Equity (Research on Economic Inequality)

LIST OF CONTRIBUTORS Alexander W. Cappelen

Norwegian School of Economics and Business Administration, Bergen, Norway

Margaret Chitiga

University of Pretoria, South Africa

John Cockburn

Poverty and Economic Policy (PEP) Research Network and Department of Economics, Laval University, Que´bec, Canada

James B. Davies

Department of Economics, University of Western Ontario, London, Ontario, Canada

Bernard Decaluwe

Poverty and Economic Policy (PEP) Research Network and Department of Economics, Laval University, Que´bec, Canada

Udo Ebert

Department of Economics, University of Oldenburg, Oldenburg, Germany

Ismael Fofana

Poverty and Economic Policy (PEP) Research Network and Department of Economics, Laval University, Que´bec, Canada

Pilar Garcı´a Go´mez

Departament d’Economia i Empresa and CRES, Universitat Pompeu Fabra, Barcelona, Spain

Nigar Hashimzade

Department of Economics, University of Exeter, Exeter, UK

Michael Hoy

Department of Economics, University of Guelph, Guelph, Ontario, Canada

Peter J. Lambert

University of Oregon, USA vii

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Ramos Mabugu

University of Pretoria, South Africa

Daniel L. Millimet

Southern Methodist University, USA

Gareth D. Myles

University of Exeter, Exeter; and Institute for Fiscal Studies, London, UK

Angel Lo´pez Nicola´s

Departamento de Economı´ a, Universidad Polite´cnica de Cartagena, Cartagena, Spain; and Departament d’Economia i Empresa and CRES, Universitat Pompeu Fabra, Barcelona, Spain

Kristian Orsini

Center for Economic Studies, Katholieke Universiteit, Leuven, Belgium

Ian Preston

University College London and Institute for Fiscal Studies, London, UK

Geoff Rowe

Statistics Canada, Ottawa, Canada

Daniel Slottje

FTI Consulting, Inc. and Southern Methodist University, USA

Amedeo Spadaro

PSE Paris-Jourdan Sciences Economiques, France; FEDEA Madrid, Spain; and Universitat de les Illes Balears, Palma de Mallorca, Spain

Paul D. Thistle

Department of Finance, University of Nevada Las Vegas, Las Vegas, NV, USA

Georg Tillmanny

Department of Economics, University of Mainz, Mainz, Germany

Bertil Tungodden

Norwegian School of Economics and Business Administration and Chr. Michelsen Institute, Bergen, Norway

Michael Wolfson

Statistics Canada, Ottawa, Canada

INTRODUCTION For equity, societies may wish to eliminate certain forms or manifestations of inequality. Horizontal equity and vertical equity in the income tax are topics which have interested me for some years. Although any shortfall from each of these objectives can be measured in terms of unwanted inequalities, equity per se is a different concept from equality. Equity relates to fairness, justice and other societal norms which give expression to the best aspirations of our collective social conscience. For example, equal access to health care for those in equal need is an accepted norm for horizontal equity in the health field. Vertical equity in this context means treating appropriately differently those who have different needs. When offered the opportunity to be Guest Editor of this volume of Research on Economic Inequality, I decided to define the focus simply as ‘‘equity’’, without placing any further restriction on topics. The papers which were ultimately included in this volume are the ones, from among those offered, which survived a rigorous refereeing process. Each has its own ‘‘take’’ on the concept of equity, and its link with equality. I hope that you, the reader, will gain from reading all of these contributions and pondering their significance. Alexander W. Cappelen and Bertil Tungodden focus on the interdependencies created by a redistributive system. In essence they ask whether, in view of these, it can be the case that increased effort on the part of any one individual (which, assuming no production interdependencies, would imply increased pre-tax income for that individual), necessarily leads to increased post-tax income (reward) for that individual. Remarkably, they show that only lump-sum redistribution schemes have this property, and that such schemes necessarily involve negative post-tax incomes for some, which they interpret as a violation of the fundamental right of a person not to work. This deep consideration of fundamentals comes with essential simplicity. Paul D. Thistle extends a long-standing result of Lerner (1944) concerning the welfare analysis of income distributions: ‘‘If it is impossible, on any division of income, to discover which of any two individuals has a higher marginal utility of income, the probable value of total satisfactions is maximized by dividing income evenly’’ (ibid., p. 29). Paul’s paper gives the background, and the subsequent discussion by other contributors which has ix

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surrounded Lerner’s result, and goes on to weaken the restrictive assumptions Lerner made, in particular assuming now that the planner may have some (if not much) information regarding the possible assignment of utility functions to individuals. Paul shows that the fundamental idea, that of ‘‘equi-probability’’, can survive (in modified form) the introduction of more modern concepts in distributional analysis than were around in Lerner’s day, such as rank and generalized Lorenz dominance, and needs-based welfare functions. Ian Preston wrote about inequality, income tax progression and labor supply in his Nuffield College DPhil thesis of 1989, but somehow moved on to other things without publishing some quite important material. Ian’s results for inequality indices which preserve the ratio dominance ordering of underlying distributions, for example, were new to economists at the time, but had been known to mathematicians since a 1967 Pacific Journal of Mathematics paper by Marshall, Walkup and Wets. Ian has been persuaded to revisit his earlier analysis for this volume. His paper ‘‘Inequality and Income Gaps’’ inter alia tells a rounded story about the ratio and gap dominance concepts, and associated orderings and welfare properties, which extend the well-known Lorenz ordering in different ways. Udo Ebert and the late and sadly missed Georg Tillmann have provided a full and somewhat startling answer to an apparently innocuous question about income tax design. For an income tax which intervenes in distribution all along the income scale (in particular, having no zero bracket amount), surely progression can remain moderate throughout? ‘‘No, it cannot’’ is the answer, ‘‘Not if you rule out a region of negative taxes with a negative marginal tax rate at some income values’’. The exposition is extremely clear and the message is thought provoking. Nigar Hashimzade and Gareth D. Myles contrast the redistributive properties of income and expenditure taxes. Heterogeneity in their model comes through differences in skill and differences in endowments. In both a static two-period model and a fully dynamic overlapping generations model, income taxes are set and then replaced with expenditure taxes calibrated to produce first the same welfare level, then the same level of government revenue. Simulation exercises with various assumed degrees of correlation between the two sources of heterogeneity indicate that, in both the static and dynamic versions of the model, Gini coefficients for lifetime income are (almost always) less in the case of income-based taxes than for expenditurebased taxes. Kristian Orsini and Amedeo Spadaro propose an index of strategic weight within couples. The index is defined for each member as the share of

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resources lost, should he or she leave the household. From these weights, the authors develop a ‘‘neutrality index’’ to determine the stance of the taxbenefit system itself toward household formation. Then, using micro data for Finland, Germany, Italy and the UK, the authors explore how strategic weights are affected by the relevant tax-benefit systems, and they are able to provide much comparative information about the family stances of the respective systems. Ample discussion is included of the limitations of the study and the future research which is now called for. James B. Davies and Michael Hoy join the ongoing debate about the best way to finance a health care system. They outline methods to determine the impact on the distribution of income of a move from completely public to totally private financing of health care, applying their methodology to a hypothetical move of this kind – in which premia that were generated through taxation are now based on age and gender, as well as on other individual characteristics related to expected health care costs – for Canada. This paper will be valued not only for its Canadian findings, but also as a useful expository source for the sort of distributional impact analysis that can be applied to such a question, and for its frank appraisal of the assumptions which the authors needed to make to get their analysis off the ground. Pilar Garcı´ a Go´mez and Angel Lo´pez Nicola´s have written a paper about equity in the utilization of health care, seeking to determine for Spain the extent to which the National Health System reforms introduced between 1987 and 2001 have led to improved equity. The authors define their equity ideal as ‘‘equal access given equal need for health care’’, and they compute inequity, using concentration indices, as the component of income-related utilization inequality which is not attributable to socio-economic needs differences. Their careful analysis permits the tracking, over the 1987–2001 period, for each of a range of health services, of an income-related inequity component and a second inequity component explained by the influence of private health insurance and privately provided health care. By this, the authors are able both to unbundle and to understand the improvements in equity that have been attained in Spain, and to point to a range of issues which remain for deeper study. Michael Wolfson and Geoff Rowe’s paper, which uses the Canadian LifePaths microsimulation model to analyze the lifetime incidence of taxes and transfers across Canadian worker cohorts, begins with a clear and thoughtprovoking general discussion of what intergenerational fairness might mean (for which, they argue, ‘‘there is no widely agreed concept’’). This discussion will be found valuable per se. The empirical results the authors derive for

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Canada suggest that under a range of scenarios for future economic growth and longevity, birth cohorts after those born in the 1920s and 1930s will experience successively smaller lifetime net transfers, both cash and in kind. These results are significantly influenced by the use of the consumer price index to update cash transfer benefit levels and income tax thresholds and other related parameters. Daniel L. Millimet, Daniel Slottje and Peter J. Lambert ask a ‘‘what if?’’ question about poverty and go on to answer it rather fully. In a paper which was handled editorially by John Bishop, Joint Managing Editor of REI, the implications of supposing that decision makers in any country and at any point in time tolerate a certain fixed amount of perceived poverty are explored. Differences in poverty aversion could fully account for observed international and intertemporal variations in objective poverty, consistent with any chosen ‘‘natural rate’’ of perceived poverty. As the authors show, poverty aversion itself can be understood in terms of political and socioeconomic factors, and an adjustment mechanism is implied such that a change in a relevant explanatory variable, which leads to changed poverty aversion, would trigger a change in distribution and restoration of the natural poverty rate. The natural rate hypothesis offers a new way to understand the influence of social, political and economic changes on measured poverty. The relationship between inequality aversion and poverty aversion is also explored with the aid of a parallel ‘‘natural rate’’ hypothesis for subjective inequality. John Cockburn, Ismael Fofana, Bernard Decaluwe, Ramos Mabugu and Margaret Chitiga report on the construction and implementation of a gender-sensitive macro-micro framework for South Africa. Their structure comprises a CGE model that can deal with non-market activities and information on time use along gender lines, and a microsimulation model based on household level data which allows the authors to account for additional heterogeneity. The outcome is a most interesting study which pins down the poverty impacts of trade liberalization in South Africa. Peter J. Lambert Editor

REDISTRIBUTION AND MARGINAL PRODUCTIVITY REWARD Alexander W. Cappelen and Bertil Tungodden ABSTRACT A fundamental ethical question is how a redistributive system should reward individual effort. Marginal productivity reward has been justified either as a way of ensuring efficiency or as a way of respecting people’s self-ownership. Both these arguments have their limitations. We show that marginal productivity reward is implied by one intuitively appealing requirement on the reward structure, which we name non-negative reward. This result can be interpreted in one of two ways. It can be seen as a new justification of marginal productivity reward that avoids the limitations of the traditional arguments. Alternatively, it can be seen as a result showing that any redistributive system that makes transfers conditional on effort, sometimes will make the reward individuals get for their additional effort completely conditional on others effort. Finally, we also show that no genuine redistributive system satisfies both non-negative reward and the liberal requirement of no forced labour.

Equity Research on Economic Inequality, Volume 15, 1–6 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15001-8

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ALEXANDER W. CAPPELEN AND BERTIL TUNGODDEN

1. INTRODUCTION A fundamental ethical question is how a redistributive system should reward individual effort. One prominent answer to this question is that people should be rewarded with their marginal productivity. This answer has traditionally been given two types of justifications. First, marginal productivity reward has been justified by efficiency considerations. Economic theory shows that deviations from marginal productivity reward create distortions that may cause Pareto-inefficiency. Second, it has been justified by equity considerations. According to some theories of distributive justice, in particular libertarianism (Nozick, 1974), marginal productivity reward is the only way of respecting people’s self-ownership (see also Kolm, 2001). Both these arguments have their limitations. The efficiency argument only provides a justification for marginal productivity reward in situations where there are incentive problems. For example, in situations where the Hicksian supply of effort is inelastic, there is no efficiency reason for rewarding effort with its marginal product. The equity argument is problematic because it relies on some very controversial normative assumptions. Only people accepting the basic idea of full self-ownership and the view that full self-ownership implies marginal productivity reward would be convinced by the libertarian equity argument. This position, however, is rejected both by utilitarians (for example, Mirrlees, 1971; Harsanyi, 1987; Broome, 1991) and liberal egalitarians (for example, Rawls, 1971; Fleurbaey, 1995; Moulin & Roemer, 1989). In this paper we present a result that may be seen as an alternative justification for marginal productivity reward that avoids the limitations of the traditional arguments. The result applies even in the absence of incentive considerations and it relies on a much less controversial normative assumption than the self-ownership argument. We show that marginal productivity reward follows from a very appealing requirement, namely that people never should have a reduction in their post-tax income when they increase their effort. We name this the non-negative reward requirement. To illustrate, consider two situations a and b, where you work harder or longer hours in b than in a and thus have a higher total pre-tax income in b than in a. The requirement then states that your post-tax income in b should not be lower than your post-tax income in a. Alternatively, the result can be seen as showing that an unavoidable consequence of any redistributive system that makes transfers to an individual conditional on his effort is that sometimes the reward individuals get for their additional effort will be completely conditional on others effort. This may be an obvious feature of a redistributive system in an economy where

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there are interdependencies in the production technology, but the result establishes that this is the case also when there are no interdependencies in the production technology. Another very appealing requirement on a redistributive system is that it should not force anyone to work, which we name no forced labour. Our second result, however, shows that this requirement is incompatible with non-negative reward in any genuine redistributive system. We present the formal framework in Section 2. In Section 3, we establish the propositions. Section 4 provides some discussion of how to interpret the results.

2. FORMAL FRAMEWORK Consider a society with a population N ¼ f1; . . . ; ng; nZ2, where person i’s effort is ei and e ¼ ðe1 ; . . . ; en Þ is the effort distribution in a particular situation e. Let O be the set of all effort distributions. We assume that all individuals can choose between all effort levels ei 2 ½emin ; emax Þ
Rþ ; where Rþ is the set of real non-negative numbers. The pre-tax income for each individual i, f i : ½emin ; emax Þ ! Rþ is continuous and strictly increasing in effort, where f i ðemin Þ ¼ 0; 8i 2 N: Note that we do not assume any interdependencies in the production technology and, moreover, we do not make any assumptions about how the choice of effort is affected by the redistributive system. Hence, each person’s pre-tax income is independent of other people’s effort and we cover cases both with and without incentive problems. Our object of study is a redistributive system F : O ! Rn ; where Fi(e) is the post-taxPincome of person i in situation e. F satisfies the balanced budget P constraint ni¼1 F i ðeÞ ¼ ni¼1 f i ðeÞ; 8e 2 O: Moreover, for F to be considered a genuine redistributive system, we assume that at least for some e 2 O and j 2 N; F j ðeÞaf j ðeÞ:

3. REWARDING EFFORT Most people support some degree of redistribution, but typically also agree that a person should be rewarded for an increase in effort. We argue that an appealing feature of any redistributive system would be that it satisfies a minimal reward condition saying that a person who increases his effort, and thus increases his pre-tax income, should not experience a decrease in posttax income. In other words, if your effort is higher in one situation than

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another, then your post-tax income should at least not be lower in the situation where you exercise more effort. Formally, we can write this requirement as follows: Non-Negative Reward (NNR): For any e; e~ 2 O and j 2 N, where e~j 4ej ! F j ð~eÞ  F j ðeÞ: One way of rewarding effort that satisfies NNR is marginal productivity reward. Marginal Productivity Reward (MPR): For any e; e~ 2 O and j 2 N, where e~j aej ! F j ð~eÞ  F j ðeÞ ¼ f j ð~ej Þ  f j ðej Þ: It turns out that the non-negative reward requirement implies that effort is rewarded with marginal productivity, that is, it is incompatible with anything else than lump-sum redistribution. Proposition 1. A redistributive system F satisfies NNR if and only if it satisfies MPR. Proof. The if part is straightforward. Hence, we will only prove the onlyif part. (i) Suppose there exist e; e~ 2 O and k 2 N such that e~k ¼ ek and F k ð~eÞ4F k ðeÞ: (ii) Consider a new situation e^ 2 O; where for some e>0, e^i ¼ ei þ
; 8i: P (iii) By the continuity of fi, for a sufficiently small e, ei Þ  i ½f i ð^ f i ðei Þo½F k ð~eÞ  F k ðeÞ: P (iv) By P the balanced budget constraint, Pi ½F i ð^eÞ  F i ðeÞ ¼ ei Þ  f i ðei Þ: By (iii), this implies that i ½F i ð^eÞ  F i ðeÞo i f i ð^ ½F k ð~eÞ  F k ðeÞ: By NNR, F i ð^eÞ  F i ðeÞ; 8i: Hence, it follows that ½F k ð^eÞ  F k ðeÞo½F k ð~eÞ  F k ðeÞ: (v) By (iv), F k ð^eÞoF k ð~eÞ: However, since e^k 4~ek ; this violates NNR. Thus the supposition in (i) is not possible. (vi) Consider any e; e~ 2 O and k 2 N such that e~k 4ek : We will now show that F k ð~eÞ  F k ðeÞ ¼ f k ð~ek Þ  f k ðek Þ: Consider e^ 2 O; where e^i ¼ ei ; 8iak and e^k ¼ e~k : By (v), F i ð^eÞ ¼ F i ðeÞ; 8iak: Hence, by the balanced budget constraint, F k ð^eÞ  F k ðeÞ ¼ f k ð^ek Þ  f k ðek Þ: By (iv), F k ð^eÞ ¼ F k ð~eÞ: Moreover, f k ð^ek Þ ¼ f k ð~ek Þ; and the result follows. ’ Note that in order to establish Proposition 1, we have not required that the post-tax income of all individuals should be positive in all situations. If some people have negative post-tax income, however, then this may be seen

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as equivalent to forcing them to work. Therefore, if we want to ensure all individuals the right to choose not to work, then the redistributive system should satisfy the following condition: No-Forced Labour (NFL): For any e 2 O and j 2 N, F j ðeÞ  0: NFL should be an appealing condition in a liberal society. However, it turns out to be impossible to combine this condition with the non-negative reward condition. Proposition 2. There does not exist any redistributive system F satisfying NNR and NFL. Proof. Proposition 1 shows that only lump-sum taxation satisfies NNR. However, any positive lump-sum tax violates NFL, and the result follows. ’ Alternatively, Proposition 2 may be seen as a characterisation of libertarianism, if libertarianism is interpreted as requiring that each person’s post-tax income always should be equal to this person’s pre-tax income. Libertarianism implies that there should be no redistribution of income in society, and thus satisfies both NNR and NFL.

4. DISCUSSION The underlying intuition of Proposition 1 is that any non-lump-sum redistribution, that is, any system of redistribution where transfers are conditional on effort creates interdependencies among the individuals in the economy, even if there are no interdependencies in the production technology. The existence of such fiscal interdependencies makes it impossible to satisfy the non-negative reward requirement. To illustrate, suppose that individual i has the pre-tax income function f ðwi ; Li Þ ¼ wi Li ; where wi is person i’s marginal productivity and Li is person i’s labour effort. Consider a very simple economy with only two individuals, person 1 and person 2, where they differ in marginal productivity, i.e., w1 aw2 (even though the proof does not rely on this assumption). Moreover, assume that the government redistributive policy is limited to a linear income tax scheme, where the tax revenues are shared equally between the two individuals in society. The post-tax incomes are then given by F 1 ¼ w1 L1 ð1  tÞ þ tððw1 L1 þ w2 L2 Þ=2Þ and F 2 ¼ w2 L2 ð1  tÞ þ tððw1 L1 þ w2 L2 Þ=2Þ: In this case, for any positive t, person 1 may receive a lower post-tax income when increasing his effort, if at the same time person 2 decreases his effort.

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In other words, the linear income tax scheme creates a fiscal interdependency between the two individuals that makes it impossible to satisfy the nonnegative reward requirement. Proposition 1 shows that this is not only a feature of a linear tax scheme with uniform transfers, but applies to any redistributive system that does not rely on lump-sum redistribution. Lump-sum redistribution, however, violates the liberal requirement of no forced labour, and thus any genuine redistributive system faces a fundamental conflict, as reported in Proposition 2. Either sometimes it has to give some people less post-tax income when they have increased their effort or sometimes it has to force people to work. Finally, let us note that there is a much weaker interpretation of the idea of non-negative reward, namely that a unilateral increase in effort by some person never should cause a decrease in his post-tax income. This very weak requirement does not imply marginal productivity reward and it is consistent with any reasonable redistribution system. We doubt, however, that it captures all of our moral intuitions on how to reward effort. We find the idea that an increase in effort should imply no decrease in post-tax income, independent of what others do, very attractive, and thus we do believe that it is of importance to observe that lump-sum redistribution is the only redistributive policy that has this feature.

ACKNOWLEDGMENTS We should like to thank Peter Lambert and Peter Vallentyne for valuable comments. The usual disclaimer applies.

REFERENCES Broome, J. (1991). Weighing goods. London: Basil Blackwell. Fleurbaey, M. (1995). Three solutions for the compensation problem. Journal of Economic Theory, 6, 96–106. Harsanyi, J. C. (1987). Bayesian decision theory and utilitarian ethics. American Economic Review, Papers and Proceedings, 68, 223–228. Kolm, S.-C. (2001). Modern theories of justice. Cambridge, MA: MIT Press. Mirrlees, J. A. (1971). An exploration in the theory of optimal taxation. Review of Economic Studies, 38, 175–208. Moulin, H., & Roemer, J. (1989). Public ownership of the external world and private ownership of the self. Journal of Political Economy, 97, 347–367. Nozick, R. (1974). Anarchy, state, and Utopia. New York: Basic Books. Rawls, J. (1971). A theory of justice. Cambridge, MA: Harvard University Press.

GENERALIZED PROBABILISTIC EGALITARIANISM Paul D. Thistle ABSTRACT For over 60 years, Lerner’s (1944) probabilistic approach to the welfare evaluation of income distributions has aroused controversy. Lerner’s famous theorem is that, under ignorance regarding who has which utility function, the optimal distribution of income is completely equal. However, Lerner’s probabilistic approach can only be applied to compare distributions with equal means when the number of possible utility functions equals the number of individuals in the population. Lerner’s most controversial assumption that each assignment of utility functions to individuals is equally likely. This paper generalizes Lerner’s probabilistic approach to the welfare analysis of income distributions by weakening the restrictions of utilitarian welfare, equal means, equal numbers, and equal probabilities and a homogeneous population. We show there is a tradeoff between invariance (measurability and comparability) and the information about the assignment of utility functions to individuals required to evaluate expected social welfare.

1. INTRODUCTION For over 60 years, Lerner’s (1944) probabilistic approach to the welfare evaluation of income distributions has aroused controversy. Lerner Equity Research on Economic Inequality, Volume 15, 7–32 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15002-X

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considered the problem of a social planner who must optimally allocate a fixed total amount of income across a given population. The social planner knows that each individual has a utility function with diminishing marginal utility of income, but does not know which individual has which utility function. The planner’s objective is to maximize expected welfare, which Lerner takes to be the sum of expected utilities. Lerner’s famous theorem is that, under ignorance regarding who has which utility function, the optimal distribution of income is completely equal. Lerner’s theorem and its interpretation have been further analyzed by a number of researchers. Breit and Culbertson (1970) extend Lerner’s twoperson diagrammatic proof to the n-person case. However, their argument relies on the rather special assumption that each individual has a ‘‘twin’’ with the same utility function. Sen (1969), McManus, Walton, and Coffey (1972), and McCain (1972) provide rigorous proofs for the n-person case. These researchers all assume the planner has an additive utilitarian social welfare function (SWF). Sen (1969) and McManus et al. consider the ‘‘maximin’’ objective of maximizing the lowest value of welfare given the income distribution. Sen (1973a, 1973b) considers general, non-utilitarian SWFs. Bennett (1981) argues that Lerner’s assumption that all assignments of utility functions to individuals are equally likely implies that the probability of gain from an equalizing redistribution is greater than one-half. Lerner’s theorem has also been criticized by a number of prominent economists, for example, Friedman (1947), Graaff (1967), Little (1957), Musgrave (1959), and Samuelson (1964).1 Freidman, Little, and Samuelson are critical of the invariance (measurability and comparability) requirements Lerner imposes on the SWF. Both Lerner and his critics exhibit some confusion on this issue. However, most of the criticism has focused on the ‘‘equi-probability’’ assumption, the assumption that all possible assignments of utility functions to individuals are equally likely. Lerner justifies equiprobability by assuming the planner is completely ignorant about which individual has which utility function. For example, Musgrave (p. 108) refers to equi-probability as an ‘‘uneasy assumption,’’ and writes ‘‘The argument, like the principle of insufficient reason, remains inconclusive.’’ Friedman (p. 409) writes ‘‘The analysis as given is not rigorous, primarily because of the appeal to ‘equal ignorance’.’’ Little (p. 59) is more harshly critical, arguing that ‘‘y from complete ignorance nothing but complete ignorance can follow y .’’ Similarly, Graaff (p. 100) writes ‘‘From absolute ignorance we can derive nothing but absolute ignorance.’’ Despite the controversy, Lerner’s observation that it may not be known with certainty which individual has which utility function remains an

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important insight. Moreover, this insight has not been much appreciated in recent research on the distribution of income. Most recent work has either explicitly or implicitly assumed that each individual’s utility function is known to the planner. For example, it is common to define the evaluation function directly over individuals’ incomes (e.g., Bishop, Formby, & Thistle, 1991, 1992). This formulation implicitly assumes that utility functions are known and that they are subsumed in the functional form of the welfare function. It is also common to assume that all individuals have the same known utility function (cf. Lambert, 2001, pp. 87–90). However, there are important restrictions in Lerner’s probabilistic welfare analysis that limit its practical application. The problem originally considered by Lerner, and by most subsequent analysts, is that of allocating a fixed amount of income. Thus, Lerner’s probabilistic approach can only be applied to compare alternative distributions that have equal means. Secondly, Lerner and most subsequent analysts have studied the ‘‘equal numbers’’ case, where the number of possible utility functions equals the number of individuals in the population. The problem is that it is not known which individual has which utility function. The objective of this paper is to generalize Lerner’s probabilistic approach to the welfare analysis of income distributions by weakening the restrictions of equal means, equal numbers, and equal probabilities. Results are obtained for general (non-utilitarian) SWFs, utilitarian SWFs, and for ordinally comparable individual utility functions. Some researchers have examined different aspects of this problem. Bishop et al. (1991) and Kakwani (1984) provide results on comparing distributions with unequal means, under the assumptions of equal numbers and equi-probability. Sen (1969) and McCain (1972) consider unequal numbers and unequal probabilities under the assumptions of a utilitarian welfare function and equal means. None of these researchers has relaxed all of the restrictions simultaneously. We also extend these results to the case where a heterogeneous population can be classified into distinct subpopulations. Generalizing Lerner’s probabilistic approach allows it to be applied to a much wider range of situations. The ‘‘equi-probability’’ assumption has been the most controversial. It seems reasonable to believe that the central planner may have some information regarding the possible assignments of utility functions to individuals. If so, then some assignments of utility functions to individuals are more likely than others. The assumption that there are an equal number of utility functions and individuals turns out to be an important restriction. It seems plausible that the number of possible utility functions may be (much) larger than the population size. Then, in addition to not knowing who has which

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utility function, it is not known which utility functions are relevant. Further, in order to weaken the restriction of equal probabilities, we first need to relax the assumption of equal numbers. There is then a tradeoff between the invariance requirements of the planner’s SWF and utility assignment information used to evaluate expected social welfare. That is, SWFs with stronger invariance requirements use less information about which individual has which utility function. The next section reviews Lerner’s analysis and discusses the criticisms of it. Section 3 relaxes the equal numbers and equi-probability assumptions, and provides the key result of the paper. Section 4 discusses efficiency-equity preferences. Section 5 considers the expected welfare evaluations. Section 6 examines heterogeneous populations. Section 7 provides brief concluding remarks.

2. PROBABILISTIC EGALITARIANISM This section reviews Lerner’s analysis and the most prominent criticisms of it. Some of the criticisms are valid, but some of the criticisms are due to misunderstanding, while still others are flawed. One objective of this section is to clear up at least some of the misunderstanding. It is also important to understand the valid criticisms, as these provide an important motivation for the generalization proposed here. The basic idea of Lerner’s probabilistic egalitarianism can be easily understood. Lerner is concerned with the problem of the socially optimal distribution of income. First, Lerner assumes that individuals’ utilities depend only on their own income, that utilities are cardinal and comparable, that each individual has diminishing marginal utility of income, and that the SWF is the sum of individual utilities. Lerner assumes that the total income is independent of the division of income. These assumptions seem unremarkable for an analysis of income distribution. Lerner’s most controversial assumption is that the planner does not know which individual has which utility function. Lerner (p. 29) concludes that ‘‘y the probable value of total satisfactions is maximized by dividing income evenly.’’ The argument for the two-person case can be seen in Fig. 1, which shows the distribution of income and the marginal utilities. Let us call these two people Ann and Bob. The width of the box, 0102, is equal to Ann and Bob’s total income. The planner is presumed to know that one individual has the utility function u1 and the other has the utility function u2, each of which is increasing and concave. Observe that the number of utility functions is equal to the number of individuals. If Ann has marginal utility MU1 and Bob has

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MU1

MU2

A

B

01

x1

D

x

Fig. 1.

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02

Probabilistic Egalitarianism.

marginal utility MU2, then a given distribution of income can be represented by the distances 01x1 and 02x1. If incomes are equalized at x; ¯ then Ann gains the area A+B, while Bob loses the area B. There is a net gain in the sum of utilities equal to A. If Bob has marginal utility MU1 and Ann has marginal utility MU2, then the same distribution of income is represented by 01x2 and 02x2. If incomes are equalized, then Ann gains the area D+E+F, while Bob loses the area C+D+F. There is a net change of E
C, which may be positive or negative. The planner, being ignorant of which is the true situation, regards each as equally likely and allocates income to maximize expected welfare, which is the expected sum of utilities. Since each situation is equally likely, the expected change is 1/2(A)+1/2(E
C) ¼ 1/2(A+E
C), which is positive since diminishing marginal utility implies A>C. The planner acts as if Ann and Bob both have the same utility function, 1/2u1+1/2u2, and divides the total income equally. Lerner, and subsequent analysts, have argued that the probability that equalizing income will yield a welfare gain is one-half, and that this is true for all initial income distributions. Bennett (1981) points out that, if incomes are initially very unequal, then a welfare gain is certain. This can also be seen in Fig. 1. The essence of Bennett’s argument is that, if the initial distribution is sufficiently unequal, then E is larger than C. If so, there is a gain from redistribution regardless of which individual has which utility function. This reinforces Lerner’s argument for equalization.

12

PAUL D. THISTLE

The criticisms of Lerner’s analysis have focused on the invariance (measurability and comparability) requirements and the equi-probability assumption.2 Lerner is responsible for some of the confusion about his invariance requirements. He writes (p. 24) ‘‘But we have no way of directly comparing the well-being of different consumers.’’ and later on the same page ‘‘y of the impossibility of measuring the satisfactions of different consumers on the same scale.’’ This seems a clear statement that utilities are not comparable. But on the next page he assumes ‘‘y the satisfactions of different people are similar in the sense that they are the same kind of thing. In other words, that it is not meaningless to say that a satisfaction that one individual gets is greater or lesser than a satisfaction enjoyed by somebody else’’ (italics in original). Thus, Lerner seems to be assuming at least ordinal level comparability of utilities. Lerner (p. 25) argues that comparability is needed since ‘‘This assumption gives meaning to the concept of maximizing the total of satisfactions experienced by all individuals in a society.’’ Lerner thus adopts a utilitarian SWF, so that the underlying individual utility functions must be cardinally measurable and fully comparable. The confusion over the invariance requirements is compounded by the assumption of ignorance. Lerner (p. 28) writes ‘‘There is no way of discovering with certainty whether any individual’s marginal utility of income is greater than, equal to, or less than that of any other individual.’’ This can be (and has been) interpreted as assuming noncomparability. Since he points out that individuals have an incentive to misrepresent their preferences, a more reasonable interpretation is that Lerner is referring to the practical difficulties in inferring individuals’ marginal utilities of income. This is analogous to the informational environment in adverse selection problems where individuals’ utility functions are private information. As Bennett (1981, p. 165) puts it ‘‘y we can assume that in a large economy the government would decide not to collect and process such information simply because of the cost involved.’’ A third possible difficulty is pointed out by Breit and Culbertson. Lerner initially states that an equal distribution of income will maximize probable total satisfaction. This is the result that Lerner actually proves. But later, Lerner (p. 32) asserts ‘‘y if it is desired to maximize the total satisfaction in a society, the rational procedure is to divide income on an equalitarian basis.’’ Breit and Culbertson interpret the omission of the word ‘‘probable’’ as a claim of a ‘‘strong theorem’’ that an equalizing redistribution increases total welfare for every assignment of utility functions to individuals. Lerner (1970) asserts that this is a misinterpretation.

Generalized Probabilistic Egalitarianism

13

Breit and Culbertson (p. 440) argue that the ‘‘strong theorem’’ also holds. They assume that every individual has a twin with the same utility function, and that the total income of every pair of twins is equal to twice the population average.3 Different sets of twins in general have different utility functions. Since each pair of twins starts with the same total income, equalizing income for each pair yields a completely equal distribution of income. Equalizing income for each pair of twins necessarily maximizes total welfare for the pair, and, adding up across pairs of twins, for society as a whole. As Lerner (1970) points out, in their quest to prove that a welfare gain is certain, Breit and Culbertson miss the point of the original analysis. Indeed, one way to interpret Bennett’s (1981) analysis is as showing that welfare must increase only if the initial distribution of income is sufficiently unequal. Little is critical of Lerner’s assumptions of cardinal and comparable utilities and a utilitarian welfare function. Little (pp. 51–52) argues that ‘‘The picture of a lot of separate satisfactions, each with a label tied round it, is not convincing.’’ and the ‘‘y thesis that one could add the welfare of different individuals to arrive at the welfare of society y has now to be abandoned.’’ Little also interprets Lerner as assuming that utilities are not comparable, then proceeding to add utilities. This leads Little (pp. 58–59) to regard Lerner’s argument as ‘‘paradoxical’’ and to regard the assumption of equiprobability as ‘‘illegitimate.’’ Little’s argument is apparently based on the view that we should be able to verify empirically whether different individuals’ utilities are comparable. But Little’s view is, at best, idiosyncratic: ‘‘So long, however, as the ‘measurement’, or estimation of satisfaction is not objective, and there is considerable room for disagreement, then it may sometimes be useful to speak of a hedonistic calculus – to speak, that is, of comparing satisfactions, and differences in satisfactions’’ (p. 34). Graaff (p. 100) also objects to Lerner’s invariance requirements, arguing that ‘‘His concept of social welfare differs from ours in that it is based on the sum of cardinally measurable satisfactions, and not on observable choices.’’ Graaff (pp. 33–35) views individuals’ utility functions as ordinal indicators of preferences. But Graaff himself adopts a welfare analysis based on Bergson–Samuelson SWFs. He recognizes that these necessarily reflect ethical judgments. He then argues (pp. 35–40) that (cardinal) measurability is not necessary to define a welfare function, and appears to take the position that Bergson–Samuelson welfare functions can be defined over noncomparable individual utility functions. This, we now know, is incorrect; utilities must be absolutely measurable and interpersonally comparable in order to define a Bergson–Samuelson welfare function.4

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PAUL D. THISTLE

Friedman’s criticism is focused on the assumption of ignorance and equiprobability: ‘‘Eliminate the assumption of ignorance and the same analysis immediately yields a justification for inequality y . And we must clearly be prepared to eliminate the assumption of ignorance’’ (p. 411) since it implies equality is a more fundamental goal than maximizing social welfare. Friedman’s argument is that, if the planner knows that Ann has the utility function u1, then the optimal distribution gives Ann 01x in Fig. 1. Lerner (pp. 28–29) is well aware of this argument, but his view is that whether Ann’s utility function is u1 or u2 is ‘‘y incapable of being discovered.’’ Friedman (p. 410) then provides an alternative argument for Lerner’s result.5 Friedman replaces equi-probability with the assumption that a person’s income is ‘‘y statistically independent of his capacity for enjoying it y .’’ Friedman then argues that individuals can, at least conceptually, be classified by their capacity for satisfaction. Statistical independence implies the average income in each class will be the same, and redistribution across classes would invalidate statistical independence. Freidman retains Lerner’s remaining assumptions, which imply that incomes within utility classifications should be equalized. One problem with this argument is that it invalidly employs a law of large numbers.6 Further, if incomes are correlated with the capacity for satisfaction, then Friedman’s argument also justifies inequality. The reason for this is that Friedman does not distinguish between the ex ante and ex post distributions across types. The positive statement that the ex ante distribution is equal (or unequal) does not imply that the normative statement that the ex post distribution should be equal.7 Samuelson attempts to avoid comparing utility functions and to avoid the use of a utilitarian welfare function. Samuelson’s solution is to reinterpret the problem as one of choosing an income distribution from behind a Rawlsian veil of ignorance. Each individual is assumed to evaluate income distributions using their own utility function; individuals’ utility functions are private information. He argues that, if every assignment of incomes to individuals is equally likely, then individuals’ risk aversion will lead to unanimous preference for complete equality. This is, of course, a different model from the one considered by Lerner. Musgrave (pp. 108–109) comes the closest to Lerner’s position. He writes ‘‘While we cannot assume that the utility schedules of individuals are known, the new welfare economics may have gone too far in its categorical rejection of interpersonal utility comparisons. Such comparisons are made continuously, and in this sense have operational meaning.’’ Musgrave then argues that the solution to this problem is to treat individuals as if they were identical, i.e., chose a particular utility function and assume that it applies to

Generalized Probabilistic Egalitarianism

15

all individuals. Given a utilitarian welfare function, equi-probability yields the same outcome, applying the average utility function to all individuals.8 Taken as a whole, Lerner’s critics make three points. First, they object to the assumption of cardinal and interpersonally comparable utility functions. Second, they object to the utilitarian SWF. Third, they object to the assumption of ignorance and equi-probability.

3. CONDITIONAL AND UNCONDITIONAL EQUI-PROBABILITY This section begins to address some of the criticisms of Lerner’s analysis. The requirement that the number of individuals and the number of utility function must be equal is relaxed. This allows the equi-probability assumption to be generalized. The set N ¼ f1; . . . ; ng is the fixed population, where n is the population size. An income vector x ¼ ðx1 ; . . . ; xn Þ is a listing of each individuals’ income, where xi is the income of the ith individual. The set of attainable income distributions is X, a compact non-empty subset of Rnþ =f0g: Mean income for x is denoted x: ¯ Each individual’s utility is assumed to be a function of her income only. The set of possible utility functions is U ¼ fu1 ; . . . ; um g; with index set M ¼ f1; . . . ; mg: The number of possible utility functions may be larger than the population size, mZn.9 This allows (but does not require) each individual to have a distinct utility function. All utility functions are assumed to be absolutely measurable and fully interpersonally comparable. Income distributions are evaluated via the central planner’s SWF. To begin we assume the SWF is a Bergson–Samuelson welfare function, and is a continuous function of individuals’ utilities.10 Several types of SWFs will be considered to reflect different judgments on the efficiency-equity tradeoff that the planner might make. All of the SWFs are assumed to satisfy anonymity, or to be symmetric in utilities. Central to Lerner’s approach is the idea that the marginal utilities of income differ across individuals. Since the planner knows each individual’s income, a specific assignment of n of the m possible utility functions to individuals is required to evaluate welfare. The evaluation of welfare can be regarded as taking place in two stages. The first step is the determination of which n of the m utility functions are required. The second step is the determination of the assignment of those utility functions to individuals.

16

PAUL D. THISTLE

The planner’s utility assignment information is represented by a probability distribution over possible assignments of utility functions to individuals. Let c ¼ ðc1 ; . . . ; cn Þ be a combination of n indices from M; let C denote the set of all such combinations. For combinations, the order in which the indices occur is not important. A combination simply selects n of the m possible utility functions. The same utility function may be selected more than once or the utility functions may all be different. There are (m+n
1)!/ n!(m
1)! such combinations.11 Let qc be the probability that the combination c identifies the correct set of utility functions. Given a combination c, a permutation of the indices is pðcÞ ¼ ðpðc1 Þ; . . . ; pðcn ÞÞ: Let P(c) be the set of all permutations of c. Permutations determine the assignment of specific utility functions to specific individuals, and are distinguished by the order of the indices. For any combination of n different items, there are n! permutations. However, if the utility function u1 is included n1 times, then there are n!/n1! distinct permutations. More generally, suppose the combination c includes S distinct indices and let ncs be the multiplicity of index s in c. Then the number of distinct permutations in c is n!/(Psncs!). Given a combination c, the conditional probability that p(c) is the correct permutation is denoted rp(c). Since the planner has only probabilistic utility assignment information, income distributions are evaluated by their expected welfare, where the expectation is taken over the possible assignments of utility functions to individuals. For the SWF W, expected welfare given the income vector x is: XX EðW jxÞ ¼ W ðupðc1 Þ ðx1 Þ; . . . ; upðcn Þ ðxn ÞÞrpðcÞ qc (1) P

P

C

PðcÞ

where C and P(c) denote the sums over all combinations in C and over all permutations in P(c). It is not assumed that all assignments of utility functions are equally likely. In particular, the probabilities are allowed to vary across combinations. For example, information on aggregate economic behavior might lead the planner to believe some combinations of utility functions are more likely than others. However, it is assumed that all permutations of a given combination are equally likely. Conditional equi-probability: If qc>0, then rp(c) ¼ (Psncs!)/n!, 8pðcÞ 2 PðcÞ and 8c 2 C: That is, for every combination of utility functions that can occur with nonzero probability, each permutation of that combination is equally likely to

Generalized Probabilistic Egalitarianism

17

give the correct assignment of utility functions to individuals. Also, while all permutations of a given combination are equally likely, those probabilities depend on the combination. Two combinations c0 and c00 will, in general, have different multiplicities, so that rp(c0 )6¼rp(c00 ). The assumption of conditional equi-probability is weaker than the assumption of equal unconditional probabilities made by Lerner, and which has been so frequently criticized. The unconditional probability of a permutation is rp(c)qc, so equi-probability requires that rp(c)qc ¼ rp0 (c0 )qc0 for 8pðcÞ 2 PðcÞ; 8p0 ðc0 Þ 2 Pðc0 Þ; and 8c; c0 2 C: To see this more clearly, let m ¼ n ¼ 2. Then the possibilities are shown in the following table: Combination

1 2 3

Permutation 1

2

1, 1 1, 2 2, 2

– 2, 1 –

Then equi-probability requires that q1 ¼ 1/2q2, q3 ¼ 1/2q2 and q1 ¼ q3 so that the unconditional probability of each distinct permutation is 1/4. Since combination 2 has two different permutations, it is twice as likely as combination 1 or 3 to be the correct combination. Conditional equi-probability leads to the following result. Proposition 1. Conditional equi-probability holds iff E(W|x) is symmetric in incomes for all x. Proof. It is enough to illustrate the proof for n ¼ 2 and m ¼ 3. The possible combinations of utility functions and their permutations are shown in the table: Combination

Permutations 1

1 2 3 4 5 6

1, 1, 1, 2, 2, 3,

2 1 2 3 2 3 3

– 2, 1 3, 1 – 3, 2 –

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PAUL D. THISTLE

Then EðW jxÞ ¼ W ðu1 ðx1 Þ; u1 ðx2 ÞÞq1 þ ½W ðu1 ðx1 Þ; u2 ðx2 ÞÞr1ð2Þ þ W ðu2 ðx1 Þ; u1 ðx2 ÞÞr2ð2Þ q2 þ ½W ðu1 ðx1 Þ; u3 ðx2 ÞÞr1ð3Þ þ W ðu3 ðx1 Þ; u1 ðx2 ÞÞr2ð3Þ q3 þ W ðu2 ðx1 Þ; u2 ðx2 ÞÞq4 þ ½W ðu2 ðx1 Þ; u3 ðx2 ÞÞr1ð5Þ þ W ðu3 ðx1 Þ; u2 ðx2 ÞÞr2ð5Þ q5 þ W ðu3 ðx1 Þ; u3 ðx2 ÞÞq6

ð2Þ

Sufficiency follows from conditional equi-probability (r1(c) ¼ r2(c)) and symmetry of W in utilities. To prove necessity, assume x16¼x2, and that E(W|x) is symmetric in incomes. Then Eq. (2) can be written as: EðW jxÞ ¼ W ðu1 ðx2 Þ; u1 ðx1 ÞÞq1 þ ½W ðu1 ðx2 Þ; u2 ðx1 ÞÞr1ð2Þ þ W ðu2 ðx2 Þ; u1 ðx1 ÞÞr2ð2Þ q2 þ ½W ðu1 ðx2 Þ; u3 ðx1 ÞÞr1ð3Þ þ W ðu3 ðx2 Þ; u1 ðx1 ÞÞr2ð3Þ q3 þ W ðu2 ðx2 Þ; u2 ðx1 ÞÞq4 þ ½W ðu2 ðx2 Þ; u3 ðx1 ÞÞr1ð5Þ þ W ðu3 ðx2 Þ; u2 ðx1 ÞÞr2ð5Þ q5 þ W ðu3 ðx2 Þ; u3 ðx1 ÞÞq6

ð3Þ

Using the fact that W is symmetric in utilities, subtracting Eq. (3) from Eq. (2) yields: ½W ðu1 ðx1 Þ; u2 ðx2 ÞÞ
W ðu1 ðx2 Þ; u2 ðx1 ÞÞðr1ð2Þ
r2ð2Þ Þq2 þ ½W ðu1 ðx1 Þ; u3 ðx2 ÞÞ
W ðu1 ðx2 Þ; u3 ðx1 ÞÞðr1ð3Þ
r2ð3Þ Þq3 þ ½W ðu2 ðx1 Þ; u3 ðx2 ÞÞ
W ðu2 ðx2 Þ; u3 ðx1 ÞÞðr1ð5Þ
r2ð5Þ Þq5 ¼ 0

ð4Þ

Since x16¼x2, each expression in brackets is non-zero. If r1(c)6¼r2(c) for any combination c for which qc>0, then E(W|x)
E(W|x)6¼0. Therefore, conditional equi-probability must hold. & Sen (1969, 1973a, 1973b) and McCain (1972) also consider the possibility that not all assignments of utility functions are equally likely. Sen and McCain both assume that the unconditional probability that individual i’s utility function is uj is independent of the individual. Let sij be the unconditional probability that individual i’s utility function is uj. Unconditional equi-probability: sij ¼ sj, 8i 2 N:

Generalized Probabilistic Egalitarianism

19

Unconditional equi-probability is more general than the conditional equi-probability assumption. Let CðjÞ ¼ fcjj 2 cg be the set of combinations that select the utility function uj. For any c in C(j), there are n permutations that assign the utility function P uj to the ith individual. Then conditional equi-probability implies sij ¼ cAC(j)qc/n, which is free of i.12 Proposition 2. Assume W is utilitarian. Unconditional equi-probability holds iff E(W|x) is symmetric in incomes for all x. Proof. Expected welfare is EðW jxÞ ¼

XX

sij uj ðxi Þ

(5)

j2M i2N

To prove equi-probability and let P sufficiency, assume unconditional P u¯ ðxÞ ¼ j2M sj uj ðxÞ: Then EðW jxÞ ¼ i2N u¯ ðxi Þ; which is symmetric in incomes. Necessity is proved for the case m ¼ 3 and n ¼ 2; the argument is essentially the same as in Proposition 1. Assume x16¼x2, and that E(W|x) is symmetric in incomes. Interchange incomes and subtract to obtain: ðs11
s21 Þ½u1 ðx1 Þ
u1 ðx2 Þ þ ðs12
s22 Þ½u2 ðx1 Þ
u2 ðx2 Þ þðs13
s23 Þ½u3 ðx1 Þ
u3 ðx2 Þ

ð6Þ

Since x16¼x2, each expression in brackets is non-zero. If s1j6¼s2j, then E(W|x)
E(W|x)6¼0. Therefore, unconditional equi-probability must hold. & That is, for a utilitarian SWF, unconditional equi-probability is equivalent to treating each individual as if she had the average utility function, u¯ ðxÞ: In his analysis of general, non-utilitarian SWFs, Sen (1973a, 1973b) assumes that each reassignment of utility functions is accompanied by a corresponding reassignment of incomes. That is, the social planner is assumed to know that income xj always belongs to the individual with the utility function uj, but, in effect, does not know that individual’s name. But symmetry of the SWF implies that individuals’ names are not relevant for the evaluation of the income distribution. Consequently, the unconditional probability with which individual i has the utility function uj (and income xj) does not affect welfare, and can be left arbitrary. Lerner, and most subsequent analysts, assume that the social planner knows individuals’ names and incomes, but not their utility functions.

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4. EFFICIENCY AND EQUITY PREFERENCE If the SWF is consistent with the Pareto principle, then it is increasing in utilities. Let W1 denote the set of all functions that are continuous, increasing, and symmetric in their arguments. If the SWF also satisfies the principle of transfers, then it is S-concave (Dalton, 1920; Dasgupta, Sen, & Starrett, 1973). Let W2 be the class of all continuous, increasing, S-concave functions. Obviously, W 2  W 1 : We will make use of the following partial orders on X. Let x~ ¼ ðx~ 1 ; . . . ; x~ n Þ be the ordered version of x, where x~ 1  x~ 2  . . .  x~ n : Then, for any x, yAX, x rank dominates y, denoted x4R y; iff x~ i  y~ i ; 8i 2 N; with least one strict Pat k inequality. The Lorenz curve for x is Lx ðk=nÞ ¼ ð1=nxÞ ¯ i¼1 x~ i : Following Shorrocks (1983) and Kakwani (1984), the generalized Lorenz curve for x is the Lorenz curve, scaled up by mean income, G x ðk=nÞ ¼ xL ¯ x ðk=nÞ ¼ P ð1=nÞ ki¼1 x~ i ; k 2 N: Then x generalized Lorenz dominates y, denote x>G y, iff Gx(k/n)ZGy(k/n), 8k 2 N; with a strict inequality for some k. That is, the generalized Lorenz curve for x must lie nowhere below the generalized Lorenz curve for y, and strictly above it at some point. Rank dominance implies generalized Lorenz dominance, and a higher mean together with Lorenz dominance implies generalized Lorenz dominance; neither converse is true.

5. EXPECTED WELFARE COMPARISONS Following Lerner, the central planner faces the problem of evaluating and comparing alternative income distributions and selecting the socially optimal distribution. Since the planner does not know who has which utility function, the planner’s objective becomes maximization of expected welfare. Expected welfare maximization yields different objective criteria for comparing income distributions depending on the characteristics of individuals’ utility functions and the planner’s SWF. We will make use of the following result. Lemma 1. (a) x4R y iff V(x)>V(y), 8V 2 W 1 : (b) x4G y iff V(x)>V(y), 8V 2 W 2 : Part (a) of the lemma states that rank dominance, x4R y; is equivalent to unanimous preference for x by every welfare function that is consistent with the Pareto principle. Part (b) states that generalized Lorenz dominance,

Generalized Probabilistic Egalitarianism

21

x4G y; is equivalent to unanimous preference for x by every welfare function that is consistent with the Pareto principle and the principle of transfers. Part (a) is proved in Saposnik (1981, 1983) and Thistle (1989). Part (b) is proved in Shorrocks (1983) and Kakwani (1984), extending Atkinson’s (1970) seminal result.13 The rank dominance and generalized Lorenz dominance criteria are equivalent to first- and second-degree stochastic dominance; see Foster and Shorrocks (1988a, 1988b), Kakwani (1984), and Thistle (1989). Suppose the planner’s SWF is Paretian and anonymous. Then the appropriate criterion for comparing income distributions is rank dominance. If the planner’s SWF is also S-concave in utilities, then the appropriate criterion is generalized Lorenz dominance. Let U1 be the set of all continuous, increasing utility functions, and let U2 be the set of all continuous, increasing, concave utility functions. Proposition 3. Assume conditional equi-probability holds. (a) If U  U1, then E(W|x)>E(W|y), 8W 2 W 1 iff x4R y: (b) If U  U2, then E(W|x)>E(W|y), 8W 2 W 2 iff x4G y: Proof. By Proposition 1, E(W|x) is symmetric in incomes. For (a), since U  U1, and W is increasing in utilities, E(W|x) is increasing in incomes, and the conclusion then follows from Lemma 1(a). For (b), since U  U 2 and W is increasing and S-concave in utilities, E(W|x) is increasing and S-concave in incomes. The conclusion then follows from Lemma 1(b). & Part (a) of Proposition 3 generalizes the result obtained by Bishop et al. (1991) under the assumptions of equal numbers, equi-probability, and a utilitarian SWF. The rank dominance criterion does not incorporate inequality aversion. If the planner’s SWF also satisfies the principle of transfers, then the appropriate criterion is generalized Lorenz dominance. Part (b) of Proposition 3 generalizes the result of Kakwani (1984) under the assumptions of equal numbers and equi-probability. Parts (a) and (b) of the proposition allow more general interpretations of first- and second-degree stochastic dominance, which are usually discussed in terms of a single fixed and known utility function. Much of the controversy surrounding Lerner’s approach has focused on his conclusion that an egalitarian income distribution is optimal. Let eðxÞ ¼ ðx; ¯ . . . ; xÞ ¯ be the n-vector with all incomes equal to the mean of x. Proposition 4. If conditional equi-probability holds and U  U 2 ; then E(W|e(x))>E(W|x), 8x6¼e(x) and 8W 2 W 2 :

22

PAUL D. THISTLE

Proof. Since eðxÞ4G x; the results follow directly from Proposition 3(b). & This extends the results of Sen (1969, 1973a, 1973b). Sen (1973a, 1973b) assumes equal numbers, which, under his assumptions, implies equi-probability. Sen (1969) employs a more general assumption on the probabilities, but at the cost of assuming a utilitarian welfare function. Propositions 3 and 4 are based on the assumption that individuals’ utilities are absolutely measurable and fully comparable, a stronger assumption than made by Lerner. These results clearly do not address Graaff ’s, Little’s, and Samuelson’s concerns on this point. We have a similar result for utilitarian SWFs. Proposition 5. Assume W is utilitarian and unconditional equi-probability holds. (a) E(W|x)>E(W|y), 8U  U1 iff x4R y: (b) E(W|x)>E(W|y), 8U  U2 iff x4G y: (c) E(W|e(x))>E(W|x), 8x6¼e(x) and 8U  U2. P Proof. We have EðW jxÞ ¼ i2N u¯ ðxi Þ: Parts (a) and (b) follow directly from the equivalence of rank dominance with first-degree stochastic dominance and generalized Lorenz dominance with second-degree stochastic dominance. Since eðxÞ4G x; part (c) follows directly from part (b). & If the invariance requirements are strengthened to ordinal level comparability, then the social welfare ordering must be a lexicographic positional dictatorship (LPD) (Gevers, 1979).14 That is, fix some assignment of utility functions to individuals. Let u~ 1  u~ 2  :::  u~ n be the utility levels, ranked from lowest to highest, when the income distribution is x. Similarly, let u^ 1  u^ 2  :::  u^ n be the ranked utility levels under distribution y. Let p be a permutation on f1; . . . ; ng; each permutation defines an LPD.15 Then x is preferred to y by the LPD defined by p, denoted x4p y; if u~ pðiÞ ¼ u^ pðiÞ ; i ¼ 1; :::; k
1 and u~ pðkÞ 4u^ pðkÞ : In the case where utility functions are known, rank dominance is equivalent to unanimity among the LPDs (Thistle, 1998). This leads to the following strong result. In particular, no restrictions on the probabilities are necessary. Proposition 6. Let utilities in U  U1 be ordinally comparable, and let x4R y: Then x4p y for all permutations p with certainty.

Generalized Probabilistic Egalitarianism

23

Proof. Let p be the permutation that defines the LPD. Then: upðc1 Þ ðx~ 1 Þ  upðc1 Þ ðy~ 1 Þ; upðc2 Þ ðx~ 2 Þ  upðc2 Þ ðy~ 2 Þ; . . . ; upðcn Þ ðx~ n Þ  upðcn Þ ðy~ n Þ

(7)

with at least one strict inequality. This inequality holds for every assignment of utility functions to individuals that has non-zero probability. Therefore, x4p y with certainty. & Rank dominance is sufficient, but not necessary, for an increase in welfare to occur with certainty. Since the possible social welfare orders are narrowly proscribed, the restrictions on the probabilities can be weakened. Moreover, since the choice of p is arbitrary, the conclusion holds for all LPDs. It should be pointed out, however, that x may be a more unequal distribution than y, so that Proposition 6 is not an egalitarian result.

6. HETEROGENEOUS POPULATIONS Friedman (1947, p. 410), in his critique of Lerner, argues that equi-probability should be replaced by the assumption that a person’s income is ‘‘statistically independent of his capacity for enjoying it.’’ Friedman then argues that individuals can be classified by their capacity for satisfaction: ‘‘Conceptually classify the individuals by their (unknown) capacities for satisfaction. Each such ‘satisfaction class’ will contain only individuals who have identical capacities, i.e., have identical utility functions.’’ (p. 410, note 6). As Lambert (2001, pp. 93–94) suggests, one possible way to classify individuals is according to ‘‘needs,’’ that is, individuals with different needs have different capacities for satisfaction. More generally, individuals can be classified according to any characteristic such that each group has a different set of possible utility functions or a different probability distribution over the set of possible utility functions. The characteristic used to classify individuals may or may not be relevant for policy. If the characteristic is relevant for policy, it may or may not be desirable to rank groups based on the characteristic.16 But so long as the characteristic affects the evaluation of welfare, we need to analyze the joint distribution of the characteristic and income. As Atkinson and Bourguignon (1987) show, this leads to either group-wise or sequential procedures for evaluation of income distributions. Atkinson and Bourguignon and the subsequent literature assume, as in Friedman, that all individuals in a group have the same known utility function.

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To classify individuals according to their ‘‘capacity for satisfaction,’’ let Nk be the set of nk individuals in group k. Then N ¼ fN 1 ; . . . ; N g g is a partition of the population N into gZ2 groups, and G ¼ f1; . . . ; gg indexes groups. Let yk ¼ nk/n be the population proportion of group k. We take the composition of the population as fixed throughout the analysis.17 Let U k  U be the set of mkZnk possible utility function for the group Nk, with corresponding index set Mk. The sets Uk are not necessarily disjoint. That is, we allow for the possibility that there may be individuals in different groups that have the same utility function. To simplify the analysis, we assume the welfare function is utilitarian and evaluate welfare on a per capita basis. Since the planner distinguishes between groups, the welfare function will not be symmetric for the full population. However, there is no reason to treat different individuals within the same group differently. The welfare function is partially symmetric in incomes with respect to the partition N if i; j 2 N k implies that interchanging xi and xj does not affect welfare. As Cowell (1980, p. 523) puts it: ‘‘We have anonymity within groups but not between them.’’18 We need to modify the unconditional equi-probability condition to apply to groups. Let skij be the unconditional probability that individual i’s utility function is uj, where iANk and jAMk. Group-wise unconditional equi-probability: sijk ¼ sjk, 8i 2 N k ; 8j 2 M k ; and 8k 2 G: That is, unconditional equi-probability holds within each group. This allows the probabilities to differ across groups, that is, jAMh, Mk does not imply shj ¼ skj : This leads to the analog of Proposition 2 for utilitarian welfare functions. Proposition 7. Assume W is utilitarian. Group-wise unconditional equiprobability holds iff E(W|x) is partially symmetric in incomes with respect to N for all x. P P Proof. Define u¯ k ðxÞ ¼ j2M k skij ukj ðxÞ: Then, by Proposition 2, i2N k u¯ k ðxi Þ is symmetric in incomes if and only if, unconditional P equi-probability P holds for group k. Expected welfare is EðW jxÞ ¼ k2G yk i2N k u¯ k ðxi Þ; which is partially symmetric in incomes with respect to N if, and only if, unconditional equi-probability holds for every group, that is, group-wise unconditional equi-probability holds. & For a utilitarian SWF, group-wise unconditional equi-probability is equivalent to treating each individual in Nk as if she had the utility function

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u¯ k ðxÞ: Since the utility functions differ across groups, expected welfare is partially symmetric in incomes. Let xk be the vector of income for the individuals in group Nk. We say x group-wise rank dominates y, denoted x4GR y; if x rank dominates y for each group, xk 4R yk ; k ¼ 1; . . . ; g: We say x group-wise generalized Lorenz dominates y, denoted x4GG y; if x generalize Lorenz dominates y for each group, xk 4G yk ; k ¼ 1; . . . ; g: Proposition 8. Assume W is utilitarian and group-wise unconditional equi-probability holds. (a) E(W|x)>E(W|y), 8U  U1 iff x4GR y: (b) E(W|x)>E(W|y), 8U  U2 iff x4GG y: (c) E(W|e(x))>E(W|x), 8x6¼e(x) and 8U  U2. Proof. Parts (a) and (b) follow from Proposition 7 and parts 1 and 2, respectively, of Proposition 1 in Atkinson and Bourguignon (1987). (c) Let ek ðxk Þ ¼ ðx¯ k ; . . . ; x¯ k Þ be the nk-vector with all elements equal to the mean of xk. The assumption x6¼e(x) implies the group means x¯ k cannot all P k be equal. Let v ðxÞ ¼ i2NP ku ¯ k ðxÞ and observe that U  U 2 implies vk is k k concave. We have v ðx¯ Þ P i2N k u¯ k ðxi Þ by part (c) of Proposition 5. Now EðW je1 ðx1 Þ; . . . ; eg ðxg ÞÞ ¼ k2G yk vk ðx¯ k Þ is concave in its arguments. Consequently, EðW jeðxÞÞ4EðW je1 ðx1 Þ; . . . ; eg ðxg ÞÞ  EðW jxÞ: & Proposition 8 can be applied whenever the groups are not ranked. This extends Proposition 5 to heterogeneous populations. Alternatively, this result extends Proposition 1 in Atkinson and Bourguignon. Finally, part (c) corrects the problems with Friedman’s (1947) alternative proof of Lerner’s result. We now turn to the case where the groups can be ranked on the basis of needs as in Atkinson and Bourguignon (1987).19 We index the groups in decreasing order of needs, so that group 1 has the greatest needs and group g is the group with the lowest needs. The ranking of groups based on needs imposes restrictions on the planner’s evaluation of social welfare, which in turn impose restrictions on individuals’ utility functions. The first restriction is that the marginal social valuation of income is positive for each group and lower for groups with lower needs. Let sk ¼ ðsk1 ; . . . ; skmk Þ: In terms of the u¯ k ; this restriction can be written as: Needs 1. 0

(a) u¯ k ðxÞ40 for all x, for all sk and 8k 2 G: 0 0 0 (b) u¯ 1 ðxÞ  u¯ 2 ðxÞ  . . .  u¯ g ðxÞ40 for all x and all (s1,y, sg).

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That is, the expected value of the marginal utility of income is positive for all groups and is greater for groups with greater needs at all incomes. Further, this must be true whatever the planner’s information about the assignment of utility functions to individuals within groups. Part (a) is the Pareto principle. Part (b) implies that a transfer from a richer individual in a group with lower needs to a poorer individual in a group with greater needs increases welfare. The second restriction is that the marginal social valuation of income is decreasing in income for each group and that the between-group difference in marginal social valuation is decreasing in income. This restriction can be written as: Needs 2. 00

(a) u¯ k ðxÞo0 for all sk and k ¼ 1, y, g. 00 00 00 (b) u¯ 1 ðxÞ  u¯ 2 ðxÞ  . . .  u¯ g ðxÞ for all x and all (s1, y, sg). Both parts of this condition can be viewed as transfer principles. Part (a) implies that transfers from richer to poorer individuals with the same group increase welfare. Part (b) implies that a progressive transfer within a group with greater needs increases welfare by more than the same transfer within a group with lower needs. Finally, the differences among groups become less important at higher income levels. These conditions impose certain restrictions on the sets of possible utility functions. Condition MU. Let hok. Then i 2 M h ; j 2 M k implies u0i ðxÞ  u0j ðxÞ for all x. That is, every possible utility function in Uh has higher marginal utility of income than every possible utility function in Uk. Condition DMU. Let hok. Then i 2 M h ; j 2 M k implies u00i ðxÞ  u00j ðxÞ for all x. That is, marginal utility falls more rapidly for every possible utility function in Uh than for every possible utility function in Uk. Together, Conditions MU and DMU imply that, for i 2 M h and j 2 M k ; the difference u0i ðxÞ
u0j ðxÞ is non-negative and non-increasing in income. This leads to the following result: Proposition 9. Let hok. 0

0

(a) Condition MU holds iff u¯ h ðxÞ  u¯ k ðxÞ for all x and all sh, sk. 00 00 (b) Condition DMU holds iff u¯ h ðxÞ  u¯ k ðxÞ for all x and all sh, sk.

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Proof. (a) Sufficiency is obvious. To see necessity, suppose that Condition MU does not hold. Then there are indices i0 2 M h and j 0 2 M k such that u0i0 ðx0 Þou0j0 ðx0 Þ for some income level x0. Letting shi0 ¼ 1 and let skj0 ¼ 1; we 0 0 have u¯ h ðx0 Þo¯uk ðx0 Þ: Part (b) follows from the same argument. & Conditions MU and DMU impose strong restrictions on the sets of possible utility functions. But recall that Atkinson and Bourguignon assume all individuals in a group have a common known utility function. The groups are then ranked according to the characteristics of their utility functions based on the conditions Needs 1 and Needs 2. Under Lerner’s probabilistic approach only the set of possible utility functions is known. Since individuals can have any of the possible utility functions, these conditions must hold for the sets of possible utility functions in order to rank groups based on the characteristics embodied in Needs 1 and Needs 2. Assuming positive and diminishing marginal utility, the Conditions MU and DMU are equivalent to assuming that Needs 1 and Needs 2 hold for the sets of possible utility functions. Thus, these restrictions are no stronger than those assumed by Atkinson and Bourguignon. Now let x1þþk ¼ ðx1 ; . . . ; xk Þ be the vector of incomes for individuals in groups 1 though k. We say x sequentially rank dominates y, denoted x4SR y if x1þþk 4R y1þþk for k ¼ 1; . . . ; g: Similarly, x sequentially generalized Lorenz dominates y, denoted x4SG y if x1þþk 4G y1þþk for k ¼ 1; . . . ; g: Since x1þþg ¼ x; sequential rank dominance and sequential generalized Lorenz dominance imply (ordinary) rank dominance and generalized Lorenz dominance. Also, group-wise rank dominance and generalized Lorenz dominance imply sequential rank dominance and generalized Lorenz dominance. Neither converse is true. Proposition 10. Assume W is utilitarian and that group-wise unconditional equi-probability holds. (a) If Condition MU holds, then E(W|x)>E(W|y), 8U  U 1 iff x4SR y: (b) If Conditions MU and DMU hold, then E(W|x)>E(W|y), 8U  U 2 iff x4SG y: Proof. The results follow from Proposition 9 and Propositions 2 and 3, respectively, in Atkinson and Bourguignon. & This generalizes Proposition 3 to the case of a heterogeneous population where population sub-groups can be ranked based on needs. Proposition 10 also allows a more general interpretation of sequential rank dominance and sequential generalized Lorenz dominance, which, following Atkinson

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and Bourguignon, are generally discussed in terms of common and known utility functions for the members of each population group.

7. CONCLUSIONS Lerner’s probabilistic approach to the welfare evaluation of income distributions has aroused comment and controversy for over 60 years. Lerner assumed that it is not known which individual has which utility function and that all assignments of utility functions to individuals are equally likely. Lerner then shows that an equalitarian division of income maximizes the probable total satisfaction of society. Most of the criticism of Lerner’s analysis has focused on the ‘‘equi-probability’’ assumption. Lerner’s observation that individuals’ preferences may not be known with certainty remains an important insight. This paper extends Lerner’s probabilistic approach to the welfare analysis of income distributions. The restrictions of a utilitarian welfare function, equal mean incomes, equal numbers, and equal probabilities are weakened or eliminated. There is a tradeoff between the invariance requirements of the planner’s SWF and the utility assignment information. This paper introduces the assumption of conditional equi-probability, which requires all permutations of a given combination to be equally likely, but allows probabilities to vary across different combinations of utility functions. The general Bergson–Samuelson welfare function has the weakest invariance requirement, absolute measurability. For Bergson–Samuelson SWFs defined over utilities, conditional equi-probability is equivalent to symmetry of expected welfare in incomes. If conditional equi-probability holds, then rank dominance and generalized Lorenz dominance can be applied as probabilistic welfare criteria. The utilitarian welfare function is invariant to linear transformations of the utility functions, a stronger invariance requirement. For utilitarian SWFs, unconditional equi-probability is equivalent to symmetry in incomes. If unconditional equi-probability holds, then rank dominance and generalized Lorenz dominance can be applied as probabilistic welfare criteria. The LPD has the strongest invariance requirement, and allows the probabilities to be unrestricted. If the invariance requirement is strengthened to ordinal comparability, then rank dominance implies greater welfare with certainty. The tradeoff only becomes apparent when the number of possible utility functions exceeds the number of individuals. In the equal numbers case, conditional equi-probability and unconditional equi-probability both reduce to Lerner’s assumption that all assignments of utility functions to individuals

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are equally likely. Even Lerner’s equi-probability assumption is weaker than the usual assumption that the assignment of utility functions to individuals is known with certainty. This paper also extends Lerner’s probabilistic approach to welfare analysis of income distributions to heterogeneous populations. The assumptions of equal mean incomes, equal number, and equi-probability are relaxed, but the assumption of a utilitarian welfare function is retained. The unconditional equi-probability condition, applied to groups within the population, is equivalent to partial symmetry in incomes. That is, expected welfare is anonymous within groups but not between groups. If group-wise unconditional equiprobability holds, then group-wise rank dominance and generalized Lorenz dominance can be applied as probabilistic welfare criteria. Under additional conditions on the possible utility functions, the groups can be ranked according to ‘‘needs.’’ Then sequential rank dominance and sequential generalized Lorenz dominance can be applied as probabilistic welfare criteria.

NOTES 1. Meade (1945) reviews Lerner’s book, but focuses primarily on other issues. Scitovsky (1971) also accepts Lerner’s analysis with little comment. 2. Boadway and Bruce (1984, pp. 162–163) provide a clear and convenient summary of invariance requirements and social welfare orderings. 3. Curiously, Breit and Culbertson (p. 440, note 9) criticize Friedman (1947) for assuming that ‘‘each individual faces another with precisely the same utility function.’’ 4. See Sen (1970, 1977) and Boadway and Bruce (1984, Chapter 5). 5. Musgrave (p. 107) repeats Friedman’s argument without comment. Scitovsky (p. 287, note 1) regards it as correcting an error in Lerner’s proof. 6. To see this, consider the two-person economy in Fig. 1. Friedman’s argument is that statistical independence implies both Ann and Bob receive the same income. Samuelson (p. 175) makes essentially the same point. 7. Similarly, Breit and Culbertson assume that each pair of utility twins has the same total income, but do not prove that they should have the same total income. 8. The same point is made in Lambert (2001, pp. 91–92). 9. As McCain (1972, p. 499) points out, the assumption of a finite set of possible utility functions is restrictive. However, the results obtained here hold for any arbitrary finite set of utility functions, hence, by a well-known theorem of analysis, can be extended to compact sets of utility functions. 10. The use of a Bergson–Samuelson social welfare function requires that utilities be absolutely measurable and fully interpersonally comparable. 11. The problem of selecting the combination of utility functions can be thought of as a problem of drawing a sample of size n from a set of m distinct objects, with replacement and without regard to order. See Chung (1974, pp. 50–52). Sampling with replacement allows the same utility function to be chosen multiple times.

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12. Under unconditional equi-probability, the probability that the combination c is correct is qc ¼ Sj2c sj : 13. This result is anticipated in Kolm (1969). 14. That is, the social welfare order is invariant to any common monotonic (not necessarily linear) transformation of utilities. 15. The best known LPD is Sen’s (1970) ‘‘lexmin’’ order, which begins with the worst off individual, proceeds to the next worst off in the event of a tie, etc. Lexmin is the special case p(i) ¼ i. 16. For example, the planner may know that individuals in different geographic areas or in different demographic groups have different ‘‘capacities for satisfaction’’ but may not consider the geographic or demographic classification important for policy. In particular, the planner may not be willing to rank groups based on the geographic or demographic classification. 17. See Jenkins and Lambert (1993) for an analysis of the case where the marginal distribution of needs is not constant. 18. The definition of partial symmetry here is slightly different from that in Cowell (1980). In the analysis here, the planner’s information or differences in needs among groups within the population determines a specific partition of the population. Thus, for our purposes, we want expected welfare to be partially symmetric with respect to that specific partition. Cowell’s definition requires that the welfare function be partially symmetric with respect to some partition of the population. 19. Bourguignon (1989) discusses the relationship between individual utility functions and household utility functions. Ebert (2000) discusses the axioms underlying Atkinson and Bourguignon’s analysis. Ok and Lambert (1999) extend Atkinson and Bourguignon’s analysis to non-utilitarian welfare functions. See Lambert (2001, pp. 72–77) for a lucid discussion of sequential generalized Lorenz dominance.

ACKNOWLEDGMENTS I would like to thank Annette Brown, John Formby, Rubin Saposnik, and especially John Bishop and Peter Lambert for helpful discussions and comments on earlier versions of this paper. Much of the paper was completed while I was on the faculty of Western Michigan University. I retain the responsibility for any remaining errors.

REFERENCES Atkinson, A. B. (1970). On the measurement of economic inequality. Journal of Economic Theory, 2, 244–267. Atkinson, A. B., & Bourguignon, F. (1987). Income distribution and differences in needs. In: G. R. Fiewel (Ed.), Arrow and the foundations of economic theory. New York: New York University Press.

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Bennett, J. (1981). The probable gain from egalitarian redistribution. Oxford Economic Papers, 33, 165–169. Bishop, J. A., Formby, J. P., & Thistle, P. D. (1991). Rank dominance and international comparisons of income distributions. European Economic Review, 35, 1399–1409. Bishop, J. A., Formby, J. P., & Thistle, P. D. (1992). Convergence of the south and non-south income distributions, 1969–1979. American Economic Review, 82, 262–272. Boadway, R., & Bruce, N. (1984). Welfare economics. Oxford: Basil Blackwell. Bourguignon, F. (1989). Family size and social utility: Income distribution dominance criteria. Journal of Econometrics, 42, 67–80. Breit, W., & Culbertson, W. P. (1970). Distributional equity and aggregate utility: Comment. American Economic Review, 60, 435–441. Chung, K. L. (1974). Elementary probability theory with stochastic processes. New York: Springer-Verlag. Cowell, F. A. (1980). On the structure of additive inequality measures. Review of Economic Studies, 47, 521–531. Dalton, H. (1920). The measurement of the inequality of incomes. Economic Journal, 30, 348–361. Dasgupta, P., Sen, A., & Starrett, D. (1973). Notes on the measurement of inequality. Journal of Economic Theory, 6, 180–187. Ebert, U. (2000). Sequential generalized Lorenz dominance and transfer principles. Bulletin of Economic Research, 52, 113–122. Foster, J., & Shorrocks, A. F. (1988a). Poverty orderings. Econometrica, 56, 173–177. Foster, J., & Shorrocks, A. F. (1988b). Poverty orderings and social welfare. Social Choice and Welfare, 5, 179–198. Friedman, M. (1953). Essays in positive economics. Chicago: University of Chicago Press. Gevers, L. (1979). On interpersonal comparability and social welfare orderings. Econometrica, 47, 75–89. Graaff, J. (1967). Theoretical welfare economics (2e). Cambridge: Cambridge University Press. Jenkins, S. P., & Lambert, P. J. (1993). Ranking income distributions when needs differ. Review of Income and Wealth, 39, 337–356. Kakwani, N. (1984). Welfare rankings of income distributions. In: R. L. Basmann, & G. F. Rhodes, Jr. (Eds), Advances in econometrics (Vol. 3). Greenwich: JAI Press. Kolm, S.-C. (1969). The optimal production of social justice. In: J. Margolis, & H. Guitton (Eds), Public economics: An analysis of public production and consumption and their relations to the private sectors. London: Macmillan. Lambert, P. (2001). The distribution and redistribution of income (3e). Manchester: Manchester University Press. Lerner, A. P. (1944). The economics of control. New York: Macmillan. Lerner, A. P. (1970). Distributional equality and aggregate utility: Reply. American Economic Review, 60, 442–443. Little, I. M. D. (1957). A critique of welfare economics (2e). Oxford: Oxford University Press. McCain, R. (1972). Distributional equity and aggregate utility: Further comment. American Economic Review, 62, 497–500. McManus, M., Walton, G., & Coffey, R. B. (1972). Distributional equity and aggregate utility: Further comment. American Economic Review, 62, 489–496. Meade, J. E. (1945). Mr. Lerner on ‘The Economics of Control’. Economic Journal, 55, 47–69. Musgrave, R. (1959). The theory of public finance. New York: McGraw-Hill.

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Ok, E. A., & Lambert, P. J. (1999). On evaluating social welfare by sequential generalized Lorenz dominance. Economics Letters, 63, 45–53. Samuelson, P. A. (1964). Abba Lerner at sixty. Review of Economic Studies, 31, 169–178. Saposnik, R. (1981). Rank dominance in income distribution. Public Choice, 36, 147–151. Saposnik, R. (1983). On evaluating income distributions: Rank dominance, the Pareto principle, and the Suppes-Sen Grading Principle of Justice. Public Choice, 40, 329–336. Scitovsky, T. (1971). Welfare and competition (rev. ed.). Homewood: Richard D. Irwin. Sen, A. K. (1969). Planners preferences: Optimality, distribution and control. In: J. Margolis & H. Guitton (Eds), Public economics. London: Macmillan. Sen, A. K. (1970). Collective choice and social welfare. San Francisco: Holden-Day. Sen, A. K. (1973a). On economic inequality. New York: Macmillan. Sen, A. K. (1973b). On ignorance and equal distribution. American Economic Review, 63, 1022–1024. Sen, A. K. (1977). On weights and measures: Informational constraints in social welfare analysis. Econometrica, 45, 1539–1572. Shorrocks, A. F. (1983). Ranking income distributions. Economica, 50, 3–17. Thistle, P. D. (1989). Ranking distributions with generalized Lorenz curves. Southern Economic Journal, 56, 1–12. Thistle, P. D. (1998). Social structure, economic performance and Pareto optimality. Theory and Decision, 45, 161–173.

INEQUALITY AND INCOME GAPS Ian Preston ABSTRACT This paper discusses inequality orderings based explicitly on closing up of income gaps, demonstrating the links between these and other orderings, the classes of functions preserving the orderings and applications showing their usefulness in comparison of economic policies.

1. INTRODUCTION It is a truism to say that inequality is about gaps between incomes and that reducing inequality is about closing these gaps up. Common means of comparison between income distributions all use criteria which do show inequality as falling when gaps close. However, explicitly asking whether the gaps reduce throughout the whole distribution in concertina-like fashion is a rare criterion to apply. This paper seeks to investigate the related orderings. The most common criteria for inequality comparison are those based on Lorenz curves, made plausible most persuasively as indicators of inequality by their link to progressive transfers of income. Progressive transfers are often seen, since the arguments of Pigou (1912) and Dalton (1920), as uncontentiously inequality reducing but this view could be challenged if there are more than two people. A transfer from the top to the middle of the Equity Research on Economic Inequality, Volume 15, 33–56 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15003-1

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income distribution1 reduces inequality between the top and the middle but increases it between the middle and the bottom.2 Regarding inequality as having fallen overall involves giving priority to the former effect –the effect on the gap between incomes of those involved directly in the transfer – for which there may be good reason, but it is not obvious that it would not be sensible to say inequality simply could not be compared.3 What convinces Dalton (1920) is the link to welfare – he is ‘‘primarily interested, not in the distribution as such, but in the effects of the distribution of income upon the distribution and total amount of economic welfare, which may be derived from income (p. 348)’’. That such transfers raise welfare is well known to be true in a typical utilitarian setting if individual welfare depends only upon own income but if income gaps matter to individual welfare then this need not be so. This issue is taken up below and links between economic welfare and the orderings based explicitly on gaps are considered. The earliest discussions of these orderings can be found outside the economic context (for example in Marshall, Olkin, & Proschan, 1967a and Barlow & Proschan, 1975). There are some useful papers from this period which are less well known than perhaps they should be and a minor function of the current paper is to bring some overlooked but highly germane mathematical literature to the attention of inequality theorists. I think particularly here of Marshall, Walkup, and Wets (1967b) which anticipates several results of this paper.4 The major function, though, is to tell a rounded story about the ratio and difference dominance concepts, and associated orderings and welfare properties, which extend the well-known Lorenz ordering in different ways. In this, I am in fact taking up again some work which I engaged in some time ago (Preston, 1989, 1990a, 1990b) and ideas which have been developed by Moyes (1994) on the ‘‘dominance in relative differentials’’ and ‘‘dominance in absolute differentials’’ concepts, for which he coined those terminologies, and by Zheng (2007). The style and manner of development, in the sequel, is intended to be somewhat in similar fashion to the way in which Rothschild and Stiglitz’s (1973) paper developed a rounded story for the Lorenz ordering, which had been begun by Kolm (1969) and Atkinson (1970) (see also Dasgupta, Sen, & Starrett, 1973). Section 2 defines the orderings and considers relations between them. Section 3 outlines classes of functions which preserve the orderings. Section 4 considers how policies map underlying variation into distributions which may be related according to the orderings. Section 5 concludes.

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2. DOMINANCE ORDERINGS 2.1. Inequality 2.1.1. Orderings on Rn It is convenient to define inequality orderings on income vectors which have been placed in order from poorest to richest. To that end let Dn ¼ fx 2 Rn jxiþ1
xi ; for i ¼ 1; . . . ; n  1g and Dnþ ¼ fx 2 Rn jxiþ1
xi ; xi 40 for i ¼ 1; . . . ; n  1g ¼ Dn \ Rnþ denote spaces of ordered vectors. The two crucial orderings of interest for this paper are defined by closing up of all gaps in relative or absolute terms. Definition 1. (a) Say that x difference dominates y , written xhA y; iff xiþ1  xi  yiþ1  yi for i ¼ 1,y, n1 and x; y 2 Dn : (b) Say that x ratio dominates y , written xhR y; iff lnðxiþ1 Þ  lnðxi Þ  lnðyiþ1 Þ  lnðyi Þ for i ¼ 1,y, n1 and x; y 2 Dnþ : If x difference dominates y then all absolute gaps are smaller and if x ratio dominates y then all relative gaps are smaller. Both orderings are discussed in Marshall et al. (1967b) where they are treated as special cases of cone orderings.5 These orderings go by different names. Moyes (1994) refers to dominance in absolute and relative differentials. Zheng (2007) refers to absolute and ratio differential conditions. In the absence of unanimity on any alternative terminology, I keep to that used in Preston (1990a). Ratio and difference dominance can obviously be nested as special cases within a more general class of orderings requiring the closing up of gaps in the value of any increasing function of incomes, say U. Zheng (2007) makes this generalisation, defining a more general class of utility gap orderings. If we choose UðxÞ ¼ lnðx þ mÞ with m 2 Rþ then we get a class of orderings which will give ratio and difference dominance as extreme cases, in line with the treatment of intermediate orderings in Kolm (1976a, 1976b).6 It is also useful to have definitions of transformations of vectors which do not change inequality. In absolute terms all gaps are maintained by a parallel shift in a vector, called a translation, and all relative gaps by multiplying all incomes by a positive constant, referred to here as a rescaling. Let en 2 Rnþ denote the vector all elements of which are unity.

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Definition 2. (a) Say that x is a translation of y iff xi ¼ yi þ l; i ¼ 1; . . . ; n or more simply x ¼ y þ len for some l 2 R and x; y 2 Dn : (b) Say that x is a rescaling of y iff xi ¼ lyi ; i ¼ 1; . . . ; n; or more simply x ¼ ly for some l 2 Rþ and x; y 2 Dnþ : We can link the inequality orderings defined above to changes in income vectors which do unambiguously close up gaps. Definition 3. (a) Say that x is an absolute lower end elevation of y iff, for some k and some l40, xi ¼ yi þ l for i ¼ 1,y, k and xi ¼ yi for i ¼ k þ 1; . . . ; n with x; y 2 Dn : (b) Say that x is a relative lower end elevation of y iff, for some k and some l41, xi ¼ lyi for i ¼ 1,y, k and xi ¼ yi for i ¼ k þ 1; . . . ; n with x; y 2 Dnþ : Combining absolute or relative lower end elevations with translations or rescalings are the only ways to secure difference or ratio dominance. We state this formally. Theorem 1. (a) xhA y iff x can be obtained from y by a finite series of absolute lower end elevations and a translation. (b) xhR y iff x can be obtained from y by a finite series of relative lower end elevations and a rescaling. Proof of Theorem 1. (a) Sufficiency follows from the facts that any lower end elevation reduces absolute gaps for i ¼ 1,y, k and leaves them unchanged for i ¼ k þ 1; . . . ; n whereas any translation leaves absolute gaps unchanged. To see necessity, suppose xhA y: Then x can be obtained from y by a series of n1 absolute lower end elevations, where the kth lower end elevation raises yi by ykþ1  yk  xkþ1 þ xk
0 for i ¼ 1; . . . ; k; and a translation by xn  yn : (b) The result follows from the above given that xhR y iff lnðxÞhA lnðyÞ: & Difference and ratio dominance are stronger inequality concepts than those prevalent in the literature. Since Pigou (1912) and, especially, Dalton

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(1920) it has been widely accepted that inequality is reduced by a sort of change which cannot necessarily be reduced to changes of the sort discussed above. Definition 4. Say that x can be obtained from y by an (elementary) progressive transfer7 if, for some k and some l40; xk ¼ yk þ l; xkþ1 ¼ ykþ1  l and xi ¼ yi ; i ¼ 1; . . . ; k  1; k þ 2; . . . ; n and x; y 2 Dn (Muirhead, 1903; Pigou, 1912; Dalton, 1920). Well-known results link progressive transfers to the most widely accepted criterion for inequality comparison, that of Lorenz dominance. Pk Definition 5. Say that x LorenzPdominates y, written xhL y; iff i¼1 n ½xi  yi 
0 for k ¼ 1,y, n1, i¼1 ½xi  yi  ¼ 0 and x; y 2 Dn : The Lorenz ordering is equivalent to a relation known as majorisation (Marshall & Olkin, 1979) which is widely used outside of economic contexts. A famous result establishes that xhL y iff x can be obtained from y by a finite series of progressive transfers (Hardy, Littlewood, & Po´lya, 1934; Atkinson, 1970). The Lorenz ordering can be extended to comparisons which do not involve equal means by allowing progressive transfers to be combined with translations and rescalings. Definition 6. (a) Say that x absolute Lorenz dominates y, written xhLA y; iff xhL y þ len for some l (Shorrocks, 1983; Moyes, 1987). (b) Say that x relative Lorenz dominates y, written xhLR y; iff xhL ly for some l40 (Lorenz, 1905). 2.1.2. Orderings on Distributions We can also define analogous orderings more generally on spaces of distribution functions or, equivalently, quantile functions. Such a setting clearly subsumes that of the earlier section, allowing for comparison of income vectors of different dimensions but also of inequality in continuous distributions. Let D denote the space of nondecreasing functions from ½0; 1 to R and Dþ denote the space of nondecreasing functions from ½0; 1 to Rþ : Let DC denote the space of differentiable, nondecreasing functions from ½0; 1 to R and DC þ denote the space of differentiable, nondecreasing functions from ½0; 1 to Rþ :

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If x is distributed according to distribution function F x : R ! ½0; 1; let xx : ½0; 1 ! R be the corresponding quantile function, or inverse distribution function, defined by xx ðpÞ ¼ supfxjF x ðxÞ  pg: We can now define the corresponding orderings defined on distributions. Definition 7. (a) Say that F x hA F y iff xx ðpÞ  xy ðpÞ is nonincreasing for p 2 ½0; 1 and xx ; xy 2 D: (b) Say that F x hR F y iff lnðxx ðpÞÞ  lnðxy ðpÞÞ is nonincreasing for p 2 ½0; 1 and xx ; xy 2 Dþ : Marshall et al. (1967a) and Barlow and Proschan (1975) say that F x is star-shaped with respect to F y if xy ðF x ðxÞÞ=x is increasing. Arnold defines an ordering identical to hR which he calls star-shaped ordering, star ordering or simply -ordering. Suppose that the distributions under comparison and their inverses are differentiable with associated densities f x and f y : Then x0x ðpÞ ¼ 1=f x ðF 1 x ðpÞÞ so that F x hA F y iff f x ðxx ðpÞÞ
f y ðxy ðpÞÞ for p 2 ½0; 1: We can also define absolute and relative Lorenz curves using the quantile functions (see Gastwirth, 1971): Rq R1 LA x ðqÞ ¼ 0 xx ðpÞdp  q 0 xx ðpÞdp Rq R1 LR x ðqÞ ¼ 0 xx ðpÞdp= 0 xx ðpÞdp and thus define Lorenz orderings. Definition 8. A (a) Say that F x hLA F y iff LA x ðqÞ
Ly ðqÞ for all q 2 ½0; 1 and xx ; xy 2 D: R (b) Say that F x hLR F y iff LR x ðqÞ
Ly ðqÞ for all q 2 ½0; 1 and xx ; xy 2 Dþ :

2.1.3. Relations Between Orderings The fact that difference and ratio dominance imply but are not implied by absolute and relative Lorenz dominance is long established. Theorem 2. (Marshall et al., 1967a, 1967b; Jakobsson, 1976; Thon, 1987; Arnold, 1987) (a) If xhA y then xhLA y: (b) If xhR y then xhLR y:

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39

(c) If F x hA F y then F x hLA F y : (d) If F x hR F y then F x hLR F y : The point is that an absolute or relative lower end elevation can always be implemented by a translation or rescaling followed by a finite series of progressive transfers. A lower end elevation obviously raises mean income. Consider a translation or rescaling which leads to the same increase in mean income and following this by redistributing the income increase to those at the lower end by transferring the income gains at the top end down the distribution to those at the bottom. It is not possible on the other hand to implement a progressive transfer by a series of lower end elevations and translations or rescalings. A progressive transfer anywhere other than at the extremes of the distribution raises some income gaps at the same time as it reduces others and we have shown that lower end elevations cannot raise income gaps. We can illustrate the relation between these orderings by showing areas of dominance in comparisons within the standard simplex as in Sen (1973) and many later papers. Imagine looking down at the origin from a point along the ray of equality in the positive orthant of income space with n ¼ 3. Any allocation of a given total income, which we normalise to unity, can be represented as a point in the simplex illustrated in Fig. 1. If we take an

Fig. 1.

Dominance Orderings Illustrated in the Standard Simplex.

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arbitrary initial income vector then the six possible permutations give the vertices of the irregular hexagonal shape shown in the figure. As is well known, the convex hull of these six points represents the set of income vectors which, permuted into appropriate order, Lorenz dominate the initial income vector. Now consider which set of points, appropriately permuted, ratio dominate the initial vector. Ratios between incomes for any two individuals are constant throughout planes containing the third axis, and these planes intersect the simplex along rays passing through its vertices. Points of greater equality between these two are those lying between such rays and the bisecting ray through the same vertex. Hence the area in which all ratios are nearer to unity is the star-shaped8 area outlined in bold within the Lorenz hexagon. Since this fits inside the hexagon, coinciding only at its vertices, it is diagrammatically plain that ratio dominance implies without being implied by Lorenz dominance in comparisons of vectors with equal means. Differences between any two incomes are maintained in planes which cut the simplex along lines perpendicular to its sides. Hence, constructing, as in the ratio-based case, an area in which all differences are diminished gives the inverted Y-shape outlined with dots inside the hexagon. Again this fits entirely inside the Lorenz hexagon except at its vertices. It contains however some points inside and some outside the ratio-based star shape (the areas shaded on the diagram), demonstrating that neither ratio nor difference dominance implies the other.

2.2. Welfare Dalton’s conviction that progressive transfers reduce welfare was motivated by the recognition that if social welfare was the sum of individual utilities which depend only on own income and do so in a concave fashion then such transfers raise social welfare. In comparisons between vectors with equal total income, Lorenz dominance can be identified with improvement in utilitarian social welfare (Hardy et al., 1934; Atkinson, 1970). We can extend this observation to comparisons involving vectors with different means by defining a generalisation of Lorenz dominance. Definition 9. (a) Say xhGL y; iff Pk that x generalised Lorenz dominates y , written n i¼1 ½xi  yi 
0 for k ¼ 1,y, n and x; y 2 D (Kolm, 1969; Shorrocks, 1983).

Inequality and Income Gaps

(b) Say that F x hGL F y ; iff and xx ; xy 2 D:

41

Rq

0 ½xx ðpÞ

 xy ðpÞdp
0 for all q 2 ½0; 1

This ordering is called supermajorisation in the noneconomic context (Marshall & Olkin, 1979). Kolm does not use the term generalised Lorenz dominance but refers to a social preference for distributions which generalised Lorenz dominate others as isophily. Generalised Lorenz dominance is also strongly linked to utilitarian social welfare. Suppose social welfare W : Dn ! R is the sum of individual utilities which are continuous, increasing, concave functions of individual incomes, ui : R ! R: Clearly xhGL y implies W ðxÞ
W ðyÞ: In fact W ðxÞ
W ðyÞ for all social welfare functions with these properties iff xhGL y (Kolm, 1969; Marshall & Olkin, 1979; Shorrocks, 1983). What, though, if utilities are not formed in a purely self-regarding way? Suppose individual utilities ui ðxi ; x  exi Þ depend not only on own income but also on the gaps between own income and the incomes of others.9 For example, suppose individual utilities have the form ui ðxi ; xÞ ¼ ui ðxi Þ þ cðxiþ1  xi Þ where ui has the usual continuous, increasing and concave properties but c is strongly enough decreasing. It is easy to construct an example where a progressive transfer in the middle of the income distribution does not increase social welfare because of the harm done to the utilities of individuals with incomes below the recipient of the transfer. In such a context an absolute lower end elevation, however, would always still increases social welfare because no income would fall and no gap increase. Lower end elevations are the natural basis for welfare comparisons corresponding to the difference and ratio dominance orderings. Let us define two orderings which correspond to income changes which should unambiguously increase social welfare even if income gaps matter to individual well being. Definition 10. (a) Say that xhA y iff xiþ1  xi  yiþ1  yi ; i ¼ 1; . . . ; n  1 and xn
yn with x; y 2 Dn : (b) Say that xhR y iff lnðxiþ1 Þ  lnðxi Þ  lnðyiþ1 Þ  lnðyi Þ; i ¼ 1; . . . ; n  1 and xn
yn for x; y 2 Dnþ : These say that no element in the vector is reduced and either all absolute or all relative gaps are reduced. The link to lower end elevations is obvious.

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Theorem 3. (a) xhA y iff x can be obtained from y by a finite series of absolute lower end elevations. (b) xhR y iff x can be obtained from y by a finite series of relative lower end elevations. These criteria for welfare comparison are plainly stronger than generalised Lorenz dominance since all partial sums of income are obviously increased by changes which raise all incomes. Theorem 4. If xhA y or xhR y then xhGL y We can also define similar orderings over distribution functions for which similar links will hold. Definition 11. (a) Say that F x hA F y iff xx ðpÞ  xy ðpÞ is nondecreasing for p 2 ½0; 1; xx ð1Þ
xy ð1Þ and xx ; xy 2 D: (b) Say that F x hA F y iff lnðxx ðpÞÞ  lnðxy ðpÞÞ is nondecreasing for, p 2 ½0; 1; xx ð1Þ
xy ð1Þ and xx ; xy 2 Dþ :

3. INEQUALITY AND WELFARE INDICES We have seen that progressive transfers increase the sum of concave functions of the individual elements in the vector. The class of functions defined on the vector which are such that they rise with progressive transfers is a wider class than this, first studied by Schur (1923) and known as Schur convex functions. Schur convex functions are those which are said to preserve the Lorenz order. A decreasing function of a Schur convex function is said to be Schur concave. If Lorenz dominance is felt to be a convincing criterion for judging inequality then this is the natural class of functions to use for measuring inequality and most measures proposed for this purpose do fall into this class (although there are notable exceptions such as the variance of logarithms which is infamously not Schur concave, as discussed in Foster & Ok, 1999). Similarly, if generalised Lorenz dominance is felt to be a suitable criterion for judging social welfare improvement then measures of social welfare ought to rise with progressive transfers and therefore to be Schur convex, besides having other properties such as being increasing in all incomes.

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43

In this section of the paper, we discuss the classes of functions of income vectors and distributions which preserve the orderings defined above based on income gaps. We start by defining formally what it means for a function to preserve an ordering. Definition 12. Say that a function f : X ! R preserves an ordering h iff fðxÞ
fðyÞ whenever xhy; x; y 2 X : We consider functions which are differentiable. For this purpose we need a notion of derivative for a mapping defined on a space of functions. Specifically, suppose f : DC ! R is a functional defined on the space of quantile functions. Then we assume the existence of a functional derivative10 R df : ½0; 1 ! R with the property that df cdp ¼ ðd=d
Þ fðx þ
ZÞj
¼0 for x 2 DC and differentiable functions Z : ½0; 1 ! R:

3.1. Inequality Functions which preserve the ratio and difference dominance orderings are characterised in the following result. Theorem 5. n (a) A hA iff Pn Pk differentiable function f : D ! R preserves i¼1 ð@=@xi ÞfðxÞ
0 for k ¼ 1,y, n1 and i¼1 ð@=@xi ÞfðxÞ ¼ 0 (Marshall et al., 1967b). n (b) A Pk differentiable function f : Dþ ! R preserves Pn hR iff i¼1 xi ð@=@xi ÞfðxÞ
0 for k ¼ 1; . . . ; n  1 and i¼1 xi ð@=@xi Þ fðxÞ ¼ 0 (Marshall et al., 1967b). C (c) RA differentiable function11 R 1 f : D ! R preserves hA iff q 0 df dp
0 for qo1 and 0 df dp ¼ 0: (d) A : DC þ ! R preserves hR iff R q differentiable function Rf 1 xdf dp
0 for qo1 and xdf dp ¼ 0: 0 0

Proof of Theorem 5. (a) If xhA y then we can get from y to x by Pa finite series of lower end elevations and a translation. Given ki¼1 ð@=@xi ÞfðxÞ
0 for k ¼ 1,y P , n ¼ 1, the lower end elevations all increase f and given ni¼1 ð@=@xi ÞfðxÞ ¼ P0n the translation leaves it unaffected. It is necessary for i¼1 ð@=@xi ÞfðxÞ ¼ 0 since, for any l, xhA x þ len and x þ len hA x: It is necessary for

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Pk

i¼1 ð@=@xi ÞfðxÞ
0 as f must increase with any lower end elevation. (b) Obvious, noting that ratio dominance is just difference dominance in logarithms. (c) If F x hA F y then xx ¼ xy  Z where Z 2 DC : For any Z 2 DC ; we have:

d fðx 
ZÞj
¼0 ¼  d


Z

1

df Z dp
Z 1  Z ¼  Zð1Þ df dp þ 0

0

0

q

Z0


Z

q

 df dp dq

0

Since, for any R 1 l 2 R; F x hA F y and F y hA F x if xx ¼ xy  le; we must have 0 df dp ¼ 0: Then d fðx 
ZÞj
¼0 ¼ d


Z

q

Z0


Z

0

q

 df dp dq

0

R q and for this to be positive for all increasing Z requires 0 df dp
0 for all q. (d) Obvious, noting that ratio dominance is just difference dominance in logarithms. & The results for orderings on Rn were derived by Marshall et al. (1967b), although the proof and the interpretation here are quite different. The classes of indices derived here are obviously broader than that of Schur convex functions, which are characterised by: @ @ fðxÞ
fðxÞ @xi @xiþ1 Functions appropriate as indices of inequality are, of course, those which preserve the reverse orderings, "A and "R ; and indices which preserve "R but not "LR include, for example, the variance of logarithms. 3.2. Welfare Just as progressive transfers raise welfare as well as reducing inequality, we consider welfare functions which are increased by lower end elevations.

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45

Theorem 6.  n (a) A Pk differentiable function f : D ! R preserves hA iff i¼1 ð@=@xi ÞfðxÞ
0 for k ¼ 1,y, n 1.  n (b) A Pk differentiable function f : Dþ ! R preserves hR iff i¼1 xi ð@=@xi ÞfðxÞ
0 for k ¼ 1,y, n1 (Marshall et al., 1967b).  C (c) A R q differentiable function f : D ! R preserves hA iff 0 df dp
0 for qo1.  C (d) A R q differentiable function f : Dþ ! R preserves hR iff 0 xdf dp
0 for qo1.

Proof of Theorem 6. (a) If xhA y then we can get from y to x by a finite series of lower end Pk elevations. Arbitrary lower end elevations increase f iff i¼1 ð@=@xi ÞfðxÞ
0 for k ¼ 1,y, n 1. (b) Obvious, noting that ratio dominance is just difference dominance in logarithms. (c) If F x hA F y then xx ¼ xy þ eZð1Þ  Z where Z 2 DC : For any Z 2 DC ; we have
Z 1  Z 1 d fðx 
½eZð1Þ  ZÞj
¼0 ¼ Zð1Þ df dp  df Z dp d
0 0  Z q
Z q Z0 df dp dq ¼ 0

0

Rq For this to be positive for all increasing Z requires 0 df dp
0 for all q. (d) Obvious, noting that ratio dominance is just difference dominance in logarithms. & Again these results are partly anticipated by Marshall et al. (1967b) though the treatment is quite different. The conditions for functions to preserve the welfare orderings differ only from those to preserve the equality orderings in that the requirements for invariance to translation and rescaling are dropped. The requirement for nonnegativity of partial sums of derivatives remains. Functions which preserve hA and hR need not be increasing in all incomes but must increase with positive translations and scalings up of incomes, respectively.

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There is a tradition of linking inequality indices with measurement of social welfare going back at least to Dalton (1920) and exemplified by Kolm (1969), Atkinson (1970) and Blackorby and Donaldson (1978, 1980, 1984). To expound the key results here we need to define properties of functions implying certain sorts of response to translations and rescalings. Let e 2 DC þ denote the quantile function which is constant at unity. Definition 13. (a) A differentiable function f : Dn ! R is translatable iff there exists an increasing function g : R ! R and a function c : Dn ! R such that f ¼ gðcðxÞÞ and cðx þ len Þ ¼ cðxÞ þ l: (b) A differentiable function f : Dnþ ! R is homothetic iff there exists an increasing function g : R ! R and a function c : Dnþ ! R such that f ¼ gðcðxÞÞ and cðlxÞ ¼ lcðxÞ: (c) A differentiable function f : DC ! R is translatable iff there exists an increasing function g : R ! R and a function c : Dn ! R such that f ¼ gðcðxÞÞ and cðx þ leÞ ¼ cðxÞ þ l: (d) A differentiable function f : DC þ ! R is homothetic iff there exists an increasing function g : R ! R and a function c : Dnþ ! R such that f ¼ gðcðxÞÞ and cðlxÞ ¼ lcðxÞ: The notion of the equally distributed equivalent income function due to Kolm (1969) and Atkinson (1970) is a crucial one in this literature. For comparisons of vectors define this as w : Dn ! R by fðwðxÞen Þ ¼ fðxÞ and for comparisons of distribution functions define it as w : DC ! R by fðwðxx ÞeÞ ¼ fðxx Þ: Clearly w preserves the same orderings as does f. If f is Schur convex and translatable then subtracting w from mean income gives an index which is Schur concave and invariant to translation. If f is Schur convex and homothetic then the proportional difference between mean income and w gives an index which is Schur concave and invariant to rescaling. In the first case we have an absolute inequality index linked to measurement of welfare and in the latter a relative inequality index – both ideas are found in Kolm (1969) and developed by later authors (Atkinson, 1970; Blackorby & Donaldson, 1978, 1980, 1984). Given that progressive transfers leave mean incomes unchanged it is natural to construct inequality indices intended to preserve the Lorenz ordering by comparison to mean income but this will not work if the index is intended to preserve the orderings based on gaps. Lower end elevations do not leave mean income unchanged. However, we can construct suitable indices by comparison to the maximum income.

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47

Theorem 7. (a) If a differentiable function f : Dn ! R is translatable and preserves hA then yðxÞ ¼ xn  wðxÞ preserves "A : (b) If a differentiable function f : Dnþ ! R is homothetic and preserves hR then yðxÞ ¼ 1  wðxÞ=xn preserves "R : (c) If a differentiable function f : DC ! R is translatable and preserves hA then yðxÞ ¼ xð1Þ  wðxÞ preserves "A : (d) If a differentiable function f : DC þ ! R is homothetic and preserves hR then yðxÞ ¼ 1  wðxÞ=xð1Þ preserves "R : Proof of Theorem 7. (a) If f is translatable that yðx þ Pn then wðx þ len Þ ¼ wðxÞ þ l so P k len Þ ¼ yðxÞ and ð@=@x ÞyðxÞ ¼ 0: For kon, i i¼1 i¼1 ð@=@xi Þ Pk yðxÞ ¼  i¼1 ð@=@xi ÞfðxÞ  0: (b) P If f is homothetic then wðlxÞ ¼ lwðxÞ Pkso that yðlxÞ ¼ yðxÞPand n k ð@=@x Þx yðxÞ ¼ 0: For kon, i i i¼1 i¼1 ð@=@xi Þxi yðxÞ ¼  i¼1 ð@=@xi Þxi fðxÞ  0: (c) If f is translatable then wðx þ leÞ ¼ R1 R q wðxÞ þ l so that R q yðx þ leÞ ¼ yðxÞ and 0 dy dp ¼ 0: For qo1, 0 dy dp ¼  0 df dp  0: (d) If yðlxÞ ¼ yðxÞ and R 1 f is homothetic then wðlxÞ R q ¼ lwðxÞ soR that q xdy dp ¼ 0: For qo1, xdy dp ¼  xdf dp  0: & 0 0 0 Thus, we have a way of constructing inequality indices preserving ratio and difference dominance orderings from social welfare measures with appropriate properties. To take the simplest example, if social welfare is measured by the homothetic and translatable function giving mean income fðxÞ ¼ x¯ ¼ P ð1=nÞ ni¼1 xi ; which is invariant to progressive transfers and therefore yields no interesting Schur concave inequality measure, then the construction Pn just outlined gives measures x  x ¼ ð1=nÞ ½x  xi  and 1  x=x ¯ ¯ n¼ n n i¼1 P 1  ð1=nÞ ni¼1 ½xi =xn ; the mean absolute and relative shortfall from the top income, which do preserve "A and "R ; respectively. A social welfare function which isPtranslatable, homothetic and strictly Schur convex is fðxÞ ¼ ð2=nðn þ 1ÞÞ ni¼1 ðn  iÞxi : The Kolm (1969) procedure gives a relative inequality index 1  wðxÞ=x¯ ¼ G ¼ ð2=nðn þ 1ÞxÞ ¯ Pn i½x  x equal to the well-known Gini coefficient. The procedure out¯ i i¼1 P lined above gives the alternative 1  wðxÞ=xn ¼ ð2=nðn þ 1Þxn Þ ni¼1 ði  nÞ ½xi  xn  which approaches Gx=x ¯ n  3½1  x=x ¯ n  for large n. There exist, though, functions which are Schur convex yet preserve the gap-based

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inequality orderings. Take the social welfare function fðxÞ ¼ ð2=nðn P þ 1ÞÞ Pn n ix : This is Schur concave yet 1  wðxÞ=x ¼ ð2=nðn þ 1Þx Þ n n i¼1 i i¼1 i½xn  xi  is still an inequality measure consistent with "R :

4. INEQUALITY-REDUCING POLICIES Often the purpose to which the inequality orderings are to be put is to compare outcomes under two policy regimes in which incomes are determined by different mappings from some underlying source of variation. For such cases, general results can be derived relating the properties of these mappings to the resulting gaps. Let us assume the underlying variation is in a single dimension and denote the variable in question by z 2 R; distributed according to Fz, drawn from a class of distribution functions F: The outcomes of interest in the two regimes are denoted x and y, where x ¼ fx ðz; F z Þ and y ¼ fy ðz; F z Þ with fx : R  F ! R and fy : R  F ! R continuous and increasing in their first arguments. Then xx ðpÞ ¼ fx ðxz ðpÞÞ and xy ðpÞ ¼ fy ðxz ðpÞÞ: Theorem 8. (a) If x ¼ fx ðz; F z Þ; y ¼ fy ðz; F z Þ with fx : R  F ! R and fy : R  F ! R continuous and increasing in their first arguments then the following are equivalent (i) F x hA F y for all F z 2 F: (ii) fx ðz; F z Þ ¼ gðfy ðz; F z Þ; F z Þ for some function g : R  F ! R such that, for all F z 2 F; gðfy ðxz ðpÞ; F z Þ; F z Þ  fy ðxz ðpÞ; F z Þ is nonincreasing in p for all p 2 ½0; 1: (b) If x ¼ fx ðz; F z Þ; y ¼ fy ðz; F z Þ with fx : R  F ! Rþ and fy : R  F ! Rþ continuous and increasing in their first arguments the following are equivalent (i) F x hR F y for all F z 2 F: (ii) fx ðz; F z Þ ¼ gðfy ðz; F z Þ; F z Þ for some function g : Rþ  F ! Rþ such that, for all F z 2 F; gðfy ðxz ðpÞ; F z Þ; F z Þ=fy ðxz ðpÞ; F z Þ is nonincreasing in p for all p 2 ½0; 1: Proof of Theorem 8. (a) Sufficiency of the condition in (ii) for F x hA F y for all F z 2 F is obvious.

Inequality and Income Gaps

49

If, for some F z 2 F; fx ðz; F z Þ is not a function of fy ðz; F z Þ then there exist p0 ; p1 2 ½0; 1 with p1 4p0 ; such that fy ðxx ðp0 Þ; F z Þofy ðxz ðp1 Þ; F z Þ but fx ðxz ðp0 Þ; F z Þafx ðxz ðp1 Þ; F z Þ: Then it cannot be that, for z distributed as Fz, xx ðpÞ  xy ðpÞ is nonincreasing in p for p 2 ½p0 ; p1 : If fx ðz; F z Þ is a function of fy ðz; F z Þ but there is an Fz and p1 4p0 such that gðfy ðxz ðp1 Þ; F z Þ; F z Þ  fy ðxz ðp1 Þ; F z Þ4 gðfy ðxz ðp0 Þ; F z Þ; F z Þ  fy ðxz ðp0 Þ; F z Þ then again it cannot be that, for z distributed as Fz, xx ðpÞ  xy ðpÞ is nonincreasing in p for p 2 ½p0 ; p1 : (b) Obvious given ratio dominance is difference dominance in logarithms. & Functions g : R ! R such that g(x)/x is increasing are called star-shaped (Bruckner & Ostrow, 1962). If the functions fx and fy, are differentiable in z then the conditions in the theorem reduce to a comparison of derivatives or elasticities – specifically, gðx; F z Þ  x is decreasing in x iff qg/qx is less than unity and gðx; F z Þ=x is decreasing in x iff @ ln g=@ ln x is less than unity. If the functions fx and fy are additively or multiplicatively separated then the role of Fz becomes irrelevant. Finding distributions Fz such that dominance fails in either direction is less restricted and the theorem can be extended to cover not only the inequality orderings based on gaps but also Lorenz dominance. In particular, suppose F includes all distributions with support within Z; x ¼ fx ðzÞcx ðF z Þ; y ¼ fy ðzÞcy ðF z Þ and fx ðzÞ ¼ gðfy ðzÞÞ ¯  Z then we can find a counterwith g(z)/z increasing over an interval Z example in which there is ratio dominance in the reverse direction by ¯ Since ratio dominance implies choosing Fz with support wholly within Z: relative Lorenz dominance then this means g(z)/z falling everywhere is a necessary condition not only for difference dominance but also for Lorenz dominance to hold for all F z 2 F: Theorem 9. (a) If x ¼ fx ðzÞ þ cx ðF z Þ; y ¼ fy ðzÞ þ cy ðF z Þ with fx : R ! R and fy : R ! R continuous and increasing and cx : F ! R and cy : F ! R then the following are equivalent (i) F x hA F y for all Fz with support in Z (ii) F x hLA F y for all Fz with support in Z (iii) fx ðzÞ ¼ gðfy ðzÞÞ for some function g : R ! R such that g(x )x is nonincreasing in x for all xAg(Z)

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(b) If x ¼ fx ðzÞcx ðF z Þ; y ¼ fy ðzÞcy ðF z Þ with fx : R ! Rþ and fy : R ! Rþ continuous and increasing and cx : F ! Rþ and cy : F ! Rþ then the following are equivalent (i) F x hR F y for all Fz with support in Z (ii) F x hLR F y for all Fz with support in Z (iii) fx ðzÞ ¼ gðfy ðzÞÞ for some function g : R ! R such that g(x )/x is nonincreasing in x for all xAg(Z) For cx ¼ cy ¼ 1, the second part of this theorem is the result of Jakobsson (1976). Sufficiency of the condition on g for F x hLR F y to hold for all Fz was recognised by Fellman (1976) and Kakwani (1977). Eichhorn, Funke, and Richter (1984) and Arnold (1987) extend this result to drop the assumption that fx and fy are continuous and increasing. 4.1. Applications 4.1.1. Progressive Taxation and Inequality 4.1.1.1. Fixed Pre-Tax Incomes. Suppose z denotes pre-tax incomes, assumed distributed in a way unaffected by taxation. Let the tax function be t(z) so that post-tax incomes are zt(z). By Theorem 9, the post-tax distribution absolute Lorenz dominates and difference dominates the pretax distribution whatever Fz iff t(z) is increasing in z which is to say that marginal tax rates are everywhere positive (Moyes, 1988). This is a property that Fei (1981) calls minimal progression. The post-tax distribution relative Lorenz dominates and ratio dominates the pre-tax distribution whatever Fz iff t(z)/z is increasing in z which is to say that marginal tax rates are everywhere above average tax rates. This is the property usually characterised as progression. The post-tax distribution dominates the pre-tax distribution iff the tax is progressive in the sense of taking a greater share of the incomes of the rich all the way along the distribution. This result, proved for example in Jakobsson (1976), captures an old idea. Seligman (1894) dates the first recorded occurrence of progressive taxation to Solonic Athens and the first written recognition that it ‘‘will lessen the disparity of fortunes’’ to Guiccardini’s sixteenth century discussion of Florentine taxation, reprinted in Guicciardini (1932).12 One tax system will reduce inequality further than another, in the sense of relative Lorenz dominance and ratio dominance, iff the elasticity of posttax income to pre-tax income – known as residual income progression (Musgrave & Thin, 1948) – is everywhere lower. This is among the results due to Jakobsson (1976).13 Suppose we have a linear tax on pre-tax income,

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t(z) ¼ tzG so that post-tax income is z(1t)+G. Then the elasticity is z=ðz þ G=ð1  tÞÞ so an increase in t reduces inequality. 4.1.1.2. Fixed Pre-Tax Wages. Changes in taxation change work incentives and therefore the distribution of earnings given a fixed distribution of wages. The inequality-reducing effect of progressive taxation is less obvious in such a context. However, the same theorems still provide the tools for assessing necessary and sufficient conditions for reduction in the inequality of incomes.14 Let z now denote wages, distributed again according to F z 2 F: Let individual hours of work be h and taxes be t(zh) so that post-tax income is zht(zh) assuming no other source of income. Chosen hours under the given tax system, h ¼ Z(z), may decline with wage but we assume at least that post-tax income does not, zZ0 ðzÞð1  t0 ðzZðzÞÞ40 – the so-called Mirrlees condition. Then, by Theorem 9, the post-tax distribution under one tax system Lorenz dominates and ratio dominates that under another iff the elasticity of post-tax income to the wage is lower at each wage. This elasticity is the product of residual income progression at zZ(z) and one plus the elasticity of hours Z(z) to z (wherever Z(z)>0). Two new considerations emerge when considering the impact of a progressive tax change. Firstly, labour supply responses may make the distribution of earnings less equal. Secondly, even if residual income progression falls at each level of earnings, labour supply responses could move individuals into less progressive parts of the tax system so that residual income progression need not fall at each wage rate. As an example, consider the case of CES preferences with a linear tax, t(zh) ¼ tzhG. Post-tax incomes are: bzs ð1  tÞs ðzð1  tÞ þ GÞ zð1  tÞ þ bzs ð1  tÞs The elasticity is: ðs  1Þ

zð1  tÞ z þ zð1  tÞ þ bzs ð1  tÞs z þ G=ð1  tÞ

An increase in t reduces the second term but increases the first and there is no guarantee that the expression as a whole falls. Preston (1990b) shows that this is possible for parameter values which are not unreasonable. In

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principle, there exist distributions of pre-tax wages such that inequality is not reduced. 4.1.2. Immigration and Inequality To take a slightly different example, consider the effect of immigration on income inequality in the pre-existing resident population of a country. Suppose what is now fixed is the distribution of productive abilities, zA[0,1], distributed in the resident population of size N according to Fz. The economy employs n(z) workers of type z to produce aRsingle type of 1 output according to a CES technology whereby output is ½ 0 znðzÞs dz1=s with so1. This output is traded internationally at a fixed world price which we normalise to 1. Demand for labour of type z is determined by equating its marginal value product to the wage w(z): znðzÞs1


Z

1

znðzÞs dz

ð1=sÞ1 ¼ wðzÞ

0

Prior to immigration, this defines an equilibrium wage distribution equating demand for labour of type z to its supply, n(z) ¼ Nfz(z). For this to involve wages increasing in z requires that we restrict attention to distributions Fz such that 1+(s1)q ln fz(z)/q ln z40 everywhere.15 Now assume that there is immigration of M ¼ mN workers with ability distributed according to distribution function Iz with density iz. The economy reaches a new equilibrium at which the ratio of new to old wages at labour type z is (1+miz (z)/fz(z))s1. Theorem 8 can be applied. The distribution of wages across pre-existing resident workers is made more equal, in the sense of ratio dominance, whatever Fz iff immigration policy is such as to guarantee iz(z)/fz(z) is increasing at all z so that immigrants are more concentrated in higher earning groups than in the population already resident.

5. CONCLUSION This paper has drawn attention to and argued a case for the interest of inequality orderings based explicitly on closing up of income gaps. Drawing where necessary on earlier papers, the links between these and other orderings have been outlined, the classes of functions preserving the orderings have been characterised and applications have been presented showing their use in comparison of economic policies.

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NOTES 1. Progressive transfers are sometimes called Robin Hood transfers. The Robin Hood of legend stole from the rich to give to the poor. No one would disagree that that reduces inequality. He never, however, stole from the rich to give to the middle or stole from the middle to give the poor. 2. Blum and Kalven (1953), for example, discuss income redistribution in this sort of way. 3. One might raise a similar objection to Sen’s (1976, 1978) strengthened criterion for comparisons of ordinal inequality for cases of more than two persons – STOIC. Recognising this makes it clearer why he finds a link with Lorenz dominance. 4. I am myself grateful to an anonymous referee for bringing the pertinence of this paper and its precedence in proving certain results to my attention. 5. x and y are cone ordered if the difference between them lies in a specified convex cone. If xhA y or xhR y; for example, then the differences between the absolute or relative gaps in the two vectors lie in the particular cone defined by the nonnegative orthant. Majorisation, discussed below, is also a cone ordering. This is a framework which yields useful insights but we do not adopt it here. 6. Kolm regards the view that equal absolute increases in income preserve inequality as ‘‘leftist’’ and the view that equal proportional increases preserve inequality as ‘‘rightist’’. This categorisation could be questioned, particularly if we consider the implications for views on decreases rather than increases in income. Is it more leftist to think that equal absolute cuts in income, as through a poll tax, preserve inequality? While it seems certainly true that the leftist would prefer a given positive sum to be distributed through equal absolute increases than through equal proportional ones it is not obvious that this reflects a view about how inequality should be measured. 7. Progressive transfers are sometimes defined as any transfers from richer to poorer individuals, not necessarily next to each other in the ordering of incomes. The term ‘‘elementary progressive transfer’’ is from Arnold (1987). 8. The coincidence between the name of the star-shaped ordering and the shape of the figure is purely fortuitous. The origin of the name lies in the connection with starshaped functions, as explained below. 9. This sort of dependence is sometimes referred to as envy but that is a somewhat tendentious term, envy, one of the seven deadly sins, being condemned in most ethical codes. The term envy is suggestive of a wish to bring down the incomes of those better off. It need not be supposed that such sentiments are necessarily implied by demoralisation arising from accentuated feelings of social inferiority – indeed the perception that those on higher incomes deserve the high social position that one cannot attain may be precisely the source of deterioration in psychological well being. 10. Suppose that f extends continuously to a function on the space of all continuous functions on the unit interval. Since this is a Banach space under suitable norm k  k we could then, for example, take df to be the Fre´chet derivative defined by:

lim

Z!0

kfðx þ ZÞ  fðxÞ  dfðxÞk ¼ 0. kZk

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11. The assumption that the quantile function is differentiable or even continuous, implicit in the stated domain for f, is probably stronger than needed. However, given the use made of integration by parts in the proof, it would be necessary to introduce a generalisation of the notion of derivative for x, and a careful treatment of the issues involved is beyond the scope of this paper. 12. This is not to say, of course, that one can date this far back recognition of formal criteria for inequality comparison and their relation to properties of the tax system but Guiccardini does say, for example, in discussing the advantages of a particular progressive tax structure that ‘‘so doing, not only shall such benefits follow as I have said, but also the ranks of each shall be equally preserved, since we are all citizens of the same rank, and thus all shall become truly equal as we reasonably should be’’ (‘‘E cosı´ faccendo, non sole ne seguiranno tante utilita´ e tanti beni che ho io detto, ma ancora si conservera´ equalmente el grado di ognuno, perche´ tutti siamo cittadini e di uno medesimo grado, e cosı´ diventereno tutti veramente pari, come ragionevolmente dobbiamo essere’’ ibid., p. 206). 13. Keen, Papapanagos, and Shorrocks (2000) extend Jakobsson’s results to cover the case where taxes on certain ranges of income are zero. 14. We should be wary of linking changes in income inequality to welfare in this context since individual well being depends on both income and hours. 15. If this condition were to fail then it would be appropriated to alter the definition of equilibrium rather than to assume wage might be decreasing in z. Assuming workers of higher ability can do the jobs of less able workers then a sensible definition of equilibrium would equate demand for labour of type z and above to supply of such labour and the equilibrium wage distribution over and around ranges of ability where the condition fails would have flat sections. We assume away this complication here.

ACKNOWLEDGMENTS I am grateful for helpful comments from Tim Besley, Chris Gilbert, Terence Gorman, Chris Harris, Peter Lambert, James Mirrlees, Stephen Nickell, Hyun Shin, seminar participants and an anonymous referee. The paper draws in large part upon my doctoral thesis, for the funding of which I am grateful to the Economic and Social Research Council.

REFERENCES Arnold, B. C. (1987). Majorization and the Lorenz order: A brief introduction. Berlin: SpringerVerlag. Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2, 244–263. Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing: Probability models. New York: Holt, Rinehart and Winston.

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Blackorby, C., & Donaldson, D. (1978). Measures of relative inequality and their meaning in terms of social welfare. Journal of Economic Theory, 18, 59–80. Blackorby, C., & Donaldson, D. (1980). A theoretical treatment of indices of absolute inequality. International Economic Review, 21, 107–136. Blackorby, C., & Donaldson, D. (1984). Ethically significant ordinal indexes of relative inequality. In: R. L. Basmann & G. F. Rhodes (Eds), Advances in econometrics, Vol. 3: Economic inequality: Measurement and policy (pp. 131–147). Greenwich: JAI Press. Blum, W. J., & Kalven, H. (1953). The uneasy case for progressive taxation. Chicago: University of Chicago Press. Bruckner, A. M., & Ostrow, E. (1962). Some function classes related to the class of convex functions. Pacific Journal of Mathematics, 12, 1203–1215. Dalton, H. (1920). The measurement of the inequality of incomes. Economic Journal, 30, 348–361. Dasgupta, P., Sen, A. K., & Starrett, D. (1973). Notes on the measurement of inequality. Journal of Economic Theory, 6, 180–187. Eichhorn, W., Funke, H., & Richter, W. F. (1984). Tax progression and inequality of income distribution. Journal of Mathematical Economics, 13, 127–131. Fei, J. C. H. (1981). Equity oriented fiscal programs. Econometrica, 49, 869–881. Fellman, J. (1976). The effect of transformations on Lorenz curves. Econometrica, 44, 823–824. Foster, J. E., & Ok, E. A. (1999). Lorenz dominance and the variance of logarithms. Econometrica, 67, 901–907. Gastwirth, J. L. (1971). A general definition of the Lorenz curve. Econometrica, 37, 1037–1039. Guicciardini, F. (1932). La decima scalata. In: R. Palmarocchi (Ed.), F. Guiccardini, Opere, Vol. VII: Dialogi e discorsi del regimmento di Firenze. Bari: G. Laterza. Hardy, G., Littlewood, J., & Po´lya, G. (1934). Inequalities. Cambridge: Cambridge University Press. Jakobsson, U. (1976). On the measurement of the degree of progression. Journal of Public Economics, 5, 161–168. Kakwani, N. C. (1977). Applications of Lorenz curves in economic analysis. Econometrica, 45, 719–727. Keen, M., Papapanagos, H., & Shorrocks, A. (2000). Tax reform and progressivity. Economic Journal, 110, 50–68. Kolm, S.-C. (1969). The optimal production of social justice. In: H. Guitton & J. Margolis (Eds), Public economics (pp. 145–200). London: Macmillan. Kolm, S.-C. (1976a). Unequal inequalities I. Journal of Economic Theory, 12, 416–442. Kolm, S.-C. (1976b). Unequal inequalities II. Journal of Economic Theory, 13, 82–111. Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American Economic Association, 9, 209–219. Marshall, A. W., & Olkin, I. (1979). Inequalities: Theory of majorization and its applications. New York: Academic Press. Marshall, A. W., Olkin, I., & Proschan, F. (1967a). Monotonicity of ratios of means and other applications of majorization. In: O. Shisha (Ed.), Inequalities: Proceedings of a symposium (pp. 177–190). New York: Academic Press. Marshall, A. W., Walkup, D. W., & Wets, R. J.-B. (1967b). Order-preserving functions: Applications to majorization and order statistics. Pacific Journal of Mathematics, 23, 569–584. Moyes, P. (1987). A new concept of Lorenz domination. Economics Letters, 23, 203–207.

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Moyes, P. (1988). A note on minimally progressive taxation and absolute income inequality. Social Choice and Welfare, 5, 227–234. Moyes, P. (1994). Inequality reducing and inequality preserving transformations of income: Symmetric and individualistic transformations. Journal of Economic Theory, 63, 271–298. Muirhead, R. (1903). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society, 21, 144–157. Musgrave, R. A., & Thin, T. (1948). Income tax progression 1929–1948. Journal of Political Economy, 56, 498–514. Pigou, A. C. (1912). Wealth and welfare. London: Macmillan. Preston, I. (1989). The redistributive effect of progressive taxation. DPhil thesis, University of Oxford. Preston, I. (1990a). Ratios, differences and inequality indices. IFS Working Paper W90/9. Preston, I. (1990b). Income redistribution and labour supply specification. IFS Working Paper W90/14. Rothschild, M., & Stiglitz, J. (1973). Some further results on the measurement of inequality. Journal of Economic Theory, 6, 188–204. Schur, I. (1923). U¨ber eine Klasse von Mittelbildungen mit Andwungen auf die Determinanttheorie. Sitzungsber Berlin Mathematische Gesellschaft, 22, 9–20. Seligman, E. R. A. (1894). Progressive taxation in theory and practice. Publications of the American Economic Association, 9, 7–222. Sen, A. K. (1973). On economic inequality. Oxford: Clarendon Press. Sen, A. K. (1976). Welfare inequalities and Rawlsian axiomatics. Theory and Decision, 7, 243–262. Sen, A. K. (1978). Ethical measurement of inequality: some difficulties. In: W. Krelle & A. F. Shorrocks (Eds), Personal income distribution (pp. 81–94). Amsterdam: North-Holland. Shorrocks, A. F. (1983). Ranking income distributions. Econometrica, 50, 3–17. Thon, D. (1987). Redistributive properties of progressive taxation. Mathematical Social Sciences, 14, 185–191. Zheng, B. (2007). Utility gap dominances and inequality orderings. Social Choice and Welfare, 28, 255–280.

HOW PROGRESSIVE IS PROGRESSIVE TAXATION? AN AXIOMATIC ANALYSIS$ Udo Ebert and Georg Tillmanny ABSTRACT There is a consensus in the general public that income taxes should be everywhere progressive. Starting from the basic properties normally required, we examine the possibilities of designing everywhere progressive income tax schedules. An axiomatic analysis investigates the (in)consistency of these requirements with further restrictions on the degree of progression. It turns out that everywhere progressive tax schedules have to be maximally progressive or almost proportional in some income range.

1. INTRODUCTION In the theory of optimal income taxation the maximization of a given social welfare function allows us to derive the form and the structure of an optimal

$

This paper is based on an unpublished discussion paper (Ebert & Tillmann, 2004) and it was completed after Georg Tillmann’s death. Udo Ebert owes him a debt of gratitude for his friendship and his collaboration.

Equity Research on Economic Inequality, Volume 15, 57–71 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15004-3

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tax schedule. It has turned out that these schedules are almost always regressive for some income ranges (cf. Tresch, 2002). This is in particular true for Mirrlees’ (1971) optimal nonlinear income tax which is regressive even for the top incomes. On the other hand there seems to be a consensus among voters and politicians that income taxes should be everywhere progressive and that the marginal tax rate should increase with income.1 According to this view, income taxation is an instrument which mainly is to be used for redistribution and for generating a more equal income distribution. This paper investigates the possibilities for defining everywhere or almost everywhere progressive income taxes. The schedules considered have to satisfy the usual properties required for income taxation. Furthermore, several conditions on the degree of progression are introduced. Based on an axiomatic analysis the existence of corresponding tax schedules is examined and their general structure is described. Musgrave and Thin (1948) have suggested four local measures of progression. We will employ residual progression: Using this measure Jakobsson (1976) has shown that one income tax is everywhere more progressive than another one if and only if its net income distribution Lorenz dominates the other net income distribution for arbitrary gross income distributions. An increase in the degree of progression implies an increase in redistribution and yields a decrease in the level of inequality (of net income distributions). This result nicely demonstrates the meaning and relevance of residual progression. Residual progression is therefore the proper measure whenever the redistribution of income is to be examined. Now the questions arise how progressive an income tax should be and how progressive it can be. The first question is related to equity. In the literature two general principles are suggested in order to justify and to design taxes: the benefit principle2 and the ability-to-pay principle. Since we do not consider the government’s expenditure here, we concentrate on the ability-to-pay principle. Given this general framework we put lower and upper bounds and further restrictions on the degree of progression. Thus the analysis is normative and based on general postulates. We then deal with the second question. At first sight it seems that we do not face any problems when a progressive income tax is to be designed: One can choose a tax schedule leading to constant residual elasticity for any degree of progression. Thus progression can remain moderate all the way along the income scale. But things are a little bit more complicated. Such a tax schedule calls for a region of negative tax liabilities and inevitably has a negative marginal tax rate for the lowest incomes. This property is not a mere pathology which can be neglected since this region need not be small,

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but it is an undesired feature of the income tax as the transfer is increasing, and not decreasing with income. One could argue that the introduction of a threshold could remedy this problem: The constant progression schedule can be modified to have a zero bracket amount, i.e. zero taxes up to the point at which the transfer becomes zero. Then indeed the negative tax rates are avoided, but another problem arises. The tax is proportional in the region below the threshold and no longer progressive. Thus we have to deal with this problem in more detail. We will impose a set of usual properties on income tax schedules and will then perform an axiomatic analysis, which demonstrates the limits of progressive taxation. Besides continuity as a regularity condition we require that net income is strictly positive and that the tax schedule is not a transfer everywhere. Furthermore, we postulate that the tax liability has to be increasing in income, i.e. with a taxpayer’s ability-to-pay, and we exclude rank reversals due to taxation by bounding the marginal tax rate from above. Finally, the tax schedule is to be progressive. These properties present a minimal set of necessary properties and define feasible tax schedules. Then we introduce further requirements. It turns out that – whenever one wants to put bounds or further restrictions on the degree of progression – one runs into difficulties. In principle, tax functions can be found for any pattern of progression, but they do not necessarily fulfill the ability-to-pay principle (i.e. the marginal tax rate may be negative for low incomes!). It is impossible to design tax schedules satisfying the usual properties and being only ‘‘moderately’’ progressive. In order to get feasible schedules one has to admit maximal progression at some incomes. Similarly, if one requires that the degree of progression is increasing with income, the tax has to be almost proportional in some income ranges. Thus the analysis shows that – given the ability-to-pay principle – further restrictions (above the normal requirements) cannot easily be implemented. The paper is organized as follows: Section 2 describes a minimal set of basic properties tax schedules should satisfy. In Section 3 further requirements are introduced. Their implications are derived and their consistency with the basic properties is investigated. Finally, Section 4 presents some discussion and offers some conclusions.

2. BASIC PROPERTIES OF TAX SCHEDULES In this section we consider the standard properties we want to impose on income taxes. An income tax schedule is a function T : Rþ ! R

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representing the tax liability TðX Þ of X
0 where X is taxable income. Income is assumed to be exogenous. Now we introduce the properties a feasible tax schedule has to satisfy. B1. (Regularity) T is continuous for all X and continuously differentiable3 for all but a finite number of (strictly positive) incomes. B2. (Positive net income; tax) TðX ÞoX for all X>0 and there is X0 such that TðX 0 Þ40: Continuity excludes any jump in tax liability. The restriction of differentiability is typically met in the real world where piecewise differentiable or piecewise linear income taxes tend to prevail (see e.g. Messere, 1998). The first part of B2 guarantees that net income is always strictly positive when gross income is strictly positive. As an implication we obtain T(0)r0. Subsidies T(X)o0 are admitted, but we postulate that the tax liability is strictly positive for some incomes. Next we turn to equity principles and present two conditions on marginal tax rates. B3. (Ability-to-pay) T 0 ðX Þ
0 for all X
0: B4. (No reranking) T 0 ðX Þ  1 for all X
0: The principle of vertical equity requires that individuals with higher income also have to pay higher taxes (Moyes (1988) labels the condition ‘‘minimal progression’’). According to B3, the tax liability has to be (weakly) increasing in income. This property is related to the ability-to-pay principle and puts the idea of the ‘‘appropriately unequal treatment of unequals’’ (see Lambert, 2001, p. 175) in concrete forms. The principle of horizontal equity is satisfied in our framework a priori since income is the sole indicator of a taxpayer’s ability-to-pay. According to B4, net income should (at least weakly) increase in gross income. Then the ranking of incomes is not changed by taxation, a property which is also postulated by vertical equity. Furthermore, some incentives to increase income are to be left. It is an obvious restriction. The properties examined up to now are standard in tax theory and have no direct implications for the degree of progression. Therefore we finally introduce B5. (Progression) T(X) is progressive for all X>0. Progression is defined in the usual way: A tax schedule T is progressive ¯ Þ ¼ TðX Þ=X is strictly at X>0 if and only if the average tax rate4 TðX

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increasing in income at X. It is a local property and requires an increasing tax burden (measured by the average tax rate). It should be mentioned that it is B5 which rules out taxes with a zero bracket amount. This property is fundamental in the following. It will not be relaxed later in the paper. ¯ Þ=dX might be used as an indicator of progression.5 The derivative dTðX But residual progression seems to be more attractive since it is related to the intensity of the redistribution of income. Residual progression r(X) is defined by the corresponding income elasticity of net income.6 It is well known that the definition of the elasticity can be rearranged (see Lambert, 2001): rT ðX Þ ¼

ð1  T 0 ðX ÞÞX 1  T 0 ðX Þ ¼ ¯ Þ X  TðX Þ 1  TðX

(R)

Thus residual elasticity is determined by the marginal and average tax rate at X and indicates whether the tax is progressive. This relationship will be used in the proofs below at various places. We have for X>0: the tax T is progressive at X 30  rT ðX Þo1: In other words, for a progressive tax schedule a one percent increase in gross income leads to an increase of less than one percent in net income. For later use we define the set R ¼ fr :
Rþ ! ½0; 1Þ
r continuous for all X but a finite number of (strictly positive) incomes}. The properties B1–B5 are basic properties for progressive income tax schedules and are typically satisfied. A linear income tax represents a simple example satisfying these properties: T 1 ðX Þ : ¼ aX  b for 0oao1 and b>0. In the following we want to consider the set T ¼ fT : Rþ ! Rj T satisfies B1–B5}. We call T 2 T a feasible (progressive) tax schedule.

3. THE DEGREE OF PROGRESSION Now we suggest and examine some properties which restrict the degree of progression. In this paper we assume that the general public is interested in redistribution by means of income taxation, but that extreme cases are to be avoided. One extreme situation can be described by r(X)1, i.e. by a proportional income tax T2(X): ¼ aX for 0oao1. In this case there is no redistribution at all (measured by Lorenz dominance). We postulate that redistribution is noticeable, i.e. there is e1>0 such that r(X)r1e1o1 for all X. The constant e1 may be arbitrarily small, but guarantees at least a minimal degree of redistribution. The other extreme situation is given by r(X)0. Then the only tax schedule satisfying this condition is

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T3(X): ¼ Xb for b>0. Here redistribution is complete. Everybody ends up with the same income b. We want to exclude this case of maximal progression, too, and introduce a lower bound e2>0 for r(X). Combining both aspects we obtain a postulate for ‘‘moderate’’ progression which may well be found acceptable by typical voters and politicians favoring redistribution: P1. (Moderate progression) There are e1 and e2 such that 0oe2rr (X)r1e1o1 for all X. In order to examine the implications of P1 we reconsider the linear tax T1(X) and recognize that rT 1 ð0Þ ¼ 0 and rT 1 ðX Þ goes to one when X tends to infinity. In other words, the range of rT 1 is equal to ½0; 1Þ and therefore the linear income tax does not satisfy P1. This result is surprising but has to be expected in view of Proposition 1: Proposition 1. There is no feasible tax satisfying P1. The basic properties B1–B5 and moderate progression P1 are inconsistent. We obtain a typical impossibility result. At the same time we learn that there are limits to the redistribution of income. Obviously we cannot choose a feasible income tax for an arbitrary pattern of progression. Therefore, in the following we want to explore the possibilities of designing progressive taxes. Then we have to weaken P1 in order to get feasible tax schedules. But at first we ‘‘invert’’ the problem: We start from a given pattern of progression, a function of the residual elasticity rðX Þ 2 R and ask the question if there exists any tax function T(X) leading to r(X) (i.e. rT (X) ¼ r(X) for all X>0) and whether it fulfills the basic properties. We establish Proposition 2. For every r 2 R [which satisfies P1] there is a function T : Rþþ ! R; which is continuous and piecewise differentiable, such that rT ðX Þ ¼ rðX Þ for all X>0. If T(0), T 0 ð0Þ exist,7 TðX Þ satisfies B1– B2, B4–B5 [and P1] and there is exactly one X0>0 such that T(X0) ¼ 0. This result is comforting. It shows that for an arbitrary pattern of progression one can find a tax function T(X) generating it. Furthermore, T(X) automatically satisfies all basic properties, but B3. Of course, if r 2 R is chosen appropriately, B3 can be fulfilled along with all other properties: e.g. rðX Þ ¼ ½ð1  aÞX =½ð1  aÞX þ b for 0oao1 and b>0 leads to the linear income tax T1(X) which is feasible (but does not satisfy P1).

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It is clear that – given B1–B2, B4–B5 – the properties B3 and P1 cannot be satisfied simultaneously (cf. Proposition 1). Thus the reason for the inconsistency of B1–B5, and P1 is a conflict between the ability-to-pay principle B3 and the requirement of moderate progression. There are two possibilities: one can do without B3 or one can weaken P1. (By assumption progression B5 is fundamental and non-negotiable.) Ignoring B3, i.e. admitting negative tax rates, leads to a strange type of tax schedule: one gets T(0) ¼ 0 and a subsidy for the lowest incomes X>0 which is increasing (!) with income on some interval ð0; X¯ Þ (see Ebert and Tillmann (2004) and cf. the discussion in the introduction). This seems to be unjust and is not too interesting. Therefore in the following we will alter P1. At first we still postulate a minimal degree of progression, but allow for maximal progression: P2. (Minimal progression) There is 0oe1o1 such that 0  rðX Þ  1 
1 o1

for all X

We know that T3(X) (as an extreme case) satisfies this property. Therefore we can expect to obtain a possibility result: Proposition 3. (a) There exist feasible tax functions T(X) satisfying P2. (b) If T(X) satisfies P2 there is X0>0 such that T(X0) ¼ 0, and8 limX !1 T 0 ðX Þ ¼ 1: The feasible tax schedule fulfilling P2 can be described precisely: In this case low incomes are subsidized, but as an implication of B3 the subsidy is decreasing with income (which leads to maximal progression at X ¼ 0) and the marginal tax rate goes to one if income tends to infinity, i.e. it is almost one for high incomes. Example T3(X) is not the only tax schedule fulfilling P2. There are more attractive ones, e.g. ( aX  b for X  b=a T 4 ðX Þ ¼ 1

X  ðb=aÞ X for X
b=a for 0oao1, b>0, and 0oeo1. In this case we obtain rT 4 ðX Þ 2 ½0; 1  a for XA[0, b/a] and rT 4 ðX Þ ¼
for XA[b/a,N] (i.e. P2 is satisfied). Furthermore, T4(X)o0 for Xob/a and T 04 ðX Þ ¼ 1 
X
1 tends to one for X-N. Thus dropping the strictly positive lower bound of r(X) allows us to get feasible income taxes guaranteeing a minimal degree of redistribution. Next we introduce another way of restricting the degree of progression. r(X) is by

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definition an elasticity: An increase of gross income X by one percent increases net income by r(X) percent. Progression implies that r is smaller than unity. One can argue that r(X) should decrease or at least not increase with income X. Therefore, assuming that the tax functions T(X) are twice and the functions of the residual elasticity r(X) are once piecewise continuously differentiable we suggest the property P3. (Nondecreasing progression) r(X) is nonincreasing ðr0 ðX Þ  0Þ for all X. which reflects this idea.9 In this case the degree of redistribution does not decrease with income. A direct implication is the requirement r(X)rr(0) for all X, i.e. the degree of progression for the lowest income forms an upper bound. Furthermore, this property rules out (piecewise) linearity and it has an immediate consequence: Lemma 1. [P3 and rT (X)>0] or decreasing progression [r0T ðX Þo0; the strict form of P3] implies that T 0 ðX Þ strictly increases (i.e. T 00 ðX Þ40 for all X>0). The Lemma shows that – given B3 – the property P3 implies that T(X) is convex. The converse is not true: Consider the tax function T 5 ðX Þ : ¼ aX  gX
for g40; 0oao1, and eo1: then T 00 ðX Þ40; but also r0T 5 ðX Þ40 for all X. Therefore the property P3 is weaker than the assumption that the marginal tax rate is increasing. Now we combine both ideas of refining the concept of progression: We impose P3 and restrict the range of r again. Then we obtain the following results: Proposition 4. (a) There is no feasible tax function T(X) satisfying P3 and the condition 0orT (X)o1 for all X. (b) A feasible tax function T(X) satisfies P3 and the condition 0rrT (X)o1 for all X if and only if there is b>0 such that T(X) ¼ T3(X) ¼ Xb. (c) There exist feasible tax functions T(X) satisfying P3, 0orT (X) and rT (0) ¼ 1. Then T(0) ¼ 0, T(X)>0 and T 00 ðX Þ40 for all X>0 and limX !1 T 0 ðX Þ ¼ 1: Part (a) shows that the ability-to-pay principle (B3) and mild progression ð0orðX Þ  rð0Þo1Þ are not compatible with each other. Therefore we extend the range of r(X): If maximal progression is admitted (0rr(X))

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exactly one tax schedule satisfies the conditions imposed in (b). T3(X) implies the leveling of incomes and is not acceptable in practice. Thus we admit r(0) ¼ 1 in (c). Then the tax function can be proportional for X ¼ 0 and ‘‘nearly proportional’’ for low incomes. Indeed, this proceeding is successful. We obtain convex tax schedules. An example is T 6 ðX Þ : ¼ X 2 =ðX þ 1Þ: It satisfies rT 6 ðX Þ ¼ 1=ðX þ 1Þ: Furthermore, it is interesting to note, that the marginal tax rate for this type of schedule must go to one for high incomes though r(X) could be constant and strictly positive for high incomes. It also turns out that incomes are never subsidized. Finally we get a further, simple result by inspection of Propositions 3 and 4(c): Corollary 1. Assume that limX !1 T 0 ðX Þo1 for a feasible tax schedule T(X). Then T(X) cannot satisfy P2 or P3. Both properties, minimal and nonincreasing progression, require that the marginal tax rate tends to 100% for high incomes. In the next section we will discuss some further aspects.

4. DISCUSSION AND CONCLUSION We have used the terms ‘‘low incomes’’ and ‘‘high incomes’’ (X-N). These terms are vague, but it has to be stressed that the corresponding income ranges are not necessarily negligible or irrelevant in practice. The reason is simple: One can scale up or down any given income interval appropriately by defining another tax schedule which possesses the same properties as the original one. Suppose e.g. that incomes are subsidized on the interval ð0; aÞ or that the marginal tax rate is greater than 99% on the interval (a, N) ^ Þ: for a given schedule T(X). Then one can define a new tax schedule TðX ¼ gTðX =gÞ for g>0. In this case, the essential properties of T at X ¯^ X^ Þ ¼ TðX ¯ Þ; are inherited by T^ at X^ ¼ gX : One obtains T^ 0 ðX^ Þ ¼ T 0 ðX Þ; Tð ^ and rT^ ðX Þ ¼ rT ðX Þ: If e.g. g ¼ 10:000; it means that X measures income in 10.000h. Thus the results presented above are also relevant for tax policy since we can find tax schedules used in practice which possess these properties. Finally we comment on the property limX !1 T 0 ðX Þ ¼ 1 implied in Propositions 3 and 4(c). If the marginal tax rate tends to one for X-N, one would expect that the tax schedule is highly progressive. This need not be the case. Consider e.g. the tax schedule T 7 ðX Þ : ¼ ðX þ 1Þ  ðX þ 1Þ


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for 0oeo1. It is feasible and we get T 07 ðX Þ 

1

X ðX þ 1Þ
1 ; and r0T 7 ðX Þ  0. ; r ðX Þ ¼ T 7 ½ðX þ 1Þ
 1 ðX þ 1Þ1


Therefore we obtain T 07 ð1Þ ¼ 1; but rT 7 ð1Þ ¼
: Though the marginal tax rate goes to one, any (nonextreme) degree of progression e, 0oeo1, can be attained in the limit. The above analysis demonstrates that a great variety of feasible tax schedules exists. But whenever one wants to restrict the pattern of progression further, problems arise. Taxes with an easy-to-understand degree of moderate progression have an undesired property (negative tax rates). Once we seek to rule out this feature, in fact no schedule survives: A feasible tax schedule cannot satisfy the property ‘‘moderate progression’’ (P1). Therefore we relax conditions, one by one, to investigate the sort of taxes which are after all possible. It turns out that one has to admit the possibility of maximal progression: Then a feasible tax schedule fulfilling P2 subsidizes low incomes and taxes all other incomes. We find maximal progression at an income of zero since the subsidy is (absolutely) decreasing with income. Similarly, if it is required that residual progression does not increase with income (P3), we have to admit the possibility that the tax schedule is proportional at X ¼ 0 (leaving aside the particular situation in which we get T 3 ðX Þ ¼ X  b). In this case all incomes are taxed. The income tax is convex in income. Moreover, P2 and P3 imply that the marginal tax rate tends to one for high incomes. Most of the restrictions on the degree of progression, which have been considered in this paper, are problematic at the boundaries of the income range.

NOTES 1. See Roemer (1999) for a political economy of progressive income taxation and Lambert (2001) for a discussion of the ‘progressive principle’ and its justification. 2. Ebert and Tillmann (2007) derive tax schedules by means of the benefit principle. 3. We assume that in X ¼ 0 the right limit exists and that there is nZ0 such that in X i ; i ¼ 0; :::; n; the left and the right limits exist. ¯ 4. Below we assume that the limit Tð0Þ exists. 5. This measure has also been suggested in Lambert (1984) as appropriate for exploring the revenue responsiveness properties of a progressive income tax as incomes grow.

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6. rT (X) may be discontinuous at a finite number of (strictly positive) incomes. Again we then consider the left and right limits. 7. In most cases the limits Tð0Þ and T 0 ð0Þ will exist, but it is well known that there are functions f (X), differentiable for all X>0, for which these limits do not exist (e.g. f (X) ¼ sin(1/X)). For the rest of the paper we exclude these cases. 8. We have to assume that limX !1 T 0 ðX Þ exists. 9. This condition is necessary and sufficient for an equiproportionate growth in all incomes to reduce after-tax inequality (see Moyes, 1989).

ACKNOWLEDGMENT Helpful comments and suggestions by Peter Lambert and a referee are gratefully acknowledged.

REFERENCES Dieudonne´, J. A. (1969). Foundations of modern analysis. New York: Academic Press. Ebert, U., & Tillmann, G. (2004). How progressive is progressive taxation? Wirtschaftswissenschaftliche Diskussionsbeitra¨ge V-257-04. University of Oldenburg, Oldenburg. Ebert, U., & Tillmann, G. (2007). Distribution-neutral provision of public goods. Social Choice and Welfare, forthcoming. Jakobsson, U. (1976). On the measurement of the degree of progression. Journal of Public Economics, 5, 161–168. Lambert, P. J. (1984). Non-equiproportionate income growth, inequality, and the income tax. Public Finance, 39, 104–118. Lambert, P. J. (2001). The distribution and redistribution of income (3rd ed.). Manchester: Manchester University Press. Messere, K. C. (Ed.) (1998). The tax system in industrialized countries. Oxford: Oxford University Press. Mirrlees, J. A. (1971). An exploration in the theory of optimum income taxation. Review of Economic Studies, 38, 175–208. Moyes, P. (1988). A note on minimally progressive taxation and absolute income inequality. Social Choice and Welfare, 5, 227–234. Moyes, P. (1989). Equiproportionate growth of incomes and after-tax inequality. Bulletin of Economic Research, 41, 287–294. Musgrave, R. A., & Thin, T. (1948). Progressive taxation in an inflationary economy. Journal of Political Economy, 56, 498–514. Roemer, J. E. (1999). The democratic political economy of progressive income taxation. Econometrica, 67, 1–19. Tresch, R. W. (2002). Public finance, a normative theory. Amsterdam: Academic Press.

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APPENDIX At first we prove some technical results used later on. Lemma A. ¯ ¯ (1) If Tð0Þ ¼ 0 and T 0 ð0Þ exists, then Tð0Þ exists and Tð0Þ ¼ T 0 ð0Þ: ¯ (2) Let TðX Þ satisfy B2, B4, and B5 and let Tð0Þ exist. (a) If Tð0Þ ¼ 0 then (i) 1oT 0 ð0Þ  1 ) rT ð0Þ ¼ 1 (ii) ½T 0 ð0Þ ¼ 1 and rT ð0Þ exists ) rT ð0Þ 2 ½0; 1 (b) Tð0Þo0 ) rT ð0Þ ¼ 0 ¯ ¯ (3) If T 0 ð1Þ exists, then Tð1Þ exists and Tð1Þ ¼ T 0 ð1Þ: 0 (4) T ð1Þo1 ) rT ð1Þ ¼ 1: Proof. ¯ Þ ¼ Tð0Þ: ¯ (1) T 0 ð0Þ ¼ limX !0 ðTðX Þ  Tð0ÞÞ=ðX  0Þ ¼ limX !0 TðX 0 0 00 (2) (a) (i) If T ð0Þ ¼ 1 we get TðX Þ ¼ Tð0Þ þ T ð0ÞX þ T ðZÞX 2 =2 with Z 2 ð0; X Þ by Taylor’s formula and then TðX Þ ¼ X þ T 00 ðZÞX 2 =2: B2 yields that T 00 ðZÞo0: Then T is not progressive. Suppose now that 1oT 0 ð0Þo1: Then 1  T 0 ðX Þ ¯ Þ X !0 1  TðX 1  lim T 0 ðX Þ ¼1 ¼ 1  lim T 0 ðX Þ

rT ð0Þ ¼ lim rT ðX Þ ¼ lim X !0

(a)

(b)

by ð1Þ

(ii) Suppose that T 0 ð0Þ ¼ 1: For T 0 ðX Þo0 we have ¯ Þ: This implies that Tð0Þ ¯ ¯ Þ ¼ 1: 04T 0 ðX Þ4TðX ¼ limX !0 TðX Since rT ð0Þ exists by assumption, the limit limX !0 rT ðX Þ ¼ ¯ ÞÞ exists, too. We obtain 0  rT ð0Þ limX !0 ð1  T 0 ðX ÞÞ=ð1  TðX  1: Some examples in Ebert and Tillmann (2004) demonstrate that for every a 2 ½0; 1 there is TðX Þ such that rT ð0Þ ¼ a: Now suppose that Tð0Þ ¼ : Ao0: (i) If T 0 ð0Þ 2 R; the numerator 1  T 0 ð0Þ is finite and we get ð1  T 0 ð0ÞÞ ¼0 X !0 ð1  TðX Þ=X Þ

rT ð0Þ ¼ lim

since TðX Þ=X ! 1

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69

(ii) Suppose that T 0 ð0Þ ¼  1: We define GðX Þ : ¼ TðX Þ þ A: Then Gð0Þ ¼ 0 and G 0 ðX Þ ¼ T 0 ðX Þ: Taylor’s formula yields Gð0Þ ¼ GðX Þ þ G0 ðX Þð0  X Þ þ G00 ðZÞX 2 =2 with Z 2 ð0; X Þ and thus GðX Þ þ G 00 ðZÞX 2 =2 ¼ G 0 ðX ÞX : If G 0 ð0Þ ¼ þ1 then G 00 ðX Þo0 in a small neighborhood of 0. Then 0  G 0 ðX ÞX ¼ GðX Þ þ G 00 ðZÞX 2 =2oGðX Þ and GðX Þ ! 0 implies that G 0 ðX ÞX ! 0: If G0 ð0Þ ¼ 1 then G 00 ðX Þ40 in a neighborhood of 0 and 0
G0 ðX ÞX ¼ GðX Þ þ G 00 ðZÞX 2 =24GðX Þ: GðX Þ ! 0 implies that G 0 ðX ÞX ! 0: Thus always limX !0 0 G ðX ÞX ¼ 0: Now limX !0 rT ðX Þ ¼ limX !0 ðð1  T 0 ðX ÞÞX Þ= ðX  TðX ÞÞ ¼ limX !0 ðX  G0 ðX ÞX Þ=ðX  TðX ÞÞ ¼ 0 since limX !0 ðX  TðX ÞÞ ¼ A40: (3) Assume that limX !0 T 0 ðX Þ ¼ : B exists. Then for all e40 there exists X(e) such that B 
 T 0 ðX Þ  B þ
for all X
X ð
Þ: On the other ¯ Þ ¼ ðTðX ð
ÞÞ þ ½TðX Þ  TðX ð
ÞÞÞ=X and TðX Þ  TðX ð
ÞÞ ¼ TðX Rhand X 0 T ðZÞ dZ: X ð
Þ Then we obtain ðB 
Þ

ðX  X ð
ÞÞ TðX Þ  TðX ð
ÞÞ  X X ðX  X ð
ÞÞ  ðB þ
Þ and X

¯ Þ¼B lim TðX

X !1

¯ (4) Since Tð1Þ ¼ T 0 ð1Þ by (3) we obtain limX !1 rT ðX Þ ¼ ð1  lim 0 ¯ ÞÞ ¼ 1: T ðX ÞÞ=ð1  lim TðX Proof of Proposition 1. B1, B2, B4, and B5 allow us to apply Lemma A (2). rT ð0Þ ¼ 0 or rT ð0Þ ¼ 1 and P1 lead to a contradiction. Thus T 0 ð0Þ ¼ 1 which contradicts B3. & Proof of Proposition 2. (i)

Existence: Let rðX Þ 2 R: If there is a (tax) function T(X) leading to the residual progression rðX Þ; it must satisfy (cf. the definition (R)): T 0 ðX Þ ¼ 1  rðX Þ þ

rðX Þ TðX Þ X

(*)

It is a linear inhomogeneous first-order differential equation. As 1r(X) and r(X)/X are continuous for all X>0 there is a (up to a constant) unique solution T(X) (Dieudonne´, 1969).

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(ii) T(X) is differentiable for all X>0. (iii) Now assume that rðX Þ is continuous in the intervals ½0; X 1 Þ; ðX 1 ; X 2 Þ; . . . ; ðX n ; 1Þ: There is always a (up to a constant) unique solution of (*) in each interval. These solutions can be combined such that the resulting tax function T(X) is continuous and almost everywhere differentiable. Then B1 is satisfied if we assume that Tð0Þ and T 0 ð0Þ exist. (iv) There is a unique solution T(X) s.t. TðZ 0 Þ ¼ T 0 for every ðZ 0 ; T 0 Þ: If T 0 ¼ Z 0 the solution is T 1 ðX Þ ¼ X : It satisfies T 1 ð0Þ ¼ 0: Now choose T 0 s.t. 0oT 0 oZ 0 : Then the solution T 2 ðX Þ fulfills T 2 ðX ÞoX for all X>0 since T 1 and T 2 must not intersect. This proves B2. (v) Rearranging (R) we obtain T 0 ðX ÞX  TðX Þ ¼ ð1  rðX ÞÞ ðX  TðX ÞÞ: Since rðX Þo1 and TðX ÞoX ; the function TðX Þ is progressive B5. (vi) We rewrite (R) again and obtain X ð1  T 0 ðX ÞÞ ¼ rðX ÞðX  TðX ÞÞ: Then rðX Þ ¼ 0 implies T 0 ðX Þ ¼ 1: rðX Þ40 and B2 yield 0 T ðX Þo1: Thus we get B4. (vii) There is X 0 40 such that TðX 0 Þ ¼ 0: Suppose TðX Þ40 for all X>0, (*) yields that T 0 ðX Þ40: B2 then implies that Tð0Þ ¼ 0: If T 0 ð0Þ exists, ¯ we obtain T 0 ð0Þ ¼ 1  rð0Þ þ rð0ÞTð0Þ or ðT 0 ð0Þ  1Þð1  rð0ÞÞ ¼ 0: 0 0 For 0  T ð0Þ  1 we get T ð0Þ ¼ 1 or rð0Þ ¼ 1; i.e. in each case rð0Þ ¼ 1 in view of Lemma A (2) (a) (i). Then T cannot be progressive. (viii) There exists at most one X0 such that TðX 0 Þ ¼ 0: (*) implies that T 0 ðX 0 Þ ¼ 1  rðX 0 Þ ¼ 0 and T 0 ðX Þ41  rðX Þ for X 4X 0 : (ix) If P1 is imposed, B3 cannot be satisfied because of Proposition 1. & Proof of Proposition 3. See Proposition 2 and example T 4 ðX Þ: ( aX  b for X  b=a T 4 ðX Þ ¼ 1

X  ðb=aÞ X for X
b=a ¯ If T 0 ð1Þ exists, then Tð1Þ ¼ T 0 ð1Þ: Suppose that T 0 ð1Þo1; then rT ð1Þ ¼ 1 by Lemma A (4), a contradiction. Thus T 0 ð1Þ ¼ 1: Proof of Lemma 1. Differentiate (*):    0 TðX Þ  X TðX Þ 00 0 T ðX Þ ¼ r ðX Þ þ rðX Þ X X Then T00 (X)>0 for [r0 (X)r0 and rðX Þ40] or r0 (X)o0.

&

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Proof of Proposition 4. (a) Since rT ð0Þ40 we get T 0 ð0Þ ¼ 1 by Lemma A (2) (a) (ii), a contradiction to B3. (b) If rT ð0Þ ¼ 0 then r0T ð0Þ ¼ 0 and thus TðX Þ ¼ X  b is the only function satisfying (*). (c) Example T 6 ðX Þ guarantees existence. If rT ð0Þ40 then Tð0Þ ¼ 0 by Lemma A (2) (b). B3 implies T 0 ðX Þ
0: The conditions 0orT ðX Þ and r0T ðX Þ  0 imply T 00 ðX Þ40 (Lemma 1). Thus TðX Þ40 for X 40: Since rT ð1Þo1 we obtain T 0 ð1Þ ¼ 1 by Lemma A (4). &

INEQUALITY AND THE CHOICE OF THE PERSONAL TAX BASE Nigar Hashimzade and Gareth D. Myles ABSTRACT It is possible to employ either income or expenditure as the base for personal taxation. A considerable literature has developed that investigates the relative efficiency of these bases. The answer is usually in favor of the expenditure tax since it does not distort the choice between consumption and saving. In contrast, the literature is almost silent on the relative equity of the two bases. We investigate the redistributive consequences of the choice in models with two sources of heterogeneity: skill in employment and lump-sum endowment. The Gini coefficient is used to measure the degree of equity achieved by the tax bases in static and dynamic settings. Income taxes and expenditure taxes that generate equal welfare or equal revenue are compared. In the static economy the income tax leads to lower inequality except when skill and endowment are negatively correlated. Inequality is always lower with the income tax in the dynamic economy. These results support the choice of income as the base for personal taxation if reduction in inequality is a priority of policy.

1. INTRODUCTION Equity will feature high on any list of the properties that a good tax system should possess. Horizontal equity simply requires that equals are treated Equity Research on Economic Inequality, Volume 15, 73–97 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15005-5

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equally. The interpretation of vertical equity is more open to debate. The idea that vertical equity implies redistribution from the fortunate to the less fortunate is generally accepted. What is disputed is how to define the fortunate, and the extent of justifiable redistribution. Since Mirrlees (1971), the theory of taxation has focused on the possession of a high level of (unobserved) skill as the characteristic of good fortune and has viewed (observed) income as the market signal of skill. Within this literature attention has focused on the link between the redistributive motives of the government and the structure of the optimal tax function (see Hashimzade & Myles, 2007). The choice of the personal tax base from an equity perspective has received little attention. The argument for employing expenditure, rather than income, as the base for taxation has a long and distinguished history. There are claims that it can be traced back to Hobbes (1660) (see Batina & Ihori, 2000), but certainly both Mill (1888) and Ramsey (1927) argued that saving should be exempt from taxation – precisely the feature that distinguishes an expenditure base from an income base. Some of the strongest arguments in favor of an expenditure tax were made by Kaldor (1955) and the Meade (1978) review of taxation in the UK. The use of an expenditure tax was also proposed in the US (see US Treasury Department, 1942). Despite this, expenditure taxation has been adopted in just two countries (India and Sri Lanka), and then only briefly. Most academic discussion has focused on the efficiency benefit of expenditure taxation, with little said on the equity aspects. One exception is Kaldor (1955), but his discussion of ‘‘taxable capacity’’ does not correspond well to modern concepts of tax theory. The contribution of this paper is to provide an assessment of the relative success of expenditure taxation and income taxation in achieving equity objectives. Why might an expenditure tax be preferred to an income tax? At least three reasons are normally cited. First, an income tax distorts the choice between consumption and saving but an expenditure tax does not. Second, an expenditure tax allows integration of the tax treatment of the personal and corporate sectors. Third, an expenditure tax removes the need to distinguish between capital gains and income. The second and third points may have relevance from an administrative perspective. From the perspective of economic analysis the major point is the first. If income is the basis for taxation then the return to saving is taxed. The taxation of income from saving raises the relative price of future consumption. This provides a disincentive to save and, it is generally claimed, reduces the aggregate level of saving and hence of national income. If expenditure forms the base for taxation, savings are only taxed when expenditures are made. This

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eliminates the distortion in the saving decision. This point is developed further in Auerbach (2006). Economic analysis of the choice of tax base has employed a range of models to address this efficiency argument. The starting point for understanding much of the analysis is the result of Chamley (1986) and Judd (1985) that the long-run tax on capital should be zero. The inefficiency of the tax on capital income is emphasized by the welfare calculations of Chamley (1981) and his observation that the replacement of a capital tax by a lumpsum tax leads to an increase in consumption and welfare. These results point to an efficiency advantage for the expenditure tax rather than the income tax. Additional results have been obtained from simulations using overlapping generations economies. Altig, Auerbach, Kotlikoff, Smetters, and Walliser (2001) employ the Auerbach–Kotlikoff model (overlapping generations with each consumer living 55 years) and show that both a flat tax and a consumption tax raise national income compared to a proportional income tax. Furthermore, the consumption tax raises national income by more. Endogenous growth models have also displayed the property that a switch from an income tax to an expenditure tax raises the growth rate (see the survey in Myles, 2000). The literature has much less to say on the equity implications on the choice between the tax bases. Comments have been made about the morality issues (an income base taxes what you put into the economy, an expenditure base taxes what you take out) but this is not what normally determines the choice between tax instruments. One approach to an assessment of the equity implication has been to calculate the effects of reform using data from tax filing. Feenberg, Mitrusi, and Poterba (1997) contrast income taxes and retail sales tax with various exemptions and find that the average tax burden rises for most of the low income groups when a retail sales tax is used. However, such analysis does not take account of re-optimization by consumers or equilibrium adjustments. The theory of equity requires taxes to compensate for differences in lifetime utility generated as the consequence of unchangeable characteristics that are not the result of economic choices. For example, the Mirrlees (1971) model of income taxation summarized such characteristics in the level of skill. Having a higher level of skill raises economic opportunities and therefore puts high skill consumers in a potentially better situation – but it remains a choice whether to take advantage of the opportunity. The first-best tax system involves a lump-sum tax levied on the value of these unchangeable characteristics to provide compensation for those less fortunate in the allocation (i.e. those with lower skill in the Mirrlees’s model).

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From this perspective an income tax can be viewed as an approximation to the first-best lump-sum tax on earning potential. The potential for greater earned income is not the only source of inequality. Inequality can also be due to unearned wealth (such as bequests). It is worth noting that unearned wealth is not subject to tax when income is chosen as the tax base. In contrast, an expenditure tax does tax this wealth when it is consumed. The taxes, therefore, have different impacts on the two sources of inequality and it may be thought that the expenditure tax will be more redistributive since it taxes both sources (earned and unearned) of finance for consumption. Some theoretical work on these lines has been undertaken by Correira (2005) who combines the two sources of inequality. Her main result is to show that an increase in the consumption tax with a corresponding reduction in the income tax raises efficiency. What we do in this paper is build upon the recognition of the two sources of inequality and their interaction with the choice of tax base in achieving redistribution. This is undertaken by extending the standard model of income taxation to incorporate variation in initial wealth and variation in skill across the population. We then contrast the success of the income tax to that of the expenditure tax in reducing inequality. There is clearly an open question here about which will be the most successful. The income tax does not tax initial wealth but the expenditure tax is a blunter tool when it comes to taxing skill. A priori, there is apparently a trade-off between the relative benefits of the two instruments. It is helpful at this point to describe how we implement the analysis. The idea of judging the redistributive success of alternative tax instruments is clearly open to a number of potential interpretations. To make the idea concrete a framework for coherent comparison has to be developed. What we choose to do is to measure inequality using the Gini coefficient applied to lifetime income. We then contrast the value of the Gini achieved by income taxation to that achieved by expenditure taxation. To ensure comparability we make these comparisons at both equal levels of welfare and at equal levels of government revenue. That is, we set the income tax rate, compute the level of welfare (or revenue) and then find the expenditure tax rate that generates the same level of welfare (or revenue). The Gini coefficients are then computed and contrasted. These comparisons are made in both a static economy and a dynamic economy. It is worth noting that government revenue is distributed as a lump-sum grant to consumers and that the grant is the only income for the poorest households. Holding revenue constant is therefore equivalent to holding welfare constant for a Rawlsian social welfare function. Since we make our welfare comparison using the

Inequality and the Choice of the Personal Tax Base

77

utilitarian criterion these two experiments span the range of values for the importance given to equity. The key element in the dynamic economy is the process through which skill is transmitted from parent to child. We choose to model this directly via the probability that a high-skill parent has a high-skill child (and similarly for a low-skilled parent). An extended approach could consider the education decision as standing between innate ability (transmitted probabilistically from parent to child) and labor market skill. The level of education is determined partly by parental wealth, partly by incentives, and partly by government policy as in Blumkin and Sadka (2005). The first of these factors will typically enhance inequalities in ability, whereas education policies are invariably redistributive (see Hanushek, Leung, & Yilmaz, 2003). Incentives can work in either direction. Recent evidence (Ja¨ntti et al. (2005)) shows there are substantial earnings persistence across generations, which suggests that the redistributive effect of education is limited. In any case, the probabilities we use can be understood as a reduced form representation of this set of interactions. From this perspective we use a range of transmission probabilities in order to encompass the possible mappings between wealth, education, and skill. The second section of the paper presents the comparison in a static economy which is an extension of the standard Mirrlees’s framework. Section 3 contrasts the two taxes in an overlapping generations model with bequests. Conclusions are given in Section 4.

2. STATIC ECONOMY This section contrasts the success at achieving equity of the income and expenditure taxes in a static economy. The economy has two periods and a population of consumers who differ in income and initial endowment. In the first period each consumer makes a labor supply decision and allocates income between consumption and saving. Consumers are retired in the second period and finance consumption from saving. The economy is static, but the fact that saving plays a key role in smoothing consumption across the lifecycle allows the effect of income and expenditure taxes to be distinguished. 2.1. Model Consumers are differentiated by two characteristics: initial endowment and skill in employment. The level of skill is measured by the wage rate received.

78

NIGAR HASHIMZADE AND GARETH D. MYLES

Types and Labeling.

Table 1.

wL wH

eL

eH

LL HL

LH HH

The endowment of consumer h is denoted eh and the wage received per unit of labor supply is denoted wh. A consumer is described by the pair {eh, wh}. The initial endowment can take one of two values, eL and eH, with eLoeH. eL is called the low endowment and eH the high endowment. The level of skill can also take two values. The low skill level is wL and the high skill level is wH, with wLowH. The economy, therefore, has four types of consumer. The labeling of these types is summarized in Table 1. The population size is fixed so it is the proportion of each type that is relevant for measuring welfare and inequality. Let ph denote the proportion of P population that is of type h, hA{LL, LH, HL, HH}. By definition h ph ¼ 1: Using the labeling of types we have
X 2 X ph e2h
ph e h (1) s2e ¼ Similarly, s2w ¼

X

ph w2h



X

ph wh

2

(2)

and sew ¼

X

ph eh wh


X

ph e h

X

ph wh

(3)

The correlation between endowment and skill plays a key role in the interpretation of our results. The correlation coefficient is defined by r ¼ sew/sesw. Each consumer lives for two periods. They work during the first period of life and are retired in the second period. In the absence of taxation the first- and second-period budget constraints for a consumer of type h are x1h þ sh ¼ ‘h wh þ eh

(4)

x2h ¼ ð1 þ rÞsh

(5)

and

Inequality and the Choice of the Personal Tax Base

79

where ‘h is labor supply, sh is saving, and r is the (fixed) interest rate. These per-period budget constraints combine to give the lifetime budget constraint x1h þ

x2h ¼ ‘ h w h þ eh 1þr

(6)

The labor supply and consumption choices are made to maximize the utility function Uðx1h ; x2h ; ‘h Þ ¼ a lnðx1h Þ þ ð1
aÞ lnð1
‘h Þ þ d lnðx2h Þ

(7)

This specification of utility assumes that all consumers have the same preferences, so we abstract from the issue of capabilities affecting inequality (Foster & Sen, 1997). We adopt a specific functional form to permit the numerical comparison of the tax bases. The degree of inequality in the population is measured by using the Gini coefficient applied to the discounted value of lifetime income, G ¼1


1 XX minfI j ; I k g H 2m j k

(8)

where I j  ‘j wj þ ej þ rsj =ð1 þ rÞ and m is mean income. We interpret one tax system as being more successful in reducing inequality than an alternative system if it generates a lower value of the Gini coefficient. We are not the first to relate income taxation to economic indices. For example, Kanbur and Keen (1989) consider how the income tax should be chosen to minimize the value of a poverty or inequality measure. What has not been analyzed previously is how income and expenditure taxes perform as determined, in our case, by the value of the Gini with income taxation relative to the Gini with expenditure taxation. Using the population proportions the Gini coefficient can be written as 1 XX Hpj pk minfI j ; I k g H 2I j k 1 XX p p minfI j ; I k g ¼1
HI j k j k

G ¼1


(9)

P where I ¼ j pj I j : From this point onward let the low wage be given by wL ¼ 0 and the high wage by wH ¼ w. Also, we consider only tax systems that are linear. Hence,

80

NIGAR HASHIMZADE AND GARETH D. MYLES

there is a constant marginal rate of tax and a common lump-sum subsidy for all consumers. This applies to the income tax and the expenditure tax. 2.2. Income Tax The introduction of income taxation modifies the budget constraints in the two periods of life to x1h þ sh ¼ eh þ wh ‘h ð1
tÞ þ g

(10)

x2h ¼ ð1 þ rð1
tÞÞsh þ g

(11)

and

where t is the tax rate and g the lump-sum grant. Note that the endowment is not taxed since it is not income and that the treatment of interest income in Eq. (11) reduces the return to saving. Combining these two budget constraints provides the lifetime budget constraint x1h þ

x2h 2 þ rð1
tÞ ¼ eh þ wh ‘h ð1
tÞ þ g 1 þ rð1
tÞ 1 þ rð1
tÞ

(12)

The lifetime budget constraint reveals how second-period incomes are discounted at the net-of-tax rate of interest, and hence that the relative price of second-period consumption is increased. This change in relative price distorts the allocation of consumption across the lifecycle. Using this budget constraint it is now possible to derive the optimal choices of each individual. Consider first an individual of type LL or LH who has a low level of skill. Since wh ¼ 0 for h 2 fLL; LHg it must be that ‘h is also zero. The consumption choices of a low-skill consumer then solve the optimization problem max U h ¼ a lnðx1h Þ þ d lnðx2h Þ s:t: x1h þ

fx1h ;x2h g

x2h 2 þ rð1
tÞ ¼ eh þ g 1 þ rð1
tÞ 1 þ rð1
tÞ (13)

This optimization has the solution for the consumption levels in the two periods of life   a 2 þ rð1
tÞ 1 xh ¼ eh þ g (14) aþd 1 þ rð1
tÞ

Inequality and the Choice of the Personal Tax Base

x2h

  d 2 þ rð1
tÞ ð1 þ rð1
tÞÞ eh þ g ¼ aþd 1 þ rð1
tÞ

81

(15)

and the solution for saving   d g d eh þ ð2 þ rð1
tÞÞ
1 sh ¼ aþd 1 þ rð1
tÞ a þ d

(16)

The high-skill consumers will choose to supply a strictly positive amount of labor for tax rates below some strictly positive cut-off point. All the numerical computations that follow are for values below the cut-off. Hence, while recognizing that corner solutions can arise, we consider only interior solutions for high-skill consumers. For the consumers with wh ¼ w40 this implies optimal choices are derived from max U h ¼ a lnðx1h Þ þ ð1
aÞ lnð1
‘h Þ þ d lnðx2h Þ s:t: Eq: ð12Þ

fx1h ;x2h ;‘h g

The resulting levels of consumption and labor supply are   a 2 þ rð1
tÞ 1 eh þ wð1
tÞ þ g xh ¼ 1þd 1 þ rð1
tÞ

x2h

  d 2 þ rð1
tÞ ð1 þ rð1
tÞÞ eh þ wð1
tÞ þ g ¼ 1þd 1 þ rð1
tÞ

  1
a eh g 2 þ rð1
tÞ 1þ þ ‘h ¼ 1
1þd wð1
tÞ wð1
tÞ 1 þ rð1
tÞ and the quantity of saving is   d 2 þ rð1
tÞ g eh þ wð1
tÞ þ g sh ¼
1þd 1 þ rð1
tÞ 1 þ rð1
tÞ

(17)

(18)

(19)

(20)

(21)

The tax policy is assumed to be purely redistributive so the revenue raised by the government is returned as a lump-sum transfer to consumers. All consumers receive the transfer regardless of income or endowment. Denote the transfer by g. The value of the transfer is calculated from the

82

NIGAR HASHIMZADE AND GARETH D. MYLES

government’s two-period budget constraint " # X g r X ¼t gþ ph w‘h þ p sh 1þr 1þr h h h

(22)

In equilibrium g is obtained by taking into account the dependence of the optimal choices of the consumers on the tax and transfer.

2.3. Expenditure Tax With expenditure taxation the budget constraints in the two periods of life become x1h ð1 þ tÞ þ sh ¼ eh þ wh ‘h þ g

(23)

x2h ð1 þ tÞ ¼ ð1 þ rÞsh þ g

(24)

where t is the constant rate of expenditure taxation. Notice how the expenditure tax treats the endowment and labor income symmetrically, and the fact that income from saving is not taxed except as expenditure on consumption. The allocation of consumption across time is not distorted by the tax. Combining these two constraints into the lifetime budget constraint gives   x2h 1 2þr 1 eh þ wh ‘h þ g ¼ xh þ (25) 1þr 1þr 1þt The lifetime budget constraint reflects the distortion introduced into the consumer choice between leisure and consumption. The optimal labor supply of an individual with a low skill level remains ‘h ¼ 0: The choices of consumption and savings are given by   a 1 2þr eh þ g x1h ¼ (26) a þ d1 þ t 1þr x2h ¼

  d 1þr 2þr eh þ g a þ d1 þ t 1þr

(27)

and   d 2þr g eh þ g sh ¼
aþd 1þr 1þr

(28)

Inequality and the Choice of the Personal Tax Base

83

We again choose to remain within the range of parameter values for which the labor supply of an individual with a high skill level is strictly positive. Consumption, labor supply, and savings are then   a 2þr 1 eh þ wh þ g xh ¼ (29) ða þ dÞð1 þ tÞ þ 1
a 1þr

x2h ¼

  dð1 þ rÞ 2þr eh þ wh þ g ða þ dÞð1 þ tÞ þ 1
a 1þr

  1
a eh g 2þr 1þ ‘h ¼ 1
þ ða þ dÞð1 þ tÞ þ 1
a wh wh 1 þ r

(30)

(31)

and sh ¼

  dð1 þ tÞ 2þr g eh þ wh þ g
ða þ dÞð1 þ tÞ þ 1
a 1þr 1þr

(32)

The value of the transfer to every consumer is computed from the government budget constraint which, for expenditure taxation, is given by  X  x2 g gþ ¼t ph x1h þ h (33) 1þr 1þr h 2.4. Contrast The intention is to contrast the success of the alternative tax bases at achieving redistribution. As noted in Section 1, we need to be careful in the way we conduct the comparison in order for the results to be meaningful. The process adopted is to set the income tax at a fixed rate and compute the level of welfare this generates. The expenditure tax is then derived that leads to the same level of welfare. The government budget constraint implies the equilibrium transfers for these tax rates which allows the value of the Gini coefficient to be calculated. This provides a comparison of the redistribution achieved for income and expenditure tax bases at an equal welfare level. The exercise is then repeated for a pair of taxes that generate identical levels of government revenue (and through the government budget constraint provide an identical value of the lump-sum transfer).

84

NIGAR HASHIMZADE AND GARETH D. MYLES

The second important aspect is to ensure that we make the comparison for a sufficiently wide range of the underlying parameters. Recall that the economy has both skill and endowment differences between consumers. Numerically testing a range of specifications revealed that the parameter that distinguishes different cases is the coefficient of correlation between skill and endowment. We therefore conduct our equal welfare (and equal revenue) comparisons for the full range of values of the correlation coefficient between
1 and 1. The details of our calculations are as follows. We consider two values of the income tax rate (t ¼ 0.1 and t ¼ 0.3). We set the low wage and low endowment level at 0. The high endowment is set at e ¼ 1. For each tax rate we consider high wages of w ¼ 1 and w ¼ 5. We set the probability of the wage–endowment pairs (0,0) and (1,1) at p and the probability of the pairs (0,1) and (1,0) at q. The population variances of the wage and of the endowment are (p+q)2 and the correlation between the two is 1
4q. Hence q ¼ 0 gives perfect positive correlation between endowment and skill, and q ¼ 1/2 gives perfect negative correlation. By varying q between 0 and 1/2 we are then able to cover the range of correlation coefficients. The contrast between the two tax bases is illustrated in Figs. 1 and 2 for w ¼ 1. The correlation coefficient is measured on the horizontal axis and the value of the Gini coefficient on the vertical axis. There is a single curve for the income tax (GI) and two curves (GEW and GER) for the expenditure tax. GEW is the value of the Gini at the same welfare level as achieved by the income tax and GER is the value of the Gini at the same revenue level as the

0.6 0.5 0.4

GI GEW

0.3

GER

0.2 0.1 0 -1

-0.5

0

Fig. 1.

0.5

1

t ¼ 0.1, e ¼ 1, w ¼ 1.

Inequality and the Choice of the Personal Tax Base

85

0.5 0.4 GI

0.3

GEW 0.2

GER

0.1 0 -1

-0.5

0

Fig. 2.

0.5

1

t ¼ 0.3, e ¼ 1, w ¼ 1.

income tax. The results show that when e ¼ w ¼ 1 the expenditure tax generates a lower value of the Gini coefficient than the income tax (and hence achieves an equilibrium with less inequality) when there is a negative correlation between endowment and skill. When the correlation becomes sufficiently positive the income tax generates a lower Gini coefficient. There is very little difference between the comparison with equal welfare and that with equal revenue. For these parameter values the choice between the two tax bases is dependent upon the value of the correlation coefficient. The outcome of the comparison is different when eow. This is illustrated in Figs. 3 and 4 for w ¼ 5. In these cases the income tax produces a lower value of the Gini index for the entire range of values for the correlation between skill and endowment. The reason for this change in outcome is that the increase in labor income relative to endowment income permits the income tax to be more successful at redistributing since it is levied on an increased proportion of total income. The results show that the relative success of the two tax bases is dependent upon the relative values of labor income and initial endowment and the coefficient of correlation between these values. It is an interesting observation that the expenditure base only achieves a lower value of the Gini coefficient when there is negative correlation – in all other cases the income base is preferable. The relative performance of the income tax is better with positive correlation because in this case a higher average tax is levied on those who are both skilled and receive a high endowment. Hence the tax on income is a good proxy for a tax on the unobserved endowment.

86

NIGAR HASHIMZADE AND GARETH D. MYLES 0.5 0.45 0.4 GI 0.35

GEW GER

0.3 0.25 0.2 -1

-0.5

0

Fig. 3.

0.5

1

t ¼ 0.1, e ¼ 1, w ¼ 5.

0.5

0.4 GI GEW

0.3

GER

0.2

0.1 -1

-0.5

0

Fig. 4.

0.5

1

t ¼ 0.3, e ¼ 1, w ¼ 5.

It is likely that the empirical evidence would determine that the correlation is positive in practice, thus providing a preference for the income base. Researching the evidence would also reveal that in practical terms initial endowments invariably arise from bequests. To argue that these interactions are adequately captured within the static model would seem to be pushing its interpretation too far. Instead, a better approach is to

Inequality and the Choice of the Personal Tax Base

87

model bequests explicitly by adopting an intertemporal model that embodies a bequest motive.

3. DYNAMIC ECONOMY The analysis of the static economy has demonstrated how the correlation between endowment and skill affects the choice between the tax bases. In practice non-earned initial endowments arise primarily from bequests which, in turn, depend on the earning capacity of predecessors. This implies an endogenous correlation between skill and endowment related to the transmission mechanism of skill between generations. The static model captures some of the consequences of inequality but it does not reflect the fact that the endowments and skills are linked via the choices of dynasties of households. It is therefore necessary to study a dynamic economy in which parents choose to leave bequests to their children. This allows the accumulation of wealth over time, the development of inequality, and the formation of an endogenous intertemporal link between skill and endowment. What is key in this economy is the mechanism by which skills are transmitted between generations. We now repeat the comparison of the tax bases in a dynamic economy where the transmission mechanism can be made explicit.

3.1. Model We adopt an infinite-horizon economy that is populated by heterogenous agents. The agents have identical preferences but differ in skill and endowment. Each agent lives two periods. In the first period an agent receives an endowment and labor income which he divides between consumption and saving. In the second period he divides his savings between consumption and bequest. The bequest becomes the endowment of his descendant. There is no population growth, and the total size of the population is normalized to unity, with equal proportions of young and old agents in every time period. With government intervention the agents pay tax and receive a transfer in every period. We consider two tax schemes: an income tax levied on labor income and interest income, and an expenditure tax levied on consumption in every period. For simplicity, wages and the interest rate are exogenously fixed. The wage for skilled workers is normalized to unity, and that for unskilled workers is normalized to zero, so that in equilibrium unskilled workers do not supply labor.

88

NIGAR HASHIMZADE AND GARETH D. MYLES

The preferences of a consumer are described by the lifetime utility function uðÞ ¼ Uðx1 ; ‘Þ þ dV ðx2 ; bÞ

(34)

Uðx1 ; ‘Þ ¼ a ln x1 þ ð1
aÞ lnð1
‘Þ

(35)

V ðx2 ; bÞ ¼ b ln x2 þ ð1
bÞ ln b

(36)

where

and

with x1 and x2 consumption in the first and in the second period of life, respectively, ‘ labor supply, and b the bequest. An infinitely lived government collects taxes and redistributes the revenues equally among all agents in every period. We assume that the government can commit to a policy of a constant tax rate and a constant transfer. There is no borrowing constraint on the government. From the solution to each agent’s optimization problem we can express the bequest as a function of endowment. Because the bequest becomes the endowment of the next generation in a given dynasty, this function can be viewed as a law of motion for the endowment. The functional form of the law of motion depends on whether the bequestor is skilled or unskilled. Therefore, in every generation the law of motion of the endowment switches randomly between two regimes. We assume the probability that the descendant of a skilled worker is skilled is equal to pss, and that the probability the descendant of an unskilled worker is unskilled is equal to puu. The process of these random switches is a two-state Markov chain with the transition matrix " # pss 1
puu P¼ (37) 1
pss puu The process is ergodic and irreducible if pss o1; puu o1; and pss þ puu 40; with ergodic probabilities 2 3 1
puu " # 62
p
p 7 p1 ss uu 7 6 p¼6 1
p (38) 7 p2 4 5 ss 2
pss
puu

Inequality and the Choice of the Personal Tax Base

89

b

45ο eu

Fig. 5.

es

e

Convergence to Steady State Bequests.

The ergodic probabilities can be interpreted as unconditional probabilities of being in each regime (see Hamilton, 1994, Chapter 22). Hence, in the long run on average p1 agents are skilled and p2 ¼ 1
p1 are unskilled. Any initial distribution of endowments in the long run converges to a bimodal distribution, with peaks at the stationary points of the two regimes. This is illustrated in Fig. 5 where eu and es are the long-run bequests of the unskilled and skilled, respectively. The government will run an ‘‘on average’’ balanced budget if it computes the amount of transfer taking p1 skilled and p2 unskilled agents, with corresponding stationary endowments, as the tax base.

3.2. Taxation With an income tax the first- and second-period budget constraints of an agent with endowment e are x1 þ s ¼ e þ w‘ð1
tÞ þ g

(39)

x2 þ b ¼ sð1 þ rð1
tÞÞ þ g

(40)

90

NIGAR HASHIMZADE AND GARETH D. MYLES

The wage of unskilled agents is set at zero so they supply no labor. The optimal choices of an unskilled agent are    a 1 1 xu ¼ eþg 1þ , aþd 1 þ rð1
tÞ    db 1 ½1 þ rð1
tÞ eþg 1þ ð41Þ x2u ¼ aþd 1 þ rð1
tÞ

bu ¼

‘u ¼ 0

(42)

d g su ¼ x1u
a 1 þ rð1
tÞ

(43)

   dð1
bÞ 1 ½1 þ rð1
tÞ eþg 1þ aþd 1 þ rð1
tÞ

The solution to the optimization problem of a skilled agent is    a 1 s e þ wð1
tÞ þ g 1 þ x1 ¼ 1þd 1 þ rð1
tÞ

xs2

   db 1 ½1 þ rð1
tÞ e þ wð1
tÞ þ g 1 þ ¼ 1þd 1 þ rð1
tÞ

(44)

(45)

(46)

a xs1 1
a wð1
tÞ

(47)

d g ss ¼ xs1
a 1 þ rð1
tÞ

(48)

‘s ¼ 1


   dð1
bÞ 1 ½1 þ rð1
tÞ b ¼ e þ wð1
tÞ þ g 1 þ 1þd 1 þ rð1
tÞ s

(49)

The long-run average tax revenue is TR ¼ t½p1 ðw‘s þ rss Þ þ p2 rsu 

(50)

Inequality and the Choice of the Personal Tax Base

91

and the transfer is computed from the government budget constraint TR ¼ g. The budget need not balance every period so we are implicitly assuming that the government can borrow and lend at the rate of interest r. With the expenditure tax the first- and second-period budget constraints of an agent with endowment e are x1 ð1 þ tÞ þ s ¼ e þ w‘ þ g

(51)

x2 ð1 þ tÞ þ b ¼ sð1 þ rÞ þ g

(52)

Using the fact that unskilled agents supply no labor,    a 1 1 eþg 1þ x1u ¼ a þ d1 þ t 1þr x2u

   db 1 1 eþg 1þ ¼ a þ d1 þ t 1þr

   dð1
bÞ 1 eþg 1þ ð1 þ rÞ bu ¼ aþd 1þr The solution to the optimization problem of a skilled agent is    a 1 1 eþwþg 1þ x1s ¼ 1 þd1þt 1þr x2s ¼

   db 1 1 eþwþg 1þ ð1 þ rÞ 1 þ d1 þ t 1þr ‘s ¼ 1


bs ¼

a xs1 ð1 þ tÞ 1
a w

   dð1
bÞ 1 eþwþg 1þ ð1 þ rÞ 1þd 1þr

(53)

(54)

(55)

(56)

(57)

(58)

(59)

The long-run average tax revenue is TR ¼ t½p1 ðx1s þ x2s Þ þ p2 ðx1u þ x2u Þ and the transfer is computed from TR ¼ g.

(60)

92

NIGAR HASHIMZADE AND GARETH D. MYLES

3.3. Contrast This section contrasts the two tax bases. This is done using two different approaches. First, we consider the dynamic evolution of the economy beginning from an arbitrary assignment of initial endowments. Second, we analyze the instantaneous stationary equilibrium with population proportions equal to the ergodic probabilities. In both cases we focus upon the value of the Gini coefficient using equal welfare and equal revenue comparisons. Figs. 6–9 depict the value of the Gini coefficient for income taxation and the two Gini coefficients for expenditure taxation: one expenditure Gini is at the same welfare level as for the income tax, the other Gini for expenditure is at the same government revenue level. Two income tax rates are considered (t ¼ 0.2 and t ¼ 0.4) and two different probabilities for a high-skill parent to have a high-skill offspring (pss ¼ 0.2 and pss ¼ 0.8). The ergodic probabilities that these generate imply long-run average proportions for high-skill of 5/13 and 5/7, respectively. These simulations compute the Gini coefficient for 100 generations of 100 families, with zero initial endowment and a uniform distribution of skills (0 or 1 with equal probability) for the families in the first generation. We plot only from generation 10 since by this point the effect of the assumptions on initial distribution has disappeared. In every period the agents (families) choose their optimal consumption, leisure, and bequest given their endowment and skills (wage income). The bequest becomes the endowment of the agent’s offspring, whose skill is determined randomly, according to Eq. (34). 0.375

0.35

0.325

0.3

0.275

GI

Fig. 6.

GER

GEW

t ¼ 0.2, pss ¼ 0.2, puu ¼ 0.5.

Inequality and the Choice of the Personal Tax Base

93

0.35

0.3

0.25

0.2

0.15 GI

Fig. 7.

GER

GEW

t ¼ 0.4, pss ¼ 0.2, puu ¼ 0.5.

0.275

0.225

0.175

0.125

0.075

GI

Fig. 8.

GER

GEW

t ¼ 0.2, pss ¼ 0.8, puu ¼ 0.5.

The economy does not reach a steady state since there is always randomness in the ability of offspring. What is observed in all the figures is that the Gini for income taxation is on average below the two Ginis for expenditure taxation. Increasing t and reducing pss emphasizes this effect. The results confirm the observation made in the static setting that the income tax leads to a lower value of the Gini. It should be observed that in this model for pss ¼ 0.8 there is a positive correlation between wage income and endowment driven by the fact that

94

NIGAR HASHIMZADE AND GARETH D. MYLES 0.25

0.2

0.15

0.1

0.05 GI

Fig. 9.

GER

GEW

t ¼ 0.4, pss ¼ 0.8, puu ¼ 0.5.

0.55

0.7

GI

GI

0.6

GER

GER

0.45

GEW

GEW 0.5 0.35 0.4 0.25 0.3

0.2

0.15 0

0.2

0.4

0.6

0.8

1

Fig. 10.

0

0.2

0.4

0.6

0.8

1

pss ¼ 0.2.

high-skill parents leave a higher bequest and are more likely to have highskill offspring. In contrast, for pss ¼ 0.2 the correlation between wage income and endowment is negative. In all cases in the long-run equilibrium the average endowment of both skilled and unskilled is less than the wage of the skilled. Hence, the outcome in the dynamic economy (lower Gini with the income tax) is consistent with the one in the static economy.

Inequality and the Choice of the Personal Tax Base

95

0.7

GI

0.5

GI

0.6

GER

GER 0.5

GEW

0.4

GEW 0.3

0.4 0.3

0.2

0.2

0.1

0.1

0 0

0.2

0.4

0.6

0.8

1

Fig. 11.

0

0.2

0.4

0.6

0.8

1

pss ¼ 0.8.

The results for the cross-section, ‘‘stationary’’ analysis confirm the observations from the dynamic process. In Figs. 10 and 11 we plot the Gini for an economy with the (instantaneous) proportion of skilled agents equal to p1, the ergodic probability, or the long-run average proportion of skilled, for a fixed pss, and puu varying from 0.01 to 0.99. In every case the Gini for the income tax is below the two Ginis for the expenditure tax. This emphasizes that the few cases in which the expenditure base is observed to produce a lower Gini than the income base during the dynamic evolution are consequences of particular random realizations of the economy. The long-run stationary outcome confirms that the expected position is for the income base to ensure a lower value of the Gini.

4. CONCLUSIONS The intention of the paper was to contrast the relative success of alternative bases for personal taxation. In a static model with inequality arising from skill in employment and from initial endowment the income base performed better in all cases considered if there was positive correlation between the sources of inequality. The expenditure base only bettered the income base when there was negative correlation and a low level of income from employment. These results were strengthened in the dynamic model. The

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income base performed better except for a small number of realizations of the economy, and was clearly better in the long-run equilibrium. If the choice over the tax base rests on the reduction of inequality these results provide evidence in favor of an income base. It seems natural to question the extent to which policy recommendations can be drawn from these stylized models. Both models capture the fact that inequality of income has two dimensions – earned and unearned – and the dynamic model also involves accumulation of inequality over time through the role of bequests. We would agree that the static model is limited by the lack of transmission of inequality across generations. For this reason we prefer to focus upon the outcome of the dynamic model. Reassuringly, the results of the dynamic model not only support those from the static model but are actually more decisive. The income tax performed better than the expenditure tax for all the parameter combinations considered (many of which have not been reported in the paper). The dynamic model was simplified by the assumption of a fixed interest rate but this can be rationalized by assuming a small open economy or a constant marginal product for capital. The advantage remains that it avoided intermixing issues of redistribution and dynamic inefficiency. We therefore feel that our conclusions on the advantage of the income tax are robust.

ACKNOWLEDGMENTS The paper has emerged from discussions of the Mirrlees Review of UK Taxation. We wish to thank members of the Review, especially Richard Blundell, Stephen Bond, and James Mirrlees. The paper has also benefited from discussion at seminars in Exeter, Lancaster, and Manchester. The comments of the three anonymous referees and the editor Peter Lambert have also been helpful.

REFERENCES Altig, D., Auerbach, A., Kotlikoff, L., Smetters, K., & Walliser, J. (2001). Simulating tax reform in the United States. American Economic Review, 91, 574–595. Auerbach, A. J. (2006). The choice between income and consumption taxes: A primer. University of California. Batina, R. G., & Ihori, I. (2000). Consumption tax policy and the taxation of capital income. Oxford: Oxford University Press.

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Blumkin, T., & Sadka, E. (2005). Income taxation with intergenerational mobility: Can higher inequality lead to less progression? European Economic Review, 49, 1915–1925. Chamley, C. (1981). The welfare cost of capital income taxation in a growing economy. Journal of Political Economy, 89, 468–496. Chamley, C. (1986). Optimal taxation of capital income in a general equilibrium with infinite lives. Econometrica, 54, 607–622. Correira, I. H. (2005). Consumption taxes and redistribution. CEPR Discussion Paper No. 5280. Feenberg, D., Mitrusi, A., & Poterba, J. (1997). Distributional effects of adopting a national retail sales tax. In: J. Poterba (Ed.), Tax policy in the economy (Vol. 11). Foster, J. E., & Sen, A. (1997). On economic inequality. Oxford: Clarendon Paperbacks. Hamilton, J. D. (1994). Time series analysis. Princeton: Princeton University Press. Hanushek, E. A., Leung, C. K. Y., & Yilmaz, K. (2003). Redistribution through education and other transfer mechanisms. Journal of Monetary Economics, 50, 1719–1750. Hashimzade, N., & Myles, G. D. (2007). The structure of the optimal income tax in the quasilinear model. International Journal of Economic Theory, 3, 5–33. Hobbes, T. (1660). Leviathan (reprinted by Penguin Classics, 1985). Ja¨ntti, M., Bratsberg, B., Roed, K., Raaum, O., Naylor, R., O¨sterbacka, E., Bjo¨rklund, A., & Eriksson, T. (2005). American exceptionalism in a new light: A comparison of intergenerational earnings mobility in the Nordic countries, the United Kingdom and the United States. Memo. 34/2005, University of Oslo. Judd, K. L. (1985). Redistributive taxation in a simple perfect foresight model. Journal of Public Economics, 28, 59–83. Kaldor, N. (1955). An expenditure tax. London: George Allen and Unwin. Kanbur, R., & Keen, M. (1989). Poverty, incentives, and linear income taxation. In: A. Dilnot, & I. Walker (Eds), The economics of social security. Oxford: Clarendon Press. Meade, J. E. (1978). The structure and reform of direct taxation. London: George Allen and Unwin. Mill, J. S. (1888). Principles of political economy. New York: Appleton. Mirrlees, J. A. (1971). An exploration in the theory of optimum income taxation. Review of Economic Studies, 38, 175–208. Myles, G. D. (2000). Taxation and economic growth. Fiscal Studies, 21, 141–168. Ramsey, F. P. (1927). A contribution to the theory of taxation. Economic Journal, 37, 47–61. US Treasury Department (1942). Proposal for a ‘‘consumption expenditure tax’’, www.taxhistory.org/Civilization/Documents/Spending/hst9369/9369-1.htm

STRATEGIC WEIGHT WITHIN COUPLES: A MICROSIMULATION APPROACH Kristian Orsini and Amedeo Spadaro ABSTRACT Individual strategic weight plays an important role in the intra-household allocation of resources; however, empirical studies invariably find such weight difficult to define in a plausible and computable way, given the available data. This paper proposes a framework for the calculation of household members’ strategic weight that can be easily computed using a microsimulation model. The index proposed for each member as the share of resources the household would lose should he or she abandon it. The causes of strategic weight differentials are analysed in four EU countries with significantly different employment structure and tax-benefit systems (Finland, Germany, Italy and the United Kingdom), using EUROMOD, an integrated EU-15 microsimulation model.

1. INTRODUCTION What advantage is there in individualising income tax or social benefits, as opposed to splitting or pooling them? Does it matter whether family and Equity Research on Economic Inequality, Volume 15, 99–132 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15006-7

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other personal circumstances are taken into account when calculating inwork benefits or tax credits? What are the likely consequences of each policy option in terms of personal income and welfare distribution, as opposed to household distribution? How does redistribution policy affect the household decision-making process and the welfare of individuals within families? With regard to reforms of the tax or redistribution system, much of the economic and political debate has focused on such questions in all European countries over the past three decades. Economists have for long been ill-equipped to tackle these issues, insofar as they have become accustomed to treat households as if they were individuals, and to use household data in a similar fashion. The need to analyse policy impacts at an individual level forced researchers to propose alternatives to the unitary model, in order to explicitly take into account the existence of various decision-makers whose preferences quite likely differ. One broad class of model represents multi-person household behaviour in a non-cooperative framework.1 Such models show that if negotiation between spouses is viewed as a repeated game, non-cooperative behaviour may occur if household members have divergent interests which cannot be reconciled. Contributions belonging to this family of models and inspired by the marriage market models of Becker (1974), such as those made by Grossbard-Shechtman (1984) or Grossbard-Shechtman and Neuman (1988), clearly show how strategic weight is related to individuals’ relative income and conditions within the marriage market. Other types of models start from the a priori assumption that spouses know each other’s preferences well and that they exploit the gains to be had from cooperation during their long-term relationship as a couple.2 The nature of the bargaining process is thus cooperative, and game-theoretic support (the Folk theorem) is provided for Pareto efficiency and appears to be a natural extension of the unitary setting. Models of this type focus on efficient intra-household outcomes by employing an explicitly axiomatic approach to bargaining solutions, such as Nash bargaining, and by specifying outside options for each individual in the household (Manser & Brown, 1980; McElroy & Horney, 1981; Haddad & Kanbur, 1994; Konrad & Lommerud, 2000; Lundberg & Pollak, 1993). A further type of model simply takes for granted that the equilibrium outcome is Pareto efficient, without taking into account any bargaining rules. This is the case of the collective model (Chiappori, 1988, 1992; Bourguignon, Browning, Chiappori, & Leche`ne, 1993)3 in which the spouses engage in a bargaining process which not only affects their behaviour, but also each spouse’s well being. The principal appeal of the collective model is

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that it provides a single framework for analysing the decision-making process and intra-household allocations, and economic behaviour and distribution are therefore analysed within a single and theoretically consistent framework. As a result, several empirical studies have explicitly adopted the collective framework to analyse the labour supply and welfare distribution effects of reforms of the tax-benefit system.4 The contribution made by these papers is significant, particularly in the field of welfare evaluation, where the unitary approach remains fundamentally unchallenged. In both cooperative and non-cooperative models, the difficulties in computing the strategic weights of each of the spouses continue to be the key issue. The lack of available data, theoretical restrictions and dependence on the tax-benefit schedule5 (which assigns a different implicit weight to each household member on the basis of various economic and socio-demographic characteristics) make it hard to define a criterion for computing strategic weight. Without wishing to question the validity of the solutions proposed by various authors6 (which basically rely on estimation or calibration procedures), in this paper we propose an alternative, highly intuitive, approach; this is based on the hypothesis that each spouse’s strategic weight is proportional to the share of resources lost by the household if he or she abandons it. The underlying rationale is that individual control over money is important for the decision-making process within the household and the subsequent distribution of resources and welfare; thus, a substantial body of literature suggests that an individual’s strategic weight within the household is related to his/her contribution to its financial resources (see Browning, Bourguignon, Chiappori, & Leche`ne, 1994; Phipps & Burton, 1992, 1993; or Blumber (1988)). The essential idea is similar to that contributed to game theory literature by Shapley (1953). His index (the Shapley value) captures the importance of adding a player to the winning coalition of a game (and thereby determining his strategic weight).7 Similarly, we propose an index aimed at capturing the strategic importance of each of the individuals in a given household by removing him or her from the coalition represented by the marriage. However, this is not totally symmetric to the computation of the Shapley value, for several reasons. Firstly, even if we assume that household members play a cooperative game and that the surplus is shared in accordance with the index we propose, the outside options are not identical for those individuals entering a coalition (e.g. marrying) as for those leaving it (e.g. divorcing). Secondly, we do not construct any type of bargaining game (whether cooperative or non-cooperative). We simply claim that this index

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may approximate the ex ante strategic weights in any ‘‘household game’’. For example, it can be used as a proxy of individual strategic weight for a policy evaluation exercise in a collective framework. It would therefore be possible, in a discrete labour supply model, to compute a set of alternative strategic weights and to use these variables as determinants of private consumption shares, without having to rely on a calibration method. Such an approach would be consistent with the view that a household member’s strategic weight is an endogenous variable, partially determined by his or her behaviour (but also by the ‘‘caring’’ or ‘‘egoistic’’ preferences of the partner). Additionally, and we believe this is our most important contribution, our index permits a comparative analysis of the performance of redistribution systems in equalising or disequalising the strategic weight of household members, both within and across countries. These two aspects have crucial implications with regard to evaluating redistribution policies. Interestingly, this index may also reveal social planners’ preferences with respect to family policy and intra-household resource allocation. The computation of this strategic weight index is based on microsimulation techniques, since it intrinsically relies on a counterfactual premise. Microsimulation models are powerful instruments whose analytical potential in the various fields of economic research have not yet been fully explored (Bourguignon & Spadaro, 2006). The advantage of using a microsimulation model lies in its capacity to fully describe the current economic situation, as well as potential counterfactuals, thereby capturing the complex effects of taxes and benefits. The paper is devoted to the computation of the strategic weight of each household member. Specifically, we examine how strategic weight differentials depend on household characteristics, employment patterns (which to some extent reflect individual preferences) and the tax-benefit systems (which, by contrast, represent social preferences). To this end, we consider four European countries with profoundly different tax-benefit systems: Finland, Germany, Italy and the United Kingdom. The paper is structured in the following way. Section 2 introduces our definition of household members’ strategic weight. Section 3 describes the data selection and EUROMOD, the microsimulation model used to derive strategic weights. Section 4 presents some results regarding the attitude of social planners toward the family, as inferred from the tax-benefit system. Section 5 analyses strategic weight differentials, focusing in particular on the role of the labour market and of the tax-benefit systems. Section 6 presents the conclusions reached.

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2. DETERMINING INDIVIDUAL STRATEGIC WEIGHT In what follows, we assume that households simply exist because, for whatever reason, it is convenient for individuals to form them. Let us assume that no public good is at stake and that agents’ behaviour is purely egoistic,8 thus, they will form part of the household only as long as this continues to be a ‘‘convenient strategy’’. In other terms, household members will not accept ‘‘commanding’’ a share of resources lower than their marginal contribution to overall household welfare. The ‘‘strategic weight’’ of each individual within the household is hence determined by a hypothetical counterfactual, corresponding to the share of resources that would be lost if he or she were to ‘‘withdraw’’ from the household. In formal terms, the weight of an individual i may be defined as: li ¼

YDðnÞ
YDðn
iÞ YDðnÞ

(1)

where YD(n) and YD(n
i) represent household disposable income, with and without household member i. Logically, the strategic weight of an individual depends on two major factors: his/her own original income and the weight assigned to him/her by the tax-benefit system. Since disposable income may be divided into gross income GY() and net transfers NT(), we have that: li ¼

GYðnÞ þ NTðnÞ
ðGYðn
iÞ þ NTðn
iÞÞ YDðnÞ

(2)

or simply: l i ¼ mi þ t i

(3)

GYðnÞ
GYðn
iÞ YDðnÞ NTðnÞ
NTðn
iÞ ti ¼ YDðnÞ

(4)

where: mi ¼

Normalising the indexes with respect to their sum permits a better comparison of the strategic weight of each household member relative to the others. Thus, the strategic weight of member i can be computed as: li ¼

li nk P lk k¼1

(5)

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The following relation also holds: li ¼ mi þ ti

(6)

where Pnk both right-hand-side terms have also been normalised with respect to k¼1 lk : The earlier decomposition allows us to capture the weight that a taxbenefit system assigns to each household member, given their prevailing roles in society in terms of age and gender. Alternatively, the proposed index can be employed as a mechanism for revealing social planners’ preferences with regard to household formation. If the tax-benefit system is perfectly neutral with respect size, li P to householdP can be reduced to the income share of person i and li ¼ 1. Thus, li>1 indicates a system which favours household formation, as the share of disposable income lost by the household if a member leaves exceeds his/her P gross income, and vice versa for lio1. For confirmation, let us take the following example9: the disposable income of each individual is (1
t)Y+bna, where (1
t)Y is the net income and bna is a subsidy equal to b times household size raised to a. Hence, assuming that all household members have the same net income: li ¼

ð1
tÞY þ b½naþ1
ðn
1Þaþ1  n½ð1
tÞY þ bna 

(7)

If a ¼ 0, then li ¼ 1/n, which corresponds to a neutral tax-benefit system. On the other hand, if the parameter a is larger than 0, the tax-benefit system favours, overall, household formation. We can therefore define the sum of the unstandardised li as a neutrality index; an index close to 1 means that the tax-benefit system approaches neutrality with respect to family size (and composition), while an index lower than 1 implies a tax-benefit system which discriminates against families. In turn, an index greater than 1 implies a profamily tax-benefit system. Obviously, the approach proposed has several shortcomings. The treatment of children, for example, is not fully satisfactory. The possibility of abandoning the household is an option available to adult household members, but not to children, especially younger ones; thus, it is not possible to compute the strategic weight of children. Further research should probably address the issue of how parents bargain over their children. The latter may be viewed as a type of public good into which both parents invest resources and subsequently bargain over their respective shares of the ensuing residual income. A priori, it seems likely that the parent who is most likely to obtain custody would in some way ‘‘incorporate’’ the children’s strategic weight

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into his or her own weight. In the following analysis we will adopt this approach and assume that children will follow the mother in the case of her leaving the household.10 Secondly, we have not considered the possibility of behavioural reactions. When one member leaves the household, the other may decide to increase his/her labour supply; alternatively, the entry of a new member may cause a corresponding decrease. This hypothesis is extremely fragile, given that labour supply behaviour is a crucial element in the analysis of outside options. The explicit inclusion of behavioural reaction would require the definition of a full model of household members’ labour supply and the game they play to allocate household resources. This would be extremely complicated and is beyond the scope of the present paper. Thirdly, we ignore the role of alimony and child support, which is usually established by the courts or agreed between the spouses in the case of divorce. Once more, this decision is debatable, since in theory it means neglecting an important influence on the threat point of each household member. Unfortunately, however, such information is lacking in the microdatasets available. Our intuition is that public goods, behavioural reactions and alimony legislation are all likely to reduce strategic weight differentials; the strategic weight we assume may therefore be considered as a special case of a more complex and realistic rule which takes the neglected factors mentioned above into account.

3. DATA SELECTION AND MICROSIMULATION SOFTWARE As explained in the previous section, the index is based on a counterfactual situation, represented by the effects upon disposable income of one of the household members leaving it (either alone or with the children). These counterfactuals are simulated using EUROMOD, an EU-wide integrated microsimulation model which permits the simulation of the tax system and most benefits unrelated to previous employment history (principally family benefits, housing allowances and income support).11 The present paper focuses on four EU countries, namely Finland, Germany, Italy and the UK; these were selected in order to permit us to analyse a sufficiently large variety of tax-benefit systems and social models,

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with different gender distributions of market and home production roles (see Esping-Andersen, 1990, 1999). Data for Finland are provided by the Income Distribution Survey, which contains a combination of register data and information gathered through interviews by Statistics Finland. The dataset refers to 1998 and contains detailed socioeconomic information for 25,010 individuals resident in 9,345 households. German data come from the German Socioeconomic Panel (GSOEP), established by the German Institute for Economic Research (DIW) in 1984. Unlike in Finland, only interviews are used to collect the annual data. The 1998 dataset supplies information regarding 18,772 individuals in 7,677 households. Italian data are collected every two years by the Survey of Household Income and Wealth (SHIW), conducted by the Bank of Italy. In this paper we use the 1995 dataset, which provides information about 23,924 individuals living in 8,135 households. Finally, data for the UK come from the Family Expenditure Survey, and are produced by the Office for National Statistics. It collects information for 15,586 individuals and 6,797 households over the period 1995–1996. For each country, we selected a subsample of married and cohabiting adult couples (i.e. aged at least 18) with and without children, irrespective of their activity status. Children were defined as single persons aged under 30 and living with their parents. This very broad definition was intended to avoid the exclusion of a significant number of households with grown-up children in Italy. For the sake of simplicity, we excluded single parents and three-generation households. Table 1 shows the sample size, before and after this selection, for the four countries. The proportion of individuals in the sample subsequently included in the subsample varies from 71.6% in Italy to 59.9% in Finland, which is in fact the country with the greatest proportion of single households. Table 2 offers some descriptive statistics for the subsamples in the four countries considered. Since only heterosexual couples were selected, the number of females is identical to the number of males. Average age appears to be very similar across the panel, with females being approximately two years younger than their male partners. With regard to the proportion of males and females in employment, significant variation is apparent across the different ‘‘social models’’. Finland’s male employment rate is almost 10% higher than that for Italy and the UK. However, it is in the female employment rate that differences are most striking: in Finland the rate of female employment is almost twice than that of Italy, while Germany and the UK occupy an intermediate position. It should be remembered that the above data refer to a period from the mid- to late 90s, and that female

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Table 1. Weighted Sample Before and After Selection. Finland

Germany

Italy

UK

Before selection No. of individuals No. of households

5,086,139 2,355,000

78,956,258 32,289,963

57,206,842 19,816,115

57,443,762 24,490,138

After selection No. of individuals No. of households

3,046,674 992,192

57,934,344 19,507,731

40,976,950 12,470,477

39,245,363 13,304,952

Share of total sample Individuals Households

59.9 42.1

73.4 60.4

71.6 62.9

68.3 54.3

Source: Authors’ calculations, based on EUROMOD.

employment rates have significantly increased in recent years in all countries except Finland. Regarding household typologies, it is noticeable that childless households are the dominant household form in all countries except Italy.12 Indeed, Italy is characterised by a particularly high incidence of households with grown-up children. Finland, Germany and the UK have similar shares of households with one and two children. Finland and Italy, moreover, have a significant proportion of households with three or more children (above 11%).

4. SOCIAL PREFERENCES AND THE NEUTRALITY INDEX Before examining the distribution of strategic weight per se, it is interesting to analyse the distribution of the neutrality index, as defined in Section 2. Thus, the tax-benefit system awards a ‘‘family bonus’’ when the neutrality index is greater than 1, but applies a ‘‘family penalty’’ when this figure is lower than 1. In the first case the tax-benefit system is obviously ‘‘pro-family’’, whereas in the second case it is ‘‘anti-family’’. Table 3 shows the average neutrality index: with respect to the four household typologies analysed (i.e. couples without children, couples with one child, couples with two children and couples with three or more children), Italy dominates Finland, which in turn dominates the UK, which in turn dominates Germany. Italy is in fact the only country which appears to have a slightly pro-family tax-benefit system. In the case of households

108

Descriptive Statistics (Weighted).

Table 2. Finland

Italy

UK

Males

Females

Males

Females

Males

Females

Males

Females

989,338 49.8 74.5 35.09 29.57

989,338 47.5 69.7 36.82 30.24

17,487,514 50.1 66.7 39.9 33.1

17,481,694 47.4 49.0 40.0 21.8

12,467,897 50.6 65.8 58.8 7.3

12,467,897 46.8 35.8 54.5 6.0

13,303,374 48.4 64.4 71.5 22.2

13,303,374 45.9 53.5 72.1 22.7

43.9 22.2 21.8 12.1

Source: Authors’ calculations, based on EUROMOD.

53.8 20.5 19.4 6.3

28.7 27.6 32.6 11.1

48.8 20.2 21.9 9.2

KRISTIAN ORSINI AND AMEDEO SPADARO

No. of adult individuals Average age % adults in employment % secondary education % tertiary education % no children % one child % two children % three or more children

Germany

Strategic Weight Within Couples

Table 3.

109

Average Strategic Weight by Number of Children. Finland

Germany

Italy

UK

Couples without children

0.958

0.936

1.022

0.945

Couples with children One child Two children Three or more children

0.928 0.911 0.889

0.857 0.822 0.739

1.015 1.037 1.077

0.904 0.861 0.845

Source: Authors’ calculations, based on EUROMOD.

with three or more children, the sum of the strategic weight is 0.739 for Germany, 0.845 for the UK, 0.889 for Finland and 1.077 for Italy. For couples without children the differences are slightly more contained, and the tax-benefit system approaches neutrality. Germany and the UK are again the two systems which are furthest from neutrality (0.936 and 0.945, respectively), while Finland and Italy are closer (in absolute value) to neutrality: the sum of strategic weight is 1.022 for Italy and 0.958 for Finland. The magnitude of the family ‘‘penalty’’ therefore increases with household size; it is greatest for households with numerous children and lowest for childless households. Italy displays the opposite trend, as households with numerous children apparently receive a larger family ‘‘bonus’’ than households with few children. Obviously, differences in the neutrality index do not only result from the tax-benefit system, but may well be produced by demographic factors or differences in employment levels. Therefore, the information contained in Table 3 is further disaggregated in Table 4. In the latter, we focus exclusively on working-age households and disaggregate the previous figures by female employment status (i.e. in employment or not in employment), arguably one of the most significant factors affecting gender-based strategic weight differences. Germany still appears to have the most anti-family tax-benefit system. In particular, the family ‘‘penalty’’ appears to be extremely consistent in households with children where the mother is not in employment. Finland and the UK display identical features, while Italy is again an outlier having slightly pro-family tax-benefit system. Family ‘‘neutrality’’ is observed for childless couples in which the female is in employment: Italy and the UK approach unity, while Germany and Finland continue to penalise such couples. One last issue, of great political and also policy relevance, is how the level of the penalty or bonus varies as a function of income. Fig. 1 shows the sum

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KRISTIAN ORSINI AND AMEDEO SPADARO

Table 4.

Average Strategic Weight by Female Employment Status (Working-Age Households). Finland

Germany

Italy

UK

Couples without children Female partner not in employment Female partner in employment

0.942 0.953

0.866 0.971

1.035 1.001

0.881 0.993

Couples with children Female partner not in employment Female partner in employment

0.818 0.927

0.745 0.869

1.085 0.977

0.794 0.918

Source: Authors’ calculations, based on EUROMOD.

1.2

1.2

Finland

1.1

1.1

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

Germany

0.6 1

2

3

4

5

6

7

8

9

10

1

2

3

1.2

4

5

6

7

8

9

10

Couples without children Couples with children

Couples without children Couples with children 1.2

Italy

United Kingdom

1.1

1.1

1

1

0.9

0.9

0.8

0.8

0.7 1

2

3

4

5

6

7

8

9

Couples without children Couples with children

Fig. 1.

10

0.7 1

2

3

4

5

6

7

8

9

10

Couples without children Couples with children

Neutrality Index by Disposable Income Deciles (Couples With and Without Children).

of female and male strategic weights as a function of disposable income. Interestingly, all the systems studied tend towards neutrality as income increases. In Finland, Germany and the UK, however, the approach is bottom-up: at lower income levels the tax-benefit system produces a higher

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family penalty, which is reduced as income increases. The size of the penalty, moreover, is higher in the case of households with children. This situation could be interpreted as providing support for the somewhat conservative view that the welfare state (in particular, income support) encourages family disruption and lone motherhood and therefore contributes to social instability. However, what does the anti-family or pro-family nature of the taxbenefit system imply in terms of the strategic weight of the household members? Are the benefits of the family ‘‘bonus’’ equally shared, or does the system award extra strategic weight to one of the household members? In other words: does increasing family as a whole necessarily mean increasing the welfare of each member? Furthermore, which elements of the tax-benefit system affect the distribution of strategic weights? These questions will be discussed in the following section.

5. STRATEGIC WEIGHT In the following analysis, individual strategic weights have been standardised with respect to their total value, as defined in Eq. (5). This facilitates comparison not only across household members, but also across countries. The average male-female strategic weight differential appears to be lowest in Germany and highest in Italy (the normalised strategic weight for females and males is 0.506 and 0.494, respectively, in Germany, compared to 0.354 and 0.646 in Italy). The case of Italy is broadly in line with our expectations, given the differential in male and female employment rates and, therefore, in access to primary income. The results are more surprising for Germany. Male employment rates are similar in Germany and the UK, whereas the British female employment rate is higher than the German one. Nevertheless, the relative strategic weight for German females (0.506) is always higher than that for British women (0.406), and even their Finnish counterparts (0.471), despite the fact that the latter have significantly higher employment rates. Table 4 shows the normalised average strategic weight for females and males, disaggregated for households with children and households with one, two and three or more children. It is immediately apparent that the strategic weight of females without children is quite similar in Germany, the UK and even Italy (varying from 0.344 to 0.369). In households with children, however, the pattern is extremely different. Having one, two or three or more children raises the strategic weight of German mothers to 0.484, 0.547 and

112

KRISTIAN ORSINI AND AMEDEO SPADARO

0.674, respectively. In these countries, it is clear that other aspects of the system play a role at least as important as the employment rate in explaining gender-based strategic weight differentials. At the opposite extreme is Italy, where the presence of children does not appear to be an influence, while Finland and the UK are located between these two extremes. Average strategic weight differentials, however, tend to be somewhat uninformative, given the fundamental heterogeneity of employment statuses and earning capacities in the households sampled. An interesting question concerns the pattern of strategic weight differentials with respect to total income. Figs. 2 and 3 show, respectively, the pattern of strategic weights, by household disposable income, in households without and with children. For couples without children the profile is remarkably flat; this is surprising, as the share of female employment may be expected to rise in line with increasing disposable income. Germany and the UK display a very similar pattern; the strategic weight of males is always between 0.6 and 0.7, while that of females ranges from 0.3 to 0.4. In Finland the gender-based strategic weight differential is far more contained (approximately 0.45 for females and 0.55 for males), although this gap widens in the higher income deciles. Italy, on the other hand, displays a highly atypical pattern: the strategic weight for females is initially very low (0.27 in the first income decile), then 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Finland

Males Females 1

2

3

4

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

5

6

7

8

9

Males Females

Males Females 1

10

Italy

Germany

2

3

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

4

5

6

7

8

9

10

United Kingdom

Males Females

0 1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

Fig. 2. Strategic Weight by Household Disposable Income Decile (Households Without Children).

Strategic Weight Within Couples 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

113 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Finland

Males Females 1

2

3

4

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

5

6

7

8

9

Males Females 1

2

3

4

5

6

7

8

9

10

Males Females 1

10

Italy

Germany

2

3

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

4

5

6

7

8

9

10

United Kingdom

Males Females 1

2

3

4

5

6

7

8

9

10

Fig. 3. Strategic Weight by Household Disposable Income Decile (Households With Children).

increases in the second and third decile, to fall again in the fourth decile. Finally, from the fifth decile onwards it increases more or less linearly. Within the higher income deciles, however, the gender-based strategic weight gap approaches the levels of the other countries studied. When observing couples with children, inter-country differences become more evident. Finland, Germany and the UK show a typical X pattern: in the lower deciles, mothers have a higher strategic weight, which is then progressively reduced, while the strategic weight of fathers increases symmetrically over the whole range. What does vary across the countries observed is the crossing point i.e. the point where fathers’ strategic weight surpasses that of mothers. In the UK this occurs in the second decile, in Finland in the fifth decile and in Germany in the seventh decile. In general, the differences appear to be largely contained, even more so than in the case of households without children. This evidence suggests that the tax-benefit system more than compensates for the lower employment rate typically experienced by mothers (with the exception of Finland, where the employment rate gap of mothers tends to be less extreme). Two features are worthy of comment: the extremely high strategic weight of mothers in the lowest decile in Germany, and the heterogeneous pattern

114

KRISTIAN ORSINI AND AMEDEO SPADARO

of strategic weight differentials in Italy. The first is probably a result of the generous income support benefits for lone mothers. In the second, the pattern is once more somewhat difficult to explain, but may be related to the specific characteristics (e.g. age or labour market participation) of households in the different income deciles. A priori, demographic variables, labour market participation and the taxbenefit system all contribute to shaping the pattern of strategic weights. In order to more accurately separate the role of market and state institutions in determining strategic weight differentials, it is useful (for households of working age only) to look at the influence of female employment status upon strategic weight differentials. Obviously, differences in male employment rates are also significant, but these tend to principally affect retirement behaviour; within primary working age, male employment rates are quite similar. In the following analysis we therefore concentrate on the crucial role of female employment.

5.1. Female Employment Table 5 shows the standardised strategic weight for females and males of working age (20–60), disaggregating this information by the employment status of the female partner. It is immediately noticeable that, in general, the gender-based strategic weight gap for childless couples in which the female works tends on average to be both quite small and fairly similar across countries, ranging from 0.434 (United Kingdom) to 0.475 (Italy). The lower strategic weight of working female spouses is probably due to gender differences in working hours as well as in hourly wages, which still penalise women. However, in childless households in which female partners do not work, their strategic weight falls to 0.183 in Italy, 0.215 in the United Kingdom, 0.288 in Germany and 0.362 in Finland. These differences across countries are not only a result of the various tax-benefit systems: some of the greater strategic weight enjoyed by, for example, Finnish women could reflect their earlier entry into the labour market and, consequently, access to contributory benefits (particularly pensions). In households with children, on the other hand, even if the female partner does not work, the differential between the strategic weight of the male and female partners is much narrower, mainly due to the tax and benefit entitlements children generate. The greatest strategic weight once more corresponds to Italian males (0.759), whereas in Germany the index for mothers

Normalised Average Strategic Weight by Female Partner Employment Status and Presence of Children. Finland

Germany

Italy

United Kingdom

Male

Female

Male

Female

Male

Female

Male

Female

Couples without children Female partner not in employment Female partner in employment

0.638 0.549

0.362 0.451

0.712 0.550

0.288 0.450

0.817 0.525

0.183 0.475

0.785 0.566

0.215 0.434

Couples with children Female partner not in employment Female partner in employment

0.557 0.505

0.443 0.495

0.478 0.456

0.522 0.544

0.759 0.518

0.241 0.482

0.655 0.521

0.345 0.479

Strategic Weight Within Couples

Table 5.

Source: Authors’ calculations, based on EUROMOD.

115

116

KRISTIAN ORSINI AND AMEDEO SPADARO

outweighs that of fathers even when the former do not work (0.522 and 0.478 for females and males, respectively). The UK and Finland occupy an intermediate position. In the case of working mothers, the gap is even narrower than that for childless couples. Here, the additional strategic weight produced by children (which we assign to mothers) makes the distribution almost egalitarian. In Germany, the strategic weight of mothers again outweighs that of fathers, but in the remaining countries the figure falls fractionally short of 0.5. It can thus be observed that amongst working-age couples in which the female partner is in employment, the distribution of strategic weight tends to be quite egalitarian. This does not mean that the tax-benefit system plays an insignificant role: it may well compensate for shorter average working hours and lower average wages among mothers. The impact of net transfers is therefore equally important for non-working-age families, working-age families in which the mother is in employment and working-age families in which the female does not work. In the next section we will specifically address the issue of net public transfers.

5.2. Net Public Transfers Using the framework established above, normalised strategic weights may be decomposed, for both males and females, into a market component (original income) and a public transfers component (net transfers).13 Table 6 presents this decomposition for the four countries studied. Italy is remarkable for the significant role of net transfers in defining strategic weights within childless households. This is unsurprising: as children tend to stay longer with their families than in the rest of Europe, and family formation tends to be considerably delayed, childless households are on average older than in the other European countries considered, and thus they display a higher share of transfers related to old age. Net transfers here are positive (on average) for both female and male spouses, although the size of the transfer tends to reinforce the strategic weight differential of original income. Again, this was foreseeable: since retirement benefits are employment-related, they tend to reproduce strategic weight differential patterns similar to those generated by original income. This also appears to be the case in Finland, while in Germany and the UK net transfers tend to have a very small average effect. At least for the UK, this could be partially explained by the fact that the primary source of income for many retired

Strategic Weight Within Couples

117

people lies in private rather than public pensions, and thus reflects original income. Net transfers also tend to be negative for families with children. The different age structure of households with and without children is likely to have an influence, since adults in households with children tend to be active in the labour market. Germany is noticeable for the significant role of net transfers in determining strategic weight; in particular, it appears that taxes strongly reduce the relative strategic weight of males and increase that of females. At the other extreme is Italy, where public transfers apparently play only a marginal role in the case of households with children, and relative strategic weight is basically determined by market incomes. This is also consistent with the Italian welfare state model, which is strongly biased towards pensions, with only minor child-related benefits and income support schemes. Only in households with three or more children is the strategic weight of mothers increased through the tax-benefit system. The United Kingdom and Finland, on the other hand, display similar patterns for households with children: in both cases transfers reduce the relative strategic weight of males to increase that of. Once again, this is probably due to the interaction between employment and earning differentials and progressive taxation. As in the previous section, it is possible to analyse the role of transfers and original income across income deciles. Figs. 4 and 5 show the profile of strategic weights, by income decile, before and after public transfers to households without and with children, respectively. For each decile, strategic weight has been decomposed into market and net transfer components. The figures show how strategic weight is modified by net transfers: the dotted line represents strategic weight calculated using gross income, whereas the solid line represents strategic weight calculated using disposable income i.e. gross income plus net public transfers. An examination of Fig. 4 reveals that the pattern is quite similar across countries i.e. public transfers ‘‘harmonise’’ strategic weight. Strategic weight calculated using gross incomes tends to increase with income decile, while public transfers increase strategic weight differentials in lower deciles and reduce them in upper deciles. The decile in which the effect changes varies across countries: in Italy, for example, net transfers are positive for both men and women up to the ninth decile; this household typology is on average older than its counterparts in the other countries analysed. In the UK, on the other hand, the effect is reversed in the fifth and sixth deciles, probably due to the lesser role of public old age benefits. In Finland and Germany the switch occurs between the sixth and the eighth decile. From a gender-based

118

KRISTIAN ORSINI AND AMEDEO SPADARO Finland, Females

Finland, Males 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Disposable income Original income

1

2

3

4

5

6

7

8

9

Disposable income Original income

1

10

2

3

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Disposable income Original income

1

2

3

4

5

6

7

8

9

1

10

2

3

4

5

6

7

2

8

9

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

1

10

2

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0 2

3

4

5

6

7

9

10

3

4

5

6

7

8

9

10

8

3

4

5

6

7

8

9

10

9

10

United Kingdom, Females

Disposable income Original income 1

8

Disposable income Original income

United Kingdom, Males 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

7

Italy, Females

Disposable income Original income 1

6

Disposable income Original income

Italy, Males 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

5

Germany, Females

Germany, Males 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

4

9

10

Disposable income Original income

1

2

3

4

5

6

7

8

Fig. 4. Strategic Weights Computed for Gross Market Income and Disposable Income, by Household Disposable Income Decile (Households Without Children).

Strategic Weight Within Couples

119 Finland, Females

Finland, Males 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

Disposable income Original income

1

2

3

4

6

5

7

8

9

10

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

Disposable income Original income

1

2

3

Disposable income Original income

1

2

3

4

6

5

7

8

9

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

10

Original income

2

3

4

6

5

7

8

9

10

Original income

2

3

4

5

6

7

9

10

1

2

3

4

5

6

7

8

9

10

8

9

10

Disposable income Original income

1

2

8

3

4

5

6

7

United Kingdom, Females

Disposable income

1

8

Original income

United Kingdom, Males 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

7

Italy, Females 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

Disposable income

1

6

Disposable income

Italy, Males 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

5

Germany, Females

Germany, Males 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

4

9

10

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

Disposable income Original income

1

2

3

4

5

6

7

8

9

10

Fig. 5. Strategic Weights Computed for Gross Market Income and Disposable Income, by Household Disposable Income Decile (Households With Children).

120

KRISTIAN ORSINI AND AMEDEO SPADARO

perspective, net public transfers have an ambiguous effect. As Table 6 shows, strategic weight is increased for both males and females, although (except in the UK) the increase is greater for the former, in both absolute and relative terms. The decile patterns show that net public transfers constantly increase strategic weight differentials based on original income in Finland and in Germany. Original labour market differences are thus duplicated through employment-related benefits. In the case of Italy, however, net transfers tend to increase strategic weight differentials based on original income in the very bottom and top deciles. In the UK, by contrast, net transfers reduce gender-based strategic weight differentials in the two lowest income deciles and increase them in the rest of the distribution. Fig. 5 depicts a similar pattern to Fig. 4, with some exceptions. For males in Finland and Germany, net public transfers decrease, on average, their strategic weight over the whole income range. The same applies to the UK, starting from the second income decile (in the first income decile positive net transfers still have a positive effect on the strategic weight of males). The extent of the reduction is considerable in Germany and the UK, especially in Table 6.

Average Impact of Net Transfers on Standardised Strategic Weight (by Number of Children). Finland Male

No children Original income Transfers % change

0.574 0.374 0.200 53.554

Female 0.426 0.325 0.101 31.058

Germany Male

Female

0.631 0.369 0.509 0.331 0.122 0.039 23.919 11.717

Italy Male

Female

0.655 0.345 0.373 0.206 0.282 0.138 75.610 67.123

United Kingdom Male

Female

0.641 0.612 0.029 4.814

0.359 0.332 0.026 7.905

0.626 0.374 0.567 0.665 0.393 0.826
0.039
0.019
0.258
5.795
4.777
31.283

0.433 0.432 0.000 0.054

One child Original income Transfers % change

0.525 0.475 0.515 0.485 0.721 0.536 1.036 0.431
0.196
0.062
0.521 0.054
27.158
11.466
50.259 12.564

Two children Original income Transfers % change

0.512 0.488 0.453 0.547 0.645 0.355 0.583 0.417 0.793 0.497 1.240 0.386 0.762 0.371 0.974 0.347
0.281
0.009
0.787 0.161
0.116
0.016
0.391 0.069
35.474
1.771
63.487 41.782
15.278
4.294
40.113 19.999

Three or more children 0.473 Original income 0.745 Transfers
0.272 % change
36.552

0.527 0.326 0.674 0.632 0.368 0.522 0.478 0.408 1.173 0.344 0.731 0.324 0.803 0.278 0.120
0.847 0.330
0.099 0.044
0.282 0.200 29.317
72.195 95.860
13.586 13.681
35.062 72.037

Source: Authors’ calculations, based on EUROMOD.

Strategic Weight Within Couples

121

the lowest deciles. This is probably related to the generous income assistance available for single-earner households; if based solely on original income, males would have an extremely high strategic weight. However, access to income support and generous supplements for children reduces the loss of income that the household would experience if the male partner were to leave. In Finland and Italy the reduction in males’ strategic weight is much lower. In Finland this is mainly due to the presence of a second earner in the household, while in the case of Italy, the lack of a safety net reduces the equilibrating effect of public transfers upon strategic weight. This also explains why the strategic weight for males is considerably higher in the lowest deciles (i.e. in the part of the distribution characterised by lower female employment rates). With respect to childless couples, the effect of transfers switches from positive to negative earlier in the distribution. This is once more due to the different age structure of households with children. The presence of children also explains why strategic weight is so markedly increased by public transfers: lone mothers have access to significantly greater income resources than single males (although of course their needs are much greater). This explains why in the lowest income deciles the strategic weight of females is raised above that of males. In the following section we will attempt to confirm the explanations offered above by examining the effect of each transfer component separately.

5.3. Decomposing Net Transfers In this section we will explore in detail how various instruments contained in tax-benefit systems affect intra-household strategic weight differentials, making intensive use of the microsimulation model. Instruments have been classified into broad groups: (i) taxes and social security contributions, (ii) income support and housing benefits, (iii) family benefits, (iv) old age and sickness benefits, and (v) unemployment benefits. For each group of measures we simulate the strategic weight that would result if these did not exist; this allows us to estimate the specific contribution of each element of the taxbenefit system. The analysis is, once more, performed for households both with and without children. Tables 7 and 8 display the difference between the baseline strategic weight and the strategic weight resulting from the removal of the specific instrument. The results are again disaggregated for households with and without

122

KRISTIAN ORSINI AND AMEDEO SPADARO

Table 7. Average Impact on Individual Strategic Weight of Different Instruments, by Income Decile (Households Without Children). Finland

Germany

Italy

United Kingdom

Male

Female

Male

Female

Male

Female

Male

Female

Taxes/SSC 1 0.00 2 0.00 3 0.00 4 0.00 5 0.00 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


0.04
0.02
0.01
0.01
0.02 0.00
0.02
0.02
0.01
0.03

0.04 0.02 0.01 0.01 0.02 0.00 0.02 0.02 0.01 0.03


0.02 0.02
0.06
0.04
0.01
0.02
0.04
0.02 0.00
0.03

0.02
0.02 0.06 0.04 0.01 0.02 0.04 0.02 0.00 0.03

0.00
0.01
0.01
0.02
0.01
0.03
0.01
0.02
0.01
0.01

0.00 0.01 0.01 0.02 0.01 0.03 0.01 0.02 0.01 0.01

Housing/S.A. benefits 1
0.01 0.01 2 0.00 0.00 3 0.00 0.00 4
0.01 0.01 5 0.00 0.00 6 0.00 0.00 7 0.00 0.00 8 0.00 0.00 9 0.01
0.01 10 0.03
0.03


0.07
0.03
0.01 0.00
0.01 0.01
0.01
0.01 0.00 0.00

0.07 0.03 0.01 0.00 0.01
0.01 0.01 0.01 0.00 0.00


0.09
0.02
0.07
0.02 0.01 0.00
0.02
0.01 0.01 0.00

0.09 0.02 0.07 0.02
0.01 0.00 0.02 0.01
0.01 0.00


0.04
0.03
0.01 0.00
0.01
0.01 0.00
0.01 0.00 0.00

0.04 0.03 0.01 0.00 0.01 0.01 0.00 0.01 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Old age/sickness benefits 1 0.01
0.01 2 0.01
0.01 3 0.01
0.01 4 0.01
0.01 5 0.01
0.01

0.09 0.12 0.15 0.09 0.10


0.09
0.12
0.15
0.09
0.10

0.24 0.18 0.16 0.19 0.18


0.24
0.18
0.16
0.19
0.18

0.02 0.04 0.01 0.00 0.01


0.02
0.04
0.01 0.00
0.01

Family benefits 1 0.00 2 0.00 3 0.00 4 0.00 5 0.00 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00

Strategic Weight Within Couples

123

Table 7. (Continued ) Finland

Germany

Italy

United Kingdom

Male

Female

Male

Female

Male

Female

Male

Female

0.00 0.01 0.00 0.00 0.03

0.00
0.01 0.00 0.00
0.03

0.08 0.04 0.04 0.04 0.02


0.08
0.04
0.04
0.04
0.02

0.16 0.13 0.10 0.07 0.03


0.16
0.13
0.10
0.07
0.03

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

Unemployment benefits 1 0.00 0.00 2 0.00 0.00 3 0.01
0.01 4
0.01 0.01 5 0.00 0.00 6 0.00 0.00 7 0.00 0.00 8 0.00 0.00 9
0.01 0.01 10 0.03
0.03


0.01 0.00 0.00 0.02 0.00 0.03
0.01 0.00 0.00 0.00

0.01 0.00 0.00
0.02 0.00
0.03 0.01 0.00 0.00 0.00

0.02 0.03
0.03
0.01 0.02 0.00
0.01 0.00 0.01 0.00


0.02
0.03 0.03 0.01
0.02 0.00 0.01 0.00
0.01 0.00

0.00 0.00 0.00 0.00 0.00
0.01 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00

6 7 8 9 10

Note: Figures are in italics for absolute changes in the range (0, 0.1], underlined for absolute changes in the range (0.1, 0.4] and in bold for absolute changes in the range (0.4, N). Source: Authors’ calculations, based on EUROMOD.

children. Different fonts have been used for the figures to facilitate their reading; this makes immediately clear which instruments play a significant role in reshaping intra-household strategic weight differentials. For childless families, the situation is relatively simple; since such households tend, on average, to be older the main benefits they receive are pensions, and thus the tax system has only a marginal influence upon strategic weight, particularly in the case of Finland. When it does play a significant role it is the female partner who is principally favoured. In both Germany and in Italy, the existence of family-based provisions in the tax system (e.g. joint taxation or deductions for dependent spouses) tends to increase the income loss that the household would experience if the female spouse were to leave, although this effect is rather modest. Income support and housing benefits, by contrast, are important. Their effect is to reduce the income loss that female partners would suffer if their male partners were to leave the household (in Germany and the UK) or, alternatively, to reduce the income to which employed partners (in this case male) having a dependent spouse or child are entitled. As all such benefits

124

KRISTIAN ORSINI AND AMEDEO SPADARO

Table 8. Average Impact on Individual Strategic Weight of Different Instruments, by Income Decile (Households With Children). Finland

Germany

Italy

United Kingdom

Male

Female

Male

Female

Male

Female

Male

Female

Taxes/SSC 1
0.07 2
0.03 3
0.03 4
0.02 5
0.02 6
0.02 7 0.00 8
0.02 9 0.00 0.02 10

0.07 0.03 0.03 0.02 0.02 0.02 0.00 0.02 0.00
0.02


0.11
0.20
0.13
0.19
0.12
0.10
0.09
0.08
0.07
0.06

0.11 0.20 0.13 0.19 0.12 0.10 0.09 0.08 0.07 0.06


0.03
0.04
0.06
0.04
0.04
0.03
0.02
0.02
0.02
0.03

0.03 0.04 0.06 0.04 0.04 0.03 0.02 0.02 0.02 0.03


0.02
0.02
0.05
0.05
0.04
0.06
0.04
0.02
0.03
0.02

0.02 0.02 0.05 0.05 0.04 0.06 0.04 0.02 0.03 0.02

Housing/S.A. benefits 1
0.08 0.08 2
0.05 0.05 0.04 3
0.04 4
0.02 0.02 5
0.02 0.02 6
0.01 0.01 7 0.00 0.00 8
0.01 0.01 9 0.01
0.01 10 0.05
0.05


0.18
0.22
0.17
0.19
0.11
0.09
0.07
0.06
0.01 0.00

0.18 0.22 0.17 0.19 0.11 0.09 0.07 0.06 0.01 0.00

0.01 0.00
0.01 0.01
0.01
0.01 0.00 0.00 0.00 0.00


0.01 0.00 0.01
0.01 0.01 0.01 0.00 0.00 0.00 0.00

0.04
0.04
0.05
0.06
0.04
0.05
0.03
0.01
0.02
0.01


0.04 0.04 0.05 0.06 0.04 0.05 0.03 0.01 0.02 0.01

Family 1 2 3 4 5 6 7 8 9 10

0.02 0.04 0.03 0.02 0.03 0.02 0.02 0.03 0.00
0.02


0.08
0.07
0.04
0.05
0.03
0.02
0.03
0.01
0.01 0.00

0.08 0.07 0.04 0.05 0.03 0.02 0.03 0.01 0.01 0.00


0.05
0.06
0.06
0.02
0.02
0.02
0.01
0.01 0.00 0.00

0.05 0.06 0.06 0.02 0.02 0.02 0.01 0.01 0.00 0.00

0.03 0.02
0.04
0.03
0.03
0.04
0.03
0.01
0.02
0.01


0.03
0.02 0.04 0.03 0.03 0.04 0.03 0.01 0.02 0.01

Old age/sickness benefits 1 0.00 0.00 2 0.01
0.01 3 0.01
0.01

0.02 0.01 0.02


0.02
0.01
0.02

0.04 0.04 0.03


0.04
0.04
0.03

0.01 0.04 0.01


0.01
0.04
0.01

benefits
0.02
0.04
0.03
0.02
0.03
0.02
0.02
0.03 0.00 0.02

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Table 8. (Continued ) Finland

Germany

Italy

United Kingdom

Male

Female

Male

Female

Male

Female

Male

Female

0.01 0.01 0.00 0.01
0.01 0.01 0.02


0.01
0.01 0.00
0.01 0.01
0.01
0.02

0.01 0.02 0.01 0.02 0.02 0.00 0.00


0.01
0.02
0.01
0.02
0.02 0.00 0.00

0.05 0.06 0.05 0.06 0.06 0.05 0.02


0.05
0.06
0.05
0.06
0.06
0.05
0.02

0.01 0.01
0.02 0.00 0.01
0.01 0.00


0.01
0.01 0.02 0.00
0.01 0.01 0.00

Unemployment benefits 0.02
0.02 1 2 0.02
0.02 3 0.00 0.00 0.02
0.02 4 5 0.01
0.01 6 0.00 0.00 7 0.00 0.00 8
0.01 0.01 9 0.01
0.01 10 0.02
0.02

0.01 0.01 0.03 0.01 0.02 0.01 0.01 0.03 0.00 0.01


0.01
0.01
0.03
0.01
0.02
0.01
0.01
0.03 0.00
0.01

0.02 0.02
0.01 0.01
0.01
0.01 0.00 0.00 0.00 0.00


0.02
0.02 0.01
0.01 0.01 0.01 0.00 0.00 0.00 0.00

0.00 0.02 0.01 0.01 0.01
0.02
0.01 0.00
0.01 0.00

0.00
0.02
0.01
0.01
0.01 0.02 0.01 0.00 0.01 0.00

4 5 6 7 8 9 10

Note: Figures are in italics for absolute changes in the range (0, 0.1], underlined for absolute changes in the range (0.1, 0.4] and in bold for absolute changes in the range (0.4, N). Source: Authors’ calculations, based on EUROMOD.

are means-tested, their effect is strongest in lower income deciles; in higher income deciles, as female partners have access to private sources of income (from either current or previous employment) they are ineligible for meanstested benefits. Finally, public pension systems tend to reproduce inequalities in access to private sources of income produced throughout working life. Since childless households are mainly older households, retirement income has a strong influence upon strategic weights. This effect of pensions is particularly strong in Italy, given the old age bias of the Italian welfare system. The same is true (to a lesser extent) in Germany. In the UK, public pensions mainly affect the lower income deciles, since higher income households have largely opted out of the state system in order to join private pension schemes. Finally, the effect of pensions on the strategic weight of males and females in Finland appears to be much less biased than in the other countries. This is mainly due to the combination of a flat rate universal old age allowance,

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coupled with the historically high participation of females in the labour market. In households with children the situation is much more complex, and here the tax system plays an important role. In Germany, the prevailing joint tax system, characterised by significant tax deductions for dependent children (for higher income groups), significantly increases the strategic weight of the female partner. This effect is highest in the second income decile and decreases progressively as household income (and the income of the female partner) increases. The Italian and British tax systems are basically individualised, but elements of family-based taxation remain in the case of the child tax credit and in the deductions for married couples (dependent spouse). In the UK there also exists a special tax credit for lone parents. These elements tend to increase the strategic weight of the female spouse. As the income of mothers increases, however, the tax advantages (i.e. deductions for dependent spouse) for couples with children either disappear or become relatively less important. Finally, although the tax system in Finland is totally individualised, it nevertheless reduces the strategic weight of male partners, especially in the lowest income decile. This is mainly due to the fact that taxation reduces the weight of the private resources of male spouses to the ‘‘advantage’’ of non-working females. Housing benefits and social assistance (as income support) are particularly important in the case of households with children. Most income support schemes, in fact, include fairly generous child-related supplements as well as special allowances for lone parents. The most generous income support scheme is clearly the German one. The Finnish benefit system is also quite generous, but the number of recipients (as well as the size of the transfer) is smaller, given the higher employment rates for both males and females. In the case of the UK, we have included Family Credit (a tax credit) within aggregate income support and housing benefit: this explains why the effect of these instruments tends to be significant in all income deciles. Finally, Italy lacks a well-developed system of income support; employed workers are entitled to social transfers if their wages are below a certain threshold, but the effect of this scheme is extremely limited. A similar scheme also provides income supplements to employed parents of dependent children. These child benefits are quite strictly means-tested and their effect is significant only in the lower income deciles. Family income support is also means-tested in the case of Germany, and higher income groups usually prefer the more favourable tax deduction scheme. In Finland and in the UK, on the other hand, child benefit is universal, although its impact is moderate over the whole range of the distribution.

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What seems a priori illogical is the negative effect on women’s strategic weight of removing family benefits in the lowest income deciles. This is in fact largely explained by interactions between the tax and benefit systems i.e. cutting off child benefit leads to increased housing benefit and income support. The above also demonstrates the limitations of our approach: in highly complex welfare states it is impossible to measure the precise impact of a specific instrument, especially since every instrument has been designed taking into account the other instruments which exist in the tax-benefit system. However, this paper by no means attempts to measure the overall impact of this system upon the individual strategic weight of spouses; instead, the aim is simply to demonstrate the diverse effects of particular elements of the tax-benefit system upon the strategic weight of partners within a family.

6. CONCLUSIONS Employing a highly intuitive concept of intra-household strategic weight, based on microsimulation techniques, we have computed the strategic weight of each spouse and examined its dependence on the tax-benefit system in four European countries between which that system differs greatly. The results show that these differences play an important role in determining such strategic weights. We believe our proposed index may be of great utility in the empirical evaluation of redistribution systems, as we have shown. Naturally, we understand and accept the limitations discussed in Section 2. For example, the framework adopted is completely static; that is to say, when calculating the strategic weight of one of the partners, we did not consider the possibility that the other partner may adjust his/her behaviour in the labour market, and nor did we consider the role of household production or of public goods. Moreover, the decision to ‘‘assign’’ children to mothers may be questionable. Traditionally, however, children are assigned to female spouses on the basis of socially dominant gender roles, and women’s ‘‘control’’ over children may well compensate for their lower strategic weight with sole regard to income (Lundberg & Pollak, 1993). It is important to note, however, that strategic weight should not be interpreted as a sharing rule, but instead as simply one factor among several which may affect the intra-household distribution of part or all of its resources. With regard to a sharing rule, it would be reasonable to assume that part of total household income is used to purchase non-private goods and services, and

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that only a residual share is allocated in accordance with strategic weight differentials (see Chen & Wolley, 2001). Bearing such limitations in mind, our approach provides further clarification of how social and individual preferences interact to determine strategic weight within the household, and of the distribution of strategic weight differentials. Individual preferences principally affect individuals’ labour supply strategies, which play a significant role in determining earning capacity and, consequently, strategic weight differentials. However, differences in male and female employment rates are only one of the factors affecting strategic weights within a couple. Net transfers, both positive and negative, also play a significant role in reshaping strategic weight differentials. While some measures are largely neutral, others tend to reduce existing inequalities or exacerbate intra-household strategic weight differentials. On this point, it is interesting to note that a pro-family tax-benefit system might have ambiguous effects on the welfare of individuals within the family. If such a system is intended to reduce the outside options of the ‘‘weak’’ partner, the effect on the individuals within the household might be far from desirable. This is particularly evident in the Italian case: the pro-family system implicitly encourages family formation and preservation, but does so at the cost of reducing the strategic weight of the weak partner. At the other extreme is Germany, whose system unexpectedly appears to penalise family stability. However, the policies which reduce incentives for family preservation simultaneously produce a more equitable distribution of strategic weight, and possibly of resources. This effect is particularly important for the lowest deciles, where strategic weight differentials are most important and where the unequal distribution of resources (influenced by the unequal strategic weights of the partners) may perversely affect individual welfare, producing poor individuals within non-poor families, for example. However, it is also in the lowest income deciles where public policies may significantly adjust strategic weights. In higher income deciles the strategic weight of spouses tends to be far more equal; individual preferences (and the distribution of human capital and talents) are the principal factors shaping strategic weight differentials in higher income groups. The marginal role of public policies is also demonstrated by the fact that the distribution of strategic weight is similar within highly diverse institutional situations. The index presented in this paper may therefore be employed as a straightforward tool to analyse the impact of tax-benefit systems on relative strategic weight, to compare their effect across countries and to assess the

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impact of tax-benefit reforms which may affect differently the strategic weight of individuals within the household. More ambitiously, this index could be used as a starting point for the elaboration of a more realistic sharing rule i.e. one which takes into account dynamic strategies e.g. individual responses to the threat of family breakup, as Rubinstein (1982) remarks, adult control over younger children and economies of scale in the purchase of public goods and services. Empirically, it would be interesting to discover if there exist natural experiments within countries which could be used to validate the index proposed here or if empirical regularities may be found to suggest that couples in which, say, the female’s strategic weight is high, adapt their behaviour, and that such changes are to be expected. This and other related topics must, however, be left for future research.

NOTES 1. See, for example, Leuthold (1968), Ashworth and Ulph (1981), Bourguignon (1984), Chen and Wolley (2001), Rubinstein (1982) and Binmore (1985). See Donni (2006) for an extensive review of non-cooperative models and their properties. 2. Lundberg and Pollak (2003) have shown, however, that if current decisions affect spouses’ future strategic weight, then inefficient outcomes are possible. For a discussion, see also Lundberg and Pollak (1994), Ott (1992) and Donni (2006). 3. See Vermeulen (2002) for a complete survey. 4. See the special issue of the Review of Economics of the Household (Vol. 4, No. 2, June 2006) on the collective model and its application to the evaluation of tax reforms. 5. This last point is highly relevant to policy analysis. Several papers suggest a correlation between the tax-benefit system and the strategic weight. In a study by Beblo, Beninger and Laisney (2003), to cite merely one of these, the calibrated strategic weight is then regressed (together with other demographic variables) on the ratio of the earnings potentials of the spouses (i.e. the average disposable income when switching from 0 to 40 h, given the alternative labour supply strategies available to the partner). The coefficients of the regression are then used to predict the strategic weight under alternative scenarios. A change in the tax-benefit system would in fact alter the earnings potentials and hence the strategic weight. 6. On the contrary, we wish to stress the importance of conducting further research in these directions. 7. The Shapley value has been also applied to the decomposition of inequality by Shorrocks (1999) and Sastre and Trannoy (2002). 8. We will discuss the implications of this strong hypothesis at the end of this section. 9. This example has been suggested by an anonymous referee who we are logically and unfortunately unable to acknowledge.

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10. Alternatively, children can be seen as a commitment mechanism. They have long-term implications, not least because they generate a liability to child support which is not modelled here in any way. 11. For a detailed description of EUROMOD, see Sutherland (2001). 12. It should be noted that childless households could be comprised by younger couples, as well as older couples whose children have already left the household. 13. Replacement incomes in this case have been treated as net transfers; arguably, however, they could be considered as deferred wages.

ACKNOWLEDGMENTS This is a completely revised version of the paper ‘‘Sharing resources within the household: a multi-country microsimulation analysis of the determinants of intra-household ‘strategic weight’ differentials and their distributional outcomes’’, PSE Working Paper No. 2005-04. We are grateful to Vincenzo Atella, Dani Cardona, Andre´ Decoster, Jacques Lecacheux, Holly Sutherland and Luc Gladiateur for their in-depth comments. We are indebted to four anonymous referees for their useful comments. All errors or omissions are entirely the responsibility of the authors. This paper was written as part of the MICRESA (Micro Analysis of the European Social Agenda) project, financed by the Improving Human Potential programme of the European Commission (SERD-2001-00099). For the countries considered in this paper, EUROMOD relies on the following microdata: the Income Distribution Survey supplied by Statistics Finland; the German Socio-Economic Panel Study made available by DIW; the Survey of Household Income and Wealth, provided by the Bank of Italy; and the Family Expenditure Survey, supplied by the British Office for National Statistics. We are indebted to our present and former colleagues of the EUROMOD team. Amedeo Spadaro gratefully acknowledges financial support from the Spanish Government – MCYT (SEJ2005-08783-C04-03).

REFERENCES Ashworth, J., & Ulph, D. (1981). Household models. In: B. Charles (Ed.), Taxation and labour supply (pp. 117–133). London: Allen and Unwin. Beblo, M., Beninger, D., & Laisney, F. (2003). Family tax splitting: A microsimulation of its potential labour supply and intra-household welfare effects in Germany. ZEW Discussion Paper, No. 03-32, Manheim. Becker, G. (1974). A theory of marriage: Part II. The Journal of Political Economy, 82, S11–S26.

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Binmore, K. (1985). Bargaining and coalitions. In: A. Roth (Ed.), Game-theoretic models of bargaining (pp. 259–304). Cambridge: CUP. Blumber, R. L. (1988). Income under female versus male control: Hypotheses from a theory of gender stratification and data from the third world. Journal of Family Issues, 9(1), 51–84. Bourguignon, F. (1984). Rationalite´ individuelle ou rationalite´ strate´gique: le cas de l’offre familiale de travail. Revue E´conomique, 35(1), 147–162. Bourguignon, F., Browning, M., Chiappori, P.-A., & Leche`ne, V. (1993). Intrahousehold allocation of consumption: Some evidence on French data. Annales d’Economie et Statistique, 29, 137–156. Bourguignon, F., & Spadaro, A. (2006). Microsimulation as a tool for evaluating redistribution policies. Journal of Economic Inequality, 4(1), 77–106. Browning, M., Bourguignon, F., Chiappori, P.-A., & Leche`ne, V. (1994). Income and outcomes: A structural model of intrahousehold allocation. The Journal of Political Economy, 102(6), 1067–1096. Chen, Z., & Wolley, F. (2001). A Cournot-Nash model of family decision making. The Economic Journal, 111(October), 722–748. Chiappori, P.-A. (1988). Rational household labor supply. Econometrica, 56(January), 63–89. Chiappori, P.-A. (1992). Collective labor supply and welfare. The Journal of Political Economy, 100(June), 437–467. Donni, O. (2006). Les mode´les non-coope´ratifs d’offre familiale de travail: The´orie et e´vidence. L’Actualite´ Economique: Revue D0 analyse E´conomique, 82, 181–206. Esping-Andersen, G. (1990). The three worlds of welfare capitalism. Princeton, NJ: Princeton University Press. Esping-Andersen, G. (1999). Social foundations of postindustrial economies. New York: Oxford University Press. Grossbard-Shechtman, A. (1984). A theory of allocation of time in markets for labor and marriage. Economic Journal, 94, 863–882. Grossbard-Shechtman, S., & Neuman, S. (1988). Women’s labor supply and marital choice. Journal of Political Economy, 96, 1294–1302. Haddad, L., & Kanbur, R. (1994). Are better-off households more unequal or less unequal. Oxford Economic Papers, 46, 445–458. Konrad, K., & Lommerud, K. (2000). The bargaining family revisited. Canadian Journal of Economics, 33, 471–487. Leuthold, J. (1968). An empirical study of formula income transfers and the work decision of the poor. Journal of Human Resources, 3, 312–323. Lundberg, S., & Pollak, R. (1993). Separate spheres bargaining and the marriage market. The Journal of Political Economy, 101(December), 988–1010. Lundberg, S., & Pollak, R. (1994). Noncooperative bargaining models of marriage. The American Economic Review, 84(2), 132–137. Lundberg, S., & Pollak, R. (2003). Efficiency in marriage. Review of Economics of the Household, 1, 153–167. Manser, M., & Brown, M. (1980). Marriage and household decision-making: A bargaining analysis. International Economic Review, 21, 31–44. McElroy, M., & Horney, M. (1981). Nash-bargained household decisions: Towards a generalisation of the theory of demand. International Economic Review, 22, 333–349. Ott, N. (1992). Intrafamily bargaining and household decisions. Berlin/Heidelberg: SpringerVerlag.

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Phipps, S., & Burton, P. (1992). What is mine is yours? The influence of male and female income on patterns of household expenditure. Discussion Paper 92-12, Department of Economics, Dalhousie University. Phipps, S., & Burton, P. (1993). Collective models of household behaviour: Implications for economics policy. Paper presented at the Status of Women Economic Equality Workshop, Ottawa, 29–30 November. Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica, 50, 97–109. Sastre, M., &, Trannoy, A. (2002). Shapley inequality decomposition by factor components: Some methodological issues. Published in Moyes, P., Seidl, C., & Shorrocks, A. (2002). Shapley, L. S. (1953). A value for n-person games. In: H. W. Kuhn, & A. W. Tucker (Eds), Contributions to the theory of games (Vol. II, pp. 307–317). Princeton: Princeton University Press. Shorrocks, A. F. (1999). Decomposition procedures for distributional analysis: A unified framework based on the Shapley value. Unpublished paper, University of Essex. Sutherland, H. (2001). Final report EUROMOD: An integrated European tax-benefit model. EUROMOD working paper EM9/01. Vermeulen, F. (2002). Collective household models: Principles and main results. Journal of Economic Surveys, 16, 533–564.

PROGRESSIVITY IMPLICATIONS OF PUBLIC HEALTH INSURANCE FUNDING IN CANADA James B. Davies and Michael Hoy ABSTRACT We adopt a standard distributional impact methodology, based on Atkinson’s cost of inequality approach, to estimate the degree of implicit redistribution created through public funding of health insurance in Canada. The first stage of the exercise is to determine the public health insurance benefits received by families of various age and composition and to add these to measured after-tax incomes. In our base case, which uses the Atkinson Mean Logarithmic Deviation as inequality index, we find that accounting for public health insurance benefits implies a reduction in inequality equivalent to 2.4% of per capita income. We then model the implications of moving to a hypothetical fully privatized system while proportionately refunding to individuals the tax revenues saved in doing so. This would give rise to a further 2.4% equivalent per capita income reduction resulting from increased inequality in the distribution of aftertax income. Thus, for this scenario, moving from public financing of health insurance in Canada to a fully privatized system implies an overall increase in inequality equivalent to a loss of 4.8% of per capita income. This corresponds to an increase of about 25% in existing inequality. Not

Equity Research on Economic Inequality, Volume 15, 133–167 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15007-9

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surprisingly, the impact of publicly financed health insurance in reducing inequality is strongest for the elderly.

1. INTRODUCTION In recent years, there has been considerable debate about the best way to finance health care. At the same time, there have also been some important changes in funding practices. As noted in Wagstaff et al. (1999, p. 269), ‘‘It is well known that during the last decade or so, there has been a shift in many OECD countries away from public sources of finance (for health care) to private sources’’. One of the principle arguments for doing so is to reduce the burden of taxation. If the tax system is progressive, however, it is also important to measure the equity benefits of publicly funded health care in order to be able to make an informed choice regarding the tradeoff between reduced taxes, with the accompanying efficiency benefit to the economy, and any welfare loss due to reduced equity. Our goal in this paper is to measure this latter cost using the Canadian health care and income tax systems as an example. More specifically, in this paper we study the distributional impact of a hypothetical move from completely public to totally private financing of health care, applying our methods to Canada. In a private system, premiums would be based on age and gender, as well as on other individual characteristics related to expected health care costs. In a public system, premiums tend to be more uniform or even absent. In Canada, in particular, essentially all funding comes from the government’s general tax revenues (see Aba, Goodman, & Mintz, 2002, p. 2). Here, we do a standard distributional impact analysis of switching between these radically different methods of funding. We adopt some simplifying assumptions which we believe, for the most part, lead to fairly conservative estimates of the reduction in inequality generated by a public health care system in comparison to a private system. For example, we assume that premiums would only depend on age and gender under a private system, which may lead to underestimation of the fees that would be paid by poor people, who may on average have higher health risks, or others with pre-existing health problems. One feature, however, that may lead to an over-estimate of the equalizing impact of a public system is that impact analysis does not allow for behavioural changes.1 After a move to a private system, lower income households may opt for lower levels of coverage and lower premiums. In contrast, we assume they

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would have to pay the full actuarial cost of unchanged coverage, perhaps tending to exaggerate the disequalizing impact of moving to a private system. There are also equity effects that could in principle be incorporated in impact analysis but which are not included in our calculations. For example, although it is a matter of dispute, some studies indicate that lower income people receive less care than higher income groups in public systems. If so, then they could perhaps get the same level of coverage under a private system with lower premiums than we assign them in our calculations. We neglect this aspect in part because the evidence on inequities of this type is mixed. Also, such inequities are not a necessary aspect of a public health care system, but are consequences of the methods of delivery and the information available to individuals.2 In Canada, public health care is funded largely out of general tax revenues and is shared by provincial and federal governments. The Canada Health Act goes so far as to forbid explicit user charges for medically necessary doctor and hospital services. In 1977, the federal government altered the EPF (Established Programs Financing), which was used to transfer funds to provinces based specifically upon postsecondary education and health care expenditures, in favour of a block grant covering both areas in a way to be determined by the provinces. Further changes were made in 1996–1997 when the EPF was abandoned altogether in favour of the CHST (Canada Health and Social Transfer) which pooled even more programs into a block grant.3 This complicates the question of assigning these tax costs to determine the distributional impact of the required ‘‘additional’’ tax collections needed to finance a publicly provided health care system. If all taxes rise together to create the needed revenue, the incidence may be approximately proportional to income – in line with the well-known result that the tax system as a whole typically has roughly proportional incidence (see e.g., Gillespie, 1980; Pechman, 1985). In contrast, if a payroll tax is earmarked to partially fund health care, or if personal income tax is the marginal source of funds, the distributional impact may deviate from proportionality. An additional complication is that in a world of private health insurance, it is possible that premia would qualify for income tax deductions or credits. This could increase the effective regressivity of the funding burden; that is if the value of this tax relief rose more than in proportion to income. Also, in health care systems that are largely privatized, some provision of health insurance is usually provided to low income individuals (e.g., Medicaid in the US). Reducing the extent to which individuals qualify for such benefits, however, can actually lead to increased costs of health coverage due to the shift of care from visits to doctor’s offices to more expensive visits to emergency

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departments and increased hospitalizations. Hence, the expected savings in tax-financed health provision from increased privatization may not be experienced to the extent expected (e.g., see Butler, Johnson, & Rimsza, 2006). In any case, the distribution of the funding burden is likely to be more regressive under the case of private insurance than for publicly provided insurance, where premiums depend on level of coverage and personal characteristics rather than earnings or income. We assess the benefit of publicly provided health care for each family to be the avoidance of private health insurance premiums that would be required for the same level of health care based on age and gender, net of additional tax burdens imposed to fund the system. This is equivalent to assuming that insurance premiums in a hypothetical private health insurance plan would be based only on age and gender and that individuals would all purchase the same coverage (i.e., for the same health benefits) as is currently provided in the public system. These and other assumptions are discussed in detail in the paper. It is perhaps not surprising that we find that inequality in disposable income is lower under a public health care system than under a private system. But we should want to know more than this. Is the increased welfare resulting from reduced inequality of sufficient magnitude to be a serious consideration in deciding whether to maintain a publicly provided health care system? To answer such questions we must make some value judgements, and we must be clear about how much importance is placed on equality. We do this by adopting the framework of utilitarian social welfare functions (swf ’s). We illustrate the approach by using the additive iso-elastic family of swf ’s, which generate the well-known Atkinson inequality indices. The Atkinson indices allow one to vary the degree of inequality aversion, and to translate inequality changes readily into equivalent changes in per capita income through their ‘‘cost of inequality’’ interpretation. This gives us a flexible tool that makes the welfare impact of inequality changes comparable with those of efficiency changes. It is well established that the cost of providing public health care is particularly high for those in older age groups. Therefore, we consider separately the subgroup of the population for those with family heads aged 65 and older and perform a decomposition analysis by age group (families with heads aged under 65 and families with heads aged 65+). We do indeed find that the equality enhancing effect of public health care provision is especially strong for the older age group. The effects on between-group inequality levels depend very much on the particular inequality index and decomposition method chosen. These results prove interesting in a number of respects.

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Overall, our computations indicate that public health care, as funded in Canada, reduces inequality considerably. The remainder of the paper is organized as follows. The next section outlines our methods. Section 3 presents results for the Canadian case. In Section 4 we then discuss those results, considering their limitations and also how they might differ under other assumptions and in other countries. Conclusions are provided in Section 5.

2. METHODOLOGY Due to the progressivity of the Canadian income tax system, after-tax incomes are distributed more equally than are before-tax incomes.4 Many government transfers, such as old age security and welfare payments, are also progressive. The incidence of other government programs, such as health care and education, however, is less well studied due to measurement problems as well as lack of appropriate data.5 The report ‘‘National Health Expenditures in Canada 1975–1994’’ (1996) provides data on public health expenditures on individuals by age and gender allowing us to ascertain what the relevant private health insurance premiums would have to be to cover people of different ages and genders. We assume that, in the absence of public health insurance, individuals would be charged premiums for private coverage based on their age and gender and that these premiums would equal the relevant age- and gender-based expenditures. There are several important assumptions implicit in this approach which we list below and then discuss. 1. In the absence of publicly provided health care, people would purchase the same type of private insurance coverage regardless of their income and this coverage level would be equal to that required to provide existing levels of care. 2. This approach presumes that the cost of health insurance would be equal to the amount that is required to finance existing levels of care at existing delivery costs as generated by the public health care system. 3. This approach also presumes that insurance premiums would not depend on any factors other than age and gender. While it is necessary to make simplifying assumptions to make progress here, it must be recognized that the above are strong assumptions. In the case of the first assumption noted above, it is not likely that everyone would wish to purchase the same level of coverage in a private insurance scenario, and even if that were so it is not likely that the coverage level chosen would just

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happen to coincide with the particular services provided by the existing public health system.6 As for the second assumption, it is possible that private health insurance could be linked to efficiencies in the delivery of health care which could lead to lower costs, although the opposite is also a possibility. Finally, considering assumption 3, private insurers are likely to use more than age and gender as categorization variables. Pre-existing health problems, behavioural traits such as smoking, and results of diagnostic tests (e.g., persistent high blood pressure) are likely to influence health insurance premiums. We will discuss the impact of adopting more general assumptions in the last section of the paper. The assumptions we have adopted allow for a clear basis on which to develop benchmark comparisons. If there were no public health insurance system, then substantial tax revenues would be freed up and we need to account for this. In 1994, for example, public health expenditures in Canada were $52 billion. This represents 49% of the aggregate personal income taxes paid according to the Survey of Consumer Finance (1994), which we use in the calculations reported later in this paper. In those calculations we assume that in the absence of a public health care system, income taxes would be reduced by equal proportionate reductions in the amount paid across all income groups.7 This type of tax cut preserves the existing degree of liability progression, and hence has been referred to as an LP-neutral tax cut. Since higher income individuals generally have higher tax liabilities both in absolute terms and as a fraction of pre-tax income, an LP-neutral tax cut leads to an increase in relative inequality. As an alternative, consider a tax cut that returns the same percentage increase in post-tax income to everyone (i.e., one that preserves residual progression, termed an RP-tax cut). Pfahler (1984) showed that, given any existing progressive (strictly convex) income tax schedule, an LP-neutral tax cut leads to a less equal distribution than would an RP-neutral tax cut (see also Lambert, 2001, pp. 219–224). Moreover, if in addition the existing pre-tax income distribution is positively skewed, then the majority would favour an RP-neutral tax cut. Thus, we recognize that our suggested tax-cut, being an LP-neutral one, is not the only one that could be considered. Moreover, our choice may exaggerate the inequality implications of moving to a private health insurance scheme. We return to this point again in the concluding section. In order to assess the relative effects on economic welfare and inequality under a public and hypothetical private health insurance scenario, we use Atkinson’s (1970) cost of inequality framework.8 Let Yede be the ‘‘equally distributed equivalent income’’: that is, the income that if received by all would generate the same social welfare as the actual income distribution

Progressivity Implications of Public Health Insurance Funding in Canada

139

Y1, y , Yn. The gap between Yede and mean income, m, is an appealing measure of the ‘‘cost’’ of inequality as it reflects the fraction of income that could be eliminated while maintaining the same level of welfare as obtained by the existing distribution of income provided incomes were equally distributed. Thus, the difference in this measure for our two income distributions that are generated by different (hypothetical) health care systems provides a useful measure of the relative efficiency of the two systems in generating welfare. Moreover, this measure provides for a useful comparison with any measures of market inefficiency for either or both systems. Thus, the Atkinson inequality measure, defined as
 Y ede A¼1
(1) m represents the percent reduction in mean income that could be allowed if income were to be distributed equally without reducing social welfare. This measure varies between 0 (complete equality) and 1 (complete inequality – one person holds all the income). It can be used to assess the impact of inequality on welfare from the viewpoint of widely varying social welfare functions. Atkinson illustrated with the additive (Utilitarian) social welfare function with iso-elastic utility function; that is, U(y) defined by yð1
eÞ ea1; e40 1
e ¼ lnðyÞ e ¼ 1

UðyÞ ¼

ð2Þ

whose properties are so familiar to economists in other contexts. Here, the parameter e reflects aversion to inequality, and ranges from 0 (complete insensitivity to inequality) to N (sensitivity to inequality is so strong it approaches the Rawlsian case). Applying Eq. (2) in a Utilitarian social welfare framework, we get the associated inequality measures: " #1=ð1
eÞ
 1 X yi ð1
eÞ Ae ¼ 1
ea1; e40 (3) n m In the case of e ¼ 1 we obtain the particular member of the Atkinson family which isP ordinally equivalent to the so-called mean logarithmic deviation MLD ½
ð1=nÞ lnðyi =mÞ: Thus, we also refer to this particular member of the Atkinson family as the AMLD measure, with formula given below:  X
 1 y ln i AMLD  A1 ¼ 1
exp (4) n m

140

JAMES B. DAVIES AND MICHAEL HOY

In the calculations reported in this paper we use the Atkinson measure, which is attractive because of its explicit ethical basis, flexibility, and ready interpretation in welfare terms.9 In order to illustrate how this framework helps us to assess inequality in welfare terms, consider the following example. Suppose the AMLD index of some income distribution A were 0.18 while for some other distribution B, with the same per capita income level, the degree of inequality were 0.13. One would say that in A the equivalent of 18% of income per capita is effectively ‘‘lost’’ due to inequality, while the ‘‘cost of inequality’’ is only 13% in the case of distribution B. Thus, moving from A to B is equivalent in welfare terms to a 5% increase in per capita income. Measured inequality, and the cost of inequality, of course depend on how averse one is to inequality. In terms of the Atkinson measures we illustrate this point with a simple two-person case using parameter values e ¼ 1 and e ¼ 2 in Fig. 1. Consider the initial income distribution of y1 ¼ $18,000 and y2 ¼ $54,000, implying an average income of $36,000. This pair of incomes Y2

.

(18000, 54000)

e=1

e=2 Y2 + Y1 = 72,000 Y1 27,000

31,180

36,000

Fig. 1. The Equally Distributed Equivalent Income Per Capita is $31,180 for e ¼ 1 and $27,000 for e ¼ 2. Thus, the Per Capita Cost of Inequality is $4,820 (or 13.4% of Total Income) for e ¼ 1 and $9,000 (orP25% of Total Income) for e ¼ 2. The Underlying Welfare FunctionPis W ¼ i ðyð1
eÞ =ð1
eÞÞ for e40; ea1 and i W ¼ i lnðyi Þ for e ¼ 1.

Progressivity Implications of Public Health Insurance Funding in Canada

141

represents approximately the average after-tax incomes of the poorest 50% and the richest 50% of the population (see Table 1) in Canada in 1994. For parameter value e ¼ 1, the measure of inequality is A1 ¼ 0.134 while for e ¼ 2 it is A2 ¼ 0.25. As illustrated in the graph, the same level of social welfare could, if incomes were equally distributed, be obtained with average income level of $31,180 for the case of e ¼ 1 (i.e., 13.4% less income) and with average income of $27,000 (i.e., 25% less income) for the case of e ¼ 2. The cost of inequality is thus regarded as higher if one has higher inequality aversion.10 While it is not necessary to take the social contractarian view of the Utilitarian Welfare framework in order to justify use of the Atkinson index, we do find it helpful to refer to the risk measurement literature in order to help judge what are reasonable values for the parameter e. The iso-elastic form of U is often used to estimate the degree of relative risk aversion. Estimates vary across individuals and studies, but values of e ¼ 1 to e ¼ 2 are generally considered reasonable.11 Since we do not wish to exaggerate the importance of inequality, we avoid the use of higher values in our calculations, and focus mainly on the results for e ¼ 1. We also indicate outcomes for the even more conservative view of inequality implied by e ¼ 0.5. We ascertain the benefit from public health care in reducing the degree of inequality in ‘‘net’’ incomes as follows. First, we find the degree of income inequality in measured after-tax incomes using the Atkinson indices noted above. Then we determine the actuarial value of the health insurance coverage, or ‘‘health insurance benefit’’, that the public system provides for each family, based on the number, age, and gender of its members. (See the next section for more details.) We add this benefit to their after-tax incomes in order to generate our net income value in the presence of public health care. Recognizing that in the absence of a public health care system individuals would be required to pay privately for heath insurance but would avoid having to pay for health care through the tax system, we then determine the distribution of net after-tax income that would result if income tax payments were reduced by 49% across all families. Since higher income families pay higher income taxes, this change in taxes will lead to greater benefits for higher income families than for lower income families and so increase measured inequality. The degree of inequality in this hypothetical income distribution (with no public health insurance) relative to that in existing net incomes (i.e., including public health care benefits) provides a measure of the effect of public health care funding in reducing inequality. Further complications could arise in measuring the impact of how governments may alter the tax system in moving to a world of private health

142

JAMES B. DAVIES AND MICHAEL HOY

Table 1. Decile Means – 1994 Family Incomes, Taxes, and Health Care Benefits. Decile

After-Tax Income

Income Tax Paid

Gross Health Care Benefit

Net Health Care Benefita

All ages 1 2 3 4 5 6 7 8 9 10

7,157 13,204 17,786 23,126 28,427 33,968 40,373 47,876 58,514 87,086

166 626 1,607 3,001 4,999 7,015 9,440 12,396 16,504 30,567

2,119 4,399 4,404 5,133 4,397 4,209 4,233 4,239 4,460 4,822

2,037 4,091 3,614 3,658 1,941 762
405
1,852
3,650
10,198

Top 5% Top 1% Overall

102,075 146,493 35,750

38,723 70,364 8,632

5,072 5,384 4,241


13,956
29,191 0

6,434 13,479 19,728 25,850 31,312 37,027 43,263 50,689 61,382 89,874

114 1,046 2,509 4,589 6,470 8,555 10,937 13,625 17,962 31,919

1,492 1,867 2,202 2,472 2,657 2,957 3,237 3,493 3,849 4,356

1,435 1,353 969 217
522
1,247
2,137
3,202
4,977
11,328

104,896 149,352 37,903

40,400 73,390 9,772

4,560 4,613 2,858


15,292
31,449
1,944

10,630 12,993 14,483 16,685 20,170 23,120 27,028 32,428 41,398 66,675

145 124 400 932 1,052 1,298 2,517 4,197 7,491 19,448

7,408 7,397 7,435 8,587 11,067 11,644 11,535 11,890 12,253 12,314

7,337 7,336 7,239 8,129 10,550 11,006 10,298 9,828 8,572 2,758

Under age 65 1 2 3 4 5 6 7 8 9 10 Top 5% Top 1% Overall Age 65 and older 1 2 3 4 5 6 7 8 9 10

Progressivity Implications of Public Health Insurance Funding in Canada

143

Table 1. (Continued ) Decile

Top 5% Top 1% Overall

After-Tax Income

Income Tax Paid

Gross Health Care Benefit

Net Health Care Benefita

80,548 125,541 26,553

26,738 53,335 3,757

12,581 12,995 10,153


557
13,212 8,306

Sources: Columns 2 and 3: Statistics Canada (Household Surveys Division) – Economic Families, 1994 Incomes; column 4: Health Canada. National Health Expenditures in Canada. Policy and Consultation Branch – 1996; column 5: author’s calculation. a Net health care benefit is equal to gross health care benefit less 49% of income tax paid.

care. For example, it is possible that governments would provide income tax deductions or partial credits for health insurance premia. Such tax relief could either increase or reduce the disequalizing impact of switching to the private system depending on patterns of expenditure on health insurance. (If this spending did not vary with income, credits would be equalizing and deductions could be equalizing as well if marginal tax rates did not rise too sharply with income. Once expenditures are allowed to rise with income, results become less clear-cut.) Also, there is likely to be significant variation in such spending even among families at the same income level and with the same demographic structure. Loomis and Revier (1988) outline a method for analysing the impact of selective tax or subsidy measures that could be applied to analyse the impact of tax relief for health insurance expenditures when there is this real-world heterogeneity. In addition to being sensitive to assumptions noted earlier in this section, our results depend on two further important aspects. First, in an actual privatization of health care the tax relief might not be distributed as we have assumed. Second, a tax reduction of this size can be expected to have incentive effects on labour supply and other income generating activities. Thus, both the distribution of before- and after-tax money income would likely change as a result of the tax reduction. We discuss how our results might differ if these factors were taken into account later.

3. RESULTS We perform two experiments. Our first experiment is to consider how including the monetized value of public health provision changes the measured level of inequality. We do this by determining the health insurance premiums

144

JAMES B. DAVIES AND MICHAEL HOY

that are inferred for each family based on the number, age, and gender of family members.12 We will refer to this as the gross health benefit HBi for each family, i. HBi is, under our assumptions, the actuarially fair private insurance premium that would have to be paid in order to obtain access to the existing level of health care services. Let Y Bi represent before-tax income, A B YA i be after-tax income, and Ti be income tax paid (i.e., Y i ¼ Y i
T i ). In each of the Tables 2–4 and 6–8, the first set of data on incomes is simply based on Y A i ; measured after-tax incomes. The second set of columns is based on after-tax incomes plus the imputed value of health benefits YA i þ HBi ; which we will refer to as income under public health, and so reflects the impact of accounting for these benefits when measuring income inequality. Comparing these two sets of results allows us to infer how much more equally distributed disposable income is if one accounts for the benefits of having one’s health insurance premiums effectively paid. Unless there is a sufficiently strong and positive relationship between family income and imputed health care benefits, the degree of inequality will be less once these benefits are included in income. This effect occurs because an equal absolute increase in income leads to a reduction in relative inequality.13 Our second experiment is to compare the income statistics, and in particular the values of inequality indices, of the incomes Y A i þ HBi ; which more accurately reflect real or full disposable income in the presence of the publicly financed health insurance plan, with a set of hypothetical incomes reflecting the scenario should the public system be replaced entirely by private health insurance. In the third set of columns, we model these hypothetical incomes should the public insurance system be replaced entirely by a private one (hence HBi is not added to after-tax incomes since individuals must purchase their health coverage out of their disposable income). However, since the government does not have to finance the public health system, a proportion (49%) of income tax is assumed to be rebated to every family according to the LP-neutral tax-cut approach previously discussed. So the statistics provided in this third set of columns are based on Y A i þ 0:49T i ; which we refer to as income under private health. In Table 1, we see that the gross health care benefits are in fact somewhat positively correlated with income. Note, for example, that families in the lowest decile on average receive the smallest health care benefit. This occurs because small families (and single individuals in particular) are overrepresented in the lowest decile. However, a somewhat smaller absolute increase in income to a low income earner than to a higher income earner can still reduce relative inequality if that transfer represents a larger fraction of original income. This is demonstrated in the second set of columns of Table 2

Decile

1 2 3 4 5 6 7 8 9 10 Top 5% Top 1% Overall Gini CV Atkinson (e ¼ 1) Atkinson (e ¼ 0.5) Atkinson (e ¼ 2) Theil

After-Tax Income

Family Incomes, 1994, All Ages. After-Tax Income Under Public Health After-Tax Income Under Private Health

Income ($)

Share (%)

Cumulative share (%)

Income ($)

Share (%)

Cumulative share (%)

Income ($)

Share (%)

Cumulative share (%)

7,157 13,204 17,786 23,126 28,427 33,968 40,373 47,876 58,514 87,086

2.00 3.69 4.97 6.47 7.95 9.50 11.29 13.39 16.37 24.36

2.00 5.70 10.67 17.14 25.09 34.59 45.89 59.28 75.64 100.00

9,277 17,603 22,189 28,258 32,824 38,177 44,606 52,115 62,973 91,908

2.32 4.40 5.55 7.07 8.20 9.55 11.15 13.03 15.75 22.98

2.32 6.72 12.27 19.34 27.54 37.09 48.24 61.27 77.02 100.00

7,239 13,511 18,575 24,600 30,884 37,415 45,012 53,967 66,623 102,106

1.81 3.38 4.64 6.15 7.72 9.36 11.26 13.49 16.66 25.53

1.81 5.19 9.83 15.99 23.71 33.06 44.32 57.81 74.47 100.00

102,075 146,493 35,750

14.29 4.11

107,147 151,877 39,992

13.41 3.81

121,102 181,068 39,992

15.15 4.54

0.354 0.681 0.205

0.322 0.627 0.181

0.374 0.742 0.229

0.102

0.089

0.114

0.449

0.396

0.480

0.203

0.176

0.231

Progressivity Implications of Public Health Insurance Funding in Canada

Table 2.

145

Decile

Top 5% Top 1% Overall Gini CV Atkinson (e ¼ 1) Atkinson (e ¼ 0.5) Atkinson (e ¼ 2) Theil

Family Incomes, 1994, Heads Aged Under 65.

After-Tax Income

After-Tax Income Under Public Health After-Tax Income Under Private Health

Income ($)

Share (%)

Cumulative share (%)

Income ($)

Share (%)

Cumulative share (%)

Income ($)

Share (%)

Cumulative share (%)

6,434 13,479 19,728 25,850 31,312 37,027 43,263 50,689 61,382 89,874

1.70 3.56 5.21 6.82 8.26 9.77 11.41 13.37 16.19 23.71

1.70 5.25 10.46 17.28 25.54 35.31 46.72 60.10 76.29 100.00

7,926 15,346 21,930 28,322 33,969 39,984 46,500 54,182 65,231 94,230

1.94 3.77 5.38 6.95 8.33 9.81 11.41 13.29 16.00 23.12

1.94 5.71 11.09 18.04 26.37 36.18 47.59 60.88 76.88 100.00

6,490 13,993 20,961 28,105 34,491 41,231 48,637 57,384 70,208 105,558

1.52 3.28 4.91 6.58 8.07 9.66 11.39 13.44 16.44 24.72

1.52 4.80 9.71 16.29 24.36 34.02 45.41 58.84 75.28 100.00

104,896 149,352 37,903

13.84 3.95

109,456 153,966 40,761

13.43 3.78

124,747 185,414 42,704

14.61 4.35

0.349 0.661 0.209

0.336 0.639 0.197

0.366 0.715 0.230

0.101

0.095

0.112

0.480

0.433

0.509

0.198

0.187

0.222

JAMES B. DAVIES AND MICHAEL HOY

1 2 3 4 5 6 7 8 9 10

146

Table 3.

Decile

1 2 3 4 5 6 7 8 9 10 Top 5% Top 1% Overall Gini CV Atkinson (e ¼ 1) Atkinson (e ¼ 0.5) Atkinson (e ¼ 2) Theil

Family Incomes, 1994, Heads Aged 65 and Over.

After-Tax Income

Income ($)

Share (%)

10,630 12,993 14,483 16,685 20,170 23,120 27,028 32,428 41,398 66,675

4.01 4.89 5.45 6.28 7.60 8.71 10.19 12.20 15.58 25.08

80,548 125,541 26,553

15.22 4.78

After-Tax Income Under Public Health

Cumulative Income ($) share (%) 4.01 8.90 14.35 20.63 28.23 36.95 47.14 59.34 74.92 100.00

Share (%)

18,038 20,389 21,918 25,272 31,236 34,764 38,563 44,318 53,651 78,989

4.92 5.55 5.97 6.88 8.52 9.48 10.52 12.06 14.61 21.49

93,129 138,536 36,706

12.73 3.82

After-Tax Income Under Private Health

Cumulative Income ($) share (%) 4.92 10.47 16.44 23.32 31.84 41.32 51.84 63.90 78.51 100.00

Share (%)

Cumulative share (%)

10,701 13,054 14,680 17,143 20,687 23,758 28,265 34,490 45,079 76,231

3.78 4.59 5.17 6.03 7.29 8.37 9.97 12.13 15.87 26.81

3.78 8.37 13.53 19.57 26.86 35.23 45.19 57.33 73.19 100.00

93,686 151,748 28,399

16.55 5.41

0.318 0.687 0.148 0.080

0.260 0.542 0.104 0.055

0.341 0.776 0.170 0.094

0.257 0.175

0.184 0.118

0.288 0.208

Progressivity Implications of Public Health Insurance Funding in Canada

Table 4.

147

148

JAMES B. DAVIES AND MICHAEL HOY

[see column entitled ‘‘After-tax Income under Public Health’’] where we see that the share of income for all deciles 1 through 6 is higher when public health care benefits are included in income. We find that the cumulative share of income is higher throughout the distribution (i.e., we have Lorenz dominance), which implies that all relative inequality indices must agree that accounting for imputed health care benefits reduces measured income inequality. Note that the AMLD measure indicates an inequality level of 0.205 for (unadjusted) after-tax incomes but falls to 0.181 when (imputed) government-provided health care benefits are included. Thus, the perceived cost of inequality falls by 2.4% of per capita incomes if one includes health care benefits in income. This drop is quantitatively important as it eliminates more than 10% of the cost of inequality in ‘‘measured’’ after-tax incomes. The way that public health care benefits are funded has an important effect on the distributional changes that one would expect in a move to private health insurance. For example, the average income tax paid by families in the first two deciles is only $166 and $626, respectively, while in the tenth (highest income) decile the amount is $30,567. Therefore, if one were to deduct the share of income tax (49%) that is required to fund public health care from each family’s tax bill, the result would be a more unequal distribution of aftertax incomes. The quantitative impact of this exercise is reported in the third set of columns of Table 2 [After-tax Income under Private Health]. We see that (hypothetical) after-tax incomes are higher for each decile, as expected, since tax payments are reduced, but the decile shares and the inequality measures indicate that the distribution is less equal than existing after-tax incomes with or without the adjustment to include publicly provided health care. To determine the distributional implications of moving to a privately funded health insurance system, we compare the values in the second set of columns of Table 2 [After-tax Income under Public Health] to those in the third [After-tax Income under Private Health]. Note that incomes in the second set of columns, Y A i þ HBi ; are inflated relative to measured after-tax incomes in order to reflect the monetary benefit of publicly provided health care, while incomes in the third set of columns, Y A i þ 0:49T i ; are inflated relative to measured after-tax incomes because the equivalent amount of money used to finance publicly provided health care is ‘‘given back’’ to individuals via hypothetical tax cuts. Thus, since average incomes are the same in the second and third sets of columns, the link between the inequality analysis and welfare analysis as discussed in the second section of this paper is consistent.14 All the inequality values are higher for the private health care scenario than under existing public health care. The AMLD measure (i.e., the

Progressivity Implications of Public Health Insurance Funding in Canada

149

Atkinson measure with parameter value e ¼ 1) indicates that if one were to move from the existing public health care system to a purely private one, the cost of inequality would rise by the equivalent of 4.8% of per capita income (i.e., from 18.1% of income to 22.9%), an increase of about 25% of existing inequality. Since the AMLD measure embodies a fairly conservative attitude concerning the cost of inequality, this is a substantial difference. It suggests that the equity benefit from funding health care benefits through the tax system rather than relying entirely on a private health insurance system is equivalent to finding a way to raise per capita or total income by 4.8%. From our data sources, health care expenditures represent $4,241 per family and average income is $35,750 per family, implying that the overall importance of health care expenditure is approximately 12% of income. Achieving an equity benefit equivalent to a 4.8% increase in income through allocation of 12% of income seems quite impressive. In Table 2, we also provide results using the Atkinson inequality index with parameter values e ¼ 0.5 and e ¼ 2. The corresponding cost of inequality that would be generated by moving to a private health care system would be equivalent to a per capita income loss of 2.5 and 8.4%, respectively. These comparisons show how the value of a public health care system in reducing inequality depends (naturally) on how averse one is to inequality. It is well documented that health care spending is higher for older individuals. Therefore, we separated our sample of families into those with heads less than 65 years of age and those 65 years of age or older and did the same analysis as above separately on these groups. The results are reported in Tables 3 and 4. Comparing Tables 3 and 4 we see, as expected, that gross health care benefits are substantially higher for families headed by older individuals. Including public health care benefits increases average real income for the age group 65 years and over from $26,553 to $36,706 while only from $37,903 to $40,761 for families in the under 65 years age group. Another way of seeing this point is to look at the net health care benefit from the public system computed in Table 1 for the average family in the under 65 group (
$1,944) with that for the average family in the 65 years and older group (+$8,306). Thus, public funding of health care represents a substantial transfer of income to older families from younger families. Also note that after-tax incomes are more equally distributed for families with heads 65 years of age and older. Despite this fact, the equality enhancing implications of publicly provided health care are especially effective for the 65+ age group, for which inequality according to the AMLD is less due to publicly provided health care by the difference 0.066 (i.e., 0.170–0.104), equivalent to 6.6% of per capita incomes of this group. For the remaining

150

JAMES B. DAVIES AND MICHAEL HOY

families (with heads under age 65), the equality enhancing effect of public health care is the equivalent of 3.3% of per capita income (i.e., 0.230–0.197). Given the differential impact of public financing of health care on the ‘‘young’’ and ‘‘old’’ age groups, we perform two common types of decomposition analysis on our results. The first is based on the generalized entropy measures of inequality Ea. This family of inequality measures depends on the degree of inequality aversion, a: 
 
a P yi 1 Ea ¼
1 aa0; 1 Naða
1Þ m
 1X m ln E0 ¼ a¼0 (5) N i yi

 1 X yi y E1 ¼ ln i a¼1 N i m m For the values ao1, the entropy measure Ea is ordinally equivalent to the Atkinson measure Ae, where a ¼ 1
e. The two are related according to the following relationship: Ae ¼ 1
½ða2
aÞE a þ 11=a A1 ¼ 1
expð
E a Þ

ao1; aa0 a¼0

(6)

Among relative inequality measures, only the family of generalized entropy measures (and scalar multiples of these) are additively decomposable (see Shorrocks, 1984). This property requires that, if one partitions the population into subgroups (indexed k ¼ 1, 2, y , K), then overall inequality, I, can be expressed as a weighted sum of the inequality values calculated for subgroups, Ik, P plus a term representing ‘‘between-group’’ inequality, IB (i.e., I ¼ k wk I k þ I B ). If the weights wk are the population shares of the subgroups, then only E0 (i.e., a ¼ 0) satisfies this complete set of properties. The results of our decomposition for the generalized entropy measure E0 are reported in Table 5. The between-group term is reported as a percentage of the overall value of inequality. This value is reduced from 3.9 to 0.0005% when including the public health benefits in income. Moving to the private insurance scenario, the between-group measure of inequality is 5% of overall inequality. These results reflect the fact that mean income differences between the age groups are lowest when using after-tax incomes that include public health benefits ($36,706 for the ‘‘old’’ versus $40,761 for the ‘‘young’’) and highest under private health insurance ($28,299 for the ‘‘old’’ versus $42,704 for the ‘‘young’’). In fact, it is a property of E0 that its between-group

Progressivity Implications of Public Health Insurance Funding in Canada

Table 5. Income Definition

After-tax income

Group

Inequality Decomposition by Age Group. Decomposition Based on Entropy Measures Mean income

E0

All

35,750

0.229

Ageo65

37,903

0.234

AgeZ65

26,553

0.160

Between After-tax income under public health

3.9%

All

39,992

0.199

Ageo65

40,761

0.219

AgeZ65

36,706

0.109

Between After-tax income under private health

0.005%

All

39,992

0.260

Ageo65

42.704

0.261

AgeZ65

28,399

0.186

Between

151

5.0%

Decomposition Based on Atkinson Measures A0.5 (equiv income)

A1 (equiv income)

A2 (equiv income)

0.102 (32,103) 0.101 (34,075) 0.080 (24,428) 3.88%

0.205 (28,421) 0.209 (29,981) 0.148 (22,623) 2.24%

0.449 (19,698) 0.480 (19,709) 0.257 (19,729) 0.094%

0.089 (36,433) 0.095 (36,889) 0.055 (34,687) 1.08%

0.181 (32,753) 0.197 (32,731) 0.104 (32,888) 0.11%

0.397 (24,155) 0.433 (23,111) 0.184 (29,952) 1.6%

0.114 (35,433) 0.112 (37,921) 0.094 (25,729) 3.88%

0.229 (30,833) 0.230 (32,882) 0.170 (23,571) 3.09%

0.480 (20,795) 0.509 (20,957) 0.228 (21,924) 1.85%

Note: Between means between group inequality according to the index approach for E0 and according to the cost of inequality approach (i.e., applicable for the Atkinson based decomposition approach). Values are in percentage of overall inequality terms.

inequality value, E B0 ; is based P on the ratios of the overall mean income to the subgroups means ðE B0 ¼ k wk lnðm=mk ÞÞ: Although the Atkinson measures do not lend themselves to additive decomposability based on the index measures of inequality per se, they can be used to decompose inequality in another manner (see Blackorby, Donaldson, & Auersperg, 1981; Lambert, 2001, pp. 113–114). In this case, one measures between-group inequality by comparing the equally distributed equivalent incomes of the subgroups rather than their mean incomes. Let xk represent the equally distributed equivalent income for subgroup k (and x for the population as a whole), as defined implicitly in Eq. (1). The cost of inequality

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is then Ck P ¼ mk
xk for subgroup k and C ¼ m
x overall. It follows that C ¼ C B þ k wk C k where CB is the ‘‘between-group cost of inequality’’ and the weights wk are the population weights. We report (in Table 5) the percentage of overall inequality that CB accounts for (i.e., ðC B =CÞ  100). The corresponding index valueP of the between-group inequality, IB, for the Atkinson measure is I B ¼ C B = k wk xk : As when we used the entropy-based decomposition approach, we see a substantial decrease in between-group inequality when comparing after-tax income plus public health benefit either to measured after-tax incomes or the after-tax incomes associated with a private health system for the cases where the inequality aversion parameter is e ¼ 0.5 and e ¼ 1 (the AMLD measure). The reason for this pattern, however, is not the same as for the entropy-based comparison where reduced between-group inequality was due to a reduced difference of mean income for the young to the old. The Atkinson-based decomposition is driven by the differences in equally distributed equivalent incomes of the groups rather than mean incomes. In fact, in the case of e ¼ 1, the equality enhancing effect of including public health benefits in after-tax income is so strong for the old that their equally distributed equivalent income becomes higher than that for the young even though the mean income of the young is higher by about 10%. So between-group inequality in the case of the measure A1 is due to the older group having a higher equally distributed equivalent income rather than a lower mean income, a reversal relative to the cases when E0 or A0.5 is used as the basis of comparison. The above discussion sets up well the pattern-breaking decomposition analysis based on the measure A2. In this case, the value of between-group inequality is substantially higher when adding public health benefits to measured after-tax income (from 0.094% of the overall cost of inequality to 1.6% as a result of including public health benefits). The reason this happens is that including benefits from public health does more to reduce inequality for the old. The inequality measure A2 is sufficiently sensitive to this advantage that the equally distributed equivalent income is much higher for the old relative to that of the young ($29,952 versus $23,111). In a sense, from a between-group perspective, the public health system increases inequality by making the individuals in the old age group too well off relative to the young. However, it is important to note that the overall level of inequality is still at its lowest in these comparisons for the definition of income that includes public health benefits. Also, part of the reason the equally distributed equivalent income is so much higher for the old when public health benefits are included is that the Atkinson measure of inequality with e ¼ 2 places so much weight on the lowest incomes (see Chiu, 2007, for details). Even for

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after-tax incomes not including public health benefits, mean income for the lowest decile of the distribution for the old is higher than for the young (see Table 1). The inequality measure A2 places enough weight on this aspect that equally distributed equivalent income is even slightly higher for the old relative to the young when using measured after-tax incomes ($19,729 versus $19,709). One important criticism of using families as the sample unit is that individuals in families of different size and composition but with the same family income do not experience the same standard of living. Thus, one needs to adjust incomes for family size. This cannot be done simply by dividing family income by the number of individuals in the family. We must account for economies of scale in meeting certain economic needs, such as housing, for the family members. The standard method uses household equivalence scales, which allow one to assign an equivalent per capita income to each member of the family based on family income and composition. We applied the OECD equivalence scales to the families in our sample and generated equivalent per capita after-tax incomes.15 In doing this we follow standard practice and assume that economies of scale within the household do not apply to health benefits. Therefore, we do not apply the household weights used to derive equivalized incomes to the gross health benefits included in the second set of columns of Tables 6–8. Instead, we added the unadjusted per capita value of gross health benefits for the family to each person’s income after the equivalization procedure was applied to after-tax incomes. The reason for making the calculations this way is that families would in fact require this amount of money to purchase their health insurance privately and no economies of scale would be relevant to this expenditure.16 The net income [After-tax Income under Private Health] in the third set of columns of Tables 6–8 is computed by three steps: (a) adding to the after-tax incomes of column set 1 the 49% of tax paid to cover public health care costs, (b) deducting the amount required to pay for health insurance privately, and then, (c) applying the equivalizing procedure to get per capita equivalent incomes. Although we adjust family income according to an equivalence scale which is not simply the inverse of the number of family members, except for that part of income which is the imputed health benefit from publicly provided health insurance, in computing inequality statistics we weight individuals equally regardless of family type that they belong. However, as Ebert (1997, 1999) has established, this approach for weighting incomes and individuals across different family types creates problems (paradoxes) when assessing welfare implications of redistributions of income between different types of family units. His proposed method of weighting individuals by the

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Table 6. Equivalent Incomes, 1994, All Ages. Decile

After-Tax Equivalent Income

After-Tax Equivalent Income Under Public Health

After-Tax Equivalent Income under Private Health

Share (%)

Cumulative share (%)

Income ($)

Share (%)

Cumulative share (%)

Income ($)

Share (%)

Cumulative share (%)

1 2 3 4 5 6 7 8 9 10

5,675 9,680 12,015 13,981 15,986 18,176 20,858 24,235 29,129 42,465

2.96 5.03 6.25 7.27 8.32 9.46 10.85 12.61 15.15 22.10

2.96 7.99 14.24 21.51 29.84 39.29 50.14 62.76 77.90 100.00

6,751 11,187 14,282 16,351 17,899 19,896 22,525 25,926 30,797 44,126

3.22 5.33 6.81 7.79 8.54 9.48 10.74 12.36 14.68 21.04

3.22 8.55 15.36 23.16 31.70 41.18 51.92 64.28 78.96 100.00

4,298 8,107 9,934 12,127 15,085 17,882 21,162 25,209 31,156 48,063

2.23 4.20 5.15 6.28 7.82 9.26 10.97 13.06 16.14 24.90

2.23 6.43 11.57 17.86 25.67 34.94 45.90 58.97 75.10 100.00

Top 5% Top 1% Overall

49,797 73,024 19,219

12.97 3.80

51,499 74,868 20,973

12.29 3.57

57,551 89,214 19,301

14.92 4.63

Gini CV Atkinson (e ¼ 1) Atkinson (e ¼ 0.5) Atkinson (e ¼ 2) Theil

0.292 0.575 0.138

0.269 0.537 0.125

0.350 0.719 0.211

0.069

0.062

0.105

0.304

0.270

0.507

0.141

0.126

0.213

JAMES B. DAVIES AND MICHAEL HOY

Income ($)

Decile

Equivalent Incomes, 1994, Heads Aged Under 65.

After-Tax Equivalent Income

After-Tax Equivalent Income Under Public Health

Cumulative Income ($) share (%)

Income ($)

Share (%)

1 2 3 4 5 6 7 8 9 10

5,377 9,263 11,782 14,040 16,242 18,490 21,218 24,618 29,555 42,775

2.78 4.79 6.10 7.26 8.41 9.56 10.97 12.74 15.29 22.10

Top 5% Top 1% Overall

49,998 72,570 19,334

12.94 3.76

Gini CV Atkinson (e ¼ 1) Atkinson (e ¼ 0.5) Atkinson (e ¼ 2) Theil

0.299 0.578 0.144 0.072

0.285 0.554 0.133 0.066

0.340 0.679 0.192 0.095

0.320 0.146

0.284 0.134

0.493 0.192

2.78 7.57 13.67 20.93 29.33 38.89 49.86 62.60 77.90 100.00

Share (%)

After-Tax Equivalent Income under Private Health

6,371 10,272 12,806 15,082 17,305 19,610 22,346 25,789 30,789 44,017

3.12 5.02 6.27 7.38 8.47 9.59 10.93 12.62 15.07 21.52

51,250 73,844 20,437

12.55 3.62

Cumulative Income ($) share (%) 3.12 8.14 14.41 21.79 30.26 39.85 50.79 63.41 78.48 100.00

Share (%)

Cumulative share (%)

4,089 8,212 11,161 13,833 16,513 19,069 22,337 26,374 32,273 48,993

2.02 4.05 5.50 6.82 8.15 9.39 11.01 13.01 15.92 24.13

2.02 6.06 11.57 18.39 26.53 35.93 46.94 59.95 75.87 100.00

58,395 89,479 20,283

14.40 4.42

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Table 7.

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Table 8. Equivalent Incomes, 1994, Heads Aged 65 and Over. Decile

After-Tax Equivalent Income

After-Tax Equivalent Income Under Public Health

Cumulative Income ($) share (%)

Share (%)

1 2 3 4 5 6 7 8 9 10

9,260 11,630 12,775 13,802 14,874 16,376 18,499 21,569 25,978 39,855

5.02 6.30 6.92 7.48 8.06 8.91 10.00 11.67 14.07 21.59

Top 5% Top 1% Overall

47,851 75,863 18,459

12.99 4.12

Gini CV Atkinson (e ¼ 1) Atkinson (e ¼ 0.5) Atkinson (e ¼ 2) Theil

0.241 0.549 0.092 0.049

0.179 0.416 0.057 0.030

0.415 1.001 0.266 0.144

0.175 0.108

0.105 0.066

0.500 0.316

14,675 18,016 19,283 20,244 21,449 22,301 24,303 27,407 31,844 45,655

5.99 7.35 7.87 8.26 8.75 9.14 9.89 11.16 12.98 18.62

53,815 81,907 24,515

11.00 3.35

Cumulative Income ($) share (%) 5.99 13.34 21.20 29.46 38.21 47.35 57.24 68.40 81.38 100.00

Share (%)

Cumulative share (%)

3,075 4,600 5,543 6,815 8,002 10,127 12,734 16,298 21,707 39,285

2.40 3.59 4.33 5.32 6.24 7.94 9.91 12.70 16.93 30.65

2.40 5.99 10.32 15.63 21.88 29.81 39.73 52.42 69.35 100.00

49,639 87,102 12,815

19.41 6.81

JAMES B. DAVIES AND MICHAEL HOY

Income ($)

5.02 11.32 18.24 25.72 33.77 42.69 52.68 64.35 78.41 100.00

Share (%)

After-Tax Equivalent Income under Private Health

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inverse of the equivalence scale for the family type to which they belong avoids such problems. However, our approach is justified by the fact that our problem here involves implicit redistribution through health benefits that are not subject to adjustments from the household equivalence scales. We see in Table 6 that the inequality indices for equivalized incomes are generally less than if one uses family incomes. However, the order of magnitude in the reduction of the AMLD index resulting from inclusion of public health care benefits, 0.138 to 0.125 (i.e., approximately a 10% reduction) is similar to that found when using family incomes. The incomes in the third set of columns [After-tax Income under Private Health] are the equivalized income values generated from after-tax incomes if taxes were reduced in order to reflect the absence of public health expenditures but individuals had to purchase health insurance privately. Unlike the case when using family incomes rather than equivalent incomes, the most relevant comparison using equivalized incomes is between the first and third set of columns (rather than the second and third). This follows because in Tables 6–8, we have deducted the health care costs that are presumed to result from private insurance when there is no public insurance. Since these expenditures are not subject to economies of scale, we did not want to apply the equivalizing procedure for such funds. Therefore, rather than comparing the inequality indices in column sets 3 to 2 in order to infer how important public health care is in equalizing income and promoting social welfare, one should make the comparison between column sets 3 and 1. This still leads to a substantial difference in the value of inequality with and without publicly financed health care. For example, the cost of inequality implied by the AMLD index would rise from 13.8% of per capita income to 21.1% in the absence of public health insurance. One must be cautious, however, in making these comparisons and extending them to the notion of social welfare because of the equivalizing procedure.17

4. DISCUSSION In this section, the implications of various aspects of our methodology and assumptions are considered. Perhaps, the most critical assumptions we have made have to do with our method of imputing the value of public health insurance to individuals. Also, we realize that the issues of financing through taxation rather than private insurance premiums are not the only important equity issues concerning the delivery of health care services, be they funded publicly or privately. Another very relevant issue is the relationship between

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income and the take-up rate of services available. Several studies have investigated whether the extent to which individuals use (or are offered) public health care services varies by income. We discuss this issue as well, albeit rather briefly, in this section. A common method of assessing equity in health care provision is to determine relative usage of health care by individuals of different incomes. For example, Dunlop, Coyte, and McIsaac (2000), using data from the same survey as this study uses, found that individuals from lower income groups were more likely to be frequent users of primary care physicians in Canada, but that after adjusting for differences in health need, those with lower incomes and fewer years of schooling were less likely to visit specialists. If low income individuals make less intensive use of health care facilities and programs, then at least from the perspective of usage the provision of health care may be inequitable in that the incidence of benefits is regressive. However, for public health care provision to be regressive in an overall (financial) sense, it must be that the benefits to lower income individuals are a lower fraction of their income than for higher income individuals rather than simply being of lower absolute amount. The opposite relationship between income and health care usage is, of course, also possible. For example, Barer, Manga, Shillington, and Siegel (1982) found that hospital use was highest for the lowest income class and relatively stable for all other income classes, thus indicating a progressive incidence of this aspect of publicly provided medical care. In terms of overall incidence, a study by van Doorslaer et al. (2000) investigating the equity in the delivery of health care concludes that for most European countries, ‘‘y (even) y after controlling for the fact that also the need for health care tends to be more concentrated at the bottom end of the income distribution, little evidence of an inequitable overall health care distribution emerges’’. See also the paper in this volume by Go´mez and Nicola´s (2007) that provides an analysis regarding utilitsation by income under public and private health insurance scenarios for Spain and thus represents a useful complement to our research. Although the above-mentioned types of studies address important equity issues concerning the incidence on the take-up rate of public health care for people with different incomes, our focus on distributional implications is concerned with the relative financial costs of public versus private health insurance. These two different perspectives are complementary to understanding the overall equity effects of health care provision. Another very useful approach is to analyse how different sources of funding (e.g., social insurance, employee and employer contributions, indirect taxes, direct taxes, private insurance costs, etc.) for health care have different

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distributional implications. In a series of papers, including Wagstaff and van Doorslaer (1997), Wagstaff et al. (1999), and van Doorslaer et al. (1999), it has been demonstrated how different systems of financing health care are more or less regressive. These studies show how different combinations of public and private sources of funds for health care imply different degrees of progressivity and regressivity in the system compared to a (hypothetical) funding system that elicits payments in proportion to an individual’s income. This basic approach also allows for a decomposition of inequality into components of vertical progression, horizontal equity and re-ranking, based on the seminal work of Aronson, Johnson, and Lambert (1994). This work is also complementary to our own, which studies the distributional impact of the benefits of public health care as well as funding effects. For Canada, however, the particular source of tax funds used to finance the public system is not at all clear, even from the perspective of identifying federal versus provincial sources.18 We have presumed that tax cuts made possible by eliminating the public health care system would occur through the income tax and would be done by a proportionate decrease in all tax rates. This represents a certain amount of tax flattening, although not a move entirely to a flat rate tax system. We believe this is a plausible scenario given the trend towards the flattening of income tax systems, as documented in Davies and Hoy (2002). Moreover, the province of Alberta recently introduced provincial tax reforms moving it to a flat rate tax system (see McMillan, 2000 for details). In contrast, one could argue that general taxes, including provincial sales taxes and the federal GST (goods and services tax), may be reduced. As noted earlier, such taxes tend to be distributionally neutral and so any reduction would have no impact on inequality. Thus, one could imagine a possible range of inequality impacts from tax reduction that range from zero to our estimates as worthy of consideration. This is one reason we computed separately the effects from considering the benefits of the public health system and the implied tax reductions when measuring the relative equity implications of public versus private systems. There is an indirect effect of replacing public with private insurance in regard to the relative cost and coverage of health care between low and high income individuals that deserves more discussion. If a menu of policies with different coverage levels and costs were offered under private insurance, as one would expect, then on average low income individuals would tend to purchase lower coverage health insurance plans with associated lower costs.19 If these lower coverage and lower cost policies provided a lower level of health care services (and expenditures) than the existing public system,

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then the subjective value of the public system could, for low income individuals, be less than is implied by the expenditures we have used for them.20 Another way of dealing with this issue is to recognize that forcing all individuals into the same health care coverage, as is implicitly done with a public system, creates an efficiency loss with some people holding more health insurance than they would like while others hold less. Such efficiency effects could be measured and compared to our equity effects. Of course, there are other efficiency issues involving asymmetric information which may make one or the other system more efficient. One such issue is that adverse selection may well reduce the efficiency of a private system while the enforced pooling of a public system can avoid this pitfall (see Hoy, 2006 for a more elaborate discussion of this point). Even if, in a fully privatized system, individuals did purchase the same insurance coverage as exists in the public system, private insurance premiums could differ from the public health care costs because in a private system costs of delivery would be different. These costs could be lower, due to more incentives arising from competition to reduce costs, or could be higher if certain economies of scale are lost as a result of privatization and/or the presence of advertising and other marketing costs are sufficiently high. Another factor that may lead to higher costs resulting from privatization is that the public health care system is effectively a monopsonist in terms of its labour input and this advantage is lost in a private system. Another aspect of the implicit pricing and valuation of insurance premiums made in this paper is that private insurance premiums are assumed to depend only on the age and gender of family members. Private insurance companies selling individual polices, however, would tend to use finer information concerning the health status of individuals in order to categorize them into risk classes with appropriately differentiated premiums. Taking account of such differences would imply more inequality under a system of private health insurance. Adverse distributional impacts of categorical discrimination in general terms are demonstrated by Hoy (1984), and Bossert and Fleurbaey (2002), while for the particular use of information from genetic tests, see Hoy and Lambert (2000) and Hoy and Ruse (2005). Data limitations concerning individuals’ health status do not allow us to take such possible behaviour by insurers into account but doing so could well lead to substantially higher levels of inequality in the hypothetical private health care scenario. However, this effect may be attenuated if health insurance is largely provided through employment. The introduction of such a sizable (49%) reduction in income taxes would likely lead to incentive effects with respect to labour supply and other

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income earning decisions. Thus, one might observe changes in the beforetax, and hence also the after-tax, distributions of income. These changes could lead to either a more or less equally distributed before-tax and/or after-tax income distribution. To take account of such incentive effects is beyond the scope of this paper. However, the methodology that we have used allows one to compare the equity effects of public financing of health care to the efficiency effects of tax reductions,21 such as those found by the study of Fullerton and Rogers (1993) measuring the efficiency effects of the 1986 tax reforms (TRA86) in the US.

5. CONCLUSION In this paper, we apply a standard distributional impact analysis to measure the implications for Canada of moving from its existing public system of health care to a fully privatized system based on health insurance premiums assessed according to age and gender. The implication of including the health care benefits received through the public system, as quantified by implied health insurance premiums that would have to be paid under a private system, is an increase in equality that in our base case is equivalent to an increase of 2.4% of per capita incomes. Reduced government expenditures from moving to a private health care system would allow for a reduction in taxes equivalent to 49% of income tax paid. If the government used these savings to reduce income taxes and made the cuts proportional to individuals’ tax payments, as we assumed in our calculations, then the overall reduction in the degree of inequality in after-tax incomes under the public system in our base case is equivalent to an increase of 4.8% of per capita incomes. Of course, tax cuts could be implemented differently. If the tax cuts were made in a neutral fashion with respect to the after-tax distribution of income, then the lower value of a 2.4% gain in per capita incomes should be associated with the public health care system. We suggest that tax cuts may well be made in a manner that has a distributional impact in between these two extremes, and so suggest that the range of 2.4–4.8% in equivalent per capita income is a reasonable one to infer regarding the distributional impact of the public heath care system. Since for our sample (Canada, 1994) health care expenditures represent 12% of income, the equity benefit of using income taxes to finance health care in Canada rather than rely on private insurance is substantial for any number in this range. There are many provisos and caveats to this conclusion. First and foremost, like any normative study involving the distribution of income, one must choose

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a norm or ethical view on how important income inequality is to society. We believe we have been quite conservative in our choice of ethical standard, adopting the Atkinson measure with a moderate aversion to nequality, to generate our base case alluded to above. Another important caveat is that we have adopted an impact analysis which, although quite common for measuring the distributional impact of public policies, has the disadvantage of assuming that individuals’ behaviour would be the same under the two systems. It is extremely unlikely that Canada would move to a purely private health care system, at least in the near future. How relevant are our calculations in light of this? Whether a specific private–public mixed system would generate a large increase in inequity depends very much on its specific design features. A mixed system with a sufficiently high level of health care provided free of charge to all (or just to low income individuals) might well not be substantially worse from a distributional perspective than the existing public system and could even be better. In contrast, bringing some health care expenditures, like prescription drugs, under the umbrella of publicly funded care may have important equity benefits. One could use the same methodology here to assess how this would affect inequality and social welfare. An argument sometimes advanced in favour of moving towards private funding of health care, besides wanting to lower the overall tax burden, is that private health care can lead to efficiency through competition and greater variety of choices in what is included in health care plans. Again, we do not dispute such claims but rather emphasize that our analysis suggests that publicly provided health care, which is funded out of income taxes, has a strong progressive effect on equality and that this effect should not be ignored. Proposals to replace the system, either partially or fully, with a private alternative must demonstrate that there is a very strong efficiency rationale for doing so, before a balanced assessment of efficiency and equity considerations could sanction such a change.

NOTES 1. Other examples of impact studies include Duclos and Tabi (1998), who analyse the implications of several social policies on income inequality; Countryman (1999), who analyses the distributional implications of the Canadian unemployment system; Davies and Hoy (2002), who compare the distributional effects of hypothetical flat rate tax schemes to an existing graduated rate tax scheme. 2. For studies concerning these issues, see Barer et al. (1982), Dunlop et al. (2000), and Van Doorslaer et al. (2000).

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3. The CAP (Canada Assistance Plan), which was a cost-sharing arrangement between provincial and federal governments for supporting social assistance and welfare programs, was also rolled into the CHST, thus delinking further sources of funding with health expenditures (see Snoddon, 1998 for details). 4. See Duclos and Tabi (1998), and Davidson and Duclos (1997) for studies of this effect. We do not perform statistical inference as is done in the latter of these studies. 5. Good examples of studies concerning the equity implications of publicly subsidized post-secondary education are Mehmet (1978) and Meng and Sentance (1982) and see Barer et al. (1982) for a study on publicly funded health care. 6. Of particular relevance to our study is that many studies show that higher income individuals typically purchase higher levels of health care in a private market (see, for example, Blomqvist & Carter, 1997); i.e., that health care is a normal good. 7. The National Accounts indicate that federal and provincial governments received $98.5 billion of personal income tax revenue in 1994. The public health expenditures of $52 billion are 53% of this total. We have also done our calculations assuming that all income tax payments fall by 53%, instead of the 49% figure implied by the SCF, and find that the results are very similar to those reported here. 8. See also Kolm (1969, pp. 186–187) who first proposed this and other indices as measures of relative injustice per dollar of social income. 9. Note that the choice of utility function being iso-elastic is necessary if one wants to satisfy the desirable property that the percentage cost of inequality, i.e., A in Eq. (1), be invariant to equal proportionate changes in all incomes (see Lambert (2001), pp. 98–99). For further discussion on this family of indices, see Jenkins (1991). 10. We use the three parameter values e ¼ 2, e ¼ 1, and e ¼ 0.5 in our calculations. For this simple example, the cost of inequality is 6.7% for the case of e ¼ 0.5 (i.e., the same level of welfare can be achieved with average incomes of $33,588 if it were equally distributed). 11. A number of studies have tried to infer policy makers’ e from studies of government policies. As reported by Lambert (2001, Chapter 5), the values thus obtained range from about 1.4 to 2.0. A wider range of values is obtained using alternative methods. Stern (1977) surveys a variety of estimation methods and reports values of e ranging from 0.4 to 10.0. Blake (1996) even argues on the basis of studies of relative risk aversion that e could lie in the range 7.9–47.1. See also Palsson (1996) for a discussion of interpersonal differences in degree of risk aversion. 12. For example, in 1994 the value (average expenditure) of public health care for a single female in the age category 65+ was $7,382 while for a family of four, including a male and female adult in the age category 45–64 ($1,546 and $1,591, respectively) and two children in the age category 0–14 ($592 each), the value is $4321 for the family. See Table 22B of National Health Expenditures in Canada: 1975–1994 (1996). 13. A simple and extreme example illustrates this point. If family A and B have incomes of $30,000 and $60,000, respectively, but then each family receives an equal absolute increase of $100,000, then the distribution becomes $130,000 and $160,000, respectively, which reflects less relative inequality (i.e., the ratio of family incomes goes from 2:1 to approximately 1.23:1). 14. There is one proviso here, however, and that is the implicit assumption often made in such welfare comparisons that the utility functions of different individuals

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are the same. This is not necessarily an innocuous assumption in the context of heath care provision and financing. 15. The particular OECD scale we adopted uses a weight of 1 for a single adult family; for a family of size two add 0.7 to the weight if the second member is an adult and 0.5 if the second member is a child; add 0.5 to the family weight for each additional family member, whether that member is a child or an adult. So, for example, a family of size 4 (2 adults, 2 children) with family income level $70,000 implies a per capita equivalized income of $70,000/2.7 ¼ $25,926 for each person in the family. There are, however, many variations to this approach (e.g., see Figini, 1998, p. 5, footnote 3). 16. See Steckmest (1996), Harding (1995), and Smeeding et al. (1993) for a discussion of this point. 17. Note in particular that the average income is not the same in these two columns (i.e., column sets 2 and 3) when using equivalized incomes, as it was when comparing family incomes. If our study involved only income transfers (between family types) that were fully subject to the economies of scale implicitly recognized by the family equivalence scales, we could avoid this difficulty by adopting Ebert’s (1997) suggested procedure of weighting individuals accordingly, as noted above. Also, see Decoster and Ooghe (2003) who apply these different approaches (weighting with individuals, equivalent individuals, and not weighting at all) to Belgian data and find that ‘‘using the number of equivalent individuals as weights y leads to fanciful results with respect to the choice of equivalence scale’’ (ibid, p. 193). 18. With the exceptions of Quebec, and more recently Alberta and Ontario, the basis for provincial taxation of income is the use of a given fraction of individual’s federal income tax payable. This ties the two sources together and reduces the concern for individuals as to whether tax cuts will come from one level of government or the other or both. 19. See Blomqvist and Carter (1997) for an analysis of this question and also a review and critique of previous empirical studies relating income to demand for health care. 20. However, private choices may not reflect true subjective values in the presence of borrowing constraints. Low income individuals could prefer higher levels of health care than they would purchase in any given period but could be prevented from spending more due to borrowing constraints. Thus, it is not clear by how much, if at all, our calculations may overstate the benefits of public health care to lower income individuals and hence imply greater redistributive effects of the system than actually exist. 21. For example, Fullerton and Rogers (1993) compute the gain from replacing entirely the federal personal income tax with non-distortionary lump-sum taxes to be 2.02% of lifetime income or, when discounting welfare gains for all generations, 0.68% of lifetime income.

ACKNOWLEDGMENTS We thank an anonymous referee and the editor, Peter Lambert, for very helpful remarks. As usual, of course, any errors or limitations of this work

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are the responsibility of the authors. Both authors thank SSHRC for funding and a succession of first-rate research assistants; namely, Jeremy Lise, Laura Pearson, and Warren Goodlet.

REFERENCES Aba, S., Goodman, W., & Mintz, J. (2002). Funding public provision of private health: The case for a copayment contribution through the tax system. C.D. Howe Institute Commentary No. 163. Aronson, J. R., Johnson, P., & Lambert, P. J. (1994). Redistributive effects and unequal tax treatment. Economic Journal, 104, 262–270. Atkinson, A. (1970). On the measurement of inequality. Journal of Economic Theory, 2, 244–263. Barer, M. L., Manga, P., Shillington, E. R., & Siegel, G. C. (1982). Income class and hospital use in Ontario. Ontario Economic Council, Occasional Paper No. 14. Blackorby, C., Donaldson, D., & Auersperg, M. (1981). A new procedure for the measurement of inequality within and among population subgroups. The Canadian Journal of Economics, 14(4), 665–685. Blake, D. (1996). Efficiency, risk aversion and portfolio insurance: An analysis of financial asset portfolios held by investors in the United Kingdom. The Economic Journal, 106, 1175–1192. Blomqvist, A. G. & Carter, R. A. L. (1997). Is health care really a luxury? Journal of Health Economics, 16, 207–229. Bossert, W., & Fleurbaey, M. (2002). Equitable insurance premium schemes. Social Choice and Welfare, 19, 113–125. Butler, R. J., Johnson, W. G., & Rimsza, M. E. (2006). Medicaid disenrollment costs: Maricopa County, AZ. Pediatrics, forthcoming. Chiu, H. (2007). Intersecting Lorenz curves, the degree of downside inequality aversion, and tax reforms. Social Choice and Welfare, forthcoming. Countryman, G. J. (1999). The effect of unemployment benefits on income inequality in the Canadian provinces. Canadian Public Policy, 25, 539–556. Davidson, R., & Duclos, J.-Y. (1997). Statistical inference for the measurement of the incidence of taxes and transfers. Econometrica, 65, 1453–1465. Davies, J. B., & Hoy, M. (2002). Flat rate taxes and inequality measurement. Journal of Public Economics, 84, 33–46. Decoster, A. & Ooghe, E. (2003). Weighting with individuals, equivalent individuals or not weighting at all: Does it matter empirically? Research on Economic Inequality, 9, 173–190. Duclos, J.-Y., & Tabi, M. (1998). Ine´galite´ et redistribtuion du revenu, avec une application au Canada. Unpublished mimeo. Dunlop, S., Coyte, P. C., & McIsaac, W. (2000). Socio-economic status and the utilisation of physicians’ services: Results from the Canadian National Population Health Survey. Social Science & Medicine, 51, 123–133. Ebert, U. (1997). Social welfare when needs differ: An axiomatic approach. Economica, 64, 233–244.

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PUBLIC AND PRIVATE HEALTH INSURANCE AND THE UTILISATION OF HEALTH CARE IN SPAIN Pilar Garcı´ a Go´mez and Angel Lo´pez Nicola´s ABSTRACT This paper reports an analysis of the evolution of equity in the utilisation of health care in Spain over the period 1987–2001, a time span covering the development of the modern Spanish National Health System. Our measures of utilisation are the probabilities of visiting a doctor, using emergency services and being hospitalised. For these three measures, we obtain indices of horizontal inequity from microeconometric models of utilisation that exploit the individual information in the Spanish National Health Surveys of 1987 and 2001. We find that by 2001, the system had improved insofar as differences in income no longer lead to differences in utilisation given the same level of need. However, tenure of private health insurance leads to differences in utilisation given the same level of need, and its contribution to inequity has increased over time, both because insurance is more concentrated among the rich and because the elasticity of utilisation for the three services has also increased.

Equity Research on Economic Inequality, Volume 15, 169–195 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15008-0

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1. INTRODUCTION Spanish society has undergone a major overhaul in the three decades that have elapsed since the death of Franco. The transformation from dictatorship to democracy and the devolution of government to the regions have combined with the sheer passage of time to transform an obsolete public sector into one comparable to that of other developed countries. The health care system is one of the areas where reforms have been far reaching; and in this paper, we aim to evaluate the change between 1987 and 2001 in one of the indicators that serve to assess its performance: the existence and degree of inequities in health care utilisation. The choice of these two dates is motivated by the fact that the most comprehensive package of reforms for the health care system was systematised and put forward by the 1986 General Health Act. This suggests 1987 as an obvious baseline period. Fourteen years later, the main features of the new health care system – taxfunded universal insurance and a modernised primary care network – had been fully developed across Spain, so 2001 is an appropriate period to compare with the baseline. One of the goals stated in the General Health Act is the elimination of socio-economic health inequalities in the utilisation of health care (Article 3). Although this objective is stated in terms of inequalities, our outcome of interest is equity in utilisation, defined as equal access given equal need for health care. In line with the recent literature (Van Doorslaer, Koolman, & Jones, 2004; Van Doorslaer, Koolman, & Puffer, 2002), our methodology consists in calculating indices of socioeconomic inequality in health care utilisation and subsequently decomposing these indices into the part that can be attributed to socio-economic differences in need and the part that can be attributed to other socioeconomic differences. According to the criterion expressed above, the latter component of inequality is interpreted as an index of inequity. Our empirical application uses data from the 1987 and 2001 editions of the National Health Survey or Encuesta Nacional de Salud (CIS, 1987, 2001). The comparison of two cross sections of the Spanish population has a limited ability to reflect the causal effect of a multi-faceted package of reforms. Nevertheless, our contention is that the implementation of these reforms should change the joint distribution of utilisation and socioeconomic characteristics after controlling for health care needs, and in fact our results show that by 2001, the system had improved insofar as differences in income no longer lead to differences in utilisation given the same level of need. However, tenure of private health insurance (PHI) leads to differences in utilisation given the same level of need, and its contribution

Public and Private Health Insurance and the Utilisation of Health Care in Spain 171

to inequity has increased over time, both because insurance is more concentrated among the rich and because the responsiveness of utilisation to private insurance has also increased. Section 2 presents the main characteristics of the health system and the reforms that have taken place in the recent past and provides a brief review of previous relevant studies. Section 3 presents the methodology that we adopt for the measurement of inequities in health care utilisation and the explanation of their changes over time. Section 4 presents the empirical results and Section 5 discusses the implications of our results.

2. THE TRANSITION OF THE SPANISH HEALTH CARE SYSTEM AND PREVIOUS LITERATURE ON INEQUITIES IN UTILISATION 2.1. Institutional Changes and the Role of Private Insurance At the end of the dictatorship in 1975, the Spanish health system was based on a social security scheme paid by employers and employees and complemented by a network of health care centres owned by different organisations. One of the characterising features of the pre-democratic system was a strong bias towards hospital care. While the 1970s had witnessed the creation of a public network of modern hospitals, primary and preventive services in the public network were underdeveloped: general practitioners were typically available for two and a half hours per day at isolated outlets which lacked administrative and diagnostic support (EOHCS, 2000). The arrival of democracy unleashed the latent demand for a better health care system and important legislative and managerial changes ensued. The Ministry of Health was created in 1977 and the 1978 Constitution consecrated public coverage for all citizens. Momentum gathered after 1983 when the government initiated a series of reforms to integrate the different networks. In 1986, the General Health Act transformed the social security system into a National Health System. Thus, two main structural reforms with a potential impact on socio-economic inequalities in utilisation of health care occurred during the period studied in this paper. Firstly, the system was finally consolidated as a taxfunded universal coverage National Health System within which individuals are entitled to a comprehensive set of benefits including not only primary and specialised inpatient and outpatient care, but also subsidised medicines with zero co-payments for specific groups such as pensioners or disabled

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persons and reduced co-payments for drugs for chronic diseases including AIDS. Secondly, primary care has been totally reformed by replacing the obsolete outlets mentioned above with team-based practices staffed by doctors and nurses who have received specific training in family medicine and whose activities not only include curative care, but also preventive care, health promotion, follow-up of patients and services targeted to particular population groups such as the mentally ill and drug users. Although by 1987 the whole of the population was covered by the National Health System, the material implementation of the primary care reform (i.e. the replacement of the obsolete outlets with modern primary care centres) all over Spain was slow: while it was planned as far back as 1984 and turned into law in 1986, only 50% of the population was covered by the modern centres in 1992 and the proportion reached 81% by 2000 (EOHCS, 2000). This is in fact the most important reform to have taken place during the period under study. For these reasons, it seems appropriate to evaluate the change between 1987 and 2001. In this study, we intend to pay special attention to the role of PHI as a determinant of inequities in health care. The concern about the equity effects of PHI is partly justified by the fact that expenditure on PHI has received public subsidies in the form of tax bonuses. Prior to 1999, the subsidy operated via personal income tax: individuals received a 15% rebate on insurance premiums (and on any other expenditure on health care). Currently, it operates via corporate tax: premiums are considered tax-free in-kind salary and companies can deduct from profits the cost of collective policies (thus obtaining a 35% tax bonus on their cost). The current fiscal treatment of PHI is explained by the recent history of the health system, since prior to the reforms discussed above some groups, notably the self-employed, were excluded from public insurance. In this context, the subsidies fulfilled a similar role to the tax deductions for the purchase of (principal) private insurance in the US, since they facilitated access to the only form of health insurance available to a group of the population. This would also explain why, unlike in systems such as the Canadian, PHI carriers are allowed to offer all – or any subset – of the comprehensive range of services covered by public insurance. Coupled with the existence of universal public insurance, this confers on PHI the nature of a duplicate in the Spanish system (it is noteworthy that insurance for services not covered by the public scheme – i.e. services for which PHI has a supplementary role1 such as dental care – are marketed separately from other policies). A similar situation is found in, among other countries, the UK, Portugal, Greece and Italy.

Public and Private Health Insurance and the Utilisation of Health Care in Spain 173

The services covered by PHI are mostly provided by Preferred Provider Organisation (PPO) type networks. The professionals within these networks receive a discounted fee for service from the insurer, and are allowed to run consultancies in the public network. To a lesser extent, there is also some vertical integration between insurers and providers in the form of Health Maintenance Organisations whose staff are paid on a full-time salaried basis. There are some aspects of the Spanish system for which the services of the typical duplicate PHI policy differ from the equivalent services in the public scheme. Firstly, whereas the public scheme requires patients to visit a GP before being referred to a specialist, PHI policies allow patients to resort to a specialist in the private network without a GP referral. Secondly, the choice of provider, particularly for outpatient services, is wider under private coverage. As for inpatient services, hospital amenities tend to be superior under private coverage (e.g. individual hospital rooms). These two differences constitute the marketing strong points for PHI policies. In contrast, these features are somehow offset by the fact that, thirdly, outpatient medical treatments prescribed by a doctor in the public network are heavily subsidised (the co-payments vary from 40 to 0%) whereas prescriptions by doctors visited under private coverage are not. And fourthly, private insurance policies cover some but not all hospital expenses. According to OCU (1997), many companies limit to 30 days the number of hospital days that will be paid for within a given year, with stricter limits to the number of days in intensive care. The OCU report also reveals that the public sector covers a much more comprehensive list of treatments than any of the policies offered by the private sector. The subsidies for PHI might induce undesired effects in terms of (in)equity, because PHI alters the patterns of utilisation, as shown by Rodrı´ guez and Stoyanova (2004). Moreover, for the particular case of specialist visits, Jones, Koolman, and Van Doorslaer (2007) and Van Doorslaer et al. (2002) have obtained evidence that supports the notion that PHI in Spain actually generates pro-rich inequity in utilisation. After presenting these institutional features, it is important to consider the way in which socio-economic factors can lead to unequal utilisation between two individuals with the same need for health care, and how the changes in the Spanish system might have altered the underlying mechanism. In 1987, public health care offered a relatively poor alternative to private health care, so individuals naturally sought private care when need arose. Private care was paid out of pocket or was covered by a private insurance policy, so, prior to 1987, we can expect rich and/or privately insured individuals to be more likely to use health care than poor individuals who are otherwise equal in terms of need. The gradual improvement in the public network would

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lead us to expect such socio-economic differences to disappear by 2001. However, a key feature of private care is the possibility of visiting a specialist without needing a GP referral. In the reformed Spanish system of 2001, this would lead us to expect a negative effect on the probability of using a GP and a positive effect on the probability of using a specialist for both income and PHI, because for a given level of need, poorer/not privately insured individuals would be more likely to use the services of a GP than the services of a specialist.

2.2. Previous Studies for Spain Apart from the studies cited above, there is a growing body of literature on the evaluation of the reforms in the Spanish National Health System since the Health Act of 1986 in terms of inequities in utilisation. The pioneering work of Rodrı´ guez, Calonge, and Ren˜e´ (1993) offered evidence, with data from 1987, on the degree of inequity in public health care consumption as measured by the expenditure devoted to doctor visits and hospitalisations in the public network. A similar method was followed by Aba´solo Alesso´n (1998) with data for 1993. More recently, Urbanos (1999, 2001a, 2001b) has considered the dynamics of inequity and analysed data for 1987, 1993, 1995 and 1997 within a unified methodological framework. Urbanos considers actual consumption data (number of visits and inpatient days) as well as an expenditure aggregate, and her results suggest a decrease in inequity during the period 1993–1995. Moreover, for 1997, she finds that the inequity indices for visits to GPs and specialists and inpatient days are not statistically significant. In contrast, she finds that there is a significant degree of pro-rich inequity in emergency visits and that individuals without PHI are likely to over-utilise public health care outlets, especially GP visits. Aba´solo, Manning, and Jones (2001) test the existence of equity in the utilisation of public-sector GPs in Spain in 1993 by analysing whether different socioeconomic characteristics influence the probability that the individual visited a public-sector GP during a two-week period. They find that individuals with PHI were less likely to visit a GP. Van Doorslaer et al. (2002) find a significant degree of pro-rich inequity in specialist visits and pro-poor inequality in GP visits using data from the Spanish sample of the 1996 wave of the European Community Household Panel (ECHP). Van Doorslaer et al. (2004) and Jones et al. (2007) again find that there is a significant degree of pro-poor inequity in both the probability of visiting and the conditional number of visits to a GP, whereas there is pro-rich inequity in both the

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probability of contacting a specialist and the conditional number of visits. Masseria, Koolman, and Van Doorslaer (2004) obtain point estimates that would suggest evidence of pro-rich inequity in hospital admissions using data from the ECHP, but the null hypothesis of no statistical significance cannot be rejected from these estimates. This paper contributes to the existing literature on a series of fronts. First, unlike Rodrı´ guez et al. (1993), Urbanos (1999, 2001a, 2001b) and Aba´solo et al. (2001), we do not restrict the analysis to publicly provided health care. The reason is that, as discussed above, privately provided health care and PHI have received public subsidies during the period considered. Secondly, most of the existing studies do not address the equity effects of PHI, and this paper offers some methodological advantages with respect to those that do so, such as Van Doorslaer et al. (2002), which will be discussed later on. A third contribution is that we use two comparable health surveys with rich information on health status spanning 14 years since the General Health Act. Despite the obvious limitations of all before–after evaluations, this is a plausible empirical strategy to approximate the effects of the evolution of the system on equity.

3. METHODS 3.1. Measuring and Decomposing Inequalities in Health Care Utilisation The operational concept of inequity used in the recent literature is socio-economic inequality in utilisation not justified by socio-economic inequalities in need. Therefore, it is necessary to compute measures of socioeconomic inequality in utilisation, decompose these measures and subsequently decide which components might be justified by the unequal needs. The literature on health inequalities has recently adopted a standard tool for the measurement of socio-economic inequalities in health or health care utilisation: the concentration index (CI) (Wagstaff, Van Doorslaer, & Paci, 1989). The CI has a similar interpretation to the more familiar Gini index for pure inequality. In fact, the two inequality measures differ in that the ranking variable is a measure of socio-economic status (usually income) (CI) rather than health/utilisation (Gini). The CI ranges between –1 and 1. A value of –1 would mean that all health/health care utilisation is concentrated in the poorest person, whereas a value of 1 would result if all health/ utilisation were concentrated in the richest person. If health/utilisation is equally distributed over income in the sense that the pth percentage of the

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population ranked by income has exactly the pth percentage of total health/ utilisation for any p then the CI is equal to zero.2 Suppose we are interested in calculating the CI for a measure of health care utilisation on income using individual data from the population of interest. Let yi denote a measure of utilisation for the ith individual, i ¼ 1, 2, y, N, and R0i denote the cumulative proportion of the population ranked by income up to the ith individual (their ‘‘relative income rank’’). The CI of utilisation on income can be written in terms of the covariance between the measure of utilisation and the relative income rank (see e.g. Van Doorslaer & Jones, 2003):
 2 CI ¼ (1) covðyi ; R0i Þ y¯ where y¯ ¼ Eðyi Þ: We consider three types of health care utilisation: visits to doctors, use of emergency services and hospitalisations. For each of these services, our measure of utilisation consists in the probability of utilisation at least once within a given time period. In the case of visits to doctors the time period is 15 days, whereas for the other two services the time period is one year. For 2001, we will also consider separately the probabilities of having visited a GP or a specialist, since the survey provides information on the speciality of the doctor in the last visit, so we will analyse five types of health care services. While the health surveys offer information on the number of events for each of the three services, we abstain from considering measures of equity in the number of events. This is motivated by the fact that the distributions for the numbers of events are concentrated on 0 and 1. For instance, less than 5% (6% for 2001) of individuals report more than one visit to the doctor and less than 2% (1% for 2001) report more than two. The case of hospitalisations is even more extreme in this respect, as only for 2001 do we find individuals reporting more than one event, and these individuals make up less than 2% of the sample. Furthermore, the studies that have considered both the probability of contact and the conditional number of events have found that, where there are inequities, these operate in the same direction for both dimensions of utilisation (Van Doorslaer et al., 2004). For each of the three types of health care, we specify a linear probability model (LPM) in the following way: yji ¼ 1 ðindividual i reports 1 or more episodes of health care jÞ X j ¼ aj þ bk xki þ
ji k

ð2Þ

Public and Private Health Insurance and the Utilisation of Health Care in Spain 177

where 1(
) is the indicator function, j ¼ 1,2,3 (in the case of 1987) and j ¼ 1,2,3,4,5 (in the case of 2001) refer to doctor visits, hospitalisations and emergency visits (in the case of 1987) and doctor visits, hospitalisations, emergency visits, GP visits and specialist visits (in the case of 2001) and i is an individual subscript. It follows that the probability of utilisation of service j by individual i, P(yji ¼ 1), can be written as X j Pðyji ¼ 1Þ ¼ aj þ bk xki (3) k

Our choice for the LPM is justified on the grounds that the linearity in parameters is particularly useful for our purposes of decomposing inequalities in the probability of utilisation (this property has been exploited by Masseria et al. (2004) in their study of inequity in the utilisation of inpatient services). Moreover, the well-known limitation of the LPM model producing predicted probabilities outside the [0,1] interval is irrelevant in our case, since we are only interested in the parameters of the model, which are consistently estimated by OLS. Further, we have verified that a comparison of the marginal effects of the LPM with those implied by a probit model does not reveal substantive differences. As shown by Wagstaff, Van Doorslaer, and Watanabe (2003), if the probability of utilisation is described by Eq. (3), then an inequality index for the probability of utilisation is given by X
j x¯ k  X j j CI ¼ bk j CI0k ¼ Zk CI0k (4) ¯ k P k k The term in brackets is the elasticity of P with respect to xk evaluated at the population means and CI0 k denotes the concentration index of xk against income. Moreover, if we denote the elasticity of the probability of utilisation with respect to the explanatory variable xk as Zjk 

bjk x¯ k ¯j P

(5)

then we can rewrite the decomposition in such a way that the CI is simply a weighted sum of the inequality in each of its determinants, with the weights equal to the elasticities, as expressed in the last part of Eq. (4). As mentioned by Van Doorslaer and Koolman (2004), the decomposition in Eq. (4) clarifies how each correlate xk of utilisation contributes to total income-related utilisation inequality: this contribution is the product of two factors: (i) its

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impact on utilisation (as measured by the elasticity) and (ii) how unequally it is distributed over income (as measured by the CI). Measures of horizontal inequity are easily obtained from the decomposition of income-related inequality in the utilisation presented in Eq. (4) (Van Doorslaer et al., 2004; Gravelle, 2003). All that is required is an agreement on what variables in the model of utilisation can be considered as legitimate determinants of unequal utilisation from a normative point of view – we shall call these variables need variables – and what variables do not satisfy this condition, i.e. non-need variables. The first group typically includes demographics, marital status and health indicators. The non-need variables will comprise variables that do not reflect need for health care once the need variables are controlled for. This group typically includes markers of socio-economic status. In our case, we use a measure of income and an indicator of tenure of PHI. Let w denote the (1  L) vector of need variables and z denote the (1  P) vector of non-need variables. The vector of explanatory variables in the models for utilisation is simply the concatenation of w and z, i.e. x ¼ (w,z) ¼ (w1, w2, y, wL, z1, z2, y, zP) ¼ (x1, x2, y, xL+1, xL+2, y, xK) and its dimension is (1  K), with K ¼ L+P. An index of horizontal inequity in utilisation for service j, HIj, is given by the part of the overall CI for service j that can be attributed to the non-need variables that determine the utilisation of that service. From Eq. (4), HIj is defined as HI j ¼

K X k¼Lþ1

Zjk CI0k ¼ CIj 

L X

Zjk CI0k

(6)

k¼1

This method differs in an important way from the method of ‘‘indirect standardisation’’ by Wagstaff and Van Doorslaer (1996). The method of indirect standardisation consists in first computing the CI of actual utilisation and then deducting from it the CI of predicted utilisation, where predicted utilisation is obtained from the estimation of an econometric model for utilisation as a function of need variables. This procedure has been criticised on the grounds that the omission of variables which, despite not qualifying as need indicators from a normative point of view, are nevertheless associated with utilisation, may lead to biased estimation (Schokkaert & Van de Voorde, 2004; Gravelle, 2003). This is particularly relevant for the purposes of this study. Since we wish to evaluate the impact of PHI on utilisation, and since PHI tenure is strongly associated with income and other socio-economic characteristics, omission of income – a non-need variable – from the utilisation equation may lead to biased

Public and Private Health Insurance and the Utilisation of Health Care in Spain 179

estimates for the impact of PHI. The existing studies for the case of Spain mostly rely on the indirect standardisation method. Indeed, only Van Doorslaer et al. (2004) and Van Doorslaer, Masseria, and Koolman for the OECD Health Equity Group (2006) use the method discussed above, but their analysis does not consider the effect of PHI. In relation to the point discussed in the previous paragraph, we must note that the literature on utilisation generally treats PHI as an endogenous variable (see Vera-Herna´ndez, 1999, for the case of Spain). This is motivated by the recognition that unobserved factors that affect the purchase of PHI are correlated with unobserved factors that affect utilisation. Our steps to address this issue consist in enriching the specification for utilisation with a wide set of health status indicators in an attempt to capture all relevant risk factors. This should purge the estimate for the effect of PHI of biases arising from the omission of the utilisation equations of health factors that simultaneously drive the propensity to purchase PHI. We subsequently test this assumption.

3.2. Decomposing Inequity Over Time The previous section shows how horizontal inequity in utilisation can be expressed as the contribution of non-need variables to an index of socioeconomic inequality in utilisation. It is then straightforward to use the approach proposed by Wagstaff et al. (2003) in order to decompose the difference in inequity between two periods. The method is a derivation of the well-known Oaxaca decomposition whereby the difference between the CIs of the population at period t and period t1 can be written as DHIj ¼ HIjt  HIjt1 ¼

K X k¼Lþ1

Zkt ðCI0kt  CI0kt1 Þ þ

K X

CIkt1 ðZkt  Zkt1 Þ

k¼Lþ1

(7) Then, the contribution of any particular variable, say income, within the vector z to the difference in inequity is given by DHIjincome ¼ Zincome;t ðCI0income;t  CI0income;t1 Þ þCI0income;t1 ðZincome;t  Zincome;t1 Þ

ð8Þ

In practice, we shall compute the difference in inequity (and contributions towards this difference) between 2001 and 1987. Moreover, in order to assess the relative importance of the inequality versus the health

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elasticity component in the contribution of each non-need variable in z, we also compute the relative excess elasticity compared with year 1987, i.e. (Zk2001Z  k1987)/|Z  k1987|, and the relative excess inequality, ðCI0k2001  CI0k1987 Þ=CI0k1987 ; for k ¼ L+1, y, K. 3.3. Statistical Inference Many of the statistics that we are going to report are non-linear functions of the data whose sampling distributions are hard to obtain. For this reason, we have used bootstrapping methods in order to derive standard errors. The bootstrap estimates for standard errors are computed following the five-step approach used by Van Doorslaer and Koolman (2004). The number of replications has been set to 500.

3.4. Data and Variable Definitions We use the 2001 and the 1987 editions of the Encuesta Nacional de Salud or ENS (CIS, 1987, 2001). These are nationwide surveys that collect information on health and socio-economic characteristics of individuals. The surveys contain separate samples for adults (16+) and children. The analysis in this paper is based on the adult samples. The sampling scheme is a multi-stage stratified process whereby primary strata are autonomous communities (2001 edition) or provinces (1987 edition). Within primary strata, substrata are defined according to residence area population size. Within substrata, municipalities (primary sampling units) and sections (secondary sampling units) are selected according to a proportional random sampling scheme. Finally, individuals are randomly selected from the sections. The survey documentation includes weighting factors that correct for the fact that the number of observations within the primary strata is not proportional to actual population. We use these weights whenever a nationwide statistic is computed. The information contained in the data files does not allow the identification of all the primary sampling units (because municipalities with a population below 100,000 are not identified). Similarly, information about the secondary sampling units is omitted, so it is impossible to control for cluster effects at either the municipality level or the section level. The ranking variable is equivalised total monthly income earned by the household (hereafter, income). In the ENS, this is measured as a categorical

Public and Private Health Insurance and the Utilisation of Health Care in Spain 181

variable with 12 response categories in 1987 and 6 response categories in 2001. In order to obtain a continuous measure for income and also overcome the fact that for both editions there is a substantial proportion of item non-response, we specify an interval regression model using a wide range of explanatory variables referring to both the respondent and the head of household. These variables are the relationship between interviewee and head of household, education of head of household, occupation of head of household, employment status of head of household, tenure of PHI, age and gender of the head of household and regional dummies. Except for the upper quantiles, the distributions for the predictions of income compare well with data from the Continuous Household Expenditure Survey (Encuesta Continua de Presupuestos Familiares or ECPF) of 1987 and data from the Spanish sample of the 2001 wave of the ECHP. The evolution of income inequality as measured by the Gini index also compares well with external sources.3 The initial 1987 ENS sample included 29,647 individuals. From the initial sample, five observations were dropped as income could not be predicted, and after deletion of those not responding to one of the relevant questions the final sample contains 29,185 observations in the visits to doctor estimation, 28,849 in hospitalisation and 29,122 in use of emergency services. In turn, the initial 2001 ENS sample included 21,067 individuals from all the autonomous communities, although the observations from Ceuta and Melilla were dropped as there were no individuals from these two regions in the 1987 sample. From the remaining 20,748, after deletion of those not responding to one of the relevant questions the final sample contains 20,644 in the visits to doctor estimation, 20,635 in hospitalisation, 20,636 in emergency visits, 20,644 in GP visits and 20,644 in specialist visits.

4. EMPIRICAL RESULTS As discussed in Section 3.1, we specify and estimate LPM for the probability of visiting a doctor during the last fortnight, hospitalisation over the last 12 months and emergency services utilisation over the last 12 months. The explanatory variables in the models are: (i) the logarithm of equivalent household income; (ii) 14 age–gender categories corresponding to age groups 16–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, 65–69, 70–74, 75–79 and 80+ for men and women (the omitted category corresponds to women aged between 16 and 19); (iii) three marital

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PILAR GARCI´A GO´MEZ AND ANGEL LO´PEZ NICOLA´S

status categories: never married or divorced, married, and widowed (never married or divorced is the omitted category); (iv) five categories of selfassessed health: very good (omitted category), good, fair, bad, and very bad; (v) six chronic illnesses: cholesterol, high blood pressure, diabetes, bronchitis or asthma, heart diseases and allergy; (vi) whether daily activities or leisure had been limited by any of the chronic diseases in the last 12 months; (vii) whether daily activities or leisure had been limited because of pain in the last two weeks; (viii) whether the individual had had to stay in bed for more than half a day in the last two weeks; (ix) whether the individual had had an accident in the last year and (x) tenure of PHI. Table A1 shows summary statistics of the variables included in the model. Table A2 contains the parameter estimates for the equations corresponding to each of the services by OLS. Table A3 reports the results for the tests, based on Hausman (1978) and outlined in Wooldridge (2003), of the assumption of exogeneity of PHI in the specified utilisation equations. These tests require the use of excluded instruments for PHI and, in line with previous studies (Vera-Herna´ndez, 1999; Jones et al., 2007), we use occupational characteristics of the head of the household as variables that affect the purchase of PHI but do not directly affect the respondent’s utilisation of health care. The first line in each of the 1987 and 2001 panels in Table A3 reports the test for the null hypothesis of no significance of these instruments in the reduced form equation for PHI. The remaining statistics are the t-values for the tests of significance of the reduced form equation for PHI residual in each of the utilisation equations (i.e. tests for the null of exogeneity of PHI in these equations). All these statistics are robust to the in-built heteroscedasticity of the LPM. As the figures in the table reveal, the P-values for the null hypothesis are above 5% level except in the case of emergency visits in 2001. This suggests that the inferences for emergency visits should be treated with caution. The estimates in Table A2 conform to a priori expectations. Men are in general less likely to use health care than women of the same age, and, conditional on the wide set of health indicators, the probability of utilisation does not increase with age. Interestingly, in 1987, women aged 20–29 were more likely to have used hospital care than women in any other female age group (all else held equal). However, in 2001, the age group of women most likely to have used a hospital is 25–34. This reflects the delay in fertility decisions of Spanish women over the last two decades. Income significantly and positively affected the probability of utilisation of any doctor in 1987 and specialists in 2001. In contrast, income negatively affected the probability of visiting GPs in 2001. The estimates associated with the health

Public and Private Health Insurance and the Utilisation of Health Care in Spain 183

variables (all actually reflecting some form of bad health) have the expected (positive) sign and many are statistically significant. For instance, all else held equal, an individual who self-assesses his/her health as poor is about 20% more likely to have visited a doctor in either of the two periods, and 14% (20%) more likely to have used a hospital in 1987 (2001). In 1987, private insurance is positively and significantly associated with hospital use (all else held equal). In 2001, it is positively associated with – in addition to hospitalisations – the use of emergency services and specialists, but negatively associated with the use of GPs. In fact, an individual with private insurance was about 5% more likely (1% less likely) to visit a specialist (GP) than an individual with the same observed characteristics without private insurance. The estimates for the models permit the calculation of the inequality measures presented in Tables 1A and 1B. Note that in both 1987 and 2001, the utilisation of the three types of services (visits to doctors, emergencies and hospitalisations) have unequal utilisation distributions which are all pro-poor. The concentration indices are statistically significant and the point estimates are greater for 2001, revealing that the degree of pro-poor inequality is exacerbated over time. Fig. 1 presents the contribution of each group of variables to the overall CI. These figures reveal that a very large portion of the CI is explained by need, which is concentrated among the poor. The second row of Table 1A presents the inequity measure for each of the services as defined in Section 3.1. For each of the services, HI (inequity index) is the part of the CI (inequality index) explained by income and tenure of PHI (i.e. the non-need variables in our specifications for the probability of utilisation). Note that in 1987, the HI indices for total visits and hospitalisations reveal a significant degree of pro-rich inequity. In these cases, both income and tenure of PHI contribute positively to the HI index. This means, in 1987, that while overall utilisation is concentrated among the poor, rich individuals and/or individuals who enjoyed PHI (who tend to be richer than average) had more chances of using these health services than poor individuals and/or individuals without PHI at the same level of need. In contrast, the HI indices for the three services are statistically not different from zero in 2001, implying that for a given level of need, there are neither pro-rich nor pro-poor differences in the chances of utilisation explained by income or insurance status. In order to analyse the changes over time for these indices in more detail, it is useful to isolate the sources of their changes. As discussed in Section 3.2,

184

Table 1A.

Concentration Indices and Inequity Indices and Changes Over Time. 1987

Visits

Hospital

Emergency visits

Visits

Hospital

Emergency visits

GP visits

Specialist visits

0.0626 0.0146 0.0115* 0.0031

0.0342 0.0246 0.0125 0.0121

0.0219 0.001 0.0011 0.0021

0.0959 0.0002 0.0102 0.0099

0.0847 0.0281 0.0078 0.0203

0.0465 0.0065 0.0182 0.0117

0.1478 0.0479 0.0439 0.0039

0.0121 0.0991 0.0602 0.0388

Note: Values significantly different from zero (at Po0.05) in bold typeface. *At Po0.10.

Table 1B.

CI2001–CI1987 HI2001–HI1987 Relative excess Relative excess Relative excess Relative excess

elasticity income elasticity PHI inequality income inequality PHI

Changes Over Time (2001–1987). Total Visits

Hospital

Emergency Visits

0.0333 0.0149 2.0125 1.8760

0.0504* 0.0035 0.2870 0.4902 0.1293 0.1141

0.0246 0.0055 20.1116 6.1485

Note: Values significantly different from zero (at Po0.05) in bold typeface. *At Po0.10.

PILAR GARCI´A GO´MEZ AND ANGEL LO´PEZ NICOLA´S

CI HI Income PHI

2001

1987 1987 1987 2001 2001 2001 2001 2001

Public and Private Health Insurance and the Utilisation of Health Care in Spain 185

Specialist visit GP visit Emergency Hospital Visits Emergency Hospital Visits −0.2

Log income

−0.15

Demographics

Fig. 1.

−0.1

−0.05

Marital status

0

0.05

Need variables

0.1

0.15

Private insurance

Contributions to Concentration Indices.

the contribution of each covariate to the index is given by the product of the elasticity of the probability of utilisation and the CI of the covariate. So, it might be the case that the impact of income, say, on the chances of using a particular service does not change but income becomes better distributed. This would lead, ceteris paribus, to a reduction in the contribution of income to the degree of pro-rich inequality in the chances of utilisation. Table 1B presents the relevant decompositions for the two non-need covariates that we have used in the specification. The table offers a clear indication of the direction in which the relevant magnitudes have evolved over time. First note that the distribution of equivalised household income has become more equal. Relative to 1987, the CI of log equivalised household income is 13% smaller in 2001. Tenure of PHI, however, has evolved in the opposite direction. Relative to 1987, the distribution of PHI is 11% more pro-rich. Doctor visits: As seen in Table 1A, the HI for the probability of visiting a doctor is positive and significant in 1987, with both income and PHI contributing positively. In 2001, the HI index is not statistically significant, but this is the result of two antagonistic effects. While in 2001, the contribution of income is negative (and not significant), the contribution of PHI is still positive and significant. In Table 1B, we can see that the change in the contribution of income is driven by a 200% reduction in the size of the elasticity of the probability of utilisation (and also the decrease in income inequality). In contrast, as well as becoming more concentrated among the

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rich, tenure of PHI exerts a greater impact on the probability of utilisation. The relative change in elasticity is about 180%. Hospitalisations: The case of hospitalisations is similar to that of doctor visits. There is a reduction in the contribution of income driven by a 28% reduction in elasticity (plus the reduction in income inequality) but the PHI elasticity of the probability of utilisation actually increases by 50%. In 2001, the contribution of PHI is statistically significant, but the lack of significance of the income contribution renders the HI insignificant. Emergencies: The HI index is not statistically significant in either 1987 or 2001. But while in 1987 the contributions of income and PHI are both insignificant, in 2001 the contribution of PHI is positive and significant. However, as noted above, the exogeneity assumption of PHI in the equation for emergencies in 2001 is rejected, so these inferences are to be taken with caution. In addition to these three services, we have obtained evidence for GP visits and specialist visits separately for the year 2001 (unfortunately the data for 1987 do not distinguish between GP visits and specialist visits). The results are consistent with the evidence obtained by Van Doorslaer et al. (2004), Rodrı´ guez and Stoyanova (2004) and Jones et al. (2007). That is, GP visits are concentrated among the poor. This is not only due to need being concentrated among the poor, since the HI index is negative and significant. That is, the poor and those without PHI have more chances of visiting the GP than the rich and/or PHI holders with the same level of need. Of course, this imbalance is compensated by the existence of a good degree of pro-rich inequity in the probability of visiting a specialist. Indeed, the inequity index for the probability of visiting a specialist in 2001 is greater than any of the other HI indices presented in Table 1A. Note that roughly two-fifths of this index is accounted for by the contribution of PHI.

5. CONCLUSIONS AND WAYS FORWARD The results presented in the previous section suggest that the Spanish health system seems to have achieved the goal of ensuring equal utilisation of doctors, hospitals and emergency services for equal need. In fact, the reason why the HI indices for the three services are not statistically significant in 2001 is that the contribution of income is negative (doctor visits and emergencies) and/or insignificant (all three services). With the necessary caveats derived from the fact that this is a pure before–after evaluation exercise, at least as far as the point estimates are concerned, it seems that the reforms

Public and Private Health Insurance and the Utilisation of Health Care in Spain 187

during the period 1987–2001 have reduced the income elasticity for the probabilities of utilisation of the three services. Coupled with a reduction in pure income inequality, this means that income, by 2001, does not lead to differences in utilisation for the same level of need. This is clearly an improvement with respect to 1987, a year for which our estimates show a positive and significant contribution of income to inequity in the utilisation of doctors. On closer examination, however, we note that the contribution of PHI to inequality in utilisation is positive and significant for the three services. The data reveal that tenure of PHI has become more concentrated among the rich and, simultaneously, our estimates suggest an increase in the PHI elasticity of the probability of utilisation for the three services. This leads to a positive and significant contribution of PHI to our measure of inequity in 2001 for the three services. Moreover, if we consider the chances of visiting a specialist in 2001, the data reveal a substantial degree of inequity with positive contributions of both income and PHI. These findings are consistent with previous results in the literature using data for periods prior to 2001 (Urbanos, 2001b; Aba´solo et al., 2001; Van Doorslaer et al., 2002, 2004; Jones et al., 2007), and contribute to confirm the existence of a clear pattern. An open issue for future research is the exact causal mechanism leading to a greater responsiveness of utilisation with respect to PHI. One hypothesis that is worthy of investigation is that in the Spanish health system of 2001, PHI generates a strong ‘‘access’’ effect (Jones et al., 2007) allowing individuals to use private services that are perceived as being of superior quality. This explanation would also be consistent with the reported fact that tenure of PHI has become more concentrated among the rich. The implications of these findings for the policy goals stated in the Health Act of 1986 depend on a value judgement about whether public policy should be concerned with the inequity effect of PHI. After all, the services afforded by PHI are privately provided. A crucial point here is that these services are partially publicly financed through the tax bonuses to PHI. Should the public purse subsidise better access to some citizens? If so, does it matter that these citizens tend to be richer than average? Obviously, equity is not the only relevant issue when assessing the appropriateness of PHI subsidies. Other considerations include the desire to support a private sector that might introduce competition into the health care market, or the wish to deviate demand to private outlets in order to decongest the public network. Concerning the latter, the evidence for the Spanish case (Lo´pez Nicola´s & Vera Herna´ndez, 2004) suggests that the subsidies are far from selffinancing: their study shows that for each euro given away as a subsidy for

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the purchase of PHI, the public health care network experiences a reduction in utilisation worth h0.12. Similar evidence is available for the UK (Emmerson, Frayne, & Goodman, 2001), where tax bonuses were eliminated recently. While the overall picture obtained in this paper is that the Spanish National Health Service has advanced towards making utilisation equitable, further research must find evidence to justify the subsidies for PHI, an element of the system that this research shows to generate a significant degree of inequity.

NOTES 1. Mossialos and Thomson (2002) offer a useful taxonomy for the possible roles of PHI. 2. To emphasise the conceptual similarity between the CI and the Gini index, think of the familiar plot for the Lorenz curve for income distribution, where the vertical axis represents the cumulative percent of income and the horizontal axis represents the cumulative percent of the population ranked by income. If the vertical axis is replaced by the cumulative percent of health care use then we obtain a concentration curve of health care use on income. Since health care can be concentrated among either the rich or the poor, this curve can lie above or below the diagonal (in contrast the Lorenz curve always lies below the diagonal). Similar to the Gini index – defined as twice the area between the diagonal and the Lorenz curve and taking values between 0 and 1 – the CI is defined as twice the area between the diagonal concentration curve, so it ranges between 1 and 1, and a value of 0 implies no income-related inequality in health care use. 3. Additional details on predictive power and goodness-of-fit are available from the authors on request.

ACKNOWLEDGMENTS This paper derives from the project ‘‘La dina´mica del estado de salud y los factores sociecono´micos a lo largo del ciclo vital. Implicaciones para las polı´ ticas pu´blicas’’, which is supported by the Fundacio´n BBVA. Support from Ministerio de Educacio´n project SEJ2005-09104-C02-02 is thankfully acknowledged. We are grateful to Guillem Lo´pez, Vicente Ortu´n, David Casado, Andrew Jones, Xander Koolman, Eddy van Doorslaer, Peter Lambert and three anonymous referees for useful comments and suggestions. The views expressed in this paper are those of the authors and not necessarily those of the funders or the authors’ employers.

Public and Private Health Insurance and the Utilisation of Health Care in Spain 189

REFERENCES Aba´solo Alesso´n, I. (1998). Equidad horizontal en la distribucio´n del gasto pu´blico en sanidad por grupos socioecono´micos en Canarias. Un estudio comparado con el conjunto espan˜ol. Hacienda Pu´blica Espan˜ola, 147, 3–28. Aba´solo, I., Manning, R., & Jones, A. (2001). Equity in utilization of and access to publicsector GPs in Spain. Applied Economics, 33, 349–364. Centro de Investigaciones Sociolo´gicas, Encuesta Nacional de Salud 1987. Centro de Investigaciones Sociolo´gicas, Encuesta Nacional de Salud 2001. Emmerson, C., Frayne, C., & Goodman, A. (2001), Should private medical insurance be subsidized? Health Care UK. King’s Fund. European Observatory on Health Care Systems. (2000). Health care systems in transition. Spain. Gravelle, H. (2003). Measuring income related inequality in health: Standardisation and the partial concentration index. Health Economics, 12(10), 803–819. Hausman, J. (1978). Specification tests in econometrics. Econometrica, 46, 1251–1271. Jones, A., Koolman, X., & Van Doorslaer, E. (2007). The impact of supplementary private health insurance on the use of specialists in European countries. Annales d’Economie et de Statistiques, 83. Lo´pez Nicola´s, A., & Vera Herna´ndez, M. (2004). Are tax subsidies for private medical insurance self-financing? Evidence from a microsimulation model for outpatient and inpatient episodes. Economics and Business Working Paper #632. Pompeu Fabra University. Masseria, C., Koolman, K., & Van Doorslaer, E. (2004). Income related inequality in the probability of a hospital admission in Europe. ECuity III Working Paper #13. Mossialos, E., & Thomson, S. M. S. (2002). Voluntary health insurance in the European Union: A critical assessment. International Journal of Health Services, 32(1), 19–88. OCU. (1997). Seguros de asistencia sanitaria. Dinero y Derechos, 44, 27–32. Rodrı´ guez, M., Calonge, S., & Ren˜e´, J. (1993). Spain. In: F. Rutten, E. Van Doorslaer & A. Wagstaff (Eds), Equity in the finance and delivery of health care. An international perspective. New York: Oxford University Press. Rodrı´ guez, M., & Stoyanova, A. (2004). The effect of private insurance access on the choice of GP/specialist and public/private provider in Spain. Health Economics, 13(7), 689–704. Schokkaert, E., & Van de Voorde, C. (2004). Risk selection and the specification of the risk adjustment formula. Journal of Health Economics, 23(6), 1237–1259. Urbanos, R. (1999). Ana´lisis y evaluacio´n de la equidad horizontal interpersonal en la prestacio´n pu´blica de servicios sanitarios. Un estudio del caso espan˜ol para el periodo 1987–1995. PhD thesis. Universidad Complutense de Madrid. Urbanos, R. (2001a). Measurement of inequity in the delivery of public health care: Evidence from Spain (1997). Fedea. Documento de Trabajo 2001–15. Urbanos, R. (2001b). Explaining inequality in the use of public health care services: Evidence from Spain. Health Care Management Science, 4, 143–157. Van Doorslaer, E., & Jones, A. (2003). Inequalities in self-reported health: Validation of a new approach to measurement. Journal of Health Economics, 22(1), 61–87. Van Doorslaer, E., & Koolman, X. (2004). Explaining the differences in income-related health inequalities across European countries. Health Economics, 13(7), 609–628. Van Doorslaer, E., Koolman, X., & Jones, A. (2004). Explaining income-related inequalities in doctor utilisation in Europe. Health Economics, 13(7), 629–648.

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Van Doorslaer, E., Koolman, X., & Puffer, F. (2002). Equity in the use of physician visits in OECD countries: Has equal treatment for equal need been achieved. In: Measuring up: Improving health systems performance in OECD countries. Paris: OECD. Van Doorslaer, E., Masseria, C., & Koolman, X. for the OECD Health Equity Group. (2006). Inequalities in access to medical care by income in developed countries. Canadian Medical Association Journal, 174, 177–183. Vera-Herna´ndez, M. (1999). Duplicate coverage and the demand for health care: The case of Catalonia. Health Economics, 8(7), 579–598. Wagstaff, A., & Van Doorslaer, E. (1996). Measuring and testing for inequity in the delivery of health care. School of Social Sciences, University of Sussex (mimeo). Wagstaff, A., Van Doorslaer, E., & Paci, P. (1989). Equity in the finance and delivery of health care: Some tentative cross-country comparisons. Oxford Review of Economic Policy, 5(1), 89–112. Wagstaff, A., Van Doorslaer, E., & Watanabe, N. (2003). On decomposing the causes of health sector inequalities with an application to malnutrition inequalities in Vietnam. Journal of Econometrics, 112(1), 207–223. Wooldridge, J. (2003). Introductory econometrics. A modern approach. Mason, Ohio: Thomson, South-Western.

Public and Private Health Insurance and the Utilisation of Health Care in Spain 191

APPENDIX Tables A1–A3 Table A1.

Descriptive Statistics. 1987

Visits Hospital Emergency visits GP visits Specialist visits Log income F20_24 F25_29 F30_34 F35_39 F40_44 F45_49 F50_54 F55_59 F60_64 F65_69 F70_74 F75_79 F80 M16_19 M20_24 M25_29 M30_34 M35_39 M40_44 M45_49 M50_54 M55_59 M60_64 M65_69 M70_74 M75_79 M80 Married Widowed Cholesterol High blood pressure

2001

Mean

SE

N

Mean

SE

N

0.178 0.070 0.109 – – 10.663 0.054 0.049 0.039 0.037 0.038 0.038 0.048 0.038 0.038 0.039 0.024 0.018 0.014 0.049 0.053 0.049 0.039 0.037 0.036 0.035 0.045 0.032 0.032 0.029 0.018 0.012 0.011 0.620 0.077 0.061 0.098

0.382 0.255 0.311 – – 0.482 0.226 0.215 0.193 0.190 0.190 0.191 0.214 0.191 0.191 0.193 0.154 0.135 0.118 0.215 0.224 0.217 0.195 0.190 0.186 0.183 0.207 0.177 0.177 0.169 0.133 0.111 0.105 0.485 0.266 0.240 0.297

29,185 28,849 29,122

0.235 0.086 0.191 0.159 0.076 11.483 0.044 0.045 0.051 0.045 0.045 0.036 0.038 0.031 0.031 0.041 0.034 0.024 0.020 0.036 0.044 0.052 0.047 0.048 0.042 0.034 0.038 0.027 0.030 0.028 0.026 0.020 0.014 0.580 0.079 0.109 0.143

0.424 0.280 0.393 0.366 0.265 0.449 0.204 0.207 0.221 0.207 0.207 0.186 0.191 0.173 0.174 0.199 0.180 0.152 0.139 0.185 0.205 0.221 0.211 0.213 0.200 0.182 0.190 0.163 0.169 0.165 0.160 0.140 0.118 0.494 0.269 0.311 0.350

20,961 20,952 20,954 20,961 20,961 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978

29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218

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PILAR GARCI´A GO´MEZ AND ANGEL LO´PEZ NICOLA´S

Table A1. (Continued ) 1987

Diabetes Bronchitis/asthma Heart Allergy Limited by chronic Limited by pain SAH good SAH fair SAH poor SAH very poor Bed Accident Private insurance

2001

Mean

SE

N

Mean

SE

N

0.040 0.062 0.044 0.056 0.180 0.083 0.537 0.245 0.069 0.013 0.043 0.074 0.134

0.195 0.241 0.205 0.230 0.385 0.275 0.499 0.430 0.253 0.114 0.203 0.262 0.340

29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218 29,218

0.055 0.049 0.051 0.077 0.091 0.150 0.550 0.225 0.072 0.016 0.072 0.084 0.118

0.227 0.215 0.221 0.266 0.288 0.357 0.497 0.418 0.259 0.127 0.259 0.277 0.323

20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978 20,978

Linear Probability Model Results for the Probability of Doctor Utilisation in 1987 and 2001. 1987

Log income F20_24 F25_29 F30_34 F35_39 F40_44 F45_49 F50_54 F55_59 F60_64 F65_69 F70_74 F75_79 F80 M16_19 M20_24 M25_29 M30_34 M35_39 M40_44 M45_49 M50_54 M55_59 M60_64 M65_69 M70_74

Total visits

Hospital

0.0078* 0.0239 0.0283 0.0167 0.0005 0.0204 0.0195 0.0003 0.0171 0.0059 0.0278* 0.0630 0.0005 0.0190 0.0109 0.0209* 0.0215* 0.0372 0.0365 0.0326 0.0340 0.0413 0.0188 0.0027 0.0154 0.0124

0.0034 0.0288 0.0467 0.0030 0.0026 0.0443 0.0626 0.0623 0.0711 0.0688 0.0739 0.0824 0.0800 0.0793 0.0066 0.0077 0.0197 0.0476 0.0522 0.0422 0.0555 0.0388 0.0365 0.0635 0.0456 0.0426

2001 Emergency visits Total visits 0.0005 0.0041 0.0033 0.0098 0.0236* 0.0607 0.0681 0.0657 0.0636 0.0713 0.1048 0.1117 0.0981 0.1264 0.0026 0.0052 0.0146 0.0388 0.0491 0.0558 0.0698 0.0624 0.0800 0.0833 0.0943 0.0820

0.0098 0.0093 0.0030 0.0079 0.0229 0.0091 0.0260 0.0284 0.0037 0.0482 0.0370* 0.0718 0.0338 0.0261 0.0335* 0.0654 0.0625 0.0428 0.0340* 0.0505 0.0403 0.0413 0.0354 0.0201 0.0446* 0.0221

Hospital

Emergency visits

GP visits

Specialist visits

0.0027 0.0106 0.0523 0.0561 0.0152 0.0255 0.0352 0.0209 0.0490 0.0239 0.0343 0.0278* 0.0272 0.0514 0.0059 0.0077 0.0113 0.0179* 0.0056 0.0229* 0.0020 0.0173 0.0191 0.0132 0.0111 0.0034

0.0143 0.0194 0.0060 0.0059 0.0736 0.0798 0.1108 0.0703 0.1162 0.1423 0.1013 0.1415 0.1630 0.1660 0.0246 0.0303 0.0325* 0.0564 0.0690 0.0886 0.0798 0.0933 0.1329 0.1339 0.1267 0.1246

0.0288 0.0059 0.0188 0.0265* 0.0220 0.0359 0.0050 0.0030 0.0116 0.0252 0.0231 0.0402* 0.0421* 0.0505* 0.0388 0.0590 0.0493 0.0414 0.0325 0.0474 0.0427 0.0337* 0.0507 0.0212 0.0312 0.0086

0.0189 0.0152 0.0158 0.0186 0.0009 0.0268 0.0310 0.0254* 0.0078 0.0231 0.0139 0.0316 0.0084 0.0244 0.0053 0.0064 0.0132 0.0014 0.0015 0.0031 0.0024 0.0076 0.0154 0.0011 0.0135 0.0307*

Public and Private Health Insurance and the Utilisation of Health Care in Spain 193

Table A2.

1987 Hospital

0.0275 0.0027 0.0263 0.0359 0.0347 0.0647 0.0508 0.0383 0.0458 0.0166 0.0219 0.1849 0.0242 0.1304 0.2114 0.1717 0.2016 0.0663 0.0101

0.0348 0.0039 0.0520 0.0362 0.0123* 0.0106* 0.0126 0.0034 0.0582 0.0044 0.0687 0.0082 0.0134 0.0440 0.1461 0.1786 0.0385 0.0830 0.0160

2001 Emergency visits Total visits 0.0751 0.0657 0.0295 0.0228 0.0103 0.0006 0.0159 0.0265 0.0681 0.0263 0.0649 0.0316 0.0215 0.0510 0.1273 0.1866 0.0700 0.2985 0.0041

0.0303 0.0147 0.0117 0.0013 0.0167 0.0465 0.0298 0.0260* 0.0267* 0.0297 0.0293 0.2564 0.0505 0.1530 0.2073 0.0231 0.1780 0.0580 0.0441

Hospital

Emergency visits

GP visits

Specialist visits

0.0003 0.0277 0.0198 0.0019 0.0127* 0.0067 0.0185* 0.0165 0.1011 0.0293 0.0558 0.0024 0.0170 0.0926 0.2029 0.1032 0.0603 0.0651 0.0328

0.1145 0.1056 0.0169 0.0077 0.0100 0.0074 0.0007 0.0653 0.1038 0.0116 0.0901 0.1102 0.0333 0.1364 0.2102 0.0544* 0.0420 0.4220 0.0423

0.0319 0.0116 0.0055 0.0015 0.0339 0.0584 0.0482 0.0318 0.0154 0.0223 0.0260 0.1877 0.0295 0.0783 0.0948 0.0189 0.1216 0.0082 0.0119*

0.0016 0.0263 0.0062 0.0028 0.0172 0.0119* 0.0184* 0.0059 0.0422 0.0074 0.0033 0.0687 0.0210 0.0747 0.1125 0.0419 0.0564 0.0498 0.0560

Note: Values significantly different from zero (at Po0.05) in bold typeface. *Po0.10.

PILAR GARCI´A GO´MEZ AND ANGEL LO´PEZ NICOLA´S

M75_79 M80 Married Widowed Cholesterol High blood pressure Diabetes Bronchitis or asthma Heart Allergy Limited by chronic Limited by pain SAH good SAH fair SAH poor SAH very poor Bed Accident Private insurance

Total visits

194

Table A2. (Continued )

Public and Private Health Insurance and the Utilisation of Health Care in Spain 195

Table A3.

Tests for the Assumption of Exogeneity of Private Health Insurance in the Utilisation Equations. 1987

Het.-robust F stat. for null hypothesis of joint no significance of instruments in reduced form P-value

F(6.28004) ¼ 112.11

0

Total visits

Hospital

Emergency visits

1.17

0.1

0.71

0.24

0.92

0.47

Het.-robust t-value for null hypothesis of no significance of residual from reduced form in utilisation equation P-value

2001 Het.-robust F stat. for null hypothesis of no significance of instruments in reduced form P-value Total visits Het.-robust t-value for null hypothesis of no significance of residual from reduced form in utilisation equation P-value

F(6.20584) ¼ 9.71

0 Hospital

Emergency GP visits Specialists visits

1.05

1.71

2.44

0.24

1.91

0.29

0.08

0.015

0.81

0.056

Note: All test statistics are robust to heteroscedasticity. The set of excluded instruments used for testing are a set of six occupational dummy variables for the head of the household.

AGING AND INTERGENERATIONAL FAIRNESS: A CANADIAN ANALYSIS Michael Wolfson and Geoff Rowe ABSTRACT Population aging in many countries has become a fundamental concern of public policy. One reason is fears that increasing numbers of elderly will place disproportionate burdens on their children in order to fund public pensions and health-related services. This analysis first discusses basic principles for assessing this question of intergenerational fairness. It then applies an empirically-based overlapping cohort dynamic microsimulation model for a quantitative analysis of the flows of taxes and cash and in-kind transfers for successive birth cohorts. The simulations cover both exogenous factors – specifically trends in life expectancy and the strength of the economy, and policy-related factors – specifically raising the age of entitlement to public pensions from age 65 to 70, and price versus relative wage indexing. The analysis concludes, among other points, that intergenerational differences are significantly smaller than intra-generational variations, and that the parents of the baby-boom generation are likely to benefit from the largest lifetime net transfers of any birth cohort from 1890 to 2010.

Equity Research on Economic Inequality, Volume 15, 197–231 r 2007 Published by Elsevier Ltd. ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15009-2

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To portray America as riven by generational warfare, young against old, is therefore an exaggeration. Worse, it obscures a deeper divide, of class rather than age. yThe big problem of the American welfare state is not that the old get too much, but that the rich do. (Economist, January 11, 1997)

INTRODUCTION Population aging is increasingly recognized as a worldwide phenomenon. And the pace of aging over the past few decades, especially in the richest countries, is unprecedented in human history. While there are many reasons why increased longevity and modest family sizes should be welcomed, population aging is more often a source of concern. The essential fear is that future cohorts of elderly, in particular those of the post WW II baby boom, will be placing an intolerable financial burden on future working age generations. A claim capturing this concern is that the baby boom generation is the first in history who cannot expect their children to be better off than they are. In this paper, we examine these questions for Canada, looking decade by decade at the financial circumstances of successive birth cohorts born during the 20th century. More specifically, for each decadal birth cohort, we have estimated the total amount of income and payroll taxes they pay over their lifetimes, and the corresponding amounts of income transfers, especially old age pensions, and transfers in kind they receive in the forms of education and health care services. It takes the better part of a lifetime to accrue a pension or to save adequately for retirement. As a result, a widely accepted criterion for good public policy in this area is that the rules underpinning public pensions and other major age-sensitive programs should be reasonably stable and predictable. Such stability enables individuals to plan better their own private savings over their life course. On the other hand, this kind of stability in public sector rules is very difficult to achieve because the future is inherently unknowable. Still, by indexing and other provisions, governments have de facto indicated what the responses will be in future to at least some unknown vicissitudes – for example, in the case of the indexing of benefit levels and income tax thresholds, to future and as yet unknown rates of inflation. It would be reassuring for future public pensions, health care, and income tax policy – the three large government programs most sensitive to population aging – to be based on a set of rules or principles (to the extent possible) that individuals could count on for their long term financial planning. In turn, this means that these rules or principles would be unlikely to

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be amended in future, by whatever democratic coalitions might emerge. In a phrase, this entails (as a necessary, but not sufficient condition) that the rules and principles should be designed in such a way that they are currently, and will continue to be, broadly perceived as inter-generationally fair. (It is also important that the rules be fair within generations, a point to which we return later.) This is a challenging objective for at least two fundamental reasons. First, there is no widely agreed concept of inter-generational fairness. Second, the future is inherently unknowable, so that even with an agreed concept of inter-generational fairness, it is extraordinarily difficult, if not impossible, to examine such a criterion for all possible eventualities. In other words, it is impossible to assess the inter-generational fairness of a given system of rules or principles under all possible future scenarios. However, it is possible to make a reasoned effort, and to consider a few of the most important areas of uncertainty. In this spirit, the following analysis provides a series of birth cohort-specific quantitative reconstructions of the histories, and projections of the interactions, of successive birth cohorts with Canada’s major tax and cash and in kind transfer programs. The essential objective is to provide the information to support judgments as to the intergenerational fairness of these major public programs.1 In addition to a ‘‘baseline’’ or status quo scenario for the future evolution of these programs, two further policy-related scenarios will be examined. Neither represents a specific policy option currently under discussion in Canada. Rather they represent two stylized and simplified versions of policy options either under discussion or implemented in other countries. The first policy alternative essentially raises the age of entitlement to public pensions from 65 to 70. The second shifts a range of tax and cash transfer program indexing provisions from the status quo consumer price index (CPI) to the average wage (AW). Since a fundamental objective of this analysis is to assess the likely intergenerational fairness of major age-sensitive public programs to the unknown vicissitudes of the future, we have also posited several alternative scenarios for the socio-economic milieu within which future program structures would apply. Again, we rely on a few highly stylized scenarios. In general, we can distill two main axes of uncertainty from the literature on public pensions and inter-generational equity – whither longevity, and whither the economy.2 More concretely, we have therefore constructed four (2
2) ‘‘exogenous’’ socio-economic scenarios within which to embed our examination of the intergenerational patterns of public policy – high and low projections of future mortality rate improvements, and high and low future levels of employment.3

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The vast majority of published literature on inter-generational fairness and the inter-generational impacts of public programs has been extremely simplified. In particular, it has typically involved just one representative (or average) individual (or maybe two, a male and a female) for each birth cohort (e.g. Kotlikoff, 1992). This is an extremely restrictive assumption, and one that we will show yields seriously misleading results. This analysis eschews such representative agents, and instead is fully microanalytic. It is based on Statistics Canada’s LifePaths microsimulation model (Statistics Canada). LifePaths is much more than a casual extension of some sort of spreadsheet analysis. Rather, it is an ‘‘industrial strength’’ policy-oriented microsimulation model that has been developed over more than a decade in partnership with a number of central policy ministries of the Canadian Government. In the following section, we review some of the main concepts of intergenerational fairness. Then we briefly outline the LifePaths model. The main part of the analysis describes the scenarios – both policy and exogenous – in greater detail and then moves onto the key results.

JUDGING INTER-GENERATIONAL FAIRNESS AND SUSTAINABILITY There is no widely agreed approach to judging whether a society’s tax/ transfer system is inter-generationally fair or sustainable.4 But there is a considerable literature addressing this question. One strand builds on conventional economic theory, and dates back at least implicitly to Ramsay (1928). The basic ‘‘axiom’’ in these inter-temporal utility function-based analyses (Basu & Mitra, 2005) is that inter-generational equity is achieved when all generations have identical utility. Unfortunately, these kinds of formal analyses are highly abstract and embody such simplifying assumptions as to render them of no practical use in the context of applied analysis.5 Kotlikoff and others have popularized the notion of ‘‘generational accounting’’ (e.g. Kotlikoff, 1992; Kotlikoff & Burns, 2004). Within this framework, generational inequity arises when the taxes required of future as yet unborn generations – to pay off current government debt (including unaccounted items such as the unfunded longer term liabilities of the U.S. Social Security pension and Medicare programs) as well as to finance government services that continue at current levels – exceed the taxes being paid by the

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generations alive today. In general, this is a reasonable principle. Note that it applies to the entire public sector, and not just to the age-sensitive programs being examined here. However, as just noted, the methods specifically used to estimate generational accounts (representative agents, constant exponential growth for all time) are dubious. There are, in any case, several norms which appear commendable, generally drawn from public policy documents:  Inter-generational golden rule (e.g. Canada, 1980, Summary, p. 54) – One generation, when it becomes old and frail, should not expect to be treated any better by its children (when they are of working age at that future time) than it treated its parents’ generation in their old age (when they themselves were of working age).6  Sustainability (Canada, 1980, Summary, p. 54; House of Commons, 1983, p. 15) – The world that parents bequeath to their children should be at least as good (e.g. economically productive) as the one they in their turn had inherited.7  Neutrality – Each generation should pay for its own pensions, i.e. there should be no inter-generational transfers at all.  Musgrave (1981) – Per capita transfers to the elderly should be a fixed proportion of per capita wages less taxes of the working age population.  House of Commons (1983, p. 17) – Pensioners should expect to share in real economic growth when it occurs, but correspondingly should not be completely immune from economic recessions.  Majority norm – ‘‘If a retirement income system is not, and is seen not to be, fair in its treatment of successive generations, it will be changed sooner or later’’ (Canada, Summary, 1980, p. 54). In other words, a tax/transfer system is sustainable and fair if it is the outcome of a continuing democratic consensus. Fig. 1 (Wolfson, Rowe, Gribble, & Lin, 1998) provides a convenient schema for illustrating these norms. Birth year is shown on the vertical axis, and calendar time along the horizontal. Each horizontal bar represents one generation or birth cohort born at time b. In turn, the lifetimes of the bth birth cohort have been divided into three broad phases: childhood (Cb), working (Wb), and elderly (Eb). Inter-generational transfers then arise, in this analysis, only from government tax/transfer activities (both cash and in kind), and generally speaking involve either Wb-Cb+1 or Wb-Eb1 flows, as indicated by the short vertical arrows in the diagram. There are several challenges for assessing inter-generational fairness in terms of Fig. 1. The first is that the boxes in Fig. 1 (along the vertical axis),

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Birth Cohort 1890

C

1910 1930 1950

W

E

C

W

E

C

W

E

C

W

E

C

W

E

C

W

1970 1990 1890

Fig. 1.

1990

2090

E

Calendar Year

Basic Generational Accounting Framework.

in reality, should not all be shown as the same size. Some birth cohorts are larger than others. Second, the state of the economy varies significantly from one time period to the next along the horizontal axis. The arrows in Fig. 1 focus on the sequence of contemporaneous (i.e. point-in-time) transfers occurring across generations. But the diagram has no representation of savings and investment (or dis-saving and dis-investment), in the sense for example of the future productivity (or increased environmental degradation) of the society. How much wealth and income a society is able to generate in future years is a crucial aspect of assessments of inter-generational fairness, and is implicit in the first two norms. Nevertheless, the diagram is still helpful in thinking about the various norms for inter-generational fairness just outlined. The first norm implies that the public pensions and health care services expected by the current working age generation, when it becomes elderly in the future, should not make any larger claim on resources, relative to the size of the economy, than the transfers it is financing for the current elderly. In terms of Fig. 1, this norm implies that the sequence of transfers indicated by the vertical arrows from Wb to Eb1 should be non-increasing over time (in proportion to the size of the economy). The second norm suggests that it is unfair to bequeath to future generations any kind of substantial liability, such as a large public debt, or a degraded physical, human, environmental or other kind of capital stock. This norm is consistent with lifetime consumption or disposable income that rises from one generation to the next. In other words, each generation of parents is sacrificing at least somewhat so their children can have a better life. This norm encompasses much more than income taxes and cash and in

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kind transfers made through the public sector. Still, if each generation (e.g. Eb which had been Wb earlier during its working years) succeeded in leaving its successors (Wb+1) a wealthier and more productive economy, then it should be possible for Wb+1 to transfer to Eb an amount that is higher than the amount Wb had transferred to Eb1 in its turn. In terms of Fig. 1, this means that transfers from those of working age to elderly should be increasing (or at least non-decreasing) from one generation to the next. Note that this norm is inconsistent with the ‘‘anonymity’’ version of inter-generational equity posited by Basu and Mitra (2005), though it is consistent with the norm implicit in Kotlikoff-style generational accounting. The third norm takes a different approach, basically saying that the fairest system is one in which there are no inter-generational transfers at all. However, there exists no ‘‘extra-planetary banker’’ who can initially loan funds to children to fund their consumption and education while they are growing up, take savings from them when they ‘‘graduate’’ into their working years first to pay down their ‘‘growing up’’ and educational loans, and then to accumulate savings for their retirement, and finally gradually disburse their accumulated savings after they have retired. Instead, the savings and dis-savings of each generation during its life course inevitably involve de facto contemporaneous inter-generational transfers (albeit mediated in complex ways both via government taxes and transfers, financial markets, and intra-family transfers). Still, this norm is (in our view, naively) involved in analyses that compare, for example, the internal rates of return to different generations for their Social Security contributions and benefits, and implicitly raises concerns when they are not all the same (e.g. Beach & Davis, 1998). This norm could also be taken as the essence of a strong form of the Kotlikoff-style generational accounting. In these analyses, the key ‘‘empirical’’ result is what the tax rate (presumed constant from today forward) would have to be for all future unborn generations in order to amortize government debt (broadly defined). And the presumption, when this tax rate is found to be much higher than that being paid by currently living generations (as is the case in the U.S., but not necessarily in Canada; see Oreopoulos & Vaillancourt, 1998), is that taxes on those currently alive should be immediately raised, or their government benefits cut, such that the two tax rates (those of the living, and those of the yet unborn) become equal. The fourth norm (Musgrave, 1981), in a more precise and focused way, provides a kind of balance point between the first and second norms. According to this norm, the sequence of transfers Wb to Eb1 are in some general sense constant, but not constant in simple money terms. Rather, this norm entails a kind of relative effort and relative benefit constancy. It

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adjusts automatically in the event of population aging by reducing net transfers to the elderly; and it adjusts for higher than anticipated per capita economic growth by raising net transfers. The fifth norm was developed by a Special Parliamentary Committee formed in 1983 to review the results of what at the time in Canada was referred to as the ‘‘great pension reform debate’’. After much (often in camera) discussion amongst the members of this all party committee, these Members of Parliament agreed on recommending that public pensions (as well as income tax thresholds for retirement saving incentives) should be indexed in such a manner that they are higher when    

real average wage growth is higher, labor force participation is higher, unemployment is lower, and the old-age dependency ratio is lower,

and would be lower in the opposite circumstances. One metaphor used by committee Members8 to understand this norm in their own terms was in reference to an extended family in an agrarian society: When the harvest was good, everyone benefited including the family’s elderly, even if they were too frail to have contributed much labor. Correspondingly, when the harvest was poor, everyone was expected to make do with less. This norm itself is, in fact, a specific and more precise articulation of the both of the first two norms, and fully in the spirit of the Musgrave notion. Interpreting the sixth ‘‘majority’’ norm only in the context of Fig. 1 is difficult. The main reason is that the population of eligible voters at any point in time includes not only members of different generations, but also individuals within a generation who are in widely different circumstances. In a word, each generation is heterogeneous. It could be, for example, that a tax/transfer system is (‘‘point in time’’) progressive in a way that lower and middle income individuals from several adjacent generations (all of whom are of voting age at that point in time) have more in common than those with high and low incomes within a given generation. Thus, ‘‘block voting’’ by generation, or generational politics, may not be in many individuals’ selfinterest. As a result, the democratic majority norm need not be consistent with any of the other norms.9 If we step back from the details, and do not take the numeraire for measurement too literally, the first five norms, in the end, are quite similar. And they do, in this sense, align with the Ramsay (1928) implicit assumption that inter-generational fairness or equity requires some sort of equal

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treatment across generations. This, however, is the easy part. The challenge is how to operationalize ‘‘equal treatment’’ in the real world where, among other things, the population size of successive birth cohorts varies, along with rates of economic growth, and patterns of working and saving. In this regard, the Musgrave norm begins moving toward a more practical or operational form by taking account of two factors – per capita wages and tax rates, which in turn will vary with the economic productivity, the employment to population ratio, and the age structure of the society. The House of Commons norm depends on essentially identical factors, since ‘‘per capita wages’’ specified in the Musgrave norm depend primarily on real average wages, labor force participation and unemployment rates – the factors explicitly mentioned in the House of Commons norm. In turn, the implication of the first five norms is that any assessment of intergenerational fairness requires specific data for each of a sequence of overlapping birth cohorts. In particular, the key data are the incomes net of transfers received less taxes paid, over complete lifetimes, of successive birth cohorts. Moreover, in line with Ramsay (1928), ‘‘ywe do not discount later enjoyments in comparison with earlier ones, a practice which is ethically indefensible and arises merely from the weakness of the imagination’’. The quantitative analysis developed in the following sections uses the average wage as the numeraire – in other words not in nominal dollars, not in constant dollars (i.e. deflated by the CPI), not in present discounted values (i.e. deflated by an interest or time-preference rate), but in ‘‘wage-relative’’ dollars (i.e. deflated by the average wage). The sixth norm reminds us that while these kinds of generational data are analytically necessary, they are by no means sufficient. We need an analytical framework that can also unpack and reflect the great heterogeneity of individuals’ life course experiences within any given generation. Given the conceptual discussion so far on norms of inter-generational fairness, it could be argued that two fundamentally distinct notions are still being confounded – in two words, levels and risks. How would the analysis unfold if we considered these norms in terms of a pair of questions: (1) if there were no uncertainty, what should the levels of available resources (consumption) be for successive generations; and (2) how should the risks associated with various kinds of uncertainties be shared between generations?10 For example, if the default assumption is that the inter-generational ‘‘contract’’ implicit in a society’s package of tax and transfer programs is written in nominal dollars, then the answer to the ‘‘level’’ question would be clear and easy to understand, but in practice it would be subject to major risks due to the uncertainties of future inflation rates.

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In effect, the levels question is the easier one – either a Ramsay approach with some sort of equality between generations, or a kind of golden rule approach with increasing levels over time. The risks question is far more difficult, and what the norms outlined above, in particular the Musgrave and House of Commons norms, are doing is beginning to specify how levels of inter-generational transfer should be automatically adjusted in the face of a range of specific kinds of risks or uncertainties – such as faster or slower economic growth, more or less rapid population aging, and higher or lower unemployment rates. In other words, these norms embody answers to both kinds of questions – what fair levels of inter-generational transfers ought to be, and what fair methods of sharing risks should be – at least for a few obvious kinds of risks, or more properly unknowns: future inflation rates, life expectancy trends, per capita wage growth, etc. One further and most interesting kind of risk is the marginal utility of money. The Ramsay (1928) analysis, and most subsequent mainstream economic analyses, make explicit reference to this notion by assuming the existence of well-defined and well-behaved utility functions, and then using formal mathematics when examining inter-generational equity questions. However, the debate on the way in which technical progress and ‘‘new goods’’ should be handled in the construction of the Consumer Price Index, i.e. the way that inflation risk should be removed from inter-generational contracts, shows the practical impossibility of ever addressing this question.11 The empirical evidence on subjective well-being, in contrast, suggests that individuals’ ‘‘utility’’ is more likely driven by a mix of their relative position within their social group, and person-specific homeostatic set-points. These latter realities give further support to the use, in this analysis, of the average wage as the numeraire for assessing inter-generational differences in levels. One implication of reframing the question of appropriate norms for judging inter-generational equity into the pair of questions – on levels and on risks – is that there can never be a completely specified norm. The simple reason is that the risks are inherently unknowable in full. Perhaps a more practical approach – call it an ‘‘evolutionary’’ approach to inter-generational equity – is to plan on the norms having to evolve as new kinds of risks and uncertainties emerge and become evident. The most obvious case was (not so much the ‘‘baby boom’’, but rather) the ‘‘baby bust’’ decline in fertility in the late 1960s. The Social Security and Canada Pension Plan actuaries did not anticipate this when these public pension plans were first set up, yet now changes in population age structure are at the heart of much of the discourse on inter-generational equity.

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Finally, the rather general points of the preceding paragraphs serve to emphasize the overall weakness of the literature in this area of inter-generational fairness. The formal theoretical work is far too abstract to be of use; the sociological and political science writings, while illuminating, offer no practical guidance; and most of the quantitative empirical work either rests on unrealistic simplifying assumptions (e.g. infinite horizon constant exponential growth in generational accounting), or is too partial (e.g. the internal rate of return calculations for Social Security in the U.S.).

AN OVERVIEW OF THE LIFEPATHS MICROSIMULATION MODEL In order to assess Canada’s tax/transfer system in the light of the norms just outlined, we draw on Statistics Canada’s LifePaths model. LifePaths is a computer simulation model designed explicitly to encompass both inter- and intra-generational analyses simultaneously. Each LifePaths simulation run generates a representative microcosm of the Canadian population. In other words, LifePaths is microanalytic. The basic units of observation are individuals, and the focus is on microlevel dynamics – how individuals move among various mixtures of socio-economic states over their life courses. And empirically, LifePaths is metasynthetic – drawing upon multiple data sets, covering diverse subject matters, and using each in order to assemble the best possible overall estimate of the information of interest.12 The basic unit of analysis in LifePaths is an individual life history or stylized biography, as shown in Fig. 2. The ‘‘state space’’ of attributes or individual characteristics is shown along the vertical axis, with age and calendar time coincident along the horizontal. The third axis indicates a representative sample of individuals in the population of interest. These are not all unrelated individuals; rather, they are juxtaposed to show that family structure is also included. Given these microlevel life histories as the basic building blocks, LifePaths assembles large representative samples of individuals (grouped into nuclear families) in a sequence of overlapping birth cohorts (Fig. 3). Each ‘‘layer’’ in the diagram represents one birth cohort, while the sequence of layers represents successive birth cohorts. A typical population pyramid showing age structure by sex at a point in time corresponds to a vertical slice through the overlapping birth cohorts along the line for ‘‘today’’.13

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population sample

person j+1 person j child 2 child 1 spouse

state space

Nuptiality Fertility Education Labour Market Disability Institutionalization …. etc time, age

Fig. 2.

State Space and Longitudinal Microdata Sample Generated by a LifePaths Simulation. Birth Cohort

“today”

Calendar Year Heterogeneous Individuals

Fig. 3.

Overlapping Birth Cohorts with Heterogeneous Members.

LifePaths essentially creates a large sample of representative individual life histories, where the individuals have been born throughout the 20th century in accord with historical population data. The historical reconstruction and subsequent projection processes proceed by data synthesis using longitudinal microsimulation: each individual’s life history is synthesized, starting at birth and then recursively generating the suite of events and characteristics shown along the vertical axis of Fig. 2 over time until death. Then another family of

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individuals is synthetically generated, and again, and again, until a very large sample (e.g. 1,000,000s) is generated. The result is our ‘‘fitted’’ population microcosm (for years prior to ‘‘today’’), plus microlevel extrapolations of each life history beyond ‘‘today’’ (if still alive) over coming decades. The result is a very large longitudinal sample of synthesized individuals that – when appropriately cross-tabulated or otherwise examined – reproduces a diversity of observed data, such as population characteristics from censuses, mortality and fertility rates dating back to about 1900, age- and sex-specific employment/population ratios since the 1970s, and aggregate wages and income taxes back to the 1920s. Underlying any LifePaths simulation is a detailed set of empirically based state transition dynamics. As a result, dynamics are represented by transition probabilities (more precisely, by transition probability functions of a range of time-varying covariates/co-evolving characteristics). For example, the nuptiality transitions explicitly modeled are shown in Fig. 4. The different states are given by the boxes, while the arrows indicate the possible transitions. For each arrow, there is an empirically estimated

Common law union

Single

Married

Separated CLU

Separated

Divorced CLU

Divorced

Married (2nd)

Widowed

Widowed (2nd)

Separated (2nd)

Divorced (2nd)

Fig. 4.

Nuptiality States and Transitions.

Widowed CLU

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transition probability function of time-varying covariates. The transition probability functions have been estimated initially from survey data and then (where possible) adjusted so that LifePaths as a whole reproduces the distribution of families by marital status observed in Canada’s 1996 population census. Some added detail on LifePaths is given in the appendix, and further information is available at www.statcan.ca/english/spsd/LifePaths.htm.

EXOGENOUS SCENARIOS Given this background discussion, we turn to the heart of this analysis. First, in order to assess the impact of exogenous changes on the projected inter-generational profiles of major government programs on Canadian birth cohorts, a series of four scenarios characterizing the socio-economic milieu have been constructed – high and low mortality, and high and low economic circumstances. Mortality As noted above, the mortality process is simulated in terms of hazard rates. These hazards, or transition probability functions, are differentiated by birth year, age, sex, as well as institutional status. Up to 2004, observed data are used. Under the high mortality/lower life expectancy scenario, Statistics Canada’s ‘‘high mortality’’ scenario in the official demographic projections (Statistics Canada, 2005) is used up to 2051, the end of that projection period. For those members of birth cohorts who survive beyond 2051 in these simulations, mortality rates remain constant at their 2051 levels. For the lower mortality/higher life expectancy scenario, the low age-sex specific mortality hazards from the demographic projections were used from 2005 to 2051. For years after 2051, mortality hazard rates (differentiated by age and sex) were assumed to continue improving at the constant rate embodied in the demographic projections for the interval from 2050 to 2051.14 These two scenarios result in considerable divergence in life expectancy, as shown in Table 1. Life expectancies for each sex differ by about three years for the cohort born in the 1990s, and by almost five years for those born in the 2002–2011 interval.15

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Table 1.

211

High and Low Life Expectancy Scenarios. Simulated Life Expectancies

Cohort

Scenario

Females

Males

Low life expectancy High life expectancy Difference

87.1 89.9 2.9

82.2 85.2 3.0

Low life expectancy High life expectancy Difference

87.6 92.2 4.6

83.1 88.0 4.9

Born in 1992–2001

Born after 2001

Strength of the Economy The other major axis of exogenous uncertainty that will be considered is the strength of the economy. This can be conceptualized in a variety of ways, but for this analysis we focus on employment. A ‘‘strong’’ economy is defined as one where employment levels are higher; while a weak economy is one where employment is lower. In order to implement these alternative employment scenarios, advantage was taken of the fact that the employment dynamics module in LifePaths is based on a set of mutually interacting transitions, each one corresponding to an arrow in Fig. 5, where these rates are in turn functions of calendar year dummy variables for each of the years from 1976 to 2004, as well as a range of other factors (age, sex, educational attainment, duration in employment state, province of residence, presence of a spouse, and spouse’s employment status). The year dummy variables appear both on their own, and as interaction terms respectively with age (linear and quadratic terms, age 65, age 65+), presence of pre-school children, low education level (oHigh School), and presence of pre-school children
low education level. Given this detailed and richly specified structure for the employment dynamics module, the ‘‘high employment’’ scenario is based simply on the assumption that the most recent business cycle peak year, 2004, will apply for the years 2005 and on when evaluating the set of employment state transition probability functions as a ‘‘fixed effect’’ for all future periods. The ‘‘low employment’’ scenario makes an analogous assumption, but in this case uses the year of the most recent business cycle trough, 1993, as a fixed effect for all future periods after 2011. Actual transition hazards for

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Paid employee

Self employed

Fig. 5.

Not employed

Employment States and Transition Possibilities.

$ 20,000

$17,500

$15,000 Low Life Expectancy Low Employment High Life Expectancy Low Employment

$12,500

Low Life Expectancy High Employment High Life Expectancy High Employment

$10,000 1970

Fig. 6.

1980

1990

2000

2010

2020

2030

2040

2050

Simulated Earnings (2001$) per Capita for Mortality and Employment Scenarios.

1994–2004 are still used. From the 2004 business cycle peak, a smooth transition has been assumed for the dummy variables to the 1993 business cycle trough over the interval 2005–2011. After that, the dummies remain constant at their 1993 levels. Fig. 6 shows the effects of these two employment scenarios on per capita earnings. For most of the projection period, the divergence in employment

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transition dynamics, between those of the 2004 peak and the 1993 trough business cycle years, amounts to over $2,000 (in 2001 dollars) or over 10% of per capita earnings. Fig. 6 also shows the effects on earnings of the two life expectancy scenarios. Since most of the variation in mortality rates arises after prime working ages, and the differences do not affect the total population that greatly (even though they change life expectancy by as much as almost five years), there is no appreciable difference in per capita earnings as a result of differences in life expectancy.

PROVISION FOR RETIREMENT IN THE CANADIAN SYSTEM In addition to incorporating a wide variety of socio-economic characteristics, this LifePaths analysis must also realistically model Canada’s major tax and transfer programs. In this section, we first give a brief overview of Canada’s current public pension system, and then describe the taxes and in kind transfers that have also been explicitly modeled. Canada’s public pension system is often described as having three tiers. The first tier is a pair of cash transfers to the elderly (generally age 65+) based only on their current income, and financed out of general taxation. One is a taxable ‘‘demogrant’’ called the Old Age Security (OAS) pension. It started in 1952 paying monthly benefits to those over age 70. This entitlement age was subsequently lowered to 65, and at July 2006 rates, annual benefits are $5,904 per year (subject to a sufficient period of prior residency). The other basic cash transfer is an income-tested benefit, the Guaranteed Income Supplement (GIS) program, starting in 1967, and an extension, the Spouse’s Allowance (SPA) program, starting in 1976. They provide nontaxable monthly benefits to Canadians age 65 and over (or age 60–64 with a spouse age 65 or over in the case of SPA). Together, these major programs provide basic income guarantees of up to $14,139 and $18,884 for Canada’s senior individuals and couples in 2006. As a result of a number of ad hoc increases over the years, their combined benefit levels have become such that very few of Canada’s elderly have incomes below the ‘‘low income line’’. The next tier is the Canada and Quebec Pension Plans (C/QPP), an earnings-related public pension plan that pays out a retirement pension essentially equal to 25% of average (updated) pre-retirement earnings. (While there are two plans, one for Quebec and one for the rest of Canada,

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they have virtually identical contribution and benefit provisions, and are completely integrated from the viewpoint of individuals moving between them.) The maximum pension in 2006, $10,135, is based on 25% of the average over the past five years of the year’s maximum pensionable earnings (YMPE). This in turn is equal to the average annual wage in Canada, and was $40,500 in 2004.16 The plans are financed by a payroll tax. Until recently, the rate was set so as to assure a reserve equal to the payout of about two years of benefits. Recently, the payroll tax rate has been increased so that accumulated funds are projected to rise to about 4.4 times benefits in 2010, and about 6.3 times in 2050 (OSFI 2005b). Still, overall, the plans remain funded essentially on a pay-as-you-go basis. The third tier of Canada’s public pension system is a set of tax incentives for private saving for retirement, either via individual accounts called Registered Retirement Savings Plans (RRSPs) or employer-sponsored plans (Registered Pension Plans or RPPs). The tax expenditure (foregone income tax revenue) in respect to these provisions amounted to about $19 billion in 2005 (Canada, 2006), while the total cost of OAS/GIS was about $30 billion in the same year (OSFI, 2005a), and C/QPP also paid out about $30 billion (for retirement and survivor pensions, based on OSFI 2005b). Thus, income tax incentives are a significant component of the public system, and they are used disproportionately by those in upper income brackets. Beyond the public system, and the significant volume of private saving accumulated under registered plans for retirement purposes, home ownership is a significant form of de facto saving for retirement. However, about half of all Canadians enter retirement without owning a house, and with relatively little in the way of accumulated savings of any form. They are therefore highly dependent on the public pension system.17 Beyond public pensions and other provisions for retirement, this analysis also takes explicit account of personal income taxes (both federal and provincial), payroll taxes, (un)employment insurance transfers, and in kind education and health care benefits. In the latter two cases, benefits are imputed based on highly simplified formulae. Health care in kind service benefits are assumed to vary only by age and sex, while education in kind service benefits vary only by the type of educational institution attended (Cameron & Wolfson, 1994). These unit costs are projected simply in line with the growth in average wages. It is, of course, well known that non-demographic factors are typically far more important in determining the trends in these unit costs (Evans, McGrail, Morgan, Barer, & Hertzman, 2001). However, consideration of these factors is beyond the scope of this analysis.18

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POLICY SCENARIOS As noted earlier, the core of this analysis is the simulation of the impacts of Canada’s major age-sensitive tax/transfer programs on inter-generational fairness according to several basic norms. The four scenarios to test the robustness of the policy scenarios to unknown future uncertainties (high and low life expectancy and high and low employment) were outlined above. From the policy perspective, we consider two stylized alternative policy scenarios in addition to the status quo scenario, as follows. Extended Work One approach to the aging of the population is to redefine retirement, essentially by raising the age of entitlement to public pensions. At the time von Bismark first set an age for pensions in 1889 at age 70 (it was subsequently lowered to age 65 in 1916, see SSA http://www.ssa.gov/history/ ottob.html) hardly anyone even survived to that age. In 1983, the U.S. amended the law so that the age of entitlement for full Social Security retirement pensions would begin rising gradually to age 67.19 More recently, Mankiw (2006), for example, has called for further change in this direction. In Canada, the Lazar Report (Canada, 1980) considered whether the age of entitlement to public pensions (both C/QPP and OAS) should be raised gradually,20 but concluded that the uncertainties were such that instead, some sort of trigger criteria for considering this kind of change, with a 10-year lead time, would be more appropriate. The criteria could include dependency ratios, taxpayer burdens, or labor force participation rates (Canada, 1980, p. 328). More recently, the Swedes reformed their public pension system in a way that implicitly indexes pension benefits to life expectancy – by requiring that the benefit about to come into pay at the point of formal retirement be based on an actuarial annuity calculation, in turn based on whatever mortality rates are then currently projected (Flood, 2003). In order to reflect this broad class of possible options for responding to concerns about the costs of public pensions, we have defined an ‘‘extended work’’ scenario. This is implemented in the model by ‘‘delayed aging’’ of persons for purposes of employment transitions and for public pension (C/QPP, OAS, and GIS/SA) eligibility and take-up. This delayed aging occurs not only in future, but also in the past. It is as if the policy of increasing the age of entitlement to public pensions in Canada had started in 1976, and proceeded at a very gradual rate until 2005 when everyone’s entitlement would be at age 70.

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More specifically, delayed aging is implemented by creating an artificial alternative age variable to be used by all the appropriate simulation modules, including both those governing behavioral dynamics and those determining program eligibility and participation. This alternative age variable kicks in at age 55 and remains fixed at age 55 for as long as five years. The onset age of 55 was chosen because it is an age where employment rates are high. In effect, by starting the ‘‘delayed aging’’ process at age 55, the decline in age-specific employment to population ratios observed after age 55 could be reasonably attenuated and thereby generate a more realistic scenario in line with the likely behavioral impacts of increasingly delayed entitlement to public pensions. The general intention is to implement delayed aging gradually: first, delaying the aging of the cohort that turned 55 in 1976 by two months; then, delaying the aging of the cohort that turned 55 in 1977 by four months, and so on – gradually implementing the full five-year delay over a period of 30 years (1976–2005). However, many of the relevant modules in the LifePaths model are not sensitive to fractional ages. As a result, the gradual 30-year phase-in was implemented by: first, delaying the aging of only a (randomly chosen) 1/6th of the cohort that turned 55 in 1976 by one year; then, delaying the aging of only a (randomly chosen) 2/6th of the cohort that turned 55 in 1977 by one year; y; delaying the aging of all of the cohort that turned 55 in 1981 by one year; delaying the aging of all of the cohort that turned 55 in 1982 by one year and further delaying the aging of a (randomly chosen) 1/6th of that cohort by an additional one year; y and so on. All members of cohorts that turn 55 on or after 2005 experience delayed aging of a full five years.21 In terms of the norms for inter-generational equity outlined earlier, this policy scenario is a rather arbitrary and approximate response to population aging. It does not offer an explicit adjustment mechanism, as in the Swedish reforms, that automates and thereby clarifies for successive cohorts the ‘‘inter-generational contract’’ with regard to retirement pensions.

Relative Indexing Another broad set of approaches to concerns about growing public pension costs in the face of population aging is to change the way the dollar value of pensions is updated from one year to the next, i.e. the indexing provisions. For example, both the Musgrave (1981) and the House of Commons (1983) norms for inter-generational fairness described above reflect forms of indexing. Canada has a somewhat complex and unusual system of indexing provisions. For the major earnings-related public pension, C/QPP, benefits

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are implicitly indexed to AW during working years. Then, after retirement when the pension comes into pay, it is indexed by the CPI. However, in Canada the earnings-related pension constitutes less than half of all the publicly provided old age cash benefits. The other major programs, OAS and GIS/SA, are indexed to the CPI. Moreover, the OAS is now subject to a degree of income testing, and the threshold where the income testing begins is itself indexed to the CPI. As a result, any real average wage growth results in these public pensions declining relative to the size of the economy. In contrast, the U.S. public pension system, for example, which is dominated by Social Security, is much closer to being fully wage indexed (even though, as with Canada’s C/QPP, pensions in pay are indexed to the CPI). Similarly, in many European countries, retirement pensions were substantially wage indexed, though over the last decade a number have moved away from AW indexing and closer to CPI indexing. On the one hand, CPI rather than AW indexing means that in future, pension costs will be lower. On the other hand, CPI compared to wage indexing means that for pensioners, their pension incomes will be lower, and they will be more likely to fall below a low income line. The importance of indexing provisions has been well known to the economically informed for decades. For example, as early as the 1980s, officials in the IMF (Heller, Hemming, & Kohnert, 1986) projected that Canada was relatively unique in not facing a pension affordability problem – essentially because of the CPI indexing of the OAS and GIS. However, there have been virtually no analyses showing the counterpart implication of falling relative individual income levels among the future elderly (with the exceptions of Murphy & Wolfson, 1991; Wolfson & Murphy, 1997). Given the importance of indexing scenarios from these earlier analyses, the second stylized and illustrative policy scenario explores wage indexing as an alternative to the current price indexing of major government programs – including not only public pensions but also the income tax system and its associated set of refundable income tax credits which de facto are very much like cash transfers. This scenario, in principle, also moves the system in a direction that is much closer to most of the norms for inter-generational equity outlined above. The shift to wage indexing is assumed to occur in 2001.

SIMULATION RESULTS In this section we present the main results from a series of LifePaths simulations, based on the exogenous and policy scenarios just described. In all

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cases, the focus is on the net balance between income and payroll taxes paid, and cash transfers plus in kind health and education benefits received. These are lifetime net balances, summed over representative samples of individuals in each decadal birth cohort. The sums are net present discounted values, where the discount rate is the same as the growth rate of average wages. This growth rate, in turn, is assumed at 1% per annum – slightly lower than the 1.1% and 1.2% assumed by the Chief Actuary in his previous two actuarial reports on the CPP (OSFI, 2005b).22 Graph 1 shows these lifetime net present values (NPVs) (2001 $000s) on the vertical axis, for each decadal birth cohort along the horizontal axis. The different curves correspond to four different points in the NPV distributions for each birth cohort – the first quartile (Q1), the median, the mean, and the third quartile (Q3). In this case, we have shown the ‘‘base’’ policy scenario, and the low life expectancy and low employment exogenous scenarios.23 To begin with the middle of the distribution of lifetime NPVs, the median curve peaks with the 1920s and 1930s birth cohorts at over $150,000. These are the birth cohorts who experienced the first benefits from the fully phased

400.0 300.0 200.0 100.0 0.0 1890s 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s

1990s 2000s 1980s

(100.0) (200.0)

Q1 Median Mean Q3

(300.0) (400.0)

Graph 1.

Net Present Values of Lifetime [TransfersTaxes]; Scenario ¼ le emp base.

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in C/QPP (introduced in 1966 and fully phased in by 1976), after having made minimal payroll tax ‘‘contributions’’, as well as being the first generation to benefit from improvements to the OAS and the introduction of the GIS. But after this point, median lifetime NPVs tail off, and become slightly negative for the cohort being born in the current decade. From this perspective, the status quo system (under the specific ‘‘low–low’’ exogenous life expectancy and employment scenario) is not balancing the first two fairness norms outlined above – successive birth cohorts after the 1920s are receiving declining net transfers. But this graph also indicates dramatic differences across individuals within each birth cohort. The mean NPV is generally lower than the median. This reflects a negative skewness in the NPV distribution, and in turn the fact that taxes are unbounded above, while cash and in kind transfers are bounded below at zero. More importantly, the curves in Graph 1 for the first and third quartiles show a very wide dispersion in NPVs, on the order of $400,000. This is an extraordinarily clear support of the old adage, ‘‘beware of the mean’’. The usual analyses of inter-generational fairness (e.g. Kotlikoff, 1992), which are based on representative agents, completely ignore these tremendous variations within generations. Graph 2 reinforces this point by showing two measures of dispersion, the inter-quartile range for the same low–low scenario as in Graph 1, and the standard deviation of NPVs, for each birth cohort. Additionally, for the standard deviations, four different curves are plotted, one for each of the exogenous scenarios.24 Two key messages arise. The first is that both indicators of dispersion give similar results – there is a great deal of heterogeneity in individual circumstances within each birth cohort. Indeed, that variation within birth cohorts is far larger than that between birth cohorts (e.g. the mean or median) shown in Graph 1. Second, the extent of this variation is essentially unaffected by which of the exogenous scenarios is chosen. Whether life expectancy is high or low, and whether employment is high or low, has almost no effect on the dispersion of lifetime NPVs. A major growth of income taxes occurred in the 1940s war years and subsequently with the growth of the ‘‘welfare state’’. Similarly, government expenditures on health, education, and old age pensions and benefits became significant only in the 1960s. As a result, the early cohorts starting with those born in the 1890s had little opportunity over their lifetimes to be ‘‘exposed’’ to large government tax/transfer programs. In turn, the opportunity for

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500 450 400 350 300 250 q3 - q1 le emp base le EMP base LE emp base LE EMP base

200 150 100 50 0

1890s 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s

Graph 2.

Inter-Quartile Range of NPV of Tax – Tran and Standard Deviation of NPVs by Exogenous Scenario, Base Policy Scenario.

dispersion in the resulting lifetime net benefits was relatively small for the 1890s cohort, grew significantly up to the 1930s birth cohort, and has continued to grow for later cohorts, but much more slowly, as the welfare state programs to which these cohorts have been and are projected to be exposed are largely mature. While Graph 2 shows little effect from the exogenous life expectancy and employment scenarios, Graph 3 shows that sex does make a big difference. In this case, we are looking at the same scenario set as in Graph 1 – the status quo policy scenario, and the low–low exogenous scenario, though for clarity the mean NPV curves have been dropped. Graph 3 therefore shows six curves: the three quartiles for males and for females. The dashed lines for females are almost everywhere above the solid lines for males. The median NPVs for females in the 1920s and 1930s birth cohorts are on the order of $300,000 higher than those of their male counterparts, though this declines to about $200,000 for the current decadal birth cohort.

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500 400 300 200 100 0 1890s 1900s 1910s

1920s

1930s 1940s

1950s

1960s 1970s 1980s 1990s

2000s

-100 -200 -300 -400

m-q1 m-med m-q3 f-q1 f-med f-q3

-500

Graph 3.

Males and Females by Quartile of NPV; Scenario ¼ le emp base.

First quartile males (those with high incomes so therefore paying more income tax and receiving less transfers) end up with NPVs of $300,000 or lower for the 1970s and successive birth cohorts, while the corresponding birth cohorts of females have NPVs about $200,000 or higher. These massive transfers from men to women are intuitively plausible when one considers that with women’s greater life expectancy and generally higher morbidity, they consume more in kind health care services and receive more survivor and old age demogrant (OAS) benefits; and with women’s generally lower incomes, they pay less in taxes and receive more in income-tested benefits. Even though the exogenous scenarios have virtually no effect on the dispersion in lifetime NPVs (Graph 2 above), they do have an impact on the typical net present value of taxes minus transfer for successive birth cohorts. Graph 4 shows the impacts on the mean (solid lines) and the median (dashed lines) NPVs of the high and low life expectancy scenarios (‘‘LE’’ and ‘‘le’’, respectively) and high and low employment scenarios (‘‘EMP’’ and ‘‘emp’’, respectively) for the status quo (‘‘base’’) policy scenario (for both sexes combined). The main result here is that the strength of the economy has a much larger impact than the pace of improvement in life expectancy. Not surprisingly, higher life expectancy increases the NPVs of transfers minus taxes, as individuals living longer have more years of entitlement to public pension benefits and use more health care services, but are not paying correspondingly more

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200 150 100 50 0 1890s 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s

2000s

(50) le emp base le EMP base LE emp base LE EMP base le emp base le EMP base LE emp base LE EMP base

(100) (150) (200) (250) (300)

Graph 4.

Medians and Means by Exogenous Scenario.

income and payroll taxes over their longer lifetimes. On the other hand, a stronger economy reduces NPVs as income taxes in particular are higher, while the demogrant (OAS) and income tested (GIS) portions of the public pension system are relatively unaffected. In quantitative terms, for the baby boom and subsequent birth cohorts, a change in life expectancy of as much as five years has impacts on lifetime NPVs that are only about one fifth as large as an improvement in employment with the effect of raising per capita wages by about 10%. Finally, Graph 5 shows how the two stylized policy alternatives compare. Since the low and high employment scenarios had a much larger impact than the high and low life expectancy scenarios, we focus on only the two exogenous employment scenarios (both assuming low life expectancy change). The light lines show the status quo (‘‘base’’) scenarios; the dashed lines show the scenario where individuals work longer and the age of entitlement to pensions rises gradually from 65 to 70 over the period 1976–2005; and the heavy lines show the scenario where indexing has been shifted from a price index basis to an index of average wages, while leaving the age of entitlement at 65. The most dramatic result here is the relatively weak impacts of the working longer/delayed retirement scenarios compared to the wage indexing

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200 150 100 50 0 1890s 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s (50) (100) (150) (200)

le le le le le le

emp base emp WORK emp INDEX EMP base EMP WORK EMP INDEX

(250)

Graph 5.

Lifetime NPVs for Three Policy and Two Employment Scenarios.

scenarios. The shift to delayed retirement (from light solid to dashed lines) is much smaller than the shift from price to wage indexing (from light to heavy solid lines) – on the order of a reduction of $20,000 compared to an increases well over $100,000 in lifetime NPVs of transfers minus taxes. Given the increasing policy discourse in many quarters on the importance of delaying retirement, these results are a sobering indication that such a change may not be as ‘‘helpful’’ as many expect. Rather, and as shown earlier, an improvement in the economy (from ‘‘emp’’ to ‘‘EMP’’) is quantitatively much more important, and tends to shift all the curves up on the order of $100,000. Thus, a stronger economy (of the order posited in the exogenous scenarios simulated here, in turn based on the actual low and high points in the Canadian economy since the 1990s) turns out roughly to offset the shift from price to wage indexing. Finally, in terms of the basic focus of this analysis, on inter-generational fairness, the shift from price to wage indexing has the effect of leveling out the curves of NPVs across generations. (Recall that these NPVs are discounted, based on the growth rate of average wages.) In terms of the norms of inter-generational fairness outlined above, these wage indexed scenarios appear most in accord.

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CONCLUDING COMMENTS Population aging is more often a source of concern for public policy than cause for celebration. One reason is the expectation that future cohorts of the elderly, particularly the post WW II baby boom generation, will place intolerable burdens on future working age generations in their retirement years in order to finance their public pensions and insured health care services. However, this analysis suggests the opposite. Under current program rules, and a range of scenarios for future economic growth and longevity, birth cohorts after those born in the 1920s and 1930s will experience successively smaller lifetime net transfers (both cash, and in kind for health and education). The main factor underlying this (perhaps) unexpected result is the index broadly used to update cash transfer benefit levels and income tax thresholds and other related parameters. This index is the CPI. However, if history is any guide, nominal wages and the economy more generally will most likely grow faster than inflation. In other words, we can likely expect real per capita economic growth. In such scenarios, CPI-indexed benefits will gradually shrink relative to the average incomes of those of working age, and CPI-indexed tax bracket thresholds will result in taxpayers gradually finding themselves in ever higher tax brackets (‘‘bracket creep’’), hence paying a larger proportion of their incomes in income tax. While there is great concern about the effects of increasing longevity on pension costs and hence on inter-generational fairness, our simulations suggest that for quite a wide range of life expectancy scenarios, this has a much smaller impact than the strength of the economy – judged by the range of employment over the most recent business cycle – specifically the 1993 trough and the 2004 peak. Also, notwithstanding the focus of this analysis on widely expressed concerns regarding inter-generational fairness, our results show that differences within generations are far larger than those between generations. Women’s net lifetime transfers minus taxes are hundreds of thousands of dollars greater than those for men, while the differences between the poor and the rich within any given generation are larger still. Finally, one of the most widely discussed responses to population aging, in the context of public pensions, is raising the age of entitlement and otherwise encouraging delayed retirement. One of the least discussed issues, on the other hand, is the nature of the indexing of pensions as well as income taxes. That these government programs should be indexed to the CPI is largely taken for granted. However, our analysis suggests that the impact of

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the indexing provisions is far larger than delaying the age of entitlement from age 65 to 70. Continuing with CPI indexing results in a continuing fall from one generation to the next in the net lifetime value of transfers minus taxes. Moving to wage indexing results in a leveling off of these net values – a situation much more in accord with the norms for inter-generational fairness found in both the economics literature and in major Canadian policy documents. Still, under the scenarios examined here, cohorts born after the 1930s never receive the net transfers minus taxes that the 1920s and 1930s birth cohorts do.

NOTES 1. Of course, inter-generational transfers occur in many ways, from unrequited payments among family members of different generations, to broader investments (or dis-investments) in the productive capacity of the economy and the quality of the environment. The latter are beyond the scope of this analysis, even though they may enter into policy debates about the inter-generational fairness of the taxes and transfers being examined here. 2. A third major axis, which is beyond the scope of this analysis, is the future health or disability status of the population, over and above life expectancy. This has been treated in Wolfson and Rowe (2004). 3. Employment is only one of several ways to measure the strength of the economy. Another would be per capita economic growth rates, in turn usually linked to productivity growth. Similarly, there is considerable interest in the role of immigration among demographic factors. Alternative scenarios of this sort are easily feasible with LifePaths, the analytical tool being used. The focus here on life expectancy and employment is simply for the convenience of a manageable range of scenarios for this initial exploratory analysis. 4. A widely agreed norm for intra-generational fairness is progressivity, i.e. that the tax/transfer system is generally redistributive from those with higher to those with lower (more often contemporaneous than lifetime) income. 5. For example, simplifying assumptions include no heterogeneity within generations, generations not overlapping each other in time, and the existence of welldefined smooth precise utility functions in the first place. Indeed, the thrust of the Basu and Mitra analysis is to show formally the impossibility of a social welfare function that at one and the same time obeys the axiom of anonymity, which they equate with inter-generational equity, and even the weakest of Pareto principles which would allow future generations to be better off than their parents – a proposition which seems intuitively obvious. 6. ‘‘(t)hose now working could build up a moral claim on future pension entitlements by making transfers to the current elderly of at least the same magnitude as they would expect to receive when their time came. This would set in motion a kind of intergenerational golden rule’’ (House of Commons, 1983).

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7. This is essentially identical to the concept of ‘‘sustainable development’’ articulated by the Brundtland Report (Bruntland et al., 1987, p. 27), defined as development that ‘‘meets the needs of the present without compromising the ability of future generations to meet their own needs’’. 8. Personal communication with Wolfson. 9. Indeed, Wolfson et al. (1998) show such an example. Also, as one referee has commented, majority support for a rule or norm is not necessarily an assurance that it is fair. 10. This way of framing the issue is more in line with current discussions of the socalled ‘‘crisis’’ in private defined benefit pension plans, though in that case, there is the added factor of the differential risks borne by the employer as plan sponsor, and workers as plan beneficiaries. 11. The ‘‘Boskin Committee’’ for the U.S. Senate (Advisory Committee, 1996) highlighted the importance of this question in the context of the U.S. Social Security system. Wolfson (1999), however, has shown the practical impossibility of ever constructing a CPI that will suffice for inter-generational comparisons given that the time spans involved are such that major ‘‘new goods problems’’ are inevitable. 12. The term ‘‘metasynthesis’’ is used in contrast to the epidemiological term ‘‘meta-analysis’’, which refers to the combination of results from a number of data sets, all of which pertain to the same question. Metasynthesis, in contrast, refers to the combination of results from data sets covering diverse subject matters. The estimation of GDP and the range of tables comprising the System of National Accounts (SNA) is an excellent example of metasynthesis – drawing together data from a wide variety of sources in order to produce the best possible estimate of a given set of concepts. The main difference is that the concepts in the SNA are aggregate, while those which are the object of LifePaths are micro and distributional – a representative sample of individual life course trajectories. 13. Although the diagram implies that time is discrete, LifePaths represents and models all events in continuous time. 14. Since the mortality rates underlying the demographic projections are based on a smooth mathematical function, using the rate of change over the last single year is reasonable and convenient for extrapolating the underlying longer term trend. 15. The Chief Actuary’s projections in his most recent report (OSFI, 2005b) are 80.7 and 84.1 for males and females, respectively. Note that Chief Actuary’s are period life expectancies in 2050, rather than cohort life expectancies used here, in turn based on mortality projections extending to the end of the 21st century. 16. The C/QPP also provide pre-and post-retirement survivor pensions, orphan and disability pensions, and a lump sum death benefit. However, in this analysis we consider only the retirement pension and the post-retirement survivor pension. These comprise about three-quarters of the total benefits provided by the plans. 17. Note that while private tax-assisted employer-sponsored pension plan saving (RPPs) is explicitly modeled in LifePaths, private tax-assisted retirement savings via RRSPs and home ownership are not. 18. Future versions of this analysis could build on the EUs projection approaches which explicitly model improvements in health status and hence declining agespecific health care costs, for example. See DG ECFIN (2005).

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19. This is based on a phase in according to an individual’s year of birth – age 65 if born in 1937 or earlier, then rising in two-month steps per year of birth to age 67 if born in 1960 or later. 20. The report strongly recommended against any lowering of this age. 21. It should be noted that this scenario increases income and payroll tax revenues, as a result of greater employment in the 55–70 age range, and reduces payouts of public pensions in the 65–70 age range. Consequently, the government’s fiscal balance improves. Notwithstanding, no adjustments are made to income or payroll taxes or to any other aspect of cash transfers. While this is likely an unrealistic scenario, it is simpler and aids interpretation of results. 22. The results are sensitive to the choice of discount rate. For this kind of analysis, from a social and inter-generational perspective, as contrasted for example to an individual perspective on a short or medium term investment choice, it is arguable that the growth rate in per capita wages is the most appropriate discount rate. And as noted earlier, this kind of indexing is closest to enabling assessment of the ‘‘equal utility’’ type of inter-generational equity norm. 23. Even though the LifePaths simulations cover everyone in Canada, these graphs cover only persons who survived to at least age 15 and were born in a province west of Newfoundland. The reason, simply, is that immigrants receive no transfers and pay no taxes until they arrive in Canada, and Newfoundlanders receive no transfers and pay no taxes until after Confederation 1949. These two cases create anomalous spikes in the frequency distribution of transfers minus taxes at zero. 24. Note that this dispersion does not include the further effects of differential mortality by income. This is well known, for example Wolfson, Rowe, Gentleman, and Tomiak (1993). More recently, the Chief Actuary (OSFI, 2006) has estimated that life expectancy at age 65 in 2001 varies by 4.5 years for males and 3.6 years for females between those with low incomes (roughly under $10,000) and those with high incomes (roughly over $50,000).

REFERENCES Advisory Committee to Study the Consumer Price Index. (1996). (‘‘Boskin Committee’’: M. J. Boskin, E. R. Duhlberger, R. J. Gordon, Z. Grilliches, & D. Jorgenson), Toward a more accurate measure of the cost of living. Final Report to the Senate Finance Committee, Washington D.C., December 4. Basu, K., & Mitra, T. (2005). Possibility theorems for aggregating infinite utility streams equitably. CAE Working Paper #05-05; http://www.arts.cornell.edu/econ/cae/05-05.pdf (referenced Nov 12/06). Beach, W. W., & Davis, G. E. (1998). Social security’s rate of return from the Heritage Foundation, http://www.heritage.org/Research/SocialSecurity/CDA98-01.cfm (referenced Nov 12/06). Bruntland, G. et al. (1987). Our common future, http://www.are.admin.ch/imperia/md/content/ are/nachhaltigeentwicklung/brundtland_bericht.pdf?PHPSESSID=e6d4ef5966d56;fa8532c fc13cf38e2bb (referenced Nov 12/06); also Oxford University Press.

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Cameron, G., & Wolfson, M. C. (1994). Missing transfers: Adjusting household incomes for non-cash benefits. IARIW 23rd General Conference, St Andrews. Canada. (1980). The retirement income system in Canada: Problems and alternative policies for reform (Lazar Report), Ottawa. Canada. (2006). Tax expenditures per http://www.fin.gc.ca/taxexp/2005/taxexp05_2e.html# Table1, referenced July 27, 2006. DG ECFIN. (2005). Annex, the 2005 EPC projections of age-related expenditure (2004–2050) for the EU-25 member states: Underlying assumptions and projection methodologies. Report prepared by the Economic Policy Committee and the European Commission (DG ECFIN), Special Report No 4/2005, accessed at http://ec.europa.eu/economy_finance/ publications/european_economy/2005/eespecialreport0405_en.htm, July 27, 2006. Evans, R. G., McGrail, K., Morgan, S., Barer, M. L., & Hertzman, C. (2001). Apocalypse no: Population aging and the future of the health care system. Canadian Journal on Aging, 20(Suppl. 1), 160–191. Flood, L. (2003). Can we afford the future? An Evaluation of the New Swedish Pension System. http://www.sesim.org/Documents/Flood_Natsem_2003.pdf referenced Nov 12/06. Heller, P. S., Hemming, R., & Kohnert, P. W. (1986). Aging and social expenditures in the major industrial countries, 1980–2025. Occasional paper No. 47, International Monetary Fund, Washington D.C., September 1986. House of Commons. (1983). Report of the parliamentary committee on pension reform (Frith Committee), Ottawa. Kotlikoff, L. J. (1992). Generational accounting: Knowing who pays, and what, for what we spend. NY: Free Press. Kotlikoff, L. J., & Burns, S. (2004). The coming generational storm: What you need to know about America’s economic future. Cambridge, MA: MIT Press. Mankiw, N. G. (2006). Mr Paulson’s Challenge. Wall Street Journal, May 31, A12. Murphy, B., & Wolfson, M. C. (1991). When the baby boom grows old: Impacts on Canada’s public sector. Statistical Journal of the United Nations Economic Commission for Europe, 8(1). Musgrave, R. A. (1981). A reappraisal of financing social security. In: F. Skidmore (Ed.), Social security financing. Cambridge, MA: MIT Press. Oreopoulos, P., & Vaillancourt, F. (1998). Applying generational accounting to Canada: Findings and fallacies. In: M. Corak (Ed.), Government Finances and Generational Equity, Statistics Canada Cat. No. 68-513-XPB, Ottawa. OSFI. (2005a). Actuarial Report (7th) on the Old Age Security Program as at 31 December, 2003, http://www.osfi-bsif.gc.ca/app/DocRepository/1/eng/reports/oca/oas7_e.pdf, referenced July 27, 2006. OSFI. (2005b). Actuarial Report (21st) on the Canada Pension Plan as at 31 December, 2003, http://www.osfi-bsif.gc.ca/app/DocRepository/1/eng/oca/reports/21/CPP2104_e.pdf, referenced July 27,2006. OSFI. (2006). Old age security program mortality experience, Actuarial Study No. 5, http:// www.osfi-bsif.gc.ca/app/DocRepository/1/eng/oca/studies/Mortality_Exp_No5_e.pdf, referenced July 27, 2006. Ramsay, F. P. (1928). A mathematical theory of savings. Economic Journal, 38, 543–559. Statistics Canada. (2005). Population projections for Canada, provinces and territories, Catalogue no. 91-520-XIE. Statistics Canada – LifePaths: www.statcan.ca/english/spsd/LifePaths.htm

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Wolfson, M. C. (1996). LifePaths: A new framework for socio-economic accounts. IARIW 24th General Conference, Lillehammer, Norway, August. Wolfson, M. C. (1999). New goods and the measurement of real economic growth. Canadian Journal of Economics, 32(2), 447–470. Wolfson, M. C., Rowe, G., Gribble, S., & Lin, X. (1998). Historical generational accounting with heterogeneous populations. In: M. Corak (Ed.), Government Finances and Generational Equity, Statistics Canada Cat. No. 68-513-XPB, Ottawa. Wolfson, M. C., & Murphy, B. (1997). Aging and Canada’s public sector: Retrospect and prospect. In: K. Banting & R. Boadway (Eds), Reform of retirement income policy: International and Canadian perspectives. Kingston: School of Policy Studies, Queens University. Wolfson, M. C., & Rowe, G. (2004). Disability and informal support: Prospects for Canada. In: S. B. Cohen & J. M. Lepkowski (Eds), Eighth Conference on Health Survey Research Methods, National Center for Health Statistics, Hyattsville, MD. (http://www.cdc.gov/ nchs/data/misc/proceedings_hsrm2004.pdf referenced March 5, 2006). Wolfson, M. C., Rowe, G., Gentleman, J., & Tomiak, M. (1993). Career earnings and death: A longitudinal analysis of older Canadian men. Journal of Gerontology: Social Sciences, 48(4), S167–S179.

APPENDIX: DATA AND METHODS This analysis draws on extensions to the LifePaths (Wolfson, 1996) family of models being developed at Statistics Canada. These are dynamic Monte Carlo microsimulation models which generate representative population cohorts. The cohorts are built up as longitudinal samples of millions of synthetic but highly realistic individual biographies or life paths – particularly in respect to their educational participation and attainment, employment, earnings, fertility, nuptiality, government taxes and transfers, and mortality trajectories over their lifetimes – hence their LifePaths. The analysis starts with the cohort born in the 1890s, and extends for two centuries, to the ultimate demise of the children being born in the 2002–2011 decade. A major effort has been made to ground the analysis using quantitative data. However, the combination of an absence of detailed historical data, with the need to make long-run projections, means that relatively stylized representations of the main socio-demographic processes and components of Canada’s tax/transfer system have had to be used. LifePaths is in a constant state of development and refinement. The most recent version was employed in the analysis reported here. However, a reasonably up-to-date description of most of the components dealing with demography, education, employment, and earnings can be found on the Statistics Canada website at www.statcan.ca/english/spsd/LifePaths.htm.

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Components of the model employed for this study that are not described on the website include Income Taxes and Cash Transfers, Other Sources of Income, and In Kind Transfers. The following provides a brief description of these: Income Taxes and Cash Transfers Federal income taxes have been implemented explicitly using historical tax regulations. Structural changes through time and legislated changes have been implemented, as have surtaxes and surtax reductions from the inception of the income tax in Canada in 1917 to present. Income taxes are calculated at year end using the simulated detail on each individual’s income: including income from working (both employment and self-employment), pension income (CPP/QPP Retirement Benefits, CPP/QPP Survivors Benefits, CPP/ QPP Death Benefits, RPP Benefits, OAS Benefits, and Unemployment/ Employment Insurance (UI/EI) Benefits). Net Income is determined after repayment of social benefits (Family Allowances, OAS Benefits, UI/EI Benefits). Deductions and exemptions (recently converted to non-refundable income tax credits) accounted for include basic personal amount, age amount, pension income amount, married and equivalent to married amount, dependent amount, education amount, CPP/QPP contributions, and UI/EI Premiums. Refundable income tax credits that have been taken into account explicitly include: Child Tax Credit, Federal Sales Tax Credit, and Goods and Services Tax Credit. Major sources of provincial transfer income have been included: Provincial Family Allowances, Quebec Newborn Allowance, and Quebec Child Supplements. However, provincial income taxes have been modeled simply as a weighted proportion of basic federal income taxes. The main programs that are currently not implemented are Provincial GIS top-ups and Provincial Child Tax Benefit Programs. Current CPI or CPI – 3% partial indexing is assumed to continue into the future, under one of the scenarios to be considered. This is a critical assumption, as shown in Wolfson and Murphy (1997). Other Sources of Income Selected special sources of income are imputed at year end just before the year’s income tax calculation takes place. These include components of income that are otherwise difficult to model: provincial Social Assistance (‘‘welfare’’), workers compensation, veterans’ benefits, investment and

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dividend income, and alimony. The imputation equations were estimated from census microdata, and take account of sex, age, immigration status, student and employment status, education level, marital status and number of children at home, as well as weeks worked and earnings in the previous 12 months. The imputation was carried out for three separate source groups: Other Transfer Income, Investment Income, and Other Miscellaneous Income. In each case, imputation was carried out in two steps: First, it was determined whether the imputed value was to be non-zero using a logistic regression equation. Then, if it was to be non-zero, a random value was imputed from an appropriate distribution using three quartile regression equations to reflect the location, dispersion and asymmetry of the empirical distribution. The last step in the imputation process involved rescaling the imputed values to values more appropriate to the simulated calendar year of imputation. For that purpose, Other Transfer Income was rescaled by the consumer price index, Investment Income was rescaled by the bank rate and Other Miscellaneous Income was rescaled by the average industrial wage. In Kind Transfers The major in kind government transfers are health care and education. These are modeled based on unit costs by age, and sex in the case of health care, and unit costs based on the kind of educational institution attended (elementarysecondary, community college, university; Cameron & Wolfson, 1994).

CHANGING POVERTY OR CHANGING POVERTY AVERSION? Daniel L. Millimet, Daniel Slottje and Peter J. Lambert ABSTRACT Supposing that decisionmakers in any country and at any point in time tolerate a certain fixed level of perceived poverty, differences in poverty aversion are called for to explain observed international and intertemporal variations in poverty statistics. Under the Natural Rate of Subjective Poverty hypothesis advanced in this paper, variations in the degree of poverty aversion are estimable and can be explained by political and socioeconomic factors. The methodology is applied to US data from 1975 to 1998 and across nations using cross-section data from the mid-1990s. Factors such as the political affiliation of government officials, public expenditure, per capita income, and economic growth account for much of the variation in poverty aversion implied by our hypothesis. The relationship between inequality aversion and poverty aversion is also explored, with the aid of a parallel ‘‘natural rate’’ hypothesis for inequality (Lambert et al., 2003). Our findings provide a new framework in which to interpret observed correlations between poverty, inequality, and social welfare.

Equity Research on Economic Inequality, Volume 15, 233–268 Copyright r 2007 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15010-9

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Many individuals and organizations both in Canada and abroad understandably want to know how many people and families live in ‘poverty,’ and how these levels change. Reflecting this need, different groups have at different times developed various measures which purported to divide the population into those who were poor and those who were not. In spite of these efforts, there is still no internationally-accepted definition of povertyy This is not surprising, perhaps, given the absence of an international consensus on what poverty is and how it should be measuredy The underlying difficulty is due to the fact that poverty is intrinsically a question of social consensus, at a given point in time and in the context of a given countryy It is through the political process that democratic societies achieve social consensus in domains that are intrinsically judgmental. Ivan P. Fellegi, Chief Statistician of Canada, September 19971

1. INTRODUCTION Poverty is an illusive term, one which economists and policymakers have long struggled to define and measure, as evidenced by the quote above. Similar sentiments have been voiced by policymakers in the UK and elsewhere. Nonetheless, the media in many countries regularly publish or broadcast news of changes in the poverty rate (however defined). Implicit in such (usually stark) reports is the presumption that the level of poverty is an exogenous event, occurring within the confines of the existing social and institutional framework. That is, it is presumed that policymakers are merely bystanders, compelled into action only in the wake of a pessimistic report. Our primary hypothesis is that such a view is incorrect. Rather, as stated in the quote above, poverty is determined through social consensus. Specifically, we maintain that decisionmakers in any country and at any point in time tolerate a certain fixed level of poverty. However, the extent of poverty inherent in the current income distribution is entirely subjective. Thus, while the subjective level of poverty – the level of poverty perceived by policymakers – is, we posit, constant over time and place, objective or absolute measures of poverty may change depending on the preferences dictated by social consensus (or some unilateral decisionmaker in a nondemocracy). Under such a view of the world, preferences for poverty (i.e., poverty aversion) are time- and country-specific. Moreover, to maintain a constant level of subjective poverty, periods of greater aversion to poverty should be characterized by lower objective poverty (i.e., the type reported in the media). Conversely, periods of lower poverty aversion should be characterized by greater objective poverty. As a result, policymakers are not

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reacting to changing objective poverty levels; rather, such levels are being explicitly determined by policymakers according to social mandates. Such a claim is of course hardly new.2 The innovation proffered in this paper is that the degree of poverty aversion is quantifiable and the determinants of intertemporal and international variations in poverty aversion are estimable. Our ability to identify the socially determined level of poverty aversion stems from the assumption that subjective poverty is constant across time and space. We will refer to this assumption as the Natural Rate of Subjective Poverty (NRSP) hypothesis from now on. According to the NRSP hypothesis, subjective poverty is held constant, whilst poverty aversion is time- and country-specific. Objective poverty accordingly varies from time to time and from place to place in such a way as to maintain this state of affairs as an ‘‘equilibrium.’’ We should note from the outset that our characterization of some poverty measures as ‘‘objective’’ in what follows is necessarily simplistic. All measures of poverty – even those such as the headcount ratio which are purported to be absolute measures – entail implicit assumptions regarding preferences surrounding the issue of poverty. Given the manner in which such indices are treated by some, however, it is not unreasonable to characterize them as objective. Two well-known poverty indices which we characterize as objective for present purposes are the headcount ratio (proportion of the population who are poor) and the normalized poverty deficit (aggregate income shortfall of poor persons or households expressed per capita of the overall population and normalized by the poverty line). Both of these poverty statistics are widely quoted in applied work; the headcount ratio is particularly popular with the media. The headcount ratio is insensitive to the extent of shortfall of incomes from the poverty line; the normalized poverty deficit is insensitive to the distribution of income among the poor. Several parametric families of poverty indices have followed upon Sen’s (1976) axiomatic treatment of the poverty measurement issue, in which the parameter purports to capture aversion to poverty (see Zheng’s (1997) comprehensive survey article). Any one of these is a potential candidate for our subjective measure. Sen himself argued that the incidence, intensity, and inequality of poverty all matter and he isolated a particular poverty index which is a mix of the headcount ratio, income gap ratio and Gini coefficient of income among the poor. Kakwani (1980) generalized Sen’s index by introducing a ‘‘sensitivity parameter,’’ increases in which make the index more sensitive to transfers of income among those with large poverty gaps and also more sensitive to small income changes at the bottom end of the

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distribution. Clark et al. (1981) proposed two parametric families, in one of which the parameter measures aversion to inequality in poverty gaps and in the other, to inequality in basic (censored) incomes; this latter parameter has been called ‘‘aversion to inequality in poverty’’ by Foster and Sen (1997, p. 178); see also Chakravarty (1983a, 1983b) on this. The so-called FGT family of Foster, Greer, and Thorbecke (1984, p. 761) has a parameter which is described by the authors as an indicator of ‘‘aversion to poverty,’’ but it has a strange property: the more averse to poverty is the observer, the lower the poverty value assigned to any fixed income distribution. Only in Zheng (2000b) is the concept of poverty aversion placed on rigorous footing. Zheng (2000b, p. 121) identifies a family of constant poverty aversion indices with formal properties: ‘‘The notion of ‘poverty aversion’ that researchers have in mind means a lot more than just ‘disliking poverty’.’’ The Zheng index is our favored ‘‘subjective’’ measure of poverty.3 The paper unfolds as follows. Section 2 gives a brief overview of the poverty measures used in the analysis and describes the NRSP hypothesis and estimation strategy. In Section 3, we analyze the intertemporal variation in poverty aversion in the US over the last quarter of the 20th century under the natural rate hypothesis. Section 4 similarly examines the empirical heterogeneity observed in the level of poverty aversion across countries in the mid-1990s under the natural rate hypothesis. Section 5 considers relationships with other recent literature and provides concluding remarks which point to opportunities for future research.

2. MODEL 2.1. Preliminaries For the case of a discrete income distribution F ¼ {y1, y2, y, yN}, Zheng (2000a, 2000b) discusses the following constant distribution-sensitivity (CDS) measure of poverty: 1 X gðz
yi Þ ½e
1 g40 N i¼1 q

PgF ¼

(1)

where z is the poverty line, q (qoN) is the number of individuals with income below the poverty line, y is income, and g is the measure of distribution-sensitivity. Distribution-sensitivity measures the decrease in poverty as a result of a progressive income transfer. Zheng (2000a) shows that the distribution-sensitivity in Eq. (1) is constant and given by g. The

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author further argues that distribution-sensitivity is an appropriate formal definition of poverty aversion (see also Zheng (2000b)). We can re-write Eq. (1) in terms of the ratio of each individual’s income to the poverty line as q 1 X gzð1
si Þ PgF ¼ ½e
1 (2) N i¼1 where si ¼ yi/z. If the data (discussed below) is partitioned into K groups, and if si is assumed constant within each group, Eq. (2) can be re-written as K X K
 X q 1X nk gzð1
sk Þ PgF ¼
þ egzð1
si Þ ¼
H F þ (3) e N N k¼1 i2k N k¼1 where HF is the headcount index, nk is the number of individuals in group k, and sk is the ratio of income to the poverty line for those in group k. The measure PgF differs from the headcount index (HF) and other summary statistics-based poverty indices in its explicitly ethical foundation. It embodies the poverty aversion parameter of a decisionmaker; thus, it is referred to as subjective in contrast to, for example, the headcount index. Note that @PgF 40 8F (4) @g Thus, a more poverty-averse social decisionmaker will perceive greater poverty in any given distribution. Although the headcount index entails ethical judgments as well, this index is regarded as authoritative by many; we call it ‘‘objective’’ for the purposes of the present study as noted above. For robustness, we also utilize the normalized poverty deficit as an objective poverty measure. For the same income distribution, F, this measure is given by q 1 X
z
yi  NPDF ¼ (5) N i¼1 z for discrete data and NPDF ¼

X
nk  k

N

ð1
sk Þ ¼ H F


X
nk  k

N

sk

(6)

for data partitioned into k groups. The NPD, which is equivalent to the Foster–Greer–Thorbecke (FGT) measure with a ¼ 1, entails ethical judgments just as the headcount index does, but it is not distribution-sensitive and we characterize it as objective for present purposes as well.

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According to the PgF measure, two entirely different income distributions F1 and F2 could be attributed the same level of subjective poverty by two different decisionmakers: g

g

PF11 ¼ PF22 g1 ag2

(7)

The relationships in Eqs. (4) and (7) are at the crux of the NRSP hypothesis.

2.2. The Natural Rate of Subjective Poverty To analyze differences in poverty a version either within a particular country over time or across countries, let Fi be the income distribution function for observation i (i may index either years or countries). Given the natural rate of subjective poverty, p, we first identify the poverty aversion parameter, gi, such that the subjective poverty in distribution Fi equals p: g

PF11 ¼ p

8i

(8)

We then analyze the determinants of the poverty aversion parameters, gi, identifying the empirical factors associated with the changing degree of aversion. If x is a vector of possible explanatory variables and xj the jth component, we wish to estimate a function c(x) such that gi  cðxi Þ

(9)

where xi indicates the values of x for observation i; or, at least, to sign the partial derivatives qc/qxj. The x’s we examine later include variables reflecting the political and economic climate of a particular country or period, such as income, population, education, unemployment, female empowerment, and corruption. With the explanatory variables in x and function c(x) determined, new political or social conditions that alter one of the explanatory variables, say xij ; will cause the level of subjective poverty to diverge from the historical natural rate of poverty p. For example, suppose qc/qxj>0 and that xij increases to xij þ Dxij : Then gi increases to gi+Dgi, where Dgi ¼ ð@c=@xj ÞDxij 40: This causes the level of subjective poverty to increase since the decisionmaker is now more averse to poverty: " ! # g @PFi i gi þDgi ¼pþ PF i Dgi 4p (10) @gi

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Given the new degree of poverty aversion gi+Dgi for observation i; can the natural rate of poverty p be restored? Yes, if redistributive policies (e.g., directly through the tax system or indirectly through increased transfer payments, government sponsored training programs, raising the minimum wage, etc.) are undertaken that improve the incomes of those below the poverty line and consequently alter the income distribution, from Fi to Gi say, where: g þDgi

PGi i

g

g þDgi

¼ PFi i ¼ poPFi i

(11)

The condition in Eq. (11) requires Gi to contain objectively less poverty than Fi (so that a decisionmaker with poverty aversion gi+Dgi is less concerned about poverty in Gi than in Fi). Taking the headcount index as our measure of objective poverty, then Gi should have a lower headcount index than Fi (i.e., H Gi oH F i ). If this is the mechanism whereby the natural rate p is restored, then according to the NRSP, our measures of objective poverty should be inversely related to the same set of explanatory variables, x. For example, we should be able to express the headcount ratio for observation i as: H F i  oðxi Þ

(12)

and if qc/qxj>0 (as assumed previously), then qo/qxjo0. This constitutes the testable implication of the NRSP.4

3. POVERTY AVERSION IN THE UNITED STATES 3.1. Data To examine the intertemporal variation in poverty and poverty aversion in the US, we use Census Bureau statistics on the extent of poverty (and poverty thresholds) over the period 1975–1998.5 Table A1 in the appendix contains the annual cumulative percentage of the total population and subpopulation of individuals over age 65 with income below a certain fraction of the poverty line. Combining this data with the Zheng index for partitioned data in Eq. (3) (and ignoring inequality within quantiles6), we find the value of g that achieves a given level of subjective poverty, p, by conducting a grid search over potential values. To do this, we compute the value of Eq. (3) for g between 1.0  10
06 and 0.15 with a step size of 1.0  10
06.

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We perform this exercise for several possible values of p since we do not presume to know the ‘‘true’’ value of the natural rate p. Tables A2 and A3 in the appendix report the values of g which yield a Zheng index value of 0.02, 0.04, 0.06, 0.08, and 0.10 for the total population and the sub-population aged 65 and over, respectively.7,8 Finally, to ensure a consistent measure of objective poverty, we use the headcount index reported in the same Census Bureau table, as well as the NPD measure estimated using Eq. (6). Table 1 contains the relevant summary statistics and sources for the potential determinants of poverty aversion we examine below.

3.2. Results 3.2.1. Preliminaries To analyze those factors associated with the level of poverty aversion in the US, we first must ensure our analysis is robust to the choice of p. Thus, we use several values for p, ranging from 0.02 to 0.10. Table 2 presents the correlation matrix between the time-specific poverty aversion parameters for each value of p, g0.02 refers to the value of g such that PgF ¼ 0:02; etc. For all values of p, the correlations are extremely close to unity, implying that over a wide range of p, the arbitrary choice of p does not appear to be problematic. Also included in Table 2 are the correlations between the timespecific aversion parameters and our two measures of objective poverty. In all cases, the correlations between the g’s and the objective poverty measures are negative and close to unity in absolute value. Consequently, periods of higher objective poverty are characterized by less poverty averse decisionmakers in the US, as the NRSP theory predicts. To further illustrate these points, Fig. 1 plots g0.04, g0.06, g0.08, and g0.10 versus our two measures of objective poverty (the headcount ratio and the normalized poverty deficit) for both the entire population as well as the over 65 sub-population.9 The relationships are downward-sloping (although not monotonically), and within each panel the four cases are nearly parallel to one another. Fig. 2 plots the level of aversion over time. The top two panels plot g0.04, g0.06, g0.08, and g0.10 for the two samples, marking times of presidential changes. As in Fig. 1, the four cases yield similar insights into relative changes in the degree of poverty aversion over this period. The bottom panels re-plot g0.02 and g0.10 against time, super-imposing one atop the other (i.e., with the axes re-scaled) to illustrate how each measure yields virtually identical inferences concerning changes in relative poverty aversion. As a result, not knowing the actual NRSP, p, does not impede our

Variable President (1 ¼ Democrat) Senate (# Democrats) Representatives (# Democrats) Annual growth rate (GDP) Median household income (1000s 97 US$) Total public education expenditures (% GDP) Unemployment rate % HS+, males % HS+, females % 4 years college+, males % 4 years college+, females Union share Minimum wage (96 US$)

Summary Statistics: US Sample.

Years

Mean

Std. Dev.

Source

1975–1998 1975–1998 1975–1998 1975–1998 1975–1998 1975–1998 1975–1997 1975–1998 1975–1998 1975–1998 1975–1998 1975–1998 1975–1997

0.46 52.79 256.50 0.03 41.86 0.14 0.07 0.74 0.74 0.23 0.17 0.16 3.30

0.50 5.99 27.32 0.02 16.00 0.08 0.01 0.06 0.07 0.03 0.03 0.06 0.44

http://www.policsci.com/almanac/history/polidivs.htm http://www.policsci.com/almanac/history/polidivs.htm http://www.policsci.com/almanac/history/polidivs.htm http://www.bea.doc.gov http://www.census.gov http://www.bea.doc.gov http://stats.bls.gov http://nces.ed.gov http://nces.ed.gov http://nces.ed.gov http://nces.ed.gov http://www.demographia.com http://epinet.org/datazone/minimumwage.html

Changing Poverty or Changing Poverty Aversion?

Table 1.

241

242

Table 2.

g0.02 g0.04 g0.06 g0.08 g0.10 Headcount NPD

DANIEL L. MILLIMET ET AL.

Poverty Aversion (Whole Population): Correlation Matrix, 1975–1998. g0.02

g0.04

g0.06

g0.08

g0.10

Headcount

1.0000 0.9026 0.9234 0.9284 0.9430 –0.8792 –0.9406

1.0000 0.9705 0.9715 0.9712 –0.9375 –0.9781

1.0000 0.9781 0.9790 –0.9212 –0.9783

1.0000 0.9837 –0.9310 –0.9836

1.0000 –0.9419 –0.9887

1.0000 0.9690

ability to make inferences regarding intertemporal variation in poverty aversion. The decline in overall poverty aversion (depicted in the top-left panel of Fig. 2), along with the negative correlation between poverty aversion and objective poverty (listed in Tables 2 and 3), can be interpreted in the context of the recent rise in (objective) poverty in the US.10 Possible explanations have ranged from structural changes in the labor market (Cutler & Katz, 1991), negative inner city neighborhood effects (Cutler & Glaeser, 1997), and an increase in female labor force participation (Topel, 1994) and femaleheaded households (Blank & Hanratty, 1992), to name but a few.11 However, the NRSP hypothesis maintains that these are at best only indirect explanations for the rise in poverty. To understand the rise in objective poverty, one must analyze the determinants of poverty aversion. The NRSP hypothesis asserts that it is poverty aversion among policymakers that leads to actions (or inactions) that determine the level of objective poverty. For example, Blank and Hanratty (1992) argue that the lack of generous transfer payments (e.g., welfare) is responsible for the rise in poverty. This is entirely consistent with the NRSP hypothesis at work. The NRSP hypothesis may also shed light on another puzzle: the inability of some state governments to effectively reach poor residents. Ravallion (1999b, p. 373) states that, ‘‘As a rule, governments of poor states (provinces or countries) do not seem to be very good at targeting public spending to their poor. Yet anti-poverty programs often target poor states, in the hope of reaching poor people.’’ However, if poverty aversion differs across states or, more to the point, if state governments have different aversion levels than the federal government, and subjective poverty is equalized across states, then states with low levels of poverty aversion should have high objective poverty according to the NRSP. Moreover, state governments

gamma_0.04 gamma_0.08

0.4

Poverty Aversion

Poverty Aversion

0.3

gamma_0.06 gamma_0.10

0.25

0.2

0.15

0.1

0.3

0.2

0.1 0.11

0.12

0.13 0.14 Headcount Index

0.1

0.15

Whole Population

0.12 0.14 Headcount Index

0.16

Population Aged 65+

gamma_0.06 gamma_0.10

gamma_0.04 gamma_0.08

gamma_0.04 gamma_0.08

0.3

gamma_0.06 gamma_0.10

0.4

Poverty Aversion

Poverty Aversion

gamma_0.06 gamma_0.10

0.25

0.2

0.15

0.1

Changing Poverty or Changing Poverty Aversion?

gamma_0.04 gamma_0.08

0.3

0.2

0.1 0.04

0.05

0.06

0.07

0.03

0.035

0.04

Normalized Poverty Deficit

Normalized Poverty Deficit

Whole Population

Population Aged 65+

Poverty Aversion and Objective Poverty.

243

Fig. 1.

0.045

gamma_0.04 gamma_0.08

gamma_0.06 gamma_0.10

0.4

Poverty Aversion

0.25 0.2 0.15 0.1

0.3

0.2

0.1 1975

1980

1985 Year

1990

1975

1998

1980

Whole Population gamma_0.02

1985 Year

1998

1990

Population Aged 65+ gamma_0.02

gamma_0.10

0.08

0.28

gamma_0.10

0.11

0.38

gamma_0.02

0.06

gamma_0.10

gamma_0.02

0.24

0.1 0.34 0.09

0.22 0.05

0.2 1975

1980

1985 1990 Year

Whole Population

Fig. 2.

1998

0.32 0.08

0.3 1975

1980

1985

1990 Year

Population Aged 65+

Poverty Aversion in the US: 1975–1998.

1998

DANIEL L. MILLIMET ET AL.

0.36

0.26 0.07

gamma_0.10

Poverty Aversion

0.3

244

gamma_0.06 gamma_0.10

gamma_0.04 gamma_0.08

Changing Poverty or Changing Poverty Aversion?

Table 3.

g0.02 g0.04 g0.06 g0.08 g0.10 Headcount NPD

245

Poverty Aversion (Population Aged 65+): Correlation Matrix, 1975–1998. g0.02

g0.04

g0.06

g0.08

g0.10

Headcount

1.0000 0.8668 0.9105 0.9097 0.9162
0.8842
0.9544

1.0000 0.9558 0.9600 0.9515
0.7960
0.9559

1.0000 0.9715 0.9715
0.8135
0.9719

1.0000 0.9839
0.7635
0.9592

1.0000
0.7711
0.9651

1.0000 0.8982

with low poverty aversion will not find it ‘‘optimal’’ to direct federal aid to combat poverty since this would only push the states out of equilibrium. Finally, we note that overall aversion to poverty is negatively correlated with aversion to poverty in the sub-population aged 65 and over. The pairwise correlation between the overall g’s and the sub-population g’s (for a fixed value of p) range from
0.11 (for p ¼ 0.04) to
0.35 (p ¼ 0.02). Interestingly, then, it appears as if policymakers do not focus on poverty as a whole, but rather focus on poverty within subgroups of the population at any given time.12 3.2.2. Correlates of US Poverty Aversion We now shift our focus to exploring the empirical factors associated with the observed variation in poverty aversion.13 To proceed, Figs. 3 and 4 present time plots of various US attributes and social policy choices and poverty aversion. Several interesting associations emerge. First, the number of Congressional representatives and senators affiliated with the democratic party is positively correlated with overall poverty aversion. The correlation coefficients are 0.59 and 0.63, respectively. However, a democratic Congress is negatively correlated with poverty aversion for the over 65 sub-population (correlation coefficients of
0.36 and
0.25, respectively). Second, perhaps not surprisingly, union share is positively correlated with overall poverty aversion (0.81), but negatively correlated with over 65 poverty aversion (
0.47). Third, while we find little correlation between lagged growth in per capita income and overall poverty aversion (
0.09 and
0.04 using a three-year and five-year moving average, respectively), we do find a large positive correlation between lagged growth and aversion to poverty in the over 65 sub-population (correlations of 0.34 and 0.42 using the same moving averages). Finally, in terms of policy outcomes, we find significant

246

Poverty Aversion (Whole Population) and Select US Attributes: 1975–1998.

DANIEL L. MILLIMET ET AL.

Fig. 3.

42000

0.32

40000 38000 1998

8

0.34 6

0.32

4 1998

0.34

20

0.32

15

0.3 1975 1980 1985 1990 Year Panel C gamma_0.10

3-year Moving Average

0.38

0.04

0.36 0.02 0.34 0

0.32 0.3 1975 1980 1985 1990 Year Panel E 0.38

25

-0.02 1998

0.36

3.5

0.34 0.32 0.3 1975 1980 1985 1990 Year Panel H

3 2.5 1998

5-year Moving Average

0.38

0.04

0.36

0.03

0.34

0.02

0.32

0.01

0.3 1975 1980 1985 1990 Year Panel F gamma_0.10

Minimum Wage 4

10 1998

0 1998

Expenditure 40

0.38 0.36

30

0.34 20 0.32 0.3 1975 1980 1985 1990 Year Panel I

10 1998

Poverty Aversion (Population Aged 65+) and Select US Attributes: 1975–1998.

247

0.3 1975 1980 1985 1990 Year Panel G

200 1998

0.36

Union Share (% non-ag., private employment)

0.3 1975 1980 1985 1990 Year Panel B

gamma_0.10

unemployment rate 10

0.36

Fig. 4.

0.32

30

GDP Growth (Per Capita)

44000

0.34

0.3 1975 1980 1985 1990 Year Panel D

250

Union Share

0.38

Government Education Expenditure (% of GDP)

Poverty Aversion

0.36

gamma_0.10

0.34

gamma_0.10 46000

0.38

0.38

0.36

median family income, 97$ Median Household Income Poverty Aversion

gamma_0.10

45 1998

300

House (# of democrats) Poverty Aversion

0.32

gamma_0.10

# democrats

0.38

GDP Growth (Per Capita) Poverty Aversion

50

Senate (# of democrats) Poverty Aversion

55 0.34

Unemployment Rate Poverty Aversion

Poverty Aversion

0.36

0.3 1975 1980 1985 1990 Year Panel A

Poverty Aversion

gamma_0.10 60

Minimum Wage Poverty Aversion

# democrats

Changing Poverty or Changing Poverty Aversion?

gamma_0.10 0.38

248

DANIEL L. MILLIMET ET AL.

associations between poverty aversion and the minimum wage (correlation coefficient of 0.77 for overall aversion;
0.57 for over 65 aversion) and government expenditure on education as a fraction of GDP (0.85 for overall aversion;
0.42 for over 65 aversion). To further test the NRSP hypothesis and better analyze the determinants of poverty aversion in the US, Tables 4 (whole population) and 5 (over 65 sub-population) present the results of some simple AR(1) regressions using ln(g0.10), ln(H), the natural logarithm of the headcount ratio, and ln(NPD), the natural logarithm of the NPD, as the dependent variables.14 The most important result to examine – which is at the crux of the NRSP hypothesis – is whether changes in various attributes that alter the poverty aversion of decisionmakers also result in changes in the level of objective poverty, such that the natural rate of poverty is maintained. Thus, factors associated with greater aversion should also be associated with lower levels of objective poverty. Examining Tables 4 and 5 verifies that this is in fact so. In almost every case, the coefficients are identical in terms of statistical significance, but of the opposite sign, in the model using g0.10 as the dependent variable and the models using our objective poverty measures.

Table 4.

Determinants of Poverty Aversion (Whole Population) and Objective Poverty: Semi-log AR(1) Specificationa.

Independent Variable

Dependent Variable g0.10

President (1 ¼ Democrat) ln (Senate (# Democrats)) ln (House of Reps. (# Democrats)) ln (Median household income) Unemployment rate Growth rate Female LFPR % HS+, males % HS+, females % 4 years college+, males % 4 years college+, females r Observations

0.05
0.07 0.18
0.27
0.06
0.01
0.03
0.18 0.12 0.16
0.01

[p ¼ 0.00] [p ¼ 0.48] [p ¼ 0.07] [p ¼ 0.24] [p ¼ 0.00] [p ¼ 0.02] [p ¼ 0.05] [p ¼ 0.00] [p ¼ 0.00] [p ¼ 0.00] [p ¼ 0.16]
0.86

Headcount
0.05
0.06 0.04 0.02 0.04 0.00
0.00 0.16
0.10
0.11 0.02

[p ¼ 0.00] [p ¼ 0.47] [p ¼ 0.56] [p ¼ 0.95] [p ¼ 0.00] [p ¼ 0.43] [p ¼ 0.78] [p ¼ 0.00] [p ¼ 0.00] [p ¼ 0.01] [p ¼ 0.06]
0.85 22

NPD
0.07
0.08 0.11 0.16 0.06 0.00 0.02 0.23
0.16
0.17 0.03

[p ¼ 0.00] [p ¼ 0.57] [p ¼ 0.39] [p ¼ 0.58] [p ¼ 0.00] [p ¼ 0.13] [p ¼ 0.28] [p ¼ 0.00] [p ¼ 0.00] [p ¼ 0.00] [p ¼ 0.02]
0.91

a p-values associated with the test H0: b ¼ 0 in brackets. Refer to the text and/or appendix for variable definitions.

Changing Poverty or Changing Poverty Aversion?

249

Table 5. Determinants of Poverty Aversion (Population Aged 65+) and Objective Poverty: Semi-log AR(1) Specificationa. Independent Variable

Dependent Variable g0.10

President (1 ¼ Democrat) ln (Senate (# Democrats)) ln (House of Reps. (# Democrats)) ln (Median household income) Unemployment rate Growth rate Female LFPR % HS+, males % HS+, females % 4 years college+, males % 4 years college+, females r Observations a


0.01 0.16
0.32
0.79
0.01 0.02 0.01
0.32 0.25 0.22
0.07

[p ¼ 0.73] [p ¼ 0.36] [p ¼ 0.06] [p ¼ 0.18] [p ¼ 0.34] [p ¼ 0.00] [p ¼ 0.68] [p ¼ 0.00] [p ¼ 0.00] [p ¼ 0.01] [p ¼ 0.05]
0.86

Headcount
0.02 0.21 0.25
0.06 0.01
0.02
0.01 0.29
0.28
0.11 0.09

[p ¼ 0.58] [p ¼ 0.30] [p ¼ 0.22] [p ¼ 0.90] [p ¼ 0.51] [p ¼ 0.00] [p ¼ 0.79] [p ¼ 0.01] [p ¼ 0.00] [p ¼ 0.31] [p ¼ 0.02]
0.83 22

NPD 0.00 0.08 0.25 0.12 0.01
0.03 0.01 0.39
0.34
0.27 0.11

[p ¼ 0.97] [p ¼ 0.72] [p ¼ 0.24] [p ¼ 0.87] [p ¼ 0.46] [p ¼ 0.00] [p ¼ 0.73] [p ¼ 0.00] [p ¼ 0.00] [p ¼ 0.02] [p ¼ 0.02]
0.86

See Table 4.

According to the specific point estimates, several interesting findings emerge. First, overall poverty aversion and overall objective poverty are significantly associated with the political affiliation of the president, although independent of the political affiliation of Congress at standard significance levels. As one might expect, a Democrat-controlled White House is associated with periods of greater (lower) poverty aversion (objective poverty). Second, during periods of greater economic mobility, overall poverty aversion (objective poverty) is lower (higher); whilst poverty aversion (objective poverty) among those over 65 is higher (lower). The fact that overall aversion to poverty falls during periods of economic growth is consistent with the positions in Ravallion and Lokshin (2000), Be´nabou and Ok (2001), and Hirschman and Rothschild (1973). These studies argue that preferences for redistribution depend not just on the median voter’s current position in the income distribution, but also his/her expectations of future income mobility.15 However, the positive effect of economic growth on aversion to poverty among those over 65 is possibly due to the same mentality that causes charitable giving to increase with income. Via an increase in poverty aversion, the benefits of economic growth are passed along to those no longer in the workforce. Third, we find a significant, negative association between the unemployment rate and overall poverty aversion. Thus, during times of low

250

DANIEL L. MILLIMET ET AL.

unemployment, poverty aversion intensifies. Again, this is consistent with the observed rise in charitable giving as incomes increase. It is also consonant with the findings in Blank and Blinder (1986), which report a similar increase in (objective) poverty as unemployment worsens. Finally, we find significant effects of education levels. An increase in the share of males (females) with at least a high school diploma is associated with a decline (increase) in poverty aversion for both samples; conversely for objective poverty. College completion rates for males, on the other hand, have a positive effect on poverty aversion in both samples and there is a negative effect of female college completion rates on poverty aversion for those over 65. The fact that an increase in males with only a high school degree lowers poverty aversion, but increases in college-educated men increase poverty aversion is not surprising. Moreover, the fact that an increase in the share of (at least) high school educated females increase poverty aversion is also not surprising given the literature on women being more risk averse than men (see, e.g., Jianakoplos and Bernasek (1998), as well as the findings in Ravallion and Lokshin (2000) that women tend to favor redistribution). However, the fact an increase in college-educated women is associated with diminished aversion to poverty amongst the sub-population aged 65 and over is perhaps unexpected.

4. INTERNATIONAL DIFFERENCES IN POVERTY AVERSION If one accepts the NRSP hypothesis, it may apply to not only intertemporal comparisons within a given country, but also to cross-sectional comparisons across countries. In its widest sense, subjective poverty may be constant across both time and countries. 4.1. Data To test the NRSP hypothesis and analyze heterogeneity in terms of poverty aversion across countries, we use data from the World Development Report 2000/2001 (WDR) and 1999 World Development Indicators published by the World Bank. Table A4 in the appendix contains the percentage of individuals living on less than $1/day and $2/day for 51 countries.16 The countries are primarily low income and/or market transition economies.17 We assume all countries have an identical poverty line of $2/day. According to the

Changing Poverty or Changing Poverty Aversion?

Table 6.

251

Summary Statistics: International Sample.

Variable Annual population growth, 1995–2015 Enrollment rate (combined 1st, 2nd, and 3rd level), 1995 Adult literacy rate, 1995 Real GDP (per capita), 1995 % Females in gov’t, ministerial level, 1995 % Females in gov’t, subministerial level, 1995 Corruption index (CPI), 1998

Mean

Std. Dev.

Source

1.81

0.94

http://www.undp.org/hdro

56.42

18.50

http://www.undp.org/hdro

70.18 3062 6.19

25.46 2147 4.87

http://www.undp.org/hdro http://www.undp.org/hdro http://www.undp.org/hdro

8.28

7.09

http://www.undp.org/hdro

3.29

1.26

http://www.gwdg.de/uwvw

WDR (2000), 2.8 billion of the world’s 6 billion individuals live on less than $2/day; 1.2 billion on less than $1/day. In addition, there is considerable variation across countries not only in the percentage of individuals surviving on incomes below these thresholds at any given time, but also in the trend for these figures. For example, the number of individuals living on less than $1/day fell by 130 million in East Asia over the period 1987–1998. Over this same time span, the number in Sub-Saharan Africa rose by over 50 million (see also Ravallion, 1994b). As in the previous section, we combine the data listed in Table A4 with the Zheng index for partitioned data in Eq. (3) and find the value of g that achieves a given level of subjective poverty, p, by conducting a grid search over potential values. As before, we perform this exercise for p ¼ 0.02, 0.04, 0.06, 0.08, and 0.10. Table A5 in the appendix reports the values of g.18,19 Table 6 contains the relevant summary statistics and sources for the variables we analyze as possible determinants of country-specific poverty aversion.

4.2. Results 4.2.1. Preliminaries As in the prior section, we must verify our analysis is robust to the choice of p. Table 7 is analogous to Table 2 and presents the correlation matrix between the country-specific poverty aversion parameters for each value of p. As in Table 2, the g’s are nearly perfectly correlated. Moreover, the correlations between the aversion parameters and our two measures of

252

DANIEL L. MILLIMET ET AL.

Table 7.

g0.02 g0.04 g0.06 g0.08 g0.10 Headcount NPD

International Poverty Aversion: Correlation Matrix. g0.02

g0.04

g0.06

g0.08

g0.10

Headcount

1.0000 0.9997 0.9991 0.9982 0.9972 –0.8810 –0.8152

1.0000 0.9998 0.9993 0.9986 –0.8865 –0.8237

1.0000 0.9999 0.9995 –0.8911 –0.8310

1.0000 0.9999 –0.8949 –0.8374

1.0000 –0.8981 –0.8430

1.0000 0.9519

objective poverty are close to minus one. Thus, as with the time series data from the US, countries with higher objective poverty are characterized by less poverty averse social policymakers, as the NRSP theory predicts.

4.2.2. Correlates of Country-Specific Poverty Aversion Table 8 presents the estimates from two different cross-sectional regression models where the dependent variables used within each model are the natural logarithms of g0.10, the headcount index, and the NPD.20 The variables we examine as potential determinants of the country-specific level of poverty aversion are: annual population growth, literacy and school enrollment rates, real per capita GDP, the proportion of females at various levels of the government, and corruption.21 Due to data availability, Model I (omitting corruption) has 50 observations, while Model II (including corruption) has 35 observations. Note that, as in the previous section, in almost every case the coefficients are of the opposite sign and have the same level of statistical significance in the models using g0.10 as the dependent variable and the models using our objective poverty measures. Examining the results from both models, we find significant, negative (positive) effects of population growth on poverty aversion (objective poverty) and significant, positive (negative) effects of per capita GDP and corruption on poverty aversion (objective poverty). The lack of concern for hardship in countries with high population growth may reflect the perception of policymakers that such hardship is self-induced through excess fertility rates (e.g., Lanjouw & Ravallion, 1995). In any event, the negative consequences of high population growth are disconcerting given the World Bank’s projection that world population will increase by two billion over the next 25 years, with over 97% occurring in developing countries (WDR, 2000).

Determinants of International Poverty Aversion and Objective Povertya.

Independent Variable

Dependent Variable Model I

Population growth Literacy rate Enrollment rate Real GDP (per capita) % females in gov’t, ministerial level % females in gov’t, subministerial level Corruption ¯2 R Observations a

Model II

g0.10

Headcount

NPD

g0.10

Headcount

NPD


0.26 (
2.50)
4.39  10–04 (
0.08) 2.44  10–03 (0.30) 0.32 (2.15)
0.01 (
0.62)

0.24 (2.51)
1.01  10–03 (
0.20)
5.50  10–04 (
0.08)
0.25 (
1.87) 0.01 (0.47)

0.31 (2.59) 5.46  10–04 (0.09)
2.58  10–03 (
0.28)
0.35 (
2.08) 0.01 (0.59)


0.29 (
2.40) 2.81  10–03 (0.42)
0.01 (0.32) 0.32 (1.81)
0.01 (
0.71)

0.24 (2.15)
0.01 (
0.92) 4.73  10–03 (0.48)
0.23 (
1.36) 0.01 (0.44)

0.33 (2.45)
3.54  10–03 (
0.46) 0.01 (0.60)
0.34 (
1.70) 0.01 (0.66)


2.26  10
03 (
0.211)


0.01 (
0.64)

1.34  10–03 (0.11)


0.01 (
0.62)

0.13 (1.93) 0.51

0.50 50

0.51

0.51

1.01  10–03 (0.09)


0.13 (
2.02) 0.51

Changing Poverty or Changing Poverty Aversion?

Table 8.

0.01 (0.58)


0.15 (
1.98) 0.51

35

Estimation is by OLS. T-statistics in parentheses.

253

254

DANIEL L. MILLIMET ET AL.

The positive association between per capita income and poverty aversion is not surprising. The fact that social decisionmakers become more concerned over the fate of the least fortunate as per capita incomes rise is consonant with the findings in the previous section with respect to the negative effect of unemployment on poverty aversion in the US. Finally, we find an unexpected positive association between corruption and poverty aversion. One possible explanation for this finding is reverse causation. If poverty averse governments implement measures aimed at combatting poverty, these programs may create new opportunities for rents to be extracted by corrupt officials.22

5. CONCLUDING REMARKS This study began by noting that defining and measuring poverty is perhaps a fraught exercise. Sawhill (1988, p. 1082) concludes that ‘‘it should be clear by now that poverty is in the eye of the beholder and reflects off the green eyeshades of the statistician.’’ However, rather than being discouraged, we embrace this fact. We do this by fully admitting that the amount of poverty inherent in a particular income distribution is subjective. For a given distribution, policymakers averse to poverty will ‘‘see’’ greater poverty than those less averse. In addition, if we assume that all societies tolerate a constant level of subjective poverty, then the amount of objective poverty will move inversely with the level of poverty aversion mandated by social consensus. We refer to this assumption as the NRSP hypothesis. The hypothesis offers more than an intellectual exercise. Applying the NRSP hypothesis to Zheng’s (2000a, 2000b) measure of subjective poverty, we are able to quantify the level of poverty aversion maintained by policymakers in a given economy. We then verify – using both time-series data from the US and cross-sectional data from 51 countries – that poverty aversion and objective poverty (measured by the headcount ratio and the normalized poverty deficit) have a strong, inverse relationship. Thus, both data are consistent with the NRSP hypothesis. Finally, we examine the determinants of poverty aversion. In the US, we find significant effects of various economic and political variables such as the political affiliation of the president and Congress, economic growth, unemployment, and education levels. In our cross-section of countries, we find significant effects of population growth, per capita income, and corruption. The study we have undertaken here complements the analysis of Lambert, Millimet, and Slottje (2003) and Millimet, Slottje, and Lambert (2000), in

Changing Poverty or Changing Poverty Aversion?

255

which a parallel hypothesis for inequality is articulated and explored. According to the Natural Rate of Subjective Inequality (NRSI) hypothesis posited therein, social planners maintain a fixed and constant value of subjective inequality at all times and in all places, this being measured a` la Atkinson (1970) as the percentage of total income that could be given up without welfare loss, the rest being distributed equally. To explain this hypothesis, inequality aversion must be time- and location-specific, with adjustment processes from changes in political and socioeconomic explanatory variables via inequality aversion to the income distribution explaining observed differences in objective inequality (measured by the Gini coefficient in Lambert et al. (2003) and Millimet et al. (2000)). All of this research begs an intriguing question: do social decisionmakers obeying our NRSP hypothesis also obey the NRSI hypothesis? In other words, can policymakers simultaneously arrange their countries’ affairs to maintain both subjective inequality and poverty at their respective natural rates?23 An affirmative answer would provide a new perspective on the old and vexed question of links between inequality, welfare, and poverty. Perhaps not surprisingly, we find a strong positive correlation in the US between our measure of overall poverty aversion and the level of inequality aversion reported in Millimet et al. (2000) (correlation coefficient 0.75). We also find a weak positive correlation between the level of country-specific poverty aversion and the level of inequality aversion reported in Lambert et al. (2003) (correlation coefficient 0.15). On the other hand, the correlation between aversion to poverty among those over age 65 in the US and inequality aversion in the US is –0.50. Fig. 5 plots inequality aversion and poverty aversion over time for each of the two US samples.24 The correlation of 0.75 in the US between poverty and inequality aversion offers insight into recent findings regarding the linkages between inequality and poverty. Gottschalk and Danziger (1984), among others, have attributed the increase of late in (objective) poverty in the US to burgeoning inequality. Sawhill (1988, p. 1092) states that ‘‘this has merely substituted one puzzle for another’’ since we are unsure why inequality has risen. However, combining the NRSP and NRSI hypotheses provides a coherent explanation for both phenomena. Social attitudes in the US, responding perhaps to the increase in high school educated males and college educated females, have become less averse to both inequality and poverty. Consequently, objective measures of each (e.g., the headcount ratio and the Gini index) have both risen. Other researchers have also been concerned with the link between poverty, inequality, and well-being. Atkinson (1987) discusses the relationship

DANIEL L. MILLIMET ET AL. inequality aversion 0.55

0.26

0.5

0.24

0.45

0.22

0.4

0.35

0.2 1975

1980

gamma_0.10

gamma_0.10

1985 1990 Year Entire Population

1998

inequality aversion

0.38

0.55

0.36

0.5

0.34

0.45

0.32

0.4

0.3

0.35 1975

1980

1985 1990 Year Population Aged 65+

1998

Fig. 5. Poverty and Inequality Aversion in the US: 1975–1998.

e_0.10

gamma_0.10

gamma_0.10 0.28

e_0.10

256

Changing Poverty or Changing Poverty Aversion?

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between the size of the pie, the cost of inequality and the ‘‘cost of poverty.’’ Massey (1996), in his presidential address before the Population Association of America, emphasized the dual rise in poverty and inequality, as well as the increase in the spatial concentration of the impoverished. Kakwani (1999) argues that inequality and poverty indices can be derived from common underpinnings in terms of deprivation; but see also Ravallion (1999a). There is also a growing literature on the linkages between inequality and poverty trends in transition economies (see, e.g., Milanovic (1998), World Bank (2000), and, most recently, Ivaschenko (2002)). Our framework offers a fresh perspective, suggesting the examination of the dual effects of the various political and socioeconomic changes that typically characterize such transitions on poverty and inequality aversions. Moreover, Ravallion (1994a) characterizes social welfare functions as inclusive measures of well-being (i.e., including the whole population) and poverty indices as exclusive measures (giving zero weight to the incomes of the non-poor). The author investigates empirically the correlations between measures of poverty and social welfare in developing countries, finding these to be very high, giving reasons and identifying factors which in practice tend to blur the theoretical differences between exclusive (poverty) and inclusive (social welfare) measures. Our twin NRSI and NRSP hypotheses provide an alternative explanation. One should expect to simultaneously observe high poverty and high social welfare given that aversion to inequality and poverty are highly correlated (these aversions both being determined by the same set of economic and political variables). On the other hand, the strong, negative correlation between aversion to poverty for the over 65 sub-population and inequality aversion – as well as the negative correlation between overall poverty aversion and poverty aversion for those over 65 reported in Section 3 – suggests that policymakers in the US tend to focus on the economic status of either younger or older cohorts at a particular time. The nature of politics may hinder the government’s ability to simultaneously address the needs of both groups. Clearly, more research is warranted, not only in terms of the relationship between poverty aversion across population sub-groups, but also addressing simultaneous changes in the level of and aversion to poverty and inequality within a coherent framework.

NOTES 1. Re-printed from http://www.statcan.ca/english/concepts/poverty/pauv.htm 2. Sawhill (1988, p. 1073) states that despite the growth in poverty-related research, ‘‘discussions of poverty have become more, not less, ideological.’’ Moreover,

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anecdotal evidence of the subjectivity involved in poverty measurements abounds. For example, assessments of the US’s War on Poverty are divided along partisan lines. Conservatives claim that either the war has been won or that the program actually increased poverty; liberals that greater action is required (Sawhill, 1988). In addition, in the inequality literature, Epstein and Spiegel (2001, p. 472) discuss the implications of deviations from an ‘‘acceptable level of inequality’’ or ‘‘natural inequality.’’ Lambert et al. (2003) propose a natural rate of subjective inequality that is constant across countries. 3. Each of the headcount ratio, normalized poverty deficit and Watts index, which we have characterized as objective, involves an implicit choice of parameter in one or other of the families referred to here. Thus, the headcount ratio and normalized poverty deficit belong to the FGT family, whilst the Watts index is an increasing transformation of an index in Clark et al.’s second family. See Zheng (1997). 4. One should resist the temptation to conclude that the negative relationship predicted by the NRSP hypothesis is mechanical in nature. If there were an exact relationship between Zheng’s poverty index, the poverty aversion parameter, g, and either of our ‘‘objective’’ measures of poverty, Q, so that PgF ¼ gðg; QF Þ; say, with qg/qg>0 and qg/qQF>0, which held across all income distributions, then certainly any xj which had a positive effect on poverty aversion would necessarily have a negative effect on objective poverty, since we hold g(g,QF) constant and equal to p. This would indeed void the test of NRSP. However, the headcount and NPD are entirely insensitive to the distribution of income among the poor, whereas Zheng’s index most certainly is not; thus, there could be no such relationship. 5. The validity of the poverty lines used by the US is beyond the scope of this paper. Future research may examine the possible simultaneous determination of poverty aversion and poverty lines by decisionmakers. 6. Ignoring within-quantile inequality is unfortunate, but necessary, given the data available. This restriction may be addressed in future research, utilizing large time-series of cross-section data from the UK or the CPS in the US. For now, we note that we have tested the robustness of the results to different assumed equal share values within quantiles. The results are unaltered. 7. The corresponding values of PgF are not presented in the table, but in all cases we are able to find a value of g which brings PgF to within 72.8  10
04 of the desired value. 8. As suggested by an anonymous referee, we also obtained values of g for values of the Zheng index of 0.15, 0.20, 0.25, and 0.30. While these are available upon request, we note that corresponding values are strongly correlated with the values for g obtained using a value of the Zheng index of 0.10. Specifically, using the total population (sub-population of individuals over age 65), the correlation is above 0.99 (0.95) in all cases. 9. Note, for the reader’s ease, we multiply g, the poverty aversion parameter, by 1,000 in the plots. 10. The headcount index has risen from 11.4% in 1978 to 15.1% in 1993 and the Watts measure (NPD) rose by 57% (52%) over the same period (Table A1). See also Levernier, Partridge, and Rickman (2000), Blank and Hanratty (1992) and Sawhill (1988). 11. Sawhill (1988) provides a nice survey.

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12. Ideally one would want to compute a measure of poverty aversion for those under age 65 and those over age 65. However, US poverty data from the census is only defined (by age) amongst the total population and the over 65 population. While one could use data on the total population by age category to estimate poverty rates for those under age 65, there is no corresponding poverty threshold (to our knowledge) defined for this sub-group. Nonetheless, we can reasonably infer that if overall poverty aversion is negatively correlated with poverty aversion for the over 65 sub-population, then the correlation between poverty aversion amongst only those under 65 and those over 65 is even more negatively correlated. 13. We use the word ‘‘determinants’’ loosely as we do no attempt to deal with issues of endogeneity. 14. For robustness, we also estimated the models using ln(g0.30) as the dependent variable. The pattern of signs on the coefficients is unchanged, and the majority of the statistically significant results remain. The results are available upon request. 15. Alternatively, Gottschalk and Danziger (1984) and others have argued that greater economic growth has led to a widening of the income distribution and consequently higher objective poverty (see Sawhill (1988) for a review). We return to this point in Section 5. 16. Again, we abstract from the choice of these ‘poverty lines’ and take them as given. See footnote 5. 17. We do not attempt to limit our analysis to countries deemed democratic. While the process by which the social consensus is mapped into the level of poverty aversion by policymakers may be less obvious in non-democracies, such avenues do exist. For example, ‘‘fair wage’’ models and models based on social custom argue that societal standards and perceptions of fairness may affect the income distribution through employment decisions, work effort conditional on employment, propensity for collective action on the part of workers, wage-setting practices of employers, as well as other channels (see, e.g., Agell & Lundborg, 1992; Ackerlof & Yellen, 1990; Blinder & Choi, 1990; Naylor, 1989; Ackerlof, 1980). Moreover, it is not trivial to distinguish between democracies and non-democracies. Finally, since (as we shall see) the data based on the full sample support our natural rate hypothesis, if indeed the relevant avenues are missing in non-democracies, then the results would be even stronger upon restricting our attention to the sub-sample of democratic regimes. 18. The corresponding values of PgF are not presented, but in all cases we are able to find a value of g which brings PgF to exactly the desired value. 19. Again, we also obtained values of g for values of the Zheng index of 0.15, 0.20, 0.25, and 0.30. While these are available upon request, we note that corresponding values are strongly correlated with the values for g obtained using a value of the Zheng index of 0.10. Specifically, the correlation is above 0.89 in all cases. 20. For robustness, we also estimated the models using ln(g0.30) as the dependent variable. The pattern of signs on the coefficients is unchanged, and the majority of the statistically significant results remain. The results are available upon request. 21. The corruption measure is obtained from Transparency International. According to their website: ‘‘The CPI [Corruption Perception Index] is a means of enhancing understanding of levels of corruption from one country to another. It does not attempt to assess the degree of corruption practiced by nationals outside their own countries. In an area as complex and controversial as corruption, no single

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source, or polling method, has yet been developed that combines a perfect sampling frame, large enough country coverage, and a fully convincing methodology to produce comparative assessments. This is why the CPI has adopted the approach of a composite index. It is a ‘poll of polls’. It consists of credible surveys using different sampling frames and varying methodologies and is the most statistically robust means of measuring perceptions of corruption. The 1998 CPI includes data from the Economist Intelligence Unit (Country Risk Service and Country Forecasts), Gallup International (50th Anniversary Survey), the Institute for Management Development (World Competitiveness Yearbook), the Political & Economic Risk Consultancy (Asian Intelligence Issue), the Political Risk Services (International Country Risk Guide), World Development Report (Private Sector Survey), and the World Economic Forum (Global Competitiveness Report). The index ranges from 0 (least corrupt) to 10 (most corrupt).’’ 22. For example, De Soto (1989) and Carino (1986) examine the effect of various government interventions on corruption. See also Acemoglu and Verdier (2000). 23. Relatedly, one may ask why policymakers would choose to do so. Such a question ventures into political economy dimensions. For example, voters may evaluate policymakers by several factors, among which is included a constraint on the perceived level of inequality and poverty. Exploration of such behavior is an interesting issue for future research. 24. Inequality aversion is given by e0.10, the value of e necessary for the Atkinson index of inequality to be equal to 0.10 (Millimet et al., 2000).

ACKNOWLEDGMENTS The authors wish to thank John Bishop, an anonymous referee, and Buhong Zheng for insightful comments, as well as conference participants at the 6th International Meeting of the Society for Social Choice and Welfare, Cal Tech University, July 2002, and at the John Formby retirement conference, Alabama, May 2003, and seminar participants at the University of Oregon and University of British Columbia.

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Lanjouw, P., & Ravallion, M. (1995). Poverty and household size. Economic Journal, 105, 1415–1434. Levernier, W., Partridge, M. D., & Rickman, D. S. (2000). The causes of regional variations in U.S. poverty: A cross-county analysis. Journal of Regional Science, 40, 473–497. Massey, D. S. (1996). The age of extremes: Concentrated affluence and poverty in the twentyfirst century. Demography, 33, 395–412. Milanovic, B. (1998). Income, inequality and poverty during the transition from planned to market economy. Washington, DC: The World Bank. Millimet, D. L., Slottje, D., & Lambert, P. J. (2000). Inequality aversion, income inequality, and social policy in the US: 1947–1998. Mimeo, Southern Methodist University. Naylor, R. (1989). Strikes, free riders, and social custom. Quarterly Journal of Economics, 104, 771–785. Ravallion, M. (1994a). Measuring social welfare with and without poverty lines. American Economic Review (AEA Papers and Proceedings), 84, 359–364. Ravallion, M. (1994b). Is poverty increasing in the developing world? Review of Income and Wealth, 40, 359–376. Ravallion, M. (1999a). Comment on Kakwani’s inequality, welfare and poverty: Three interrelated phenomena. In: J. Silber (Ed.), Handbook of income inequality measurement (pp. 629–634). Norwell, MA: Kluwer Academic Publishing. Ravallion, M. (1999b). Are poorer states worse at targeting their poor? Economics Letters, 65, 373–377. Ravallion, M., & Lokshin, M. (2000). Who wants to redistribute? The Tunnel Effect in 1990s Russia. Journal of Public Economics, 76, 87–104. Sawhill, I. V. (1988). Poverty in the U.S.: Why is it so persistent? Journal of Economic Literature, 26, 1073–1119. Sen, A. (1976). Poverty: An ordinal approach to measurement. Econometrica, 44, 219–231 Reprinted as Chapter 17 in Sen (1982). Topel, R. H. (1994). Regional labor markets and the determination of wage inequality. American Economic Review, 84, 17–22. World Bank. (2000). Making transition work for everyone: Poverty and inequality in Europe and Central Asia. Washington, DC. World Development Report 2000/2001: Attacking Poverty (2000). World Bank and Oxford University Press. Zheng, B. (1997). Aggregate poverty measures. Journal of Economic Surveys, 11, 123–162. Zheng, B. (2000a). Poverty orderings. Journal of Economic Surveys, 14, 427–466. Zheng, B. (2000b). Minimum distribution-sensitivity, poverty aversion and poverty orderings. Journal of Economic Theory, 95, 116–137.

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APPENDIX Table A1. Year

1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1978 1977 1976 1975

Poverty Rates in the US, 1975–1998.

Whole Population

Population Aged 65+

% with income below 50% of poverty line

% with income below 75% of poverty line

% with income below poverty line

% with income below 50% of poverty line

% with income below 75% of poverty line

% with income below poverty line

0.051 0.054 0.054 0.053 0.059 0.062 0.061 0.056 0.052 0.049 0.052 0.052 0.053 0.052 0.055 0.059 0.056 0.049 0.044 0.038 0.036 0.035 0.033 0.037

0.085 0.090 0.093 0.093 0.101 0.105 0.102 0.097 0.091 0.084 0.088 0.090 0.094 0.094 0.097 0.102 0.101 0.091 0.083 0.073 0.069 0.070 0.070 0.073

0.127 0.133 0.137 0.138 0.145 0.151 0.148 0.142 0.135 0.128 0.130 0.134 0.140 0.136 0.144 0.152 0.150 0.140 0.130 0.117 0.114 0.116 0.118 0.123

0.023 0.022 0.021 0.019 0.025 0.024 0.023 0.022 0.021 0.020 0.019 0.019 0.021 0.020 0.017 0.022 0.025 0.020 0.021 0.024 0.017 0.017 0.019 0.020

0.047 0.046 0.049 0.047 0.056 0.056 0.056 0.052 0.052 0.046 0.047 0.053 0.047 0.050 0.046 0.053 0.060 0.063 0.063 0.066 0.053 0.054 0.058 0.057

0.105 0.105 0.108 0.105 0.117 0.122 0.129 0.124 0.122 0.114 0.120 0.125 0.124 0.126 0.124 0.138 0.146 0.153 0.157 0.152 0.140 0.141 0.150 0.153

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Table A2.

Poverty Aversion, US (Whole Population).

Year

g0.02

g0.04

g0.06

g0.08

g0.10

1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1978 1977 1976 1975

0.00006 0.00006 0.00006 0.00006 0.00005 0.00005 0.00005 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00005 0.00006 0.00006 0.00007 0.00007 0.00008 0.00008 0.00008 0.00007

0.00012 0.00011 0.00011 0.00011 0.00010 0.00010 0.00010 0.00010 0.00011 0.00012 0.00011 0.00011 0.00011 0.00011 0.00011 0.00010 0.00010 0.00011 0.00012 0.00014 0.00014 0.00014 0.00014 0.00014

0.00016 0.00015 0.00015 0.00015 0.00014 0.00014 0.00014 0.00015 0.00015 0.00016 0.00016 0.00016 0.00015 0.00015 0.00015 0.00014 0.00014 0.00016 0.00017 0.00019 0.00019 0.00019 0.00020 0.00019

0.00020 0.00019 0.00019 0.00019 0.00018 0.00017 0.00018 0.00018 0.00019 0.00020 0.00020 0.00019 0.00019 0.00019 0.00018 0.00018 0.00018 0.00020 0.00021 0.00023 0.00024 0.00024 0.00024 0.00023

0.000230 0.000230 0.000220 0.000220 0.000210 0.000200 0.000210 0.000220 0.000230 0.000240 0.000230 0.000230 0.000220 0.000230 0.000220 0.000210 0.000210 0.000230 0.000250 0.000270 0.000280 0.000280 0.000280 0.000270

Table A3.

Poverty Aversion, US (Population Aged 65+).

Year

g0.02

g0.04

g0.06

g0.08

g0.10

1998 1997 1996 1995 1994 1993 1992

0.00011 0.00011 0.00011 0.00011 0.00010 0.00010 0.00010

0.00019 0.00020 0.00019 0.00020 0.00017 0.00017 0.00017

0.00026 0.00026 0.00026 0.00027 0.00024 0.00024 0.00024

0.00032 0.00032 0.00032 0.00033 0.00029 0.00029 0.00029

0.00037 0.00037 0.00037 0.00038 0.00034 0.00034 0.00034

Changing Poverty or Changing Poverty Aversion?

265

Table A3. (Continued ) Year

g0.02

g0.04

g0.06

g0.08

g0.10

1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1978 1977 1976 1975

0.00010 0.00010 0.00011 0.00011 0.00010 0.00010 0.00010 0.00011 0.00010 0.00009 0.00009 0.00009 0.00008 0.00010 0.00010 0.00009 0.00009

0.00018 0.00018 0.00020 0.00019 0.00019 0.00019 0.00019 0.00020 0.00017 0.00016 0.00016 0.00016 0.00016 0.00018 0.00018 0.00017 0.00017

0.00025 0.00025 0.00027 0.00026 0.00025 0.00026 0.00025 0.00027 0.00024 0.00022 0.00023 0.00022 0.00022 0.00025 0.00025 0.00024 0.00023

0.00030 0.00031 0.00033 0.00032 0.00031 0.00031 0.00031 0.00033 0.00030 0.00027 0.00028 0.00028 0.00027 0.00031 0.00031 0.00029 0.00029

0.00035 0.00036 0.00038 0.00038 0.00036 0.00036 0.00036 0.00038 0.00034 0.00032 0.00033 0.00032 0.00031 0.00036 0.00036 0.00034 0.00034

Table A4. Country

Bangladesh Bolivia Brazil Burkina Faso Chile China Colombia Costa Rica Cote d’lvoire Dominican Republic Ecuador Egypt, Arab Rep. El Salvador Estonia Ethiopia

International Poverty Rates. Year

1996 1990 1997 1994 1994 1998 1996 1996 1995 1996 1995 1991 1996 1995 1995

% With Income Below $1/Day

% With Income Below $2/Day

0.291 0.113 0.051 0.612 0.042 0.185 0.110 0.096 0.123 0.032 0.202 0.031 0.253 0.049 0.313

0.778 0.386 0.174 0.858 0.203 0.537 0.287 0.263 0.494 0.160 0.523 0.527 0.519 0.177 0.764

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DANIEL L. MILLIMET ET AL.

Table A4. (Continued ) Country

Guatemala Honduras India Indonesia Jamaica Kazakhstan Kenya Lesotho Madagascar Mali Mauritania Mexico Moldova Mongolia Nepal Niger Nigeria Pakistan Panama Paraguay Peru Poland Romania Russian Federation Rwanda Senegal Sierra Leone South Africa Sri Lanka Tanzania Turkmenistan Uganda Venezuela Yemen, Rep. Zambia Zimbabwe

Year

% With Income Below $1/Day

% With Income Below $2/Day

1989 1996 1997 1999 1996 1996 1994 1993 1993 1994 1995 1995 1992 1995 1995 1995 1997 1996 1997 1995 1996 1993 1994 1998 1983–5 1995 1989 1993 1995 1993 1993 1992 1993 1998 1996 1990–1

0.398 0.405 0.442 0.152 0.032 0.015 0.265 0.431 0.602 0.728 0.038 0.179 0.073 0.139 0.377 0.614 0.702 0.310 0.103 0.194 0.155 0.054 0.028 0.071 0.357 0.263 0.570 0.115 0.066 0.199 0.209 0.367 0.147 0.051 0.726 0.360

0.643 0.688 0.862 0.661 0.252 0.153 0.623 0.657 0.888 0.906 0.221 0.425 0.319 0.500 0.825 0.853 0.908 0.847 0.251 0.385 0.414 0.105 0.275 0.251 0.846 0.678 0.745 0.358 0.454 0.597 0.590 0.772 0.364 0.355 0.917 0.642

Changing Poverty or Changing Poverty Aversion?

Table A5. Country Bangladesh Bolivia Brazil Burkina Faso Chile China Colombia Costa Rica Cote d’lvoire Dominican Republic Ecuador Egypt, Arab Rep. El Salvador Estonia Ethiopia Guatemala Honduras India Indonesia Jamaica Kazakhstan Kenya Lesotho Madagascar Mali Mauritania Mexico Moldova Mongolia Nepal Niger Nigeria Pakistan Panama Paraguay Peru

267

International Poverty Aversion. g0.02

g0.04

g0.06

g0.08

g0.10

0.02893 0.06320 0.13477 0.01896 0.13089 0.04305 0.07550 0.08378 0.05264 0.16504 0.04211 0.06643 0.03811 0.13540 0.02830 0.02729 0.02624 0.02258 0.04063 0.12049 0.20223 0.03399 0.02587 0.01887 0.01673 0.12717 0.04959 0.08259 0.05009 0.02495 0.01897 0.01709 0.02685 0.08329 0.05013 0.05357

0.05692 0.12239 0.25231 0.03744 0.24701 0.08412 0.14488 0.16019 0.10262 0.30732 0.08225 0.13004 0.07448 0.25368 0.05568 0.05363 0.05161 0.04454 0.07971 0.23002 0.37675 0.06666 0.05087 0.03728 0.03308 0.24109 0.09641 0.15894 0.09767 0.04916 0.03745 0.03378 0.05291 0.15904 0.09728 0.10402

0.08405 0.17802 0.35621 0.05545 0.35104 0.12336 0.20900 0.23032 0.15016 0.43179 0.12059 0.19104 0.10927 0.35838 0.08221 0.07907 0.07616 0.06591 0.11732 0.33018 0.52936 0.09809 0.07505 0.05523 0.04905 0.34397 0.14072 0.22981 0.14297 0.07268 0.05547 0.05009 0.07821 0.22843 0.14177 0.15166

0.11034 0.23044 0.44911 0.07303 0.44503 0.16092 0.26855 0.29508 0.19547 0.54204 0.15726 0.24958 0.14260 0.45207 0.10791 0.10367 0.09994 0.08670 0.15357 0.42224 0.66432 0.12837 0.09846 0.07274 0.06466 0.43753 0.18277 0.29587 0.18618 0.09553 0.07305 0.06603 0.10279 0.29239 0.18386 0.19678

0.13585 0.27998 0.53297 0.09019 0.53058 0.19693 0.32409 0.35517 0.23873 0.64072 0.19241 0.30584 0.17458 0.53669 0.13285 0.12749 0.12299 0.10697 0.18854 0.50727 0.78484 0.15757 0.12114 0.08985 0.07994 0.52315 0.22276 0.35766 0.22745 0.11775 0.09021 0.08161 0.12669 0.35165 0.22379 0.23961

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DANIEL L. MILLIMET ET AL.

Table A5. (Continued ) Country Poland Romania Russian Federation Rwanda Senegal Sierra Leone South Africa Sri Lanka Tanzania Turkmenistan Uganda Venezuela Yemen, Rep. Zambia Zimbabwe

g0.02

g0.04

g0.06

g0.08

g0.10

0.16841 0.11561 0.09670 0.02526 0.03260 0.02091 0.06562 0.06637 0.03933 0.03882 0.02613 0.05872 0.08446 0.01669 0.02882

0.30672 0.22169 0.18436 0.04978 0.06401 0.04122 0.12681 0.12918 0.07702 0.07601 0.05145 0.11362 0.16323 0.03298 0.05661

0.42376 0.31950 0.26440 0.07360 0.09430 0.06097 0.18409 0.18875 0.11319 0.11169 0.07600 0.16514 0.23694 0.04891 0.08342

0.52502 0.41005 0.33792 0.09676 0.12356 0.08017 0.23788 0.24534 0.14794 0.14596 0.09981 0.21365 0.30611 0.06449 0.10933

0.61415 0.49421 0.40583 0.11928 0.15183 0.09888 0.28855 0.29921 0.18137 0.17893 0.12294 0.25946 0.37121 0.07973 0.13439

A GENDER-FOCUSED MACRO-MICRO ANALYSIS OF THE POVERTY IMPACTS OF TRADE LIBERALIZATION IN SOUTH AFRICA$ John Cockburn, Ismael Fofana, Bernard Decaluwe, Ramos Mabugu and Margaret Chitiga ABSTRACT Despite the general presumption in favor of trade liberalization, the question of how to implement it in a way to ensure equitable income distribution and sustainable poverty alleviation in developing countries is at the core of the current trade debate. We build a macroeconomic framework that integrates both market and non-market activities, while distinguishing male and female workers throughout, in order to evaluate impacts of tariffs elimination on men and women in South Africa. Our

$

This work emanates from the medium-term sub-programme (2001–2005) being implemented by the African Centre for Gender and Development (ACGD) of the United Nations Economic Commission for Africa (ECA). This work also benefited from funding from the Poverty and Economic Policy (PEP) Research Network, financed by the International Development Research Centre (IDRC).

Equity Research on Economic Inequality, Volume 15, 269–305 r 2007 Published by Elsevier Ltd. ISSN: 1049-2585/doi:10.1016/S1049-2585(07)15011-0

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study reveals a strong gender bias against women with a decrease in their labor market participation, while men participate more in the market economy. This strong result is due to the fact that female workers are concentrated in contracting sectors that were initially among the protected sectors and that benefit little from the fall in input prices. In contrast, male workers are more concentrated in the expanding exportintensive sectors. Female labor market participation drops particularly for Black African women, as they are more concentrated in contracting sectors. As male labor market participation and real wages increase more than for their female counterparts, their income share increases within the household. Women continue to suffer nonetheless from a heavy time use burden given their increased domestic work with trade liberalization.

1. INTRODUCTION Over the past decade, developing countries especially in Sub-Saharan Africa have committed themselves to meeting targets in various international and bilateral agreements including the millennium development goals (MDGs). Many countries have implemented policy reforms aimed at achieving these goals. These policy reforms, including trade liberalization, will have significant repercussions on the economy of these countries and on income distribution and poverty reduction. Although the principal argument in favor of openness to trade has been the benefit brought to all nations, its partisans recognize that it creates winners and losers in all countries. The problem of the distribution of gains from trade in the developing countries, where national income is already unequally distributed, is at the core of the current trade debate. Gender poverty and inequality has become an important issue in developing countries. Many studies show that, compared to men, women are more vulnerable to chronic poverty because of gender inequalities in the distribution of income, access to productive inputs such as credit, asset management and labor market conditions. Several other studies have focused on a variety of gender issues, including the impact of trade liberalization on gender inequalities. Most of these studies1 note a significant increase in female labor market participation during the last decade, corresponding to the period of liberalization in the majority of the developing countries. The feminization of work in export sectors was found to be stronger in the industrial sector and semi-industrialized economies, than in agricultural sectors economies. In semi-industrialized countries,

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some reservations have been expressed about the welfare impacts, mostly concerning the conditions under which female work grows. In agricultural economies, many studies2 mention that market opportunities benefit men more than women, because of the difficulties for women to access productive assets (loans, land, new technologies, knowledge, etc.). Recently, gendered macroeconomic models3 have been used to analyze the economy-wide impact of trade liberalization on male and female welfare. These studies conclude that trade liberalization expands female work and income more than their male counterparts in the economies analyzed. Although, the expansion of female market work is seen as enhancing their negotiating power within the household, it could constitute for them a burden if there is not an equivalent reduction in their domestic work. Its perverse effects on female leisure and domestic work leave some skeptical of its benefits for women, children and other household members. Fiscal policy is a key policy instrument in influencing men and women’s welfare and their prospects for economic empowerment. It can contribute to narrowing or widening gender gaps in time use, incomes, health, education, nutrition, etc. There is also increasing concern about how gender inequality can constrain the outcomes of macroeconomic policy. Recent studies4 show that economic reforms with decreased incentives can reduce women’s output or restrict access to education, and thus hinder women’s ability to develop their human resources. They also observe that ignoring household nonmarket work may affect macroeconomic outcomes by constraining labor mobility and the supply response, as well as affecting the demand for close market substitutes to home produced commodities.5 Therefore, interactions between male and female work on the one hand, and market and non-market activities on the other hand, may play key roles in policy impact analysis. Therefore, the analysis of the impact of trade reform policy on income distribution and poverty reduction in South Africa, and its differentiated impacts on women and men is of crucial importance. Conventional economics and most economic statistics ignore the enormous volume of unpaid work and the undeniably valuable output of services by the household or ‘‘care’’ economy. Households devote a large proportion of their time to produce ‘‘home’’ commodities, which can neither be purchased nor sold on the market and which, therefore, are consumed entirely by the household themselves. Although, many of these commodities have their equivalents in the market economy, economics is generally blind to the unpaid work and production of women (and men) within households. Advances in economic theory have stressed that important productive activities occur within the household, and that more attention should be

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devoted to distinguishing domestic work activities from leisure activities, as it is not likely that home production and leisure activities will be affected in the same way by changes in technology, wage rates or socioeconomic variables. Although these gender-related development issues have prompted serious debate, the absence of appropriate gender-focused macroeconomic analytical tools has prevented quantitative analysis. A related constraint is the inadequate data and statistical indicators for effective gender-sensitive policy-making, monitoring and evaluation.6 We address this deficiency by developing a gender-focused Computable General Equilibrium (CGE) for the South African economy that distinguishes male and female workers throughout, as well as breaking down market and non-market activities. This approach allows us to evaluate impacts of trade liberalization on male and female time allocation between work (at the market and at home) and leisure, as well as on household welfare. CGE models are powerful tools to capture, in a general equilibrium framework, all direct and indirect effects of macroeconomic shocks (wherever the shock occurs in the economy) on sectoral production and factor demands.

2. OVERVIEW OF SOUTH AFRICAN CHARACTERISTICS AND POLICY ON TRADE, POVERTY AND GENDER ISSUES 2.1. International Trade South Africa was reintegrated into the world economy following a credible transition to democracy symbolized by the elections in 1994. The new South African government immediately adopted the Reconstruction and Development Programme (RDP), which set the broad framework of the new government’s economic and social policy. This was followed in 1996 by the launching of the Growth, Employment and Redistribution (GEAR) programme, which defined policy instruments and objectives for the five years until 2001. The pace of trade liberalization quickened after South Africa became a signatory to the Marrakech Agreement. Initial progress in rationalizing the very complex tariff regime and lowering the overall level of nominal and effective protection was relatively fast. Between 1990 and 1999, the number of tariff lines was reduced from 12,500 in 200 tariff bands to

Gender-Focused Macro-Micro Analysis

Table 1.

Number of lines Number of bands Minimum rate (%) Maximum rate (%) Unweighted mean rate (%) Standard deviation (%) Coefficient of variation (%)

273

Reform of South African Tariffs. All Rates (1990)

All Rates (1996)

All Rates (1999)

Positive Rates (1999)

12500 200 0 1389 27.5 n.a. 159.8

8250 49 0 61 9.5 n.a. 134.0

7743 47 0 55 7.1 10.0 140.3

2463 45 1 55 16.5 8.6 52.2

Source: Lewis (2001).

7,743 in only 47 tariff bands. In fact, if the numerous cases of zero tariffs are ignored, the number of tariff lines had been reduced to fewer than 2,500 by 1999. At the same time, the maximum existing tariff has been reduced from almost 1,400 to 55 percent and the average economy-wide tariff fell from 28 to 7.1 percent (Table 1). The aggregate response of trade to liberalization has been quite dramatic. The average annual growth rate of the trade ratio, as measured by the sum of export and import values to GDP (in current prices), was 5.5 percent between 1993 and 1996, 0.8 percent between 1997 and 1999 and 9.8 percent between 2000 and 2002 (Davies & van Seventer, 2003). Closer inspection shows that the trade ratio started to grow in 1992, perhaps reflecting the post-apartheid reintegration. The slowdown in 1997–1999 was probably related to the Asian crisis, but may also reflect the ending of the initial impetus provided by the ending of apartheid. The acceleration after 1999 likely reflects both world recovery and domestic liberalization policies starting to make an impact. A broad look at the performance of exports in the apartheid, transition and liberalized periods suggests that the reforms may have stimulated export growth. During the pre-democracy period (1981–1990), the value of exports declined by an average of 2.6 percent. Between 1991 and 1996, export growth averaged 6.4 percent per year. During the liberalized period (1997–2002), exports grew by only 3.7 percent per annum. However, this latter figure masks a sharp downturn in the mining sector in recent years. As to the composition of exports, the share of manufacturing products increased from 41.2 percent in 1991–1996 to 53.3 percent in 1997–2001, while the share of mining diminished from 42.3 percent in 1991–1996 to 26.9 percent in 1997–2001. Gold, the main South African export, still accounted

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for more than 20 percent of total exports in 1997–2001, down from more than 35 percent in 1991–1996 (TIPS, 2002). The performance of imports in the transition and liberalized periods suggests that the reforms may have also stimulated import growth, albeit marginally. TIPS (2002) shows that imports grew by an average of 11.7 percent in the transition period between 1991 and 1996, but grew by only 0.1 percent between 1997 and 2001. The relatively low growth in the latter years is puzzling given that tariffs were falling in this period, although GDP growth was muted. Imports, just as exports, are dominated by manufactured and mining products, accounting for over 86 percent of imports over the two periods. In terms of trade competitiveness, South Africa has on average experienced a 50 percent decline in terms of trade over the two periods, with the exclusion of gold (Ndlela & Nkala, 2003). Although the terms of trade inclusive of gold have increased by about 20 percent during the same period, the overall decline in the terms of trade reflects a critical weakness in the structure of the country’s trade composition. Like many developing countries, a large proportion of exports consist of unprocessed raw materials with, in the case of South Africa, the mining industry contributing the greatest proportion to the country’s total exports. The proportion of manufactured goods in exports has however experienced a significant rise, with a higher proportion of raw materials being processed before export. Major export commodities are gold, diamonds, platinum, wool, sugar, manganese and chrome ores, asbestos, atomic energy materials and base minerals such as coal, antimony, copper and iron ore. Exports of chemicals, metal products, machinery, transport equipment and manufactured goods have increased, particularly to Africa, in recent years.

2.2. Income Distribution and Poverty South Africa has one of the worst income distributions in the world. The Gini coefficient, which measures the degree of income inequality, was 0.56 in 1995 and 0.57 in 2000, implying that the income distribution has also been getting worse across the country. In addition, the Gini coefficient not only takes high values for the country as a whole, but also for individual population categories, suggesting a high degree of inequality within each major ethnic group. The Gini coefficient is higher for Africans than for Whites. More significantly, according to ILO (1999), income distribution within population groups worsened between 1990 and 1995 while inequality decreased between groups. This may reflect the fact that the end

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of apartheid-based discrimination has created new employment opportunities for highly skilled Africans. Income is also unevenly distributed among rural and urban areas. There is general agreement that poverty has grown worse since liberalization. The World Bank (1999) notes that extreme poverty is concentrated mainly in rural areas, where over 75 percent of the households cannot meet their minimum food requirements. In urban areas poverty is much less acute, with only about 10 percent of the households below the poverty line. The same study argues that poverty has a strong gender dimension, showing that female-headed households have a 50 percent higher poverty rate than male-headed households. In addition, unemployment figures have shown that females suffer more from unemployment than males. Although no concrete evidence is available, there is a general consensus that this pattern has persisted over time. The UNDP (2000) gives the rate of poverty as 45 percent. This is despite the fact that South Africa is classified as an upper middle-income country. Poverty differs greatly by region and by race, with the majority of the poor being Black Africans. According to Klasen and Woolard (1998), there is a strong correlation between unemployment and poverty. They estimate that the unemployment rate among the 20 percent poorest households is 53 percent compared to 4 percent in the case of the richest 20 percent households. The problem is not restricted to persons with low levels of formal education. Although education reduces the likelihood of unemployment, rates are extremely high amongst African women, irrespective of whether or not they have completed secondary education. It should be noted, however, that significant differences exist in the quality of education that has been provided to different population groups. This is a legacy of deliberate discrimination under the apartheid system. Only tertiary education seems to substantially reduce the risk of unemployment for both men and women.

2.3. Gender in the South African Economy Male and female time allocation is presented in Fig. 1. At the national level, men are more active in the labor market than women, contributing roughly 60 percent of total market labor. Women, meanwhile, perform more than 75 percent of domestic unpaid work. Looking at employment in formal versus informal sectors, we note that, in broad terms, women are concentrated in informal services and trade. In 1995, 33 percent of economically active African women were own account

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100% 80% 60%

Female

40%

Male

20% 0% Market work

Fig. 1.

Domestic work

Leisure

Gender Time Allocation in 2000. Source: Statistics South Africa (2001b).

workers compared to 6 percent of men. Women are generally concentrated within the low profit activities, generally earn less and tend to have smaller activities in the informal sector (Baden, Hasim, & Meintjes, 1998). Although in general more women than men work in the informal sector, the sectoral distribution of men and women in the informal sector as well as the occupations are very similar to the formal sector. Valodia (2000) gives more corroborating evidence validating this. A broad look at the participation of women in formal employment in the apartheid, transition and liberalized periods suggests that female participation rates have been on a general increase. Standing, Sender, and Weeks (1996) show that this trend started in the apartheid era, with female labor force participation increasing from 23 percent to 41 percent between 1960 and 1991. According to the World Bank (2002), female labor force as a percentage of total labor force has moved from 37 percent in 1990 to 38 percent in 2000. According to Casale and Posel (2002), the post-apartheid period from 1995 to 1999 witnessed a continued feminization of the labor force in South Africa. In 1995, 38 percent of all females between the ages of 15 and 65 were either working or actively looking for work. By 1999, this had increased to 47 percent. A gender segregated labor market in South Africa may be explained by discrimination against women in education and training during the apartheid period. However, post-apartheid primary and secondary enrolment and literacy rates suggest a dramatic improvement in these indicators for women (World Bank, 2004). Men and women tend to work in different sectors. Some sectors are male-intensive (i.e. mining, food, beverage and tobacco, heavy manufacturing and construction), while others are female-intensive (i.e. textile, private services). Women are engaged primarily in tertiary

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activities, while men are spread throughout primary and secondary sectors. This trend between men and women has not changed much, as seen in the 2001 census data represented in Fig. 2. As shown in Table 2, unemployment rates for women are much higher than for men. This is true for all population groups, especially in urban areas where unemployment was estimated at over 28 percent for women, compared to 24.1 percent for men. Higher female unemployment may be explained, inter alia, by lower education and literacy rates. In situations of declining demand during the liberalized and deflationary period, women were pushed into the informal sector. Overall, the post-apartheid period and increased globalization have been associated with higher female participation rates in the labor force. However, we notice that the feminization of the labor force is accompanied by an increase in female unemployment. Where employment has grown, this seems to have been mostly in self-employment in the informal sector. Accordingly, given that there has been no appreciable increase in the demand for female labor in the formal sector, these findings may reflect an increasing number of women who are ‘‘pushed’’ into the labor market (Casale & Posel, 2002). Data on earnings distribution by gender in the apartheid period are sparse but are generally thought to confirm discrimination along racial lines. Fallon and Lucas (1998) find that, while education and experience are important determinants of earnings, other factors such as discrimination by race and gender and barriers to mobility (i.e. geographic location and formal/informal economic activity) are associated with larger differentials than usually found in studies for other countries. In a recent study, Rospabe (2002) shows that Black Africans earn the lowest incomes, followed by Coloureds and Indians, while Whites have the highest earnings. According to the 1997 October Household Survey, African workers earned, on average, 63 percent less than White workers. As later surveys have shown, this racial wage gap, though still significant, is smaller in community, social and personal services than in other sectors. The gap has tended to narrow in the long run, though data should be interpreted with caution due to methodological changes (see Hofmeyr, 1993; Crankshaw, 1997). According to ILO (1999), during the last few years the gap seems to have remained unchanged. The continuing increase of the relative wages of African workers in community services may be due to policy changes in the public sector after the end of apartheid. The same narrowing in the globalized era has not been perceived in the gender wage gaps from available anecdotal evidence. There is a growing literature showing gender differences are also seen in terms of earnings.

Fig. 2.

Land transport

Membership organisations

Undetermined

Private households

foreign governments

Exterritorial orgs

Other service

Sports, culture, recreational

Male

community; social, personal

Male

Health, social work

Education

Administration, defence

Other business

Research, devlpt

Computers

Rent machinery

Real estate

Auxiliary finance

Insurance, Pensin

Financial

Post, telecomm

Transport sppt

Air transport

Water transport

ric ul Fo ture re st Fi ry Pe M shin tro ine g le um coa & l M Min ga in s e e m Go O eta ld th l Fo M er m ore Te od ine ini s xt ; B S ng ile ev er , c , T vic lo o e th ba ,l c ea o Fo the M ot r nf w ct ea r, r F M uel M ine ; n r M fr. al M n. e me nf le ta r. c l M ele tric nf ct al r. ro M tran nic; nf sp El r. f or ec ur t tri nit ci ur ty e ;g a C W s; on a te s W tru r /s ct al io R e, t n Sa eta rad H le il tr e ot el veh ade , r ic es le ta s; ur an t

Ag

278 JOHN COCKBURN ET AL.

100% Female

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

100% Female

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

Employment by Sector and Gender. Source: Calculation from the 2001 Census.

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Table 2. Unemployment (Official Definition) by Race and Gender (2001). Population Group and Area

Unemployed Rate (%) Male

Female

All population groups Urban Non-urban

24.8 24.1 26.4

28.0 28.6 26.9

African Urban Non-urban

30.0 31.0 28.6

32.3 35.7 27.9

Colored Urban Non-urban

21.1 23.9 8.8

22.8 23.7 17.1

Indian/Asian Urban Non-urban

13.9 13.5 31.4

23.0 22.9 30.1

White Urban Non-urban

5.6 5.7 4.9

7.8 8.0 5.4

Source: Statistics South Africa (2001a).

According to Fig. 3, there are substantial monthly earning differentials in favor of men. Women are estimated to earn 65–95 percent less than men in formal sector employment (Valodia, 1996). Using the October household survey for 1999, Rospabe (2002) shows that the cumulative earnings distribution of female workers is first order dominated by the distribution of income for male workers. Further, it was found that women’s earnings were more severely affected in manufacturing than in other sectors, with women’s earnings equal to 73 percent of men’s in metropolitan areas. This is mainly because of the lower positions of women (Pillay, 1993 cited in Budlender, 1995). Budlender (1997) also found that, even for those with the same qualification, there was substantial discrimination in earnings between men and women. Rospabe (2002) estimated the average earnings gap between males and females to be about 20 percent. These differences are attributed to differences in productivity between the two genders and to labor market discrimination against women (Rospabe, 2002).

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Men

Women

14000 12000 10000 8000 6000 4000 2000 0 Formal White

Fig. 3.

Formal urban (African)

Informal urban (African)

Informal non-urban (African)

Domestic (urban) (African)

Domestic (non-urban) (African)

Agricultural (formal) (African)

Agricultural (informal) (African)

Mean Monthly Income by Gender (1999). Source: Statistics South Africa (1999). Market work

Domestic work

Personal care

Extra-leisure time

100% 80% 60% 40% 20% 0% Male

Female

African

Fig. 4.

Male

Female

Coloured

Male

Female

Indian

Male

Female White

Male

Female All

Household and Gender Time Allocation.

The 2000 South African survey of time use shows that men have more market labor and leisure time. Women do more of the work of rearing and caring for children, caring for other household members, cooking and cleaning (Fig. 4).

3. BUILDING A GENDER-FOCUSED INTEGRATED MACRO-MICRO MODEL Our gender-focused integrated micro-macro model is constructed in three steps. First, we prepare an accounting framework that brings together

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market and non-market activities using macro- and microeconomic datasets for South Africa. Then, we incorporate into a standard CGE model labor market segmentation between male and female workers. These are considered as different factors of production in the same way workers are differentiated according to skill or geographical location in other contexts. Finally, we introduce non-market activities and leisure time into the model with the recognition that women are more likely to perform household work, while men are more active in the labor market and have more leisure time.

3.1. Building a Gender-Focused Social Accounting Matrix with Household-Level Data A CGE model is generally built on the basis of a social accounting matrix (SAM). A gender-focused SAM further distinguishes labor factors by gender. Integrating real households from a representative survey of the population requires vectors of household income and expenditures, as well as data on their market and non-market time allocation. In this process, we use both macro- and microlevel datasets, which we reconcile in a single framework. Fig. 5 illustrates the procedure used in building a gender-focused SAM with household-level data on income, expenditures and the allocation of time to various activities. We first bring together the Supply and Use Tables (SUT) and the integrated economic accounts (IEA), both for year 2000, in a single framework: a standard SAM (step one). Then, household-level data on income and expenditure as well as male and female market work, are computed from household surveys, i.e. the Income and Expenditure Survey (IES) and the September Labor Force Survey7 (LFS), once again both for year 2000 (step two). We then reconcile these household-level data and the standard SAM to generate a gender-disaggregate SAM (step three). Fourth, the time use survey (TUS) for year 2000 is combined with household income and expenditure data, and individual market work data, to impute time spent by individuals in non-market activities, i.e. domestic work, leisure and personal care activities (step four). Fifth, household non-market work, leisure and personal care time are incorporated into the gender-disaggregate SAM to generate a gender-focused SAM (step five). The concept of a National Satellite Account of Household Production (NSAHP) is used to incorporate non-market activities (household production of services and leisure activities) into the standard SAM as recommended by the 1993

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Integrated Economic Accounts for 2000

Supply and Use Tables for 2000 Step 1

Income and Expenditure Survey for 2000

Labor Force Survey for 2000

Step 2

Standard Social Accounting Matrix for 2000 Gender Disaggregated Data on Household Income + Expenditure + Market

Step 3

Gender-Disaggregate Social Accounting Matrix for 2000

Step 4

NSAHP=Non-SNA Prod + SNA Prod + Leisure =GHP

Step 5

Extended Gender-Aware Social Accounting Matrix with NSAHP for 2000

Fig. 5.

Time Use Survey for 2000

Step 6

Gender-Aware CGE Micro Simulation Model Integrated approach

From NSAHP to a Gender-Focused CGE Microsimulation Model.

System of National Accounts of the United Nations. The sixth and final stage is to distinguish each individual household within the SAM in order to obtain a gender-focused SAM with real households. In this procedure, time spent by individuals on non-market work and leisure activities is converted into monetary value by assigning a price. The opportunity cost approach is used to impute a unitary value to the time spent by individuals on various non-market activities. This price is approximated to the ‘‘expected’’ wage rate that an individual would have received if he or she had sold his/her time (or labor services) to the market rather than performing non-market activities. The expected wage rate is predicted for each individual in the household based on individual characteristics (age, gender, etc.). The estimated value of non-market labor is used as an indicator of the value of household production. Therefore, home-produced goods ‘‘directly’’ require neither capital nor inputs by assumption. Substitution and complementarity between durable and non-durable goods in the home production of services are ‘‘indirectly’’ integrated in the consumption decisions of households.

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3.2. The Gender-Focused Integrated Macro-Micro Model This study uses a CGE model based on the neoclassical-structuralist specification presented in Decaluwe, Martens, and Savard (2001). The model seeks to explain production, consumption and prices in an economy in which consumers and producers respond to relative prices based on welfare and profit maximizing consumption and production behavior, and markets simultaneously adjust relative prices in order to clear markets. Though, most of the equations have strong microeconomic foundations, the conceptualization of the economy also allows a strict macroeconomic analysis such that the behavior of agents is consistent with macroeconomic constraints. The model incorporates additional features of particular interest for developing countries. The model explicitly treats trade and transportation margins for commodities that enter the market sphere. A constant trade and transportation margins coefficient is added to each transaction, included in the price, and the corresponding revenues generated are a source of demand for the trade and transportation sector. Labor markets have been treated to reflect empirical evidence in developing countries and South African specificities. Initially, there are eight categories of workers distinguished by their residential area (urban and rural), age (child and adult) and skill categories in the case of adult workers (high, medium and low). The model explicitly treats unemployment as a consequence of labor market imperfections in South Africa. Most standard CGE models make the implicit assumption that male and female workers are perfect substitutes in market production and thus do not distinguish them. However, many studies underline the fact that there is segmentation in the labor market between men and women, and different levels of market work flexibility according to the domestic tasks they perform. Also, it is observed that male and female workers tend to concentrate in different sectors and occupations, which further undermines the hypothesis of perfect substitutability. Finally, it is widely recognized that there is often a gender bias against women in the labor market in term of wage earnings and job opportunities. Indeed, the 2002 report on men and women in South African shows that the unemployment rate is higher for women than for men within each population group, and in both urban and rural areas. Formal sector work is far more common for men than for women. Employed women tend to cluster into a small number of industries compared to men; and women are significantly more likely than men to be employed in clerical jobs while men are primarily employed as operators.

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Mean hourly earnings are higher for men than women across all population groups. Therefore, the first step of the modeling exercise will consist in the segmentation of the labor market into male and female workers to highlight the gender bias observed in the South African economy. fem Therefore, male labor (LDmal i ) and female labor (LDi ) are imperfect substitutes in the aggregate sector i labor demand (LDi ). The conditional demand of male and female labor depends on initial sectoral shares, wage rates and their degree of substitution in sectoral production. fem LDi ¼ f ðLDmal i ; LDi Þ

The gross earnings of male and female workers are equal to the volume of labor services demanded by productive sectors valued at market wage rates. Household labor income (Yh) consists of male and female wage incomes. Assuming labor market imperfections and the presence of unemployment, only a proportion of the total hours supplied by households to the labor market is hired. LSh is household h labor supply, w and u the rate of wage and the rate of unemployment, respectively. fem mal Y h ¼ f ðLSmal ; wfem ; umal ; ufem Þ h ; LSh ; w

We introduce non-market activities into the model with the recognition that women are more likely to perform household work while men are more active in the labor market and have more leisure time. Furthermore, modeling non-market activities alongside market activities makes it possible to assess (i) the importance of household production of services which are intensive in female work. These services, which are not sold in the market and therefore entirely consumed by the household, enter in competition with their market substitutes,8 (ii) the impact of constraints faced by women at the household level (because of their involvement in family tasks) that may negatively affect their labor market participation and the performance of the overall economy, (iii) the impacts on female leisure time. Increased female participation in the labor force will not necessarily improve their welfare if they still perform most of the domestic work and must therefore reduce their leisure time, and (iv) the impact on child education at the household level. If children, especially girls, are required to assume the household tasks of female adults who have entered the labor market, their education and leisure time could be negatively affected. Men and women substitute the time devoted to leisure and to the production of home goods, which are imperfect substitutes for market goods.9 fem Male (LZmal h ) and female domestic work (LZh ) are imperfect substitutes in home good production (Zh), which, by assumption, does not require either

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intermediate goods or capital.10 fem Z h ¼ f ðLZmal h ; LZh Þ

The relative demand for male and female labor in home production deand afem pends on their relative share (amal h h ) in home production, male and mal female expected wage rates (w and wfem ) and the degree of trade-off between men and women in home production represented by the elasticity of substitution11 (eh). LZmal fem mal h ¼ f ðamal ; wfem ;
h Þ h ; ah ; w LZfem h The value of home-produced goods is equal to the value of the labor devoted to their production, where non-market labor is valued at its opportunity cost as measured by the expected market wage rates. An extended linear expenditure system is specified to derive household demand for home goods subject to full income; where ‘mal and ‘fem represent h h z m male and female leisure time, respectively; C h and C h;i are home produced goods and market goods consumptions, respectively. z mal fem U h ¼ f ðC m h;i ; C h ; ‘h ; ‘ h Þ

Men and women allocate their total available time in two steps. First, the total exogenous time (hours) available for market and non-market activities are allocated to domestic activities (according to home goods production requirement and the degree of substitutability among men and women in home production), to leisure activities (the demand for male and female leisure is derived from the utility function) and to market activities as residuals. Second, the hours of labor supplied to the market is allocated between work and unemployment.12

4. SIMULATIONS AND RESULTS Our first simulation involves the elimination of all import tariffs where government revenue is held constant through the introduction of an endogenous adjustment in indirect taxes. Trade liberalization emerges as one of the key policy issues of the GEAR agenda discussed in previous sections. Although other trade barriers still exist, tariffs constitute the principal

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protectionist measure in South Africa. The removal of tariffs in South Africa modifies the entire price structure and, consequently, factor returns. The impact on households depends on their factor endowments and their consumption patterns. Trade liberalization also has differential impacts on men and women depending on the sectors in which they are intensively employed and the household to which they belong.

4.1. Trade and Output Effects The initial impact of the removal of all tariffs is a fall in the domestic price of imports that is particularly strong in the highly protected sectors. Local consumers react to the fall in import prices by increasing their imports by sector roughly in the same proportion as the fall in sectoral tariff rates. Given a fixed current account balance, the increase in imports leads to a 4.9 percent exchange rate depreciation, which partially offsets the fall in import prices in these sectors and leads to an increase in the domestic price of imports in some other sectors (see Appendix 1). Of course, this import surge comes at the expense of domestic competitors, who experience a decline in the volume and price of their sales on the local market. Given the imperfect substitution between local and imported goods (CES), as well as the relatively small initial import intensities (imports/domestic consumption), the changes here are proportionally much smaller than the variations in import volumes. Nonetheless, the sectors with the most substantial reductions in local sales are the highly protected sectors. The exchange rate depreciation also results in a 1.8 percent increase in export volume. Exports increase most in the export-intensive sectors, i.e. the sectors with the highest initial export intensity ratios (Exports/Output). These sectors are identified in italics in Appendix 1. Variations in exports and domestic sales determine changes in total output. Given their loss in domestic sales, the highly protected sectors also experience the strongest output declines. Output prices are averages of export prices, which are assumed fixed, and domestic prices, weighted by the share of sales on each of these markets. Thus, it is unsurprising that they fall strongly in most of the highly protected sectors, while they increase in sectors with initially low tariff rates. Note that these are after-tax output price variations and thus include a 13.4 percent increase in the indirect tax rate required to balance the government’s budget, whereas the import and domestic sales price variations are shown net of indirect taxes.

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4.2. Factor Effects We now examine how the trade and output effects above influence factor prices and unemployment rates, crucial components of the ultimate welfare and poverty effects. To understand these results, note that factor prices are driven by valueadded prices as the source of their remuneration. While changes in valueadded prices generally reflect output price variations, their evolution is more positive (less negative) when input costs rise less (fall more) than output prices. Thus value-added prices generally fall most among the highly protected sectors whereas they increase among sectors with low initial tariffs. However, export-oriented industries are among the sectors with the strongest increases in value-added prices. Indeed, beyond the modest increase in their output prices, these sectors benefit more from falling input costs, given the high share of their inputs that come from the initially highly protected sectors. The contrary is true for the high value-added (low input) agricultural sector, in which value-added prices fall. The rest of this table shows the shares of total income that each factor derives from each of the sectors (Appendix 2). The relationship between the wage rate and the unemployment rate is represented by a downward-sloping relation (the ‘‘wage curve’’). As a result, rising (falling) wage rates are associated with falling (rising) unemployment rates. Essentially, rising demand for certain types of labor translates into increased wages and employment, whereas falling demand has the opposite effect. Consequently, we focus our analysis here on the wage impacts with the understanding that the unemployment effects are generally the mirror image. To explain wage impacts, we refer throughout to the value-added price variations and factor intensities in Appendix 2. Whereas public sector employment and wage rates are assumed fixed, private sector workers are assumed to be mobile between sectors with wage rates that equalize across all private sectors. We note substantial differences in private sector wage and unemployment rate changes according to the gender, skills and location of workers (Table 3). Male wage rates generally evolve more favorably than female wage rates, with the exception of high-skilled urban and low-skilled rural workers. Female workers are penalized by their greater participation in garments, as well as health and social work, for which value-added prices fall (Appendix 2). In contrast, male workers benefit from their strong participation in mining activities, which offsets their dependency on agricultural wages, especially in rural areas. Among child workers, in both rural and urban South Africa, the decline in wage rates for girls can be traced primarily

288

Table 3.

Wage and Unemployment Rate Variations.

Urban High skill

Child

0.05 0.01 0.04

0.02
0.01 0.01


0.09
0.09
0.09

Change in unemployment rates Males 0.14
0.53 Females
0.10
0.10 All 0.05
0.38


0.24 0.07
0.10

0.83 0.37 0.52

Rural

Rural All

All

High skill

Medium skill

Low skill

Child

0.02 0.01 0.02


0.01
0.04
0.02

0.02
0.06 0.00


0.12
0.09
0.11


0.24
0.64
0.31


0.01
0.06
0.03

0.02 0.00 0.01


0.31
0.08
0.23

0.13 0.40 0.25


0.09 0.58 0.04

1.17 0.88 1.05

1.85 6.59 2.77

0.09 0.56 0.23


0.27
0.03
0.18

JOHN COCKBURN ET AL.

Low skill

Change in wage rates Males
0.01 Females 0.01 All
0.01

Medium skill

Urban All

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289

to their greater participation in agriculture, whereas boys diversify into a number of services sectors where prices generally rise modestly. Capital is assumed to be sector-specific because of the short-term horizon of our analysis. As a result, variations in the rates of returns to capital closely follow changes in the value-added prices of their respective sectors. These rates fall most in the highly protected sectors and increase in the expanding export-oriented sectors (Appendix 2).

4.3. Time Allocation Analysis We have already noted that men are more active in the labor market than women, whereas women are more heavily involved in domestic work. We also noted that men and women tend to work in different sectors. Most sectors are male intensive with the notable exceptions of textiles and garments and a number of service sectors. Households respond to the changes in real wage rates for male and female workers by changing their allocation of time between market and nonmarket activities. Labor market participation decisions depend on labor and non-labor income effects, which are taken at the household level. As a consequence, higher real wage rates will not necessarily induce an increase in the labor market participation of workers as labor income from other members, non-labor income and non-market activities may also play important roles. Women, especially in urban areas, increase their market participation while male market participation stagnates (Table 4). Male and female market participation in rural areas fall as their real wage rates decrease. Female market participation increases within the Black population category, because of their low endowment of high- and medium-skilled workers that win from tariff elimination in South Africa, and decrease within other household categories. Men and women work more at home, as they substitute market goods with rising prices by home produced goods. Although females already do more domestic work than men, they continue to carry out most of the domestic tasks, especially in urban areas. Their market and non-market work increase is roughly double that of men, at the expense of their pure leisure time. As a large proportion of their time spent outside market work is devoted to leisure activities rather than domestic work, men perform even less domestic work with trade liberalization, especially in urban areas and within female-headed household categories.

290

Table 4. Change in Hours Worked (Percent Variation). Market Work

Domestic Work

Urban Urban Urban Urban All Rural Rural Rural Rural All high medium low child urban high medium low child rural skill skill skill skill skill skill

All

Urban Urban Urban Urban All Rural Rural Rural Rural All All high medium low child urban high medium low child rural skill skill skill skill skill skill


0.01
0.02

0.01 0.07

0.01 0.03

0.00 0.00 0.04
0.03


0.04
0.04


0.04
0.55
0.02
0.54 0.00
0.03

0.00
0.01 0.03 0.08

0.01 0.00


0.09
0.03
0.04
0.01 0.05 0.03

0.03 0.23

0.01
0.05

0.89 0.47

0.87 1.11

0.56 0.07 0.54 0.14

Head of household Male head Male
0.01 Female 0.00


0.01
0.01

0.01
0.01 0.07
0.16

0.00
0.01 0.04
0.02


0.06
0.02


8.04
0.07

0.00
0.02 0.00
0.02

0.00
0.01 0.03 0.08

0.01
0.02


0.06 0.00
0.02
0.05
0.01
0.02

0.04 0.21

0.03
0.10

1.02 0.52

0.90 1.01

0.61 0.09 0.47 0.08

Female head Male
0.01 Female
0.01

0.00
0.02

0.09 0.04

0.04 0.09

0.03 0.04 0.04
0.11


0.03
0.05

0.00
2.85
0.03
4.66 0.00
0.07

0.02 0.02

0.04 0.09

0.01 0.01


0.17
0.08
0.10
0.06 0.05 0.10 0.08 0.30

0.00
0.02

0.69 0.42

0.83 1.19

0.47 0.04 0.60 0.20

Population group Black Male
0.01 Female 0.00

0.00
0.01

0.00 0.09

0.01 0.03

0.00 0.00 0.06
0.03


0.04
0.04


0.04
0.79

0.00
0.02 0.00
0.03

0.00 0.04

0.03 0.06


0.02
0.02


0.10
0.04
0.05
0.01 0.05 0.03

0.04 0.25

0.01
0.05

0.90 0.47

0.86 1.11

0.53 0.08 0.55 0.14

Colored Male
0.01 Female 0.00

0.00 0.00

0.02
0.02 0.04
0.13

0.00 0.00 0.02
0.08


0.04
0.01

0.00
5.76
0.04 0.00
0.14 0.00
0.06
0.02

0.04 0.00


0.02
0.11


0.08
0.02
0.04
0.01 0.03 0.06 0.05 0.15

0.01
0.04

0.91 0.35

0.87 1.01

0.57 0.10 0.26 0.13

0.00 0.00

0.00 0.00

0.00 0.00 0.00 0.00
0.02
0.02

0.08 0.00

0.02 0.00


0.07
0.03
0.03 0.00
0.02
0.02

0.00 0.10


0.05 0.00

1.03 0.00

0.84 1.15

0.68 0.09 0.54 0.07

0.00
0.03 0.00 0.11

0.01 0.10


0.09
0.02
0.03 0.05 0.04 0.05

0.04 0.23

0.11
0.24

0.86 0.45

0.94 1.20

0.68 0.04 0.73 0.10

0.44 0.00


0.06
0.04
0.01 0.00 0.00 0.00

0.02 0.00


0.01 0.00

0.51 0.00

0.87 0.00

0.42 0.04 0.00 0.00

Asian Male Female

0.00 0.00


0.02 0.00

0.01
0.01 0.00 0.00

0.00 0.02 0.00
0.02

White Male Female

0.00 0.00


0.01
0.13

0.02 0.00

0.00 0.00

0.00 0.03


0.08 0.03

0.00 0.00

0.00
0.02 0.00 0.03

Unspecified Male
0.04 Female 0.00


0.62 0.00


0.44 0.00

0.00
0.13 0.00 0.00

0.03 0.00


0.10 0.00

0.00 0.00

0.00
0.02
0.13 0.00 0.00 0.00

0.02 0.01

0.04 0.00

JOHN COCKBURN ET AL.

South Africa Male
0.01 Female 0.00

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291

4.4. Income, Consumption and Welfare Effects With the CGE microsimulation approach, we obtain income variations for each individual household, which we can then group in a variety of ways. We present results grouped according to residential area, population group and the gender of the household head. We first note that wages are the principal source of income in South Africa, followed by various forms of transfers (from other households, government, etc.), although there are substantial differences between household groups. Overall, incomes do not change significantly (see Table 5). Incomes evolve more favorably in urban than rural areas, as a consequence of rising wage rates and market participation, and the capital remuneration effects. Maleheaded households benefit from trade reform policy, whereas female-headed households suffer from a significant drop in the returns to their capital. All population groups except ‘‘White’’, which shows a stagnation in income, benefit from free trade in terms of income. The ‘‘Asian’’ population group is the big winner, as they benefit from a significant increase of the returns to their capital. In addition to its income effects, trade liberalization influences household welfare by changing consumer prices. While pre-tax prices fall both for imports and, in the face of increased import competition, domestic goods, consumer prices increase by 0.9 percent due to exchange rate depreciation and the increase in the sales tax required to offset lost tariff revenues. The required increase in the initial indirect tax rate (surtax) is quite small (13.4 percent) due to the relative small share of tariffs in government revenue and the average sale tax of 4.5 percent. However, consumption prices for agriculture goods increase less than services and manufacturing goods, as they present the smallest average tax rate. Each household is affected differently by consumer price reductions according to its consumption patterns. In this respect, we note that consumer prices increase for all household, consequently, tariff elimination on imports leads to a welfare loss in South Africa.

4.5. Poverty and Inequality Analysis The advantage of the integrated CGE microsimulation approach is its capacity to capture the heterogeneity of household income sources and consumption patterns in order to perform the between- and within-group distribution, poverty and inequality analysis. The model is used to generate

292

Table 5. South Africa

0.04
0.21 0.00 0.22 0.05 0.92
0.23

Residential Area

Head of Household

Population Group

Urban

Rural

Male head

Female head

Black

Colored

Asian

White

Unspecified

0.09
0.21 0.00 0.44 0.09 0.89
0.21


0.27
0.16 0.00
1.22
0.13 1.05
0.35

0.06
0.23 0.00 0.40 0.07 0.90
0.24


0.04 0.00 0.00
0.10
0.02 0.99
0.15

0.04 0.04 0.00 0.07 0.04 0.86
0.17

0.05 0.08 0.00 0.02 0.07 0.79
0.11

0.16 0.05 0.00 0.23 0.12 1.19
0.17

0.00
0.29 0.00 2.67 0.05 0.99
0.31

0.46 0.12 0.00 1.68 0.05 0.72
0.33

JOHN COCKBURN ET AL.

All incomes Income taxes Transfers out Savings Consumption Consumer price index EV/initial income

Household Income and Expenditure Effects (in Percent).

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293

the post-simulation data. Then these data and the base year data drawn from the income and expenditure survey are used to compute and compare standard consumption-based poverty and inequality indicators. Foster–Greene–Thorbecke (FGT) poverty indicators (i.e. headcount index, poverty gap and squared poverty gap) and the Theil inequality index are adopted. We define the poverty line as 3,864 South African rands per year in 2000 prices, a lower bound poverty line suggested by Hoogeveen and O¨zler (2004). Post-liberalization consumption data are deflated by the Laspeyres economy-wide consumer price index to account for the change in the general price level. Results presented in Table 6 suggest that the impacts of complete tariff removal on poverty are small. Poverty and inequality increase slightly. Poverty indicators increase more in rural areas than in urban areas. This is confirmed by the increasing inequality in rural areas. Poverty increase more among female-headed, colored and Black households, whereas they increase slightly or remain stable for male-headed, Asian, White and unspecified households. Our analysis until now has been at the household level. However, given our preoccupation with the gender impacts of trade liberalization, we exploit the microsimulation aspect of our analysis, including detailed information on all individuals in the sample households, to analyze poverty Table 6.

Poverty and Inequality Indexes (in Percent). Initial Values

Variation

P0

P1

P2

Theil index

P0

P1

P2

53.0

25.3

15.0

1.6

0.29

0.26

0.20

0.06

42.4 68.3

18.4 35.4

10.2 22.1

1.6 1.0

0.23 0.37

0.21 0.34

0.14 0.27


0.01 0.07

Head of household Male Female

43.6 65.8

19.5 33.4

11.1 20.5

1.6 0.8

0.19 0.43

0.22 0.32

0.15 0.26

0.03 0.03

Population group Black household Colored household Asian household White household Unspecified household

61.0 36.2 6.4 0.1 11.4

29.5 14.7 2.3 0.0 3.1

17.6 7.8 0.8 0.0 0.8

1.1 0.8 0.3 1.0 1.7

0.31 0.45 0.00 0.00 0.00

0.30 0.19 0.04 0.00 0.08

0.23 0.12 0.03 0.00 0.04

0.07 0.01 0.01 0.06
0.06

South Africa Residential area Urban Rural

Notes: P0 ¼ poverty headcount; P1 ¼ poverty gap; P2 ¼ poverty severity.

Theil index

294

JOHN COCKBURN ET AL.

and inequality impacts separately for men, women and children. Note that we do not attempt to integrate issues of intra-household allocation and simply assume that income and consumption are shared evenly. Thus, men, women and children are considered to be poor if they belong to a poor household, i.e. a household for which consumption expenditure per capita is less than the poverty line. It can be shown that these results are robust for a wide range of poverty lines. Table 7 indicates that, in South Africa, 63 percent of children and 51 percent of women are poor (live in poor households), as compared to only 44 percent of men. This hierarchy is reproduced for all household categories, with the exception of female-headed households, in which the incidence

Table 7.

Poverty Indexes by Gender and Age. Men

Women

Children

P0

P1

P2

P0

P1

P2

P0

P1

P2

Base year values (%) South Africa 43.8 Urban area 35.1 Rural area 61.5 Male headed 36.6 Female headed 66.0 Black 51.8 Colored 30.8 Asian 5.5 White 0.0 Unspecified 0.0

19.9 14.9 30.2 15.6 33.2 23.8 11.9 2.0 0.0 0.0

11.5 8.1 18.5 8.7 20.3 13.9 6.1 0.8 0.0 0.0

50.8 41.6 65.9 41.9 59.4 60.1 34.6 2.9 0.2 7.9

23.9 18.1 33.4 18.7 28.9 28.5 14.3 1.0 0.1 2.1

14.0 10.0 20.5 10.6 17.3 16.8 7.7 0.3 0.1 0.6

62.7 51.7 73.7 53.6 72.6 68.9 43.0 12.3 0.0 21.8

31.2 22.8 39.7 24.9 38.1 34.7 17.6 4.3 0.0 5.8

19.0 12.8 25.4 14.6 23.9 21.3 9.3 1.6 0.0 1.6

Variations after simulation (%) South Africa 0.22 0.22 Urban area 0.26 0.17 Rural area 0.13 0.32 Male headed 0.19 0.19 Female headed 0.30 0.31 Black 0.23 0.26 Colored 0.42 0.17 Asian 0.00 0.03 White 0.00 0.00 Unspecified 0.00 0.00

0.16 0.11 0.24 0.13 0.25 0.19 0.10 0.02 0.00 0.00

0.31 0.26 0.39 0.23 0.38 0.35 0.37 0.00 0.00 0.00

0.26 0.21 0.34 0.21 0.31 0.31 0.18 0.02 0.00 0.05

0.19 0.15 0.27 0.15 0.23 0.23 0.12 0.01 0.00 0.03

0.32 0.15 0.50 0.14 0.53 0.33 0.55 0.00 0.00 0.00

0.30 0.25 0.35 0.26 0.35 0.33 0.22 0.07 0.00 0.15

0.23 0.17 0.29 0.19 0.28 0.26 0.15 0.05 0.00 0.08

Notes: P0 ¼ headcount index; P1 ¼ poverty gap; P2 ¼ squared poverty gap (poverty severity index).

Gender-Focused Macro-Micro Analysis

295

of poverty is less among women than among men. Note that this does not reflect intra-household allocation, as this is ignored. Instead, it indicates that there tends to be a higher ratio of men to women in poor female-headed households than in non-poor female-headed households. The results of our trade liberalization scenario in the bottom half of Table 7 indicate that poverty increases slightly more among women and children than among their male counterparts. In particular, the elimination of import tariffs is likely to increase more among women and children living in poverty than men. This gender and age bias in the poverty results is particularly strong for individuals in rural areas, female-headed and Black households. It can be shown also that those results are robust for a wide range of poverty lines.

5. CONCLUSIONS South Africa is in the midst of an ambitious trade liberalization program, notably in the context of various regional and international trade agreements. These policies are likely to have wide-ranging effects on the South African economy, in particular its international trade, production, government revenues, factor markets, household incomes and consumer price structure. To analyze the poverty impacts on South African men, women and children, we construct a CGE microsimulation model including 4,000 actual households from a nationally representative household survey and featuring the explicit modeling of male and female market and domestic work activities and leisure time. South Africa has a very discriminatory tariff structure with rates varying from 0 to 112.8 percent. The high protection sectors are predominantly comprised of light manufacturing activities such as garments, beverages and tobacco, structural metal, electrical equipment and household appliances. These sectors are found to suffer from a contraction in output and valueadded prices subsequent to trade liberalization. In contrast, export-oriented sectors such as mining, transport and communication equipment, machinery and medical instruments expand as a result of the import-driven exchange rate depreciation and the fall in input costs. As male workers tend to be more heavily involved in export-oriented sectors, whereas women work more in the highly protected light manufacturing activities and services, male wage rates rise with respect to female

296

JOHN COCKBURN ET AL.

wage rates. An interesting contrast emerges between urban and rural workers. While urban wage rates tend to perform better than rural wage rates, results vary substantially between skill categories. Medium- and urban lowskilled workers, especially men, are the big winners from our trade experiment. In contrast, high- and rural low-skilled, and child workers fare worse as a result of their dependency on wages from the agricultural sector in rural areas, and from social services in urban areas. Consequently, wage effects are in favor of the more skilled workers in rural areas and in favor of the less skilled urban workers. As capital is assumed to be immobile in the short run, rates of return closely mirror the evolutions in sectoral value-added prices. The upshot of all these changes is an increase in the incomes of urban and male-headed households relative to their rural and female-headed counterparts. These results compound with a greater reduction in consumer prices among urban and male-headed households to generate for them a smaller increase in poverty and a reduction in inequality.

NOTES 1. Elson and Pearson (1981), Standing (1989), Cagatay and Ozler (1995), Joekes (1995, 1999) and Ozler (2000, 2001). 2. Gladwin (1991) and Fontana, Joekes, and Masika (1998). 3. Fontana and Wood (2000), Fontana (2001, 2002) for Bangladesh and Zambia; Fofana, Cockburn, and Decaluwe (2003, 2005) for Nepal; and Siddiqui (2004) for Pakistan. 4. Haddad, Brown, Richter, and Smith (1995), Cagatay, Elson and Grown (1995) and Palmer (1994). 5. Elson (1995), Sinha (1999, 2000) and Fofana et al. (2003). 6. Latigo and Ironmonger (2004). 7. The year 2000 Income and Expenditure Survey (IES) is based on the same sample of households as the September 2000 Labor Force Survey (LFS: 2). 8. We observe some complementarity between market and non-market productive activities. 9. Gronau (1977) and Solberg and Wong (1992) assume that home goods are perfect substitutes for market goods. However, in other versions of Gronau’s model, these goods are imperfect substitutes. For other assumptions to simplify the modeling aspects, see Fofana et al. (2003). 10. Domestic paid labor, capital goods and intermediate goods are included in the household utility function and indirectly substitute to domestic unpaid labor which is referred here as home goods. 11. We assume that there are very limited substitution possibilities between men and women in the production of home goods, reflected by a low elasticity of substitution (0.5) between male and female domestic work. 12. For details on technical aspect, refer to Fofana et al. (2003).

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297

ACKNOWLEDGMENTS The contribution of both Dr. Alfred Latigo and Mr. Omar Abdourahaman from the ACGD/Economic Commission for Africa in providing comments for this study is greatly appreciated. However, the opinion expressed in this paper is the only responsibility of the authors without engaging the ACGD or the Economic Commission of Africa.

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Fontana, M. (2002). Modeling the effects of trade on women: The case of Zambia. Working Paper 155. Institute of Development Studies, Brighton. Fontana, M., Joekes, S., & Masika, R. (1998). Global trade expansion and liberalization: Gender issue and impacts. Bridge Report no. 42. IDS, Brighton, UK. Fontana, M., & Wood, A. (2000). Modeling the effects of trade on women at work and at home. World Development, 28(7), 1173–1190. Gladwin, C. (1991). Structural adjustment and the African women farmers. Economic performance in Latin America and the Caribbean. New York: Oxford. Gronau, R. (1977). Leisure, home production, and work – The theory of the allocation of time revised. Journal of Political Economy, 85(6), 1099–1124. Haddad, L., Brown, L. R., Richter, A., & Smith, L. (1995). The gender dimensions of economic adjustment policies: Potential interactions and evidence to date. World Development, 23(6), 881–896. Hofmeyr, J. F. (1993). African wage movements in the 1980s. South African Journal of Economics, 61(4), 266–280. Hoogeveen, J. G., & O¨zler, B. (2004). Not separate, not equal poverty and inequality in postapartheid South Africa. World Bank, 1818H Street NW, Washington, DC 20433, USA. ILO. (1999). ILO report on social impact of globalization. Geneva: ILO. Joekes, S. (1995). Trade-related employment for women in industry and services in developing countries. UNRISD Occasional Paper, Geneva. Joekes, S. (1999). A gender-analytical perspective on trade and sustainable development. In: UNCTAD, Trade sustainable development and gender. New York and Geneva: UNCTAD. Klasen, S., & Woolard, J. (1998). Levels, trends and consistency of employment and unemployment figures in South Africa. Working Paper, unpublished. University of Munich/ University of Port Elizabeth. Latigo, A., & Ironmonger, D. (2004). The missing link in growth and sustainable development: Closing the gender gap. An Issues Paper presented at the ADB/ECA Symposium of African Ministers of Finance, Planning and Economic Development, 24 May 2004, Kampala, Uganda. Lewis, J. (2001). Reform and opportunity: The changing role and patterns of trade in South Africa and SADC. Africa Region Working Paper Series no. 14. The World Bank, Washington, DC. Ndlela, T., & Nkala, P. (2003). Determinants of exports from SADC and the role of market access. Paper presented at the Trade and Industrial Policy Strategies (TIPS), 2003 Annual Forum at Glenburn Lodge, Muldersdrift. Ozler, S. (2000). Export orientation and female share of employment: The evidence from Turkey. World Development, 28(7), 1239–1248. Ozler, S. (2001). Export led industrialization and gender differences in job creation and destruction: Micro evidence from the Turkish manufacturing sector. Unpublished paper, Department of Economics, UCLA. Palmer, I. (1994). Social and gender issues in macro-economic policy advice. Social Policy Series no. 13. GTZ, Eschborn. Rospabe, S. (2002). An evaluation of gender discrimination in employment, occupation attainment and wage in South Africa in the late 1990s. Development Policy Research Institute, University of Cape Town, mimeo.

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Siddiqui, R. (2004). Modelling gender dimensions of the impact of economic reforms on time allocation among market work, households work and leisure. Research Report no. 185. Pakistan Institute of Development Economics, Islamabad, Pakistan. Sinha, A. (1999). Gender awareness in macroeconomic analysis. An Indian experiment presented at the conference on Feminist Economics at Calton University, Ottawa, Canada. Sinha, A. (2000). Gender in macroeconomic framework, a CGE model analysis. Presented at the 2nd Annual Gender Planning Network Meeting, Kathmandu. Solberg, J. E., & Wong, D. C. (1992). Family time use: Leisure, home production, market work, and work related travel. The Journal of Human Resources, 27(3), 485–510. Standing, G. (1989). Global feminization through flexible labor. World Development, 17(7), 1077–1095. Standing, G., Sender, J., & Weeks, J. (1996). Restructuring the labor market: The South African challenge. An ILO country review. Geneva: ILO. Statistics South Africa. (1999). October household survey South Africa. Statistics South Africa. (2001a). Labor force survey. February 2001 Statistical release P0210. Statistics South Africa. (2001b). A survey of time use: How South African women and men spend their time. Pretoria, South Africa. TIPS. (2002). A review of the changing composition of the South African economy. Report compiled by Trade and Industrial Policy Strategies. United Nations Development Programme. (UNDP). (2000). Human development report 1997. New York, USA. Valodia, I. (1996). Work, Chapter 3. In: D. Budlender, (Ed.), The women’s budget (pp. 53–96). Cape Town: IDASA. Valodia, I. (2000). Economic policy and women’s informal and flexible work in South Africa. Paper presented at the Tips 2000 Annual Forum. World Bank. (1999). South Africa country assistance strategy: Building a knowledge partnership. The World Bank Group, Africa Region, Washington. World Bank. (2002). Gender stats – Database for gender statistics. http://devdata.worldbank. org/genderstats World Bank. (2004). World development. http://devdata.worldbank.org

300

APPENDIX 1. TRADE AND OUTPUT EFFECTS Sectors

Tariff

Sectoral Shares VA

1.1 0.0 0.0 0.0 4.0 7.6 3.2 5.5 112.8 6.7 17.2 1.9 11.7 0.9 7.7 1.9 0.7 1.2 1.4 6.4 1.4 1.5 1.5

3.3 2.1 4.7 6.8 0.5 0.2 0.4 0.8 1.4 0.2 0.7 0.1 0.1 0.5 0.9 0.7 1.5 1.0 1.2 0.2 0.6 0.1 0.6

Exp

1.6 0.0 13.7 13.7 1.5 0.2 0.6 0.5 0.4 1.0 1.5 0.4 0.7 0.6 1.3 1.1 1.1 5.2 5.4 0.9 1.0 0.3 1.1

2.6 9.9 24.8 34.7 1.8 0.2 0.3 1.2 1.6 0.4 1.1 0.5 0.1 0.8 2.4 0.4 3.4 3.7 1.8 0.4 0.3 0.2 0.4

Volume Changes Imp

7.0 0.0 73.0 65.8 11.9 6.1 9.1 6.4 3.4 28.7 18.0 40.2 34.8 13.2 12.6 17.0 7.5 39.2 28.8 32.4 18.9 24.8 17.8

12.4
5.9 85.3
5.8 87.5
0.4 86.8
0.4 16.4
1.6 6.8 3.6 4.5
2.8 16.8
0.3 14.1 147.7 17.4 0.4 18.5 14.8 47.7
2.3 8.4 7.3 19.3
4.1 24.3 3.8 7.4
2.8 24.3
5.2 34.6
1.0 13.8
2.6 22.0 2.4 7.9
2.6 16.3
2.8 7.7
1.7

Price Changes

Exp Output Dom 2.9 0.0 0.0 0.0 2.6 2.7 2.6 2.7 5.3 2.1 2.0 3.4 2.5 3.7 3.2 3.5 2.1 2.3 2.4 2.3 2.7 3.0 2.4


0.5 0.0 0.4 0.3
0.8
1.0
1.1
1.0
4.9
1.9
2.7 1.9
2.1 1.4 0.2 0.8
0.5 1.4 0.3
0.6 0.5 0.8 0.5

Imp

Dom Output


1.0 3.7 0.3 0.0 4.9 0.8 2.7 4.9 2.8 1.9 4.9 2.2
1.1 0.9 0.6
1.1
2.5 0.6
1.2 1.6 0.5
1.5
0.6 0.2
5.9
50.7
6.0
2.5
1.7 0.2
2.9
10.5 0.1 0.7 3.0 0.9
2.3
6.1 0.0 0.9 4.0 0.5
0.6
2.6 0.2 0.6 2.9 0.6
1.0 4.2 1.3 0.9 3.7 2.4 0.0 3.5 1.6
1.2
1.4 1.0 0.3 3.4 1.4 0.5 3.4 1.1 0.4 3.3 1.9

0.6 0.8 1.3 1.2 0.8 0.6 0.6 0.6
5.4 0.7 0.3 1.6 0.1 0.9 0.8 0.7 1.6 2.7 1.8 1.4 1.5 1.3 2.0

JOHN COCKBURN ET AL.

AGRICULTURE Gold and uranium Other mining MININGa Meat and vegetables Dairy Grain milling Other food Beverages and tobacco Textiles Garments Leather Footwear Wood Paper Printing Petroleum Basic chemicals Other chemicals Rubber products Plastic products Glass products Non-metallic mineral

Imp

IPR EIR

2.2 0.4 0.8 0.4 0.4 0.1 0.1 0.1 0.1 0.1 0.0 0.2 0.2 0.1 0.9 0.5 0.1 0.3 0.2 18.8 2.4 0.4 1.6 1.3 11.1 2.0 6.2 3.9 10.0

3.1 0.1 1.8 4.3 5.8 0.5 0.6 0.9 0.2 0.2 0.3 0.7 6.1 3.0 4.9 8.5 3.6 0.3 5.4 74.9 0.0 0.0 0.1 0.2 0.1 2.0 2.8 1.6 0.8

10.5 0.4 0.7 2.6 1.4 0.1 0.2 0.2 0.1 0.1 0.0 0.4 0.7 0.4 3.8 1.2 1.1 1.1 1.8 47.7 0.4 0.0 0.0 0.0 0.2 2.6 5.2 1.1 2.9

17.2 2.5 20.3 72.2 60.7 35.8 42.9 56.9 11.9 27.0 39.8 28.9 77.8 83.5 23.4 64.6 85.1 11.3 75.1 29.4 0.0 0.2 0.5 1.9 0.1 20.6 7.6 6.6 1.4

46.1 11.7 10.0 71.4 32.9 14.1 25.4 20.3 6.4 12.8 11.5 23.6 33.7 57.9 21.2 23.3 69.0 39.9 68.5 24.1 3.6 0.4 0.1 0.2 0.3 27.4 14.5 5.1 5.5


1.2 25.2
0.9
0.3
0.4 5.5 2.0
1.4 12.8
2.6
1.9 6.0
0.8
0.8 2.1
1.7
0.3 3.0
0.7 0.6 0.0
6.9
5.0
5.4
5.7
5.6
4.7
5.4
7.2

2.1 2.2 2.6 4.0 3.0 1.8 2.5 3.2 1.9 2.8 3.2 2.4 3.4 3.9 1.6 2.9 3.4 2.6 2.2 2.6 2.9 3.0 2.6 2.6 3.2 3.0 2.7 3.0 3.4

1.5
0.4 0.6 3.3 1.4
2.7
0.7 2.2
2.2 0.7 1.2
1.6 1.7 3.4
0.9 2.1 3.3
0.7 1.0
0.1
0.1
0.6 0.0
0.2 0.2 0.9 0.6 0.3
0.2

1.1 4.4
0.8
13.1 0.4 2.6 2.1 2.6 0.8 2.2
3.1
5.1
1.7
2.1 1.9 4.2
2.4
8.7 0.4 3.5 1.0 3.3
2.2
5.0 1.0 2.3 3.2 4.4
1.5
0.8 2.0 4.9 3.2 4.9
1.0
2.0 0.0 2.5
0.7 1.5
0.3 0.0
0.6 4.9 0.0 4.9
0.2 4.9 0.2 4.9 0.1 4.9 0.2 4.9 0.2 4.9
0.4 4.9

2.8 1.4 1.7 1.0 1.4 0.4 0.3 1.9 0.6 1.4 1.3 0.2 1.1 1.7 1.6 2.3 2.5 0.7 2.0 0.8 0.8 0.4 1.4 1.3 0.8 0.9 1.4 1.0 0.1

3.1 1.7 1.8 1.8 1.8 0.6 1.0 2.1 0.8 1.6 1.4 0.6 1.5 1.8 2.1 2.4 2.6 0.9 2.6 1.3 0.8 0.4 1.4 1.3 0.8 1.4 1.7 1.1 0.2

301

0.5 20.7 2.2 2.2 2.7 10.6 7.2 0.7 14.9 1.3 1.5 10.5 2.6 0.5 5.7 0.0 0.0 7.0 2.4 3.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Gender-Focused Macro-Micro Analysis

Iron and steel Structural metal Other fabricated metal General purpose machinery Special purpose machinery Household appliances Electric motors Electricity distribution Insulated wire and cable Accumulators Lighting equipment Other electrical equipment Communication equipment Medical instruments Motor vehicles Motor vehicle parts Other transport equipment Furniture Other manufacturing INDUSTRYa Electricity and gas Water Building Construction Trade services Hotel and restaurant Transport services Post and telecommunications Financial services

302

APPENDIX 1. (Continued ) Sectors

Tariff

Sectoral Shares VA

Real estate Other business General government Health and social work Other services SERVICEa ALLa

Imp

IPR EIR

Exp

0.0 6.0 0.2 0.4 0.6 1.5 0.0 2.9 1.0 0.6 5.5 3.4 0.0 16.5 0.0 0.5 0.0 0.7 0.0 1.9 0.1 0.3 0.6 2.6 0.0 4.8 0.9 0.8 4.0 4.0 0.0 71.1 9.8 15.0 3.1 4.0 2.5 100.0 100.0 100.0 16.1 15.8

Volume Changes

Price Changes

Imp

Exp Output Dom


5.6
5.5 0.0
6.7
6.7
5.6
0.3

3.0 3.2 3.3 2.7 3.2 3.0 1.8

0.1 0.4 0.0
0.7
0.2 0.1 0.0

0.0 0.3 0.0
0.8
0.3
0.1
0.3

Imp 4.9 4.9 0.0 4.9 4.9 4.9 2.3

Dom Output 0.9 0.8 0.5 0.7 0.4 0.7 0.7

0.9 0.9 0.5 0.8 0.5 0.8 1.0

Notes: VA ¼ value added; Imp ¼ imports; Exp ¼ exports; Dom ¼ local sales of domestic output; IPR ¼ import penetration ratio; EIR ¼ export intensity ratio. a Average variation for volumes – Laspeyres index for prices.

JOHN COCKBURN ET AL.

Sectors

VA Price

Share in Male Wages Urban

Rural

Share in Female Wages Urban

Rural

Hi Med Lo Kid Hi Med Lo Kid Hi Med Lo Kid Hi Med Lo
1.0 0.0 0.7 0.5
0.5
0.5
1.2
0.7
11.4
0.6
0.5 1.3
2.0 0.5 0.3 0.3
2.9 2.2 0.1
0.2 0.1 0.4 0.9 2.9

0.1 1.1 1.8 5.8 2.2 5.1 4.0 11.0 0.4 0.5 0.3 0.5 0.5 0.2 0.4 0.9 1.7 0.4 0.1 0.3 0.5 0.6 0.1 0.1 0.0 0.2 0.2 1.0 0.5 1.0 1.1 0.9 0.8 0.5 1.2 0.6 3.0 0.4 0.1 0.6 0.7 0.9 0.1 0.3 0.5 0.5 1.0 1.9

4.6 5.4 2.3 7.7 1.3 0.5 0.5 2.8 1.0 0.7 1.4 0.0 0.0 1.0 0.6 1.2 0.1 0.2 1.4 0.0 1.5 0.4 0.3 3.5

50.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

14.2 13.4 33.3 75.8 0.4 0.0 0.8 0.2 0.0 0.2 2.9 11.6 7.3 0.0 0.3 2.9 12.3 7.5 0.0 0.5 0.6 0.4 1.0 0.0 0.2 0.7 0.0 0.2 0.0 0.0 0.4 0.3 0.3 0.0 0.2 0.3 1.5 1.4 0.0 0.1 0.1 0.4 0.4 0.0 0.3 0.0 0.3 0.0 0.0 0.1 0.1 0.3 0.3 0.0 1.2 0.0 0.1 0.2 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.3 1.8 1.9 0.0 0.2 0.0 0.4 0.4 0.0 1.0 0.0 0.2 0.2 0.0 1.7 0.0 0.1 0.0 0.0 0.1 1.9 0.4 0.0 0.0 0.3 0.0 0.6 0.5 0.0 1.9 0.0 0.5 0.0 0.0 0.0 0.2 0.0 0.1 0.0 0.7 0.0 0.2 0.0 0.0 0.0 0.1 0.8 0.6 0.0 0.1 0.8 1.4 0.3 0.0 1.2

0.5 0.2 0.5 0.7 0.5 0.0 0.1 0.9 0.3 0.9 3.9 0.1 0.3 0.4 0.6 1.1 0.0 0.3 0.4 0.1 1.2 0.1 0.1 1.1

2.4 0.1 0.3 0.4 2.1 0.0 0.1 1.4 0.1 0.2 2.4 0.2 0.3 0.2 0.9 0.5 0.0 0.1 2.8 0.0 3.6 0.0 0.3 0.1

88.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

1.7 0.0 0.0 0.0 1.3 0.0 0.0 0.0 0.0 0.0 0.7 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Share Returns Kid

8.3 20.1 100.0 0.0 0.0 0.0 2.7 0.1 0.0 2.7 0.1 0.0 0.9 0.7 0.0 0.0 0.2 0.0 0.6 0.1 0.0 1.2 2.3 0.0 0.8 0.2 0.0 0.7 0.0 0.0 7.2 0.9 0.0 0.0 0.1 0.0 0.7 0.1 0.0 1.2 1.0 0.0 0.4 1.6 0.0 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 0.2 0.0 0.0 0.1 0.0 0.2 1.0 0.0 0.1 0.0 0.0 0.8 0.2 0.0 0.2 0.0 0.0

4.8 1.4 6.5 7.9 0.5 0.2 0.4 0.7 2.2 0.1 0.2 0.1 0.1 0.3 1.1 0.4 2.7 1.3 0.9 0.1 0.1 0.1 0.9 3.2


1.5 0.0 1.2 1.0
1.3
1.5
2.3
1.6
15.8
2.4
3.1 3.3
4.1 1.9 0.5 1.0
3.4 3.6 0.4
0.8 0.5 1.2 1.5 4.5

303

AGRICULTURE Gold and uranium Other mining MINING Meat and vegetables Dairy Grain milling Other food Beverages and tobacco Textiles Garments Leather Footwear Wood Paper Printing Petroleum Basic chemicals Other chemicals Rubber products Plastic products Glass products Non-metallic mineral Iron and steel

Capital

Gender-Focused Macro-Micro Analysis

APPENDIX 2. FACTOR EFFECTS

304

APPENDIX 2. (Continued ) Sectors

VA Price

Share in Male Wages Urban

Share in Female Wages

Rural

Urban

Rural

Hi Med Lo Kid Hi Med Lo Kid Hi Med Lo Kid Hi Med Lo
0.1 0.4 0.6 0.4
0.8
0.2 2.6
3.0 0.7 1.1
1.3 0.7 1.3
0.8 1.1 0.3
0.2 0.8
0.6
0.3
1.2 0.0
0.1 0.1 2.1

0.3 1.0 0.5 0.0 0.7 0.6 1.2 1.0 1.4 0.0 0.0 0.3 0.6 0.5 1.2 0.0 0.0 0.0 1.0 0.7 0.9 0.0 0.0 0.8 0.1 0.1 0.1 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.1 0.2 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.4 0.1 0.0 13.8 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.1 0.0 0.0 0.0 1.5 1.0 0.3 0.0 1.2 0.3 0.4 1.0 1.5 0.0 0.3 0.8 0.5 0.3 0.2 0.0 0.0 0.0 0.4 0.4 0.7 0.0 0.0 0.7 0.1 0.2 0.4 0.0 0.7 0.1 20.2 19.0 25.8 21.0 8.4 13.9 2.3 1.8 1.0 0.0 0.0 0.7 0.4 0.2 0.0 0.0 0.5 0.8 0.6 4.5 0.8 11.4 0.2 3.2 0.6 1.5 10.9 5.9 0.6 2.8 8.1 12.2 16.3 2.7 9.6 13.2 0.5 0.9 0.5 0.0 0.6 1.8

0.0 0.1 0.2 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 9.2 1.4 1.0 0.9 9.5 7.5 0.7

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 24.2 0.0

0.0 0.1 0.0 0.0 1.3 0.1 0.0 0.0 0.2 1.2 0.0 0.0 0.1 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.3 0.0 0.0 0.0 0.1 0.1 0.0 0.0 0.1 0.1 0.0 0.0 0.0 1.1 0.0 0.0 0.1 0.1 0.0 0.0 0.2 0.1 0.0 2.0 0.1 0.1 0.0 0.0 0.4 0.1 0.0 0.1 0.3 0.6 0.0 0.2 0.4 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.3 0.0 0.0 0.2 0.4 0.4 0.0 13.9 16.7 18.8 0.7 0.4 0.9 0.7 0.0 0.0 0.1 0.0 0.0 0.0 0.5 0.2 0.0 0.1 0.3 0.2 0.0 9.5 16.8 19.2 2.2 1.0 2.7 1.1 0.0

0.0 0.0 0.0 0.2 0.6 0.1 0.0 0.0 0.3 0.0 0.0 0.2 0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.4 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.4 0.0 0.2 0.0 3.2 18.6 9.9 0.0 0.3 0.0 0.0 1.2 0.3 0.0 0.5 0.0 0.0 0.6 0.5 6.2 24.4 15.8 0.2 5.1 1.9

Share Returns Kid 0.0 0.2 0.0 0.6 0.0 0.1 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 1.0 0.0 0.4 0.0 0.0 0.0 0.2 0.0 0.2 0.0 19.4 0.0 3.5 0.0 0.6 0.0 1.3 0.0 1.2 0.0 10.2 0.0 3.1


0.5 1.0 3.9 1.7
3.5
1.0 4.8
5.1 1.4 2.4
2.9 2.4 4.7
1.7 3.3 3.6
0.9 1.8
2.5
0.4
1.8 0.1
0.3 0.3 3.0

JOHN COCKBURN ET AL.

Structural metal Other fabricated metal General purpose machinery Special purpose machinery Household appliances Electric motors Electricity distribution Insulated wire and cable Accumulators Lighting equipment Other electrical equipment Communication equipment Medical instruments Motor vehicles Motor vehicle parts Other transport equipment Furniture Other manufacturing INDUSTRY Electricity and gas Water Building Construction Trade services Hotel and restaurant

Capital

0.7 0.5
0.3 0.8 0.1 0.0
0.6
0.1 0.2 0

4.6 7.4 6.0 0.0 5.0 1.5 0.9 0.0 12.7 4.0 1.0 0.0 1.7 0.1 0.5 0.0 7.7 2.4 1.7 0.0 23.5 31.1 18.9 0.0 1.4 0.3 1.1 0.0 6.4 1.1 2.3 8.3 75.6 69.0 61.9 28.4 100 100 100 100

11.6 6.0 4.5 0.0 0.3 0.2 1.2 0.0 9.0 0.5 0.1 0.0 0.3 0.0 0.0 0.0 0.3 1.5 0.8 0.0 19.6 27.7 19.9 0.0 3.3 0.4 0.8 0.0 18.8 1.4 1.9 0.0 74.6 60.3 50.0 24.2 100 100 100 100

4.3 1.8 0.6 0.0 3.3 0.3 0.3 0.0 2.1 4.8 0.3 0.0 0.1 3.2 0.9 0.0 8.7 9.3 1.1 0.0 3.5 1.2 0.0 0.0 2.0 0.5 1.0 0.0 0.0 0.0 0.0 0.0 6.8 3.8 4.3 0.1 1.8 1.8 2.2 0.0 20.5 35.3 13.2 0.0 8.3 26.2 20.7 0.0 9.0 2.0 2.8 2.1 13.3 2.3 3.0 0.0 20.9 3.2 33.8 6.8 58.3 3.5 24.4 0.0 85.2 82.1 78.4 11.2 95.1 70.5 69.9 0.0 100 100 100 100 100 100 100 100

Notes: VA ¼ value added; Hi, Med, Lo, Kid ¼ high, medium, low skilled and child workers. a Laspeyres price index.

7.5 5.2 13.5 12.4 1.1 4.2 1.9 2.3 67.9 100

1.2 0.8
0.5 0.8 0.5 0.0
1.3
0.2 0.4 0

Gender-Focused Macro-Micro Analysis

Transport services Post and telecommunications Financial services Real estate Other business General government Health and social work Other services SERVICES ALLa

305