Econometrics, Statistics And Computational Approaches in Food And Health Sciences

Z l

zi.

Further, from the properties of concentrated likelihood functions and the fact that z t = 0 (i = 2,..., K) it follows that the asymptotic covariance between yjT^ and ^/Tvec (6V) is zero except when i= 1 i.e. except for the intercept term. However, from (3.23) it is clear that the y4FM[vec (f5)] depends only on the covariance between y/T\ec(fiv) and y/T SlB where 0lB are the unconstrained parameters in the matrix B. Hence, the last two terms in (3.23) are zero whenever the coefficients of the intercept are assumed to be different for each equation and (3.8) specializes to (3.10). General Considerations. There are several aspects of the results contained in Proposition 2 that deserve some discussion. First, if the third moments of the actual distribution vanish, then the asymptotic covariance matrices R and JR* differ only in that the matrix (7 + i7)(0®f2) is replaced by the matrix D 4 of the fourth moments in i?J2. It seems rather unrealistic, however, that this condition would be met in practical applications since serious departures from multivariate normality are also likely to entail the loss of the symmetry property of the distribution function especially in cross section data. Second, the coefficient of the intercept term is assumed to be different in each equation in most econometric models and hence the results given in the Corollary are of considerable practical

Wald Tests and Systems of Stochastic Equations use. It is interesting to note that under this assumption, the matrix R*2 has precisely the same form as in the symmetric distribution case but the additional term appearing in Rf2 does not vanish entirely due to the non-zero covariance between the estimated coefficients of the intercept term and the elements of the reduced form error variance matrix. Third, there are some situations in which the coefficients of the intercept term may be constrained across equations (e.g. in a dynamic earnings function with labour market experience) so that it would be necessary to evaluate Rf2 ifl the general form given by (3.8). These computations can be carried out by noting that the third term could alternatively be written as (3.34)

-

(

/ + / 7 ) ( / G ® f i f i ' - 1 ) ( ^ ^ - ) / ? 1 1 ( ^ ^ - ) ' (fl" 1 ® J>)(/G®z)Z>3

_(/+i7)(/c®Oi?'-1)(-^?-)^n(-^^-)'(fi-1®/x)(/c®z)/>3 which also reveals the dependence of this covariance term on both the variance covariance matrix of the coefficients of the endogenous variables and on the covariance between the estimated elements of B and C. Moreover, in spite of its formidable appearance, the expression (3.34) is not particularly difficult to compute since many of the matrices involved are simply selection operators. Finally, it should be mentioned here that in general it is quite difficult to test the appropriateness of the multivariate normality assumption partly due to the complications arising with the use of other multivariate distribution functions that do not impose the symmetry condition and specialize to be multivariate normal distribution under some suitable conditions. In any event, one could in practice examine some elements of D3 and D 4 and if they appear to be inconsistent with the multivariate normality assumption, then inferences could be based on standard errors obtained from the estimated matrix R* which is robust to distributional misspecification. Indeed, in several experiments that we conducted using dynamic panel data models,5 it was found that the performance of the statistics Wand W* (that utilize the matrices R and R*, respectively) were quite similar in that they detected complicated error structures like a random effect with homoscedastic (or heteroscedastic) transitory components following a (fifth order) moving average process (see also below) even when the elements d3i and d4i where (3.35)

d3i = E(ul)M

i = l , . . . , 10

dM = £(uf,)/(xf

i= 1

and (3.36)

10

were in the range [ — 2, 2] and [3, 18], respectively (see Chambers, Mallows and Stuck [1976]). However, as d4l were increased to take values in the interval 5

The model simulated was similiar to that in Bhargava and Sargan [1983] with 500 individual units on whom data are available for ten time periods, one time invariant regressor, one time varying variable and the coefficient of the lagged dependent variable being 0.50.

41

42

A. Bhargava

[10, 200], the results obtained using W were indeed quite misleading whereas W* afforded correct inferences. Thus, the adverse consequences of distributional misspecification appear to be determined by the degree to which the actual distribution differs from the multivariate normal distribution and it would seem prudent in applied work to at least inspect some elements of D3 and D4 before drawing conclusions on the basis of test statistics that rely on the multivariate normality assumption. We elaborate on this issue in the next Section by the means of an empirical application where the panel data definitely contain several extreme observations. However, it might be of interest to note that within these limited simulations, alternative formulations for the constraints made negligible differences to the values of the Wald criteria mainly because the constraints were invariably formulated in a manner which ensured that the continuity properties of the derivatives were not violated in the neighborhood of some parameter values. 4.

AN EMPIRICAL APPLICATION TO PANEL DATA

An important aspect of panel data is that individual units are usually observed at regular time intervals so that the errors affecting the dependent variable must be distributed according to some univariate laws. The multivariate distribution assumption, on the other hand, serves a most useful purpose in that it enables the consistent estimation of all the parameters in the model without the need of being specific about the behaviour of the transitory and permanent components over time. Now, given the complexities arising in the analysis of individuals' behaviour in uncertain economic environments, it would seem unreasonable to postulate a priori the form of the serial covariance matrix since the violation of the constraints by the data could also lead to inconsistent estimation of all the parameters in the model. The fact that the stochastic processes affecting panel data models shed considerable light on the economic behaviour of individual units, then, suggests that a fruitful strategy in the analysis of panel data would be test, whenever possible, alternative specifications for the transitory and permanent components on an unconstrained estimate of the serial covariance matrix by a sequence of Wald tests.6 We stress, however, that the large number of individual units comprising typical panels ensures that the parameters are precisely estimated and hence, a "preliminary analysis," based on visual inspections of the correlation matrices or otherwise is inadequate in determining the appropriate error structure; it should not be viewed as a substitute for the rigorous testing of the various null hypotheses by the means of Wald tests. We now turn to the dynamic earnings function7 that explains the log of indi6 Note that this would not be possible within the fixed effects framework unless T is large due to the incidental parameters (see Bhargava et al. [1982]). 7 Note that in some cases it might be preferable to model this relationship as

ykk = 'Z?=oZkj8j+'£T=o'£"=iXhj,Uj,+uhk

h=

\,...,H {Continued on next page)

Wald Tests and Systems of Stochastic Equations

viduals' incomes using log of schooling, an occupational dummy, log of annual hours of employment, log of one period lagged incomes, and time dummies as regressors. The detailed estimates using data on 961 individuals for 10 time periods from the Michigan Panel Survey of Income Dynamics are reported in Bhargava and Sargan [1983] and here, we note that the (quasi) likelihood function (apart from an irrelevant constant) (4.1)

L = - y In det Q* - y tr [O*" 1 U*' £/*]

where JJ* = (u0 • U), u0 being the a H x 1 vector of the errors on the reduced form for the initial observations, U being the H x T matrix of the errors on the dynamic equation (see also footnote 7), and Q* being the variance matrix of the rows of [/*, cannot be concentrated in the usual Koopmans and Hood [1953] way since that would leave the parameters in the reduced form unidentified. Instead, we now have the concentrated likelihood function8

(4.2)

L*=-flndet(-^)

which needs to be optimized over all the structural form parameters and the matrices R22 and i?| 2 c a n De obtained using the theory developed above. In testing various restrictions on Q*, however, we focus on the Tx T submatrix Q since the first row of Q* is likely to have a different structure. The appropriate Wald criteria for testing the random effects specification9 on Q for this dynamic model under the assumptions of multivariate normality and distributional misspecification for the errors were calculated to be W= 324.7 and W* = 103.8, respectively, each being distributed as a Chisquare variable with (Continued) and J*< = 2i'=oZ*Jrj + 2r=ix»j.i9j + a ^<-i+"i.. h = l,...,H; t=k + l,...,T where k is the length of the lag necessary to ensure that the systematic part of the inital observation is well approximated and hence the parameter estimates are not adversely affected by an inadequate set of instruments for the initial observations. In our example, however, given that there is only one time varying regressor and that the coefficient of the lagged dependent variable is quite small (0.16), it was felt reasonable to write down the reduced form for the first observation. 8 Essentially, we now need to estimate most of the parameters in (4.1) which is slightly inconvenient but the Wald criteria are still simpler to compute than the corresponding likelihood ratios proposed by Bhargava and Sargan [1983] in the nonlinear cases. Moreover, since it is difficult to assert a priori the type of stochastic processes affecting these relationships and the fact that the likelihood function can possess several local maxima under the null means that the present approach is likely to be more useful in tackling practical problems. 9 That is, the elements on the principal diagonal are equal and the remaining elements are all equal to one another. Note that the presence of the lagged dependent variable requires the use of our extension of the Hotelling result under normality [see (2.12)].

43

44

A. Bhargava

—±— '- —2 = 43 degrees of freedom. Thus, the simple random effects formulation is again found to be inconsistent with the data and the relatively lower value of W* indicates that the fourth moments of the distribution function are being underestimated by the formula (J + I7)(£5*(g)£5*) that is appropriate under the multivariate normality assumption. An inspection of the estimated Q* matrix (see Table 1) clearly reveals that the hypothesis that the elements on the principal diagonal are all equal (except, of course, the first entry which is expected to be different) seems to be rather unsuitable and indeed the appropriate Wald criteria for testing these stationarity restrictions were calculated to be W=92>.\ and W* = 25.6 each being distributed with eight degrees of freedom. Thus, the error process appears to be somewhat more complex than that usually postulated in time series analysis and its non-stationarity is consistent with the alternative formulations where the random effect has a time coefficient and also where the transitory components are heteroscedastic, the latter being under investigation here. TABLE 1 THE ESTIMATED SERIAL COVARIANCE MATRIX AND THE MOMENTS OF THE RESIDUALS FROM THE DYNAMIC EARNINGS FUNCTION USING PSID"

Q*

0.2050

0.1361 0.1585

0.1246 0.1151 0.1494

0.1234 0.1099 0.1121 0.1535

0.1206 0.1084

0.1087 0.0967

0.1140 0.1215 0.1780

0.1022 0.1060 0.1168 0.1702

0.1043 0.0981 0.1029 0.1013 0.1122 0.1106 0.1483

0.1049 0.0941 0.0989 0.1048 0.1148 0.1162 0.1152 0.1742

0.0998 0.0886 0.0996 0.0997 0.1110 0.1103 0.1112 0.1193 0.1834

0.0979 0.0957 0.1027 0.1000 0.1105 0.1082 0.1194 0.1261 0.1372 0.2342

-0.442 -0.454 -0.563 -0.698 -0.996 -1.070 -0.146 -0.512 -0.527 -1.674 dl 4.560

5.023

5.514

7.643

" fl = 961, T=9, m=2, n = 10,

8.470 b

8.306

4.205

4 = Z L . fil/Hof ;

6.276

5.334

12.414

' £ , = 2?=i HiJHaf.

Next, let us initially assume that the transitory components of the random effects model (4.3)

uht = 5h + vh,h=

1,..., H; t = 1,..., T

follow the q th order moving average process

Wald Tests and Systems of Stochastic Equations « » * = E 0A«-o>0. = l ;

(4.4)

45

h=l,...,H;t=l,...,T

i=0

where eht are independently and identically distributed with zero mean and variance a2 and, since Q is a Tx T matrix, we further assume that q^T—2 in order to ensure that the parameters in (4.4) are identified. Note that the models (4.3) and (4.4) imply that the elements along any of the first (q +1) diagonals of the upper triangle are equal to one another but the elements on different diagonals are unequal. Thus, the rejection of the most general moving average (MA) process also entails, for example, the rejection of the hypothesis that the vht are generated by the stationary first order autoregression and in general the Wald criterion for testing the random effects model with transitory components following an MA(q) T T( T+ 11 process is asymptotically distributed as a Chi-square variablew ith —v '— 2 — q degrees of freedom.

Columns 2 and 3 in Table 2 report the values of W

and W*, respectively, for testing the random effects model with moving average errors, the order of the MA process being given in Column 1. Before attempting to test any of these hypotheses, however, it is necessary to decide the overall significance level since the hypotheses are sequential and indeed we shall not consider testing the transitory components for following an MA(16) process, for example, if we had previously rejected the MA(7) process. Now, it seems rather unreasonable to fix the overall size at the usual five per cent level and test each of

TABLE 2 VALUES OF THE WALD CRITERIA FOR TESTING THE VARIOUS CONSTRAINTS

<7* 7 6 5 4

W 120.0 120.5 129.3 139.2

W*<

W

W*°

54.4

22.0 34.6 35.7

11.2

60.4 66.9

2

158.9 175.8

83.3 94.0 101.2

1

324.1

103.4

3

41.0 57.4 89.3 119.3

19.0 21.0 34.3 42.2 56.4 67.2

" Order of the Moving Average. b Random effects model with MA(q) errors under normality (degrees of freedom=43— q). c Random effects model with MAfe) errors under distributional misspecification. d Random effects model with a modified heteroscedastic MA(g) process under normality (degrees of freedom=34—q). ' Random effects model with a modified heteroscedastic MA(?) process under distributional misspecification.

A. Bhargava

46

these hypotheses at approximately 0.07 per cent level since the power of such a procedure are likely to be extremely low (see also Sargan [1980]). In view of the outright rejection of the random effects model, however, if we regard the hypotheseis of second or third order moving average as the most "stringent" that we wish to test (see Anderson [1971]) and let the overall size be ten per cent, then each hypothesis could be tested at slightly less than two per cent significance level which would appear to be a much more reasonable approach. Thus, the random effects model with transitory components following the MA(7) process is again seen to be inconsistent with the data and this finding is not unexpected in view of the overwhelming evidence against the stationarity hypothesis. Finally, turning to the case where the variance of the transitory components a1 is dependent on time, we note that in the absence of additional constraints on the o2' s, it is not really straightforward to translate the model (4.3) and (4.4) in terms of testable constraints. However, if we first make no assumptions on the variances but instead assume the correlation pattern to be that of the MA{q) process i.e. assume that Q has elements of the form (4.5)

a>st =
s,t =

l,...,T,

when co(s_t) are the elements of the variance covariance matrix of the stationary MA(q) process, then we obtain the constraints that for \s — f|
(co (s+li) ( S+k) - <7iyi2(a>0+k)u+k)

- a1)112

whereas, for \s — t\>q, we have cost = aj, and the associated Wald criterion is asymptotically distributed as a Chisquare variable with

•T(T-l)_2_q

degrees

of freedom. Columns 4 and 5 in the Table report the values of W and W*, respectively, for testing the above constraints, the length of the MA process being given in Column 1. By using the sequential procedure described above, the use of W leads to the acceptance of the modified heteroscedastic MA(4) process whereas W* accepts the modified MA(3) process. Since W* is robust to distributional misspecification and our sample contains several outliers (some due to coding errors) it would seem sensible to rely on W* in reaching the conclusion that the error process on the estimated dynamic earnings function is not inconsistent with the random effects model with transitory components that are generated by a modified heteroscedastic third order moving average process. Note that this does not imply that the model (4.3) and (4.4) with an heteroscedastic MA(3) process is consistent with the data though it is possible to add further constraints into the set given above that are implied by specific forms of heteroscdasticity to test the validity of this hypothesis. However, within the framework of these nonlinear restrictions, the issue of an appropriate choice for a2 turned out to be quite important and further theoretical research might facilitate the determination of a formulation which is somewhat less sensitive to other forms of misspecification in the model. In any event, the various tests conducted above

Wald Tests and Systems of Stochastic Equations

establish that the error process affecting this dynamic earnings function is indeed quite complicated and the formulations used in previous studies are likely to be inadequate in explaining the dynamics of individuals' incomes. The conclusion drawn from the use of such models, therefore, should be viewed with some caution and we hope to develop the appropriate tests for the various specifications and report our findings in a sequel to this paper. 5.

CONCLUSION

In this paper, we have presented several results that enable the applications of Wald tests to systems of stochastic equations where the hypotheses of interest also relate to the parameters in the variance matrix. The chief advantages of our formulation are that the methods can be implemented rather easily since it is only necessary to optimize the usual concentrated likelihood function with respect to the structural form parameters and that the results extend to other asymptotically normally distributed econometric estimators. In view of the serious consequences of incorrectly enforcing covariance restrictions, it seems reasonable to argue that the testing of the implied constraints should precede, whenever possible, efficient estimation in the presence of these restrictions. The Wald statistics have the distinct advantage of not requiring the repeated estimation of the system in order to test different null hypotheses and indeed in the context of panel data their use may simply be inevitable since it is generally difficult to assert the appropriate form of the serial covariance matrix given that it contains valuable information about the responses of individual units to the changing economic environments. University of Pennsylvania,

U.S.A.

REFERENCES ANDERSON, T. W., The Statistical Analysis of Time Series (New York: John Wiley and Sons, 1971). AND C. HSIAO, "Estimation of Dynamic Models with Error Components," Journal of American Statistical Association, 76 (June, 1981), 598-606. AND H. RUBIN, "The Asymptotic Properties of Estimates of the Parameters of a Single Equation in a Complete System of Stochastic Equations," Annals of Mathematical Statistics, 21 (1950), 570-582. BHARGAVA, A., L. FRANZINI AND W. NARENDRANATHAN, "Serial Correlation and the Fixed

Effects Model," Review of Economic Studies, 49 (October, 1982), 533-549. AND J. D. SARGAN, "Estimating Dynamic Random Effects Models from Panel Data Covering Short Time Periods," Econometrica, 51 (November, 1983), 1635-1660. BYRON, R. P., "Testing Structural Specifications Using the Unrestricted Reduced Form," Econometrica, 42 (September, 1974), 869-883. CHAMBERS, J. M., C. L. MALLOWS AND B. W. STUCK, " A Method for Simulating Stable Random Variables," Journal of American Statistical Association, 71 (June, 1976), 340-344. ENGLE, R. F., D. F. HENDRY AND J. F. RICHARD, "Exogeneity," Econometrica, 51 (March, 1983), 277-304.

47

48

A. Bhargava

HOTEUUNG, H., "Relations Between Two Sets of Variates," Biometrika, 28 (1936), 321-377. KOOPMANS, T. C. AND W. C. HOOD eds., Studies in Econometric Methods (New York: John Wiley and Sons, 1953). , H. RUBIN AND R. B. LEIPNIK, "Measuring the Equation Systems of Dynamic Economics," in, T. C. Koopmans, ed, Statistical Inference in Dynamic Economic Models (New York: John Wiley and Sons, 1950). LILLARD, L. A. AND R. J. WILLIS, "Dynamic Aspects of Earnings Mobility," Econometrica, 46 (September, 1978), 985-1011. MACURDY, T. E., "The Use of Time Series Processes to Model the Error Structure of Earnings in a Longitudinal Data Analysis," Annals of Applied Econometrics, 18 (January, 1982), 83-114. MANN, H. B. AND A. WALD, "On the Statistical Treatment of Linear Stochastic Difference Equations," Econometrica, 11 (July-October, 1943), 173-220. RICHARD, J. F., "A Note on the Information Matrix of the Multivariate Normal Distribution," Journal of Econometrics, 3 (February, 1975), 57-60. RUBIN, H., "Systems of Linear Stochastic Equations," Unpublished Ph. D . thesis, University of Chicago (1948). SARGAN, J. D., "The Identification and Estimation of Sets of Simultaneous Stochastic Equations," Discussion Paper, London School of Economics (1976). , "Some Tests of Dynamic Specification for a Single Equation," Econometrica, 48 (May, 1980), 879-898. TUKEY, J. W., "A Survey of Sampling from Contaminated Distributions," in, I. Olkin, ed., Contributions to Probability and Statistics I (Stanford: Stanford University Press, 1960). WALD, A., "Tests of Statistical Hypotheses Concerning Several Parameters when the Number of the Observations is Large," Transactions of the American Mathematical Society, 54 (November, 1943), 426-482. ZELLNER, A., "An Efficient Method of Estimating Seemingly Unrelatd Regression Equations and Tests for Aggregation Bias," Journal of American Statistical Accosiation, 57 (1962), 348-368.

Review of Economic Studies (1991) 58, 129-140 © 1991 The Review of Economic Studies Limited

0034-6527/91/00090129S02.00

Identification and Panel Data Models with Endogenous Regressors ALOK BHARGAVA University of Houston First version received December 1987; final version accepted March 1990 {Eds.) This paper provides sufficient conditions for the identification of both static and dynamic models containing endogenous regressors from panel data by utilizing the restrictions across time periods on the parameters. It is shown that identification is achieved under quite weak conditions even in the presence of a general pattern of correlation between the errors and the time-varying variables. Efficient estimation procedures for the models considered and some specification tests are outlined. Finally, static formulations relating individuals' intakes of nutrients in the previous 24 hours to household incomes are estimated using (ICRISAT) panel data from rural India.

1. INTRODUCTION While panel data provide valuable information at the individual level, the extraction of this information generally requires the development of statistical methods that are wellsuited to the special features of such data sets. Thus, for example, the fact that typical panels comprise of a large number of individual units observed for a few time periods, has led researchers to employ a body of asymptotic distribution theory that relies only on the increase in the number of individuals for its validity (e.g. Amemiya and MaCurdy (1986), Anderson and Hsiao (1981), Bhargava and Sargan (1983), Chamberlain (1984), Hausman and Taylor (1981), Hsiao (1986), etc.). There are, of course, several other features of such data sets that can be incorporated into the existing econometric methodology to enhance the elucidation of economic relationships. For example, an important aspect of econometric modelling using panel data is the estimation of models containing endogenous explanatory variables. In fact, the treatment of the relationship to be estimated in different time periods as different "equations" gives rise to crossequations restrictions on the unknown parameters. These restrictions can be exploited to identify models which might seem unidentified from the use of conventional criteria. This is particularly useful in practical applications where the data are available only on a few exogenous time varying variables. Recently, Bhargava and Sargan (1983) have developed a framework which allows the use of cross-equation restrictions in dynamic panel data models to achieve identification of the parameters; sufficient conditions for identification have been derived under the assumption of a random-effects type correlation structure for the endogenous time-varying variables. Whilst the latter assumption allows identification under very weak conditions and improves the efficiency of the estimation procedures, the data may not always support its imposition. Analogously, in static models the identification conditions derived by Hausman and Taylor (1981) invoke a simple random effects decomposition for the error terms. The violation of either of these sets of assumptions in empirical

50

A. Bhargava applications could invalidate even the consistency properties of the estimators. Indeed, using the Michigan Panel Survey of Income Dynamics, the error structure affecting a dynamic earnings equation was found to be a third-order Moving Average process with heteroscedastic variances over time (Bhargava (1987)). Similarly, in estimating static demand functions for nutrients (see Section 4 below), the weights of the individuals may be correlated not only with the individual effects but also with the time-varying part of the error terms. Thus it would seem important from an empirical standpoint to provide identification conditions and develop estimation and test procedures that place minimal restrictions on the underlying correlation patterns. The structure of this paper is as follows. Section 2 considers the static model with some endogenous time-invariant and time-varying variables appearing as regressors. Identification conditions are derived under the assumptions of a general form of correlation between the time-varying variables and the errors and also where a random-effects type decomposition is imposed upon the correlation structure. Section 3 proves a theorem on identification in dynamic models in the situation where the time-varying variables are assumed to be correlated in a general way with the error terms. In Section 4, the methods developed for static models are applied to repeated 24-hour recall data on the intakes of nutrients from rural south India. The income elasticities of nutrients are estimated in a static framework and the results underscore a definite relationship between the intakes of nutrients and household incomes. 2.1. IDENTIFICATION IN STATIC MODELS WITH A GENERAL CORRELATION PATTERN We proceed by considering the single equation static model n

yhi =ir=o 1 7izih+ I j6.-x.-hi + "(w

(h = l,...,H;t=l,..,T)

(1)

where z's and the x's are, respectively, the time-invariant and the time-varying variables with coefficients y and )3, uhl are the error terms that are distributed identically across individual units with zero mean and variance covariance matrix ft, H and T are, respectively, the number of individual units and the number of time periods for which the data are available. Furthermore, it is assumed that the first (m, + l) time-invariant variables (including an overall constant term) z, and the first n, time-varying variables x, are uncorrelated with the error terms uhl while the remaining m2 time-invariant and n2 time-varying variables are correlated with the w's in some general way. As noted in the Introduction, the random-effects decomposition on the error terms uh, will not be imposed a priori in this model. Instead, the cross-equations restrictions present in the system will be seen to identify (1) under some fairly weak assumptions on the exogenous variables z, and x,. Now rewriting the system in a simultaneous equations framework with unrestricted reduced forms for the non-exogenous variables z2 and x2 we obtain the system -yh+TjZjh+X, 7 !, C2,x2/.r+Xr=i C1,x1,„ + r,z l / , = w,,, -z2h

(2)

+ Y.J=lG,xu„ + G*zlh = u2h -x2h,

+ 1 / 1 , F,jXlhj + F?zUl = uVu

(3) (f = l , . . . , T )

(4)

where yh is a Tx 1 vector of the dependent variable, T,, T 2 , Cu and C2, are respectively, T x ( m , + 1), Txm2, Txnt and Txn2 coefficient matrices. Similarly, G,(t = 1 , . . . , T), G*,F0(t=l,..., T;j = l,..., T),and F*(t = \,..., T) are m , x n , , m 2 x ( m l + l ) , n 2 x n l

Panel Data Models with Endogenous Regressors

51

and « 2 x (m, + 1) matrices, respectively. Also, uxh, u2i,, and uJh, (t = 1 , . . . , T) are, respectively, I x l , m2x 1, and w2x 1 vectors of errors. The proofs of the propositions in the paper are collected together in the appendix. Denning Z + = [X,: Z,], where X, and Z, are H x (n, T) and H x (w, + 1 ) data matrices, we state our first proposition: Proposition 1. The model (2) is identified if (i) P\imH^oc(Z+'Z+/H) definite, (ii) n , g l , (iii) T S 2 (iv) 77ie matrix (5) is of rank (m2+n2), where

is positive

Gi

G.

•••

Gi

G->

G2

• ••

G2

•••

GT

GT

•••

GT

-F\\

F2t

'''

^Vi

F\2

F22

'''

FT2

'''

F\T

FIT

'''

/Vr-

.

(5)

There are several interesting aspects of these results. Firstly, even though the timevarying endogenous variables are assumed to be correlated in a free way with error terms, the rank condition (iv) should be easily satisfied in practice since (5) is a (m2 + n2) x T2n, matrix. Secondly, the number of exogenous time-varying variables in the model can be smaller than the number of endogenous time-invariant variables insofar as T is not very small. This provids an interesting contrast to the sufficient conditions derived by Hausman and Taylor (1981) where n, should be greater than m2 as a result of not utilizing the cross-equation restrictions. Thirdly, identification is achieved more easily in situations where the endogenous regressors are largely the time-varying variables. This is because each of the endogenous variables x2h, appears only once in the system (2) i.e. in the /-th equation. Thus the number of endogenous variables included in each equation is only (m2+n2). Fourthly, the rank condition can sometimes be violated in practical applications due to a lack of correlation between the time-varying and the time-invariant variables (see Bhargava and Sargan (1983)). Thus it may be desirable to verify its validity. This can be done using a Wald-type procedure (Sargan (1980)) and by noting that this condition is equivalent to the condition that the matrix Plim (Z*'Z+/H) is of full rank, where Z* = [Z,: Z 2 : X 2 ]. Finally, when the variance matrix ft of w u is assumed to be unrestricted, the maximum likelihood estimates of the parameters appearing in (2) are asymptotically equivalent to the efficient instrumental variables procedure which is essentially the Three Stage Least Squares estimator with cross-equation restrictions on the coefficients. Formally, writing (2) in matrix notation as AX*'=U'

(6)

where A is a Tx[T(n + l) + m + l] coefficient matrix and X* is the [T(n + l) + m + \]x H data matrix i.e. X* = [ Y: Z , : Z 2 : X,: X 2 ] and let «' = (y':j8')

and

R=

{X*'Z+)(Z+'Z+Y\Z+'X*).

Then the efficient estimator of 8 is given by S=[S'(n-'®R)ST'S'(Q.-'®R)s

(7)

where, S and s are selection matrices such that, \ec(A) = S8-s.

(8)

The asymptotic variance covariance matrix of 8 can be approximated by [S'(£ll®R)SY' with the obvious estimator of fl from (6) replacing the true value. For efficient estimates in the presence of restrictions on Cl, a logical procedure would be to start with ft unrestricted, then test restrictions on the serial covariance matrix implied

52

A. Bhargava by a random-effects type specification with correlated (possibly heteroscedastic) transitory components using Wald statistics (see Bhargava (1987)). The free parameters in (2) and in II can then be estimated by an iterative procedure such as maximum likelihood under multivariate normality assumption for the errors. 2.2. IDENTIFICATION UNDER A RANDOM-EFFECTS TYPE DECOMPOSITION FOR THE TIME-VARYING VARIABLES The results presented above are widely applicable since there are no restrictions placed on the decomposition of the error terms and on the pattern of correlation between the time-varying variables and the errors. In some practical applications, however, there may only be a few time observations available (e.g. T = 2 in the empirical application below) and investigators might be reluctant to treat many of the time-varying variables as exogenous. Further, it is plausible that the estimation procedures, assuming the time-varying variables to be correlated with the errors in a general way, may not be very efficient especially if the number of endogenous variables is large. In such circumstances, it would seem desirable to make some specific assumptions on the decomposition of the error terms (Hausman and Taylor 1981)) and/or on the pattern of correlation between the individual effects and the time-varying variables (Bhargava and Sargan (1983)). We now follow the latter approach for static models and assume that xih, = CiVh + vfhl

(i = «1 + l , . . . , n 2 ; / J = l , . . . , H ; r = l , . . . , T )

(9)

where 17' are the random effects and v*'s are uncorrelated with the errors. This formulation affords the use of xthl, where xth, = xiht-^=lxm.JT

(i = n1 + l,...,n;h

= l,...,H;t

=

2,...,T)

as additional ( T - l ) n 2 instrumental variables while creating only the n2 time-means of the correlated x's as endogenous variables in the system. Indeed, for the static model being considered, this will obviate the need for the presence of exogenous time-varying variables which is certainly of practical use. The extended model can now be written as

-^/,+r 2 z 2h +xr=i c2,x2hl+Y^=x cuxxh,+rxzlh -z2H+Z!=iG,xlhl

+ G*zlh+Zl=2G:xlh,

= ulh

(10)

= u2h

(11)

-*2(,+lT=i F,Xihl + F?Zih + 21J'=2 F*X2hl = u3h -x2h, + X2h, + X2h=0

(12) (f=l,...,T).

(13)

+

Defining Z = [X,: X2: Z,], we have the following result: Proposition 2. The model (10) is identified if (i) P\imH^x,(Z+'Z+/H) definite, (ii) Tig 2, (iii) The matrix (14) is of rank m2, where [G,

G2

• • • GT

Gt

Gt

•••

Grl

is positive (14)

Propositions 1 and 2 provide sufficient conditions for the identification of static models under a general form of correlation between the time-varying variables and the error terms and also for a random-effects type decomposition for the time-varying variables, respectively. The choice between the two formulations will normally be determined by the special features of the model to be estimated as well as by the length of the panel. Note that in the absence of covariance restrictions, (10) can be efficiently estimated using the estimator (7) by redefining the matrix of instrumental variables as Z + = [X, :Z, :X2] and treating z2 and x2 as endogenous.

Panel Data Models with Endogenous Regressors

53

Lastly, it would be desirable in practical work to test the validity of the decomposition (9). First, note that the model (10)-(13) is mathematically equivalent to the system (2)-(4) with x2h, included as instrumental variables in equations (3) and (4). Thus the likelihoodratio test proposed by Bhargava and Sargan (1983) can be used to test the exogeneity of X2 variables. Under the null hypothesis, the statistic is asymptotically distributed as a Chi-square variable with [T{T-l)n2] degrees of freedom. Indeed, if the null is not rejected, we can further test the exogeneity of time means x2 so that the testing procedures are in fact sequential (Wald (1947)). Of course, these hypotheses can also be tested using Instrumental Variables estimates (see Sargan (1975)). Define Z\ = [X, :Z, :X2], Z2 = [ X , : Z , : X2 ] and ZX, = [X,: Z,] and let the corresponding projection matrices be Qx, Q2 and Q}, where Qt = ZtiZt'Zty'Zt1', etc. Then, denoting by w3 the residuals from estimating equation (2) using instrumental variables Z\ and so on, we have that tr[n _1 {" 2 '(?2W 2 -" 3 '(?3" 3 }] and t r [ i l ' { " " Q . " ' - u2'Q2u2}'] (15) are asymptotically distributed as Chi-square variables with [ T( T -1) n2] and [ Tn2] degrees of freedom, respectively. In practical work, however, the choice of a consistent estimator of ft, the rounding-off errors in matrix inversion and the possible mis-specification of the relationship may cause these criteria to assume negative values. In such circumstances, it would be useful to reformulate the test criteria and perhaps also apply likelihood-ratio tests prior to reaching definite conclusions. 3. IDENTIFICATION IN DYNAMIC MODELS WITH A GENERAL CORRELATION PATTERN Many economic relationships are dynamic in nature. The inclusion of the lagged values of the dependent variable is often necessary for capturing the influence of the past realisations of the time-varying variables on the current levels of the dependent variable. In analysing food consumption patterns, for example, economic theories of "habit persistence" imply that the demand functions are dynamic (see Gorman (1967)). Similarly, outside economic forces such as "cost of protection" measures in studying wage determination ensure that the previous wage levels are relevant in determining the current wages. We now address the problems of identification in dynamic models in the presence of endogenous time-invariant and time-varying variables. The previous work of Bhargava and Sargan (1983) imposed a random-effects decomposition for the correlation between the time-varying variables and the error terms while specifiying a reduced-form equation for the first observations on the individual units. The following proposition assumes that the time-varying variables are correlated with the errors in a general way. The corollary covers the situation where the fcth observations on the dependent variable are treated as the initial ones partly to improve the prediction of the "systematic" part. Assuming that (T +1) observations are available on the variables and treating the first (/ = 0) observations as the initial ones, we obtain the model -yoi, +I, 7 lo M!*W.< + M*'ZW, = "o;,

(16)

Byh + r2z2h+Y1J=l C2lx2h,+J1Ji=l Cuxlhl + Tlzlh = ulh

(17)

-Z21, + i r = o G ' x i ' " +

G

*zi'.

= u

2i<

(18)

-x2iu+lJ=0F,jX„,j + F?Zu, = Uih, (t=l,...,T) (19) where, /x and /x* are, respectively, n, x 1 and (m, + 1) x 1 coefficient vectors, the remaining matrices and vectors are defined above and B is a Tx(T+\) matrix with elements bit = a,

b,; I+1 = - 1 ,

bjj = 0 otherwise,

(20)

54

A. Bhargava a being the coefficient of the lagged dependent variable. Also, reverting to the definition of Z+ as Z + = [Z,: X,], we have the following proposition: Proposition 3. The model (17) is identified if (i) P\in\H^oc(Z+'Z+/H) is positive definite, (ii) « , g l , (iii) I S 4 , (iv) The matrix (20) is of rank (m2+n2), where G„

G0

•••

G„

G,

G,

•••

G,

•••

GT

GT

•••

GT

-F00

^io

•• '

FTO

Fol

F\i

'' '

FT\

'''

FQT

FlT

•••

Fj-,,

Corollary. If the k-th observations are treated as the initial observations, then (17) is identified under conditions (i), (ii), and (iv) with (iii) replaced by (iii)* T g 3 + /e. The general form of correlation between the time-varying variables and the error terms would seem to be a more satisfactory formulation in situations where the data cover reasonably long time periods. Furthermore, if the null hypothesis of a random effects decomposition for the correlation pattern for the time-varying variables cannot be rejected, the efficient estimates of the parameters may be obtained by including XT variables in the set of instruments. Of course, in some applications, it may be inevitable to invoke the random effects decomposition for identification purposes due to the short length of the panel especially in dynamic models (see Bhargava (1991)). We now turn to an empirical application of the methods proposed in the paper using a very short panel (T = 2) and note that for the general form of correlation, the estimator (7) again provides efficient estimates of the parameters on redefining the coefficient matrix A. 4. AN APPLICATION TO THE DATA FROM RURAL SOUTH INDIA ON THE INTAKES OF NUTRIENTS IN THE PREVIOUS TWENTY-FOUR HOURS An important procedure for analysing the nutritional well-being of individuals is to survey some sub-populations regarding their food intakes in the previous 24 hours. The interviewers, especially in less-developed countries, often assess the quantities consumed by carrying with them utensils of different sizes and obtain estimates of the various foods consumed by each member of the households. The resulting data are then converted into data on intakes of nutrients using some standard tabulations (e.g. Gopalan et al. (1971) for Indian foods). Samples of some of the foods consumed by the households are sometimes examined in a laboratory to cross-check the accuracy of the tabulations. For rural south India, four rounds of such nutritional surveys were conducted by the International Crops Research Institute for Semi-Arid Tropics (ICRISAT) in 1976 and 1977 in six villages (Binswanger and Jodha (1978)). Complete data on the intakes of nine nutrients, namely, Energy, Protein, Calcium, Iron, Carotene, Ascorbic Acid, Riboflavin, Niacin and Thiamine in three of the villages are available to us. Recently, there has been a growing interest in quantifying the effects of increases in households' incomes on the intake of nutrients by the individual members in lessdeveloped countries. The knowledge of such income elasticities of nutrients is particularly important in assessing the efficacy of the policies of international agencies such as the World Bank which provide aid to these countries. Most of the previous studies using simple statistical techniques on the ICRISAT data have been unable to find any systematic relationship between the intakes of nutrients and household incomes (Ryan et al. (1984) and Behrman and Deolalikar (1987)). Indeed, it has been suggested in the latter study

Panel Data Models with Endogenous Regressors that the lack of correlation may be due to the consumption of foods for their "status value" or "taste" rather than for their nutritive content even at such low income levels. However, averaging the two rounds during the year to produce an annual figure for each individual and estimating dynamic demand systems by maximum likelihood for five nutrient groups, Bhargava (1991) reports a definite causal link between nutrients' intakes and household incomes. The estimated short-run income elasticities of nutrients were approximately in the range [0-05,0-20]. While these estimates are perhaps lower than may have been expected by some policy makers, they do support the case for raising incomes of the poor in less-developed countries in order to improve nutrition (see below). Whilst a dynamic framework for modelling the demand for foods and nutrients has considerable theoretical and empirical appeal, the quantities consumed of the latter pertain to the previous 24 hours. Further, no interviews were conducted by ICRISAT following periods of religious festivities in order to estimate individuals' intakes of nutrients for a "typical" day. Thus the interviews took place roughly at six-month intervals. Now, in a dynamic model where the lagged value of the dependent variable appears as a regressor, this implies that the annual figure produced by averaging the two rounds of data available for each of the years is representative of food intakes for the year as a whole. This may be questionable in some cases especially if households living close to subsistence level spread their consumption of more nutritious foods over the year so as to coincide with religious festivities (Bhargava (1991)). Also, seasonal factors affect food availability and consumption in a developing country like India. Thus such factors will make the period in which the interviews actually took place very relevant in a dynamic framework. It would therefore seem important to examine the robustness of the empirical results obtained using dynamic models by relating the individuals' intakes of nutrients to the current levels of household incomes and other characteristics. The income elasticities of nutrients within a static framework can be estimated using instrumental variables (or maximum likelihood) in the systems represented by (2)-(4) or (10)-(13) depending on the exogeneity properties of the independent variables. Tables I, II and III report the estimated relationships for the intakes of six nutrient groups using available data on 364 individuals from the three Indian villages. Tables I and II in fact treat the individuals' weights as fully endogenous and correlated in the random-effects fashion as in (9), respectively. Table III assumes the weights to be pre-determined; the heights of the individuals are invariably treated as predetermined since they are unlikely to be influenced by the day-to-day variations in food intakes. The nutrients' intakes are expressed in percentages of Recommended Daily Allowances (e.g. Stigler 1945)); the Vitamin A&C group consists of Carotene and Ascorbic Acid and the Vitamin B group comprises of Riboflavin, Thiamine and Niacin (see Bhargava (1991)). Note that individuals under the age of ten years in 1976 were excluded from this sample. The regressors in the tables are the two constants for the years, dummy variables for two of the villages, the number of adult equivalents in the households and its square, the non-rental incomes of the households and the height and weight of the individuals. A computer program was written in Fortran to estimate the class of static models considered in this paper and was implemented on the Supercomputer (IBM 3090) at Cornell University. The Chi-square values are the sample criteria for the statistics given in equation (15) and the tables are organized in a decreasing order of generality of the endogeneity assumption on the weight variable. There are several interesting features of these empirical results. Firstly, using a sequential testing procedure with the Chi-square misspecification tests, the accepted estimates of the Energy, Calcium, and Vitamins A&C relationships are contained in

55

56

A, Bhargava

TABLE I Efficient estimates of income elasticities of nutrients for rural India with the weight variable treated as fully endogenous'

Variable Const. 1 Const. 2 Dum. I 2 Dum. 2 2 Adeq.3 Adeq. Sq. Income Height Weight 1 2 3 4

Energy

Protein4

Calcium

7-322 (2-977) 0-033 (0-023) -0114 (0-039) -0-185 (0-029) -0-378 (0-105) 0-086 (0-033) 0-049 (0-020) -1113 (0-814) 0-751 (0-300)

3-613 (3-561) -0-050 (0-027) -0-372 (0-047) -0-179 (0-034) -0-252 (0-122) 0043 (0-038) 0-063 (0-023) -0-092 (0-975) 0-434 (0-359)

2-548 (6-433) -0-015 (0-035) 0-064 (0-085) -0-260 (0-063) -0-779 (0-224) 0161 (0-069) 0-096 (0-038) -0-212 (1-759) 0-764 (0-650)

Iron

-14-68 (5-490) 0013 (0-036) -0-858 (0069) -0-440 (0-048) 0-007 (0-175) -0-008 (0-054) -0053 (0-033) 4-749 (1-506) -0-908 (0-555)

Vits. A&C

Vit. B4

-4-552 (5-745) -0-014 (0-047) 0-081 (0-077) 0041 (0-057) -0-929 (0-204) 0-238 (0-063) 0103 (0-039) 1-687 (1-572) -0-251 (0-580)

5-183 (4-092) -0046 (0-029) -0-299 (0-054) -0194 (0-039) -0-204 (0-142) 0-014 (0-044) 0-127 (0-027) -0-615 (1-120) 0-549 (0-413)

H = 364; T = 2; all variables in logarithms. Dummies for villages. Number of adult equivalents. Protein and Vit. B relationships are appropriately specified—see the Chi-square tests in Table II.

TABLE II Efficient estimates of income elasticities of nutrients for rural India with a random effects decomposition for the weight variable

Const. 1 Const. 2 Dum. 1 Dum. 2 Adeq. Adeq. Sq. Income Height Weight

xH2Y 1 2 3 4

Energy4

Protein3

Calcium 4

4-574 (2-406) 0-037 (0-022) -0-135 (0-037) -0-181 (0-029) -0-389 (0-104) 0-085 (0-032) 0-047 (0-019) -0-351 (0-624) 0-466 (0-239) 4-52

1-044 (2-819) -0-047 (0-027) -0-391 (0-044) -0-174 (0-034) -0-250 (0-122) 0-042 (0-038) 0-060 (0-023) 0-620 (0-766) 0168 (0-280) 9-26

3-480 (4-720) -0016 (0-035) 0-071 (0-079) -0-261 (0-063) -0-778 (0-225) 0161 (0-070) 0-097 (0-039) -0-470 (1-275) 0-861 (0-465) 0-73

Chi-square tests for the random effects decomposition. See text. H 0 is rejected—see Table I. H0 is accepted—see Table III.

Iron -12-47 (3-820) 0-013 (0-036) -0-858 (0-069) -0-440 (0-049) 0006 (0-175) -0-008 (0-054) -0-053 (0-033) 4-750 (1-510) -0-908 (0-555) -ve2

Vits. A&C 4

Vit. B3

-5-393 (4-827) -0-013 (0-047) 0-074 (0-074) 0-042 (0-057) -0-929 (0-205) 0-238 (0-063) 0-102 (0-039) 1-921 (1-322) -0-338 (0-481) 2-22

1-952 (3-251) -0-042 (0-029) -0-322 (0-051) -0-188 (0-039) -0-202 (0-142) 0-012 (0-044) 0-124 (0-027) 0-281 (0-883) 0-213 (0-323) 9-79

Panel Data Models with Endogenous Regressors

57

TABLE III Efficient estimates of income elasticities of nutrients for rural India with the weight variable treated as predetermined Variable Const. 1 Const. 2 Dum. 1 Dum. 2 Adeq. Adeq. Sq. Income Height Weight X2(2)2 1 2 3

Energy1

Protein

Calcium 1

Iron

Vits. A&C

Vit. B

4-049 (1-099) 0-037 (0-022) -0139 (0-033) -0-180 (0-029) -0-379 (0-104) 0-085 (0-032) 0 046 (0-019) -0-205 (0-273) 0-412 (0-088) 0-46

1-762 (1-289) -0-048 (0-026) -0-386 (0-039) -0-175 (0-034) -0-251 (0-122) 0-042 (0-038) 0061 (0-023) 0-422 (0-320) 0-242 (0-104) -ve3

-2-468 (2-331) -0010 (0-034) 0-027 (0-071) -0-253 (0-062) -0-776 (0-221) 0160 (0-069) 0-096 (0-038) 1-175 (0-578) 0-243 (0-187) 0-54

-6-845 (1-766) 0-003 (0-034) -0-796 (0-055) -0-448 (0-046) 0-012 (0-168) -0007 (0-052) -0044 (0-031) 2-573 (0-439) -0-095 (0-142) -ve

0-520 (2-134) -0-021 (0-047) 0-120 (0-064) 0-035 (0-056) -0-927 (0-201) 0-239 (0-062) 0-108 (0-039) 0-278 (0-530) 0-277 (0-171) 1-07

2-918 (1-496) -0043 (0-029) -0-315 (0-045) -0-190 (0-039) -0-203 (0-141) 0-012 (0-043) 0-125 (0-027) 0-014 (0-372) 0-313 (0-120) -ve3

Energy, Calcium and Vits. A&C are correctly specified. Chi-square tests for exogeneity under a random effects decomposition. Not Applicable.

Table III whereas those for Protein and Vitamin B are given in Table I. The rather high level of noise present in these data seems to widen the confidence limits for the test statistics. This is a common feature of 24-hour recall data and is usually attributed to excessive intra-individual variation. Thus it is perhaps not surprising that the exogeneity null hypothesis is accepted in three of the cases. The estimates of the income elasticities from the three tables, on the other hand, are close to one another thereby indicating that the violation of the exogeneity assumption is probably quite minor. It might be added that within the limitations imposed by the negative values of the test criteria based on Instrumental Variables estimates, the data appear to support a general correlation pattern over a random-effects decomposition for the weight variable in the Protein and the Vitamin B relationships. Secondly, the Iron relationship is very poorly determined in all three of the tables and this is perhaps due to errors in assessing iron intakes and absorption by the human body. In fact, combining Calcium and Iron produced poor results for the mineral group as a whole. The Chi-square statistics in many of the cases assume negative values which may be due to the generally poor fits as well as to the rounding-off errors involved in matrix inversion. Finally, it is interesting to note that the estimates of income elasticities range from 0-046 for Energy to 0-127 for Vitamin B. Now, the nutritional requirements of the human body are such that the energy needs must be satisfied prior to the absorption of other nutrients—especially protein (see Hutchinson (1969) and Sukhatme (1974)). Thus one may view the nutritional requirements of the body as being "hierarchical" in the sense discussed in the economics literature, for example, by Gorgescu-Roegen (1966) and Lancaster (1971). However, since most foods contain all of these nutrients (except Ascorbic Acid), it would be necessary to modify the assumption in theoretical analyses that the consumer can demand exact quantities of some of the nutrients without consuming

58

A. Bhargava

several others in the process. In any event, one would expect the share of foods that are good sources of the desirable nutrients to rise (in comparison to the energy intakes) with households' incomes. This in turn might be reflected in the income elasticities of nutrients which should be greater for the nutrients that are usually associated with more expensive foods. Interestingly, the income elasticity of Energy is estimated to be the lowest whereas the elasticities of Vitamin A&C and Vitamin B groups are the highest. Thus in the static framework, there is again support for a causal relationship between the intakes of nutrients and households' incomes as well as some indication of a hierarchical structure in the demand for nutrients. A further discussion of the magnitudes of these elasticities from a policy viewpoint should focus on the other needs of these villagers such as those for clothing and housing. Also, the level of "noise" due to the intra-individual variation in 24-hour recall data and the possibility of dynamic misspecification should be taken into account. This is beyond the scope of the present paper. APPENDIX Proof of Proposition 1. We multiply the matrix of coefficients in (2) (also given by A in (6)) by a Tx[T(n2+ l) + m 2 ] transformation matrix [IT:H2:H3l:H32:-:H3T]

(A.l)

and show that the a priori constraints force (A.l) to take the form where H2 = 0, H3, = 0 (/ = 1 , . . . , 7"). Defining q to be a T x 1 vector of ones and d, to be a T x l vector containing one in the r-th position and zeros elsewhere, the constraints on (2) are that r , = <jy„

r2 = qy'2,

C„ = d,j8'„

C2, = d,p'2

(f = l , . . . , T ) .

(A.2)

Writing the transformed version of y as {y- y*), etc we have the set of transformed equations r l + H 2 G* + I ^ 1 H 3 , F * = , ( y i - y * ' ) T2-H2 = q(y'2-yV) C „ + W 2 G , + E 7 = 1 HyFj, = C*, C2,-H3,

= Cf,

(A.3) •

(A.4)

(r = l , . . . , T )

(A.5)

(f = l , . . . , 7").

(A.6)

Simplifying, these can be rewritten as qy*' + H2G* + l.7,^H3,F*

=0

(f = l , . . . , T )

H2 = qyf d,0f' + tf2G, + l J _ , H 3 / F , , = O d,P*'-H3,

=0

(A.7) (A8)

(/ = 1 , . . . , T ) (t = l,...,T).

(A.9) (A.10)

Combining these, we have d,Pt' + qy$'+Zj,l'ijPVFi,

=o

qyV + qyt'G* + Zl_ldlp?F*

= 0.

(t = i,...,T)

(A.ii) (A.12)

Now relaxing the constraints in (A.ll) by replacing d: by q, it immediately follows that /3f = 0. The remaining restrictions from these equations can be put in the form r f G , + /3fF„=0

(j=l,...,T;t

= l,...,T)

(A.13)

Then assuming the rank of the matrix (5) given in the text to be (m2 + n2), it follows from (A.13) that y*' = 0 and /3f' = 0. Finally, from (A.12), we have that •y*' = 0 and hence the parameters are all identified. || Proof of Proposition 2. The Tx [T+m2 + (T+ l)n2] transformation matrix now takes the form t / T : H 2 : H 3 : H f : Hf :• • • : « £ ] .

(A.14)

Panel Data Models with Endogenous Regressors

59

The a priori constraints are still given by (A.2). The transformed equations can be written as r, + H2G* + H3lF* = q(y't-y*')

(A.15)

V2-H2 = q(y'2-yf)

(A.16)

ru + H2G, + HiF, = C* C2,-H*

= Cl

(t = l,...,T)

(A.17)

(t = \,...,T)

(A.18)

H* = 0

(A.19)

H2G* + H3F* + H* = 0 -H3 + l^H*

(t = 2,...,T)

(A.20)

= 0.

(A.21)

From (A.19), j8f = 0 a n d Cf, = C2, (t= 1 , . . . , T) so that (A.21) implies that H* = 0 (t = 2

T) and hence

H3 = 0. Thus we have qyf G, + d,B*' = 0

(f = l , . . . , r )

(A.22)

and qyf'G* = 0 (t = 2,...,T). (A.23) Thus /3* = 0 and if the rank of the matrix (14) is m2, then from (A.22) and (A.23), we must have y* = 0. Thus H2 = 0 and -yf = 0. || Proof of Proposition 3. The Tx[(T+

l) + m2+ Tn2] transformation matrix now takes the form

[h0:(IT + HJ: H2: H3l: H32:- • •: H3T],

(A.24)

where h0 is a T x 1 vector, Ht is a T x T matrix and the remaining matrices have the same dimensions as in Propositions 1 and 2. Defining d* to be a ( T + 1) x 1 vector with 1 in first position and zeros otherwise, and writing B, to the transformed version of the matrix B, the transformed set of equations take the form -h0d*' + (I + H,)B = Bl

(A.25)

/i oM *' + (/ + H , ) r , + H 2 G* + I ^ 1 H3,F* = q(y\-y*') {l + Hl)V2-H2

(A.26)

= q(y'2-yf)

(A.27)

h0vi>0+H2G0 + lJ=1 H3JFjo = 0 h<,fL', + (I + Hl)Cl, + H2G,+Y.J_lH3JFil

(A.28)

= C*

(/ + H , ) C 2 , - H 3 , = CJ,

(/ = 1 , . . . , T ) ((=1,...,T).

(A.29) (A.30)

From these equations, we obtain H2 = qyr+Hiqy2

(A.31)

H3, = d,p*' + H,d,p'2 h0vL', + d,Bf' + HldlB\ + H2G, + 'Zj,l"3jFi,=0

(/ = 1 , . . . , T )

(t = l,...,T)

ftoM*' + 9 - y * ' + H l 9 y i + H 2 G* + l 7 . , H3JF* = 0.

(A.32) (A.33) (A.34)

(A.33) can now be re-written for (/ = 1 , . . . , T) as h0ri + d,Br + Hld,B\ = [(qyr + Hlqy2)G,+Zj_ldiBrF)l

+ Hl2Zj_ldlB2Fl,].

(A.35)

Now relaxing the constraints on C 2 , as in Proposition 1, (A.35) is identical to (B.12) in Bhargava and Sargan (1983). Thus we can show that the transformed a, a* is 0 provided that n , > 0 , so that h„ = 0, H, = 0 , and (A.35) implies that B* = 0. Finally, substituting for h0, H, and B* in (A.35), and assuming that the rank of the matrix (21) in the text to be (m 2 + n 2 ), we can deduce that •y* = 0 and Bf. Consequently, from (A.34), we must have yf = 0. ||

Acknowledgements. I would like to dedicate this paper to Professor Terence Gorman who has done so much to stimulate the interest of his students in empirical problems. This revision has benefited from the comments of K. Hassett, F. Hayashi, three anonymous referees and, especially, a Managing Editor.

60

A. Bhargava

REFERENCES AMEMIYA, T. and MACURDY, T. (1986), "Instrumental-Variable Estimation of an Error Components Model", Econometrica, 54, 869-880. ANDERSON, T. W. and HSIAO, C. (1981), "Estimation of Dynamic Models with Error Components", Journal of American Statistical Association, 76, 598-606. BEHRMAN,J. R. and DEOLALIKAR, A. (1987), "Will Developing Country Nutrition Improve with Incomes? A Case Study for Rural South India", Journal of Political Economy, 95, 492-507. BHARGAVA, A. (1987). "Wald Tests and Systems of Stochastic Equations", International Economic Review, 28, 789-808. BHARGAVA, A. (1991), "Estimating Short and Long Run Income Elasticities of Foods and Nutrients for Rural South India", Journal of Royal Statistical Society, Series A (forthcoming). BHARGAVA, A. and SARGAN, J. D. (1983), "Estimating Dynamic Random Effects Models from Panel Data Covering Short Time Periods", Econometrica, 51, 1635-1660. BINSWANGER, H. and JODHA, N. S. (1978) Manual for Instruction for Economic Investigators in ICRISAT's Village Level Studies (Hyderabad: International Crops Research Institute for Semi-Arid Tropics). CHAMBERLAIN, G. (1984), "Panel Data", in Griliches, Z. and Intriligator, M. (eds). Handbook of Econometrics, Volume 2 (Amsterdam: North Holland). GEORGESCU-ROEGEN, N. (1966) Analytical Economics: Issues and Problems (Cambridge: Harvard University Press). GOPALAN, C , RAMA, B. V. and BALASUBRAMANIAN, S. C. (1971) Nutritive Value of Indian Foods (Hyderabad: National Institute of Nutrition). GORMAN, W. M. (1967), "Tastes, Habits and Choices", International Economic Review, 8, 218-222. HAUSMAN, J. A. and TAYLOR, W. E. (1981), "Panel Data and Unobservable Individual Effects", Econometrica, 49, 1377-1398. HSIAO, C. (1986) Analysis of Panel Data (New York: Cambridge University Press). HUTCHINSON, R. (1969) Food and the Principles of Dietetics (12th Edition) (London: Edward Arnold). LANCASTER, K. (1971) Consumer Demand: A New Approach (New York: Columbia University Press). RYAN, J. G., BINDINGER, P. D., RAO, N. P. and PUSHPAMMA, P. (1984) Determinants of Individual Diets and Status in Six Villages of South India (Hyderabad: International Research Institute for Semi-Arid Tropics). SARGAN, J. D. (1975), "Testing for Misspecification After Estimating Using Instrumental Variables" (Mimeo, London School of Economics). SARGAN, J. D. (1980), "Some Tests of Dynamic Specification for a Single Equation", Econometrica, 48,879-898. STIGLER, G. J. (1945), "The Cost of Subsistence", Journal of Farm Economics, 27, 303-314. SUKHATME, P. V. (1974), "The Protein Problem, its Size and Nature", Journal of Royal Statistical Societv A, 137, 166-199. WALD, A. (1947) Sequential Analysis (New York: Dover). WORLD BANK (1981) World Development Report (Washington: World Bank).

Review of Economic Studies (1982), XLIX, 533-549 © 1982 The Society for Economic Analysis Limited

0034-6527/82/00420533$00.50

Serial Correlation and the Fixed Effects Model A. BHARGAVA L. FRANZINI and W. NARENDRANATHAN London School of Economics This paper generalizes the Durbin-Watson type statistics to test the OLS residuals from the fixed effects model for serial independence. Also generalized are the tests proposed by Sargan and Bhargava for the hypothesis that the residuals form a random walk. A method for efficient estimation of the parameters is also developed. Finally, an earnings function is estimated using the Michigan Survey of Income Dynamics in order to illustrate the uses of the tests and the estimation procedures developed in this paper.

1. INTRODUCTION AND SUMMARY The use of panel data in elucidating economic relationships is quite appealing to economists since most theories pertain to the behaviour of the individual unit and panel data provides valuable information at the individual level. The fact that several heterogeneous units are observed for a relatively few time periods is recognised by econometricians and the so-called "random effects" and the "fixed effects" frameworks have been proposed in order to take account of the individual differences when estimating economic relationships from panel data. Whilst the former treats the effects as randomly distributed variables thus generally providing more efficient estimates of the parameters, it is required that some or all of the independent variables must be uncorrelated with the effects (see Hausman and Taylor (1981)). This assumption is perhaps a bit strong in some cases since one would expect individual units with a "high" individual component, for example, to possess some permanent characteristics which in turn might also influence their level of independent variables. The fixed effects model, on the other hand, does not rely upon the orthogonality assumptions since the the individual effects are introduced as parameters to be estimated (the covariance-analysis or the dummy variables technique). For both frameworks, however, a common problem is likely to be that the error terms of individual units are serially correlated due to the possible omission of relevant variables. Whilst Lillard and Willis (1978) have discussed the first order autoregression within the random effects framework, this paper attempts to tackle the problem of testing the serial independence of errors on afixedeffects model by extending the well-known results of Anderson (1948) and Durbin and Watson (1950, 1971). The recent work of Sargan and Bhargava (1982a) is also extended to panel data thereby allowing researchers to choose between model specification in levels versus differences by the means of the most powerful invariant tests (see also Sargan and Bhargava (19826)). We proceed by generalizing the Durbin-Watson and the Berenblut-Webb (1973) statistics to panel (Section 2). There are several advantages with the use of these tests. Firstly, the independent variable need not be orthogonal to the effects so that these tests may be applied to any static fixed effects model. Secondly, Kiefer (1980) has pointed out that for the fixed effects model, maximum likelihood estimates may not possess the

62

A. Bhargava, L. Franzini and W. Narendranathan

usual asymptotic properties due to the incidental parameters. All the tests proposed in this paper, however, have exact finite sample properties thereby circumventing these type of problems. Thirdly, it is possible to tabulate tight lower and upper bounds on the criteria (Tables I and II) so that the residuals from Ordinary Least Squares (OLS) can be tested for serial independence without any significant computational burden. And, lastly, since the Berenblut-Webb statistic is generally more powerful when the coefficient of serial correlation is close to one, an investigation of the exact powers of these tests (when data are available on only thirty individuals) reveals that the two tests perform equally well (Table III). Thus only the Durbin-Watson statistic would need to be calculated in practice (of course, as the number of individuals increases, the tests are equivalent so that there is little to choose between them). Section 3 discusses efficient estimation in the presence of serial correlation. The Generalized Least Squares (GLS) estimator is extended to panel data and is shown to perform very satisfactorily by Monte Carlo methods (Table IV). The difficulty here is that since the intertemporal variance-covariance matrix cannot be consistently estimated as the number of time periods is small (see Kiefer (1980)), we are forced to work out analytically the inconsistency in the estimate of serial correlation and adjust the preliminary estimate obtained from the Durbin-Watson statistic. In Section 4, we consider the appropriateness of model specification in first differences by testing the hypothesis that the residuals from the levels equation from a random walk. The tests proposed are a generalization of those developed by Sargan and Bhargava (1982a) and have the further desirable properties that a simple bounds test is feasible (Tables V and VI) and, as the number of individual units increases, it becomes possible to test both the hypotheses that the errors are serially independent and/or they form a random walk using only the sample criterion for the generalized Durbin-Watson statistic. For comparison with Section 2, we also report the powers of the three tests for random walk residuals in Table VII. Section 5 illustrates the uses of the tests and estimation procedures developed in this paper by estimating an earnings function for the U.S. using the Michigan Panel Survey of Income Dynamics. This empirical example is also meant to stress the ease with which hypothesis testing and estimation can be carried out for such large data sets and to point out how the storage limits on modern computers need not be exceeded in carrying out the computations. Finally, the conclusion summarizes the methodology developed in this paper. Before proceeding, it is perhaps worth pointing out that the errors on static regression equations can be serially correlated if the true relationship is in fact a dynamic one. The estimation of dynamic models from panel data, however, is much more complex than its counterpart in time series analysis since a typical panel consists of only a few observations over time. The role of the assumptions made on the initial observations on the dependent variable, therefore, becomes quite crucial (see Anderson and Hsiao (1981)). Further research, which takes account of the systematic part of the initial observations as well as the possibility of correlation between the independent variables and the individual effects, would seem to be necessary in order to resolve this very important case. 2. TEST STATISTICS The Durbin-Watson statistic for panel data We consider the model yi, = Si+i

xiityi + uit

uit = puit-i + eil

(t = l,...,T;i

= l,...H)

(1)

(t = l,...,T;i

= l,...,H)

(2)

63

Serial Correlation and the Fixed Effects Model

where eit are independently normally distributed with mean zero and variance a2, St are the fixed effects (or dummy variables), x's are the non-stochastic regressors and H and T are, respectively, the number of individual units and the number of time periods. Rewriting (l)'in matrix notation y=X*/3 + u

(3)

where y' = ( y n , . . . , yir, y 2 i , . . . , V2T, ••-, y m , . . . , y^r), u' = (ulu ..., ulT, u2i, •.., U2T, • • •, "HI. • • •, UHT), X* = (C • X), X being the HT x n matrix of the x's and C = (IH ® s), IH being the HxH identity matrix and s is a T x 1 vector of ones, and /?' = (8' • y') is the 1 x (H + n) vector of parameters to be estimated. Before estimating (1) on the assumption that the errors are generated by (2), it would seem apt to proceed by testing the null hypothesis that p = 0 against the alternative that | p | < l i.e. testing that the «„'s are serially independent against that alternative hypothesis that they are generated by the stationary first-order autoregression. A popular method of testing this hypothesis in time series analysis is by using the Durbin-Watson statistic d and we define its generalization to panel data by ^ .Ii-llt-2("'t~»'»-l) T Up — ir^ VH V Li-i Lt=i "'<


where w„ are the OLS residuals from estimating the fixed effects model (3) (or equivalently, by first subtracting off individual means from the variables, as described in Appendix A, and then running OLS of transformed y's on the transformed x's). By defining the matrices, M = InT-X*(X*'X*r1X*' (5) and A* = (IH®A) where A is the TxT

(6)

Durbin-Watson matrix, we can rewrite (4) in matrix notation as dp =

_,

u'A*u .,. uu

J dp=

u'MA*Mu TT} •

or (7)

M MU

Now to show that dP has the same desirable properties as the Durbin-Watson statistic d, we note that the density of (2) is proportional to exp [ ^ { ( 1 + P 2 ) I " i i r . i "?<-p2(Sf=i «?i +If = 1 "?r)-2p If =1 l l 2 «,«,.,_!>]

(8)

against which no Uniformly Most Powerful (UMP) test exists (follows from Anderson (1948)). However, by following Durbin and Watson (1950) and Wallis (1972) we can approximate (8) by exp r~2{(l +P2) l " i I^-i

"2»-P(X"I

«a + l "

I "2T)~2P

Efli lj=2 "ft"«-i}J

(9)

Then dP is a UMP test for the hypothesis that p = 0 against the one sided alternatives 0 < p < 1 (-1 < p <0) whenever the regressors are the eigen-vectors of the matrix A*.

64

A. Bhargava, L. Franzini and W. Narendranathan

Moreover, for arbitrary regressors, dP is a locally most powerful invariant test in the neighbourhood of p =0 (follows from Durbin and Watson (1971)). Next, we turn to the actual testing of the hypothesis that p = 0 using the sample criterion for dP calculated from (4). While it is true that modern computers have made possible an exact Durbin-Watson test in time series analysis (i.e. where the exact distribution of d is calculated using the Imhof routine, see, e.g. Koerts and Abrahamse (1969)), such a procedure is both impractical and unnecessary for panel data. Indeed, in order to calculate the exact distribution of dp, we need to calculate the non-zero eigen roots of the HTxHT matrix MA*. Thus, if the data were available on fifty individual units over ten time periods (H = 50, T = 10), then MA* is a 500 x 500 matrix and would exceed the storage limit of most modern computers. On the other hand, by constructing an argument similar to that of Durbin and Watson (1950), it is possible to set lower {dpi) and upper (dPU) bounds on dP quite independently of the regressors in the model (but, of course, depending on H, T and n). In order to do so, we note that the matrix C of the fixed effects forms the eigen-vectors of the matrix A* corresponding to the H zero eigen-roots. The non-zero eigen-roots of A* are given by Aq = 4 s i n 2 ( ^ )

(q = l , . . . r - l )

(10)

each occurring with a multiplicity of H (the number of individual units in the model). Thus in order to calculate the lower bound (dPL) on dP, we need to include the smallest (HT-H — n) eigen-roots given by (10) as the weights in the Imhof routine (see Koerts and Abrahamse (1969)) to calculate Pr[zZ~H~"^-r)z^0]=a

(11)

where z\ are independently distributed central chisquare variates and a is the size of the test. (11) can be evaluated for say three values of r and dPL corresponding to the given value of a can be found on inverse interpolation. Similarly, dPU can be calculated by including the largest (HT—H — n) roots (it is worth pointing out that the Imhof routine has provision for weights occurring with some multiplicity so that the A,'s appearing in (11) represent the ( T - l ) roots given by (10) except that the multiplicity factor is assumed to be set to H for all but the largest root (in calculating dPL) for which it is set to {H — n),H>n). As in the Durbin-Watson (1950) case, the null hypothesis of serial independence is rejected if the sample criterion dP calculated from (4) is less than dPL, the null is accepted if dP is greater than dPU and for dPL
Serial Correlation and the Fixed Effects Model

65

TABLE I Five per cent significance points ofdPL and dPU when T = 6 H

50

100

150

n

dpL

dpu

dpi.

dpu

dpL

dpu

1 3 5 7 9 11 13 15

1-8091 1-7954 1-7805 1-7665 1-7523 1-7380 1-7211 1-7063

1-8231 1-8376 1-8517 1-8657 1-8812 1-8956 1-9118 1-9267

1-8660 1-8592 1-8523 1-8444 1-8386 1-8304 1-8283 1-8163

1-8731 1-8799 1-8867 1-8937 1-9018 1-9086 1-9158 1-9227

1-8907 1-8859 1-8819 1-8770 1-8720 1-8671 1-8631 1-8580

1-8958 1-8998 1-9046 1-9094 1-9145 1-9185 1-9233 1-9284 1000

500

250

H n

dpL

dpu

dpL

dpu

dpL

dpu

1 3 5 7 9 11 13 15

1-9158 1-9135 1-9100 1-9070 1-9044 1.9021 1-8987 1-8956

1-9183 1-9217 1-9240 1-9265 1-9296 1.9321 1-9354 1-9379

1-9409 1-9393 1-9378 1-9363 1.9349 1-9333 1-9319 1-9304

1-9413 1-9427 1-9441 1-9455 1.9468 1-9482 1-9497 1-9511

1-9579 1-9573 1-9567 1-9551 1.9544 1-9538 1-9531 1-9524

1-9586 1-9593 1-9560 1-9606 1-9614 1-9621 1-9628 1-9630

TABLE II Five per cent significance points of dPL and dPU when T = 10 H

50

100

150

n

dpL

dpu

dpL

dpu

dpL

dpu

1 3 5 7 9 11 13 15

1-8512 1-8421 1-8338 1-8258 1-8164 1-8072 1-7999 1-7903

1-8596 1-8688 1-8769 1-8851 1-8945 1-9029 1-9126 1-9209

1-8953 1-8907 1-8862 1-8826 1-8780 1-8734 1-8698 1-8651

1-8991 1-9037 1-9081 1-9118 1-9164 1-9209 1-9275 1-9294

1-9156 1-9117 1-9076 1-9059 1-9047 1-9003 1-8971 1-8946

1-9160 1-9206 1-9244 1-9245 1-9284 1-9318 1-9341 1-9375

H

250

500

1000

n

dpL

dpu

dpL

dpu

dpL

dpu

1 3 5 7 9 11 13 15

1-9336 1-9321 1-9303 1-9286 1-9270 1-9255 1-9241 1-9217

1-9354 1-9370 1-9390 1-9405 1-9421 1-9445 1-9459 1-9474

1-9528 1-9520 1-9509 1-9501 1-9492 1-9484 1-9476 1-9468

1-9536 1-9544 1-9552 1-9561 1-9572 1-9580 1-9588 1-9569

1-9668 1-9667 1-9663 1-9657 1-9652 1-9648 1-9642 1-9639

1-9677 1-9679 1-9682 1-9686 1-9700 1-9705 1-9710 1.9712

66

A, Bhargava, L. Franzini and W. Narendranathan

The Berenblut-Webb Statistic The Berenblut-Webb statistic g has the desirable property that it is a locally most powerful invariant test in the neighbourhood of p = 1. Its computation, however, requires also the estimation of the differenced version of the levels equation (1) i.e. the estimation of Ayi( = Z; = 1 A^, r ; + AMir

(f = 2 , . . . , T ; i = l

H)

where Ayj( = yit - y„-i and Axy, = xijt - xtjt-i (t = 2,...,T;j = l,...,n,i generalized Berenblut-Webb statistic can then be defined as At

(12) = l,...,H).

The

A

ee gp = —

(13)

WW

where e and u are, respectively, the OLS residuals from estimating (12) and (1). It can be easily shown that the bounds for gP coincide with those for dP (see Bhargava et al. (1980)) and that gP = dP whenever the regressors are the eigen-vectors of A* or if we assume large sample behaviour in H. Thus the only conceivable advantage in the use of gP could be for the case where H is moderately small. While H is likely to very large for typical panels, we report in Table III the exact powers of dP and gP when H = 30, T = 10, n = 2 and a = 0-05, the data set being similar to that described in Appendix A. TABLE III Exact powers of dp and gP when testing H0:p = 01 P

dp

0-25 0-40 0-50

0-9616 0-9999 1000

gP Power 0-96076 0-9999 1-000

Notes:

L K = 30, r=10,n = 2,a=0-05.

2. Exactlimit= 1-82188. 3. Exact limit =1-80966.

Clearly the two tests perform equally well and their powers are very high in spite of H being only 30. In practice, therefore, it would be unnecessary to calculate gP and dP can be expected to be quite powerful in detecting serial correlation. 3. ESTIMATION AND SIMULATION RESULTS Estimation The null hypothesis that the errors are serially independent (or that they form a random walk) would probably be rejected quite frequently in favour of the alternative hypothesis that they are generated by the first order autoregression. It is therefore desirable to develop an estimation procedure in order to obtain efficient estimates of the parameters. On the standard assumption that the w„'s given by (2) have a constant variance (|p| < 1), the Generalized Least Squares (GLS) estimator (in the serial correlation sense) can be defined as b = (X*'n*~ 1 X*)" 1 X*'a*" 1 y (14) where ft* = (JH ® ft) is an HT x HT matrix, ft being the usual Tx.T variance-covariance

Serial Correlation and the Fixed Effects Model

67

matrix of the stationary first order autoregression i.e. ft has elements of the form <»tk=Z 21-p

(15)

From the standpoint of actual computations, (14) is a rather inconvenient expression and the GLS estimates can be obtained by first rewriting (1) and (2) as Vl-p2yll = Vl-p25I+Vl-p2i;=1%1y/+ell

(i = 1 , . . . , H)

(16a)

and (Yu - pyu-i) = (1 - P)SI + Zy"-i (xiit -pxu-Jy,

+ e„

(i = 1 , . . . , H; t = 2 , . . . , T) (16b)

and then eliminating the dummy variables 5, by the use of the symmetric idempotent matrix C + = (I„ ® C*) where C* = IT-W(W'WT1W'

(17)

and w i s a T x l vector given by vv' = ( V T ^ , l - p , . . . , l - p ) = ( ^ = £ , l , . . . , l ) ( l - p ) .

(18)

It is easy to show that this transformation is equivalent to transforming, for example, the dependent variable as V

^[rV-pH2>'-- [ T(^2p] I '-'fr»-^-- )

«-'

">

(19a

T).

(19b)

>

and f

()

'"

_Py

^ Q-P2)yn (1-P) v r , , " - " [ T ( l - p ) + 2p]~[T(l-p) + 2 p ] I ' = 2 ( y " ~ W ' - l ) l)

(i = l , . . . , / f ; f = 2

The JC'S can be similarly transformed and an OLS run of the transformed y's on the transformed x's will produce efficient estimates of the parameters. Alternatively, equations (1) and (2) may be transformed as (16a) and (16b) and an OLS subroutine which also eliminates the dummy variables 5( (by subtracting off individual means) can be used on these transformed variables to produce the GLS estimates (see also Appendix A and Section 5). The above discussion of the estimation problem assumes that p is known. In practice, however, p will usually be unknown and, in view of Kiefer's results, it is not possible to estimate it consistently by maximum likelihood type procedures unless the number of time periods (T) becomes very large. The latter condition is unlikely to be fulfilled in practice so that it would seem necessary to develop a procedure specifically for the first order autoregression (an earlier version of Nickell (1981) had also suggested a procedure but, as pointed out in Bhargava et al. (1981), the procedure suggested below is much more efficient). Assuming large sample behaviour in H (but not in T) we can write E(dP)=E\1^?iU;-Ui'-^]

(20)

where ut. = 1/T £ ( = 1 uit (i = 1 H) and n)t's are the OLS residuals from estimating (1). Now using the Nagar (1959) approximation for (20) and noting that all cross terms

A. Bhargava, L. Franzini and W. Narendranathan

68

are divided by H (and hence can be ignored), we have E\\/{HT) E(dP) =

!?_! lJ=2 (uit - uu-!)2]

E^/iH^Z^Zltiuu-u,.)2]

Taking expectations inside the square brackets and cancelling out a2, we have, to

BGt) ._2a=eKl=«GL_.

0(1/T),

(21)

[l-(l/T 2 )I, , '. 1 I,1 l( , 1 '-"]

Thus if we define, as in time series analysis, an estimate pD (which is consistent as T -» oo) by Pd = l - y

(22)

then

Bte,,.,..

<1Z£KIZ1) r

.

(23)

[r-(i/r)ir.,i, ,l(,"-"] Or, from Appendix B, v( ^ 1 E(pD) = 1 - r

L

r

(l-p)CT-l) — — 1+p 2 p ;( l - p 'r—. )1 + 2 p ( l - p 2)] 1+p l-p T(l-p) J

p

(24)

T(l-pr

Note that since dP will invariably be calculated to test the errors for serial independence, pD can be easily calculated from (22) and substituting this value on the left-hand side of (23) or (24), a very good estimate of p (say pD) can be obtained by solving the equation iteratively for p. Since this correction procedure for p is somewhat unconventional, we investigate its performance by Monte Carlo methods in the next subsection. Simulation results We study the properties of the model given by (1) and (2) by Monte Carlo methods (see Appendix A for details). Table IV reports the results for H = 50, T = 10, n = 2 and 50 replications. The biases in the estimates of the two y's were found to be negligible and hence are not tabulated (see also Breusch (1980)). The standard errors, however, indicate that for large values of p, the true OLS standard errors are considerably higher than those estimated by the OLS program and that the two step GLS (which uses the corrected pf>) produces standard errors that are very close to the true GLS standard errors. Thus there is a considerable advantage in using the suggested two step GLS procedure (although not reported in the Table, we also found that if the initial observations are deleted—as implied by Nickell (1981), then the resulting estimator entailed a very substantial loss in efficiency especially for small values of p). The biases in the estimates of pD and pD are also reported in Table IV. Clearly pD tends to be badly biased whereas pD tends to be very close to its true value. Thus it would seem reasonable to conclude that the estimation procedure developed above, although specific only to the first autoregression, is likely to perform quite satisfactorily in practice. We shall illustrate the use of this procedure by the means of an empirical example in Section 5.

Serial Correlation and the Fixed Effects Model

69

TABLE IV Simulation results for the fixed effects model with serially correlated errors1

(D-25

p

Parameter

0-50

0-75

Ti

Y2

n

T2

GLS(p)

0-0218

00235

0-0223

0-0237

OLS(p)

0-0216

0-0247

0-0263

0-0291

Estimator

0-90

yi

y-i

Yi

y^

0-0229

0-0228

0-0225

0-0218

0-0339

0-0363

00406

0-0426

True standard errors

Mean of the estimated standard errors GLS(p*D)

0-0206 (0-001)

0-0234 (0-001)

0-0222 (0-001)

0-0237 (0-001)

0-0227 (0-001)

0-0228 (0-001)

0-0224 (0-001)

0-0218 (0-001) 2

OLS

0-0188 (0-001)

0-0223 (0-001)

0-0196 (0-001)

0-0232 (0-001)

0-0215 (0-001)

0-0254 (0-001)

0-0231 (0-001)

0-0273 (0-002)

Bias in the estimate of p PD

P*D

-0-0660 (0-0486)

-01216 (0-0440)

-01959 (0-0323)

-0-2575 (0-0422) 2

-0-0183 (0-0618)

-0-0173 (0-0580)

-0-0264 (0-0467)

-0-0419 (0-0658)

Notes: 1. H = 5 0 , T = 1 0 , n=2 and 50 replications. 2. Standard deviations are in parentheses.

4. TESTS FOR RANDOM WALK RESIDUALS The hypothesis that the errors on the fixed effects model (1) form a random walk is of considerable interest since its acceptance would imply that the estimates of the parameters obtained from the differenced version of the model (equation (12)) are the most efficient. Also, investigators have found that for very high values of serial correlation, the distribution of the estimator (of p) corresponds closer to that when the true coefficient is, in fact, one (see, e.g. Evans and Savin (1981)). Thus if the residuals are found to be highly positively correlated (which would be indicated by a small value of dP), the researchers may wish to test if they form a random walk. We shall now show that dP, gP and RP (defined below) can be used to test the random walk null hypothesis by the means of another bounds test. It should be emphasised however, that as the number of individual units becomes large (a common feature of panel data), the three tests are equivalent (see Appendix C) so that only dp will be used in practice in order to test the random walk hypothesis as well. This is in contrast with the ordinary time series case, studied by Sargan and Bhargava (1982a), where the tabulated bounds were very wide apart and it was seen to be desirable to calculate the exact distribution of the BerenblutWebb statistic. Rewriting equation (3) as y = CS+Xy + u

(25) where C = (IH ® s) is the matrix of the fixed effects and X consists of the independent variables, we now wish to test the null hypothesis that the H„'S are generated by Ui, = Ui,-i + ei,

(26)

A. Bhargava, L. Franzini and W. Narendranathan

70

against the alternative that Ui, = pult-i + elt

(|p|
(27)

Observe that the problem remains invariant with respect to transformations of the form y* = a0 + a1y+Xa2 (28) where a'0 = (a01,..., a0H), a'0i = m,(l, 1 , . . . , 1) (i = l,...,H), - o o o n , 0 and - o o < a2/ < °o (/ = 1 , . . . , n). Thus at the first stage, the set of first differences D*y can be chosen as a maximal invariant (see Lehmann (1959), Bhargava (1982)) where D* = (IH®D)

(29)

and D i s a ( T - l ) x T matrix with elements of the form dkj = -\

if k=j

= 1 if; =fc+ l = 0 otherwise. Also the approximation of the density (8) by (9) implies that f l * _ 1 - n r 1 = (l-p)2/m'+pA* so that the most powerful invariant test is given by the critical region f fcb

f

• •• f oo

-h(P*y

-D*Xy, a) dyx dy2 • • • dyn da

ps-^

>r

(30)

f • • • [ -f0(D*y -D*Xy, a) d7l dy2... dyn da •'o J—oo J—oo a where/o and/i are the respective densities under the null and the alternative. Proceeding along the lines of Sargan and Bhargava (1982a) it is easily seen that the statistic R r ~

(3D

where e are the OLS residuals from the differenced equation (12), F* = (IH®F)

(32)

and F i s a ( r - l ) x ( T - l ) symmetric matrix with elements of the form

Fik = (T-j)k/T if/afc (y = i,...,r-i;fc = i,...,r-i), = Fki

(; = l , . . . , T - l ; f c = l , . . . , r - l )

is a Uniformly Most Powerful test against the one sided alternatives in (27) whenever the regressors are the eigen-vectors of A*. Moreover, for the eigen-vector case, we also have that Rp = gP = dP

(33)

where gP and dp are now being considered under the random walk null hypothesis (see, Sargan and Bhargava (1982a)). For general jc's, (33) is replaced by RpSgp^dP

(34)

and it is possible to tabulate lower (RpL) and upper (RPU) bounds for RP by extending

Serial Correlation and the Fixed Effects Model

71

the argument presented in Section 2. Now the non-zero eigen-roots of F* are given by Mq

= l/[4sin2(|^)]

(q = l,...,T-l)

(35)

each occurring with a multiplicity of H (note that (fj.q = 1/Aq). Thus in order to calculate the lower and upper bounds we need to include, respectively, the largest and the smallest (HT—H- n) eigen-roots in evaluating p\L^xH~n

(1 - m)z} S o] = 1 - a.

(36)

The Imhof routine can be used to evaluate (36) and the bounds are found on iterpolation as described above. The null hypothesis that the residuals form a random walk is accepted if RP is less than RPL, the null hypothesis is rejected if RP is greater than RPU and for RPL
50

100

150

RPL

Rpu

RPL

Rpu

RPL

Rpu

1-0126 1-0069 0-9987 0-9930 0-9871 0-9811 0-9741 0-9669

10266 1-0454 10667 10889 1-1135 1-1386 1-1654 1-1928

0-9644 0-9600 0-9587 0-9552 0-9515 0-9483 0-9462 0-9432

0-9707 0-9800 0-9869 0-9994 1-0095 10194 10269 1-0355

0-9433 0-9417 0-9399 0-9377 0-9357 0-9336 0-9320 0-9300

0-9479 0-9538 0-9595 0-9620 0-9665 0-9774 0-9810 0-9887

H

250

500

1000

RPL

RPU

RPL

Rpu

RPL

Rpu

0-9235 0-9219 0-9210 0-9200 0.9187 0.9170 0-9163 0-9156

0-9231 0-9270 0-9300 0-9335 0-9392 0-9425 0-9480 0-9510

0-9033 0-9020 0-9016 0-9012 0-9007 0-9002 0.8998 0-8993

0-9044 0-9058 0-9070 0-9075 0-9101 0-9103 0-9123 0-9152

0-8892 0-8890 0-8888 0-8885 0-8883 0-8881 0-8878 0-8876

0-8900 0-8905 0-8915 0-8926 0-8937 0-8945 0-8956 0-8967

72

A. Bhargava, L. Franzini and W. Narendranathan

TABLE VI Five per cent significance points ofRPL and Rpu when T= 10 H

50

100

150

RPL.

Rpu

RPL

Rpu

RPL

Rpu

06562 0-6536 O-6510 0-6485 0-6460 0-6434 0-6409 0-6383

0-6592 0-6735 0-6890 0-7061 0-7245 0-7422 0-7615 0-7890

0-6216 0-6196 0-6187 0-6178 0-6168 0-6147 0-6138 0-6129

0-6232 0-6286 0-6931 0-6443 0-7045 0-7098 0-7110 0-7161

0-6064 0-6058 0-6051 0-6045 0-6038 0-6031 0-6023 0-6016

0-6077 0-6260 0-6320 0-6398 0-6445 0-6509 0-6540 0-6580

H

250

500

1000

RPL

Rpu

RPL

Rpu

RPL.

Rpu

0-5897 0-5892 0-5885 0-5880 0-5878 0-5875 0-5873 0-5870

0-5910 0-5963 0-5986 0-6001 0-6036 0-6051 0-6079 0-6107

0-5781 0-5779 0-5777 0-5775 0-5773 0-5771 0-5769 0-5767

0-5788 0-5796 0-5807 0-5824 0-5837 0-5841 0-5858 0-5865

0-5682 0-5680 0-5679 0-5678 0-5678 0-5677 0-5677 0-5676

0-5686 0-5691 0-5697 0-5704 0-5708 0-5715 0-5721 0-5728

practice for gP and dp. However, since a typical panel consists of a large number of individuals, it would be reasonable to take probability limits as H -* oo. For this important case in applied research, the inequality (34) can be replaced by the equality (33) (the interested reader is referred to Appendix C for proofs). Thus only the Durbin-Watson statistic dp calculated above need be used in testing the random walk null hypothesis thereby saving on additional computations necessary for the calculation of gP or RP both of which require also the estimation of the differenced equation (12). Furthermore, the preliminary estimate of serial correlation is also obtained from dP (see equation (22)) which obviates the need for storage of the vector of residuals in order to calculate a preliminary estimate of p. Finally, as a matter of interest, Table VII reports the powers TABLE VII Exact powers of dp, gP and RP when testing H0: p = 1 p

dp

g3P

RP

Power 0-50 0-75 0-80 0-85 0-90

100 0-95164 0-82462 0-5926 0-33323

Notes: 1. H=30, 7=10, n=2,a=Q05. 2. Exact Limit =0-73049. 3. Exact Limit =0-71173. 4. Exact Limit =0-69654.

100 0-96163 0-84739 0-62073 0-35219

100 0-96380 0-85306 0-62832 0-35749

Serial Correlation and the Fixed Effects Model

of RP, gP and dP (using the same data set as that used in calculations reported in Table IV; H = 30, T = 10, n = 2 and a = 0-05). The power of dP is seen to be very slightly lower than that of RP or gP (RP is a locally most powerful invariant test in the neighbourhood of p = 1 and gp is a locally most powerful test in the neighbourhood of p — 0, see Sargan and Bhargava (1982a)) and since the three tests are equivalent as H-*oo, there would seem to be a strong justification in the use of dP alone to test the random walk null hypothesis. We now turn to Section 5 where all the tests and estimation procedures developed in this paper are illustrated by the means of an empirical example.

5. AN ILLUSTRATION From the Michigan Survey of Income Dynamics, data were taken on male heads of households who were not unemployed, reported positive earnings throughout the sample period, were not retired or full-time students and were not included in the SEO sample. Thus we obtained data on 962 individuals (if = 962, T= 10). An OLS program was written and subroutines to calculate dP and p% were attached to it. The most salient feature of the program is that data are read in individual by individual since the data tramsformation like the elimination of the dummies can be carried out separately for each individual. This obviates the need of reading in the typically very large matrix X (here 10,000 x 12) which makes enormous savings on the storage space required in the execution of the program (details available on request). Column 2 in Table VIII reports the results for the run on the levels equation after the dummy variables were eliminated by subtracting off individual means. As noted by Hausman and Taylor (1981), years of schooling and other fixed attributes, being constant throughout the sample period, drop out due to the fixed effects. From the vector of residuals, the sample criterion for dP was calculated to be 1.3331. The appropriate lower limit dpL for testing against positive serial correlation is 1-96 (Table II) and clearly dP
73

74

A. Bhargava, L. Franzini and W. Narendranathan TABLE VIII Regression results using the Michigan survey of income dynamics (dependent variable is log of income appropriately transformed) 1. Regressors

2. OLS (Levels)

3. (Differences)

4. GLS(p£)

EXP1

0-0977 (0-0022) -0-0005 (0-0001)

0-1024 (0-0075)

0-09876 (0-0031)

-0-0006 (0-0001)

RURAL 2

-0-0279 (0-0199)

-0-0133 (0-0235)

-00005 (0-0001) -00212 (0-0220)

OCC.l 3

01692 (00391)

0-0562 (0-0445)

01166 (0-0420)

OCC.2

0-1269 (0-0372)

0-0589 (0-0424)

00960 (00399)

OCC.3

-0-0292 (0-0392)

0-0032 (0-0442)

-0-0012 (0-0418)

OCC.4

0-0476 (0-0375)

0-0280 (0-0426)

0-0427 (0.0402)

OCC.5

00809 (0-0348)

0-0235 (0-0400)

0-0553 (0-0375)

OCC.6

0-0525 (0-0361)

0-0070 (0-0406)

0-0336 (0-0384)

OCC.7

-00195 (0-0381)

-0-0233 (0-0419)

-0-0152 (0-0400)

OCC.8

-0-2076 (0-0502)

-0-1357 (0-0571)

-0-1670 (0-542)

ANHRS 4

0-5799 (0-0133)

0-4996 (0-0127)

0-5455 (0-0129)

582-24

767-53

560-84

(EXP squared)

RSS 5 DF

6

8646

8646

8646

d P =l-3331

g P =l-3186

R P =l-3035

Notes': 1. Experience=Age-(years of schooling)-6. 2. For city size S 10,000 people. 3. Dummies for occupational groups (see Lillard and Willis (1978)). 4. Log of annual hours of employment. 5. Residual sum of squares. 6. Degrees of freedom.

6. CONCLUSION In this paper, we have developed a methodology which can be easily implemented to test the OLS residuals from a fixed effects model for serial correlation and to estimate the parameters efficiently in its presence. The proposed tests have the optimum properties of their counterparts in time series analysis and, since typical panel data sets are very large, we have placed considerable emphasis on the feasibility of the recommended procedures. To recapitulate the ideas presented in this paper, the research strategy suggested for typical panels is:

Serial Correlation and the Fixed Effects Model

75

(i) Test H0: p = 0 by comparing the sample criterion for dP with dPU. If dP > dPU, the residuals are serially independent (test for negative serial correlation also) and the levels equation (1) yields efficient estimates. (ii) If dP < dPL., test H0: p = 1 by comparing dP with RPL. If dP < JRPL, the residuals form a random walk and the estimates of the parameters form the differenced equation (12) are efficient, (iii) If dP>RPU, then let pD = l-(dP/2) and use (23) or (24) in order to find a corrected estimate p%. Then transform the variables as described by (16a, 16b) and estimate by OLS after eliminating the dummy variables. Since the fixed effects model has been much used in previous studies and serially correlated errors lead to incorrect estimates of the standard errors of the estimated coefficients, we hope that this extension to panel data of some well-known as well as some recently developed procedures will prove to be quite useful in applied research.

APPENDIX A The model y.-< = St + yixn, + y2Xi2, + uit

(t = 1 , . . . , 10; / = 1 , . . . , 50)

uit = puu-i + eit

(f = 1 , . . . . 10; / = 1 , . . . . 50)

was generated as follows. First {viu, vi2t} (f = 1 , . . . . 15; » = 1 , . . . . 50) were drawn from a Bivariate Normal distribution with mean zero, variance one and correlation 0-5 (Box-Muller). Then the JC'S were generated by xijt = 0-lt+pijXii,-1 + v,j,

(/ = 1, 2; t = 1 , . . . , 15; / = 1,. . ., 50)

where the pu (y'=,l,2) were drawn from a Uniform distribution in (0,1). Next, the {e«} (t = 1 15; / = 1 , . . . , 50) were drawn from an independent Normal distribution with zero mean and variance 0-25. The w's were then generated by Ui, = puu-i + ei,

(t = 1 , . . . , 15; / = 1 , . . . ,50).

Finally, the y 's were generated by y„ = S; + l-8*u' + 0-8xi2t + uu

(f = 1 , . . . , 15; i = 1 , . . . , 50)

where 8t are Uniform in (0,2). The first five observations were then discarded. For the OLS run, the fixed effects were eliminated by transforming the variables as {yi( - y,,}, {xij,-Xy.}

(i = l,...,H;t

= l,...,T;J

=

l,...,n)

where y.-- = r;E, T =iyir,

xu. = j;Zt=iXii<

(' =

1

H;j =

l,...,n)

and the computations were carried out using the transformed variables. For GLS, the variables were first transformed as described by (16a, 16b) and then the above OLS procedure was used.

76

A. Bhargava, L. Franzini and W. Narendranathan

APPENDIX B lk

Zl-i lli p ~" = r+2 z™ (T-j)p1 T\

= T +

2Tp(l-p ) _ 2 p [ 1 +

2 p + 3p2 +

. . .+

(r

_1)p-2]

1-p =

T(l+p)-2TpT 1-p

d T_2 2p — [p(l+p + - • -+p )J dp

T(l+p)-27pr i-/3

„ rd-rpr"1)(l-p) + (p-pr)l -*py (1- -Pf

r(-V)--2p(l--p

)

(i -Pf Thus B(PD)==

( 1 - -p)(T- -1)

i-,

1/ "

~Tu,

rl (i-p) 2 (l-p)GT-i) 'l+p\ 2p(l-p 7 )l p) + Tix-pYi

[*-(&)

APPENDIX C We wish to show that the three test statistics , «p=

uA*u -,-

,

ee

.

gp=^7T

and

_ i< P =

ee „

p

^

are equivalent as H -» oo. First, replacing the OLS estimator of /? by the true population value, we have u'A*u u'JVV

d

P = ..I*T*>

5SP= F

u'D*'D*u .,.,».. u'N*u

. and

„ i?P

u'D*'D*u u'D*'F*D*u

where N* = (IH®N) and N = IT-(1/T)ss', s being a T x l vector of ones. The equivalence of dP and gP follows from the fact that A*~D*'D* and the equivalence of gP and RP follows from noting that D*'F*D* = (I„®D'FD) =

[IH®D'(DD'TlD]

= N* X

l

since F = {DD')~ and D'(DD')~ D =AT (see Sargan and Bhargava (19826)). First version received August 1981; final version accepted March 1982 (Eds.). This paper is a revised version of the ICERD Discussion Paper (Bhargava et al. (1981)). We are grateful to Tony Atkinson, Terence Gorman, David Hendry, Steve Nickell, Denis Sargan, Tony Shorrocks and Paul Taubman for helpful comments and encouragement. This revision has also benefitted from the the comments of the two referees and, especially, the Managing Editor. Bhargava's research was financed, in part, by an ICERD grant.

Serial Correlation and the Fixed Effects Model

REFERENCES ANDERSON, T. W. (1948), "On the Theory of Testing Serial Correlation", Skandinavisk Aktuarietidskrift, 31, 88-116. ANDERSON, T. W. and HSIAO, C. (1981), "Estimation of Dynamic Models with Error Components", Journal of American Statistical Association, 76, 598-606. BERENBLUT, 1.1, and WEBB, G. I. (1973), "A New Test for Autocorrelated Errors in the Linear Regression Model", Journal of Royal Statistical Society, Series B, 1, 33-50. BHARGAVA, A. (1982), "The Theory of the Durbin-Watson Statistic with special reference to the Specification of Models in Levels as against in Differences" (forthcoming Ph.D. thesis, LSE). BHARGAVA, A., FRANZINI, L. and NARENDRANATHAN, W. (1980). "Durbin-Watson-Sargan type Tests for Serial Correlation in Models Estimated from Panel Data I" (ICERD Working Paper). BHARGAVA, A., FRANZINI, L. and NARENDRANATHAN, W. (1981), "Serial Correlation and the Fixed Effects Model" (ICERD Discussion Paper, No 81/33). BREUSCH, T. S. (1980), "Useful Invariance Results for Generalized Regression Models", Journal of Econometrics, 13, 327-340. DURBIN, J. and WATSON, G. S. (1950), "Testing for Serial Correlation in Least Squares Regression I", Biometrika, 37, 409-428. DURBIN, J. and WATSON, G. S. (1971), "Testing for Serial Correlation in Least Squares Regression III", Biometrika, 58,1-19. EVANS, G. B. A. and SAVIN, N. E. (1981), "Testing for Unit Roots 1", Econometrica, 49 (3), 753-779. HAUSMAN, J. A. (1978), "Specification Tests in Econometrics", Econometrica, 46, 1251-1272. HAUSMAN, J. A. and TAYLOR, W. E. (1981), "Panel Data and Unobservable Individual Effects", Econometrica, 49 (6), 1377-1398. KIEFER, N. M. (1980), "Estimation of Fixed Effects Models for Time Series of Cross-Sections with Arbitrary Intertemporal Covariance", Journal of Econometrics, 14,195-202. KOERTS, J. and ABRAHAMSE, A. P. J. (1969) On the Theory and Applications of the General Linear Model (Rotterdam: Rotterdam University Press). LEHMANN, E. L. (1959) Testing Statistical Hypotheses (New York: John Wiley). LILLARD, L. A. and WILLIS, R. J. (1978), "Dynamic Aspects of Earning Mobility", Econometrica, 46, 985-1011. NAGAR, A. L. (1959), "The Bias and Moment Matrix of the General k-Class Estimators of the Parameters in Simultaneous Equations", Econometrica, 27, 573-595. NICKELL, S. J. (1981), "Biases in Dynamic Models with Fixed Effects", Econometrica, 49 (6), 1417-1426. SARGAN, J. D. and BHARGAVA, A. (1982a), "Testing Residuals from Least Squares Regression for being Generated by the Gaussian Random Walk", Econometrica (forthcoming). SARGAN, J. D. and BHARGAVA, A. (19826), "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors when the Root lies on the Unit Circle", Econometrica (forthcoming). WALLIS, K. F. (1972), "Testing for Fourth Order Autocorrelation in Quarterly Regression Equations", Econometrica, 40 (4), 617-636.

77

II. Food Intakes, Health and Productivity in Developing Countries

81

J. R. Statist. Soc. A (1991) 154, Parti, pp. 157-174

Estimating Short and Long Run Income Elasticities of Foods and Nutrients for Rural South India By A L O K B H A R G A V A f University of Houston,

USA

[Received September 1989. Revised March 1990] SUMMARY

This paper estimates expenditure-income elasticities of six categories of foods using the Institute for Crops Research in Semi-Arid Tropics panel data on households from rural south India. The results underscore the importance of distinguishing between the short and long run effects particularly for groups like milk and meat. The demand for intake of nutrients is next analysed using two time observations on individuals under three formulations. A simple dynamic demand system is specified for five nutrient groups which is then extended to incorporate the differences in quality of foods consumed by expressing the intake of nutrients as ratios to energy intake by the individuals. Lastly, an interdependent formulation is estimated under special assumptions on the pattern of correlation between the individual effects and the remaining nutrients. The limited length of the panel data raises some issues of identification in the third case that are also resolved. Overall, these data provide support for the view that increases in household incomes will in turn improve the intakes of nutrients. Keywords: DYNAMIC DEMAND MODELS; FOOD AND NUTRITION POLICIES; INCOME ELASTICITIES; MAXIMUM LIKELIHOOD ESTIMATION; PANEL DATA

1. INTRODUCTION The problems of undernutrition in developing countries are recognized to be of utmost importance by researchers in many disciplines as well as by the international agencies which provide aid and support to these countries. Since important policy decisions should be based on the circumstances prevailing in these countries, considerable effort has been devoted to analysing the dietary habits of at least some of the residents. A good example of the influence of statistical analysis of the data on policy decisions is the work by Sukhatme (1974) which challenges the view that improved nutrition is synonymous with increased intakes of protein. Rather, the inability of households to purchase food has been blamed for malnourishment (Sukhatme (1974), p. 167). The problems of nutrition are well known to economists in developed countries as well partly because of the analysis of 'minimum cost diets' by Stigler (1945) that in turn influenced the work on 'quality differentials' by Gorman (1980), Griliches (1961) and Lancaster (1966). The analysis of nutritional well-being of individuals is on the periphery of several disciplines since food consumption habits are determined, among other things, by the nutrient requirements of the human body, the amount of money budgeted for food, cultural patterns, individual specific needs, etc. It should therefore be the case that a 1Address for correspondence: Department of Economics, College of Social Sciences, University of Houston, Houston, TX 77204-5882, USA. © 1991 Royal Statistical Society

0035-9238/91/154157

$2.00

82

A. Bhargava

multidisciplinary approach incorporating the various determinants of nutritional intake in the statistical analysis would enhance the value of the empirical results. Now, it is well known that it is practically impossible to define the optimal level of nutrient intake for an individual and the results from biomedical experiments can only recommend what may appear to be reasonable levels for the nutrients. An apparent shortcoming in these recommendations is the lack of substantive evidence on the manner in which different nutrients interact within the human body. The interactions between energy and protein, however, are recognized by many writers; Hutchinson (1969) notes that 'protein when divorced from carbohydrate in the diet is of no use in repairing the wear and tear of body protein'. Sukhatme's criticism of the emphasis on protein enrichment of diets in poor countries is in the same spirit. A drawback in the analysis of data on nutritional intakes is the unavailability of successive observations (panel data) on the same individuals that could afford a systematic control of the individual-specific differences. Thus previous researchers have relied mainly on cross-sectional data (Langier, 1969; Timmer and Alderman, 1979) and in some situations restrictive assumptions have been invoked to avoid biases induced by the interindividual and intra-individual differences (Sukhatme, 1974). Fortunately, the Institute for Crops Research in Semi-Arid Tropics (ICRISAT) has surveyed individual members of 240 households in six south Indian villages with regard to their consumption of food in the previous 24 hours (Binswanger and Jodha, 1978). In each village, 40 households representing different socioeconomic groups were surveyed twice a year for 2 years (1976-77). The data on annual household food expenditures and four successive 24-hour recall observations on individuals' intakes of nutrients in three of the villages were made available to researchers. Recently, Behrman and Deolalikar (1987) have analysed the ICRISAT consumption data from the standpoint of estimating expenditure elasticities (Engel curves) for six food categories and for nine nutrients. Although the point estimates of the former appear to be reasonable, there is practically no correlation between nutrient intake by individuals (or households) and household incomes (or expenditures) within static regression models (see also Ryan etal. (1984)). (Their results are sensitive to the specification of the model in levels versus differences since level is not controlling for individual effects. Also, it is well known that the within variance obscures relationships in 24-hour recalls (Liu etal., 1978).) This has led these researchers to conclude that 'the World Bank (1981)-type optimism about the nutrients improvements to be expected with income gains . . . seems fundamentally misleading' (Behrman and Deolalikar (1987), p. 505). Given the serious policy implications of their conclusions, this paper re-examines the role of incomes in determining the nutritional well-being of these Indian villagers. We estimate models which facilitate a distinction between the short and long run effects as emphasized by Gorman (1967), Nerlove (1972) and Phlips (1974). The analysis also incorporates some of the relevant socioeconomic and biomedical factors affecting the intakes of nutrients and elaborate econometric and computational techniques are used to estimate the relationships. The empirical results establish a causal link between the intake of nutrients and household incomes. This in turn provides support for the case advocated by the World Bank (1981) for improving nutrition in less developed countries by raising the incomes of the poor. The structure of this paper is as follows. Section 2 estimates short and long run expenditure elasticities for six food groups (grains, sugar, pulses, vegetables, milk

Short and Long Run Income Elasticities

and meat) using household level data. Section 3 proceeds by estimating simple dynamic models for intakes of five nutrient groups (energy, protein, calcium and iron, vitamins A and C, and vitamin B). It is then argued that the demand for more nutritious foods would entail a change in the proportions in which the other nutrients are consumed in comparison with energy intakes. Thus the dynamic model is re-estimated with the intakes of nutrients expressed as ratios to energy intakes. Section 4 develops an interdependent system for the five nutrient groups incorporating some suggestions of Hutchinson (1969), Stigler (1945), Sukhatme (1974) and Lancaster (1971). The present approach is somewhat different since it is impossible to consume even very basic foods like grains and not to consume, for example, riboflavin that is abundant in some more nutritious foods. Thus, in specifying a simultaneous equations system for the five nutrient groups, the identification of the parameters cannot be achieved by excluding any of the endogenous or the predetermined variables from the equations. Instead, specific assumptions are made on the pattern of correlation between the individual specific effects and the time varying variables (Bhargava and Sargan, 1983). These assumptions provide additional instrumental variables which enable the identification of the system given only two time observations (Appendix A). The robustness of the empirical results can be examined by using dietary surveys from less developed countries that are repeated more frequently (Beaton etal., 1979; Block, 1982; Freudenheim etal., 1987; Nelson etal., 1989; Bhargava, 1989). 2. ESTIMATING EXPENDITURE ELASTICITIES OF FOODS FROM HOUSEHOLD DATA 2.1. Habit Persistence in Diets Although dietary habits in the Indian subcontinent have changed in the last few decades owing to overall increases in household incomes, one nevertheless senses a remarkable amount of continuity in the eating habits of the people. In general, these habits depend on the geographic location, caste and income group of the households. An example of the continuity is the practice of vegetarianism as a result of which generations have abstained from eating meat. Similarly, typical meals consist of rice or wheat (or some other grain like bajra) together with some pulses and vegetables (and meat). It is important to note that the proportions in which these foods are consumed depends on the notion that households have regarding their relative affluence. Thus, for example, households regarding themselves as poor would be accustomed to consuming rice with a very small quantity of pulses and practically no vegetables unless there is a substantial drop in the relevant prices or if they have received payments in kind. In contrast, wealthy rural households will generally consume some rice mixed with a greater proportion of pulses as well as some vegetables (and meat). The children in these households usually supplement their meals with some milk. Now, if a hypothetical household regarding itself as marginally wealthy began to experience successive drops in income, then it would be reasonable to expect an immediate reduction in its consumption of milk (and meat). This would be gradually followed by a lowering of the proportions in which vegetables and pulses are consumed though the extent to which the proportions change will depend on the degree to which the lowering of incomes is perceived as a permanent drop by the members of the household.

83

84

A. Bhargava From the above discussion, the two important aspects of analysing data on rural Indian households are, firstly, the perceptions of the households of their relative position within their village or their permanent incomes. Secondly, it is important to incorporate the fact that changes in eating habits will occur with some lag. From an empirical standpoint, these factors underscore the need for a clear distinction between the short run and the long run effects of changes in household incomes on the pattern of food consumption. In particular, it is very likely that the long run expenditure elasticities of more nutritious foods are considerably higher than their short run counterparts. However, some of these distinctions may not be fully visible in estimates using only two time observations. (It would have been useful to obtain the data for the entire 9 years. However, only the data on food consumption for the years in which the 24-hour recall surveys were carried out were compiled very accurately.) 2.2. Habit Persistence and Demand A nalysis The notion of habit persistence in empirical economic analysis has been long recognized in the works of Duesenberry (1949), Friedman (1957), Stone (1954) and Houthakkar and Taylor (1970). A formal treatment of short and long run models of utility and demand may be found in Gorman (1967), Pollak (1970), Phlips (1974) and Deaton and Muellbauer (1980). The reasoning underlying the long run class of models is that choices depend on tastes and tastes in turn depend on past choices. This is certainly consistent with the behaviour of the rural Indian households previously described. From the standpoint of estimating Engel curves, the previous work has relied on cross-sectional data (Prais and Houthakkar, 1955) which do not permit a distinction between the short and the long run effects. In this section, we focus on food consumption and assume that households maximize utility subject to the usual budget constraint. Habit formation may now be incorporated by assuming that the past choices affect current consumption with their influence declining geometrically over time. This is equivalent to introducing the past or the lagged value of the dependent variable as an explanatory variable into the model (Pollak, 1970). The resulting short run demand function can be then written as Q, = h(PnmnQ,_{)

(1)

where Q, and P, are respectively the vectors of quantities demanded and prices in time period /, Q,_x is the past value of Q, and m, is the total expenditure in time period /. The estimation of such a (dynamic) model from panel data entails the treatment of the initial values of the dependent variable (Qt) as endogenous in the system in so far as the number of time periods for which the data are available is small (Anderson and Hsiao (1981), Bhargava and Sargan (1983) and below). Thus for every food group we specify the model m

2

yn = S ZyOj +

n

YJTJ

**A, + «/.

(1=1,...,//)

(2)

and m

n

yn = Y^Zuyj+Y^X^k

+ Oiyn + Un

(/= 1... . , / / ) .

(3)

85

Short and Long Run Income Elasticities

Here, yn and yn are expenditures in 1976 and 1977 respectively of the /th household on the relevant food group (// = 94), the z are the time invariant regressors (z,0 being a constant term), the x are the time varying variables such as number of adult equivalent members and total expenditure, un and ua are random error terms that are jointly distributed with mean zero and a finite (unrestricted) 2 x 2 variancecovariance matrix, and a is the coefficient of the lagged dependent variable. The unknown parameters 7, /3 and a in equation (3) will be estimated by an iterative maximum likelihood estimation procedure that filters out of the likelihood function the nuisance parameters <5 and 6 in equation (2) (Bhargava and Sargan, 1983). (Estimates of the instrumental variables were used as initial values in the numerical optimization of the log-likelihood function. A Fortran program written previously by the author was extended to use the vector version of the optimizing routine E04JBF of the Numerical Algorithms Group (1989) library.) It is not necessary to assume that the errors u„ are normally distributed for estimation or inferences (Bhargava, 1987) and they need not conform to the simple random effects decomposition ",v = »?, + «>»

(i=l,...,H;

t=l,2)

(4)

where 17, are the individual or household-specific random variables. 2.3. Random Effects and Exogeneity Assumptions It is helpful to elaborate on the complications arising from the presence of the random effects r/, in model (2)-(3). Firstly, the 77, represent individual or householdspecific permanent characteristics that cannot be modelled within the equations to be estimated. In the analysis of individuals' intakes of nutrients presented later, the 77, could reflect the metabolic rates and/or the chemical work performed by the subjects, the latter being unmeasurable (Waterlow, 1989). These factors clearly affect the intakes of nutrients (>>„). And since, in short panel data, the correlation between y] and u2 cannot be ignored, yx is treated as an endogenous variable in the system. Secondly, some of the explanatory variables (the z or x) are likely to be determined outside the system and are therefore independent of the error terms w„. Again in explaining the individuals' intakes of nutrients, the size (or income) of the households may be appropriately treated as predetermined. Thirdly, some of the x (or the z) might be influenced by the random effects. For instance, 77, may affect the weight of the individual in the above example. This is because the characteristics determining the weight of a person may also be systematically affecting the individual's intakes of nutrients like energy and protein. For the time varying variables, a possible pattern of correlation is Xij, = KJr)i + x*Jt

(j = 1, . . . , / • ; / = 1, ...,H;t=

1, 2)

(5)

where the x*, are uncorrelated with the error term «„ (and 77,) and K, are constants. Here, the xUl are correlated with the u„ but this correlation is due to the random effects 77,. Thus a high realization of 77, will in turn raise (or lower) the levels of the observed time varying variables. The deviations of xijt from their time means, however, are uncorrelated with the error terms and can be used as additional instrumental variables (Bhargava and Sargan, 1983). Variables of this type will be referred to as 'special' endogenous time varying variables. In contrast, the correlation between yx and u2 is of a general type and thus j , is a 'fully' endogenous variable of the system.

86

A. Bhargava

Finally, it would be desirable to assume a general form of correlation between the errors and thex. Unfortunately, this seems infeasible for a dynamic model given only two time observations. However, a static formulation can be estimated from two observations with some fully endogenous time varying variables. The empirical results for the intakes of nutrients problem indicate that the consequences of the incorrect enforcement of the decomposition (5) depend on the various properties of the models postulated (Bhargava, 1991). This is discussed further in Section 4. 2.4. Empirical Results for Rural South Indian Households Table 1 reports the results for equation (3) estimated using data on six food groups (grains, sugar, pulses, vegetables, milk and meat) using household data from three villages. The regressors are dummy variables for two of the villages, number of adult equivalent members, its square and total expenditure. Food prices vary between villages but no data are available on price variations within villages. Thus price variables are not included in these relationships since they would be perfectly collinear with the village dummy variables. The relationship for grains is specified in logarithms since no household had a zero consumption and this transformation is useful for estimation involving cross-sectional data. The short and long run elasticities at sample means are also reported in Table 1; the latter is set equal to the former whenever the coefficient a is statistically insignificant at the 5°7o level. For the meat

Maximum

likelihood

TABLE 1 estimates of household expenditure

Variable

Constant Dummy 1 Dummy 2 No. of adult equivalents (No. of adult equivalents)2 Expenditure a Short run elasticity§§ Long run elasticity*

xW* 2L*°

Grains $

Sugar

0.97 (0.61) 0.67 (0.09) 0.30 (0.08) -0.23 (0.13) 0.06 (0.05) 0.841 (0.058) -0.197 (0.111) 0.841 0.703 0.543 453.7

2.27 (5.88) - 24.09 (4.27) -7.54 (2.68) 3.17 (1.16) -0.24 (0.08) 0.035 (0.007) 0.347 (0.098) 0.640 0.980 1.452 -905.2

elasticities

offoodst

Estimates for the following foods: Pulses Vegetables Milk 36.45 (25.45) - 59.26 (20.82) -9.28 (5.39) -1.22 (1.72)

25.68 (6.0) - 22.92 (3.40) -4.28 (2.80) -1.94 (0.56)

—

—

0.062 (0.012) -1.075 (0.680) 1.674 1.674 0.328 -1100.8

0.056 (0.007) 0.027 (0.098) 0.813 0.813 0.241 -850.8

f94 households, two time periods; asymptotic standard errors are given in parentheses. J Sum of expenditures on rice, wheat, jowar, bajra and maize in logarithms. § Vegetarians excluded. §§ Elasticities calculated at sample means. * Long run elasticities (elasticity/(l - a)). ** x2-test for the exogeneity of the expenditure variable against alternative (5). ° Twice the maximized value of the log-likelihood function.

-66.37 (2.55) -0.50 (3.42) -4.45 (3.19) 12.10 (0.77) -0.74 (0.07) 0.062 (0.007) 0.927 (0.128) 1.094 14.980 0.238 -1223.1

Meat§ -5.83 (5.18) 5.87 (2.39) 0.21 • (2.35) 0.36 (0.51)

— 0.016 (0.006) 0.612 (0.120) 0.579 1.492 5.033 -763.7

Short and Long Run Income Elasticities

food group, the estimates exclude 12 vegetarian households who consumed no meat and the parameters were estimated more precisely. The noteworthy features of the results in Table 1 are that, firstly, the coefficients of the expenditure variable are invariably significant at any reasonable critical level. (The inclusion of the value of households' assets as a proxy for savings in the model did not alter the results.) Secondly, the long run elasticities of sugar, meat and, especially, milk are all higher than their short run counterparts. Thirdly, the long run expenditure elasticity for grains is lower than the short run elasticity (Houthakkar and Taylor, 1970) though the standard error for a is rather .large. This suggests a slight tendency of a reduction in grain consumption in the long run as a result of increases in expenditures (or household incomes). Fourthly, a is insignificant in the pulses and the vegetables relationships. The prices of vegetables in India are greatly influenced by seasonal factors. Thus it is perhaps not surprising that the annual data used here cannot distinguish between the short and long run effects. For pulses, most households may have become accustomed to consuming them in roughly the same proportions though the more wealthy households might be consuming more expensive varieties. Fifthly, the square of expenditure was significant in the grains and the meat equations but the results were qualitatively the same. However, the relationships are generally quadratic in the households' size variable. (The expenditure variables were also expressed in per capita terms with the adult equivalent scale, but the results in Table 1 provided a better fit because the relationship was non-linear.) Also, dummy variables for the caste and the education level of the head of the household were generally insignificant. This may be due to the loss of half the observations because the lagged value of the dependent variable was included as a regressor. Lastly, likelihood ratio tests (see later) for the exogeneity of the expenditure variable against the alternative of correlation pattern (5) do not reject the null hypotheses; the criterion assumes a value slightly lower than the critical level (at 5%) only in the relationship for meat. In summary, the results presented in this section support the hypothesis of habit persistence in the diets of these Indian villagers. Also, from the estimated elasticities, it is reasonable to expect that nutritional surveys would indicate that members of relatively wealthy households are better nourished. 3. ESTIMATING EFFECTS OF INCOME ON INTAKE OF NUTRIENTS 3.1. Some Issues in Modelling Demand for Nutrients The problems associated with the measurement of nutrient intakes and absorption by the human body are widely recognized in the nutritional literature (Nutrition Reviews, 1976; Shils and Young, 1988). For example, it is difficult to assess accurately the nutritive content of vegetables consumed since the manner in which they are processed could enhance or reduce (or even destroy) the vitamins present. Moreover, the absorption of any nutrient usually depends on the levels of other nutrients in the foods consumed. In fact, the absorption of calcium from spinach is hindered by oxalic acid and in general it cannot be measured without examining the excreta. In contrast, the absorption of iron is increased by ascorbic acid in the meal. Analogously, there are formidable difficulties in specifying a generic 'health production function' linking health ('output') to the intake of various nutrients ('inputs'); the former cannot be satisfactorily defined from an empirical viewpoint.

87

88

A. Bhargava

The four rounds of nutritional surveys carried out by the ICRISAT attempted to reduce the problems in measuring nutritive content of foods consumed in these villages by comparing some of the nutritive values with the tabulations of Gopalan etal. (1971). An important feature of these data is that the same individuals were interviewed biannually and food intakes in the previous 24 hours were converted into nutrients. Naturally, this contains far more detailed information on the nutrient intakes by individuals than annual household expenditures on food groups. Thus it is of interest to analyse these data, while controlling for the individual specific differences. The effects of large internal variances, however, are notorious for obscuring relationships in 24-hour recall dietary surveys (Liu etal., 1978). In the present situation, the estimated association between intakes of nutrients and household incomes might be weakened if there is excessive internal variation in the data. It has long been recognized in demand analysis that goods may be demanded for the characteristics that they possess (Gorman, 1980). The simplest examples found in the literature (Lancaster, 1971; Ironmonger, 1972) refer to the demand for nutrients like vitamins that must be satisfied through the consumption of foods. The recent applications of such models to economic data has produced reasonable results (Pudney, 1981). In contrast, non-linear programming solutions to the diet problem have appeared previously though the results are dependent on very specific assumptions about the shapes of indifference curves (Langier, 1969). A starting point for modelling the demand for nutrients would be to treat them analogously to other commodities (e.g. foods) and to estimate 'reduced form' relationships with household and village endowments and household expenditures as predetermined variables (Behrman and Deolalikar, 1987). Incorporating habit persistence would lead to model (2) and (3) above except that the dependent variables would now be the intakes of a particular nutrient. For comparison, eliminating the endogenous variable yn in equation (3), we obtain the unrestricted reduced form m

yn^YiZ&i

I n

+ Yi E XuoPu+Vii

( ' = J> • • • . # ) •

(6)

Relationship (6) allows the current level of intake of a nutrient to depend on the past values of the explanatory variables. Further, model (6) is consistent with more elaborate structural models which incorporate the interactions between different nutrients. For example, in the protein-energy relationship discussed by Sukhatme (1974), a dynamic structural model explaining the demand for dietary energy would relate energy to the predetermined variables as well the intakes of protein (and vice versa). Then, eliminating nutrient appearing as an explanatory variable, we obtain model (6) relating the demand for each nutrient to all the past and current values of the predetermined variables in the model. The direct estimation of such unrestricted relationships using cross-sectional data, however, entails the risk of imprecise estimation of the parameters. The criterion of relying on ^-values to decide the importance of a variable may leave few relevant variables explaining the dependent variable. However, a procedure exploiting the panel nature of the data can enhance the efficiency of the estimates (Section 4). This section estimates simple dynamic models and the interdependence in the intakes of nutrients is fully recognized in Section 4.

Short and Long Run Income Elasticities

3.2. Data Manipulation In this section, data on the intakes of nine nutrients, namely energy, protein, calcium, iron, carotene, thiamine, niacin, riboflavin and ascorbic acid, are used to estimate directly the effects of household incomes on intakes of nutrients in a dynamic framework. The explanatory variables are household income, number of adult equivalents, two dummy variables for the villages and the height and weight of the individuals in the two time periods as in equations (2) and (3). (The incomes excluding rent of the households were used instead of the expenditure variable since there were difficulties in matching all the observations on households with those on individuals. Also, the square of the number of adult equivalent members was insignificant in most of the relationships estimated in Sections 3 and 4.) Given that the recollection of the younger members about food intakes may be inaccurate, it was decided to retain only individuals who were aged 10 years or older in 1976. Also, the two rounds were averaged to produce a figure for the year and we thus obtained data on 364 individuals for 2 years. (Data from individuals with single observations in each of the years were retained.) The preliminary results for the nine nutrients indicated that the variation in the data was much too large to afford precise estimation of the parameters for all the nutrients. The nutrients were therefore grouped by expressing the data on a particular nutrient in terms of the percentages of the recommended daily allowances (Stigler, 1945; Langier, 1969; Ryan etal., 1984). Five groups were then obtained, namely energy, protein, (calcium and iron), (carotene and ascorbic acid —referred to as vitamins A and C) and vitamin B (comprising thiamine, riboflavin and niacin). (If calcium and iron were considered individually, poor results were obtained for both. Also, a combination of all vitamins into a single group did not produce an improvement in the results.) The rationale for combining calcium and iron was alluded to earlier in that the absorption of these minerals is greatly influenced by the presence of other nutrients. Also, vitamins A and C were combined as the diets contained practically no fruits so that the prime sources of these nutrients were leafy vegetables.

3.3. Empirical Results for Simple Dynamic Relationships Table 2 reports the results for the dynamic relationships (3) in logarithms for the five nutrient groups. In each case, the estimated coefficient of incomes is statistically significant though the elasticities seem low. The estimates of the lagged dependent variable a in the energy and calcium and iron relationships, however, are unacceptably large and the optimization routine indicated that some of these models were not well specified (the instrumental variables estimates were sometimes quite different from the maximum likelihood estimates). An examination of the unrestricted reduced form (6) estimates for each of these groups showed that the lagged values of incomes were statistically significant in explaining the current nutrient intake for all but the vitamins A and C relationship. For vitamin B, both the lagged and the current values of incomes were significant at the 5% level. The only individual specific regressors in Table 2 are the heights and the weights of the individuals; the remaining variables are common to all members of the households. This will probably leave much of the variation in the data unexplained. Now, the facts that the human body can use its own adipose tissue to meet energy

89

A. Bhargava

90

TABLE 2

Maximum likelihood estimates of income elasticities of nutrients in the simple dynamic models^ Variable

Constant Dummy 1 Dummy2 No. of adult equivalents Income Weight Height a 2L*

Estimates for the following nutrients: Calcium and iron Vitamins A and C

Energy

Protein

-0.646 (3.230) -0.007 (0.093) -0.274 (0.051) -0.064 (0.064) 0.066 (0.032) -0.169 (0.332) -0.159 (0.518) 1.409 (0.608) 1937.9

1.362 (1.821) -0.069 (0.149) -0.293 (0.048) -0.164 (0.049) 0.106 (0.034) 0.098 (0.165) -0.391 (0.476) 0.947 (0.358) 1793.9

10.617 (5.241) 0.794 (0.379) 0.641 (0.323) 0.052 (0.119) 0.007J (0.048) 0.109 (0.131) -3.609 (1.744) 2.387 (0.790) 1482.2

0.114 (0.362) -0.207 (0.126) 0.071 (0.079) -0.365 (0.065) 0.095 (0.047) 0.113 (0.155) 0.198 (0.048) 0.454 (0.330) 730.0

Vitamin B 1.208 (1.928) -0.230 (0.082) -0.283 (0.049) -0.169 (0.051) 0.127 (0.027) 0.203 (0.051) -0.119 (0.437) 0.582 (0.205) 1496.2

t All variables are in logarithms; 364 individuals; two time periods. t Significant with inclusion of the square of income.

needs and that many of these households are living close to the subsistence level together imply that most of these individuals are consuming low quantities of nutrients in comparison with their dietary energy intakes. Thus, a possible procedure for reducing the high level of unexplained variation would be to re-estimate the simple relationships in Table 2, but now expressing the intakes of nutrients as ratios to the energy intakes. Thus, for example, individuals with high basal metabolic rates will probably consume higher quantities of energy but the proportions of their intakes of other nutrients will be determined by the incomes of the household to which they belong. Such ratios have been used in other nutritional studies. Table 3 reports the results for the nutrient/energy ratios. For both the protein and the vitamin B equations, incomes significantly influence the proportions in which these nutrients are consumed and the short and the long run elasticities are as expected. The calcium and iron and vitamins A and C relationships, however, are not as supportive in so far as the income and long run effects are concerned. However, the appropriate comparisons of the maximized values of the likelihood functions in Tables 2 and 3 show that the data support the transformation of nutrients in the form of ratios to energy intakes. Moreover, the large estimates of a in the first three relationships of Table 2 and the lack of similarity between these results and those reported in the first two columns of Table 3 indicate that the former models are misspecified. Indeed, the conversion of the intakes of nutrients in ratio forms partially incorporates the interdependence between the nutrients and in turn enhances the performance of the simple models. This transformation also causes a distinction between the relative and the absolute income elasticities of nutrients which is discussed later.

Short and Long Run Income Elasticities

91

TABLE 3

Maximum likelihood estimates of relative income elasticities of nutrient/energy ratios^ Variable Protein Constant Dummy 1 Dummy 2 No. of adult equivalents Income Income2 Weight Height a 2L*

-0.400 (0.760) -0.087 (0.062) -0.013 (0.015) -0.069 (0.016) 0.042 (0.010)

— 0.004 (0.063) 0.048 (0.210) 0.623 (0.224) 3222.7

Estimates for the following nutrients: Calcium and iron Vitamins A and C - 10.661 (0.800) -0.197 (0.059) -0.057 (0.076) -0.111 (0.071) 0.291 (0.187) -0.017 (0.009) -0.269 (0.067) 2.176 (0.037) -0.103 (0.191) 1837.0

-4.128 (3.298) 0.056 (0.155) 0.393 (0.078) -0.241 (0.082) 0.081 (0.069)

— -0.167 (0.237) 0.607 (0.237) 0.128 (0.323) 759.3

Vitamin B -2.074 (0.586) -0.125 (0.042) 0.012 (0.029) -0.067 (0.030) 0.288 (0.058) -0.013 (0.003) 0.003 (0.059) 0.152 (0.059) 0.505 (0.164) 2294.5

t All variables are in logarithms; the square of income is included in the calcium and iron and vitamin B equations.

4. INCORPORATING INTERDEPENDENCE BETWEEN NUTRIENTS 4.1. Hierarchical Structure of Nutritional Wants The intakes of energy, protein, minerals and vitamins are all essential for maintaining proper health of a human body. Households living close to the subsistence level, however, may not be able to afford adequate quantities of all the desirable nutrients. Consequently, it would be necessary for them to rank various foods from the viewpoint of satisfying the most immediate needs of their members. Indeed, it is quite common in these villages to find separate arrangements especially for staple products like grains and pulses that are relatively good sources of energy and protein. Such agreements are often formed on the basis of the work performed during the harvest seasons but even for semi-skilled services such as those provided by barbers and carpenters some payments are made in kind. These undoubtedly reduce the risk of facing hunger. The income earned from other sources may then be spent on more nutritious foods like vegetables, milk and meat, though the quantities actually purchased will be determined by food prices and by household incomes. The situation facing these households could perhaps be characterized by the well-known phenomenon of the 'hierarchy of human wants' (for example Georgescu-Roegen (1966)). From the standpoint of empirical work, the examples illustrating hierarchy in the economics literature (Lancaster, 1971; Ironmonger, 1972) cannot be easily translated into practical procedures for analysing individuals' demands for nutrients. Firstly, characteristics like energy, protein, minerals and vitamins are generally found in most foods though in different proportions. Thus the demand for any particular

92

A. Bhargava

nutrient is accompanied by automatic increases in intakes of other nutrients. Secondly, although it is true that the demand for vitamins will manifest itself only after a household has attained a certain level of income, it is not straightforward to model the levels at which this will be observed. Indeed, with the exception of vitamin C, the remaining nutrients on which the data are available are found in minute quantities even in grains and pulses. Thus a simple hierarchical formulation where the demand for energy, protein, calcium and iron, vitamins A and C and vitamin B are satisfied in that order would simply be misleading. It is essential to distinguish between the intakes of minerals and vitamins (through staple foods), and the demand for foods that are rich sources of these nutrients. Lastly, the non-market arrangements prevailing in these villages complicate the models of demand for nutrients; some of the demand functions may be viewed as 'conditional' demand functions arising from utility maximization subject to quantity restrictions (Pollak, 1969). If the arrangements pertain solely to staple foods, then it might be reasonable to introduce the quantities consumed of the two vital nutrients (energy and protein) as 'explanatory' variables into the demand functions for the remaining nutrients. This would only be an approximate empirical procedure since some minerals and vitamins are present in the staple foods. However, precise data on the non-market arrangements are unavailable and agreements about vegetables (especially if they can be preserved as pickles) will invalidate these formulations. Thus an alternative approach is pursued here. 4.2. Interdependence in Nutritional Intake It was noted by Stigler (1945) that 'the optimum quantity of any nutrient depends on the other nutrients available' and that 'the ultimate health function will doubtless be very complex'. Although knowledge about the nutritional requirements of human beings has advanced in the last four decades, there are still large gaps in the understanding of the manner in which the various nutrients interact to maintain good health. Moreover, some biomedical evidence suggests that the nutritional needs of the human body can influence the tastes of individuals. Now, the primary purpose of this study is to investigate the link between individuals' intakes of important nutrients and household incomes. Given the difficulties in quantifying the health value of nutritional intake, it is reasonable to separate out the issue of the specification of a health production function. Instead, we approach the data on the intake of nutrients from the standpoint of demand analysis, recognizing that the quality of foods consumed must depend on both the physiological needs of the individuals as well as on households' incomes. The fact that the consumption of more nutritious foods entails the intake of small quantities of the nutrients cheaply available, then, suggests that it would be very informative to quantify the effects of household incomes on the intake of any specific nutrient, holding the quantities consumed of the other nutrients constant. Such a formulation would seem consistent with the notions of interdependence in nutritional intakes advanced by Hutchinson (1969), Stigler (1945) and Sukhatme (1974). However, there are problems in identifying the system because the remaining nutrients appear as endogenous explanatory variables in every relationship. But if these problems could be circumvented perhaps under the special correlation patterns (5), then the income elasticities of nutrients may be obtained from solving the interdependent system. Since we have only two

93

Short and Long Run Income Elasticities

time observations, the special form of endogeneity of the time varying variables will be maintained as an assumption in this investigation. 4.3. The Model and its Identification It will be convenient to rewrite model (1) and (2) in a slightly different form owing to the special endogenous nature of some of the time varying variables. Thus we write the complete system 2

V,, +fi.'Zn + Y, /*i'*«« + ^2 'xni = M/i

(/= 1,...,//),

(7)

1=1

Byi + y;zi + fcxi22 + (31'xin = ui2

(/= 1,...,//),

- xi2 + j] F,xn, + F2+x?22 + Fzn = ul3 -xU2 + x+2+x0 = 0

(/= 1,...,//),

( / = l , . . . , / / ; j = n-k-\,...,/!).

(8) (9) (10)

Here, B=(a, - 1 ) , zn is an ( w + l ) x l vector of exogenous time invariant variables, and xiU and xi2l are k x 1 and (n — k) x 1 vectors of exogenous and special endogenous time varying variables respectively, /x, y and j3 are all vectors of unknown coefficients and the F a r e matrices of unknown coefficients in the reduced form (9). Also, the correlation pattern (5) is assumed for the endogeneity of the time varying variables, and x,+22 are the deviations of xi22 from their time means, i.e. with T = 2 x

m

=

(xi22 ~ xn\)>

2-

Correlation structure (5) adds only n — k time means as endogenous variables in the system and the xtj2 provide precisely the same number of instrumental variables that can be used for estimating the system. A likelihood ratio test can be applied to test the validity of the exogeneity assumption for the time varying variables against the alternative pattern (5). The test statistic is 2(L*dog - L*og) + H log(det W22)

(11)

where L* represents the maximized value of the log-likelihood functions under the treatment of the time varying variables as, respectively, special endogenous and exogenous, and W22 is an estimate of the unrestricted variance matrix corresponding to the errors on equation (9). Expression (11) is asymptotically distributed as a X2-variable with 2{n — k) degrees of freedom. Now assuming no endogenous time invariant variables in the model, and defining the data matrix of the exogenous variables as Z+ =

[Zl:Xi:X2+],

we have the following result on identification (see Appendix A for the proof). Proposition.

If

(a) Plimw^„ (Z+'Z+/H) is positive definite, (b) k > 0 and (c) T=2, then model (8) is identified.

94

A. Bhargava

4.4. Empirical Results Table 4 reports the results for each of the five nutrient groups where the remaining four nutrients appear as explanatory variables. First, focusing on the exogeneity of the nutrient variables with correlation structure (5) as the alternative hypothesis, the vitamins A and C relationship clearly accepts the null hypothesis for all the four regressors at any reasonable significance level. The vitamin B equation would also accept the null hypothesis at about the 4% level but a closer examination revealed that it is the vitamin A and C group that is mainly increasing the value of the test statistic; thus it is reasonable to accept the null hypothesis. The calcium and iron relationship, however, rejects the exogeneity null hypothesis at the 5% level and the results in Table 4 treat the nutrients as special endogenous variables. Similarly, the exogeneity null hypotheses are rejected in the energy and protein relationships. It was noted earlier that decisions to consume foods containing high quantities of vitamins are likely to succeed those regarding staple foods. Thus the acceptance of the exogeneity null hypotheses for the vitamin groups might be viewed as an indication of a hierarchical structure in the demand for these nutrients. (The coefficients for the other nutrients are expected to be non-zero because the nutrients are present in minute quantities in most foods.) Secondly, the relationships are generally non-linear in household incomes and the TABLE 4 Maximum likelihood estimates of relative income elasticities of nutrients in the interdependent Variable

Income Income2 No. of adult equivalents Weight Height Energy Protein Calcium and iron Vitamins A and C Vitamin B a 2L* X2(8)

Energy

Protein

-0.352 (0.086) 0.020 (0.005) 0.049 (0.021) 0.175 (0.058) -0.811 (0.083)

0.329 (0.088) -0.019 (0.005) - 0.026 (0.020) -0.227 (0.049) 0.635 (0.065) 1.013 (0.132)

— 0.760 (0.090) 0.219 (0.043) 0.012 (0.016) -0.108 (0.051) 0.031 (0.043) 7734.1 37.02

— - 0.098 (0.035) -0.030 (0.017) 0.287 (0.044) 0.084 (0.047) 7737.2 22.81

Estimates for the following nutrients: Calcium and iron Vitamins A and C 0.324 (0.057) -0.022 (0.003) -0.013 (0.061) -0.333 (0.096) 1.668 (0.223) 1.019 (0.166) -0.227 (0.223)

— 0.072 (0.043) 0.376 (0.147) 0.148 (0.080) 7080.1 17.55

0.082 (0.058)

— -0.284 (0.085) -0.075 (0.139) 0.015 (0.067) 0.785 (0.301) -1.099 (0.352) 0.422 (0.099)

— 0.388 (0.193) 0.332 (0.122) 849.5 2.58

system^

Vitamin B 0.124 (0.004) -0.004 (0.001) -0.006 (0.020) 0.023 (0.007) -0.352 (0.010) - 0.029 (0.005) 1.084 (0.007) 0.046 (0.024) 0.015 (0.016)

0.022 (0.024) 2655.4 16.96

t All the variables are in logarithms; the energy, protein and calcium and iron equations treat the other nutrients as special endogenous variables —see the x2-values; the coefficients of the constant term and the village dummy variables are not reported.

Short and Long Run Income Elasticities

coefficients are statistically significant. These results support the hypothesis that, with increases in household incomes, foods containing greater proportions of the last four nutrient groups will be consumed. The negative sign of the income coefficient and the positive sign of its square in the energy relationship further confirm this. Thirdly, solving the interdependent system (7)-(10) but retaining terms up to the first order, the respective income elasticities of the five nutrient groups are 0.129, 0.179, 0.125, 0.176 and 0.316. The first-order approximation is necessary here as the squared income term appears as a regressor in four of the equations. Its rigorous justification would also require the calculation of the joint variance-covariance matrix of the parameters of the whole system. (The simultaneous estimation of the complete system is necessary for computing the covariance matrix of the estimated parameters in different equations. To economize on storage space, the full data set is never read into the computer. Thus the simultaneous estimation of the equations will require a considerable amount of additional programming.) The seemingly low estimates of the income elasticities may be rationalized to some degree by the nature of the 24-hour recall data. Furthermore, we might reasonably expect households with low incomes to spread their consumption of more nutritious foods over the year especially to coincide with religious festivities. The fact that no interviews were conducted during festival periods, then, suggests that the income elasticities of nutrients may have been underestimated. Fourthly, the long run effects are much larger for the calcium and iron and the vitamins A and C relationships. Since the diets in these villages contained virtually no fruits, the implications for the intake of vitamins A and C are encouraging. The vitamin B relationship, however, does not afford a distinction between the short and the long run effects. (For income elasticities in static models, see Bhargava (1991).) In summary, the results in Table 4 show that, in these villages, foods containing higher proportions of the desirable nutrients are consumed with increases in household incomes. This conclusion is conditional on the assumed form of endogeneity (5) for the remaining nutrients appearing as regressors. This condition might seem restrictive but has commonly been invoked in dynamic error components models (for example Anderson and Hsiao (1981)). Although statistical tests for the hypotheses maintained cannot be applied to the present models with two time observations, the non-rejection of the exogeneity null hypotheses in the last two relationships suggests that the conclusions may not be critically dependent on the correlation patterns postulated. 5. CONCLUSION This paper has estimated short and long run income elasticities of foods and nutrients using data from south India. The specifications for food groups are consistent with the economic hypothesis of habit formation and the data provided good support for the theory. The analysis of demand for nutrients, however, is very complicated. The incorporation of the interdependence in nutritional intakes led to models that showed significant effects of household incomes on the intake of nutrients. The estimated income elasticities of nutrients from the dynamic interdependent system, while sensitive to the approximations used, seem somewhat larger than their static counterparts. Nevertheless, the results demonstrate better nutrition with increases in household incomes, thereby supporting the position of the World

95

96

A. Bhargava Bank (1981) for raising incomes in developing countries. Finally, the analyses of the various aspects of nutrition in developing countries will be greatly facilitated by the availability of surveys that continuously record food intakes for several days and are also repeated several times during the year. These are routine features of epidemiological surveys in developed countries (for example Freudenheim etal. (1987) and Nelson etal. (1989)) though the number of subjects observed has typically been small. In less developed countries, the internal variances in intakes of nutrients tend to be much larger and seasonal factors can create serious food shortages. Thus the benefits from elaborate nutritional surveys such as the accurate assessment of the incidence of undernutrition and more precise estimation of parameters that are of interest in policy making should offset the costs. ACKNOWLEDGEMENTS The author is indebted to Jere Behrman, Marc Nerlove, Bob Pollak and Amartya Sen for helpful discussions and to two referees for many thoughtful criticisms of an earlier draft. Thanks are also due to the Cornell Theory Center for supercomputer time. APPENDIX A: PROOF OF THE PROPOSITION We premultiply equation (8) by a 1 x 2(n — k) vector [h0: I + h,: h2: hf]

(A.l)

and show that h0, hu h2 and h* are all zero. The set of transformed equations can be written as -h0d{ + (l+hi)B h0a' + (l+hi)y;+h2P

= Bl, = y;-yf,

(A.l) (A.3)

*„/*,' + h2F{ = 0,

(A.4)

/!„/*,' + (1 + A.JjS,' + h2F2 = B( - Bf,

(A.5)

(1+*,)&'-Ar=02'-/3?',

(A.6)

+

hen?' + h2F2 +hf^0,

(A.7)

h2 = h*. (A.8) Here d2 = (0, 1), B = (a, — 1), Bt is the transformed version of B with a replaced by a, = a — a*, h0 and A, are scalars, h2 and h* are I X (n — k) vectors and 7* and j3* are the transformed versions of 7 and fi respectively. From equation (A.2), on equating the coefficients, we immediately have that A. = 0,

h0 = a*.

(A.9)

Thus we may rewrite the previous equations as «V +h2F=-yf,

(A. 10)

a*/xi' + h2F, = 0,

(A. 11)

Short and Long Run Income Elasticities a*ii{+h2F2

= -0t',

(A.12)

h?=P?, a*ti'

97

(A. 13) +

+h2{I+F2 )

= 0.

(A. 14)

On combining equations (A.8) and (A. 13), we have hf = h2 = /3f which can be satisfied only if hf = h2 = 0. Thus, from equation (A. 11), a* = 0 and, consequently, /3f — 0, (3f — 0 and 7* = 0. Hence all the parameters in the model are identified.

REFERENCES Anderson, T. W. and Hsiao, C. (1981) Estimation of dynamic models with error components. /. Am. Statist. Ass., 76, 598-606. Beaton, G. H., Milner, J., Corey, P., McGuire, V., Cousins, M., Stewart, E., de Ramos, M., Hewitt, D., Grambsch, P. V., Kassim, N. and Little, J. A. (1979) Sources of variance in 24-hour dietary recall data: implications for nutrition study design and interpretation. Am. J. Clin. Nutr., 32, 2546-2559. Behrman, J. R. and Deolalikar, A. B. (1987) Will developing country nutrition improve with incomes?: a case study for rural south India. J. Polit. Econ., 95, 492-507. Bhargava, A. (1987) Wald tests and systems of stochastic equations. Int. Econ. Rev., 28, 789-808. (1989) Malnutrition and the role of individual variation with evidence from India and the Philippines. To be published. (1991) Identification and panel data models with endogenous regressors. Rev. Econ. Stud. ,58, in the press. Bhargava, A. and Sargan, J. D. (1983) Estimating dynamic random effects models from panel data covering short time periods. Econometrica, 51, 1635-1660. Binswanger, H. and Jodha, N. S. (1978) Manual for Instruction for Economic Investigators in ICRISAT's Village Level Studies. Hyderabad: International Crops Research Institute for Semi-Arid Tropics. Block, G. (1982) A review of validation of dietary assessment methods. Am. J. Epidem., 115, 492-505. Deaton, A. S. and Muellbauer, J. (1980) Economics and Consumer Behavior. Cambridge: Cambridge University Press. Duesenberry, J. S. (1949) Income, Saving, and the Theory of Consumer Behavior. Cambridge: Harvard University Press. Freudenheim, J. L., Johnson, N. E. and Wardrop, R. L. (1987) Misclassification of nutrient intake of individuals and groups using one-, two-, three-, and seven-day food records. Am. J. Epidem., 126, 703-713. Friedman, M. (1957) A Theory of the Consumption Function. Princeton: Princeton University Press. Georgescu-Roegen, N. (1966) Analytical Economics: Issues and Problems. Cambridge: Harvard University Press. Gopalan, C , Rama, B. V. and Balasubramanian, S. C. (1971) Nutritive Value of Indian Foods. Hyderabad: National Institute of Nutrition. Gorman, W. M. (1967) Tastes, habits and choices. Int. Econ. Rev., 8, 218-222. (1980) A possible procedure for analyzing quality differentials in the egg market. Rev. Econ. Stud., 47, 843-856. Griliches, Z. (1961) Hedonic price indexes for automobiles: an econometric analysis of quality change. In Price Indexes and Quality Change: Studies in New Methods of Measurements (ed. Z. Griliches). Cambridge: Harvard University Press. Houthakkar, H. S. and Taylor, L. D. (1970) Consumer Demand in the United States, 2nd edn. Cambridge: Harvard University Press. Hutchinson, R. (1969) Food and the Principles of Dietetics, 12th edn. London: Arnold. Ironmonger, D. S. (1972) New Commodities. Cambridge: Cambridge University Press. Lancaster, K. (1966) A new approach to consumer theory. J. Polit. Econ., 74, 132-157. (1971) Consumer Demand: a New Approach. New York: Columbia University Press. Langier, J. D. (1969) Economical and Nutritional Diets using Scarce Resources. East Lansing: Michigan State University Press.

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A. Bhargava Liu, K., Stamler, J., Dyer, A., McKeever, J. and McKeever, P. (1978) Statistical methods to assess and minimize the role of intra-individual variability in obscuring the relationship between dietary lipids and serum cholestrol. J. Chron. Dis., 31, 399-418. Nelson, M., Black, A. E., Morris, J. A. and Cole, T. J. (1989) Between-and-within subject variation in nutrient intake from infancy to old age: estimating the number of days required to rank dietary intakes with desired precision. Am. J. Clin. Nutr., 50, 155-167. Nerlove, M. (1972) Lags in economic behaviour. Econometrica, 40, 221-251. Numerical Algorithms Group (1989) Library of Computer Programs, Mark 12. Oxford: Numerical Algorithms Group. Nutrition Reviews (1976) Present Knowledge in Nutrition, 4th edn. Washington DC: Nutritional Foundation. Phlips, L. (197'4) Applied Consumption Analysis. Amsterdam: North-Holland. Pollak, R. A. (1969) Conditional demand functions and consumption theory. Q. J. Econ., 83, 70-78. (1970) Habit formation and dynamic demand functions. J. Polit. Econ., 78, 60-78. Prais, S. J. and Houthakkar, H. S. (1955) The Analysis of Family Budgets. Cambridge: Cambridge University Press. Pudney, S. E. (1981) Instrumental variable estimation of a characteristics model of demand. Rev. Econ. Stud., 48, 417-433. Ryan, J. G., Bindinger, P. D., Rao, N. P. and Pushpamma, P. (1984) Determinants of Individual Diets and Nutritional Status in Six Villages of South India. Hyderabad: International Crops Research Institute for Semi-Arid Tropics. Shils, M. E. and Young, V. R. (1988) Modern Nutrition in Health and Disease, 7th edn. Philadelphia: Lea and Febiger. Stigler, G. J. (1945) The cost of subsistence. / . Farm Econ., 27, 303-314. Stone, J. R. N. (1954) Linear expenditure system and demand analysis: an application to the pattern of British demand. Econ. J., 64, 511-527. Sukhatme, P. V. (1974) The protein problem, its size and nature. J. R. Statist. Soc. A, 137, 166-199. Timmer, C. P. and Alderman, H. (1979) Estimating consumption parameters for food policy analysis. Am. J. Agric. Econ., 61, 982-994. Waterlow, J. C. (1989) Nutritional adaptation and variability. Eur. J. Clin. Nutr., 43, 203-205. World Bank (1981) World Development Report. Washington DC: World Bank.

NOTES DOES H O U S E H O L D CONSUMPTION B E H A V E AS A M A R T I N G A L E ? A T E S T F O R R U R A L SOUTH INDIA AJok Bhargava and Martin Ravallion* Abstract—The hypothesis that consumption evolves over time as a martingale process is tested on household panel data for three villages in south India. A novel feature of the methodology is that it gives consistent estimates of dynamic effects in short panels. The estimated coefficients of lagged consumption are generally smaller than unity and a number of the lagged income and wealth variables are statistically significant. The results are inconsistent with the proposition that consumption equals permanent income. This is also true when the data are disaggregated by household wealth. I.

Introduction

An intertemporally optimal consumption plan will equate ex ante the marginal rate of substitution between current and future consumption with the marginal rate of transformation. The latter depends on the subjective rate of time preference relative to the real rate of interest. With a quadratic instantaneous utility function and a rate of time preference equal to the rate of interest, future changes in consumption should be uncorrelated with currently available information, including consumption itself; consumption should evolve over time as a martingale process (see Hall, 1978; Hayashi, 1987). Then consumption will equal permanent income, the annuity value of assets plus the present value of expected future income (Flavin, 1981). The earliest tests of the permanent income hypothesis (PIH) used aggregate time series data (Hall, 1978; Flavin, 1981). Since it is a hypothesis about individualor household-level behavior, panel data sets seem more appropriate for testing the PIH, and there have been a number of attempts to do so (see Hayashi, 1987), of which Hall and Mishkin (1982) were the first. They assumed quadratic preferences and that the rate of time preference equals the rate of interest (the latter is Received for publication May 10, 1991. Revision accepted for publication May 22, 1992. * University of Houston and World Bank, respectively. We are grateful to the Resource Management Program of ICRISAT for access to their data, subject to the usual disclaimer. For their comments, we are grateful to Angus Deaton, Jonathon Morduch, Lawrence Summers, and the Review's referees. These are the views of the authors, and should not be attributed to any other person or organization, including the World Bank.

generally not assumed in aggregate time series tests). Their results for household panel data in the United States suggest that changes in food consumption are correlated with lagged income. Two strands of recent empirical work using panel data sets have adopted different approaches. Building on Campbell's (1987) alternative test of PIH based on savings behavior, Deaton (1990) reports tests using a two-year panel of household data for Cote d'lvoire. This approach can allow consistent tests of the full set of martingale restrictions though the Campbell/Deaton implementations do employ a stationarity assumption for incomes which might be restrictive in some settings. Computational costs also appear to entail a rather restricted set of variables used in testing orthogonality. Zeldes (1989) develops a new formulation in which the instantaneous utility function has constant relative risk-aversion, and uses this to test for liquidity constraints using U.S. panel data. Morduch (1990) uses this approach to investigate the effects of such constraints on the consumption and production behavior of Indian households. While the Zeldes approach allows tests for liquidity constraints (assuming rational expectations) it does not actually test the PIH, since consumption cannot be derived as a function of permanent income for such a preference specification. Our task is to explore a different approach which allows consistent estimates in short panels of a test equation of the martingale hypothesis. We apply this to the consumption expenditures of 109 households from rural India that were repeatedly observed for 6 years. This is a setting in which the performance of consumption smoothing arrangements has bearing on a number of measurement and policy issues (Chaudhuri and Ravallion, 1993; Lipton and Ravallion, forthcoming). Unlike past tests using panel data, the methodology used here allows us to clearly distinguish the two possible reasons why consumption might not behave as a martingale: it does not have a unit root, and its changes over time are correlated with other lagged information. Section II outlines our approach and describes the estimation methods for the resulting models. In section III the data are briefly described, and the results are presented. Copyright © 1993

100

A. Bhargava and M. Ravallion the martingale property; a logical statistical procedure would be to estimate the relationship without imposing The previous investigations of the PIH using panel a — 1 and without requiring the p's to be zero. The data have employed a variety of specifications and estimates from the unrestricted model can then be estimation methods for the test equation. A common utilized in testing these null hypotheses separately or feature of these studies is the small number of time sequentially. The estimation procedure will need to observations on the households. The estimation meth- assume the effects as randomly distributed and must ods, however, differ in the treatment of the treat the initial observations (Cn) as endogenous varihousehold-specific effects as "random" or "fixed." ables in short panels. Also, the unit root restriction has frequently been A potential drawback in the use of the random imposed a priori on the data. It seems likely that the effects formulation is the possibility of correlation bedecision to reject or accept the martingale hypothesis is tween a large number of the explanatory variables and influenced by the postulated model and the estimation the random effects. In such circumstances, it might method. The relative merits of alternative assumptions seem attractive to treat the effects as fixed parameters may be discussed within the difference equation: in the estimation. From the viewpoint of testing the martingale hypothesis, an alternative approach would m c be to impose a = 1 and test the null hypothesis that „ = E *kzik + aCu-\ + PiYn-i Pi = " ' = Pn = 0 within a static framework with k~\ n fixed effects. Thus the changes in consumption could + LPjXJi,-i+ii, + uil (i) be regressed on the previous levels of income and wealth variables with a dummy variable for each housewhere Cjt is the real expenditure on consumer goods hold and the significance of the p's may be tested using (food or non-food) by household i in time period t, Yit "t" type tests. The violation of the assumption that is the real income of household i in the tth time a = 1, however, will adversely affect the consistency of period, and Xju is the j ' t h component of a vector of the estimated coefficients, the estimated standard er(n - 1) wealth variables. The z's are time invariant rors and the stochastic properties of the «,-,. variables, z, being a constant term. ixt is a householdFurther, the estimation of static models with fixed specific effect which can be treated in the estimation as effects and serial correlation in the errors is complia randomly distributed variable or as a fixed parame- cated by the fact that the covariance matrix of the u,,'s ter. The K„ are general random error terms with zero cannot be consistently estimated for small T because mean and a finite variance-covariance matrix. of the incidental parameters (Kiefer, 1980). While the It is essential to control for the unobserved differ- Durbin-Watson type finite sample tests for serial indeences between the households by treating the /i,.'s as pendence are still valid, the standard errors of the random variables or as fixed parameters. There are estimated coefficients can be estimated in the presence arguments for and against each option. Treating the of serial correlation using "bias corrected" procedures ji,'s as fixed parameters introduces the problem of in some cases (Bhargava et al., 1982). Thus the testing "incidental" parameters originally discussed by of the martingale property within the fixed effects Neyman and Scott (1948). In particular, the estimation framework is likely to present serious difficulties. of a dynamic model from a short panel generally leads A procedure sometimes used to eliminate the ranto inconsistent estimates (Anderson and Hsiao, 1981). dom effects is to difference the model. This may not be The treatment of the effects as randomly distributed applicable if the random effects depend on time so that variables circumvents the incidental parameter prob- the effects cannot be easily removed by differencing lem since only the variance (covariance matrix) of these (Bhargava, 1987). Moreover, an unrestricted serial covariables need be estimated. There is, however, the variance matrix for the composite error term (/u., + uu) possibility that the explanatory variables are correlated obviates the need for assuming that these variables are with the random effects. The endogeneity of explana- normally distributed for inference purposes. tory variables can be treated within a simultaneous In summary, there are arguments that can be made equations framework (Bhargava and Sargan, 1983, and for and against each of these approaches. As an alterBhargava, 1991). native to the fixed effects model with the untested unit In choosing an estimator, it is desirable to distin- root restriction imposed, it would seem reasonable to guish between the two implications of the martingale try estimating the unrestricted model (1) treating the hypothesis, namely that a = 1 due to the equality of household specific effects as randomly distributed with time preference and interest rates, and that the previ- an unrestricted variance-covariance matrix. The endoously available information is irrelevant for current geneity of explanatory variables such as household consumption expenditures (P\ = • • • — /?„ = 0). This incomes should be tackled in the empirical analysis, has clear implications for the econometric testing of though there will be limits to how far this can be done II. An Econometric Formulation

Household Consumption as a Martingale: A Test for Rural South India in practice. We will also compare this new estimator to the usual fixed effects estimator of the test equation. III. Estimates of the Test Equation for Rural South India The panel data used in the analysis were collected by the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) in three villages (Aurepalle, Kanzara and Shirapur) of south India over the period 1976-1981. The setting and the data are discussed in detail by Walker and Ryan (1990) and we have a complete set of observations on 109 households for 6 years. Farm profits and labor earnings are the main sources of income and these variables show considerable variation over time, partly because of the monsoon. The villages differ in a number of respects, which could be relevant for the capacity of households to smooth their consumption. Aurepalle is in the state of Andhra Pradesh and credit is mainly obtained from traditional sources (professional moneylenders and large farmers). Kanzara and Shirapur are both in Maharashtra where government sponsored cooperative societies have played a major role in allocating credit, accounting for nearly half of total credit distribution. The rural public employment schemes operating in that state appear to have helped households buffer their consumption against income fluctuations. Also, Kanzara tends to have a more reliable rainfall. The data set also includes a detailed accounting of the households' wealth, comprising of value of the land owned, livestock, farm implements, buildings, farm stocks, consumer durables, jewelry, financial assets, and liabilities. All variables were deflated by villagespecific price indices. Pooling all households across all three villages {H = 109, T = 6), we obtained the following dynamic random effects estimate of equation (1), treating lagged income as endogenous (the time varying variables consist of the lagged values of the nine components of non-human wealth and the lagged household incomes mentioned above; standard errors in parentheses): C„ =

.432C„_1 + .011 Incomeil_l + .006La/tdf,_, (.024) (.024) (.002) + .Ql(> Livestockil_l — .023 Implements,/(_1 (.017) (.015) + .058Buildingsil_l .l57Stocki,_1 (.012) (.058) + .216 Durablesil_l — .003 Jewelry•jl_l (.063) (.023) + .011Fin Assetsu_x + .005 Liabilities jl_1 (.027) (.015) + residual. (2)

101

The coefficient on lagged consumption is significantly less than unity, and a number of the right-hand side variables have coefficients that are significantly different from zero. These results can be compared to a fixed effects model imposing a = 1 a priori: Q< ~ Q i - i = .025 Incomeil_1 + .032 Land il_1 (.029) (.009) + .004 Livestock a_x + .002 Implements,-,_, (.066) (.022) + .0%i Buildingsu_l .586Stocku_1 (.056) (.144) - .235Durables,-,_i — .035Jewelryil_1 (.116) (.035) + J2Q2Fin Assets!,_! — .041 Liabilities il_1 (.061) (.030) + household dummy variables + residual. (3) Most coefficients are quite different between the two estimators, though the joint F-test on the latter estimate still rejects the orthogonality restrictions (F(10,539) = 5.65). The differences between (2) and (3) could well reflect the incorrect imposition of the unit root restriction on the fixed effects model.1 The dynamic random effects estimates for food and non-food expenditures separately, and for the three villages are presented in table 1. The model was estimated under the alternative assumptions that the lagged household incomes are pre-determined variables and they are simultaneously determined with current consumption expenditures. The Chi-square values in the table are the test statistics for the exogeneity null hypothesis and the estimation accordingly treats incomes as pre-determined or endogenous. The exogeneity of the lagged incomes is rejected in all of the villages for the food and non-food expenditures. This rejection may in part be due to errors in measuring incomes. The lagged incomes generally influence the current consumption expenditures. The coefficients of lagged consumption expenditures are invariably significant and are below unity in the food relationships. The estimated a for Aurepalle in the non-food expenditures is negative and greater than unity in absolute value whereas that for Shirapur exceeds unity. This type of instability is absent in the food expenditures. Some of the lagged components of non-human wealth have statistically significant coefficients in all of the relationships. This is especially true for buildings, stock, consumer durables and financial 1 We do not estimate the fixed effects model with lagged consumption as a regressor since it is known that the coefficients of all the explanatory variables will then be biased, and that the bias may be large (Nickell, 1981).

A. Bhargava and M. Ravallion

102

TABLE 1 . — M A X I M U M LIKELIHOOD ESTIMATES O F F I R S T O R D E R AUTOREGRESSIONS FOR CONSUMPTION EXPENDITURES INCLUDING LAGGED M E A S U R E S OF W E A L T H AS REGRESSORS U S I N G I C R I S A T D A T A O N R U R A L INDIAN H O U S E H O L D S

Aurepalle Food Constant

763.5 (2.22) 0.009 Income _ [ (0.013) Land j 0.002 (0.002) Livestock 1 0.030 (0.013) Implements _ [ 0.020 (0.011) 0.032 Buildings _ i (0.016) Stock_ j -0.087 (0.080) Cons. Dur. l 0.011 (0.036) Jewelry 1 -0.005 (0.014) -1.281 Fin. Assets t (0.339) -0.005 Liabilities t (0.018) Consumption , 0.572 (0.038) 2L*° -2992.6 51.67 Chi-square (6) b a b

Kanzara

Non-food

Food

1352.6 (231.5) -0.087 (0.032) O.003 (0.007) -0.087 (0.033) 0.044 (0.013) 0.132 (0.062) 0.580 (0.200) 0.459 (0.115) -0.012 (0.031) 0.367 (0.819) 0.006 (0.257) -1.825 (0.257) -3087.5 46.29

709.8 (1.95) - 0.041 (0.017) -0.001 (0.003) 0.004 (0.029) 0.016 (0.039) 0.070 (0.013) - 0.402 (0.075) 0.379 (0.069) 0.078 (0.035) 0.094 (0.015) 0.041 (0.016) 0.628 (0.044) -3015.3 104.9

Non-food 616.5 (3.67) 0.024 (0.024) 0.001 (0.004) 0.087 (0.038) 0.051 (0.045) 0.083 (0.011) -0.294 (0.081) -0.061 (0.037) 0.179 (0.042) 0.035 (0.027) -0.017 (0.029) 0.340 (0.064) -3258.6 82.92

Shirapur Food 1137.6 (1.91) 0.046 (0.010) 0.008 (0.004) 0.012 (0.020) 0.053 (0.032) -0.059 (0.031) 0.102 (0.074) 0.198 (0.118) -0.108 (0.058) 0.049 (0.052) 0.003 (0.014) 0.446 (0.054) -3235.1 49.65

Non-food 77.95 (149.7) 0.037 (0.020) -0.003 (0.003) -0.060 (0.023) 0.003 (0.030) 0.059 (0.040) 0.071 (0.077) -0.550 (0.185) - 0.040 (0.069) 0.068 (0.065) 0.042 (0.011) 1.212 (0.142) -2977.4 101.76

Twice the maximized value of the log-likelihood function. Chi-square test for the exogeneity of the income variable.

TABLE 2 . — M A X I M U M LIKELIHOOD ESTIMATES O F THE F I R S T O R D E R AUTOREGRESSIONS FOR CONSUMPTION EXPENDITURES DISAGGREGATED BY THE A V E R A G E W E A L T H OF HOUSEHOLDS

Wealth Group 1 Food Constant

3414.2 (370.6) 0.051 Income t (0.037) Land l 0.051 (0.034) 0.049 Livestock l (0.053) 0.037 Implements _ l (0.205) Buildings j 0.010 (0.126) Stock , 0.190 (0.134) -0.035 Cons. Dur. t (0.045) Jewelry [ 0.982 (0.283) -0.069 Fin. Assets , (0.047) 0.023 Liabilities , (0.059) -0.643 Consumption [ (0.077) - 2807.6 2L* Chi-square (6) 98.76

Wealth Group 2

Wealth Group 3

Non-food

Food

Non-food

Food

331.2 (185.0) 0.144 (0.044) 0.062 (0.025) 0.088 (0.048) -0.244 (0.178) 0.258 (0.189) 0.489 (0.115) 0.025 (0.061) -0.236 (0.658) -0.016 (0.043) -0.022 (0.077) -0.212 (0.164) -3011.2 37.13

1209.6 (299.6) -0.018 (0.044) 0.004 (0.008) 0.047 (0.021) 0.024 (0.045) -0.086 (0.119) 0.155 (0.108) -0.037 (0.032) 0.167 (0.107) -0.005 (0.019) 0.070 (0.045) 0.414 (0.081) -3105.1 27.14

1710.6 (205.0) 0.053 (0.052) 0.019 (0.010) -0.002 (0.019) -0.064 (0.065) 0.370 (0.173) 0.368 (0.128) 0.026 (0.059) -0.180 (0.173) -0.028 (0.033) 0.085 (0.071) -0.517 (0.149) -3202.0 39.58

1828.2 (302.9) -0.094 (0.027) -0.001 (0.002) 0.013 (0.021) 0.005 (0.012) -0.223 (0.076) 0.217 (0.055) 0.006 (0.023) 0.039 (0.025) 0.002 (0.017) 0.179 (0.029) 0.463 (0.063) -3579.9 44.09

Non-food 970.1 (311.5) -0.179 (0.038) 0.001 (0.002) 0.042 (0.034) 0.013 (0.017) -0.063 (0.085) 0.107 (0.074) 0.028 (0.030) 0.002 (0.025) - 0.009 (0.019) 0.222 (0.034) 0.726 (0.034) -3632.6 36.81

Household Consumption as a Martingale: A Test for Rural South India

assets. There are some limitations in interpreting the signs and the magnitudes of the estimated coefficients since the formulation for testing the martingale property may be an unsatisfactory approximation for the process determining the consumption expenditures. It is often argued that if the rejection of the martingale hypothesis is caused by liquidity constraints, then this hypothesis may be accepted for the well-off households (Hayashi, 1987). Of course, the rejection could also arise from a failure of the rational expectations assumption. Nonetheless, a disaggregation of the sample by wealth could afford insights into the role of liquidity constraints. We constructed three groups on the basis of household wealth during the 6 year period. Table 2 contains the results for the three wealth groups. T h e autoregression coefficients for Wealth Groups 1 (the poorest) and 2 are negative but the processes do not seem non-stationary. Again, some components of wealth and household incomes appear with significant coefficients in these relationships. The martingale property is not supported by the data on any of the three groups. In summary, using a consistent estimator of a dynamic random effects model for consumption, we find that the martingale hypothesis for how consumption evolves over time is convincingly rejected for these data. Changes in consumption from one year to the next are correlated with ex-ante information, including lagged consumption. Thus these data are inconsistent with the simplest formulation of the permanent income hypothesis, equating consumption with the annuity value of assets plus the stochastically self-fulfilling expectations of future incomes. REFERENCES Anderson, T. W., and C. Hsiao, "Estimation of Some Dynamic Models with Error Components," Journal of American Statistical Association 76 (1981), 598-606. Bhargava, Alok, "Wald Tests and Systems of Stochastic Equations," International Economic Review 28 (1987), 789-808. , "Identification and Panel Data Models with Endogenous Regressors," Review of Economic Studies 58 (1991), 129-140.

103

Bhargava, Alok, L. Franzini, and W. Narendranathan, "Serial Correlation and the Fixed Effects Model," Review of Economic Studies 49 (1982), 533-549. Bhargava, A., and J. D. Sargan, "Estimating Dynamic Random Effects Models from Panel Data Covering Short Time Periods," Economelrica 51 (1983), 1636-1660. Campbell, J. Y., "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Economelrica 55 (1987),1249-1273. Chaudhuri, S., and Martin Ravallion, "How Well Do Static Indicators Identify the Chronically Poor?" Journal of Public Economics (1993). Deaton, Angus, "Saving and Income Smoothing in the Cote d'lvoire," mimeo, Woodrow Wilson School, Princeton University, 1990. Flavin, M. A., "The Adjustment of Consumption to Changing Expectations about Future Welfare," Journal of Political Economy 89 (1981), 974-1009. Hall, Robert E., "Stochastic Implications of the Life Cycle—Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy 86 (1978), 971-987. Hall, Robert E., and Frederic S. Mishkin, "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households," Economelrica 50 (1982), 461-481. Hayashi, F., "Tests for Liquidity Constraints: A Critical Survey and Some New Observations," in Truman F. Bewley (ed.), Advances in Econometrics, Fifth World Congress Volume 2 (Cambridge: Cambridge University Press, 1987). Kiefer, N. M., "Estimation of Fixed Effects Models for TimeSeries of Cross-Sections with Arbitrary Intertemporal Covariance," Journal of Econometrics 14 (1980), 195-202. Lipton, Michael, and Martin Ravallion, "Poverty and Policy," in Jere Behrman and T. N. Srinivasan (eds.), Handbook of Development Economics, Volume 3 (Amsterdam: North-Holland, forthcoming). Morduch, J., "Risk, Production and Saving: Theory and Evidence from Indian Households," mimeo, Department of Economics, Harvard University (1990). Neyman, I., and E. L. Scott, "Consistent Estimates Based on Partially Consistent Observations," Economelrica 16 (1948), 1-32. Nickell, S. J., "Biases in Dynamic Models with Fixed Effects," Economelrica 49 (1981), 1417-1426. Walker, T. S., and J. G. Ryan, Village and Household Economies in India's Semi-Arid Tropics (Baltimore: Johns Hopkins University Press, 1990). Zeldes, S. P., "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy 97 (1989), 305-346.

105

Community and International Nutrition Dietary Intakes and Socioeconomic Factors Are Associated with the Hemoglobin Concentration of Bangladeshi Women1 Alok Bhargava,*2 Howarth E. Bouis1" and Nevin S. Scrimshaw** 'From the Department of Economics, University of Houston, Houston, Texas 77204-5882; TInternational Food Policy Research Institute, 2033 K Street NW, Washington, D.C. 20006 and "International Nutrition Foundation, Box 500, Charles Street Station, Boston, Massachusetts 02114 ABSTRACT Iron deficiency anemia affects a large number of women in developing countries, especially during child-bearing years. The hemoglobin concentration is useful for identifying iron deficiency anemia. The main objectives of this study were, first, to extend algorithms for calculating bioavailable iron from mixed diets, taking into account the enhancers and inhibitors of iron absorption under alternative assumptions on body iron stores. Second, a comprehensive longitudinal model was developed for the proximate determinants of hemoglobin concentration that included the subjects' dietary intakes, nutritional status, morbidity and socioeconomic factors and the unobserved between-subject differences. The model for hemoglobin concentration was estimated using three repeated observations on 514 free living women in Bangladesh. Socioeconomic factors affecting the iron intake from meat, fish and poultry and from all animal sources were also modeled. The main results were that bioavailable iron, women's height and mid upper arm circumference and intake of iron tablets were significant predictors of hemoglobin concentration. Increases in household incomes were associated with higher intake of iron from meat, fish and poultry and from all animal sources. The algorithms for estimating bioavailable iron showed the importance of assumptions regarding body iron stores and underscored the need to develop suitable algorithms for subjects in developing countries. J. Nutr. 131: 758-764, 2001. KEY WORDS: • bioavailable iron • iron deficiency anemia • socioeconomic factors • longitudinal data • random effects models Iron deficiency anemia (IDA) is widely prevalent in low and middle income countries. It is estimated that 3.5 billion persons have IDA (UNICEF/WHO 1999). IDA hinders normal human functions in all age groups. For example, IDA lowered labor productivity of Indonesian rubber tappers (Basta et al. 1979) and Sri Lankan tea pickers (Gardner et al. 1977), adversely affected birth outcomes (Bhargava 2000) and impaired the cognitive development of children (Lozoff 1988, Pollitt 1993). The productivity loss and human costs associated with IDA are enormous (UNICEF/UNU/WHO/MI 1999). Poor diet quality and low bioavailability of dietary iron are important factors that contribute to IDA (Tatala et al. 1998); iron loss due to parasitic infection and menstrual bleeding and pregnancy can exacerbate IDA in women. For the design of effective policies, it is essential to adopt a multifactorial approach to analyzing the proximate determinants of IDA under actual living conditions. Thus, for example, the success of iron fortification programs is likely to vary with the intakes "ofmeat,

1 Supported by grants from the Danish International Development Assistance and the U.S. Agency for International Development, Office of Women in Development, to the International Food Policy Research Institute. 2 To whom correspondence should be addressed. E-mail: bhargava @ uh.edu 3 Abbreviations used: FeBIO, bioavailable iron; FeMFP, iron from meat, fish and poultry; FeTOT, total iron; Hb, hemoglobin; IDA, iron deficiency anemia; MFP, meat, fish and poultry; MUAC, mid upper arm circumference.

fish, poultry (MFP) and vitamins A and C, which enhance nonheme iron absorption, and of phytates and tannins, which inhibit it (Garcia-Casal et al. 1998, Hallberg et al. 1989 and 1997, Monsen et al. 1978). The algorithms developed for calculating iron bioavailability in the presence of enhancers such as meat and vitamin C were recently extended to incorporate the inhibitory effects of phytates, which chelate iron, thereby reducing its absorption (Tseng et al. 1997). Although iron intake by the poor in Bangladesh comes from staple foods such as rice, contamination iron from pots, small quantities from green and yellow vegetables and animal products, the phytate content of the meal is typically high. Thus, algorithms for calculating iron bioavailability and taking into account the enhancers and inhibitors of iron absorption at each meal are specially useful for subjects in developing countries. However, the inhibitory effects of phytate intakes have been customarily calculated from data on healthy subjects with —500 mg of iron stores (Brune et al. 1992, Hallberg et al. 1989). By contrast, iron absorption rates in the presence of enhancers were tabulated for body stores 0, 250 and 500 mg by Monsen et al. (1978); alternative assumptions on body iron stores lead to different estimates of absorbable iron. Hemoglobin concentration (Hb) is a widely used measure for assessing IDA (Khusun et al. 1999, UNICEF/WHO 1999). Although measures such as serum ferritin and erythrocyte

0022-3166/01 $3.00 © 2001 American Society for Nutritional Sciences. Manuscript received 28 February 2000. Initial review completed 12 May 2000. Revision accepted 28 November 2000.

A. Bhargava, H.E. Bouis and N.S. Scrimshaw

106

protoporphyrin provide additional insights into iron status, there are logistics and other difficulties in transporting venous blood samples from a large number of subjects living in remote areas of developing countries. Thus, modeling t h e proximate determinants of H b measured in the field through a fingerprick can be valuable for deciding on t h e allocation of resources among instruments such as government policies t h a t encourage MFP production, the provision of elemental iron tablets, and so on. Thus far, only a few studies in t h e nutrition literature have attempted to quantify the effects of dietary intakes o n serum iron measures (Doyle et al. 1999, D u et al. 2000). Also, most previous analyses did not incorporate other confounding factors and did not address in detail the methodological issues surrounding the bioavailability of iron. Dietary intakes and supplements, morbidity from infectious disease and genetic factors are likely to affect H b status. Therefore, we developed and estimated comprehensive longitudinal models for the proximate determinants of the H b status of Bangladeshi women. Because the success of interventions will be influenced by the way in w h i c h dietary intakes change with incomes, we also estimated a model for assessing t h e impact of increases in household incomes o n iron intake from MFP (FeMFP) and for iron intake from all animal sources.

MATERIALS A N D

METHODS

Subjects. The study was conducted in 16 villages in Jessore, 10 in Saturia and 18 in Mymensingh, Bangladesh (Bouis et al. 1998). One of the purposes of the research was to investigate the nutritional impact of the adoption of agronomically improved vegetables in Saturia and fish pond management strategies in Jessore and Mymensingh. At each site, the new technologies were introduced through nongovernment organization programs that provided credit and training to women. The selection of households was done in a complex manner to ensure that the selected households were representative of the three sites. Initially, there were 990 households, of which 33 did not participate in all four survey rounds. The sample size was further reduced because some women were not available for Hb measurements during one or more survey rounds. A comparison of the households in the census sample with nationally representative surveys for Bangladesh (Rahman et al. 1996) indicated that households in our sample were representative of households in the threes sites and not atypical of rural Bangladesh. The study design was approved in 1996 by a human subjects committee of the Bangladesh Medical Research Council in Dhaka. The surveys began in June 1996, and the fourth survey round was completed by September 1997. Because Hb was measured in survey rounds 2, 3 and 4, we analyzed the data from these rounds. Overall, there were 664 women in the age group 15-49 y (one from each household) for whom three observations separated by 4-mo intervals were available. Because observations on nutritional, anthropometric and other variables were missing for some women in the three survey rounds, models for Hb were estimated using the complete data on 514 women. The models for women's intake of FeMFP and for iron intake from all animal sources were estimated using the data on 514 women. For the simple autoregressive models estimating between- and withinsubject variations in Hb, data on 664 women in three survey rounds were used; Hb data on a subset of 71 women on 4 consecutive d in the fourth survey round were also analyzed. Economic, demographic and morbidity variables. Background information was compiled on household members' age, relationship with the head of the household, occupation, education and other items. Detailed information was gathered in the four survey rounds on economic variables such as household assets, incomes, food and nonfood expenditures, wages and so on; a variable was constructed for the average per capita monthly expenditures for each round. In poor countries, expenditure data are more reliable measures of economic well-being than are incomes. The reproductive history of each woman was investigated, and the current pregnancy and lactation

status was recorded. In each survey round, the women were questioned about symptoms such as fever, cough, diarrhea and any diseases in the past 2 wk; women with mucus and blood in the diarrhea were questioned. Work toss due to chronic illness during the year was also assessed. Anthropometry and hematology. Weight and arm circumferences of the women were measured in each survey round; height was measured at the start of the study. Spring scales accurate to 0.25 kg were used to measure the subjects' weight in light clothing. An adjustable wooden measuring board was used to measure height to the nearest 0.1 cm with the woman standing in upright position. A paper tape was used to measure the mid upper arm circumference (MUAC). Hb status was measured in the three survey rounds with a fingerprick sample of capillary blood obtained by a physician and analyzed immediately using a portable photometer (HemoCue; HemoCue Inc., Mission Viejo, CA). Nutritional intakes and bioavailable iron. In each of the three survey rounds, food intakes were measured using the 24-h recall method for the four meals consumed (i.e., breakfast, lunch, dinner and snacks). The person primarily responsible for preparing the meals was questioned about the recipes, ingredients and amounts of dishes consumed by household members and guests. The women's intakes of 40 nutrients at each meal were estimated using the food composition database of Calloway et al. (1994) for six countries. For estimating the bioavailable iron, taking into account nutrient interactions at each meal, we focused on the intakes of dietary iron, iron from animal sources, ascorbic acid, phytates and tannins from tea. Because most women did not consume any snacks, the data on snacks were aggregated with nutrient intakes at lunch. Moreover, because tea consumption was negligible in this population, the inhibitory effects of phytates were the prime concern. To calculate the bioavailable iron, algorithms (Monsen et al. 1978, Monsen and Balintfy 1982, Tseng et al. 1997) were suitably extended. The enhancing effects of MFP and ascorbic acid were programmed to calculate bioavailable iron at each meal under the assumptions that the women's iron body stores were 0, 250 and 500 mg. In comparison with normal subjects with iron stores of 500 mg, the absorption rates for heme and nonheme iron were 25 and 50% higher for subjects with iron stores o( 250 and 0 mg, respectively (Monsen et al. 1978, Table 1). The mathematical formulas for body stores of 0 and 250 mg have not been used in previous studies and may be more realistic for undernourished populations. Further, the algorithm of Tseng et al. (1997) for calculating the inhibitory effects of phytate intakes assuming an iron store of 500 mg contained a mathematical error. The correct formulas for the 0-, 250and 500-mg iron stores in the presence of enhancers and inhibitors of iron absorption in the meal are presented as eqs. 3-5. A Fortran program for meal-by-meal calculations is available from the first author; the program also sums the bioavailable iron (and other nutrients) at three or more meals to produce figures for the 24-h period. Computer programs for statistical packages, such as those developed by Tseng et al. (1997) for SAS (1996), can be easily modified on the basis of these mathematical formulas. In the following equations, FeTOT indicates the total iron intake, and FeBIO indicates the bioavailable iron. Heme iron was assumed to constitute 40% of FeMFP (Monsen et al. 1978). Using the notation of Monsen and Balintfy (1982), let the enhancing factor (EF) for a meal be given by E F - (M + F + P) + A A

(1)

where.M, F and P are the edible quantities of MFP (in g), respectively, and AA is the intake of ascorbic acid (in mg). If EF is >75, then EF was assumed to be 75. To take account of the inhibitory effects of phytates, using the data of Hallberg et al. (1989), Tseng et al. (1987) calculated the "correction term" (CT) (0 ^ CT ^ 1) that gives the proportion of FeBIO. However, Tseng et al. (1997) defined C T incorrectly when phytate intake was ^2.88 mg, because in the data of Hallberg et al. (1989), phytate intakes were either 0 or >2.88 mg. Let PHY be the total phytate intake (in mg) during the meal. Then, for PHY of ^ 2.88 mg, we defined CT as 1 {i.e., we assumed that there were no inhibitory effects of phytate intake for such small values). By contrast,

107

Hemoglobin Concentration of Bangladeshi Women TABLE 1 Selected variables in three survey rounds of Bangladeshi women from Saturia, Mymensingh and Jessore sites'! Variable Age, y Pregnant (yes = 1, no = 0) Height, m Hemoglobin, g/L Mid upper arm circumference, cm Weight, kg Fe tablets (yes = 1, no = 0) Energy intake, kJ/d Protein intake, g/d Phytate intake, mg/d Ascorbic acid, mg/d Fe, mg/d Fe (meat, fish, poultry), mg/d Fe (animal source), mg/d Fe (bioavailable: enhancers; zero body Fe stores), mg/d2 Fe (bioavailable: enhancers + inhibitors; zero body Fe stores), mg/d Fe (bioavailable: enhancers; 250 mg body Fe stores), mg/d Fe (bioavailable: enhancers + inhibitors; 250 mg body Fe stores), mg/d Fe (bioavailable: enhancers; 500 mg body Fe stores), mg/d Fe (bioavailable: enhancers + inhibitors; 500 mg Fe stores), mg/d

Round 2

Round 3

514 33.29 ± 7.80 0.05 ± 0.22 1.50 ± 0 . 0 5 117.3 ± 14.3 22.88 + 2.17 42.03 ±6.11 0.22 ± 0.41 9719 ± 3231 52.58 ± 16.99 2298 ±817 41.85 ±39.31 6.93 ± 3.00 0.33 ± 0.47 0.38 ± 0.49

514

119.4 22.91 42.26 0.22 8929 49.15 2229 61.33 7.99 0.23 0.29

: : : : : : : : : : :

14.6 2.19 6.07 0.42 2562 16.27 838 47.04 4.36 0.31 0.35

514

115.4: 23.25 : 42.83 : 0.27: 10,082 : 54.19: 2328: 79.31 : 7.91 : 0.26: 0.32:

13.6 2.22 6.32 0.44 2730 16.0 705 103.1 3.60 0.36 0.41

0.85 ± 0.54

0.98: 0.68

0.99: 0.63

0.20 ±0.13

0.22 : 0.13

0.22: 0.13

0.56 ± 0.33

0.64 : 0.41

0.64: 0.38

0.14 ±0.09

0.14 : 0.09

0.15: 0.08

0.39 ± 0.22

0.44: 0.28

0.45: 0.26

0.10 ±0.07

0.10: 0.06

0.11 : 0.06

1 Values are means ± SD. 2 See eqs. 3-5 in the text.

the algorithm of Tseng et al. (1997) would inadvertently imply that PHY intakes in the interval of 0-2.88 mg increase iron absorption. For other values of PHY, CT was defined by C T = io [ - 0 ' 2 8 6 9 losi°(pHY)+al295]

(2)

where log10 is logarithm to the base 10. Thus, high values of PHY intake reduce FeBIO in a curvilinear fashion (Brune et al. 1992, Tseng et al. 1997). Assuming that body iron stores were 0, 250 and 500 mg, the FeBIO can be calculated, respectively, from the following three equations (Monsen et al. 1978; Table 1): FeBIO (0) = 0.140 FeMFP + [5 + 26.804 log n {(EF + 100)/100}] X C T [FeTOT - 0.4 FeMFP]/100

(3)

FeBIO (250) = 0.112 F e M F P + [4 + 14.296 log n {(EF + 100)/100}] X C T [ F e T O T - 0 . 4 FeMFP]/100

(4)

FeBIO (500) = 0.092 FeMFP + [3 + 8.93 log n {(EF + 100)/10O}] X C T [FeTOT - 0.4 FeMFP]/100

(5)

where logn is natural logarithm. Note that because the absorption of heme iron was assumed to be not affected by the presence of other nutrients in the meal, the formulas for calculating FeBIO simultaneously take into account the effects of enhancers and inhibitors on nonheme iron absorption (i.e., the order in which the adjustment is made for enhancers and inhibitors is immaterial). Also, the inhibitory effects of phytate intake in eqs. 3-5 assumed body iron stores of 500 mg; this issue is further discussed later.

A model for the proximate determinants of Hb concentration. The Hb status of a woman is influenced by previous nutritional intakes, sicknesses, pregnancy and lactation status, dietary supplements and genetic factors. The intake of heme iron and interactions between nonheme iron and ascorbic acid, vitamin A, beta-carotene and phytates in the meal affect iron absorption and, ultimately, the Hb level. In developing countries, economic constraints on household food consumption adversely affect the quality of diet, thereby hindering iron absorption. Determination of within-subject variability in 24-h recall data at a given time requires two or three random repetitions within a limited time period. In our study, we obtained useful information on within-subject variability during the entire study by using the women's dietary intakes in each of the three survey rounds. Longitudinal studies that measure subjects' dietary intakes over more extended periods of time would be prohibitively expensive. It is therefore important to introduce anthropometric variables such as the MUAC, height and weight in models that explain Hb status because they reflect the history of nutritional intakes and infections. Moreover, recent sicknesses, especially those involving blood loss, can reduce Hb (Scrimshaw et al. 1959). By contrast, iron supplements can raise Hb within a short time frame (Viteri 1999). The model for Hb should account for all of these factors. The effects of dietary intakes and other factors on Hb status can be analyzed using longitudinal data by estimating autoregressive regression models that include previous measurement on Hb as an explanatory variable. Denoting the ith subject's Hb in time period t by Hb it (i — 1, 2, . . . , n; t = 2, 3), we postulated the autoregressive model for Bangladeshi women: Hb,-, = OQ (constant) + a\ (age) + a2 (pregnancy indicator) + a3 (height) + a4 (MUAC) + a5 (weight) + <% (FeBIO) + a7 (diarrhea with blood indicator) + a8 (Fe tablets indicator) + 0$ (Hb)lt_t + uit

(6)

108

A. Bhargava, H.E. Bouis and N.S. Scrimshaw

where a 0 , . . . , a9 are the regression coefficients, uit is an error term (see eq. 7) and Hb ([ _ i is the previous measurement of Hb status, with coefficient Og. There were several attractive features of the model in eq. 6 for Bangladeshi women's Hb status using three repeated observations in an 8-mo period. First, the short-run, or immediate, impact of a change in a variable such as the FeBIO on Hb was given by a 6 ; the long-run impact was [a 6 /(l — a,)]. Generally, one would expect 0 < a, < 1, so the long-run effect would be greater than the short-run impact. Moreover, for small estimated values of %, the 8-mo observation period was sufficiently long for much of the long-term effect to materialize. Second, the error term uit in eq. 6 can be decomposed in a random effects fashion as: u« = S, + v„

(7)

where 5s are women-specific random effects, and v's are independently distributed random variables. Because Hb is influenced by genetic factors (Garner et al. 2000) and other unobserved characteristics, one would expect the between-subject variance (of Sf) to be an important parameter in the model that explains differences in Hb status. Third, Hb measurements using capillary blood often exhibit large within-subject variation that can obscure the effects of explanatory variables (Liu et al. 1976, Morris et al. 1999). In contrast with a single observation on the subjects, however, maximum likelihood estimates computed using repeated observations in a random effects framework can alleviate some of these problems. Fourth, interesting hypotheses can be tested using the model given in eq. 6. For example, economic factors are likely to affect diet quality of the Bangladeshi women; diet quality in turn would determine the quantity of FeBIO that would be expected to predict Hb status. Autoregressive models for iron intake from MFP and iron from all animal sources. To investigate the effects of economic variables on Hb status, we postulated an autoregressive model for the intake of FeMFP; such models are consistent with theories of "habit persistence" in diets that are important for analyzing dietary patterns, especially in traditional societies (Bhargava 1991, Gorman 1967). The model can be written as: FeMFP,, = b0 (constant) + b[ (age) + b2 (household size) + b3 (household size)2 + b4 (BMI) + b5 (monthly average per capita expenditure) + b6 (FeMFP)^, + u&

(8)

Note that household size (and its square) were included in the model in eq. 8 because women in poor households with a large number of children were likely to consume inadequate quantities of FeMFP. The household per capita total expenditure, which changed with the survey rounds, was potentially important for explaining women's intake of FeMFP. Women's height and weight were introduced into the model because they reflected the energy requirements (James and Schofield 1990). In eq. 8, height and weight were combined as the body mass index (BMI; in kg/m2) due to the results of a statistical test (Bhargava 1994). In rural populations subsisting in poverty, BMI can be a measure of chronic undernutrition and so associated with a variety of adverse outcomes (James and Ralph 1994). Econometric procedure. Because there were only three time observations available for the women, statistical estimation was based on the assumptions that the number of women was large but the number of survey rounds was fixed. Thus, initial observations on the dependent variables were treated as endogenous variables (correlated with the errors, Bhargava and Sargan 1983). The enors in eqs. 6 and 8 were assumed independent across women but correlated over time with a positive definite variance-covariance matrix. The random effects decomposition for the u values given in eq. 7 was a special case of this model. The joint determination of the three observations on Hb (or FeMFP) implied that econometric techniques used for simultaneous equations were likely to be useful in this application. Details of the

maximum likelihood estimation method are presented elsewhere (Bhargava and Sargan 1983). Here, we note that the profile loglikelihood functions of the models in eqs. 6 and 8 were optimized using numerical scheme E04 JBF from the Numerical Algorithm Group (1989); asymptotic standard errors of the parameters were obtained by approximating second derivatives of the function at the maximum. The maximized values of the logarithm of the likelihood function were used to test hypotheses regarding the coefficients of the variables included in the models for Hb and FeMFP.

RESULTS Descriptive statistics. T h e sample means of selected variables i n three survey rounds for 514 Bangladeshi w o m e n are given in Table 1. Striking features of t h e intake data were t h e low FeMFP intakes and t h e high phytate intakes. For example, in the first survey round, t h e average daily F e T O T intake was 6.93 ± 3.00 mg, of w h i c h only 0.33 ± 0.47 mg was FeMFP. Further, assuming 0-mg iron body stores a n d taking into account enhancers of iron absorption, t h e average daily FeBIO was 0.85 ± 0.54 mg. However, this was reduced t o 0.20 ± 0.13 mg w h e n the effect of p h y t a t e intake was incorporated; t h e suitability of t h e algorithm for incorporating inhibitory effects of phytate intakes in undernourished populations is addressed in Discussion. Similarly, assuming 250-mg iron stores, t h e average daily FeBIO fell from 0.56 ± 0.33 t o 0.14 ± 0.09 mg when phytate intakes were taken into a c c o u n t . T h e s e intakes ate well below the "safe" level of 2 mg r e c o m m e n d e d for a woman who weighs 50 kg ( F A O / W H O 1988). T h e average daily intake of FeMFP by 514 w o m e n at percentiles 1, 5, 10, 15, 2 5 , 50, 75 and 90 was 0.009, 0.030, 0.058, 0.080, 0.111, 0.209, 0.338 and 0.513 mg, respectively. T h e corresponding values for H b at these percentiles were 81.4, 97.0, 103.5, 106.1, 111.7, 118.0, 125.0 a n d 130.3 g/L, respectively. Using 120 g Hb/L as a cutoff p o i n t for IDA, > 5 5 % of the w o m e n would be classified as h a v i n g I D A . For t h e 71 women who were p r e g n a n t during o n e or more of t h e three survey rounds, t h e respective H b m e a s u r e m e n t s were 76.7, 88.7, 99.3, 101.9, 104.0, 111.3, 116.0 a n d 122.8 g/L; hemodiiution and iron cost of pregnancy are likely t o diminish the H b status of pregnant women. Autocorrelations and between- and within-subject variations in Hb concentration. Table 2 presents t h e results for a simple autoregressive model fot the natural logarithm of H b ; t h e constant term was t h e only additional explanatory variable in eq. 6. T h e point estimate of the coefficient of t h e lagged dependent variable using t h e data in t h t e e survey rounds was 0.18 (SE = 0.058). T h i s was smaller t h a n t h e corresponding estimate 0.248 (SE = 0.112) for the 4-d observations; b o t h estimates wete statistically significant. T h e difference in estimates seemed reasonable because nutritional a n d o t h e r factors such as women's pregnancy status and a n t h r o p o m e t r i c indicators changed over t h e three survey rounds. T h e ratio of between to within variance was 0.536 (SE = 0.133) for t h e three survey rounds and 0.417 (0.207) for 4 consecutive d observations. T h e between-subject variations in H b were relatively large; individual characteristics such as t h e subjects' height, M U A C and weight may a c c o u n t for some these differences. Underlying genetic factors ( G a m e r et al. 2000) may also have conttibuted to t h e b e t w e e n - w o m e n differences. Last, the within-subject variance was large, especially in comparison with studies i n w h i c h simple r a n d o m effects models were estimated for venous blood samples (Morris et al. 1999). However, t h e autocorrelations were n o t estimated in previous studies.

Hemoglobin Concentration of Bangladeshi Women

Results from the autoregressive model explaining Bangladeshi women's Hb concentration by demographic and nutritional variables. The results from estimation of the autoregressive model given in eq. 6 for women's Hb status are presented in Table 3, where body iron stores were assumed to be 0 mg (similar results were obtained when iron stores were assumed to be 250 and 500 mg and hence are not reported). Table 3 presents results for the cases where, first, only the enhancers of iron absorption were taken into account and, second, the inhibitory effects of phytates in the meal were also incorporated in calculating FeBIO. The subjects' age, height, MUAC, weight, FeBIO and the previous measurement of Hb were transformed into natural logarithms. The logarithmic transformation reduced internal variation in the data (Nelson et al. 1989). The estimated coefficients of the variables in logarithms were short-run "elasticities" (percentage change in the dependent variable resulting from a 1% change in an independent variable). The long-run elasticity with respect to an explanatory variable can be obtained by dividing the shortrun elasticity by (1 — dg), where dg was the coefficient of Hb in the previous time period. There was a significant decline in Hb with age in the model where only the enhancers of iron absorption were taken into account in calculating FeBIO; the coefficient was not statistically significant when the inhibitory effects of phytates were incorporated. Hb of pregnant women was significantly lower (P < 0.05). An additional indicator (0-1) variable was included for women who were lactating during the survey rounds. However, it was not statistically significant. The women's height and MUAC were positively associated with Hb status; these coefficients were statistically significant. Height is a good indicator of early nutrition, whereas MUAC can approximate lean body mass. It was not surprising that these two variables were positively associated with Hb. By contrast, weight was negatively associated, which may have

TABLE 2 Maximum likelihood estimates of a simple first-order autoregressive model with random effects for the natural logarithm of Bangladeshi women's hemoglobin concentration measured in three survey rounds and hemoglobin concentration measured for a subset of the women on four consecutive days in the fourth survey roundi Hemoglobin Three survey rounds? Independent variable n Constant Lagged dependent variable, 9'L Between/within variance Within variance Proportion of variance due to between subject differences 2 (log-likelihood function) 1

Coefficient 664 3.897* 0.180* 0.536* 0.009 0.435 8591.62

SE

0.323 0.068 0.167

— — —

Four consecutive days3 Coefficient 71 3.575* 0.248* 0.417* 0.006

SE

0.598 0.125 0.207

—

0.409 1393.33

Values are slope coefficients and standard errors. * P < 0.05. Hemoglobin concentration measured at 3-mo intervals. 3 Hemoglobin concentration measured on four consecutive days in the third survey round. 2

109

TABLE 3 Maximum likelihood estimates of a first order autoregressive model with random effects for Bangladeshi women's hemoglobin concentration in 3 survey rounds explained by anthropometric and morbidity variables and by the intake of bioavailable Fe assuming 0 mg body Fe stores^ Hemoglobin Fe enhancers only Independent variable n Constant Age,2 y Pregnant (yes = 1; no = 0) Height,2 m MUAC.2 cm Weight.2 kg Fe bioavailable,2,3 mg/d Diarrhea with blood (yes = 1; no = 0) Indicator for Fe tablets (yes = 1; no = 0) Lagged dependent variable,2 g/L Between/within variance Within variance 2 (log-likelihood function)

Coefficient

Fe enhancers + inhibitors

SE

Coefficient

SE

514 3.558* -0.018* -0.047* 0.343* 0.325* -0.203* 0.012*

0.076 0.008 0.013 0.124 0.022 0.017 0.006

514 3.649* -0.020 -0.047* 0.330* 0.312* -0.196* 0.015*

0.305 0.018 0.014 0.134 0.029 0.026 0.006

-0.038

0.044

-0.038

0.045

0.026*

0.009

0.026*

0.009

0.182* 0.444* 0.009 6769.89

0.004 0.055

0.173* 0.462* 0.009 6772.09

0.057 0.133

— —

— —

1 Values are slope coefficients and standard errors. * P < 0.05. 2 These variables and dependent variable were in natural logarithms. 3 See equation (3) in the text for the algorithm.

been due to the presence of pregnant women in the sample; the indicator variable did not account for pregnancy trimesters. In the first column, where only the enhancers of iron absorption were used for calculating the FeBIO, the coefficient of FeBIO was positive and significant at the 5% level. Moreover, this coefficient showed a 20% increase in the second column where the inhibitory effects of phytate intakes were also taken into account. The maximized value of the logarithm of the likelihood function was higher when the inhibitory effects of phytate intake were incorporated. The indicator variable for woman with bloody diarrhea was negative but not significantly associated with Hb status; parity and the average birth interval were also insignificant. However, the indicator variable for women taking iron tablets during the survey round was positive and significant. In Bangladesh, iron tablets were often sold together with birth control pills. The results reported in Table 3 set the indicator variable for iron tablets to 1 only when the women answered the specific question regarding iron tablets intake. Last, maximized values of the logarithms of the likelihood functions were slightly higher when it was assumed that the women had 0-mg body iron stores than in the cases where the iron stores were assumed to be 250 or 500 mg. Although this was not direct evidence for the actual iron stores, the results suggested that the average woman probably had iron stores lower than 250 mg. Results from autoregressive models explaining Bangladeshi women's iron intake from MFP and from all animal sources by economic, demographic and nutritional variables.

A. Bhargava, H.E. Bouis and N.S. Scrimshaw

110 TABLE 4

Maximum likelihood estimates of a first order autoregressive model with random effects for Bangladeshi women's iron intake from meat, fish and poultry (MFP) and iron intake from animal source in 3 survey rounds explained by anthropometric, demographic and economic variables' Fe intake, mg

Independent variable n Constant Age, 2 y Household size2 Household size squared 2 Monthly average percapita 2 expenditure, Taka3 BMI,2 kg/ml Lagged dependent variable, 2 mg Between/within variance Within variance 2 (log-likelihood function)

Fe from MFP, mg

Fe from all animal sources, mg

Coefficient

SE

Coefficient

SE

514 -2.907* -0.679* 0.932* -0.197*

0.060 0.015 0.033 0.034

514 -3.718* -0.622* 1.291* -0.310*

0.232 0.130 0.078 0.031

0.650* 0.747*

0.012 0.023

0.708* 0.771*

0.071 0.056

0.077* 0.070* 1.972 -1152.32

0.037 0.033

0.130* 0.030 1.687 -863.95

0.052 0.044

1

Values are slope coefficients and standard errors. * P < 0.05. These variables and dependent variable were in natural logarithms. 3 $1.00 = 42Taka. 2

The results from estimation of the model in eq. 8 for intake of FeMFP and iron from all animal sources are given in Table 4Because some women did not consume any MFP in one or more survey rounds but consumed some milk and animal products, the two sets of results give a better description of the food consumption patterns. The zero intakes of iron by some women were set to 0.01 mg before the logarithmic transformation; a sensitivity analysis was performed to investigate whether this assumption affected the results, but it did not. The interesting aspects of the results were that 1) age had a large negative coefficient that was statistically significant in both models; older women consumed lower quantities of animal products. This finding was also consistent with the slight decline in Hb with age in Table 3. 2) There was a nonlinear effect of household size on intake of FeMFP and iron intake from all animal sources. This was an expected finding because larger households typically consist of a greater number of children growing up in poverty; the diet quality in such households is generally poor. 3) The coefficients of monthly average per capita expenditure were large and significant; a 1% increase in households' monthly expenditure was associated with 0.65 and 0.71% increases in FeMFP intake and iron intake from all animal sources, respectively. The corresponding longrun income elasticities were 0.70 and 0.87. These results suggested that women's iron intakes improved significantly with increases in household incomes. 4) The subjects' BMI was a significant predictor of FeMFP and from all animal sources. In a long time frame, however, systematically higher intakes of FeBIO may contribute to a gain in lean body mass, thereby increasing the BMI. At the given data points, the possible reverse causality from higher intake of FeMFP to BMI was investigated by testing the null hypothesis that the correlation between the random effects (8;) in eq. 8 and BMI was 0; the hypothesis was accepted for

FeMFP (likelihood ratio statistic, 0.30, df, 3; P = 0.999). Similar results were obtained for iron intake from all animal sources. 5) The coefficients of lagged dependent variables were 0.077 and 0.130, respectively, in the models for intake of FeMFP and iron intake from all animal sources; both coefficients were statistically significant. The ratios of between to within variance were not statistically significant in either model. This was in part due to the large within-subject variation in iron intake from animal sources. DISCUSSION IDA is widely prevalent in low and middle-income countries (UNICEF/WHO 1999). Using the recent longitudinal survey from Bangladesh, the intake of FeBIO were calculated under alternative assumptions of women's iron stores. For example, the mean intake of FeBIO in survey round 2 was 0.20 mg/d, taking into account the meal-by-meal nutrient interactions and assuming negligible body iron stores; mean intakes of FeBIO were 0.14 and 0.10 mg/d, respectively, when the body stores were assumed to be 250 and 500 mg. Furthermore, high phytate content of the meals reduced FeBIO intake from 0.85 to 0.20 mg/d with the assumption of zero iron stores. The inhibitory effects of phytates were calculated using algorithms based on data on healthy populations with iron stores of - 5 0 0 mg (Hallberg et al. 1989, Tseng et al. 1997). It is plausible that inhibitory effects of phytates and tannins differ in populations with lower iron stores. For example, Murphy et al. (1992) adjusted nonheme iron intakes of toddlers in Egypt, Kenya and Mexico for the presence of tannins in the meal, although the data were not available by meals. The authors estimated that average FeMFP intakes of toddlers in Egypt, Kenya and Mexico were 0.64, 0.05 and 0.37 mg/d, respectively (Murphy et al. 1992, Table 4). However, the corresponding FeBIO intakes incorporating the effects of tannins in the three populations were 0.49, 0.61 and 0.37 (mg/d), respectively. It is perhaps surprising that despite the lowest average intake (0.05 mg/d) of FeMFP in Kenya, these toddlers had the highest intake (0.61 mg/d) of FeBIO. It would seem critical to conduct studies in undernourished populations to derive suitable algorithms for iron absorption from mixed diets. The second objective of the study was to develop comprehensive longitudinal models for the Hb status of Bangladeshi women and to model the socioeconomic determinants of the intake of FeMFP. From the results in Table 3 for Hb status, the short- and long-run elasticities of Hb with regard to FeBIO were 0.015 and 0.018, respectively. Using the sample means in round 2 in Table 1, a doubling of FeBIO to 0.40 mg/d would result in a long-run increase of 3.6% in Hb. Because the sample mean of Hb was 117.3 ± 11.6 g/L, the average woman would then not be classified as having IDA. Moreover, a 10-fold increase of FeBIO from 0.20 mg to the "safe" level of 2.0 mg (FAO/WHO 1988) would be associated with a 18% increase in Hb, which would greatly reduce the prevalence of IDA. The magnitude of such increases is likely to be underestimated because within-subject variation in iron intakes results in measurement errors that bias the estimated coefficients downward (Liu et al. 1976). At any rate, there is evidence that even minor improvements in Hb have beneficial effects on child-bearing, time allocation, morbidity from infections, work productivity and cognition (UNICEF/UNU/ WHO/MI 1999). IDA among the poor in part results from high prices of animal products, which reduces the intake of heme iron. Also,

Hemoglobin Concentration of Bangladeshi Women

prices of fresh vegetables and fruits show large seasonal fluctuations, making t h e m less affordable outside t h e harvest season. Thus, the e n h a n c i n g effects of vitamin C for iron absorption may be applicable primarily to t h e well-off groups and not to those most likely t o have I D A . Cereal staples, such as rice, in Bangladesh have low iron and a high phytate content. T a k e n together, these factors suggest that to reduce IDA, one would need to evaluate the cost-effectiveness of instruments such as iron fortification of rice, increased consumption of MFP and easier access to iron tablets. Because women in our sample who took iron tablets had —2.5% higher H b levels and the costs of daily iron supplementation were ~ $ 0 . 2 5 per woman per m o n t h (Levin et al. 1993), women, especially those of child-bearing age, would be good candidates for daily or weekly iron supplementation (Allen 2000, Beard 1998). ACKNOWLEDGMENTS The authors would like to thank the participants in the surveys and the staff of Data Analysis and Technical Assistance in Dhaka, Bangladesh, for making this study possible. We also thank K. Hallman, N. Hassan, N. Islam, E. Payongayong and A. Quisumbing for their help and P. Reeds for valuable suggestions. LITERATURE CITED Allen, L. H. (2000) Anemia and iron deficiency: effects on pregnancy outcome. A m . J. Clin. Nutr. 7 1 : 1280S-1284S. Basta, S. S., Soekirman, M. S., Karyadi, D. & Scrimshaw, N. S. (1979) Iron deficiency anemia and the productivity of adult males in Indonesia. A m . J . Clin. Nutr. 32: 9 1 6 - 9 2 5 . Beard, J . L. (1998) Weekly iron intervention: the case for intermittent iron supplementation. A m . J . Clin. Nutr. 68: 2 0 9 - 2 1 2 . Bhargava, A. (1991) Estimating short and long run income elasticities of f o o d s and nutrients for rural south India. J . R. Stat. Soc. A 154: 4 1 7 - 4 3 2 . Bhargava, A. (1994) Modelling the health of Filipino children. J. R. Stat. Soc. A 157: 4 1 7 - 4 3 2 . Bhargava, A. (2000) Modeling the effects of maternal nutritional status and socioeconomic variables on the anthropometric and psychological indicators of Kenyan infants from age 0 - 6 months. A m . J . Phys. Anthropol. 1 1 1 : 8 9 104. Bhargava, A. & Sargan, J . D. (1983) Estimating dynamic random effects models from panel data covering short time periods. Econometrica 5 1 : 1 6 3 5 1660. Bouis, H. E., Briere, B., Guitierrez, L , Hallman, K., Hassan, N., Hels, 0 . , Quabili, W., Quisumbing, A., Thilsted, S., Zihad, Z. H. & Zohir, S. (1998) Commercial Vegetable and Polyculture Fish Production in Bangladesh: Their Impacts on Income, Household Resource Allocation, and Nutrition. International Food Policy Research Institute, Washington, D.C. Brune, M , Rossander-Hulten, Hallberg, L , Gleerup, A. & Sandberg, A.-S. (1992) Iron absorption from bread in humans: inhibiting effects of cereal fiber, phytate, and inositol phosphates with different numbers of phosphate groups. J. Nutr. 1 2 2 : 4 4 2 - 4 4 9 . Calloway, D. H., Murphy, S. P. & Bunch, S. (1994) User's Guide t o the International Minilist Nutrient Data Base. Department of Nutritional Sciences, University of California, Berkeley, CA. Doyle, W., Crawley, H., Robert, H. & Bates, C. J. (1999) Iron deficiency in older people: interactions between f o o d and nutrient intakes with biochemical measures of iron: further analysis of the National Diet and Nutrition Survey of people aged 65 years or over. Eur. J . Clin. Nutr. 53: 5 5 2 - 5 5 9 . Du, S., Zhai, F., Wang, Y. & Popkin, B. M. (2000) Current methods of estimating dietary iron bioavailability do not work in China. J. Nutr. 130: 193-198. FAO/WHO (1988) Requirements of Vitamin A, Iron, Folate and B 1 2 : Report of a Joint FAO/WHO Expert Consultation. Food and Agriculture Organization, Rome, Italy. Garcia-Casal, M. N., Layrisse, M., Solano, L , Baron, M. A., Arguello, F., Llovera, D., Leets, I. & Tropper,.E. (1998) Vitamin A and /3-carotene can improve nonheme iron absorption from rice, wheat and corn by humans. J . Nutr. 128: 646-650.

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Gardner, G. W., Edgerton, V. R., Senewratne, B., Barnard, J . J . & Chiro, Y. (1977) Physical w o r k capacity and metabolic stress in subjects with iron deficiency anemia. A m . J . Clin. Nutr 30: 9 1 0 - 9 1 7 . Garner, C , Tatu, T., Reittie, J. E., Littlewood, T „ Darley, J „ Cervino, S . , Farrall, M., Kelly, P., Spector, T. D. & Thein, S. L. (2000) Genetic influences on F cells and other hematologic variables: a twin heritability study. Blood 95: 3 4 2 - 3 4 6 . G o r m a n , W. M. (1967) Tastes, habits a n d choices. Int. E c o n . Rev. 8 : 2 1 8 - 2 2 2 . Hallberg, L , Brune, M. & Rossander, L. (1989) Iron absorption in m a n : ascorbic acid and d o s e - d e p e n d e n t inhibition by phytate. A m . J . Clin. Nutr. 49: 1 4 0 144. Hallberg, L , Hulten, L & Gramatkovski, E. (1997) Iron a b s o r p t i o n f r o m t h e whole diet in men: h o w effective is t h e regulation of iron absorption? A m . J . Clin. Nutr 66: 3 4 7 - 3 5 6 . James, W.P.T. & Ralph, A. (1994) The functional significance of l o w body m a s s index. Eur. J . Clin. Nutr. 48(suppl. 3). James, W.P.T. & Schofield, E. C. (1990) Human Energy Requirements. O x f o r d University Press, O x f o r d , U.K. Khusun, H., Yip, R., Schultink, W. & Ditlion, D.H.S. (1999) World Health Organization hemoglobin cut-off points for the detection of anemia are valid for an Indonesian population. J . Nutr. 1 2 9 : 1 6 6 9 - 1 6 7 4 . Levin, H., Pollitt, E., Galloway, R. & McGuire, J . (1993) Micronutrient deficiency disorders. In: Disease Priority in Developing Countries (Jamison, D., Mosley, W., Measham, A. & Bobadila, J . , eds.), Oxford University Press, Oxford, U.K. Liu, K., Dyer, J . , M c Keever, J . & McKeever, P. (1976) Statistical methods t o assess and minimize the role of intra-individual variability in obscuring the relationship between dietary lipids and serum cholesterol. J. Chron. Dis. 3 1 : 399-418. Lozoff, B. (1988) Behavioral changes in iron deficiency. A d v . Pediatr. 35: 331-360. Monsen, E. R. & Balintfy, J . L. (1982) Calculating dietary iron bioavailability: refinement a n d computerization. J. A m . Diet. Assoc. 8 0 : 3 0 7 - 3 1 1 . Monsen, E. R., Hallberg, L., Layrisse, M., Hegsted, D. M., C o o k , J . M., Mertz, W. & Finch, C. A. (1978) Estimation of available dietary iron. A m . J . Clin. Nutr. 31: 134-141. Morris, S., Ruel, M. T., C o h e n , R. J . , Dewey, K. G., d e la Briere, B. & Hassan, M. N. (1999) Precision, accuracy, and reliability of hemoglobin assessment with use of capillary b l o o d . Am. J . Clin. Nutr. 69: 1243-1248. Murphy, S. P., Beaton, G. H. & Calloway, D. H. (1992) Estimated mineral intakes of toddlers: predicted prevalence of inadequacy in village populations in Egypt, Kenya, a n d Mexico. A m . J . Ciin. Nutr. 56: 5 6 5 - 5 7 2 . Nelson, M., Black, A. E., Morris, J . A. & Cole, T. J . (1989) Between-and-within subject variation in nutrient intake f r o m infancy to o l d age: estimating t h e number of d a y s t o rank dietary intakes with desired precision. A m . J . Clin. Nutr. 50: 1 5 5 - 1 6 7 . Numerical Algorithm G r o u p (1989) Numerical Algorithm Group Library, Mark 13. Oxford University, Oxford, U.K. Pollitt, E. (1993) Iron deficiency and cognitive function. Annu. Rev. Nutr. 13: 521-537. Rahman, H. Z „ Hossain, M. & Sen, B. (1996) 1 9 8 7 - 1 9 9 4 : Dynamics of Rural Poverty in Bangladesh. Bangladesh Institute of Development Studies, Dhaka, Bangladesh. SAS Institute (1999) Statistical Analysis Software Version 6.12. SAS Institute, Inc., Cary, NC. Scrimshaw, N. S., Taylor, C. E. & Gordon, J . E. (1959) Interactions of nutrition and infection. A m . J . M e d . Sci. 237: 3 6 7 - 4 0 3 . Stoltzfus, R., Chwaya, H. M., Tielsch, J. M., Schulze, K. J „ A l b o n i c o , M. & Savioli, L. (1997) Epidemiology of iron deficiency anemia in Zanzibari schoolchildren: the importance of hookworms. A m . J . Clin. Nutr. 65: 1 5 3 - 1 5 9 . Tatala, S., Svanberg, U. & M d u m a , B. (1998) Low dietary iron availability is a major cause of anemia: a nutrition survey in the Lindi district of Tanzania. A m . J . Clin. Nutr. 68: 1 7 1 - 1 7 8 . Tseng, M., Chakraborty, H., Robinson, D. T., Mendez, M. & Kohlmeier, L. (1997) Adjustment of iron intake for dietary enhancers and inhibitors in population studies: bioavailable iron in rural and urban residing Russian w o m e n a n d children. J . Nutr. 127: 1 4 5 6 - 1 4 6 8 . UNICEF/UNU/WHO/MI (1999) Preventing Iron Deficiency in W o m e n and C h i l dren: Background a n d Consensus on Key Technical Issues a n d Resource for Advocacy, Planning and Implementing National Programmes. International Nutrition Foundation, Boston, MA. UNICEF/WHO (1999) Prevention and Control of Iron Deficiency Anaemia in W o m e n and Children. World Health Organization, Geneva, Switzerland. Viteri, F.E., Ali, F. & Tujague, J . (1999) Long-term iron supplementation i m proves and sustains nonpregnant w o m e n ' s iron status a s well or better t h a n currently r e c o m m e n d e d short-term daily supplementation. J Nutr. 129: 2 0 1 3 2020.

/. R. Statist. Soc. A (1992) 155, Part 2, pp. 221-231

Malnutrition and the Role of Individual Variation with Evidence from India and the Philippines By ALOK BHARGAVAT University of Houston, USA [Received May 1990. Final revision May 1991] SUMMARY This paper estimates the proportions of variations in the intakes of dietary energy and protein due to interindividual and intraindividual differences using four rounds of 24-hour recall data from India and the Philippines. The variances are estimated in a dynamic error components framework assuming that the number of individuals tends to infinity. It is noted that these proportions are affected by socioeconomic factors in developing countries and that the relative contribution of the within variation is likely to decline with rises in incomes. A comparison of the maximum likelihood estimates for the two countries and a breakdown of the samples by household incomes supports this hypothesis. Some implications of the results are also discussed. Keywords:

BETWEEN AND WITHIN VARIATIONS; DIETARY SURVEYS; DYNAMIC ERROR COMPONENTS MODELS; ECONOMETRIC MODELS; EPIDEMIOLOGICAL METHODS; LONGITUDINAL DATA; MAXIMUM LIKELIHOOD ESTIMATION; PROTEIN-ENERGY MALNUTRITION

1.

INTRODUCTION

The pathological conditions marasmus and kwashiorkor resulting from dietary energy and protein deficiencies are prevalent in many less developed countries (Shils and Young, 1988). The long-term effects of these conditions can be particularly harmful for the younger members of the populations. The definition of recommended daily allowances (RDAs) of the various nutrients is thus an important task for international agencies such as the Food and Agriculture Organization (FAO) and the World Bank. Initially, the interindividual differences in the population were emphasized by the FAO and the RDAs were increased to 'safe' levels (Food and Agriculture Organization, 1970). The improvements in the techniques for assessing human nutrient requirements and the recent availability of intake data from developing countries will no doubt afford more precise adjustments in the RDAs (Food and Agriculture Organization, 1985). The incorporation of the interindividual differences in the RDAs protects individuals with higher requirements from undernutrition and, at a large-scale level, poor countries from food shortages. The upward revisions in the RDAs were criticized by Sukhatme (1974) who stressed that the intraindividual (within) variation in energy and protein intakes was the dominant component. Sukhatme and Margen (1978, 1982) subsequently postulated an autoregulatory mechanism in the human body which controls the efficiency with ^Address for correspondence: Department of Economics, University of Houston, Houston, TX 77204-5882, USA. © 1 9 9 2 Royal Statistical Society

0035-9238/92/155221

$2.00

A. Bhargava

114

which food intakes are converted into expendable energy. The large contribution of the within variation and the serial correlation in energy and protein intakes of 35 British army recruits (Edholm et al., 1970) and 12 people living in Antarctica (Acheson et al., 1980) were construed as supporting the 'adaptation' hypothesis. The main implication of the theory is that, in the range governed by the within variance, human beings can perform their normal functions without feeling nutritional stress. Now, the connection between the within variation and autocorrelation in nutritional intakes and biological adaptation seems rather tenuous given the limited understanding of biologists about the latter process (Waterlow, 1986,1989). Furthermore, the striking physiological dissimilarities between the subjects in developing countries and those in Britain and Antarctica cast doubt on the relevance of the empirical results for the design of food policies for developing countries. Yet the Sukhatme-Margen hypothesis has been influential among some policy makers (James, 1989) and it has been suggested that the RDAs of vital nutrients can be reduced without affecting the subjects' health. The estimation of interindividual and intraindividual variances in the intakes of nutrients is an important topic in epidemiological research partly because the prediction of individuals' habitual food intakes is complicated by the within variation (e.g. Block (1982) and Liu et al. (1978)). Most epidemiological studies have estimated variance components models under the assumption that the random fluctuations are serially uncorrelated. Also, the diverse socioeconomic factors underlying the patterns of food consumption have seldom been incorporated into the analyses. The estimation of variance components models allowing for temporal dependence in the random errors by using data from developing countries is therefore of interest and could shed some light on the influence of socioeconomic factors on the variances. The structure of this paper is as follows: Section 2 outlines the properties of the model used for estimating the interindividual and intraindividual variances and the autocorrelation in nutrient intakes. The profile log-likelihood function is presented in a compact form for numerical optimization. The socioeconomic factors underlying the variations in nutrient intakes in developing countries are analysed in Section 3 where it is argued that poor households will tend to reduce their food consumption in response to drops in incomes or rises in food prices. The 24-hour recall data from India and the Philippines are briefly described in Section 4.1. The empirical results are presented in Tables 1-5 and are discussed in Sections 4.2 and 5. 2. THE MODEL The variations in nutrient intakes due to the interindividual and intraindividual differences can be estimated in the presence of serial correlation within the model (Sukhatme and Margen, 1978, 1982): yit = 8, + uit, /= 1 , 2 , . . . , / / , /= 1, 2, . . ., T, (1) with uit = ««„_! + eit, 1 = 1 , 2 , . . . , / / , t= 1, 2, . . ., T. (2) Here, yit may represent the nitrogen balance or the energy balance of the /th individual in the tth time period measured in deviations from an overall mean, 5, are normally distributed individual-specific random variables with mean 0 and constant variance,

Malnutrition and Individual Variation: India and the Philippines

115

«„ are first-order stationary Markoff processes with unknown coefficient a (| a | < 1) and eit are assumed to be independently normally distributed with constant variance a2. The statistical implications of this model are that the variance of yit, namely var(6,) + var(e„)/(l -a2), depends on the coefficient a of the stationary Markoff process (2), but a itself does not influence the level (6,) to which the yit converge in a probabilistic sense. This in turn has the asymmetry implication that the proportion of variation explained by the intraindividual variation depends explicitly on a, but the proportion of variation due to the interindividual differences is influenced by a only through the within variance. As some temporal dependence in the random errors is likely to be a common feature of nutritional intake data, it is desirable to reformulate the model in a manner enabling a more symmetric treatment of the two variances. 2.1. Reformulation of Model Suppose that equation (1) is replaced by yit = 5,/(l -a)

+ uit,

i= 1,2

, H,

/ = 1 , 2 , . . ., T,

(3)

where the uit are as in equation (2) (Anderson and Hsiao, 1981). Then individuals will gradually move in a probabilistic sense to their respective levels 5,7(1 -a) which depend on both the individual-specific component <5, and on the autocorrelation coefficient a. The model given by equations (3) and (2) can equivalently be written as a 'dynamic error components' model: yn = 5,/(l -a)

+ un,

i ' = l , 2 , . . ., H,

(4)

and yit = ayil_l + 5, + e„,

/= 1, 2, . . . , / / ,

t = 2, 3, . . ., T.

(5)

In this formulation, the.y„ are again a realization of a stationary process with constant variance v a r ( ^ ) = var(5,)/(l - a)2 + var(e„)/(l - a2).

(6)

Defining the ratio of the between variance to the within variance as p2 = var(5,)/var(e„),

(7)

the proportions of variations 8X and 62 due to interindividual and intraindividual differences respectively are given by

0, = p\l+a)/{(l+a)P2 d2 = (l-a)/{(l+a)p2

+

(l-a)},

(°) +

(l-a)}.

Model (4) and (5) has the appealing property that the previous levels of individuals' intakes affect the current intakes. The proportions due to interindividual and intraindividual variations now depend on a, the former becoming dominant for values of a close to 1. It should be qualified, however, that neither model (1) and (2) nor that given by equations (4) and (5) can adequately represent nutritional adaptation (Healy, 1989). Nutritional adaptation can perhaps be investigated in clinical experiments (Keys et al., 1950) by using modern calorimeters. The resulting data may then be analysed by non-linear dynamic formulations to capture the threshold of stress. The

116

A. Bhargava

primary purpose of this paper is to quantify the influence of socioeconomic variables on the variations in nutrient intakes. As some of the food policy debate has centred on these parameters, the estimation of dynamic variance components models by maximum likelihood with data from developing countries seems an advance over the previous work. The fitting of non-linear dynamic models to more elaborate data sets remains an important topic for future research. 2.2. Maximum Likelihood Estimation Recent developments in statistical theory have enabled the estimation of models of the type given by equations (4) and (5) (or (1) and (2)) where the number of individuals (H) is large but the number of time observations (7) is fixed (Anderson and Hsiao, 1981; Bhargava and Sargan, 1983). The initial observations yn, however, must be treated as variables that are jointly determined with the remaining yits in the maximum likelihood estimation of the parameters. Although a sample covering a large number of individuals affords inferences on the entire population, the costs of extended surveys would be prohibitive. Thus the distribution theory assuming only H to be large is quite useful. In applications involving nutritional data, it will be necessary to take account of the differences in mean intakes across groups formed on the basis of age, sex, household incomes, etc. This may be achieved by including dummy (or 0-1) variables in equations (4) and (5) for the subgroups. Alternatively, the above models may be viewed as representing the deviations of an individual's intakes from the time means of the various subgroups. A general method for estimating dynamic models by treating the >>/r as a system of T simultaneous equations is developed in Bhargava and Sargan (1983). For model (4) and (5), the profile log-likelihood function can be compactly written as L = -O.SHlnX

- 0.5HTlns2,

(9)

where A and s2 are defined in Appendix A, which also describes the numerical optimization procedure used in the estimation. 3. SOCIOECONOMIC ANALYSIS OF INDIVIDUAL VARIATION The notion that households base their consumption decisions on 'normal' or 'permanent' rather than current incomes is a standard postulate in the economics literature (Duesenberry, 1949; Friedman, 1957). In empirical work, the permanent income is often approximated by a weighted average of the past incomes and by taking into account the expected future earnings. It is usually assumed that the households can borrow from credit markets and thus spend on the basis of their future incomes as well. The applications of such models of course require some approximations. The results, however, should not be adversely affected by assumptions capturing the socioeconomic conditions. The incomes of most households living in less developed countries tend to exhibit large fluctuations due to factors such as poor harvests or low crop prices. A large negative realization of the transitory component of income, for example, can frustrate a household from drawing up its consumption plans on the basis of permanent income. This in part is due to the very limited nature of the credit markets

Malnutrition andiJinfclividual Variation: India and the Philippines

especially for unskilled workers who accumulate very low levels of savings. Also, the daily wages of the non-land-owning workers in rural areas are determined by the demand and supply conditions in the regions. Thus a poor household cannot offset a loss in income by borrowing. Now, it would be reasonable to expect that households living close to the subsistence level satisfy the needs of their members for food before expenditures on other items such as clothing and housing. This is the well-known phenomenon of hierarchy in human wants and has appeared since the writings of Plato. Its implications for economic behaviour are discussed by Georgescu-Roegen (1966) and Lancaster (1971); an application to the food consumption and household income relationship is contained in Bhargava (1991). Indeed, if poor households are forced into varying their food expenditures to match earnings, then the contribution of the within variation in the nutrient intakes will be high for their members. In contrast, a decline in the income of a well-off household may cause reductions in expenditures on other items. The effects of income fluctuations and the basic need for staple foods, when combined, provide a basis for explaining the variations in nutrient intakes in developing countries. Indeed, if a sample were disaggregated by household incomes, then the relative contribution of the within variance should decline with income increases as the diets stabilize. Further, in a comparison involving two countries, the relative contribution of the within variation would be expected to be smaller for the country with relatively higher or stable incomes. This should be so in as much as there are no striking physiological or cultural differences. Thus it seems reasonable to compare the populations from the southern regions of India and the Philippines, but a comparison of these groups with the inhabitants of Antarctica or Britain would not seem very insightful (Waterlow, 1989). 4. EMPIRICAL RESULTS FOR DYNAMIC ERROR COMPONENTS MODELS 4.1. The Data The International Crops Research Institute for Semi-Arid Tropics surveyed 240 households in six villages in south India twice during the years 1976 and 1977 (Binswanger and Jodha, 1978). The data on intakes of dietary energy and protein and on socioeconomic variables such as household sizes and incomes in three of the villages are available to us. Individuals missing from any of the rounds and infants under the age of 1 year at the time of the first round were omitted from the sample, leaving complete data on 368 individuals in four time periods. Since some food was consumed outside the home, the errors may be treated as independently distributed. The development of estimation methods allowing for household-specific random variables is an important topic that will be investigated in future research (the analysis is complicated by the differing number of individuals in the households so that the system of equations for the yit has unequal numbers of equations when indexed by households). The data set from the Bukidnon region of the Philippines is based on a survey of 448 households living within a radius of 20 miles during the years 1984 and 1985 (Bouis and Haddad, 1990). The surveys were conducted at 4-month intervals and the intakes of dietary energy and protein in four rounds are available on 2047 individuals who were older than 1 year. In view of our emphasis on the socioeconomic aspects of

117

A. Bhargava

118

nutritional variability, four income groups were constructed for the Indian sample and the Philippine sample was broken down into five income groups. The groups were formed by making the number of individuals in each group roughly equal and sufficiently large for the use of asymptotic distribution theory. Similarly, three age groups (1-10.0,10.01-30.0 and over 30 years) were created for India and five groups (1-5.0,5.01-10.0,10.01-15.0,15.01-30.Oand 30 years) forthe Philippines to account for the differences in mean intakes by age. The sample means of energy and protein intakes in kilocalories and grams respectively and the estimated standard deviations by age and income subgroups are reported in Table 1. 4.2. Empirical Results The maximum likelihood estimates (MLEs) of the variances and autocorrelation coefficients in the intakes of dietary energy and protein for India and the Philippines are presented in Table 2. The intakes were transformed into natural logarithms partly because of the amount of heteroscedasticity in the data (Nelson et al., 1989). The estimated ratio (between variation)/(within variation) (p2) and the contribution of the intraindividual variation (02) to the total variation are reported in Table 2. Firstly, the values of 62 are about 25% lower for the Philippines in both the energy and the protein relationships. The per capita gross domestic product (GDP) of the TABLE 1

Summary of the sample means and standard deviations of the data T Group

No. of individuals

India Income 1

92

Income 2

90

Income 3

85

Income 4

101

All

368

Philippines Income 1

405

Income 2

421

Income 3

404

Income 4

412

Income 5

405

All

2047

No. of

Energy intake (kcal)

Protein intake (g)

Group

1740 (800) 2054 (759) 2011 (762) 2191 (856) 2003 (815)

44.7 (22.7) 59.8 (24.0) 57.5 (23.5) 62.1 (27.5) 56.1 (25.5)

Age 1

85

Age 2

141

Age 3

142

1774 (839) 1809 (921) 1838 (892) 1947 (968) 1937 (946) 1861 (915)

49.1 (24.2) 51.6 (25.8) 52.8 (26.7) 56.5 (27.3) 56.1 (26.5) 53.2 (26.2)

Age 1

451

Age 2

429

Age 3

304

Age 4

369

Age 5

494

individuals

Energy intake (kcal)

Protein intake (g)

1407 (594) 2048 (748) 2321 (798)

40.6 (19.2) 56.7 (23.8) 64.8 (26.0)

1186 (585) 1485 (623) 1802 (702) 2384 (904) 2449 (903)

34.7 (17.4) 43.3 (19.3) 51.5 (20.8) 67.2 (25.6) 69.4 (26.3)

{Numbers in parentheses are standard deviations; see the text for the definition of groups; income group 1 consists of the poorest households; age group 1 consists of the youngest members in the samples.

Malnutrition and Individual Variation: India and the Philippines

MLEsfor Parameter

c a P

s*2

e2L* 2

TABLE 2 the dynamic error components

MLEsfor India for the following intakes: Energy Protein 6.308 (0.391) 0.162 (0.052) 0.387 (0.098) 0.124 0.650 2704.0

3.008 (0.225) 0.229 (0.057) 0.245 (0.084) 0.164 0.719 2366.4

119

model] MLEsfor the Philippines for the following intakes: Energy Protein 7.046 (0.147) 0.046 (0.019) 0.744 (0.060) 0.154 0.551 12467.3

3.627 (0.076) 0.051 (0.019) 0.744 (0.056) 0.155 0.548 12394.1

tAU variables are in logarithms; the sample size H= 368 and T= 4 for the Indian data and H=2047 and T= 4 for the Philippine data; the numbers in parentheses are the estimated asymptotic standard errors; c is the coefficient of the overall constant term; a is the coefficient of the lagged value of the dependent variable (^,r_i); p2 is the (between variation)/(within variation) ratio (7); 62 is the proportion explained by the within variation (8); s*2 is the maximized value of s2 given in Appendix A; 2L* is twice the maximized value of the log-likelihood function (9).

Philippines at 1980 international prices for the year 1984 is 1472 as opposed to the figure 579 for India in 1976 (Summers and Heston, 1988). This aggregate comparison does not address the income disparities in the two countries. However, regional level comparisons suggest that the per capita GDP in the Bukidnon region is about 1.5 times higher than in the southern districts of India. Moreover, in contrast with the Indian climate, there are no dry seasons in the Bukidnon region. The smaller contribution of the within variation for the Philippine data is thus in accordance with the analysis presented here. The results in Table 3 introduce dummy (0-1) variables for age and income groups, for the subject's sex and for the third and the fourth survey rounds in equations (4) and (5). The relative contribution of the within variation rises substantially mainly because of the reduction in the between variation brought about by incorporating the differences in mean intakes of these subgroups. The values of 62 for the two countries are very close in the energy relationships though 02 remains larger for India in the protein equation. Moreover, the income dummy variables are significant in the energy and protein relationships at the 5% level for the Indian sample but are significant only in the protein relationship for the Philippines. A possible explanation of the latter set of results is that the diets of the poor households in the Philippines are deficient only in protein. Tables 4 and 5 present the results for India and the Philippines respectively when the samples are disaggregated by per capita household incomes. First, for India, the estimated 62 clearly decreases with rises in household incomes. The very low value reported in the protein equation for income group 2 is close to the boundary solution (p 2 = 0) which may be due to the modest sample size. The likelihood ratio statistics for the null hypothesis of constancy of the parameters across different income groups are distributed in large samples as x2-variables with 18 degrees of freedom. The values of the test statistics for energy and protein were respectively 90.4 and 117.8 so that the null hypotheses are rejected even at the 1% significant level.

A. Bhargava

120

MLEs Parameter

c

+ l

2

l

3

'4

with dummy

TABLE 3 variables for income and age groups,

MLEs for India for the following intakes: Energy Protein 6.109 (0.334) 0.114 (0.032) 0.138 (0.039) 0.068 (0.037) 0.156 (0.036)

2.653 (0.176) 0.110 (0.029) 0.235 (0.048) 0.165 (0.044) 0.215 (0.046)

0.331 (0.039) 0.454 (0.043)

0.258 (0.040) 0.370 (0.045)

0.093 (0.029) -0.030 (0.031) 0.125 (0.048) 0.125 (0.048) 0.118 0.857 2983.4

0.029 (0.031) -0.029 (0.031) 0.203 (0.053) 0.061 (0.044) 0.160 0.916 2588.6

'5 72 73 74 75 *3

u a P2

s*2

h

2L*

two rounds and

sex]

MLEs for the Philippines for the following intakes: Energy Protein 6.591 (0.135) 0.106 (0.012) 0.011 (0.026) -0.019 (0.029) 0.038 (0.025) 0.031 (0.027) 0.245 (0.025) 0.429 (0.031) 0.690 (0.029) 0.696 (0.029) -0.056 (0.014) 0.008 (0.015) 0.045 (0.019) 0.187 (0.023) 0.152 0.830 14267.8

3.113 (0.068) 0.092 (0.012) 0.062 (0.030) 0.035 (0.028) 0.102 (0.028) 0.106 (0.029) 0.236 (0.030) 0.407 (0.030) 0.640 (0.031) 0.659 (0.029) -0.072 (0.015) 0.060 (0.015) 0.058 (0.019) 0.239 (0.026) 0.151 0.789 14049.4

Ti and y are respectively the coefficients of the dummy variables for the income and age groups; £ are the coefficients of dummies for rounds 3 and 4 and \p is the coefficient of the dummy variable for the subject's sex.

The results for the Philippines indicate only a tendency for 02 to decline with household incomes. It should be noted that the proximity of the Bukidnon region to the sea affords choices between dry and fresh varieties of fish. The prices of fresh fish are usually higher than the dried types though the protein content of the latter is high. Thus, if households respond to losses in incomes or rises in fish prices by substituting the fresh variety by dried fish, then the contribution of the within variation in protein intakes need not differ systematically across income groups. Lastly, the null hypotheses of the constancy of the parameters across the income groups were rejected at the 1% level. 5. CONCLUSION In this paper, the interindividul and intraindividual variances and the auto-

121

Malnutrition and Individual Variation: India and the Philippines TABLE 4 MLEs for the four income groups using Indian data with age group dummies Parameter Income i?roup 1 Energy Protein c 72 73

a P2

s*2

h

2L*

4.915 (0.662) 0.296 (0.077) 0.395 (0.086) 0.3O5 (0.095) 0.037 (0.067) 0.162 0.934 646.5

2.597 (0.332) 0.304 (0.085) 0.389 (0.092) 0.231 (0.099) 0.041 (0.073) 0.224 0.937 530.2

MLEs for the following income groups: and intakes: Income, group 2 Income group 3 Income group 4 Energy Protein Energy Protein Energy Protein 6.995 (0.682) 0.299 (0.069) 0.406 (0.078) 0.042 (0.094) 0.192 (0.115) 0.093 0.827 802.1

2.721 (0.366) 0.157 (0.061) 0.270 (0.063) 0.277 (0.095) 0.005 (0.062) 0.129 0.990 727.2

7.269 (0.644) 0.334 (0.079) 0.476 (0.095) -0.009 (0.089) 0.239 (0.130) 0.099 0.810 729.3

3.189 (0.406) 0.305 (0.082) 0.392 (0.088) 0.119 (0.109) 0.152 (0.126) 0.132 0.839 644.3

7.079 (0.641) 0.403 (0.087) 0.537 (0.090) 0.021 (0.089) 0.294 (0.131) 0.115 0.766 795.1

3.214 (0.389) 0.261 (0.083) 0.401 (0.076) 0.129 (0.103) 0.207 (0.131) 0.149 0.788 702.4

TABLE 5 MLEs for the five income groups from the Philippines with age dummies] Parameter Income group 1 Energy Protein c a P2

s*2

h

2L*

MLEs for the following income groups and intakes: Income group 2 Income group 3 Income group 4 Energy Protein Energy Protein Energy Protein

Income group 5 Energy Protein

6.697 3.129 6.963 3.258 6.269 3.339 6.517 3.387 6.694 3.178 (0.307) (0.140) (0.287) (0.144) (0.272) (0.150) (0.317) (0.142) (0.302) (0.155) 0.101 0.008 0.035 0.083 -0.009 0.037 0.068 0.018 0.042 0.088 (0.044) (0.041) (0.041) (0.042) (0.039) (0.044) (0.044) (0.045) (0.040) (0.043) 0.150 0.272 0.197 0.194 0.256 0.176 0.157 0.361 0.249 0.307 (0.047) (0.062) (0.052) (0.056) (0.062) (0.056) (0.053) (0.076) (0.064) (0.071) 0.124 0.135 0.162 0.158 0.146 0.190 0.165 0.136 0.163 0.145 0.845 0.783 0.827 0.814 0.799 0.841 0.848 0.728 0.787 0.732 3178.1 2941.6 2818.0 2850.6 2828.7 2463.4 2762.9 2917.7 2656.2 2794.3

|To save space the coefficients of the age dummies are not reported.

correlation coefficients for intakes of energy and protein were estimated for data from India and the Philippines. The analysis incorporated some socioeconomic factors affecting food consumption. The contribution of the intraindividual variation was seen to decline with rises, in household incomes. Also, the interindividual differences in the two populations seem generally small and quite close when the differences in the mean intakes by age and income groups are incorporated. The main implications of these results for developing countries are, firstly, that the iarge contribution of the within variation and the autocorrelation in intakes do not justify reductions in the RDAs (Sukhatme and Margen, 1978, 1982). Secondly, minor upward revisions seem necessary to accommodate the interindividual differences (Sukhatme, 1974).

A. Bhargava

122

T h e definition of the RDAs is a complex issue demanding further improvements in methods of measuring the h u m a n nutritional needs. The within variation, however, is a standard feature of daily intake data arising in part from the nutrient composition of foods. A n alternative approach for quantifying the usual intakes in epidemiological applications may b e to discuss the issues within the framework of weekly allowances. This is beyond the scope of the present analysis. ACKNOWLEDGEMENTS T h e author is indebted t o A . B. Atkinson, G. H . Beaton, J . - P . Habicht, M . J. R. Healy, W . P . T . James, N . E. Johnson, A. K. Sen, J. C. Waterlow and three referees for helpful comments and encouragement. Thanks are also d u e to the Cornell Theory Center for time on their supercomputer. APPENDIX A Function (9) can be defined in terms of the elements of several matrices. Let q be a Tx 1 vector of Is a n d B b e a ( T - 1) x /"matrix: Bu = -a, Bu,+, = - 1 andB tj = 0otherwise. Also, let Y be the Hx Tmatrix containing the yits, U be the Hx (7*- 1) matrix of the error terms on equation (5) and 1H be the HxH identity matrix. Then defining Q = IH-qq'/H, the Tx T second-moment matrix of the deviations of the yus from an overall mean is W= Y'QY/H. Further, partition W&s W= [w>,: W2], where w, is a T x 1 vector with its first element wM and W2 is the Tx (T- 1) matrix containing the remaining columns of W. Lastly, let A, /x and K be given by A = {1 + / o 2 ( 7 " - l ) } / ( l - a 2 ) + p 2 / ( l - a ) 2 , P2d-«) p2+{(l-a)/(l+a)}{l+(7"-l)p2}

=

" and

K

=

(l-a){l+(T-l)p2}p/p2.

Then the MLE of the variance a2 of the e„s is (Bhargava and Sargan, 1983) s2 =(T- l/T)[tr{U'U/(T+ Woofl + (T-

\)H}-p2q'U'Uq/H(T1){1 +(T- l)p2}] l)p2}/\T-2p2w{B'q/\(l-a)T+pAq'BWB,q/(l-a)2T\K.

A is the determinant of the covariance matrix of the composite errors on equations (4) and (5) and K is the first entry in its inverse. Function (9) can be optimized with respect to the unknown parameters by using 'vectorized' numerical algorithms (Navon et al., 1988; Numerical Algorithms Group, 1989) on supercomputers. The observations are read individual by individual to create second-moment matrices and the function is defined in terms of these matrices. Subroutine E04JBF of the Numerical Algorithms Group library numerically approximates the derivatives and is used for optimization. Lastly, equation (8) is a convenient parameterization as the maximum can occur at p2 = 0 in small samples. REFERENCES Acheson, K. J., Campbell, I. T., Edholm, O. G., Miller, D. S. and Stock, M. J. (1980) A longitudinal study of body weight and body fat changes in Antarctica. Am. J. Clin. Nutr., 33, 972-977.

Malnutrition and Individual Variation: India and the Philippines

Anderson, T. W. and Hsiao, C. (1981) Estimation of some dynamic models with error components. / . Am. Statist. Ass., 76, 598-606. Bhargava, A. (1991) Estimating short and long run income elasticities of foods and nutrients for rural south India. J. R. Statist. Soc. A, 154, 157-174. Bhargava, A. and Sargan, J. D. (1983) Estimating dynamic random effects models from panel data covering short time periods. Econometrica, 51, 1635-1660. Binswanger, H. P. and Jodha, N. S. (1978) Manual for Instructions for Economic Investigators in ICRISA T's Village Level Studies. Hyderabad: International Crops Research Institute for Semi-Arid Tropics. Block, G. (1982) A review of validation of dietary assessment methods. Am. J. Epidem., 115, 492-505. Bouis, H. E. and Haddad, L. J. (1990) Agricultural Commercialization, Nutrition and the Rural Poor: a Study of Philippine Farm Households. Boulder: Riener. Duesenberry, J. S. (1949) Income, Saving and the Theory of Consumer Behaviour. Cambridge: Harvard University Press. Edholm, O. G., Adam, J. M., Healy, M. J. R., Wolff, H. S., Goldsmith, R. and Best, T. W. (1970) Food intake and energy expenditures of army recruits. Br. J. Nutr., 24, 1091-1107. Food and Agriculture Organization (1970) 8th Report of Expert Committee on Nutrition. Geneva: World Health Organization. (1985) Energy and protein requirements. Technical Report 724. World Health Organization, Geneva. Friedman, M. (1957) A Theory of the Consumption Function. Princeton: Princeton University Press. Georgescu-Roegen, N. (1966) Analytical Economics: Issues and Problems. Cambridge: Harvard University Press. Healy, M. J. R. (1989) Nutritional adaptation and variability. Eur. J. Clin. Nutr., 43, 209-210. James, W. P. T. (1989) Nutritional adaptation and variability. Eur. J. Clin. Nutr., 43, 205-208. Keys, A., Brozek, J., Henschel, A., Mickelsen, O. and Taylor, H. L. (1950) The Biology of Human Starvation, vols 1 and 2. Minneapolis: University of Minnesota Press. Lancaster, K. (1971) Consumer Demand: a New Approach. New York: Columbia University Press. Liu, K., Stamler, J., Dyer, A., McKeever, J. and McKeever, P. (1978) Statistical methods to assess and minimise the role of intra-individual variability in obscuring the relationship between dietary lipids and serum cholesterol. J. Chron. Dis., 31, 399-418. Navon,I. M., Phua, P . K. H. and Ramamurthy, M. (1988) Vectorisation of conjugate gradient methods for large scale minimisation. In Proc. Supercomputing 1988. Gainesville: Institute of Electronic and Electrical Engineers Computer Society. Nelson, M., Black, A. E., Morris, J. A. and Cole, T. J. (1989) Between- and within-subject variation in nutrient intake from infancy to old age: the number of days required to rank dietary intakes with desired precision. Am. J. Clin. Nutr., 50, 155-167. Numerical Algorithms Group (1989) Library of Computer Programs, Mark 12. Oxford: Numerical Algorithms Group. Shils, M. E. and Young, V. R. (1988) Modern Nutrition in Health and Disease, 7th edn. Philadelphia: Lea and Febiger. Sukhatme, P. V. (1974) The protein problem, its size and nature. / . R. Statist. Soc. A, 137, 166-199. Sukhatme, P. V. and Margen, S. (1978) Models of protein deficiencies. Am. J. Clin. Nutr., 31, 1237-1256. (1982) Autoregulatory homeostatic nature of energy balance. Am. J. Clin. Nutr., 35, 355-365. Summers, R. and Heston, A. (1988) A new set of international comparisons of real product and prices for 130 countries, 1950-85. Rev. Inc. With, 34, 1-25. Waterlow, J. C. (1986) Metabolic adaptations to low energy and protein intakes. Ann. Rev. Nutr., 6, 495-526. (1989) Nutritional adaptation and variability. Eur. J. Clin. Nutr., 43, 203-205.

123

JOURNAL OF

Econometrics

ELSEVIER

Journal of Econometrics 77 (1997) 277-295

^ ^ ^

= = = = = = =

Nutritional status and the allocation of time in Rwandese households Alok Bhargava Department of Economics, University of Houston, Houston, TX 77204-5882, USA

Abstract This paper analyzes the activity patterns of adult men and women in approximately 110 Rwandese households surveyed four times in 1982-83. Dynamic models are separately estimated for men and women for the time spent sleeping and resting, performing heavy activities, doing housework, and on agriculture. The models postulate simultaneity between men and women's activities and investigate the differential feedbacks. The main findings are that low incomes and high food prices reduce the households' energy intakes, thereby forcing the adults to spend additional time resting and sleeping. Second, both men and women share the workload in spite of poor nutritional status. Third, for women, there is substitution between housework and agriculture, the former tasks being relegated to other household members. Lastly, energy intakes of twice the Basal Metabolic Rate seem inadequate for the sustenance of active adults. The policy implications of the results are discussed. Key words: Health; Nutrition; Time allocation; Dynamic models; Food policies J EL classification: C23; 112; J24; 0 1 2

1. Introduction The measurement of h u m a n energy expenditures is an i m p o r t a n t topic in biological sciences; its relevance for denning energy requirements was underscored by the expert committee of the F A O / W H O / U N U ( F A O , 1985). The F A O approach to energy needs is reflected in the phrase 'Requirements for what?'. Since Lavoisier's discovery of the role of oxygen in energy metabolism

This study was supported by Research Committee of the World Bank. The author thanks Q. Khan, C. Muller, M. Ravallion, and J. Yu for their help, but retains the responsibility for views in the paper. This revision has benefited from the comments of three referees. 0304-4076/97/$ 15.00 © 1997 Elsevier Science S.A. All rights reserved PU S 0 3 0 4 - 4 0 7 6 ( 9 6 ) 0 1 8 1 6 - 7

126

A. Bhargava and Rubner's work on the heat produced in oxidation of food, physiologists have developed sophisticated methods for measuring energy expenditures (Durnin, 1991). For example, modern calorimeters afford accurate measurement in laboratories and the doubly labelled water method is useful for free living poulations. A knowledge of energy expenditures of the inhabitants of less developed countries is useful for the design of food policies. Since resources available for data collection are limited, the expenditures are typically calculated from time allocation surveys. The data have provided some useful insights. For example, Berio (1984) suggests that women bear the greater burden of economic development. The behavioral mechanisms through which men and women share work are not explored in the analysis. Interpreting some biomedical evidence on Gambian women, however, Beaton (1984) concludes that low energy intakes induce behavioral changes amongst the poor. Consequently, it is superficial to distinguish between the biological and social sciences approaches to time allocation; a unified framework is useful for data analysis. The importance of research in bio-chemistry of food for economic development policies was recognized by Leibenstein (1957) who argued that higher wages of workers will improve their nutritional status and hence productivity. The 'wage efficiency hypothesis' has since been refined (Mirrlees, 1975). In countries such as Rwanda, the population subsists on agriculture and energy deficiencies are prevalent. The link between wages and labor productivity is affected by the intra-household distribution of food; the earners' intakes need not increase proportionately with wages. Further, while higher wages ultimately affect productivity via improvements in health (Fogel, 1994), the lags underlying health processes are complex (Bhargava, 1994). Lastly, many adults work on their own land and perform housework without receiving monetary compensation. An analysis of the determinants of time allocation in Rwandese households is therefore of interest. Modelling the relationship between the adults' time allocation and nutritional status presents several difficulties. Firstly, while recording daily activities at a disaggregated level is insightful, there is a large amount of internal variation in the data. Also, energy expenditures are available only for broad categories of activities (FAO, 1985). Secondly, individual food intakes are difficult to quantify in Rwanda since household members share the food from the same plate. Thirdly, alternative formulations for sharing the work between men and women are available in social sciences (e.g., Becker, 1991; Sen, 1983; Simon, 1986). Lastly, due to differences in data collection procedures, the effects of variables such as food prices on time allocation can be assessed only indirectly in a longitudinal framework. The structure of this paper is as follows: Section 2 describes the data from Rwanda. Section 3 outlines a framework for analyzing the activities data and the dynamic model is briefly described. The empirical results for the households'

Nutrition and Allocation of Time in Rwandese Households energy intakes, adults' weights, and the time spent sleeping and resting, on heavy activities, performing housework, and on agricultural activities are discussed in Section 4. Finally, in Section 5, the issue of 'Requirements for what?' is reexamined in light of the empirical results.

2. The data The longitudinal study in Rwanda was conducted by the Ministry of Planning with assistance from the French government during 1982-83 (Republique Rwandaise, 1986). The food intakes in 270 households (three from each of the 90 'sectors') were recorded for seven consecutive days. The surveys were repeated four times at four-month intervals. The heights of adults were recorded once and the weights were measured in each round. The time spent by household members on over 600 activities for fourteen consecutive days was recorded in each survey round. Since food intakes are observed for seven days, the activity data on the same days are used in the analysis. Further, for comparisons with other studies and to reduce variation in the data, the activities were mapped into the 25 broad categories defined by FAO (1985). The activities that were difficult to match were put into 5 groups formed on the basis of energy expenditures, expressed as multiples of the Basal Metabolic Rate (BMR is the minimal energy necessary for sustaining life). The data for seven days were then averaged to produce a figure for an 'average' day of the week, i.e., average activity levels in the four survey rounds are analyzed in this paper. Some information on education, land holding, and other variables is contained in the data set. Single observations for the survey period are available on the value of households' consumption and production. The prices of seven food groups and information on wages earned by a subset of household members are recorded once. The 'lead' young adult man and woman were selected from each household; the adults need not be a couple but were likely to be the ones performing the demanding tasks. Retaining individuals with four time observations, complete data were obtained on approximately 110 adults. The sample mean are reported in Table 1.

3. A framework for time allocation at the susistence level 3.1. Nutrient deficiencies, work performance, and time allocation The deficiencies of certain nutrients in the diet diminish the physical work capacity of individuals. For example, iron deficiencies are known to reduce the maximum volume of oxygen consumed (Spurr, 1983); field studies have shown

127

A. Bhargava

128

Table 1 Sample means of the variables in the four rounds of data from Rwanda Variable

Women

Men

Proportion of time spent sleeping, resting, and sitting quietly

0.547 (0.107)

0.509 (0.086)

Proportion of time spent on heavy activities

0.187 (0.088)

0.180 (0.073)

Proportion of time spent on housework

0.014 (0.050)

0.131 (0.069)

Proportion of time spent on agriculture

0.100 (0.088)

0.140 (0.079)

Average energy expenditure

1.992 (0.437)

2.184 (0.298)

Household size

5.991 (2.248)

Age

34.223 (19.315)

Total value of consumption

51881 (25319)

Total value of production

43271 (31248)

Energy intakes Protein intakes

32.017 (16.157)

11161 (5340) 361.6 (201.7)

Weight

48.817 (12.787)

48.269 (11.636)

Height

157.259 (15.625)

152.975 (11.637)

19.350 (3.033)

20.333 (3.592)

Body mass index (BMI)

The sample means are calculated using four time observations on 116 men and 119 women. Tables 3-6 analyze a subset of these data. Numbers in parentheses are estimated standard deviations for the pooled samples. Heavy activities require at least thrice as much energy as sleep. Average energy expenditure is in terms of Basal Metabolic Rate. Consumption and production are annual figures in Rwandese francs for the households. Households' energy and protein intakes per day are measured, respectively, in kcals and grams. Weight and height are in kilograms and centimeters, respectively.

positive effects of iron supplementation on labor productivity (Basta et al, 1979; Gardner et al, 1975). In countries such as Rwanda, energy deficiencies are of paramount importance since they restrict behavior and affect health by hindering the absorption of nutrients (Bhargava, 1991). For an historical perspective, see Fogel (1994).

Nutrition and Allocation of Time in Rwandese Households

129

The physiological changes resulting from inadequate energy intakes are complex. Waterlow (1986), for example, has suggested that the (low) ratio of an individual's BMR to body weight (fat-free mass) in developing countries reflects 'metabolic economy'. However, this is not necessarily the case in an undernourished sample from India (Soares and Shetty, 1991). A high BMR to body weight ratio for the malnourished is consistent with a long-run elasticity of BMR with respect to weight that is less than unity (Bhargava and Reeds, 1995). The energy necessary for performing an activity can be expressed as a multiple of the individual's BMR. The latter is related to body weight (Schofield, 1986). From a policy standpoint, the effects of nutritional status on work performance are of interest. Since the Rwandese households spend most of their time on subsistence activities, the link between nutritional status and time allocation is important. 3.2. Modelling the effects of economic variables on time allocation Myrdal (1968) observed the vicious circle of poverty and poor work performance in developing countries caused by chronic food shortages. Mirrlees (1975) extended the theoretical wage-consumption analysis, though emphasizing the need for an empirical treatment. Since improved nutrition enhances the 'capabilities' of individuals to undertake useful tasks (Sen, 1985; Anand and Ravallion, 1993; Dasgupta, 1993), modelling the determinants of time spent on various activities is of interest. The treatment of leisure (L) as an argument in the utility function yields the demand for leisure as a function of goods prices (p), wage rate (w), and nonlabor income (^4), i.e., L = h(p,w,A).

(1)

It would be desirable to adopt a flexible approach in the analysis of longitudinal time allocation data from Rwanda. Firstly, a large proportion of the food consumed by households is their own produce or is received in the form of gifts. Also, energy deficiencies are apparent in Table 1 from the sample means of Body Mass Index (BMI is defined as weight in kilograms divided by the square of height in meters; James et al., 1988). In such circumstances, it is likely that energy expenditures are driven by the intakes. The food available to many households will be inadequate and can thus be viewed as pre-allocated (Pollak, 1969). The indicators of nutritional status are important explanatory variables in time allocation models since they capture the effects of current and past nutritional deficiencies. Secondly, due to own-production of food and the gifts received, minor fluctuations in food prices may not have immediate effects on leisure. However, prices will gradually influence the 'habitual' leisure. Thirdly, since a single observation on wages is available for roughly a third of the households, it might

130

A. Bhargava seem difficult to examine the effects of wages on time allocation. However, one can control for earnings of the household members by including total consumption during the sample period as a regressor in the longitudinal models. The link between nutritional status and time allocation can be investigated using the present data set by splitting the estimation problems into two stages. At the first stage, the households' average energy intakes in the four survey rounds are explained in a cross-sectional framework by variables such as household size, regional dummy variables, food prices, and measures of household incomes. The estimated relationship will provide a large-scale view of the effects of economic variables on food availability. The equilibrium quantity of food consumed through market and nonmarket arrangements, however, may be insufficient for essential activities of the household members. The second stage, then, models the determinants of time allocated to leisure and productive activities in a longitudinal framework. Since the choice between work and leisure is affected by health, biological and behavioral factors play important role in model specification. In particular, the mechanism by which energy deficiencies restrict activities and factors underlying the sharing of work between men and women merit a systematic treatment. 3.3. A dynamic framework for longitudinal time allocation data The joint nature of household labor supply decisions was formulated from an empirical standpoint by Mincer (1962). The analysis is suitable for time allocation decisions since, at the subsistence level, members share the work. The joint activity patterns, however, complicate the application of Becker (1965) type models of household production (Pollak and Wachter, 1975). It would seem difficult to specify a model for time allocation, analogous to the 'characteristics' model of demand (Pudney, 1981), in terms of latent price variables. The division of tasks within a household affects the relationship between time allocation and nutritional status for all the members. For example, women with young children may substitute agricultural activities by housework; the latter is less strenuous and older children can help in gathering wood, fetching water, etc. Further, men and women share the additional (seasonal) workload according to certain rules. Since fertility rates are high in Rwanda, a model of joint time allocation decisions would be useful for assessing if women face a disproportionate burden in times of growth (Berio, 1984). Now, inadequate energy intakes will force a reduction in the individuals' energy expenditures. This might be achieved in the short run by decreasing the effort on strenuous tasks; a gradual increase in the proportion of time spent on lighter activities will follow. If energy deficiencies persist over time, the individuals will begin to lose weight and further curtail expenditures. The latter might entail avoiding heavy activities altogether; there is evidence that the undernourished cannot endure strenuous work (Gardner et al., 1975). The

Nutrition and Allocation of Time in Rwandese Households

131

proportion of time spent resting and sleeping will show an upward tendency even in the short run. An apparent shortcoming in exclusively focusing on the equality between energy intakes and expenditures is that important health aspects are omitted from the discussion. For example, micro-nutrient intakes are essential for maintenance of the immune system; repeated sicknesses can diminish individuals' work capacity (see also Floud et al., 1991). In the present data, morbidity can be inferred from resting patterns; hence the dynamic aspects of time allocation and nutritional status are important. The nutritional status of an individual may be represented by height and weight in time allocation models. In response to work opportunities, however, adults might increase activities in spite of poor health. Higher energy and protein intakes facilitate expenditures in the short run. Also, given the interrelationships between height and weight, it is desirable to test if these variables can be combined (Bhargava, 1994). Lastly, an equation for weight is useful for studying the dynamics of nutritional status. 3.4. The model and its estimation The model for time allocation can be represented by the following equations (h= 1, ...,J;i= 1, ...,N; t = 2,3,4): k

c

h = £ zhjPj + un, m

(2)

n

Wit = £ Zijyj + £ xljt£j + txt Wit- i + XxHi + u2it, J=I

1

Pu = I J=I

(3)

J=I

r

ztjlj + X xijt0j + a2Pit-1

+- k2 Wit + X3H( + u 3 „.

(4)

J=I

Here, Ch is the hth household's average energy intake in four survey rounds; there are J households on whom cross-sectional data are available. Wit is ith individual's weight in the tth survey, Ht is the height, and Pit is the proportion of time spent on a certain activity in the tth survey round (the subscript for different activities is suppressed for brevity). Thus N individuals are repeatedly observed in four survey rounds. The z's and x's are, respectively, time-invariant and time-varying regressors; the coefficients are denoted by lower case Greek letters. The error terms affecting (2) are independently distributed with zero mean and finite variance. The errors in Eqs. (3) and (4) are assumed independent across individuals but correlated over time with a positive definite variance-covariance matrix (u2i, and u3it can be correlated with one another). The random effects decomposition

A. Bhargava

132

for u2it, for example, is a special case, i.e., u2it = 5i + v2it,

(5)

where (5's are individual-specific random effects and v's are independently distributed random variables. Note that lagged dependent variables (including initial observations Wn and Pn) are treated as endogenous in the system (Anderson and Hsiao, 1981). Some of the time-varying regressors are also endogenous in the sense that they are correlated with random effects. The exogeneity hypotheses can be tested using likelihood ratio statistics. Details of identification of model parameters and computation of maximum likelihood estimates are presented elsewhere (Bhargava and Sargan, 1983). It is important to explore the mechanism by which men and women share the work. For example, additional work available during a survey round is likely to be distributed amongst household members on the basis of their work capacity. Otherwise, the arrangements may not be sustainable and a breakdown could threaten members' survival. Since observations on some members are incomplete, results for the lead adult man and woman are presented in the next section.

4. The empirical results 4.1. The results for households' average energy intakes Table 2 presents the results for households' average energy intakes in the four survey rounds. Since Rwanda is divided in six geographical zones, five dummy variables were included in the models; the variables for zones 3 and 5 and 6 were insignificant. The results in the first two columns assume the regressors to be exogenous; the third column treats the total value of consumption as an endogenous variable and reports the instrumental variables estimates. All variables were transformed into natural logarithms to reduce heteroscedasticity (e.g., Nelson et al, 1989). Household size is positively associated with energy intakes. While some nonlinearity is implicit in the logarithmic specification, square of household size was insignificant. The total value of consumption is an approximate measure for household incomes. The point estimate of income elasticity of energy intakes in the first column is 0.56. The total value of production, however, is insignificant. Note that since energy intakes influence productive activities, consumption may be correlated with the error term. This problem is tackled in the third column where the size of land owned by the household is used as an additional instrument. Land holding is fixed in Rwanda by the government and there is variation in land quality. The estimate of income elasticity is higher in column 3 though its standard error is larger as well.

Nutrition and Allocation of Time in Rwandese Households

133

Table 2 Cross-sectional results for average household energy intakes Variables

Specification 1

Specification 2

Specifical

6.476 (0.509)

6.204 (0.661)

5.376 (1.909)

Zone 2

-0.119 (0.041)

- 0.107 (0.062)

-0.110 (0.045)

Zone 4

-0.186 (0.041)

- 0.197 (0.059)

-0.179 (0.044)

0.234 (0.041) 0.558 (0.040) 0.002 (0.022)

0.154 (0.139) 0.667 (0.182)

-0.120 (0.102)

Constant

Household size

Price beans

- 0.146 (0.091)

0.253 (0.061) 0.545 (0.053) - 0.006 (0.032) - 0.047 (0.032) - 0.093 (0.130)

Price sweet potatoes

- 0.095 (0.046)

- 0.020 (0.062)

-0.101 (0.048)

0.477 (0.077)

0.568 (0.114)

0.476 (0.077)

Total consumption Total production Average wage rate

Price traditional beers

_~_

Sample size

251

119

Adjusted R2

0.757

0.721

—

251

—

All variables are in logarithms. Zone 2 and 4 are indicator variables. Specification 1 and 2 are estimated by least squares. Specification 3 treats consumption as endogenous using land size as an additional instrument. Standard errors are in parentheses.

Higher prices of sweet potatoes significantly decrease households' long-run energy intakes. Due to poor quality of land in Rwanda, some quantities of staple foods are purchased at market prices. It is interesting to note that price of traditional beers has the opposite effect on energy intakes. Thus expenditures on beer (consumed mainly by men) appear to divert scarce resources from staple foods. Lastly, the results in second column include a measure for wages earned by household members; the wage variable is insignificant. The reduction in sample size decreases the precison of the estimates; prices of beans and sweet potatoes are insignificant as well. The treatment of wages and consumption as endogenous variables led to insignificance of all the regressors (the results are not reported). There are difficulties in finding suitable instruments for predicting wages in poor countries; shifts in demand for labor contribute to fluctuations in wages (cf. Bliss

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A. Bhargava

and Stern, 1978; Deolalikar, 1988). However, measures of economic activity in the 90 sectors of Rwanda are not included in the data set. 4.2. Results for body weight The empirical results for the body weight of men and women are presented in Table 3. The height variable significantly affects weight; the short-run coefficient for women is almost thrice as large. Since fertility rates are high, these differences may be due to short-term accumulation of subcutaneous fat. The inclusion of household size and energy and protein intakes as regressors in the model affords an approximate treatment of the impact of food intakes on weight. It would be desirable to include individual intakes and take into account ages of the household members. Since food is shared from a common plate in Rwanda, an alternative approach would be to use energy expenditures of members as surrogates for their intakes; members' weight and average activity Tables 3 Maximum likelihood estimates of the weight relationship in Rwanda Variable

Men

Women

Constant

- 3.063 (0.812) 0.004 (0.019) 0.834 (0.249)

- 7.078 (0.440) - 0.009 (0.025) 1.947 (0.077)

Protein intakes

0.004 (0.019)

0.004 (0.022)

Energy intakes

0.007 (0.026)

0.003 (0.030)

Time dummy 3

- 0.008 (0.013)

- 0.026 (0.013)

Time dummy 4

- 0.025 (0.013)

- 0.007 (0.013)

0.670 (0.123)

0.282 (0.040)

Household size Height

Lagged dependent variable (Between/within) variance

0.091

0.984

(0.152)

(0.221)

Within variance

0.011

0.010

Chi-square (4)

9.9

0.7

All variables in logarithms. The numbers in parentheses are the estimated asymptotic standard errors. Chi-square(4) is the test for exogeneity of energy intakes. Time dummies 3 and 4 are, respectively, indicator variables for 3rd and 4th survey rounds (see the text).

Nutrition and Allocation of Time in Rwandese Households levels are relevant regressors. The estimation of such a formulation, however, is infeasible; activities of children were not recorded and observations on adults are often incomplete. The statistical insignificance of household size and energy and protein intakes should thus be interpreted with caution. The coefficient of previous weight is significant in equations for men and women. While the estimate for men is higher, the ratio of between to within variance is low, indicating small between-subject differences. Note, however, that maximum likelihood estimation using modest sample sizes often entails underestimation of the between variance. The indicator variables for survey rounds appear with negative signs; coefficients in fourth and third rounds are, respectively, significant for men and women (there is no dummy variable for the second survey round as the initial observation on the dependent variable has its own intercept and a constant is included). The results indicate a tendency of weight loss over time. Since work availability in the last two survey rounds is low, shortfalls in energy intakes seem responsible for weight changes. Lastly, exogeneity hypothesis for energy intakes is not rejected in the models for men and women. While within-subject variation is similar for the sexes, overall variation in the data is high. The acceptance of exogeneity hypotheses may in part be due to the wide confidence intervals for likelihood ratio statistics. 4.3. Results for the resting and sleeping patterns The empirical results for the proportion of time spent by the adults resting, sleeping, and sitting quietly are in Table 4; logistic transformation of the dependent variable ensures a smooth relationship with explanatory variables. The adults' height and weight were initially introduced as separate regressors. The use of likelihood ratio statistics generally led to acceptance of the hypothesis that the two variables can be combined as the Body Mass Index (BMI). Moreover, in models where coefficients of height and weight were unrestricted, collinearity amongst the regressors was evident; estimates with BMI are reported in the tables. First focusing on the results for men, the time spent resting increases with age (coefficient of age squared was insignificant). Also, resting time of the lead adult is positively associated with household size. Secondly, estimated coefficients of the value of household consumption and individuals' BMI are negative and significant. The coefficient of BMI is strong and this variable reflects cumulative effects of energy deficiencies in the medium term. It therefore appears that adult males in poor households spend additional time resting and sleeping to avoid weight loss. Thirdly, the lime spent resting by men is negatively associated with average energy expenditure of the lead woman in the household. Since household consumption is taken into account, a possible explanation is that men decrease

135

136

A. Bhargava Table 4 Quasi maximum likelihood estimates for the proportion of time spent sleeping, resting, and sitting quietly Variable Constant

Men

Women

-0.915 (0.876)

1.387 (1.356)

Age

0.129 (0.044)

-0.006 (0.047)

Household size

0.149 (0.075)

0.095 (0.078)

- 0.308 (0.093)

0.038 (0.078)

0.042 (0.075)

0.070 (0.069)

Average men's or women's energy expenditure

—0.316 (0.163)

—0.165 (0.094)

BMI

- 0.623 (0.161)

0.025 (0.139)

Energy intakes

-0.031 (0.102)

-0.174 (0.105)

Time dummy 3

0.211 (0.060)

0.153 (0.044)

Time dummy 4

0.121 (0.067)

0.117 (0.047)

Lagged dependent variable

0.322 (0.095)

0.021 (0.083)

(Between/within) variance

0.007 (0.063)

0.364 (0.163)

Total consumption Protein intakes

Within variance Chi-square (12)

0.192 15.8

0.090 18.8

The dependent variable is the logistic transformation. Women's (men's) average energy expenditure is included in the equation for men (women). Chi-square (12) is the test for the exogeneity of men's (or women's) average energy expenditure, BMI, and energy intakes.

their resting time to offset high demand for women's activities. This demonstrates the joint nature of activity patterns; a decline in men's leisure would facilitate subsistence tasks. While the type of work undertaken is explored below, marginal product of labor is likely to be low due to poor nutritional status. However, no further measures of adult productivity are available in the data set. Fourthly, energy intakes are statistically insignificant. Note that 24-hour recall data from developing countries exhibit high within-subject variation in

Nutrition and Allocation of Time in Rwandese Households intakes by the poor (Bhargava, 1992). This variation does not appear to diminish in the average intakes, presumably due to chronic food shortages in Rwanda. The likelihood ratio test accepts the joint exogeneity of women's average energy expenditures and men's BMI and energy intakes. However, if the latter variables are treated as exogenous, the exogeneity of women's (men's) expenditures was rejected in some of the models. We also estimated static versions of the models used in this paper since they require less restrictive exogeneity assumptions. However, the results were quite similar. Lastly, the coefficients of indicator variables for third and fourth survey rounds are positive and significant indicating low work availability. Also, time spent resting is significantly influenced by its lagged value; long-run effect of a change in an independent variable is about 1.33 times greater than the short-run impact. The between subject variance is insignificant, however. In contrast with the results for men, only a few variables are significant in explaining women's resting patterns. The average energy expenditure of men and women's energy intakes are estimated with negative coefficients that are marginally significant. The indicator variables for survey rounds and the between subject variance are significant. Notice that the estimated within subject variance is twice as large for men. This might be due to the fact that the agricultural tasks performed by men are seasonal in nature.

4.4. Results for heavy activities Table 5 contains results for the proportion of time spent on heavy activities (with a continuity correction for extreme values; Cox, 1970) requiring at least thrice as much energy as the BMR. From the viewpoint of assessing the effects of poor nutritional status on time allocation, this model complements the specification for resting patterns. Notice that proportion of time spent by men (women) on heavy activities is positively associated with time spent by women (men) (see also Ashenfelter and Heckman, 1974; Hausman, 1981; Lundberg, 1988). The coefficients are statistically significant. Also, BMI is significant for men and might have been significant in the model for women if the sample size were greater. The energy intakes are significant for men; dummy variables for survey rounds are mainly negative though their coefficients are insignificant. While the coefficients of lagged dependent variables are insignificant, between subject variances are significant. The statistical insignificance of some of the parameters may be due to greater variation in heavy activities. Unlike rest and sleep, these activities are strongly influenced by geographical location of the household, land quality, etc. In fact, within variances in Table 4 are about twice the corresponding estimates in Table 3.

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A. Bhargava

138

Table 5 Quasi maximum likelihood estimates for the proportion of time spent on heavy activities Varible

Men

Constant

0.635 (2.690) - 0.166

2.506 (2.207) 0.009

Age

Women

(0.081)

(0.076)

-0.186 (0.132)

0.049 (0.133)

0.204 (0.138)

0.040 (0.142)

-0.056 (0.073)

-0.016 (0.106)

Men's or women's time on heavy activities

0.113 (0.064)

0.142 (0.043)

BMI

0.709 (0.309)

0.314 (0.217)

Energy intakes

0.136 (0.067)

-0.162 (0.152)

Time dummy 3

- 0.069 (0.080)

- 0.045 (0.061)

Time dummy 4

- 0.106 (0.080)

0.068 (0.062)

Lagged dependent variable

0.051 (0.078)

0.013 (0.086)

(Between/within) variance

0.303 (0.138)

0.637 (0.253)

Household size Total consumption Protein intakes

Within variance Chi-square (12)

0.342 16.7

0.179 17.6

The dependent variable is the logistic transformation with a continuity correction for extreme values. Women's (men's) time on heavy activities is included in the equation for men (women). Chisquare (12) is the test for the exogeneity of men's (or women's) heavy activities, BMI, and energy intakes.

4.5. Results for agricultural and household activities The determinants of time allocated to agricultural and household activities are investigated in Table 6. The models underscore joint nature of time allocation decisions; men's agricultural actvities depend on their effort on housework and on time spent by women on agriculture. The women's housework is influenced by their agricultural activities. In contrast, women's agricultural

139

Nutrition and Allocation of Time in Rwandese Households

Table 6 Quasi maximum likelihood estimates for the proportion of time spent on agricultural and household activities Men

Women

Variable

Agriculture

Housework

Agriculture

Constant

0.858 (1.384)

0.917 (2.496)

1.635 (1.763)

Age

0.331 (0.107)

0.139 (0.094)

0.518 (0.097)

-0.148 (0.164)

- 0.360 (0.155)

-0.116 (0.154)

0.149 (0.067)

- 0.076 (0.165)

0.234 (0.163)

- 0.203 (0.120)

- 0.070 (0.116)

- 0.084 (0.126)

Household size Total consumption Protein intakes Men's or women's agriculture

0.239

-0.113

0.153 (0.041)

(0.062)

(0.049)

Housework

0.032 (0.090)

—

BMI

0.937 (0.327)

0.773 (0.247)

0.773 (0.194)

Energy intakes

0.226 (0.115)

0.253 (0.166)

-0.134 (0.181)

Time dummy 3

-0.117 (0.091)

-0.122 (0.065)

-0.150 (0.072)

Time dummy 4

-0.176 (0.090)

- 0.089 (0.067)

- 0.023 (0.075)

Lagged dependent variable

0.068 (0.081)

0.009 (0.067)

- 0.027 (0.074)

(Between/within) variance

0.633 (0.233)

0.802 (0.278)

0.624 (0.225)

0.427

0.208

0.256

18.7(16)

7.7(12)

32.8(16)

Within variance Chi-square

-0.152 (0.060)

Men's (women's) agriculture appears in the equation for women's (men's) agriculture. Women's agriculture is included in the women's housework equation. Degrees of freedom of the chi-square test for the exogeneity of agriculture, housework, BMI, and energy intakes are in parentheses.

activities are influenced by their housework and by the time spent by men on agriculture. Since a small proportion of men's time is spent on household activities, the empirical results for housework were poor and are omitted from the table.

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A. Bhargava First considering the results for men's agriculture, age, total value of consumption, BMI, energy intakes, women's agriculture, time dummies, and between-subject variance are all significant. The coefficient of age is positive and contrasts with the negative estimate obtained for heavy activities in Table 4. The inclusion of square of age indicated a nonlinear relationship though the additional term was not significant at 5% level. The housework performed by men is insignificant; dropping this variable from the model did not alter the results. In the model for women's housework, coefficient of household size is significant; a greater number of members in the household is associated with reduction in the lead woman's effort on housework. This phenomenon was explored further by controlling for the number of children in age groups 1-5 and 5-10 years. The estimates were less precise as the sample size was reduced to 85 women because of missing data. However, the results confirmed that children in the household enable women to increase their resting time. Since poor nutritional status diminishes adult productivity, larger families might be viewed favorably in Rwanda; children enhance the subsistence capacity of the household (Schultz, 1973). The coefficients of women's agriculture and BMI are significant in explaining housework which contrasts with some of the findings in previous tables. The household and agricultural activities seem to cover salient aspects of women's role in subsistence agriculture. Notice the substitution between agricultural and household activities. This is not the case for men. Thus men share additional work by performing tasks outside the house. The remaining tasks are completed by other members including children. Finally, the results for women's agriculture are broadly consistent with the estimates obtained for housework. The coefficient of men's agriculture is significant and positive whereas that of housework is negative. The subsititution between agricultural and household activities is of a similar order of magnitude in the two models. The BMI is positively associated with agriculture; household size is insignificant. The coefficients of dummy variables for third survey rounds are negative and significant in the two columns. The coefficients of lagged dependent variables are insignificant though the between-subject variances are invariably significant.

5. Conclusion This paper has proposed a dynamic framework for analyzing the determinants of time allocation at the subsistence level. The models for energy intakes, body weight, and activity patterns capture different aspects of the relationship. In spite of exchange of food amongst households, high food prices cause energy deficiencies. Further, poor nutritional status hampers the capacity of adults to undertake subsistence tasks. Since weight loss was evident during the sample

Nutrition and Allocation of Time in Rwandese Households period, energy intakes of twice the BMR appear inadequate for subsistence activities of the lead adults. The productivity of adults will benefit from programs alleviating energy deficiencies. This might be achieved by subsidizing foods such as sweet potatoes and beans. Significant improvements in health and productivity will facilitate family planning programs in Rwanda, once the present conflict is resolved. Since men and women share the work, special programs for women might not be necessary. At a general level, the results indicate that it would be fruitful to discuss the issue of 'Requirements for what?' (FAO, 1985) in a dynamic framework. Firstly, in populations facing energy deficiencies, intakes determine the expenditures. At a given point in time, energy expenditures cannot afford a full assessment of the nutrient levels necessary for maintaining long-term health. Dietary guidelines for poor countries should reflect the importance of nutrients for various human functions. Secondly, in situations where energy needs are satisfied, modern intervention programs address protein and micronutrient deficiencies. The latter increase morbidity and reduce physical work capacity. The diminished capacity of individuals together with limited market opportunities will gradually lower their expenditures and intakes. The coexistence of marginal undernutrition and poverty results in suboptimal energy expenditures. It is important to formulate the dynamic interactions between the energy, protein, and micronutrient intakes. Such considerations will enhance the efficacy of dietary recommendations (see also Bhargava and Reeds, 1995). Finally, for populations enjoying unrestricted food supplies, a knowledge of energy expenditures is useful. While epidemiologic research in developed countries has focused on habitual intakes (e.g., Willett, 1990), recent studies suggest underreporting (or underconsumption on the days sampled) of nutrients such as fat and cholesterol (Bingham, 1994). Future work, verifying the intakes data by energy expenditures and biological markers, can facilitate the prevention of diseases associated with overnutrition.

References Anand, S. and M. Ravallion, 1993, Human development in poor countries: On the role of private incomes and public services, Journal of Economic Perspectives 7, 133-150. Anderson, T.W. and C. Hsiao, 1981, Estimation of dynamic models with error components, Journal of the American Statistical Association 76, 598-606. Ashenfelter, O. and J. Heckman, 1974, The estimation of income and substitution effects in a model of family labor supply, Econometrica 42, 73-85. Basta, S.S, M.S. Soekirman, D. Karyadi, and N.S. Scrimshaw, 1979, Iron deficiency anemia and the productivity of adult males in Indonesia, American Journal of Clinical Nutrition 32, 916-925.

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Beaton, G.H., 1984, Adaptation to and accomodation of long term low energy intake, in: E. Pollitt and P. Amante, eds, Energy intake and activity (Alan R. Liss, New York, NY) 395^103. Becker, G.S., 1965, A theory of allocation of time, Economic Journal 75, 493-517. Becker, G. S., 1991, A treatise on the family (Harvard University Press, Cambridge, MA). Berio, A.-J., 1984, The analysis of time allocation and activity patterns in nutrition and rural development planning, Food and Nutrition Bulletin 6, 53-68. Bhargava, A., 1991, Estimating short and long run income elasticities of foods and nutrients for rural south india, Journal of the Royal Statistical Society A 154, 157-174. Bhargava, A., 1992, Malnutrition and the role of individual variation with evidence from India and the Philippines, Journal of the Royal Statistical Society A 155, 221-231. Bhargava, A., 1994, Modelling the health of Filipino children, Journal of the Royal Statistical Society A 157,417-432. Bhargava, A. and P. Reeds, 1995, Requirements for what? Is the measurement of energy expenditure a sufficient estimate of energy needs?, Journal of Nutrition 125, 1358-1362. Bhargava, A. and J.D. Sargan, 1983, Estimating dynamic random effects models from panel data covering short time periods, Econometrica 51, 1635-1660. Bingham, S.A., 1994, The use of 24-h urine samples and energy expenditure to validate dietary assessment, American Journal of Clinical Nutrition 59, 227S-231S. Bliss, C. and N. Stern, 1978, Productivity, wages and nutrition, I and II, Journal of Development Economics 5, 331-362 and 363-398. Cox, D.R., 1970 Analysis of binary data (Chapman and Hall, London). Dasgupta, P., 1993, An inquiry into well-being and destitution (Oxford University Press, New York, NY). Deolalikar, A.B., 1988, Nutrition and labor productivity in agriculture: Estimates for rural south India, Review of Economics and Statistics 67, 406-413. Durnin, J., 1991, Practical estimates of energy requirements, Journal of Nutrition 121, 1907-1913. FAO/WHO/UNU, 1985, Energy and protein requirements, World Health Organization technical report series no. 724 (WHO, Geneva). Floud, R., K. Wachter, and A. Gregory, 1991, Height, health and history (Cambridge University Press, Cambridge). Fogel, R.W., 1994, Economic growth, population theory and physiology: The bearing of long-term processes on the making of economic policy, American Economic Review 84, 369-395. Gardner, G.W., V.R. Edgerton, B. Senewiratne, J.R. Bernard, and Y. Ohira, 1975, Physical work capacity and metabolic stress in subjects with iron deficiency anemia, American Journal of Clinical Nutrition 30, 910-917. Hausman, J.A., 1981, Labor supply, in: H. Aaron and J. Pechman, eds., How taxes affect economic behavior (Brookings Institution, Washington, DC). James, W.P.T., A. Ferro-Luzzi, and J.C. Waterlow, 1988, Definition of chronic energy deficiencies in adults, European Journal of Clinical Nutrition 42, 969-981. Leibenstein, H., 1957, Economic backwardness and economic growth (Wiley, New York, NY). Lundberg, S., 1988, Labor supply of husbands and wives: A simultanoeous equations approach, Review of Economics and Statistics 67, 224-234. Mincer, J., 1962, Labor force participation of married women, in: G.H. Lewis, ed., Aspects of labor economics (Princeton: University Press, Princeton, NJ). Mirrlees, J., 1975, A pure theory of underdeveloped economies, in: R. Reynolds, ed., Agriculture in development theory (Yale University Press, New Haven, NJ). Myrdal, G., 1968, Asian drama: An enquiry into the poverty of nations (Allen Lane, Middlesex). Nelson, M., A.E. Black, J.A. Morris, and T.J. Cole, 1989, Between-and-within subject variation in nutrient intake from infancy to old age: Estimating the number of days to rank dietary intakes with desired precision, American Journal of Clinical Nutrition 50, 155-167.

Nutrition and Allocation of Time in Rwandese Households

Pollak, R., 1969, Conditional demand functions and consumption theory, Quarterly Journal of Economics 83, 70-78. Pollak, R. and M. Wachter, 1975, The relevance of household production functions and its implications for the allocation of time, Journal of Political Economy 83, 255-277. Pudney, S., 1981, Instrumental variable estimation of a characteristics model of demand, Review of Economic Studies 48, 417-433. Republique Rwandaise, 1986, Enquete national sur le budget et la consommation des manages (Ministry of Planning, Rwanda). Schoefield, W.N., 1986, Predicting basal metabolic rate, new standards and review of previous work, Human Nutrition Clinical Nutrition 39C, Suppl. 1, 5-41. Schultz, T.W., 1973, Fertility and economic values, in: T.W. Schultz, ed., Economics of the family (Chicago University Press, Chicago, IL). Sen, A., 1983, Economics of the family, Asian Development Review 1, 14-26. Sen, A., 1985, Commodities and capabilities (North-Holland, Amsterdam). Simon, H.A., 1986, Rationality in psychology and economics, Journal of Business 59, S209-S224. Soares, M.J. and P.S. Shetty, 1991, Basal metabolic rates and metabolic economy in chronic undernutrition, European Journal of Clinical Nutrition 45, 363-373. Spurr, G.B., 1983, Nutritional status and physical work capacity, Yearbook of Physical Anthropology, 1-35. Waterlow, J.C, 1986, Metabolic adaptation to low intakes of energy and protein, Annual Review of Nutrition 6, 495-526. Willett, W., 1990, Nutritional epidemiology (Oxford University Press, Oxford).

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Issues and Opinions in Nutrition T h e views expressed i n t h i s section are t h o s e of t h e a u t h o r s and n o t necessarily those of t h e Editor, the Editorial Board of T H E JOURNAL OF N U T R I T I O N or the A m e r i c a n I n s t i t u t e of N u t r i t i o n . Readers are invited t o respond to t h e s e essays b y Letter to t h e Editor, so t h a t T H E JOURNAL can serve as a forum for the discussion of these topics.

Requirements for What? Is the Measurement of Energy Expenditure a Sufficient Estimate of Energy Needs?1 ALOK

BHARGAVA2

AM> PETER J.

REEDS*

Department of Economics, University of Houston, Houston, TX 77204-5882, and *(JSDA/ARS Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, TX 77030 Knowledge of the current nutritional status of populations and, ideally, of specific subgroups within a population is essential information for those engaged in long-term economic and health planning. Failing some generally acceptable, specific and practicable index of the status of a specific nutrient, information is frequently presented in terms of intakes in relation to some estimate of requirement or need. The FAO/WHO/UNU (1985] expert committee strongly, and rightly, stated that information on free-living energy expenditure was crucial for the definition of the energy requirements of different groups of humans. Partly as a consequence of this recommendation, and partly as a result of the wide application of the doubly labeled water method for estimating energy expenditure, there are now extensive published data on the energy expenditure of humans of a variety of ages and nutritional and physiological states living in different environments, both "advantaged" and "disadvantaged" (e.g., Bianca et al. 1994, Butte et al. 1990, Goldberg et al. 1991b, James and Schofield 1990, Schultink et al. 1993, Shultz and Schoeller 1994). This information is both invaluable and important but, we would argue, not necessarily sufficient to define an individual's (or indeed the population's) energy requirements, defined in this paper as energy needs. Energy requirements are a combined function of the individual's genotype, growth, health and physiological status and, critically, physical activity. Ideally, the last factor should be appropriate for optimal performance within a particular environment. However, the satisfaction of these requirements may be constrained by the availability of suitable sources of energy, often itself a function of the socioeconomic status of the individual or population under exami0022-3166/95 $3.00 © 1995 American Institute of Nutrition. J. N Manuscript received 15 November 1994.

nation. There is, moreover, a necessary thermodynamic equality between energy intake and energy expenditure and storage, so that failing the availability of appropriate quantities of food, energy expenditure or storage, or both, must change. To draw useful implications from measurements of energy expenditure it is important to recognize the importance of the time frame (usually <10 d) in which these measurements are made. Over this time scale they frequently represent measurements of energy intake. We would argue that measurements of energy expenditure must be viewed in light of other aspects of individual health and function (Bhargava 1994). It seems to us that, without due consideration of the socioeconomic environment and other factors involved in nutritional status, there is a real danger of gaining a false impression of energy requirements (and hence the adequacy of current intake) when this estimate is based solely on measurements of expenditure. In other words, measurements of energy expenditure must be placed in a broader analytical framework than is often the case (Beaton 1984). To illustrate this point, we wish to discuss three circumstances in which, for different underlying

'This work is a publication of the USDA/ARS Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, TX. This project has been funded in part with federal funds from the U.S. Department of Agriculture, Agricultural Research Service under Cooperative Agreement no. 58-6250-1003. The contents of this publication do not necessarily reflect the views or policies of the U.S. Department of Agriculture, nor does mention of trade names, commercial products or organizations imply endorsement by the United States government. Alok Bhargava's research was supported in part by the World Bank. To whom correspondence should be addressed. :. 125: 1358-1362, 1995.

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reasons, measurements of energy expenditure may give a false view of energy requirements. These are: 1) Measurements made in a population with a historically poor socioeconomic status. In these populations, the availability of food has been restricted over a long period of time, and the individual's energy expenditure (which is in balance with intake) reflects changes in behavior, especially physical activity, that conserve energy. 2) Measurements made under circumstances in which deficiencies of other dietary factors, notably protein and micronutrients, may have influenced the individual's physiological function. In this circumstance, physical activity, and its attendant expenditure of energy, may be constrained by other nutritional inadequacies and hence may not necessarily reflect energy requirements. 3) Measurements made in populations whose nutrient intakes are unrestrained by economic factors. In the third circumstance, measurements of expenditure are more useful estimates of "requirements" but, even so, are fundamentally measurements of immediately preceding and current energy intake.

ENERGY DEFICIENCY, EXPENDITURE AND ADAPTATION In his insightful discussions of adaptation, Waterlow (1985, 1986a and 1986b) emphasized two main points. First, uncritical use of the word adaptation must be avoided. This is because the term adaptation is often taken to imply benefit, and not all forms of adaptation are advantageous. Waterlow took physical stunting as an illustration and presented two alternative interpretations. On the one hand, he argued that reduced linear growth is an inevitable result of a nutrient intake that has not allowed the individual to realize his or her growth potential. On the other hand, Waterlow emphasized that the stunted individual has, by definition, a lower absolute nutrient requirement, so that such an individual could be regarded as having adapted successfully. Waterlow's second point was that adaptation may involve changes in metabolic and physiological function that act over different time scales. There are difficulties in assessing chronic energy deficiencies using biological indicators alone (Beaton 1984). For example, in the study of 130 Indian males by Soares and Shetty (1991), the ratio of basal metabolic rate (BMR) to body weight (WT) [or fat free mass (FFM)] was not the lowest for the undernourished (cf. Waterlow 1986a). Apart from nonlinearities in this relationship, it is likely that the proportionate change in BMR as a result of a 1% change in WT ("elasticity") is smaller than one. Furthermore, different activity rates for lean body mass, visceral tissue and fat complicate the functional form, and the

subjects' age and height (HT) are potentially important determinants of BMR. We estimated a quadratic function in WT for BMR using least squares (e.g., Cramer 1946) on the Soares-Shetty data: BMR = -301.97 + 187.13 WT - 1.16 (WT)2 (1247.2) (49.62) (0.44) 3.83 HT (661.96)

25.36 Age (10.81)

Residuals (1)

where BMR is measured in megajoules per day, weight is in kilograms, and height is in meters; the numbers in parentheses are standard errors. Squared weight is statistically significant even at the 1 % level though height is insignificant. There is a significant decline in BMR with age (the individuals are in the age group 18-30 y). A similar model replacing WT with FFM, however, led to a statistically insignificant estimate of the squared FFM, implying a linear relationship between BMR and FFM. The estimates for a simple log-linear version with FFM as a regressor were Log (BMR) = 6.30 - 0.12 log (Age) (0.24) (0.04) + 0.71 log (FFM) + Residuals (0.05)

(2)

From these results, the elasticity of BMR with respect to FFM (e.g., Hicks 1946) is 0.71. Thus one would frequently observe a high BMR/FFM ratio among the undernourished. Furthermore, models using alternative procedures for adjusting BMR for WT and FFM will often lead to conflicting conclusions,- the time span over which the observations are made may also be important. To fully understand the long-term consequences of energy deficiencies, therefore, it is essential to examine the effects of nutritional status on behavioral outcomes such as the individuals' activity patterns. As noted by Waterlow (1986a), the distinction between biological and behavioral adaptation is critical when we consider energy deficiency. In the short term, an inadequate energy intake will lead to the loss of body mass, thus the observation of Bianca et al. (1994) that the equal, and high, levels of energy expenditure of Gambian men with a low or normal body mass index might well result from a relatively short period of inadequate intake and, by that token, might truly reflect the energy requirements of both groups. The men with the low body mass index will have consumed energy at a rate beneath their requirements and hence have lost body mass. However, this loss of body mass can only be of limited duration, in strict contrast with the increase in body mass accompanying a persistently excessive intake. If the inadequate intake persists, energy expenditure eventually

Estimation of Energy Needs must fall in order to enable the individual to survive, and the only aspect of expenditure over which a person has ready control is the level and nature of physical activity. But an individual must perform some basic tasks in order to survive, so that behavioral adaptation involves curtailing less essential, though desirable, forms of activity. Societal adaptations, such as work sharing, also may evolve. If, at this time, energy expenditure is measured, the individual will be found to be in energy balance, and the simple conclusion is that the individual's energy requirement is low. However, it is under this circumstance that other information becomes critical and an important distinction between actual activity (and energy expenditure) and desirable activity becomes necessary. The actual energy expenditure conveys little information about requirements, because it is constrained by energy intake, and the current intake does not necessarily allow the individual to function optimally within the environment. For example, Bhargava (19961 noted that in Rwanda, poorly nourished adults (i.e., with a low body mass index| not only spent more time resting and sleeping but pursued only tasks that incurred a moderate energy expenditure. Their actual expenditure represented the minimum needed for survival but could hardly be regarded as being optimal for the environment. Similarly, Sigman et al. (1989) concluded that the majority of the Kenyan children that they studied had higher energy intakes than the FAO/UNU/WHO recommendations, yet they were underweight for their age. An interpretation of this could be that the children had maintained their physical activity in the face of an intake that was insufficient for both activity and adequate growth. The distinction between desired and actual activity levels is noted in FAO/UNU/WHO (1985) and could be of crucial importance to policy makers. However, the idea became overshadowed by the emphasis that was placed on the use of energy expenditure, measured inevitably over a short period of time, to justify estimates of appropriate energy intakes. The problem, of course, is that estimating desired or optimal levels of activity involves judgments about the social environment. The measurement of energy expenditure is objective and gives direct information. Even so, in chronically undernourished populations, measurements of energy expenditure reflect the results of poor nutrition whereas interventions should, at the very least, attempt to deal with the causes. From a policy standpoint, nutritional surveys in poor countries can enhance our understanding of the magnitude of undernutrition by questioning the subjects about their preferred activity levels. For example, the subjects' willingness to participate in "food for work" programs would indicate the prevalence of energy deficiencies. The potential gains from improved "quality of diet" can be investigated by inquiring about the individuals' perceptions of the resulting gains in (labor) productivity.

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ENERGY EXPENDITURE AND MICRONCITRIENT DEFICIENCIES The increase in production of cereals has enabled many population groups in developing countries to meet their energy needs (International Food Policy Research Institute 1990). Some countries in Africa have been less successful, with intermittent energy deficiencies resulting from drought, high food prices, low incomes and a poor food distribution system. Although it is true that diets supplying inadequate amounts of energy almost always provide inadequate quantities of protein and micronutrients, diets that supply sufficient amounts of energy do not always provide adequate amounts of micronutrients. For example, the U.S. Agency for International Development (1992) surveys of child development in Egypt, Kenya and Mexico identified an energy deficiency only in Kenya. This was, however, short lived and the result of a drought. On the other hand, the diets consumed by all three populations of children seemed to be deficient in some micronutrients (see also Allen 1994). The relationship between energy expenditure and micronutrient status represents a long-term phenomenon. To illustrate some of the difficulties, consider Waterlow's (1986b) discussion on the energy costs of walking in a tropical climate. From experiments, it is known to be 15-20% more efficient to walk at 100 m/min than at 40 m/min (FAO/UNU/ WHO 1985). Waterlow suggests that the slow pace observed in developing countries is comfortable, and he conjectures that at the practical level it is "efficient" in terms of energy use. This hypothesis presumably stems from equating energy intakes and expenditures in a short time frame. An alternative explanation would be that habitually low iron status reduces the vigor with which individuals perform tasks (Basta et al. 1979), so that subjects with a low hemoglobin concentration are forced to walk at a slower pace because it reduces the oxygen demand per unit of time even though the slow pace entails a higher energy expenditure per unit of distance traveled. This is a rational behavioral response because staple foods are inexpensive relative to foods that are good sources of iron. Moreover, this phenomenon is consistent with the notion of "hierarchy in human wants" that has appeared in the Western literature since the writings of Plato (e.g., Plato 1982). Behavioral factors underlying nutrient intakes are influenced by such considerations, because the absorption of protein and micronutrients critically depends on whether the subjects' dietary energy needs are satisfied. The relationship between energy expenditures and micronutrient intakes also has to be viewed in a dynamic time framework. At a given time, energy expenditure will be a good reflection of energy intake,

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and during a short period of energy deficiency the abundant energy stores of the body can be used. However, to sustain activity levels, it is necessary for individuals to consume adequate quantities of many micronutrients within a certain time interval because, unlike energy, the body's stores of these nutrients (including amino acids] are limited. Thus, low intakes of micronutrients in the past influence the level of activity that can be sustained in the present and hence influence the estimate of energy requirements that are developed from measurements of expenditure. The assessment of the relationship between micronutrient status and energy expenditure is also complicated by socioeconomic factors. Consider the following. In developing countries, educated persons in white-collar occupations have a lifestyle that involves a moderate expenditure of energy. However, because nutrient densities typically are positively associated with income (Bhargava 1991), it is likely that the "quality" of the diet consumed by the professional groups performing light activities is better than that of laborers whose activities involve greater energy expenditure. Thus a random sample encompassing both groups could show negative correlations between energy expenditure and micronutrient intake but positive correlations within each group (Basta et al. 1979). The results of the former exercise could be interpreted satisfactorily only by considering other aspects of both nutritional status (in this case the nutrient composition of the diet) and the lifestyle of the subjects.

ENERGY INTAKES AND EXPENDITURES IN DEVELOPED COUNTRIES The problems associated with measurements of energy expenditure in the so-called developed world are somewhat different. Food availability is not limited by economic constraints, and the evidence regarding the deleterious effects of high intakes of fat and cholesterol has motivated much research (e.g., Willett 1990) into factors that regulate overall food intake and selection. As a result of this research, it has become clear that underreporting of food intake is extremely frequent (Goldberg et al. 1991a, Mertz et al. 1991). Furthermore, there are more subtle effects than a mere underreporting of total intake. For example, dietary intervention programs developed by the National Cancer Institute and the U.S. Department of Agriculture have increased subjects' awareness of the adverse effects of excessive fat and cholesterol intakes (Henderson et al. 1990). However, on the basis of 7-d food records of a sample of 37 Houston women, Bhargava et al. (1994) concluded that the educational program had apparently had different effects on the subjects' weekday and weekend intakes (see also Tarasuk and Beaton 1992).

Because such effects will not be visible in 3- or 4-d food records, the collection of 7-d records is appealing. It is under this circumstance that measurements of free-living energy expenditure (made over 10-d periods) are extremely useful (e.g., Bingham 1994, Black et al. 1991, Goldberg et al. 1991a). Even so, the measurement of energy expenditure under these circumstances is fundamentally a measurement of intake. Further information, particularly about body composition, will be needed to make an interpretation in terms of energy requirements. For instance, the nutritional conclusions drawn from data showing equal energy expenditure in lean and obese individuals will be different. The former individuals might be consuming food at or slightly below their requirements, whereas the latter are consuming (or have consumed) energy in excess of their requirements. In summary, the emphasis on measuring energy expenditure is extremely useful for estimating energy requirements, provided that the applications recognize the socioeconomic circumstances of the subjects. This is especially true in developing countries where energy expenditures are influenced by few work opportunities, poor diet quality and other undesirable environmental factors. By considering three specific cases, we have argued the need for a suitable analytical framework for interpreting data on energy expenditure in terms of energy requirements. From a health policy viewpoint in Western countries, a better understanding of cultural factors affecting food consumption and the interrelationships between nutritional status and biological markers (Schulte 1987) will enhance disease prevention. Increased collaboration among researchers in the relevant disciplines could facilitate this intricate task.

ACKNOWLEDGMENTS The authors would like to thank M. J. Soares for providing the original data from India and the reviewers and the Editor for helpful comments. The views contained in the paper are exclusively those of the authors.

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Estimation of Energy Needs Bhargava, A. (1994| Modelling the health of Filipino children. J. R. Stat. Soc. A 157: 417-432. Bhargava, A. (1996) Nutritional status and the allocation of time in Rwandese households. J. Econometrics (in press) Bhargava, A., Forthofer, R., McPherson, S. &. Nichaman, M. (1994) Estimating the variations in dietary intakes on weekdays and weekends. Stat. Med. 13: 113-126. Bianca, P. D., Jequier, E. & Schutz, Y. (1994) High level of freeliving energy expenditure in rural Gambian men: lack of behavioral adaptation between low and normal BMI groups. Eur. J. Clin. Nutr. 48: 273-278. Bingham, S. A. (1994) The use of 24-h urine samples and energy expenditures to validate dietary assessment. Am. J. Clin. Nutr. 59: 227S-231S. Black, A. E., Goldberg, G. R., Jebb, S. A., Livingstone, M.B.E., Cole, T. J. &. Prentice, A. M. (1991) Critical evaluation of energy intake data using fundamental principles of energy physiology: 2. Evaluating the results of published surveys. Eur. J. Clin. Nutr. 45: 583-599. Butte, N. F., Wong, W. W., Ferlic, L., Smith, E. O., Klein, P. D. & Garza, C. 11990) Energy expenditure and deposition of breast-fed and formula-fed infants during early infancy. Pediatr. Res. 28: 631-640. Cramer, H. (1946) Mathematical Methods of Statistics. Princeton University Press, Princeton, NJ. FAO/UNU/WHO (1985) Energy and Protein Requirements, World Health Organization Technical Series no. 724. WHO, Geneva, Switzerland. Goldberg, G. R., Black, A. E., Jebb, S. A., Cole, T. J., Murgatroyd, P. R., Coward, W. A. & Prentice, A.. M. (1991a) Crucial evaluation of energy intake data using fundamental principles of energy physiology: 1. Derivation of cut-off limits to identify underrecording. Eur. J. Clin. Nutr. 45: 569-581. Goldberg, G. R., Prentice, A. M., Coward, W. A., Davies, H. L., Murgatroyd, P. R., Sawyer, M. B., Ashford, J. & Black, A. E. (1991b) Longitudinal assessment of the components of energy balance in well-nourished lactating women. Am. J. Clin. Nutr. 54: 788-798. Henderson, M. M., Kushi, L. H., Thomson, D. J., Gorbach, D. J., Clifford, C. C , Insull, W., Moskowitz, M. & Thomson, R. (1990) Feasibility of a randomized trial of a low fat diet for the prevention of breast cancer. Prev. Med. 19: 115-133. Hicks, J. (1946) Value and Capital. Oxford University Press, Oxford, U.K.

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International Food Policy Research Institute (1990) Research Report 1990. International Food Policy Research Institute, Washington, DC. James, W.P.T. & Schofield, E. C. (1990) Human Energy Requirements. Oxford University Press, Oxford, U.K. Mertz, W., Tsui, J. C , Judd, J. T., Reiser, S., Hallfrisch, J., Morris, E. R., Steele, P. D. & Lashley, E. (1991) What are people really eating? The relation between energy intake derived from estimated diet records and intake determined to maintain body weight. Am. J. Clin. Nutr. 54: 291-295. Plato (1982) Republic (Jowett, B., transl.). Modern Library, New York, NY. Schulte, P. A. (1987) Methodologic issues in the use of biologic markers in epidemiologic research. Am. J. Epidemiol. 126: 1006-1016. Schultink, J. W., Van Raaij, J. M. & Hautvast, J. G. (1993) Seasonal weight loss and metabolic adaptation in Beninese women: the relationship with body mass index. Br. J. Nutr. 70: 689-700. Schultz, L. O. &. Schoeller, D. A. (1994) A compilation of total daily energy expenditure and body weights in healthy adults. Am. J. Clin. Nutr. 60: 676-681. Sigman, M., Neumann, C , Jansen, A. A. & Bwibo, N. (1989) Cognitive abilities of Kenyan children in relation to nutrition, family characteristics, and education. Child Dev. 60: 1463-1474. Soares, M. J. & Shetty, P. S. (1991) Basal metabolic rates and metabolic economy in chronic undernutrition. Eur. J. Clin. Nutr. 45: 363-373. Tarasuk, V. &. Beaton, G. H. (1992) Statistical estimation of dietary parameters: implications of patterns in within-subject variation—a case study of sampling strategies. Am. J. Clin. Nutr. 55: 22-27. U.S. Agency for International Development (1992) Functional Implications of Malnutrition. Final Report, Human Nutrition Collaborative Research Program. United States Agency for International Development, Washington, DC. Waterlow, J. C. (1985) What do we mean by adaptation? In: Nutritional Adaptation in Man (Blaxter, K. L. &. Waterlow, J. C , eds.), pp. 1-12. John Libbey, London, U.K. Waterlow, J. C. (1986a) Metabolic adaptation to low intakes of energy and protein. Annu. Rev. Nutr. 6: 495-526. Waterlow, J. C. (1986b) Notes on the new international estimates of energy requirements. Proc. Nutr. Soc. 45: 351-360. Willett, W. (1990) Nutritional Epidemiology. Oxford University Press, Oxford, U.K.

III. Child Health and Cognitive Development in Developing Countries

J. R. Statist. Soc. A (1994) 157, Part 3, pp. 417-432

Modelling the Health of Filipino Children By ALOK BHARGAVAt University of Houston, USA [Received October 1992. Revised July 1993] SUMMARY This paper estimates dynamic models for nutrient intakes, height, weight and morbidity spells by using longitudinal data on 312 children between the ages 1 and 10 years from the Bukidnon region of the Philippines. The analysis attempts to integrate the biomedical aspects of anthropometric assessment with the behavioural factors affecting health. The time dimension of child health is emphasized and a triangular system of equations for height, weight and morbidity spells is estimated. The empirical results show positive associations between protein intake and the children's heights and a negative association between ^-carotene intake and an index of morbidity. Also, the susceptible children can be identified by using anthropometric variables. Keywords: ANTHROPOMETRIC ASSESSMENT; DIETARY SURVEYS; DYNAMIC ECONOMETRIC MODELS; EPIDEMIOLOGICAL METHODS; GROWTH; INCOME ELASTICITIES; LONGITUDINAL DATA; MAXIMUM LIKELIHOOD ESTIMATION; MICRONUTRIENTS; MORBIDITY INDICES

1. INTRODUCTION The assessment of how well children are nourished (nutritional status) is an important task in biomedical research. In developed countries, anthropometric measures are compared against national standards available by age and sex to provide insights into the physiological development of children. Simple interventions such as changes in dietary habits can prevent diseases in later years. It is not surprising that much effort has been spent on developing widely applicable growth standards (e.g. Tanner et al. (1966), Hamill et al. (1977), Waterlow et al. (1977) and Cole (1988, 1990, 1991)). The problems affecting growth of children in less-developed countries are of a different complexion. In areas affected by food shortages, measures such as weight and arm circumference are used to identify children at risk of mortality (Sommer and Loewenstein, 1975). The recent trends in agricultural production have enabled many population groups to meet their energy needs via the consumption of staple foods (International Food Policy Research Institute, 1990). However, deficiencies in protein and micronutrient intakes remain prevalent; their effects on children's physiological and mental development are largely unknown. Also, poor sanitation and environmental conditions exacerbate the consequences of malnutrition. Detailed knowledge of the mechanisms linking the behavioural factors affecting food consumption to children's health is useful from a policy standpoint. This has been emphasized by many researchers (Mosley and Chen, 1984; Martorell and ^Address for correspondence: Department of Economics, College of Social Sciences, University of Houston, Houston, TX 77204-5882, USA. E-mail: [email protected] © 1994 Royal Statistical Society

0035-9238/94/157417

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Habicht, 1986). The estimation of such relationships is complicated for several reasons. Firstly, the socioeconomic environment of the households must influence the variables selected to represent health. For example, although the ratio of a child's weight to height is a good measure of the current nutritional status, its use may be inappropriate where food shortages have reduced linear growth. In contrast, if the energy needs are met, then morbidity spells and cognitive performance are suitable indicators. The second set of difficulties addressed in the paper emanates from complicated lags between food consumption and the ultimate nutritional status. It is known that malnourished children tend to catch up in physiological growth if their circumstances improve (Tanner, 1986a). The immunological and other systems, however, may be damaged by undernutrition spells. In addition, indicators of health such as height, weight and sickness are differentially affected by episodes of nutritional stress and environmental trauma. Thus it is essential to incorporate biomedical features in statistical models for health. Thirdly, it is important to balance the emphasis on the biomedical and socioeconomic determinants of health. This is not an easy task, at least at a general level (Cox, 1992). For example, biomedical researchers often postulate simple relationships between functional outcomes and nutrient intakes (United States Agency for International Development, 1990). In contrast, social scientists model households' decisions over a range of variables (e.g. Behrman and Deolalikar (1988)). This paper tackles some of these difficulties in the course of developing a model for the health of Filipino children. The data are described in Section 2. The model for nutrient intakes is discussed in Section 3. In Section 4, the relationships between three components of health, namely height, weight and morbidity spells, and the explanatory variables are examined. The model is presented in Section 5.1 and some methodological issues are addressed in Section 5.2. The empirical results are discussed in Section 6. The conclusions are given in Section 7. 2. THE DATA The data from the Bukidnon region of the Philippines were collected during 1984-85 by surveying 448 households living within a 20-mile radius (Bouis and Hadad, 1990). Four nutritional surveys were conducted at 4-month intervals and foods consumed in the previous 24 hours by all members of the households were recorded. The children's height and weight were measured in each round. For adults, weight was recorded four times and height was measured in the first survey round. In each survey, information on whether individuals suffered from colds, cough, fever, diarrhoea and headaches during the previous fortnight and the duration of three of the sicknesses were recorded; the medicines taken, type of doctors consulted, the overall expenditures and those on health are known. The time to travel to the nearest hospital, doctor and paramedic facility were recorded; data on the type of toilet facility, primary source of water, access to electricity, etc. are available. The time spent by women on housework during the previous 4 months was recorded in each survey. Also, parental education and the wife's nutritional knowledge (measured through questions) are included in the data set. To minimize the potential dependence in errors affecting the children within a household, the data

Modeling the Health of Filipino Children

for the youngest child (in the age group 1-10 years) were retained. Thus there are four time observations on 312 children. 3. MODELLING DETERMINANTS OF CHILDREN'S NUTRITIONAL INTAKES The children's growth patterns and health are affected by genetic factors, nutritional intakes, how much time mothers spend on housework, sanitation and environmental and medical facilities. Food consumption decisions, however, are based on behavioural considerations and on the economic constraints faced by the households. The development of a model for the children's nutrient intakes is an important aspect of modelling health. Also, care by mothers in preparing food can increase the intake of essential nutrients such as ^-carotene (Sommer, 1986). The main staple foods in the Bukidnon region of the Philippines are corn and rice. The poorest households consume a greater proportion of corn since three crops can be grown locally during the year. The corn is husked and turned into grits and is consumed after boiling in water. Some salt is usually added to the cooked corn and, as the region is close to the sea, dried or fermented fish (Bangoong) is occasionally mixed. Also, vegetables are sometimes consumed with the corn depending on the season and prices. In contrast, the more wealthy households consume rice as the staple together with (Monggo) beans and the richest households regularly add vegetables, fish or meat. As in many countries, the diets in the Bukidnon region exhibit 'habit persistence' in that that food consumption patterns respond gradually to income or price changes. This phenomenon is recognized in the economics literature (e.g. Duesenberry (1949), Friedman (1957) and Gorman (1967)). The resulting models are dynamic; the previous intakes affect the current intakes and it is possible to distinguish between the short and long run effects of independent variables (Bhargava, 1991a). Since the households consume a large number of foods, an analysis of children's intakes of essential nutrients is useful for assessing the effect of income and other variables on health. The intakes relationship is presented within the model for child health in Section 5.1; the empirical results are discussed in Section 6.1. 4. MODELLING DETERMINANTS OF HEIGHTS, WEIGHTS AND MORBIDITY PATTERNS 4.1. Some Aspects of Production Functions Relevant for Child Health The notion of production functions is used in economics to express the maximum amount of a commodity that can be produced by using different input combinations. The inputs are usually entered in aggregate forms as capital and labour in the empirical specifications. The problems in viewing the relationships between nutrient intakes and health measures as 'health production functions' were originally discussed by Stigler (1945). Naturally, there are differences between the optimal use of inputs by firms and biological processes determining the ingestion of nutrients and the ultimate health. However, certain models of production that incorporate the features of the process are relevant for health. For example, Chenery (1949) modelled the engineering process of pipeline transportation and specified the technical details. Similarly, Johansen (1959, 1972) emphasized the 'fixed' nature of technology, once a plant has been constructed. Such formulations are useful for

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health; a child's height is fixed in the (24-hour) observation period and the degree to which weight or morbidity can change is constrained by biological factors. 4.2. Time Dimension of Child Health The children's health is continually affected by nutritional intakes and other variables. At any point in time, the precise effects of intakes may be evident only in blood assays. However, consistent deficiencies will eventually reduce growth and increase morbidity. A basic difficulty in modelling health is that one is explaining the dependent variable which summarizes the history of intakes and sicknesses by the realization of independent variables in specific time intervals. In this respect, health differs from the production of commodities where the lags between the use of inputs and the final output are amenable to statistical modelling; the lag structure for health components is very complex. The lag patterns in health could be better approximated if data were available on a large number of children over a long time span with the details of intakes, anthropometric variables and medical conditions recorded at short intervals. A longitudinal study of this type would be too expensive. Thus investigators are forced to rely on a few time observations separated by several months. The problem is exacerbated by large day-to-day variation in nutrient intakes (Liu et al., 1978). In spite of inadequacies in the data, the estimated relationships between health indicators and explanatory variables provide insights into the probable causes of the differences observed. Further, in a longitudinal setting, the distributions of indicators shift over time. The dynamic interrelationships between current and past measurements on health and their dependence on genuinely time varying explanatory variables are informative. The shortcomings of the data may be reduced by ordering the health components by using a time-dependent criterion. 4.3. Stages in Health and Their Determinants The height of a child reflects the history of nutritional intakes and sicknesses. The child's weight can be predicted from the height by using approximations for relative proportions of lean body mass and fat. The sickness spells reflect the inability of the body to cope with nutritional and other forms of stress. Thus morbidity depends on the nutritional status that is embodied in the height and weight variables. The environmental and sanitation factors affect sicknesses via the rapid transmission of bacterial diseases. The dynamic aspects of health can be modelled by viewing the health indicators height, weight and sickness spells as sequential stages of health. The term sequential underscores the degree to which the health components are fixed in the short run; the lags underlying the indicators become shorter as one proceeds in this sequence. This is in contrast with the production of commodities where processes are often disaggregated into stages over time. The three health components, however, are always measurable; it is appropriate to divide health into stages on the basis of the differential time effects of the independent variables. Thus children's heights are fixed in the survey period. The weight can respond to current intakes and morbidity levels. The sickness spells in the preceding fortnight are 'flow' variables that are influenced by the 'stock' of health (height and weight). Since the health

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indicators are affected by their previous levels, the models are assumed to be dynamic. The interrelationships between the health indicators are 'triangular' since height partly determines weight, and height and weight explain morbidity. It is appropriate to refer to such formulations as 'health functions' since they are broadly consistent with the analysis in the anthropometric literature (Tanner, 1986b). However, the anthropometric approach might require some modification since the current morbidity can lower a child's weight and height may depend on previous morbidity. The nutrient intakes are important determinants of health. The intakes of protein, calcium and iron are relevant for the height relationship; the energy and protein intakes are likely to affect weight. The /3-carotene and ascorbic acid intakes can improve the children's immune systems (Shils and Young, 1988). Lastly, genetic factors are likely to affect height and weight; morbidity is influenced by the hygiene and environmental conditions. 5. STATISTICAL FORMULATION OF MODEL FOR CHILD HEALTH 5.1. Model for Nutrient Intakes and Health Components The determinants of children's nutrient intakes and health indicators may be represented by a system of dynamic equations. Assuming that the parameters are identified and the number of children in the sample is large, the equations can be estimated by maximum likelihood for a fixed number T of time observations. However, it is necessary to assume that the initial observations on the dependent variable are correlated with the errors ('endogenous' variables). Otherwise, the estimated parameter will be inconsistent for small T (Anderson and Hsiao, 1981; Bhargava and Sargan, 1983). Denoting the children by suffix /' and survey rounds by t ( / = 1 , . . ., 312; t-2, 3, 4), the system is m

n

Hit = a0 + 2 IjZij + 2 q

I

Mit = c0 + 2

+ QxMit_x + uUt,

(1)

+ 62Hit + B3MU + w2,„

(2)

r

Wit - 6 o + X l VjZij + 2 j=i

PkXmt + ^Hit_x kkXikt + a2Wtt-i

k=\ P

KjZij + 2

HkXiu + <*3MY-I + 9AHh + d5Wit + u3it

(3)

and s

h

Nu = d0 + 2 jZij + 2 faxikt + ouAk-i + 66Hit + 6-jWi, + u4it. j=\

k=\

Here Hit, Wu, Mit and Nit are respectively the height, weight, an index of morbidity and the nutrient intakes for the fth child in the rth time period, z are time invariant variables including an overall constant term, x are time varying variables and include 'macro-variables' such as 0-1 indicators for the survey rounds. «„ are stochastic error terms with zero means and finite covariance matrices. The regression coefficients are denoted by Greek letters. The morbidity index Mit is defined by adding the duration of three sicknesses in

(4)

A. Bhargava

158 Household Variables

Children's Characteristics

Environmental Factors

Niacin

Beta Carotene A s c o r b i c Acid

Triangular System of Health Components

Nutritional Intakes

Fig. 1. Graphical representation of the empirical model for child health: bold arrows represent relationships between all the variables in boxes or circles; empty arrows represent the influence of specific variables on outcomes; shaded arrows show short-term feed-backs

the previous fortnight and taking a logistic transformation of the proportion of time for which a child is sick (with a continuity correction for extreme values; Cox (1970)). This index is in the spirit of Rand Corporation (1983) and Cox et al. (1992). It would have been preferable to assign higher weights to fever and diarrhoea than to cold, cough and headaches. However, the severity of diarrhoea is unknown though the incidence was low (about 3%). Also, the temperatures of sick children were not measured. Overall, the index seems a reasonable measure of intensity of the sicknesses. The empirical model is illustrated in Fig. 1. 5.2. Some Methodological Issues A child's height, weight and nutrient intakes are influenced by its age. This is also true of sicknesses that become less severe as the immune systems develop. Age is not strictly a time varying variable; the children's ages in subsequent periods are known. Instead, age in months at the first survey can be included as a time invariant variable in the model together with a set of (0-1) variables for survey rounds. This procedure will automatically remove the influence of age from the regressors. Second, the children's nutritional status is relevant for the morbidity and intakes relationships. Although height and weight can be introduced as separate regressors,

Modeling the Health of Filipino Children

159

their interrelationship suggests that it might be preferable to use a combination such as the ratio of weight to squared height (body mass index (BMI); Cole (1991)). A more general approach, encompassing the arguments of Cole (1991) and Kronmal (1993), would be to estimate the model without restricting the coefficients of height and weight. The validity of the BMI transformation can be tested by a likelihood ratio test. For example, if height and weight appear in logarithmic forms in equation (3), the null hypothesis is 04 + 205 = 0.

Third, it is important to investigate the potential correlation between regressors and the errors (endogeneity). Random effects are a common source of the problem; let the errors be given by uu = 5, + v„

(5)

where the 5s are individual specific random variables and the us are general random variables (distributed with zero means and finite variances). The 6s are correlated with the lagged dependent variables and possibly with some regressors. In a longitudinal setting, macro-variables (which are constant across individuals) and time invariant variables do not aid identification of the parameters; identification depends on the time varying variables ('instruments'). The estimation of models containing several endogenous regressors using inappropriate instruments may not afford valid inferences (see Cebu Study Team (1992)). The sources of endogeneity and the time sequence of household decisions can facilitate the classification of variables into the exogenous and endogenous categories. Fourth, the estimation of equations (l)-(4) by a maximum likelihood procedure requires a 'reduced form' for the initial observations: m

4

t\

y,\ = <*i + 2 hz-'j + YA 2 J fktX-M + um.

(6)

Similar equations are necessary for the time means of regressors that are correlated with the random effects. The ('exogeneity') hypothesis of zero correlation between «2 regressors and the random effects can be tested by a likelihood ratio test. Given T time observations, the test statistic is asymptotically distributed under the null hypothesis as a x 2 - var i a ble with Tn2 degrees of freedom. The random effects decomposition (5) can also be tested; the likelihood ratio statistic is distributed as a x2-variable with 7 X r + l ) / 2 - 2 degrees of freedom (see Bhargava and Sargan (1983) and Bhargava and Bouis (1992)). Fifth, in empirical work, exogeneity of regressors is tested before the validity of the random effects decomposition (5). This sequential approach is in the spirit of Wald (1947) and Anderson (1970). There seems little point in testing whether a model satisfies the random effects restrictions if the parameters are inconsistently estimated because of the failure of exogeneity assumptions. Sixth, the violation of the multivariate normality assumption for the errors does not affect the consistency of the maximum likelihood estimates under general conditions (Mann and Wald, 1943). The asymptotic variance-covariance matrix (AVM) of statistics involving the elements of the dispersion matrix Q depends on the third- and fourth-order moments of the actual errors (Hotelling, 1936). A robust

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A. Bhargava

version of the Wald (1943) statistic is used to test the random effects decomposition; the model is estimated by maximum likelihood assuming normality and without restricting £2. Alternative forms for fi can be tested with analytical expressions for the AVM of fl under misspecification of the distribution function (Bhargava, 1987). Lastly, the above procedures have performed well in previous studies using moderately large samples. Some of the shortcomings might be circumvented by invoking other simplifying assumptions (e.g. Gilks et al. (1993)). However, the endogeneity of the lagged dependent variables and some explanatory variables complicates the application of the Gibbs sampler to structural relationships. Overall, our aim is to develop a substantive model of child health incorporating the factors that are often analysed in isolation in different disciplines. 6. EMPIRICAL RESULTS FOR HEALTH OF FILIPINO CHILDREN 6.1. Estimated Models for Nutrient Intakes The maximum likelihood estimates of the parameters in equation (4) for intakes of dietary energy, protein, calcium, iron, ^-carotene, ascorbic acid, riboflavin, thiamine and niacin are presented in Table 1 (the derivation of such models is discussed in Bhargava (1991a, b). All variables are in natural logarithms (the zero intakes of ascorbic acid by some children were set equal to 1 before the logarithmic transformation). The regression coefficients measure the percentage change in the dependent variable resulting from a 1% change in an independent variable (short run elasticity). The initial observations (and the lagged dependent variables) are treated as variables that are correlated with the errors (endogenous). Firstly, the likelihood ratio test of the exogeneity null hypothesis for total expenditure, height and weight cannot reject the null hypothesis for the intakes; the remaining repressors are assumed to be exogenous in this test. The random effects decomposition is then tested by using likelihood ratio statistics reported in the next row of Table 1. Since the tests are sequential, the significance level is 2.5%. The tests do not reject the random effects formulation in the /3-carotene and thiamine relationships; the sample criterion for the iron intakes is slightly above the critical level 17.5. The simple random effects model is rejected for the remaining nutrients, possibly owing to the violation of the normality assumption. The next row reports robust Wald statistics that are more supportive of the simple random effects model (the degrees of freedom are smaller as the restrictions implied by initial observations are not included in this test). In view of the importance of between- and withinsubjects variation in nutritional studies, the constrained estimates are reported. Secondly, the between-subjects variances are small in comparison with the within-subjects variances of the intakes. This has been reported in previous studies using simple models that exclude explanatory variables (Nelson et al., 1989). The behavioural factors affecting the children's intakes are introduced in our empirical model; the regressors capture many aspects of the between-children differences. The between-subjects variances calculated from the fitted residuals are thus lower. It is interesting to note that the within-subjects variation remains high. This in part is due to the nutrient composition of foods. Another source of variation in the intakes of nutrients such as /3-carotene and ascorbic acid by children in developing countries is the seasonal fluctuation in the availability and prices of fruits and vegetables.

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Modeling the Health of Filipino Children

Maximum Parameter

Constant Age Mother's housework Total household expenditure Height Weight T3 T4 Lagged dependent variable 2 P a*1 X 2 d2) X2(8) X2(4) X 2 U)

TABLE 1 likelihood estimates of the nutrient intakes relationships for Filipino children "f Energy

Protein

Calcium

Iron

^-carotene Ascorbic Riboflavin acid

Thiamine

Niacin

2.104 (0.182) 0.009 (0.052) 0.029 (0.014) 0.080 (0.029)

-1.935 (0.180) O.024 (0.066) 0.042 (0.016) 0.132 (0.035)

0.892 (2.227) 0.026 (0.104) 0.011 (0.021) 0.228 (0.047)

-3.600 (1.858) 0.005 (0.086) 0.033 (0.017) 0.195 (0.039)

9.003 (0.501) -0.102 (0.081) -0.020 (0.034) 0.210 (0.045)

8.520 (5.936) 0.182 (0.282) -0.031 (0.056) 0.020 (0.123)

-5.553 (1.837) -0.082 (0.092) 0.017 (0.019) 0.243 (0.042)

-6.602 (2.378) -0.107 (0.109) 0.013 (0.023) 0.328 (0.051)

-3.603 (0.229) 0.001 (0.081) 0.027 (0.021) 0.359 (0.045)

0.674 (0.037) 0.250 (0.120) -0.044 (0.031) 0.062 (0.031) 0.100 (0.049)

0.889 (0.023) 0.097 (0.151) -0.050 (0.034) 0.132' (0.042) 0.091 (0.048)

0.393 (0.658) 0.359 (0.283) 0.024 (0.057) -0.001 (0.059) 0.133 (0.051)

0.758 (0.547) 0.248 (0.234) -0.009 (0.047) -0.005 (0.049) 0.133 (0.050)

-2.778 (0.106) 3.263 (0.468) -0.164 (0.122) -0.450 (0.130) 0.053 (0.048)

-2.816 (1.751) 2.271 (0.750) -0.160 (0.142) -0.505 (0.151) 0.096 (0.053)

0.619 (0.536) 0.357 (0.212) -0.120 (0.049) 0.025 (0.053) 0.131 (0.047)

0.728 (0.697) 0.516 (0.300) -0.101 (0.061) -0.032 (0.064) 0.096 (0.047)

0.700 (0.030) 0.249 (0.178) -0.032 (0.054) 0.088 (0.056) 0.082 (0.050)

0.119 (0.051) 0.181 1.22 25.39 17.08 33.35

0.131 (0.057) 0.239 5.13 30.41 12.93 26.25

0.063 (0.047) 0.451 9.63 40.60 16.85 13.78

0.049 (0.044) 0.320 7.09 18.24 8.35 26.21

0.134 (0.054) 4.216 9.79 12.36 7.64 6.94

0.120 (0.058) 2.916 8.30 24.60 11.30 4.66

0.074 (0.045) 0.344 8.07 34.28 11.60 16.83

0.040 (0.039) 0.528 6.52 15.13 4.31 17.04

0.094 (0.052) 0.438 5.45 23.64 7.05 8.18

T312 children in four time periods; all variables are in natural logarithms; asymptotic standard errors are in parentheses; age was measured in months, mother's housework as the number of days spent in the 4-month period; T3 and T4 are dummy variables for the third and fourth survey rounds; p2 is the (between/within)-variance ratio; a2 is the within-subjects variance; x2(12) is the likelihood ratio statistic for exogeneity of total household expenditure, height and weight; x2(8) is the likelihood ratio statistic for the random effects decomposition; x2(4) is the robust Wald statistic; x 2 (l) is the likelihood ratio statistic for the BMI restriction.

Thirdly, the likelihood ratio test for BMI transformation rejects the null hypothesis for all nutrients except ascorbic acid. Also, the intakes increase with height, and mother's housework in the 4-month period significantly increases the intakes of energy, protein and iron. The housework variable is insignificant in the @carotene and ascorbic acid relationships; the large within-subjects variation in the intakes of these nutrients is probably responsible for the poor fit. Fourthly, with the exception of ascorbic acid intakes, the expenditure (income) elasticities of nutrients are statistically significant. The elasticities of the vitamin B group are high, especially for the niacin intakes where the point estimate is 0.36. The phenomenon of poor households switching from corn to rice as the staple is apparent. From a health viewpoint, the bioavailability of nutrients is important. Since the elasticities of calcium and iron are respectively 0.23 and 0.20, there is evidence of improved child nutrition with increases in household incomes. Lastly, the estimated coefficients of the lagged dependent variables are small partly because the surveys are separated by 4-month intervals. Also, the intakes of

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/3-carotene and ascorbic acid are lower in the last time period (there are two dummy variables for the survey rounds since an overall constant term, is included and equation (6) for the initial observations has its own intercept term). If the intakes are low for an extended period, these variables might appear with significant (negative) coefficients in the morbidity relationship. We note that the parents' education, current morbidity and the child's sex were not significant in these models. 6.2. Estimated Relationships for Three Health Components 6.2.1. Results for height The maximum likelihood estimates of the parameters in the height relationship under alternative sets of exogeneity assumptions are presented in Table 2. First focusing on the model specification aspects, the results in the second column assume the protein and calcium intakes to be correlated with the random effects; these variables are treated as exogenous in the third column. The likelihood ratio statistic for the exogeneity null hypothesis is just about at the 2.5% significance level. The results in the two columns are similar so the test is not crucial. The likelihood ratio

Maximum

likelihood

Parameter

Constan t Age Father's height Mother's height Mother's housework Protein Calcium T3 T4 Lagged dependent variable X2(8)§ X2(8)§§ X 2 (l)*

TABLE 2 estimates for the height

relationship^

Nutrient intakes endogenous t

Nutrient intakes exogenous

0.126 (0.122) 0.030 (0.004) 0.063 (0.018) 0.067 (0.019) 0.0003 (0.0005) 0.001 (0.001) -0.0002 (0.0010) 0.005 (0.001) 0.0003 (0.0010) 0.813 (0.017) 17.67

0.120 (0.096) 0.020 (0.006) 0.050 (0.011) 0.044 (0.012) 0.002 (0.0006) 0.002 (0.001) 0.0013 (0.0010) 0.004 (0.003) 0.003 (0.001) 0.805 (0.024) 62.94 7.11

tSee the notes to Table 1. tThe intakes of protein and calcium are assumed to be correlated with the random effects. §Likelihood ratio statistic for the exogeneity of protein and calcium intakes. §§Likelihood ratio for the random effects decomposition. •Likelihood ratio statistic for the null hypothesis that the coefficients of parents' heights are the same.

Modeling the Health of Filipino Children

statistic for the simple random effects specification is far above its critical level and hence Wald tests were not pursued. Secondly, the heights of the parents are significant and the coefficients are close. The mother's height is usually the dominant variable but for children in the age group 1-10 years the length at birth seems less relevant. The likelihood ratio test for the equality of the coefficients of parents' heights rejects the null hypothesis (the estimates were similar under the equality restriction). Thirdly, the protein intakes are significant though the calcium intakes are not. Given the long lags underlying height, it is desirable to minimize the influence of the within-subjects variation in intakes. A possible procedure would be to treat the average intake in the four time periods as a time invariant variable. With the inclusion of indicator variables for the rounds, this is equivalent to assuming that (apart from the random effects) the intakes differ across rounds by a fixed amount. This assumption is quite stringent. Its use, however, led to improvements in the empirical results and both the protein and the calcium intakes were statistically significant. Lastly, the coefficient of the lagged dependent variable is high (0.81); the long run effects of explanatory variables are (in absolute terms) six times greater than the short run impact. The small coefficient for protein, for example, implies a relatively large equilibrium effect. 6.2.2. Results for weight Next, turning to the weight relationship (Table 3), the parents' heights and weights are introduced as separate regressors in the second column. The coefficients for father's height and weight are opposite in signs and the coefficient for mother's height is insignificant. The third column combines the father's height and weight as the BMI and drops mother's height from the model. The null hypothesis is not rejected; the sample criterion of the likelihood ratio statistic is 0.52 which is well below the (5%) critical level of a x 2 -variable with two degrees of freedom. A possible explanation of these results is that the father's BMI captures his current nutritional status and, to a certain extent, his 'productivity' (earnings capacity). The mother's past intakes are less relevant for predicting the child's current weight. Secondly, an increase in the mother's housework coefficient appears to increase children's weights, presumably through the preparation of food and improvements in hygiene. The energy and protein intakes are not significant in the two columns (there are no apparent energy deficiencies in the Bukidnon region; see Bhargava and Bouis (1992)). However, the protein intakes affect weight via their effects on height (Table 2). The index of current morbidity has a small negative coefficient which is significant. The coefficient of the lagged dependent variable is 0.74; the long run elasticities with respect to the explanatory variables are about 1.33 times the short run counterparts. Thirdly, the coefficient of height is 0.37 which is significant and is close to previous findings for children in similar age groups (Ehrenberg, 1968). The coefficient for age, however, is small and insignificant. Overall, the collinearity between age and height complicates the separation of the effects of height and age on weight. The measurement of children's arm circumference and skinfold thickness (reflecting lean body mass and fat respectively) would have been useful. Alternatively, we could

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A. Bhargava

Maximum

TABLE 3 likelihood estimates for the weight relationship t

Parameter

Constant Age Father's height Mother's height Father's weight Mother's weight Father's BMI Mother's housework Height Current morbidity Energy Protein T3 T4 Lagged dependent variable X2(2)§§ X2(8)*

Results with parents' height and weight %

Results with father's BMI and mother's weight §

-0.908 (0.149) 0.001 (0.008) -0.116 (0.011) 0.024 (0.017) 0.055 (0.016) 0.025 (0.013)

-0.832 (0.142) 0.001 (0.009)

— 0.003 (0.001) 0.373 (0.026) -0.006 (0.002) 0.007 (0.007) -0.002 (0.006) 0.015 (0.006) -0.021 (0.005) 0.736 (0.027) 0.52 56.30

0.027 (0.013) 0.055 (0.031) 0.003 (0.001) 0.374 (0.088) -0.006 (0.002) 0.007 (0.007) -0.002 (0.007) 0.015 (0.006) -0.002 (0.006) 0.736 (0.055) 56.71

tSee the notes to Table 1. JThe coefficients of the parents' heights and weights are assumed to be unrestricted. §Father's height and weight are combined as the BMI (weight/height2) and mother's height is dropped. §§Likelihood ratio statistic for the null hypothesis that the father's height and weight can be combined as the BMI and mother's height can be dropped. •Likelihood ratio statistic for the random effects decomposition.

replace height by an age-adjusted variable such as the 'Z-score' (Cole, 1990). This procedure may not significantly improve the results since age in months is an informative variable for predicting the height and weight of children in the age group 1-10 years. 6.2.3. Results for morbidity Table 4 presents the results for the index of morbidity assuming that the variancecovariance matrix of the errors is that implied by the simple random effects model; the constraints are not rejected at the 2.5% significance level by the likelihood ratio tests. The second column reports the results when height and weight are included

165

Modeling the Health of Filipino Children TABLE 4 Maximum likelihood estimates for the morbidity Parameter

Constant Age Open pit toilet Distance§§ Mother's housework Height Weight BMI /3-carotene T3 T4 Lagged dependent variable P2 a*2 X 2 (l)* X2(8)**

relationship^

Results with height and weight t

Results with BAf/§

-16.564 (3.880) -0.528 (0.172) 0.177 (0.089) 0.059 (0.017) 0.054 (0.037) 4.374 (1.142) -2.020 (0.474)

-15.642 (3.169) -0.462 (0.046) 0.174 (0.088) 0.060 (0.017) 0.055 (0.036)

—

-0.035 (0.019) -0.249 (0.100) -0.103 (0.102) 0.051 (0.046) 0.061 (0.043) 1.519 4.86 17.32

— — -2.069 (0.495) -0.034 (0.017) -0.239 (0.099) -0.089 (0.093) 0.045 (0.047) 0.067 (0.044) 1.517

—

16.47

tSee the notes to Table 1. tThe coefficients of children's height and weight are assumed to be unrestricted. §The height and weight are combined as the BMI (weight/height2). §§Average time of travel (in minutes) to the nearest hospital, paramedic facility and doctor. •Likelihood ratio statistic for combining the height and weight as the BMI. **Likelihood ratio statistic for the random effects decomposition.

as separate regressors; the BMI is used in the next column. The likelihood ratio statistic for the BMI transformation is 4.86; the null hypothesis is not rejected at the 2.5% significance level. It is interesting that the unrestricted coefficient for weight in the second column of Table 4 is about half the estimated coefficient for height (with the opposite sign). The data indicate that it is preferable to combine the children's height and weight as the BMI as opposed to weight divided by height. This is perhaps remarkable since James et al. (1988) have advocated the use of BMI for assessing chronic energy deficiencies. Also, the diseases in Bukidnon region are typically less serious than the water-borne diseases found in the urban regions of the Philippines. It is interesting to find in the present setting that children with BMI lower than the average for their age (in months) are sick more frequently. Secondly, the estimated coefficient of age is negative and significant indicating

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A. Bhargava

a decline in sicknesses with age. Also, morbidity is higher in households that rely on open pit toilets which probably increase the transmission of diseases. Thirdly, the time (in minutes) to travel to the nearest hospital, paramedic facility or doctor increases morbidity. Since areas far from medical facilities are sometimes overpopulated, a variable for population density was also included; it was found to be insignificant. Fourthly, the /3-carotene intakes appear with a significant negative coefficient. This was not true for the ascorbic acid intakes. Thus there is weak evidence that the consumption of fresh vegetables reduces children's sicknesses. In view of the seasonal fluctuations in prices, greater production of vegetables by land owning households is likely to be beneficial for the children's health. Fifthly, there do not appear to be significant between-children differences in the morbidity patterns. This may in part be due to the inclusion of the salient determinants of health in the model. However, a greater number of children in the sample might have reduced the standard error of the between-subjects variance. Lastly, the exogeneity null hypothesis for height, weight and the /3-carotene intakes is not rejected at the 5°7o level in the morbidity relationship (the statistic is not reported in Table 4). This is perhaps not surprising since the random effects are likely to reflect the sanitation and environmental facilities available to the households. 7. CONCLUSION A dynamic framework has been proposed to analyse the effects of behavioural and environmental factors on the health of Filipino children. Since the health components are differentially affected by nutritional intakes and other variables, a triangular system of equations for height, weight and morbidity spells was estimated. The inclusion of relatively fixed health components as regressors reduced some of the deficiencies inherent in health and nutrition data. From a policy viewpoint, increasing protein and /3-carotene intakes seem important for improving child health. This may be achieved by increasing household incomes or through food programmes for children from the poorest households; greater production of vegetables by land-owning households would be helpful. The time to travel to the nearest medical facility and open pit toilets increase morbidity. Within the information available on sicknesses, the BMI appears to be useful for identifying vulnerable children. In future work, we hope to extend the present framework to health indicators such as the children's head circumference and cognitive performance by using data from Egypt, Kenya and Mexico (United States Agency for International Development, 1990). ACKNOWLEDGEMENTS The author would like to thank H. Bouis, T. Cole, P. Reeds and J. Yu for their help and the faculty members of Nuffield College, Oxford, for useful discussions. This revision has benefited from the thoughtful criticisms of the two referees and R. Kronmal.

Modeling the Health of Filipino Children REFERENCES Anderson, T. W. (1970) The Statistical Analysis of Time Series. New York: Wiley. Anderson, T. W. and Hsiao, C. (1981) Estimation of dynamic models with error components. J. Am. Statist. Ass., 76, 598-606. Behrman, J . R . and Deolalikar, A. (1988) Health and nutrition. In Handbook of Development Economics (eds H. Chenery and T . N . Srinivasan), pp. 633-711. Amsterdam: North-Holland. Bhargava, A. (1987) Wald tests and systems of stochastic equations. Int. Econ. Rev., 28, 789-808. (1991a) Estimating short and long run income elasticities of foods and nutrients for rural south India. / . R. Statist. Soc. A, 154, 157-174. (1991b) Identification and panel data models with endogenous regressors. Rev. Econ. Stud., 58, 129-140. Bhargava, A. and Bouis, H. (1992) Maximum likelihood estimation of between and within variations in energy and protein intakes from infancy to adolescence for the Philippines. Statist. Med., 11, 533-545. Bhargava, A. and Sargan, J. D. (1983) Estimating dynamic random effects models from panel data covering short time periods. Econometrica, 51, 1635-1660. Bouis, H. and Haddad, L. (1990) Agriculture Commercialization, Nutrition and the Rural Poor: a Study of Philippine Farm Households. Boulder: Riener. Cebu Study Team (1992) A child health production function estimated from longitudinal data. J. Dev. Econ., 38, 323-351. Chenery, H. (1949) Engineering production functions. Q. J. Econ., 63, 507-531. Cole, T. J. (1988) Fitting smoothed centile curves to reference data (with discussion). J. R. Statist. Soc. A, 151, 385-418. (1990) The LMS method for constructing normalized growth standards. Eur. J. Clin. Nutr., 44, 45-60. (1991) Weight-stature indices to measure underweight, overweight, and obesity. In Anthropometric Assessment of Nutritional Status (ed. J. H. Himes), pp. 83-111. New York: Wiley-Liss. Cox, D. R. (1970) Analysis of Binary Data. London: Chapman and Hall. (1992) Causality: some statistical aspects. J. R. Statist. Soc. A, 155, 291-301. Cox, D. R., Fitzpatrick, R., Fletcher, A. E., Gore, S. M., Spiegelhalter, D. J. and Jones, D. R. (1992) Quality-of-life assessment: can we keep it simple (with discussion)? J. R. Statist. Soc. A, 155, 353-393. Duesenberry, J. S. (1949) Incomes, Savings, and the Theory of Consumer Behavior. Cambridge: Harvard University Press. Ehrenberg, A. S. C. (1968) The elements of lawlike relationships. / . R. Statist. Soc. A, 131, 280-302. Friedman, M. (1957) A Theory of the Consumption Function. Princeton: Princeton University Press. Gilks, W. R., Clayton, D. G., Spiegelhalter, D. J., Best, N. G., McNeil, A. J., Sharpies, L. D. and Kirby, A. J. (1993) Modelling complexity: applications of Gibbs sampling methods in medicine. / . R. Statist. Soc. B, 55, 39-52. Gorman, W. M. (1967) Tastes, habits and choices. Int. Econ. Rev., 8, 218-222. Hamill, P. V. V., Drizd, T. A., Johnson, C. L., Reed, R. B. and Roche, A. F. (1977) NCHS growth curves for children birth-18 years. In Vital and Health Statistics, ser. 11, no. 165. Washington DC: United States Government Printing Office. Hotelling, H. (1936) Relations between two sets of variates. Biometrika, 28, 321-377. International Food Policy Research Institute (1990) Research Report. International Food Policy Research Institute, Washington DC. James, W. P. T., Ferro-Luzzi, A. and Waterlow, J. C. (1988) Definition of chronic energy deficiencies in adults. Eur. J. Clin. Nutr., 42, 969-981. Johansen, L. (1959) Substitution versus fixed production coefficients in the theory of economic growth. Econometrica, 27, 157-176. (1972) Production Functions. Amsterdam: North-Holland. Kronmal, R. A. (1993) Spurious correlation and the fallacy of the ratio standard revisited. J. R. Statist. Soc. A, 156, 379-392. Liu, K., Stamler, J., Dyer, A., McKeever, J. and McKeever, P. (1978) Statistical methods to assess and minimise the role of intra-individual variability in obscuring the relationships between dietary lipids and serum cholesterol. J. Chron. Dis., 31, 399-418.

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A. Bhargava Mann, H. B. and Wald, A. (1943) On the statistical treatment of linear stochastic difference equations. Econometrica, 11, 173-220. Martorell, R. and Habicht, J.-P. (1986) Growth in early childhood in developing countries. In Human Growth (eds F. Falkner and J. M. Tanner), vol. 3, pp. 241-259. New York: Plenum. Mosley, W. H. and Chen, L. (1984) An analytical framework for the study of child survival in developing countries. Popln Dev. Rev., 10, suppl., 25-48. Nelson, M., Black, A. E., Morris, J. A. and Cole, T. J. (1989) Between-and-within subject variation in nutrient intake from infancy to old age: estimating the number of days to rank dietary intakes with desired precision. Am. J. Clin. Nutr., 50, 155-167. Rand Corporation (1983) Measurement of Physiologic Health for Children, vols 1-5. Santa Monica: Rand Corporation. Shils, M. E. and Young, V. R. (1988) Modern Nutrition in Health and Disease, 7th edn. Philadelphia: Lea and Febiger. Sommer, A. (1986) Nutritional Blindness. New York: Academic Press. Sommer, A. and Loewenstein, M. S. (1975) Nutritional status and mortality: a prospective validation of the QUAC stick. Am. J. Clin. Nutr., 28, 287-292. Stigler, G. J. (1945) The cost of subsistence. J. Farm Econ., 27, 303-314. Tanner, J. M. (1986a) Growth as a target seeking function. In Human Growth (eds F. Falkner and J. M. Tanner), vol. 1, pp. 167-179. New York: Plenum. (1986b) Use and abuse of growth standards. In Human Growth (eds F. Falkner and J. M. Tanner), vol. 3, pp. 95-108. New York: Plenum. Tanner, J. M., Whitehouse, R. H. and Takaishi, M. (1966) Standards from birth to maturity for height, weight, height velocity, and weight velocity. British children, 1965 — 1. Arch. Dis. Childhd, 41, 454-471. United States Agency for International Development (1990) Nutrition Collaborative Research Program: Annual Report. Washington DC: United States Agency for International Development. Wald, A. (1943) Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Am. Math. Soc, 54, 426-482. (1947) Sequential Analysis. New York: Dover Publications. Waterlow, J. C , Buzina, R., Keller, W., Lane, J. M., Nichaman, M. Z. and Tanner, J. M. (1977) The presentation and use of height and weight data for comparing the nutritional status of groups of children under the age of 10 years. Bull. Wrld Hlth Organizn, 55, 489-498.

Modeling the Effects of Nutritional and Socioeconomic Factors on the Growth and Morbidity of Kenyan School Children ALOKBHARGAVA* University of Houston,

Houston,

Texas

77204-55882

ABSTRACT This paper estimates dynamic models for the height, head circumference, weight, and morbidity of approximately 110 Kenyan school children (6-9 years) in a multivariate longitudinal data framework. Dynamic models allow anthropometric dimensions to depend on the respective measurements in the previous period. The system of 4 equations specified for height, head circumference, weight, and morbidity incorporates the interrelationships among these variables; explanatory variables in the model consist of nutritional, socioeconomic, demographic, and environmental factors. The model parameters are estimated using the principle of maximumlikelihood, while controlling for the unobserved between-children differences. The main findings are, first, that calcium intakes are positively associated with height while protein and energy intakes are associated with weight. Vitamin A intakes are negatively associated with morbidity. Second, socioeconomic status plus the cash income of the household is a significant predictor of height, head circumference, and morbidity. Third, maternal height is positively associated with children's height and maternal body mass index (BMI) is positively associated with children's weight. Fourth, parents' scores on psychological tests, mother's age, and children's hemoglobin concentration are negatively associated with morbidity while mothers' morbidity is positively associated with children's morbidity. Implications of the modeling results are discussed. Am. J. Hum. Biol. 11:317-326, 1999. © 1999 Wiley-Liss, Inc.

A large number of children in less developed countries are undernourished (FAO/ WHO, 1992). Undernutrition during the critical preschool years affects all dimensions of human development. For example, undernourished children face growth faltering early in life (Waterlow, 1994), are more likely to succumb to infections and disease (Scrimshaw et al., 1959; Mata, 1978), and typically grow into adults with a reduced physical working capacity (Spurr, 1983). Moreover, cognitive development is intertwined with physical growth; measures such as the body mass index (BMI) and head circumference are important predictors of cognitive abilities in populations such as in Kenya (Bhargava, 1998). The use of growth reference values for children in developed countries (Tanner et al., 1966; Cole, 1988, 1990) has facilitated identification of children at risk of mortality

©1999 Wiley-Liss, Inc.

in developing countries (Sommer and Loewenstein, 1975). Public policies such as those providing antenatal care and medical facilities at the time of delivery can enhance child survival. Diets of surviving children, however, often do not meet the children's energy needs. More frequently, the diets are inadequate in protein and micronutrients essential for growth (Scrimshaw, 1994). Further, the problem of poor diet quality is compounded by loss of important nutrients during illnesses related to poor sanitation and environmental conditions. In such circumstances, the design of public policies is

Contract grant sponsor: Research Committee of the World Bank. Correspondence to: Alok Bhargava, Department of Economics, University of Houston, Houston, TX 77204-5882. E-mail: [email protected] Received 3 September 1997; Revision received 13 March 1998; Accepted 18 March 1998

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A. Bhargava been born within the previous 10 months. Thus, 292 households were eligible; the study design was approved by an appropriate H u m a n Subjects Committee. There were approximately 110 children in the sample for whom longitudinal data, comprising of 3 observations separated by 3month intervals, were available.

complex; for i n t e r v e n t i o n s to be costeffective, a knowledge of the proximate determinants of growth and morbidity is essential. From a policy standpoint, it would be useful to investigate the effects of nutritional intakes on growth and morbidity in a broad framework. The analysis should incorporate the inter-relationships between anthropometric indicators and the role of various nutrients in maintaining health should be reflected in the statistical models (Allen, 1993). For example, weight is influenced by height because height approximates skeletal size (Ehrenberg, 1968; Cole, 1988; Tanner, 1986). To quantify the effects of energy and protein intakes on weight, the model should include height as an explanatory variable. This is important because empirical associations are sensitive to the exclusion of relevant explanatory variables. Furthermore, since weight changes slowly over time, the weight in the previous period is an important predictor of current weight, i.e., the model for weight should be a dynamic one. Longitudinal data from the Embu region of Kenya afford an opportunity to investigate in a dynamic framework the associations between anthropometric and morbidity variables of school children and the underlying nutritional, familial, demographic, socioeconomic, and environmental factors. The longitudinal analysis also controls for unobserved between-children differences. The empirical results could be useful in identifying specific nutritional, socioeconomic, and environmental factors that play an important role in sustaining growth and health status.

Children's nutritional intakes The children's intakes of 40 nutrients were estimated by averaging food intake data available for two consecutive days each month. On the day of the interview, food intakes during the past 24 hours were assessed by the 24-hour recall method; food intakes were recorded for the interview day and some of the food portions were weighed. The intakes were then converted into nutrient intakes using food composition tables for Kenya (Murphy et al., 1991). Laboratory analyses of certain indigenous recipes were conducted to assess the validity of the tabulated food conversion factors. Three data points were created for nutrient intakes; the time interval between data points was three months. Thus, each of the three-time observations was calculated by averaging six food records, i.e., two food records per month during the three-month period. The separation of data points by three months was motivated by t h e fact t h a t many socioeconomic and health variables were available approximately at threemonth intervals. The three-month interval also provides a more complete picture of the children's sicknesses. Lastly, averaging has the desirable effect of reducing within subject variation in nutrient intake data (Liu et al., 1978; Nelson et al., 1989).

MATERIALS AND METHODS Subjects The data are derived from surveys sponsored by the U.S. Agency for International Development in 1984—85 in the Embu region of Kenya (USAID, 1992). Of the 2,059 households in the region, households were selected to participate in the study if there was a toddler (approximately 18 months old) or a school aged child (6-9 years) present; households were also included if the lead female in the household was pregnant but had not completed the first trimester. A household was ineligible if the lead female was over 40 years old, or her last pregnancy occurred over 5 years ago, or if a child had

Morbidity index Sicknesses of children were recorded weekly during the observation period. Typically, mothers reported illnesses and the data were verified by medical personnel. Reliability of the data was good; there was 95% agreement between different enumerators about the nature of illnesses for a subset of children (Neumann et al., 1991). The length of time for which a child was sick with conditions such as lower or upper respiratory infections, fever, diarrhea, eye or ear infections, etc., were recorded; illnesses were typically classified as "mild", though in a few instances, they were classified as "severe". The number of days for which a child

Growth and Morbidity of Kenyan School Children was sick with different symptoms in the three-month interval were added to form an index of morbidity (Eand Corporation, 1983; Bhargava, 1994); the number of days sick was doubled if the illness was "severe". While the morbidity index assigns equal weights to different sicknesses, the duration and intensity of illnesses were reflected in the different values assumed by the index at the three data points. Anthropometry and hematology

Height, weight, arm and head circumferences, and skinfold thicknesses (triceps, biceps, and subscapular) were taken on each child on a monthly basis; electronic scales were used to measure weight. Two independent measurements were taken on the anthropometric variables. Correlations between the measurements were greater than 0.95; thus only the first set was used. Monthly measurements were averaged to produce figures corresponding to the three data points used in the longitudinal analysis. Blood analyses measured hemoglobin concentration, white blood cells, etc. Typically, one observation was available for hemoglobin concentration during the sample period. Thus variables such as hemoglobin concentration were treated as time invariant explanatory variables in the longitudinal analysis. Parental anthropometry, morbidity, and hematology

Body weight of parents was recorded on a monthly basis; height was measured once during the observation period. The monthly measurements were averaged to produce figures for the three-month intervals. Thus, parental weight was a time varying explanatory variable in the models whereas height was a time invariant variable. Episodes of sicknesses in mothers were recorded weekly; an index of female morbidity, similar to the one for children, was constructed from the sickness records. Sicknesses were recorded roughly at monthly intervals for fathers; an index of morbidity was also constructed for the fathers. Hemoglobin concentration of the parents was measured at least once during the observation period.

Socioeconomic, demographic, and sanitation variables

Observations on parental age, education, earnings, etc., were linked with the data for children. The adults took a revised version of the Weschler Adult Intelligence Scale and the Ravens Progressive Matrices (Ravens, 1965). The scores on psychological tests are useful measures of functional abilities. Socioeconomic status (SES) of the household was assessed by adding the number of household possessions. Cash income received by the head of the household was recorded on a scale from 1-5. SES and cash income were combined to form an index that reflected household possessions and current earnings; the index assumed different values at the three data points. The data set contained detailed demographic information on household members. Relationship of each member to the head of the household was recorded. Reproductive history of the mothers was investigated. Ages of all children in the household were in the data set; pregnancy status of women was recorded every three months during the observation period. Sanitation and hygiene practices of the household were assessed in the survey. Source of drinking water was recorded; water was tested for bacterial contamination for a small proportion of the households. The type of toilet facility used was recorded. Overall, the data contained information on over 300 variables for approximately 110 children at three data points t h a t were separated by three-month intervals. Because observations were missing on different variables for different children, the models estimated for height, head circumference, weight, and morbidity of the children used complete data on the maximum number of children in the sample. Thus, there were minor differences in the number of observations used to compute maximumlikelihood estimates of the parameters in the models for the four health indicators; sample sizes ranged from 92-109. A multi-disciplinary framework for modeling the health indicators

A n t h r o p o m e t r i c dimensions s u c h as height, head circumference, and weight, and sicknesses emphasize different dimensions of child health. For example, height is gradually influenced by the history of nutri-

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A. Bhargava

ent intakes and infections. By contrast, weight responds more quickly to changes in dietary intakes and is a suitable indicator of the medium-term nutritional status. Similarly, the duration and intensity of sicknesses is informative in a short time frame, though capacity of children to resist disease is likely to depend on their long-term nutritional status (Mata, 1978; Adair et al., 1993; Scrimshaw, 1996). Nutritional intakes are likely to differentially affect anthropometric and sickness indicators. For example, calcium intakes are likely to be important for linear growth; energy and protein intakes would influence body weight. Moreover, deficiency of nutrients, such as protein, iron, and zinc, in the diet may adversely affect brain development (Pollitt et al., 1993; Scrimshaw, 1993). While brain mass cannot be measured easily, head circumference increases with brain size (Dobbing et al., 1968; Tanner, 1989). Head circumference is a proxy for brain development in undernourished populations. At a given point in time, anthropometric dimensions may be viewed as indicating the children's "stock" of health; morbidity is a "flow" variable since intensity of sickness can vary on the same day (Bhargava, 1994). For example, if a child consumes inadequate food on a particular day, then the child's height would not be affected, arm circumference would not change noticeably, body weight can change somewhat, and morbidity can assume very different values. Thus, anthropometric dimensions and morbidity are interdependent processes and some of these variables are "fixed" in relation to others. For example, a model explaining weight should include height and arm circumference as explanatory variables to approximate, respectively, skeletal size, and lean tissue mass. The model should be dynamic since the child's weight in the previous time period will affect current weight; unobserved between-children differences should also be taken into account. The empirical model for health indicators Assuming that N children are observed in three survey rounds, the inter-dependent system for height (HT), head circumference (HD), weight (W), and the morbidity index (M) is given by dynamic equations (l)-(4) (i = 1, ..., N; t = 2,3):

HT it = 2

z

HDit = 2

z

ij •Yj + 2

j=i

x

j=i

ij Kj + 2

j=i

j=i

«t £j + « i HT it _! + u l i t

Xyt M-j + a 2

HD

it-i

+ Xx HT it + u 2 i t m3 W

it = 2

(2)

n3 Z

H j + 2

X

ijt ^j + «3 W it _!

+ k2 HT it + \ 3 AM it + X4 M it + u 3 i t (3) m4 M

it = 2

j=l

n4 Z

tj TJ + 2

j=l

^jt Vj + <*4 M it~l

+ \ 5 H T i t + \ 6 W i t + u4it.

(4)

The z's and x's are, respectively, time invariant and time varying explanatory variables; z's could be background variables such as parents' heights while nutrient intakes t h a t vary over time are included in the x's. AM is arm circumference; coefficients of regressors are denoted by Greek letters. Econometric procedure Because the number of time observations is small, statistical estimation theory assumes that the number of children (N) is large but the number of time observations is fixed. Thus, initial observations on the dependent variables were treated as endogenous variables (correlated with the errors, Bhargava et al., 1983). The errors on equations (l)-(4) were assumed independent across children, but correlated over time with a positive definite variance-covariance matrix. The random effects decomposition for the u's is a special case. For example: Ulit = 8; + V U t

(5)

where 8's are children specific random effects and v's are independently distributed random variables (Laird et al., 1982). The joint determination of anthropometric and morbidity indicators implies t h a t certain regressors are potentially correlated with the error terms; unobserved factors affecting such variables could be related to the random effects. It is necessary to test the exogeneity of some regressors and estimate

Growth and Morbidity of Kenyan School Children equations in the presence of endogenous variables. This can be achieved by rewriting the dynamic model in a simultaneous equations framework, i.e., by defining a "reduced form" for the initial observations and a system of (T-l) "structural" equations for remaining time periods (Bhargava et al., 1983): m

T Z

Yil = 2

j=0

T

ij £j + X 2

j=l k=l

^ k Xijk + U n

(i=l,...,N) B

Y'+

Cz

(6) Z' + C x

X'

(T-l)xT TxN (T-l)x(m+l) (m+l)xN (T-l)xnT nTxN

= U' . (T-l)xN

Here, Y, Z, and X are, respectively, matrices containing observations on the dependent, time invariant and time varying variables. B is a (T-l)xT lower triangular matrix of coefficients: By = a, B; i + 1 = - 1 , By = 0 otherwise, ( i = 1,. . . ' , T - l ; j = 1.....T). The matrices C z and C x contain coefficients of time invariant and time varying regressors, respectively. U contains the error terms. Details of the maximum-likelihood estimation method are presented elsewhere (Bhargava et al., 1983). It should be noted that the profile log-likelihood function is optimized using a numerical scheme and the asymptotic standard errors of the parameters are obtained by approximating second derivatives of the function at the maximum. The exogeneity hypothesis of zero correlation between n 2 time varying regressors (x2) and the random effects can be tested by a likelihood ratio test. Given three repeated observations on the children, the statistic is asymptomatically distributed under t h e null hypothesis as a Chi-square variable with (3n2) degrees of freedom. RESULTS Descriptive statistics Sample means of selected variables in the Kenyan longitudinal data are reported in Table 1. With the exception of age, hemoglobin concentration, and household size,

173

TABLE 1. Sample means (standard deviations) of selected variables in the Kenyan longitudinal data1 Time period 1 83.12 (5.36) 8.24 Household size, n (2.33) 121.17 Hemoglobin, g/L (12.76) Height, cm 114.50 (5.89) Head circumference, 50.73 cm (1.52) Weight, kg 24.00 (6.26) Morbidity index 35.82 (49.48) Energy intake* Kcal 1530.46 (326.25) Protein intake, g 45.79 (11.03) Calcium intake, mg 240.23 (90.21) Iron intake, mg 15.39 (4.03) Vitamin A intake, 455.33 (igRE (283.06) SES+ Cash income 2.58 index (0.69) Sample size 102 x There are 59 boys and 43 girls in this Variable Age, months

Time period 2

Time period 3

115.97 117.48 (5.86) (5.64) 50.90 50.93 (1.32) (1-34) 25.36 26.52 (7.13) (6.44) 25.93 19.61 (32.21) (29.48) 1339.88 1403.11 (321.73) (269.33) 35.48 43.70 (11.08) (9.65) 182.41 243.27 (65.07) (76.09) 12.66 14.68 (3.75) (3.16) 381.08 631.63 (265.58) (304.72) 2.45 2.49 (0.62) (0.67) 102 102 longitudinal sample.

means are separately reported for the three time periods. Sample means for time period two show a drop in nutrient intakes; observations in this interval correspond to the period when households in the Embu region faced food shortages caused by a drought (Cohen et al., 1987). Means were also calculated separately for 59 boys and 43 girls; the statistics did not reveal significant sex differences and are not reported. Height Table 2 presents maximum-likelihood estimates of the dynamic model for height. The variables were transformed into natural logarithms to reduce heteroscedasticity (Nelson et al., 1989); the reported coefficients are the short run elasticities (percentage change in the dependent variable resulting from 1% change in an explanatory variable). Absolute values of the t-statistics are reported in parentheses below the estimated coefficients. The coefficients significant at 5% and 10% levels are, respectively, marked with asterisk and plus signs. Because height changes gradually over time, one would expect the coefficient of the

A. Bhargava

174 TABLE

2. Maximum-likelihood estimates for height1

Variable/Parameter Constant Sex Maternal height No. of Children < 16 yrs SES+ Cash Income Morbidity Calcium Lagged dependent variable Chi-square (6)4'6 Sample Size

of the

model

Estimated coefficients2,3 0.314* (26.17) -0.001 (0.50) 0.019t (9.50) -0.006* (2.00) 0.007* (2.33) -0.001 (1.00)

o.ooit

(1.700) 0.917* (45850.00) 7.69 109

Estimated coefficients are the short run elasticities, and absolute values of asymptotic t-statistics are in parentheses. 2 *P < 0.05. 3 t P < 0.10. 4 Chi-square (6) is the likelihood ratio test statistic for the exogeneity of calcium intakes and morbidity in the model. 5 The random effects specification has a more complex structure than that given in the text [equation (5)].

lagged dependent variable to be large in this model. The point estimate 0.92 (P < 0.05) implies that the long run elasticity of height with respect to an explanatory variable is about 12 times greater than the short run estimate reported in Table 2. The between/ within variance ratio is not reported because errors affecting height have a more complex structure than the simple random effects specification given in equation (5). In addition to the random effects, familial factors are captured in the model for height by including parental heights; paternal height was not significant and was subsequently dropped from the model. The indicator variable for the child's sex is not significant. Both socioeconomic indicators are significant (P < 0.05). Thus, long-term nutritional status appears to be adversely affected by poverty and a large number of children in the household. Calcium intakes are significantly (P < 0.10) associated with height. However, protein and iron intakes are not significant. Linear growth of children in over-crowded households can be reduced by sicknesses. However, the coefficient of morbidity is not significant (previous morbidity was also not significant). The exogeneity hypothesis for calcium intakes and morbidity is accepted using the likelihood ratio test. This could be due to many

TABLE

3. Maximum-likelihood estimates for head circumference1

of the

model

Estimated coefficients2 0.752* (368.86) Sex 0.008* (2.65) Paternal head circumference 0.155* (571.39) Maternal head circumference 0.145* (430.76) SES+ Cash Income 0.008* (2.04) Height 0.066* (67.62) Lagged dependent variable 0.421* (789.12) 4 5 Chi-square (3) 2.91 Sample Size 94 Estimated coefficients are the short run elasticities, and absoVariable/Parameter Constant

lute values of asymptotic t-statistics are in parentheses. 2 *P < 0.05. 4 Chi-square (3) is the likelihood ratio test statistic for the exogeneity of height. 5 The random effects specification has a more complex structure than that given in the text [equation (5)].

reasons including the fact t h a t the confidence intervals for the likelihood ratio statistics are wide. Head circumference The results for head circumference in Table 3 show strong familial effects; coefficients of parental head circumference are large and significant (P < 0.05). This suggests that brain size probably has a familial component which, in undernourished populations, is the likely result of poverty and micronutrient deficiencies persisting for generations. Boys tend to have larger head circumferences than girls and the coefficient of height is significant (P < 0.05). The estimated coefficient of the lagged dependent variable (0.42) is approximately half t h e corresponding e s t i m a t e in t h e height relationship (Table 2). While errors in measuring head circumference may be greater than those in measuring height (Gould, 1981), the long-run elasticities of height appear to be considerably larger than the corresponding elasticities for head circumference. Body weight The results for weight are reported in Table 4. Specifications 1 and 2 treat the protein/energy ratio, height, arm circumference, and morbidity as, respectively, exog-

Growth and Morbidity of Kenyan School Children

TABLE

4. Maximum-likelihood

Variable/Parameter Constant Paternal body mass index (Paternal body mass index) 2 Maternal body mass index SES+ Cash Income (SES+ Cash Income)2 Protein/Energy Ratio Height Arm Circumference Morbidity Lagged dependent variable Chi-square (12)4'5 Sample Size

estimates

of the model for

175 weight1

Estimated coefficients2,3 Specification 1 Specification 2 -5.958* -4.095* (62.14) (83.57) -0.004* -0.056* (4.00) (3.50) 0.003* — (3.00) 0.096* 0.106* (5.64) (6.63) 0.023 0.017 (0.66) (0.32) -0.022 -0.008 (1.05) (0.28) 0.049* 0.062* (9.80) (5.17) 1.416f 1.074* (236.0) (153.43) 0.606* 0.562* (25.25) (455.17) -0.002 -0.004* (1.00) (2.00) 0.149* 0.161* (4.14) (7.67) 23.25t 25.06* 103 103

1 The estimated coefficients are short run elasticities, and absolute values of asymptotic tstatistics are in parentheses. 2 *P < 0.05. 3 t P < 0.10. 4 Chi-square (12) statistic tests the exogeneity of protein/energy ratio, height, arm circumference and morbidity. In Specification 2, this null hypothesis is rejected and these variables are treated as endogenous. 5 The simple random effects specification is rejected in this model.

enous and endogenous variables. While maternal BMI has a positive coefficient in Specification 1, paternal BMI appears with a negative sign. In Specification 2, the relationship between weight and paternal BMI is seen to be a non-linear (quadratic) one. Similarly, weight is a quadratic function of the SES plus cash income though the coefficients are not significant. These results reveal certain aspects of non-linearities underlying the medium-term nutritional stat u s of t h e children. The e s t i m a t e s of threshold points, however, would be imprecise because of the modest number of children in the sample. Including energy and protein intakes separately into the model produced a negative coefficient for energy intake; a likelihood ratio test accepted the null hypothesis that these variables can be combined as the protein/energy ratio. In developing countries, the ratio of protein to energy intakes is an indicator of diet quality (Bhargava et al., 1995). Because height is an explanatory variable in the model for weight, one may

conclude that Kenyan children consuming better diets are heavier. Height and arm circumference are estimated with large and significant coefficients (P < 0.05). Although height is widely used in anthropometric research to explain weight (Ehrenberg, 1968; Tanner, 1986; Cole, 1991), arm circumference is an important variable because it approximates lean body mass. While restrictions on food intake would have immediate effects on body fat, the effects on arm circumference would be smaller, at least in the short run. Thus, in comparison with a low BMI, a small arm circumference indicates that the child h a s suffered nutritional deprivation for a longer period (James et al., 1994). Current morbidity is seen to be negatively associated with weight (P < 0.05) in Table 4. The coefficient of weight in the previous period is smaller than the respective coefficients estimated in the height and head circumference relationships. Note that skinfold thicknesses were not a significant predictor in the model for body weight.

A. Bhargava

176 TABLE

5. Maximum-likelihood for morbidity

estimates index1

Variable/Parameter

Constant Hemoglobin Maternal age Paternal score on cognitive tests Maternal score on cognitive tests No latrine SES+ Cash Income (SES+ Cash Income)2 Vitamin A Maternal morbidity BMI Lagged dependent variable (Between/Within) Variance 4 Within variance Chi-square (9)6 Sample Size

of the

model

Estimated coefficients 2 , 3

21.554* (122.47) -0.594* (16.97) -0.924* (16.21) -0.219* (4.87) -0.835* (23.19) 1.599t (1.70) -3.284* (15.42) 2.415* (14.56) -0.240* (8.57) 0.238* (4.33) -2.673* (46.09) 0.075 (0.95) 0.151 (1.10) 1.395 5.22 102

l Estimated coefficients are the short run elasticities, and absolute values of asymptotic t-statistics are in parentheses. 2 *P < 0.05. 3 t P < 0.10. 4 Random effects specification is accepted. 5 Chi-square (9) tests the exogeneity of vitamin A intakes, maternal morbidity, and BMI.

Morbidity index Table 5 presents the estimates for the morbidity index. Parental scores on psychological tests are significant predictors of morbidity of children (P < 0.05). The coefficient of the maternal score is four times greater (in absolute value) than the estimate for the father. Also, the age of the mother is negatively associated (P < 0.05) with morbidity. Because mothers are primarily responsible for child care, their knowledge and day to day experiences appear to enhance the health of children. Nutrition plays an important role in the model explaining morbidity; vitamin A intakes are negatively associated (P < 0.05) with morbidity. While iron intake is not significant, hemoglobin concentration has a large significant coefficient (P < 0.05). In this population, iron intakes may not be approximating the serum iron levels because absorption of iron is diminished by short-

falls in ascorbic acid intakes, adverse impact of intestinal parasites, increased requirement during periods of rapid growth, etc. While drawing blood from children to measure plasma level of vital nutrients is invasive and can lower participation rates, blood analyses are specially useful when the bio-availability of nutrients is poor. Children in households with no latrine facilities suffer from greater sicknesses (P < 0.05). There is also a slight decline in morbidity in households t h a t have access to piped water. Unfortunately, the data on water contamination were available only for a few households; the parameter estimates for this case are not included in Table 5. Maternal morbidity is positively associated (P < 0.05) with the sickness in children, which might be due to less time available for care. Also, bacterial diseases can be transmitted through family members. Paternal morbidity, however, is not a significant predictor of child morbidity. It is likely that paternal morbidity results in less time available for productive activities, i.e., father's morbidity lowers the household income. The empirical relationship between children's morbidity and SES and cash income is quadratic; both terms are significant (P < 0.05). Children's BMI is significant (P < 0.05) and indicates that children with good medium-term nutritional status are sick less frequently. However, this causation could run in the opposite direction, especially in the long run. While the likelihood ratio test for exogeneity of vitamin A intakes, maternal morbidity, and the BMI accepts the null hypothesis, certain alternative specifications were also estimated. For example, current BMI was replaced by lagged BMI in one of the specifications. This, however, raised further issues relating to the model specification aspects. For instance, a model containing current height and lagged weight as separate regressors was preferable to the specification where both height and weight were lagged one period. While the coefficients of height and weight were dependent on the model specified for the morbidity relationship, the results for other variables were largely unaffected. Coefficient of the lagged dependent variable and between/within variance ratio are not significant. Overall, sicknesses appear to be associated mainly with environmental factors; the capacity of children to resist infection seems to depend on their nutritional

Growth and Morbidity of Kenyan School Children status and on the ability of parents to recognize the mechanisms spreading disease. DISCUSSION An empirical model for health indicators of Kenyan school children was developed. The model incorporates the inter-relationships between height, head circumference, weight, and morbidity; the resulting specification is consistent with the anthropometric assessment literature. The effects of various nutrients on health indicators postulated in the nutrition literature were explored. Because the data contain detailed information on the parents and the household, the multidisciplinary analysis controlled for many confounding factors that are often analyzed in different disciplines. The empirical associations indicate the importance of a high quality diet. Heights were positively associated with calcium intakes, the ratio of protein to energy intakes was a predictor of weight, and vitamin A intakes and hemoglobin concentration were negatively associated with morbidity. Moreover, the indicator variable for poor sanitation (no latrine) was positively associated with morbidity in children; home environment, reflected in parental scores on psychological tests, was negatively associated with morbidity. From a policy perspective, the availability of skilled labor is an essential ingredient of economic development. Also, skill acquisition is a cumulative process requiring longterm investments. Because the cognitive development of children was influenced by their anthropometric dimensions, morbidity and the school environment (Bhargava, 1998), it is important for policy makers to formulate policies that simultaneously address issues of nutrition, health, and education. For example, the benefits from food supplementation programs are likely to be magnified by concomitant investments in the educational infrastructure. Moreover, policies improving sanitation facilities would prevent nutrient loss due to infections thereby raising the efficacy of food supplementation programs. In the long run, comprehensive policies that enhance children's health status and facilitate skill formation in developing countries are likely to be cost-effective.

ACKNOWLEDGMENTS This research was supported by the Research Committee of the World Bank. While retaining the responsibility for the views in the paper, the author thanks Martin Ravallion, Nevin Scrimshaw, Marian Sigman, two reviewers, and the Editor for helpful comments. LITERATURE CITED Adair L, Popkin BM, VanDerslice J, Akin J, Guilkey D, Black R, Briscoe J, Flieger W. 1993. Growth dynamics in the first year of life. Eur J Clin Nutr 47:42-51. Allen LH. 1993. Nutritional influences on linear growth: a general review. Eur J Clin Nutr 48:S75S89. Bhargava A. 1994. Modelling the health of Filipino children. J R Statist Soc A 157:417-432. Bhargava A. 1998. A dynamic model for the cognitive development of Kenyan schoolchildren. J Ed Psychol 90:162-166. Bhargava A, Reeds PJ. 1995. Requirements for what? Is the measurement of energy expenditure a sufficient estimate of energy needs? J Nutr 125:1358-1362. Bhargava A, Sargan JD. 1983. Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51:1635-1660. Cohen JM, Lewis DB. 1987. Role of government in combating food shortages: lessons from Kenya 1984—85. In: Glantz M, editor. Drought and hunger in Africa. Cambridge: Cambridge University Press, p 269-296. Cole TJ. 1988. Fitting smooth centile curves to reference data (with discussion). J R Statist Soc A 151:385-418. Cole TJ. 1990. The LMS method for constructing normalized growth standards. Eur J Clin Nutr 44:45-60. Cole TJ. 1991. Weight-stature indices to measure underweight, overweight, and obesity. In: Himes JH, editor. Anthropometric assessment of nutritional status. New York: Wiley-Liss. p 83-111. DobbingJ. 1968. Effects of experimental undernutrition on development of the nervous system. In: Scrimshaw NS, editor. Malnutrition, learning and behavior. Cambridge: MIT Press, p 181-202. Ehrenberg ASC. 1968. The elements of a lawlike relationship. J R Statist Soc A 131:280-302. Espinosa MP, Sigman MD, Neumann CG, Bwibo NO, McDonald MA. 1992. Playground behaviors of schoolage children in relation to nutrition, schooling, and family characteristics. Dev Psychol 28:1188-1195. FAO/WHO. 1992. Nutrition and development. A global assessment. Rome: Food and Agriculture Organization. Gould SJ. 1981. The mismeasure of man. New York: Norton. Guzman M. 1968. Impaired physical growth and maturation in malnourished children. In: Scrimshaw NS, editor. Malnutrition, learning and behavior. Cambridge: MIT Press, p 42-54. James WPT, Mascie-Taylor GCN, Norgan NG, Bistrian BR, Shetty PS, Ferro-Luzzi A. 1994. The value of arm circumference measurements in assessing chronic energy deficiency in third world adults. Eur J Clin Nutr 48:883-894.

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Laird N, Ware J. 1982. Random effects models for longitudinal data. Biometrics 38:963-974. Liu K, Dyer J, McKeever J, McKeever P. 1978. Statistical methods to assess and minimize the role of intraindividual variability in obscuring the relationship between dietary lipids and serum cholesterol. J Chron Dis 31:399-418. Mata L. 1978. Children of Santa Maria Cauque. Cambridge: MIT Press. Monckeberg F. 1975. Effects of malnutrition on physical growth and brain development. In: Prescott JW, Read MS, Coursin D, editors. Brain function and malnutrition: neurophysiological method of assessment. New York: John Wiley, p 15-52. Murphy PM, Weinberg-Anderson SW, Neumann C, Mulligan K, Calloway DH. 1991. Development of research nutrient data bases: an example using food consumed in rural Kenya. J Food Composit Anal 4:217. Nelson M, Black AE, Morris JA, Cole TJ. 1989. Between-and-within subject variation in nutrient intake from infancy to old age: estimating the number of days to rank dietary intakes with desired precision. Am J Clin Nutr 50:155-167. Neumann C, McDonald MA, Sigman M, Bwibo N, Marquandt M. 1991. Relationships between morbidity and development in mildly to moderately malnourished Kenyan toddlers. Pediatrics 88:93-942. Pollitt E, Gorman KS, Engle PL, Martorell R, Rivera J. 1993. Early supplementary feeding and cognition. Mon Soc Res Child Develop 58 (serial number 235), no. 7. Rand Corporation. 1983. Measurement of physiologic health for children, Vol 1-5. Santa Monica, CA: Rand Corporation. Ravens JC. 1965. The coloured progressive matrices test. London: Lewis. Scrimshaw NS. 1993. Early supplemental feeding and cognition: a retrospective comment. In: Pollitt E, Gorman KS, Engle PL, Martorell R, Rivera J, editors.

Early supplementary feeding and cognition. Mon Soc Res Child Develop 58 (serial number 235), no. 7. p 111-115. Scrimshaw NS. 1994. Malnutrition, brain development, learning and behavior. Mimeographed: United Nations University, Tokyo. Scrimshaw NS. 1996. Nutrition and health from womb to tomb. Nutr Today 31:55-67. Scrimshaw NS, Taylor CE, Gordon JE. 1959. Interactions of nutrition and infection. Am J Med Sci 237:367-403. Sigman M, Neumann C, Jansen AAJ, Bwibo N. 1989. Cognitive abilities of Kenyan children in relation to nutrition, family characteristics, and education. Child Dev 60:1463-1474. Sommer A, Loewenstein MS. 1975. Nutritional status and mortality: a prospective validation of the QUAC stick. Am J Clin Nutr 28:287-292. Spurr GB. 1983. Nutritional status and physical work capacity. Yrbk Phys Anthropol 1-35. Tanner JM. 1986. Use and abuse of growth standards. In: Falkner F, Tanner JM, editors. Human growth. Vol 3. New York: Plenum, p 95-108. Tanner JM. 1989. Foetus into Man. Cambridge: Harvard University Press. Tanner JM, Whitehouse RH, Takaishi M. 1966. Standards from birth to maturity for height, weight, height velocity, and weight velocity. British children 1965-1. Arch Dis Child 41:454-471. USAID. 1992. Functional implications of malnutrition. Kenya project, final report. Washington: United States Agency for International Development. Waterlow JC. 1994. Causes and mechanisms of linear growth retardation (stunting). Eur J Clin Nutr 48:S1S4. Youdim MBH, Ben-Shachar D, Yehuda S. 1989. Putative biological mechanisms of the effects of iron deficiency on brain biochemistry and behavior. Am J Clin Nutr 50:607-617.

AMERICAN JOURNAL OF HUMAN BIOLOGY 15:209-219 (2003)

Coliforms in the Water and Hemoglobin Concentration Are Predictors of Gastrointestinal Morbidity of Bangladeshi Children Ages 1-10 Years ALOK BHARGAVA, 1 * H O W A R T H E . B O U I S , 2 KELLY HALLMAN, 3 AND BILQIS A. H O Q U E 4 1 Department of Economics, University of Houston, Houston, Texas 77204, USA 2 International Food Policy Research Institute, Washington, DC 20006, USA Population Council, New York, New York 10017, USA 4 Environmental and Population Research Centre, Dhaka, Bangladesh

ABSTRACT The presence of pathogens in the water and children's poor nutritional status are likely to increase morbidity in developing countries. Understanding the interactions between the environmental and nutritional factors is important from the standpoint of improving child health. In this study, we analyzed the effects of fecal and total coliforms in the water available at the source and that stored in the household on the spells of gastrointestinal morbidity of 99 Bangladeshi children at three time points in an 8-month period. Fecal and total coliforms in the stored water were significant predictors (P < 0.05) of morbidity that was modeled using dynamic random effects models. Moreover, children with better hemoglobin status experienced lower morbidity. An empirical model for the proximate determinants of hemoglobin concentration showed significant negative associations between children's hookworm loads and hemoglobin. While the children's intakes of bioavailable iron, iron from meat, fish, and poultry, and iron from animal sources were not significant predictors of hemoglobin status in this population, the need for broader interventions for improving child health was apparent. Am. J. Hum. Biol. 15:209-219, 2003.

O 2003 Wiley-Liss, Inc.

Water-borne diseases are widely prevalent in less-developed countries, where the water available at the source and that stored in the household are often contaminated by various pathogens (Mintz et al., 2001). Improper disposal of fecal matter exacerbates water contamination levels and unhygienic practices such as handling water with unclean hands increase pathogens in the stored water. Furthermore, the diets of children are frequently deficient in micronutrients such as iron and vitamins A and C, which are important for the functioning of the immune system (Scrimshaw and SanGiovanni, 1997). While nutritional deficiencies are likely to gradually depress the immune system, the effects of water-borne diseases are evident in episodes of diarrhea, dysentery, and other illnesses such as cholera and typhoid that are a major cause of child mortality. By contrast, the effects of iron deficiencies are apparent in low hemoglobin (Hb) and ferritin concentrations. It is recognized by researchers that iron deficiencies and anemia adversely affect several dimensions of children's health and intellectual development (UNICEF/WHO, 1999; Lozoff, 1988). While testing water for certain diseasecausing pathogens is complicated by their

2003 Wiley-Liss, Inc.

short survival time, quantitative measures based on fecal and other coliforms are useful indicators of water contamination. Moreover, contact with animal and human waste increases the exposure to geohelminths such as hookworms that thrive on blood, thereby contributing to anemia. Because iron status depends on the intake of bioavailable iron that is found in high proportions in expensive foods such as animal products, it is important to jointly investigate the factors affecting child health for the formulation of cost-effective policies. In particular, it is important to quantify the extent to which strategies such as reducing water contamination and anthelmintic Abbreviations: AA, ascorbic acid; BMI, body mass index; CT, correction term; EF, enhancing factors; FeBIO, bioavailable iron; FeMFP, iron from meat, fish, and poultry; FeTOT, total iron; Hb, hemoglobin; MFP, meat, fish, and poultry; PHY, phytate. Contract grant sponsors: Neys van Hoogstraten Foundation, the U.S. Agency for International Development. Correspondence to: Alok Bhargava, Department of Economics, University of Houston, Houston, TX 772045019. E-mail: [email protected] Received 6 August 2002; Revision recieved 13 November 2002; Accepted 20 November 2002 Published online in Wiley InterScience (www. interscience. wiley.com). DOI: 10.1002/ajhb. 10141

180

A. Bhargava et al. treatment can enhance child health. Improvements in diet quality should no doubt be the long-term goal of food policies in developing countries. Previous analyses of diarrheal morbidity among children in developing countries have investigated the effects of fecal and other coliforms in water (Feachem et al., 1978; Tomkins et al., 1978; Van Derslice and Briscoe, 1995; Moe et al., 1998). While Van Derslice and Briscoe (1995) emphasized contamination of the water at the source, Moe et al. (1998) underscored the presence of pathogens in stored water and in the food consumed. These analyses, however, did not take into account measures of children's nutritional status such as Hb concentration that is often an indicator of resistance to diseases (Chandra et al., 1977; Bhargava, 1999). Anemia is likely to reduce the bactericidal capacity and blood T-cells, thereby increasing susceptibility to infections (Keusch, 1991; Kuvibidila et al., 1993). With reductions in energy deficiencies in many developing countries, addressing protein and iron deficiencies merits higher priority. Thus, for example, Bhargava et al. (2001) explained the Hb concentration of Bangladeshi women by the intakes of bioavailable iron, anthropometric indicators, and other variables. However, information on intestinal parasites was not available in the data. In a study of Tanzanian school children, Bhargava et al. (submitted) found that hookworm and schistosomiasis loads were negatively associated with Hb status, although dietary intakes were not measured in the study. Analyses of data investigating the effects of water contamination, Hb concentration, nutrient intakes, and intestinal parasitical loads on children's health status are likely to provide useful policy insights. In this study, we analyzed longitudinal data on 99 Bangladeshi children ages 1-10 years at three time points. Children's gastrointestinal morbidity covered the spells and duration of seven symptoms, i.e. diarrhea, dysentery, vomiting, stomachache, typhoid, cholera, and acidity (indigestion) in the previous 1 month. Water samples from the source and from the storage container were analyzed for fecal and total coliforms, as defined in American Public Health Association (1992). Children's Hb concentration was measured in the three survey rounds. Dietary intakes were assessed using the 24-hour recall method for four meals; we

were able to calculate the hioavailable iron intake, taking into account the enhancers and inhibitors of iron absorption. Children's stool was tested for intestinal parasites such as hookworm, ascaris, etc. The elaborate information allowed estimation of dynamic random effects models for morbidity spells. Dynamic models were also estimated for children's Hb status to investigate the effects of hookworm loads and hioavailable iron intakes on Hb status. MATERIALS AND METHODS Subjects The study was conducted in 10 villages in Saturia Thana, Manikgonj Province, Bangladesh with the primary purpose to investigate the nutritional impact of adoption of improved vegetables. Because new technologies were introduced through nongovernmental organization programs, selection of households was done in a complex manner to ensure that the selected households were representative. Initially, there were 330 households, of which 17 did not participate in all three survey rounds. Due to the costs of testing the water for coliforms and stool for intestinal parasites, water at the source and in the storage pot was tested for approximately 67% of the households in all three rounds. However, a comparison of the households in the sample with representative surveys for Bangladesh (Rahman et al., 1996) indicated that our households were representative of rural Bangladesh. The study design was approved in 1999 by a Human Subjects Committee of the Bangladesh Medical Research Council in Dhaka. The surveys began in June, 1999, and the third survey round was completed by May, 2000. Because observations on nutritional, anthropometric, and other variables were missing for some of the children age 1-10 years in one or more survey rounds, the models for morbidity and Hb status were estimated using complete data on 99 children in the three survey rounds. Economic, demographic, and morbidity variables The surveys compiled background information on household members such as their age, occupation, and education. Detailed information was gathered in the

Gastrointestinal Morbidity of Bangladeshi Children three survey rounds on economic variables such as household assets, incomes, food and nonfood expenditures, and wages; a variable was constructed for the average per capita monthly expenditures. In the three survey rounds the mothers were questioned regarding the occurrence and duration of seven symptoms in the previous 1 month—diarrhea, dysentery, vomiting, stomachache, acidity, typhoid, and cholera; up to three episodes per subject were recorded. An index of morbidity was constructed on the basis of this information (Rand Corp., 1983) by calculating the length of period for which the child was sick with up to three of the seven symptoms in (up to) three episodes of morbidity during each survey round. Thus, the morbidity index reflected the intensity and duration of gastrointestinal sicknesses in the previous month and was expected to be more informative than, for example, a dichotomous variable indicating whether a child had diarrhea. Anthropometry and hematology

Children's weight and height were measured in each survey round. Spring scales were used to measure weight in light clothing, accurate to 0.25 kg. An adjustable wooden measuring board was used to measure height to the nearest 0.1 cm with the child standing in upright position. The Hb status was measured in the three survey rounds; a finger-tip sample of capillary blood was obtained by a physician and analyzed immediately using a portable photometer (HemoCue, Mission Viejo, CA). All children received a free supply of iron tablets for 30 days at the end of the study. Tests for coliform colonies in the water and for intestinal parasites in the stool

Water samples were taken from the source and from the storage container. At the source, water was collected from running water after 10 minutes of pumping; the storage containers were shaken gently before taking the water samples. The samples were collected in the morning in sterilized bottles that were transported using insulated boxes packed with ice the same afternoon to a laboratory in Dhaka. Approximately 7% of the samples were collected in duplicate. The water samples were tested using the membrane filtration method that estimated the number of coliform colonies present using the guidelines in

American Public Health Association (1992). The first m-Endo media (DIFCO, Germany) was added to the water sample from the source and from the storage container in Petri dishes to estimate the colonies of total coliforms. For the source water, 100 ml was filtered using an electric vacuum pump; 50 ml of water was filtered for the stored water. The Petri dishes were placed the same evening in an incubator for 24 hours at 35° C. A xlO magnification was used to determine microbial density. Water samples from the source and the storage container were also poured in Petri dishes to test for fecal coliforms using the m-FC media (DIFCO, Germany). The water samples filtered from the source and stored water were, respectively, 200 ml and 5 ml for these tests. The Petri dishes were placed in the second incubator for 24 hours at 45° C. Following the 24-hour incubation period, the colonies of fecal coliforms were counted. All Petri dishes containing the coliform colonies were placed in an autoclave to kill the pathogens prior to disposal. The children's stool samples were collected using sterilized plastic containers and tested for hookworm and other infections such as Ascaris lumbricoides and Trichuris trichiura. For hookworm, slides for stool samples were prepared by the Kato-Katz technique using plastic templates, following the guidelines in World Health Organization (1991). A cellophane piece that had been soaked overnight in glycerol/malachite solution was placed on top of the sample. The slide was left for 7-10 minutes at room temperature before reading under a microscope. Hookworm eggs were counted and expressed as eggs per gram of stool (epg). Similarly, epg were estimated for other parasite species. All infected children were offered free treatment against the species with which they were infected. Nutritional intakes and bioavailable iron

In all three survey rounds, food intakes were measured using the 24-hour recall method for the four meals consumed, i.e., breakfast, lunch, dinner, and snacks. Because most children did not consume snacks, the data on snacks were aggregated with the intakes at lunch. The intakes of 40 nutrients at each meal were estimated using the food composition database of Calloway et al. (1994). For estimating the bioavailable

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iron taking into account nutrient interactions at each meal, the algorithms of Monsen et al. (1978), Monsen and Balintfy (1982), and Tseng et al. (1997) were extended (Bhargava et al., 2001). In the equations that follow, iron intake from meat, fish, and poultry is denoted by FeMFP, the total iron intake by FeTOT and the bioavailable iron by FeBIO. Heme iron was assumed to constitute 40% of FeMFP (Monsen et al., 1978). Using the notation of Monsen and Balintfy (1982), let the enhancing factor (EF) for a meal be given by: EF = (M + F + P) + AA

(1)

where M, F, and P are, respectively, the edible quantities of meat, fish, and poultry in grams and AA is the intake of ascorbic acid in mg. If EF > 75, then EF was assumed to be 75. To take account of the inhibitory effects of phytates, Tseng et al. (1987) calculated the "correction term" CT (0 < CT < 1) that gives the proportion of FeBIO. We used a modification of the algorithm of Tseng et al. (1997) (Bhargava et al, 2001). Let PHY be the total phytate intake in mg during the meal calculated using the food composition database of Calloway et al. (1994). Then, for PHY > 2.88 mg, CT was defined by C T = 1 0 [ - ° ' 2 8 6 9 1 ° S I O ( P H Y ) + 01295]

(2)

where logi0 is logarithm to the base 10. Assuming that children's body iron stores were 0, 250, and 500 mg, the bioavailable iron (FeBIO) can be calculated, respectively, from the following three equations: FeBIO (0) = 0.140 FeMFP + [5 + 26.804 log n {(EF + 100)/100}] CT x [FeTOT -0.4FeMFP]/100 (3) FeBIO (250) = 0.112FeMFP + [4 + 14.296 log n {(EF + 100)/100}] CT x [FeTOT - 0.4FeMFP]/100 (4) FeBIO (500) = 0.092 FeMFP + [3 + 8.93 log n {(EF+100)/100}]CTx [FeTOT - 0.4FeMFP]/100 (5) where logn is natural logarithm. Note that the inhibitory effects of phytate intake in Eqs. (3-5) assumed body iron stores of 500 mg.

Empirical model for the proximate determinants of children's gastrointestinal morbidity The presence of pathogens in the water is likely to cause sicknesses such as diarrhea, stomachache, and vomiting. More serious illnesses such as cholera and typhoid are caused by pathogens that typically do not survive for long periods in water. Thus, quantitative measures for fecal and total coliform colonies provide useful information on water contamination. Moreover, recovery from gastrointestinal illnesses is likely to be influenced by the purity of water consumed during convalescence; water contamination can increase the duration of sicknesses. Also, children's food intakes in the illness period are likely to be reduced due to anorexia and infections are likely to contribute to poor absorption of nutrients (Chen and Scrimshaw, 1983). The vicious cycle of malnutrition and infection has been emphasized in the nutritional literature (Scrimshaw et al., 1959, 1968; Esrey et al., 1988) and should be reflected in empirical models for child morbidity. The contamination of water at the source is likely to affect all households utilizing the source. By contrast, further contamination of the stored water would depend on hygiene practices in the household. While Briscoe and Van Derslice (1993) argued that household members may develop immunity from familial contamination, the biological underpinnings of such a process would be complex. Moreover, young malnourished children may be at greater risk of illnesses because of lower immunity to infections. The relative impact of coliforms can be investigated by including quantitative measures for fecal and total coliforms in water samples from the source and from the stored water as explanatory variables in the models for child morbidity. At a given point in time, children's morbidity is likely to be influenced by their nutritional status that can be approximated by weight, height, Hb concentration, and nutrient intakes. Weight reflects the history of energy imbalances and is likely to be lowered by illnesses that reduce dietary intakes and increase protein loss. Height of a child reflects the quality of diet since height is influenced by the long-term intakes of protein, calcium, and zinc that are present in more nutritious foods. While current morbidity can lower weight, the effects of

Gastrointestinal Morbidity of Bangladeshi Children sicknesses on future linear growth are likely to be very gradual. It would therefore seem inappropriate to combine height and weight as the BMI in a model explaining child morbidity (Kronmal, 1993). Instead, one can test if the data support the transformation of weight and height as BMI (Bhargava, 1994). Children's iron status can be approximated by their Hb concentrations; ferritin concentrations typically increase in response to infections (Kuvibidila et al., 1994; Bhargava et al., submitted). Lastly, the model should take into account the between-children differences due to unobserved differences in the environmental, nutritional, and other factors. Denoting the i t h child's morbidity by an index M it (i = 1,2,... ,n; t = 2,3), we postulated the model (Model 1) for Bangladeshi children: Mit = a0 (Constant) + ai(Age) it + a2(Age)ft + a 3 (Height)it + a4(Hemoglobin)it + a 5 (Weighty + a$ (Fecal coliforms in source) it + a7 (Fecal coliforms in storage) it + a 8 (M) i t _ 1 + u i t (6) where a 0 ,... ,as are the regression coefficients, u it is an error term (see Eq. (7), below), and M i t _! is the previous measurement on the morbidity index ("lagged dependent variable"), with coefficient a8. The fecal coliform colonies in the water from the source and that stored in the household were replaced by the respective numbers of colonies of total coliforms in an alternative version of Model 1. The quadratic relationship between children's age and morbidity was a flexible formulation in view of the likely increases in resistance to diseases with age and the increased exposure to contaminated food and water. The error term u i t affecting Model 1 in Eq. (6) can be decomposed in a random effects fashion as: Uit = 5; + Vit

(7)

where the 8's are children-specific random effects and v's are independently distributed random variables. Lastly, because gastrointestinal morbidity can also affect body weight, the possible correlation between weight and the children specific random effects (§;) in Eq. (6) was tested by a likelihood ratio test.

Also, the intakes of vitamins A and C and an indicator variable for the child's sex were included as explanatory variables in Eq. (6). Empirical model for the proximate determinants of children's hemoglobin concentration The children's Hb concentration is often a useful indicator of iron status and has been found to be negatively associated with child morbidity in the analysis of data from developing countries (Chandra et al., 1977; Bhargava, 1999). Factors such as the intake of bioavailable iron and parasitical loads are likely to affect the Hb status. However, there are uncertainties in the estimates of bioavailable iron because the algorithms were based on data on well-nourished populations. It would therefore be of interest to estimate alternative versions of the model for children's Hb status by replacing the bioavailable iron intake by the iron intake from meat, fish, and poultry or by the iron intake from all animal sources. This is important in small studies using nutritional data compiled by the 24-hour recall method that exhibits high within-subject variability (Nelson et al., 1989). The potential differences in children's Hb status due to genetic factors (Garner et al., 2000) can be partially accounted for in the model by including random effects, as in Eq. (7). The empirical model (Model 2) for children's Hb status can be written as: Hbit = bo (Constant) + bi(Age) it + D2(Hookworm)it + b3 (Bioavailable iron) it + b 4 (Height) it + b 5 (Hb) i t _ 1 +u 2 i t (8) The intake of bioavailable iron in Model 2 was replaced by FeMFP and by the iron for all animal sources in two alternative versions of Model 2. Note that children's weight was dropped from Model 2 because it was not a significant predictor in any of the specifications; height (or height-for-age) was likely to better reflect diet quality. Also, it was conceivable that children's gastrointestinal morbidity in the previous month could lower the current Hb concentrations, i.e., the association between Hb and morbidity in Model 1 may be due to reverse causation. This issue was investigated by including

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morbidity as an explanatory variable in Eq. (8) and testing if its coefficient was statistically different from zero. Statistical and econometric procedures For computing descriptive statistics such as the sample means and standard deviations, the software package SPSS (Chicago, IL) was used. Because there were only three time observations available on the children, statistical estimation was based on the assumptions that the number of children (n) was large but the number of survey rounds was fixed. Thus, initial observations on the dependent variables (morbidity and Hb) were treated as endogenous variables (correlated with the errors; Bhargava and Sargan, 1983). The errors in Eqs. (6) and (8) were assumed independent across children but correlated over time with a positive definite variance-covariance matrix. The random effects decomposition for the u's in Eq. (7) was a special case of this model. The joint determination of the three observations on morbidity (or Hb) implied that econometric techniques used for simultaneous equations were likely to be useful. Details of the maximum likelihood estimation method are presented in Bhargava and Sargan (1983). Here, we note that the profile log-likelihood functions of the models in Eqs. (6) and (8) were optimized using a numerical scheme (E04 JBF) from Numerical Algorithm Group (1989); asymptotic standard errors of the parameters were obtained by approximating second derivatives of the function at the maximum. The maximized values of the logarithm of the likelihood function were used to test hypotheses regarding the coefficients of the variables included in the models for children's morbidity and Hb status. RESULTS Descriptive statistics The sample means of selected variables in three survey rounds for 99 Bangladeshi children in the age group 1-10 years are presented in Table 1. The mean number of fecal coliform colonies in the water from the source was in the neighborhood of 12 per 100 ml of water in the three survey rounds. By contrast, the average colonies of fecal coliforms in the stored water in

the three survey rounds were 38, 64, and 174, respectively. The average total coliform colonies in the water from the source in the three survey rounds were 39, 26, and 43, respectively. The corresponding means for total coliform colonies in the stored water in the three survey rounds were 93, 142, and 455, respectively. These tabulations indicate the importance of hygiene in handling the stored water. Moreover, Survey round 3 coincided with a dry spell where the water was stored for long periods and hence was highly contaminated. The average levels of Hb were below the cutoff point 120 g/L for anemia (Khusun et al., 1999); approximately 75% of the children were anemic. The mean hookworm eggs per gram of stool in the three survey rounds were 101, 158, and 128, respectively. Approximately 40% of the children were infected with hookworm, although only 10% had hookworm loads greater than 400 eggs per gram of stool that would be regarded as heavy infections. In Table 1 the bioavailable iron intake were estimated under alternative assumptions that the children's body stores of iron were 0, 250, and 500 mg; the computations incorporated the effects of enhancers and inhibitors of iron absorption and also where only the enhancers were accounted for. For example, the minimum and maximum values of bioavailable iron intakes in the presence of enhancers and inhibitors and assuming zero body iron stores in Survey round 1 were 0.03 mg and 0.53 mg, respectively. The maximum values were close to the requirements of bioavailable iron for children in these age groups (FAO/WHO, 1988, table 5.4), thereby indicating that there was sufficient variation in the intakes data. Further, the bioavailable iron intakes were critically dependent on the assumptions regarding body iron stores and on the corrections for phytate intakes that assumed 500 mg of body iron stores. Because some of these assumptions may not be appropriate for undernourished populations, Table 1 also reports the intake of FeMFP and iron intake from all animal sources. The FeMFP and iron intake from all animal sources were closer to the intakes of bioavailable iron when both the enhancers and inhibitors of iron absorption were taken into account. Lastly, the average child was sick for 1 day with one of the seven gastrointestinal symptoms in the previous 30 days.

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TABLE 1. Sample means and standard deviations of selected variables for Bangladeshi children in three survey rounds* Survey round 1 n = 99 Age, y Sex, 0-l(Male = 1) Height, m Weight, kg Hemoglobin, g/L Hookworm, eggs per g stool Fecal coliforms at source, colonies per 100 ml Fecal coliforms in stored, colonies per 100 ml Total coliforms at source, colonies per 100 ml Total coliforms in stored, colonies per 100 ml Morbidity index, score Fe (from meat, fish and poultry), mg/d Fe (animal sources), mg/d Fe (bioavailable: enhancers + inhibitors; zero body Fe stores), mg/d Fe (bioavailable: enhancers; zero body Fe stores), mg/d Fe (bioavailable: enhancers + inhibitors; 250 mg body Fe stores), mg/d Fe (bioavailable: enhancers; 250 mg body Fe stores), mg/d Fe (bioavailable: enhancers + inhibitors; 500 mg body Fe stores), mg/d Fe (bioavailable: enhancers; 500 mg body Fe stores), mg/d Per capita monthly expenditure, Taka

6.56 ± 2.15 0.39 1.071 ± 1.35 15.64 ± 4.04 115.3 ± 10.8 100.7 ± 172.4 12.58 ± 30.51 38.25 ± 56.86 38.54 ± 64.14 92.83 ± 117.02 0.49 ± 1.51 0.08 ± 0.22 0.18 ± 0.33

Survey round 2 Survey round 3 n = 99 n = 99

1.08 16.20 111.4 158.1 13.94 64.43 26.34 142.33 1.29 0.13 0.21

± ± ± ± ± ± ± ± ± ± ±

1.34 1.11 ± 1.32 4.21 16.92 ± 4.21 12.7 114.5 ± 11.5 268.7 128.2 ± 226.9 41.43 11.09 ± 19.79 72.68 174.05 ± 220.21 64.64 43.32 ± 55.51 126.53 454.76 ± 523.19 5.01 1.13 ± 4.46 0.16 0.11 ± 0.18 0.33 0.23 ± 0.24

0.12 ± 0.09 0.50 ± 0.42

0.09 ± 0.05 0.38 ± 0.24

0.13 ± 0.08 0.58 ± 0.40

0.08 ± 0.06 0.34 ± 0.26

0.07 ± 0.03 0.27 ± 0.16

0.09 ± 0.05 0.39 ± 0.25

0.06 ± 0.04 0.24 ± 0.17 636 ± 277

0.05 ± 0.03 0.19 ± 0.11 643 ± 586

0.07 ± 0.04 0.28 ± 0.17 907 ± 1053

*Values are means ± standard deviations.

Results from the model explaining Bangladeshi children's gastrointestinal morbidity by demographic, nutritional, and environmental variables The results from estimating Model 1 given in Eq. (6) for children's morbidity are presented in Table 2. The results are presented for the two cases where the fecal coliform colonies in the water from the source and in the stored water were included, and where the total coliform colonies replaced the respective fecal coliform colonies. The children's age, height, weight, and hemoglobin were transformed into natural logarithms; the coliforms were also transformed into natural logarithms, with the zero values being set to unity, i.e., the logarithm of the number of coliform colonies in uncontaminated water was zero. The logarithmic transformation reduced internal variation in the data (Nelson et al., 1989). Moreover, the estimated coefficients of the variables expressed in logarithms can be converted to the short-run "elasticities" (percentage change in the dependent variable resulting from a 1% change in an independent variable) by dividing the respective coefficients by the average score on the index of morbidity. The long run elasticity with

respect to an explanatory variable can be obtained by dividing the short run elasticity by (l-a 8 ), where a8 is the coefficient of morbidity in the previous period. The results in Table 2 for the two specifications using fecal and total coliforms as explanatory variables were similar. First considering the results from Model 1 with fecal coliforms, both age and age-squared were significant predictors of gastrointestinal morbidity (P < 0.05); the duration and intensity of sicknesses for children in our sample declined with age, although at a decreasing rate. The children's Hb status was an important predictor of morbidity, i.e., anemic children were likely to have more episodes of gastrointestinal illnesses and stayed sick for a longer duration. Children's height was not a significant predictor of morbidity but weight was a significant predictor, indicating that children that were lighter for their age were sick more frequently. The fecal coliforms in the water from the source were not significantly associated with gastrointestinal morbidity. By contrast, the fecal coliforms in the stored water were a significant predictor of morbidity (P < 0.05). These findings support the descriptive statistics in Table 1, where the stored water was

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A. Bhargava et al. Table 2, indicating that the between-children differences were uncorrelated with children's weight. Note that the intakes of Vitamin A and C and an indicator variable for the child's sex were not significantly associated with morbidity in this population.

heavily contaminated and are discussed further in the Discussion. The estimated coefficient of morbidity in the previous period ("lagged depended variable") was negative, indicating cyclical fluctuations in morbidity, presumably due to seasonal factors and the acquired immunity to various illnesses. The between to within variance ratio was statistically significant, indicating that some of the unobserved between-children differences in child morbidity were not accounted for by the explanatory variables. The results in the second column of Table 2 for Model 1 with total coliforms replacing the fecal coliforms were similar. The main differences were that height was also significantly negatively associated with morbidity in the model with total coliforms. Thus, both height and weight were significantly negatively associated with morbidity, showing the inappropriateness of combining these variables as the BMI. The difference between the maximized values of the loglikelihood functions for Model 1 with fecal and total coliforms was small; the version of the model with total coliforms as explanatory variables had a slightly higher value of the log-likelihood function. The null hypothesis of exogeneity of body weight was accepted in both versions of Model 1 in

Results from the models explaining Bangladeshi children's Hb status by demographic, health, and nutritional variables Table 3 presents the results for Model 2 for children's Hb concentration explained by the intakes of bioavailable iron, FeMFP, or iron from all animal sources, together with other variables. Children's age was not a significant predictor of Hb status in all three versions of the model. By contrast, hookworm eggs per gram of stool were significantly negatively associated with Hb status in all specifications (P < 0.05). The intakes of bioavailable iron, FeMFP, and iron intake from all animal sources were not significant predictors of Hb status. This was presumably due to the modest number of children in the sample and is discussed in the Discussion. The children's height was a significant predictor of Hb status in the first two

TABLE 2. Maximum likelihood estimates of dynamic random effects model for Bangladesh children's gastrointestinal morbidity in the 3 survey rounds explained by demographic, anthropometric, nutritional, and environmental variables*Dependent variable: Morbidity index n == 99 Model 1: Explained by fecal coliforms Coefficient

Independent variable Constant Age, y Age-squared, y Hemoglobin, g/L Height, m Fecal coliforms at source, colonies per Fecal coliforms in stored, colonies per Total coliforms at source, colonies per Total coliforms in stored, colonies per Weight, kg Lagged dependent variable, score Between/within variance Within variance Chi-square statistic, 0 df = 3 2(maximized log-likelihood function) a

100 ml 100 ml 100 ml 100 ml

35.559* -11.334* 4.091* -8.834* -1.515 0.271 0.204*

— —

-2.541* -0.421* 0.851* 9.204 2.22 -788.98

SE 0.296 0.151 0.078 0.126 1.029 0.149 0.082

— —

0.103 0.079 0.375

— —

Model 1: Explained by total coliforms Coefficient 38.690* -12.435* 4.674* -10.575* -4.554*

— —

0.018 0.388* -2.346* -0.418* 0.836* 9.244 0.48 -788.79

Values are slope coefficients and standard errors; see Eq. [6] in the text for an explanation of the Model 1. The independent variables were in natural logarithms. chi-square test for the exogeneity of the time mean of weight. *P < 0.05.

b c

SE 0.309 0.159 0.078 0.137 1.003

— —

0.106 0.107 0.106 0.072 0.341

—

Gastrointestinal Morbidity of Bangladeshi Children specifications in Table 3 where the intake of bioavailable iron and FeMFP were used as explanatory variables, respectively. The lagged dependent variables were not statistically different from zero in the three versions of the model. These results were likely to be due to the modest number of children in the sample and also because Hb measured using capillary blood typically has a high withinsubject variability leading to poor precision of the estimates (Liu et al, 1976; Bhargava et al., 2001). The between to within variance ratio was significantly different from zero only in the model containing the bioavailable iron intake. Comparing the maximized values of the logarithm of the likelihood functions, the third specification that used the intake of iron from all animal sources as an explanatory variable achieved the highest value. Thus, the data on Bangladeshi children indicated that iron intake from animal source was a better indicator of diet quality, perhaps because of the uncertainty in algorithms for estimating bioavailable iron intake in undernourished subjects. Lastly, the children's morbidity index was not a significant predictor of Hb status, indicating that the associations between Hb status and morbidity in Table 2 were not the result of reverse causation.

187

DISCUSSION The quality of water available at the source and that stored in the house are typically poor in a less-developed country such as Bangladesh. Sanitation and hygiene practices increase the transmission of diseases via further contamination of the stored water and also increase the prevalence of helminth infections that lead to blood loss. Children's poor iron status can lower their capacity to fight infections. Using a longitudinal dataset on 99 free-living Bangladeshi children, we analyzed the effects of environmental and nutritional factors on children's gastrointestinal morbidity. The water samples from the source were contaminated by fecal and total coliforms and poor hygiene practices compounded the problems for the stored water. For example, in Survey round 3, where the water was stored for long periods, the mean levels of fecal coliform colonies in the water from the source and in the stored water were, respectively, 11 and 174 per 100 ml. These large differences underscored the need for simple interventions such as washing hands before handling water (Hoque et al., 1995) and for the use of storage containers with

TABLE 3. Maximum likelihood estimates of dynamic random effects model for Bangladeshi children's hemoglobin concentration in the 3 survey rounds explained by demographic, dietary, and anthropometric variables and a,h hookworm egg counts

Dependent variable: hemoglobin concentration, g/L n = 99 Model 2: explained by Fe bioavailable Independent variable Constant Age, y Hookworm, eggs per g of stool Fe bioavailable, mg/d Fe from meat, fish and poultry, mg/d Fe from all animal sources, mg/d Height, m Lagged dependent variable, g/L Between/within variance Within variance 2(maximized log-likelihood function) a

Coefficient

SE

Model 2: explained by Fe from meat, fish and poultry Coefficient

SE

Coefficient

SE

5.398* 0.019

0.574 0.036

5.315* 0.016

0.586 0.058

5.482* 0.014

0.603 0.066

-0.014* 0.011

0.005 0.012

-0.011*

0.003

-0.010*

0.004

—

—

—

—

—

—

0.002

0.008

—

—

—

—

0.352*

0.159

-0.146 0.555* 0.006

0.109 0.281

1150.66

—

—

0.361* -0.131 0.526 0.006

—

0.161 0.128 0.347

—

1151.13

Values are slope coefficients and standard errors; see Eq. [8] in the text for an explanation of Model 2. The dependent and the independent variables were in natural logarithms. *P < 0.05.

b

Model 2: explained by Fe from all animal sources

0.015 0.342

0.009 0.190

-0.161 0.600 0.006

0.126 0.372

1155.21

—

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A. Bhargava et al. narrow mouths and tight-fitting lids (Mintz et al., 2001). The empirical results in Table 2 implied that a 50% reduction in fecal coliforms would reduce children's gastrointestinal morbidity by approximately 10%, assuming that the average child had the score of 1 on the morbidity index as in Table 1. Such reductions are feasible given the median household in Survey round 3 had 20 and 118 colonies of fecal coliforms in the water from the source and the stored water, respectively. Providing subsidized soap to the poorest households and introducing new technologies for water storage would be useful strategies for reducing children's gastrointestinal morbidity. Further, the modeling results in Table 2 showed that the fecal and total coliforms in the stored water were important predictors of children's gastrointestinal morbidity. This was also true for fecal coliforms in the water from the source when the variable representing the coliforms in the stored water was dropped from the model. These results indicated the importance of providing clean water at the source and for improving hygiene during storage. In circumstances where it is difficult or expensive to provide clean water at the source, water treatment using sodium hypochlorite solutions would be a useful strategy of reducing pathogen levels (Dunston et al., 2001). A cost-benefit analysis of alternative strategies given the levels of water contamination, child morbidity, and available resources would be useful for policy design. The inappropriate disposal of fecal matter exacerbates the spread of parasites, such as hookworm, that thrive on blood. The empirical results in Table 3 imply that a 50% reduction in hookworm load would lead to approximately a 1% increase in children's Hb concentration. Because approximately 10% of the children were heavily infected with hookworm, anthelmintic treatment can reduce the loads of the infected children (Stoltzfus et al., 1997; Beasley et al., 1999). This, in turn, is likely to improve children's iron status as reflected in their Hb and ferritin concentrations (Bhargava et al., submitted). Because children with better Hb status experienced lower morbidity, the coordination of sanitation policies with those encouraging the use of soap and better technologies for water storage are likely to have synergistic effects on child health.

Lastly, iron deficiencies are widely prevalent in poor countries and hamper children's physical and intellectual development (UNICEF/WHO, 1999). The nutrient intakes data for Bangladeshi children in Table 1 underscored the inhibitory effects of phytate intakes for iron absorption. While appropriateness of the algorithms needs to be further investigated in clinical settings, children's intakes of bioavailable iron, FeMFP, and iron from all animal sources were not significant predictors of Hb status. By contrast, hookworm loads were negatively associated with the Hb status. Because hookworm infection can be treated by chemotherapy, it would seem logical that anthelmintic treatment should precede iron supplementation (Bhargava, 2001). This, however, should not be viewed as assigning lowering priority to improving diet quality in developing countries; anthelmintic treatment can only restore children's Hb to the "normal" levels. Iron deficiencies can be reduced by food policies that increase the long-term intakes of bioavailable iron. Such policies include greater consumption of animal products and fresh fruits and vegetables that enhance non-heme iron absorption from staple foods such as rice and wheat. The results in this article underscore the importance of exploiting synergisms between the dietary and environmental factors for improving child health in Bangladesh.

ACKNOWLEDGMENTS The authors thank the participants in the surveys and the staff of Data Analysis and Technical Assistance in Dhaka, Bangladesh, for making this study possible. While retaining responsibility for the views in the article, the authors thank W. Quabili for help with data preparation and the two reviewers for many helpful comments.

LITERATURE CITED American Public Health Association. 1992. Standard methods for the examination of water and wastewater, 18th ed. Washington, DC. Beasley NM, TomkinsAM, Hall A, KihamiaCM, LorriW, Nduma B, Issae W, Nokes C, Bundy DAP. The impact of population level deworming on the hemoglobin levels of schoolchildren in Tanga, Tanzania. Trop Med Int Health 4:744-750. Bhargava A. 1994. Modelling the health of Filipino children. J R Statist Soc A 157:417-432.

Gastrointestinal Morbidity of Bangladeshi Children

Bhargava A. 1999. Modelling the effects of nutritional and socioeconomic factors on the growth and morbidity of Kenyan school children. Am J Hum Biol 11:317-326. Bhargava A. 2001. Nutrition, health and economic development: some policy priorities. Food Nutr Bull 22:163-168. Bhargava A, Sargan JD. 1983. Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51:1635-1660. Bhargava A, Bouis HE, Scrimshaw NS. 2001. Dietary intakes and socioeconomic variables are associated with the hemoglobin concentration of Bangladeshi women. J Nutr 131:758-764. Calloway DH, Murphy SP, Bunch S. 1994. User's guide to the international minilist nutrient data base. Department of Nutritional Sciences, University of California, Berkeley, CA. Chandra RK, Au B, Woodford G, Hyam P. 1977. Iron status, immunocompetence and susceptibility to infection. In: Jacob A, editor. Ciba Foundation symposium on iron metabolism. Amsterdam: Elsevier, p 249-268. Chen LC, Scrimshaw NS (eds). 1983. Diarrhea and malnutrition. New York: Plenum. Cole TJ. 1991. Weight-stature indices to measure underweight, overweight and obesity. In: Himes JH, editor. Anthropometric assessment of nutritional status. New York: Wiley-Liss. p 83-111. Dunston C, McAfee D, Kaiser R, Rakotoarison D, Ramebeloson L, Hoang AT, Quick RE. 2001. Collaboration, cholera, and cyclones: a project to improve point-of-use water quality in Madagascar. Am J Public Health 91:1574-1576. Esrey SA, Habicht JP, Latham MC, Sisler DG, Casella G. 1988. Drinking water source, diarrheal morbidity, and child growth in villages with both traditional and improved water supplies in rural Lesotho, Southern Africa. Am J Public Health 78:1451-1455. FAO/WHO. 1988. Requirements of vitamin A, iron, folate and vitamin B 12 . Report of a joint FAO/WHO expert consultation. Rome: Food and Agriculture Organization. Feachem RG, et al. 1978. Water, health and development. London: Tri-med Books. Garner C, Tatu T, Reittie JE, Littlewood T, Darley J, Cervino S, Farrall M, Kelly P, Spector TD, Thein SL. 2000. Genetic influences on F cells and other hematologic variables: a twin heritability study. Blood 95:342-346. Hoque BA, Mahalanabis D, Alam MJ, Islam S. 1995. Post-defecation handwashing in Bangladesh: practice and efficiency perspectives. Public Health 109:15-24. Keusch GT. 1991. Nutritional effects on response of children in developing countries to respiratory tract pathogens: implications for vaccine development. Rev Infect Dis 13(Suppl):S486-S489. Khusun H, Yip R, Schultink W, Dillion DHS. 1999. World Health Organization hemoglobin cut-off points for the detection of anemia are valid for an Indonesian population. J Nutr 129:1669-1674. Kronmal RA. 1993. Spurious correlation and the fallacy of the ratio standard revisited. J R Statist Soc A 156:379-392. Kuvibidila S, Yu L, Ode D, Warrier RP. 1993. The immune response in protein-energy malnutrition and single nutrient deficiencies. In: Klurfeld DM, editor. Nutrition and immunology. New York: Plenum, p 121-148. Kuvibidila S, Yu L, Warrier RP, Ode D, Mbele V. 1994. Usefulness of serum ferritin levels in the assessment

of iron status in non-pregnant Zairean women of childbearing age. J Trop Med Hyg 97:171-179. Liu K, Dyer J, McKeever J, McKeever P. 1976. Statistical methods to assess and minimize the role of intraindividual variability in obscuring the relationship between dietary lipids and serum cholesterol. J Chron Dis 31:399^118. Lozoff B. 1988. Behavioral changes in iron deficiency. Adv Pediatr 35:331-360. Mintz E, Bartram J, Lochery P, Wegelin M. 2001. Not just a drop in the bucket: expanding access to pointof-use water treatment systems. Am J Public Health 91:1565-1570. Moe CL, Sobsey MD, Samsa GP, Mesolo V. 1991. Bacterial indicators of risk of diarrhoel disease from drinkingwater in the Philippines. Bull WHO 69:305-317. Monsen ER, Balintfy JL. 1982. Calculating dietary iron bioavailability: refinement and computerization. J Am Diet Assoc 80:307-311. Monsen ER, Hallberg L, Layrisse M, Hegsted DM, Cook JM, Mertz W, Finch CA. 1978. Estimation of available dietary iron. Am J Clin Nutr 31:134-141. Nelson M, Black AE, Morris JA, Cole TJ. 1989. Betweenand-within subject variation in nutrient intake from infancy to old age: estimating the number of days to rank dietary intakes with desired precision. Am J Clin Nutr 50:155-167. Numerical Algorithm Group. 1989. Numerical Algorithm Group Library, Mark 13. Oxford: Oxford University. Rahman HZ, Hossain M, Sen B (eds.). 1996. 1987-1994: Dynamics of rural poverty in Bangladesh. Bangladesh Institute of Development Studies, Dhaka, Bangladesh. Rand Corporation. 1983. Measurement of physiologic health of children, Vol. 1-5. Santa Monica, CA. Scrimshaw NS, SanGiovanni JP. 1997. Synergism of nutrition, infection, and immunity: an overview. Am J Clin Nutr 66:464S-477S. Scrimshaw NS, Taylor CE, Gordon JE. 1959. Interactions of nutrition and infection. Am J Med Sci 237:367-403. Scrimshaw NS, Taylor CE, Gordon JE. 1968. Interactions of nutrition and infection. Monograph, Geneva: WHO. Stoltzfus R, Chwaya HM, Tielsch JM, Schulze KJ, Albonico M, Savioli L. 1997. Epidemiology of iron deficiency anemia in Zanzibari schoolchildren: the importance of hookworms. Am J Clin Nutr 65:153-159. Tomkins A, Drasar BS, Bradley AK, Williamson WA. 1978. Water supply and nutritional status in Northern Nigeria. Tran R Soc Trop Med Hyg 72:239-243. Tseng M, Chakraborty H, Robinson DT, Mendez M, Kohlmeier L. 1997. Adjustment of iron intake for dietary enhancers and inhibitors in population studies: bioavailable iron in rural and urban residing Russian women and children. J Nutr 127:1456-1468. UNICEF/WHO. 1999. Prevention and control of iron deficiency anaemia in women and children. Geneva: World Health Organization. Van Derslice J, Briscoe J. 1995. All coliforms are not created equal: a comparison of the effects of water source and in-house water contamination on infant diarrheal disease. Water Res 29:1983-1995. World Health Organization. 1991. Basic laboratory methods in medical parasitology. Geneva: WHO.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 111:89-104 (2000)

Modeling the Effects of Maternal Nutritional Status and Socioeconomic Variables on the Anthropometric and Psychological Indicators of Kenyan Infants From Age 0-6 Months A L O K BHARGAVA* Department of Economics, University of Houston, Houston, Texas 77204-5882, and World Health Organization, CH-1211 Geneva 27,

Switzerland

KEY WORDS humans; growth; malnutrition; Brazelton Neonatal Behavioral Assessment Scale; Bayley Motor Scale; Bayley Infant Behavior Record; socioeconomic factors ABSTRACT This paper presents a comprehensive empirical analysis of the factors affecting growth and psychological development of over 100 infants from birth to age 6 months in the Embu region of Kenya. The analysis was divided into four parts. First, infants' birth weight, and length and head circumference as measured few days after birth, were modeled using multiple regression models. Maternal prepregnancy body mass index (BMI), gestation period, and parity were associated with infants' anthropometric measurements (P < 0.05). Second, the scores on seven clusters of the Brazelton Neonatal Behavioral Assessment Scale were explained by health and socioeconomic indicators. While the models had poor predictive power, the scores were comparable to those reported in the literature for Puerto Rican and African American infants. The third part of the analysis modeled infant growth between 1-6 months by analyzing longitudinal data on length, head circumference, and weight. Dynamic models were postulated for the effects of nutritional, socioeconomic, and environmental factors and morbidity on anthropometric variables. The results showed that infants' calcium intakes were positively associated with length (P < 0.05). Maternal BMI and hemoglobin concentration were positively associated with infant weight (P < 0.05); infant morbidity was negatively associated with weight (P < 0.05). Lastly, the infants' scores at 6 months on the Bayley Motor Scale and on eight items from the Bayley Infant Behavior Record were explained using anthropometric, socioeconomic, and psychological variables. The infants' arm circumference and intake of protein were significant predictors of scores on the Bayley Motor Scale. In addition, time spent by the mother talking to the infant was positively associated with the scores on the Bayley Infant Behavior Record. The empirical results have implications for identifying vulnerable children in developing countries. Am J Phys Anthropol 111:89-104, 2000. © 2000 Wiley-Liss, inc.

A large number of children in developing countries are undernourished (Food and Agriculture Organization, 1996). Undernutrition suffered during the formative years affects individuals' activities over their entire life span. Different disciplines are therefore concerned with the effects of undernutri2000 WILEY-LISS, INC.

tion at different stages of life. Physiologists, for example, study the physical work capacGrant sponsor: Organization of Economic Cooperation and Development, Paris, France. Correspondence to: Alok Bhargava, Department of Economics, University of Houston, Houston, TX 77204-5882. E-mail: bhargava® uh.edu Received 25 November 1998: accepted 27 August 1999.

192

A. Bhargava ity of undernourished adults in developing countries. Studies have shown that adults with a poor nutritional status (low body mass index (BMI)) have lower oxygen uptake and reduced physical work capacity (Spurr, 1983). Similarly, field studies have shown that anemic individuals take longer to complete agricultural tasks (Basta et al., 1979). Because economists are concerned with raising labor productivity, the link between nutrition and adult productivity has been discussed in the economics literature (Leibenstein, 1959; Bhargava, 1997; Strauss and Thomas, 1998). Although the link between nutrition and labor productivity is an important one, food policies can improve adult productivity in a limited way, in comparison with the benefits from targeting children. For example, while one can obtain higher agricultural output per worker by providing anemic individuals with iron-fortified foods (Basta et al., 1979), it would be more difficult to train such workers into skilled occupations. For creating a well-trained labor force, it is necessary that, starting from a very early age, children receive adequate quantities of energy, protein, and micronutrients (Pollitt, 1993; Pollitt et al. 1993; Scrimshaw, 1998); education and health environments play a vital role in cognitive development (Bhargava, 1998). The early development of children has been studied by many researchers in nutrition and psychology (Waterlow, 1988; RoveeCollier and Lipsitt, 1992; Pollitt et al., 1993; Grantham-McGregor, 1995). Because the human brain shows rapid growth during the first 2 years, a diet high in protein and micronutrients is likely to facilitate brain development (Monckeberg, 1975). Since these nutrients are found in relatively expensive foods, maintaining an adequate supply of vital nutrients in a rather short time interval during childhood presents a challenge to policy makers in international organizations and national governments. The task of identifying young children whose brain development might have been compromised by nutrient deficiencies is complicated by several factors. First, psychological tests for infant development such as the Bayley tests are known to have poor reliability; infants tested a week apart can score

quite differently on the same components of the test (Horner, 1988). Second, while the rate of linear growth of children in developing countries begins to falter at an early age (Waterlow, 1994), comparisons using psychological measures are ambiguous because neurological development is a complex process, and many of its dimensions cannot be quantified. Modeling the interrelationships between children's anthropometric measures and the scores on psychological tests can provide useful insights. The purpose of this paper was to develop a comprehensive empirical model for the proximate determinants of physical and mental development of infants in the Embu region of Kenya. The analysis considered the anthropometric and psychological indicators of development in the period from birth to age 6 months and used appropriate statistical techniques when modeling the effects of socioeconomic, nutritional, and environmental variables on infant development. First, the proximate determinants of birth weight, and length and head circumference as measured a few days after birth, were modeled; nutritional, socioeconomic, and demographic variables were used in the multiple regression analysis. Second, the scores obtained by the infants within a week of birth on the Brazelton Neonatal Behavioral Assessment Scale (NBAS) (Brazelton, 1984) were modeled using similar explanatory variables. Third, the dynamics of growth in the period of 1-6 months were modeled in a longitudinal framework, using six repeated observations. The principle of maximum likelihood was used to estimate parameters of dynamic models for length, head circumference, and weight; the infants' z-scores for weight-forage were also modeled in a dynamic framework. Finally, the scores obtained on the Bayley Motor Scale and eight items from the Bayley Infant Behavior Record (Bayley, 1969) were modeled using regression analysis. MATERIALS AND METHODS Subjects The data were derived from surveys sponsored by the U.S. Agency for International Development in 1984-1985 in the Embu region of Kenya (Sigman et al., 1989). Of the 2,059 households in the region, households

Anthropometric and Psychological Indicators of Kenyan Infants were selected to participate in the study if there was a toddler (approximately 18 months old) or a school-age child (6-9 years) present; households were also included if the lead female in the household was pregnant but had not completed the first trimester. A household was ineligible if the lead female was over 40 years old, or her last pregnancy occurred over 5 years ago, or if a child had been born within the previous 10 months. Thus, 292 households were eligible. Over 100 infants born during the observation period were followed longitudinally from birth until age 6 months. The study was approved by a Human Subjects Committee of the University of California, Los Angeles (Neumann et al., 1992). Anthropometry and psychological measurement The infants were weighed at birth and, within a few days after birth, measurements were taken on length, head circumference, and arm circumference; skinfold thicknesses were measured at triceps, biceps, and subscapular sites. Afterwards, anthropometric variables were measured every month. Typically, two sets of measurements were taken by different enumerators; correlations between the measurements were close to 0.95. Trained observers completed the Brazelton NBAS few days after birth (Brazelton, 1984). The scale consisted of two parts. First, there were elicited responses on 18 items that were scored from "low" to "high" on a scale of 1-3. The second part of the scale consisted of 27 behavioral items that were scored on a scale of 1—8. Because higher scores on behavioral items did not indicate better performance, the scores were redefined on a progressive scale (Lester et al., 1982). Further, using the progressive scoring system, the 27 behavioral items were grouped into six clusters: Habituation, Orientation, Motor, Range of State, Regulation of State, and Autonomic Stability (Lester et al., 1982); the mean score on the 27 items was also used as an indicator. The number of abnormal responses on the 18 items in the first part of the test constituted the score on the seventh (Reflex) cluster, where higher scores indicated worse performance. The test for motor development given at 6 months consisted of 33 items selected from

the Bayley Motor Scale (Bayley, 1969). There were no ambiguities in scoring in this component of the test because the scores were dichotomous (infants either passed or failed the items). Motor development was defined by the number of items on which infants passed the test; this score was used as a dependent variable in the fourth part of the analysis. Interobserver reliability of the scores was high (Whaley et al., 1998). For the analysis of data from the Bayley Infant Behavior Record, eight items were selected: Endurance, Activity, Banging Toys, Manipulating, Body Motion, Energy and Coordination, Coordination of Gross Muscle Movement, and Coordination of Fine Muscle Movement. For 6-month-old infants, it was appealing to focus on items that would be less affected by within-infant variability. For example, the score on Responsiveness to Examiner was more likely to be affected by swings in infant moods than the scores on Endurance or Energy and Coordination. For a subset of 22 infants, the interobserver reliability ranged from 0.72-0.86 for factors extracted using principal components analysis (Whaley et al., 1998). Infant-caregiver interaction was assessed using a time-sampling procedure. The proportion of time for which the mother, an adult, or an older sibling looked, held, touched, and talked to the infant in a 30-min period was recorded at 60-day intervals. Thus, three repeated observations were available for each infant on four interaction variables (look, hold, touch, and talk). The observations were subsequently averaged over time to produce mean levels of the interaction variables for the 6-month observation period; averaging also reduced the within-subject variation in the measurement of care-giving. Measurement of nutritional, socioeconomic, and demographic variables and morbidity Length of the gestation period was estimated by the method of Dubowitz and Dubowitz (1977). Breast-feeding patterns of the infants were investigated in the questionnaire. Mothers were asked about duration and frequency of breast feeding. Most infants received supplemental foods after a

193

194

A. Bhargava few months. The intakes of supplemental foods were converted into intakes of 41 nutrients, using food composition tables (Murphy et al., 1991). Sicknesses of the infants were recorded on a weekly basis. Each month, the numbers of days for which an infant was sick with different symptoms were combined to form an index of morbidity (Bhargava, 1994, 1999). A separate index was created for diarrhea, though the incidence of diarrhea was low. For each infant, detailed information was available on the nutritional status of the mother before and after the birth. Measurements on weight, arm circumference, and skinfold thicknesses at biceps, triceps, subscapular, suprailiac, abdomen, and thigh sites were taken every month (similar measurement were taken on the fathers). Maternal height and head circumference were measured once during the observation period. Maternal nutrient intakes were assessed on a monthly basis, using the 24-hr recall method and by weighing certain food portions on the day of the survey. Sicknesses were recorded on a fortnightly basis; an index of morbidity was constructed for the mothers. Blood analyses measured the hemoglobin concentration and white blood cell count, at least once during the observation period; intensity of hookworms in the stool was measured once. Education levels of the parents were available in the data; parents took the revised version of Wechsler's Adult Intelligence Scale (Wechsler, 1981) and Raven's Progressive Matrices (Raven, 1965). Sanitation and hygiene practices of the household were recorded. An index of socioeconomic status was constructed on the basis of household possessions and cash income. The data covered more than 100 infants. However, the number of observations used to estimate various models differed because of missing observations on the explanatory variables in the models. For further details of the study design, see Neumann et al. (1992). A framework for modeling anthropometric and psychological indicators: proximate determinants of birth weight, length, and head circumference A majority of pregnant women in developing countries have themselves suffered from

undernutrition during childhood, which can limit their capacity to produce healthy infants. Episodes of undernutrition and morbidity during pregnancy can adversely affect fetal development and hinder postnatal growth. For understanding the effects of undernutrition on child development, it is important to begin with an analysis of factors contributing to intrauterine growth retardation. Babies born in developing countries are typically shorter, weigh less, and have a smaller head circumference than their counterparts in affluent societies (Falkner et al., 1994). In some cases, however, head circumference is proportionately less reduced; such infants have shown a greater propensity for catch-up growth (Miller, 1992). This could be due to better maternal nutrition in earlier phases of pregnancy. Further, maternal nutritional status is likely to deteriorate with parity in developing countries because the diet is often deficient in energy, protein, and micronutrients necessary to sustain energy expenditures for subsistence activities (Bhargava, 1997). Birth outcomes would therefore depend on the maternal prepregnancy nutritional status and the timing of undernutrition and sicknesses during the pregnancy. Because the biological relationships between maternal nutritional status and fetal development are complex (Tanner, 1989), epidemiological investigation can provide useful insights. There have been several studies analyzing the effects of maternal undernutrition on outcomes such as birth weight (Milner, 1988). For the Kenyan data analyzed in this paper, Neumann and Harrison (1994) reported positive correlations between maternal size (height and weight) and birth weight. However, the data contain information on maternal hemoglobin concentration, hookworm infestation, and morbidity that are measures of health status (Mata, 1978; Scrimshaw, 1998). Moreover, maternal micronutrient intakes and demographic variables such as number of preceding live births are potentially important predictors of infant weight, length, and head circumference.

Anthropometric and Psychological Indicators of Kenyan Infants

Modeling the scores on the Brazelton Neonatal Behavioral Assessment Scale Development of the central nervous system is a complex process, and it is often difficult to assess the effects of undernutrition on neurological development, even using advanced techniques (Levitsky and Strupp, 1995). Thus, researchers often use head circumference as a proxy for brain growth, even though the time profiles of changes in brain mass and head circumference are known to differ (Dobbing and Sands, 1978). It is useful to seek additional measures of infant development for identifying vulnerable children early in life (Bornstein and Lamb, 1992). The Brazelton NBAS is a widely used instrument for evaluating infant behavior (Brazelton, 1984). However, the scores on different test items have different interpretations. Lester et al. (1982) redefined the NBAS scores on a progressive scale; six clusters, namely, Habituation, Orientation, Motor, Range of State, Regulation of State, and Autonomic Stability have been suggested, using principal components analysis. This grouping has the advantage of reducing within-infant variation; the scores on clusters are amenable to multivariate modeling. Simple correlations between explanatory variables and scores on the Brazelton NBAS clusters, however, are often ambiguous. For example, Oyemade et al. (1994) reported that the score of African American infants on the Motor cluster was negatively correlated with "high partner interaction," whereas it was positively correlated with "high degree of happiness of spousal partner." Similarly, certain other correlations between the scores on NBAS clusters and explanatory variables reported by these authors were difficult to interpret. A systematic approach would be to introduce a set of potentially relevant explanatory variables into a multivariate model explaining the scores; important predictors can be retained on the basis of statistical tests.

falter in undernourished populations within few weeks after birth (Adair et al., 1993; Hernandez-Beltran et al., 1996). Longitudinal studies relating maternal nutritional and health status and environmental factors to anthropometric measurements of infants can provide insights into the causes of growth retardation. It would be useful to model the dynamics of infant weight, length, and head circumference in the period from 1-6 months. Thus, for example, the effects of maternal nutritional status on nutrient composition and volume of breast milk have been investigated in field studies (e.g., Jelliffe and Jelliffe, 1978; Brown et al., 1986; Prentice et al., 1994). Because breast milk is the primary source of nourishment for infants in the age group 1-6 months, indicators of maternal nutritional status such as BMI, arm circumference, protein intakes, and hemoglobin concentration are potentially important factors explaining infant growth. Furthermore, unobserved betweeninfant differences are important for modeling growth because they partly reflect genetic differences and also environmental factors that cannot be controlled for. Models ignoring unobserved differences can yield inconsistent parameter estimates, especially in dynamic formulations where anthropometric measurements in a given period depend on past measurements. Assuming that n infants were observed 6 times at monthly intervals, the system of equations estimated for length (LE), head circumference (HD), and weight (W) is given by equations (1-3) (i = 1,. . ., n; t = 2 , . . ., 6): m1

p1

z

LE it = 2 i j ^ j

The first 2 years of a child's life are critical from the standpoint of physical growth and brain development; linear growth begins to

+

j=l

+

2xijtCj

LE a _!

ai

+ \ j Mit

m2

K +

ij j

2

x

«t u j + «2 HD it _!

j=i

+ XJJ LE it m3

j=l

+ ulit

p2

z

j=i

W it = 2

m

u ;

j=l

HDit = 2 Dynamic modeling of length, head circumference, and weight in the period of 1-6 months

195

(2)

'

+ \ 3 M it

+ u 2it

p3

Z

ij $3 + 2 Xijt *l*j + <*3 Wit_j j=l

+ \ 4 L E l t + \ 5 AM i t

+X 6 M i t

+u 3 i t

n )

v o ;

196

A. Bhargava Here, the z's and x's are, respectively, timeinvariant and time-varying explanatory variables; the coefficients are denoted by Greek letters. Background variables such as maternal height that did not change during the survey period were included in the z's. Nutrient intakes, that changed with the month, were included in the x's. M and AM were, respectively, an index of infant morbidity and arm circumference. While M and AM were time-varying, they were written separately to facilitate the discussion of the model. The system in equations (1-3) embodied several interrelationships between the anthropometric indicators. For example, infant weight was explained by length because the latter approximates skeletal size (Ehrenberg, 1968; Tanner, 1986; Cole, 1991). Moreover, arm circumference was included in the model because it is a proxy for lean body tissue (Bhargava, 1999). While weight would respond quickly to shortfalls in energy intake and sickness spells, the inclusion of length and arm circumference as explanatory variables controlled for many factors that could not be easily observed. Moreover, since current weight would depend on weight in the previous period, the model for weight in equation (3) was a dynamic relationship. An alternative to modeling the dynamics of infant weight by equation (3) would be to model the z-scores for weight-for-age. This approach was suggested by a reviewer and was also explored using the Kenyan data on infants in the period from 1-6 months. Modeling the scores on Bayley Motor Scale and Bayley Infant Behavior Record In affluent societies, children in the age group 3-24 months are sometimes examined on the Bayley Motor Scale and the Bayley Infant Behavior Record (Bayley, 1969). This is less common in poor countries, in part because of the costs associated with testing. From a policy viewpoint, it is important to identify vulnerable children early in life. Thus, a model for the proximate determinants of scores on Bayley scales at 6 months would be of interest. Because the infants were previously examined on the Brazelton NBAS, one can also investigate the predic-

tive power of NBAS for the scores on the Bayley scales. The scores on eight items selected from the Bayley Infant Behavior Record were Endurance, Activity, Banging Toys, Manipulating, Body Motion, Energy and Coordination, Coordination of Gross Muscle Movement, and Coordination of Fine Muscle Movement. Proximate determinants of the scores were analyzed using regression models. Scores on the last two items were transformed so that higher scores implied better coordination (Wolf and Lozoff, 1985). An alternative approach would be to use principal components analysis for clustering items (Kaplan-Estrin et al., 1994). However, the clusters are often difficult to interpret. Econometric procedure For multiple regression models, the procedure PROC REG by SAS (1997) was used to estimate model parameters. Dynamic models for infant length, head circumference, and weight given by equations (1-3), were estimated by the principle of maximum likelihood (Bhargava and Sargan, 1983). A computer program was developed in Fortran to compute the likelihood functions; model parameters were estimated by optimizing the likelihood function, using the routine E04 JBF from the Numerical Algorithm Library (NAG, 1989). The estimation theory assumed that initial observations of the dependent variables were endogenous variables (correlated with the errors) and that the errors (uit) were independent across infants but correlated over time with a positive definite variance covariance matrix. The random effects model is a special case: u it = 8; + v it

(4)

where 8's are infant-specific, normally distributed random variables and v's are independently normally distributed random variables. The exogeneity hypothesis of zero correlation between n2 time-varying regressors (x2) and random effects was tested by likelihood ratio tests. With six time observations in the data set, the statistic was asymptotically distributed as a chi-square variable with 6n 2 degrees of freedom.

Anthropometric and Psychological Indicators of Kenyan Infants

TABLE

197

1. Regression models explaining infant birth weight and length and head circumference measured after birth by maternal nutritional status and demographic characteristics1

Dependent variable Independent variable Constant Indicator for sex2 Dubowitz,3 w Maternal prepregnancy BMI,3 kg/m2 Maternal hemoglobin,3 g/1 Maternal hookworms/g3 Parity Parity squared Indicator for birth order 1 Infant age, days Adjusted R2 Sample size, n

Birth weight (kg) Coefficient SE

Length ( cm) SE Coefficient

-4.286*

0.984

2.620*

1.068* 0.274* 0.136 -0.014 0.007

0.249 0.104 0.093 0.009 0.005

0.285* 0.094* -0.013 -0.007* -0.0003

0.094 0.038 0.034 0.003 0.0019

-0.102*

0.051

-0.007 0.002* 0.27 99.0

0.019 0.0004

0.33 102.0

0.363

shortly

Head circumftjrence (cm) SE Coefficient 2.487* 0.022* 0.168* 0.101* 0.033 -0.004 0.012* -0.0008*

0.249 0.006 0.064 0.026 0.023 0.002 0.0004 0.0004

0.002* 0.51 99.0

0.0004

1

Values are slope coefficients ± standard errors. Boy, 1; girl, 0. These variables and the dependent variable were in logarithms; coefficients of these explanatory variables are elasticities. *P<0.05. 2 3

RESULTS Results for birth weight, length, and head circumference The results for birth weight, and length and head circumference measured few days after birth, are reported in Table 1. Maternal prepregnancy BMI, hemoglobin concentration, and hookworms were transformed into natural logarithms (Nelson et al., 1989). Estimated coefficients of these variables were thus the elasticities (proportionate change in the dependent variable resulting from 1% change in the independent variable). The models were also estimated with variables in levels. Coefficients significant at the 5% level were marked with asterisks. There were several noteworthy features of the results. First, the elasticity of birth weight with respect to gestation period exceeded unity (birth weight was approximately 200 g less than the 50th U.S. percentiles; National Center for Health Statistics, 1977). The point estimates of elasticities of infant length and head circumference with respect to gestation period were, respectively, 0.29 and 0.17. Thus, longer gestation periods had the greatest impact on birth weight, followed by length and head circumference. The elasticity of birth weight with respect to the maternal prepregnancy BMI was 0.27 (P < 0.05). Thus, good initial nutritional status was associated with higher birth weight. Hookworm intensity was nega-

tively associated with birth weight, though the coefficient was not significant at the 5% level (P = 0.077). The indicator (0-1) variable for first-born infants showed a lower birth weight (P < 0.05). However, the number of live births (parity) was not significantly associated with birth weight. This was also true for the square of parity (see below). The prepregnancy BMI was statistically significant (P < 0.05) in the relationships for length and head circumference measured a few days after birth. The point estimate of the elasticities was close to 0.10. Because the infants were measured at slightly different ages, age in days was included as a regressor; age was a significant predictor (P < 0.05) of length and head circumference. The coefficients of the indicator variable for first-born infant and the parity variable were not statistically significant in the model for infant length. The overall fit of the model for length was worse than that for weight and head circumference. This could be due to the fact that infant length at birth is often not very different for undernourished and affluent populations (Karlberg et al., 1994). Thus, it is more difficult to relate observed differences in maternal characteristics to infant length. Sex of the infant was not significant in the models for birth weight and length, but was significant in the model for head circumfer-

A. Bhargava

198 TABLE Brazelton

2. Regressions models explaining Neonatal Behavioral Assessment

Dependent variable Independent variable Constant Dubowitz, w Maternal prepregnancy BMI, kg/m2 Infant BMI, kg/m2 Infant head circumference., cm Infant arm circumference, cm Adjusted R2 n

the scores on Reflex, Habituation, Orientation, and Motor clusters of Scale by maternal nutritional status and demographic characteristics1

Reflex2 Coefficient SE -6.241 0.048 -0.179 -0.089 0.493 -0.449 0.003 85.0

9.766 0.151 0.116 0.215 0.269 0.412

Habituation 3 Coefficient SE 4.297 0.016 0.102 0.087 0.161 -0.023 0.028 74.0

5.809 0.087 0.069 0.129 0.158 0.247

Orientation Coefficient SE 2.272 0.041 0.088 -0.107 -0.035 0.132 -0.008 85.0

5.267 0.082 0.062 0.116 0.145 0.222

Motor Coefficient SE 6.614 0.019 0.073* -0.025 -0.156* 0.190 0.068 85.0

2.627 0.041 0.031 0.058 0.072 0.111

1

Values are slope coefficients ± standard errors. Reflex was the cluster based on 18 elicited responses. Habituation, Orientation, and Motor clusters were defined by Lester et al. (1986). *P<0.05.

2 3

ence, indicating that boys had a greater head circumference than girls. The relationship between parity and head circumference was a quadratic one, and both terms were significant (P < 0.05). However, the coefficient of the indicator variable for first-born was not significant in this model. Maternal hookworms infestation was estimated with a negative sign that was not significant at 5% level. However, hookworm intensity was a significant predictor (P < 0.05) of infant length. The effects of maternal weight gain and sicknesses during the three trimesters on birth weight, length, and head circumference were investigated using the models in Table 1. However, these variables were not statistically significant. This partly reflected the difficulties in identifying sicknesses that affect fetal growth. Spells of mild undernutrition during the pregnancy may not be as important as, for instance, the general maternal health status represented by variables such as BMI, hemoglobin concentration, and hookworm infestation. While hemoglobin was not an important predictor in the results in Table 1, it was significant in certain versions of the model. However, socioeconomic variables were not significant predictors of anthropometric measurements, presumably because such factors were reflected in maternal health status. Results for scores on the Brazelton NBAS The empirical models explaining the scores on the Reflex, Habituation, Orientation, and Motor clusters of the Brazelton NBAS are

presented in Table 2 (the results for Range, State, Autonomic Stability, and Mean Score were similar and hence were omitted). It was evident, however, that the explanatory variables did not explain the variation in scores. The R-squared (adjusted for degrees of freedom) were often close to zero and assumed slightly negative values for some models. Coefficients of some explanatory variables were statistically significant. For example, maternal prepregnancy BMI was positively associated with scores on the Motor cluster. But in this model, infant head circumference had a negative coefficient that was significant (P < 0.05). Moreover, the results were not robust to changes in model specification; statistical significance of explanatory variables seemed more due to chance than a substantive finding. The poor fit of the model for scores on the Brazelton NBAS raised the issue of validity of the scores. First, one could question the reliability of the tests; infants might have scored differently if tested at another point in time. The role of within-subject variation in test scores can be investigated by designing studies that repeatedly test infants over a few days. However, multiple observations on the Brazelton NBAS would be expensive. Furthermore, using averages as dependent variables may not improve the fit of the models. Second, genetic and cultural factors may have influenced scores on the Brazelton NBAS. A comparison of Kenyan infants' scores with those for other populations might reveal some unusual aspects of the study. In

Anthropometric and Psychological Indicators of Kenyan Infants

TABLE 3. Sample means and standard deviations of the scores on Brazelton for Kenyan, Puerto Rican, and African American

Mean

SD

Variables Reflex Habituation Orientation Motor Range Regulation of State Autonomic Stability n

3.757 4.980 4.323 4.497 3.704 5.112 5.494 115.0

2.501 1.481 1.352 0.651 0.983 1.126 0.685

1 2 3

Behavioral

Puerto Rico2 Mean SD

Kenya Country

Neonatal infants1

199

2.050 7.050 4.850 4.050 3.850 5.700 6.950 37.0

Scale

clusters

U.S.3 Mean

SD

7.400 6.020 5.330 3.830 5.900 6.920 228.0

1.060 1.550 0.740 0.740 1.260 1.160

Values are means ± standard deviations. From Lester et al. (1982), SD not reported by the authors. From Oyemade et al. (1994).

Table 3, the mean scores of Kenyan infants on the seven clusters are presented along with the results for 228 African-American infants (Oyemade et al., 1994) and for a sample of 37 infants from Puerto Rico (Lester et al., 1986); the latter researchers did not report standard deviations. The mean scores on the clusters were similar for the three populations, though there were some differences. Kenyan infants appeared to do worse than their counterparts in Puerto Rico and U.S. on most clusters. On Motor Development, however, the scores were slightly better for Kenya than for Puerto Rico. The estimated standard deviations for Kenyan and U.S. infants were of a similar order of magnitude. For example, the coefficients of variation for the Motor cluster for Kenya and the U.S. were, respectively, 0.145 and 0.139. It would seem reasonable to conclude that the Brazelton NBAS was appropriately designed for the Kenyan population. This, however, does not imply that scores on the Brazelton NBAS were useful indicators of infant development in the Kenyan population. It might be preferable to use anthropometric indicators for identifying vulnerable children at early ages. However, this argument is conditional on the assumption that the scores on the Brazelton NBAS were poor predictors of later psychological outcomes. Because the infants took the Bayley scales at 6 months, this issue is discussed below. Results for the dynamics of infant length in the period of 1-6 months The empirical results for infant length are presented in Table 4. With the exception of

TABLE 4. Maximum likelihood estimates of dynamic random effects model for infant length in the period from 1-6 months explained by maternal nutritional status, and infant nutrient intakes and morbidity1'2

Dependent variable Independent variable Constant Sex3 Maternal hemoglobin,4 g/L Maternal BMI,4 kg/m2 Infant calcium intake, 4 mg/day Infant morbidity index 4 Indicator time period 3 Indicator time period 4 Indicator time period 5 Indicator time period 6 Lagged dependent variable, 4 cm Between/wi thin-variance Within-variance Chi-square (6)5 2x log-likelihood function n

Length (<:m) SE Coefficient 2.466* 0.009* 0.011 0.025 0.001* -0.0001 0.024* 0.041* 0.061* 0.068* 0.356* 0.564* 0.0006 9.52 -4,375.03 102.0

0.224 0.003 0.013 0.015 0.0006 0.0008 0.005 0.007 0.009 0.011 0.059 0.161

1

Values are slope coefficients ± standard errors. The 102 infants were observed six times at monthly intervals. Boy, 1; girl, 0. 4 These variables and the dependent variable were in logarithms. 5 Chi-square is the likelihood ratio test statistic for exogeneity of morbidity index; degrees of freedom — 6. *P<0.05. 2 3

indicator variables for sex and the survey periods, the explanatory variables were transformed into logarithms. Coefficient of the sex indicator variable was significant (P < 0.05), showing that boys were slightly longer than girls. Maternal BMI and hemoglobin concentration were positively associated with infant length, though the coefficients were not significant at the 5% level. Calcium intake from weaning was positively associated with length (P < 0.05); calcium intakes were positively associated with height in a Filipino sample (Bhargava, 1994)

200

A. Bhargava TABLE 5. Maximum likelihood estimates of dynamic random effects model for infant head circumference in the period from 1-6 months explained by maternal nutritional status, and infant nutrient intakes, 12 morbidity, and length '

Head circumference (cm) Dependent variable and model Independent variable Constant Sex3 Maternal hemoglobin,4 g/1 4 Maternal head 4circumference, cm Maternal BMI, kg/m2 4 Maternal morbidity index Infant morbidity index 4 Infant length, 4 cm Indicator time period 3 Indicator time period 4 Indicator time period 5 Indicator time period 6 Lagged dependent variable, 4 cm Between/within-variance Within-variance Chi-square 5 2 x log-likelihood function n

Specification 1 Coefficient 0.479* 0.007* 0.018 0.136* -0.0002 -0.0006 -0.0003 0.211*

0.475* 0.268* 0.0003 18.83 -4,371.85 92.0

SE 0.185 0.002 0.011 0.048 0.009 0.0005 0.0006 0.033

0.039 0.088

Specification I2 Coefficient 1.516* 0.015* 0.031* 0.225* 0.008 -0.0003 -0.0007 0.016* 0.037* 0.049* 0.052* 0.298* 1.040* 0.0003 8.98 -4,845.03 102.0

SE 0.121 0.002 0.011 0.016 0.012 0.0006 0.0006 0.003 0.005 0.006 0.007 0.052 0.216

1

Values are slope coefficients ± standard errors. The 92 infants were observed six times at monthly intervals. Boy, 1; girl, 0. 4 These variables and the dependent variable were in natural logarithms. 5 Likelihood ratio statistics in Specifications 1 and 2 test, respectively, the exogeneity of infant morbidity and length, and infant morbidity (degrees of freedom, 12 and 6, respectively). *P<0.05. 2 3

and also for school-age children from this Kenyan population (Bhargava, 1999). Indicator variables for the 4 survey months were estimated with significant positive coefficients (P < 0.05); these estimates confirmed steady growth during the 1-6-month period (at most four such indicator variables can be included). Coefficient of the lagged dependent variable was significant (P < 0.05); the long-run elasticity of length with respect to an explanatory variable was approximately 1.5 times the short-run elasticity reported in Table 4. For example, doubling an infant's calcium intake was associated with a 1% increase in infant length in a short time frame. The long-run impact would be to increase length by 1.5%. While the magnitude of these elasticities was small, length is known to respond very gradually to nutritional intakes. The between/within-variance ratio was significant (P < 0.05) in the model for length. Thus, unobserved between-infant differences played an important role in this model. Note that many other explanatory variables were also introduced into the dynamic model.

However, the coefficients of households' socioeconomic status and cash income, maternal morbidity and hookworms, parity, parents' scores on cognitive tests, an index for the duration of breast feeding, etc., were not significant predictors of infant length. Results for the dynamics of infant head circumference in the period of 1-6 months The results for head circumference presented in Specification 1 of Table 5 showed that boys had a greater head circumference than girls, which was also the case for measurements just after birth (Table 1). The elasticity of infant head circumference with respect to maternal head circumference was 0.14 (P < 0.05). Paternal head circumference was not a significant predictor, which could be due to the greater number of missing observations on the fathers that had lowered the sample size used in the estimation. Maternal BMI, hemoglobin concentration, and morbidity and infant morbidity were not significant predictors of head circumference.

Anthropometric and Psychological Indicators of Kenyan Infants Infant length was a significant predictor (P < 0.05) of head circumference in Specification 1 in Table 5; systemic bone growth is likely to increase cranial vault thickness (Lieberman, 1996). However, in Specification 2 of Table 5, length was dropped from the model to allow for possible differences in the mechanisms governing cranial and long bone growth. While the four indicator variables for time periods were not significant in Specification 1, they were significant in Specification 2, presumably because increase in length partly accounted for the growth in head circumference in Specification 1. Moreover, in contrast with the results for Specification 1, maternal hemoglobin concentration was a significant predictor of infant head circumference in Specification 2. Thus, maternal iron status appears to have had a beneficial effect on the growth in infant head circumference in the period of 1—6 months. The between/within-variance ratio was large in Specification 2, presumably indicating that omitting length from the model led to an increase in the unobserved between-infant differences. Likelihood ratio statistics accepted the null hypothesis that the random effects affecting length and morbidity were uncorrelated with those affecting head circumference. Results for the dynamics of infant weight in the period from 1-6 months The results for infant weight are in Table 6. The indicator variable for sex was not significant in this model. Maternal BMI and hemoglobin concentration were significant predictors of growth in weight in the period of 1-6 months (P < 0.05). This presumably reflected the fact that the breast milk of well-nourished mothers contained greater quantities of fat and possibly other nutrients that enhance infant growth (Jelliffe and Jelliffe, 1978; Brown et al., 1986). However, other indicators of maternal nutritional status such as protein intakes and skinfold thicknesses were not significant predictors of infant weight. Paternal BMI was also not significantly associated with infant weight. Infant sicknesses were negatively associated (P < 0.05) with body weight; arm circumference and length were significant predictors (P < 0.05) of weight. The use of

201

TABLE 6. Maximum likelihood estimates of dynamic random effects model for infant weight in the period from, 1-6 months explained by maternal nutritional status, and infant nutrient intakes, morbidity, and length and arm circumference1-2

Dependent variable Independent variable Constant Sex 3 Maternal hemoglobin,4 g/1 Paternal BMI,44 kg/m22 Maternal BMI, kg/m Maternal morbidity index 4 Infant calcium intake, 44 mg Infant morbidity index Infant arm circumference,4 cm Infant length, 4 cm Lagged dependent variable, 4 kg Between/within-variance Within-variance Chi-square(18) 5 2 X log-likelihood function n

Weight (kg) Coefficient SE -5.066* 0.006 0.077* 0.023 0.087* 0.0009 0.002 -0.006* 0.666* 0.973* 0.283* 0.008 0.0061 24.14 -2,469.18 81.0

0.545 0.008 0.026 0.025 0.019 0.0026 0.002 0.002 0.060 0.118 0.039 0.047

1

Values are slope coefficients ± standard errors. The 81 infants were observed six times at monthly intervals. Boy, 1; girl, 0. 4 These variables and the dependent variable were in logarithms. 5 Likelihood ratio statistic tests the exogeneity of infant morbidity, arm circumference, and length; degrees of freedom = 18. *P<0.05. 2 3

length to predict body weight is common in the anthropometric assessment literature (Ehrenberg, 1968; Tanner, 1986; Cole, 1991). However, because the arm circumference is an approximation for lean body tissue, its inclusion greatly improved the fit of the model for weight (Bhargava, 1999). In contrast with the results for length and head circumference, the between/within-variance ratio was not significant in the model for weight; unobserved between-infant differences were apparently accounted for by explanatory variables such as length and arm circumference. The results from estimating dynamic models for the z-scores for weight-for-age, based on the tabulations for the U.S. (National Center for Health Statistics, 1977) and the U.K. (Freeman et al., 1995), are presented in Table 7. Four indicator variables were included in the model for the time periods. Infant length and arm circumference were omitted from the set of explanatory variables; previous z-score was treated as an endogenous variable in the estimation. Maternal BMI and hemoglobin concentration and some of the time indicator variables

A. Bhargava

202

TABLE 7. Maximum likelihood estimates of dynamic random effects model for z-scores for weight-for-age based on NCHS and U.K. reference standards explained by maternal nutritional status, and infant nutrient intakes1'2

Dependent variable, with model Independent variable Constant Maternal hemoglobin,5 g/1 Paternal BMI,55kg/m22 Maternal BMI, kg/m Maternal morbidity index5 Infant calcium intake, mg/day 5 Infant morbidity index5 Indicator time period 3 Indicator time period 4 Indicator time period 5 Indicator time period 6 Lagged dependent variable, 5 cm Between/within-variance Within-variance 2 X log-likelihood function n

z-scores for weight-for-age NCHS standards 3 U.K. standards 4 Coefficient SE Coefficient SE -8.381* 0.021* 0.069 1.757* -0.007 0.023 -0.050 -0.051 -0.553* -0.238 -0.293 -0.037 0.310* 1.465 -300.26 90.0

2.480 0.007 0.060 0.778 0.042 0.036 0.041 0.182 0.184 0.190 0.192 0.052 0.104

-8.134* 0.016* 0.051 1.880* 0.011 0.023 -0.023 -0.120 -0.339* -0.456* -0.486* 0.284* 0.417* 0.586 160.18 90.0

1.684 0.004 0.040 0.516 0.027 0.022 0.028 0.114 0.117 0.120 0.119 0.056 0.139

1

Values are slope coefficients ± standard errors. The 90 infants were observed six times at monthly intervals. National Center for Health Statistics (1977). 4 Freeman et al. (1995). 5 These variables and the dependent variable were in natural logarithms. *P<0.05. 2 3

were significantly associated with the zscores for weight-for-age. However, the lagged dependent variable was not significant in the model based on the National Center for Health Statistics (NCHS) reference standards. Also, infant morbidity index was not significantly associated with the z-scores for weight-for-age. Overall, the results in Table 6 and 7 were similar. However, the dynamic model for infant weight incorporated the interrelationships between total body weight, skeletal size (length), and lean body tissue (arm circumference), while addressing the issues of endogeneity of certain explanatory variables. This approach was in the spirit of previous contributions to the anthropometric assessment literature (Tanner, 1986; Ehrenberg, 1968; Cole, 1991). Results for scores on Bayley Motor Scale and Bayley Infant Behavior Record The results for scores on the Bayley Motor Scale are reported for three specifications in Table 8. Specification 2 replaced the infants' protein intakes with protein intake from animal sources that has been used as an indicator of diet quality in Kenya (e.g., Neumann et al., 1992). Specification 3 included mean scores on the Brazelton NBAS as an

explanatory variable. The scores on the Bayley Motor Scale were positively associated (P < 0.05) with protein intake and arm circumference. In Specification 2, protein intake from animal sources was a significant predictor (P < 0.05). Infant morbidity was negatively associated with the scores, though the coefficient was not significant at the 5% level (P = 0.10). Infant length, weight, and head circumference were not significant predictors of motor development. The four interaction variables (look, touch, hold, and talk), measuring mother-infant interaction were not significant predictors of scores on the Bayley Motor Scale. In Specification 3, the coefficient of the mean score on the Brazelton NBAS was estimated with a negative sign but was not significant. This was also true when the mean score was replaced by the score on the Motor cluster of the Brazelton NBAS. Thus, the scores on the Bayley Motor Scale were better predicted by infants' nutritional and health status. Early psychological measures lacked the predictive power to warn clinicians and policy makers of potential developmental problems. The results for scores on eight items from the Bayley Infant Behavioral Record in Table

Anthropometric and Psychological Indicators of Kenyan Infants

TABLE

203

8. Regression models explaining scores on Bay ley Motor Scale at 6 months by infants' nutritional morbidity, and mean score on the Brazelton Neonatal Behavioral Assessment Scale1-2

status,

Scores on 33 items from the Bayley Motor Scale Specification 1 Specification 2 Specification 3

Dependent variable, with model

Coefficient

SE

-0.028 0.126

8.321 0.071

0.075 0.840* -0.007

0.137 0.292 0.004

Coefficient

SE

Coefficient

SE

0.819

8.181

2.379 0.131

10.222 0.083

0.209* 0.078 0.790* -0.007

0.088 0.135 0.285 0.004

0.036 0.952* -0.008* -0.281 0.088 82.0

0.168 0.361 0.004 0.608

Independent variable Constant Infant protein intake, g/day Infant animal protein intake, g/day Infant length, cm Infant arm circumference, cm Infant morbidity index Mean score on Neonatal Behavioral Assessment Scale Adjusted R2 n

0.107 100.0

0.129 100.0

1

Values are slope coefficients ± standard errors. The number of items on which the infants passed the test. *P<0.05. 2

TABLE 9. Regression by infants' nutritional

models explaining scores on eight items from the Bayley Infant Behavior status, morbidity, and mean score on the Brazelton Neonatal Behavioral

Dependent variable, with model Independent variable Constant Maternal interaction (talk) Infant protein intake, g/day Infant animal protein intake, g/day Infant length, cm Infant arm circumference, cm Infant morbidity index Mean score on Neonatal Behavioral Assessment Scale Adjusted R2 n

Record at 6 Assessment

months Scale1'2

Score on eight items from Bayley Infant Behavior Record Specification 1 Specification 2 Specification 3 Coefficient SE SE Coefficient Coefficient SE 10.438 11.195* 0.297*

11.231 4.367 0.097

-0.004 1.093* 0.001

0.184 0.399 0.006

0.173 100.0

13.178 12.049*

11.555 4.499

0.209 0.003 0.930* 0.001

0.124 0.190 0.408 0.006

0.118 100.0

7.524 10.860* 0.334*

12.964 4.955 0.107

0.083 1.122* -0.001

0.213 0.467 0.006

-0.516 0.192 82.0

0.792

1

Values are slope coefficients ± standard errors. The items were Endurance, Activity, Banging toys, Manipulating, Body Motion, Energy and Coordination, Coordination of Gross Muscle Movement, and Coordination of Fine Muscle. *P<0.05. 2

9 showed protein intake and arm circumference to be significant predictors (P < 0.05). In contrast with the results for the Bayley Motor Scale, time spent by the mother talking to the infant was a significant predictor of scores. The remaining three interaction variables were not significant. Infant morbidity was not significant in the three specifications in Table 9. The total protein intake was a significant predictor of the scores. The fit of the models left a substantial amount of variation in the data unexplained. This is likely to be a common feature in the analysis of psychological data collected at an early age, partly due to within-subject variation. Nevertheless, the results for the Bayley scales were an improvement over those for

the Brazelton NBAS. Even so, variables such as maternal anthropometric indicators were not significant predictors of scores on the Bayley scales. DISCUSSION This paper studied in detail the proximate determinants of anthropometric and psychological measures of Kenyan infants from birth to age 6 months. The analysis used infant birth weight, and length and head circumference, as indicators of the intrauterine growth environment. The scores on the Brazelton NBAS were analyzed, and the dynamics of physical growth in the period from 1-6 months was investigated by modeling infant length, head circumference, and

204

A. Bhargava

weight. Lastly, the scores on Bayley Motor Scale and the Bayley Infant Behavior Record were analyzed. There are several implications of the empirical results. First, maternal nutritional status was an important predictor of infants' anthropometric measurements at birth. Mothers with a high prepregnancy BMI and free from hookworm infestation were likely to produce babies that were longer, heavier, and with a larger head circumference. Parity was associated with anthropometric measurements in a nonlinear way. Thus, supplying fortified foods to undernourished pregnant women is likely to be beneficial for infant health. Second, the scores on the Brazelton NBAS for the Kenyan infants were not systematically associated with the measures of maternal or infant nutritional status. A comparison of the results for Kenyan infants with those for African American and Puerto Rican infants suggested that, even in undernourished populations such as those from the Embu region, the Brazelton NBAS may not facilitate identification of vulnerable children. This is partly because maternal undernutrition and infection did not appear to have caused neurological defects in Kenyan infants; the Brazelton NBAS may be useful in identifying such problems. Because the Brazelton NBAS is expensive to administer, it would not seem cost-effective to examine infants in sub-Saharan Africa using this test. Third, the dynamic models for length, head circumference, and weight, estimated using data from 1-6 months, showed that maternal nutritional status, and infant nutrition and morbidity, were important factors predicting growth. For example, maternal hemoglobin was positively associated with infant weight and head circumference, maternal BMI was positively associated with infant length and weight, maternal head circumference was a predictor for infant head circumference, infants' calcium intakes were positively associated with length, and infant morbidity was negatively associated with weight. Because the longitudinal analysis controlled for many confounding

factors affecting growth, the empirical results underscored the importance of good maternal nutritional status for infant growth. Fourth, the analysis of scores on the Bayley Motor Development Scale and eight items from the Bayley Infant Behavior Record showed that nutritional status was positively associated with higher scores on the tests. Moreover, the analysis offered insights into the usefulness of arm circumference as a measure for identifying vulnerable children. The quality of diet was an important predictor of scores on the Bayley scales. However, care is needed in interpreting this finding, because weaning can increase the risk of infection (e.g., Mata, 1978). Finally, because psychological measures for young infants may not be very reliable, the physical and mental development of children should be approached in an integrated framework. It is important for researchers to jointly utilize anthropometric and psychological data for identifying vulnerable children in developing countries. While anthropometric measures were seen to be better indicators of early development, the scores on cognitive tests of school-age children from this population were informative from a policy viewpoint (Bhargava, 1998). ACKNOWLEDGMENTS While retaining responsibility for the views expressed, the author is indebted to Nancy Butte, Tim Cole, Peter Reeds, Aristomene Varoudakis, two anonymous reviewers, and the editor of this journal for helpful suggestions. I dedicate this paper to the loving memory of my father, T.N. Bhargava, who passed away on January 19,1999. LITERATURE CITED Adair L, Popkin BM, VanDerslice J, Akin J, Guilkey D, Black R, Briscoe J, Flieger W. 1993. Growth dynamics in the first year of life. Eur J Clin Nutr 47:42-51. Basta S, Soerkirman M, Karyadi D, Scrimshaw N. 1979. Iron deficiency anemia and the productivity of adult males in Indonesia. Am J Clin Nutr 32:916-925. Bayley N . 1969. Bayley scales of infant development. New York: Psychological Corporation. Bhargava A. 1994. Modelling the health of Filipino children. J R Stat Soc [A] 157:417^32.

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Wechsler D. 1981. Wechsler adult intelligence scale— revised. New York: Psychological Corporation. Whaley SE, Sigman M, Espinosa MP, Neumann CG. 1998. Infant predictors of cognitive development in an undernourished Kenyan population. J Dev Behav Pediatr 19:169-177. Wolf AW, Lozoff B. 1985. A clinically interpretable method for analyzing the Bayley infant behavior record. J Pediatr Psychol 10:199-214. World Health Organization. 1994. An evaluation of infant growth. Geneva: World Health Organization.

Journal of Educational Psychology 1998, Vol. 90. No. 1,162-166

Copyright 1998 by the American Psychological Association, Inc. 0022-0663/98/S3.00

A Dynamic Model for the Cognitive Development of Kenyan Schoolchildren Alok Bhargava University of Houston The author presents an integrated analysis of the scores obtained on cognitive tests and school examinations by approximately 110 Kenyan children (aged 6-9 years) in the Embu region of Kenya. A dynamic multivariate model, controlling for the unobserved between-children differences, is formulated for the scores and is estimated using three repeated observations. Children's body mass index, head circumference, hemoglobin concentration (i.e., measures of biological development), and grade level are important predictors of the scores on higher order cognitive tests. The family household's socioeconomic status is positively associated with cognitive scores, and children's morbidity is negatively associated. Only grade level and school attendance, however, are significant predictors of scores on school examinations. The implications of the results are briefly discussed.

Economic development and well-being of inhabitants of less developed countries depend on education levels (e.g., literacy rates) attained by the population. Children's ability to learn concepts is likely to depend on their nutritional status and the school and home environments. Economists are, therefore, interested in analyzing the effects of socioeconomic, nutritional, environmental, and educational variables on the cognitive development of children. Typically, such relationships are complex and demand the specification and estimation of several multivariate models using econometric techniques. The results from such integrated analyses of psychometric and other health indicators are valuable for allocating scarce resources in the education and health sectors. The diets of many children in less developed countries are deficient in protein and vital micronutrients such as iron and zinc. Because these nutrients affect brain development, much effort has been made in the fields of nutrition and psychology to assess their impact on cognitive development (e.g., Grantham-McGregor, 1995; Levitsky & Strupp, 1995; Monckeberg, 1975; Pollitt, Gorman, Engle, Martorell, & Rivera, 1993; Scrimshaw, 1994; Wachs et al., 1995; Youdim, Ben-Shachar, & Yehuda, 1989). Most analyses of children's cognitive development, however, do not simultaneously address the effects of socioeconomic, nutritional, health, and educational variables on child development. Doing so is particularly appealing when longitudinal data sets are used because one can also tackle the unobserved betweenchildren differences underlying cognitive development. Previous analyses of longitudinal data on children in the Embu region of Kenya have reported simple correlations between the aggregate cognitive test scores and energy This study was supported by the Research Committee of the World Bank. I thank Martin Ravallion, Nevin Scrimshaw, and Alexander Siegel for helpful comments. Correspondence concerning this article should be addressed to Alok Bhargava, Department of Economics, University of Houston, Houston, Texas 77204-5882. Electronic mail may be sent to [email protected].

intake from animal sources (Espinosa, Sigman, Neumann, Bwibo, & McDonald, 1992; Sigman, Neumann, Jansen, & Bwibo, 1989). Certain anthropometric measures and family characteristics were also found to be correlated with test scores. These models, however, do not exploit the longitudinal nature of the data. Multiple observations on health indicators afford a systematic investigation of the dynamics of cognitive development; the importance of dynamic formulations in applied work is now recognized by many psychologists (e.g., Vallacher & Nowak, 1994). I present an integrated analysis of the scores obtained by Kenyan children on cognitive tests and school examinations; the influence of dietary, familial, educational, and socioeconomic factors are modeled within a dynamic random-effects framework Furthermore, the model for test scores is consistent with the "cumulative deficit hypothesis" (e.g., Guzman, 1968) that has been advanced for underprivileged children. In this framework, cognitive development is viewed as a continuous and a dynamic process (i.e., past learning affects children's capacity to assimilate knowledge in the current period). In assessing children's physical health in developing countries, data are often collected on height, weight, and sicknesses (Bhargava, 1994). However, analyses based on these health indicators shed little light on children's capacity to grasp abstract concepts. More critical are measures of brain development, such as the growth in head circumference (Tanner, 1989). Nutrient intakes, hemoglobin concentration, home and school environments, and socioeconomic factors are also important variables for explaining children's cognitive development, especially when the goal is to inform education and health policies.

Method Participants The data were derived from surveys sponsored by the U.S. Agency for International Development (USAID; 1992) in 1984 to

A. Bhargava

208

1985 in the Embu region of Kenya. Of the 2,059 households in the region, a sample of 292 households with children were selected for the study. The children for whom the measurements on cognitive tests and school examinations were available were in the 6- to 9-year age group.

Measures and

Econometric

Procedure

Assuming that N children are observed in three survey rounds, the dynamic model for scores on cognitive tests can be written as (with i = 1,. ..,N;t = 2, 3):

Procedures

The children were given a battery of cognitive tests three times during the academic year 1984 to 1985. The verbal comprehension component was similar to the Peabody Picture Vocabulary Test (Dunn & Dunn, 1981) adapted to urban settings in East Africa. The children also took the Raven Coloured Progressive Matrices (Raven, 1965), and arithmetic and digit span tests. Behavioral cooperation was assessed by trained observers assigning scores (on a scale ranging from 1 to 8) for cooperativeness, goal directedness, attention span, and an overall judgment of the test. The scores on school examinations in the three terms during the observation period were also recorded. Children's "standard" assumes discrete values of 1, 2, and 3 for these respective grade levels; kindergarten is set equal to 0.5. School attendance was recorded for the academic year; the number of days for which a child was absent was obtained from the attendance records. Observations on classroom behavior were made by recording children's behavior using a time-sampling procedure of 10 s. Observers recorded whether the child talked to another child, played with an object, or was off task in the 10-s interval. The intake of approximately 40 nutrients in the three survey rounds was estimated by averaging the intake data available for 2 consecutive days every month. Initially, food intakes were assessed by the recall method and by weighing food portions; these intakes were converted into nutrient intakes using food composition tables (Murphy, Weinberg-Anderson, Neumann, Mulligan, & Calloway, 1991) and by laboratory analyses of indigenous recipes. Sicknesses of children were recorded every 2 weeks during the observation period. The number of days for which a child was sick with different symptoms was combined to form an index of morbidity (Bhargava, 1994). Children's height, weight, arm and head circumference, and skinfold thickness were measured monthly; electronic scales were used to measure weight. Two independent measurements were taken for these anthropometric variables. The correlations between the measurements were greater than .95; thus, only the first set is used. These monthly measurements were averaged to produce figures corresponding to the three data points at which the cognitive tests were given. In addition, blood analyses measured the children's hemoglobin levels, white blood cells, and so on at least once during the sample period; intensity of hookworms in the stool was recorded once. For each child, data on parents' education, age, and earnings were recorded; the parents took a revised version of the Wechsler Adult Intelligence Scale and the Raven Coloured Progressive Matrices. Sanitation and hygiene practices of the household were recorded. An index of socioeconomic status (SES) was constructed on the basis of household possessions and cash income. Parents' anthropometric measurements, episodes of sicknesses, and blood assays and pregnancy status of women were also available in the data set. For further details of the study design, see USAID (1992). Overall, there were longitudinal data on approximately 120 children. However, because of missing observations on certain variables, sample sizes used in the estimation ranged from 77 to 109.

+ XfHTi, + \2HD„ + V,W„ + \tMu + «,„ (1) where z and x are, respectively, time-invariant and time-varying regressors; and HTt„ HDit, Wu, and Mit are, respectively, height, head circumference, weight, and morbidity of the (th child in time period t. The coefficients of regressors are denoted by Greek letters. Because the number of survey rounds is small, the estimation theory assumes that the number of children (N) is large but the number of time observations is fixed. Thus, initial observations on the dependent variables are treated as endogenous variables (correlated with the errors; Bhargava & Sargan, 1983). The errors («,,) affecting the dynamic model (Equation 1) are assumed independent across children but correlated over time with a positive definite variance-covariance matrix. The conventional random-effects model is a special case of this formulation;

«,, = °, + v„,

(2)

where 8 is the specific random effect and v is the independently distributed random variable. The joint determination of test scores and health indicators such as head circumference implies that certain regressors are potentially endogenous variables. This is because unobserved factors affecting such variables could be related to the random effects (8) affecting Equation 1. It is thus necessary to test the exogeneity of some regressors and estimate equations in the presence of endogenous variables. This can be achieved by rewriting the dynamic model in a simultaneous equations framework. A reduced form for initial observations and a system of (T - 1) structural equations for remaining time periods can be defined as follows (Bhargava & Sargan, 1983): m

y« = 2

T

(7"-l)Xr

V

jk *ijk + ",1 (' = 1

N)

(3)

j=\ k=\

j=0

B

T

*
Y'

+

TXN

C,

Z'

( T - l ) X ( m + l) +

Cx

X'

(T - 1) X nT nTXN

(m+l)XAr =

U'

(4)

(T - 1) X N

Here, Y, Z, and X are, respectively, matrices containing observations on the dependent, time-invariant, and time-varying variables. B is a (T — 1) X T lower triangular matrix of coefficients: B a = a , S i i i + 1 = -l,fi 1 J = 0. Otherwise,;' = 1 , . . . , T - 1; j = 1,. . . , T.

Cognitive Development of Kenyan Schoolchildren

The matrices Cz and Cx contain coefficients of time-invariant and time-varying regressors, respectively. U contains the error terms. Details of the estimation methods for dynamic models are presented elsewhere (Bhargava & Sargan, 1983). It should be mentioned here that maximum likelihood estimates are computed using a numerical scheme to optimize the profile likelihood function. Asymptotic standard errors of the parameters are obtained by numerically approximating second derivatives of the function at the maximum. The exogeneity hypothesis of zero correlation between, for example, n2 time-varying regressors (x2) and random effects is tested by a likelihood ratio statistic. With three time observations available in the data, the statistic is asymptotically distributed as a chi-square variable with 3n2 degrees of freedom. Results and Discussion The sample means of selected variables used in the analysis are presented in Table 1; these statistics revealed minor boy-girl differences. The parameters of models for scores on cognitive tests and school examinations are reported, respectively, in Tables 2 and 3. Empirical Results for Children's on Cognitive Tests

Scores

Table 2 presents maximum likelihood estimates of the dynamic random-effects model for scores on cognitive tests; asymptotic standard errors also are reported. Total score was subsequently disaggregated into three components (i.e., a score combining digit span, Raven matrices, and arithmetic scores [DRA]; word meaning; and behavioral

209

cooperation). The variables were transformed into natural logarithms to reduce heteroscedasticity (Nelson, Black, Morris, & Cole, 1989); the reported coefficients are thus short-run elasticities (percentage change in the dependent variable resulting from 1% change in an explanatory variable). In the model explaining total scores on cognitive tests, the coefficients of head circumference, body mass index (calculated from height and weight data), and morbidity were statistically significant (p < .05). That is, biological development depending on children's nutritional status (measured by uieir body mass index and head circumference) proved to be an important predictor for higher order cognitive development as reflected by the DRA measures (Binet & Simon, 1916). That the intakes of energy, protein, and iron were not significant predictors was probably because many of the important determinants of test scores such as households' SES, parents' scores, and children's grade level are modeled in the present analysis (cf. Sigman et al., 1989). Also, there is typically a large amount of within-subject variation in nutrient intakes (arising from the nutrient composition of foods), which obscures statistical relationships (e.g., Nelson et al., 1989). The empirical results for DRA scores contrast with those for word meaning. Although head circumference appeared with a large and significant (p < .05) coefficient in the DRA model, this coefficient was statistically not different from zero in the word-meaning relationship, which better reflects learning from the environment (e.g., Gottlieb, 1983; Vygotsky, 1987). Hemoglobin concentration was significant (p < .05) in the model for DRA; body mass index was

Table 1 Sample Means and Standard Deviations of Selected Variables in the Kenyan Data M

Fathers

Girls

Boj 'S

Variable

SD

M

SD

M

SD

Mothers M

SD

Cognitive test score* 68.03 13.91 68.34 16.98 106.05 24.71 90.16 18.85 School examination scorea 36.81 25.98 37.32 24.10 b Hemoglobin 118.68 11.98 122.59 13.97 143.58 13.46 118.02 16.26 Height (cm) 116.58 5.41 114.97 7.28 162.53 20.48 153.98 5.89 Head circumference (cm) 51.28 1.40 50.21 1.49 55.75 1.57 53.55 1.38 Weight (kg) 20.44 2.28 19.74 3.07 54.83 6.94 51.78 8.35 Morbidity' 28.05 37.40 24.06 39.49 30.35 38.95 50.50 53.78 Aged 6.99 0.45 6.81 0.47 38.85 7.08 34.78 9.14 e Household size 8.34 2.38 8.46 2.46 1 SES + cash income 2.53 0.71 2.70 0.70 Standard* 1.10 0.55 1.30 0.66 Energy (kcal) 1499.49 326.09 1319.79 281.37 Protein (g) 43.62 11.94 38.12 10.14 Iron (mg) 14.99 4.06 13.11 3.30 Note. There are 48 boys and 35 girls included in these calculations. SES = socioeconomic status. 'Raw scores. b Measured per deciliter of blood. 'Weighted index based on number of days for which a person is sick, with different symptoms counting as additional sickness days. d Age on July 1,1984, is in years. 'Number of persons in household. Index based on household possessions and income. g Grade level (kindergarten = 0.5).

210

A. Bhargava

Table 2 Maximum Likelihood Estimates of the Models for Scores on Cognitive Tests Total score Variable/parameter Coefficient SE Constant -1.077 Hemoglobin 0.089 b Parents' score 0.108* Standard 0.169** C SES + cash income 0.082** Head circumference 0.647** Body mass index 0.351** Morbidity11 -0.014** Lagged dependent variable 0.191* Between/within variance ratio 0.412* Within variance 0.012 9.800 xV/= 9f n 104

0.665 0.104 0.065 0.038 0.042 0.037 0.166 0.006

Digit span + Raven matrices + arithmetic Word meaning Coefficient SE Coefficient SE -6.523 3.046 -0.456 2.723 0.234** 0.108 0.098 0.149 0.151** 0.075 0.135 0.140 0.279** 0.061 0.231** 0.057 0.057 0.078 0.197** 0.064 1.658** 0.856 0.029 0.664 0.410* 0.231 0.698** 0.261 -0.023** 0.010 -0.006 0.009

Behavioral cooperaldon" Coefficient : SE 0.784 -0.022 0.178* 0.085** -0.018 0.322 0.146 -0.015

2.330 0.130 0.095 0.032 0.050 0.548 0.205 0.009

0.112

0.083

0.105

0.151

0.148

0.037

0.092

0.264

0.779** 0.031 17.870** 104

0.379

0.382 0.026 0.650 104

0.311

0.072 0.029 12.400 106

0.091

Note. All variables are in logarithms. Children were observed in three survey rounds. SES = socioeconomic status. "Includes cooperativeness, goal directedness, attention span, and judgment of the test. 'Corresponds to respective components for children. c Based on household possessions. d Index based on number of days for which the child is sick in each survey round. likelihood ratio test statistic for exogeneity of head circumference, body mass index, and morbidity. *p < .10. **p < .05. significant (p < .05) in the models for DRA and word meaning. However, the anthropometric indicators were not significant predictors of the scores on behavioral cooperation. Table 3 Maximum Likelihood Estimates of the Model for Scores on School Examinations Specificati ion V Variable/parameter

Coefficient

SE

Specification 2b Coefficient

SE

2.875** 1.437 -0.604 5.467 Constant Hemoglobin -0.135 0.220 — Absent0 -0.093** 0.039 -0.093** 0.038 0.231** 0.103 0.277** 0.100 Standard -0.028 0.183 Parents' score — SES + cash income -0.055 0.125 -0.056 0.130 Head circumference 1.145 1.373 — Body mass index 0.345 0.521 0.495 0.493 Morbidity -0.012 0.021 -0.009 0.019 Lagged dependent variable 0.246** 0.121 0.181* 0.116 BetweenAviuiin variance ratio 0.0623 0.144 0.211 0.185 Within variance 0.120 0.122 2 X (d/=9and6, respectively) 5.13 5.38 n 77 81 Note. SES = socioeconomic status. "Chi-square statistic tests exogeneity of head circumference, and morbidity. b Chi-square statistic tests exogeneity of body mass index and morbidity. c Number of days for which the child is absent from school. *p < .10. **p < .05.

Results for Scores on School

Examinations

Table 3 reports maximum likelihood estimates of the model for scores on examinations during the three school terms. Two qualifications are necessary here. First, the data on examinations were available for a smaller number of children, and information is limited to the total score. Second, because examination scores were compiled using records from 15 schools, the scores could reflect schoolspecific scoring bias (Goldstein & Thomas, 1996; Ceci, 1991). Indicator variables for schools were included in the model for examination scores. However, coefficients of these indicators were all nonsignificant, implying that the school environment is similar for most children; thus, the between-school differences were not represented in Table 3. In contrast with the results for cognitive test scores, the coefficients of anthropometric variables were not significant in Table 3. Overall, on the basis of results in Tables 2 and 3,1 conclude that nutrition can relatively affect children's biological development and higher order cognitive function. The effects of nutrition on the scores on vocabulary tests were less strong. Moreover, school performance, as measured by the examination scores, could not be predicted by nutritional variables, probably because the examination scores do not fully reflect children's abilities. Thus, cognitive tests are useful measures for identifying children in developing countries whose cognitive development might be compromised by nutrient deficiencies. References Bhargava, A. (1994). Modelling the health of Filipino children. Journal of the Royal Statistical Society A, 157, 411-432.

Cognitive Development of Kenyan Schoolchildren

Bhargava, A., & Sargan, J. D. (1983). Estimating dynamic random effects models from panel data covering short time periods. Econometrica, 51, 1635-1660. Binet, A., & Simon, T. (1916). The development of intelligence in children. Baltimore: Williams & Wilkins. Ceci, S. J. (1991). How much does schooling influence general intelligence and its cognitive components? A reassessment of the evidence. Developmental Psychology, 27, 703-722. Dunn, L. M., & Dunn, L. M. (1981). Peabody Picture Vocabulary Test—Revised. Circle Pines, MN: American Guiding Service. Espinosa, M. P., Sigman, M. D., Neumann, C. G., Bwibo, N. O., & McDonald, M. A. (1992). Playground behaviors of school-age children in relation to nutrition, schooling, and family characteristics. Developmental Psychology, 28, 1188-1195. Goldstein, H., & Thomas, S. (1996). Using examination results as indicators of school and college performance. Journal of the Royal Statistical Society A, 159, 149-163. Gottlieb, G. (1983). The psychobiological approach to developmental issues. In M. Haith & J. J. Campos (Eds.), Infancy and developmental psychobiology (Vol 2, pp. 1-26). New York: Wiley. Grantham-McGregor, S. (1995). A review of the studies of the effect of severe malnutrition on mental development. Journal of Nutrition, 125, 2233S-2238S. Guzman, M. (1968). Impaired physical growth and maturation in malnourished children. In N. S. Scrimshaw (Ed.), Malnutrition, learning and behavior (pp. 42-54). Cambridge, MA: MIT Press. Levitsky, D. A., & Strupp, B. J. (1995). Malnutrition and the brain: Changing concepts, changing concerns. Journal of Nutrition, 125, 2212S-2220S. Monckeberg, F. (1975). Effects of malnutrition on physical growth and brain development. In J. W. Prescott, M. S. Read, & D. Coursin (Eds.), Brain function and malnutrition: Neurophysiological method of assessment. New York: Wiley. Murphy, P. M., Weinberg-Anderson, S. W, Neumann, C , Mulligan, K., & Calloway, D. H. (1991). Development of research nutrient data bases: An example using food consumed in rural Kenya. Journal of Food Composition and Analysis, 4, 2-17. Nelson, M., Black, A. E., Morris, J. A., & Cole, T. J. (1989). Between-and-within subject variation in nutrient intake from

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infancy to old age: Estimating the number of days to rank dietary intakes with desired precision. American Journal of Clinical Nutrition, 50, 155-167. Pollitt, E., Gorman, K. S., Engle, P. L., Martorell, R., & Rivera, J. (1993). Early supplementary feeding and cognition. Monographs of the Society for Research in Child Development, 58(7, Serial No. 235). Raven, J. C. (1965). The Coloured Progressive Matrices Test. London: Lewis. Scrimshaw, N. S. (1994). Malnutrition, brain development, learning and behavior. Tokyo: United Nations University. Sigman, M., Neumann, C , Jansen, A. A. J., & Bwibo, N. (1989). Cognitive abilities of Kenyan children in relation to nutrition, family characteristics, and education. Child Development, 60, 1463-1474. Tanner, J. M. (1989). Foetus into man. Cambridge, England: Harvard University Press. U.S. Agency for International Development. (1992). Functional implications of malnutrition (Kenya project, final report.) Washington, DC: Author. Vallacher, R. R„ & Nowak, A. (Eds.). (1994). Dynamical systems in social psychology. San Diego, CA: Academic Press. Vygotsky, L. S. (1987). Thinking and speech. In R. W. Rieber & A. S. Carton (Eds.), Collected works ofL. S. vygotsky (Vol. 1, pp. 39-285). New York: Plenum. Wachs, T. D., Bishry, Z., Moussa, W., Yunis, R, McCabe, G., Harrison, G., Sweifi, E., Kirksey, A., Galal, O., Jerome, N., & Shaheen, F. (1995). Nutritional intake and context as predictors of cognition and adaptive behavior of Egyptian school-age children. International Journal of Behavioral Development, 18, 425^150. Youdim, M. B. H., Ben-Shachar, D., & Yehuda, S. (1989). Putative biological mechanisms of the effects of iron deficiency on brain biochemistry and behavior. American Journal of Clinical Nutrition, 50, 607-617. Received February 12, 1997 Revision received August 6, 1997 Accepted August 12, 1997 •

Anthelmintic treatment improves the hemoglobin and serum ferritin concentrations of Tanzanian schoolchildren

Alok Bhargava, Matthew Jukes, Jane Lambo, C. M. Kihamia, W. Lorri, Catherine Nokes, Lesley Drake, and Donald Bundy Abstract To investigate the relationships between helminth infections and iron status among school-aged children, 1,115 Tanzanian children in grades 2 through 5 were randomly assigned to treatment or control groups. The children in the treatment group were screened for infection with Schistosoma h a e m a t o b i u m and hookworm at baseline, 3 months, and 15 months; infected children were given albendazole against hookworm and praziquantel against schistosomiasis. The control group received a placebo and did not undergo parasitological screening until 15 months after the baseline. Hematological variables were compared between the treatment and control groups. The main results were, first, that the hemoglobin concentration significantly improved after treatment for hookworm (p < .001) by 9.3 g/L in children treated for hookworm only and by 8.8 g/L in children treated for hookworm and schistosomiasis. The ferritin concentration also improved in children treated for schistosomiasis (p = .001) or hookworm (p = .019). Second, a longitudinal analysis of the data from the children in the control group showed that hookworm and schistosomiasis loads were negatively associated with hemoglobin and ferritin concentrations. Moreover, ferritin concentrations increased as C-reactive

Alok Bhargava is affiliated with the Department of Economics, University of Houston, Houston, Texas, USA. Matthew Jukes, Jane Lambo, and Lesley Drake are affiliated with the Partnership for Child Development, Imperial College School of Medicine, London. C. M. Kihamia and Catherine Nokes are affiliated with the Tanzanian Partnership for Child Development (UKUMTA), Dar es Salaam, Tanzania. W. Lorri is affiliated with the Tanzania Food and Nutrition Centre, Dar es Salaam, and Donald Bundy is affiliated with the Tanzania Food and Nutrition Centre, Dar es Salaam, and the World Bank, Washington, DC. Address queries to the corresponding author: Alok Bhargava, Department of Economics, University of Houston, Houston, TX 77204-5019; telephone (713) 743 3837; fax (713) 743 3798; e-mail: [email protected]. Mention of the name of firms and commercial products does not imply endorsement by the United Nations University.

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protein levels increased. Overall, the results showed that anthelmintic treatment is a useful tool for reducing anemia in areas with high hookworm and schistosomiasis endemicity. The empirical relationship between ferritin and C-reactive protein indicated that simple procedures for adjusting cutoff points for the use of ferritin as an indicator of low iron stores were unlikely to be useful in this population.

Key w o r d s : Anemia, anthelmintic treatment, ferritin, hemoglobin, iron deficiency, longitudinal data, schistosomiasis, schoolchildren, Tanzania

Introduction Iron deficiency and iron-deficiency anemia are widely prevalent in low-income countries [1]. Iron-deficiency anemia adversely affects the physical and mental development of children [2-4] and may consequently hamper economic development [5]. In sub-Saharan Africa, helminth infections contribute significantly to the prevalence of anemia [6-8]. School-age children bear the largest b u r d e n of these diseases; there is a high prevalence of anemia (hemoglobin < 120 g/L) in schoolchildren across sub-Saharan Africa [9]. Treatment for hookworm can improve hemoglobin concentration and iron stores [10, 11], but there are mixed results regarding the effect of t r e a t m e n t for schistosomiasis on hemoglobin concentration [12-14] and iron stores [13]. However, observational studies [15] have demonstrated a relationship between schistosomiasis and iron stores. For b o t h hookworm and schistosomiasis, it m a y b e necessary to administer iron supplementation in addition to anthelmintic treatment to see an improvement in iron status [13]. The aim of the current study was to investigate further the effects of anthelmintic treatment on the iron status of school-age children; the methodology for assessing iron status was also i m p o r t a n t for the investigation. Thus far, there is no general agreement

Food and Nutrition Bulletin, vol. 24, no. 4 © 2003, The United Nations University.

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on the interpretation of indicators of iron stores or on the choice of indicators to define iron deficiency in populations where subclinical parasitic infections are endemic. For example, the disease environment can complicate the interpretation of ferritin as a measure of iron stores [16-18]. Some researchers have suggested that the cutoff points for ferritin should be increased in populations where C-reactive protein levels are elevated [18]. Such adjustments maybe misleading in situations where, for example, ferritin increases unabatedly with increases in C-reactive protein levels. The current study aimed to investigate the relationships among children's hemoglobin, ferritin, and C-reactive protein status by assessing the impact of treatment for hookworm and schistosomiasis on these indicators over a period of 15 months and by analyzing these relationships in children in the control group during the observation period.

Methods Participants

at the beginning of the study (treatment group), and the other was not screened until the end of the study (control group). Children were randomized to these groups after stratification according to sex and the four grade levels in the 10 schools. Following the baseline parasitology survey, children in the treatment group were selected to take further part in the study if they were either "uninfected" (< 50 eggs per gram of stool for hookworms and < 5 eggs per 10 ml of urine for schistosomiasis) or "heavily infected" (> 400 eggs per gram of stool for hookworm and/or > 50 eggs per 10 ml of urine for schistosomiasis). Children with "moderate infections" (> 50 and < 400 eggs per gram of stool for hookworm, > 5 and < 50 eggs per 10 ml of urine for schistosomiasis) took no further part in the study, partly because the broader objective of the study was to assess the impact of anthelmintic treatment on cognitive function. Hereafter, "infected" refers to "heavily infected," as defined above. Children infected with hookworm were given 400 mg of albendazole (SmithKline Beecham, Brentford, UK) for three consecutive days. A single dose of praziquantel (40 mg/kg of body weight; E. Merck Pharmaceutical Division, Darmstadt, Germany) was given against schistosomiasis. The chemotherapy was repeated at survey round 2 for children in the treatment group who had become infected since survey round 1.

The data were collected in Tanzania as part of a larger study to investigate the effects of anthelmintic treatment on schoolchildren's cognitive function and educational achievement [ 19]. The study was conducted in 10 schools in the coastal area of Bagamoyo and Kibaha In survey round 3, children in the control group districts, and measurements were taken at baseline, 3 were also tested for hookworm, schistosomiasis, and months, and 15 months. A school was eligible if more other parasitic infections; all infected children in the than 100 children were enrolled in grades 2 through 5, control and treatment groups were treated at the end if it was accessible by road during the rainy season, of the study. All children received three vitamin B and if it had a relatively high (> 20%) prevalence of tablets containing mixtures of 1 mg of thiamine, 1 mg Schistosoma haematobium, as estimated by self-report of riboflavin, and 10 mg of nicotinamide in the three questionnaires. Children were eligible to participate survey rounds; the nurses who treated the children in the study if they were 9 to 15 years old and were were blinded to the nature of the tablets administered. enrolled in grades 2 through 5. Children were excluded Overall, 1,115 children entered the trial, 270 with heavy if the parent or guardian refused consent, or if the child infections, 116 with no or very light infections, and had severe clinical symptoms of infections, physical or 729 in the control group, whose infection status was mental handicaps, or other chronic diseases. The study unknown at baseline (fig. 1). design was explained to the children and parents in Kiswahili, and the children and the parents signed a Demographic and socioeconomic variables written consent form before participation. The ethics committees of the Institute of Child Health, London, The child's date of birth was recorded from the school the Tanzania Ministry of Health, and the Tanzania register. Children for whom only the year of birth was Ministry of Education and Culture approved the known were assigned a birth date of June 15. Detailed study design. The surveys started in May 1997, and background information was collected for the houseeach round lasted approximately three months. Survey holds, including the construction materials of the roof, round 2 commenced in September 1997 and was com- walls, and floor. The source of drinking water, availpleted by December 1997. Survey round 3 started in ability of toilet facilities, and number of key household October 1998 and was completed by December 1998. possessions (bicycle, radio, refrigerator) and livestock A total of 2,004 children in grades 2 through 5 were were recorded. The information was collected through eligible for participation in the study. Of these, 1,650 interviews with children and validated for a subsample children returned the signed consent form and were by observation in the home and interviews with parincluded in the longitudinal study (fig. 1). The chil- ents. An overall index of economic wealth was created dren were then divided into two equal groups; one by summing the scores across selected variables. The group was screened for their parasitological status investigators designed and carried out the surveys.

Hemoglobin and Serum Ferritin Concentrations of Tanzanian Schoolchildren

EliH'blcrhiklTii in p irlu.ip-Tin:: •.rhocl-in 2('(U)

Chi'drtn 'ctu'nns l o n w n : 1(j'in« (n.-165(ii R-riHomira'.ion So-Mod fo-t'c.ilrnr-nl gniup 'i-H-l'') 1 Ava'l.ibln L-.i basdinr in--S'. -;)

I

I I lookjvorm -- -100 esfi=.'K ifool or Sc hr.'osorm -••50 (^RS/ 10 ml urinr (n=27(i)

Hookworm bctwcc n 50 and '100 i-CBs/ij ".tool anc Sch-ilowma between 5
I IcmaloiOHy and rinlhroprjmrhy fn-?70)

Baseline May-August

1997

Albcnii i?ok- O'llv in 56) I'ldzRpantc! orly in-79) AlbL'nd.i7olr a-id pr.izii|LintH (n-135)

First follow up, 3 months (mean=108 days) after baseline

Hi'mnlnlngy. iinlrirupomclry and parasitosis, (n-2'1-1) Missing data (n 2fi)

Viiamm B only ;n 183) Albendazole only (n 37) P'S7Kju.i:ilcl on!y !n~19) Albendazole and pr.!/,iqi.,,Hi'H ;n-

Second follow up, 15 months (mean=448 days) after baseline

Hcirkitulogy. iinthiupomclry, and parasitology (n-228) iVVsiinR data (n- 52)

S( It r lev fur (ortiol ,;m ip (n-801i /wail.ih r- al h.Tii Irir- (n---7.""j) Huok'.vurm •-. 50 r-f;^'^ *'uol and 5rhistor.oir.i . • 5 c w / 1 0 il jrinr f-i-:116)

Hom.itolog> and .inth-opurrviy
Vilamin B or;iy ,'-i I ' f )

Hematology, anthropometry, and parasitology .n KMi) Mining ri.r..i
Vlt'imin B only (n 68) Albendazole only f n - 3 ' ) Piazii:uairi>' only 'i-=6) Albendazole ::nd praziriuanlr1 T - 1 )

Hematology, iinll ro:>omr--iy .'rid p d asr.o'OiiV

(:i=103) Mus ni" d i: i (n-13)

FIG. 1. Randomization of children to treatment and control groups and retention in trial

I IcmsloioHy -Hid .irthmiiumtltv (n=/29j

V-lar •:;•, C only in

Hrnid'olof,'/ ,
(n-fio;

Vitamin B only (n

He-iialok',
215

A. Bhargava et al.

216 Anthropometry and hematology

Parasitology

The children's weight, height, mid-upper-arm circumference, and skinfold thickness were measured in each survey round by trained observers. Electronic scales (Soehnle, Germany) were used to measure weight to the nearest 0.1 kg; the scales were intermittently checked for accuracy. The children were weighed barefoot in school uniforms. Height was measured twice with a portable stadiometer (CMS Weighing Equipment, London) with the child standing upright. If the observations differed by more than 2 mm, a third measurement was taken. The correlation between the two measurements was very high (> 0.98). Left midupper-arm circumference was measured to a precision of 2 mm with a waxed paper insertion tape (TALC, St. Albans, UK). Duplicate measurements of triceps skinfold thickness were taken with Holtain calipers (CMS Weighing Equipment, London). In each survey round, the nurses drew 2 ml of blood with sterilized syringes and transferred the blood to a prelabeled tube that had a drop of EDTA to prevent clotting. A cuvette was filled immediately with blood for analysis with a portable photometer (HemoCue, Sheffield, UK). If the hemoglobin was < 80 g/L, the child's blood was retested on the next day, and if the second value was also < 80 g/L, the child was referred to a physician. The nurses prepared a malaria thick smear, and the dried slides were placed in a box with ice packs along with the tubes containing blood. The boxes were immediately transferred to the local storage area, and the tubes containing the blood samples were centrifuged at 3,000 revolutions/min. Aliquots of 250 ul of plasma were pipetted into three separate tubes; the samples were stored in a freezer at -20°C. The slides for malaria diagnosis were processed within three days of collection and were stained with 3% Giemsa stain, which was prepared in the laboratory by diluting 1.5 ml of Giemsa stock with 150 ml of buffered water. The slides were immersed for 45 minutes, washed and dried, and then read under an oil-immersion objective. The results were recorded as the number of parasites per 200 white blood cells. Ten fields were examined. Ferritin and C-reactive protein were measured by sandwich enzyme-linked immunosorbent assay (ELISA) using capture and horseradish peroxidase-conjugated antibodies to ferritin and C-reactive protein (Dako, Cambridge, UK). The C-reactive protein and ferritin standards were supplied by Behring Diagnostic (Milton Keynes, UK) and Dako, respectively. The substrate used was 3, 3', 5, 5'-tetramethylbenzidine dihydrochloride (Sigma, Poole, Dorset, UK). Samples and quality controls were diluted in phosphate-buffered saline containing 0.05% Tween 20 and were run in duplicate.

Three urine samples were taken at each survey round from children in the treatment group on three consecutive days during school hours; the children brought stool samples to the school in a prelabeled container. For children in the control group, urine and stool analyses were performed in the third survey round. Approximately 20 ml of the urine sample was transferred to a universal tube with a pinch of Borax to stop bacterial growth without distorting the eggs. The urine and stool samples were placed in plastic bags and transported to the local laboratory for examination of parasite eggs. For S. haematobium, a 10-ml sample was filtered through a 12-mm-diameter polycarbonate membrane with a 12-um pore size (Costar, UK). The slides were read under a microscope at low power. The number of eggs counted was expressed per 10 ml of filtered urine as an indicator of infection intensity. Two sets of observations were made, and the results were averaged to produce a more reliable estimate of egg count. A random sample of 10% of the urine samples was analyzed for accuracy by the chief technician at the laboratory. The stool samples were examined for hookworm and other infections, such as Ascaris lumbricoides and Trichuris trichiura. For hookworm, duplicate slides containing approximately 25 mg of stool were prepared using the Kato-Katz technique [20]. A cellophane piece that had been soaked overnight in glycerol/malachite solution was placed on top of the sample. The slide was left for 7 to 10 minutes at room temperature before it was read under a microscope. Hookworm eggs were counted and expressed as eggs per gram of stool. Similarly, the number of eggs per gram of stool was estimated for other parasite species. The duplicate observations on hookworm egg counts were averaged for the data analysis. Statistical analyses Two lines of analysis are presented here. First, the effects of anthelmintic treatment on hemoglobin and ferritin were assessed by analyses of data from three survey rounds, performed separately for the treatment and control groups. Data from the treatment group were analyzed according to baseline infection status. Because the control group's baseline infection status was not known, these children could not be included in one of the analyses for the treatment group. Second, a longitudinal analysis of children in the control group at the three time points was performed to estimate the relationship of schistosomiasis and hookworm egg counts to hemoglobin, ferritin, and C-reactive protein, taking into account the interrelationships among these three variables.

Hemoglobin and Serum Ferritin Concentrations of Tanzanian Schoolchildren The first line of analysis used three-way praziquantel treatment x albendazole treatment x survey round repeated-measures analysis of variance (ANOVA) to test the null hypotheses that treatment had no effect on hemoglobin, ferritin, and C-reactive protein. A statistical software package [21] was used to compute the descriptive statistics and perform the ANOVAs. The longitudinal analysis of hemoglobin, ferritin, and C-reactive protein status for 602 children in the control group was conducted by using random-effects models [22]. Econometric methods [23] were used to estimate three models, assuming a random-effects error structure that allowed for between-children differences. The advantage of using econometric techniques was that they permitted child-specific random effects to be correlated with some of the explanatory variables in the model. For example, poor diet quality due to low income may affect children's hemoglobin status; low income can also affect C-reactive protein levels by its effects on hygiene and sanitation. Thus, C-reactive protein was potentially correlated with the errors on the model for hemoglobin status. Standard statistical techniques do not allow such correlations and would result in inconsistent parameter estimation. The dependent variables in the three models were hemoglobin, ferritin, and C-reactive protein concentrations. For all three models, explanatory variables included household possessions and socioeconomic status, age, height, malarial parasite count, and hookworm and schistosoma egg counts. The interdependence of hemoglobin, ferritin, and C-reactive protein status was incorporated according to the following two a priori considerations:

217

First, ferritin is known to increase with C-reactive protein levels [16], although the rate of increase may vary with C-reactive protein levels. The model for ferritin included both the C-reactive protein level (CRP) and the square of the C-reactive protein level (CRP2) as explanatory variables to investigate whether ferritin increased with C-reactive protein at a decreasing or an increasing rate. Second, hemoglobin status can be an important indicator of the ability to resist infection [24, 25]. Thus, the model for C-reactive protein included hemoglobin status as an explanatory variable. C-reactive protein was also included as an explanatory variable in the model for hemoglobin to test for possible effects of infection on hemoglobin levels.

Results Descriptive statistics The sample means of selected variables for 602 children in the control group and 331 children in the treatment group with complete observations in all three survey rounds are presented in table 1. The sample means for the two groups in the first survey round were very close. The differences in the means between the two groups were statistically significant only for the number of possessions (p = .03), which was slightly higher in the treatment group.

TABLE 1. Selected variables in three survey rounds of Tanzanian schoolchildren in the treatment and control groups" Control group (N = 602)1' Variable

Round 1

Age (mo) 146.1 ± 14.6 Household possessions1 1.36 + 0.78 Socioeconomic status index'' 59.98 ± 11.9 Malaria (prevalence) 33% Malaria (merozoites/200 28.3 ± 80.0 white blood cells) Hookworm (eggs/g stool) — Schistosomiasis (eggs/10 ml — urine) Hemoglobin (g/L) 114.7+ 12.6 C-reactive protein (mg/L) 2.39 ±3.82 Ferritin (ug/L) 30.8 ± 25.4 Height (m) 1.37 ±0.90 Weight (kg) 31.1 ±6.4 a. b. c. d.

Round 2

Treatment group (N == 331)b

Round 3

Round 1 146.9 ± 15.5 1.47 + 0.76 61.07 ± 11.8 38% 29.6 ± 47.0

Round 2

Round 3

49%

43%

51%

38%

— —

845 ± 1500 204.6 ± 509

423 + 929 192.0 + 375

79 ± 297 5.48 ± 39

165 ± 566 107.8 ± 370

112.8 ±11.9 2.09 ± 3.50 27.3 ± 19.8 1.39 ±0.90 31.9 ±8.5

116.1 ± 14.0 2.06 ± 3.07 30.2 ±21.9 1.43 ±0.90 35.4 ±7.6

115.0 ± 13.6 2.10 ±2.97 30.0 ± 24.8 1.37 ±0.83 31.0 ±5.6

115.8 ± 11.9 2.09 ±3.31 28.0 ± 20.6 1.39 ±0.81 32.0 ±5.9

121.0 ± 12.5 2.07 ± 3.38 31.6 ±20.7 1.43 ± 0.85 35.4 ±6.7

Plus-minus values are means ± SD. Complete data were available in all three survey rounds from these children. One point each was given for ownership of a bicycle, radio, or refrigerator. The socioeconomic status index was based on the quality of materials used for construction of walls, roof, and floor; the source of drinking water; and the type of fuel used.

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A. Bhargava et al.

Impact of anthelmintic treatment on hemoglobin, ferritin, and C-reactive protein

The means for the three hematological variables, hemoglobin, ferritin, and C-reactive protein, in survey rounds 1,2, and 3 are presented in tables 2 and 3 for the treatment and control groups, respectively. In table 2, children in the treatment group were classified according to the type of treatment received. For comparison, children in the control group in table 3 were classified according to infection status in the same way as the treatment group. However, children in the control group were classified according to their infection status in survey round 3; because of ethical considerations, these were the only parasitological data taken from these children. Table 2 shows that the baseline hemoglobin concentration was lower in infected children than in uninfected children by approximately 4 g/L for those infected only with schistosoma and by approximately 7 g/L for those infected either with hookworm alone or with both species of helminth. After treatment, the hemoglobin concentrations were at approximately the same levels in all groups. The results of ANOVA showed a significant improvement in hemoglobin after albendazole treatment (albendazole x survey round interaction: F(l, 326) = 15.1,p < .001). Mean Hb levels in children treated for hookworm increased by 9.3 g/L (P < 0.001) over the course of the study compared with an increase of only 2.7 g/L for the uninfected group. The effect of praziquantel treatment (F(l, 326)

= 1.0, p = .36) and the interaction between albendazole treatment and praziquantel treatment (F(l, 326) = 0.81, p = .44) were not significant. Anthelmintic treatment also had a significant impact on the number of children suffering from anemia (hemoglobin < 120 g/L). Before treatment, 67% (189/ 284) of infected children were anemic; after treatment, only 44% (118/266) were anemic. The proportions of children with more severe anemia were also reduced. The prevalence of children with hemoglobin < 110 g/L fell from 36% (102/284) to 14% (37/266); the prevalence of children with hemoglobin < 100 g/L fell from 11% (31/284) to 3% (8/284). The full distribution of hemoglobin levels in infected children before and after treatment is illustrated in figure 2. Ferritin levels also improved after the treatment. There was a significant increase (table 2) in ferritin levels following treatment for hookworm (albendazole X survey time interaction: F(l, 326) = 4.0,p = .019) and for schistosomiasis (praziquantel x survey time interaction: F(l,326) = 6.7,p = .001). There was no significant interaction between the two treatments (albendazole x praziquantel X survey time interaction: F(l, 326) = 1.0, p > .36). The analysis of C-reactive protein levels found these to be unrelated to levels of infection with hookworm or schistosoma in the treatment group (F(l, 326) < 0.02, p > .8 in both cases); there was no effect of either albendazole or praziquantel treatment on C-reactive protein levels (F(l, 326) < 7.9, p > .39 in both cases). By contrast, the levels of the three hematological

TABLE 2. Sample means and standard deviations of hemoglobin, C-reactive protein (CRP), and ferritin concentrations in the treatment group, classified according to baseline infection status" Infection status and treatment Hookworm and S. haematobium; albendazole and praziquantel ( N = 135)

Variable

Uninfected (N=116)

Hookworm only; albendazole only (N=56)

Schistosoma haematobium only; praziquantel only (N = 79)

Hemoglobin (g/L) Baseline 3 mo 15 mo

119.0 ±11.7 116.4 ±10.2 121.7 ±12.7

111.2 ±16.4 113.6 ±12.6 120.5 ± 12.6

114.4 ±13.6 114.7 ±14.5 119.0 ±13.7

112.1 ±15.2 115.6 ±13.0 120.9 ±11.4

Ferritin (pg/L) Baseline 3 mo 15 mo

43.2 ± 40.4 33.3 ± 24.3 32.0 ±21.6

26.3 ±28.1 23.7 ± 14.9 32.5 + 22.2

30.5 ±31.0 26.8 ±18.6 31.1 ±25.6

24.4 + 17.2 27.4 + 23.5 32.2 + 20.6

CRP (mg/L) Baseline 3 mo 15 mo

2.73 ±3.12 2.24 ± 3.07 2.22 ± 3.57

2.04 ± 3.29 1.67 + 2.54 1.74 ± 2.40

1.92 ±2.26 1.91 ±2.81 1.61 ± 1.97

2.08 ±3.13 2.25 + 3.94 2.53 + 3.91

a. "Infected" means "heavily infected" as defined in the text: > 400 eggs per gram of stool for hookworm and > 50 eggs per 10 ml of urine for schistosoma.

Hemoglobin and Serum Ferritin Concentrations of Tanzanian Schoolchildren

120

>, 80

40

60 80 100 120 140 160 180 Hemoglobin (g/L)

FIG. 2. The distribution of Hb levels in children infected with intestinal helminths before and 15 months after anthelmintic treatment (Hb < 120 g/L is the definition of anemia for this age group) variables in infected, untreated children (control group; table 3) did not change over time relative to those in uninfected children. Those who were infected in survey round 3 had lower levels of hemoglobin than the uninfected children throughout the study (main effect of hookworm infection: F(l, 448) = 13.9,p < .001; main effect of schistosoma infection: F( 1,448) = 4.4, p = .036; interaction between the two infections: F ( l , 448) = 4.3, p = .039). There was a significant improvement in hemoglobin concentration over time (main effect of survey round: F ( l , 448) = 4.12, p = .045), but this improvement was similar in all four groups (all survey round x infection status interactions were not significant: F(l,448) < 1.9, p> . 15 in all cases). The ferritin concentration in the control group,

like the hemoglobin concentration, was lower in children infected with hookworm throughout the study (main effect of hookworm infection: F(l,448) = 32.0, p < .001). Unlike hemoglobin, the level of ferritin did not improve in untreated children over time (main effect of survey r o u n d : F ( l , 448) = 1.64, p = .20). Similarly, children infected with hookworm had significantly lower levels of C-reactive protein than other children (F(l, 448) = 5.3, p = .021); infection with schistosoma had no effect on C-reactive protein levels (F(l, 448) = 0.14, p = .71). C-reactive protein levels decreased over time in the control group (F(2, 448) = 3.14, p = .044), b u t this decline did not vary according to infection status (all infection x time interactions: F(2,448)<1.5,p>.23). The effect of treatment was most apparent when the pattern over time of the hematological variables in the control and treatment groups was compared. However, it was not immediately apparent that these two groups were comparable, because parasitological classifications were made at different time points and the baseline infection status of the control group was unknown. Nevertheless, the comparison was somewhat justified by the consistency in hemoglobin, ferritin, and C-reactive protein levels of infected children across the two groups. For example, the mean hemoglobin levels of infected children were similar in the two groups at baseline (approximately 113 g/L), as were the hemoglobin levels of uninfected children in the two groups (approximately 119 g/L), suggesting that these groups had similar levels of infection. Furthermore, the relationship between infection status and hemoglobin in the control group was relatively stable over time, sug-

TABLE 3. Sample means and standard deviations of hemoglobin, C-reactive protein (CRP), and ferritin concentrations in the control group, classified according to baseline infection status" Infection status

Variable Hemoglobin (g/L) Baseline 3 mo 15 mo Ferritin (\xg/V) Baseline 3 mo 15 mo

Uninfected (N = 70)

Hookworm only (N=115)

Schistosoma haematobium only (N = 48)

Hookworm and S. haematobium (N = 220)

119.0 ±11.1 117.7 ±12.2 120.8 ±11.8

112.9 ± 12.1 110.3 ± 11.7 114.1 ±14.5

114.8 ±11.3 112.6 ±10.0 115.9 ±9.9

112.7 ±13.0 110.8 ±11.9 113.0 ±14.5

40.8 ± 34.3 32.2 ± 23.7 37.6 ± 28.4

26.2 ± 22.6 24.3 ±18.9 27.2 ±25.1

38.8 ±33.3 33.3 ± 19.3 34.1 ±20.4

26.8 ±19.1 24.2 ±17.1 25.4 ± 15.4

CRP (mg/L) 2.21 ± 3.88 3.25 ± 5.36 2.10 ±2.87 3.20 ± 5.88 Baseline 1.82 ±2.83 2.32 ±4.00 1.88 ±2.47 2.83 ±5.61 3 mo 2.27 ± 3.43 2.32 ± 2.88 1.97 ±2.72 2.60 ± 4.94 15 mo a. "Infected" means "heavily infected" as defined in the text: >400 eggs per gram of stool for hookworm and >50 eggs per 10 ml of urine for schistosoma.

219

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A. Bhargava et al.

gesting that the infection levels were stable. Since prima facie evidence for the comparability of the two groups has been established, the results of the comparison will be examined. Treatment against hookworm improved levels of hemoglobin and ferritin in infected children; treatment against schistosomiasis improved levels of ferritin. Similarly, hemoglobin and ferritin levels in infected but untreated children did not improve over the same time period. Thus, anthelmintic treatment had a specific and beneficial effect on children's iron status. Results for the longitudinal random-effects models for hemoglobin, ferritin, and C-reactive protein status of children in the control group Table 4 presents the results from estimating randomeffects models using the data on hemoglobin, C-reactive protein, and ferritin status of 602 children in the control group. The independent and dependent variables were transformed into natural logarithms to reduce heteroscedasticity [26]. This procedure leads to estimated coefficients that are "elasticities" (percentage change in the dependent variable resulting from a 1% change in an explanatory variable). Certain hypotheses were tested using chi-square statistics. The aim of these analyses was to investigate the

relationships a m o n g h o o k w o r m , schistosomiasis, and the outcome variables (hemoglobin, C-reactive protein, a n d ferritin c o n c e n t r a t i o n s ) , taking into account the interdependence in the outcome variables. For the analysis of hemoglobin concentration, the elasticities of h o o k w o r m eggs per gram of stool and schistosoma eggs per 10 ml of urine were -0.006 and -0.004, respectively; both coefficients were statistically significant (p < .05). Calculations based on these coefficients imply that reducing the hookworm load by 50%, for example, would predict an increase of 1.2% in hemoglobin concentration. The negative coefficient of C-reactive protein was statistically significant. The results for C-reactive protein levels showed that the n u m b e r s of h o o k w o r m eggs per gram of stool and schistosoma eggs per 10 ml of urine were not significantly associated with C-reactive protein status. By contrast, high levels of malaria parasites were associated with high C-reactive protein levels (p < .001). H e m o g l o b i n status was a significant predictor of C-reactive protein with a negative coefficient, indicating that children with higher hemoglobin levels had lower C-reactive protein levels. The model for ferritin concentration included the same explanatory variables as the models for hemoglobin and C-reactive protein but assumed a quadratic relationship between ferritin and C-reactive protein.

TABLE 4. Longitudinal random effects model for the hemoglobin and ferritin concentration and C-reactive protein (CRP) of 602 Tanzanian schoolchildren in the control group in three survey rounds explained by socioeconomic and anthropometric variables and helminth infections," malaria, and age Dependent variable Hemoglobin (g/L) Independent variable Constant Age (mo) Household possessions6 Socioeconomic status indexc Malaria (merozoites/ 200 white blood cells) Height (m) Hookworm (eggs/g stool) Schistosomiasis (eggs/10 ml urine) Hemoglobin (g/L) CRP (mg/L) CRP2 (mg2/L2) Ferritin (pg/L) X2,df=3<<

Coefficient

Ferritin (ug/L)

CRP (mg/L)

SE

Coefficient

SE

Coefficient

SE

3.962* -0.078* 0.008 0.0006* 0.001

0.288 0.046 0.006 0.0003 0.003

3.610* -0.363 0.043 0.001 -0.005

1.429 0.224 0.028 0.002 0.012

13.060* -0.782 -0.053 0.001 0.117*

3.329 0.432 0.054 0.004 0.023

0.232* -0.006* -0.004*

0.058 0.001 0.002

0.293 -0.049* -0.005

0.304 0.007 0.007

-0.338 -0.022 0.009

0.624 0.013 0.014

— -0.006*

— — 1.25

— 0.002

— —

—

—

-1.631*

0.447

0.158* 0.023*

0.010 0.006

—

—

— — —

— — —

4.72

7.88"

a. Values are slope coefficients and standard errors. The dependent and independent variables are in natural logarithms. b. One point each was given for ownership of a bicycle, radio, or refrigerator. c. The socioeconomic status index was based on the quality of materials used for construction of walls, roof, and floor; the source of drinking water; and the type of fuel used. d. Chi-square test for the exogeneity of the time means of C-reactive protein in the models for hemoglobin and ferritin concentrations, and for exogeneity of time means of hemoglobin concentration in the model for C-reactive protein. *p<.05.

Hemoglobin and Serum Ferritin Concentrations of Tanzanian Schoolchildren

The results indicated that children with higher hookworm egg counts had lower levels of ferritin. Both CRP and CRP2 were estimated with positive coefficients that were statistically significant. These associations suggested that children's ferritin concentration increased at an increasing rate with C-reactive protein levels in this population; the implications of this finding are discussed below.

Discussion This paper presents an analysis of the data from a randomized school-based intervention in coastal regions of Tanzania, where hookworm and schistosomiasis infections were widely prevalent. The results showed the effectiveness of anthelmintic treatment on children's hemoglobin and ferritin status. There were clear and independent effects of praziquantel treatment and albendazole treatment on ferritin concentration and of albendazole treatment on hemoglobin levels. This extends the results of previous studies in showing that praziquantel treatment can improve the iron status of infected schoolchildren. Further, for the design of control programs, the results indicated that children's iron status can be increased to the level of that of uninfected controls after just two rounds of anthelmintic treatment over a course of 15 months. Given that children's iron status is also compromised by malaria [27], and that their diets are likely to be iron deficient [28], one might expect that removal of intestinal parasites would not be sufficient for hemoglobin levels to recover without iron supplementation [13]. That hemoglobin levels recovered to the levels of those in uninfected children after two rounds of anthelmintic treatment has encouraging implications for reducing anemia in areas of high helminth endemicity. Such treatments are inexpensive and can be delivered in school health programs [29]. Of course, improving diet quality should be the long-term objective of food and nutrition policies. The second question addressed by our study was the relationship between ferritin and C-reactive protein. The results showed that ferritin increased at an increasing rate with C-reactive protein. The implication of this result is that using ferritin alone as an indicator of iron status may provide useful information in children with low C-reactive protein concentrations but overestimate iron status in those with higher C-reactive protein concentrations. Thus, if we classify children with ferritin levels < 30 |xg/L as having low iron stores [18], then of the 602 children in the control group at baseline, 217 had ferritin > 30 u.g/L and would seem to have adequate iron stores. However, 108 (18%) of these children were anemic (hemoglobin < 120 g/L). By contrast, if we restricted the analysis of ferritin to the 400 children with (nonelevated) C-reactive protein < 2.2 mg/L [30],

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then only 7 children (1%) were anemic. The presence of malaria parasites appeared to be a reason for the elevated C-reactive protein levels, and our study supports the conclusions of others [31] that cutoff points should be used with caution in defining iron deficiency in areas of endemic malaria infection. However, ferritin can be used more accurately as an indicator of iron status if C-reactive protein levels are taken into account. Another possibility is to disaggregate ferritin into types H and L subcomponents [32], because infections are known to differentially affect these components [33]. A final issue arising from our results concerned the methods used to investigate the relationship between iron status and helminth infections. We analyzed both longitudinal observational data and data from an intervention study. In the latter, anthelmintic treatment led to an average increase of 8.3 g/L in hemoglobin, an increase of approximately 7.3% from baseline. However, according to calculations made on the basis of estimated parameters from the longitudinal observational model, we would expect an approximately 3% increase in hemoglobin to result from this reduction in worm load. This underprediction by the longitudinal model for hemoglobin may be a result of improvements in nutrient absorption due to the reduction in parasitic loads in treated children. This emphasizes the fact that intervention studies not only investigate the relationship between variables but also can change the relationship; there is a need to use alternative methodological approaches to fully understand the interrelationships. It also suggests that cross-sectional analyses may underestimate the potential benefits of removing helminth infections.

Acknowledgments We gratefully acknowledge the hard work of all the staff of the MAKWAMI Project: Damaris Ngorosho, Chacha Musabi, Charles Deus, Christina Mwita, Erasto Tuntufye, Eliza Charles, Fausta Ngowi, Juliet Mdusi, Asnat Mchopa, Husna Tuli, Selemani Kungulilo, Zuhura Mfaume, Muhsin Iddi, and Gordian Rwegasira. We would also like to thank the primary school students who participated in the study, their teachers and the village leaders, and the District Education Officers, District Medical Officers, and District Health Management Teams of Bagamoyo and Kibaha districts. ELISA analysis was conducted by Vincent Assey, Michael Maganga, and Dr. Ndosi at the Tanzania Food and Nutrition Centre, Dar es Salaam. The comments of two anonymous reviewers and research support from the J. S. MacDonnell Foundation and the Research Committee of the World Bank are gratefully acknowledged.

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Hemoglobin and Serum Ferritin Concentrations of Tanzanian Schoolchildren

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AMERICAN JOURNAL OF HUMAN BIOLOGY 17:280-292 (2005)

Original Research Article Modeling the Effects of Health Status and the Educational Infrastructure on the Cognitive Development of Tanzanian Schoolchildren ALOK BHARGAVA, 1 * MATTHEW J U K E S , 2 DAMARIS NGOROSHO, 3 CHARLES KHILMA, 3 AND DONALD A.P. BUNDY 4 'Department of Economics, University of Houston, Houston, Texas 2 Partnership for Child Development, Imperial College, London, United Kingdom 3 Tanzanian Partnership for Child Development (UKUMTA), Dar es Salaam, Tanzania "The World Bank, Washington, DC

ABSTRACT This paper models the proximate determinants of school attendance and scores on cognitive and educational achievement tests and on school examinations of over 600 schoolchildren from the Control group of a randomized trial in Tanzania, where children in the Intervention group heavily infected with hookworm and schistosomiasis received treatment. The modeling approach used a random effects framework and incorporated the inter-relationships between school attendance and performance on various tests, controlling for children's health status, socioeconomic variables, grade level, and the educational infrastructure. The empirical results showed the importance of variables such as children's height and hemoglobin concentration for the scores, especially on educational achievement tests that are easy to implement in developing countries. Also, teacher experience and work assignments were significant predictors of the scores on educational achievement tests, and there was some evidence of multiplicative effects of children's heights and work assignments on the test scores. Lastly, some comparisons were made for changes in test scores of treated children in the Intervention group with the untreated children in the Control group. Am. J. Hum. Biol. 17:280-292, 2005. c 2005 Wiley-Liss, Inc.

A large number of children in developing countries fail to complete primary education. It was estimated that only 50% of the eligible children in Tanzania competed primary school (International Bureau of Education, 1997). Because learning is a cumulative process, children dropping out of school are unlikely to pursue education and would not be a part of the skilled labor force that is essential for economic development (Bhargava, 2001). The factors hindering school completion include poor health status, inadequate educational infrastructure, poverty drawing children into household tasks, and lack of opportunities in skilled occupations. Because children's intellectual development is a complex process covering aspects analyzed in various disciplines, it is essential to use a multidisciplinary framework for quantifying the factors affecting child development. Thus, for example, while a hungry child is unlikely to comprehend the material presented in school, it is also the case that a poor educational environment may not stimulate even the well-nourished children.

s 2005 Wiley-Liss, Inc.

While an informed policy discussion entails information on various factors affecting children's development, researchers in different disciplines have emphasized different aspects. For example, certain psychologists have argued that intestinal parasites such as hookworm and schistosomiasis may adversely affect cognitive development (Watkins and Pollitt, 1997). Although the underlying biological pathways remain unclear, the effects of anthelmintic treatment on children's scores on cognitive tests have been investigated in randomized trials (Dickson et al., 2000; Simeon et al., 1995). The results have been ambiguous in part because the studies were conducted in a short time frame and also because there are complex interactions between health status,

•Correspondence to: Alok Bhargava, Department of Economics, University of Houston, Houston, TX 772045019. E-mail:[email protected] Received 8 April 2004; Revision Received 11 January 2005; Accepted 26 January 2005 Published online in Wiley InterScience (www. interscience. wiley.com). DOl: 10.1002/ajhb.20142

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A. Bhargava et al. socioeconomic variables, and the educational infrastructure. For example, anthelmintic treatment can improve children's iron status that, in turn, can reduce sicknesses. If the school environment is stimulating, then anthelmintic treatment can enhance child development through an alternative set of mechanisms. It is therefore useful to analyze the data from Control and Intervention arms of randomized trials in a broad analytical framework (Bhargava et al., 2003). Ideally, researchers would prefer to analyze the effects of health status and educational infrastructure on several indicators of cognitive development measured over time. The meager resources for longitudinal studies, however, limit the choices. While cognitive tests have been used as indicators of child development, there are difficulties in ensuring that children in less-developed countries are acclimatized to the tasks. When the relevant factors are accounted for, analysis of cognitive data can provide useful insights (Bhargava, 1998). Further, children regularly take school examinations in subjects such as arithmetic, science, and language, and these scores can be recorded without substantial costs (Goldstein and Thomas, 1996). Educational achievement tests, such as those in reading, spelling, and arithmetic, are similar in spirit to school examinations but are typically monitored by outside staff. An analysis of the scores on cognitive and educational achievement tests and on school examinations can afford insights into the relative merits of using these instruments in developing countries. This paper presents a comprehensive analysis of factors affecting children's cognitive development using a longitudinal data set from 10 schools in the rural coastal regions of Tanzania. The data from Control group were analyzed by specifying models for school attendance and for the scores on cognitive and educational achievement tests and on school examinations. The inter-relationships between psychological, biological, and socioeconomic variables were modeled. A random-effects framework was employed to estimate the model parameters and to address the joint determination of children's test scores and school attendance. Lastly, the changes over the study period in the test scores of children in the Intervention group that received treatment against hookworm and/or schistosomiasis were compared with the changes for the untreated children to

shed further light on the effects of anthelmintic treatment. MATERIALS AND METHODS Subjects

The study was conducted in 10 schools in the Bagamoyo and Kibaha districts of rural coastal Tanzania in 1997-1998 (Partnership for Child Development, 2002). The schools were eligible if more than 100 children were enrolled in grades 2-5 and were accessible by road during the rainy season. Children were eligible to participate if they were between 9 and 15 years old. The Institute of Child Health, London, and the Tanzania Ministry of Health approved the study design. A total of 1,232 children were observed at the baseline and then at 3 and 15 months after the baseline (survey rounds 1, 2, and 3, respectively). Approximately half the children were randomized into the Intervention group, and 270 children that were "heavily" infected with hookworm and schistosomiasis received treatment (Bhargava et al., 2003, Table 2). This paper focuses on modeling the data on test scores and school examinations for children in the Control group and briefly discusses the differences in changes in the scores of children in the Control and Intervention groups. Socioeconomic variables and measures of health status

The child's date of birth was recorded from the school register, and detailed background information was collected by interviewing the households. An index of socioeconomic status was constructed by summing the households' scores on the quality of materials used for construction, furniture, etc. Children's weight and height were measured in each survey round. Electronic scales were used to measure weight to the nearest 0.1 kg; height was measured using a portable stadiometer (Partnership for Child Development, 2002). In each survey round, nurses drew 2 mL of blood using sterilized syringes. Hemoglobin concentration was measured in grams per liter of blood (g/L) using a portable photometer. The C-reactive protein levels were measured by sandwich ELISA and expressed in milligrams per deciliter of blood (mg/dL). The urine samples were taken for the Control group only in the third survey round because

Cognitive Development of Tanzanian Schoolchildren highly infected children were immediately treated for ethical reasons. The schistosomiasis egg counts were expressed per 10 mL of filtered urine as indicators of infection intensity. Similarly, children's stool was tested for hookworm and for other parasites in the third survey round; hookworm egg count per gram of stool was used as the measure for infection. Cognitive and educational achievement tests, school examinations, and the educational infrastructure

The cognitive tests, adapted to the Tanzanian environment, consisted of several tasks measuring analytical and motor skills and were given in the three survey rounds to approximately half the children that were randomly selected (Partnership for Child Development, 2002). Briefly, digit span (forward and backward) asked children to repeat strings of numbers after the examiner read them out. Corsi block was a visual-spatial analogue of the digit span forward test. The Stroop test measured the time taken to correctly point at "ticks" and "crosses" and to label them with the correct or the opposite label. The Grooved Pegboard tasks assessed motor skills by measuring the time for completion of tasks using the dominant and nondominant hands. The verbal fluency test asked the children to name as many foods and animals in 1-min periods, with a point given for nonduplicate answers. The silly sentences test asked the children for "yes" or "no" responses to questions and recorded the number of correct answers; the mean response time in correctly answering the questions was analyzed. Lastly, children's mean reaction time was measured in tasks that entailed choosing the picture that matched the auditory signal. The educational achievement tests were given in survey rounds 1 and 3 and consisted of a letter, word, and sentence reading score in Kishwahili. This test was designed to measure children's comprehension, and the scores were adjusted for incorrect answers. The spelling test consisted of 50 questions. There were written and oral tests in arithmetic; total arithmetic score was used in the analysis. Children's scores on school examinations during the terms were matched with the time points of the survey rounds 2 and 3; the scores in arithmetic, science, geography, and civics were modeled. The enumerators visited eight of the 10 the schools and recorded variables reflecting the educational infrastructure and teacher

qualifications. The proportions of children in various grades sitting on the floor were recorded. The number of teachers, their years of experience, and the numbers of blackboards, desks, chairs, pictures, and textbooks in the classroom were recorded. In addition, the numbers of work assignments in each subject for the grades were investigated. The empirical analysis utilized indices based on this information. The average number of years of teaching experience was constructed for each school, and the numbers of work assignments in the children's grades were computed. Empirical models for children's school attendance and test scores

Children's cognitive development in poor societies is affected by their health status, socioeconomic factors, and the educational infrastructure. Poverty can force parents to assign household tasks to children that can interfere with school attendance. Even in an impoverished environment, however, a child must learn language in order to convey the basic needs to adults (Vygotsky, 1987). Thus, one might observe greater differences between children from poor and well-off households on tasks such as arithmetic that require gradual acquisition of skills through instruction in school or at home. Because children are periodically tested in school examinations, those performing poorly are likely to get discouraged from continuing school. Socioeconomic variables such as household income can make a critical difference in determining the length of stay in school. Further, while anthropometric variables such height and weight are suitable indicators of nutritional status (Cole, 1991), the C-reactive protein levels provide quantitative measures of infections (van den Broek and Letsky, 1999). Poor diet quality entails low intakes of micronutrients such as iron that is important for cognition (Lozoff, 1988; Pollitt, 1993); hemoglobin concentration is a useful indicator. Lastly, the educational infrastructure is likely to play a role in stimulating children's interest (Ceci, 1991); measures such as teachers' years of experience and work assignments are likely to be important for cognitive development. The effects of various factors on children's cognitive development were modeled using a four-equation system. Let SchAtt^, Cog;t, Educ^, and SchExam« be, respectively, the

227

228

A. Bhargava et al. measurements for the ith child in time period t (i = 1,..., N; t = 1, 2, 3) on the proportion of school attendance, and the scores on cognitive tests, educational achievement tests, and on school examinations. The respective empirical models for these outcome variables can be represented by equations (l)-(4): SchAtt;, =
school examinations in four subjects. In equation (2), school attendance was excluded because it was not a statistically significant predictor. Lastly, the models in equation (3) for the scores on educational achievement tests were estimated taking into account the teachers' experience and the number of work assignments in the grades. In addition, a variable interacting children's heights with the work assignments was included as an explanatory variable in these models to investigate the presence of multiplicative effects. Some issues in model specification

Cog;, =

feo(Constant)+6i(Grade); 4- 62(SES index); + ^(Hookworm), + 64 (Schistosomiasis); + ^(Height);, -I- &6(C -reactive protein);, + 67 (Hemoglobin);, + u2u, (2)

The children in the study from rural regions of Tanzania were enrolled in 10 different schools. Although there did not seem clear advantages in attending a particular school, the models in equations (l)-(4) need to take into account the possible effects of between-school differences. Moreover, the school attendance variable in equations (3) Educ;, = Co (Constant) -fci (Grade); and (4) could be correlated with the error + C2(SES index); 4- C3 (Hookworm); terms u^u and unt, respectively. For example, parents concerned with children's edu+ C4 (Schistosomiasis); + C5 (Height);, cation may send them regularly to school and participate in the learning process. The + C6(C—reactive protein);, unobserved parental characteristics could + C7 (Hemoglobin);, lead to correlations between errors on the + c8(SchAtt);, +u3it, (3) models for test scores and school attendance. Such issues merit a treatment from the standpoint of model formulation, estimation, SchExam;, = do (Constant) + d\ (Grade); and diagnostic testing. In explaining school attendance by equa+ d 2 (SES index); tion (1), one can control for between-school + d3 (Hookworm); differences by including a complete set of + (^(Schistosomiasis); nine indicator variables. Moreover, issues arising in incorporating the school infra+ d5 (Height);, structure were closely related to the hand+ de(C- reactive protein);, ling of school indicator variables; the children were enrolled in four grades in 10 + ^(Hemoglobin);, different schools, so that it was possible to + d8 (SchAtt);, + uiit. (4) include up to 39 indicator variables. While the inclusion of a large number of indicator Here, (a 0 ,..., a4, b0,..., bn, c 0 ,..., c8, and variables can exacerbate multi-collinearity do,..., dg) are regression coefficients, and problems, it was unfeasible to treat these u\u, u2.it, u^t, and uAit are random-error effects as randomly distributed variables terms that are discussed below. "Rest before because of the asymptotic distribution theschool" was an indicator variable that was ory used and the temporal correlation in equal to 1 if the child reported resting as the unequally spaced data. Instead, it was useful activity before and after school. The model in to directly introduce in the models measures equation (2) was estimated for scores on of school infrastructure such as work assigneight cognitive tests. Equations (3) and (4) ments and investigate if such variables interwere estimated, respectively, for the scores acted with children's heights that reflect on three educational achievement tests and their health status.

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Cognitive Development of Tanzanian Schoolchildren An econometric reformulation of the models

For exposition of the estimation methods and testing procedures, we rewrite the random-effect model containing "endogenous" explanatory variables that are potentially correlated with the errors as: k\

m

k

(i = l,...,N;t

= l,...,T),

(5)

where, z values are time-invariant variables, x\ and x2 are, respectively, exogenous and endogenous time-varying variables (ki + k2 = k); slope coefficients are denoted by Greek letters. In equation (3) for the scores on educational achievement tests, for example, children's grade and the school indicator variables were time invariant variables; height, C-reactive protein, and hemoglobin concentration were time-varying exogenous variables. School attendance was a potentially endogenous time-varying variable. The errors affecting equation (5) are often decomposed in the simple random-effects fashion as: uit = 8; + vit,

(6)

where 8 values are children-specific random variables that are distributed with zero mean and constant variance, and v values are independently distributed random variables with zero mean and constant variance (e.g., Laird and Ware, 1982). The estimation methods assumed that the errors affecting the models in equations (l)-(4) were independent across children but correlated over time with a positive definite variance—covariance matrix, i.e., the random-effects decomposition in equation (6) was a special case. This formulation was more flexible partly because the surveys were conducted at unequal intervals so that the v^ values were likely to be serially correlated in a complex manner. The asymptotic distribution theory assumed that the number of children was large but the number of time period was fixed (Bhargava and Sargan, 1983).

Further, the model in equation (5) can be rewritten as a "system of T equations," where each equation corresponds to the observations in a time period, with equality restrictions on parameters in different time periods. This reformulation enabled the application of simultaneous equations methods (Bhargava, 1991; Bhargava and Sargan, 1983). Moreover, one can distinguish between two sets of assumptions for the potential endogeneity of time-varying variables. First, the x2 values may be correlated with the Uu in a general way, i.e., x2 were "fully" endogenous variables. Let Xi and X2 be, respectively, the kj x 1 and k2 x 1 vectors containing the exogenous and endogenous time varying variables, and let Z be the m x 1 vector of time-invariant variables. We can write the "reduced form" for the fully endogenous variables X2 as: T

X2u = Z_jFtj Xuj +F*t Zi + U2it (i = l,...,N;t

= l,...,T)

(7)

where FtJ•. (t = 1 , . . . , T; j = 1 , . . . , T) and F*t (t = 1,..., T) are, respectively, k 2 x ki and k2 x m matrices of coefficients; U2u is the k2 x 1 vector of errors. While the reduced form equation (7) was a general formulation for correlations between timevarying endogenous variables and the errors on equation (5), sufficient conditions for identification of model parameters were stringent especially for applications with a small number of time observations (Bhargava, 1991). Thus, the second set of assumptions invoked a "special" form for the endogeneity, where only the childrenspecific random-effects 8; values were correlated with x2Qt, i.e., X2ijt = ^ ( 5 ; +Xf2ijt

(i = l,...,N;t=l,...,T; j = k1 + l,...,k)

(8)

where x*2ijt were uncorrelated with 8;. The formulation (8) allowed children to possess unobserved characteristics that in turn could influence the levels of the explanatory variables. The advantage in assuming this

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A. Bhargava et al. correlation pattern was that the deviation of *2ijt from their time means:

in equation (7) predicted the endogenous variables; under the special endogeneity assumptions for X2, only the time means of the endogenous variables in equation (10) X 2ijt = x2ijt — Xftj were predicted by the reduced form. (t = 2,...,T;j = k1 + l,...,k; FORTRAN programs were developed to estii = l,...,N), (9) mate the alternative models using stepwise procedures (Bhargava, 1991). Further, while we used the correlation where pattern in equation (8) to tackle endogeneity, it would be helpful to describe the diagnostic tests for discriminating between T exogeneity assumptions. The assumption that all k variables were exogenous would x%j = ^x2ijt/T {j = ki + l,...,k; yield Tk instrumental variables. Assuming i = l,...,N) (10) X2 to be special endogenous variables would reduce the number of instruments to [Tk — were uncorrelated with the random effects and k2], whereas assuming X2 to be fully endohence could be used as additional [(T — l)k2] genous would decrease the number of instru"instrumental" variables to facilitate para- ments to Tki. Thus, we can proceed by meter identification and estimation (see maintaining the most general hypothesis below). Note that while one can use a "fixed" that X2 were fully endogenous and test if effects estimator (i.e., with indicator variables the constraints implied by special form of for each child) to circumvent certain endo- endogeneity were accepted (Wald, 1947). If geneity problems, the increase in the number this null hypothesis cannot be rejected, then of parameters with sample size leads to the we can test if the time means of X2 were problem of "incidental parameters" (Neyman correlated with the random effects (5;). For and Scott, 1948). Moreover, the coefficients of large N, the statistics for testing special form time-invariant variables such as socioeco- of endogeneity and for lack of correlation nomic status cannot be estimated in the fixed between time means of X2 and random effects were distributed as Chi-square varieffects framework. ables with [T(T - l)k2] and Tk2 degrees of freedom, respectively. Estimation of model parameters and the diagnostic tests

Assuming that the variance-covariance matrix of the error terms uu in equation (5) was unrestricted and equality restrictions on model parameters in the T time periods, the appropriate estimation method would depend on the exogeneity assumptions. First, if all the k time-varying variables were exogenous, then the Seemingly Unrelated Regression Equations estimator (Zellner, 1962) incorporating parameter restrictions would produce efficient estimates. Second, when some of the time varying variables were endogenous in equation (5), the exogenous variables can be used as "instrumental variables" for predicting the endogenous variables (Sargan, 1958). A "Three Stage Least Squares" type estimator (Zellner and Theil, 1962) was used to estimate model parameters incorporating the cross-equation restrictions. In the fully endogenous variables case, the reduced form

RESULTS Descriptive statistics and t-tests

The sample means of selected variables of the Tanzanian schoolchildren in the 3 survey rounds are presented in Table 1. Hookworm and schistosomiasis infections are widely prevalent in this population. More than 30% of the children had over 400 hookworm eggs per gram of stool and thus were heavily infected. The data on hemoglobin concentration showed that 60% of the children had readings lower than 120 (g/L) and hence were anemic. The sample means of the scores on various cognitive and educational achievement tests and school examinations are in Table 2. The sample means of the scores on cognitive and educational achievement tests showed an increase over the survey rounds and a decline in time taken to complete the tasks. Application of paired i-tests showed statistically significant changes at the 5% level

Cognitive Development of Tanzanian Schoolchildren TABLE

231

1. Sample means and standard deviations of selected variables in 3 survey rounds of Tanzanian school children" Round 2

Round 1 Variable Age, m o n t h s Grade Socioeconomic status index Hookworm, b eggs per g r a m of stool Schistosomiasis, 1 " eggs per 10 ml of urine Hemoglobin, g/L C-reactive protein, mg/dL Height, m Weight, kg Proportion school attendance

Mean

SD

146.08 3.09 62.15

14.57 1.08 5.75

— — 115.22

12.72 3.77 0.91 6.45 0.10

2.43 1.37 30.96 0.887

Mean

— — 113.33 2.11 1.39 31.96 0.887

Round 3 SD

Mean

SD

11.92 3.47 0.90 6.68 0.14

727.1 189.6 117.18 2.10 1.43 35.22 0.872

1378 500.1 13.80 3.23 0.90 7.62 0.17

"Values are means and standard deviations; N = 662. Measured in survey round 3 only.

b

TABLE 2. Sample means of the scores on the components of cognitive and educational examinations of Tanzanian school children0.

achievement

tests and school

Round 2

Round 1

Round 3

Variable

Mean

SD

Mean

SD

Mean

SD

Cognitive t e s t s ' Digit span Corsi block Stroop Pegboard dominant time c Pegboard non-dominant time Verbal fluency Mean response time Mean reaction time

11.57 9.96 40.33 78.17 94.24 27.48 0.66 3.79

3.07 2.02 8.52 31.86 37.92 8.08 0.22 0.30

12.27 10.62 35.51 64.67 79.94 29.77 0.63 3.67

2.80 2.19 7.87 17.42 28.54 8.39 0.22 0.23

12.98 11.31 32.90 59.48 72.27 31.30 0.59 3.57

2.94 2.26 6.35 11.04 25.00 8.20 0.13 0.21

Educational achievement tests'* Sentence reading Total arithmetic Spelling

26.06 24.47 35.68

15.51 5.41 16.63

— — —

37.59 27.34 42.01

14.23 5.97 14.77

34.32 44.15 45.04 43.35

22.65 20.59 18.87 18.53

School examinations" Arithmetic Science Geography Civics

— — — —

49.88 48.60 47.85 46.28

24.60 21.53 22.44 22.92

"Values are means and standard deviations. Differences between survey round 1 and 3 in the scores on the eight cognitive tests were significant at the 5% level; N — 413. c Time is in seconds. d Educational tests were given in survey rounds 1 and 3 and the differences between survey rounds 1 and 3 were significant for all three scores; N = 680. °N = 373.

between survey rounds 1 and 3 in the scores on eight cognitive tests and the three educational achievement tests for the children in the Control group. This was also true for the children that were treated against hookworm and/or schistosomiasis in the Intervention group (results not shown). However, using independent £-tests, none of the differences in changes in cognitive and educational achievement test scores between

survey rounds 1 and 3 for Control and Intervention groups were significant at the 5% level. Results from the model for school attendance

The results from estimating the random effect model in equation (1) for the logistic transformation of the proportion of time the child attended school (Cox, 1971) during each

A. Bhargava et al.

232

of the three survey rounds are in Table 3; the results are reported for the cases with and without the nine indicator variables for the schools. The index of socioeconomic status, C-reactive protein levels, and hemoglobin concentration were transformed into natural logarithms to reduce heteroscedasticity (Nelson et al., 1989). The estimated coefficients of the transformed variables were the "elasticities" (percentage change in the dependent variable resulting from a 1% change in an independent variable). The indicator variables for school numbers 1, 2, 3, 4, and 7 were estimated with coefficients that were significant at the 5% level. The results in Table 3 show that children's socioeconomic status was a significant predictor of school attendance {P < 0.05) in both versions of the model. Thus, reducing poverty was likely to be beneficial for increasing school attendance. The coefficient of the variable indicating that the children were mainly "resting" before and after school was positive, although it as not statistically significant at the 5% level. Children's hemoglobin concentration was a significant predictor of school attendance at the 5% level

in the model without school indicators; it was significant at the 10% level in the version including the school indicators. While children with high intestinal parasitic loads in this population had lower hemoglobin concentration (Bhargava et al., 2003), on controlling for children's hemoglobin status, the hookworm and schistosomiasis egg counts were not significant predictors of school attendance. Coefficients of C-reactive protein were estimated with negative signs but were not statistically significant. Results for the scores on cognitive tests

Results for the scores on eight cognitive tests are reported in Tables 4 and 5. Except for the child's grade, all variables were transformed into natural logarithms. The zero counts of hookworm and schistosomiasis eggs were set equal to 1 prior to logarithmic transformation. Sensitivity analysis showed that this procedure did not change the results. The main findings were that children's grade and height were significant predictors (P < 0.05) of the scores on cognitive tests. The only exception was the model

TABLE 3. Efficient estimates from the random effects model for the logistic transformation of the proportion of school attendance of Tanzanian school children in three survey rounds explained by socioeconomic variables, infections, hemoglobin concentration, and indicator variables for the schools°b

Dependent variable

Independent variable Constant Socioeconomic status, index Rest before and after school0 C-reactive protein, mg/dL Hemoglobin, g/L Indicator School 1 Indicator School 2 Indicator School 3 Indicator School 4 Indicator School 5 Indicator School 6 Indicator School 7 Indicator School 8 Indicator School 9

Model with indicator variables for schools

Model without indicator variables for schools

Proportion of school attendance

Proportion of school attendance

Coefficient

SE

Coefficient

SE

-7.786* 1.882* 0.200 -0.034 0.532 0.809* 0.817* -0.526* -0.538* -0.076 0.370 -0.739* -0.098 -0.025

2.564 0.524 0.112 0.028 0.327 0.210 0,168 0.156 0.168 0.150 0.196 0.160 0.190 0.168

-9.797* 2.102* 0.130 -0.029 0.761*

2.361 0.491 0.119 0.028 0.332

— — — — — — — — —

^Values are slope coefficients and standard errors {N = 680, T — 3). The dependent and all the independent variables, except for the school indicators, were in natural logarithms; coefficients of the independent variables in logarithms are the elasticities (percentage change in the dependent variable resulting from a 1% change in an independent variable). ^ e s = 1; No = 0. *P < 0.05.

b

233

Cognitive Development of Tanzanian Schoolchildren

TABLE 4. Efficient estimates from the random effects models for Tanzanian children's scores on cognitive tests in three survey rounds explained by socioeconomic and a,b,c anthropometric variables, infections, and hemoglobin concentration

:Dependent Digit span (forward + backward) Independent variable Constant Grade Socioeconomic status Hookworm, eggs/g of stool Schistosomiasis, eggs/10 m L of u r i n e Height, m C-reactive protein, mg/dL Hemoglobin, g/L

Corsi block

variable

Stroop (forward + backward)

Pegboard d o m i n a n t time

Coefficient

SE

Coefficient

SE

Coefficient

SE

Coefficient

SE

-2.654* 0.034* -0.062 0.0004

0.997 0.012 0.136 0.004

-1.000 0.018* -0.102 -0.003

0.816 0.009 0.102 0.003

9.820* -0.042* -0.110 -0.002

0.719 0.008 0.102 0.003

9.717* -0.034* -0.227 -0.004

0.982 0.013 0.144 0.004

0.003 1.048* -0.010* 0.023

0.004 0.166 0.005 0.072

0.004 0.691* -0.003 0.064

0.003 0.139 0.005 0.063

0.0007 -1.058* 0.004 -0.080

0.003 0.122 0.003 0.051

-0.013* -0.724* 0.008* -0.168*

0.005 0.164 0.004 0.068

a

Values are slope coefficients and standard errors (JV = 359, T = 3). Except for Grade, all variables were in natural logarithms; coefficients of indenpendent variables in logarithms are the elasticities. The coefficient of school indicator variables and school attendance were not significant, and hence these variables were dropped from the models. *P < 0.05. c

TABLE 5. Efficient estimates from the random effects models for Tanzanian children's scores on cognitive tests in three survey rounds explained by socioeconomic and anthropometric variables, infections, and hemoglobin concentrationa'b'c Dependent variable Pegboard non-dominant time Independent variable Constant Grade Socioeconomic status Hookworm, eggs/g of stool Schistosomiasis, eggs/10 m L of u r i n e Height, m C-reactive protein, mg/dL Hemoglobin, g/L

Verbal fluency

Mean Response time

Mean Reaction time

Coefficient

SE

Coefficient

SE

Coefficient

SE

Coefficient

SE

10.704* -0.031* -0.212 -0.007

1.048 0.013 0.150 0.005

-3.646* 0.029* -0.078 0.002

1.160 0.014 0.160 0.005

9.503* -0.035* 0.196 -0.005

1.040 0.013 0.145 0.005

10.074* -0.006 0.079 0.000

0.286 0.004 0.042 0.001

-0.005 -0.948* -0.002 -0.120

0.005 0.177 0.005 0.745

0.008 1.343* 0.0001 0.115

0.005 0.194 0.006 0.086

0.002 -0.633* 0.013* -0.133

0.005 0.176 0.005 0.077

-0.002* -0.417* 0.004* -0.020

0.001 0.048 0.001 0.020

a

Values are slope coefficients and standard errors (N — 359, T = 3). Except for Grade, all variables were in natural logarithms; coefficients of independent variables in logarithms are the elasticities. T h e coefficients of school indicator variables and school attendance were not significant, and hence these variables were dropped from the models. *P < 0.05.

for mean reaction time, where grade was an insignificant predictor. While height is a good indicator of the long-term nutritional status and was a significant predictor in all models, the coefficients of body weight were not statistically different from zero. Moreover, statistical tests indicated that height and weight should not be combined as the Body Mass Index (Bhargava, 1994). Coefficient of the school attendance variable was not significantly different from zero in

all eight cognitive tests and hence was dropped from the models. Similarly, none of the indicator variables for school was statistically significant. The index of socioeconomic status was not a significant predictor in Tables 4 and 5. The C-reactive protein levels were significantly associated with the scores on digit span, Grooved Pegboard dominant time, and the mean response and reaction times. The prevalence of malarial parasites was high in

A. Bhargava et al.

234

this population and malarial parasites can elevate C-reactive protein levels (Bhargava et al., 2003). Thus, it was plausible that malaria was responsible for poor performance on some of these tasks. Hemoglobin concentration was a significant predictor of the scores only on the Grooved Pegboard using the dominant hand. The coefficients of hookworm and schistosomiasis egg counts were insignificant in all models. In the models for Grooved Pegboard dominant time in Table 4 and the mean reaction time in Table 5, coefficients of schistosomiasis were significant but estimated with unexpected negative signs.

Results for scores on educational achievement tests The results for children's scores on sentence reading, arithmetic, and spellings are in Table 6; nine indicator variables for the schools are included in these models. Children's grade level, height, and school attendance were significant predictors of all three scores. The time spent in school was likely to enhance performance on educational achievement tests that were similar in spirit to the school examination but were monitored by outside examiners. The index of socioeconomic status was not significant at the 5% level in the three models, although omission of the insignificant indicator

variables for the schools led to its significance in the models for total arithmetic and spelling. The null hypotheses t h a t the random effects affecting test scores were not correlated with those the affecting school attendance were rejected at t h e 5% level in the models for arithmetic and spelling; t h e estimation methods treated school attendance as a n endogenous variable, using as instruments the exogenous variables in the models and deviations of t h e time-varying endogenous variable (i.e., school attendance) from its time mean. Hemoglobin concentration was a significant predictor of t h e scores on sentence reading, total arithmetic, and spelling. The hookworm and schistosomiasis egg counts were estimated with negative coefficients in all three models but were not statistically significant at t h e 5% level. Results for the scores on school examinations The results for children's scores on school examinations in arithmetic, science, geography, and civics are in Table 7. The child's grade level was significantly negatively associated with the arithmetic and civics scores. The index of socioeconomic status was not a significant predictor of the examination scores. Coefficients of hookworm and schistosomiasis egg counts were not significant in these models. Children's height was a

TABLE 6. Efficient estimates from the random effects modes for Tanzanian children's achievement tests in two survey rounds explained by socioeconomic and anthropometric hemoglobin concentration, and school attendanceab

scores on variables,

educational infections,

Dependent variable Sentence relading" Independent variable Constant Grade Socioeconomic status Hookworm, eggs/g of stool Schistosomiasis, eggs/10 m L of urine Height, m C-reactive protein, mg/dL Hemoglobin, g/L Proportion school attendance Chi-square statistic 11

Total arithmetic"

Spelling0

Coefficient

SE

Coefficient

SE

Coefficient

SE

-17.160* 0.202* 0.131 -0.007 -0.003 3.511* 0.001 0.404* 0.040* 5.84

2.237 0.023 0.295 0.008 0.009 0.354 0.014 0.169 0.001

-2.111* 0.101* 0.081 0.001 0.003 0.802* -0.002 0.150* 0.010* 14.95*

0.695 0.007 0.093 0.002 0.003 0.111 0.004 0.052 0.004

-11.932 0.122* 0.353 -0.007 -0.004 2.543* 0.001 0.239* 0.022* 14.95*

1.737 0.020 0.264 0.007 0.008 0.259 0.009 0.120 0.007

'"Values are slope coefficients and standard errors (N — 680, T — 2). 'Except for Grade, all variables were in natural logarithms; coefficients of independent variables in logarithms are the elasticities. P A complete set of nine School indicator variables were included in the models though for brevity their coefficients are not reported. Chi-square test for the exogeneity of proportion school attendance, df — 2. *P < 0.05.

235

Cognitive Development of Tanzanian Schoolchildren TABLE 7. Efficient estimates from the random- effects models for Tanzanian children's scores on school examinations in two survey rounds explained by socioeconomic and anthropometric varibles, infections, hemoglobin concentration, and school attendance0. Dependent variable Arithmetic 0 Independent variable Constant Grade Socioeconomic status Hookworm, eggs/g of stool Schistosomiasis, eggs/10 mL ofurine Height, m C-reactive protein, mg/dL Hemoglobin, g/L Proportion school attendance Chi-square statistic 11

Science 0

Geography 0

Civics 0

Coefficient

SE

Coefficient

SE

Coefficient

SE

Coefficient

SE

-1.564 -0.202* 0.620 -0.009

4.208 0.053 0.526 0.014

-5.343 0.029 0.747 -0.004

3.904 0.048 0.510 0.013

-3.710 -0.023 0.662 -0.007

2.933 0.035 0.368 0.010

-9.162* -0.079* 0.694 0.001

3.421 0.041 0.436 0.011

-0.027 0.505 -0.048* 0.244 -0.032 13.12*

0.015 0.682 0.025 0.304 0.027

-0.002 0.768 -0.028 0.479 -0.031 6.25*

0.015 0.630 0.022 0.270 0.021

-0.018 0.840 0.003 0.163 -0.025 5.53

0.011 0.478 0.018 0.207 0.014

-0.020 1.753* -0.032 0.380 -0.016 1.67

0.013 0.558 0.020 0.233 0.015

a

Values are slope coefficients and standard errors (iV - 294, T — 2). for Grade, all variables were in natural logarithms; coefficients of independent variables in logarithms are the elasticities. A complete set of nine School indicator variables were included in the models though for brevity their coefficients are not reported. Chi-square test for the exogeneity of proportion school attendance, df — 2. *P < 0.05.

b Except C

significant predictor of the scores in civics, and hemoglobin concentration was not a significant predictor of the scores. The C-reactive protein level was negatively and significantly associated with the scores in arithmetic. In contrast with the results for the educational achievement tests, school attendance was not a significant predictor of the scores on school examinations.

Results for the scores on educational achievement tests taking into account interactions between health status and the educational infrastructure

Table 8 presents the results for the scores on educational achievement tests where the models included teachers' years of experience, number of work assignments, and a

TABLE 8. Efficient estimates from the random effects models for Tanzanian children's scores on educational tests in two survey rounds explained by socioeconomic and anthropometric variables, infections, hemoglobin concentration, school attendance, and interactions between health status and school infrastructure"' '"' Dependent variable Total arithmetic

Sentence reading Independent variable Constant Grade Socioeconomic status Teacher experience Work assignments Hookworm, eggs/g of stool Schistosomiasis, eggs/10 mL of urine Height, m Work assignments x height C-reactive protein, mg/dL Hemoglobin, g/L Proportion school attendance

Coefficient 24.143* 0.198* 0.269 0.026 0.212* -0.007 0.005 4.717* -0.042* 0.016 0.420* 0.033*

Spelling

SE

Coefficient

SE

Coefficient

SE

4.041 0.032 0.373 0.017 0.100 0.010 0.011 0.737 0.020 0.017 0.201 0.012

-0.978 0.110* 0.094 0.013* -0.037 -0.001 -0.0002 0.510* 0.008 0.001 0.154* 0.020*

1.218 0.010 0.114 0.005 0.030 0.002 0.003 0.225 0.006 0.005 0.059 0.006

-15.216* 0.132* 0.742* 0.012 0.044 -0.009 0.006 2.786* -0.009 0.006 0.264 0.033*

3.188 0.028 0.341 0.016 0.078 0.009 0.010 0.575 0.016 0.011 0.150 0.008

"Values are slope coefficients and standard errors (N - 507, T = 2).

b Except for Grade, all variables were in natural logarithms; coefficients c School indicator variables were omitted from these models. d

Chi-square statistics were suppressed. *P < 0.05.

of independent variables in logarithms are the elasticities.

236

A. Bhargava et al. term interacting children's height with work assignments. The sample sizes were lower because of missing data for 2 schools. Teachers' experience was a significant predictor of the total arithmetic scores; the number of work assignments was significantly associated with the scores on sentence reading. Moreover, the variable interacting work assignments with height was a significant predictor of the scores on sentence reading providing some evidence on interactions between measures of children's health status and the educational infrastructure. The proportion of school attendance was a significant predictor of all three scores. Moreover, the results for educational achievement tests in Tables 6 and 8 were similar despite a reduction in sample sizes. Lastly, the results for school examinations from models containing variables approximating the educational infrastructure were similar to those in Table 7 and hence were omitted.

DISCUSSION This paper analyzed the data from a comprehensive longitudinal study in Tanzania covering cognitive, health, and educational variables for children attending primary schools. The analytical framework for modeling the scores on cognitive and educational achievement tests and school examinations provided useful insights. Firstly, from a methodological standpoint, educational achievement tests are closer in spirit to the material taught in school but are administered by trained outside staff. By contrast, the design of cognitive tests entails an elaborate culture-specific input from psychologists; the scores on school examinations are easy to compile. However, the empirical results for the scores on school examinations identified only a few proximate determinants of children's performance and school attendance was not a significant predictor of these scores. By contrast, school attendance was a significant predictor of the scores on the three educational achievement tests suggesting inadequacies in the school examination systems. Moreover, variables such as children's heights and hemoglobin concentration were invariably significant in the models for the educational achievement tests though hemoglobin concentration was mostly insignificant in the models for cognitive test scores. From our comprehensive

analysis of the Tanzania data, it seems reasonable to conclude that educational achievement tests are very suitable instruments for assessing children's intellectual development in poor countries. Secondly, the allocation of meager resources typically available for health and education in developing countries entails trade-offs between programs such as those for food supplementation, anthelmintic treatment, and for the educational infrastructure. The results for models explaining children's scores on educational achievement tests by work assignments, height, and interaction between these variables (Table 8) provided useful insights. Coefficients of the variables in the model for sentence reading suggested that shorter children may benefit more from work assignments though this can be true only up to a certain extent. For wider applicability of such results, it would be necessary to calculate threshold points that require larger sample sizes for precise estimation of the model parameters. Thirdly, the results for school attendance showed that improving the socioeconomic status of the households is likely to increase school attendance. This is especially relevant in the wake of the AIDS pandemic in African countries where many children are being orphaned; a decline in the socioeconomic status due to parental morbidity and mortality is likely to interfere with school attendance and can adversely affect health status. Recent evidence from Ethiopia suggests that subsidies to households fostering orphaned children would facilitate school participation (Bhargava, 2005). Thus, greater resources should be devoted for increasing children's school participation though magnitudes of the subsidies would depend on the educational infrastructure and HIV prevalence rates in the country. Finally, although several randomized trials offering anthelmintic treatment to infected children to assess gains in cognitive performance have been carried out (Dixon et al., 2000), less emphasis has been placed on data analyses to model the underlying pathways. The test scores of children in the Control and Intervention groups of our study increased over the 18-month observation period though the differences in the changes in scores of the treated and untreated children were not statistically significant. Unlike the markers for iron status, such as hemoglobin and ferritin concentration, that were directly affected by anthelmintic treatment (Bhargava et al.,

Cognitive Development of Tanzanian Schoolchildren 2003), children's cognitive development depends on a wide range of factors. Our analysis identified the importance of children's regular school attendance, height, and hemoglobin concentration for the test scores. Thus, in addition to anthelmintic treatment, future trials should investigate the benefits of iron supplementation and possibly special instruction in the classroom for children's cognitive development. In the wake of the AIDS pandemic, large-scale interventions are necessary for maintaining the future supply of skilled labor and hence for economic growth in Tanzania. ACKNOWLEDGMENTS

The research was supported by grants from the J.S. MacDonnell Foundation and the Research Committee of the World Bank. While retaining the views expressed in the paper, the authors thank the participants and our field collaborators for making the study possible and Professor J. Sachs for useful suggestions. This revision has greatly benefited from the detailed comments of two reviewers and the editors. LITERATURE CITED Bhargava A. 1991. Identification and panel data models with endogenous regressors. Rev Econ Stud 58:129-140. Bhargava A. 1994. Modelling the health of Filipino children. J R Stat Soc A 157:417-432. Bhargava A. 1998. A dynamic model for the cognitive development of Kenyan schoolchildren. J Educ Psychol 90:162-166. Bhargava A. 2001. Nutrition, health and economic development: some policy priorities. Food Nutr Bull 22:173-177. Bhargava A. 2005. AIDS epidemic and the psychological well-being and school participation of Ethiopian orphans. Psychol Health Med (in press). Bhargava A, Sargan JD. 1983. Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51:1635-1660. Bhargava A, Jukes M, Lambo J, Kihamia CM, Lori W, Nokes C, Drake L, Bundy DAP. 2003. Anthelmintic treatment improves the hemoglobin and serum ferritin concentrations of Tanzanian schoolchildren. Food Nutr Bull 24:332-342. Ceci SJ. 1991.How much does schooling influence intelligence and its cognitive components? A reassessment of the evidence. Dev Psychol 27:703-722.

Cole TJ. 1991. Weight-stature indices to measure underweight, overweight and obesity. In: Himes JH, editor. Anthropometric assessment of nutritional status. New York: Wiley-Liss. p 83-111. Cox DR. 1971. Analysis of binary data. London: Chapman Hall. Dickson R, Awasthi S, Williamson P, Demellweek C, Garner P. 2000. Effects of treatment for intestinal helminth infection on growth and cognitive performance in children: systematic review of randomized trials. Br Med J 320:1697-1701. Goldstein H, Thomas S. 1996. Using examination results as indicators of school and college performance. J R Stat Soc A 159:149-163. International Bureau of Education. 1997. World data on education. Geneva, Switzerland: UNESCO, International Bureau of Education. Laird NM, Ware JH. 1982. Random effects models for longitudinal data. Biometrics 38:963-974. Lozoff B. 1988. Behavioral changes in iron deficiency. Adv Pediatr 35:331-360. Nelson M, Black AE, Morris JA, Cole TJ. 1989. Betweenand within-subject variation in nutrient intake from infancy to old age: estimating the number of days to rank dietary intakes with desired precision. Am J Clin Nutr 50:155-167. Neyman J, Scott E. 1948. Consistent estimates based on partially consistent observations. Econometrica 16: 1-32. Partnership for Child Development. 2002. Heavy schistosomiasis is associated with poor short-term memory and slower reaction times in Tanzanian schoolchildren. Trop Med Int Health 7:104-117. Pollitt E. 1993. Iron deficiency and cognitive function. Annu Rev Nutr 13:521-537. Sargan JD. 1958. The estimation of economic relationships using instrumental variables. Econometrica 26:393-415. Simeon DT, Grantham-McGregor SM, Callender JE, Wong MS. 1995. Treatment of Trichuris trichiura infections improves the growth, spelling scores and school attendance in some children. J Nutr 125: 1875-1883. van den Broek NR, Letsky EA. 1999. Etiology of anemia in pregnancy in south Malawai. Am J Clin Nutr 72:247S-256S. Vygotsky LS. 1987. Thinking and speech. In: Rieber RW, Carlton AS, editors. Collected works of L.S. Vygotsky, Vol 1. New York: Plenum. Wald A. 1947. Sequential analysis. New York: Dover Publications. Watkins WE, Pollitt E. 1997. "Stupidity or worms": do intestinal worms impair mental performance? Psychol Bull 121:171-191. Zellner A. 1962. An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. J Am Stat Assoc 57: 348-368. Zellner A, Theil H. 1962. Three-stage least squares: simultaneous estimation of simultaneous equations. Econometrica 30:54-78.

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Psychology, Health & Medicine, August 2005; 10(3): 2 6 3 - 2 7 5

R Routledge

Taylor & Francis Group

AIDS epidemic and the psychological well-being and school participation of Ethiopian orphans

ALOK BHARGAVA Department of Economics, University of Houston, USA

Abstract This paper modeled the proximate determinants of the scores on 60 items from Minnesota Multiphasic Personality Inventory-2 (MMPI) and of school participation of approximately 1,000 children who had lost their mothers due to AIDS and from other causes using the data from a survey in Ethiopia. The scores on MMPI items reflecting emotional and social adjustment, and school participation before and after maternal deaths were modeled in a multi-disciplinary framework incorporating the time sequence of events. The main findings were that while AIDS orphans scored lower on MMPI items, variables such as presence of the father, household income, feeding and clothing conditions, and attitude of the fostering family were significant predictors of children's scores. Secondly, girls were at a disadvantage in terms of the scores on MMPI items. Third, variables such as income and good feeding and clothing conditions were significant predictors of school participation. Fourth, school participation before maternal death was an important predictor of subsequent school participation probabilities. An ordinal regression model was estimated to address certain methodological problems. Overall, the results indicated that economic subsidies to fostering households would enhance child welfare in Ethiopia. Keywords: AIDS epidemic, child welfare, economic policy, psychological well-being, school participation

Introduction The AIDS epidemic is having a major toll in sub-Saharan Africa leaving a large number of orphaned children. It is estimated that by 2010, there will be over 25 million orphans of AIDS in Africa (TJSAID/UNICEF/UNAIDS, 2002). The effects of parents dying in their prime are devastating for young children. Furthermore, orphaned children need a supporting environment enabling them to overcome the emotional and economic losses (Ansell & Young, 2004). This is difficult where families cannot meet their own children's basic needs for nutrition, clothing, and education. It is therefore unrealistic to expect fostering households to possess the resources for ensuring orphaned children's well-being and school participation. While international organizations such as the World Bank have recognized the importance of channeling resources to needy children (Subbarao & Coury, 2004), there is an urgent need for developing cost-effective interventions for children in various age groups (Bhargava Correspondence: Alok Bhargava, Professor of Economics, Department of Economics, University of Houston, Houston, TX 772045019, USA. Tel: + 1 (713) 743 3837. Fax: + 1 (713) 743 3798. E-mail: bhargava @ uh.edu ISSN 1354-8506 print/ISSN 1465-3966 online © 2005 Taylor & Francis Group Ltd DOI: 10.1080/13548500412331334181

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A. Bhargava & Bigombe, 2003). For example, subsidies for fees, uniforms and supplies to families fostering school-aged children are likely increase school participation. However, there is paucity of evidence on factors affecting orphaned children's psychological well-being and school participation (Monasch & Boerma, 2004). Apart from imparting the necessary skills, school participation is likely to alleviate children's isolation. Moreover, small-scale interventions by non-governmental organizations in African countries suggest that educational programs can enhance children's understanding of the HIY transmission routes (Bhargava & Bigombe, 2003). While the economics literature on child labor has addressed issues such as the effects of child wages and subsidies on school participation (Ravallion & Wodon, 2000), the consequences of poor adult health on children's income-generating activities and school participation are largely unexplored. Parental death due to AIDS is preceded by morbidity spells that can hamper children's school attendance; evidence from Tanzania indicated that households' socioeconomic status was an important predictor of school attendance (Bhargava, Jukes, Ngorosho, Khilma, & Bundy, submitted). A decline in cash earnings due to parental sickness is likely to increase children's income-generating activities and adversely affect their well-being. Furthermore, there have been epidemiological studies in African countries investigating risk factors for HIV transmission such as the presence of other sexually transmitted infections and multiple sex partners (Carael & Holmes, 2001). While the dangers of HIV transmission can be communicated via the media (Demographic and Health Survey, 2000), it is difficult for poorly educated individuals to adhere to safe sex practices (Ndubani & Hojer, 2001). Moreover, increased attrition of the skilled labor force due to premature AIDS deaths implies that children will eventually need to replenish the labor market with skills that are important for economic growth (Bhargava, Jamison, Lau, & Murray, 2001). Multi-disciplinary research investigating the effects of behavioral and socioeconomic factors on children's school participation and the scores on items from the Minnesota Multiphasic Personality Inventory-2 (MMPI) (Butcher & Williams, 2000) can provide useful insights for policy formulation. The MMPI items typically cover several aspects of children's emotional and social adjustments in different settings (Butcher, 1995); issues such as the gender differences in the MMPI scores (Hathaway & Monachesi, 1953; Williams, Butcher, Ben-Porath, & Graham, 1992) can be addressed in the empirical analyses. From the standpoint of child development, physical growth of children in developing countries is often compromised by inadequate nutrient intakes and sicknesses spells; such factors are reflected in the high prevalence rates for "stunting" and "wasting" (Waterlow, 1994). Moreover, nutritional status is important for brain development (Pollitt, 1993; Scrimshaw, 1996); school attendance enhances children's learning and cognitive development (Bedi & Marshall, 1999; Bhargava et al., submitted). While the educational infrastructure is poor especially in rural areas of African countries, parental input can offset some of the disadvantages (Bhargava, 1998). However, the AIDS epidemic is reducing the time that parents can devote to children. Instead, children often become caregivers to the dying parents. Furthermore, premature parental death is likely to have adverse consequences for children's psychological well-being and school participation; girls might be assigned additional housework while boys may spend more time on remunerative activities. While orphaned children from better-off households may be buffered against food shortages and can continue in school, it is important to investigate children's welfare using several measures. Demographic, socioeconomic, and behavioral variables are likely to affect

Psychological Well-being of Ethiopian Orphans children's school participation and the scores on MMPI items. This paper analyzed the data from the National Survey on die Prevalence and Characteristics of Orphans in Ethiopia (MOLSA/Italian Corporation/UNICEF, 2003) to elucidate the links between children's fostering environment, school participation, and well-being.

Methods Participants The National Survey of Prevalence and Characteristics of Orphans in Ethiopia was conducted in 2 0 0 1 - 0 2 using a stratified sampling approach in the nine Administrative Regions and two Administrative Cities (MOLSA/Italian Corporation/UNICEF, 2003). The households were visited by trained "supervisors" who had a degree is social sciences and prior experience in data collection, and by trained "data collectors" that had completed at least high school education and were experienced in data collection. The questions were read out in Amharic (or the local language) and the responses were recorded by die enumerators. The enumerators were trained in Addis Ababa and a manual was developed to streamline die protocol. Of die 11,932 households surveyed, 3,883 were found to be fostering at least one maternal orphan (orphans widi bodi parents deceased were included). An orphan was randomly selected from each household and die head of die household answered questions on demographic and socioeconomic aspects. The survey administered 60 items from die MMPI to assess die emotional and social adjustment of orphans over die age of 10 years. The analysis of child well-being and school participation was restricted to tiiis sub-sample. Economic, demographic, and morbidity variables The demographic and economic modules of die questionnaire inquired characteristics of die orphan's own family and of die fostering family. Education levels of die deceased mothers and that of die head of die fostering household were recorded. Mondily income of the head of the household was investigated using 11 categories. The age of die mother at die time of deatii, number of days for which she was critically sick, number of children mat she had, and the number of children in die fostering households were determined. Furuiermore, questions were asked about die nature and duration of maternal sicknesses, fever spells, diarrhea, cough with blood, skin spots, swollen neck and armpits, tuberculosis, and paralysis prior to deatii. Based on die responses, a "verbal autopsy" was conducted to conclude if die mother had died of an AIDS-related illness. The reliability of this procedure for a subset of die sample was 0.97 (MOLSA/Italian Corporation/UNICEF, 2003). The children were asked questions about dieir sicknesses, vaccination status, household environment, and well-being. For example, questions pertaining to die attitude of die fostering family towards die orphans, if food was unequally distributed and if die children had adequate food intake and domes to wear were answered by die children. Moreover, die school participation of die children before and after modiers' deadis was investigated. The questionnaire also inquired if children had engaged in income-generating work before and after dieir mother's deatii. The children's HIV status was not investigated in die study in part because motiier-to-infant HTV transmission was unlikely to be responsible for children's HIV status; in die absence of anti-retroviral dierapy, die median survival time for HIVpositive infants is typically 12.4 mondis (Spira et al., 1999).

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A. Bhargava Measures of emotional and social adjustment The selection of the MMPI items was based on the constructs of emotional and social adjustment that were appropriate for the Ethiopian setting. Initially, 80 emotional adjustment items were selected to cover aspects such as the control and expression of emotions, and manifestations such as extreme worry, sleep disturbance and loneliness. The 80 social adjustment items covered social perception, attitude, and behavior in adapting to the social surroundings. The items were translated into Amharic by a translator from the Institute of Language Studies at the University of Addis Ababa and two psychologists from the University of Addis Ababa specializing in psychometrics and counseling assessed the construct validity. Subsequently, the items were tested on three groups of children, namely juvenile delinquents, institutionalized orphans, and school children living with both biological parents for criterion validity. The items-test correlations were examined and only items with correlation coefficients greater than .40 were selected. This procedure led to the selection of 30 items in each of the emotional and social adjustment categories. The responses to the 60 items were converted to the usual MMPI format, that is, whether the children "Agree ( = 1 ) " or "Disagree ( = 2 ) " with the questions. For most questions, higher scores reflected better outcomes though in some cases the responses were transformed so that "Disagree" was the desirable response. The emotional adjustment items included items such as "Almost everyday something happens to frighten me", "I feel that I deserve severe punishment for the mistakes I committed" and "I have a tragic loss in my life that I know I will never get over". Examples of social adjustment items were "Most of the time I feel lonely even when I am with others", "I dislike having people around me" and "It is safer to trust nobody". The mean scores on emotional and social adjustment items were modeled; the averages enabled us to retain children who had failed to answer a few questions. Due to missing observations on certain questions pertaining to the school participation and income-generating work, complete data were available on 848 children for modeling the proximate determinants of school participation, and on 1027 children for the analysis of the scores on MMPI items. Empirical models for the proximate determinants of school participation and psychological well-being The Ethiopian orphans' well-being and school outcomes were modeled using a threeequation model, where the first and second equations specified latent variables that were unity if the child was participating in school before and after the death of the mother, respectively; the observed variables were zero otherwise. Because learning is a cumulative process, the model for school participation after maternal death included an indicator variable for whether the child was previously in school. This indicator variable was potentially "endogenous" (correlated with the error term) and the statistical problems were tackled by estimating an ordinal regression model. The explanatory variables for school participation before maternal death pertained to the previous living arrangements; the variables recorded for fostering households were included in the model for school participation after maternal death. The third equation modeled mean scores on MMPI items in the two situations where the indicator variable for school participation after maternal death was excluded from the model and where it was included as potentially an endogenous variable. The empirical model for the ith child (i= 1, 2, . . . , ri) can be written as:

Psychological Well-being of Ethiopian Orphans

243

(School Participation before), = a0 + ai (Maternal age at death), + a2 (Mother died of AIDS), + a3 (Mother illiterate), + a4 (Number of children of deceased), + a5 (Sex orphan), + a6 (Father preparing meals), + a7 (Income-generating work before),+ u, (1) (School Participation after), = b 0 + b! (Mother died of AIDS), + b 2 (Sex orphan), (2) + b 3 (Father preparing meals),+ b 4 (Family size in foster household), + b 5 (Monthly income of foster household), + b 6 (Feeding conditions good), + b 7 (Dressing well),+ b 8 (Head of foster household illiterate), + b 9 (Income-generating work after), + b 1 0 (School participation before),+ v,

(2)

and (Mean scores on MMPI items),r=c 0 + c 1 (Mother died of AIDS), + c 2 (Sex orphan), + c 3 (Father preparing meals),+ c 4 (Monthly income of foster household), + c 5 (Monthly income of foster household) 2 ,+ c 6 (Feeding conditions good), + c 7 (Dressing well), + c 8 (Head of foster household illiterate), + c 9 (Food unequally distributed), + c 10 (Family's attitude is not sympathetic), + w,-

(3)

Statistical and modeling procedures The differences in the means of variables for AIDS orphans and for orphans from other causes were tested using independent r-tests available in the software package SPSS (1999). For dichotomous variables, the non-parametric procedures due to Mann and Whitney (1947) or Wilcoxon (1945) available in SPSS (1999) were used. The errors on equations (1) and (2) were random variables that were assumed to be distributed according to the logistic distribution with zero means and constant variances; errors on equation (3) were assumed to be normally distributed with zero mean and constant variance. The unknown coefficients were estimated separately for each equation. Equations (1) and (2) were estimated by maximum likelihood using the binary logistic option in SPSS (1999). However, the variable "School participation before" was potentially an endogenous variable in equation (2) because the underlying factors such as unobserved child characteristics affecting school participation before maternal death might be related to factors affecting subsequent school participation. Because this problem cannot be easily addressed within models where both the dependent variable and the endogenous explanatory variable are dichotomous, the salient features of die models in equations (1) and (2) were incorporated to form an ordinal regression where the dependent variable assumed values 1 - 4 for the states depending on whether the children were or were not in school. The four states were: {(Yes, No), (No, No), (Yes, Yes) and (No, Yes)}. Thus, it was assumed that children who were participating in school before the death of their mothers but not after had the least desirable outcomes. By contrast, in the last state, school participation after maternal death for children not previously in school was the best possible outcome in terms of the fostering arrangements. The ordinal regression model was estimated by maximum likelihood using an algorithm (McCullagh, 1980); omer reformulations of the dependent variable in the ordinal model produced similar results. Lasdy, die models for the mean scores on 30 emotional adjustment items, 30 social adjustment items and on the combined 60 items were estimated using the multiple regression method.

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A. Bhargava Results Descriptive statistics and differences between AIDS and non-AIDS orphans The sample means and standard deviations of the variables used in the analysis are reported in Table I. The ^-statistics for differences in the means of variables for orphans due to AIDS and orphans from other causes are also presented for comparing the means of the dichotomous variables, the non-parametric test statistics are reported. There were 230 boys (48%) and 249 girls (52%) in the AIDS orphan group, and 276 boys (48%) and 298 girls (52%) among other orphans, so the sex ratios were very similar. However, there were significant differences (p < .05) between the two groups of orphans in variables such as the mother's age at death that was significantly lower for AIDS orphans; the number of days for which the mother was critically sick was significantly higher for the AIDS group. The proportion of illiterate mothers dying from AIDS was significantly lower than maternal deaths from other causes. The family size in the fostering households and the numbers of children of the deceased mother were significantly lower for the AIDS group. A significantly lower proportion of AIDS orphans reported that the feeding conditions were good or satisfactory in the fostering households; similar results were obtained for the question inquiring if the orphans were dressing well. There were no significant differences in the responses investigating whether food was unequally distributed in the household. While there were insignificant differences between the two groups in school participation before maternal death, there were significant differences after the mothers' deaths; a greater proportion of AIDS orphans were participating in school following maternal deaths. In the four categories for children participating in school before and after maternal death, that is, {(Yes, No), (No, No), (Yes, Yes) and (No, Yes)}, the numbers of orphans in these groups (with the percentages in parentheses) were 79 (11%), 32 (4%), 558 (74%), and 83 (11%), respectively. Lastly, participation in income-generating work more than doubled for both types of orphans after maternal deaths. However, there were no significant differences between AIDS and other orphans. The mean scores on 60 MMPI items investigating the emotional and social adjustment aspects were significantly lower for the AIDS orphans. The Cronbach a coefficient (Cronbach, 1984) for assessing internal consistency of the responses to the 30 emotional adjustment items was .86, and was .80 for the 30 social adjustment items, reflecting a high degree of consistency. School participation before and after maternal death The maximum likelihood estimates from binary logistic models for orphans' school participation before and after maternal death controlling for children's ages are in Table II. For school participation before maternal death, the coefficient of mother's age at time of death was positive and statistically significant (p < .05). Thus, mothers' premature deaths appeared to have hindered children's school participation. However, the variables representing mothers' death due to AIDS and sex of the orphan were not significant predictors of school participation before maternal death. The coefficient of the indicator variable for whether the mother was illiterate was estimated with a significant negative sign indicating that illiterate mothers were only half as likely to send their children to school. The coefficient of children's income-generating work was negative but not significantly different from zero. In the second set of columns in Table II, the results for children's school participation after maternal death provided useful insights and the fit of the model was better than that for

Table I. Sample means and standard deviations of selected variables for maternal orphans due to AIDS and other causes in the Ethiopian Survey of prevalence and characteristics of AIDS orphans.

Mother's age at death, years Number of days mother critically sick Number of children of the deceased mother Deceased mother was illiterate,0, 0 = No, 1 = Yes Father preparing meals for the orphan, 0 0 = No, 1 = Yes Sex of the orphan, 0 1 = Boy, 2 = Girl Monthly income of the fostering household, 1-11 Head of foster household is illiterate,0 0 = No, 1 = Yes Family size in the foster household Feeding conditions are good or satisfactory,0 0 = No, 1 = Yes Food is unequally distributed, 0 0 = No, 1 = Yes Whether dressing well,0 0 = No, 1 = Yes Family's attitude is not sympathetic,0 0 = No, 1 = Yes Mean MMPI scores on 30 emotional adjustment items, 1 = Agree, 2 = Disagree Mean MMPI scores on 30 social adjustment items, 1 = Agree, 2 = Disagree Mean MMPI scores on all 60 items, 1 = Agree, 2 = Disagree Going to school before mother's death, 0 0 = No, 1 = Yes Going to school after mother's death, 0 0 = No, 1 = Yes Income generating work before mother's death, 0 0 = No, 1 = Yes Income generating work after mother's death, 0 0 = No, 1 = Yes Ordered variable for school participation categories, 1 - 4 d

AIDS orphans" (« == 479)

Other orphans 8 (« == 574)

M

SD

M

SD

tb

34.35 94.85 3.14 0.32 0.35 1.52 1.91 0.31 5.24 0.41 0.31 0.41 0.02 1.47 1.48 1.47 0.79 0.87 0.09 0.23 2.89

7.77 145.9 1.88 0.47 0.48 0.50 1.76 0.46 2.50 0.49 0.46 0.49 0.15 0.21 0.19 0.18 0.41 0.33 0.28 0.42 0.70

35.69 56.97 3.62 0.39 0.34 1.52 1.87 0.32 5.75 0.47 0.28 0.47 0.03 1.50 1.50 1.50 0.75 0.82 0.08 0.26 2.83

8.91 97.63 2.19 0.49 0.47 0.50 1.76 0.47 2.88 0.50 0.45 0.50 0.18 0.21 0.18 0.18 0.43 0.38 0.27 0.44 0.77

2.55 -4.53 3.83 2.36 -0.23 -0.13 -0.34 0.15 2.95 2.13 -0.95 2.05 0.98 2.09 2.16 2.32 - 1.35 -2.12 -0.47 1.11 - 1.19

"There were 230 boys and 249 girls in the AIDS orphans group, and 276 boys and 298 girls among the other orphans. Degrees of freedom = 1051 for the (-tests, assuming constant variances, ^on-parametric tests were used to test the differences in dichotomous variables. 4 See notes to Table III.

i-statistics for differences in means (Other -AIDS) p-value .011

< .001 < .001 .018 .816 .894 .735 .882 .003 .033 .343 .041 .325 .037 .031 .021 .178 .034 .636 .268 .234

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A. Bhargava

Table II. Maximum likelihood estimates from binary logistic regression models for children's school participation before and after the deaths of their mothers using the Ethiopian Survey of prevalence and characteristics of AIDS orphans. Dependent variable (0 = No, l = Y e s ) : school participation before mother's death (n = 848) Explanatory variables Constant Mother's age at death, years Mother died of AIDS, 0 - 1 Mother was illiterate, 0 - 1 Number of children of the dead mother Sex of the orphan, 1-2 Father preparing meals for the orphan, 0 - 1 Income generating work before mother's death, 0 - 1 Family size in foster household Monthly income of foster household, 1-11 Feeding conditions are good or satisfactory, 0 - 1 Whether dressing well, 0 - 1 Head of foster household is illiterate, 0 - 1 Income generating work after mother's death, 0 - 1 School participation before mother's death, 0 - 1

Coefficient

SE

0.862 0.035* 0.001 - 0.726* - 0.072 -0.013 -0.167 - 0.365

0.487 0.012 0.182 0.180 0.048 0.176 0.184 0.287

-

.053

Dependent variable (0 = No, l = Y e s ) : school participation after mother's death {n- 753) Coefficient

SE

1.059

0.605

-

-

0.485*

0.245

-

-

- 0.5554* 0.004

0.004 0.307* 0.880* 0.870* - 0.226 - 1.651* 1.236* .306

0.249 0.271

0.044 0.162 0.307 0.292 0.254 0.256 0.281

*p < 0.05.

school participation before maternal death. AIDS orphans had significantly higher chances of school participation than orphans whose mother had died due to non-AIDS-related illnesses. Second, girls were significantly less likely than boys to participate in school following the death of their mothers. The presence of the father in the household and family size of the fostering households did not significantly affect the chances of school participation after maternal death. Third, monthly income, and good feeding and dressing conditions in the fostering household were significant predictors of school participation following maternal death. Fourth, while the illiteracy status of the head of the fostering household was not a significant predictor, children's participation in income-generating work after maternal death appeared to have reduced their school participation chances by approximately 80%. This was in contrast with the results for school participation before maternal death where incomegenerating work was not significantly associated. Fifth, the indicator variable for whether the orphan was in school before maternal death was significantly associated with school participation after maternal death; such children were 3.5 times more likely to be in school after maternal deaths. Because the factors underlying school participation such as children's abilities and motivation would affect school participation before and after maternal death, it was desirable to treat this variable as an endogenous explanatory variable. Table III reports the maximum likelihood estimates of the ordinal regression model for the four states of school participation before and after maternal death. The coefficients of the three "threshold" variables were significant indicating differences in means among the four states. The coefficients of the explanatory variables were consistent with the results presented in Table II. Girls had lower chances of school participation than boys, and good

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Psychological Well-being of Ethiopian Orphans Table III. Maximum likelihood estimates from an ordinal regression model for four categories of children's school participation before and after the deaths of their mothers using the Ethiopian Survey of prevalence and characteristics of AIDS orphans 8 Dependent variable ( 1 - 4 ) : ordinal variable for school participation before and the mother's death (n = 752) Explanatory variables Threshold 1 Threshold 2 Threshold3 Mother's age at death, years Mother died of AIDS, 0 - 1 Mother was illiterate, 0 - 1 Sex of the orphan, 1-2 Monthly income of foster household, 1-11 Feeding conditions are good or satisfactory, 0 - 1 Father preparing meals for the orphan, 0 - 1 Whether dressing well, 0 - 1 Head of foster household is illiterate, 0 - 1 Income generating work before mother's death, 0 - 1 Income generating work after mother's death, 0 - 1 R2

Coefficient

SE

- 3.819* - 3.374* 1.016* —0.031* 0.192 0.172 - 0.403* 0.071 0.474* 0.087 0.508* —0.351 —0.404 —1.287* .166

0.541 0.536 0.513 0.010 0.171 0.180 0.172 0.049 0.208 0.182 0.206 0.194 0.322 0.224

"The four ordinal variables assumed the values 1, 2, 3, and 4 for respective answers to the questions whether they were participating in school before and after the deaths of their mothers: (Yes, No), (No, No), (Yes, Yes), and (No, Yes). *p < 0.05.

feeding and clothing conditions were positively associated with school participation states. However, household income was not a significant predictor in this model. While the coefficient of the income-generating work before maternal death was not statistically significant, the coefficient of income-generating work after maternal death was negative and statistically significant. Thus, income-generating work before maternal death did not appear to have been as detrimental to school participation as the work following maternal death. This phenomenon may have been partly due to the facts that learning is a cumulative process, and children's school participation declines with age. Children's emotional and social adjustment Table IV presents the results from multiple regression models for children's mean scores on MMPI items measuring emotional and social adjustments, and for the mean scores on all 60 items. First, the negative coefficient of the indicator variable for the child's sex showed that girls scored significantly lower than boys on emotional adjustment items; girls might be more sensitive to the emotional loss and more willing to record their feelings. The presence of father in the household and the indicator variable for whether the children were dressing well had positive and statistically significant effects on the scores on emotional adjustment. Moreover, the coefficient of indicator variable for unsympathetic attitude of the fostering family was estimated with a significant negative coefficient. Second, for the mean scores on social adjustment items, AIDS orphans were at a disadvantage. Again, girls scored significantly lower than boys, which may in part be due to greater housework load following maternal deaths. There were non-linearities in the effects of household incomes on the mean scores on social adjustment items; both income terms

to

Table IV. Multiple regression models for children's mean scores on MMPI items using the Ethiopian Survey of prevalence and characteristics of AIDS orphans. Dependent variable : mean MMPI scores on 30 emotional adjustment items (n = 1027) Explanatory variables Constant Mother died of AIDS, 0 - 1 Sex of the orphan, 1 - 2 Father preparing meals for the orphan, 0 - 1 Monthly income of foster household, 1-11 Monthly income( squared Feeding conditions are good or satisfactory, 0 - 1 Food is unequally distributed, 0 - 1 Whether dressing well, 0 - 1 Head of foster household is illiterate, 0 - 1 Family's attitude is not sympathetic, 0 - 1 R2 *p < 0.05.

Dependent variable : mean MMPI scores on 30 social adjustment items in = 1027)

Dependent variable: mean MMPI scores on all 60 items (n -= 1027)

Coefficient

SE

Coefficient

SE

Coefficient

SE

1.488* - 0.020 - 0.027* 0.066* -0.016 0.001 0.080* - 0.023 0.057* - 0.003 -0.153* .141

0.028 0.013 0.013 0.013 0.012 0.001 0.016 0.015 0.015 0.014 0.038

1.558* -0.021* - 0.023* 0.024* - 0.029* 0.003* 0.045* - 0.044* 0.014 - 0.001 - 0.208* .096

0.024 0.011 0.011 0.012 0.011 0.001 0.014 0.013 0.013 0.012 0.033

1.522* -0.021* - 0.025* 0.046* - 0.022* 0.002* 0.063* - 0.032* 0.034* - 0.001 -0.180* .133

0.024 0.011 0.011 0.011 0.010 0.001 0.014 0.013 0.013 0.012 0.032

C3 TO

s 6)

Psychological Well-being of Ethiopian Orphans were statistically significant. Good feeding conditions were significantly associated with higher scores on social adjustment items, whereas unequal distribution of food was negatively associated. Third, the estimated coefficients in the model for the mean scores on all 60 MMPI items were more precise than the results for emotional and social adjustment items, and many coefficients were statistically significant. For example, the negative coefficients of variables indicating that the mother had died of AIDS, the indicator variable for girls, unequal distribution of food, and unsympathetic attitude of the fostering family were all statistically significant. Moreover, the coefficients of the variables inquiring if the father was preparing meals, if feeding conditions were good, and if the child was dressing well were significantly positively associated with the mean scores on 60 items. The R2 was higher in the model for the scores on all 60 items indicating a better goodness of fit than in the model for the scores on social adjustment items. Finally, the results for models for the scores on MMPI items where children's school participation after maternal deaths was included as an explanatory variable were very similar to those in Table IV (results not shown). School participation was positively and significantly associated with the scores on emotional adjustment items and with the scores on all 60 items thereby indicating the beneficial effects of school participation for children's well-being. Discussion This paper presents an analysis of the factors affecting orphaned children's school participation before and after maternal death and of the scores on MMPI items reflecting the emotional and social adjustments using the data from a recent survey from Ethiopia. The analysis took into account the time sequence of events and specified a three-equation model for school participation and the scores on MMPI items. The findings from this study support the view that increasing school participation of orphans would enhance their wellbeing. Because remunerative activities following maternal death appeared to have hindered school participation, policies such as subsidies of $40 per annum to support orphans' fees and other expenses in African countries are likely to increase school participation (Bhargava & Bigombe, 2003). The second main finding was that the economic status of the fostering household was important for increasing school participation and for child welfare. While there was some evidence of unequal food distribution in fostering households, the effects were small in comparison with the beneficial effects of greater food availability, resources for clothing, and emotional support. More elaborate studies such as those comparing the well-being of fostered orphans with biological children in the households would provide further insights for policy formulation. Finally, girls were more affected than boys by the emotional loss as reflected in the MMPI scores and were less likely to be participating in school after maternal deaths. While sex differences in MMPI scores have been reported in previous studies (Gumbiner & Flowers, 1997), larger sample sizes would be necessary to investigate the factors underlying the sex differences among Ethiopian orphans. Furthermore, the lack of economic opportunities for adolescent females is an urgent problem because it can lead to their engaging in commercial sex. Thus, approaches to sex education incorporating cultural aspects such as aunts ("Senga") communicating about sex education in Uganda (Muyinda, Nakuya, Pool, & Whitworth, 2003) are likely to reduce risky behavior. In view of wide spread poverty in Ethiopia, vocational training programs for adolescents are likely to be effective for moving

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girls out of poverty. International agencies such as the World Bank should support largescale vocational training programs so that they can replenish the labor force lost due to AIDS deaths. In view of the large number of HIV-positive adults in sub-Saharan Africa who are likely to die within the next decade, such policies are critical for maintaining economic growth. Acknowledgements Without implication, the author thanks Gobena Daniel of the University of Addis Ababa for generously sharing the data, and the World Bank for partial support for the analyses. This revision has benefited from the detailed and thoughtful comments of the two reviewers and the Editor. References Ansell, N.j & Young, L. (2004). Enabling households to support successful migration of AIDS orphans in South Africa. AIDS Care, 16, 3 - 1 0 . Bedi, A., & Marshall, J. (1999). School attendance and student achievement in rural Honduras. Economic Development and Cultural Change, 7, 657-682. Bhargava, A. (1998). A dynamic model for the cognitive development of Kenyan schoolchildren. Journal of Educational Psychology, 90, 162-166. Bhargava, A., & Bigombe, B. (2003). Public policies and the orphans of AIDS in Africa. British Medical Journal, 326, 1387-1389. Bhargava, A., Jamison, D., Lau, L., & Murray, C. (2001). Modeling the effects of health on economic growth. Journal of Health Economics, 20, 423-440. Bhargava, A., Jukes, M., Ngorosho, D., Khilma, C , & Bundy, D. (in press) Modelling the effects of health status and the educational infrastructure on the cognitive development of Tanzanian school children. American Journal of Human Biology Butcher, J. N . (1995). International adaptations of the MMPI-2. Minneapolis: University of Minnesota Press. Butcher, J. N., & Williams, C. L. (2000). Essentials of MMPI-2 andMMPI-A interpretation. Minneapolis: University of Minnesota Press. Carael, M., & Holmes, K. (2001). (Eds.). The multicentre study of factors determining the different prevalences of HIV in sub-Saharan Africa. AIDS, IS, Supplement 4. Cronbach, L. J. (1984). Essentials of psychological testing (4th ed.). New York: Harper and Row. Demographic and Health Surveys (2000). Demographic and Health Survey Ethiopia 2000. Washington, D.C.: Macrointernational. Gumbiner, J., & Flower, J. (1997). Sex differences on the MMPI-1 and MMPI-2. Psychological Reports, 81, 4 7 9 482. Hathaway, S., & Monachesi, E. (1953). Analyzing and predicting juvenile delinquency with the MMPI. Minneapolis: University of Minnesota Press. Mann, H., & Whitney, D. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18, 5 0 - 6 0 . McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Statistical Society B, 42, 109-142. MOLSA/Italian Corporation/UNICEF (2003). Survey of the prevalence and characteristics of AIDS orphans in Ethiopia. Addis Ababa: Ministry of Labour and Social Affairs. Monasch, R., & Boerma, J. (2004). Orphanhood and childcare patterns in sub-Saharan Africa: An analysis of national surveys from 40 countries. AIDS, 18, S55-S65. Muyinda, H., Nakuya, J., Pool, R., & Whitworth, J. (2003). Harnessing the Senga institution of adolescent sex education for the control of HIV and STD's in rural Uganda. AIDS Care, 15, 159-167. Ndubani, P., & Hojer, B. (2001). Sexual behavior and sexually transmitted diseases among young men in Zambia. Health Policy Planning, 16, 107-112. Pollitt, E. (1993). Iron deficiency and cognitive function. Annual Review of Nutrition, 13, 5 2 1 - 5 3 7 . Ravallion, M., & Wodon, Q. (2000). Does child labour displace schooling? Evidence on behavioural responses to an enrollment study, Economic Journal, 110, C I 5 8 - C I 7 5 . Scrimshaw, N . S. (1996). Health and nutrition from womb to tomb. Nutrition Today, 31, 5 5 - 6 7 .

Psychological Well-being of Ethiopian Orphans

Spira, R , Lepage, P., Msellati, P., Van De Perre, P., Leroy, V., Simonon, A., et al. (1999). Natural history of Human Immunodeficiency Virus Type 1 infection in children: A five-year prospective study in Rwanda. Pediatrics, 104, 1-9. SPSS (1999). SPSS for Windows version 10. Chicago, IL: SPSS, Inc. Subbarao, K., & Coury, D. (2004). Reaching out to Africa's orphans: A framework for public action. Africa Region Human Development Series. Washington, D.C.: The World Bank. USAID/UNICEF/UNAIDS (2003). Children on the brink 2002. New York: UNICEF. Waterlow, J. C. (1994). Causes and mechanisms of linear growth retardation (stunting). European Journal of Clinical Nutrition, 48, S 1 - S 4 . Wilcoxon, F . (1945). Individual comparisons by ranking methods. Biometrics, 1, 8 0 - 8 3 . Williams, C , Butcher, J., Ben-Porath, Y., & Graham, J. (1992). MMPI-A Content Scales: Assessing psychopathology in adolescents. Minneapolis: University of Minnesota Press.

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IV. Population Health and Economic Growth

Econometrics Journal (2001), volume 4, pp. 273-286.

Stochastic specification and the international GDP series ALOK BHARGAVA

Department of Economics, University of Houston, Houston, TX 77204-5019, USA E-mail: bhargavaSuh.edu Received: November 2000

Summary This paper investigates the stochastic properties of GDP series based on purchasing power comparisons for 125 countries from the Penn World Table (PWT) and a GDP series based on exchange rate conversions in 1987 constant dollars for 107 countries from the World Development Indicators (WDI) in the period 1965-90. Because many health and demographic variables are compiled at irregular intervals, models for economic growth are often estimated using data that are separated by 5-year intervals. Panel data on the GDP and growth rate series were analyzed using alternative econometric methodologies. First, the stochastic properties of the series were analyzed by applying classical tests for unit roots in a fixed effects framework. A new ratio was developed for the case where heterogeneous drift parameters are present under the null hypothesis. The 5% critical values of the most powerful invariant tests for unit roots are tabulated for different numbers of countries and time periods. Second, a dynamic random effects framework was used for testing the stochastic specification for the GDP and growth rate series. A sequence of Wald statistics was applied to test various structures for the variance covariance matrix of the GDP and growth rate series. Overall, the GDP series from PWT and WDI showed various forms of non-stationarity. Moreover, GDP growth rates at 5-year intervals possessed simple stochastic properties making them amenable to econometric modeling. Keywords: Unit roots.

Economic growth, Fixed effects models, Random effects models, Panel data,

1. INTRODUCTION The availability of aggregate panel data for countries in the post-war period (Penn World Table (PWT), Summers and Heston, 1991, World Development Indicators (WDI), World Bank, 1998) has spurred much empirical research in the economic growth literature. Panel data on developing and developed countries have been extensively used to investigate the contributions of factors such as investment in capital stock, measures of literacy, health indicators, political conditions, etc. to economic growth (e.g. Barro and Sala-i-Martin (1995), Caselli etal. (1996), Barro (1997)). Because the countries are at different stages of health and demographic transition, empirical analyses of the data can yield insights into the likely effects of such factors on economic growth (Barro (1997), Bhargava et al. (2001)). The quality of the data in PWT and WDI, however, can be poor especially for less developed countries where many of the variables are 'projections' from statistical models. For example, the purchasing power parity indices commonly used for constructing the real GDP series in the PWT are based on information on a subset of 68 countries. Furthermore, most countries face different © Royal Economic Society 2001. Published by Blackwell Publishers Ltd, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Maiden, MA, 02148, USA.

256

A. Bhargava socioeconomic and infrastructural constraints that are difficult to approximate in the analyses. Thus, pooling of data across countries can lead to spurious results, especially if the investigators fail to address stochastic properties of the dependent variable in econometric modeling (Sargan (1964)). Such problems are exacerbated in models explaining aggregate variables such as the GDP levels. Easterly et al. (1993) have argued that it is preferable to analyze GDP levels rather than annual growth rates because the latter are subject to considerable variation. However, econometric modeling of the GDP levels entails the use of data on physical capital stock that are only available for a few developing countries. Also, there are conceptual difficulties in measuring the physical capital stock (Summers and Heston (1991)). Thus, the stochastic properties of GDP and growth rate series are important since it would be simpler to model GDP growth rates in practical situations. The stochastic properties of GDP and growth rate series have received some attention in the literature (Sala-i-Martin (1996), Durlauf and Quah (1998)). However, since health indicators such as life expectancy and fertility rates are compiled at irregular intervals, the use of annual data in growth regressions is often problematic. The purpose of this paper is to investigate the stochastic properties of the GDP and growth rates series from the PWT and WDI separated by 5-year intervals. The analysis will facilitate econometric modeling of GDP levels or growth rates and highlight the effects of data smoothing procedures on the stochastic properties of the GDP series. The structure of this paper is as follows: Section 2 describes the data used in the analysis. The econometric framework using fixed effects models is outlined in Section 3.1. A new ratio is developed for testing the unit root null hypothesis in the presence of heterogeneous trends. The 5% limits of the two test statistics (Rip and /?2/>)> for the respective cases where the trends are excluded and where they are included in the model, are tabulated. The random effects framework for analyzing the stochastic properties of the GDP and growth rate series is outlined in Section 3.2. A sequential procedure based on Wald statistics for testing various types of error structures on dynamic random effects models is discussed in Section 3.3. The empirical results from the fixed effects models for the GDP and growth rate series from PWT and WDI are presented in Section 4.1. The results from the random effects models are in Section 4.2. Overall, the results indicate that the GDP levels series exhibit various types of non-stationarity that can be parsimoniously modeled in a random effects framework. More importantly, GDP growth rates at 5-year intervals were found to possess simple stochastic properties making them amenable to econometric modeling.

2. THE DATA The data used in the analysis were from the PWT and the WDI. The GDP series in the PWT are in '1985 international dollars' and were based on purchasing power comparisons for a subset of 68 countries. The GDP series from the WDI, based on the official exchange rates, was in 1987 constant dollars. The WDI GDP series is likely to show greater variability because exchange rate fluctuations can induce large distortions, especially for small countries. However, the PWT GDP series involves estimation of the purchasing power parity indices for countries where the data were not available (Summers and Heston (1991), Ahmad (1992)). It is therefore of interest to assess the effects of data interpolation on the stochastic properties of the commonly used GDP series. © Royal Economic Society 2001

Stochastic Specification and the International GDP Series

257

While it is possible to analyze annual data on GDP and growth rate series, most empirical growth models use observations that are separated by 5 years because many explanatory variables are not measured annually. Thus, we analyzed panel data that were separated by 5 year intervals i.e. six time observations on the countries (for the years 1965, 1970,1975, 1980, 1985, 1990) were used. The models with fixed effects were also estimated using the annual observations on the GDP and growth rate series. The GDP data covered 125 countries in the PWT and 107 countries in the WDI.

3. THE ECONOMETRIC FRAMEWORK The GDP series on countries are aggregated data that are likely to exhibit a high degree of persistence. We begin by investigating the stochastic properties of the GDP series by testing for alternative forms of non-stationarity. The models fitted to the GDP series will also be estimated for growth rates. A comparison of the properties of the GDP and growth rate series would be helpful in the selection of the appropriate modeling approach. The analysis of the GDP series in this paper used three sets of methodologies that are described later.

3.1. Non-stationarity in the fixed effects framework The classical von Neumann (1941) ratio or the Durbin and Watson (1950) statistic can be used to test for a unit root against stationary alternatives in a fixed effects framework as proposed by Bhargava et al. (1982). The main advantage in using this test is that it is a uniformly most powerful test against the stationary first order autoregression in small samples. Moreover, the model includes country specific fixed effects (dummy variables) that capture differences in the mean GDP levels or growth rates. Let yit be the natural logarithm of the real per capita GDP (i = 1 , . . . , N; t = 1 , . . . , T). Then we can write the first order autoregression as: yit = fi+

u

it

(1)

with uit — auit-i + eit

(2)

where, f\ are country specific dummy variables and e,-,s are independently normally distributed random variables with zero mean and constant variance. The Durbin-Watson statistic for panel data is defined as: KlP=ap=

EN

sr^T

,

-,2

^t-ilyit-yu-x)

T.t^Uiyit-yt)2

where yt = J2t=i yit/T(i = 1, • • •, N). Note that dummy variables for (T — 1) time periods can also be included in equation (1) to partially control for trends affecting the series during the sample period. The unit root null hypothesis a — 1 can be tested by comparing the sample criterion for R\p with the exact limit. For calculating the exact distribution of RIP, it is useful to analytically derive the eigenvalues of the symmetric (T — 1) x (T — 1) matrix F that has the elements Fij = (T-j)i/T j>i; i= l T-l. (4) © Royal Economic Society 2001

258

A. Bhargava The eigenvalues (Xk) of F are then used as weights in the Imhof (1961) program (Koerts and Abrahamse (1969)) to evaluate •NT-N ?T[RIP


=Pr

J2 (l-rkk)z2k<0

1- Y

(5)

where y is the size of the test, Zk are independent standard normal variates, and

**=, • L , ( t = i

r

<6>

)-

4sin z {§£} Because of the fixed effects in model (1), each eigenvalue A.* appears with a multiplicity of N. The unit root null hypothesis is rejected for 'large' values of R\p. Table 1 presents the 5% significance limits of R\p for various values of N and T. For the intermediate values not reported in the table, the critical limits can be interpolated. The test given by R\p can be applied to panel data where the investigator wishes to test the null hypothesis that the ys follow a simple random walk against a stationary alternative, allowing the means of the ys to differ across countries. If dummy variables for time periods are included in (1), then the bounds in Tables 1 and 2 from Bhargava et al. (1982) can be used for testing the null hypothesis. Note that it is also possible to tabulate the distribution of Ri p using simulation methods, though the exact calculations will usually be more accurate. In addition to the differences in GDP levels across countries, it is plausible that growth rates exhibit some form of heterogeneity across countries. A possible mechanism is the presence of country-specific time trends in the means and variances of the GDP series, proposed by Lee et al. (1997). Thus, for example, equation (1) may be replaced by yu = fi+ Pa + uit

(7)

where the us are given by (2). Then, under the null hypothesis a = 1, equation (7) implies Ay,-, = ft + eit

(8)

whereas, under the alternative, the means of the ys depend on country specific time trends. The finite sample framework is well-suited to testing the unit root null hypothesis because of the large number (2N) of 'incidental' parameters (coefficients of fixed effects and country specific trends) that need to be estimated. An increase in the number of parameters with the sample size (N) vitiates some of the desirable properties of asymptotic procedures when T is fixed (Neyman and Scott (1948)). By contrast, we can define a locally most powerful test for the null hypothesis a = 1 in the neighborhood of the null that is invariant with respect to the values of the incidental parameters and is valid for fixed values of N and T. The test is based on the ratio:

R2p

=

E\,T

N

T

(=1

t=2

,

^E[(r-Uytt-c-UyiT-(T-f)yn-(T-Dff,--°-5(yn

+ wr))]2

(9) The exact distribution of RZP is again a weighted average of independently distributed chi-square variables and can be calculated using the Imhof algorithm. The eigenvalues of the matrix F M Q © Royal Economic Society 2001

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Stochastic Specification and the International GDP Series Table 1. Five percent significance points of R\p and R^p for testing the unit root null hypotheses in the two cases, respectively, where heterogeneous drift are excluded and included in the model a ' b . N == 25

N --= 50

N --= 75

N =:100

RIP

T =A

R\p 1.551

RIP

2.595

1.415

2.525

R\p 1.366

2.499

1.340

2.484

T =5

1.326

2.240

1.200

2.156

1.155

2.124

1.130

2.105 1.609

RIP

RIP

RIP

RIP

T=l

1.025

1.748

0.918

1.661

0.879

1.626

0.858

r = io

0.762

1.309

0.677

1.232

0.647

1.202

0.630

1.186

r = i5

0.532

0.920

0.471

0.860

0.448

0.836

0.436

0.823

r = 20

0.409

0.708

0.361

0.660

0.343

0.642

0.334

0.630

r = 25

0.332

0.576

0.292

0.536

0.272

0.519

0.270

0.511

r = 30

0.280

0.485

0.246

0.450

0.234

0.437

0.227

0.429

r =4

1.323

2.475

T =5

1.114

T=l

0.845

r = io

N = 125

N == 150

N == 175

1.311

2.468

1.301

2.462

2.093

1.103

1.595

0.835

2.085

1.094

1.586

0.828

0.619

1.174

0.612

1.166

0.606

r = i5

0.429

0.815

r = 20

0.328

0.623

0.423

0.809

0.323

0.618

r = 25

0.265

0.505

0.262

r = 30

0.223

0.424

0.220

N =:200 1.294

2.458

2.078

1.087

2.073

1.580

0.822

1.575

1.160

0.602

1.155

0.419

0.804

0.416

0.800

0.320

0.615

0.318

0.612

0.501

0.259

0.498

0.257

0.495

0.421

0.219

0.418

0.216

0.419

Notes: a N is the number of countries and T is number oftimeperiods. The unit root null hypotheses are rejected if the sample criteria for R\p or Rxp are greater than the tabulated limits.

can be used as the weights in the Imhof program; F is defined by (3) and, with 5 defined as a (T — 1) x 1 vector of ones, Mo is given by

Mo = IT-I - Y~[ss'-

(10)

The eigenvalues of the matrix FMQ can be calculated analytically; Bhargava (1986) proved that when T is an even integer, the non-zero eigenvalues are given by fik(k = 1 , . . . , T — 2). M2*=

A

. *

(* = i , . . . , ( r / 2 ) - i )

and Wik-\ =

A . 2, nk , 4sin 2 {^P r }

(ft=l,...,(772)-l).

For the case where 7" is odd,

H2k= . . -2L , ,

4sin {^}

© Royal Economic Society 2001

(* = i , . . . , ( r - i ) / 2 )

(11)

260

A. Bhargava and Wt-1 =

. 2\ „

k

,

(k = l,...,(T-l)/2).

(12)

4sur [YZ\\ The exact distribution of R2p can be calculated by noting that each /^(A: = 1 T - 2) appears with multiplicity N. Thus, the N(T — 2) non-zero eigenvalues can be used as weights in the Imhof program to evaluate (5). The 5% significance points of R2p are also presented in Table 1. The test would reject the unit root null hypothesis for 'large' values of R2p. In contrast with the asymptotic procedures of the type proposed by Dickey and Fuller (1979) (e.g. Harris and Tzavalis (1999)), the test based on R2p is invariant with respect to the values of nuisance parameters both under the null and alternative hypotheses. Moreover, the test is valid for fixed values of N and T and allows for trends in the mean of the series under the null and alternative hypotheses. Further, if the unit root null hypothesis cannot be rejected, then the F statistic for testing the hypothesis that coefficients (ft) of the heterogeneous trends in equation (8) are zero is given by:

[E£iE,r=2(y.-»-y,->-i)2]

F(N, NT - 2JV) = (T - 2)

(13)

In practical applications, the ratios (9) and (13) can be easily computed and compared with the exact limits of R2p in Table 1 and the significance points of the F-distribution, respectively.

3.2. Non-stationarity in a random effects framework In equations (1) and (2), the variance covariance matrix of the errors (w,() cannot be consistently estimated for large N and fixed T because the number of parameters increases with the sample size N (Kiefer (1980)). It is therefore useful to treat the country specific effects as randomly distributed variables and estimate the parameters of dynamic random effects models for GDP and growth rate series, as proposed by Bhargava and Sargan (1983). Equations (1) and (2) can be re-formulated as: yn=gi

+m

(i = i,...,N)

yu =8t+ ayn-i + vit

(t = 2,...,

(14) T; i = 1 , . . . , N)

(15)

where vit=Si

+ wit.

(16)

Here, Si are country specific random effects and wi, are the 'transitory' components of the errors that can possess complex stochastic properties over time (see equation (17)). However, the errors across countries are assumed to be independent in such applications. While disaggregating the sample by geographical regions can reduce possible dependence in the errors, this is typically infeasible because it is desirable to have many countries in the sample for the estimation. Further, given the fixed number of time observations (T), the initial observations (v,i) must be treated as endogenous variables in maximum likelihood estimation (see Anderson and Hsiao (1981), Bhargava and Sargan (1983)). Alternative assumptions on yu lead to different estimators. © Royal Economic Society 2001

Stochastic Specification and the International GDP Series

261

We consider two sets of assumptions: yn are drawings from a normal distribution such that the process (v,i, v,2, • • •, yn) is stationary. In this formulation, it is necessary to assume that — 1 < a < 1. The second assumption is that yn are drawings from a normal distribution with an arbitrary variance but the covariance between y,i and the remaining (y,2, • • •, yn) is the same. This non-stationary formulation has the advantage that a can exceed unity, which is useful in applications analyzing aggregate data. The model given by equations (14)—(16) has implications for 'convergence' hypotheses of the per capita GDP series. Previous researchers have noted that high values of a imply slower convergence (e.g. Barro and Sala-i-Martin (1995), Islam (1995), Nerlove (2000)). However, the discussion has not addressed the role of country specific random effects (Si) in determining the equilibrium GDP level. Consider the dynamic random effects model (14)-(16), where y,i are drawings from a stationary distribution. Then, apart from an overall mean (and time dummies), the equilibrium level of GDP of a country is given by [Si/(I — a)]. A country can start at some GDP level but will converge in the long run to this equilibrium level. This is not the case under the second assumption where yn an arbitrary variance and when a > 1. Because of the unobserved country specific components of the error term in (16), dynamic random effects models allow long-term differences in equilibrium GDP levels.

3.3. Wald statistics for the variance covariance matrix of the errors on dynamic random effects models The stochastic properties of the v,-f affecting equations (14) and (15) can be further investigated using a sequence of Wald statistics based on maximum likelihood estimation of the dynamic model (Bhargava (1987)). As emphasized by Sala-i-Martin (1996), this is important in the context of empirical growth models because variances of the transitory components (wn) of the vu need not be constant over time. Typically, 'shocks' to the economic system are likely to cause heteroscedasticity over time in the errors. Moreover, in as much as the coefficient of <$,• in (16) could depend on time, the models for growth rates will also be affected by country specific random effects. This is a parsimonious formulation in comparison with the model with heterogeneous trends in equation (7) that involves a large number of (incidental) parameters. We postulate that the Wit follow a qt\\ order moving average process: i

Wi, = J2kieHt-i)^0

=U

(i = l,...,N;t=l,...,T).

(17)

7=0

It was further assumed that the variance of the es depends on time in a linear or in an exponential fashion as proposed in Bhargava (1987). Wald statistics, that are robust to the misspecification of the distribution function of the vs, are used in the analysis. The robustness property is useful because researchers have reported bimodal distributions for GDP series (e.g. Quah (1996)). In such circumstances, the fourth order moments of the GDP series are likely to differ from the usual value of 3 for the normal distribution. The constraints implied by (17) and by heteroscedasticity in the errors es can be tested using the maximum likelihood estimate of the unrestricted variance covariance matrix of the us. In contrast with the model containing time varying explanatory variables considered by Bhargava and Sargan (1983), some of the model parameters may not be identified in simple autoregressive models due to a failure of the rank condition. Because the model is non-linear in parameters, © Royal Economic Society 2001

262

A. Bhargava the rank condition is sufficient for identification but is not necessary (Sargan (1983)). However, identification can be achieved by regressing the real GDP on the population variable that is commonly assumed to be exogenous in growth models (Solow (1956)). This formulation would afford an identified model where Wald statistics can be applied to an unconstrained estimate of the variance covariance matrix of the errors. To ensure reliable inferences, one can compare the results from using Wald statistics from the model for real per capita GDP with those where real GDP is regressed on the logarithm of the population variable.

4. EMPIRICAL RESULTS FOR THE PENN WORLD TABLE AND WORLD DEVELOPMENT INDICATORS GDP SERIES 4.1. Stochastic properties of the GDP and growth rate series in a fixed effects framework The GDP data from the PWT were based on purchasing power comparison and covered 125 countries at 5-yearly intervals in six time periods (1965-90); GDP series from the WDI covered 107 countries and were in constant 1987 dollars, converted using the official exchange rates. The ratio R\P given by (3) for the natural logarithm of the PWT and WDI GDP series were, respectively, 0.4277 and 0.4585. The five percent significance limit for testing the unit root null hypothesis was interpolated to be 0.94 from Table 5 in Bhargava et al. (1982). Thus, the unit root null hypothesis cannot be rejected for both the GDP series. By contrast, R\p for the corresponding GDP growth rates were 1.511 and 1.925, respectively. The unit root null hypothesis was firmly rejected for growth rates. Moreover, the significance limit at 5% for testing serial independence (i.e. a = 0) was 1.87 from Table 1 in Bhargava et al. (1982). Thus, one would accept the null hypothesis that the WDI GDP growth rates were serially independent; there was slight positive serial correlation in growth rates based on the PWT GDP series. The aforementioned results indicated a high degree of persistence in the GDP series from both the PWT and WDI. One would expect persistence to be higher in the former series because of the methods used to smooth the data and also because movements in exchange rates were likely to induce further noise in the WDI GDP series. The ratio R\p did not control for the macro trends affecting the GDP series, i.e. means in different time periods were assumed to be the same. Including time dummies in the model, the sample criteria for R\p for the two GDP series were 0.456 and 0.488, respectively. This slight increase did not alter the conclusions in any significant way. It therefore seemed likely that trends affecting aggregate GDP series were of a more complex nature. Next, we postulated the presence of country specific trends as in (7) and tested the unit root null hypothesis using the ratio (9). The sample criteria of R2P for the PWT and WDI GDP series were 1.366 and 1.527, respectively. The exact significance limit of R2p for PWT where N = 125(7 = 6) was calculated to be 1.812; the limit for the WDI series where N = 107 was 1.820. The unit root null hypothesis was accepted in both cases, though the sample criteria for Rzp were substantially higher than the corresponding results for R\p. The F statistics (13), for testing that the N coefficients of the drift terms are zero, were 4.791 and 4.450, respectively, for the PWT and WDI GDP series. Thus, the null hypotheses of zero drifts were rejected; the data appeared to contain a fair amount of heterogeneity (similar conclusions were reached using annual observations). This, however, should not be interpreted as implying that we have arrived at a reasonable specification for the GDP series. For, the model (7) fitted AT country specific dummy variables and another N drifts parameters to the data. Moreover, insofar as T was fixed, © Royal Economic Society 2001

Stochastic Specification and the International GDP Series further analysis of stochastic properties of the error terms such as the changes in variances over time is infeasible in the fixed effects framework due to the incidental parameters. From an econometric modeling standpoint, the estimated coefficients of country specific time trends reflect the time path of economic and demographic variables affecting GDP. Econometric models should be able to capture some of these trends in a parsimonious way. Because the properties of parameter estimates in the fixed effects model are adversely affected by incidental parameters, it is useful to investigate stochastic properties of the GDP series in a random effects framework. In the next section, we use dynamic random effects models to estimate the model parameters and test alternative specifications for the errors.

4.2. Stochastic properties of the GDP series in a dynamic random effects framework Table 2 presents the maximum likelihood estimates of the first order non-stationary autoregression for the natural logarithm of per capita GDP and growth rate series from the PWT and WDI. The models for GDP included four dummy variables for time periods; for growth rates, at most three such variables can be included. There are several noteworthy features of the results. First, coefficients of the lagged dependent variables for the logarithm of the GDP exceeded unity for both the PWT and WDI data series. The ratio of between/within variance [i.e. var((5,)/var(w,,) in (16)] was not significantly different from zero which could be due to the modest number of countries in the data set Fisher (1973). Second, the likelihood ratio statistics rejected the constraints implied by the non-stationary first order autoregression against the alternative that the variance covariance matrix of the errors (us) was of a more general type for both the series. However, as noted in Section 3.3, the parameters of the dynamic model with unrestricted variance covariance matrix may not be identified. Third, for growth rates, the coefficient of the lagged dependent variable for PWT data was small but significantly different from zero; the coefficient using WDI GDP series was insignificant at the 5% level. The between/within variance ratio was not statistically significant for the PWT data but was significant for the WDI. Because of the modest number of countries in the sample, statistical errors in estimating parameters such as the between/within variance ratio were likely to be large. Fourth, both the PWT and WDI growth rate series accepted the constraints implied by the non-stationary random effects model; growth rate series thus appeared to have attractive stochastic properties. The results broadly supported the conclusions reached in Section 4.1, where most powerful invariant tests were applied in the fixed effects framework. The empirical results for the first order stationary model are presented in Table 3; the coefficient of the lagged dependent variable was constrained to be smaller than unity in this formulation. However, the estimated coefficients of the lagged GDP were very close to unity; the estimated between/within variance ratio was very close to zero indicating a boundary solution. Taken together, the results suggest that the stationary model is too restrictive a formulation for GDP series. By contrast, parameter estimates from the model for growth rates were similar in Tables 2 and 3. For growth rates, the main difference between the estimates was that the PWT GDP data accepted the constraints implied by the stationary model whereas the WDI data rejected these constraints. In view of the different procedures used to create the two GDP series, one would expect some dissimilarities between the empirical results. This issue is further addressed later. Table 4 presents the results for testing various stochastic specifications on an unconstrained estimate of the variance covariance matrix of the errors vs on equations (14) and (15) affecting the PWT and WDI GDP series using a sequence of Wald statistics. The statistics were computed © Royal Economic Society 2001

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Table 2. Maximum likelihood estimates of the first order non-stationary random effects model for the logarithm of the real per capita GDP and GDP growth rates at 5-year intervals using the data from Penn World Table (PWT) and World Development Indicators (WDI)a-b. PWT Variable

WDI

Levels -0.294 (0.352)

Growth rates

Time dummy 3

-0.001 (0.018)

—

Time dummy 4

-0.050 (0.021)

-0.010 (0.004)

-0.026 (0.024)

-0.003 (0.004)

Time dummy 5

-0.147 (0.025)

-0.027 (0.004)

-0.153 (O.029)

-0.025 (0.004)

Time dummy 6

-0.150 (0.048)

-0.034 (0.004)

-0.103 (0.030)

-0.011 (0.005)

Lagged dependent variable

1.060 (0.048)

0.298 (0.079)

1.167 (0.061)

0.154 (0.078)

Between/within

0.343 (0.343)

0.090 (0.085)

2.633 (1.671)

0.220 (0.117)

0.0152

0.0008

0.0193

0.0009

Constant

variance ratio Within variance 0

Likelihood ratio test for non-stationary random effects model No. of countries No. of time periods

48.11

0.027 (0.004)

10.78

Levels -1.062 (0.430) 0.001 (0.022)

51.40

Growth rates 0.026 (0.004)

—

15.66

125

125

107

107

6

5

6

5

Notes: a The GDP seriesfromthe PWT is in '1985 international dollars' whereas the seriesfromthe WDI is in constant 1987 dollars based on exchange rate conversions.b Asymptotic standard errors are in parentheses.c Degrees of freedom are 17 for Levels and 11 for Growth rates models. under the assumption that the true distribution function of the errors was non-normal. The results for growth rates are suppressed because the tests accepted the null hypotheses of serially independent errors in equation (17). For the GDP levels series where T = 6, the ws in equation (17) can be assumed to follow at most a third order moving average (MA(3)) process. Moreover, Wald tests were sequential in the sense that we would not test the null hypothesis that the errors follow an MA(2) process if we had previously rejected the MA(3). It is desirable to test the sequential hypotheses at an overall significance level that is higher than the conventional level 5% (e.g. 10%; see Anderson (1971)). First considering the results for the PWT GDP data, Wald statistics firmly rejected the random effects models with MA(3) errors if the errors given by (17) are assumed to possess constant variance over time. Thus, it was necessary to work with a more general formulation allowing the variances of the ws to change over time. The next set of results in Table 4 assumed that the variances changed linearly over time. The Wald test accepted the null hypothesis that the errors © Royal Economic Society 2001

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Table 3. Maximum likelihood estimates of the stationaryfirstorder autoregression for the logarithm of the real per capita GDP and GDP growth rates at 5-year intervals using the data from Penn World Table (PWT) and World Development Indicators (WDI)a,b. PWT Variable Constant

Time dummy 3

Levels

WDI Growth rates 0.028

0.146

0.027

(0.017)

(0.003)

(0.017)

(0.003)

0.010

-0.028 (0.018)

Time dummy 5

-0.118 (0.018)

Time dummy 6

-0.118 (0.018)

Lagged dependent variable Between/within variance ratio Within variance Likelihood ratiod

Growth rates

0.224

—

(0.018) Time dummy 4

Levels

0.019

—

(0.022) -0.010 (0.003) -0.027 (0.003) -0.023 (0.004)

0.013 (0.025) -0.093 (0.022) -0.041 (0.023)

-0.003 (0.004) -0.025 (0.004) -0.012 (0.004)

0.990

0.253

0.994

0.108

(0.001)

(0.062)

(0.001)

(0.062)

0.0°

0.138

0.0°

0.286

(0.0)

(0.071)

(0.0)

(0.103)

0.0200 146.87

0.0007 18.66

0.0233 130.86

0.0008 41.06

test for stationary random effects model No. of countries No. of time periods

125

125

107

107

6

5

6

5

a

Notes: The GDP series from the PWT is in '1985 international prices' whereas the series from the WDI is in constant 1987 dollars based on exchange rate conversions.b Asymptotic standard errors are in parentheses. c Boundary solution. d Degrees of freedom are 18 for Levels and 12 for Growth rates models. followed an MA(3) process. Further, the null hypothesis that errors were generated by an MA(2) process was also accepted. However, the data firmly rejected the MA(1) model. The diagonal elements of the variance covariance matrix accepted the linear and exponential formulations for variances of the tos over time. The results for GDP data from WDI in Table 4 supported the conclusions from the PWT data. Again, Wald statistics rejected specifications assuming homoscedastic variances of the ius. In the heteroscedastic case, the MA(2) process was accepted by the WDI data. The Wald statistics were also applied to the model where GDP was regressed on the population variable. The conclusions were broadly similar indicating that the structure of the unconstrained variance covariance matrix of the errors was not critically affected by the identification problems discussed in Section 3.3. Lastly, the third and fourth order moments of the residuals from the dynamic models were computed. While the results were close for the two GDP series, the fourth order © Royal Economic Society 2001

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Table 4. Stochastic properties of the unconstrained estimated serial covariance matrix of the first order autoregression for the logarithm of real per capita GDP series using the data from the Penn World Table and World Development Indicatorsa. Penn World Table ]Robust

Wald statistics for moving average error specificationb Homoscedastic variances over time

Order of the moving average

3

2

1

Wald statistic

24.45

24.48

25.68

Degrees of freedom

10

11

12

Heteroscedastic variances over timec Order of the moving average

3

Wald statistic

8.34

Degrees of freedom

2

1

15.16

8

24.21

9

10

World Development Indicators Robust Wald statistics for moving average error specification Homoscedastic variances over time Order of the moving average

3

2

1

Wald statistic

26.81

31.61

43.77

Degrees of freedom

10

11

12

Heteroscedastic variances over time Order of the moving average

3

Wald statistic

9.05

Degrees of freedom

8

2 15.93 9

1 33.59 10

Notes: aThere are 125 countries in the Penn World Table and 107 countries in the World Development Indicators with six time observations. b The statistics are robust with respect to distributional misspecification. c Error variances are assumed to follow a linear pattern over time.

moments of the residuals from the WDI GDP series were affected by currency re-evaluations for certain countries such as Jordan in the 1970s. However, retaining or dropping Jordan from the WDI sample did not alter the conclusions reached via the application of robust Wald statistics.

5. CONCLUSION In this paper, the stochastic properties of aggregate GDP series from PWT and WDI for several countries were analyzed using different estimation and test procedures for the fixed and random effects frameworks. In so doing, we developed the distribution theory of the locally most powerful invariant test statistic for a unit root in the presence of heterogeneous drift parameters. The 5% significance limits of the new ratio /?2P and the earlier generalization of the Durbin-Watson statistic (RIP) were tabulated. Some of the difficulties in estimating random effects models with unconstrained variance covariance matrices were addressed. The sequence of Wald statistics accepted a second order moving average process with heteroscedastic variances for the transitory components of the errors for both the PWT and WDI GDP series. © Royal Economic Society 2001

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From an empirical standpoint, one would expect the GDP series based on exchange rate conversions to show greater variability; GDP series constructed using purchasing power comparisons are likely to be smoother. The econometric methods used in the paper indicated that these differences were relatively small provided that one took into account the influence of outliers in the exchange rate based series that can significantly affect higher order moments. Further, the 5-year growth rates exhibited simple stochastic properties making them amenable to econometric modeling. This conclusion is useful because reliable data on physical capital stock are seldom available for developing countries. Because the 5-year growth rates are less variable than the corresponding annual figures, and because some of the explanatory variables used in empirical growth models are projections from statistical models, the use of 5-year growth rates as dependent variables would seem attractive in applied work.

ACKNOWLEDGEMENTS This study was supported by the Global Program on Evidence for Health Policy of the World Health Organization, Geneva. While retaining responsibility for the views expressed, the author would like to thank an anonymous referee and the Editor for helpful comments.

REFERENCES Ahmad, S. (1992). Regression estimates of per capita GDP based on purchasing power parities. Working Paper #WPS 956, International Economics Department, The World Bank. Anderson, T. W. (1971). Statistical Analysis of Time Series. New York: John Wiley. Anderson, T. W. and C. Hsiao (1981). Estimation of dynamic models with error components. Journal of the American Statistical Association 76, 598-606. Barro, R. J. (1997). Determinants of Economic Growth. Cambridge: MIT Press. Barro, R. J. and X. Sala-i-Martin (1995). Economic Growth. New York: McGraw-Hill. Bhargava, A. (1986). On the theory of testing for unit roots in observed time series. Review of Economic Studies 53, 369-84. Bhargava, A. (1987). Wald tests and systems of stochastic equations. International Economic Review 28, 789-808. Bhargava, A., L. Franzini and W Narendranathan (1982). Serial correlation and the fixed effects model. Review of Economic Studies 49, 533-49. Bhargava, A., D. Jamison, L. J. Lau and C. J. L. Murray (2001). Modeling the effects of health on economic growth. Journal of Health Economics 20, 423-40. Bhargava, A. and J. D. Sargan (1983). Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51, 1635-60. Caselli, R, G. Esquivel and R Lefort (1996). Reopening the convergence debate: a new look at the crosscountry growth empirics. Journal of Economic Growth 1, 363-89. Dickey, D. A. and W A. Fuller (1979). Distributions of estimators of autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427-31. Durbin, J. and G. S. Watson (1950). Testing for serial correlation in least squares regression I. Biometrika 37, 409-28. Durlauf, S. N. and D. T. Quah (1998). The new empirics of economic growth. NBER Working Paper Number 6422 (http://www.nber.org/papers/w6422). © Royal Economic Society 2001

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A. Bhargava Easterly, W., M. Kramer, L. Pritchett and L. Summers (1993). Good policy or good luck? Country growth performance and temporary shocks. Journal of Monetary Economics 32, 1-25. Fisher, R. A. (1973). Statistical Methods for Research Workers, 14th edition, New York: Hafner. Harris, R. D. F. and E. Tzavalis (1999). Inference for unit roots in dynamic panels where the time dimension is fixed. Journal of Econometrics 91, 201-26. Imhof, P. J. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika 48, 419-26. Islam, N. (1995). Growth empirics: a panel data approach. Quarterly Journal of Economics 110,1127-70. Kiefer, N. M. (1980). Estimation of fixed effects models for time-series of cross-sections with arbitrary intertemporal matrix. Journal of Econometrics 14, 195-202. Koerts, J. and A. P. J. Abrahamse (1969). On the Theory and Application of the General Linear Model. Rotterdam: Rotterdam University Press. Lee, K., M. H. Pesaran and R. Smith (1997). Growth and convergence in a multi-country empirical stochastic Solow model. Journal of Applied Econometrics 12, 357-92. Nerlove, M. (2000). Growth rate convergence, fact or artifact? An essay in panel data econometrics. I In J. Krishnakumar and E. Ronchetti (eds), Panel Data Econometrics: Future Directions, pp. 3-34. Amsterdam: North Holland. Neyman, J. and E. Scott (1948). Consistent estimates based on partially consistent observations. Econometrica 16, 1-32. Quah, D. (1996). Twin peaks: growth and convergence in models of income dynamics. Economic Journal 106, 1045-55. Sala-i-Martin, X. (1996). The classical approach to convergence analysis. Economic Journal 106,1019-36. Sargan, J. D. (1964). Wages and prices in the U.K.: a study in econometric methodology. In P. Hart, G. Mills and J. K. Whitaker (eds), Econometric Analysis for National Economic Planning, pp. 25-54. London: Butterworths. Sargan, J. D. (1983). Identification and the lack of identification. Econometrica 51, 1605-34. Solow, R. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics 70, 65-94. Summers, R. and A. Heston (1991). The Penn World Table (Mark 5): an expanded set of international comparisons, 1950-88. Quarterly Journal of Economics 106, 327-68. http://pwt.econ.upenn.edu. von Neumann, J. (1941). Distribution of the ratio of mean square successive difference to the variance. Annals of Mathematical Statistics 12, 367-95. World Bank (1998). World Development Indicators 1998 CD-ROM. Washington: The World Bank. http://www.worldbank.org/data/wdi/home.html.

© Royal Economic Society 2001

JOURNAL OF

HEALTH ECONOMICS ELSEVIER

Journal of Health Economics 20 (2001) 423-440 www.elsevier.nl/locate/econbase

Modeling the effects of health on economic growth Alok Bhargavaa*, Dean T. Jamison b , Lawrence J. Lau c , Christopher J.L. Murray d " Department of Economics, University of Houston, Houston, TX 77204-5882, USA b Center for Pacific Rim Studies, University of California, Los Angeles, CA, USA c Department of Economics, Stanford University, Stanford, CA, USA d Department of International Health, Harvard School of Public Health, Boston, and World Health Organization, Geneva, Switzerland Received 1 February 2000; received in revised form 1 January 2001; accepted 11 January 2001

Abstract This paper investigates the effects of health indicators such as adult survival rates (ASR) on GDP growth rates at 5-year intervals in several countries. Panel data were analyzed on GDP series based on purchasing power adjustments and on exchange rates. First, we developed a framework for modeling the inter-relationships between GDP growth rates and explanatory variables by re-examining the life expectancy-income relationship. Second, models for growth rates were estimated taking into account the interaction between ASR and lagged GDP level; issues of endogeneity and reverse causality were addressed. Lastly, we computed confidence intervals for the effect of ASR on growth rate and applied a test for parameter stability. The results showed positive effects of ASR on GDP growth rates in low-income countries. © 2001 Elsevier Science B.V. All rights reserved. JEL classification: C22; C33; E17; F43; 112; Ol 1; 047 Keywords: Economic development; Economic growth; Health; Random effects models; Panel data; Simultaneity

1. Introduction The 20fh century has seen remarkable gains in health. Average life expectancy in developing countries was only 40 years in 1950 but had increased to 63 years by 1990 (World Bank, 1993). Factors such as improved nutrition, better sanitation, innovations in medical technologies, and public health infrastructure have gradually increased the human life span. The relative contribution of these factors depends on the level of economic development; there are synergisms between the underlying factors operating in complex ways. Thus, for * Corresponding author. Tel.: +1-713-743-3837; fax: +1-713-743-3798. E-mail address: [email protected] (A. Bhargava). 0167-6296/01/$ - seefrontmatter © 2001 Elsevier Science B.V. Allrightsreserved. PII:S0167-6296(01)00073-X

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A. Bhargava et al. example, while recognizing various determinants of life expectancy, Preston (1976) emphasized economic development as the most important factor. However, since life expectancy is strongly influenced by child mortality, low-cost interventions such as the provision of ante natal care and vaccination programs in poor countries can be effective instruments for raising life expectancy. More generally, economic development depends on the level of skills acquired by the population and on capital formation. The former is influenced by child nutrition, educational infrastructure, and households' resources, including parents' physical health and cognitive attainment (e.g. Fogel, 1994; Scrimshaw, 1996; Bhargava, 1998, 1999). Capital accumulation depends on the savings rate that is also influenced by adult health. Analyses of the inter-relationships between health and economic productivity can be conducted at the individual level, at regional levels within a country, and for aggregate data on countries. In developing countries, there are numerous micro studies in biological and social sciences showing benefits of better health on productivity (e.g. Basta et al., 1979; Spurr, 1983; Bhargava, 1997; Strauss and Thomas, 1998). Quantifying the relationship between health indicators and economic productivity is more subtle in developed countries. For example, the effects of disability on employment status have been investigated in The Netherlands (Stronks et al., 1997); the relationship was stronger in physically demanding occupations where earnings are typically low. The earnings of a large proportion of the population, however, depend on their general health and well-being, including mental health. While psychologists have investigated the decline with age in components of cognitive abilities (Horn and Hofer, 1992), the effects of such factors on individuals' productivity remain largely unknown. Recently, aggregate data at the country level for the post-war period have become accessible (Penn world table (PWT), Summers and Heston, 1991; world development indicators (WDI), World Bank, 1998). Panel data on countries have been extensively used to elucidate economic relationships (e.g. Barro and Sala-i-Martin, 1995; Barro, 1997). Because many countries have experienced demographic and health transition in this period, studies can yield insights into the sources of economic growth. The quality of the data, however, can be poor especially in less developed countries, where many of the variables are 'projections' from statistical models. For example, the purchasing power parity indices commonly used for constructing the real GDP series in the PWT are based on the information on a subset of 68 countries. Further, most countries face different socio-economic and infrastructural constraints that are difficult to approximate in the analyses. Pooling data across countries can lead to spurious results, especially if the investigators fail to address stochastic properties of the dependent variable in econometric modeling (Sargan, 1964). Such problems are exacerbated in models explaining aggregate variables such as the GDP. Moreover, growth rates averaged over long time periods (e.g. 25 years) tend to describe economic activity in a way that is similar to the GDP. By contrast, the 5-year average growth rates analyzed in this paper show considerable variation but are less noisy than the annual growth rates. The purpose of this paper is to model the proximate determinants of economic growth with emphasis on variables that approximate health of the population. In so doing, we develop an analytical framework within which issues of demographic transition, human development, and capital formation can be discussed. In addition, the models incorporate the stochastic properties of the GDP series and take into account the data limitations. Section 2 describes

Modeling the Effects of Health on Economic Growth the data used in the analysis. The analytical framework for modeling the effects of health on economic growth is developed in Section 3.1. The econometric framework is outlined in Section 3.2. Issues of possible reverse causality from higher growth rates to the adult survival rates (ASR) are discussed in Section 3.3. A Wald type statistic for the stability of model parameters outside the sample period is developed in Section 3.4. In Section 4.1, average growth rates at 5-year intervals are modeled using a model similar to Barro (1997), but allowing for simultaneity and interactions between some regressors. Instrumental variables estimation methods were used and certain maintained hypotheses were tested (Bhargava, 1991a). In Section 4.2, we elaborate on the role of the interaction between lagged ASR and GDP from a policy standpoint. Stability of the estimated parameters is tested in Section 4.3 by a Wald test using out-of-sample observations for 1995 on GDP from the WDI. The conclusions and the need for collecting additional health statistics are discussed in Section 5.

2. The data The data used in the analysis were primarily from the PWT (Summers and Heston, 1991) and the WDI (World Bank, 1998). The GDP series in the PWT are in "1985 international dollars" that were based on purchasing power parities for a subset of countries; the GDP series from the WDI was based on the official exchange rates using 1987 constant dollars. The WDI GDP series is likely to show greater variability, because exchange rate fluctuations can induce distortions especially for small countries. However, the PWT GDP series involves estimation of the purchasing power parity indices for countries where the data were not available (Summers and Heston, 1991; Ahmad, 1992). Conclusion from our analysis will be strengthened if GDP series based on purchasing power parities and exchange rates yield similar results. The total fertility rate, life expectancy, and population variables were available in the PWT and WDI data sets. In addition to life expectancy, we used the ASR (probability of surviving the 60th birthday after reaching the age 15 years; mean = 0.702, S.D. = 0.14) from Bos (1998). The ASR is less sensitive to child mortality rates and was constructed from World Bank demographic files containing mortality data on countries; figures for some countries were projections from demographic models. Typically, data on total fertility rate and ASR were compiled at irregular intervals. To reduce the effects of projections on the empirical results, we analyzed panel data that were separated by 5-year intervals, i.e. six time observations on the countries (in 1965,1970, 1975,1980,1985,1990) were used (first observation in WDI series was for 1966). The education series (average years of education for population aged 15-60) for the six time periods were taken from Barro and Lee (1996). Data on geographical variables such as the area in the tropics, if the country is 'land-locked', and an index of openness to trade were from Gallup and Sachs (1998). Overall, the GDP data covered 125 countries in the PWT and 107 countries in the WDI. However, because of missing observations on explanatory variables, the sample sizes used in the estimation were lower for the models for GDP growth rates. We note that while it is feasible to estimate aggregate production functions for the countries, the data on physical capital stock were available for only 58 countries in the PWT.

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Collins and Bosworth (1996) and Nehru and Dhareshwar (1993) have imputed the data on physical capital for a larger number of countries under certain assumptions on depreciation rates. Because these assumptions are non-standard and because the focus of our analysis was on the relationship between health indicators and economic growth, we do not report the results for aggregate production functions in this paper.

3. A framework for modeling the effects of health on economic activity 3.1. The conceptual framework Preston (1976) analyzed cross-country data on life expectancy and national incomes for the approximate periods 1900, 1930, 1960 and observed that the curves showed an upward shift over time. For a given income level, life expectancy was highest in 1960s. Moreover, per capita GDP above $600 (in 1963 prices) had little impact in raising the highest life expectancy (73 years) in the 1960s. While recognizing that shifts in the curves had multiple causes, Preston attributed approximately 15% of the gains in life expectancy to income growth, but was less optimistic about the role played by nutrition and literacy. However, recent analyses of historical data suggest larger benefits from improved nutrition (Floud et al., 1991; Fogel, 1994). Furthermore, public health programs reducing sicknesses have beneficial effects on health by preventing the loss of vital nutrients due to infection (Scrimshaw et al., 1959). Life expectancy (or ASR) in a country is a broad measure of population health, though it need not accurately reflect the productivity of the labor force. For example, suppose that due to poor childhood nutrition, ability of individuals to perform productive tasks diminishes at an early age but, because of access to medical care, life expectancy is high (e.g. the Indian state of Kerala; International Institute of Population Sciences, 1995). Then productivity loss will be under-estimated if life expectancy was used as the sole indicator of health. Indices measuring disabilities of the working population in various occupations would be insightful for assessing productivity loss (e.g. Murray and Lopez, 1996). At a general level, capital formation requires that a high proportion of the skilled labor force remains active for a number of years; experience is important for technical innovations that take years of investments in research and development. Because detailed information on such variables cannot be utilized in national comparisons, a broader view of health is helpful for interpreting the results. In particular, investments in education and training critically depend on survival probabilities; expenditure on children's education may be influenced by parents' subjective probabilities of child survival. All these factors are potentially important for explaining economic growth (e.g. Bloom and Canning, 2000). Panel data on developing and developed countries provide an opportunity to disentangle some of the effects of demographic, health, and economic variables on growth rates, because the countries are at different stages of economic and social development. In certain developing countries, high fertility rates hamper investments in child health and education. Poor child health is likely to lead to reduced physical work capacity when the children turn into adults (Spurr, 1983). Thus, in the absence of natural resources, certain countries may not be able to escape from poverty traps. Because many developing countries have

273

Modeling the Effects of Health on Economic Growth prospered during the sample period (1965-1990), while others have not, a model for the proximate determinants of economic growth can shed light on these issues. The dependence of life expectancy on incomes up until a certain threshold suggests that it would be useful to model the GDP or growth rates using a flexible production function such as the trans-logarithmic function (Christensen et al., 1973; Sargan, 1971). Boskin and Lau (1992) estimated aggregated production functions for five developed countries using annual observations for the post-war period. Kim and Lau (1994) extended the analysis to cover four countries in the Pacific basin where good data on the physical capital stock were available. From the standpoint of modeling the effects of health on economic growth, the flexible functional form approach underscores the interaction between explanatory variables and the importance of squared terms in the model. While precise estimation of coefficients of high order terms would require large sample sizes, the work by Preston (1976) demonstrated the asymmetry in the life expectancy-incomes relationship. It is therefore likely that the impact of health indicators such as ASR on growth rates would depend on the level of GDP. Thus, ASR should be important for explaining economic growth at low levels of GDP. In more affluent settings, investments in education and training, and measures of health such as the decline in cognitive abilities with age, and age-specific disease prevalence rates, may be of greater importance. 3.2. The econometric framework for estimation of static random effects models containing endogenous regressors The methodology used for the estimation of static random effects models for GDP growth rates in situations where some of the explanatory variables are endogenous was developed by Bhargava (1991a). Let the model be given by n\

m

yn = J2ZiJyJ +YlxwPj 7= 1

7= 1

n

+ J2

x

*J
= l,...,T)

(1)

7="1 + 1

where z is time invariant variables, x\ and X2, respectively, exogenous and endogenous time varying variables, and N the number of countries that are observed in T time periods. The slope coefficients are denoted by Greek letters. In the models estimated for GDP growth rates, for example, the proportion of area of a country in the tropics is a time invariant explanatory variable. Time varying regressors consist of (lagged) total fertility rate, investment/GDP ratio, ASR, interaction between ASR and GDP, and GDP. It is important to distinguish between two sets of assumptions for the potential endogeneity of the time varying variable X2. First, X2 may be correlated with the errors uu in a general way, i.e. xi are 'fully' endogenous variables. Thus, X2jt must be treated as different variables in each time period. Let X\ and X2 be, respectively, the n 1 x 1 and /12 x 1 vectors containing the exogenous and endogenous time varying variables (ni + «2 = "), and let Z be the m x 1 vector of time invariant variables. We can write a reduced form equations for the fully endogenous variables X2 as T

x2it = J2F'JXuj + F*z' + u*> 7=1

<2>

274

A. Bhargava et al. where Ftj (t — 1 , . . . ,T;j = l,...,T) and F* (t = 1 , . . . , T) are, respectively, «2 x ni and ri2 x m matrices of reduced form coefficients; Uiu the «2 x l vector of errors. The reduced form Eq. (2) is a general formulation for correlation between the time varying endogenous variables and errors ult affecting model (1). Thus, for example, lagged GDP has often been included as an explanatory variable in models for growth rates (Barro and Sala-i-Martin, 1995; Barro, 1997). Caselli et al. (1996) have stressed that lagged GDP should be treated as endogenous. Because the error terms affecting Eq. (1) may have a complex structure (Sala-i-Martin, 1996), it is appealing to treat lagged GDP as a fully endogenous variable in the estimation. Similarly, one might postulate that the investment/GDP ratio is a fully endogenous variable; transitory components of w,, may be correlated with short-term fluctuations in the investment/GDP ratio. Moreover, one can test the hypotheses that GDP and the investment/GDP ratio are exogenous variables using sequential procedures. As noted in Section 2, variables such as ASR and total fertility rate are typically compiled in a country at a certain points of time; the yearly values tabulated in PWT and WDI are often projections from simple statistical models. Extrapolation of a variable such as ASR implies that it cannot be treated as a fully endogenous variable; the time observations on ASR are likely to be systematically related. This will violate the rank condition for parameter identification in models where ASR is assumed to be a fully endogenous variable. An alternative assumption for endogeneity of variables such as ASR is to assume that only the country-specific random effects Sj are correlated with X2tjtX2ijt = M i + X2ijt

(3)

where jc|..r are non-correlated with 5,, and <5, are randomly distributed variables with zero mean and finite variance. This correlation pattern was invoked by Bhargava and Sargan (1983) and is in the spirit of the commonly used random effects models. Endogenous variables represented by Eq. (3) have sometimes been referred to as 'special' endogenous variables (Bhargava, 199 lb). While Eq. (3) may seem to be a restrictive formulation, it allows countries to possess unobserved 'permanent' characteristics that in turn could influence the levels of explanatory variables. For example, countries with high saving rates may invest greater resources in health and education sectors. This will cause the errors on the model for growth rates to be correlated with variables such as the education levels attained by the population. Furthermore, such assumptions are implicit in random effects models that decompose the errors ult as uit = k + vit

(4)

where % are independently distributed random variables with zero mean and finite variance. Eq. (4) is a special case of the general formulation for the errors on model (1), which only assumes that the variance covariance matrix of u,t is positive definite. The main advantage in assuming the correlation pattern (3) is that deviations of the X2ijt from their time means. x

2iit = *2y' - *2i/

(t = 2,...,T;j=m

+ l,...,n;i

= l,...,N)

(5)

Modeling the Effects of Health on Economic Growth

275

where T

x2ij = YJXJL

(j = ni + l,...,n;i

= l,...,N)

(6)

r=i

can be used as [(T — 1)«2] additional instrumental variables to facilitate parameter identification and estimation (Bhargava and Sargan, 1983). An efficient three-stage least squares type instrumental variables estimator will be used to estimate Eq. (1), assuming the two types of correlation patterns for X2jt given by Eqs. (2) and (3), and without restricting the variance covariance matrix of uu. Further, in contrast to ordinary time series case, where mis-specification tests have been applied to test the overidentifying restrictions (Sargan, 1958), it is possible to test the validity of exogeneity assumption for explanatory variables in the panel data framework. As shown in Bhargava (1991a), one can sequentially test exogeneity assumptions using statistics based on instrumental variables estimates, because the correlation pattern for special endogenous variables in Eq. (3) is nested within the general formulation (2), where the X2 are fully endogenous. The sequential Chi-square test for exogeneity would first test the validity of the special correlation pattern (3). If «2 time varying variables are postulated to be endogenous, then under the null hypothesis, the first test statistic is asymptotically distributed (for large N and fixed T) as a Chi-square variable with [T(T — 1)«2] d.f. If the null hypothesis cannot be rejected, then we can further test if the time means of X2 given by Eq. (6) are non-correlated with the random effects 5,. The test statistic for the second set of hypotheses is asymptotically distributed as a Chi-square with Tri2 d.f. (for details, see Bhargava, 1991a). The overall size of sequential tests can be based on several considerations (e.g. Anderson, 1971; Sargan, 1980). To summarize the modeling strategy used in the analysis, we proceed by assuming that lagged GDP is a fully endogenous variable and estimate the parameters using an efficient instrumental variables estimator. It is likely that the exogeneity null hypothesis will be rejected for the lagged GDP variable. We can also test whether lagged investment/GDP ratio should be treated as a fully endogenous variable. Due to the potentially low predictive power of the instrumental variables in explaining the endogenous variables in panel data models (Bhargava and Sargan, 1983, p. 1654), we also report the adjusted /{-squared for the reduced form equations for lagged GDP in each of the five time periods. Further, because of extrapolation of variables such as ASR, it would be inappropriate to formulate that ASR and the interaction between ASR and GDP are fully endogenous variables. Instead, we treat these regressors as special endogenous variables as in Eq. (3) and test if their time means given by Eq. (6) are non-correlated with the country specific random effects <5;. We recognize that it would be desirable to use additional time varying variables not included in model (1) as instruments. However, the identification conditions for such formulations in the presence of cross-equation restrictions on the parameters have not been fully worked out. Furthermore, simulation evidence suggests that it is important to incorporate the serial covariance structure of the errors affecting panel data models and select good instruments for producing reliable parameter estimates. Thus, in Section 3.3, we also develop a formulation for testing reverse causality, i.e. if lagged growth rates affect the current ASR. The results will be helpful in interpreting the outcome of the exogeneity tests in the models for growth rates.

276

A. Bhargava et al. 3.3. A formulation for investigating reverse causality from GDP growth rates to adult survival rates As noted in Section 3.1, Preston (1976) emphasized the likely effects of GDP level on life expectancy using cross-country data. By contrast, the recent literature explains GDP growth rates using lagged life expectancy as an explanatory variable. It is therefore important not only to treat lagged GDP level as a fully endogenous variable in model (1), but also to investigate possible reverse causation, i.e. if higher GDP growth rates in the previous period may be the 'cause' of higher ASR. Such an investigation would be in the spirit of Fisher (1973). Cochrane (1965) and Cox (1992) discuss certain aspects of interpreting associations in observational data as causal effects. While one can apply the approach commonly used in time series analysis for testing the significance of lagged values of ASR in the model for GDP growth rate to investigate reverse causality, this procedure would suffer from certain drawbacks. First, as noted above, ASR is based on demographic data collected at a few points in time and the remaining values are projections; the lagged values of a slowly evolving variable such as ASR will be highly correlated with current values. Second, ASR may be correlated with the country specific random effects 5, in model (1) for growth rates thereby making it more likely that the coefficients of lagged ASR will be significantly different from zero. Third, because our sample size consists of six time observations at 5-year intervals and some explanatory variables are endogenous, the purely time series approach is perhaps unappealing. The approach used in our analysis is based on developing a model for ASR and investigating whether lagged GDP growth rates are significant predictors of ASR, after controlling for many confounding factors. Because the relationship between life expectancy and GDP level is well-established, we include lagged GDP level as an explanatory variable in the model for ASR and expect it to be a significant predictor. However, this need not be true for lagged GDP growth rates. In the spirit of the discussion in Section 3.1, we also include an interaction term between lagged GDP level and growth rates. Thus, if the coefficient of lagged GDP growth rates is a significant predictor of current ASR, and ASR is also a significant predictor of growth rates in model (1), then causality could run in either direction, i.e. from GDP growth rates to ASR or from ASR to GDP growth rates. By contrast, if the coefficient of GDP growth rates is not statistically significant in the model for ASR, then causality is more likely to run from ASR to GDP growth rates. Because of the panel nature of the data, we can tackle some of the issues of simultaneity in the estimation of models for GDP growth rates and ASR. 3.4. A Wald type test for parameter stability outside the sample period A Wald type statistic can be developed in the random effects framework to test if the parameters remain constant outside the sample period. Assuming that the number of countries (AO is large, this statistic would be asymptotically equivalent to the appropriate likelihood ratio test. The Wald statistic can be computed by estimating the model for the N out-of-sample observations in time period (T +1). Coefficients estimated from model (1), using the observations in the first Tperiods, are substituted as parameter values under the null hypothesis. Formally, apart from the intercept term, let b be the (k x I) vector of efficient estimates

277

Modeling the Effects of Health on Economic Growth

of the unknown coefficients in Eq. (1) and let b* be the corresponding estimates from the cross-section regression for time period (T + 1). Then, defining the variance covariance matrix of b* by V(b*,b*), the Wald statistic for parameter stability is given by W = (b*-bY=[V(b*,b*)rl(b*-b)

(7)

Under the null hypothesis of parameter stability, W is distributed (for large AO as a Chi-square variable with k d.f.

4. Empirical results 4.1. Empirical results for models for GDP growth rates Table 1 presents the empirical results for GDP growth rates for 92 countries at 5-year intervals using the PWT GDP series; the stochastic properties of the GDP series are discussed in Bhargava (2000), where it was found preferable to model growth rates. The model is similar in spirit to Barro (1997) but, as will be apparent from the discussion, it differs in a number of important respects. Specification 1 treats the explanatory variables as exogenous; the lagged GDP was a fully endogenous variable in specification 2. The estimation method used for specification 2 was also applied under the additional assumption that lagged investment/GDP ratio was a fully endogenous variable. However, the appropriate Chi-square statistic reported in Table 1 accepted the exogeneity null hypothesis for investment/GDP Table 1 Estimated slope coefficients from static random effects models for real per capita GDP growth rates 1965-1990 at 5-year intervals using data from PWTa Variable

Specification 1

Constant Tropics Openness Logarithm of fertility rate lagged 5 years Logarithm of investment/GDP ratio lagged 5 years Logarithm of adult survival rate lagged 5 years Interaction between lagged adult survival rate and GDP Logarithm of GDP lagged 5 years GDP at which partial derivative of GDP growth rate with respect to lagged adult survival rate is zero Chi-square (20) test for exogeneity of lagged GDP Chi-square (20) test for exogeneity of investment/GDP ratio Chi-square (15) test for exogeneity of means of lagged investment/ GDP ratio, ASR, and interaction of ASR and GDP Number of countries Number of time observations

0.274 (0.041) -0.011 (0.004) 0.026 (0.005) -0.015 (0.006) 0.014 (0.002) 0.181 (0.075) -0.024(0.011) -0.026 (0.004) 2123

a

Specification 2 0.407 (0.069) -0.012 (0.004) 0.028 (0.005) -0.028 (0.008) 0.014 (0.002) 0.358(0.114) -0.048 (0.016) -0.041 (0.008) 1714

63.89 18.28 15.22 92 5

92 5

Asymptotic standard errors are in parentheses. Specification 1 treats the time varying variables as exogenous; specification 2 treats lagged GDP as a fully endogenous variable. b

278

A. Bhargava et al. ratio, conditional on the treatment of lagged GDP as a fully endogenous variable. Next, the investment/GDP ratio, ASR and interaction between ASR and GDP were treated as special endogenous variables, i.e. correlated with the country specific random effects <5,. Another Chi-square statistic reported in Table 1 accepted the exogeneity null hypothesis, conditional on the treatment of lagged GDP as a fully endogenous variable. The variance covariance matrix of the errors was unrestricted in the estimation and testing procedures. The main results can be summarized as follows. 1. The coefficient of the percentage of area of a country in the tropics was estimated with a negative sign that was statistically significant. Openness of the economy was positively associated with growth rates; the magnitude of the coefficient was robust to the use of alternative definition of openness in the PWT. The log of total fertility rate was negatively associated with GDP growth rates and was statistically significant. High fertility rates are common in developing countries and increase the demand on resources for health care and education; the work force does not increase equi-proportionately with the population. Also, high fertility rates in developing countries often reflect unwanted fertility that adversely affects households' resource allocation decisions (Bhargava, 2002). For example, the ratio of skilled to unskilled labor is likely to be negatively associated with total fertility rate due to diminished resources available for education; total fertility rate is thus likely to be negatively associated with growth rates. 2. The lagged investment/GDP ratio had a positive coefficient that was statistically significant; economic growth was affected by investments in physical capital. The fact that the coefficient of the investment/GDP ratio was small, suggests that one should not dismiss proximate determinants of growth rates because of their small magnitudes. Of course, coefficients should be statistically significant and robust to changes in model specification. However, the extent to which one can investigate adequacy of models for growth rates is limited by difficulties such as the large variation in growth rates, modest number of countries in the sample, measurement errors in the explanatory variables, etc. For example, one might have expected a variable such as the average years of education of the population (Barro and Lee, 1996) to be positively associated with growth rates. This was not the case in the present models, perhaps because variation in this variable was relatively small for a number of developing countries. 3. The lagged ASR and interaction between ASR and GDP were the significant predictors of economic growth. The impact of ASR was positive at low levels of GDP and, for example, approached zero in specification 1 when the per capita GDP was 2123 in 1985 international dollars. We discuss this issue in greater detail in Section 4.2. The empirical results were similar when ASR was replaced by life expectancy, though the model where ASR was included provided a better fit. This was perhaps not surprising since life expectancy is strongly influenced by child mortality. Because child mortality is itself affected by unwanted fertility in developing countries, the total fertility rate and ASR are better indicators of the health infrastructure. 4. The estimated coefficient of lagged GDP was negative showing a tendency of regression towards the mean. While the results in specifications 1 and 2 were close, the level of GDP at which the effect of ASR on growth rate was zero was estimated to be 1714 in 1985 international dollars due to the treatment of lagged GDP as an endogenous variable.

Modeling the Effects of Health on Economic Growth

279

Table 2 Estimated slope coefficients from static random effects models for real per capita GDP growth rates 1965-1990 at 5-year intervals using data from WDIa Variable Constant Tropics Openness Logarithm of fertility rate lagged 5 years Logarithm of investment/GDP ratio lagged 5 years Logarithm of adult survival rate lagged 5 years Interaction between lagged adult survival rate and GDP Logarithm of GDP lagged 5 years GDP at which partial derivative of GDP growth rate with respect to lagged adult survival rate is zero Chi-square (20) test for exogeneity of lagged GDP Chi-square (20) test for exogeneity of investment/GDP ratio Chi-square (15) test for exogeneity of means of lagged investment/ GDP ratio, ASR, and interaction of ASR and GDP Number of countries Number of time observations

Specification 1

Specification 2 b

0.220 (0.033) -0.014 (0.004) 0.041 (0.006) -0.023 (0.007) 0.009 (0.003) 0.192(0.061) -0.029 (0.010) -0.022 (0.004)

0.310(0.048) -0.016(0.005) 0.047 (0.007) -0.034 (0.008) 0.008 (0.003) 0.333 (0.084) -0.052 (0.014) -0.034 (0.006)

584

580

62.41 13.23 3.04

73 5

73 5

a

Asymptotic standard errors are in parentheses. Specification 1 treats the time varying variables as exogenous; specification 2 treats lagged GDP as a fully endogenous variable. b

Because the Chi-square specification test indicated that lagged GDP should be treated as a fully endogenous variable, the /{-squared values were computed from reduced form equations regressing lagged GDP on the explanatory variables; the adjusted /{-squared for the five time periods were 0.78, 0.80, 0.81, 0.83, and 0.85, respectively. While it is possible to develop a rigorous statistical test for the rank condition underlying the instrumental variable estimation, the adjusted /{-squared values suggest that the rank condition is satisfied in this model. The empirical results for GDP growth rates based on official exchange rates from the WDI are shown in Table 2. The results in Tables 1 and 2 were similar for most explanatory variables except that the level of GDP at which the effect of ASR on growth rate was zero in specifications 1 and 2 were 684 and 580, respectively, in constant 1987 dollars. These estimates were substantially lower than the corresponding figures for the PWT data when converted from 1985 international dollars to 1987 constant dollars (an 1985 international dollar is approximately equal to 1.25 constant 1987 dollars). The specification test again indicated that lagged GDP should be treated as a fully endogenous variable; the adjusted /^-squared for the five reduced form equations were 0.74,0.75,0.77,0.79, and 0.80, respectively. Because the WDI data were not interpolated for most countries, there was greater variation in the GDP series. Thus, one would expect the /{-squared values to be slightly lower in the reduced form equations for the WDI GDP series. The effects of smoothing procedures will be further apparent in Section 4.2, where we investigate the net effect of ASR on GDP growth rates.

280

A. Bhargava et al. 4.2. The net impact of adult survival rates of GDP growth rates The ASR for a country is likely to be influenced by economic development, access to and quality of medical care, and the public health infrastructure. However, beyond a certain threshold, increases in ASR are difficult to achieve and will increase the proportion of the elderly in the economy. By contrast, for countries at low levels of GDP, one would expect significant effects of ASR on economic growth due to the contribution of labor in prime years. Thus, models for growth rates should allow some forms of non-linearities. Because of the modest number of countries in the data set and because the average life expectancy in the sample was around 60 years, only the interaction between lagged ASR and GDP was found to be statistically significant. For illustrative purposes, we rewrite the net effect of a change in ASR on growth rate as fc2 + &3(GDP)

(8)

where fc2 and £3 are, respectively, the (partial) coefficients of the logarithm of ASR and interaction between logarithms of ASR and GDP in the model (1). The net effect b\ can be computed at different levels of GDP and the asymptotic confidence intervals can be approximated from Avar(foi) = Avar(62) + Avar(fc3)(GDP)2 + 2Acov(fc2, &3)(GDP)

(9)

Thus, we can tabulate the effects of a unit change in ASR on growth rates and the corresponding confidence intervals for the countries at mean GDP levels. The results for

.2 " -C

.15 "

5 0

01

.1

CL

Q C3 c 0)

.05 0 -

ra c to -C 0 +*

c

ffi 0

0 CL

-.05 ~ -.1 ~ -.15 ~ -.2 ~ 4.5

5.5

1 1 1 1 6.5 7 7.5 8 Log of G D P per capita

1— 8.5

9.5

10

Fig. 1. Net effect and confidence intervals for a percent change in ASR on GDP growth rate using PWT GDP data and assuming exogenous explanatory variables.

.2 ~ X

.15 "

S o O)

a o CD c a O)

c CO s: o

_0)C^o CD Q.

.1 ~ .05 o -.05 -.1 -.15 -.2 4.5

I 5.5

I 6

I I I I 6.5 7 7.5 8 Log of GDP per capita

I 8.5

9.5

10

Fig. 2. Net effect and confidence intervals for a percent change in ASR on GDP growth rate using PWT GDP data and assuming GDP is a fully endogenous explanatory variable.

the PWT data are presented in Figs. 1 and 2, where Fig. 2 plots the results for the case where lagged GDP was treated as a fully endogenous variable. The effect was plotted against mean of the logarithm of GDP of countries in the sample period. Corresponding results for the WDI data are in Figs. 3 and 4. .2

sz 5 o D>

a. a

.15 .1

O c

.05


0

cCO JO

o cCO o

-.05

4-,

CO D_

-.1

-.15 -.2 4.5

5.5

n 6

i r ~r 6.5 7 7.5 8 Log of GDP per capita

8.5

9.5

10

Fig. 3. Net effect and confidence intervals for a percent change in ASR on GDP growth rate using WDI GDP data and assuming exogenous explanatory variables.

A. Bhargavaet al.

282

.2 sz S o o>

.15

Q.

.05

Q

CD c
o

.1

0

-.05 . 1

4 ^

c CO

-.15

o

CO

-.2

4.5

—I 5.5

1 6

1 1 1 1 6.5 7 7.5 8 Log of GDP per capita

1— 8.5

9.5

r 10

Fig. 4. Net effect and confidence intervals for a percent change in ASR on GDP growth rate using WDI GDP data and assuming GDP is a fully endogenous explanatory variable.

The results from PWT in Fig. 1 showed significant positive effects of ASR on growth rates until the logarithm of the GDP was approximately 6.81 (907 in 1985 international dollars); the corresponding estimate from specification 2 in Fig. 2 was very close. Once these points were crossed, the net effect of ASR approached zero and subsequently assumed negative values. Note, however, that the negative effects of ASR on growth rates were not statistically different from zero in Fig. 1. However, this was not true in Fig. 2, where the net effect was negative and significant for a few countries with high GDP levels. The results using WDI GDP series in Figs. 3 and 4 were similar for low income countries, except that the threshold where the impact of ASR was zero, was reached earlier. Once the net effect of ASR turned negative, it was statistically significant for certain countries at the high end of the income distribution in Figs. 3 and 4. However, as noted in Section 3.1, this should not be construed as implying harmful effects of ASR on growth rates. Rather, some of the affluent countries, especially in Europe, had achieved high ASR while experiencing slower growth rates in the sample period, due to historical and institutional reasons. As discussed in Section 5, it would be useful to compile additional health indicators providing elaborate information especially in affluent settings. 4.3. Results for the test for reverse causality and parameter stability outside the sample period The results for the model explaining ASR using the GDP data from PWT and WDI are presented in Table 3, under alternative exogeneity assumptions on lagged GDP levels and growth rates. The proportion of the area in the tropics and total fertility rate were significantly and negatively associated with ASR. Openness of the economy and the investment/GDP

Modeling the Effects of Health on Economic Growth

283

Table 3 Tests for reverse causality based on the slope coefficients from static random effects models for log ASR in the period 1965-1990 at 5-year intervals using the data from PWT and WDIa'b Variable

PWT Specification 1

Constant Tropics Logarithm of fertility rate lagged 5 years Logarithm of GDP lagged 5 years Interaction between lagged GDP and growth rate Growth rate lagged 5 years Chi-square (24) test for exogeneity of lagged GDP and growth rate Chi-square (8) test for exogeneity of means of lagged GDP and growth rate Number of countries Number of time periods

WDI Specification 2

Specification 1

Specification 2

-0.852 (0.134) -0.089 (0.028) -0.058(0.021)

-0.746(0.211) -0.091 (0.030) -0.081 (0.030)

-0.435(0.133) -0.063 (0.032) -0.126(0.031)

-0.447 (0.237) -0.060 (0.033) -0.144(0.048)

0.087 (0.014) 0.001 (0.070)

0.078 (0.022) -0.025 (0.232)

0.050 (0.013) -0.041 (0.101)

0.055 (0.025) -0.382 (0.377)

-0.258 (0.529) 14.82

-0.033 (1.765)

0.233 (0.680) 7.31

2.593 (2.578)

4.83

92 4

3.02

92 4

73 4

73 4

a Specifications 1 and 2 treat lagged GDP and growth rate as exogenous and fully endogenous variables, respectively. b Asymptotic standard errors are in parentheses.

ratios were not significant predictors of ASR; these variables were dropped from the model to reduce multi-collinearity. As expected, lagged GDP level was a significant predictor of ASR. By contrast, lagged GDP growth rate and the interaction between GDP level and growth rate were not statistically significant. The Chi-square statistics for the exogeneity null hypothesis of lagged GDP level and growth rate accepted the null. Overall, the results in Table 3 support the view that lagged GDP growth rates do not influence the current ASR, at least in the short time frame of 5 years. Consequently, the positive associations between ASR and GDP growth rates reported in Tables 1 and 2 are more likely to reflect causality running from ASR to growth rates for low income countries. Further, because GDP data were available in the WDI for 1995 (the PWT data for 1995 are not as yet available), we applied the statistic W given in Eq. (7) to test the constancy of coefficients of the variables tropics, openness, lagged total fertility rate, investment/GDP ratio, ASR, interaction between ASR and GDP, and GDP in two situations. First, as in specification 1, these variables were assumed to be exogenous. In the second case, lagged GDP was treated as a fully endogenous variable (specification 2). The sample criteria for the W statistics in the two cases were 16.53 and 15.07, respectively. For a Chi-square variable with 7 d.f., the critical values at 5 and 2.5% are 14.1 and 16.0, respectively. Thus, the test assuming exogeneity of lagged GDP would reject the null hypothesis of parameter constancy at the conventional 5% level. The null would also be rejected using the parameter estimates from specification 2, though the sample criterion for the W statistics is somewhat closer to the 5% critical limit.

284

A. Bhargava et al. 5. Conclusion This paper modeled the proximate determinants of economic growth at 5-year intervals using panel data on GDP series based on purchasing power parities from the PWT and on exchange rate conversions from the WDI. In the conceptual framework of the analysis, the demographic literature relating life expectancy to income (Preston, 1976) was integrated with models commonly specified for economic growth (Barro and Sala-i-Martin, 1995). Appropriate econometric estimators and test procedures were used in the analysis to draw inferences. Although the health of individuals in a country can only be roughly approximated in national averages, the models showed significant effects of ASR on economic growth rates for low income countries. Thus, for example, for the poorest countries, a 1 % change in ASR was associated with an approximate 0.05% increase in growth rate. While the magnitude of this coefficient was small, a similar increase of 1 % in investment/GDP ratio was associated with a 0.014% increase in growth rate. A novel aspect of the analysis was that we estimated the threshold point beyond which ASR had typically negligible effects on growth rates; confidence intervals for the net impact of ASR highlighted the asymmetries for poor and rich countries (Figs. 1-4). Thus, for example, using the GDP data for 1990 from the PWT, the parameter estimates imply large positive effects of ASR on growth rates for countries in the sample such as Burkina Faso, Burundi and the Central African Republic. The positive effects were also significant for India, Ivory Coast and Nigeria. For highly developed countries such as USA, France and Switzerland, the estimated effect of ASR on growth rates was negative. These empirical findings in part result from the choice of the functional form, explanatory variables available for the analysis, and the standard errors of the estimated parameters. From a conceptual standpoint, it is important that future research compile more elaborate data on health indicators. Thus, for example, ASR in poor countries reflects the levels of nutrition, smoking prevalence rates, infectious diseases, health infrastructure, and factors such as accidents leading to premature deaths. By contrast, differences in ASR in middle and high income countries may be influenced by genetic factors and by access to and costs of preventive and curative health care. Because investments in skill acquisition in poor countries depend on the ASR, the years for which skilled labor remains productive is likely to be important for explaining economic productivity. Furthermore, it would be useful to augment statistics such as percentages of skilled and unskilled labor compiled for countries (International Labour Organization, 1999) by measures of physical and mental health. For example, productivity loss due to ill health can be estimated from augmenting employment surveys with a health module. Measures of cognitive function in different age cohorts may also be useful for explaining economic performance of countries. Analyses based on elaborate data sets would afford sharper insights into the likely impact of health on economic growth.

Acknowledgements This study was supported by the Global Programme on Evidence for Health Policy and by the Economics Advisory Service of the World Health Organization, Geneva, Switzerland. The authors are indebted to D. Evans for useful suggestions, and to A. Tandon and J. Wang

Modeling the Effects of Health on Economic Growth for their valuable help. This revision has benefited from the comments of a referee and the editor. The views contained in the paper are those of the authors. References Ahmad, S., 1992. Regression estimates of per capita GDP based on purchasing power parities. Working Paper #WPS 956, International Economics Department, The World Bank, Washington, DC. Anderson, T.W., 1971. Statistical Analysis of Time Series. Wiley, New York. Barro, R.J., 1997. Determinants of Economic Growth. MIT Press, Cambridge, MA. Barro, R.J., Sala-i-Martin, X., 1995. Economic Growth. McGraw-Hill, New York. Barro, R.J., Lee, J.W., 1996. International measures of school years and schooling quality. American Economic Review, Papers and Proceedings 86, 218-223. Basta, S.S., Soekirman, M.S., Karyadi, D., Scrimshaw, N.S., 1979. Iron deficiency anemia and the productivity of adult males in Indonesia. American Journal of Clinical Nutrition 32, 916-925. Bhargava, A., 1991a. Identification and panel data models with endogenous regressors. Review of Economic Studies 58, 129-140. Bhargava, A., 1991b. Estimating short and long run income elasticities of foods and nutrients for rural south India. Journal of the Royal Statistical Society A 154, 174-175. Bhargava, A., 1997. Nutritional status and the allocation of time in Rwandese households. Journal of Econometrics 77, 277-295. Bhargava, A., 1998. A dynamic model for the cognitive development of Kenyan schoolchildren. Journal of Educational Psychology 90, 162-166. Bhargava, A., 2002. Family planning, gender differences and infant mortality: evidence from Uttar Pradesh, India. Journal of Econometrics, in press. Bhargava, A., 1999. Modeling the effects of nutritional and socioeconomic factors on the growth and morbidity of Kenyan school children. American Journal of Human Biology 11, 317-326. Bhargava, A., 2000. Stochastic specification and the international GDP series. Discussion Paper, University of Houston. Bhargava, A., Sargan, J.D., 1983. Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51, 1635-1660. Bloom, D., Canning, D„ 2000. Health and wealth of nations. Science 287, 1207-1209. Bos, E., 1998. Basic demographic, health and health systems data. Technical Report, The World Bank, Washington, DC. Boskin, M., Lau, L.J., 1992. Post-war economic growth in the group-of-five countries: a new analysis. Discussion Paper, Stanford University. Caselli, E, Esquivel, G., Lefort, E, 1996. Reopening the convergence debate: a new look at cross-country growth empirics. Journal of Economic Growth 1, 363-389. Christensen, L.R., Jorgenson, D.W., Lau, L.J., 1973. Transcendental logarithmic production frontiers. Review of Economics and Statistics 55, 28^15. Cochrane, W.G., 1965. The planning of observational studies of human populations (with discussion). Journal of the Royal Statistical Society A 128, 234-265. Collins, S.M., Bosworth, B.P., 1996. Economic growth in East Africa: accumulation versus assimilation. Brookings Papers on Economic Activity 2, 135-203. Cox, D.R., 1992. Causality: some statistical aspects. Journal of the Royal Statistical Society A 155, 291-302. Fisher, R.A., 1973. Statistical Methods for Research Workers, 14th Edition. Hafner, New York. Floud, R., Wachter, K., Gregory, A., 1991. Height, Health and History. Cambridge University Press, Cambridge. Fogel, R.W., 1994. Economic growth, population health and physiology: the bearing of long-term processes on the making of economic policy. American Economic Review 84, 369-395. Gallup, J.L., Sachs, J.D., 1998. Geography and economic development. Discussion Paper, Center for International Development, Harvard University, Cambridge, MA. Horn, J., Hofer, S.M., 1992. Major ability and development in the adult period. In: Sternberg, R.J., Berg, C.A. (Eds.), Intellectual Development. Cambridge University Press, Cambridge.

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A. Bhargava et al. International Institute of Population Sciences, 1995. The national family health survey, Mumbai, India. International Labour Organization, 1999. Key indicators of labour market. International Labour Organization, Geneva, Switzerland. Kim, J.I., Lau, L.J., 1994. The sources of economic growth in the East Asian newly industrialized countries. Journal of Japanese and International Economies 8, 235-271. Murray, C.J.L., Lopez, A., 1996. The Global Burden of Disease. Harvard University Press, Cambridge. Nehru, V., Dhareshwar, A., 1993. A new database on physical capital stock: sources, methodology and results. Revista de Aanalisis Economico 8, 37-59. Preston, S.H., 1976. Mortality Patterns in National Populations. Academic Press, New York. Sala-i-Martin, X., 1996. The classical approach to convergence analysis. Economic Journal 106, 1019-1036. Sargan, J.D., 1958. The estimation of economic relationships using instrumental variables. Econometrica 26, 393^115. Sargan, J.D., 1964. Wages and prices in the UK: a study in econometric methodology. In: Hart, P., Mills, G., Whitaker, J.K. (Eds.), Econometric Analysis for National Economic Planning. Butterworths, London, pp. 25-54. Sargan, J.D., 1971. Production functions. In: Layard, P.R.G., Sargan, J.D., Ager, J.D.M.E., Jones, D.J. (Eds.), Qualified Manpower and Economic Performance, Part 5. Allen Lane, London. Sargan, J.D., 1980. Some tests of dynamic specification for single equations. Econometrica 48, 879-898. Scrimshaw, N.S., 1996. Nutrition and health from womb to tomb. Nutrition Today 31, 55-67. Scrimshaw, N.S., Taylor, C.E., Gordon, J.E., 1959. Interactions of nutrition and infection. American Journal of Medical Science 237, 367-403. Spurr, G.B., 1983. Nutritional status and physical work capacity. Yearbook of Physical Anthropology, volume 26, pp. 1-35. Strauss, J., Thomas, D., 1998. Health, nutrition and economic development. Journal of Economic Literature 36, 766-817. Stronks, K., van de Mheen, H., van den Bos, J., Makenbach, J.P., 1997. The interrelationship between income, health and employment status. International Journal of Epidemiology 26, 592-599. Summers, R., Heston, A., 1991. The Penn world table (mark 5): an expanded set of international comparisons, 1950-1988. Quarterly Journal of Economics 6, 327-368. World Bank, 1993. Investing in health. World Development Report 1993, The World Bank, Washington, DC. World Bank, 1998. World development indicators 1998 CD-ROM. The World Bank, Washington, DC.

V. Economic Demography

Indian Economic Review, Vol. XXXII, No. 2, 1997, pp. 141-153

A Longitudinal Analysis of Infant and Child Mortality Rates in Developing Countries ALOK BHARGAVA AND JIANG YU Dept. of Economics, University of Houston, Houston, TX 77204-5882, USA

ABSTRACT

Child mortality is an important indicator of economic and social development in developing countries. This paper investigates the determinant of infant and child mortality rates in 13 African and 23 non-African developing countries using data based on demographic surveys. A longitudinal analysis incorporating temporal dependence in the data and cross-country heterogeneity is performed at the country level for the period 1975-85. The main findings are that elasticities of child mortality rates with respect to female illiteracy are close to unity in African countries but are lower for non-African countries. Also, real per capita Gross National Product and government expenditures on health are inversely associated with mortality rates in African countries, some aspects of specifying models for child mortality and their implications are discussed. JEL Classification : C23, 112

1. INTRODUCTION Child mortality is an important indicator of economic and social development in less developed countries in part because it reflects the effectiveness of the health infrastructure. A knowledge of the determinants of infant and child mortality is important for the formulation of policies of national governments and of international organization providing aid. This is especially true for certain countries in Africa and Asia where child mortality remains very high. Analyses of data from such countries can facilitate a better understanding of the determinants of child mortality. In some cases, mortality might be reduced by re-allocating resources amongst alternative sectors of the economy. Previous research in demography and economics has measured the impact of socioeconomic, medical and environmental factors on child mortality. For example, female education, per capita Gross National Product, government expenditures on health, income inequality, sanitation, innoculation rates, etc are postulated to be important determinants (e.g. Preston, 1976, Cochrane, O'Hara and Leslie, 1980, Hill and Pebley, 1989, Behrman 1991 and Murthy et al., 1995). Recently, researchers have underscored

A. Bhargava and J. Yu

290

the use of child mortality rates as an indicator of human development (e.g. Sen, 1992, Anand and Ravallion, 1993, and Aturupane et al., 1994). A common problem in analyzing infant and child mortality rates from various developing countries is the lack of reliable data (e.g. Chamie, 1994). The mortality figures for many countries published by international organizations such as the World bank are " projections" from simple statistical models. Further, policy instruments such as expenditures on medical personnel and hospitals require several years to have their full impact. The effects of such variables on child mortality will therefore not be evident in purely cross-sectional analyses of the data (e.g. Bhalla and Glewwe, 1986, Isenman, 1987, Pyatt, 1987 and Ravallion, 1986). The purpose of this paper is to tackle some shortcomings in the previous analyses by utilising longitudinal data derived from demographic surveys (United Nations, 1992). The influence of previous realizations of explanatory variables is modelled by postulating time-dependent (dynamic) models for child mortality rates. The estimation of such formulations form longitudinal data covering only a few time periods is feasible (Anderson and Hsiao, 1981, Bhargava and Sargan, 1983 and Bhargava, 1991). An analysis of longitudinal data on national child mortality rates is useful for understanding the differential effects of development in various sectors. The parameters in the relationships for African and other developing countries, however, are likely to differ. This in part is due to the political circumstances in some African countries that hinder utilisation of health services. Moreover, there are differences in methods by which data on variables such as the Gross Domestic Product and Gross National Product are compiled by international agencies for African countries (Ahmad, 1994). It is therefore necessary to separately estimate the models for child mortality for African and nonAfrican countries. The structure of this paper is as follows: the conceptual framework is outlined in Section 2.1. The model is explained in Section 2.2 and some econometric issues are discussed in Section 2.3. The data are described in Section 3 and some inadequacies are noted. In Section 4, empirical results for child mortality rates in developing countries are discussed. Section 5 outlines the implications of the results public policies and for future research. 2. A LONGITUDINAL FRAMEWORK FOR INFANT AND CHILD MORTALITY RATES 2.1 The Conceptual Framework Improving the health of children in developing countries is a major goal of public policies. While high child mortality rates partly reflect shortcomings in the health infrastructure, mortality is preceded by sicknesses that hinder the normal process of child development. Although analyses of the proximate determinants of sickness spells can provide useful insights for public policies, morbidity data are unavailable on a comparable scale in different developing countries. However, data on children's anthropometric measures such as height and weight could be useful health indicators in a cross-country analysis. In this paper, we model the proximate determinants of child mortality rates to investigate the effects of differential levels of social and economic development in developing countries on child health.

Infant and Child Mortality Rates in Developing Countries

291

Prevalence of severe illnesses and poor access to medical care are likely to contribute to infant and child mortality. Further, investments in the health infrastrucure gradually reduce mortality. For example, there are delays in utilization of health facilities especially by the uneducated poor in rural areas. Since mortality rates are high for such groups, government expenditures would require several years to produce the desired effects. It is therefore important to model child mortality using dynamic formulations that are capable of representing the delayed response to policy instruments. An analysis of the national child mortality rates for developing countries would show the effects of developing different components of the infrastructure. Because child mortality reflects the ultimate effects of severe illnesses, allocating additional resources to specific sectors would enhance child survival. Also, unlike analyses based on crosssectional data, longitudinal data enable investigators to control the unobserved differences between different countries. The estimated parameters from dynamic econometric models incorporating cross-country heterogeneity would be of interest. Before outlining the dynamic model for aggregate child mortality rates, we recognize the value of studies conducted at regional and household levels. The effects of unequal distribution of health facilities within a country will be apparent in analyses based on data at the regional level (e.g. Murthy et al., 1995). The relationship between child mortality and explanatory variables estimated using household data provide direct insights into the potential causes of child mortality, historically, analyses at the country level have preceded investigations using individual data (Goldstein, 1979 and Tanner, 1981). This sequencing is natural since results from aggregate data are useful for the formulation of finer hypotheses. Results from the present analysis are also helpful for some ongoing research by the first author that models the proximate determinants of child mortality in India using data from the National Family and Health Survey (NFHS, 1995). 2.2

A Dynamic Formulation for Models of Child Mortality

The issues arising in estimation of dynamic models for child mortality rates using a few time observation can be addressed within the specification: m+1

y_ = Z it

.=1

y„

= E

f

-=1

n

z..y.

+ I

IJ ' \

m+1

T

z..£. + z 'J

I

X

k=]

=1

S + a y ikt^k

+ u (/ = 1

';f-1

H; t = 2,...7)

(1)

it

T

S vx.. + u k=1

JK UK

(/= 1

H)

(2)

'1

Here Y is the infant (for under 5 child) mortality rate (deaths per 1000 live births) in /'th country in tth time period; there are H countries in the sample tat are observed in 7 periods. The z. are characteristics of /th country that are constant in the sample period; x are time varying regressors. The model is dynamic in the sense that mortality in the previous period (y ) affects the current rate. This affords a distinction between the short and long run effects of changes in explanatory variables on child mortality.

A. Bhargava and J. Yu

292

The errors on equation (1) are assumed to be multivariate normally distributed with mean zero and a positive definite variance covariance matrix. Analogously, u. are drawings from a normal distribution with mean zero and finite variance (normality assumptions are not crucial for the consistency and asymptotic normality of structural form parameter estimates; Bhargava, 1987). The random effects model for the u's is a special case; the errors on equation (1) can be decomposed as

"/f = 5 . + ^

(/=1

H;f = 2

T)

(3)

where 5. are country specific independently distributed random variables with mean zero and variance o-2 and £ are independently distributed random variables with zero mean and variance a2. In practice, e may be correlated over time and the coefficient of 8. could depend on time. For small sample sizes, however, the decomposition (3) is useful. Child mortality rate in the previous period is treated as an endogenous variable in the system. The model, parameters are estimated by maximizing the concentrated likelihood function of model (1); this function is obtained by eliminating the "nusiance" parameters appearing in (2). A numerical scheme is used for optimization and asymptotic standard errors of the estimated parameters are calculated by numerically approximating second derivative of the likelihood function at the maximum. Since the number of observations available is small, we also compute efficient estimates of "static' models that exclude y from the set of regressors (Bhargava, 1991). The estimates from static models will provide a check on robustness of the parameter estimated from dynamic models. Note that "fixed effects' estimates are inconsistent for small T due to the classical problem of "incidental parameters". 2.3

Some Econometric Issues

The previous research on child mortality has utilized two time observations to control for "initial conditions" in the countries (Bhalla and Glewwe, 1986). However, the application of least squares to dynamic models leads to biased estimates insofar as the number of time observation (T) is small (e.g. T < 15). Since differencing the equation removes country specific random variables (S.), least squares estimates from differenced equations might seem reasonable in some applications. For consistent estimation of the parameters, it is necessary to use an instrumental variables procedure on the differenced model (Anderson and Hsiao, 1981). The formulation adopted in this paper circumvents most of the difficulties arising in practice. Lagged child mortality is included as a regressor in the model; the random effects (S's) capture the between country differences. The initial observations (y ) on child mortality are treated as endogenous i.e the errors on equations (1) and (2) are correlated. Within the present framework, it is possible to discriminate between the levels formulation and models where some variables are specified in differences (see Bhargava and Ravallion, 1993). Note that this aproach differs from the method used by Aturupane et al. (1994) where the models condition upon y . In short panels, however, it is necessary to maximize the joint likelihood function of the observations (y , y , y ). The use of conditional likelihood function will yield inconsistent parameter estimates insofar

Infant and Child Mortality Rates in Developing Countries

as y are endogenous i.e. 7 is fixed. Secondly, data on important explanatory variables such as the illiteracy rate are available only at a singly point in time; altenative projections of education stock have recently been constructed by Dubey and King (1994). In this paper, we extend the model for estimating coefficients of time varying variables on which a single time observation is available. This can be achieved by including indicator variables for time periods and treating illiteracy rate as a time invariant regressor (Bhargava, 1994). This procedure is equivalent to assuming that there are trends underlying mortality rates and explanatory variables. A knowledge of the coefficients of the trends, however, is unnecessary since the estimation method is invariant with respect to the unknown values. Lastly, the dynamic and static formulations are capable of treating some of the explanatory variables as endogenous in the system. Since our analysis relies on national averages separated by 5-year intervals, it seems reasonable to treat the explanatory variables as pre-determined. Note that the long run elasticities of child mortality rates computed from edynamic models might be close to those obtained using static formulations. This is because static models allow temporal dependence in the shocks E "S (see equation (3)); it might be difficult to distinguish between the two sets of estimates when the number of observations is small. 3. THE DATA The data on infant and child mortality rates are from the recent publication of the United nations (1992). These figures are "direct' estimates based on demographic surveys in developing countries; the data are more reliable than projections by the World Bank or the United Nations. Explanatory variables were taken from various sources, especially from STARS (1992). Some publications of the United Nations were also used to obtain additional variables. We note that data on Gross Domestic Product (GDP) of non-African countries are unavailable in the World Bank and other data sources. The tabulations by Summers and Heston (1988) for Gross National Product (GNP) and GDP are used for non-African countries to obtain real per capital GNP and government expenditures on health. However, in the latter data set, variables are expressed in "international prices". Some comparisons were made in the empirical analysis for African countries where alternative data series are available. The data on 13 African and 23 non-African developing countries in 1975, 1980 and 1985 are used in the analysis, figures 1 to 4 plot the average infant and under-five mortality rates (o and q , respectively) from United Nations (1992) for countries in Africa, Asia and South America. The countries are listed in the notes to Table 2. The decline in child mortality rates in the figures suggests the use of the natural logarithmic transformation. A loglinear specification will incorporate to some degree the possible interactions between explanatory variables. 4. THE EMPIRICAL RESULTS The empirical results from dynamic and static models for infant and child mortality rates in African and non-African developing countries are presented in Tables 1 and 2. The

293

A. Bhargava and J. Yu

294

INFANT AND CHILD MORTALITY RATES (For African countries) 140

INFANT MORTALITY (
120 100 -G-S-

80 60 40 h -B~

20

EAST AFRICA

*

WEST AFRICA

^" NORTH AFRICA

_l_

1975

1980

1985

Fig 1

CHILD MORTALITY (q 5 )

300

:; 250

x 200

-

150 100 h-

50

-

o 1975

- B - EAST AFRICA

-X

TEST AFRICA

1980

Fig 2

"^

NORTH AFRICA

1985

Infant and Child Mortality Rates in Developing Countries

295

INFANT AND CHILD MORTALITY RATES (For o t h e r developing countries) INFANT MORTALITY (
-E3

80, 60

-----

:c

40 20

- a - SOUTH ASIA

-"X- OTHER ASIAN

-S>- LATIN AMERICA

n

1980

1975

1985

Fig 3

200

CHILD MORTALITY (qs)

150

100

fc: ••-x-

---<>

-

50 SOUTH ASIA

*

OTHER ASIAN

" 0 - LATIN AMERICA

I

1975

1980

Fig 4

1985

296

A. Bhargava and J. Yu

TABLE 1

LONGITUDINAL REGRESSIONS FOR INFANT AND CHILD MORTALITY RATES FOR AFRICAN AND OTHER DEVELOPING COUNTRIES 1975-85 African Developing Countries Model

Dynamic Random EFF.

Variable

"1

Other Developing Countries

Static Random EFF.

Dynamic Random EFF.

%

%

^5

«1

1.664 (0.563)

0.420 (0.242)

%

Static Randon EFF. <1

%

0.410 (0.254)

3.156 (0.263)

3.197 (0.272)

Constant

2.573 (0.634)

2.172 (0.463)

1.287 (0.480)

Illiteracy Female

0.769 (0.188)

1.000 (0.088)

1.060 (0.200)

1.257 (0.238)

0.022 (0.070)

0.044 (0.075)

0.193 (0.160)

0.314 (0.167)

Illiteracy Male

-0.139 (0127)

-0.201 (0.080)

-0.169 (0.161)

-0.250 (0.184)

0.086 (0.067)

0.080 (0.070)

0.202 (0.156)

0.168 (0.163)

RPCGMP

-0.193 (0.067)

-0.142 (0.051)

-0.014 (0.025)

-0.014 (0.023)

-0.007 (0.007)

-0.005 (0.007)

-0.013 (0.009)

-0.010 (0.009)

RGHELEXP

-0.009 (0.033)

-0.076 (0.026)

-0.087 (0.027)

-0.166 (0.031)

-0.001 (0.014)

-0.002 (0.015)

0.018 (0.028)

0.018 (0.030)

Time Dummy 2

-

-

-0.059 (0.038)

-0.109 (0.033)

-

-

-0.189 (0.040)

-0.240 (0.042)

Time Dummy 3

-0.048 (0.017)

-0.036 (0.026)

-0.124 (0.055)

-0.168 0.049)

0.063 (0.042)

0.106 (0.050)

-0.280 (0.043)

-0.328 (0.045)

Lagged

0.110 (0.051)

0.123 (0.061)

-

-

0.802 (0.055)

0.800 (0.057)

-

-

13

13

13

13

23

23

23

23

q

N

Long Run Elasticities Illiteracy

0.864

1.140

0.193

0.314

0.217

0.162

0.0

0.0

0.0

0.0

Female RPCGMP RGMELEXP

0.087

0.087

Notes : 1. qr is the number of infants (per 1,000 live birth) dead before reaching the age of 1; g is the number of children deaa before the age of 5; Illiteracy female and Illiteracy male are, respectively, the percentage of female and male over the age of 15 years who are illiterate. RPCGNP is the real per capita GNP. RGHELEXP is the real government expenditure on helath; LAGGED q is the lagged q or q g included as a regressor in the dynamic model. Time Dummy 2 and Time Dummy 3 are, respectively, dummy variables for 1980 and 1985; Long Run Elasticity = (Short Run Elasticity)/(1-lagged q). 2. All variables are in natural logrithms, the reported coefficients are thus elasticities; Standard errors are in the parentheses. There are 3 repeated observations on 13 African countries (N = 13, T = 3) and 23 other developing countries (N = 23, T = 3). 3. The static random effects model allows serial correlation in the temporal shocks. 4. Long run elasticities are obtained from the static model if the lagged q is not statistically significant in the dynamic model. 5. Some components of GNP and GDP data for other developing countries are from Summers - Heston. 6.For country list refer to Notes in Table 2.

Infant and Child Mortality Rates in Developing Countries

297

TABLE 2

LONGITUDINAL REGRESSIONS FOR INFANT AND CHILD MORTALITY RATES FOR AFRICAN AND OTHER DEVELOPING COUNTRIES 1975-85 African Developing Countries Model

Dynamic Random EFF.

Variable

Other Developing Countries

Static Random EFF.

Dynamic Random EFF.

Static Randon EFF.

"1

05

01

qs

qi

qs

qi

qs

Constant

3.001 (0.207)

2.794 (0.876)

1.093 (0.627)

1.099 (0.745)

0.300 (0.241)

0.300 (0.255)

2.942 (0.324)

2.985 (0.333)

Illiteracy Female

0.531 (0.085)

0.706 (0.235)

0.914 (0.116)

1.082 (0.141)

0.117 (0.035)

0.133 (0.040)

0.405 (0.066)

0.496 (0.068)

Index of Hel. Prof.

0.001 (0.026)

-0.010 (0.027)

0.006 (0.016)

0.026 (0.019)

0.013 (0.017)

0.013 (0.017)

0.024 (0.042)

0.025 (0.043)

RPCGMP

-0.241 (0.056)

-0.189 (0.103)

0.001 (0.021)

-0.004 (0.019)

-0.006 (0.007)

-0.004 (0.007)

-0.012 (0.009)

-0.010 (0.009)

RGHELEXP

0.012 (0.037)

-0.058 (0.046)

-0.081 (0.035)

-0.132 (0.039)

-0.003 (0.014)

-0.001 (0.014)

0.029 (0.029)

0.028 (0.029)

Time Dummy 2

-

-

-0.057 (0.039)

-0.112 (0.033)

-

-

-0.192 (0.040)

-0.243 (0.042)

Time Dummy 3

-0.050 (0.024)

-0.035 (0.030)

-0.108 (0.051)

-0.167 0.044)

0.064 (0.037)

0.106 (0.039)

-0.284 (0.043)

-0.332 (0.045)

Lagged

0.161 (0.106)

0.138 (0.171)

-

_

0.805 (0.054)

0.797 (0.057)

-

-

13

13

13

13

23

23

23

23

0.914

1.082

0.600

0.655

0.0

0.0

0.0

0.0

q

N

Long Run Elasticities Illiteracy Female RPCGMP

0.241

RGMELEXP

0.189 0.081

0.132

Notes : 1. This table replace the Male Illiteracy by an Index of Health Professionals which is defined as Doctors + Midwives + Nurses + Paramedics in 1985. 2. Refer to Table 1 for definitions of other variable and notes on the models and data. 3. Country List: African developing countries: Benin, Bostwana, Egypt, Ghana, Burkina Faso, Kenya, Morcoco, Mali, Rwanda, Senegal, Tunisia, Uganda, Zimbabwe. Other developing countries: Bangladesh, Bolivia, Brazil, Columbia, Costa Rica, Dominican Republic, Ecuador, EL Salvador, Guatemala, Haiti, Honduras, Indonesia, Iran, Mexico, Nepal, Pakistan, Paraguay, Peru, Sri Lanka, Syria, Thailand, Trinidad and Tobago, Uruguay.

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explanatory variables in the first table are female and male illiteracy rates, real per capita GNP, real government expenditures on health, dummy variables for time periods and (in the dynamic case) the previous mortality rate. Since there are three time observations, two dummy variables are included in the static case (for 1980 and 1985) but only one in the dynamic model (for 1985); the reduced form equation (2) for initial observations has a separate intercept term. The variables are expressed in natural logarithms. The estimated coefficients of are thus the short run elasticities of infant ( a ) and under-five ( a ) mortality rates with respect to the explanatory variables. Since the dynamic model contains lagged q as a regressor, the long run elasticity is the short run impact divided by (l-a), a being the estimated coefficient of lagged q. There are several noteworthy features of the results in Table 1. Firstly, the coefficient of female illiteracy is statistically significant in the q and q relationships for African countries in both static and dynamic models. The estimated long run elasticities are close to unity for a and appear to exceed unity in the q relationship. On the other hand, male illiteracy rate is usually insignificant in the models. The results show that African countries with higher female literacy experience significantly lower infant and child mortality. The results for non-African countries also indicate beneficial effects of female literacy; the estimated elasticities are in the range 0.20-0.30. Secondly, the long run elasticities of q and q with respect to the real per capita GNP (RPCGNP) for African countries are, respectively, 0.22 and 0.16. The corresponding elasticities with respect to real government expenditures on health (RGHELEXP) are about 0.09 for q and q . One would expect different components of the RGHELEXP such as expenditures on midwives and innoculations to have differential effects on q and q . However, given the level of aggregation used to construct national figures and the small sample size, a further analysis of the present data is infeasible. Thirdly, the RPCGNP and RGHELEXP are statistically insignificant for non-African countries. This may in part be due the fact that most of the countries in the sample are in South America. The high rates of inflation during the observation period may have adversely influenced the conversion factors used by Summers and Heston (1988); both GNP and GDP variables show a relatively high degree of variability. Replacing the GNP and GDP for African countries by the corresponding figures from Summers and Heston (1988) lowered the elasticities of RPCGNP and RGHELEXP. The estimated coefficients, however, remained statistically significant. Fourthly, dummy variables for 1980 and 1985 are estimated with negative coefficients indicating a decline in mortality. The cross-sectional regressions for 1985 (when illiteracy data are available) supported the empirical results in Table 1. However, the estimates from latter regressions were not as precise and hence are not reported in this paper. Lastly, estimated coefficients of the lagged dependent variables are relatively small for African countries; estimates for other countries are significantly below unity. Thus treating the initial observations as endogenous in the system and controlling for the heterogeneity in the data yields plausible estimates when models for child mortality are specified in levels. This is in contrast with the results of Aturupane et al. (1994) where

Infant and Child Mortality Rates in Developing Countries

the coefficients of lagged mortality rate exceed unity. As noted in Section 2.3, least squares estimates of the parameters in the dynamic levels equation are misleading when T is small (T = 2). Moreover, in the presence of explanatory variables in the model, the biases in least squares estimates from the levels and differenced versions of the model cannot be analytically compared. In Table 2, male illiteracy rate is replaced by an index of health professionals (average number of doctors, nurses, midwives and paramedics per 10,000 persons). This variable appears with the correct sign but is statistically insignificant in the relationships. The estimated long run elasticities of female illiteracy are similar to the results obtained for African countries (Table 1). For non-African countries, however, the elasticities in Table 2 are in the 0.60-0.65 range. The increase in elasticities suggests that the estimated parameters for non-African countries are not robust to changes in model specification. This could be due to the differences amongst countries in the sample. Also, the number of observations used in estimation is small. Finally, we note that dynamic and static models were estimated for q . q , African and non-African countries with additional variables such as population per doctor, percentage of population with access to safe water, an index of children innoculated against titanus, dyptheria, tuberculosis and malaria, food availability, etc. These regressors were included with the significant determinants, namely female illiteracy RPCGNP, RGHELEXP and the dummy variables. Coefficients of the additional variables were insignificant even for African countries. Apart from the reasons outlined above, inequities in distribution of health facilities and services may be responsible for the lack of statistical significance of these variables; such issues are discussed in the next section. 5.CONCLUSION The models estimated in this paper for infant and child mortality rates in African and nonAfrican developing countries show the importance of female literacy. Also, per capita GNP and government expenditures on health are important for African countries. The elasticities are useful for understanding the broad effects of developing the infrastructure in different sectors of the economy. Programs for female education in areas with exceptionally high child mortality are likely to be beneficial for child health. For reasons discussed below, it would be desirable to conduct further studies for designing comprehensive policies for specific countries. Firstly, the effects of policy instruments on child mortality are likely to depend upon the distribution of services and medical facilities within a country. For example, in a country with sparsely populated rural areas and good water quality, access to medical care especially at birth will enhance child survival, in contrast, densely populated urban areas will benefit from governement investments in sanitation and water quality. Female literacy is also important in both situations. Since child mortality is an important indicator of economic and social development, the efficacy of public polices for a country will be enhanced by supplementing our results with studies based on regional and household level data. Secondly, a knowledge of the interaction effects between female literacy and variables such as governement expenditures on health would be useful from a policy standpoint. To a certain extent, the logarithmic specification embodies such non-

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linearities. However, since literacy rates are available only at a single point in time, the treatment of the interaction term as a time varying variable entails some stringent assumptions. The formulation of health policies will benefit from a coordinated effort by international agencies and national governments to compile economic, demographic and health and environmental variables at similar time intervals. Thirdly, in studies using household data, female education is sometimes found to have negligible effects on child morbidity and mortality (e.g. Behrman, 1991). This seems implausible since educated women are aware of benefits from hygiene and are more likely to use medical facilities, however, in areas where a large proportion of women are illiterate, educating a few women could have synergistic effects on child health. Thus average female education in the region might be associated with low child mortality. This interpretation is consistent with the empirical evidence presented in the paper; in a geographical sense, national averages are "regional" figures. Thus investments in female education imply large social gains (Subbarao and Raney, 1992). Finally, we note that in some preliminary analysis of NFHS (1995) data on approximately 21,000 children from the Indian state of Uttar Pradesh, female literacy was found to be a significant predictor of child survival. Thus the lack of statistical significance of female education in household level studies could be in part due to the relatively small sample size used in estimating probit or logit models by maximum likelihood. Overall, the results in the paper underscore the need for investing in female education, including programs for adult females during child bearing years. REFERENCES Ahmad, S. (1994) "Improving Inter-spatial and Inter-Temporal Comparability of National Accounts", Journal of Development Economics, 44, 53-75. Anand, S. and Ravallion, M. (1993) "Human development in poor countries: On the role of private incomes and public services', Journal of Economic Perspectives, 7, 113-150. Anderson, T. W. and Hsiao, C. (1981) "Estimation of Dynamic Models with Error Components", Journal of the American Statistical Association, 76, 598-606. Aturupane, H., Glewwe, P. and Isenman, P. (1994) "Poverty, human development and growth: An emerging consensus?", American Economic Review, (Papers and Proceedings), 84, 344-349. Behrman, J. (1991) "A Survey on socioeconomic Development, Structural Adjustment and Child health and Mortality in Developing Countries", in Child Survival Programs: Issues for the 1990's edited by Hill, K. (Baltimore: John Hopkins university Press) Bhalla, S. and Glewwe, P. (1986) "Growth and equity in developing countries: A reinterpretation of the Sri Lankan experience", Worid Bank Economic Review, 1, 35-63. Bhargava, A. (1987) "Wald Tests and Systems of Stochastic Equations", International Economic Review, 28, 789-808. Bhargava, A. (1991) "Identification and Panel Data Models with Endogenous Regressors", Review of Economic Studies, 58, 129-140. Bhargava, A. (1994) "Modelling the Health of Filipino Children", Journal of the Royal Statistical Society A, 157, 417-432. Bhargava, A. and Ravallion, M. (1993) "Does household consumption behave as a Martingale? A test for rural south India", Review of Economics and Statistics, 75, 500-504.

Infant and Child Mortality Rates in Developing Countries Bhargava, A. and Sargan, J. D. (1983) "Estimating Dynamic Random Effects Models from Panel data Covering Short Time Periods", Econometrica, 51, 1635-1660. Chamie, J. (1994) "Demography Population Data Bases in development Analysis", Journal of Development Economics, 44 , 131-146. Cochrane, S.H., O'Hara, D.J. and Leslie, J. (1980) "the Effects of Education on Health", World Bank Staff Working Paper #405. Dubey, A. and King, E. (1994) "A new Cross-Country Education Stock Series Differentiated by Age and Sex", World Bank Staff Working Paper. Goldstein, H. (1979) The Design and Analysis of Longitudinal Studies (New York; Academic Press). Hill, K. and Pebley. A. (1989) "Child Mortality in the Developing World", Populationa and Devolopment Review, 15, 657-687. Isenman, P. (1987) "A comment on growth and equity in developing countries; A reinterpretation of the Sri Lankan experience', World Bank Economic Review, 1, 521-531. NFHS (1995) The National Family and Health Survey (institute of Population Studies, Bombay, India). Murthy, M., Guio, A-C and Dreze, J. (1995) "Mortality, fertility, and gender bias in India: A district level analysis", Population and Development Review, 21, 745-782. Preston, S. H. (1976) "Causes and Consequences of Mortality Declines in Less Developed Countries During the 20th Centuary' in Population and Economic Changes in Less Developed Countries, edited by Easterlin, R.A. (Chicago: University of Chicago press). Pyatt, G. (1987) "A f.omment on growth and equity in developing countries; A reinterpretation of the Sri Lankan experience", World Bank Economic Review, 1, 515-520. Ravallion, M. (1986) "Growth and equity in Sri Lanka: A comment", Working Paper, Australian National University. Sen, A. (1992) Inequality reconsidered: (Cambridge: Harvard University Press). Subbarao, K. and Raney, L. (1992) "Social Gains from Female Education", World Bank Staff Working Paper. Summers, R. and Heston, A. (1988) "A New Set of International Comparisons of Real Product and Prices for 130 countries, 1950-85", Review of Income and Wealth, 34,1-25. STARS (1992) World Bank Data on Diskette (Washington D. C. : World bank) Tanner, J. M. (1981) A History of the Study of Human Growth (Cambridge: Cambridge University Press) United Nations (1992) Child Mortality since the 1960s: A data base for Developing countries (New York: United Nations). United Nations Development Program (1990) Human development report. (Oxford: Oxford University Press).

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JOURNAL OF

Econometrics ELSEVIER

Journal of Econometrics 112 (2003) 225-240

= ^ ^ ^ = ^ ^ ^ ^ = www.elsevier.com/locate/econbase

Family planning, gender differences and infant mortality: evidence from Uttar Pradesh, India Alok Bhargava* Department of Economics, University of Houston, Houston, TX 77204-5019, USA

Abstract This paper modeled the proximate determinants of infant survival using the National Family Health Survey data on 11,500 women from the most populous Indian state Uttar Pradesh in the period 1982-1992. A methodological framework was developed for analyzing the interrelationships between high fertility and infant mortality, gender differences in mortality, and for modeling the effects of health care and family planning variables. Probit models were estimated by maximum likelihood taking into account simultaneity of regressors and unobserved household differences. The proximate determinants of infant survival included maternal education and age at first birth, birth interval, the number of children before family planning was first used, maternal tetanus vaccination, and child's vaccinations. Indicator variables for a boy (girl) born at a birth order higher than the "ideal" number showed that unwanted births exacerbated female mortality. © 2002 Elsevier Science B.V. All rights reserved. JEL classification: C5; C33; 112; 012 Keywords: Infant mortality; Gender bias; Family planning; Probit models; Simultaneity

1. Introduction Children in less d e v e l o p e d countries suffer from v a r i o u s f o r m s o f u n d e r - n u t r i t i o n ; it is estimated that h a l f the children are stunted a n d a s m a l l e r p r o p o r t i o n suffer from wasting ( F A O / W H O , 1 9 9 2 ) . P o o r m a t e r n a l nutritional status, u n h y g i e n i c h o m e e n v i r o n m e n t , sicknesses d u r i n g p r e g n a n c y , a n d lack o f ante-natal care a r e likely to a d v e r s e l y affect intra-uterine g r o w t h ( K u r z et al., 1 9 9 3 ; B h a r g a v a , 2 0 0 0 ) . T h u s , for e x a m p l e , b a b i e s b o r n in d e v e l o p i n g countries are shorter in length a n d w e i g h less t h a n their

*Tel.: +1-713-743-3837; fax: +1-713-743-3798. E-mail address: [email protected] (A. Bhargava). 0304-4076/02/$-see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 4 0 7 6 ( 0 2 ) 0 0 1 6 2 - 8

304

A. Bhargava counterparts in affluent societies (Falkner et al., 1994). While survival chances of retarded newborns are lower, poor access to medical care and immunization programs is likely to exacerbate infant mortality. The likely causes of child mortality in developing countries have been analyzed in demographic research using data on large numbers of households (e.g. Hobcraft et al., 1983; Cleland and Sathar, 1984; Mohamed et al., 1998). While large surveys cannot observe women's nutritional status during pregnancy, analyses adopting a general framework are useful (Mosley and Chen, 1984). For example, hazard analysis of the data from Sri Lanka (Trussell and Hammerslough, 1983) has influenced subsequent research explaining child mortality by demographic, socioeconomic, and health care variables (e.g. Muhuri and Preston, 1991). The longitudinal study in Bangladesh has led to insights into the causes of excess female mortality (Chen et al., 1981; Koenig et al., 1990). An important aspect of modeling the proximate determinants of child survival is the use of a framework capable of addressing a wide range of conceptual and methodological issues; conclusions from statistical analyses depend on the postulated model and the estimation method employed. For example, inter-relationships between fertility and child mortality are often discussed in the demographic literature. While some researchers have argued that a high probability of child survival is necessary for couples to use family planning (Taylor et al. 1976), others have suggested that excess or unwanted fertility exacerbates child mortality (Scrimshaw, 1978; Cleland, 1996). From an empirical standpoint, however, it is essential to draw testable implications from such hypotheses and specify statistical models accordingly. The possible direction of causality in the fertility-mortality relationship can be investigated in a framework that tackles methodological problems such as simultaneous determination of explanatory variables, and conceptual issues such as the effects of desired fertility and access to family planning on child survival. Another important example of the relevance of model specification issues is the work by Muhuri and Preston (1991) and Muhuri (1996) emphasizing the effects of sex composition of children in the household on child mortality in Bangladesh. The model, however, is formulated in a restricted way introducing a limited number of indicator variables to represent the possible sex-composition scenarios. Moreover, the estimation method ignores problems of simultaneity that arise when the number of surviving brothers and sisters are included as explanatory variables; survival chances of older siblings and the index child are determined by similar factors. Consequently, the parameters would be inconsistently estimated. The structure of this paper is as follows: the data from the National Family Health Survey (UPS, 1995) are described in Section 2. Uttar Pradesh was selected because in 1991, it had a population of approximately 140 million and the total fertility rate was 5.1. In Section 3, a framework is developed for modeling the effects of demographic, socioeconomic and family planning and health care variables on infant (under-1) survival. First, the inter-relationships between fertility, family planning and child mortality are examined. Second, it is noted that the number of surviving older brothers and sisters should be directly introduced into models explaining infant survival. Third, a random effects estimator is used to tackle endogeneity of regressors and the unobserved between

Family Planning, Gender Differences and Infant Mortality household differences. The empirical results for infant survival in UP are presented in Section 4. The models are separately estimated for the data covering the previous 10 and 5 year periods; the latter contain additional information on ante-natal care and child vaccinations.

2. Data and definitions The National Family Health Survey (NFHS) was coordinated in 1992-1993 by the International Institute for Population Sciences with support from the U.S. Agency for International Development (UPS, 1995). The sample was representative of the population and covers approximately 90,000 ever-married women in the age group 13-49 years from 25 Indian states. There are approximately 11,500 women from Uttar Pradesh where roughly 20% of the households reside in urban areas. There was retrospective information on households' background characteristics, land holding, caste, religion, dwelling space, possessions, etc. Information was also gathered on certain sanitation and environmental variables such as the type of toilet used and source for drinking water. While variables such as number of rooms in the house may not correspond to the period during which the index child was born, changes in such variables were likely to be small for households living in poverty. The data on child mortality were compiled using information on all live births during the previous 15 years. To avoid possible errors in recalling events such as the age of a child at time of death, the present analysis utilized information on births in the period 1982-1992. For children who died, age at the time of death was imputed using alternative methods to minimize measurement errors. For every woman, information was gathered on education, age at marriage, fertility, and family planning practices. Fertility preferences were investigated by posing hypothetical questions such as "How many of these children [the ideal number] would you like to be boys and how many would you like to be girls?" The answers to such questions were translated into indicator variables. An indicator variable for boys used in the analysis assumed the value one if a boy was born at parity where the preceding number of male births exceeds the ideal number of boys; the corresponding indicator variable for girls was analogously defined. The women were asked "Do you agree or disagree that an Indian family should have no more than two children?" Use of family planning was investigated by recording the point in time when contraceptive was first used. For the 5-year period (1988-1992), detailed information was available on households' access to immunization programs and medical services. For example, variables such as whether the woman received ante-natal care, was visited by a health care worker during pregnancy, was inoculated against tetanus, etc, were in the data. There was information on whether the child was inoculated against polio, diphtheria, tetanus, etc. Place of delivery and complications during pregnancy were recorded. Two data sets were created for the analysis. In the first case, the models explained probability of infant survival by demographic and socioeconomic variables and by variables reflecting the utilization of family planning services. Secondly, information on health care

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Table 1 Child mortality figures for the data from Uttar Pradesh (1982-1992) a Total

Number of children born Number of children dead

Age at time of death Less than 30 days 1-6 months 7-12 months 13-24 months 25-36 months 37-48 months 49-60 months

Urban

Rural

Boys

Girls

Boys

Girls

21620 3165 (14.6)

2059 167 (8.1)

1898 185 (9.7)

9133 1343 (14.7)

8530 1470 (17.2)

1578 (7.3) 459 (2.1) 486 (2.2) 379 (1.8) 141 (0.6) 81 (0.4) 41 (0.2)

95 (4.6) 24 (1.2) 17 (0.8) 14 (0.7) 6 (0.3) 7 (0.3) 4 (0.2)

75 (4.0) 31 (1.6) 35 (1.8) 27 (1.4) 14 (0.7) 3 (0.1) 0 (0.0)

736 (8.1) 200 (2.2) 175 (1.9) 137 (1.5) 42 (0.5) 34 (0.4) 19 (0.2)

672 (7.9) 204 (2.4) 259 (3.0) 201 (2.4) 79 (0.9) 37 (0.4) 18 (0.2)

"Figures in parentheses are the percentage of children who died.

and immunization program use in the period 1988-1992 augmented the explanatory variables. Comparison of the results for the two cases can provide insights into the importance of health care programs for infant survival. Table 1 reports the number of children born in the period 1982-1992 and mortality in the different age groups; figures are presented separately for boys and girls in urban and rural areas. It was evident that approximately 80% of children who died in this period were less than a year old. Also, female mortality in rural areas was higher in age groups 7-12 months and 13-24 months. Further, since information on immunization and health care programs was available during the 1988-1992 period, it seemed fruitful to focus on infant (under-1) mortality. This is because a higher proportion of infant deaths would be included in the infant mortality data than in the situation where, for example, under-2 child mortality figures were used. The data covering the 4-year sub-period (1988-1991) were also analyzed to examine if exclusion of children who may have died in 1992 after the survey affected the empirical results. Excess female mortality in the age group 13-24 months was investigated using under-2 mortality figures (the results for infant and under-2 survival were very similar). Table 2 reports sample means and standard deviations of selected explanatory variables used in the models for infant survival. Sample means of boys and girls born in this population were very close to those reported for the prospective Matlab study in Bangladesh (Muhuri, 1996).

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307

Table 2 Sample means and standard deviations of selected variables3 Variable 11

Mother's education

Total number of rooms No toilet0 Mother's age at first birthd Birth interval11 Total number of children Ideal number of boys Ideal number of girls Indian families should have no more than two children0 Approve family planning0 Use family planning0 Number of children before using family planning Mother vaccinated (tetanus )0,e Child vaccinated°'e Sample size

Urban

Rural

1.520 (1.898) 2.518 (2.087) 0.214 (0.410) 20.076 (3.051) 2.265 (1.683) 4.259 (2.332) 1.796 (0.928) 1.176 (0.625) 0.645 (0.478) 0.791 (0.407) 0.313 (0.464) 3.753 (2.406) 0.682 (0.466) 0.430 (0.500) 3957

0.361 (0.949) 3.119 (2.523) 0.929 (0.256) 19.070 (2.771) 2.316 (1.558) 4.755 (2.416) 2.216 (0.944) 1.350 (0.705) 0.561 (0.496) 0.637 (0.481) 0.159 (0.366) 4.413 (2.439) 0.357 (0.479) 0.311 (0.463) 17 663

a

Standard deviations are in parentheses. Categorical variable 0-5. indicator variable (Yes = 1, No = 0). d In years. e Based on the period 1988-1992. b

3. Modeling the proximate determinants of infant survival 3.1. Family planning and the fertility-mortality

inter-relationships

The inter-relationships between fertility and child mortality are dynamic in nature and depend on the economic and social development in the region. Historically, when family planning methods and medical care were unavailable, maternal health and interactions between children's genotype and nutritional factors determined survival. Thus, a large number of children were born and a relatively small proportion survived. The prospects of child survival have improved in recent years even in backward areas such as rural

308

A. Bhargava Uttar Pradesh. This will influence parents' perception of the desired family size. For example, the statistics in Table 2 showed that 65% of urban women and 56% in rural areas agreed that Indian families should not have more than two children. Moreover, 79% of urban women and 63% rural women approved the use of family planning. The figures for actual use were 31% and 16%, respectively, presumably reflecting poor access to such services. In discussing the effects of child mortality on fertility (or vice versa), it is helpful to indicate the time frame in which implications of the theory are likely to hold. For example, some proponents of the "child survival hypothesis" have suggested that couples are unlikely to adopt family planning unless they are confident that the desired number of children will survive. This can strictly be true for irreversible procedures such as sterilization. More importantly, contraceptive use and its timing, while reflecting parental expectations regarding child survival, affect the survival chances of existing children and future births. For example, parents in affluent societies can be confident of child survival shortly after birth. By contrast, child mortality is high in developing countries and the pattern more complex. The under-5 mortality figures in Table 1 showed that 91% of children in Uttar Pradesh who died were less than 2 years old; it could take 2-3 years for survival uncertainties to be resolved. Thus, irreversible family planning procedures are unlikely to be appealing in developing countries unless couples have surpassed their reproductive goals and access to contraceptives is poor. Further, if family planning services are unavailable in the period following a birth, then risk of pregnancy would be high, once the post-partum amenorrhea due to breastfeeding is over. The ensuing pregnancy would demand rapid replenishment of vital nutrients such as iron and calcium to support fetal growth (Scrimshaw, 1996). This is difficult in developing countries because bioavailability of such nutrients from staple foods such as cereals is low; nutrient losses due to infections diminish women's capacity to produce healthy infants. Depending on parity, frequent pregnancies reduce the time available for child care and subsistence activities (Bhargava, 1997). Thus, an unmet need for family planning is likely to result in large number of children born in a relatively short interval; short birth intervals are associated with increased risk of mortality (e.g. Hobcraft et al., 1983; Gribble, 1993; Nath et al., 1994). If, however, women use family planning, then births can be spaced. This would be beneficial for health of the surviving children and improve the prospects of carrying the subsequent pregnancy to full-term. Early use of contraceptives is therefore likely to enhance infant survival. Now, at a given point in time, direction of causality in the fertility—mortality interrelationship has certain asymmetric implications for infant mortality. High mortality at low order births is likely to influence parents' decision to have more than the desired number of children. By contrast, if mortality is the result of a large number of unwanted births, then children born at higher parities would be at greater risk. There may also be gender differences; researchers have reported excess female mortality at higher parities in India (Das Gupta, 1987). However, mortality rates for first-born children are high (Bongaarts, 1987; Trussell, 1988). From a biological viewpoint, there is competition for nutrients between the fetus and the young mother's own requirements for growth (Falkner et al., 1994). Multivariate analyses can partially control for this by including

Family Planning, Gender Differences and Infant Mortality maternal age at first birth as an explanatory variable; some additional methodological issues are discussed in the next two sections. 3.2. Some aspects of model formulation for the infant survival relationship In the absence of family planning, the total number of live births to a woman will chiefly depend on her fecundity, nutritional status, age at marriage and the breast-feeding patterns. The number of surviving children is affected by demographic, socioeconomic and health care variables. Another important aspect of modeling the proximate determinants of infant survival in south Asian countries is that parents may desire a certain number of sons (Chen et al., 1981; Sen and Sengupta, 1983). This has led Muhuri and Preston (1991) and Muhuri (1996) to postulate that the surviving older brothers and sisters differentially affect survival chances of the index child. At a conceptual level, differential effects of older boys and girls on index child's survival raise some interesting questions. For, it is common in poor households for young girls to spend a proportion of their time on household tasks. This is not the case for boys especially in rural areas where adult males undertake strenuous work. Further, intra-uterine growth retardation is likely to increase with parity (Al et al., 1997; Bhargava, 2000); mothers also have less time for care of children born at higher parities. Thus older sisters can fill the child care gap. While survival chances of siblings are likely to be positively correlated, care given by girls will strengthen the coefficient of older sisters in the model explaining index child's survival. This phenomenon can be investigated to a limited extent using the data from Uttar Pradesh due to certain methodological issues. First, Muhuri and Preston (1991) represented households' sex composition by indicator variables for cases such as where 1, 2 or more older brothers or sisters are present. These variables and interactions between them were used as explanatory variables in the model explaining child mortality. The numerous sex compositions in the sample, however, cannot be captured in this way. More importantly, without an appropriate benchmark defining the indicator variables, it is difficult to interpret the coefficients. This problem can be circumvented by including the actual number of surviving older brothers and sisters as explanatory variables. Second, it is difficult to fully capture age differences between older brothers and sisters and the index child since households have different age and sex composition of children. While the age gap reflects capacity of older children to provide care, one cannot easily develop an "index" of child care. The model for infant survival can include birth interval and the number of surviving older brothers and sisters as regressors; unobserved household effects will partially reflect age distribution of children. It would be useful to collect information on time allocation patterns of girls and boys. Third, survival chances of older brothers and sisters and the index child are determined by a similar set of factors; errors affecting infant survival relationship are likely to be correlated with these explanatory variables. This will lead to inconsistent estimates of the parameters from probit or logit models. Other regressors can also be simultaneously determined. For example, inasmuch as couples have access to family planning, the number of surviving children before contraceptive is used is potentially

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310

an endogenous variable. Similarly, while birth interval has been found positively associated with child survival, researchers have argued that short birth intervals are the result of mortality of the preceding child. It is important to use suitable econometric methods for estimating the model parameters. 3.3. Sources of endogeneity and the econometric estimation A major source of simultaneity in the infant survival relationship is that the determinants of survival of older siblings and the index child are similar; the number of surviving children before a family planning method is used is potentially an endogenous variable since it reflects parental preferences about family size. If, however, the estimation method addresses the prime source of endogeneity (i.e. number of surviving children), then it is likely that statistical tests will accept exogeneity hypothesis for the decision to use family planning. Similarly, while birth interval may be affected by death of the preceding child, the problem of reverse causality can be circumvented by controlling for survival status of older siblings. A probit model explaining the survival to age one year of N live births (_yt) by m endogenous variables (Yt) and n exogenous variables (Xu) is given by y, = Y!y+X{tP + Ui, Yi=P'Xi+Vi,

(i = 1,2,. ..,N),

(i = l,2,...,tf).

(1) (2)

Eq. (1) is the "structural" model for the dichotomous variable y that is one if the child dies before reaching the age of one, and zero otherwise. The coefficients of Y and X\ are represented by m x 1 and nx\ vectors y and jS, respectively. Eq. (2) is a "reduced form" for the m endogenous variables in Eq. (1), with a m x n coefficient matrix P'; V is an m x 1 matrix of reduced form errors. It is assumed that certain exogenous variables are excluded from the structural model for identifying the parameters (e.g. Newey, 1987; Rivers and Vuong, 1988). The errors in Eqs. (1) and (2) are assumed to be jointly normally distributed. Further, assuming that there are H households in the sample with different number of live births, errors affecting Eqs. (1) and (2) will have an unbalanced structure. Treating the household effects as randomly distributed variables, the errors in Eq. (1) can be decomposed as Uhj = o'h+whj

(j=\,...Jh,h=\,2,...,H\

(3)

where <5's are household specific random effects, w's are randomly distributed variables, and Jh is the number of live births in household h. Similarly, random effects can be introduced in reduced form Eq. (2); the errors on the first endogenous variable in (2) can be written as Vikj = hh+wihj

(j=l,...,Jh;h=l,2,..-,H).

(4)

Even in the absence of random effects, estimation of the system given by Eqs. (1) and (2) is complicated because the "nuisance" parameters in the reduced form (2) cannot be eliminated by step-wise maximization (Koopmans and Hood, 1953). Thus,

Family Planning, Gender Differences and Infant Mortality researchers have used "conditional" likelihood functions assuming that the errors in Eqs. (1) and (2) are jointly normally distributed (Smith and Blundell, 1986). This entails working with the density of «,• conditional on V,in (1) and substituting a consistent estimator of P from Eq. (2) in the modified Eq. (1). Model parameters are then estimated by maximum likelihood using a numerical optimization scheme; standard errors are obtained using a Taylor series expansion. The conditional likelihood function with random effects has been developed by Vella and Verbeek (1999); software packages (e.g. LIMDEP, 1995) can be extended to estimate the parameters. Because the errors have a random effects structure, it is necessary to include two covariance terms per endogenous variable in Eq. (1). Exogeneity of a variable is tested by testing the null hypothesis that coefficients of covariance terms computed from the reduced form residuals are zero. Lastly, in instrumental variables estimation, it is desirable that the instruments are strongly correlated with the endogenous variables (Hotelling, 1936; Sargan, 1958). Because correlations are low in cross-sectional analysis, instrumental variables methods can lead to poor results. This issue was discussed by Bhargava and Sargan (1983) for dynamic models estimated using longitudinal data. Recently, Bound et al. (1995) have underscored its importance; Bollen et al. (1995) discuss certain problems arising in probit models. The approach in this paper reports the results for the cases where endogeneity of regressors is ignored and where it is addressed.

4. The empirical results Tables 3 and 4 present maximum likelihood estimates of probit models for infant survival for the periods 1982-1992 and 1988-1992, respectively. The tables contains four specifications. In Model 1, the problem of multiple children in households is ignored. Model 2 introduces random effects to capture the unobserved between household differences. The number of surviving older brothers and sisters are treated as endogenous variables in Model 3; the instruments used are the household's possessions and number of older boys and girls born before the index child. Lastly, in last column, the coefficients estimated for Model 3 are converted into the respective marginal effects of the explanatory variables. 4.1. Empirical results for the period 1982-1992 The results for Models 1 and 2 in Table 3 have some interesting features. First, the indicator variable for rural areas was estimated with a negative coefficient indicating lower survival probability in rural areas. The model parameters were broadly similar when the model was separately estimated for urban and rural samples. Second, while the sample statistics in Table 2 showed mortality of girls to be higher in rural areas, coefficient of the indicator variable for girls was not significantly different from zero. Interestingly, the indicator variable that is equal to one if a girl was born at a parity higher than the ideal number was negative and significant in all three specifications.

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Table 3 Maximum likelihood estimates of probit models for infant survival in Uttar Pradesh for the period (1982-1992) Variable

Model 1

Model 2

Model 3

Marginal

Constant

1.126* (0.097) -0.146* (0.045) 0.052 (0.038) -0.228* (0.039) -0.119* (0.035) 0.134* (0.013) 0.074* (0.013) 0.065* (0.012) 0.009* (0.004) 0.170* (0.010) -0.091* (0.006) -0.131* (0.043) 0.012* (0.005)

1.155* (0.100) -0.139* (0.050) -0.046 (0.040) -0.219* (0.041) -0.111* (0.037) 0.127* (0.013) 0.066* (0.013) 0.068* (0.013) 0.010* (0.004) 0.176* (0.007) -0.089* (0.006) -0.143* (0.047) 0.014* (0.006)

—

Covariance term 1 (girls)

—

—

Covariance term 2 (girls)

—

—

Covariance term 1 (boys)

—

—

Covariance term 2 (boys)

—

—

1.227* (0.103) -0.137* (0.051) 0.075 (0.045) -0.251* (0.044) -0.053 (0.040) 0.125* (0.016) 0.060* (0.015) 0.062* (0.014) 0.006 (0.004) 0.160* (0.006) -0.073* (0.008) -0.147* (0.049) 0.017* (0.007) 0.078* (0.003) -0.222* (0.009) 0.179* (0.008) -0.271* (0.007) 0.252* (0.039)

Indicator for rural areas Indicator for girls Indicator for girls born after the ideal number Indicator for boys born after the ideal number Number of older girls Number of older boys Mother's education Mother's age at first birth Birth interval Number of children before family planning Indicator for no toilet Number of rooms

Rho

0.267* (0.038)

-0.020* (0.007) 0.011 (0.006) -0.036* (0.006) -0.008 (0.006) 0.018* (0.002) 0.009* (0.002) 0.009* (0.002) 0.001 (0.001) 0.023* (0.001) -0.011* (0.001) -0.021* (0.007) 0.002* (0.001) 0.011* (0.001) -0.032* (0.001) 0.026* (0.001) -0.039* (0.001)

There were 21512 live births; Model 3 treats number of older boys and girls as endogenous; the last column reports the "marginal effects" for the parameter estimates in Model 3; asymptotic standard errors are in parentheses; covariances terms are conditional expectations of errors in Eq. (1); Rho is the proportion of variance due to random effects; * p < 0.05.

This suggest that survival chances of girls and boys born at low parities were similar but mortality was greater for girls born at higher parities. Third, the number of surviving older brothers and sisters were positively associated with survival chances of the index child. Since older sisters are likely to take

Family Planning, Gender Differences and Infant Mortality

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Table 4 Maximum likelihood estimates of probit models for infant survival in Uttar Pradesh for the period (1988-1992) Variable

Model 1

Model 2

Model 3

Marginal

Constant

0.912* (0.165) -0.037 (0.075) 0.114** (0.063) -0.208* (0.066) -0.016 (0.059) 0.185* (0.024) 0.125* (0.024) 0.0001 (0.020) 0.002 (0.007) 0.180* (0.016) -0.124* (0.014) 0.289* (0.047) 1.001* (0.063) -0.117 (0.072) 0.007 (0.009)

0.912* (0.164) -0.037 (0.075) 0.114** (0.063) -0.208* (0.065) -0.016 (0.060) 0.184* (0.022) 0.126* (0.023) 0.0002 (0.020) 0.002 (0.007) 0.180* (0.014) -0.124* (0.012) 0.289* (0.047) 1.001* (0.066) -0.117 (0.070) 0.007 (0.009)

—

Covariance term 1 (girls)

—

—

Covariance term 2 (girls)

—

—

Covariance term 1 (boys)

—

Covariance term 2 (boys)

—

1.103* (0.167) -0.047 (0.077) 0.170* (0.068) -0.261* (0.070) -0.035 (0.061) 0.227* (0.030) 0.162* (0.032) -0.001 (0.020) -0.001 (0.007) 0.186* (0.014) -0.138* (0.017) 0.282* (0.049) 0.988* (0.069) -0.104 (0.072) 0.006 (0.009) 0.053* (0.014) -0.280* (0.018) 0.223* (0.024) -0.094* (0.014) 0.127 (0.182)

Indicator for rural areas Indicator for girls Indicator for girls born after the ideal number Indicator for boys born after the ideal number Number of older girls Number of older boys Mother's education Mother's age at first birth Birth interval Number of children before family planning Indicator for tetanus vacc. Indicator for child vacc. Indicator for no toilet Number of rooms

Rho

— 0.001 (22.817)

-0.005 (0.008) 0.018* (0.007) -0.028* (0.008) -0.004 (0.007) 0.025* (0.004) 0.018* (0.004) -0.0001 (0.002) -0.001 (0.001) 0.018* (0.002) -0.015* (0.002) 0.031* (0.005) 0.107* (0.007) -0.011 (0.008) 0.001 (0.001) 0.006* (0.001) -0.030* (0.002) 0.024* (0.003) -0.010* (0.002)

There were 9674 live births; *p < 0.05; **p < 0.10; see notes to Table 3.

care of younger siblings, one would expect the coefficient of girls to be higher than the corresponding estimate for boys, which was the case. The null hypothesis that coefficients of boys and girls are the same was rejected by a likelihood ratio test. Maternal education, measured by a categorical variable assuming six different values, was

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A. Bhargava significantly associated with infant survival. There were some non-linearities apparent in the relationships between infant survival and maternal age at first birth and the number of surviving older sisters. For example, the squared term for older sisters was estimated with a negative coefficient that was marginally significant, indicating an adverse effect after couples have had a certain number of girls. While the overall results were similar to those reported in Table 3, the positive coefficient of the number of surviving older sisters should be interpreted in this light. Fourth, birth interval was significantly positively associated with infant survival. The number of surviving children before a family planning method was used was negatively associated. Note that if the woman did not use family planning, this variable was set equal to the number of surviving children. Because the model accounted for survival status of children born before the index child, early use of family planning was beneficial for infant survival. Fifth, the indicator variable for not having a toilet was negatively associated with probability of infant survival; having access to piped water was positively associated in certain specifications. The number of rooms was positively associated. Environmental variables are likely to gradually affect health indicators such as anthropometric measurements and morbidity (Bhargava, 1994). Because these indicators are expensive to measure in large surveys, the relationship between environmental variables and infant survival is a useful proxy for the underlying biological relationships. Sixth, the household specific random effects were statistically significant in Model 2; approximately 25% of the residual variance was due to the unobserved between household differences. However, there were only minor differences in the results for Models 1 and 2. This could be due to the fact that explanatory variables such as number of rooms in the house and maternal education accounted for many of the between household differences. The small unobserved differences suggest that latent factors common to survival chances of siblings may also be small in magnitude. Seventh, the results for Model 3 that treats the number of surviving older brothers and sisters as endogenous variables, were close to those reported for Models 1 and 2. However, coefficients of the covariance terms were statistically different from zero thereby rejecting the exogeneity null hypotheses for these variables. Coefficients of the number of older brothers and sisters in Model 3 were not noticeably different from the corresponding estimates in Model 2 that ignored endogeneity problems. The remaining estimates were close in all three specifications; the proportion of variance explained by random effects was similar in Models 2 and 3. While minor violations in statistical assumptions are not likely to dramatically alter parameter estimates because of the large sample size, the estimates were dependent on the use of number of preceding male and female births as instruments. These variables were highly correlated with the number of surviving older children and are exogenous in the absence of family planning. Even when family planning is used, it is likely that the unobserved errors affecting infant survival are related to factors such as the maternal nutritional and health status, and environmental factors such as sanitation and hygiene. Eighth, exogeneity hypothesis for the number of surviving children before a family planning method is used was tested; coefficients of the covariance terms for this variable were not statistically different from zero. This is perhaps not surprising since the

Family Planning, Gender Differences and Infant Mortality prime source of simultaneity was the number of surviving children. Once this is taken into account, statistical procedures were unlikely to find a relationship between family planning decisions and the unobserved factors affecting infant survival. Lastly, because of the presence of random effects and endogenous regressors in Model 3, standard errors of the estimated parameters were computed by a bootstrap procedure; the results were close (Bollen et al., 1995). 4.2. Empirical results for models including immunization variables (1988-1992) In addition to the variables used in Table 3, the models in Table 4 included indicator variables for whether the mother was vaccinated against tetanus and if the child was vaccinated. The estimated coefficients of these variables were large and statistically significant thereby showing the importance of health care programs for infant survival. The analysis was repeated using data for the period 1988-1991 (excluding the births in 1992) to avoid the problem that some infants may have died shortly after the survey. However, the empirical results for the past 4 and 5 years were very close. Because children are typically vaccinated around the age of 3 months, the indicator for child vaccination was dropped from the models to investigate the robustness of the results. This led to a change in coefficient of the indicator variable for maternal tetanus vaccination though the remaining estimates were similar. In contrast with the results in Table 3, coefficients of maternal education and age at first birth, indicator variable for not having a toilet and the number of rooms in the house were not statistically significant in Table 4. This could be due to the reduction in the sample size though there was also a decline in the magnitudes of these coefficients. This was not true for variables such as birth interval and number of children before a family planning method was used; the estimated coefficients of family planning related variables were more robust changes in model specification. The indicator variable for rural areas was insignificant in Table 4. The indicator variable for girls was significant though with a positive sign. By contrast, the indicator variable for girls born at a higher parity than the ideal number had a negative coefficient. These results suggest that girls born at low parities were not at a disadvantage which could be due to better maternal nutritional status and also because daughters' contribution to housework is viewed favorably. This would not be the case for girls born at high parities who face greater growth retardation and increased competition for resources, including medical care. The indicator variable for boys born after the ideal number was not significant in Table 4, suggesting the possibility of a selective neglect of girls born at high parities.

5. Conclusion The proximate determinants of infant survival were modeled in this paper using data from Uttar Pradesh, the most populous Indian state. The analysis extended previous demographic research by emphasizing the role of model formulation. Using a suitable parameterization for sex composition of older siblings and addressing issues of

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simultaneity, the empirical results yielded new insights. The number of older brothers and sisters was found to differentially affect the survival probability of the index child, with older sisters possibly filling in the child care gap. Moreover, indicator variables constructed on the basis of the stated preferences for sons and daughters indicated that unwanted fertility contributes to excess mortality of higher order births, especially of girls. Family planning programs are therefore likely to narrow gender differences in infant mortality. Further, studies explaining variation in average fertility rates in developing countries by couples' fertility preferences (Pritchett, 1994) should not be viewed as casting doubt on the efficacy of family planning programs. This is because fertility also depends on socioeconomic variables and access to family planning services; such factors are masked in analyses using cross-country data on average fertility rates. From the standpoint of the effects of maternal education on infant mortality (Bicego and Boerma, 1993; Murthi et al., 1995), it is likely that educated mothers take better care of themselves and the infant. However, the results in Tables 3 and 4 indicated that family planning and immunization programs had a greater impact on infant survival. Since a majority of women in rural Uttar Pradesh are uneducated, adult education programs would require substantial resources. Investments in family planning and immunization programs are also expensive but are likely to prevent infant mortality in a shorter time frame. Female education should be an important policy goal; parental scores on cognitive tests were predictors of Kenyan children's physical and intellectual development (Bhargava, 1998, 1999). Policies exploiting synergisms between female education and health care and family planning use are likely to be cost-effective. Finally, public policies are unlikely to have the desired -effect on children's lives unless they control unwanted fertility (Cleland, 1996). Even uneducated parents are aware of bleak employment prospects in rural areas; living conditions in urban slums are unlikely to be a motivating factor for large families. While customs can dampen the speed with which family planning programs are adopted, it is essential that such services reach the poor. Infants in developing countries survive if a minimal set of maternal health and nutritional requirements are met. Reducing infant mortality is a modest goal. Once this is achieved, policy makers can concentrate on policies that enhance children's physical and intellectual development via nutritional and educational programs (Scrimshaw, 1998).

Acknowledgements While retaining the responsibility for the views, the author would like to thank Amartya Sen for suggesting this topic and the Mac Arthur Foundation for partial support. Thanks are also due to Erwan Quintin and the two referees for helpful comments.

References Al, M.D.M., Houwelingen, A.C., Hornstra, G., 1997. Relation between birth order and the maternal and neonatal docohexaenoic acid status. European Journal of Clinical Nutrition 51, 548-553.

Family Planning, Gender Differences and Infant Mortality Bhargava, A., 1994. Modelling the health of Filipino children. Journal of the Royal Statistical Society A 157, 417-432. Bhargava, A., 1997. Nutritional status and the allocation of time in Rwandese households. Journal of Econometrics 77, 277-295. Bhargava, A., 1998. A dynamic model for the cognitive development of Kenyan school children. Journal of Educational Psychology 90, 162-166. Bhargava, A., 1999. Modelling the effects of nutritional and socioeconomic factors on the growth and morbidity of Kenyan school children. American Journal of Human Biology 11, 317-326. Bhargava, A., 2000. Modelling the effects of maternal nutritional status and socioeconomic variables on the anthropometric and psychological indicators of Kenyan infants from age 0 - 6 months. American Journal of Physical Anthropology 110, 89-104. Bhargava, A., Sargan, J.D., 1983. Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51, 1635-1660. Bicego, G.T., Boerma, J.T., 1993. Maternal education and child survival: a comparative study of survey data from 17 countries. Social Science and Medicine 36, 1207-1227. Bollen, K., Guilkey, D.K., Mroz, T.A., 1995. Binary outcomes and endogenous explanatory variables: tests and solutions with an application to the demand for contraceptive use in Tunisia. Demography 32, 111-131. Bongaarts, J., 1987. Does family planning reduce infant mortality rates? Population and Development Review 13, 323-334. Bound, J., Jaeger, D., Baker, R., 1995. Problems with instrumental variables estimation when the correlation between instruments and the endogenous explanatory variable is weak. Journal of American Statistical Association 90, 443-450. Chen, L.C., Huq, E., D'Souza, S., 1981.. Sex-bias in the family allocation of food and health in rural Bangladesh. Population and Development Review 7, 50-77. Cleland, J., 1996. Population growth in the 21st century: cause for crisis or celebration? Tropical Medicine and International Health 1, 15-26. Cleland, J., Sathar, Z.A., 1984. The effect of birth spacing on childhood mortality in Pakistan. Population Studies 38, 401-418. Das Gupta, M., 1987. Selective discrimination against female children in rural Punjab. Population and Development Review 13, 77-100. Falkner, F., Holzgreve, W., Schloo, R.H., 1994. Prenatal influences on postnatal growth: overview and pointers for research. European Journal of Clinical Nutrition 48, S15-S24. FAO/WHO, 1992. Nutrition and development. A global assessment. Food and Agriculture Organization, Rome. Gribble, J.N., 1993. Birth intervals, gestational age, and low birth weight: are the relationships confounded? Population Studies 47, 133-146. Hobcraft, J.N., McDonald, J.W., Rutstein, S., 1983. Child spacing effects of infant and early child mortality. Population Index 49, 585-618. Hotelling, H.( 1936. Relations between two sets of variates. Biometrika 28, 321-377. UPS, 1995. National Family Health Survey. International Institute for Population Sciences, Mumbai. Koenig, M.A., Phillips, J.F., Campbell, O.M., D'Souza, S., 1990. Birth interval and childhood mortality in rural Bangladesh. Demography 27, 251-265. Koopmans, T.C., Hood, W.C., 1953. Studies in Econometric Methods. Wiley, New York, NY. Kurz, K.M., Habicht, J.P., Rasmussen, K.M., Schwager, S.J., 1993. Effects of maternal nutritional status and maternal energy supplementation on length of postpartum amenorrhea among Guatemalan women. American Journal of Clinical Nutrition 58, 636-640. LIMDEP, 1995. Econometric Software Inc., New York. Mohamed, W.N., Diamond, I., Smith, P.W.F., 1998. The determinants of infant mortality in Malaysia: a graphical chain modelling approach. Journal of the Royal Statistical Society A 161, 349-366. Mosley, W.H., Chen, L., 1984. An analytical framework for the study of child survival in developing countries. Population and Development Review 10, 25-48. Muhuri, P., 1996. Estimating seasonality effects on child mortality in Matalab, Bangladesh. Demography 33, 98-110.

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Muhuri, P., Preston, S., 1991. Effects of family composition on mortality differentials by sex among children in Matlab, Bangladesh. Population and Development Review 17, 415-434. Murthi, M., Guio, A.C., Dreze, J., 1995. Mortality, fertility, and gender bias in India: a district level analysis. Population and Development Review 21, 745-782. Nath, D.C., Land, K.C., Singh, K.K., 1994. Birth spacing, breastfeeding, and early child mortality in a traditional Indian society: a hazards model analysis. Social Biology 41, 168-180. Newey, W., 1987. Efficient estimation of limited dependent variable models with endogenous explanatory variables. Journal of Econometrics 36, 230-251. Pritchett, L.H., 1994. Desired fertility and the impact of population policies. Population and Development Review 20, 1-55. Rivers, D., Vuong, Q., 1988. Limited information estimators and exogeneity tests for simultaneous probit models. Journal of Econometrics 39, 347-366. Sargan, J.D., 1958. The estimation of economic relationships using instrumental variables. Econometrica 26, 393-415. Scrimshaw, S., 1978. Infant mortality and behavior in the regulation of family size. Population and Development Review 4, 383-403. Scrimshaw, N.S., 1996. Nutrition and health from womb to tomb. Nutrition Today 31, 55-67. Scrimshaw, N.S., 1998. Malnutrition, brain development, learning and behavior. Nutrition Research 18, 351-379. Sen, A., Sengupta, S., 1983. Malnutrition of rural children and the sex bias. Economic and Political Weekly 18, 855-864. Smith, R.J., Blundell, R.W., 1986. An exogeneity test for a simultaneous equation tobit model with an application to labor supply. Econometrica 54, 679-685. Taylor, C.E., Newman, J.S., Kelly, N., 1976. The child survival hypothesis. Population Studies 30, 262-278. Trussell, J., 1988. Does family planning reduce infant mortality? An exchange. Population and Development Review 14, 171-178. Trussell, J., Hammerslough, C , 1983. A hazard-model analysis of the covariates of infant and child mortality in Sri Lanka. Demography 20, 1-26. Vella, F., Verbeek, M., 1999. Two-step estimation of panel data models with censored endogenous variables and selection bias. Journal of Econometrics 90, 239-263.

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ELSEVIER

ECONOMICS AND HUMAN BIOLOGY

Economics and Human Biology 3 (2005) 388-404 http://www.elsevier.com/locate/ehb

Healthcare infrastructure, contraceptive use and infant mortality in Uttar Pradesh, India Alok Bhargavaa'*, Sadia Chowdhuryb, K.K. Singh c " Department of Economics, University of Houston, Houston, TX 77204-5019, USA b The World Bank, Washington, DC, USA c Banaras Hindu University, Varanasi, India Accepted 14 September 2005

Abstract This paper analyzes data on approximately 30,000 women from a survey in Uttar Pradesh in 1995 together with the data from surveys of public and private providers of healthcare and family planning services. A framework was developed for analyzing the effects of quality of services on utilization, and for understanding the gradual evolution of the healthcare infrastructure. The empirical results from logistic regressions for use of female sterilization and IUD showed significant effects of quality of services in government and private hospitals, and of socioeconomic variables such as education, caste, and an index of household possessions. Secondly, models for infant mortality of children born in the preceding 3-year period showed significant effects of socioeconomic variables, quality of healthcare services and birth spacing. Lastly, analysis of data at a more aggregated (Primary Sampling Unit) level indicated differential effects of economic development on the quality of services available in the public and private facilities. © 2005 Elsevier B.V. All rights reserved. JEL classification: C5; C35; 112; 012 Keywords: Infant mortality; Contraceptives demand; Birth spacing; Healthcare; Economic development; Uttar Pradesh

1. Introduction Economic development generally entails the availability of a skilled labor force capable of exploiting the opportunities afforded by technological advancements in the production of goods and services. Creating a skilled labor force, moreover, requires resources for educating children and is facilitated by small family size especially for poor households (Bhargava, 2001). It is

Corresponding author. Tel.: +1 713 743 3837; fax: +1 713 743 3798. E-mail address: [email protected] (A. Bhargava). 1570-677X/S - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ehb.2005.09.001

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A. Bhargava, S. Chowdhury and K.ICSingh therefore natural for social scientists to be concerned with issues of high fertility in less developed countries. However, the previous demographic literature has followed different approaches for exploring the inter-relationships between fertility and child mortality. While Taylor et al. (1976) have argued that a high probability of child survival is necessary for reducing fertility, Scrimshaw (1978) and Cleland (1996) have emphasized that 'unwanted' fertility is likely to exacerbate child mortality. These views can be reconciled by recognizing that they potentially apply to different time frames. Historically, a decline in child mortality was likely to precede reductions in fertility. At a given point in time, however, households without access to health care typically have large families and experience greater child mortality especially at high parities (Bhargava, 2003). Further, following the work by Becker (1982), economists have emphasized that family planning programs in developing countries may be "endogenously" placed in response to health conditions in the region; more complex statistical techniques are necessary to tackle such problems (Angeles et al., 1998). While governments often require placement of public health facilities on basis of population (Koenig et al., 2000), the quality of services is likely to depend on economic development in the region; it is often difficult to relocate skilled medical personnel in remote areas. Moreover, in countries such as India, there has been a rapid rise in private providers of healthcare (Peters et al., 2002) that is likely to increase utilization and can in turn influence the quality of care in public facilities. Such issues merit analytical and empirical investigations; poor quality of public services in backward regions and increased role of private providers have different implications for child mortality than models emphasizing the endogenous placement of public facilities. The data set on 'performance indicators' of healthcare programs ('PERFORM') in Uttar Pradesh (SIFPSA, 1996) on approximately 40,000 households, and 2400 'fixed service delivery points' such as clinics and hospitals, and 22,000 'private agents' (e.g. doctors) offer an opportunity to model the proximate determinants of contraceptive use and infant mortality using indicators of service quality in public and private sectors. Previous analysis by Stephenson and Tsui (2002) has provided insights by modelling the demand for contraceptive use for a subset of households in five districts of Uttar Pradesh. However, the authors did not differentiate between terminal methods such as sterilization and the methods for birth spacing such as condoms and birth control pills. Because a majority of couples in rural areas rely on sterilization after surpassing their fertility goals, the proximate determinants of contraceptives for birth spacing and terminal methods are likely to be different. Moreover, little medical expertise is necessary for dispensing condoms and pills. By contrast, sterilization and intra uterine device (IUD) insertion require skilled services. Timing of couples' decisions to opt for terminal methods is likely to be influenced by the quality of the healthcare infrastructure. Another attractive feature of the PERFORM survey is that detailed information on ante-natal care, delivery, and post-natal care was compiled for all births in the 3 years preceding the survey. In addition, the women were asked if the child born was wanted or if they would have preferred to have had the child 'later' or 'never'. While responses to such questions might not fully assess the intensity of 'unwantedness' of births, such measures have been employed in previous demographic research (Bongaarts, 1990,1993; Montgomery et al., 1997; Marston and Cleland, 2003). From the standpoint of utilization of healthcare and family planning services, one can investigate if the approximate degree of unwantedness of births had a negative impact on the chances of infant survival. The structure of the paper is as follows: Section 2 describes the PERFORM data and outlines the variables used for constructing indices to approximate the healthcare infrastructure in public and private facilities. Section 3 develops the analytical framework; it is argued in Section 3.1 that in view of the biological and socioeconomic processes involved, it is appealing to analyze the

Contraceptive Use and Infant Mortality supply and demand for contraceptives rather than for children. Section 3.2 discusses the gradual evolution of the healthcare infrastructure with economic development and its impact on utilization and quality of public and private services available in the region. The empirical models are outlined in Sections 3.3 and 3.4, and certain estimation issues are briefly discussed. The results from estimating models for contraceptive use are presented in Section 4.1. The results from models for infant mortality are in Section 4.2 and those from an analysis of data on healthcare infrastructure in public and private facilities at the Primary Sampling Unit (PSU) levels are in Section 4.3. The conclusions are summarized in Section 5. 2. The data The PERFORM survey was designed to measure indicators of reproductive health at three levels. First, data were compiled on public and private providers of healthcare. Second, the work experience of staff in the delivery points was investigated. Finally, detailed information was compiled on married women who were likely to utilize healthcare and family planning services. The survey used a systematic multi-stage cluster sample of households and service delivery points. Two districts from each of the 14 administrative divisions were selected. The survey was carried out in 1995 in 1539 villages and 738 urban blocks within 1911 Primary Sampling Units (PSUs), interviewing 40,633 households, 2428 fixed service delivery points and 6320 staff members, and 22,335 individual service agents such as health workers and medical shops (SIFPSA, 1996). The Urban Block and Village questionnaires investigated the number of households, clinics, private practitioners, cooperatives, voluntary organizations, and industries in the region. The Household questionnaire investigated demographic composition of the household, land holding and other variables. For example, households were questioned about six possessions, i.e. if they owned a clock or a watch, fan, radio, television, bicycle, and a motorcycle, scooter, car, or a tractor. The affirmative answers were summed to form an index of possessions for approximating the socioeconomic status; the use of factor analysis led to very similar results. The Women's questionnaire covered variables such as marital status, reproductive history, access to healthcare and family planning services, quality of services, fertility preferences, and contraceptive use. There was detailed information on up to three births in the previous 3-year period. Vaccinations against tetanus and complications during and after the pregnancy were recorded. The Fixed Service Delivery Point questionnaire investigated the availability of services such as male and female sterilization, IUD insertion and medical termination of pregnancy. Providers were mapped to households in the PSU. The number of months of supply of contraceptives such as condoms and pills were inquired. Staff in the facilities, including doctors, nurses, and social workers, were interviewed to assess their qualifications. Several indices were constructed to approximate the healthcare infrastructure (Mensch et al., 1996). The number of allopathic doctors (i.e. trained in "Western" medicine) performing male or female sterilization, inserting IUD, and terminating pregnancies was calculated separately for government hospitals, community health centers, private hospitals, and private agents (i.e. medical personnel such as doctors and nurses). The total numbers of staff as well as the averages calculated over the respective types of facilities were used as indicators of the healthcare infrastructure. The use of averages enabled comparisons across groups though aggregate figures were sometimes used in the analyses. Similarly, the number of 'full-time equivalent' staff and those devoted to family planning services in public and private facilities were calculated; averages over the facilities and for private agents were used. The numbers of months of supply of condoms and birth control pills in public and private facilities and by private agents were

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A. Bhargava, S. Chowdhury and K.K. Singh calculated from responses of the providers. Because some private agents were "unqualified", the indices aggregated over the personnel that were trained for specific procedures such as sterilization and IUD insertion. Overall, indices based on the data from fixed service delivery points and private agents and the information on numbers of government and private hospitals and allopathic doctors provided an assessment of the healthcare infrastructure available to women in the PERFORM survey. The sample means and standard deviations of selected variables are presented in Table 1. The calculations were performed in SPSS (1999) using the data on contraceptive use and for women who had a birth in the previous 3-year period. Approximately 68% of the women had never attended school; average number of children was 3.49 in the sub-sample covering contraceptive use. Female sterilization was the most common method of family planning, with 15% women opting for the procedure; only 1.4% of men were sterilized. Percentages of couples using IUD, birth control pills and condoms were, 1.5, 1.7 and 3.7, respectively; only 0.7% of the women

Table 1 Sample means (or percentages) and standard deviations of selected variables in the models for contraceptive use and infant mortality estimated from the PERFORM survey from Uttar Pradesh" Mean Woman's age in years Ever attended school (1 = yes, 0 = no) Number of children born Number of surviving children Household possessions index (0-6) Backward caste (1 = yes, 0 = no) Woman sterilized (1 = yes, 0 = no) (%) Man sterilized (1 = yes, 0 = no) (%) Women using IUD (1 = yes, 0 = no) (%) Women using birth control pills (1 = yes, 0 = no) (%) Man using condoms (1 = yes, 0 = no) (%) Number of women with a birth in the 3-year period Children who died before reaching age of 1 year (%) Births wanted 'later' (%) Births wanted 'never' (%) Birth interval for birth in years Women vaccinated against tetanus (%) Number of women with two births in the 3-year period The second birth wanted 'never' (%) Average number of government hospitals in PSU Average number of private hospitals in PSU Average number of private allopathic doctors in PSU Average number of private doctors trained in terminal FP methods in PSU Average family planning staff—government hospitals Average family planning staff—private hospitals Average family planning staff—community health centers Months supply of birth control pills and condoms—government hospitals Months supply of birth control pills and condoms—private hospitals Months supply of birth control pills and condoms—community health centers Number of private agents trained in dispensing birth control pills in PSU

29.74 0.32 3.49 2.99 2.67 0.51 15 1.4 1.5 1.7 3.7 19,620 3.9 7.5 5.5 3.09 54 2037 5.9 0.63 0.13 0.33 0.029 2.45 1.72 11.03 0.21 0.21 0.54 0.22

S.D. 8.54 0.47 2.27 1.85 1.79

2.07

2.58 0.58 0.85 0.024 7.50 7.20 60.37 1.08 1.09 1.52 0.82

a There were 30,966 and 19,632 women in the samples for contraceptive use and infant mortality. PSU = Primary Sampling Unit.

Contraceptive Use and Infant Mortality reported using a "traditional" method such as withdrawal. These figures were comparable to the findings from other surveys in India (Ramesh et al., 1996). The data on 19,620 children born in the previous 3-year period were used for the analysis of infant mortality; 2037 of the women had an additional birth in this period. For women with one birth in the 3-year period, 7.4% reported that they would have preferred to have had the birth 'later', while 5.4% would have liked not to have had the birth ('never'). The infant mortality rate calculated from data on births in the 3-year period was 3.9% (39 per 1000 live births). Average birth interval was 3.09 years and the vaccination rate against tetanus was 54%. The average numbers of government and private hospitals for the PSU were 0.63 and 0.13, respectively. While there were several private agents operating in the PSU, on the basis of qualifications to perform sterilization, terminate pregnancies and insert IUD, average for the PSU was 0.029. Average numbers of family planning staff available in government hospitals, community health centers and private hospitals were 2.45,11.03 and 1.72, respectively; there was wide variation in staff availability that was reflected in the standard deviations in Table 1. Also, the distributions of these variables were skewed to the right and the fourth moments were above the normal values of 3. To economize on space, the supply of birth control pills and condoms were combined in Table 1; average months of supply were approximately 0.21 for government and private hospitals and private agents, and 0.54 for community health centers. 3. A framework for analyzing the effects of healthcare infrastructure on contraceptive use and infant mortality There has been a decline in child mortality rates and an increase in life expectancy over the last half century in developing countries such as India (Preston, 1976; UNDP, 1990). Improvements in maternal nutritional status and better access to healthcare afforded by economic development are likely to lower child mortality and, with some delays, decrease the fertility rates. Because the role of socioeconomic factors has been underscored in many analyses, we reappraise some analytical issues and develop a framework for analysis of the PERFORM data encompassing the economic and demographic approaches. 3.1. Demand and supply schedules for contraceptives Easterlin and Crimmins (1985) underscored the role of economic factors affecting the demand and supply of children, building on the earlier contribution of Becker (1965). With economic development, there is clearly a need to educate children for gaining employment in skilled occupations. This, together with a decline in child mortality and easier access to healthcare and family planning services, are likely to lower the desired family size. Because cultural factors play an important role in adoption of family planning methods (Cleland and Wilson, 1987; Dreze and Murthi, 2001), it is important to reappraise some of the postulates invoked in economic analyses of fertility behavior. The supply schedule is used in economics to deduce the quantities of commodities offered at different prices, holding certain relevant variables constant. However, the number of children born to a married woman mainly depends on her fecundity; fecundity, in turn, is determined by biological processes that are not easily amenable to empirical modeling. By contrast, the desired numbers of children are likely to depend on economic factors such as expenditures that households can afford on food, clothing, education and healthcare, and on social and cultural factors (Cadwell, 1982). Furthermore, the actual number of children born to a woman is influenced by efficacy of the contraceptives used. Because factors affecting the supply schedule

323

324

A. Bhargava, S. Chowdhury and K.K. Singh for children are somewhat opaque, and demand for contraception is a "derived" demand for avoiding unwanted births, it would be appealing to analyze fertility behavior employing demand and supply schedules for contraceptives rather than for the children. Further, there are differences between demand for commodities that yield utility or satisfaction and the demand for contraceptives that are inconvenient to use. It is perhaps not surprising that many couples in backward states such as U.P. rely on female sterilization after surpassing their fertility goals. This, however, does not diminish the importance of contraceptives for birth spacing. Firstly, it would take approximately two years after a birth in U.P. to ensure that the child will survive with a high probability (Bhargava, 2003). If contraceptives are unavailable in this period, the woman could become pregnant again thereby increasing her unwanted fertility; birth spacing methods are critical for achieving the exact number of desired children. Secondly, due to low iron and calcium stores among under-nourished women, birth spacing can improve intra-uterine growth and increase survival chances of children. Thus, the demand for contraceptives for birth spacing and that for terminal methods merit separate treatments; the supply of these services would also depend on different factors. Terminal methods for family planning such as sterilization require skilled services and entail risks such as excessive bleeding and sexual dysfunction. The availability of qualified staff and adequate drugs are essential for encouraging couples to opt for such procedures. Moreover, the fees for services in private clinics can hinder utilization especially if public facilities do not function smoothly when judged by criteria such as "dignity" and "respect" shown towards patients (World Health Organization, 2000). Thus, variables reflecting quality of services in public and private facilities are likely to affect the use and timing of terminal methods. For example, less educated women could delay sterilization in spite of unwanted births if women in the community have reported complications. In contrast, the demands for birth control pills and condoms are influenced by economic factors and the couples' awareness of benefits from birth spacing. The supply of these contraceptives can be increased via subsidies to non-governmental organizations (NGO) and need not entail major investments in the public healthcare infrastructure. 3.2. Gradual evolution of the healthcare infrastructure versus endogenous facility placement In India, the healthcare infrastructure has evolved gradually over time and comprises of public facilities, private providers and NGO's. Initially, healthcare was available mainly in urban areas via government facilities and from private practitioners offering services to those who can afford them. It is also common for doctors employed in public facilities to engage in private practice outside the working hours. Because life in urban areas affords opportunities such as education for children, urban areas are attractive venues for medical personnel and their families. A concentration of public and private facilities staffed by qualified personnel is likely to increase competition among providers thereby enhancing the quality of services. Even the poor seeking treatment for serious illnesses, for example, may spend their savings in private facilities if public care is viewed to be inferior. In the absence of major public investments, healthcare infrastructure in rural areas is likely to evolve very slowly. While governments often mandate placement of hospitals or community health centers based on population, quality of services is likely to depend on the allocated resources and on the willingness of qualified personnel to serve in remote areas. Low purchasing power of households in under-developed areas reduces incentives for private providers to set up facilities. To fill the healthcare gaps, NGO's supported by the government and external agencies

Contraceptive Use and Infant Mortality

325

often deliver basic services. The quality of services as measured, for example, by number of trained personnel providing healthcare, is likely to be poor. This would be reflected in lower utilization rates and higher child and maternal mortality. In contrast with the gradual evolution of the healthcare infrastructure, some economists have emphasized the role of pressure groups for placement of public facilities. If, for example, programs were placed because of high infant mortality rates, then errors affecting infant mortality relationship could be con-elated with variables such as distance to the nearest public facility. Such formulations, however, seem applicable to situations where government is the sole provider of healthcare and acts appropriately without delays. Moreover, governmental efforts to improve service quality are likely to be hampered by logistical difficulties in transferring advanced equipment to remote places that may lack even electricity. The facts that a high proportion of healthcare is privately provided in India and quality differentials in services have been unexplored suggest that it would be useful to analyze the effects of healthcare infrastructure on contraceptive use and infant mortality in a broader analytical framework. For example, the errors affecting a model for infant mortality that includes several variables approximating the healthcare infrastructure are less likely to be correlated with the explanatory variables since these have gradually evolved over time. Lastly, an analysis of the proximate determinants of healthcare infrastructure in public and private facilities can be conducted using data at the PSU level. Because the PERFORM data are available only at a single point in time (in 1995), it would not be feasible to model the gradual evolution of the healthcare infrastructure. Instead, certain issues such as the effects of economic development on quality of services available in public and private facilities can be investigated. The models are outlined in Section 3.4, following the specification of models for individual level data on contraceptive use and infant mortality. 3.3. Empirical models for contraceptive use and for infant mortality Proximate determinants of the use of family planning methods can be analyzed via binary, multinomial and ordinal regressions. As noted in Section 3.1, the supply and quality of skilled services are likely to influence decisions to opt for female sterilization and IUD use. First, the empirical model for the chances of female sterilization (or IUD use) is given by:

(Female sterilization), =«o + #i (woman's age), + ai (ever attended school), + «3(no. of surviving children), + ^ ( n o . of surviving children), + 05 (possessions index),- + c^backward caste),. + a 7 (no. of govt, hospitals), + a 8 (no. of pvt. hospitals), + a 9 (avg. qualified staffgovt.), + «io(avg. qualified staff-pvt.), + a\ i (avg. qualified staff-pvt. agent), + u\i(i = 1 , . . . , N) (1)

The variable 'ever attended school' was an indicator (0-1) variable that was unity if the woman had attended school and 'backward caste' was an indicator variable that was one if the household belonged to a scheduled caste or a tribe; an indicator variable for rural/urban location of the household was not significant in these models. The staff qualified to perform sterilization, terminate pregnancy and insert IUD were calculated for each facility; 'average qualified staff variables in Eq. (1) were averages over the respective facilities, and for private agents in the PSU.

326

A. Bhargava, S. Chowdhury and K.K. Singh The error terms uu were assumed to be distributed as a logistic distribution for the N women in the sample; uu were assumed to be normal for probit models. Second, the model for the chances of use of birth control pills is given in Eq. (2):

(Pill use),. = bo + b\ (woman's age), + ^(ever attended school), + &3(no. of surviving children), + ^(possessions index),. + ^(backward caste), 4- b6(no. of govt, hospitals), + ^7(no. of private hospitals),- + bg (months supply pills-govt.), + ^(months supply pills-CHC), + &io(months supply pills-pvt.), + fen (average supply pills-pvt. agent),- + uu(i = 1 , . . . ,N)

(2)

A similar model was estimated for condom use by replacing variables representing the supply of birth control pills by the respective supplies of condoms. While the stocks of birth control pills and condoms are potentially important for encouraging birth spacing, it is possible that they are influenced by the contraceptive demand; disaggregation of the stocks in public and private facilities could shed light on this issues. Non-linearities with respect to the number of surviving children were not evident in the models for the chances of birth control pills and condom use. Moreover, the models for IUD, birth control pill and condom use were re-estimated dropping from the sample women who were sterilized. Third, in view of the fact that female sterilization was the main method for family planning, we defined an (ordered) categorical variable as zero if the couple was not using contraceptives, 1 if the woman or the man was sterilized, and 2 if the couple was using birth control pills, condoms, or IUD (i.e. {0,1,2}). An enlarged version of the model containing the explanatory variables in Eqs. (l)and (2) was estimated by ordinal and multinomial logistic methods (McCullagh, 1980). These regressions addressed potential inter-dependence in the choice of contraceptive methods and the estimated parameters were likely to be useful for assessing the robustness of the results from binary models. Fourth, the model for chances of infant mortality for the births in 3-year period preceding the survey is given by:

(Infant mortality),- =co + c\ (woman's age), + ci(woman's age)f + C3 (ever attended school), + c4 (no. of surviving children before 3-year period), + C5 (no. of surviving children before 3-year period), + eg (possessions index),- + c-i (backward caste),. + c8(avg. no. of private allopathic doctors), 4- c9(avg. no. of trained FP-CHC), + ci0(tetanus vaccination), + cn(birth interval),.+Ci2(birth wanted 'never'^+Ms,-^' = \,...,N) (3) 'Tetanus vaccination' was an indicator variable that was one if the woman was vaccinated against tetanus during the pregnancy. The indicator variable 'birth wanted never' was one if the woman

Contraceptive Use and Infant Mortality

327

stated that she did not want that child. The model in Eq. (3) addressed some of the possible nonlinearities in woman's age, child's birth order and/or the number of surviving children. Moreover, owing to unobserved factors that can affect infant mortality, the variable 'no. of surviving children before 3-year period' may be correlated with the error terms M3, (Bhargava, 2003; Arulampalam and Bhalotra, 2004). Alternative versions of the model for infant mortality in Specification 2 replaced the surviving number of children by 'no. of children born before 3-year period'. Also, Specification 1 was estimating treating the number of surviving children before the 3-year period as an endogenous variable using a conditional maximum likelihood estimation approach (Smith and Blundell, 1986); the numbers of children born before the 3-year period and the numbers of government allopathic hospitals in the PSU were used as instrumental variables. Lastly, in Specification 3, the indicator variable 'birth wanted never' was replaced by the variable 'both births wanted never' that was one if the woman had two births in the 3-year period and stated that she would have preferred not to have had them; this variable was likely to reflect the intensity of feeling that the births were unwanted. 3.4. Proximate determinants ofpublic and private healthcare infrastructure at the PSU level While the gradual evolution of healthcare infrastructure cannot be modelled using crosssectional data on providers, the government hospitals and community health centers are established on a population basis; private providers are attracted by economic opportunities in the regions. It would be useful to analyze the proximate determinants of quality of services in public and private sectors and those offered by private agents using data at the PSU level. The model for the number of family planning staff in government hospitals is given in Eq. (4):

(Family planning staff-govt.) = d0 + d\ (rural indicator),. + d2(no. of govt, fair price shops), + d3(no. of cooperatives); + d4(no. voluntary organizations), + ds(avg. infant mortality),- + ^(avg. possessions),- + vu(i — I,... ,N)

(4)

The average infant mortality rate in the PSU was included as an explanatory variable in (4) to assess its impact on public healthcare infrastructure, as emphasized in the endogenous facility placement literature. A similar model was estimated for family planning staff in community health centers. Because healthcare services available in private facilities can be influenced by services in the public sector, the model for family planning (FP) staff in private facilities is given by:

(Family planning staff-pvt.) = eo + e\ (rural indicator),- + £2(110. of govt, fairprice shops), + e3 (no. of cooperatives),- + e^no. of voluntary organizations),+ es(avg. infant mortality),- + e6(avg- possessions),- + 27 (FP staff-govt.),+ eg(pvt. agents trained in FP), + V2i{i = 1, • • •, N).

(5)

328

A. Bhargava, S. Chowdhury and K.K. Singh In Eq. (5), the family planning staff in government facilities was an explanatory variable that might be correlated with the error terms i>2,-. Such problems can be addressed by applying instrumental variables estimators such as two-stage least squares. The numbers of private allopathic doctors, industries, and full-time equivalent staff in community health centers were used as instruments and their validity was tested using Chi-square tests for over-identifying restrictions (Sargan, 1958). Moreover, for checking robustness of the results, the variables family planning staff in government hospitals and trained private agents were dropped from the model and a 'reduced form' version was estimated. Finally, a model similar to that in Eq. (5) was estimated for services provided by private agents trained in family planning services. 4. The results from PERFORM data from Uttar Pradesh 4.1. Empirical results for contraceptive use The maximum likelihood estimates from binary logistic models for the chances of women opting for sterilization, and for use of IUD, birth control pills, and condoms are presented in Table 2; coefficients significant at the 5% level are marked with asterisks. In the model for female sterilization, the woman's age and having attended school significantly increased (P < 0.05) the chances of sterilization. There were non-linearities with respect to the number of surviving children in that birth of an additional child increased the chances of sterilization though at a decreasing rate. The households' possession index was estimated with a positive and statistically significant coefficient. While the average number of government hospitals for the PSU was not a significant predictor, the average number of private hospitals was positively and significantly associated with the chances of women opting for sterilization. The average number of private doctors trained in performing sterilization, IUD insertion and terminating pregnancies significantly increased the chances of female sterilization. By contrast, the availability of such personnel in government and private hospitals were not significant predictors of female sterilization. Because indices based on the PERFORM data on healthcare infrastructure primarily reflected the availability of services in the PSU, these results highlight the importance of access to trained medical personnel in public and private sectors for increasing the chances of female sterilization. The results for IUD use were similar in many respects to those for female sterilization but there were some differences. For example, coefficient of woman's age was estimated with a negative sign indicating that younger women were more likely to use IUD, presumably for birth spacing. Also, women from backward castes and tribes had significantly lower chances of IUD use. Coefficients of the indicator variable for school attendance and the number of surviving children were similar in the models for female sterilization and IUD use. The average number of trained private doctors and staff available in government hospitals were positively and significantly associated with IUD use. The empirical results for the use of birth control pills and condoms were similar in many respects. The relationships were linear in the number of surviving children; older women and their husbands were significantly less likely to use birth control pills and condoms, respectively. The household possessions index was positively and significantly associated with birth control pill and condom use. However, women from backward castes and tribes were less likely to use these methods. While the supplies of pills and condoms in government hospitals and community health centers were not significantly associated with pill use, the number of trained private agents was a positive and significant predictor. The number of months of supply

Contraceptive Use and Infant Mortality

329

Table 2 Maximum likelihood estimates of binary logistic regressions for the use of female sterilization, IUD, birth control pills and condoms explained by demographic, socioeconomic and healthcare infrastructural variables using the PERFORM survey*

Constant Woman's age Backward caste Ever attended school No. of children surviving (No. of children surviving)2 Household possessions index Average number of governmental hospitals Average number of private hospitals Average number of private doctors trained in terminal methods Average number of trained in FP methods—government hospitals Average number of trained in FP methods—private hospitals Months supply pills (condoms)—government hospitals Months supply pills (condoms)—CHC Months supply pills (condoms)—private hospitals Number of private agents trained in pills and condoms R2

Female sterilization

IUD

Birth control pills

Condoms

Coefficient

S.E.

Coefficient

S.E.

Coefficient

S.E.

Coefficient

S.E.

-7.043* 0.082* 0.010 0.430* 1.300* -0.150* 0.121*

0.115 0.002 0.034 0.040 0.046 0.005 0.010

-4.437* -0.036* -0.664* 0.835* 0.318* -0.040* 0.254*

0.239 0.008 0.170 0.108 0.104 0.014 0.030

-3.026* -0.063* -0.380* 0.505* 0.168*

0.199 0.007 0.091 0.097 0.029

-3.248* -0.040* -0.398* 0.930* 0.045*

0.149 0.005 0.069 0.073 0.023

0.014

0.076

-0.557*

0.283

-0.434

0.267

0.088*

0.025

0.059

0.064

-0.027

0.071

0.053*

0.024

0.080*

0.036

-

-

0.038

0.025

0.200*

0.049

-

-

-0.033

0.022

0.052

-

-

-0.064

0.136*

0.027

0.245* -0.116

0.112*

0.021 0.156

0.041

-

-

-0.052

0.134

0.008

0.010

-

-

-0.024

0.030

-0.055*

0.025

-

-

0.109

0.094

0.156*

0.023

-

-

0.188*

0.083

0.073

0.065

0.198*

0.102*

0.043*

0.118*

There were 30,966 women in this sample; slope coefficients and standard errors are reported. P < 0.05.

of condoms in private hospitals was positively and significantly associated with condom use. This was not true for the supply of condoms in government hospitals and in community health centers. Because birth control pills and condoms can be obtained in a more discreet manner from private suppliers by households that can afford them, it was perhaps not surprising that the results underscored private sources. The (pseudo) R2 (Cox and Snell, 1989) for the model for condom use was higher than that for birth control pill use, partly because greater number of

330

A. Bhargava, S. Chowdhury and K.K. Singh

Table 3 Maximum likelihood estimates of the enlarged ordinal and multinomial regression models for the categorical variable for three categories of contraceptive use explained by demographic, socioeconomic and healthcare infrastructural variables using the PERFORM survey"'h

Constant Woman's age Backward caste Ever attended school Number of children surviving (Number of children surviving)2 Household possessions index Average number of governmental hospitals Average number of private hospitals Average number of private doctors trained in terminal methods Average number of trained in FP methods—government hospitals Average number of trained in FP methods—private hospitals Months supply pills—government hospitals Months supply pills—CHC Months supply pills—private hospitals Months supply condoms—government hospitals Months supply condoms—CHC Months supply condoms—private hospitals Number of private agents trained in pills and condoms R2 a

Ordinal regression

Multinomial logistic regression (non-user group)

Multinomial logistic regression (sterilized group)

Coefficient

S.E.

Coefficient

S.E.

Coefficient

S.E.

4.549* 0.048* -0.189* 0.755* 0.085* -0.094* 0.172* -0.106

0.081 0,002 0.029 0.033 0.033 0.004 0.009 0.068

3.361* 0.024* 0.466* -1.017* -0.425* 0.042* -0.258* 0.298*

0.126 0.004 0.051 0.054 0.048 0.006 0.015 0.127

-3.979* 0.118* 0.395* -0.350* 0.941* -0.118* -0.114* 0.284*

0.160 0.004 0.057 0.061 0.062 0.008 0.017 0.137

0.079*

0.022

-0.085*

0.035

0.002

0.039

0.050*

0.021

-0.051

0.030

0.026

0.031

0.183*

0.023

-0.267*

0.033

-0.138*

0.037

-0.013

0.020

-0.026

0.030

-0.061

0.034

-0.159*

0.050

0.232*

0.075

0.095

0.085

0.033*

0.011

0.001

0.022

0.052

0.024

0.169*

0.039

-0.271*

0.058

-0.194*

0.067

-0.004

0.009

0.002

0.013

0.004

0.014

-0.051*

0.011

0.045*

0.021

-0.010

0.024

-0.001

0.045

0.038

0.070

0.074

0.079

0.031

-0.115*

0.050

-0.069

0.056

0.079*

0.179*

0.271*

0.271*

There were 30,966 women in this sample; slope coefficients and standard errors are reported. The categorical dependent variable ((0,1,2)) was 0 for non-users of contraceptives, I for female or male sterilization, and 2 for use of condoms, pills or IUD. * P < 0.05. b

Contraceptive Use and Infant Mortality

331

couples were using condoms. Lastly, dropping sterilized women from the sample led to very similar results in the models for IUD, birth control pill and condom use. The results in Table 3 for the categorical variable ({0, 1, 2}) for type of contraceptive used from ordinal and multinomial logistic regressions were broadly consistent with the results from binary models. The coefficients from ordinal regression model were very similar to those in Table 2 and all the significant coefficients remained significant in Table 3. While binary regressions explained contraception choice by the respective measures for availability, the ordinal regression incorporated availability of other methods. For the multinomial regression in Table 3, the signs of the coefficients were switched because the results are presented with respect to the group using birth control pills, condoms or IUD. The magnitudes of the coefficients were often different in the two groups of contraceptive non-users and sterilized couples. Overall, in view of the natural ordering of the categorical variable for households from U.P. with limited access to family planning services, it was perhaps not surprising that the results from ordinal regression were easy to interpret and supported the findings from binary models. 4.2. Empirical results for infant mortality The empirical results from estimating binary logistic models for infant mortality are presented in Table 4 for three alternative specifications. Specification 2 replaced the variable 'no. of children surviving before 3-year period' by the corresponding variable for the number of children born; Specification 3 replaced the indicator variable 'birth wanted never' in Specification 1 by 'both births wanted never'. The results for Specification 1 indicated that, firstly, there were significant non-linearities in infant mortality with respect to maternal age and with respect to the Table 4 Maximum likelihood estimates of binary logistic regressions for infant mortality explained by demographic, socioeconomic and healthcare infrastructural variables using the PERFORM survey*

Constant Woman's age (Woman's age)2 Backward caste Ever attended school Number of children surviving before 3-year period (Number of children surviving before 3-year period)2 Number of children born before 3-year period (Number of children born before 3-year period)2 Household possessions index Birth interval Tetanus vaccination Average number of private allopathic doctors Average number of trained in FP methods—CHC Birth wanted 'never' Both births wanted 'never' R2

Specification 1

Specification 2

Specification 3

Coefficient

S.E.

Coefficient

S.E.

Coefficient

S.E.

0.511 -0.185* 0.003* 0.241* -0.202* -0.378* 0.031*

0.676 0.049 0.001 0.087 0.107 0.072 0.010

1.383* -0.246* 0.004* 0.233* -0.140

0.691 0.051 0.001 0.086 0.107

0.527 -0.188* 0.003* 0.248* -0.194 -0.382* 0.031*

0.676 0.049 0.001 0.087 0.107 0.072 0.010

-0.116* -0.157* -0.248* -0.131* -0.029 0.025

0.028 0.023 0.085 0.060 0.016 0.211

-0.128* 0.014* -0.108* -0.140* -0.216* -0.132* -0.028 -0.128

-

-

0.045*

0.039*

0.060 0.006 0.028 0.023 0.085 0.060 0.016 0.210

-0.116* -0.152* -0.249* -0.133* -0.029

0.028 0.023 0.085 0.060 0.017

1.120* 0.048*

0.282

Specification 3 replaced the indicator variable 'birth wanted never' in Specification 1 by 'both births wanted never'. * There were 15,875 births in this sample; slope coefficients and standard errors are reported. * P < 0.05.

332

A. Bhargava, S. Chowdhury and K.K. Singh number of surviving children. Some of the non-linearities with respect to maternal age have been reported in the previous literature. Secondly, women from scheduled castes and tribes experienced significantly higher infant mortality; infant mortality was lower for better off households as reflected in the possessions index and for women that had attended school. Thirdly, longer birth intervals decreased the chances of infant mortality as reported in previous studies (Hobcraft et al., 1983). For women vaccinated against tetanus, infant mortality was significantly lower supporting the earlier findings for U.P. (Bhargava, 2003). Fourthly, average number of private allopathic doctors and the average number of staff trained in family planning methods in community health centers were estimated with negative signs that were significantly associated with chances of infant mortality at the 5 and 10% levels, respectively. Because approximately 25% of the women received ante-natal care and 85% of the babies were delivered without qualified personnel, it was perhaps not surprising to find small effects of healthcare infrastructure on the chances of infant mortality. Fifthly, the indicator variable if the women would have preferred 'never' to have the birth was estimated with a positive coefficient but was not statistically significant. The results for Specification 2, where the number of surviving children was replaced by the number of children born, were close to the results from Specification 1 for most variables. However, the coefficient of the variable for whether the woman had ever attended school was no longer significant at the 5% level. Moreover, there was slight loss in the goodness of fit in Specification 2 where the R2 declined from 0.045 for Specification 1 to 0.039. Coefficient of the indicator variable 'both births wanted never' in Specification 3 was positive and significant implying that infants whose mothers stated that they would have preferred not to have had the two children in the 3-year period had higher chances of mortality. While it would be useful to develop more elaborate measures for the degree of unwantedness of births, greater utilization of family planning services is likely to reduce infant mortality in U.P., partly because birth spacing was associated with lower infant mortality. Also, indicator variables for the sex of the child and for rural areas were not significant in the models for infant mortality. Lastly, because the survival chances of infants born to the same woman could be related, Specification 1 was re-estimated with the number of surviving children before the 3-year period treated as an endogenous variable. The numbers of children born before the 3-year period and the numbers of government allopathic hospitals in the PSU were used as instrumental variables in the probit framework. While the test for exogeneity of the number of surviving children rejected the null hypothesis, the results from this version of the model were similar to the estimates for Specification 1 in Table 4. 4.3. Empirical results for the healthcare infrastructure using PSU level data The results from estimating multiple regression models for family planning staff available in government hospitals, community health centers, private hospitals and via private agents at the PSU level are presented in Table 5. First, for government hospitals, indicator variable for rural areas was estimated with a negative and significant coefficient. While infant mortality rate in the PSU was not a significant predictor, the variable averaging households' possession index over the PSU was significant. However, the explanatory variables were not jointly significant at the 5% level. Thus, family planning services in government facilities were not significantly predicted by the explanatory variables in the model and may have b6en influenced by other variables such as indicators of economic activity not covered in the PERFORM survey. Secondly, in the results for

333

Contraceptive Use and Infant Mortality

Table 5 Efficient estimates of regression models incorporating potential inter-dependence in family planning staff available in government hospitals, community health centers, private hospitals and via private agents using Primary Sample Unit level data from the PERFORM survey" Government hospitals

Constant Rural indicator (1 = rural, 0 = urban) Number of government fair price shops Number of cooperatives Number of voluntary organizations Average infant mortality in the PSU Average household possessions index for PSU Number of family planning staff—government hospitals Number of family planning staff—private hospitals Average number of trained in FP methods—private agents Chi-square (2)b R2

Community health centers

Private hospitals

Trained agents

private

Coefficient

S.E.

Coefficient

S.E.

Coefficient

S.E.

Coefficient

S.E.

38.751* -11.015*

6.909 4.250

0.307 7.417*

0.976 0.619

12.441 0.483

8.683 5.271

-0.294* 0.006

0.079 0.048

0.417

2.108

0.522*

0.268

5.813*

2.547

-0.008

0.023

0.494 0.510

2.7J3 3.521

-0.143 -0.502

0.335 0.441

11.229* -8.836*

3.258 4.241

0.006 -0.002

0.030 0.039

-13.080

17.942

-3.288

2.339

-10.234

22.706

-0.100

0.207

-4.401*

1.587

0.229

0.212

-2.337

1.997

0.128*

0.018

0.028

0.0003

0.0002

0.0001

0.0002

-

-

0.554*

-

-

-

-

-

1.298

-

-

0.005

0.119*

3.133 0.190*

2.556

-

0.038*

a

There were 1911 PSU in this sample; slope coefficients and standard errors are reported. For the Chi-square test for mis-specification in the model for private hospitals, the number of family planning staff in government hospitals was treated as an endogenous variable using as instruments, the numbers of private allopathic doctors, industries, and full-time equivalent staff in community health centers. * P < 0.05. b

community health centers in the second column of Table 5, the rural indicator variable and number of government fair price shops were significant predictors. Moreover, in spite of the low R2, explanatory power of the variables was significant at the 5% level. Another version of the model included family planning services available in government facilities; this variable was estimated with a negative sign and was statistically significant. Thus, there seemed some interdependence in governmental decisions to allocate personnel between hospitals and community health centers. However, the results for this formulation were not included in Table 5, partly to economize on space and also because of the simultaneity issues discussed next. Thirdly, in the results for family planning services in private hospitals, the numbers of govemment fair price shops and cooperatives were positive and significant predictors, while the numbers of voluntary organizations were significantly negatively associated. As noted above,

A. Bhargava, S. Chowdhury and K.K. Singh

334

voluntary organizations are likely to operate in remote areas. Coefficient of family planning services available in government hospitals was positive and was a highly significant predictor of the services in private hospitals. This was partly an indication of the gradual evolution of the healthcare infrastructure. The model was also estimated by instrumental variable method, treating services in government hospitals as an endogenous variable; the results were similar in terms of signs and significance of the coefficients. Coefficient of trained private agents was not significant in the model explaining the availability of family planning services in private hospitals. Finally, the last column in Table 5 presents the results for private agents trained in family planning services. Only the average household possession index for the PSU was a statistically significant predictor with a positive coefficient; the coefficients were jointly significant at the 5% level. These results indicated that private agents were likely to be located in regions with economically better-off households. 5. Conclusion This paper analyzed the data from Uttar Pradesh on healthcare and family planning services, contraceptive use, and infant mortality, emphasizing gradual evolution of the healthcare infrastructure. Previous theories of demand and supply of children were extended for devising a unified framework for research in economic demography. Implications of the endogenous placement of public facilities hypothesis were examined and, in view of the increased role of private providers, a more general framework was adopted for the analysis. The empirical results underscored the importance of quality of available services for use of methods such as female sterilization and IUD; the use of birth spacing methods was significantly associated with female education, socioeconomic status, and contraceptive stocks. While terminal methods are appropriate for couples not desiring additional children, birth spacing is essential for achieving the desired number of children. Because the empirical results indicated that short birth intervals exacerbated infant mortality, it is important to facilitate birth spacing especially in remote areas. Such interventions need not entail major investments in the public healthcare infrastructure since the services can be delivered via subsidies to NGO's and private agents. More serious complications during pregnancies and deliveries can be tackled by improving the quality of services in community health centers and government hospitals and by enhancing transportation links between rural and urban areas. The analysis of demographic data and information on government and private facilities and private agents provided insights into the inter-relationships between the services and their likely impact on child mortality. While the costs of services in private facilities were not assessed in the survey, owing to the increased availability of private services, governmental facilities are likely to be under-utilized if quality of care is inferior. Thus, additional resources are essential for improving the public healthcare infrastructure and for monitoring the quality of services. It is important for policy makers to exploit the synergisms between various components of the healthcare infrastructure to achieve more equitable outcomes especially for the poor in backward regions of Uttar Pradesh. Acknowledgements While retaining the responsibility for the views, the authors thank the Research Committee of the World Bank for supporting these analyses, and Melanie Fox-Kean for assistance with the data. The present version has benefited from the comments of seminar participants at Cambridge

Contraceptive Use and Infant Mortality University, London School of Hygiene and Tropical Medicine and the World Bank, and from the suggestions of Bob Retherford, John Komlos and the referees. References Angeles, G., Guilkey, D., Mroz, T., 1998. Purposive program placement and the estimation of family planning program effects in Tanzania. J. Am. Stat. Assoc. 93, 884-899. Arulampalam, W., Bhalotra, S., 2004. Sibling death clustering in India: genuine scarring versus unobserved heterogeneity. Mimeo: Department of Economics, University of Warwick, UK. Becker, G., 1965. A theory of the allocation of time. Econ. J. 75, 493-517. Becker, G., 1982. A theory of competition among pressure groups for political influence. Quart. J. Econ. 98, 371^t00. Bhargava, A., 2001. Nutrition, health and economic development: some policies priorities. Food Nutr. Bull. 22, 173-177. Bhargava, A., 2003. Family planning, gender differences and infant mortality: evidence from Uttar Pradesh, India. J. Econometrics 112, 225-240. Bongaarts, J., 1990. The measurement of wanted fertility. Pop. Dev. Rev. 16, 487-506. Bongaarts, J., 1993. The supply-demand framework for the determinants of fertility: an alternative implementation. Pop. Stud. 47, 437-456. Cadwell, J.C., 1982. Theory of Fertility Decline. Academic Press, London. Cleland,.!., 1996. Population growth in the 21st century: cause for crisis or celebration? Trap. Med. Int. Health 1, 15-26. Cleland, J., Wilson, C , 1987. Demand theories of fertility transition: an iconoclastic view. Pop. Stud. 41, 5-30. Cox, D., Snell, E., 1989. Analysis of Binary Data, second ed. Chapman & Hall, London. Dreze, J., Murthi, M., 2001. Fertility, education, and development: evidence from India. Pop. Dev. Rev. 27, 33-63. Easterlin, R., Crimmins, E., 1985. The Fertility Revolution. University of Chicago Press, Chiacgo. Hobcraft, J.N., McDonald, J.W., Rutstein, S., 1983. Child spacing effects of infant and early child mortality. Pop. Ind. 49, 585-618. Koenig, M., Foo, G., Joshi, K., 2000. Quality of care within the Indian family welfare programme: a review of recent evidence. Stud. Fam. Plann. 31, 1-18. Marston, C , Cleland, J„ 2003. Do unintended pregnancies carried to term lead to adverse outcomes for mother and child? An assessment in five developing countries. Pop. Stud. 57, 77-93. McCullagh, P., 1980. Regression models for ordinal data. J. R. Stat. Soc. B 42, 109-142. Mensch, B., Arends-Kuenning, M., Jain, A., 1996. The impact of the quality of family planning services on contraceptive use in Peru. Stud. Fam. Plann. 27, 59-75. Montgomery, M., Lloyd, C , Hewett, P., Heuveline, P., 1997. The consequence of imperfect fertility control for children's survival, health, and schooling. Demographic and Health Surveys Analytical Reports No. 7. Macrointernational, Calverton, MD. Peters, D., Yazbeck, A., Sharma, R., Ramana, G., Pritchett, L„ Wagstaff, A., 2002. Better Health Systems for India's Poor. World Bank, Washington, DC. Preston, S., 1976. Mortality Patterns in National Populations. Academic Press, New York. Ramesh, B., Gulati, S., Retherford, R., 1996. Contraceptive use in India, 1992-93. National Family Health Survey Subject Reports Number 2. East West Center, Honolulu, Hawaii. Sargan, J.D., 1958. The estimation of economic relationships using instrumental variable. Econometrica 26, 3 9 3 ^ 1 5 . Scrimshaw, S., 1978. Infant mortality and behavior in the regulation of family size. Pop. Dev. Rev. 4, 383-403. SIFPSA, 1996. Performance indicators for the innovations in family planning services project. State seminar report. Lucknow, UP, India. Smith, R.J., Blundell, R.W., 1986. An exogeneity test for a simultaneous equation Tobit model with an application to labor supply. Econometrica 54, 679-685. Stephenson, R., Tsui, A., 2002. Contextual influences on reproductive health service use in Uttar Pradesh. India. Stud. Fam. Plann. 33, 309-320. SPSS, 1999. SPSS for Windows version 10. SPSS, Inc., Chicago, IL. Taylor, C , Newman, J., Kelly, N., 1976. The child survival hypothesis. Pop. Stud. 30, 262-278. United Nations Development Program, 1990. Child mortality since 1960's: a data base for developing countries. United Nations, New York. World Health Organization, 2000. World Health Report 2000. World Health Organization, Geneva.

335

VI. Behavior, Diet and Obesity in Developed Countries

STATISTICS IN MEDICINE, VOL. 13, 113-126 (1994)

ESTIMATING THE VARIATIONS AND AUTOCORRELATIONS IN DIETARY INTAKES ON WEEKDAYS AND WEEKENDS ALOK BHARGAVA Department of Economics, University of Houston, Houston, TX 77204-5882, U.S.A. AND RONALD FORTHOFER, SUSIE McPHERSON AND MILTON NICHAMAN School of Public Health, University of Texas Health Science Center, Houston, TX 77225, U.S.A. SUMMARY The high incidence of breast cancer in the U.S. and the possible link with dietary fat has led to the development of educational programmes for reducing women's fat intakes by agencies such as the National Cancer Institute and the U.S. Department of Agriculture. In this paper, we analyse the effects of an intervention on the intakes of 12 nutrients by 37 women in the Houston area. We estimate a dynamic random effects model by maximum likelihood to estimate the between and the within variations and the autocorrelations using 7 consecutive food records before and after the intervention programme. The main findings are that the pattern of within variations differs during weekdays and weekends. Secondly, the mean intakes of nutrients such as /J-carotene and ascorbic acid tend to be lower on weekends. Lastly, the intervention programme reduced the overall fat intakes and also increased the variation in the consumption of foods high in fats during weekdays. We discuss the implications of the results for the design of further studies.

1. INTRODUCTION The identification of relationships between the consumption of certain foods (nutrients) and diseases such as cancer and coronary heart disease is a challenge for researchers in nutritional epidemiology. Some associations have been found for high levels of cholesterol and saturated fat intakes with cardiovascular diseases (for example Reference 1, Chapter 15). The high incidence of breast cancer in the U.S. has led the National Cancer Institute to sponsor trials that assess the effects of educational programmes aimed at reducing the fat intakes by women (for example Greenwald,2 Buzzard et al.3 and Henderson et a/.4). Indeed, the statistical analyses of intake data are valuable for the design of dietary guidelines and provide useful insights for investigating the biological aspects of the associations. A common problem facing nutritional epidemiologists is the measurement of a person's 'usual' intake, and they often employ methods such as 24-hour recalls, food records and food frequencies.5 The day-to-day (within) variability in the diets makes it difficult to rely on a single or few time observations. Thus data are collected for a number of days with the length of the observation

0277-6715/94/020113-14$ 12.00 © 1994 by John Wiley & Sons, Ltd.

Received December 1991 Revised October 1992

340

A. Bhargava et al.

period usually depending on the magnitude of the within variances of intakes (for example Beaton et al.6) The predicted usual intakes, in turn, facilitate the modelling of the relationships between diet and disease. The physiological needs of the individuals and their socioeconomic and cultural environments determine food consumption. Thus, for example, the nutrient composition of meals consumed at work may differ substantially from those eaten at home on weekends. In previous studies, the mean intakes on weekdays and weekends have been postulated to differ.7 With several days data collected, for example, they include Saturday or Sunday to represent the weekend. 2 " 4 It has been assumed that the stochastic properties of the intakes remain the same throughout the week. This assumption may be inappropriate in practice and, for example, it may be easier to alter the subjects' dietary intakes on weekdays. Such issues have not been explored in epidemiologic research and may have clear implications for the development of dietary guidelines. This paper presents an analysis of the stochastic properties of the intakes of 12 nutrients collected from 37 women in the Houston area on 14 days. The intakes on 7 consecutive days were initially recorded. Then, by means of a dietary education programme, 8 the adverse effects of fat consumption and the positive effects of fibre, calcium and vegetables in the diet were emphasized. A second set of 7-day intakes was recorded after the intervention. The present analysis extends the previous epidemiologic research in at least three respects. Firstly, we represent the daily intakes by a dynamic error components model which uses a 0-1 (dummy) variable to indicate whether the observation is for a weekday or the weekend. Secondly, we estimate the variations and the autocorrelations in intakes separately for weekdays and weekends. Lastly, we examine the effects of the dietary intervention by comparing the estimated parameters of the models before and after the intervention programme. Overall, the stochastic properties of the nutrient intakes and the effects of the dietary intervention depend on whether the observations are from weekdays or the weekend. The collection of 5-day records (comprising 3 consecutive weekdays and a weekend) seems preferable to selecting 3 weekdays and including either Saturday or Sunday to represent the weekend. 2. THE DYNAMIC ERROR COMPONENTS MODEL Many researchers have emphasized the influence of previous nutritional intakes on current intakes (for example Beaton et al.6 and Sukhatme and Margen 9 ). Thus we chose to model the nutrient intakes of women in the Houston area on consecutive days by means of a stationary first-order autoregressive process with error components (or a dynamic random effects model). Also, the potential differences in food consumption patterns on weekdays and weekends merit a closer examination. A formulation that incorporates these features is: yn=7i

+ PiDl + [«V(1 - a)] + [ e a / V ( l - a 2 )]

yu = y2 + P2Dl + ayu-l

+ Si + eu

(i = 1, 2, . . . , H)

(1)

(i = 1, 2, . . . , H; t = 2, 3, . . . , T).

(2)

Here, yit is the intake of a nutrient (or the natural logarithm of the intake) by subject i in the rth period; there are H subjects in the sample each consecutively observed for T periods (H = 37, T = 7). The parameters yt and y2 are, respectively, the coefficients of the constant term in the first and the remaining (T— 1) periods. The variable Dt indicates the weekday-weekend states (0 = Monday-Friday, 1 = Saturday and Sunday) with coefficients ^ and p2 for the first and the last (T — 1) periods, respectively. We assume that the coefficient of autoregression a is less than one in absolute value. The quantity <5f denotes subject-specific random effects which we assume are independently normally distributed with zero mean and variance aj. We assume further that

Variations and Autocorrelations in Dietary Intakes

341

the general error terms (ei() are independently normally distributed with mean zero and variance <x2 and are independent of the <5,s. The variance of each yit is var(3>„) = [<x2/(l - a) 2 ] + [> 2 /(l - a 2 )].

(3)

Denning the ratio of the between to the within variance as p2 = varfo)/var(e ft ) = aj/a2,

(4)

the proportions of the total variation in yit due to the between and within variations are, respectively, 6l and 02, where 10 0, = p 2 (l + «)/[(l + a)p2 + (1 - a)]

and

02 = (1 - a)/[(l + a)p 2 + (1 - a)].

(5)

The asymptotic distribution theory used in the paper assumes that the number of subjects in the sample H is large with the number of time observations T held fixed. 1112 This necessitates the treatment of the initial observations yn as stochastic variables jointly distributed with the intakes in the remaining (T — 1) periods (2). Equation (1) postulates that the yns are drawn from a stationary distribution. This assumption is appealing for modelling the nutrient intakes, though we can estimate the dynamic model under alternative assumptions with modifications in the likelihood function. Also, we could estimate 'static' models with random effects and serial correlation in the error terms. The dynamic random effects model, however, treats the contributions of the between and within variances to the total variation more symmetrically.10 The estimation of the dynamic model (1) and (2) involves numerical optimization of the log-likelihood function. From a computational standpoint, it would be convenient to optimize the profile log-likelihood function obtained by eliminating the parameters in the 'systematic' part of the initial observations (1). The detailed derivations of these functions under different assumptions on the error components appear elsewhere. 1213 For the present model, the profile log-likelihood function depends only on the unknown parameters (y2, J?2><*> P) in (2). We can optimize it by using a standard subroutine. 14 Note that we can estimate the mean nutrient intake \x as /* = [72/(1 - a)].

(6)

We obtain the asymptotic standard errors (ASEs) of the estimated parameters by numerically approximating the second derivatives of the profile log-likelihood function with respect to the parameters at the maximum. We then derive the ASE of the estimated mean intake (6) by differentiating (6) analytically and using a first-order Taylor series expansion. The result is ASE(/J) = [AV(y2) - 2y2{AC(f2, «)/(l - a)} + yf{AV(«)/(l - a) 2 }] 1 / 2 /(l - a),

(7)

where the hats denote the estimates of the parameters and AV and AC are abbreviations for the asymptotic variance and covariance, respectively. We can investigate further the differences in the stochastic properties of the nutrient intakes on weekdays and the weekend by estimating the model (1) and (2) separately for these subperiods. The 7-day dietary records, however, commenced on a Tuesday or a Wednesday. Thus there are three consecutive weekday observations on all of the women for the estimation of the dynamic model ( 7 = 3 and 7 = 2 , respectively, for weekday and weekend intakes). We note that in the absence of time varying exogenous variables, there is some possibility of multiple identification of the modeLparameters when T = 2. An error components model assuming no autocorrelation in the intakes will also be estimated for the weekend data to check the robustness of the conclusions.

342

A. Bhargava et al. 3. THE 7-DAY FOOD RECORDS AND THE DIETARY INTERVENTION PROGRAMME

The 37 women in the sample were volunteers who responded to advertisements in local newspapers or those posted at the Medical Center at Houston. The subjects were above 18 years of age with fat intakes accounting for over 36 per cent of the calories. Only women with low-density lipoproteins below 190 were included in the study and those above this level were referred for appropriate treatment. The women were mostly employed with 35 working full-time, one part-time and one unemployed. Also, 16 were married, 14 divorced, separated or widowed and 7 were never married. All women had at least high school education, 6 had additional vocational training and 24 had some college education. The median annual income was approximately $30,000. The subjects were shown how to complete dietary questionnaires and they completed the first set of 7 consecutive food records during the months of November and December 1989. The women then attended dietary educational classes for an hour every week for 12 weeks. The programme was based on the U.S. Department of Agriculture guidelines for Americans.8 Specifically, the women received strong encouragement to reduce the percentage of calories from fat to less than 30 per cent and to reduce the consumption of foods high in cholesterol and sodium. Also, there was emphasis on the importance of fruits, vegetables, fibre and calcium in the diet. The women completed the second set of 7 consecutive records in March and April 1990 after the dietary intervention. The subjects' intakes of over 6000 foods were converted into the intakes of 28 nutrients, and two nutritionists reviewed the data. 4. THE EMPIRICAL RESULTS 4.1. Variations and autocorrelation in 7-day consecutive records Table I presents the mean intakes (per day) of dietary energy, protein, carbohydrate, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, cholesterol, fibre, calcium, /?-carotene and vitamin C. The numbers in parentheses are the estimated standard deviations. The results are tabulated for the mean intakes on 7 consecutive days, 5 weekdays and the weekend both before and after the dietary intervention. The maximum likelihood estimates of the dynamic error components model (2) for the natural logarithms of the intakes prior to the intervention appear in Table II; the corresponding results for the logarithms of intakes after the intervention are in Table III. We used the logarithmic specification partly to reduce heteroscedasticity in the data 15 and also to minimize the influence of outliers on the parameter estimates. The tables also report the estimated within variances (ff*2) and the proportion of variation due to between subject variation (0i). The asymptotic standard errors of the parameters appear in parentheses below the estimates. The noteworthy results in Table II are,firstly,that the (between/within) ratios p2 are typically smaller than one, as found in previous studies. Secondly, the estimates of the weekend dummy variable have negative coefficients that are statistically significant at the 5 per cent level in the polyunsaturated fat, /?-carotene and vitamin C relationships. Thus the consumption of these nutrients on the weekend seems lower than on weekdays. It is plausible, however, that with a larger number of subjects, we might have found the weekend dummy variable significant for some other nutrients (such as fibre). Thirdly, the autocorrelation coefficient a is significant for only the protein intakes. This contrasts with the relatively large positive autocorrelations reported by Sukhatme and Margen9

Table I. Sample means of the nutrient intakes before and after the intervention* Energy

Protein

Carbohydrate

Total fat

Saturated fat

Mono, fat

Poly, fat

Cholesterol

Fibre

Calcium

/J-carotene

Vitamin C

7-day intakes

1836-3 (732-9)

72-02 (2814)

211-35 (95-68)

75-11 (37-22)

25-49 (13-83)

27-69 (15-43)

16-30 (9-68)

234-27 (137-96)

15-89 (8-74)

705-86 (475-5)

568-92 (777-2)

99-40 (107-5)

5-weekday intakes

1815-5 (588-8)

70-85 (21-92)

213-44 (84-96)

73-24 (29-39)

24-78 (1119)

26-61 (11-63)

16-33 (909)

22407 (1160)

16-30 (8-87)

699-71 (3920)

611-67 (816-2)

105-80 (117-3)

Weekend intakes

18881 (10100)

74-94 (39-69)

20613 (118-8)

79-78 (51-84)

27-26 (18-86)

30-39 (22-14)

16-22 (1107)

259-76 (1801)

14-87 (8-36)

721-24 (641-6)

46206 (6630)

83-39 (75-98)

7-day intakes

1473-2 (526-9)

62-58 (27-13)

187-60 (74-40)

50-28 (26-73)

1606 (10-38)

1802 (10-39)

1219 (7-34)

190-89 (153-6)

14-74 (7-29)

666-41 (3981)

530-90 (941-6)

97-50 (74-94)

5-weekday intakes

1478-2 (542-5)

62-78 (27-55)

191-56 (75-21)

5004 (27-66)

15-88 (10-62)

17-77 (10-54)

12-40 (7-93)

177-29 (135-2)

15-23 (7-37)

693-42 (419-2)

553-37 (394-5)

103-90 (74-6)

Weekend intakes

1460-5 (4890)

6209 (26-22)

177-71 (71-86)

50-88 (24-41)

16-52 (9-81)

18-67 (1004)

11-66 (5-60)

224-90 (188-9)

13-51 (701)

598-89 (332-7)

474-74 (10540)

81-52 (73-94)

Before intervention

After intervention

* The numbers in parentheses are the estimated standard deviations; H = 37. Energy is measured in kilocalories per day. Protein, carbohydrate, total fat, saturated fat, monounsaturated fat, polyunsaturated fat and fibre are in grams per day. Cholesterol, calcium, ^-carotene and vitamin C are in milligrams per day.

Table II. Maximum likelihood estimates of the dynamic error components model using 7-day consecutive food records before the intervention* Energy

Protein

Carbohydrate

Total fat

Saturated fat

Mono. fat

Poly. fat

Cholesterol

Fibre

Calcium

/S-carotene

Vitamin C

72

7-436 (0-585)

3-535 (0-352)

5198 (0-414)

4-266 (0-337)

3-269 (0-249)

3-198 (0-263)

2-430 (0-210)

4-844 (0-437)

2-592 (0-211)

6-309 (0-464)

5166 (0-447)

4091 (0-324)

Pi

-0-033 (0046)

- 0036 (0-651)

-0-094 (0061)

-0-036 (0059)

0004 (0073)

-0006 (0064)

-0-168 (0-079)

0031 (0111)

- 0136 (0-093)

-0-071 (0-070)

- 0-407 (0183)

-0-291 (0-128)

0002 (0079)

0162 (0081)

0016 (0079)

- 0010 (0080)

-0-051 (0078)

0001 (0082)

0095 (0076)

0079 (0082)

0-027 (0079)

0011 (0-071)

0079 (0079)

0026 (0-072)

60

P1

0-415 (0164)

0140 (0092)

0-460 (0186)

0-420 (0-174)

0-537 (0-208)

0-358 (0150)

0-182 (0098)

0083 (0068)

0-233 (0111)

0-539 (0-205)

0090 (0-070)

0-363 (0-152)

§

P

7-4516 (11742)

4-2189 (0-8416)

5-2824 (0-8415)

4-2249 (0-6668)

31094 (0-4644)

3-1976 (0-5216)

2-6856 (0-4537)

5-2620 (0-9411)

2-6636 (0-4278)

6-3764 (0-9248)

5-6081 (0-9559)

41999 (0-6347)

£

a*1

01029

01244

0-1266

01659

01874

0-2004

0-3071

0-3797

0-2467

0-2437

1-6773

0-8109

e,

0-2943

01629

0-3220

0-2916

0-3264

0-2635

0-1873

00884

01976

0-3550

00950

0-2764

a

* All nutrients are in natural logarithms. The estimated asymptotic standard errors are in parentheses. y2 is the coefficient of the overall constant term. ft2 is the coefficient of the weekday-weekend indicator variable, a is the coefficient of the lagged dependent variable, p1 is the (between/within) variance ratio (4). ft is the mean calculated from (6). a*1 is the MLE of the within variance a2. 0t is the proportion explained by between subject variation (5). H = 37, T = 7.

> £7*

Table III. Maximum likelihood estimates of the dynamic error components model using 7-day consecutive food records after the intervention* Total fat

Saturated fat

Mono. fat

Poly. fat

5096 (0-440)

3-493 (0-329)

2-271 (0-231)

2-565 (0-242)

2-231 (0196)

4-931 (0-399)

2-610 (0-218)

5-353 (0-560)

5-906 (0-420)

4-588 (0-338)

0001 (0063)

- 0053 (0-053)

0053 (0077)

0080 (0085)

0094 (0090)

-0-004 (0109)

0-247 (0-140)

-0-141 (0069)

- 0129 (0076)

- 0-324 (0184)

-0330 (0-112)

0054 (0089)

0006 (0089)

0011 (0084)

0068 (0087)

0106 (0-087)

0041 (0088)

0040 (0080)

-0-003 (0083)

0159 (0087)

- 0085 (0-078)

-0-065 (0075)

0-309 (0146)

0-127 (0083)

0-552 (0-222)

0091 (0072)

0139 (0-087)

0086 (0-070)

0129 (0-082)

0031 (0052)

0-352 (0-145)

0-243 (0127)

0173 (0-094)

0-230 (0116)

7-2203 (1-3501)

40360 (0-7249)

5-1514 (0-8816)

3-7485 (0-7010)

2-5395 (0-5020)

2-6760 (0-4945)

2-3239 (0-3928)

4-8807 (0-7812)

2-6007 (0-4293)

6-367 (1-3241)

5-4453 (0-7663)

4-3086 (0-6159)

00950

01784

01147

0-2850

0-3547

0-3875

0-3547

0-6427

0-2088

0-2681

1-6645

0-6104

0-2564

01142

0-3617

00943

01464

0-0857

0-0857

00292

0-2589

0-2508

0-1275

0-1683

Energy

Protein

6-831 (0-638)

4013 (0-362)

0006 (0044)

* See notes to Table II.

Carbohydrate

Cholesterol

-0-010 0081

Fibre

Calcium

^-carotene

Vitamin C

346

A. Bhargava et al.

in the energy intakes of British army recruits. The present model, however, assumes that the stochastic process representing the intakes is the same throughout the week. This assumption merits closer investigation; we address this later in Section 4.2. Lastly, the estimated within variances in the intakes of /J-carotene and vitamin C are quite large and the proportion of variation due to the between subject differences (0j) ranges from a low of 0088 for cholesterol to a high of 0-355 for the calcium intakes. Overall, these results are close to the findings of previous research that assumed no autocorrelation in the intakes. This similarity seems somewhat surprising but is probably due to the insignificance of the autocorrelations in the pooled 7-day records. Next, considering the results after the dietary intervention (Table III), it is remarkable that the within variances of the total fat, saturated fat, monounsaturated fat and cholesterol intakes are almost double the corresponding estimates in Table II. The exception in the fatty acid group is polyunsaturated fat where the within variance increased only slightly. Thus, after the intervention, the subjects varied their diets to a greater extent in the consumption of foods containing high proportions of fats and cholesterol. Also, the intervention resulted in a reduction in the mean intakes of these nutrients; the estimated standard errors are large due to the modest number of subjects in the sample. Of course, it would have been useful to compare the present results with those for a (control) group of women not enrolled in the intervention programme. The influence of seasonal factors on the intakes could have been isolated by such a comparison. The autocorrelations are again mostly insignificant in Table HI with the exception of the calcium intakes. The weekend dummy variable is positive and significant at the 5 per cent level for cholesterol intakes and appears with significant negative coefficients for the intakes of fibre, /J-carotene and vitamin C. Thus there are real differences in the mean intakes of these nutrients on weekdays and the weekend before and after the intervention programme. Moreover, the stochastic properties of the intakes may differ. We can address this issue by estimating the model separately for the intakes on weekdays and the weekend. The analysis will afford some insights into the effects of the intervention programme on the pattern of food consumption during the week. 4.2. Variations and autocorrelation in intakes on 3 weekdays and the weekend Tables IV and V present the estimates of the dynamic model for the nutrient intakes on three consecutive weekdays and the weekend before and after the intervention, respectively. First, in Table IV, the estimated autocorrelations in the weekend intakes are positive, large and statistically significant, whereas those for weekdays are small and often negative. It is perhaps not surprising that the pooling of the data in the 7-day records obliterates the autocorrelation pattern in the intakes. Second, comparing the results in Tables IV and V, it is evident that the dietary intervention resulted in a reduction of the mean intakes of fat and cholesterol on both weekdays and the weekend. Third, before the intervention, the within variances of the fat and cholesterol intakes tend to be higher on weekends than on weekdays (Table IV). Interestingly, these differences almost disappear after the intervention programme (Table V) as the within variances decline on the weekend and increase on weekdays. In fact, the within variances estimated for the weekend intakes using an error components model that assumes no autocorrelation showed a similar decline after the intervention. Further, a greater number of the autocorrelations in the intakes on weekdays are negative and significant in Table V. Thus, after the intervention, the subjects tend to offset high (low) fat and

Table IV. Maximum likelihood estimates of the dynamic error components model for 3 consecutive weekdays and the weekend before the intervention* Energy

Protein

3 consecutive weekdays 8-507 2-971 (0-441) (1-498)

Carbohydrate

Total fat

Saturated fat

Mono. fat

Poly. fat

Cholesterol

Fibre

Calcium

/?-carotene

Vitamin C

7-271 (0-905)

4-412 (0-793)

3-307 (0-607)

2-955 (0-386)

2-318 (0-566)

4-312 (1-410)

2-810 (0-641)

6-707 (1-456)

4-780 (0-647)

4192 (1-087)

-0-381 (0171)

-O042 (0190)

-O058 (0192)

0078 (0122)

0130 (0-214)

0186 (0-268)

- 0051 (0-238)

-0058 (0-227)

0159 (0111)

0005 (0-243)

0142 (0-201)

0-298 (0104)

0-337 (0-372)

00

1-513 (0-967)

0105 (0197)

0-291 (0-311)

00

0036 (0-172)

0071 (0-272)

0-500 (0-567)

0-617 (0-612)

00

0-490 (0-573)

7-4505 (2-6253)

4-2344 (1-2571)

5-2641 (1-3067)

4-2329 (1-5308)

31266 (1-1393)

3-2067 (0-8430)

2-6660 (1-3051)

5-2958 (3-4708)

2-6733 (1-2148)

6-3395 (2-7337)

5-6863 (1-5123)

4-2131 (21171)

00702

00801

00762

01486

01899

01949

0-2459

0-2194

01480

01968

1-6338

0-7845

0-2019

00

0-4039

00884

0-2058

00

00448

00932

0-3112

0-3546

00

0-3311

4-421 (1084)

3-327 (0-668)

2-273 (0-253)

2-624 (0-615)

2067 (0-446)

1-952 (0-404)

1-475 (0-176)

5156 (0-874)

2-288 (0-420)

3-337 (0-864)

4-268 (0-888)

2-261 (0-513)

0-385 (0145)

0182 (0-152)

0-527 (0046)

0-339 (0145)

0-287 (0144)

0-338 (0129)

0-371 (0057)

0026 (0159)

0063 (0-157)

0-432 (0136)

0151 (0-155)

0-306 (0120)

0001 (0-012)

0009 (0064)

00

0001 (0019)

0001 (0-014)

0012 (0084)

0005 (0021)

0001 (0-015)

00

0009 (0044)

0015 (0-071)

71864 (3-4542)

40671 (1-5695)

4-8095 (0-9960)

3-9669 (1-7968)

2-8981 (1-2075)

2-9481 (11811)

2-3463 (0-4564)

5-2917 (1-7570)

2-4422 (0-8557)

5-8707 (2-9185)

50253 (1-9557)

3-7769 (1-3694)

0-2020

0-2445

01794

0-3452

0-3551

0-3932

0-5536

0-6372

0-3735

0-4170

2-2629

1-2316

00

0002

00276

00

00022

0-0011

00252

00048

00012

00

0-0127

0-0271

Weekend only

00

2

* See notes to Table II. H = 37, 7" = 3 for weekdays. H = 37, T = 2 for weekend, p = 0 denotes a boundary solution.

Table V. Maximum likelihood estimates of the dynamic error components model for 3 consecutive weekdays and the weekend after the intervention* Energy

Protein

Carbohydrate

Total fat

Saturated fat

Mono. fat

Poly. fat

Cholesterol

Fibre

Calcium

/J-carotene

Vitamin C

3 consecutive weekdays yi

8-554 (1-316)

3-819 (0-946)

3-203 (1-550)

4-581 (0-647)

2-580 (0-491)

3-650 (0-396)

2-513 (0-478)

5-759 (1020)

2-912 (0-591)

40702 (1-863)

7-130 (0-956)

4-681 (0-888)

a

-0-189 (0-182)

0048 (0-236)

0-371 (0-299)

- 0-243 (0167)

- 0032 (0188)

- 0-401 (0145)

- 0129 (0-201)

-0-195 (0-210)

- 0109 (0-223)

0-362 (0-292)

- 0-325 (0-167)

- 0088 (0-195)

P1

1193 (0-814)

0116 (0-292)

0054 (0-316)

1090 (0-725)

0-739 (0-573)

1-734 (1-003)

0-590 (0-571)

0-361 (0-438)

0-529 (0-515)

0047 (0-263

0-346 (0-357)

0143 (0-287)

P

7-1968 (2-2110)

40096 (1-9873)

50949 (40079)

3-6844 (1-0153)

2-4997 (0-9271)

2-6046 (0-5469)

2-2262 (0-8177)

4-8194 (1-6989)

2-6248 (10599)

6-3846 (5-8485)

5-382 (1-3974)

4-3015 (1-5847)


00606

01465

01264

01668

0-2542

01813

0-2617

0-4768

01630

0-2440

1-3237

0-4559

01

0-4488

01130

01054

0-3987

0-4093

0-4225

0-3130

01957

0-2981

00912

01499

01071

03

n TO

31 Weekend only 4-407 7l (1-090)

2-790 (0-558)

3-836 (0-722)

2-332 (0-554)

1-563 (0-215)

1-600 (0-242)

1-593 (0-358)

3062 (0-705)

1-731 (0-290)

3092 (0-724)

2-683 (0-538)

2-694 (0-575)

a

0-384 (0-153)

0-299 (0138)

0-257 (0-138)

0-347 (0145)

0-336 (0073)

0-362 (0079)

0-249 (0148)

0-393 (0132)

0-332 (0116)

0-520 (0118)

0-444 (0109)

0-295 (0-138)

P2

00

0003 (0019)

0003 (0019)

00

0030 (0121)

0016 (0088)

0002 (0028)

00

0010 (0064)

00

0-001 (0012)

0003 (0032)

P

71594 (3-5485)

3-9777 (1-5799)

51634 (1-9293)

3-5727 (1-6381)

2-3532 (0-5692)

2-5092 (0-6780)

21202 (0-8878)

50413 (2-2526)

2-5916 (0-8738)

6-4410 (3-0925)

4-8274 (1-8934)

3-8196 (1-5519)

a*2

01021

0-1772

01615

0-2180

0-2848

0-2615

0-2708

0-5446

0-2733

0-2770

1-6890

0-9206

0,

00

00052

00044

00

00564

00329

00039

00

00192

00

00015

00054

* See notes to Table II.

Variations and Autocorrelations in Dietary Intakes

cholesterol intakes by lower (higher) intake on the subsequent day. The doubling of the within variances of these nutrients in the 7-day records after the intervention (Table HI) results mainly from the increased variation in the consumption of foods high in fats and cholesterol on weekdays. This adjustment may have been facilitated by the fact that practically all the women in the sample worked on weekdays. Since the dietary records commenced on Tuesday or Wednesday, we cannot apply a likelihood ratio test for constancy of the model parameters on weekdays and the weekend. Finally, as a matter of general interest, Tables VI and VII report the estimates of the dynamic model using 7 consecutive records for the nutrient densities before and after the dietary intervention, respectively. Since the nutrient intakes are generally lower after the intervention, these results reflect to some degree the confounding effects of the educational programme. Note, however, that the within subject variation in fat and cholesterol densities is again doubled by the intervention. This supports our earlier finding that the subjects varied their diets in the consumption of foods high in these nutrients. We do not report the weekday and weekend results in the paper partly to economize on space and also because the maximum of the likelihood function frequently occurred at the boundary p2 = 0. This is discussed in the next section. 5. DISCUSSION The empirical results in the paper show that the stochastic properties of the nutrient intakes of 37 women in the Houston area differ on weekdays and the weekend. While the cultural, socioeconomic and work related factors that affect food consumption are likely to explain these differences, we cannot assess their precise influence in the present sample owing to the limited number of subjects. Yet, such issues have considerable importance for the design of effective dietary guidelines. It is, for example, plausible that the dietary intervention might have produced different results if the women were at home on weekdays. The incorporation of such considerations into the statistical analyses of nutritional data on a larger number of subjects in the future will enhance the development of dietary guidelines. Some research is in progress using the Women's Health Trial data set4 that consists of over 300 women among whom roughly one-third are controls. Thus, in contrast with the present analysis of the Houston sample, it is possible to compare the effects of the intervention programmes on the nutrient intakes of the women in the intervention and control groups. We note, however, that in the Women's Health Trial the weekend is represented by the recording of food intakes only on Sundays. Thus separate analyses of the weekday and weekend intakes are not feasible. The different signs of autocorrelations on weekdays and the weekend imply that the rates of convergence of the estimated mean intakes to the population values are affected by whether the observations are for a weekday or the weekend. While the weekend estimates from the present sample may be less reliable, the compilation of 7-day records is appealing. However, such surveys are expensive to conduct and may suffer from high attrition rates. In such circumstances, it might be reasonable to rely upon 5-day records that consists of 3 consecutive weekdays and the full weekend. A comparison of the empirical results obtained from 5- and 7-day food records could shed further light on this issue. Another alternative is to record the food intakes on 3 consecutive weekdays (such as Monday, Tuesday and Wednesday) followed by observations on Friday, Saturday and Sunday in the subsequent week. Such a design could reduce the subjects' perception of the effort required in completing the questionnaires, thereby improving the quality of dietary information. Overall, the weekday/weekend distinction is important; the efficacy of an intervention will be determined by the extent to which the subjects alter food consumption during weekdays and the weekend. Finally, we must mention in Tables IV and V the frequent occurrence of the maximum of the log-likelihood function at the boundary p2 = 0. This occurrence results partly from the modest

349

Table VI. Maximum likelihood estimates for nutrient densities using 7-day consecutive food records before intervention* Protein 7i

Carbohydrate

Total fat

Saturated fat

Mono, fat

Poly, fat

Cholesterol

Fibre

Calcium

^-carotene

Vitamin C

2-323 (0-229)

3-929 (0-298)

3-657 (0-283)

2-501 (0-196)

2-696 (0-202)

1-667 (0119)

4-379 (0-403)

1-558 (0144)

5-438 (0-455)

4-440 (0-411)

3-514 (0-295)

0016 (0038)

-0-060 (0026)

-0-005 (0-030)

0030 (0-042)

0028 (0035)

— 0-118 (0066)

0072 (0077)

-0-076 (0077)

-0-038 (0060)

-0-356 (0-223)

- 0-252 (0-125)

0155 (0082)

-0-028 (0078)

-0-023 (0079)

-0015 (0078)

- 0058 (0-079)

0-205 (0113)

0-415 (0167)

0-372 (0158)

0-387 (0160)

2-7487 (6-5386)

3-8210 (0-5796)

3-5671 (0-5529)

00673

00304

0-2193

0-2819

0181 (0-061)

0071 (0-083)

0-266 (0067)

0068 (0077)

0123 (0-081)

0039 (0-076)

0-562 (0-216)

00

0042 (0-059)

00

0-329 (0145)

0032 (0-054)

0-278 (0126)

2-4631 (0-3822)

2-5475 (0-3796)

20345 (0-2946)

4-7141 (0-8545)

2-1218 (0-3863)

5-8324 (0-9714)

50605 (09231)

3-6549 (0-5841)

00392

00745

00533

01744

0-2928

01860

01738

1-5347

0-7647

0-2621

0-2727

0-3335

00

00459

00

0-2738

00391

0-231

* See notes to Table II. The densities for protein, carbohydrate and fats are defined as calories from these nutrients per 1000 kcal; densities for the remaining nutrients are grams or milligrams per 1000 kcal.

> CO OfQ

P

<

Table VII. Maximum likelihood estimates for nutrient densities using 7-day consecutive food records after the intervention* Protein li

* See notes to Table VI.

Carbohydrate

Total fat

Saturated fat

Mono, fat

Poly, fat

Cholesterol

Fibre

Calcium

^-carotene

Vitamin C

2-865 (0-227)

3-752 (0-335)

3-454 (0-271)

2156 (0163)

2-352 (0189)

1-848 (0-159)

4-996 (0-360)

2-706 (0-185)

5-375 (0-507)

5-339 (0-420)

4-042 (0-296)

0008 (0046)

-0-057 (0033)

0-055 (0051)

0-085 (0090)

0096 (0-072)

- 0010 (0-070)

0-254 (0100)

-0-141 (0057)

-0-135 (0065)

- 0-338 (0-244)

- 0-335 (0-147)

0-021 (0080)

0043 (0-085)

- 0038 (0-082)

- 0016 (0-075)

- 0-042 (0080)

0030 (0-082)

-0-094 (0-076)

0093 (0-077)

0-112 (0-083)

- 0051 (0-081)

- 0011 (0-071)

0-253 (0-122)

0135 (0084)

0154 (0-081)

0-215 (0-101)

0131 (0-074)

0196 (0101)

0141 (0-084)

0167 (0094)

0173 (0100)

0-115 (0078)

0134 (0-028)

2-8071 (0-4424)

3-9216 (0-6970)

3-3284 (0-5233)

2-1214 (0-3114)

2-2573 (0-3590)

1-9056 (0-3206)

4-5665 (0-6439)

2-2901 (0-3971)

60534 (11363)

5-1374 (0-7825)

3-9982 (0-5686)

00904

0-0527

01209

01888

01989

0-2007

0-4963

0-1578

0-2005

1-6246

0-5802

01955

0-1283

01252

0-1724

01076

0-1725

01043

0-1675

01781

00940

01160

352

A. Bhargava et al. sample size used in the estimation and is exacerbated by the reduction in the number of observation times when we estimate the models separately for the weekday and the weekend intakes. We commenced the numerical procedure for optimizing the profile log-likelihood function of the dynamic model at different initial values to check the robustness of the reported results. The iterations, however, converged to the same solutions. Such problems are less likely to occur in larger samples. The availability of 5 consecutive days' food records or 3 consecutive records in adjacent weeks on a large number of subjects in the future will benefit the development of intervention programmes that incorporate the socioeconomic constraints on food consumption. From this viewpoint, the empirical analysis presented in this paper highlights important issues for attempts to alter women's dietary habits by means of educational programmes. ACKNOWLEDGEMENTS

Without implicating, the authors would like to thank Dr. Charles Brown, an anonymous referee and the editor for several helpful comments. An earlier version of this paper was presented at the National Cancer Institute and the comments of the participants were useful. Thanks are also due to the Cornell Theory Center for time on their Supercomputer. REFERENCES 1. Willett, W. Nutritional Epidemiology, Oxford University Press, New York, 1990. 2. Greenwald, P. 'Strengths and limitations of methodologic approaches to the study of diet and cancer: summary and future perspectives with emphasis on dietary fat and cancer', Preventive Medicine, 18, 163-166 (1989). 3. Buzzard, M. I., Asp, E. H., Chelbowski, R. T., Boyar, A. P., Jeffery, R. W., Nixon, D. W., Blackburn, G. L., Jochimsen, P. R., Scanlon, E. F., Insull, W., Elashoff, R. M., Butrum, R. and Wynder, E. L., 'Diet intervention method to reduce fat intake: nutrient and food group composition of selfselected low-fat diets', Journal of the American Dietetic Association, 90, 42-50 (1990). 4. Henderson, M. M., Kushi, L. H., Thomson, D. J., Gorbach, S., Clifford, C. C, Insull, W., Moskowitz, M. and Thomson, R. 'Feasibility of a randomized trial of a low fat diet for the prevention of breast cancer', Preventive Medicine, 19, 115-133 (1990). 5. Block, G. 'A review of validation of dietary assessment methods', American Journal of Epidemiology, 115, 492-505 (1982). 6. Beaton, G. H., Milner, J., Corey, P., McGuire, V., Cousins, M., Stewart, E., de Ramos, M., Hewitt, D., Grambsch, P.V., Kassim, N. and Little, J. A. 'Sources of variance in 24-hour dietary recall data: implications for nutrition study design interpretation', American Journal of Clinical Nutrition, 32, 2546-2559 (1979). 7. Hartman, A. M., Brown, C. C, Palmgren, J., Pietinen, P., Verkasalo, M., Myer, D. and Virtamo, J. 'Variability in nutrient and food intakes among older middle-aged men', American Journal of Epidemiology, 132, 999-1012 (1990). 8. United States Department of Agriculture. Nutrition and Your Health: Dietary Guidelines for Americans, bulletin no. 232, Washington D.C., 1990. 9. Sukhatme, P. V. and Margen, S. 'Autoregulatory homeostatic nature of energy balance', American Journal of Clinical Nutrition, 35, 355-365 (1982). 10. Bhargava, A. 'Malnutrition and the role of individual variation with evidence from India and the Philippines', Journal of the Royal Statistical Society, Series A, 155, 221-231 (1992). 11. Anderson, T. W. and Hsiao, C. 'Estimation of dynamic models with error components', Journal of the American Statistical Association, 76, 598-606 (1981). 12. Bhargava, A. and Sargan, J. D. 'Estimating dynamic random effects models from panel data covering short time periods', Econometrica, 51, 1635-1660 (1983). 13. Bhargava, A. and Bouis, H. 'Maximum likelihood estimation of between and within variations in energy and protein intakes from infancy to adolescence for the Philippines', Statistics in Medicine, 11, 533-545 (1992). 14. Numerical Algorithm Group. Library of Computer Programs Mark 13, Oxford University, Oxford, 1990. 15. Nelson, M., Black, A. E., Morris, J. A. and Cole, T. J. 'Between and within subject variation in nutrient intake from infancy to old age: estimating the number of days required to rank dietary intakes with desired precision', American Journal of Clinical Nutrition, 50, 155-167 (1989).

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Preventive Medicine

S C I EENNCCE E(7\\ D D I R E C T *

@ '

ELSEVIER

Preventive Medicine 38 (2004) 442-451 www.elsevier.com/locate/yprned

Behavioral variables and education are predictors of dietary change in the Women's Health Trial: Feasibility Study in Minority Populations Alok Bhargava, Ph.D.3'* and Jennifer Hays, Ph.D. b 3

Department oj'Economics, University of Houston, Houston, TX 77204-5019, USA b Department of Medicine, Baylor College of Medicine, Houston, TX 77030, USA

Abstract Background, Reducing the intakes of fats and increasing consumption of fruits and vegetables are an important goal for improving population health. Analyzing the effects of nutrition education programs on subjects' dietary intakes incorporating factors such as habit persistence in diets, unhealthy eating habits, perceptions of health risks, participation motivation, and expectancies can yield useful insights. Methods. A Food Frequency Questionnaire (FFQ) was used to measure intakes at baseline, 6 and 12 months, by 318 and 548 postmenopausal women in, respectively, the Control and Intervention groups of the Women's Health Trial: Feasibility Study in Minority Populations (WHTFSMP). Information on background, behavioral, and anthropometric variables was collected. The Intervention group met in classes led by nutritionists. Dynamic random effects models were estimated for the two groups using the data at baseline, 6 and 12 months on the intakes of carbohydrate, saturated, monounsaturated, and polyunsaturated fats, fiber, p-carotene, ascorbic acid, and calcium. Results. The nutrition education program lowered the intakes of fats while increasing fiber, (3-carotene, and ascorbic acid intakes especially in subjects scoring high on indices reflecting concerns about health, desirability of change, and participation motivation. In addition, subjects' education was a predictor of dietary intakes in the Intervention group. Conclusions. Nutrition education can be an effective tool for improving diets, but behavioral characteristics deserve greater attention in helping to design the most effective approaches for various target groups. © 2003 The Institute For Cancer Prevention and Elsevier Inc. All rights reserved. Keywords: Dietary intakes; Habit persistence; Health perceptions; Random effects models; Socioeconomic factors; Unhealthy eating

Introduction The prevalence of obesity in the United States especially among minority populations is of serious concern from a public health standpoint. Medical conditions such as hypertension, diabetes, and cardiovascular diseases diminish the quality of life and demand enormous medical resources [1,2]. Because foods high in fat are energy-dense, switching to a low-fat diet can decrease the energy intake and is a useful strategy for weight control. This strategy can also lower plasma lipids that are important risk factors for chronic diseases [3]. The extent to which nutrition education programs can facilitate dietary change is likely to be influenced by behavioral aspects such as the habit -persistence in diets [4], perception of health risks [5], expectancies and motivation for dietary change [6,7], and the participants' readiness to change [8].

* Corresponding author. Fax: +1-713-743-3798. E-mail address: [email protected] (A. Bhargava).

Nutrition education programs attempt to alter subjects' dietary intakes by inducing changes in behavioral variables, food preferences and preparation skills, goal-setting, motivation, and support for the change efforts. Thus, theoretical constructs from the psychological literature are useful for the specification of empirical models for dietary intakes. Further, randomized trials provide an opportunity to compare changes over time in dietary intakes of the Control and Intervention groups. For example, the dissemination of minimal information such as that contained in materials written by the United States Departments of Agriculture and Health and Human Services [9,10] can potentially influence intakes in the Control group. If, for example, highly educated women in the Control group reduced their fat intakes and increased the intake of essential nutrients, then greater resources can be channeled towards less educated women. There have been a few dietary intervention studies seeking to reduce women's fat intakes and increase the consumption of whole grains, fruits, and vegetables. The nutrition education program in the Women's Health Trial:

0091-7435/$ - seefrontmatter © 2003 The Institute For Cancer Prevention and Elsevier Inc. All rights reserved. doi:10.1016/j.ypmed.2003.11.014

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A. Bhargava and J. Hays

Vanguard Study lowered the fat intakes of 300 White postmenopausal women during a 24-month period [11]. The subsequent Women's Health Trial: Feasibility Study in Minority Populations (WHTFSMP) investigated dietary intakes of over 1,200 Black, Hispanic, and low socioeconomic status women in a 12-month period [12-14]. In addition to lowering fat intakes, women in the Intervention group of WHTFSMP experienced significant weight loss [15]. In previous research using the data from the Women's Health Trial, Urban et al. [16] found significant associations between adherence to low-fat diets and explanatory variables such as attendance in educational sessions, college education, and the feeling of food deprivation. However, the authors did not control for subjects' weight and did not report the associations between the explanatory variables and intakes of vital nutrients such as p-carotene, ascorbic acid, and calcium. In a study involving working women in Houston, Bhargava et al. [17] reported that following the nutrition education program, the women varied their diets to decrease the consumption of foods high in fat and cholesterol on weekdays but not on weekends, presumably due to cultural factors influencing weekend food consumption. The WHTFSMP included questions on many behavioral aspects that were likely to be associated with dietary intakes. Such questions can be combined to form indices that reflect theories pertaining to subjects' eating habits, food preparation time and budget, health beliefs, and motivation [18]. In this paper, the effects of the nutrition education program on indices reflecting behavioral aspects and the dietary intakes were analyzed using the longitudinal information at baseline, 6 and 12 months. In addition, habit persistence in diets was incorporated by estimating dynamic models for the intakes [4,19]. Comprehensive longitudinal models were estimated for the intakes of carbohydrate, and saturated, monounsaturated and polyunsaturated fats, fiber, p-carotene, ascorbic acid, and calcium by women in the Control and Intervention groups of WHTFSMP. The estimated model parameters provided insights for identifying factors that are likely to facilitate dietary change among minority and low socioeconomic status populations in the US.

Methods Subjects The WHTFSMP was a multi-center randomized trial in 1991-1995 sponsored by the National Cancer Institute involving 2,208 women in Atlanta, Birmingham, and Miami, with the goals of reducing energy intakes from fat to 20%, and increasing the consumption of fruits, vegetables, and grain products in the Intervention group [12]. The participants (28% Black, 16% Hispanic, and 54% White) were postmenopausal women in the age group 50-79 years; 40% and 60% of the subjects were randomly assigned,

respectively, to the Control and Intervention groups. Due to budget constraints on the study period, however, complete data on dietary, behavioral, and anthropometric variables at baseline, 6 and 12 months, were available for 318 women in the Control group and 548 women in the Intervention group. Data collection The goals of the WHTFSMP were to reduce fat intakes especially of saturated fat and to increase the consumption of fruits, grain products, and vegetables. The women in the Intervention group, led by a nutritionist, met weekly in groups of 8-15 for the first 6 weeks, biweekly for the next 6-weeks, and monthly thereafter for 9 months. The subjects in the Control group received minimal information on healthful eating [9]. Dietary intakes at baseline, 6 and 12 months, were measured in the two groups by a Food Frequency Questionnaire (FFQ) especially developed for this study [12,20]. The subjects' age, marital status, and reproductive history were recorded in the questionnaire. Education levels were coded into four categories that were increasing with the years of education. Similarly, household incomes were coded into three groups. Subjects' height and weight were measured at baseline and at 6 and 12 months. Height was measured with a stadiometer by rounding off to the nearest half-inch; weight was measured to the nearest pound using a calibrated balanced beam scale. The subjects were asked several questions at baseline, 6 and 12 months, regarding their eating habits, time spent on food preparation, motivation for dietary change, concerns about health, and the reasons for participation in the WHTFSMP; four indices were constructed using the responses. The index 'Unhealthy eating' was based on the answers, on a scale of 1-4 (1 = never, 4 = very often), to eight questions regarding the subjects' food cravings and preferences: (i) if they liked tasty food, (ii) had craving for rich foods, (iii) liked healthy foods, (iv) ate more than they should, (v) whether the food consumed was satisfying, (vi) felt uncomfortable with rich foods, (vii) felt deprived in the absence of rich foods, and (viii) disliked the taste of fat. The scores on eating healthy foods, felt uncomfortable with rich foods, and disliked the taste of fat were recoded so that higher scores implied less healthy eating habits. The scores on the eight questions were summed to produce the 'Unhealthy eating' index that ranged from 8 to 32 [15]. The index 'Preparation and budget' was based on the answers, on a scale of 1-4 (1 = very little, 4 = a lot), to four questions regarding the time spent on shopping for food, preparing food, trouble taken in preparing food, and the money spent on food. The scores on these four questions were summed and this index ranged from 4 to 16. The index 'Concerned about health' was based on the answers to seven questions, on a scale of 1-5 (1 = not important, 5 = very important), regarding health-related reasons for participating

Dietary Change in the Women's Health Trial in the WHTFSMP. This index summed the scores on (i) whether the subjects had a relative or a friend with cancer, (ii) were trying to lose or control weight, (iii) were concerned about their health, (iv) were concerned about their husband's health, (v) were concerned about their family's health, (vi) had high cholesterol or heart problems, and (vii) were afraid of getting cancer. The scores on the 'Concerned about health' index ranged from 7 to 35. The index 'Participation motivation' was based on the answers to questions regarding motivating factors for participating in the WHTFSMP. The subjects answered four questions, on a scale of 1-5 (1 = not important, 5 = very important), whether they felt that their participation was important for helping scientific research, learning more about nutrition, sharing activities with new people, and for helping the community. The scores on 'Participation motivation' index ranged from 4 to 20. In addition to these four indices, subjects were asked if they were consuming a lowfat diet (0 = no, 1 = yes). Also, on a scale of 1-4 (1 = not strong, 4 = very strong), subjects were asked about their 'Desirability of change' to low-fat diet.

355

energy intake are discussed by Willett [21]. Moreover, certain coefficients such as those of the indices reflecting behavioral variables were likely to differ in the two groups due to the nutrition education program. The model We postulated dynamic random effects models for the dietary intakes by n subjects at three time points (baseline, 6 and 12 months) (i = 1, 2,..., n; t = 2, 3): ln(Intake),7 = a0 + ct\ (Black),. + «2 (White),. + aj, (Education), + (^(Income),. + a5ln(Height). + aj (Eating low — fat diet),., + a-i (Desirability of change),, + agin (Unhealthy eating) ,-, + a9ln(Preparation and budget),.,

Analyticalframeworkfor modeling the proximate determinants of dietary intakes

+ aioln(Concerned about health),, + anln(Participation motivation),,

The subjects' dietary intakes are likely to be influenced by background variables, education levels, eating preferences, perceptions regarding current and future health status, motivation, budget and food prices, and the energy requirements. Several hypotheses are available in the psychology literature regarding factors that can influence dietary intakes. For example, Bandura's [6] social learning theory and social cognitive theory [7] underscored the influence of expectancies and incentives for changing behaviors; the health belief model [5] hypothesized the importance of perceptions regarding vulnerability to ill-health. Economists have emphasized habit persistence in diets [4,19]; dietary intakes are likely to depend on the intakes in the previous period. The Food preparation and budget index, reflecting time and monetary constraints, could be important for women from low-income households. The Participation motivation index may be relevant for the intakes especially by women in the Intervention group. Further, while subjects in the Control group received minimal information on healthful eating, the Intervention group met in regular sessions with nutritionists. Because the changes in the intakes over time would operate partly through changes in behavioral factors, it was of interest to compare the changes in indices of behavioral variables for the two groups. In addition, models for dietary intakes should take into account subjects' anthropometric variables such as height and weight and the energy intakes. We adopted a general formulation where the energy intake was an explanatory variable and its inclusion enabled tests of hypotheses that the intakes can be expressed as ratios to the energy intake. Alternative methods for adjusting for the

+ a12ln(Weight),., + ai3m(Energy intake),, + a14ln(Intake),.,_, + uu

(1)

Here, In represents natural logarithm and a0,..., a,4 are unknown coefficients; a0 is the coefficient of the overall constant term. The model was estimated for intakes of carbohydrate, saturated, monounsaturated and polyunsaturated fats, fiber, p-carotene, ascorbic acid, and calcium. The dietary intakes, weight, and the indices Unhealthy eating, Preparation and budget, Concerned about health, and Participation motivation were transformed into natural logarithms, partly to reduce heteroscedasticity [22], Coefficients of the variables in logarithms were thus the 'elasticities' (percentage change in the dependent variable resulting from a 1% change in the independent variables). The variables Black and White were indicator (0-1) variables for subjects' race (with coefficients interpreted in relation to the Hispanic subgroup) and were in part included in view of the results of Kristal et al. [14] showing that the fat intakes differed by race. Furthermore, the indicator variables for race and the categorical variables Education and Income were 'time invariant' and their coefficients can be estimated using the dynamic model in Eq. (1). Eating low-fat diet was an indicator variable and Desirability of change was a categorical variable that assumed different values at the baseline, 6 and 12 months. The subjects' age and agesquared were also included as explanatory variables in the models.

356

A. Bhargava and J. Hays

The models for dietary intakes contained the intakes in the previous period ('lagged dependent variable') as explanatory variables with coefficient a]4. The role of behavioral and socioeconomic variables in bringing about dietary change can be analyzed using the estimated parameters of the dynamic longitudinal model in Eq. (1). While one can estimate 'static' models for changes in intakes by excluding the previous intakes and the variables that do not change over time from the set of explanatory variables, the dynamic model was likely to provide a more comprehensive view of the factors affecting dietary intakes [15]. The uit were random error terms that can be decomposed in a random effects fashion as uu = Si + V,-,

(2)

where <5; were subject-specific random variables that were assumed to be normally distributed with zero mean and a constant variance, and v„ were normally distributed random variables with zero mean and constant variance [23]. If the unobserved subject-specific random effects (<5;) affecting the dietary intakes in Eq. (1) also influenced energy intakes, then energy intake would be correlated with the error term uit. Such problems can be tackled by the use of econometric techniques briefly described below. Moreover, the null hypothesis that the coefficient of energy intake in Eq. (1) was equal to one (i.e., a^ = 1) was tested by likelihood ratio tests. The acceptance of the null hypothesis for the particular intakes would imply that it was preferable to express the intakes as ratios to energy intake. The null hypothesis of constancy of model parameters across the Control and Intervention groups was tested using likelihood ratio statistics. Statistical and econometric methods For assessing changes between the baseline and 12month periods in the Control and Intervention groups, paired t tests were used to test the null hypotheses that there were no differences between the means of the behavioral variables, body weight, and dietary intakes. The software package SPSS [24] was used to compute descriptive and t statistics. Differences between changes in the means in the Control and Intervention groups were tested using t tests. Cronbach's a's [25] were computed for the indices Unhealthy eating, Preparation and budget, Concerned about health, and Participation motivation. Because only three time observations were available on the subjects, the estimation of the model in Eq. (1) was based on the assumptions that the number of women («) was large but the number of time periods was fixed. Thus, initial observations on the dependent variables (Intake,/ in Eq. (1)) were treated as correlated with the errors by specifying a 'reduced form' equation [26], The errors affecting the model were assumed independent across women, but correlated over time with a positive definite variance-covariance matrix. However, for comparability with previous studies,

the results were reported for the simple random effects model in Eq. (2), where the variance of the random effects ((5j) reflects the unobserved between-subject differences, while the variance of v„ captures the within-subject variation in the intakes over the three time points. The joint determination of the three time observations in the models for dietary intakes implied that econometric techniques for estimating simultaneous equations models were useful. Details of the maximum likelihood estimation method are presented elsewhere [26], We note that the profile log-likelihood functions of the model in Eq. (1) were optimized using a numerical scheme [27]; asymptotic standard errors of the parameters were obtained by approximating second derivatives of the function at the maximum. Possible correlations between the random effects (<5j) and the time means of the energy intakes were tested using likelihood ratio statistics that were distributed, for large n, as Chi-square variables with three degrees of freedom.

Results Descriptive statistics and t tests The sample means and standard deviations of the variables for subjects in the Control and Intervention groups are presented in Table 1. The significant changes (P < 0.05) between the baseline and 12 months and the differences in the changes between baseline and 12 months for the two groups are also indicated in Table 1. The sample means of background variables such as race, education, and income, and of the indices Unhealthy eating, Preparation and budget, Concerned about health, and Participation motivation were similar at baseline for the two groups. The scores on the Unhealthy eating index were significantly lower at 12 months especially for the Intervention group; the difference between changes in the Control and Intervention group was statistically significant (P < 0.05). There were large changes between the baseline and 12 months in the proportion of women reporting the consumption of low-fat diets in the Control and Intervention groups. The Desirability of change to low-fat diet showed that this variable significantly declined over time in the Control group. By contrast, there was a significant increase in the Intervention group. The Participation motivation index did not show a significant change between the baseline and 12 months for women in the Control group but had significantly increased in the Intervention group. For the Control group, changes in body weight between the baseline and 12 months were not statistically significant. By contrast, women in the Intervention group lost approximately 2.26 kg and the change was statistically significant. The declines in energy intakes were significant in both groups and the difference between the two groups was significant. Similarly, the intakes of carbohydrate and saturated, monounsaturated, and polyunsaturated fats, and the

357

Dietary Change in the Women's Health Trial

Table 1 Sample means and standard deviations of selected variables for the 318 women in Control group and 548 women in the Intervention group at baseline, 6 months and 12 monthsa"b Intervention groupi (« = 548)

Control group (n = 318) Baseline Age, year Black ( 0 - 1 ; 0 = no, 1 = yes) White ( 0 - 1 ; 0 = no, 1 = yes) Education (1 - 4 ; 1 = low, 4 = high) Income (1-3; 1 = low, 3 = high) Height, m Unhealthy eating (8-32) Preparation and budget (4-16) Eating low-fat diet (0-1) Desirability of change (1-4) Concerned about health (7-35) Participation motivation (4-20) Weight, kg Energy intake, kJ Carbohydrate, g Saturated fat, g Monounsaturated fat, g Polyunsaturated fat, g Calcium, mg P-carotene, ug Ascorbic acid, mg Fiber, g % Energy carbohydrate % Energy saturated fat % Energy monounsaturated fat % Energy polyunsaturated fat

59.67 ± 0.41 ± 0.56 ± 2.91 ± 1.96 ± 1.63 ± 21.18 ± 10.21 ± 0.44 ± 3.54 ± 28.3 ± 16.1 ± 76.77 ± 7160 ± 190.7 ± 25.8 ± 28.3 ± 16.9 ± 661.5 ± 3833 ± 94.4 ± 13.2 ± 45.4 ± 12.7 ± 14.5 ± 8.7 ±

6 months 6.31 0.49 0.50 1.01 0.48 0.06 2.8 1.8 0.50 0.68 4.9 2.9 12.2 3303 87.0 14.6 15.7 9.9 404 3849 53.2 6.1 8.2 3.0 3.0 2.5

20.44 10.13 0.58 3.20 27.1 15.6 76.53 6385 177.3 21.1 24.0 13.9 604.2 3713 95.9 12.4 47.3 12.1 13.8 8.1

± ± ± ± + + + + ± + + ± + + + + ± + ± +

2.9 1.8 0.49 0.87 5.4 3.3 12.3 3095 84.8 12.9 14.1 8.6 385 2895 55.4 6.1 8.7 2.9 3.0 2.5

12 months

20.34 10.04 0.60 3.19 27.2 15.8 76.50 6192 173.1 20.5 22.7 13.2 613.8 3747 92.7 12.4 47.7 11.9 13.4 7.8

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.8C 1.9C 0.49c 0.88c 5.5C 3.2 12.4 3235° 89.1 c 14.2" 14.6C 9.3C 411 c 3499 53.1 6.1 c 8.8° 3.0° 3.1c 2.5C

Baseline 60.52 0.36 0.58 3.00 1.98 1.63 21.26 10.27 0.38 3.38 27.8 16.2 76.08 7427 196.0 26.9 30.1 17.4 693.2 3613 93.6 13.1 44.6 13.3 15.0 8.8

± + ± ± ± + ± ± + ± ± ± ± ± ± ± ± ± + ± ± ± ± ± ± ±

6.58 0.48 0.49 0.98 0.49 0.06 2.9 1.9 0.48 0.82 5.4 3.2 12.8 3643 100 15.7 16.6 9.8 413 2847 55.0 6.3 7.7 2.8 2.9 2.5

6 months

12 months

19.18 10.38 0.91 3.59 27.7 16.7 74.11 5393 181.1 13.1 14.0 7.8 656.6 3916 103.5 13.1 56.7 8.9 9.6 5.4

19.05 10.32 0.93 3.46 27.5 16.5 73.82 5438 185.7 13.0 13.8 7.6 668.8 3712 108.1 13.3 57.8 8.7 9.3 5.2

± ± ± ± ± + ± ± ± ± ± ± + ± ± ± ± ± ± ±

2.6 1.9 0.29 0.66 5.2 3.0 12.7 2294 78.2 7.8 8.6 5.3 374 2730 56.6 6.9 9.4 2.6 3.2 2.1

± ± + ± ± ± ± ± ± + ± ± ± ± ± ± ± ± ± ±

2.6 cd 1.9 0.26cd 0.77c'd 5.6" 3.1c-d 12.8 cd 2430c'd 83.0° 8.2c'd 8.7c'd 4.8c'd 439 2735 58.4 cd 6.6d 9.5c'd 2.6c>d 3.2c'd 2.2c'd

a

Values are means ± standard deviations. Dietary intakes were based on a Food Frequency Questionnaire. Differences between baseline and 12 months were significant (P < 0.05). d Differences in the changes between baseline and 12 months in the Control and Intervention groups were significant (P < 0.05).

b c

energy derived from these nutrients were significantly lower at 12 months in the two groups. Even in the absence of counseling, women in the Control group reduced their fat intakes, though it was possible that the intakes were underreported. Lastly, the Cronbach's a's for Control and Intervention groups for the indices Unhealthy eating, Preparation and budget, Concerned about health, and Participation motivation were in the range 0.66-0.85; these statistics were close to the previous findings on the internal consistency of psychological measures [28]. Empirical results for the dietary intakes in the control group The empirical results from the dynamic random effects models for selected intakes are reported in Table 2. The models for the dietary intakes were estimated separately for Control and Intervention groups because likelihood ratio tests rejected the null hypotheses that the parameters were constant in the two groups. Another set of likelihood ratio statistics were applied to test the null hypotheses that the dietary intakes should be expressed as ratios to the energy intake. The results indicated that it was preferable to adjust for energy intakes by including the energy intake as an explanatory variable in the models, as in Eq. (1), rather than

specifying the dependent variables as ratios to the energy intake. First, focusing on the intakes of carbohydrate and saturated, monounsaturated, and polyunsaturated fats, the indicator variables for race, education, and income were not significant predictors. Height was a significant predictor of these intakes (P < 0.05) though weight was not significant in the models for carbohydrate and polyunsaturated fat intakes. Both height and weight were significant predictors of the intakes of saturated and monounsaturated fats. The application of the likelihood ratio tests proposed in Ref [29] rejected the null hypothesis that height and weight can be combined as the body mass index in these models for the dietary intakes. The Unhealthy eating index was positively associated (P < 0.05) with the intakes of saturated and monounsaturated fats but not with the intakes of carbohydrate and polyunsaturated fat. The food Preparation and budget index was positively associated with monounsaturated and polyunsaturated fat intakes. The indicator variable for whether the subject was Eating low-fat diet was positively associated with carbohydrate intake and negatively associated with the fat intakes; all the coefficients were statistically significant (P < 0.05). The categorical variable Desirability

in

Table 2 Maximum likelihood estimates of dynamic random effects models for the intakes at baseline, 6 and 12 months, of carbohydrate, saturated, monounsaturated, and polyunsaturated fats, fiber, p-carotene, ascorbic acid, and calcium by women in the Control group explained by anthropometric, socioeconomic, and behavioral variables3 The intakes of (« - 318)": Constant Black (0-1) White (0-1) Education (1-4) Income (1-3) Height, mb Unhealthy eatingb (8-32) Preparation and budgetb ( 4 - 16) Eating low-fat diet (0-1) Desirability of change (1 -4)i Concerned about healthh (7 --35) Participation motivation1' (4--20) Weight, kgb Energy intake, kJb Lagged dependent variable5 Between/within variance Within variance Chi-square (3)c

Carbohydrate, g

Saturated fat, g

Monounsaturated fat, g

Polyunsaturated fat, g

Fiber, g

-1.775* -0.063 -0.081 0.001 -0.001 0.521* 0.030 -0.058 0.064* 0.014 -0.019 0.026 -0.014 0.922* 0.003 0.985* 0.0150 1.77

-5.740* ± 0.058 ± 0.064 ± 0.005 ± -0.037 ± -0.841* ± 0.157* ± -0.011 ± -0.092* ± -0.033* ± 0.017 + -0.044 ± 0.135* ± 1.139* ± -0.002 ± 1.051* ± 0.0254 6.57

-5.250* 0.094 0.033 -0.001 -0.008 -0.883* 0.088* 0.071* -0.104* -0.032* 0.047* -0.062 0.083* 1.108* 0.011 0.820* 0.0259 3.31

-4.986* 0.114 0.053 -0.008 0.019 -0.706* -0.056 0.088* -0.121* -0.024 0.052* -0.080* 0.046 1.038* 0.059* 0.730* 0.0459 0.35

-3.121* -0.196* -0.089 0.022 0.052 0.617* -0.034 -0.042 0.126* 0.017 -0.105* 0.054 0.021* 0.733* 0.034 1.274* 0.0411 0.59

± + + + + + + + + + + + + + + +

0.099 0.067 0.067 0.009 0.018 0.126 0.019 0.032 0.014 0.008 0.020 0.017 0.048 0.014 0.017 0.143

0.393 0.084 0.083 0.011 0.024 0.192 0.054 0.026 0.019 0.011 0.032 0.037 0.046 0.017 0.017 0.147

+ ± ± ± ± ± ± ± ± ± ± ± ± ± ± +

0.045 0.085 0.084 0.011 0.022 0.148 0.021 0.023 0.018 0.010 0.017 0.033 0.041 0.015 0.016 0.120

±0.172 ± 0.107 ± 0.015 + 0.014 ± 0.029 ± 0.276 ± 0.049 ± 0.023 ± 0.023 ± 0.014 ± 0.023 ± 0.037 ± 0.039 ± 0.025 + 0.022 ±0.118

± + + ± ± ± ± ± ± ± ± ± ± ± ± ±

0.062 0.090 0.088 0.015 0.032 0.037 0.055 0.052 0.024 0.014 0.017 0.033 0.004 0.025 0.036 0.230

(3-Carotene, pg

Ascorbic acid, mg

Calcium, mg

1.366 0.129 0.179 0.056* -0.105 0.733 0.003 -0.089 0.240* 0.002 -0.049 0.123 0.148 0.715* 0.029 1.223* 0.1262 9.91*

-0.938* -0.001 -0.089 0.040* -0.001 1.486* -0.060 0.052* 0.200* 0.026 -0.180* 0.122* -0.107* 0.602* 0.177* 0.720* 0.1052 1.43

-1.884* -0.139 0.116 0.002 0.013 0.114 -0.008 -0.023 0.079* 0.039* -0.061* 0.102* 0.121 1.005* 0.012 1.089* 0.0511 0.002

± + ± ± ± ± ± ± + ± ± ± ± ± ± ±

0.972 0.210 0.207 0.027 0.057 0.395 0.127 0.069 0.042 0.024 0.080 0.085 0.147 0.042 0.055 0.282

+ 0.038 + 0.157 + 0.157 + 0.021 + 0.043 ±0.139 ± 0.051 ± 0.021 + 0.035 ± 0.020 ± 0.041 ± 0.046 + 0.012 ± 0.037 ± 0.049 ±0.181

± ± ± ± ± ± ± ± + ± ± ± + + ± ±

0.505 0.122 0.124 0.016 0.035 0.312 0.033 0.061 0.027 0.015 0.030 0.042 0.083 0.021 0.021 0.159

* Values are the slope coefficients from Eq. (1) in the text + standard errors; the slope coefficients correspond to the intakes at 6 and 12 months, while the baseline intakes were used to address the statistical issues. ^ Transformed into natural logarithms. 0 Chi-square test for exogeneity of energy intake (df= 3). *P<0.05.

03

E?

era

Table 3 Maximum likelihood estimates of dynamic random effects models for the intakes at baseline, 6 and 12 months, of carbohydrate, saturated, monounsaturated, and polyunsaturated fats, fiber, p-carotene, ascorbic acid, and calcium by women in the Intervention group explained by anthropometric, socioeconomic, and behavioral variables" The intakes of (n = 548)b: Constant Black (0-1) White (0-1) Education (1-4) Income (1-3) Height, mb Unhealthy eatingb (8-32) Preparation and budgetb ( 4 - 16) Eating low-fat diet (0-1) Desirability of change (1 - 4 Concerned about healthb (7- 35) Participation motivation11 (4--20) Weight, kgb Energy intake, kJ Lagged dependent variable'1 Between/within variance Within variance Chi-square (3)c a

Carbohydrate, g

Saturated fat, g

Monounsaturated fat, g

Polyunsaturated fat, g

Fiber, g

-1.525* -0.038 -0.052* 0.005 0.009 0.180 -0.135* -0.009 0.134* 0.020* -0.021 0.047* -0.040* 0.965* 0.014 0.784* 0.0150 8.82*

-5.419* 0.054 0.005 -0.029* -0.012 -0.612* 0.314* 0.001 -0.212* -0.035* -0.062* -0.080* 0.015* 1.109* 0.040* 0.509* 0.0440 6.02

-5.310* 0.208* 0.092* -0.040* -0.032 -0.761* 0.345* 0.006 -0.237* -0.051* -0.057* -0.128* 0.075 1.082* 0.045* 0.590* 0.0496 4.39

-5.610* 0.238* 0.131* -0.026* -0.029 -1.003* 0.245* 0.015 -0.219* -0.048* -0.006 -0.136* 0.134* 1.027* 0.047* 0.594* 0.0655 4.07

-4.053* -0.049 0.056 0.039* 0.024 0.049 -0.209* -0.016 0.179* 0.030* 0.060* 0.075* 0.083* 0.823* 0.044 0.729* 0.0517 1.10

± ± + ± ± ± ± ± ± ± ± ± ± ± ± ±

0.167 0.028 0.026 0.006 0.013 0.135 0.022 0.024 0.018 0.007 0.014 0.022 0.019 0.004 0.008 0.089

± 0.027 ± 0.040 ± 0.038 ± 0.009 ± 0.014 ± 0.066 ± 0.033 ± 0.025 ± 0.028 ± 0.008 ± 0.013 + 0.026 ± 0.007 ± 0.005 ±0.012 ± 0.069

± ± ± ± + ± + ± ± + ± ± ± ± ± ±

0.220 0.044 0.043 0.010 0.021 0.115 0.041 0.040 0.031 0.012 0.019 0.035 0.049 0.010 0.012 0.076

± ± ± ± ± ± ± ± ± ± ± ± ± ± + +

0.054 0.043 0.043 0.011 0.020 0.071 0.025 0.021 0.035 0.010 0.022 0.047 0.008 0.007 0.014 0.077

± 0.300 ± 0.048 ± 0.046 ± 0.011 ± 0.022 ± 0.051 ± 0.053 ± 0.032 ± 0.033 ± 0.013 ± 0.030 ± 0.036 ± 0.020 ±0.013 ± 0.023 + 0.105

(3-Carotene, ug

Ascorbic acid, mg

Calcium, mg

0.766 -0.001 0.032 0.042* 0.047 -0.022 -0.176 -0.086 0.100 0.053* 0.203* 0.179* 0.090* 0.674* 0.144* 0.486* 0.1805 15.58*

-1.386* -0.012 -0.068 0.052* 0.027 0.464* -0.306* -0.062 0.190* 0.021 0.171* 0.052 0.036 0.674* 0.140* 0.793* 0.0995 1.15

-1.484* -0.273* -0.056 0.013 0.047 0.728* -0.101* 0.057 0.170* 0.026 0.040 -0.003 -0.080 1.044* 0.032* 0.877* 0.0575 2.12

± 0.534 ± 0.080 + 0.077 ± 0.019 + 0.038 ± 0.323 ± 0.092 ± 0.081 ± 0.058 ± 0.023 ± 0.033 ± 0.018 ±0.013 ± 0.039 ± 0.044 + 0.110

± ± + ± ± ± ± ± ± ± + ± ± ± ± ±

0.461 0.070 0.068 0.016 0.033 0.229 0.087 0.041 0.045 0.016 0.021 0.037 0.039 0.032 0.037 0.133

±0.166 ± 0.053 ± 0.051 ± 0.013 ± 0.026 ± 0.140 ± 0.038 ± 0.050 ± 0.034 ± 0.014 ± 0.036 ± 0.041 ± 0.070 ± 0.009 ± 0.006 ± 0.090

Values are the slope coefficients from Eq. (1) in the text ± standard errors; the slope coefficients correspond to the intakes at 6 and 12 months, while the baseline intakes were used to address the statistical issues. Transformed into natural logarithms. c Chi-square test for exogeneity of energy intake (df~ 3). *P< 0.0. b

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of change to low-fat diet was negatively associated with saturated and monounsaturated fat intakes. The coefficient of the Concerned about health index was significant in the models for the monounsaturated and polyunsaturated fats with positive signs implying that women in the Control group that had greater concerns for health were consuming higher quantities of these two fats. This issue is addressed in the Discussion. The Participation motivation index was significant only for the intakes of polyunsaturated fat. The coefficients of energy intakes were large and statistically significant. The coefficients of the previous intakes ('lagged dependent variables') were small and statistically insignificant in the models for carbohydrate and saturated and monounsaturated fat intakes but was significant for the polyunsaturated fat intakes. The between/within variance ratios were large and significant in the four models. These results indicated the importance of unobserved subject-specific factors affecting dietary intakes. The Chi-square tests accepted the null hypothesis that the random effects were uncorrelated with the energy intake.

was not a significant predictor of fat intakes in the Control group. The Unhealthy eating index was negatively associated with carbohydrate intakes and positively associated with fat intakes, with statistically significant coefficients (.P < 0.05). Coefficients of the indicator variable for Eating low-fat diet were statistically significant for carbohydrate and fat intakes. The categorical variable for Desirability of change was significant and positively associated with carbohydrate intakes and negatively associated with the fat intakes. The Concerned about health index was estimated with negative coefficients that were significant in the models for saturated and monounsaturated fat intakes. Thus, women in the Intervention group that were more concerned about health had lower intakes of monounsaturated and polyunsaturated fats. Participation motivation index was significantly and positively associated with carbohydrate intakes and negatively associated with the fat intakes in Table 3. The intakes in the previous periods were estimated with small coefficients that were significant in the models for the saturated, monounsaturated, and polyunsaturated fat intakes. The between/within variance ratios were significant in the models for the carbohydrate and fat intakes.

The results from the models for the intakes of fiber, pcarotene, ascorbic acid, and calcium showed that Black women in the Control group consumed significantly lower quantities of fiber. More educated women consumed greater quantities of (J-carotene and ascorbic acid. The Unhealthy eating index was not significantly associated with the intakes of fiber, p-carotene, ascorbic acid, and calcium. The food Preparation and budget index was positively associated only with ascorbic acid intakes. Women that reported consuming low-fat diets had higher intakes of fiber, [J-carotene, ascorbic acid, and calcium. The subjects' height and weight were significant predictors of the intakes of fiber and ascorbic acid. The women in the Control group reporting greater concerns about health consumed significantly lower quantities of fiber, ascorbic acid, and calcium. Moreover, women who scored higher on the Participation motivation index consumed greater amounts of ascorbic acid and calcium. The coefficients of energy intakes were large and statistically significant in models for fiber, p-carotene, ascorbic acid, and calcium. The coefficients of the previous intakes were small and significant only in the model for ascorbic acid intakes; the between/within variance ratios were large and statistically significant (P < 0.05).

Further, the results in Table 3 showed that more educated women consumed higher quantities of fiber, p-carotene, and ascorbic acid; education was not significantly associated with calcium intakes. The calcium intakes were significantly lower for Black women presumably due to the lower consumption of dairy products [14]. Women with higher scores on the Unhealthy eating index consumed significantly lower quantities of fiber, ascorbic acid, and calcium. Subjects consuming low-fat diets had higher intakes of fiber, ascorbic acid, and calcium. The coefficient of this indicator variable in the model for (J-carotene was not statistically significant presumably due to the large within-subject variation in these intakes [30]. The Desirability of change variable was significantly associated with the intakes of fiber and p-carotene (P < 0.05). Women with higher scores on the Concerned about health index had significantly higher intakes of fiber, pcarotene, and ascorbic acid. The coefficients of the Participation motivation index were significant for the intakes of fiber and p-carotene in the Intervention group. The previous intakes were significant in the models for P-carotene, ascorbic acid, and calcium.

Empirical results for the dietary intakes in the Intervention group

Discussion

The empirical results for the selected dietary intakes by women in the Intervention group are in Table 3. The intakes of monounsaturated and polyunsaturated fats were significantly higher among Black and White women (P < 0.05). More educated women had significantly lower intakes of saturated, monounsaturated, and polyunsaturated fats. This was in contrast with the results in Table 2 where education

There were significant differences (P < 0.05) between the Control and Intervention groups of the WHTFSMP in the changes between baseline and 12 months in behavioral variables such as Unhealthy eating index, Eating low-fat diet, Desirability of change, Concerned about health index, and Participation motivation index. The intakes of energy, and saturated, monounsaturated, and polyunsaturated fats at

Dietary Change in the Women's Health Trial

12 months were reduced by greater amounts in the Intervention group. The models developed for dietary intakes in the Control and Intervention groups took into account the subjects' behavioral and socioeconomic variables and the energy intakes. For the Control group, education was significantly positively associated with the intakes of p-carotene and ascorbic acid. For the Intervention group, education was significantly positively associated with the intakes of fiber, fj-carotene, and ascorbic acid, and was negatively associated with saturated, monounsaturated, and polyunsaturated fats intakes. While more educated women in the Control group consumed higher quantities of pi-carotene and ascorbic acid, the nutrition education program for the Intervention group led to greater reductions in fat intakes by such women. These findings suggest that strategies such as providing detailed instructions for preparation of healthy meals may afford significant benefits for educated women but are less likely to result in behavior change among less educated women; low-educated women suffering from chronic conditions such as obesity are likely to require dietary and medical counseling. The Unhealthy eating index was significantly and positively associated with the intakes of saturated and monounsaturated fats in the Control group. By contrast, its coefficients were significant in all models for the Intervention group except for the (3-carotene intakes. Coefficients of the indicator variable for whether the subject was eating a low-fat diet were significant for the intakes of the three fats in Control and Intervention groups in Tables 2 and 3, respectively. However, in the Control group, for subjects reporting Eating low-fat diet, the average percentages of energy derived from fat at baseline and 12 months were, respectively, 33.6 and 31.1. The corresponding averages for the Intervention group were 34.5 and 22.5, respectively. Thus, at the baseline, subjects in the two groups had similar perceptions regarding what constituted a low-fat diet, though at 12 months, the average subject in the Intervention group was in fact consuming a low-fat diet. It would seem important to refine the questions posed to investigate 'Stages of change' in behavioral research [31,32]. For example, it would be useful to investigate the subjects' understanding of what constitutes a low-fat diet before classifying them into the five stages. The Concerned about health index was positively associated with the intakes of monounsaturated and polyunsaturated fats and negatively associated with fiber, ascorbic acid, and calcium intakes in the longitudinal models developed for the Control group. A possible explanation for these findings may be that women more concerned about health were in fact those consuming higher quantities of monounsaturated and polyunsaturated fats and lower quantities of fiber, ascorbic acid, and calcium. By contrast, in the Intervention group, the Concerned about health index was negatively associated with the intakes of saturated and monounsaturated fats and was positively associated with

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fiber, pi-carotene, and ascorbic acid intakes. Thus, subjects in the Intervention group perceiving higher health risks made the appropriate dietary changes. The results from our analysis of the WHTFSMP data underscored the role of behavioral factors on dietary intakes by minority and low socioeconomic status women in the US. While the importance of such factors has been recognized in nutrition education research [33] and by policy makers [34], there have been few studies facilitating the development of more targeted approaches to nutrition education. The results from this study, for example, showed the importance of women's perceptions regarding health and their motivation for change for improving dietary intakes. These factors can be investigated via brief questionnaires given to the subjects. Moreover, knowledge of the cultural barriers to dietary change such as the composition of family meals consumed especially on weekends [17] could provide additional insights. Education programs incorporating the responses to such questions are likely to be more effective in facilitating dietary change. Lastly, it is relatively straightforward to target lowincome populations such as those participating in the Food Stamp Program or the Supplemental Food Program for Women, Infants and Children since the States are encouraged to offer nutrition education to such households. Moreover, it may be possible to achieve dietary changes among low-income households by distributing detailed advice, recipes, and health guidelines via organization [35], The effectiveness of such programs for achieving long-term dietary changes and for reducing risks of chronic diseases merits further quantitative research, especially from a costbenefit standpoint.

Acknowledgments This research was supported through a Cooperative Agreement between the Economic Research Service of the U.S. Department of Agriculture and the University of Houston, and by a grant (R03 CA 97738) from the National Cancer Institute. While retaining the responsibility for the views, the authors thank Joanne Guthrie and the two reviewers for their detailed and most helpful comments.

References [1] Frazao E. High costs of poor eating patterns in United States. America's eating habits: changes and consequences. AIB, vol. 750. Washington, DC: U.S. Department of Agriculture, Economic Research Service; 1999. p. 5-32. [2] Nestle M, Jacobson MF. Halting the obesity epidemic: a public health policy approach. Public Health Rep 2000;115:12-24. [3] Greenwald R The potential of dietary modification to prevent cancer. Prev Med 1996;25:41-3. [4] Gorman WM. Tastes, habits and choices. Int Econ Rev 1967;8: 218-22.

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[5] Rosenstock IM, Strecher VJ, Becker MH. Social learning theory and the health belief model. Health Educ Q 1988;15:175-83. [6] Bandura A. Social learning theory. Englewood Cliffs, NJ: PrenticeHall; 1977. [7] Bandura A. Social foundations of thought and action. Englewood Cliffs, NJ: Prentice-Hall; 1986. [8] Glanz K, Rimer BK, Theory at a glance: a guide for health promotion practice. Bethesda, MD: National Cancer Institute; 1995. (Publication No. 95-3869). [9] USDA/DHSS. Nutrition and your health: dietary guidelines for Americans. Washington: Department of Health and Human Services; 1990. [10] USDA/DHSS. Nutrition and your health: dietary guidelines for Americans. Fifth ed. Washington: Department of Health and Human Services; 2000. [11] Henderson MM, Kushi LH, Thompson DJ, Gorbach SL, Clifford CC, Insull W, et al. Feasibility of a randomized trial of a low-fat diet for the prevention of breast cancer: dietary compliance in the women's health trial vanguard study. Prev Med 1990;19:115-33. [12] Bowen D, Clifford CC, Coates R, Evans M, Feng Z, Fouad M, et al. The women's health trial feasibility study in minority populations: design and baseline description. Ann Epidemiol 1996;6:507-19. [13] Coates R, Bowen DJ, Kristal AR, Feng Z, Oberman A, Hall DW, et al. The women's health trial feasibility study in minority populations: changes in dietary intakes. Am J Epidemiol 1999;149: 1104-12. [14] Kristal AR, Shattuck AL, Patterson RE. Differences in fat-related dietary patterns between black, Hispanic and white women: results from the women's health trial feasibility study in minority populations. Public Health Nutr 1999;2:253-62. [15] Bhargava A, Guthrie J. Unhealthy eating habits, physical exercise and macronutrient intakes are predictors of anthropometric indicators in the women's health trial: feasibility study in minority populations. Br J Nutr 2002;88:719-28. [16] Urban N, White E, Anderson GL, Curry S, Kristal AR. Correlates of maintenance of a low-fat diet among women in the women's health trial. Prev Med 1992;21:279-91. [17] Bhargava A, Forthofer R, Mc Pherson S, Nichaman M. Estimating the variations and autocorrelations in dietary intakes on weekdays and weekends. Stat Med 1994;13:113-26. [18] Steptoe A, Doherty S, Kerry S, Rink E, Hilton S. Sociodemographic and psychological predictors of change in dietary fat consumption in adults with high blood cholesterol following counseling in primary care. Health Psychol 1999;19:411-9. [19] Bhargava A. Estimating the short and long run income elasticities of

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British Journal of Nutrition (2004), 92, 497-506 © The Author 2004

DOI: 10.1079/BJN20041210

Socio-economic and behavioural factors are predictors of food use in the National Food Stamp Program Survey Alok Bhargava* Department of Economics, University of Houston, Houston, Texas, USA (Received 9 December 2003 - Revised 7 April 2004 - Accepted 5 May 2004)

The unhealthy dietary patterns in the USA especially among low-income households demand complex strategies for health promotion. The present paper analysed the proximate determinants of 7d food use by 919 participants in the National Food Stamp Program Survey conducted in 1996. The households' consumption of dietary energy, carbohydrate, protein, fibre, saturated, monounsaturated and polyunsaturated fats, Ca, Fe, p-carotene and vitamin C were explained by background, socio-economic and behavioural factors. Certain methodological issues arising in modelling food use data were addressed. The results showed that the subjects' knowledge of the US Department of Agriculture food pyramid, reading nutrition labels, adopting a low-fat diet, selecting fruits and vegetables, saving money at grocery stores and frequency of shopping trips were often significantly associated (P<0-05) with the densities of nutrient use. The results identified certain aspects of nutrition education programmes that deserve greater emphasis for improving diet quality. The model for energy intake indicated that disbursing half the food stamp benefits on a 2-week basis and better shopping practices can enhance food availability. Diet: Hunger: Food stamps: Behavioural factors: Poverty

Food shortages and hunger experienced by low-income households in an affluent country such as the USA are embarrassing and are alleviated by households' participation in programmes such as the Food Stamp Program (Basiotis et al. 1983; Cohen et al. 1999; Rose 1999). The Food Stamp Program provides low-income households with benefits that can be used for purchasing food from authorized retailers. In 1997, for example, this programme provided more than US$22 billion in benefits to 9 million US households. Furthermore, food pantries and the Supplemental Food Program for Women, Infants, and Children (WIC) help buffer households, especially those with young children, against deficiencies of nutrients such as Ca, Fe and vitamin C (Perez-Escamilla & Haldeman, 2002). Because the body stores of micronutrients are typically low and micronutrients are vital for functioning of the immune system (Scrimshaw & SanGiovanni, 1997), it is important that food stamp and other programmes afford adequate and balanced nutrition over time. While some low-income households may experience periodic hunger, the recent trends in consumption of energy-dense foods and decline in physical activity contribute to the obesity epidemic in the USA (Bhargava & Guthrie, 2002). Households with low education and income levels are likely to consume worse diets, in part because of their limited understanding of the nutritional

requirements and also because of the lack of ability to explore healthy foods and lifestyle choices. While promoting dietary change is a sustainable long-term strategy for improving health outcomes (Contento, 1995; Bhargava & Hays, 2004), there have been few studies exploring such issues in low-income populations. In a previous analysis of the data from the National Food Stamp Program Survey (NFSPS), Hersey et al. (2001) reported that subjects 'looking for grocery specials' were significantly more likely to belong to households meeting their RDA for vitamins A, B 6 , C and folate. In addition to the information on looking for grocery specials, the NFSPS compiled variables such as the decision-makers' selection of foods on the basis of information on labels, preference for consuming low-fat foods and fruits and vegetables, and knowledge of the US Department of Agriculture food pyramid. The effects of behavioural and economic factors on food use can provide insights into aspects that could be modified via nutrition education (US Department of Agriculture, 1999). Thus, for example, while the effects of price reductions on food use are important from a budgeting standpoint (Hersey et al. 2001), it is perhaps more important to investigate the effects of behavioural factors on food choices. This is because a low-income household may subsequently experience an increase in income that in turn would increase their

Abbreviations: AME, adult male equivalent; ENU, equivalent nutritional unit; NFSPS, National Food Stamp Program Survey; WIC, Supplemental Food Program for Women, Infants and Children. * Corresponding author: Dr Alok Bhargava, fax 4-1 713 743 3798, email [email protected]

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food intake. An understanding of what constitutes a healthy diet is essential for reducing the consumption of energydense foods that contribute to weight gain and other medical conditions (US Department of Agriculture/Department of Health & Human Services, 2000). Another important issue is the disbursement of food stamps and subsidies from supplemental programmes (Wilde & Ranney, 2000). Because of coexistence of obesity and hunger in some low-income households (Townsend et al. 2001), it would be counter-productive to encourage binge-eating in periods following the receipt of benefits. Furthermore, food shortages are likely to entail lower intakes of fresh fruits and vegetables that are relatively difficult to store and relatively expensive. If, for example, households face hunger after exhausting the monthly food stamp benefits, then it may be more effective to disburse half the benefits on a 2-week basis. At a conceptual level, food consumption decisions are influenced by factors such as the ethnicity, education and income levels of the decision-makers. Behavioural variables such as reading nutrition labels and the knowledge of what constitutes a healthy diet are likely to play an important role in determining food intake. The effects of socio-economic and behavioural factors on nutrient availability among food stamp programme participants should therefore be analysed in a multidisciplinary framework. The purpose of the present paper was to analyse the proximate determinants of the quantity and dietary quality of food used by households in the NFSPS, with the aim of identifying behaviours that could be changed via nutrition education. We estimated models for the use of carbohydrate, fibre, protein, saturated, monounsaturated and polyunsaturated fats, Ca, Fe, vitamin C and ^-carotene, which were expressed as ratios to the energy use. These densities of nutrients were explained by background, behavioural and socio-economic variables to provide insights into the proximate determinants of vital nutrient use that were likely to affect health outcomes. Certain methodological issues were also addressed in the analysis. A model was estimated for energy use to provide further insights into factors affecting the overall food situation in the households.

Methods Subjects The data were from the NFSPS conducted in 1996 with the sponsorship of the US Department of Agriculture (Cohen et al. 1999). From the national sample of 2142 food stamp participants, a random sample of 937 households was selected to complete 7d food use diaries. The food used was converted into nutrient and energy used by using a food composition database. The data on households' dietary energy and selected nutrient densities were analysed for the present paper. Experimental

methods

One week before the completion of food use diaries, the households were interviewed through a computer-assisted

personal interview; a second interview took place 1 week after the completion of the diaries. Background, socioeconomic, behavioural and nutritional variables of the households were measured. Ethnicity, age, education levels, occupation of the head of the household, and household size in terms of adult male equivalents (AME) were recorded. In addition, equivalent nutritional units (ENU) were computed from AME by taking into account meals consumed by the members outside the home. The presence of guests was also incorporated in an alternative version of the ENU. Income from various sources, such as that earned or received from Aid to Families with Dependent Children, was recorded. Participation of the household in the WIC and the period for which the household had been receiving food stamp benefits were recorded. The presence of guests at meals, number of meals consumed outside the home and meals skipped were recorded. The time between receipt of food stamp benefits and the end of the 7 d period of food use was recorded. Demographic features of the metropolitan area were included in the data set. The constructions of behavioural and dietary

indices

In the diet and behaviour module of the questionnaire, the subjects were asked several questions relating to their dietary knowledge, seeking nutrition information, eating preferences and shopping practices. Because the questions covered different dimensions of household characteristics and behaviour, five indices were created to quantify the effects of behavioural and socio-economic factors on food use (Steptoe et al. 1999; Bhargava & Hays, 2004); sensitivity analyses were performed in modelling the food data to check the robustness of the conclusions. The first index was based on answers to six questions relating to the US Department of Agriculture food pyramid. The subjects were asked if they were familiar with the food pyramid and, if so, they w,ere asked to identify the five broad food groups. Correct answers were assigned the score 1 and then were summed; the 'food pyramid' index thus ranged from 0 to 6. The 'nutrition labels' index was based on the answers to five questions on a scale of 1 to 6 (1, not important; ...; 5, important; 6, very important), relating to subjects' reading of labels on foods purchased; the score 1 was assigned if the subjects reported 5 or 6 as the answers. The first three questions related to shopping for food; how important was product safety, nutrition, and how well the food will keep. The fourth question asked if the subjects had changed their decision to buy a product in the previous 2 weeks because of information on the label. The fifth question asked if the subjects had ever changed their mind because of nutrition labels. The affirmative answers to these questions were assigned the score 1; the scores on the five questions were summed to form the 'nutrition labels' index ranging from 0 to 5. The 'low-fat diet' index was created by assigning the score 1 to affirmative answers to six questions regarding choices of low-fat foods. The questions were: if the subjects' diet was low in fat and cholesterol; if eating habits had changed to reduce fat; if they were currently limiting the amount of fat; if they had limited fat in the diet in

Predictors of Food Use the past; if they were currently eating a low-fat diet; if in the past 1 month they had thought about changes that could decrease fat in the diet. The answers to these six questions were summed to create the iow-fat diet' index ranging from 0 to 6. The 'fruits and vegetables' index was based on answers to five questions investigating the extent to which the diets consisted of fruits and vegetables. The questions were: if fruits and vegetables were a regular part of the diet; if the subjects had ever changed their eating habits to increase consumption of fruits and vegetables; if they were eating more fruits and vegetables than previously; if they had been eating more fruits and vegetables in the last year; if they chose five or more servings of fruits and vegetables. The affirmative answers were assigned the score 1 and summed for the five questions; the 'fruits and vegetables' index ranged from 0 to 5. The 'save money' index was based on subjects' answers to six questions on their shopping practices: how often the subjects looked in newspapers for grocery specials; used cents-off or store discount coupons; stocked up on items when there were bargains; compared prices at different supermarkets; visited other food stores for advertised specials; used a shopping list. Affirmative answers were scored as 1 and the 'save money' index ranged from 0 to 6. Overall, because of missing observations on eighteen of the participating households, complete data on 919 households were used in the analysis. A framework for modelling the proximate determinants of food use in the National Food Stamp Program Survey Food use among NFSPS households was likely to depend on factors such as ethnicity, income, household size, education, and on behavioural variables such as the subjects' knowledge and perceptions of the likely effects of various foods on health. Moreover, participation by the eligible households in the WIC could have enhanced dietary knowledge of the decision-makers. There were two sets of issues addressed in the empirical analysis. First, a model for dietary energy use was likely to reveal the effects of socio-economic and behavioural variables and of factors such as the time elapsed since receipt of food stamp benefits on households' overall food situation. Second, because the energy expenditures of subjects were not available in the NFSPS (James & Schofield, 1990; Goldberg et at. 1991), the proximate determinants of diet quality were investigated by modelling nutrient use expressed as the ratios to energy intake (Bhargava & Reeds, 1995), i.e. as nutrient densities. In developing a model for the households' energy use, it was essential to take into account meals consumed outside the home and those skipped for other reasons. The NFSPS constructed ENU from AME by accounting for meals eaten outside the home by each member and also by taking into account the food used by guests. The ENU were derived separately for energy and for nutrients such as Ca and Fe by assuming that the nutrient intake corresponded to the RDA (Cohen et al. 1999). The latter assumption, however, may be invalid if the subjects had a poor understanding of RDA. The choice between AME and ENU in the models

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for food use can be based on statistical criteria such as those discussed later. One might expect ENU to be preferable in the model for energy use because ENU incorporated the expected quantity of food consumed by each person. By contrast, AME may be preferable for explaining nutrient densities that may be less influenced by RDA than the actual nutrient composition of meals. Last, the empirical relationship between energy use and the explanatory variables was likely to be a multiplicative one. Moreover, certain non-linearities, such as those between household size reflected in AME (or ENU) and energy use, could arise due to 'economies in scale' in food intake. Thus, use of logarithmic transformation was helpful for the precise estimation of model parameters, especially for variables exhibiting a high degree of internal variation.

The model for energy use The model for the households' energy use (model 1) was given by equation (1) (i = 1 ., n): ln(energy intake), = ao + ai (black)j+a2 (Hispanic); + a3 (college degree); + a4 ln(income +food stamp benefits))-fas ln(AME)j + a6 (ln(AME)i)- + a7 ln(proportion meals away); + ag (guests), -l-ag (members > 60 years old)j + aio (members < 18 years old); +ai i (WIC participant), + ai2 ln(foodpyramid)i + ai3 ln(nutrition labels); -fan ln(low-fat diet); +aig ln(fruits and vegetables); + a 16 ln(save money); + a 17 (number of shopping trips); -l-aig ln(days from food stamp receipt); + ai9 ln(proportion skipped meals);+ Uj. (1) Model 1 embodied salient features of energy use by the NFSPS households. The indicator variables for ethnicity, college education, guests present during meals, presence of elderly people and/or children and participation in the WIC reflected background information. Socio-economic variables were household income, shopping practices and the number of days since receipts of monthly food stamp benefits. Behavioural variables covered the subjects' understanding of the US Department of Agriculture food pyramid, reading nutrition information on labels, consumption of a low-fat diet and fruits and vegetables, and the number of shopping trips to grocery stores. Because the variable measuring the number of monthly shopping trips ranged from 1 to 4, it was not transformed into logarithms. Random error terms u were assumed to be normally distributed with zero mean and constant variance. In addition to these variables, model 1 included AME, AME" and the proportion of meals consumed outside the home. In order to incorporate the effects of household size and presence of guests on food use, it was important to estimate an alternative version (model 2) that replaced these three variables by ENU and ENU2. Because the proportion of meals consumed outside the home was the household

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average, for households with a single member, model 2 was a special case of model 1 in the linear case where the square of AME variable was excluded from the explanatory variables. A likelihood ratio test for nested formulations could be applied to discriminate between these two versions (Cox & Hinkley, 1974). In practice, however, most households had more than one member so that models 1 and 2 were nonnested even in the linear variables case. Because a quadratic formulation in AME was likely to be useful, one would need to use complex statistical procedures to discriminate between non-nested models that are also non-linear in variables. Thus, to simplify the methodology, we estimated both models 1 and 2 and compared the maximum values of the log-likelihood functions for model selection. In view of the differences in the number of model parameters, the Akaike information criterion (Akaike, 1973) was also used to discriminate between the alternative model formulations.

The models for the nutrient densities Behavioural factors such as subjects' nutritional knowledge were likely to be more strongly associated with diet quality than energy use. The models (model 3) for nutrient densities for use of carbohydrate, fibre, protein, saturated, monounsaturated and polyunsaturated fats, Ca, Fe, [3-carotene and vitamin C were as follows: ln(nutrient/energy use); = bo + b] (black); + hi (Hispanic)i + b3 (college degree); + b4 ln(income + food stamp benefits), + bs ln(AME)i + b6 ln(proportion meals away), + b7 (members > 60 years old); + bjj (members < 18 years old); + b9 (WIC participant); + bi0 ln(food pyramid); + bii ln(nutrition labels); + b12 ln(low-fat diet); + b]3 ln(fruits and vegetables);+bi4 ln(save money), + b ^ (number of shopping trips); + b)6 ln(days from food stamps receipt); + b|7 ln(proportion skipped meals); + V;. (2) In the models for nutrient densities, the AME2 variable was dropped, since the non-linear effects of household size on energy use were found not to carry over to diet quality. Moreover, alternative versions of model 3 in equation 2 were estimated where AME and the percentage of meals consumed outside the home were replaced by ENU based on energy or the ENU based on the RDA of specific nutrients. In contrast with the model for energy use, including ENU based on RDA could lower the maximum values of the likelihood functions. This was because nutrient densities were likely to be similar for household members and need not correspond to individuals' RDA. Last, the indicator variable for guests was dropped from equation 2 because it was not a significant predictor of nutrient densities.

Statistical analysis Cronbach (1984) a were computed for the five indices used in the analysis: 'food pyramid'; 'nutrition labels'; 'low-fat diet'; 'fruits and vegetables'; 'save money'. These statistics measure the internal consistency of the variables combined to form the indices; a>0-80 are usually regarded as indicating 'high' internal consistency, especially if the numbers of items combined are small. The models 1, 2 and 3 in equations 1 and 2 were estimated using the least squares option in the procedure MIXED of the statistical package SAS (version 8, 2000; SAS Institute Inc., Cary, NC, USA). The maximized values of the log-likelihood function and the Akaike information criterion are calculated in this procedure using the estimated residual variances and the number of model parameters. Lower values of the Akaike information criteria indicate a preference for that specification. The models were estimated with zero values of the indices increased to 0-1 before the logarithmic transformation and where all the values were increased by unity before the transformation. While the results were similar in terms of statistical significance of the coefficients, Tables 2-6 report the result where only the zero values were increased to 0-1. Thus, the coefficients of the variables in logarithms were the 'elasticities' (percentage change in the dependent variable resulting from a 1 % change in the explanatory variable). The zero values of the proportion of meals consumed outside the home were set to 0-001 before the logarithmic transformation; sensitivity analyses were performed and the results were robust. Results Descriptive statistics The sample mean values of the variables used in the analysis are reported in Table 1. The average household size was 2-98; in terms of AME, ENU and ENU taking account of guests, the household sizes were 2-15, 1-79 and 1-85 respectively. Approximately 40 % of the households were black, 46% were white and 12% were Hispanic. Only 7% of the heads of households had a college degree; 33 % of the households were participating in the WIC. The average monthly income was USS667 and the average monthly food stamp benefit was US$165. The average values of the five indices were near the midpoint of the range. However, 52 % of the households scored zero on the 'food pyramid' index, 21 % scored zero on the 'low-fat diet' index and 7 % scored zero on the 'fruits and vegetables' index. These scores were low from the viewpoint of healthy eating and merit attention in nutrition education programmes. Cronbach a for 'food pyramid', 'nutrition labels', 'low-fat diet', 'fruits and vegetables' and 'save money' indices were 0-92, 0-40, 0-72, 0-61 and 0-68 respectively. Further analysis of the 'nutrition labels' index, dropping the last two items enquiring if subjects had changed their shopping practices after reading labels, led to an increase of a to 0-67. This definition of the index was also used in models 1, 2 and 3 for energy and nutrient densities, but the results were similar. The average percentage of meals consumed outside the home was 14 and those skipped was 15. Possible reasons

Predictors of Food Use Table 1. Selected variables for 919 households in the National Food Stamp Program Survey* (Mean values and standard deviations) Variable Black (yes, 1; no, 0) White (yes, 1; no, 0) Hispanic (yes, 1; no, 0) Members in the household (n) Members >60 years old (yes, 1; no, 0) Members <18 years old (yes, 1; no, 0) Guests (yes, 1; no, 0) AME ENU (based on energy) ENU (correcting for guests) College education (yes, 1; no, 0) WIC participant (yes, 1; no, 0) Time from food stamp receipt (d) Income (US$ per month) Food stamp benefits (US$ per month) Nutrient intakes Energy (kj/7d) Energy/AME(kJ/7d) Energy/ENU(kJ/7d) /3-Carotene(mg/7d) Ca(mg/7d) Carbohydrate (g/7 d) Protein (g/7d) Fibre (g/7d) Fe (mg/7 d) Saturated fat (g/7 d) Monounsaturated (g/7d) Polyunsaturated fat (g/7d) Vitamin C (mg/7 d) Proportion of skipped meals (per 7 d) Proportion of meals away (per 7 d) Behavioural and dietary indicest 'Food pyramid' index (0-6) 'Nutrition labels' index (0-5) 'Low-fat diet' index (0-6) 'Fruits and vegetables' index (0-5) 'Save money' index (0-6) Number of shopping trips (n per month) n

Mean

SD

0-40 0-46 0-12 2-98 0-27 0-61 0-30 2-15 1-79 1-85 0-07 0-33 14-73 666-84 16508

0-49 0-50 0-33 1-76 0-44 0-49 0-46 1-31 1-17 1-19 0-25 0-47 8-79 643-79 118-48

186757 96518 116491 7832 15759 5094 1614 269 313 820 764 394 2262 0-14 0-15

142 383 66513 75769 9851 12 273 4103 1216 230 261 1257 628 390 2132 0-16 0-18

2-22 3-87 2-86 2-62 3-58 2-39 919

2-31 1-20 203 1-72 1-75 1-04

WIC, supplemental Food Program for Women, Infants and Children; AME, adult male equivalent; ENU, equivalent nutritional unit. * For details of procedures, see p. 498. t For details of indices, see p. 498.

for skipping meals such as dieting, lack of food, or illness were not asked in the questionnaire. The households' average energy intake for the 7d period was 186-757 MJ; the sample mean values of energy intake in terms of AME and ENU were 96-518 MJ and 116-491 MJ respectively. Using the averages for the intakes of saturated, monounsaturated and polyunsaturated fats from Table 1, the % energy derived from the three fats were 16-5, 15-4, and 8-0 respectively, i.e. 40% energy was derived from fat. Approximately 45 % energy was derived from carbohydrate. The average number of shopping trips per month was 2-39. Empirical results for the households' energy use The results from models 1 and 2 for households' energy use are presented in Table 2; the results in the far right-hand column used ENU variables that also took into account food used by the guests. The results for the three

367

formulations in Table 2 were very similar, although the maximum values of the likelihood functions (and minimum values of the Akaike information criteria) indicated a preference for the model that included guest-corrected ENU as explanatory variables. The salient features of the results in Table 2 were, first, that the relationship between the logarithms of energy use and AME was a quadratic one, with energy use increasing with household size but at a declining rate. The indicator variable for presence of guests in model 1 was a significant predictor (P<0-05) of higher energy use. Households with children < 18 years old used significantly greater dietary energy. Second, ethnic differences in energy use were not statistically significant. Household income including the food stamp benefits was not a significant predictor, presumably because all households were food stamp participants; increases in income would decrease the benefits. Participation in the WIC and the college education of the household head were not statistically significant predictors of energy use. Third, the 'food pyramid', 'nutrition labels', 'low-fat diet' and 'fruits and vegetables' indices were not significant predictors in the models for energy use. By contrast, the 'save money' index was a statistically significant predictor in the three versions of the model. Thus, subjects taking advantage of savings offered by grocery stores, searching for bargains and using shopping lists were from households that had higher energy use. Further, the number of days from the receipt of food stamp benefits was significantly negatively associated with energy use in model 1 with AME, and was significant (P<0-10) in model 2 where ENU were included. The variable measuring the proportion of skipped meals was significantly negatively associated with energy use in all three formulations. Because the reasons for skipping meals were not covered in the questionnaire, we did not model the potential dependence between energy use and skipping meals decisions for households lacking economic resources. Last, R 2 adjusted for the number of estimated parameters were approximately 0-50, indicating that the explanatory variables accounted for 50 % of the variation in the dependent variable. Empirical results for the households' nutrient densities The results for households' dietary Ca densities are shown in Table 3 for model 3 using AME, ENU based on energy and ENU based on the RDA for Ca; this presentation was helpful for illustrating the methodological approach in the present paper. The values of the log-likelihood functions were highest when AME and proportion of meals away from home were used, followed by the model with energy-based ENU; the log-likelihood function was lowest when ENU based on the RDA for Ca were included. A similar ranking for model preference was obtained using the Akaike information criteria and the adjusted R 2 reported in Table 3. Thus, the statistical criteria favoured the inclusion of the variable AME for explaining Ca densities. While the results for the three models were close, statistical significance (P<0-05) was reached, for example, for the coefficient of the indicator variable for children < 18 years old only in the model that included the AME variable.

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Table 2. Results from regression models for households' 7d energy use in logarithms, explained by background, socio-economic and behavioural factors using alternative definitions of household sizeft (Regression coefficients with their standard errors) Models for households' energy use (kJ)§ Model 1 with household size using AME Independent variable Black (0-1) Hispanic (0-1) Members >60 years old (0-1) Members <18 years old (0-1) Guests (0-1) Ln(AME) (Ln(AME))2 Ln(ENU based on energy) (Ln(ENU based on energy))2 Ln(ENU including guests) (Ln(ENU including guests))2 College education (0-1) WIC participant (0-1) Ln(days from food stamp receipt) Ln(income + food stamp benefits) Lnjproportion of skipped meals) Disproportion of meals away) Lnjfood pyramid) Lnfnutrition labels) Ln(low-fat diet) Ln(fruits and vegetables) Lnjsave money) Number of shopping trips Constant Adjusted fl2 Log-likelihood function Akaike information criterion|| n

Coefficient 0036 0014 -0055 0-198* 0-205* 0-706* -0078

0-031 0018 -0-055* 0019 -0063* -0050* 0012 0-011 -0-021 -0004 0-086* 0-009 10-887* 0-48 -725-1 1492-2 919

SE

0-039 0-057 0-049 0062 0040 0-071 0046

0-072 0-044 0-025 0-025 0013 0-007 0010 0024 0013 0020 0-019 0-017 0-184

Model 2 with household size using ENU Coefficient

SE

0042 -0-016 -0-059 0-224* 0-190*

0038 0-056 0-047 0-054 0039

0-609* -0027

0039 0029

0-012 0-035 -0-048 0010 -0-051*

0-071 0044 0025 0-024 0012

0011 0002 -0025 -0004 0-091* 0016 11 -257* 0-50 -707-1 1454-2 919

0010 0023 0013 0019 0018 0-017 0-178

Model 2 with household size using ENU corrected for guests Coefficient

SE

0021 -0-030 - 0062 0-238*

0037 0-056 0047 0-053

0-630* - 0027 0008 0024 - 0043 0010 - 0050*

0039 0029 0070 0-043 0025 0-024 0012

0-014 0013 -0024 - 0006 0091* 0018 11-268* 0-51 -704-3 1446-6 919

0010 0023 0013 0019 0-018 0-017 0-176

AME, adult male equivalent; ENU, equivalent nutritional unit; WIC, Supplemental Food program for Women, Infants and Children. *P<0-05. tFor details of subjects and procedures, see Table 1 and pp. 498-500. t-AII the lvalues for joint significance of the regression coefficients were statistically significant (P<0-05). § See equation 1 (p. 499) for the definition of models 1 and 2. II Akaike (1973).

The AME variable was significantly negatively associated with Ca densities, indicating relatively lower use in larger households. However, participation in the WIC implied significantly higher densities of Ca. Ca densities were lower for black households in comparison with white households; the indicator variable for Hispanic households was not statistically significant. A greater score on the 'food pyramid' index was significantly associated with higher densities of Ca. The number of shopping trips per month was a significant and positive predictor of Ca density. Households where the members skipped meals had significantly lower Ca densities. Because of the similarity between the results from the three versions of model 3, we report the results for remaining nutrient densities where AME and proportion of meals away from home were included as explanatory variables. The results from model 3 for protein, fibre and Fe densities are shown in Table 4; results for carbohydrate, R-carotene and vitamin C are shown in Table 5, and those for saturated, monounsaturated and polyunsaturated fats are shown in Table 6. The results in Table 4 showed that larger households had significantly lower protein,

fibre and Fe densities. The fibre densities were significantly higher in households where an elderly member was present. Black households used significantly lower fibre densities, whereas fibre density was significantly higher in Hispanic households. Moreover, in comparison with white households, protein density was higher and Fe density was lower in black households. Participation in the WIC was significantly associated with higher Fe densities. However, calculation of absorbable Fe was not feasible in the NFSPS data because it would have required data on food use by meals (Monsen & Balintfy, 1982). Of the behavioural factors, the 'nutrition labels' index was negatively associated with protein density and was positively associated with fibre density (P<0-05). Households scoring high on the 'low-fat diet' index had significantly higher protein densities. The 'save money' index was not a significant predictor of protein, fibre and Fe densities. The number of shopping trips per month was significantly associated with fibre density. The skipped meals variable was estimated with significant negative coefficients in the models for the fibre and Fe densities.

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369

Table 3. Regression models for households' 7d calcium densities in logarithms, explained by background, socio-economic and behavioural factors using alternative definitions of household sizeft (Regression coefficients with their standard errors) Models for calcium densities§

Independent variable Black (0-1) Hispanic (0-1) Members >60 years old (0-1) Members < 18 years old (0-1) Ln(AME) Ln(ENU based on energy) Ln(ENU based on Ca) College education (0-1) WIC participant (0-1) Ln(days from food stamp receipt) Ln(income + food stamp benefits) Ln(proportion of skipped meals) Ln(proportion of meals away) Ln(food pyramid) Ln(nutrition labels) Ln(low-fat diet) Ln(fruits and vegetables) Ln(save money) Number of shopping trips Constant Adjusted R 2 Log-likelihood function Akaike information criterion|| n

Model 3 with household size using AME and proportion of meals away

Model 3 with household size using ENU based on energy

Model 3 with household size using ENU based on RDA for Ca

Coefficient

Coefficient

Coefficient

-0-257* -0046 0042 0-100* -0082* -0-019 0-112* 0001 0-012 -0-030* 0-005 0015* 0006 0014 0033* -0025 0-032* -2-690* 0-16 -467-5 973 919

SE

0-029 0043 0-036 0-046 0031 0054 0033 0-019 0019 0-009 0005 0008 0018 0010 0015 0014 0-013 0-139

SE

-0-263* - 0049 0042 0070

0029 0043 0036 0041

-0044

0026

-0018 0-110* 0001 0008 -0031*

0-054 0-033 0-019 0019 0009

0016* 0006 0016 0-033* -0-026 0030* -2-690* 0-16 -469-85 975-7 919

0008 0018 0010 0015 0-014 0013 0-136

SE

-0-267* -0053 0045 0060

0029 0-043 0-036 0-044

-0024 -0020 0-112* 0-001 0006 -0031*

0027 0-054 0-034 0-019 0-019 0-009

0016* 0-005 0017 0033* -0027 0-029* -2-661* 0-15 -470-9 977-8 919

0-008 0-018 0010 0-015 0014 0013 0-135

AME, adult male equivalent; ENU, equivalent nutritional unit; WIC, Supplemental Food Program for Women, Infants and Children. *P<005. t For details of subjects and procedures, see Table 1 and p. 500. i All the Fvalues for joint significance of the regression coefficients were statisficaliy significant (P<005). § See equation 2 on p. 500 for the definition of model 3. II Akaike (1973).

Table 5 presents the results for the use of carbohydrate, P-carotene and vitamin C densities. Black households were using significantly lower carbohydrate and P-carotene densities, while Hispanic households were using significantly higher p-carotene and vitamin C densities. Households that scored high on 'nutrition labels' index were using significantly greater carbohydrate and P-carotene densities. Skipping meals was significantly negatively associated with carbohydrate, p-carotene and vitamin C densities. Higher AME was significantly associated with lower use of P-carotene and vitamin C densities; households with elderly members had significantly greater P-carotene and vitamin C densities. The 'food pyramid' and 'fruits and vegetables' indices were positively and significantly associated with the P-carotene density. The number of shopping trips was significantly positively associated with P-carotene density. The skipped meals variable was negatively associated with vitamin C density (P<0-05). The results in Table 6 showed that black households had higher densities of monounsaturated and polyunsaturated fats than white households. By contrast, for Hispanic households, the saturated and monounsaturated fat densities were lower and the polyunsaturated fat density was higher. College education was negatively associated with monounsaturated fat density (P<0-\0). The 'nutrition

labels' index was negatively associated with monounsaturated fat density (P<005). The 'save money' index was positively associated with polyunsaturated fat density and the number of shopping trips per month was negatively associated with monounsaturated and polyunsaturated fat densities. The skipped meals variable was positively associated with monounsaturated fat density. Last, in comparison with the ENU, inclusion of the variables AME and proportion of meals consumed outside the home led to higher values of the log-likelihood functions (and lower values of the Akaike information criterion) for all densities except those of protein and monounsaturated fat use (results not shown). In these two cases, the differences between the log-likelihood functions were practically negligible. Overall, the model parameters were more precisely estimated when AME and proportion of meals consumed outside the home were included as explanatory variables in the models for nutrient densities. Discussion The present paper presents a comprehensive analysis of the effects of background, socio-economic and behavioural factors on food use in the NFSPS data. Because the

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A. Bhargava

Table 4. Regression models for households' 7d protein, fibre and iron densities in logarithms, explained by background, socio-economic and behavioural factors (Regression coefficients with their standard errors)!^ Model 3 for protein densities§ Independent variable Black (0-1) Hispanic (0-1) Members >60 years old (0-1) Members <18 years old (0-1) Ln(AME) College education (0-1) WIC participant (0-1) Ln(days from food stamp receipt) Ln(income + food stamp benefits) Ln(proportion of skipped meals) Ln(proportion of meals away) Ln(food pyramid) Ln(nutrition labels) Ln(low-fat diet) Ln(fruits and vegetables) Ln(save money) Number of shopping trips Constant Adjusted R2 n

Model 3 for fibre densities!

Model 3 for Fe densities!

Coefficient

SE

Coefficient

SE

Coefficient

SE

0073* 0-032 - 0-030 -0073* -0053* -0-039 0014 0010 0012 -0008 0003 0001 -0025* 0019* 0007 -0009 0013 - 4-800* 007 919

0-016 0-024 0020 0025 0017 0030 0019 0011 0010 0005 0003 0004 0010 0006 0008 0008 0007 0077

-0-151* 0-247* 0-148* -0001 -0-110* 0026 - 0043 - 0001 0022 - 0-037* 0-010 0014 0046* 0008 0012 0001 0-044* - 6-902* 0-18 919

0029 0043 0036 0-045 0031 0-054 0033 0019 0019 0009 0005 0008 0018 0010 0015 0014 0013 0-138

-0057* - 0036 0028 0042 -0043* -0021 0-066* -0002 0038* -0-021* -0002 -0001 0016 0-013 0011 0002 0015 - 6-797* 0-05 919

0022 0-033 0-027 0035 0-024 0-041 0-025 0014 0-014 O-007 0004 0006 0-014 0008 0-011 0-011 0010 0-105

AME, adult male equivalent; ENU, equivalent nutritional unit; WIC, Supplemental Food Program for Women, Infants and Children. *P<005. t For details of subjects and procedures, see Table 1 and p. 500. t All the F values for joint significance of the regression coefficients were statistically significant (P< 005). § See equation 2 on p. 500 for the definition of model 3.

Table 5. Regression models for households' 7d carbohydrate, /3-carotene and vitamin C densities in logarithms, explained by background, socio-economic and behavioural factorstt Model 3 for carbohydrate densities! Independent variable Black (0-1) Hispanic (0-1) Members >60 years old (0-1) Members <18 years old (0-1) Ln(AME) College education (0-1) WIC participant (0-1) Ln(days from food stamp receipt) Ln(income + food stamp benefits) Ln(proportion skipped meals) Ln(proportion meals away) Ln(food pyramid) Ln(nutrition labels) Ln(low-fat diet) Ln(fruits and vegetables) Ln(save money) Number of shopping trips Constant Adjusted R 2 n

Model 3 for B-carotene densities!

Model 3 for vitamin C densities!

Coefficient

SE

Coefficient

SE

Coefficient

SE

-0-120* 0-003 0033 0-051 -0011 0-044 - 0021 - 0003 0020 -0011* 0-001 0003 0035* 0002 0-005 0008 0006 - 3-829* 009 919

0017 0026 0022 0027 0-019 0-033 0020 0011 0011 0006 0003 0005 0011 0006 0009 0009 0008 0083

-0-176* 0-283* 0-340* 0-186 -0-177* 0008 -0-152 -0-010 - 0008 - 0052* -0-014 0046* 0-097* 0-045 0-129* 0047 0075* -4-130* 0-10 919

0075 0-112 0-093 0-118 0081 0-140 0-086 0-049 0-048 0-024 0-014 0020 0-046 0026 0038 0-037 0034 0-357

0012 0-265* 0-141* 0-159* -0-119* -0018 0071 0000 0017 - 0-044* 0009 0-018 0-054 0022 0035 0037 0027 -5070* 006 919

0048 0072 0060 0076 0052 0090 0055 0032 0031 0016 0009 0013 0030 0017 0025 0-024 0022 0-230

AME, adult male equivalent; WIC, Supplemental Food Program for Women, Infants and Children. *P<005. t For details of subjects and procedures, see Table 1 and p. 500. t All the F values for the joint significance of the regression coefficients were significant (P<0-05). § See equation 2 on p. 500 for the definition of model 3.

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371

Table 6. Regression models for households' 7d saturated, monounsaturated and polyunsaturated fat densities in logarithms, explained by background, socio-economic and behavioural factorsft Model 3 for saturated fat densities§ Independent variable Black (0-1) Hispanic (0-1) Members > 60 years old (0-1) Members < 18 years old (0-1) Ln(AME) College education (0-1) WIC participant (0-1) Ln(days from food stamp receipt) Ln(income + food stamp benefits) Lnjproportion of skipped meals) Lnjproportion of meals away) Lnjfood pyramid) Ln(nutrition labels) Ln(low-fat diet) Ln(fruits and vegetables) Ln(save money) Number of shopping trips Constant Adjusted R2 n

Model 3 for monounsaturated fat densities§

Model 3 for polyunsaturated fat densities§

Coefficient

SE

Coefficient

SE

Coefficient

SE

0-047 -0-098* -0-041 0068 -0046 -0053 - 0003 0001 -0-002 -0010 -0002 0-010 -0-023 -0-013 -0-009 0005 0002 - 5-572* 0-01 919

0029 0044 0037 0046 0032 0055 0034 0019 0019 0010 0006 0008 0018 0010 0015 0014 0013 0-140

0-119* -0067* -0027 0003 0008 -0066 -0011 -0006 -0007 0016* -0001 0002 -0030* -0013 -0014 0002 -0-017* - 5-389* 009 919

0019 0029 0024 0031 0021 0-036 0-022 0013 0013 0006 0004 0005 0012 0-007 0010 0-010 0-009 0093

0-131* 0-186* 0-028 0-042 0-045 0-052 -0-071* -0-009 0-020 0-000 -0-008 -0-004 0-012 -0-002 0010 0-036* -0-030* -6-555* 0-04 919

0031 0047 0039 0049 0034 0059 0036 0021 0020 0-010 0006 0008 0019 0011 0016 0015 0-014 0-150

AME, adult male equivalent; WIC, Supplemental Food Program for Women, Infants and Children. *P<005. t For details of subjects and procedures, see Table 1 and p. 500. tAII the F values for joint significance of the regression coefficients were statistically significant (P<0-05). §See equation 2 (p. 500) for the definition of model 3.

subjects in low-income households in the USA are typically less educated, it was important to analyse the factors affecting energy intake and diet quality in a broad analytical framework. The empirical results provided insights that can be used to refine nutrition education programmes. First, the zero scores by many households on indices of 'food pyramid', 'low-fat diet' and 'fruits and vegetables' suggested that nutrition education programmes should seek to enhance subjects' dietary knowledge. Moreover, many subjects may not understand issues such as what constitutes a low-fat diet (Bhargava & Hays, 2004). While the importance of fruits and vegetables has been emphasized in programmes such as '5 a day' (National Cancer Institute, 2001) and empirical evidence from several dietary interventions has been summarized in Agency for Healthcare Research & Quality (2001), it is essential that such advice reach a large number of low-income households. This could be achieved by distributing nutritional information and recipes for healthy meals via offices, providing food stamp benefits and through other programmes (Lutz et al. 1999). Moreover, resources allocated to nutrition education (US Department of Agriculture, 1999) can be channelled more effectively after investigating, via brief questionnaires, the behavioural and socio-economic aspects most in need of modifications. Second, the results from the model for energy use showed the importance of variables covered in the 'save money' index. It is important for decision-makers in low-income households to improve shopping practices for increasing food availability without a concomitant increase in food expenditures. However, some aspects of shopping practices may have evolved in the NFSPS data with the

households' needs for increasing food supplies to meet the members' energy needs. Even so, taking advantage of the discounts offered by grocery stores is likely to increase food availability. Third, duration from the receipt of food stamp benefits was negatively associated with energy use, thereby supporting previous findings of declines in food intakes as households moved further from the receipt of benefits (Wilde & Ranney, 2000). Disbursement of half the food stamp benefits via the electronic benefit transfer every 2 weeks is likely to stabilize food availability for many participating households. Fourth, from the standpoint of dietary quality of food used, the results showed the importance of making regular trips to grocery stores; shopping trips were significantly positively associated with Ca, fibre and (3-carotene densities, and were negatively associated with the densities of monounsaturated and polyunsaturated fat. Elderly members of households may be reluctant or unable to make regular trips, food delivery at a nominal price by grocery stores can enable members to stabilize the availability of nutrient-dense foods such as fruits and vegetables. Involvement of younger relatives in shopping for the elderly living in the vicinity could be a potentially useful strategy for improving nutrition and should be examined in future studies. Finally, the scores on the 'food pyramid' index were significant predictors of the Ca and (3-carotene densities; the 'nutrition labels' index was significantly associated with the densities of fibre, carbohydrate and (3-carotene, and was negatively associated with monounsaturated fat density. The 'fruits and vegetables' index was positively associated with pVcarotene density. Thus, it is important

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to improve subjects' understanding of the food pyramid through detailed presentations by dietitians and nutritionists. Nutrition labels could provide further guidance, such as the need to limit the consumption of energy-dense foods. Moreover, programmes such as 'Pick the tick' in New Zealand (Young & Swinburn, 2002) have been successful in reducing the salt content of processed foods. In view of the steep rise of obesity rates in the USA and the concomitant medical conditions, increased nutrition education together with greater availability of healthier foods in grocery stores would seem essential for promoting long-term health, especially of the poor.

Acknowledgements This research was supported through a cooperative agreement between the University of Houston and the Economic Research Service of the US Department of Agriculture, and by a grant from the National Cancer Institute (R03 CA 97738). While retaining the responsibility for the views in the paper, the author would like to thank Aliaksandr Amialchuk, Margaret Andrews, Joanne Guthrie, Linda Nebeling, Sharon O'Donnell, David Smallwood and Parke Wilde for their help and advice. This revision has benefited from the detailed and helpful comments from two reviewers and the editors. References Agency for Healthcare Research and Quality (2001) Efficacy of Interventions to Modify Dietary Behavior Related to Cancer Risk, http://www.ahrq.gov/clinic/epcsums/dietsumm.htm Akaike H (1973) Information theory and the extension of the maximum likelihood principle. In Second International Symposium on Information Theory, pp. 267-281 [B Petrov and F Csaki, editors]. Budapest: Akademai Kiado. Basiotis P, Brown M, Johnson SR & Morgan KJ (1983) Nutrient availability, food costs, and food stamps. Am J Agric Econ 65, 685-693. Bhargava A & Guthrie JF (2002) Unhealthy eating habits, physical exercise and macronutrient intakes are predictors of anthropometric indicators in the women's health trial: feasibility study in minority populations. Br J Nutr 88, 719-728. Bhargava A & Hays J (2004) Behavioural variables and education are predictors of dietary change in the Women's Health Trial: feasibility study in minority populations. Prev Med 38, 442-451. Bhargava A & Reeds PJ (1995) Requirements for what? Is the measurement of energy expenditure a sufficient estimate of energy needs? J Nutr 125, 1358-1362. Cohen B, Ohls J, Andrews M, Ponza M, Moreno L, Zambrowski A & Cohen R (1999) Food Stamp Participants, Food Security and Nutrient Availability. Technical Report, Economic

Research Service. Washington, DC: US Department of Agriculture. Contento I (1995) The effectiveness of nutrition education and implications, nutrition education policy, programs, and research: a review of research. / Nutr Educ 27, 279—418. Cox DR & Hinkley DV (1974) Theoretical Statistics. London: Chapman and Hall. Cronbach LJ (1984) Essentials of Psychological Testing, 4th ed. New York: Harper and Row. Goldberg GR, Black AE, Jebb SA, Cole TJ, Murgatroyd PR, Coward WA & Prentice AM (1991) Crucial evaluation of energy intake data using fundamental principals of energy physiology: 1. Derivation of cut-off limits to identify underrecording. Eur J Clin Nutr 45, 569-581. Hersey J, Anliker J, Miller C, Mullis R, Daugherty S, Das S, Bray C, Dennee P, Sigman-Grant M & Thomas HO (2001) Food shopping practices are associated with dietary quality in lowincome households. J Nutr Educ 33, S16-S26. James WPT & Schofield E (1990) Human Energy Requirements. Oxford: Oxford University Press. Lutz SF, Ammerman AS, Atwood J, Campbell MK, DeVellis RF & Rosamond WD (1999) Innovative newsletter interventions improve fruit and vegetable consumption in healthy adults. J Am Diet Assoc 99, 705-709. Monsen ER & Balintfy JL (1982) Calculating dietary iron bioavailability: refinement and computerization. J Am Diet Assoc 80, 307-311. National Cancer Institute (2001) 5 a Day for Better Health Program. National Insititutes of Health Publication no. 01-5019. Bethesda, MD: NIH. Perez-Escamilla R & Haldeman L (2002) Food label use modifies association of income with dietary quality. / Nutr 132, 768-772. Rose D (1999) Economic determinants and dietary consequences of food insecurity in the United States. J Nutr 129, 517S-520S. Scrimshaw NS & SanGiovanni JP (1997) Synergism of nutrition, infection, and immunity: an overview. Am J Clin Nutr 66, 464S-477S. Steptoe A, Dohert A, Kerry A, Rink E & Hilton S (1999) Sociodemographic and psychological predictors of change in dietary fat consumption in adults with high blood cholesterol following counseling in primary care. Health Psychol 19, 411-419. Townsend MS, Peerson J, Love B, Achterberg C & Murphy S (2001) Food insecurity is positively related to overweight in women. J Nutr 131, 1738-1745. US Department of Agriculture (1999) Promoting Healthy Eating: An Investment in the Future. Report to the US Congress. Alexandria, VA: Food and Nutrition Service. US Department of Agriculture/Department of Health and Human Services (2000) Nutrition and Your Health: Dietary Guidelines for Americans, 5th ed. Washington, DC: DHSS. Wilde PE & Ranney CK (2000) The monthly food stamp cycle: shopping frequency and food intake decisions in an endogenous switching regression framework. Am J Agric Econ 82, 200-213. Young L & Swinbum B (2002) Impact of the Pick the Tick food information programme on the salt content of food in New Zealand. Health Promot Int 17, 13-19.

373 British Journal of Nutrition (2002), 88, 719-728 © The Authors 2002

DOl: 1O.1079/BJN2OO2739

Unhealthy eating habits, physical exercise and macronutrient intakes are predictors of anthropometric indicators in the Women's Health Trial: Feasibility Study in Minority Populations Alok Bhargava1* and Joanne F. Guthrie2 1

Department of Economics, University of Houston, Houston, TX 77204-5019, USA Economic Research Service, US Department of Agriculture, 1800 M Street NW, Washington, DC 20036, USA (Received 1 October 2001 - Revised 26 March 2002 - Accepted 17 August 2002)

The increasing prevalence of obesity in the USA, especially among minority populations, is a serious public health concern. This present study analysed repeated measurements at baseline and at 6 and 12 months on 351 women in the control group and 575 women in the intervention group of the Women's Health Trial: Feasibility Study in Minority Populations. Dynamic random effects models were estimated using the three repeated observations to explain the effects of energy and macronutrient intakes, physical exercise, unhealthy eating habits and socio-economic characteristics on the subjects' body weights and waist and hip circumferences. In both the control and intervention groups, physical exercise was negatively associated with body weight and with waist and hip circumferences, while an index of unhealthy eating habits was positively associated (P<005). The proportion of energy derived from carbohydrate and from saturated and monounsaturated fat were often significant predictors of body weight and of waist and hip circumferences in the two groups. The results indicated that nutrition education programmes for improving eating habits and increasing physical exercise can reduce obesity prevalence in the USA. Dietary fat: Physical exercise: Unhealthy eating: Socio-economic factors: Random effects The rising prevalence of obesity in the USA has spurred serious public health concerns. Medical conditions associated with obesity such as hypertension, diabetes and cardiovascular diseases are becoming increasingly costly to society (Frazao, 1999). Adults, especially from less educated populations, are susceptible to obesity. While energy imbalance is generally agreed to be a cause of weight gain, the specific role of dietary fat in promoting obesity has received some attention in the literature (Bray & Popkin, 1998; Willett, 1998a; Rolls et al. 1999). Clinical studies have indicated the imprecise nature of the regulation of the fat balance in human subjects, especially among less active individuals (Flatt, 1987; Schutz et al. 1989; Shepard et al. 2001). Moreover, researchers have argued that the intakes of saturated, monounsaturated and polyunsaturated fats may differentially affect adiposity (Doucet et al. 1998). Analyses of longitudinal data from observational studies can afford insights into the likely effects of dietary factors on body weight and on waist and hip circumferences that have been used to predict clinical outcomes (Larssonef al. 1984; Jones etal. 1986; Rexrodeeta/. 1999). In the present paper, we explore these issues by developing comprehensive longitudinal models for body weight and for

waist and hip circumferences using the data from the Women's Health Trial: Feasibility Study in Minority Populations (WHTFSMP; Bowen et al. 1996). Since the subjects in the intervention group of WHTFSMP were counselled to reduce fat intakes, their dietary patterns were likely to exhibit greater variation than those in the control group. Moreover, the subjects' physical exercise patterns and measures of unhealthy eating habits and preferences were likely to reflect the difficulties in making dietary changes. These variables can be included in the models for anthropometric indicators to provide insights into the factors determining the success of dietary interventions. An important issue for consideration is that the models postulated for anthropometric indicators are likely to influence the interpretation of the empirical results. Willett (1998b), for example, suggested the use of current energy intake as an explanatory variable in models for disease status. At a given point in time, however, subjects' energy requirements are a function of their body weights and activity levels (Food and Agricultural Organization/ World Health Organization/United Nations University, 1985; James & Schofield, 1990; Bhargava & Reeds, 1995). Ideally, investigators should include a measure of

Abbreviation: WHTFSMP, Women's Health Trial: Feasibility Study in Minority Populations. * Corresponding author: Dr Alok Bhargava, fax +1 713 743 3798, email [email protected]

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A. Bhargava and J.F. Guthrie

energy imbalance in models for anthropometric indicators (Prentice, 1995). This is generally unfeasible in large studies because of the large cost. Instead, we used a statistical framework that allowed possible bi-directionality in the relationship between body weight and the current energy intake. Moreover, it was possible to discriminate between the models where the intakes of carbohydrate, saturated, monounsaturated and polyunsaturated fats and the current energy intake were included as explanatory variables and where the dietary intakes were expressed as dietary intake:energy intake. Methods Subjects The WHTFSMP was a multi-centre randomized trial, conducted in 1991-5 and sponsored by the National Cancer Institute, involving 2208 women in Atlanta, GA, Birmingham, AL and Miami, FL, USA, with a goal of reducing energy intakes from fat to approximately 2 0 % in the intervention group (Bowen et al. 1996). The participants (28% black, 16% Hispanic and 5 4 % white) were postmenopausal women in the age group 5 0 - 7 9 years; 40 and 6 0 % of the subjects were randomly assigned to the control and intervention groups respectively. Because the WHTFSMP was funded for a fixed period (Bowen et al. 1996), complete results at the baseline, 6 and 12 months on the variables used in the analysis were available for 351 women in the control group and for 575 women in the intervention group. Experimental

methods

The primary goals of the WHTFSMP were to reduce fat intakes, especially of saturated fat, and to increase the consumption of fruits, grain products and vegetables. The women in the intervention group, led by a nutritionist, met once per week in groups of eight to fifteen for the first 6 weeks, bi-weekly for the next 6 weeks and once per month thereafter for an additional 9 months. Dietary intakes at the baseline, 6 and 12 months were measured by a food-frequency questionnaire developed especially for the present study and using 4 d food records (Bowen et al. 1996; Kristal et al. 1997; Coates et al. 1999). However, to reduce costs, 50 % of the women were randomly selected at baseline and only their 4 d food records were processed. The analysis of anthropometric indicators used the nutrient intakes calculated from the food-frequency questionnaire Each subject's age, marital status and reproductive history were recorded in the questionnaire. Education levels were coded into four categories that increased with the years of education; similarly, household incomes were coded into three groups. The subject's patterns of 'mild' and 'strenuous' physical exercise for at least 30min were investigated on a scale of 1-5 (1, never; 5, everyday). The subjects answered, on a scale of 1-4 (1, never; 4, very often), eight questions regarding their food cravings

and preferences: (1) if they liked tasty food; (2) had craving for rich foods; (3) liked healthy foods; (4) ate more than they should; (5) whether the food consumed was satisfying; (6) felt uncomfortable with rich foods; (7) felt deprived in the absence of rich foods; (8) disliked the taste of fat. The scores on 'eating healthy foods', 'felt uncomfortable with rich foods' and 'disliked the taste of fat' were recoded so that higher scores implied less healthy eating preferences. The scores on the eight questions were subsequently summed to produce an index of 'unhealthy eating' that ranged from 8-32. Each subject's height, body weight and waist and hip circumferences were measured at baseline and at 6 and 12 months. Height was measured with a stadiometer by rounding off to the nearest 0-5 inches; weight was measured to the nearest pound using a calibrated balanced beam scale. Using a fibreglass tape, waist circumference was measured at the smallest horizontal circumference between the ribs and the iliac crest. Hip circumference was measured at the maximum extension of the buttocks. For the analysis, body-weight measurements were converted to kg and height and waist and hip circumferences were expressed in m.

Analytical framework and the models for weight and waist and hip circumferences The body weight of an individual responds gradually to nutrient intakes and lifestyle changes; weight in the previous time period is therefore an important predictor of the current weight. While reductions in energy intakes can induce weight loss over time, the relationship between nutrient intakes and weight is likely to be smooth in most applications. Similarly, waist and hip circumferences change slowly over time and are influenced by the history of energy imbalance, physical exercise and the previous measurements. Because of the emphasis in the WHTFSMP on fat intakes, we postulated a dynamic random effects model (model 1) for the body weight of n subjects using three repeated observations (i: = 1,2,..., n; t — 2,3): ln(WT) it = ao + a^black)) + a 2 (white)j + a3(education)j + a^income); + a5ln(unhealthy eating); + a^physical exercise); + a 7 ln(height)i + a 8 ln(carbohydrate) it + a9ln(saturated fat)it + aioln(monounsaturated fat) it + ai ^(polyunsaturated fat)it + ai 2 ln(energy intake) it + a^lnCWTXt-! + ulit,

(1)

Anthropometric Indicators in the Women's Health Trial where WT is body weight and In is the natural logarithm. Each subject's body weight, index of unhealthy eating, carbohydrate and energy intake and the intakes of saturated, monounsaturated and polyunsaturated fats were transformed into natural logarithms, partly to reduce heteroscedasticity (Nelson et al. 1989). The coefficients of the variables expressed in logarithms were thus the 'elasticities' (a term used in economics literature for the % change in the dependent variable resulting from a 1 % change in the independent variables). The model for body weight contained previous measurement of weight as an explanatory variable with coefficient a13. The uHt were random error terms that can be decomposed in a random effects fashion as: uiit = 5j + v i i , ,

(2)

where Si were subject specific random effects that were assumed to be normally distributed with zero mean and a constant variance and v lit were normally distributed error terms with zero mean and constant variance (Laird & Ware, 1982). Further, we developed a model (model 2) where the dietary intakes were expressed dietary intakexurrent energy intake. Since ln(carbohydrate:energy) can be written as ln(carbohydrate) - ln(energy), model 2 was a special case of model 1 with the restrictions on the coefficients in model 1 that: a8 + a9 -I- aio + an + a]2 = 0. These restrictions were tested using a likelihood ratio test statistic mat was distributed, for large n, as a x2 variable with 1 df. Similar models were estimated for each subject's waist and hip circumferences. Note that while pooling the data for the control and intervention groups, an indicator variable for the subjects' group was included in models 1 and 2. Because of the nutrition education programme for the intervention group, it was of interest to test whether the model parameters in the two groups were constant. The null hypotheses of parameter constancy for the control and intervention groups were rejected in all the models and hence the empirical results are presented separately for the two groups. It was also useful to estimate 'static' random effects models for the changes in weight between the baseline to 6 months and from 6 to 12 months (i.e. without including the previous weight change as an explanatory variable; Sheppard et al. 1991). The subjects' characteristics that were constant during the observation period (race, education, income, unhealthy eating, physical exercise and height) were omitted in explaining the weight changes. Thus, model 3 was developed for the two observations on weight changes that were explained by the changes in the intakes of carbohydrate, saturated, monounsaturated and polyunsaturated fats and energy. Another model (model 4) was estimated for weight changes with the explanatory variables expressed as the changes in the proportions of energy derived from carbohydrate and saturated, monounsaturated and polyunsaturated fats. Last, model 5 was specified for weight changes (time (t - 1) - time t) explained by the levels of the proportions

375

of energy derived from carbohydrate and saturated, monounsaturated and polyunsaturated fats (at time t). Statistical analysis For assessing the changes between the baseline and 6- and 12-month periods in the control and intervention groups, paired t tests were used to test the null hypotheses that there were no differences between the means of weight, waist and hip circumferences, energy and nutrient intakes and the energy derived from carbohydrate and saturated, monounsaturated and polyunsaturated fats. The software package SPSS (1999; SPSS Inc., Chicago, IL, USA) was used to compute the descriptive and t statistics. Since there were only three repeated time observations on the subjects, the statistical estimations of models 1-5 were based on the assumptions that the number of women (n) was large, but the number of time periods was fixed. Thus, initial observations on the dependent variables (e.g. WT n in model 1, see p. 720) were treated as correlated with the errors (Bhargava & Sargan, 1983). The errors (e.g. u]it) in the models were assumed independent across subjects, but correlated over time with a positive definite variance-co variance matrix. Details of the maximum likelihood estimation methods for models 1 and 2 are presented by Bhargava & Sargan (1983). The static random effects models (models 3-5) were estimated using a Generalised Least Squares estimator computed in a stepwise fashion (Bhargava, 1991). Results Descriptive statistics and t tests The sample mean values and standard deviations of the variables used in the analysis for 351 subjects in the control group and 575 subjects in the intervention group with complete information are presented in Table 1. The sample mean values of background variables such as race, education and income and the index of unhealthy eating and exercise patterns were similar in the control and intervention groups. For the control group, there were significant (P<005) changes between the baseline and 12 months in all variables except weight and waist circumference; changes between the 6- and 12-month periods were substantially smaller. The mean energy intakes declined from 7223 to 6243 kJ, constituting a 16% reduction. There was a decline of approximately 20 % in the intake of saturated, monounsaturated and polyunsaturated fats. The intakes of saturated fat (g) at percentiles 10, 30, 50, 70 and 90 were 101 v. 7-9, 170 v. 13-2, 22-6 v. 17-9, 301 v. 23-9 and 441 v. 37-3 at baseline and 12 months respectively. Even in the absence of counselling, the subjects reduced their saturated fat intakes, presumably due to the minimal information (Unites States Department of Agriculture/Department of Health and Human Services, 1990) that they received through participating as controls. The changes in the intervention group between the baseline and 12 months were statistically significant for all variables (P<005). The reduction in energy intake was approximately 27 %. The corresponding changes in

-J OS

Table 1. Selected variables for 351 women in the control group and 575 women in the intervention group at baseline, 6 months and 12 monthst§ (Mean values and standard deviations) Intervention group (n 575)

Control group (n 351) Basel ne

Age (years) Black (0-1)|| White (0-1)|| Education (1 -4)|| Income (1-3)11 Unhealthy eating (8-32)|| Physical exercise (1-5)|| Height (m) Weight (kg) Waist circumference (m) Hip circumference (m) Energy intake (kj) Carbohydrate (g) Saturated fat (g) Monounsaturated fat (g) Polyunsaturated fat (g) Carbohydrate (% energy) SFA (% energy) MUFA (% energy) PUFA (% energy)

6 months

Mean

SD

59-9 0-38 0-56 2-91 1-96 21-1 2-84 1-62 76-2 0-86 109 7223 191 25-2 28-6 17-0 45-2 12-8 14-5 8-7

6-6 0-49 0-50 1-00 0-48 2-84 1-22 006 12-5 0-11 009 3262 85-6 14-5 15-5 9-6 80 30 30 2-4

Mean

760 0-86 108 6485 180 21-6 24-3 140 47-2 12-2 13-8 80

12 months SD

12-5

on

009 3067 840 13-0 14-0 8-4 8-8 30 3-1 2-5

Mean

75-9 0-86 1-08* 6243* 174* 20-8* 22-9* 13-3* 47-5* 12-0* 13-4* 7-8*

Baseline

6 months

12 monthst

SD

Mean

SD

Mean

SD

Mean

SD

12-7 0-11 0-10 3188 87-3 140 14-3 90 8-8 3-1 3-1 2-5

60-1 0-34 0-57 2-98 1-98 21-3 2-86 1-63 760 0-87 109 7489 198 27-1 30-3 17-5 44-5 13-3 15-0 8-8

6-6 0-48 0-50 1-00 0-50 2-91 1-33 006 12-7 0-11 009 3736 104 160 16-7 100 7-7 2-8 2-9 2-5

740 0-85 107 5406 181 13-1 140 7-8 56-6 8-9 9-6 5-4

12-7 0-11 009 2284 77-9 7-7 8-5 5-3 9-4 2-6 3-2 2-1

73-8* 0-85* 107* 5448* 186* 130* 13-8* 7-6* 57-7* 8-7* 9-3* 5-2*

12-8 0-11 0-10 2423 83-0 8-2 8-6 4-8 9-6 2-7 3-2 2-2

SFA, saturated fatty acid; MUFA, monounsaturated fatty acid; PUFA, polyunsaturated fatty acid. Mean values were significantly different from baseline values for each group: *P<005. Mean values for the change between baseline and 12 months were significantly different from those of the control group except for carbohydrate intake: tP<005. $ For details of subjects and procedures, see p. 720. § Dietary intakes were based on a food-frequency questionnaire. II For details of scoring system, see p. 720.

Anthropometric Indicators in the Women's Health Trial

377

constancy in the two groups (x2 56-4, df 14, /*< 0-001). Thus, the dynamic models were estimated separately for the control and intervention groups. For the control group, the results for models 1 and 2 showed that white women and women from better-off households were significantly lighter (/ > <005). The index of unhealthy eating was positively associated with weight, while the reported frequency of mild physical exercise was negatively associated. These results underscored the importance of behavioural factors such as craving for rich foods and physical exercise for body weight. Height was a significant predictor of weight. The estimated coefficients from models 1 and 2 were significantly (P<005) lower than the value 2 that would have indicated a preference for combining (the logarithms of) height and weight as the BMI (Bhargava, 1994). The estimated coefficient of the current energy intake in model 1 for the control group was negative and statistically significant (P<005). The likelihood ratio test rejected the restrictions on the coefficients of model 1 at the 5 % significance level, though the null hypothesis was accepted at the 2-5 % level. The estimated coefficients of models 1 and 2 were close, suggesting that the conclusions based on either formulation would be similar. The standard errors of the coefficients were slightly lower in model 2 because of the coefficient restrictions. The coefficients of monounsaturated fat were positive and significant (P<0-05) in

weight and waist and hip circumferences were 3, 2 and 2 % respectively. While it was possible that the subjects underreported their energy intakes, the reported intakes of saturated, monounsaturated and polyunsaturated fat were reduced to < 50 % of the levels at the baseline. The intakes of saturated fat at percentiles 10, 30, 50, 70 and 90 were 101 v. 5-0, 17-7 v. 8-2, 24-5 v. 11-5, 32-2 v. 14-9 and 46-6 v. 23-5 at baseline and 12 months respectively. The reductions in saturated fat intakes especially by women consuming high-fat diets at the baseline were impressive. There was a 23 % increase in the % energy derived from carbohydrate. Overall, in comparison with the control group, the educational programme for the intervention group helped lower fat and energy intakes and promoted greater weight loss. Empirical results for body weight in the control and intervention groups The empirical results from estimating the models for weight of the subjects in the control and intervention groups are presented in Table 2. Model 1 included the current energy intake and the levels of carbohydrate and fat intakes. In model 2, the nutrient intakes were expressed as nutrient intakes:energy intake. Allowing for different mean values in the control and intervention groups, a likelihood ratio test rejected the null hypothesis of parameters

Table 2. Maximum likelihood estimates of dynamic random effects models for the weight of women in the control and intervention groups explained by socio-economic variables and nutrient intakesft (Slope coefficients with their standard errors) Weight (kg) Intervention group (n 575)

Control group (D351) Model 2||

Model 1

Constant Black (0-1)1 White (0-1)11 Education (1 -4)1 Income (1-3)1 Unhealthy eating (8-32)§1 Physical exercise (1 - 5 ) 1 Height (m)§ Energy intake (kJ) Carbohydrate (g)§ Saturated fat (g)§ Monounsaturated fat (g)§ Polyunsaturated fat (g)§ Carbohydrate:energy§ Saturated fat:energy§ Monounsaturated fat:energy§ Polyunsaturated fat:energy§ Lagged dependent variable§ Betweenrwithin variance Within variance

Model 1

Model 2||

Coeff

SE

Coeff

SE

Coeff

SE

Coeff

SE

2-100* 0024 -0035* 00004 -0008 0-126* -0007* 0-776* -0087* 0-033* 0018 0-046* 00006

0049 0017 0-017 0003 0005 0017 0003 0-130 0021 0013 0-013 0020 0009

2-197* 0022 -0038* 0-0008 -0010* 0-133* -0007* 0-804*

0-320 0011 0012 0002 0-005 0041 0-002 0-144

2094* 0032* -0028* -0012* -0006 0-140* -0009* 1061* -0028 0010 -0018 0034* 0007

0-190 0017 0014 0003 0009 0028 0003 0-133 0027 0018 0014 0017 0009

2-114* 0032* -0028* -0012* -0006 0-145* -0009* 1074*

0-161 0-012 0011 0003 0007 0021 0002 0-122

0-411* 8-245* 00009

0029 1-260

Coeff, coefficient. *P<0-05. t F o r details of subjects and procedures, see p. 720. $ Dietary intakes were based on a food-frequency questionnaire. || The intakes in model 2 were expressed intake:energy intake. § Transformed into natural logarithms. Tl For details of scoring system, see p. 720.

0032* 0019 0-051* -0002 0-401* 8-648* 00009

0016 0016 0019 0010 0088 3012

0-332* 9-337* 00011

0045 1-686

0010 -0018 0034* 0006 0-329* 9-399* 0-0011

0013 0012 0017 0009 0047 1-623

378

A. Bhargava and J.F. Guthrie by itself was insufficient to induce behavioural changes leading to weight loss among the more educated women. The coefficients of the index of unhealthy eating and physical exercise patterns in models 1 and 2 were similar for the control and intervention groups and were statistically significant (P<005). However, only the intakes of monounsaturated fat were positively associated with weight in the intervention group. Coefficient of weight in the previous period was slightly lower for the intervention group and the estimates of the within-subject variance were slightly higher. The coefficient of energy intake in model 1 was not statistically different from zero. Last, the subjects' age and age-squared were significant predictors of weight; the parameter estimates reported in Table 2 were not noticeably affected by inclusion of the age variables in the models.

models 1 and 2. This was not true for saturated and polyunsaturated fat intakes where the estimated coefficients in both models were not statistically different from zero. The estimated coefficients of the lagged dependent variables were approximately 040 for models 1 and 2 and were significant (P<005), thereby underscoring the need for taking into account the history of subject's' body weight when investigating the effects of nutrient intakes. The betweemwithin variance ratios were large and significant (P<005), suggesting that the between-subject differences in the sample were partially accounted for by the background variables, index of unhealthy eating, physical exercise patterns and nutrient intakes. Since weight responds gradually to small imbalances in energy intake and expenditure, it was reasonable to expect that the explanatory variables measured at three time points would not account for the entire history of energy imbalances. The results shown in Table 2 for women in the intervention group were broadly similar to the results for the control group. Black women were heavier and white women were lighter than Hispanic women (P<005). The coefficient of education was statistically significant (P<005) in models 1 and 2, suggesting that highly educated women benefited more from the counselling. Since the coefficient of education was not statistically significant in the control group, awareness of the counselling programme

Empirical results for waist and hip circumferences in the control and intervention groups The results from estimating models 1 and 2 for waist circumference of the women in the control and intervention groups are presented in Table 3. In the control group, household incomes and physical exercise patterns were negatively associated with waist circumference whereas the index of unhealthy eating habits was positively

Table 3. Maximum likelihood estimates of dynamic random effects models for the waist circumference of women in the control and intervention groups explained by socio-economic variables and nutrient intakesft (Slope coefficients with their standard errors) Waist circumference (m)§ Intervention group (n 575)

Control group (n351) Model 2||

Model 1

Constant Black (0-1)1 White (0-1)1 Education (1-4)11 Income (1-3)1 Unhealthy eating (8-32)§1 Physical exercise (1 -5)1 Height (m)§ Energy intake (kJ)§ Carbohydrate (g)§ Saturated fat (g)§ Monounsaturated fat (g)§ Polyunsaturated fat (g)§ Carbohydrate:energy§ Saturated fat:energy§ Monounsaturated fat:energy§ Polyunsaturated fat:energy§ Lagged dependent variable§ Betweemwithin variance Within variance

Model 1

Model 2||

Coeff

SE

Coeff

SE

Coeff

SE

Coeff

SE

-0-136 0033 0009 - 0004 -0016* 0051 -0007* 0-170 -0090* 0048* 0039* 0004 0012

0-173 0017 0017 0004 0008 0031 0003 0-101 0-040 0023 0-020 0026 0013

0054 0030 -0001 -0004 -0018* 0060* -0007* 0-192*

0-143 0017 0017 0-004 0008 0028 0003 0-101

-0-514* 0015 -0023 -0008* -0014 0-114* -0-010* 0-237* 0-003 -0-007 -0024 0039* -0011

0-103 0016 0015 0004 0008 0029 0002 0-110 0019 0015 0-014 0020 0010

-0-517* 0-015 -0023 -0008* -0014 0-114* -0010* 0-237*

0-132 0-015 0-015 0004 0-008 0027 0003 0-109

-

0-453* 1 -986* 00018

0-103 0-979

Coeff, coefficient. *P<005. t F o r details of subjects and procedures, see p. 720. ^Dietary intakes were based on a food-frequency questionnaire. § Transformed into natural logarithms. || The intakes in model 2 were expressed at intake:energy intake. II For details of scoring system, see p. 720.

0047* 0041* 0009 0010 0-431* 2-210* 00018

0021 0017 0-012 0011 0099 0-988

-

0-237* 4-969* 00016

0056 1008

.0-007

- 0025* 0040* -0011 0-235* 5-006* 00016

0020 0011 0008 0008 0056 1007

379

Anthropometric Indicators in the Women's Health Trial

associated (P<005). The estimated coefficient of height was small and statistically significant (P<0-05) only in model 2. Energy intake in model 1 was estimated with a negative sign that was significant. The intakes of carbohydrate and saturated fat were significant (P<005) and positively associated with waist circumference in both model 1 and 2. The coefficients of the lagged dependent variables for waist circumference were close to those for body weight reported in Table 2. In the intervention group, education was negatively associated with waist circumference. The index of unhealthy eating habits and physical exercise patterns were significantly associated with waist circumference of the women in the intervention group. Moreover, while the carbohydrate and saturated fat intakes were not significant predictors, the intake of monounsaturated fat was a significant predictor. Some of the differences between the control and intervention groups were likely to be due to the relative changes in the intakes of saturated, monounsaturated and polyunsaturated fats. This issue will be further addressed later. The coefficients of the lagged dependent variables were lower, whereas the betweemwithin variance ratios were higher in the intervention group. Table 4 presents the results for the hip circumferences of women in the control and intervention groups. Again, the index of unhealthy eating habits and physical exercise patterns were significant (P<0-05) predictors for both

groups. The magnitude of these coefficients was similar to the results for weight and waist circumference in Tables 2 and 3 respectively. Height was positively associated with hip circumference. Energy intakes were estimated with negative signs for both groups and were statistically significant. The intake of monounsaturated fat was a significant predictor of hip circumference in the control group; the fat intakes were not significant predictors in the intervention group. The coefficients of the lagged dependent variables were smaller and the betweemwithin variance ratios were larger for the control group. Empirical results for weight changes in the control and intervention groups Table 5 presents the results for the models for weight changes in the control and intervention groups. In model 3, the explanatory variables were the corresponding changes in the intakes of carbohydrate and saturated, monounsaturated and polyunsaturated fats and energy. In model 4, the explanatory variables were expressed as changes in the proportions of energy derived from carbohydrate and saturated, monounsaturated and polyunsaturated fats. The proportions of energy from these macronutrients in levels were the explanatory variables in model 5. In the results from model 3, the coefficients of energy

Table 4. Maximum likelihood estimates of dynamic random effects models for the hip circumference of women in the control and intervention groups explained by socio-economic variables and nutrient intakesft (Slope coefficients with their standard errors) Hip circumference (m)§ Intervention group (n 575)

Control group (n 351) Model 1

Constant Black (0-1)1 White (0-1)11 Education (1-4)1 Income (1-3)1 Unhealthy eating (8-32)§1 Physical exercise (1 - 5 ) 1 Height (m)§ Energy intake (kJ)§ Carbohydrate (g)§ Saturated fat (g) Monounsaturated fat (g)§ Polyunsaturated fat (g)§ Carbohydrate:energy§ Saturated fat:energy§ Monounsaturated fat:energy§ Polyunsaturated fat:energy§ Lagged dependent variable§ Between:within variance Within variance

Model 2||

Model 1

Model 2||

Coeff

SE

Coeff

SE

Coeff

SE

Coeff

SE

-0-254 0-009 -0-021 0-003 -0009 0090* -0008* 0-292* -0024 0012 - 0-004 0-034 -0010

0-135 0019 0019 0004 0008 0031 0003 0-107 0026 0015 0-015 0018 0-010

-0-213 0007 -0023 0004 -0-010 0094* -0008* 0-300*

0-145 0-019 0019 0004 0-009 0-032 0003 0-104

- 0-264* 0013 -0008 -0006* -0004 0070* - 0-005* 0-331* -0013* 0008 -00002 0011 -0003

0-062 0-010 0009 0003 0005 0-019 0002 0074 0002 0005 0011 0-015 0007

-0-249* 0012 -0008 -0006* -0004 0-071* -0-005* 0-334*

0075 0010 0009 0003 0005 0018 0002 0072

0069 6-520* 00008

0078 1-600

Coeff, coefficient. *P<005. t For details of subjects and procedures, see p. 720. X Dietary intakes based on a food-frequency questionnaire. § Transformed into natural logarithms. II The intakes in model 2 were expressed as intake:energy intake. I For details of scoring system, see p. 720.

0-011 - 0003 0037 -0012 0-067 6-598* 00008

0018 0-015 0019 0010 0078 1-604

0-279* 3-557* 0-0009

0-053 0-719

0-007 00004 0011 -0-003 0-283* 3-482* 00009

0013 0012 0013 0008 0054 0-715

Table 5. Efficient estimates of three versions of static random effects models for weight changes of the women in the control and intervention groups explained by the changes in carbohydrate, saturated, monounsaturated and polyunsaturated fat and by transformations of the explanatory variablestt§ (Slope coefficients and standard errors) Weight change (kg) Intervention group (n 575)

Control group (n 351) Model 3f|

Constant Change in carbohydrate (g) Change in saturated fat (g) Change in monounsaturated fat (g) Change in polyunsaturated fat (g) Change in energy (kJ) Change in carbohydrate (% energy) Change in saturated fat (% energy) Change in monounsaturated fat (% energy) Change in polyunsaturated fat (% energy) Carbohydrate (% energy) Saturated fat (% energy) Monounsaturated fat (% energy) Polyunsaturated fat (% energy)

Model 41

Model 3||

Model 5 f t

Model 41

Model 5 t t

Coeff

SE

Coeff

SE

Coeff

SE

Coeff

SE

Coeff

SE

Coeff

SE

-0001 0042* 0015 0052* -0003 0013*

0-001 0014 0011 0-014 0-007 0024

-0001

0001

0-172*

0057

-0-006* 0015 0008 0012 0-022* -0054*

0001 0-011 0009 0011 0-005 0-018

-0006*

0-001

0-179*

0044

-

0042* 0016 0052* -0004

-

Coeff, coefficient. *P<0-05. f For details of subjects and procedures, see p. 720. $The dependent variable and all explanatory variables were transformed into natural logarithms. § Dietary intakes were based on a food-frequency questionnaire. II Model 3 explained the changes in weight by the changes in intakes. H Model 4 explained changes in weight by the changes in the % energy derived from the intakes. f t Model 5 explained the changes in weight by the level of % energy derived from the intakes.

0014 0-011 0014 0007

-

0018 0-005 0024* 0003

0011 0009 0-012 0006

-

0016 0-001 0012 0-022*

-

-— 0011 0009 0011 0007 0-018 0006 0010 0016*

0010 0009 0011 0006

Anthropometric Indicators in the Women's Health Trial intakes were estimated with negative signs and were statistically significant (P<0-05) for both the control and intervention groups. These negative estimates were broadly similar to the estimated coefficients of energy intakes in the model for weight in Table 2. Thus, the results again suggested that weight changes might be better explained by the changes in the proportions of energy derived from carbohydrate and saturated, monounsaturated and polyunsaturated fats. The results for model 4 in Table 5 were close to those obtained from estimating model 3. Moreover, in the control group, the % energy derived from carbohydrate and monounsaturated fat was positively associated with weight changes. By contrast, the % energy derived from polyunsaturated fat was positively associated in the intervention group. Further, the results from model 5 with the explanatory variables in levels showed positive associations between energy derived from monounsaturated fat and weight changes in the control group. By contrast, a greater proportion of energy from polyunsaturated fat was associated with weight gain in the intervention group. A possible explanation of these findings was that, although some women in the intervention group had lowered their saturated fat intakes due to the nutrition education programme, they might have subsequently increased the intake of polyunsaturated fat thereby increasing the overall energy intake (Guthrie et al. 1999). Overall, while the results in Tables 2 and 5 showed significant effects of macronutrient intakes on body weight and weight changes, the results were ambiguous with regard to the evidence on the possible link between the subjects' fat intakes and body weights. Moreover, the inclusion of protein intakes in models 1 and 2 led to very similar results and indicated a preference of the conversion of dietary intakes:energy intake. Discussion This present study analysed the effects of the dietary intervention in the WHTFSMP. The proximate determinants of weight and waist and hip circumferences in the control and intervention groups were modelled using repeated measurements at baseline, 6 and 12 months. The dietary intakes calculated from the food-frequency questionnaire showed significant (P<005) reductions between baseline and 12 months in the intakes of energy and saturated, monounsaturated and polyunsaturated fats for both groups; the changes between the 6- and 12-month periods were, smaller. The reductions in intakes between baseline and 12 months were greater for the intervention group. Between baseline and 12 months, the mean body weight and waist and hip circumferences of women in the intervention group were reduced by 3, 2 and 2 % respectively. By contrast, there was only a slight reduction in hip circumference of women in the control group. The comprehensive longitudinal data provided an opportunity to model the associations between background, lifestyle and nutritional variables and the anthropometric indicators. Separate analyses were performed for the control and intervention groups because of the differences in the model parameters for the two groups. The results from the models for weight and waist and hip

381

circumferences showed the importance of physical exercise and unhealthy eating habits for the anthropometric indicators; mild exercise appeared to be helpful in reducing body weight and waist and hip circumferences. These findings merit a further consideration from those designing educational programmes for dietary improvements. For example, using the question items regarding unhealthy eating habits in the WHTFSMP, investigators can identify the women who will face greater difficulties in responding to nutrition education; such women can be offered additional guidance for making dietary changes. While the education variable was a significant predictor of anthropometric indicators in the intervention group, education was not a significant predictor in the control group. Higher education levels may have made it easier for women to understand and apply the nutrition guidance provided as part of the intervention. Given the wide prevalence of obesity among less educated women in lowincome households, special attention is necessary for devising effective education programmes for such subjects. It is essential that women receive dietary advice before they reach a stage where excess weight leads to conditions such as non-insulin-dependent diabetes mellitus. The longitudinal data analysis also attempted to separate out the effects of intakes of energy, carbohydrate and saturated, monounsaturated and polyunsaturated fat on anthropometric indicators. For example, the % energy derived from carbohydrate and saturated and monounsaturated fats was often a positive and significant predictor of the anthropometric indicators in the two groups. In the models for weight changes, higher % energy from monounsaturated fat was associated with weight gain in the control group. By contrast, energy derived from polyunsaturated fat was a positive predictor of weight gain in the intervention group. The empirical results did not point to a clear link between the intakes of the three types of fat and body weight; reporting biases in the intakes might have influenced some of the findings (Bingham, 1994; Buzzard et al. 1996). For reasons of small sample sizes, the random effects models were not separately estimated for the black, Hispanic and white women. The results from observational and experimental studies can often be combined to provide useful insights into the factors affecting body weight. For example, physical exercise was an important predictor of body weight and waist and hip circumferences in the WHTFSMP data. The importance of physical exercise has been documented in experimental studies measuring fat oxidation in subjects consuming high-fat diets (Smith et al. 2000); only a few subjects were studied for a limited number of days due to the large costs. While increased physical activity decreased the (positive) fat balance in the subjects, it was unclear whether such fat imbalances would persist for long periods in physically active individuals. Last, it is important to emphasize the guidelines encouraging the maintenance of a healthy body weight or the BMI. Because high-fat foods are energy dense, from a practical standpoint, a diet with low-energy density is likely to be moderately low in fat (United States Department of Agriculture/Department of Health and Human Services, 2000). The results from WHTFSMP indicate

A. Bhargava and J.F. Guthrie

382

that making lifestyle changes such as improving dietary habits and increasing physical exercise can be effective in reducing weight and waist and hip circumferences. In view of the high costs of caring for chronic diseases due to over-nutrition, preventive efforts, such as nutrition education, merit greater emphasis.

Acknowledgements This paper is dedicated to the memory of Professor Peter J. Reeds, who was a true scholar, mentor, critic and friend. The authors are greatly indebted to Dr Carolyn Clifford of the National Cancer Institute, who sadly passed away on 31 May 2001. Thanks are due to Dr Peter Basiotis, Professor Tim Cole, Dr Albert Oberman and the two referees for helpful comments. The views contained in this paper are exclusively those of the authors. This research was supported through a Cooperative Agreement between the Economic Research Service of the USA Department of Agriculture and the University of Houston. References Bhargava A (1991) Identification and panel data models with endogenous regressors. Review ofEconomic Studies 58,129-140. Bhargava A (1994) Modelling the health of Filipino children. Journal of the Royal Statistical Society Series A 157, 417-432. Bhargava A & Reeds P (1995) Requirements for what? Is the measurement of energy expenditure a sufficient estimate of energy needs? Journal of Nutrition 125, 1358-1362. Bhargava A & Sargan JD (1983) Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51, 1635-1660. Bingham SA (1994) The use of 24-hour urine samples and energy expenditures to validate dietary assessment. American Journal of Clinical Nutrition 59, 227S-231S. Bowen D, Clifford CC, Coates R, Evans M, Feng Z, Fouad M, George V, Gerace T, Grizzle JE, Hall WD, Heam M, Henderson M, Kestin M, Kristal A & Leary ET et al. (1996) The Women's Health Trial Feasibility Study in Minority Populations: Design and baseline description. Annals of Epidemiology 6, 507—519. Bray G & Popkin B (1998) Dietary fat intake does affect obesity! American Journal of Clinical Nutrition 68, 1157-1173. Buzzard IM, Faucett CL, leffery RW, McBane L, McGovern P, Baxter IS, Shapiro AC, Blackburn GL, Chlebowski RT, Elashoff RM & Wynder EL (1996) Monitoring dietary change in a lowfat diet intervention study: Advantages of using 24-hour dietary recalls versus food records. Journal of American Dietetic Association 96, 574-579. Coates R, Bowen DI, Kristal AR, Feng Z, Oberman A, Hall DW, George V, Lewis CE, Kestin M, Davis M, Evans M, Grizzle IE & Clifford C (1999) The Women's Health Trial Feasibility Study in Minority Populations: Changes in dietary intakes. American Journal of Epidemiology 149, 1104-1112. Doucet E, Almeras N, White MD, Despres I-P, Bouchard C & Tremblay A (1998) Dietary fat composition and human adiposity. European Journal of Clinical Nutrition 52, 2-6. Food and Agriculture Organization/World Health Organization/ United Nations University (1985) Energy and Protein Requirements. Geneva: WHO. Flatt IP (1987) Dietary fat, carbohydrate balance and weight maintenance: Effects of exercise. American Journal of Clinical Nutrition 45, 296-306.

Frazao E (1999) High costs of poor eating patterns in United States. In America's Eating Habits: Changes and Consequences, ALB no 750, pp. 5-32. Washington, DC: US Department of Agriculture, Economic Research Service. Guthrie IF, Derby BM & Levy AS (1999) What people know and do not know about nutrition. In America's Eating Habits: Changes and Consequences, AIB no 750, pp. 243-280. Washington, DC: US Department of Agriculture, Economic Research Service. lames WPT & Schofield E (1990) Human Energy Requirements. Oxford: Oxford University Press. lones P, Hunt M, Brown T & Norgan N (1986) Waist-hip circumference ratio and its relation to age and overweight in British men. Human Nutrition: Clinical Nutrition 40C, 239-247. Kristal AR, Feng Z, Coates RI, Oberman A & George V (1997) Associations of race/ethnicity, education and dietary intervention with the validity and reliability of a food frequency questionnaire. American Journal of Epidemiology 146, 856-869. Laird N & Ware I (1982) Random effects models for longitudinal data. Biometrics 38, 963-974. Larsson B, Svardsudd K, Welin K, Wilhemsen L, Bjorntorp P & Tibblin G (1984) Abdominal adipose tissue distribution, obesity and risk of cardiovascular disease and death: 13 year follow up of participants in the study of men born in 1913. Clinical Research 288, 1401-1404. Nelson M, Black AE, Morris IA & Cole TJ (1989) Between-andwithin subject variation in nutrient intake from infancy to old age: Estimating the number of days to rank dietary intakes with desired precision. American Journal of Clinical Nutrition 50, 155-167. Prentice A (1995) Obesity in Britain: Gluttony or sloth? British Medical Journal 311, 437-439. Rexrode KM, Carey VI, Hennekens CH, Walters EE, Colditz GA, Stampfer MI, Willett WC & Manson IE (1999) Abdominal adiposity and coronary heart disease in women. Journal of American Medical Association 280, 1843-1848. Rolls BI, Bell EA, Castellanos VH, Chow M, Pelkman CL & Thorwart ML (1999) Energy density but not fat content of foods affected energy intake in lean and obese women. American Journal of Clinical Nutrition 69, 863—871. Schutz Y, Flatt I-P & Jequier E (1989) Failure of dietary fat intake to promote fat oxidation: A factor favoring the development of obesity. American Journal of Clinical Nutrition 50, 307-314. Shepard TY, Weil KM, Sharp TA, Grunwald GK, Bell ML, Hill 10 & Eckel RH (2001) Occasional physical inactivity and a high-fat diet may be important in the development and maintenance of obesity in human subject. American Journal of Clinical Nutrition 73, 703-708. Sheppard L, Kristal A & Kushi L (1991) Weight loss in women participating in a randomized trial of low-fat diets. American Journal of Clinical Nutrition 54, 821-828. Smith SR, de Long L, Zachwieja JI, Nguyen T, Rood I, Windhauser M, Volaufova I & Bray GA (2000) Concurrent physical activity increases fat oxidation during shift to a high-fat diet. American Journal of Clinical Nutrition 72, 131-138. United States Department of Agriculture/Department of Health and Human Services (1990) Nutrition and Your Health: Dietary Guidelines for Americans. Washington, DC: DHHS. United States Department of Agriculture/Department of Health and Human Services (2000) Nutrition and Your Health: Dietary Guidelines for Americans, 5th ed. Washington, DC: DHHS. Willett W (1998a) Is dietary fat a major determinant of body fat? American Journal of Clinical Nutrition 67, 556S-562S. Willett W (19986) Nutritional Epidemiology, 2nd ed. Oxford: Oxford University Press.

Econometrics. Statistics and Computational Approaches m Food and Health Sciences Peter Robinson, Tooke Professor of Economic Science and Statistics. London School of Economics

Per Pinstrup-Andersen, HE. Babcock Professor of Food, Nutrition and Public Policy. Cornell University; World Food Prize Laureate

This remarkable volume is a testament to Professor Bhargava's breadth of interest and depth of scholarship, over a quarter of a century of research. It spans fundamental econometric methodology and many substantive empirical applications in health, nutrition, development and demography.

Quantitative analysis is important to establish causal links between policy changes and the resulting nutrition and health effects. In this book. Alok Bhargava presents a very rich selection of such quantitative analyses, drawing on both econometrics and applied health sciences. The author employs his thorough understanding of economics, econometrics, public health, and nutrition, together with an outstanding ability to utilize quantitative analytical models to advance our understanding of food security, nutrition, and health.

Jerry Hausman, John and Jennie S. MacDonald Professor of Economics. MIT Professor Bhargava's papers demonstrate the advantage of combining path-breaking research in econometrics and its application to important real world problems. The relationship between food intake and health and productivity in developing countries is among the most important problems faced by governments and policy analysts. I found the results in the papers in this book especially enlightening. Erik Thorbecke, H. E. Babcock Professor of Economics & Food Economics. Emeritus. Cornell University Alok Bhargava is the foremost econometrician working on food, nutritional and health issues. The statistical and technical rigor which is applied to the investigation of crucial nutritional and health questions within a multidisciplinary framework makes this a truly unique volume. Peter J. Hotez, Professor and Chairman. Department of Microbiology. Immunology and Tropical Medicine. The George Washington University As a tropical medicine expert and microbiologist specializing in parasitology. I am glad to endorse this collection of papers. While these were previously published in high impact journals, few social scientists have tackled the complex biological issues as adroitly as Professor Bhargava. Daniel L. McFadden, Nobel Laureate in Economics, University of California. Berkeley The determinants of human health, particularly the long-term effects of nutrition, are challenging to uncover due to the long latencies involved and lack of controlled experiments or definitive epidemiological data. What one can learn has to come from careful and sophisticated statistical and econometric analysis that can unravel multiple causes and trace nutritional effects over lifetimes. Alok Bhargava is the master of this subject, and his insighfs and methods have defined the field and provided persuasive evidence on the role that nutrition plays in the health and productivity in less developed countries. Peter Svedberg, Professor of Development Economics. University of Stockholm Few researchers have published up-front articles in leading journals in economics, epidemiology, nutrition, sociology, physiology, demography, as well as statistics. Alok Bhargava has. and this collection of his most prominent articles shows why. Alok is a leading bridge-builder across these disciplines, an urgent challenge for the international research community. James J. Heckman, Nobel Laureate in Economics. University of Chicago These essays by Alok Bhargava demonstrate Ihe power of modern microeconometrics in addressing basic social problems. They also illustrate the value of grounding serious research in economics in the biology and science producing the phenomenon being studied. Bhargava has developed a powerful synthesis of economics and the biology of human nutrition. This is a collection of papers thai richly repays a close read.

Sir Partha Dasgupta, Frank Ramsey Professor of Economics, University of Cambridge Reading Bhargava's articles on the biomedical basis of economic life in poor countries gives readers the thrill that really creafive works are able to give. The analysis is invariably careful and the author never claims any more than is warranted by the evidence. Most importantly, we learn from each piece. This is high quality social science. Robert W. Fogel, Nobel Laureate in Economics, University of Chicago Alok Bhargava has been one of the leading economists specializing in the impact of nutrition on health and productivity. He has brought fo this work a highly sophisticated understanding of econometric issues, which he combined with far-ranging analysis of the epidemiology and physiology of health. The book is a tour through frontiers of a wide array of issues pertaining to health and economic growth. Nevin S. Scrimshaw, President. International Nutrition Foundation; Institute Professor Emeritus. Massachusetts Institute of Technology; Senior Advisor. United Nations University; World Food Prize Laureate Bhargava is unique in his ability to apply training as an economist to the economic and social consequences of nutritional inadequacies and deficiencies in human populations. In this volume he displays a sound knowledge of nutrition as well as economics and explores a wide range of themes. His contributions in the sections on relationships between child nutrition and learning and behavior and on population health and economic growth are particularly important for public policy. In a final section he makes useful observations on the epidemic of obesity that is damaging the health of industrialized populations. Francois Bourguignon, Chief Economist and Senior Vice President. World Bank Alok Bhargava's contribution to development economics bears upon what should be one of the cornerstones of the discipline, namely health and in particular child health and nutrition. He initially approached this field as an economist and soon found the bridges between economics and health sciences rarely crossed by development experts. Having all his work in a single volume will be extremely useful for those motivated to look beyond a narrow focus on economics. David M. Cutler, Otto Eckstein Professor of Applied Economics and Dean of Social Sciences. Harvard University This work is must reading for anyone interested in food and nutrition science around the world.

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