International Consumption Comparisons
E. A. Selvanathan I S . World Scientific
i m**4
Infernofional ConsumpNon Comparisons OECD Versus LD
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International Consumption Comparisons (H>
E.
School of International Business and Asian Studies Faculty of Commerce and Management Griffith University, Australia
S. Selvanathan
School of Economics, Faculty of Commerce and Management, Griffith University, Australia
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World Scientific New Jersey • London • Singapore SL • Hong Kong
Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202,1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.
INTERNATIONAL CONSUMPTION COMPARISONS: OECD VERSUS LDC Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
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ISBN 981-02-4005-8
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DEDICATION
&4a dove made e«to>im(M4> &acni(jice&foyive cu t&e moat fineccout yifft o£ education the late Mr Veluppillai Eliyathamby the late Mrs Pooranam Eliyathamby Mr Murugesapillai Pathmanathan Mrs Parameswary Pathmanathan
ABOUT T H E AUTHORS D t E A Selvanathan is an Associate Professor in the School of International Business and Asian Studies at Griffith University, Queensland, Australia. He was educated at the University of Jaffna (BA Hons), University of Bucurest (MSc) and Murdoch University, Western Australia (PhD). He has also taught for brief periods at the University of Jaffna, Murdoch University and the University of Western Australia. For the period 1994-1997, Dr Selvanathan was the Deputy Dean (Staffing) of the Faculty of International Business and Asian Studies, Griffith University. He has co-authored three research monographs and has widely published in international refereed journals such as Review of Economic Studies, Journal of Business and Economic Statistics, Journal of Econometrics, Review of Economics and Statistics and Marketing Science. In 1988, Dr Selvanathan was awarded the prestigious Inaugural 75th Anniversary Distinguished Teaching Award, The University of Western Australia. He has also co-authored two textbooks, including an Australian best-seller in Business Statistics entitled Australian Business Statistics. Dr Saroja Selvanathan is an Associate Professor in the School of Economics at Griffith University, Queensland, Australia. She was educated at the University of Jaffna (BSc Hons), Murdoch University (MPhil) and the University of Western Australia (PhD). Dr Selvanathan has also taught for brief periods at the University of Jaffna, Murdoch University and the University of Western Australia. For the period 1996-1997, Dr Selvanathan was the Deputy Dean (Research and Postgraduate Studies) of the Faculty of Commerce and Management, Griffith University. She has authored a research monograph and has co-authored another research monograph. Dr Selvanathan has also published widely in international refereed journals such as Review of Economics and Statistics, Empirical Economics, Economic Modelling and Economic Record. She has co-authored two textbooks, including an Australian best-seller in Business Statistics entitled Australian Business Statistics.
Vll
PREFACE Understanding consumer reaction to price and income changes is of crucial importance for a host of microeconomic policy issues such as public-utility pricing, the measurement of distortions, optimal taxation and the treatment of externalities. The modern system-wide approach to applied demand analysis provides a unique approach to determine the factors that influence consumer decisions. This book presents a detailed analysis of the consumption patterns of consumers from 46 countries. The countries considered in the analysis are classified into two groups, namely, the Organisation for Economic Co-operation and Development (OECD) group — made up of a number of highly industrialized, rich countries, and the Less Developed (LD) group — made up of a number of relatively poor countries (totaling to about 9000 data points). Such a large and diverse body of data should provide convincing evidence, one way or the other, about a number of empirical regularities as well as the validity of the theory of the consumer. While the book reviews the theory of the consumer, it contributes more to the analysis of the consumption patterns of consumers around the Globe.
A Preview of the Book One of the primary objectives of applied demand analysis is to estimate demand systems to obtain income and price elasticities in order to use them to design microeconomic policies. With this objective, in Chapter 1 we present an
Vlll
overview of international consumption patterns and in Chapter 2 we present a review of the basics of demand theory. In Chapter 1, we present an overview of the OECD and LD countries and their consumer characteristics as well as a review of some of the previous international consumption studies. In Chapter 2, we present the basics of the economic theory of the consumer, discuss various consumer utility preference structures, review the differential approach to deriving demand systems and present a number of popular demand systems such as CBS, ADDS, translog and Rotterdam demand systems. In Chapter 3, we provide a preliminary data analysis of the consumption patterns in the OECD countries. We start this chapter by giving information about the data sources and the characteristics of the data set. We present a summary of the data in the form of Divisia indices. We investigate a number of empirical regularities of the consumers such as the Engel's Law, Law of demand and the famous Frisch's conjecture in these 23 OECD countries. The analysis of this chapter reveals that consumption tends to be more variable than prices and the consumers move away from those goods which have above average price increases — supports the law of demand. Furthermore, we find that the allocation of consumers' income on food decreases with their increasing income — supports Engel's law. Also the income elasticity of the marginal utility of income is not related to consumers' income - does not support Frisch's conjecture. We also derive initial estimates for income and price elasticities for the nine commodity groups in this chapter using the double-log demand systems. These initial estimates suggest that the OECD consumers consider food, housing, medical care and education as necessities; and clothing, durables, transport and recreation as luxuries. We also find that the demand for all goods in the OECD countries is price inelastic. We start Chapter 4 by giving details about the data source and the characteristics of the data for 23 LD countries. We use the same data analysis
IX
techniques introduced in Chapter 3 to present a preliminary analysis of the LDC data. The results show that the LD countries data supports the law of demand, Engel's law and does not support Frisch's famous conjecture. The elasticity estimates reveal that consumers in the LD countries consider food, housing and medical care as necessities; and clothing, durables, transport, education and recreation as luxuries. In general, demand for all goods in the LDC appear to be price inelastic. In Chapter 5, we compare the consumption patterns of the OECD and LD consumers based on the results of Chapters 3 and 4. We then combine the data sets for the two groups of countries to investigate the empirical regularities for the "World Consumers" as a whole. A comparison of the income allocation shows that OECD consumers allocate less proportion of their income on food compared to the LD consumers. OECD consumers allocate a higher proportion of their income on housing, medical care, transport and recreation than the LD consumers. Based on the pooled data, an average world consumer allocates about 33 percent of his/her income on food, 8 percent on clothing, 15 percent on housing, 8 percent on durables, 5 percent on medical care, 12 percent on transport, 7 percent on recreation, 1 percent on education and the remaining 12 percent on all other things. The results also show that both OECD and LDC data support Engel's law. Individual prices of consumer goods play a major role in consumer decisions as well as determine the rate of inflation, which impacts the economy as a whole. Thus studying the price movements is also important in understanding consumer behaviour. In Chapter 6, we study the prices and consumption of individual goods using the stochastic index numbers. According to this approach, the proportionate change in each individual price is taken to be equal to the underlying rate of inflation plus other components, which are random and nonrandom. The overall price index is then obtained by taking some
X
form of average of the individual price changes. An alternative to the stochastic approach is the functional approach whereby the form of the index is related to the underlying utility function. The attraction of the stochastic approach is that it provides standard errors for the price index. These standard errors increase with the degree of relative price variability. This agrees with the intuitive notion that when the individual prices move disproportionately, the overall rate of inflation is less well defined. We start this chapter by outlining the stochastic approach to index numbers and derive a number of theoretical results. We then apply these results to measure the price and quantity movements of the OECD and LD countries using the data presented in the previous chapters. Chapter 7 presents the final form of the estimating demand equations and tests demand theory hypotheses, demand homogeneity and Slutsky symmetry. The results show that homogeneity is universally acceptable by the OECD and LDC data and symmetry is acceptable to a lesser extent. In Chapter 2 of the book, we introduce a number of competing demand systems such as the Rotterdam, CBS, AIDS, etc. In Chapter 8, we estimate four of these demand systems using the OECD and LDC data and test the demand theory hypotheses, homogeneity and symmetry. For each country, a comparison of the performance of these four demand systems is presented using the information inaccuracies and a preferred demand system is then selected. In Chapter 9, we investigate a special form of utility structure — preference independence. The results show that preference independent utility structure is acceptable for most of the LD countries and by the majority of the OECD countries. In Chapter 9, we also give the final estimates of income and price elasticities of the nine commodity groups. The Appendix to this book, written by Wana Yang, Ken Clements and Dongling Chen, presents a shorter version of the User's Guide to the Demand Analysis Package, DAP2000. DAP2000 is an enhanced version of the Demand
XI
Analysis Package (DAP) written by S. Selvanathan, E.A. Selvanathan and Ken Clements in 1989. Features of DAP2000 include Preliminary data analysis, Hypotheses testing using both conventional asymptotic procedures and the Monte Carlo simulation approach, Estimation of demand systems and the Matrix approach to simulation (MAS), which is a recently-developed technique to evaluate demand systems. DAP2000 is extensively used in producing the results for Chapters 3, 4, 7 and 9 of this book.
E.A. Selvanathan Saroja Selvanathan January 2003
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xiii
TABLE OF CONTENTS PREFACE
vii
TABLE OF CONTENTS
xiii
LIST OF TABLES
xviii
LIST OF FIGURES
xxiv
TECHNICAL NOTES
xxvi
ACKNOWLEDGEMENTS
xxvii
CHAPTER 1: AN OVERVIEW OF INTERNATIONAL CONSUMPTION PATTERNS E^4. Selvanathan and S. Selvanathan
1
1.1 An Overview of the OECD and LD Countries 1.2 Consumption Theory 1.3 A Review of International Consumption Comparisons 1.4 A Pioneering International Consumption Study 1.5 Are Tastes Constant? References
2 6 14 17 22 26
CHAPTER 2: CONSUMER DEMAND MODELS JB^4. Selvanathan andS. Selvanathan
31
2.1 2.2
31 39
The Economic Theory of the Consumer The Structure of Preferences
xiv 2.3 Differential Approach to Deriving Demand Equations 2.4 Other Popular Demand Systems 2.5 More on the Differential Demand Equations 2.6 Aggregation and Consumer Demand References
43 52 59 63 65
CHAPTER 3: DATA ANALYSIS: OECD COUNTRIES S. Selvanathan andE^4. Selvanathan
71
3.1 DataSource 3.2 Summary Measures 3.3 Engel'sLaw 3.4 Preliminary Estimates of Income and Price Elasticities 3.5 Preliminary Estimates of the Income Flexibility 3.6 Testing the Frisch's Conjecture 3.7 The Validity of Preference Independence References
71 74 94 102 105 116 118 120
CHAPTER 4: DATA ANALYSIS: LESS DEVELOPED COUNTRIES E^4. Selvanathan and S. Selvanathan
125
4.1 DataSource 4.2 Summary Measures 4.3 Engle'sLaw 4.4 Preliminary Estimates of Income and Price Elasticities 4.5 Preliminary Estimates of the Income Flexibility 4.6 Testing the Frisch's Conjecture 4.7 The Validity of Preference Independence References
126 126 141 153 156 165 166 168
XV
CHAPTER 5: A COMPARISON OF CONSUMPTION PATTERNS IN THE OECD AND LD COUNTRIES E^4. Selvanathan and S. Selvanathan
169
5.1
Summary Measures
170
5.2
Empirical Regularities
175
5.3
Conclusion
182
CHAPTER 6: STOCHASTIC PRICE AND QUANTITY INDEX NUMBERS E~A. Selvanathan and S. Selvanathan
187
6.1 An Unweighted Average of Prices 6.2 A Budget-Share-Weighted Average of Prices 6.3 The Extended Model 6.4 A Two-Step Estimation Procedure: Step 1 6.5 A Two-Step Estimation Procedure: Step 2 6.6 AnExtension 6.7 Application of Stochastic Index Numbers to OECD and LDC 6.8 Conclusion References
189 190 193 194 196 199 205 224 224
CHAPTER 7: TESTING DEMAND THEORY HYPOTHESES: OECD AND LD COUNTRIES S. Selvanathan andE.A. Selvanathan
227
7.1
The Demand Model
228
7.2
Demand Homogeneity
230
7.3
Slutsky Symmetry
235
7.4 Summary Results References
241 245
XVI
CHAPTER 8: A COMPARISON OF ALTERNATIVE DEMAND SYSTEMS £L4. Selvanathan andS. Selvanathan
249
8.1 Four Demand Systems 8.2 Measure of Goodness-of-fit 8.3 The Preferred Demand System 8.4 Conclusion References
250 256 259 264 265
CHAPTER 9: THE STRUCTURE OF PREFERENCES: OECD AND LD COUNTRIES S. Selvanathan andE^4. Selvanathan
267
9.1 The Demand Model 9.2 Model Estimation 9.3 Estimation Results 9.4 Testing Preference Independence 9.5 Implied Income and Price Elasticities 9.6 Conclusion References
268 270 273 279 285 291 292
APPENDIX: THE DEMAND ANALYSIS PACKAGE, DAP2000 ....295 Wana Yang, Kenneth W Clements and Dongling Chen A.l Using the Package A.2 InputOptions A.3 Preliminary Data Analysis A.4 Hypothesis Testing and Estimation A.5 The Matrix Approach to Simulation References
296 297 300 301 310 319
xvii
INDEX Subject Index Author Index
321 321 324
xviii
LIST OF TABLES Chapter 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
General characteristics of the OECD and LD countries Economic characteristics of the OECD and LD countries Major studies in international consumption comparisons Characteristics of the LPW database Budget shares of eight commodities in 13 countries Prices and per capita quantities consumed of eight commodities in 13 countries Divisia moments in 13 countries Marginal shares and income elasticities for eight commodities in 13 countries Quality of budget share predictions in OECD countries and Australian states
4 5 15 18 19 20 21 23 25
Chapter 3 3.1 3.2 3.3 3.4
Details of the commodity groups Characteristics of the OECD database Budget shares of 9 commodities in 23 OECD countries Per capita quantity consumed of 9 commodities in 23 OECD countries 3.5 Prices of 9 commodities in 23 OECD countries 3.6 Divisia volume indices in 23 OECD countries 3.7 Divisia price indices in 23 OECD countries 3.8 Divisia quantity variances in 23 OECD countries 3.9 Divisia price variances in 23 OECD countries 3.10 Divisia price-quantity correlations in 23 OECD countries 3.11 Divisia moments in 23 OECD countries
72 73 75 77 79 80 82 84 85 86 88
3.12 Relative quantity log-changes of 9 commodities in 23 OECD countries 3.13 Relative price log-changes of 9 commodities in 23 OECD countries 3.14 Frequency distributions of relative consumption and relative prices of 9 commodities in 23 OECD countries 3.15 Frequencies of joint signs of relative consumption and relative price changes in 23 OECD countries 3.16 Estimates of Working's model for 23 OECD countries 3.17 Previous estimates of Working's income coefficient for food 3.18 Income elasticities of 9 commodities in 23 OECD countries 3.19 Own-price elasticities of 9 commodities in 23 OECD countries 3.20 Four sets of estimates for income flexibility in 23 OECD countries 3.21 Another set of estimates for income flexibility for OECD countries
90 91 92 93 99 101 103 104 107 114
Chapter 4 4.1 4.2 4.3 4.4
Details of the commodity groups Characteristics of the LDC database Budget shares of 9 commodities in 23 LD countries Per capita quantity consumed of 9 commodities in 23 LD countries 4.5 Prices of 9 commodities in 23 LD countries 4.6 Divisia volume indices in 23 LD countries 4.7 Divisia price indices in 23 LD countries 4.8 Divisia quantity variances in 23 LD countries 4.9 Divisia price variances in 23 LD countries 4.10 Divisia price-quantity correlations in 23 LD countries 4.11 Divisia moments in 23 LD countries 4.12 Relative quantity log-changes of 9 commodities in 23 LD countries
127 128 129 131 132 133 134 136 137 138 140 142
XX
4.13 Relative price log-changes of 9 commodities in 23 LD countries 4.14 Frequency distributions of relative consumption and relative prices of 9 commodities in 23 LD countries 4.15 Frequencies of joint signs of relative consumption and relative price changes in 23 LD countries 4.16 Estimates of Working's model for 23 LD countries 4.17 Income elasticities of 9 commodities in 23 LD countries 4.18 Own-price elasticities of 9 commodities in 23 LD countries 4.19 Four sets of estimates for income flexibility in 23 LD countries 4.20 Another set of estimates for income flexibility for LD countries
143 144 145 151 154 155 157 165
Chapter 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8
Average budget shares of 9 commodities: OECD and LD countries Average per capita quantity consumed of 9 commodities in OECD and LD countries Average prices of 9 commodities in OECD and LD countries Divisia moments in OECD and LD countries Average frequencies of joint signs of relative consumption and relative price changes in OECD and LD countries Estimates for income flexibility for the 9 commodities in 46 countries Average income elasticities of 9 commodities in OECD and LD countries Average own-price elasticities of 9 commodities in OECD and LD countries
171 173 173 175 177 180 181 181
Chapter 6 6.1 6.2
Estimates of price inflation and standard errors for Australia Estimates of relative price changes: Australia
202 204
XXI
6.3
Rate of inflation estimates and their standard errors in 23 OECD countries 6.4 Rate of inflation estimates and their standard errors in 23 LD countries 6.5 Estimates of relative price changes for the 9 commodities in 23 OECD countries 6.6 Estimates of relative price changes for the 9 commodities in 23 LD countries 6.7 Quantity index estimates and their standard errors in 23 OECD countries 6.8 Quantity index estimates and their standard errors in 23 LD countries 6.9 Estimates of relative quantity changes for the 9 commodities in 23 OECD countries 6.10 Estimates of relative quantity changes for the 9 commodities in 23 LD countries
207 209 211 212 216 218 220 221
Chapter 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9
Further characteristics of the OECD database 232 Testing homogeneity in 22 OECD countries 234 Further characteristics of the LDC database 236 Testing homogeneity in 23 LD countries 237 Testing symmetry in 22 OECD countries 240 Testing symmetry in 23 LD countries 242 Summary results: Testing demand theory hypotheses in 22 OECD countries 243 Summary results: Testing demand theory hypotheses in 23 LD countries 244 Summary of percentage acceptance of the demand theory hypotheses: 22 OECD and 23 LD countries 245
XX11
Chapter 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8
Value of the test statistics for testing homogeneity and the symmetry hypotheses for four demand models, OECD countries Summary results for testing homogeneity and symmetry for four demand models, OECD countries Value of the test statistics for testing homogeneity and symmetry hypotheses for four demand models, LD countries Summary results for testing homogeneity and symmetry for four demand models, LD countries Mean information inaccuracies, OECD countries Mean information inaccuracies, LD countries Preferred demand systems, OECD and LD countries Preferred demand systems for 22 OECD and 23 LD countries (in percentages)
252 253 254 255 261 262 263 264
Chapter 9 9.1
Estimates of the intercept terms of the model under preference independence for 9 commodities in 22 OECD countries 9.2 Estimates of the income coefficients for 9 commodities and income flexibility in 22 OECD countries 9.3 Estimates of the intercept terms of the model under preference independence for 9 commodities in 23 LD countries 9.4 Estimates of the income coefficients for 9 commodities and income flexibility in 23 LD countries 9.5 Testing preference independence in 22 OECD countries 9.6 Testing preference independence in 23 LD countries 9.7 Summary results: Testing preference independence, 22 OECD countries and 23 LD countries 9.8 Estimates of the income elasticities under preference independence for 9 commodities in 22 OECD countries 9.9 Estimates of the own-price elasticities under preference independence for 9 commodities in 22 OECD countries 9.10 Estimates of the income elasticities under preference independence for 9 commodities in 23 LD countries
274 275 277 278 280 281 284 287 288 289
xxm 9.11 Estimates of the own-price elasticities under preference independence for 9 commodities in 23 LD countries 9.12 Summary of acceptance of preference independence hypothesis: 22 OECD and 23 LD countries
290 291
Appendix A. 1 Overview of output of preliminary data analysis A.2 The comparison matrix A.3 Simulation procedure for M(k I j)
301 314 315
xxiv
LIST OF FIGURES Chapter 1 1.1
Food budget share vs logarithm of per capita GDP for 46 countries ..
7
Chapter 3 3.1
Quantity standard deviation vs price standard deviation in 23 OECD countries 3.2 Food budget shares against logarithm of per capita real consumption expenditures in OECD countries 3.3a Food budget share vs Log (Income) for pooled data from 23 OECD countries 3.3b Food budget share vs Log (Income) for pooled data from 22 OECD countries (excluding Iceland) 3.4 Relative quantity against relative price in OECD countries 3.5 Relative consumption vs relative prices for 9 commodity groups .... 3.6 Own-price elasticity against income elasticity
87 95 100 100 108 115 119
Chapter 4 4.1
Quantity standard deviation vs price standard deviation in 23 LD countries 4.2 Food budget share against logarithm of per capita real consumption expenditures in LD countries 4.3a Food budget share vs Log (Income) for pooled data from 23 LD countries 4.3b Food budget share vs Log (Income) for pooled data from 22 LD countries (excluding Hungary) 4.4 Relative quantity against relative price in LD countries 4.5 Relative consumption vs relative prices for 9 commodity groups .... 4.6 Own-price elasticity against income elasticity
139 147 152 152 158 163 167
XXV
Chapter 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9
Average budget shares of 9 commodities, OECD vs LDC Average quantity log-changes in OECD and LD countries Average price log-changes in OECD and LD countries Quantity vs price standard deviations, 46 countries Relative consumption vs relative price in 46 countries Adjusted food budget share vs the logarithm of income - Pooled data from 44 countries Income elasticities of 9 commodities: OECD vs LD countries Own-price elasticities of 9 commodities: OECD vs LD countries Income elasticities vs own-price elasticities for 9 commodities in 46 countries
171 174 174 176 177 180 183 183 184
Chapter 6 6.1 6.2 6.3 6.4
Standard errors of the inflation estimates, Australia Estimated inflation rates vs their standard errors, Australia Estimated inflation rates vs their t-values, Australia Estimated inflation rates and their 95% confidence intervals, Australia 6.5 OECD inflation rates vs their standard errors 6.6 OECD inflation rates vs their t-values 6.7 LDC inflation rates vs their standard errors 6.8 LDC inflation rates vs their t-values 6.9 OECD quantity index estimates vs their standard errors 6.10 OECD quantity index estimates vs their t-values 6.11 LDC quantity index estimates vs their standard errors 6.12 LDC quantity index estimates vs their t-values
203 204 206 206 214 214 215 215 222 222 223 223
xxvi
TECHNICAL NOTES This book contains nine chapters and an Appendix. To aid the reader, each chapter has been written so that it is more or less self-contained. Each chapter contains a number of sections, subsections and a list of references. The sections in each chapter are numbered at two levels. The first level refers to the chapter and the second to the order of occurrence of the section within the chapter. For example, Section 2.4 is the fourth section in Chapter 2. Subsections are unnumbered. Equations are indicated by two numbers, the first refers to the section and the second to the order of occurrence within that section. For example, 'equation (2.8)' of Chapter 3 denotes the eighth equation in Section 2 of that chapter (Section 3.2). This equation is referred to in Chapter 3 as 'equation (2.8)'. If this equation is referred to in another chapter, then we use the terminology 'equation (2.8) of Chapter 3'. Tables and figures are indicated by two numbers, the first refers to the chapter and the second to the order of occurrence. For example, 'Table 4.5' refers to the fifth table of Chapter 4 and 'Figure 3.2' refers to the second figure of Chapter 3. Sections of the Appendix are numbered at two levels. For example, the second section of the Appendix is referred to as Section A2. Equations in the Appendix are numbered at three levels. For example, 'equation (A2.5)' refers to equation 5 of Section A2. Tables of the Appendix are numbered at two levels. For example, Table A.2 refers to the second table of the Appendix. Matrices are indicated by a boldface uppercase symbol (e.g., X). Vectors are indicated by a boldface lowercase symbol (e.g., x). The notation [xtJ] refers to a matrix whose (i,j)th element is xy, while x = [x,] refers to a column vector whose ith element is xt.
XXV11
ACKNOWLEDGEMENTS We wish to express our profound gratitude to Professor Ken Clements of the University of Western Australia for many stimulating discussions and helpful comments in writing the various chapters of the book, and for his encouragement and support. We would also like to thank Professor Clements and his colleagues Wana Yang and Dr Dongling Chen for their contribution of the User's Guide to the Demand Analysis Package, DAP2000, as an Appendix to this book. We are also grateful to Professor Prasada Rao of the University of New England for his invaluable comments on some of the chapters of the book. We also acknowledge the comments and suggestions of the anonymous reviewers and the editor of the book, which have helped improve the quality and presentation of the book. We would like to thank Dr Renuka Mahadevan, Mrs Tanya Tietze and Dr Nerissa Salayo for excellent research assistance during various stages of the project. We would also like to thank the publishing staff at World Scientific for their patience and support throughout the duration of the project. Finally, we acknowledge the financial support of an ARC (Small) grant, Griffith University, in assisting with the data collection and preliminary analysis. Our special thanks to our loving children, Arthavan (11 yrs) and Prabha (9 yrs), for their patience, support and clerical assistance throughout the duration of this project.
CHAPTER 1
An Overview of International Consumption Patterns £L4. Selvanathan <& S. Selvanathan
With the increasing trend in the globalization of national economies, understanding the consumption patterns of the consumers of a particular country is not only important to that country but also to all other countries in the world. As the barriers to international trade reduce, exporters look for a global market for their product. Therefore, understanding consumer behaviour around the Globe is becoming much more important than ever before. Even in less developed countries, due to globalization of the local economy, a class of wealthier consumers is emerging while the size of the class of consumers living under the poverty line is also on the increase. The main aim of this book is to study the consumption patterns of consumers using a huge and diverse database consisting of 46 countries. Such a large body of data should provide convincing evidence, one way or the other, about the validity of consumption theory. The book also presents a large number of applications of recent innovations in the area. The database includes 23 countries from the Organisation for Economic Co-operation and Development (OECD) which are all high-income and highly industrialised countries, and 23 Less Developed (LD) countries which are low-income countries. The countries within each group share a number of common features among themselves. At
2
International Consumption Comparisons
the same time, however, there are obvious differences in language, religion, culture and geography. The book also analyses whether these differences are of economic importance within the two groups and whether there are any differences in consumer preferences between the high-income and low-income countries. Understanding the behaviour of consumers from such a diverse group is important for a number of reasons. First, consumer spending is considered as a good objective economic indicator to measure the health of an economy. Second, private consumption absorbs a major portion of the Gross Domestic Product (GDP) in most countries, thus having a significant influence on the state of the economy as a whole and business conditions. Finally, an understanding of the price and income responsiveness of consumption is of crucial importance for a host of microeconomic policy issues including public utility pricing, optimal taxation and introducing various welfare measures. We start this chapter with an overview of the OECD and LD countries and then in the following section provide a short review of consumption theory. In Section 1.3, we present a review of some of the international consumption studies available. In the following section, we present a review of one of the pioneering international consumption study by Lluch, Powell and Williams (1977). Finally, in Section 1.5, we look at the issue of identical tastes at crosscountry level from a study by Selvanathan (1993).
1.1
An Overview of the OECD and LD Countries
Table 1.1 presents some general information on a number of basic characteristics such as land size, language, religion, population size and population density of the OECD and LD countries and their consumers.
Chapter 1 An Overview
3
Column 1 of the table lists the names of the countries. Columns 2 and 3 give the language and religious background of the people in each country. Column 4 gives the land size of each country (in '000 square kms). As can be seen, the countries are diverse in terms of the size of the country, the languages spoken and their religious belief. Column 5 gives the population for the year 2001 and columns 6 to 8 give the distribution of the population for 3 different age groups. Column 9 presents the population density (i.e., population per square kilometer). Obviously there are similarities and differences in the population characteristics among the consumers in the 46 countries. It can be easily seen from the table that in both the OECD and LD group of countries, the percentage of consumers in the age group 15-64 is about the same, about 60 to 70 percent. While the proportion of consumers in the aging population group (over 65 years) is high in the OECD countries compared to the LD countries, implying that people in rich countries have a higher life expectancy than those in poor countries. Also, the proportion of consumers in the younger age group (0-14 years) is higher in the LD countries than the OECD countries. These kinds of differences in the consumer distribution could result in significant differences in the demand for certain commodities. Another significant difference is in terms of the population density among the 46 countries. For example, the population densities for Hong Kong and Singapore are about 3000 times higher than that of Australia. On average, the LD countries have a higher population density compared to the OECD countries. Table 1.2 presents the main economic indicators of the OECD and LD countries. Columns 2 and 3 of the table present the details about each country's trading partners (exports and imports). As can be seen, the leading economies in the OECD group, USA, UK, Japan, Germany and France are the dominant players in the OECD as well as the LD countries. Columns 4 and 5 present the rate of inflation (in 2000) and the rate of unemployment (in 2000). While the
International Consumption Comparisons
4
Table 1.1 General characteristics of the OECD and LD countries Country
Language
Religion
(2)
(3)
Area
1Ftopdation 2001
Percentage population by age group
Fbpuatjon persqkm
OOOOsqkm) (pillions) {>14yrs 15-64yrs 65-yrs (1)
(4)
(5)
OECD Countries English, Aboriginal 19.40 7713.36 Anglican, Romm Catholic 1. Australia German ai3 Roman Catholic Anglican 83.85 2. Austria 10.24 Roman Catholic Dutch, French, German 30.52 3. Belgium 31.28 9976.14 Roman Catholic, Protestant English French, Inuktitut 4. Canada 5.34 Danish 43.09 Lutheran 5. Denmark Finnish, Swedish 5.17 Frotestant 338.13 Finland 6. French 59.33 551.50 Roman Catholic Frotestant, Islam 7. France Gerrran 82.80 Lutheran, Roman Catholic 356.91 8 Germany Greek 10.60 Greek Orthodox 131.99 Greece 9. Icelandic 0.28 Lutheran 103.00 10. Iceland Roman Catholic Fbtestant Irish English 3.80 70.28 11. Ireland Italian 57.63 301.27 Roman Catholic 12. Italy Japanese, Korean, Chinese Shinto, Buddhist, Christian 126.55 377.80 13. Japan Letzburgish, French, Gerrran 0.44 Roman Catholic 2.59 14. Luxembourg Dutch, Frysian 15.89 37.33 Roman Catholic Frotestant 15. Netherlands New Zealand English, Maori 3.82 Anglican, Romm Catholic Presbyterian 270.99 16. 4.48 Norwegian 323.90 Lutheran 17. Norway Portuguese Rorran Catholic 10.05 92.39 18. Portugal Catalan Roman Catholk 40.00 504.78 19. Spain Swedish a87 Lutheran, Frotestant 449.96 20. Sweden 7.26 Romanist 41.29 Roman Catholic FTOtestant 21. Switzerland English, Welsh, Scottish, Irish 59.51 244.88 Frotestant, Roman Catholk, Islam. Hindu, Judaism 22. UK English, Spanish 275.56 Frotestant, Roman Catholkjudaism 9372.61 23 US LD Countries 39.69 Roman Catholk: Spanish Colombia 1138.91 1. 0.76 Greek Orthodox, Christian, Islam Greek, Turkish 9.25 Cyprus 2. Roman Catholic 12.92 Spanish, Cuediua 283.56 3. Ecuador 0.83 1&27 English, Fijian, Hndi Christian, Wndu 4. Fiji Roman Catholic 6.25 112.09 Spanish, English 5. Honduras 7.12 Buddhist, Confucian, Taoist, Christian, Islam Hindu English, Chinese Hong Kong 1.04 6. 10.14 Hungarian 93.03 Roman Catholic Frotestant 7. Hungary 1014 Ffindu, Islam Sikh, Christian Ffndi, English, Tanil 3287.59 8. India 65.62 Farsi, Turkic Kurdish 1648 Islam Christian 9. Iran 5.84 Hebrew, Arabk 20.77 JeiMsh, Islam 10. Israel 2.65 10.99 Frotestant, Romm Catholk English 11. Jamaica 47.47 99.02 Buddhist, Protestant, Roman Catholic Confudanist Korean 12. Korea 0.39 0.32 Rorran Catholk Maltese, English 13. Malta Roman Catholic Spanish 100.35 1958.2 14. Mexico 81.16 300 Roman Catholic Islam Filipino, English Spanish 15. Philippines Romm Catholic ftotestant Spanish, English 3.92 8.9 16. Puerto Rico Chinese, hfelay, Tanil, English Buddhist, Christian, Islam Taoist, Hindu 4.15 17. Singapore 0.62 Africaans, English, Xhosa, Zulu Christians, Ftoman Catholic 43.42 1221.04 18. South Africa 19.24 Buddhist, Hindu, Islam Christian Sinhalese, Tanil, English 65.61 19. Sri Lanka Buddhist, Confucian, Taoist, christian 22.19 35.74 Chinese, Taiwanese 20. Taiwan Thai, Chinese, Malay 61.23 513.12 Buddhist, Islam 21. Thailand Romm Catholic Spanish 23.54 22. \fenezuela 912.05 11.34 English, Bantu 390.58 Christian, Anirrist 23. Zimbabwe Source: The Wforld Fact Book', wm.ofa.gotJa^fxMi&tians/fdctixxi^ and US Bureau of the Census, International Database.
(6)
(7)
(8
(9)
21 17 17 19 19 18 19 16 15 23 22 14 15 19 18 22 20 17 15 18 17 19 21
67 68 66 68 67 67 65 68 67 65 67 68 68 67 68 66 65 67 68 65 68 65 66
12 15 17 13 15 15 16 17 18 12 11 18 17 14 14 12 15 16 17 17 15 16 13
2.52 96.96 335.52 3.14 123.93 15.29 107.58 231.99 80.31 2.72 54.07 191.29 334.97 169.88 425.66 14.10 13.83 108.78 79.24 19.71 175.83 243.02 29.40
32 23 36 33 42 18 17 33 33 27 30 22 20 33 37 24 18 32 26 21 23 32 39
63 66 60 63 54 72 69 62 62 63 63 71 67 62 59 66 75 63 67 70 70 63 58
5 11 4 4 4 11 15 5 5 10 7 7 13 5 4 10 7 5 7 9 7 5 3
34.85 82.15 45.56 45.43 55.76 6846.15 109.00 308.43 39.82 281.17 241.13 479.40 1218.75 51.25 270.53 440.45 6693.55 35.56 293.25 620.87 119.33 25.81 29.03
5
Chapter 1 An Overview Table 1.2 Economic characteristics of the OECD and LD countries
(1) OECD Countries 1. Australia 2. Austria 3. Belgium 4. Canada 5. Denmark 6. Finland 7. France 8. Germany 9. Greece 10. Iceland 11. Ireland 12. ItaJy 13. Japan 14. Luxembourg 15. Netherlands 16. New Zealand 17. Norway 18. Portugal 19. Spain 20. Sweden 21. Switzerland 22. UK 23. US LD 1. 2. 3.
Countries Colombia Cyprus Ecuador
Inflation Unemployment
Major Trading Partners
Country
Export
Import
(2)
(3)
Japan, US, Korea USJapan, China Germany, Italy, Switzerland Germany, Italy, Switzerland France, German/, Netherlands Netherlands, Germany, France US. Japan, UK Us Japan, China Germany, Sweden, UK Germany, Sweden, UK Germany, Sweden, Russia Germany, Sweden, UK Germany, Belgium, Italy Germany, UK Spain France, Nethedands, US France. US, UK Italy, Germany, France Germany, Italy, UK Germany, US, UK UK. Germany, US UK US, Germany UK, US, Germany Germany, France, US Germany, France, Netherlands US, China, Korea US, China, Korea Belgium, Germany, France Germany, France, Belgium Germany, US, UK Germany, Belgium, France Australia, USJapan Australia US, Japan UK, Netherlands, France Sweden Germany, UK Spain, Germany, France Spain Germany, France France, Germany, Italy France, Germany, Portugal Germany, UK Norway Germany, US, UK Germany, France, Italy Germany, US, France Germany, US. France US, Germany, France Canada, Mexico, Japan Canada, Mexico, Japan
2000 (4) 4.50 2.40 2.50 2.70 2.90 3.40 1.70 1.90 3.10 5.20 5.60 2.50 •0.70 2.90 2.50 2.70 3.10 2.90 3.40 1.00 1.50 2.90 3.40
Real per capita GDP in 1992
2000
inSUS
US-100
locXGDP)
(5)
(6)
(7)
(8)
6.3 3.70 10.90 6.80 5.40 9.80 9.50 10.50 11.40 1.30 4.10 10.50 4.70 2.70 2.60 6.00 3.40 4.00 14.10 4.70 2.00 5.50 4.00
18500 16989 18091 20970 18730 15619 18232 20197 8658 16324 12259 16724 19920 21144 17373 15502 17094 9005 12986 18387 21631 16302 23220
80 73 78 90 81 67 79 87 37 70 53 72 86 91 75 67 74 39 56 79 93 70 100
9.83 9.74 9.80 9.95 9.84 9.66 9.81 9.91 9.07 9.70 9.41 9.72 9.90 9.96 9.76 9.65 9.75 9.11 9.47 9.82 9.98 9.70 10.05
Food budget share 1992 (9) 0.20 0.19 0.18 0.16 0.21 0.24 0.18 0.21 0.36 0.25 0.33 0.20 0.19 0.19 0.15 0.19 0.22 028 0.20 0.20 0.27 0.21 0.12
4254 0.34 8.36 18 16.70 8.00 US, Venezuela, Ecuador US, Venezuela Mexico 9.37 51 11742 3.40 UK Greece, Russia 0.26 4.10 UK US, Italy 8.14 15 3420 10.30 96.10 US, Colombia, Venezuela US, Korea, Colombia 0.39 8.57 S288 Australia, re, Singapore 0.37 23 6.00 1.10 Australia, US, UK 4. Fiji 7.49 8 1792 28.00 11.00 US, Guatemala Japan US, Germany, Belgium 5. Honduras 0.45 21034 9.95 91 5.10 -3.80 China Taiwan Japan China, US, Japan 6. Hong Kong 0.16 866 0.37 25 5780 6.40 9.80 Germany, Samoa, Italy Germany, Russia Italy 7. Hungary 7 7.40 1633 4.40 4.00 US, Hong Kongjapan 8. India 0.53 US, Belgium Singapore 8.33 18 4161 14.00 14.50 Germany, Korea, Italy Japan, Italy, Korea 9. Iran 0.35 9.46 US, Belgium, Germany 0.24 55 12783 8.80 1.10 US, Belgium UK 10. Israel US, UK, Canada US, UK Canada 0.41 8.00 13 2978 16.00 8.80 11 .Jamaica 9.14 4.00 Japan, US, China 0.30 40 9358 2.30 US, Chinajapan 12. Korea 8.94 France, Italy, Singapore US, Singapore, Germany 0.31 33 7625 5.30 2.40 13 Malta US, Canada, Germany 8.97 34 7867 2.20 9.50 US, Japan, Germany 14. Mexico 0.28 2172 Japan, US, Korea USJapan, Taiwan 15. Philippines 0.58 7.68 9 11.00 4.30 8.87 31 US, Dominican, Netherlands US, lreland,japan 0.22 7120 9.50 5.70 16. Puerto Rico 72 17. Singapore 0.17 9.73 16736 3.00 1.40 Malaysia, USJapan Malaysia US, Hong Kong 8.26 17 3885 30.00 5.30 Germany, US, UK US, UK Japan 18. South Africa 0.36 7.93 12 19. Sri Lanka 0.59 2783 7.60 6.20 Japan, India Hong Kong US, UK Germany 9.20 42 9850 3.00 1.30 Japan, US, Korea US, Hong Kongjapan 0.28 20. Taiwan 8.52 Japan, US, China USJapan, Singapore 21. Thailand 22 5018 3.60 1.60 0.29 9.04 36 8449 US, Colombia, Brazil US, Nethedands, Brazil 22. Venezuela 0.41 13.90 16.20 South Africa UK Japan 23. Zimbabwe 7.30 6 1479 50.00 55.70 South Africa UK, Mozambique 0.30 Source: Columns 2-5 are based on year 2000 trade figures obtained from FACT sheet, Department ofForeign Affairs and Trade, Australia. GDP are from Perirvorld Tables by Heston and Summers. For Honduras, the entries are from The World Fact Book', vwiw.cxfci.Q^x^da/puHications/factbook; and GDP and budget share entries for Puerto Rico are for 1985 and for Taiwan are for 1990.
6
International Consumption Comparisons
OECD countries enjoy a lower rate of inflation combined with a lower rate of unemployment, the LD countries have a much higher rate of inflation coupled with a higher rate of unemployment, with the exception of the four Asian Tigers, namely, Hong Kong, Singapore, Korea and Taiwan. Column 6 of Table 1.2 gives the real per capita GDP (for the year 1992). As can be seen, among the LD countries, the per capita GDP of Hong Kong and Singapore are comparable with many OECD countries and are even higher than some of the OECD countries (for example, Greece and Portugal). For ease of comparison, in column 7, we present the GDP with US=100. Column 8 presents the logarithm of real per capita GDP for all countries. The last column of the table gives the food budget share for the 46 countries. Comparing columns 7 and 9, we can see an inverse relationship between the per capita real GDP and the food budget share. That is, the food budget share decreases with increasing real GDP. This is illustrated in Figure 1.1, where we plot the food budget share against the logarithm of per capita real GDP. As can be seen, a clear inverse relationship exists between food budget share and the per capita real GDP. This observation supports the famous law in consumption economics, the Engel's Law, which states that food budget share falls with increasing income. More on Engel' s law will be discussed in the later chapters.
1.2
Consumption Theory
The objective of consumption theory is to analyse the demand for goods and services in terms of income and prices. In Chapter 2, we present a detailed description of consumption theory. In this section, we present a simplified description of this theory.
Chapter 1 An Overview
y = -0.1196x+ 1.3748
Food budget share o o ro *.
0.6 -
^ $ * >
0.0 8
9
10
Ln(GDP per capita)
Food budget share vs logarithm of per capita GDP for 46 countries Figure 1.1
Consider a demand function for commodity i of the form M log # = a + P log —-1 + y log vP \Pj
(2.1)
where q-x is the quantity consumed of i; M is the consumer's money income; P is a general price index; pt is the price of i; and a, P and y are constants. The coefficient P in equation (2.1) is interpreted as the income elasticity, i.e.,
8
International Consumption Comparisons 8(log g| .)
T og yJ This elasticity describes the income sensitivity of consumption of the good. The coefficient y is the price elasticity of demand, i.e., dflogg,) '
< * * ) '
As demand curves slope downwards, this elasticity is negative. The income variable in equation (2.1) is money income (M) deflated by the general price index (P). Thus MIP is interpreted as real income. As real income is being held constant, if p/P changes, then the response of consumption to this change reflects the pure substitution effect only. As the coefficient y measures this response, it is known as the "income-compensated" price elasticity, or the compensated price elasticity for short. The size of y reflects the availability of substitutes; y will be higher (in absolute value) when there are more good substitutes available. As the two variables on the right-hand side of equation (2.1) are both expressed in real terms (real income and the relative price of i), it follows that an equi-proportional increase in the nominal variables M, p± and P has no effect on consumption. This property of the demand equation is known as the absence of money illusion of the consumer, or demand homogeneity (as the demand equation is homogeneous of degree zero in nominal variables). The key virtue of model (2.1) is its simplicity. Its parameters have a straightforward economic interpretation and the model can be easily estimated. However, it suffers from several deficiencies. The first problem is that it does
9
Chapter 1 An Overview
not give any explicit attention to consumer preferences, which lie behind the demand equation. Second, the model deals with the demand for commodity i in isolation from all other goods. The model consists of only one equation whereas in fact there is one equation for each of the n goods consumed. A related deficiency is that the model does not allow good i to be more closely related to some goods and less to others. This is because the model specifies that all crossprice elasticities d(logg,-)
i*j.
logy are zero. A simple way of rectifying the second deficiency is to extend model (2.1) by adding to it terms involving the prices of other goods. Let there be n goods with prices p\,..., p„. An extended version of (2.1) is then M log qx = a; + PJ log —
+ £ Ytj log
i=l,...,n.
In model (2.2) the coefficient pi is the income elasticity (as before) and aqogg,.)
n = —r
log
Pj
(2.2)
International Consumption Comparisons
10
is the compensated elasticity of demand for good i with respect to the price of good j . It is to be noted that (2.2) consists of n equations, which describe the demand for the n goods simultaneously. Accordingly, (2.2) is a 'system-wide' demand model (Theil, 1980). As p,qi is expenditure on good i, expenditure on all n goods is X"=i p,-<7,-..In what follows, we call this sum 'income' although strictly speaking it is total expenditure. The value of income (denoted by M, as before) is taken to be exogenous or outside the control of the consumer. Accordingly, the consumer's budget constraint takes the form
ZPiGi = M.
(2.3)
i=l
Differentiating both sides of (2.3) with respect to M yields
i=i
oM
As the income elasticity holds constant prices, it can be formulated as 3(log<7,) 3(logM)
Pi =
Using the identity d(log x) = dx/x, this elasticity can also be expressed as
&
=
-
!
&
•
(
2
'
5
)
11
Chapter 1 An Overview
We define Pitt
M
as the share of income devoted to good i. Using (2.5) and (2.6) in (2.4), we obtain
I w,A=l.
(2.7)
In words, the budget constraint (2.3) implies that a weighted-average of the n income elasticities is unity. It can also be shown that the budget constraint implies the following constraint on the price elasticities: E^fpO,
j=l,...,iL
(2.8)
The n equations in model (2.2) need to be estimated subject to constraints (2.7) and (2.8) to ensure that the estimates satisfy the budget constraint. It is to be noted that (2.7) and (2.8) are cross-equation constraints on the parameters of the demand equations. This emphasises the interrelationships between the consumption of the n goods; as income is fixed, a rise in expenditure on one good means that expenditure on at least one other must fall. Another cross-equation constraint that needs to be imposed on the parameters of model (2.2) is Slutsky symmetry, or symmetry of the substitution
International Consumption Comparisons
12
effects. This constraint, implied by the utility-maximizing theory of the consumer, takes the form dqj
%,
dPi
real income constant
*Pj
i,j=l,...,«. real income constant
To formulate this constraint in terms of the parameters of (2.2), we note that 9(logg,.) Pj) log
Yy
9(logg,) BQogpj)'
where the approximation is based on 9(log P)/3(log p,) ~ 0. As real income is held constant in (2.2), we have Pj dqt Yij
»
9i fyj
real income constant
Accordingly, Slutsky symmetry can be approximated by WiYu = WJYJI,
1,J—1,...,/X,
where we have used the definition of w} given in (2.6). To illustrate explicitly the effect of the consumer's preferences on the demand equations, consider the following algebraic form of the utility function:
13
Chapter 1 An Overview u(qu...,qn)
= I
(2.9)
a,. log(qr,--&,-),
where the a^s and bj's are coefficients satisfying X a,; = 1 and ft j < ^j. i=l
Maximizing (2.9) subject to the budget constraint (2.3) yields the following demand equations
q, = b,+
M- I Pi I
pjbj
i-l
"i
J=I
or, multiply both sides by p\, PU\
P\b\+ ai M - Z pjbj
i=l,...,n.
(2.10)
As model (2.10) expresses expenditure on i as a linear function of prices and income, it is known as the linear expenditure system (LES). This demand system was first used by Stone (1954a, 1954b). As can be seen, the form of the utility function implies the form of the demand equations. It is to be noted that the form of the utility function (2.9) is very simple. Its additive nature implies that there are no interactions between the goods in generating utility; i.e., the marginal utility of each good is independent of the consumption of all others. Such additive utility structure is called 'preference independence'. We shall
14
International Consumption
Comparisons
consider, in detail, preference independence and its implication to consumer demand in Chapters 2, 3, 4, 5 and 9. Another aspect of the LES should also be noted. That is, it cannot be used to test the homogeneity and symmetry hypotheses as these are built in or maintained hypotheses in this model. However, such restrictions may not be at great variance with the data if the model is applied to broad commodity groups. In the main, this book deals with system-wide demand models, which are closely linked to the structure of the consumer's preferences.
1.3
A Review of International Consumption Comparisons
The modern literature on international consumption comparisons probably started with Houthakker (1957) who estimates double-log Engel curves from cross-sectional data for a large number of countries. As Houthakker uses crosssectional data with no variation in prices, he does not estimate price elasticities. Subsequently, others have used time-series data for a number of countries to provide estimates of both income and price elasticities; more recently Selvanathan (1993) and Chen (2001). Selvanathan (1993) considered 18 OECD countries over the time period up to the early 1980s and Chen extended Selvanathan's analysis by adding 13 less developed countries (a total of 31 countries) with roughly the same time period. Table 1.3 provides a tabulation of the major consumption studies. We now discuss two of the most recent developments in international consumption comparisons. The first development was due to international consumption comparisons adopted by Clements and Theil (19961), who used
Published in 1996 but the research was carried out in the late 1970s at the University of Chicago.
15
Chapter 1 An Overview Table 1.3 Major studies in international consumption comparisons Authors
(1) 1.
Chen (2001)
Countries
(2) 31 OECD/LD countries
Type of Data
(3) Time series
Period
Number of commodities
Model
(6)
(4)
(5)
1960-1984
8
Working's
2.
Clements and Theil (1996)
16 countries
Cross-country
4
Working's
3.
Camaletsos (1973)
11 OECD countries
Time series
1950-1965
5
LES, GLES and IAES
4.
Coldberger and Gamaletsos (1970) 13 OECD countries
Time series
1950-1961
5
LES and DL
5.
Houthakker(1957)
30 countries
Cross-sectional
4
DL
6.
Houthakker (1965)
1 3 OECD countries
Time series
5
DL
7.
Kravis e t a l (1982)
34 countries
Cross-country
8.
Lluch and Powell (1975)
19 countries
Time-series
1946-1968
8
LES
9.
Lluch e t a l (1977)
17 countries
Time series
1953-1969
8
ELES
10. Lluch and Williams (1975)
14 countries
Time series
1955-1969
8
ELES
1 1 . Parks and B a r t e n d 973)
14 OECD countries
Time-series
1950-1967
5
variant of LES
12. Pollak and Wales (1987)
Belgium, UK and US
Time-series
1961-1978
3
QES
13. SelvanathanS(1993)
18 OECD countries
Time-series
1960-1981
10
Working's
14. Theil (1987)
3 0 countries
Cross-country
10
Working's
15. Theil and Suhm (1981)
1 5 countries
Cross-country
8
Working's
16. Theil e t a l ( 1 9 % )
30 countries
Cross-country
10
Working's
1948-1959
103 and 25
DL and LES
* LES=Linear expenditure system; GLES=Ceneralised LES; IAES=lndirect additive expenditure system; DL=double-log demand model; ELES=Extended LES; QES=Quadratic expenditure system.
data from Kravis et al (1978) on 16 countries to estimate a common system of demand equations for all countries. In comparison with the usual time-series application for a given country, here countries play the role of time periods. This idea has been built on by Theil and Suhm (1981). Under this approach, tastes are taken to be the same internationally. Although this is obviously a rather bold assumption, it is one forcibly advocated by Stigler and Becker (1977). Stigler and Becker hypothesize that tastes neither change capriciously nor differ importantly between people. In an international context, this hypothesis amounts to stating that consumers in different countries are similar irrespective of
16
International Consumption Comparisons
differences in language, religion, culture and geography. In an innovative paper, Pollak and Wales (1987) formally tested this hypothesis. They use the quadratic expenditure system with time-series/cross-country data for Belgium, the UK and the USA. On the basis of likelihood ratio and nonparametric (revealed preference) tests, they conclude that the data from these countries cannot be pooled to estimate a common demand system. That is, they reject the hypothesis of identical tastes. Selvanathan (1993) also tested Stigler and Becker (1977) hypothesis using consumption data for the 18 OECD countries. First the consumers in different countries were allowed to be idiosyncratic and 18 separate systems of demand equations were estimated, one for each country. Then it was specified that consumers in different countries have identical tastes. That is, the parameters of the demand equations were taken to be the same across countries. This involves pooling the data and estimating a common demand system for all countries. Now, the restrictions of the pooled model against the individual country model are formally tested by means of a likelihood ratio test. Selvanathan (1993) also concluded that the data from these countries cannot be pooled to estimate a common demand system. That is, the hypothesis of identical tastes should be rejected. For more on the issue of identical tastes among consumers, see Section 1.5. The second development resulted from the analysis of the extensive detailed data collected and compiled by Kravis et al (1982). A leading example of such a cross-country application is by Theil (1987) and Theil et al (1996), who used data compiled by Kravis et al (1982). These data, which are part of the International Comparisons Project sponsored by the United Nations and the World Bank, cover 34 countries and provide comparable price and volume indices for more than 100 detailed categories of consumption. This study differs from other studies reported in the literature (see Table 1.3) in one or more of the following ways: the number of commodity groups used and the level of
Chapter 1 An Overview
17
aggregation, the countries included, the time period used and the demand model used. In the next section, we discuss one of the pioneering international consumption study by Lluch et al (1977).
1.4
A Pioneering International Consumption Study
The international consumption comparisons presented in this book consider the consumption data for 23 OECD countries and 23 LD countries. However, in this section, we present results from one of the pioneering international consumption studies, which uses a different database, but includes both developed and developing countries. Relative to the OECD or LDC separately, these data exhibit more cross-country variability in income as it contains a mix of both OECD and LD countries but for only a total of 13 countries. The material presented in this section is mainly from Selvanathan (1988). In a pioneering study, Lluch, Powell and Williams (1977) - hereafter LPW - used data for 8 commodity groups in 17 countries. Table 1.4 presents an overview of the data for 13 of the 17 countries with countries ordered in terms of declining per capita GNP. (See Selvanathan, 1988, for the reasons for not considering 4 of the LPW countries.) As can be seen, the US has the highest per capita GNP, while Korea has the lowest with only 4 percent of the US value. Table 1.5 presents the budget shares at sample means of the 8 commodities in each country. Note the strong tendency for the food budget share to decline with increasing GNP, which is in accordance with Engel's law. The upper half of Table 1.6 presents the average annual price log-changes, while the lower half presents the corresponding per capita quantity log-changes. Next, we summarize these data with Divisia indices. Let wic be the budget share of i
International Consumption Comparisons
18
Table 1A Characteristics of the LPW database CNPat sample midpoint Country
Sample period (2)
(1) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
US Sweden Australia UK Israel Italy Puerto Rico Ireland Greece South Africa Panama Thailand Korea
1955-68 1955-68 1955-66 1955-68 1959-68 1955-68 1955-67 1955-68 1958-68 1955-68 1 960-68 1960-69 1955-68
GNPin 1970 US$ (3)
(3) with US=100 (4)
3669 2962 2192 1900 1468 1207 1023 1014 676 596 564 148 142
100 81 60 52 40 33 28 28 18 16 15 4 4
Source: Lluch etal. (1977, Table 3.2).
for country c at sample means (given in Table 1.5); and Dpic and DqiC be the mean price and quantity log-changes (Table 1.6). The Divisia volume and price indices for country c are then DQe = I
wicDqic,
DPC =
TwicDpic,
c=l
13,
and are presented in columns 2 and 3 of Table 1.7. As can be seen from the last row of the table, on average, per capita consumption grew at a rate of 3.5 percent per annum, while prices in these countries increased by 3.3 percent per
Chapter 1 An Overview
19 Table 1.5
Durables
Other services
Housing
Recreation
Clothing
Transport
Food
Personal care
Budget shares of eight commodities in 13 countries (Means x 100)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
US
26.7
9.5
22.7
7.3
8.1
15.2
5.5
4.9
Sweden
36.6
11.5
15.9
7.0
3.7
14.2
8.9
2.4
3.
Australia
33.3
11.0
12.7
7.8
5.7
13.1
4.3
12.1
4.
UK
39.7
10.7
18.3
6.6
2.3
10.9
7.5
4.0 10.0
Country (1) 1. 2.
5.
Israel
31.9
9.4
19.2
7.4
6.6
7.3
8.1
6.
Italy
46.3
10.1
16.6
3.2
6.3
8.1
7.5
1.8
7.
Puerto Rico
35.6
10.6
15.3
6.9
6.9
12.3
8.8
3.7
8.
Ireland
49.2
10.0
12.8
5.7
1.3
8.8
6.3
5.9
9.
Greece
46.8
12.2
18.3
3.9
3.6
6.9
6.1
2.3
10. South Africa
36.8
11.8
16.7
7.8
4.8
13.2
4.7
4.1
11. Panama
45.5
7.4
16.7
6.4
4.7
9.4
7.5
2.3
12. Thailand
57.6
8.4
8.0
3.2
5.6
7.9
7.5
1.8
13. Korea
59.9
10.4
11.4
2.8
4.2
4.7
4.4
2.2
Mean
42.0
10.2
15.7
5.8
4.9
10.2
6.7
4.4
Source: Lluch et ai 0977, Table 3.3).
annum. Columns 4-6 of the table contain the corresponding second-order moments, Divisia quantity and price variances, defined in Chapter 2. As can be seen, the Divisia quantity variances systematically exceed the price variances. We will investigate this empirical regularity with data from 46 countries in Chapters 3 and 4. The last column of Table 1.7 presents the Divisia price-
International Consumption Comparisons
20
Table 1.6 Prices and per capita quantities consumed of eight commodities in 13 countries (Mean annual log-changes x 100)
o
Country
Li-
(2)
(1)
(J
(3)
o I (4)
Q
H
(5) P r i ices
(6)
(7)
V
6
a. (8)
(9)
1.
US
1.85
1.62
1.70
0.55
3.04
1.52
2.35
4.31
2.
Sweden
4.00
2.25
3.85
1.79
2.85
3.46
4.22
3.70
3.
Australia
2.32
1.39
4.87
0.48
3.15
1.96
2.92
3.02
4.
UK
2.1 1
1 .70
4.68
1.69
3.09
2.93
4.62
3.80
5.
Israel
4.85
4.65
7.81
1.94
6.46
8.06
5.97
7.22
6.
Italy
2.52
2.1 7
3.65
-0.16
4.24
2.27
4.07
4.19
7.
P u e r t o Rico
2.62
1 .44
1.27
0.83
5.76
2.83
3.20
2.46
8.
Ireland
3.18
0.89
3.98
3.1 5
1.33
3.13
3.63
4.24
9.
Greece
2.57
1 .20
1 .59
0.67
2.48
1.87
0.55
0.69
10.
South Africa
2.27
0.20
3.50
0.32
3.90
2.40
2.49
3.40
1 1.
Panama
1.95
0.59
0.54
0.1 1
2.24
0.04
0.97
0.00
12.
Thailand
1 3.
Korea
3.24 1 3.28
Mean
0.19 14.75
-2.63
-1.64
1.33
0.06
2.43
2.02
1 1.27
12.54
16.70
12.69
13.91
14.80
1 .71
4.35
3.29
3.95
4.14
3.60
2.54
3.54
Quantities 1.
US
0.99
2.42
2.79
3.70
3.90
2.78
2.86
3.63
2.
Sweden
1.51
1.76
2.77
5.25
5.62
5.32
2.28
4.03
3.
Australia
0.78
0.66
2.34
3.14
4.09
3.12
0.10
1.89
4.
UK
1 .62
2.44
1 .98
3.08
3.75
5.53
1.37
6.48
5.
Israel
4.62
6.87
5.41
1 1.67
5.96
9.24
8.58
5.17
6.
Italy
4.09
4.62
4.62
8.51
5.96
9.46
4.28
4.47
7.
P u e r t o Rico
-0.28
3.91
3.25
4.4 5
1.40
5.13
4.89
5.89
8.
Ireland
1.91
4.88
2.51
5.85
2.71
5.32
3.72
2.47
9.
Greece
4.14
7.92
5.99
6.41
5.67
8.94
8.08
6.48
10.
South Africa
1 .04
2.20
0.57
3.21
1.81
3.32
1.22
2.48
1 1.
Panama
2.59
3.23
1.92
5.06
2.55
2.01
4.36
2.84
12.
Thailand
2.1 5
5.30
1.06
10.16
3.70
6.55
5.59
7.16
13.
Korea
1.94
2.35
2.27
6.88
4.95
1 1.55
5.69
3.31
2.08
3.74
2.88
5.95
4.01
6.02
4.08
4.33
Mean
Source: Derived
from
Lluch et al. (1977,
Tables 3.4 and
3.5).
21
Chapter 1 An Overview
Table 1.7 Divisia moments in 13 countries
Country
Divisia quantity index
Divisia price index
Divisia quantity variance
Divisia price variance
Divisia price-quantity correlation
DQ
DP
K
n
P
(2)
(3)
(4)
(5)
(6)
1.
US
2.47
1.89
0.97
0.57
0.20
2.
Sweden
2.83
3.52
2.41
0.56
-0.42 0.09
(1)
3.
Australia
1.75
2.51
1.32
1.28
4.
UK
2.52
2.88
2.15
1.33
0.05
5.
Israel
6.30
5.85
4.40
2.89
-0.31
6.
Italy
4.94
2.82
2.53
0.79
-0.30
7.
Puerto Rico
2.49
2.40
5.17
1.32
-0.30
8.
Ireland
2.97
3.11
1.95
0.73
-0.42
9.
Greece
5.71
1.93
2.86
0.50
-0.80 -0.47
10. South Africa
1.67
2.23
0.96
1.24
11. Panama
2.76
1.21
0.73
0.65
-0.15
12. Thailand
3.37
1.92
4.51
3.63
-0.38
13. Korea
2.93
13.36
5.11
1.27
0.05
Mean
3.29
3.51
2.70
1.29
-0.24
All entries in columns 2 and 3 are to be divided by 100 and columns 4 and 5 by 10000.
quantity correlation. As can be seen, most of the correlations are negative with an average of -.24. The Linear Expenditure System
Stone's (1954b) linear expenditure system discussed in Section 1.2 is probably the most popular demand system. Notable studies using this model include
22
International Consumption Comparisons
Deaton (1975), Goldberger and Gamaletsos (1970), Kravis et al (1982), Lluch and Powell (1975), Lluch et al (1977), Parks (1969), Pollak and Wales (1969,1992) and Yoshihara (1969). In this section, we reproduce the estimation results of the linear expenditure system from the LPW study. LPW uses time-series data to estimate LES (or a variant thereof, Lluch's, 1973, the extended linear expenditure system) for the 13 countries listed in Table 1.4. The model is estimated for each country independently of the others. The upper part of Table 1.8 presents the estimates of the marginal shares (i=l,...,8 goods; c=l,..., 13 countries), while the lower part gives the implied income elasticities, ri
i c
=^, w
(4.1)
ic
using the mean budget shares from Table 1.5. As can be seen from the last row of Table 1.8, on average, food and housing are necessities (r|jc < 1), clothing is a borderline case while the remaining five goods are luxuries (r|iC > 1). Notwithstanding its popularity, LES has its drawbacks. Perhaps the most important is the parameterization whereby the marginal shares are treated as constants. It is clear from (4.1) that the constancy of the marginal share implies that the income elasticity is inversely proportional to the corresponding budget share. This can give rise to problems when income is subject to large changes.
1.5
Are Tastes Constant?
One of the other areas where consumer demand analysis is gaining significance is the argument that consumer tastes are the same or similar across countries. In
Chapter 1 An Overview
23
Table 1.8 Marginal shares and income elasticities for eight commodities in 1 3 countries
Country
o U-
u
I
a
CL
H
(5)
(6)
(7)
(8)
0.14 0.05 0.13 0.03 0.07 0.07 0.1 1 0.01 0.05 0.05 0.04 0.05 0.07
0.1 7 0.25 0.22 0.28 0.12 0.12 0.18 0.17 0.1 1 0.21 0.09 0.12 0.15
0.07 0.10 0.01 0.07 0.12 0.07 0.14 0.08 0.08 0.05 0.13 0.15 0.08
0.1 1 0.02 0.14 0.1 1 0.10 0.02 0.07 0.07 0.03 0.06 0.02 0.03 0.04
0.07
0.17
0.09
0.06
1.69 1 .41 2.33 1.30 1.00 1.05 1.65 1.08 1.33 1.02 0.94 0.93 1.76
1.1 5 1.78 1.71 2.54 1.59 1.44 1.43 1.93 1.55 1.56 0.90 1.56 3.1 1
1.18 1.09 0.21 0.88 1.44 0.93 1.56 1.19 1.36 0.98 1.69 2.00 1.77
2.31 1.00 1.14 2.65 0.97 1.06 1.95 1.19 1.22 1.44 0.83 1.56 1.73
1.35
1.71
1.25
1.46
(2)
(3)
(4)
Israel Italy 7. Puerto Rico Ireland 8. Greece 9. 1 0 . South Africa 1 1. Panama 1 2 . Thailand 1 3 . Korea
0.09 0.28 0.14 0.12 0.21 0.40 0.18 0.32 0.34 0.30 0.42 0.48 0.43
0.1 1 0.07 0.05 0.07 0.10 0.09 0.1 1 0.13 0.17 0.16 0.08 0.10 0.07
0.21 0.1 5 0.22 0.26 0.17 0.17 0.14 0.1 1 0.18 0.07 0.1 1 0.01 0.09
0.1 1 0.08 0.08 0.08 0.12 0.07 0.07 0.1 1 0.05 0.12 0.1 1 0.05 0.08
Mean
0.29
0.10
0.14
0.09
1.
US
2.
Sweden Australia
0.34 0.76 0.43 0.30 0.66 0.87 0.50 0.64 0.73 0.80 0.92 0.84 0.73
1 .14 0.62 0.46 0.63 1.10 0.86 1.06 1.34 1.38 1.39 1.10 1.20 0.66
0.91 0.91 1.73 1.41 0.90 1.03 0.94 0.84 0.96 0.40 0.68 0.16 0.75
1.45 1.13 1.05 1.1 5 1.61 2.16 0.99 2.00 1.28 1.47 1.77 1.63 2.75
0.65
0.99
0.89
1.57
(1)
O (9)
M arginal shares 1.
US
2. 3.
Sweden Australia
4.
UK
5. 6.
Income elasticities
3. 4.
UK
5.
Israel Italy Puerto Rico Ireland Greece South Africa Panama Thailand Korea
6. 7. 8. 9. 10. 11. 12. 13.
Mean
Source: Marginal shares are from Lluch et al. (1977, Table 3.6) and income elasticities are derived using equation (4.1).
24
International Consumption Comparisons
this section we present some cross-country and regional results directly from Clements and Selvanathan (1994, Sec. 8), which originated from the work of Selvanathan (1993, Chapter 4). In a highly-influential paper, Stigler and Becker (1977) advocates treating tastes as fixed. Their argument has merit as the utility maximization theory usually postulates that tastes are fixed, so that it is only the observable variables income and prices that explain consumption. Stigler and Becker show that a number of examples of apparently capricious behaviour (addiction, custom, tradition, fashion etc.) can in fact be reconciled with the assumption of stable preferences. Stigler and Becker (p.89) argue that, "no significant behaviour has been illuminated by the assumption of differences in tastes. Instead, they, along with the assumption of unstable tastes, have been a convenient crutch to lean on when the analysis has bogged down. They give the appearance of considered judgement, yet really have only been ad hoc arguments that disguise analytical failures." Selvanathan (1993, Chapter 4) carried out an analysis to test the hypothesis of stable preferences by estimating demand equations for different groups of consumers and then analysing the extent to which the parameters (such as the income and price elasticities) differ across consumers. Selvanathan performed the analysis with the OECD database (consisting of 15 countries with 10 commodity groups) by estimating (i) country-specific demand equations; and (ii) common demand equations for all countries whereby the data are pooled across countries. The test then involved an analysis of the deterioration in the fit of the demand equations when the data are pooled. In other words, this amounted to investigating the extent to which the same demand equations can explain consumption in the different OECD countries. The upper part of Table 1.9 contains the results using the root-meansquared (RMS) percentage prediction error as the goodness-of-fit criterion for
25
Chapter 1 An Overview
Table 1.9 Quality of budget share predictions in OECD countries and Australian states RMS percentage prediction error Country (1) OECD Countries 1. US 2. Canada 3. Sweden 4. Denmark 5. Australia 6. France 7. Belgium 8. Norway 9. Netherlands 10. Iceland 11. Finland 1 2. Austria 13. UK 14. Spain 1 5. Italy
Weight (xl 00) (2)
51.34 5.14 1.84 1.01 2.74 10.30 1.81 .72 2.42 .04 .82 1.25 8.57 4.78 7.20
16. Unweighted mean 1 7. Weighted mean Australian states 18. NSW 1 9. Victoria 20. Queensland 21. SA 22. WA 23. Tasmania 24. U n w e i g h t e d mean 25. W e i g h t e d mean
38.53 27.31 14.79 8.29 8.47 2.61
Individual country/state (3)
Pooled country/state (4)
1.65 3.16 1.88 2.16 2.41 1.39 2.59 2.07 3.20 4.70 3.68 2.34 1.77 2.33 1.88
1.72 3.32 1.91 2.16 2.46 1.39 2.74 2.35 3.58 4.99 3.67 2.50 1.79 2.29 2.13
2.48 1.87
2.60 1.95
2.16 2.49 3.07 2.47 2.54 3.42
2.14 2.59 2.97 2.51 2.46 3.56
2.69 2.47
2.70 2.48
The column 2 weights for the OECD countries are proportional to GDPs in 1975 in international dollars; and the weights for the Australian states are proportional to total consumption expenditures in 1981. The RMS percentage prediction errors in columns 3 and 4 are 100 times the square root of the budgetshare-weighted mean of the squared relative prediction errors of the budget shares; as an approximation, these are computed as 100 times the square root of twice the information inaccuracies.
26
International Consumption
Comparisons
the 15 OECD countries. Although the RMSEs for the country-specific models (given in column 3) are in general a bit lower than those for the pooled model (column 4), the differences are not substantial. In addition, the countries have similar rankings with respect to the two sets of RMSEs. Looking at the entries in row 17 of columns 3 and 4 of Table 1.9, the weighted means of the RMSEs are 1.87 percent for the individual country models and 1.95 percent for the pooled model. Accordingly, the average "cost" of taking tastes to be identical is 1.95 - 1.87 = .08 percentage points. This is clearly quite modest and points in the direction that tastes are not too dissimilar across countries. (For a different finding, however, see Pollak and Wales, 1987.) There are many non-economic differences between some of the OECD countries (see Tables 1.1 and 1.2). For example, language, culture and climate differ substantially in some cases. It may thus come as a surprise to some that tastes in these countries are more or less similar. In an attempt to control for some of the non-economic factors, Selvanathan and Selvanathan (1994, Chap.4) conducted a similar analysis with data from different regions of the same country, the six states of Australia. The lower part of Table 1.9 summarizes the findings and the result is that tastes are even more similar within a country, as expected.
References Chen, D.L. (2001). World Consumption Economics. Singapore, London: World Scientific. Clements, K.W., and S. Selvanathan (1994). "Understanding Consumption Petterns,' Empirical Economics 19: 69-110.
Chapter 1 An Overview
27
Clements, K.W., and H. Theil (1996). 'A Cross-Country Analysis of Consumption Patterns,' Chapter 7 in H. Theil (ed.), Studies in Global Economics. Advanced Studies in Theoretical and Applied Econometrics, Boston: Kluwer Academic Publishers, 95-108. Deaton, A.S. (1975). Models and Projections of Demand in Post-War Britain. London: Chapman and Hall. Gamaletsos, T. (1973). 'Further Analysis of Cross-Country Comparison of Consumer Expenditure Patterns,' European Economic Review 4: 1-20. Goldberger, A.S., and T. Gamaletsos (1970). 'A Cross-Country Comparison of Consumer Expenditure Patterns,' European Economic Review 1: 357-400. Houthakker, H.S. (1957). 'An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel's Law,' Econometrica 25: 532-551. Houthakker, H.S. (1965). 'New Evidence in Demand Elasticities,' Econometrica 33: 277-288. Kravis, LB., A.W. Heston and R. Summers (1978). International Comparisons of Real Product and Purchasing Power. Baltimore, Md.: The John Hopkins University Press. Kravis, I.B., A.W. Heston and R. Summers (1982). World Product and Income: International Comparisons of Real Gross Product. Baltimore, Md.: The John Hopkins University Press. Lluch, C. (1973). The Extended Linear Expenditure System,' European Economic Review 4: 21-32. Lluch, C, and A.A. Powell (1975). 'International Comparisons of Expenditure Patterns,' European Economic Review 5: 275-303. Lluch, C, A.A. Powell and R.A. Williams (1977). Patterns in Household Demand and Saving. Oxford: Oxford University Press.
28
International Consumption Comparisons
Lluch, C, and R.A. Williams (1975). 'Cross Country Demand and Savings Patterns: An Application of the Extended Linear Expenditure System,' Review of Economics and Statistics 57: 320-328. Parks, R.W. (1969). 'Systems of Demand Equations: An Empirical Comparison of Alternative Functional Forms,' Econometrica 37: 629-650. Parks, R.W., and A.P. Barten (1973). 'Cross-Country Comparison of the Effects of Prices, Income and Population Composition on Consumption Patterns,' Economic Journal 83: 834-852. Pollak, R.A., and TJ. Wales (1969). "Estimation of the Linear Expenditure System,' Econometrica 37: 611-628. Pollak, R.A, and T.J. Wales (1987). Pooling International Consumption Data,' Review of Economics and Statistics 69: 90-99. Pollak, R.A., and T.J. Wales (1992). Demand System Specification and Estimation. New York and Oxford: Oxford University Press. Selvanathan, S. (1988). A System-Wide Analysis of International and Interregional Consumption Patterns. Ph.D. Thesis, The University of Western Australia. Selvanathan, S. (1993). A System-Wide Analysis of International Consumption Patterns. Advanced Studies in Theoretical and Applied Econometrics, Boston: Kluwer Academic Publishers. Selvanathan, S., and E.A. Selvanathan (1994). Regional Consumption Patterns: A System-Wide Approach. London: Avebury Publishers. Stigler, A.J., and A.S. Becker (1977). 'De Gustibus Non Est Disputandum,' American Economic Review 67: 76-90. Stone, R. (1954a). The Measurement of Consumers' Expenditure and Behaviour in the United Kingdom, 1920-1938. Vol. 1, Cambridge: Cambridge University Press. Stone, R. (1954b). 'Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand,' Economic Journal 64: 511527.
Chapter 1 An Overview
29
Theil, H. (1980). The System-Wide Approach to Microeconomics. Chicago: The University of Chicago Press. Theil, H. (1987). 'The Economics of Demand Systems,' Chapter 3 in H. Theil and K.W. Clements (eds.), Applied Demand Analysis: Results from System-wide Approaches. Cambridge, MA: Ballinger Publishing Company. Theil, H., and F.E. Suhm (1981). International Consumption Comparisons: A System-wide Approach. Amsterdam: North-Holland Publishing Company. Theil, H., D.L. Chen and C. Moss (1996). Studies in Global Econometrics. Boston: Kluwer Academic Publishers. Yoshihara, K. (1969). Demand Functions: An Application to the Japanese Expenditure Pattern,' Econometrica 37: 257-274.
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CHAPTER 2
Consumer Demand Models E.A. Selvanathan <& S. Selvanathan
One of the primary objectives of applied demand analysis is to estimate demand systems to analyse the income and price responses on consumer demand. With this objective, this chapter presents a review of the basics of demand theory. Section 2.1 presents the basics of the economic theory of the consumer. In Section 2.2, various structures of consumer preferences are discussed, and in Section 2.3, we discuss Theil's (1980) differential approach to derive the differential demand equations. Section 2.4 presents a number of flexible functional forms. In Section 2.5, we discuss the recently developed differential demand systems such as the CBS demand system (Keller and van Driel, 1985) and even simpler demand systems (Selvanathan, 1985). Finally, in Section 2.6, we briefly outline recent developments on issues associated with aggregation in consumer demand.
2.1
The Economic Theory of the Consumer
The objective of consumption theory is to analyse the demand for goods and services in terms of income and prices. Such a relationship between the quantity demanded, income and prices is called a demand equation. A most straight-
32
International Consumption
Comparisons
forward way of generating demand equations is to derive them by maximizing the consumer's utility function subject to his/her budget constraint. Let qu..., qn be the quantities consumed of n goods and let ph..., pn be the corresponding prices. Then,
M= z,Piqi
(i.i)
i=l
is the total expenditure, which shall be referred to as 'income1 for short. Equation (1.1) is also known as the budget constraint. The proportion of income spent on good i, Wi=ML
(1.2)
M is called the budget share of good i. These budget shares are positive and, in view of (1.1), they all sum to one. That is, I
w,=l.
(1.3)
The consumer chooses the n x 1 quantity vector q = [q{] to maximize the utility function u(q), subject to the budget constraint (1.1), written in vector form as p'q = M, where p = [p{] is the (n x 1) price vector. Thus the maximization problem takes the Lagrangian expression, u*(q,X) = u(q)-X(p'q-M),
(1.4)
33
Chapter 2 Consumer Demand Models
or, in scalar form, u*(qu ...,q„,X)
= u(qu
...,qn)-X
where X is the Lagrangian multiplier. The solution to this maximization problem leads to a Marshallian demand equation for good i: qx =
qi(M,pu...,pn),
i=l,...,n.
(1.5)
The first-order conditions for the above maximization problem are the budget constraint (1.1) and du
.
i=l,...,n.
(1.6)
i=l,...,n.
(1.7)
Re-arranging (1.6), we can write X =
du
tyPi^Y
The right-hand side of (1.7) can be interpreted as the change in utility for a $1 increase in income, where this increase comes from the increase in the expenditure on any commodity i, i=l,2,.. .,n. Therefore, one could interpret X in (1.4) as the marginal utility of income. We assume that there is a generalised diminishing marginal utility so that the Hessian matrix of the utility function
34
International Consumption Comparisons
is negative definite. As Hessians are symmetric, U is a symmetric negative definite n x n matrix. The main emphasis of this book is the utility-based approach to demand analysis. However, there is an older, more traditional approach that directly specifies the demand equations without any reference to the utility function (see, for example, Cassel, 1932; and Stone, 1954a). A popular example of such directly specified demand equations is the double-log demand system: log # = oti + rii log M + 2X-logpj,
i=l,...,«,
(1.8)
where 0Cj is an intercept term. The coefficient rj; is the income elasticity of commodity i, defined as
^=
*i±*L dM/M
=
*Q?*5LI, d(logM)
!=!,...,«.
(i.9)
The income elasticity answers the question, if income rises by 1 percent with prices held constant, what is the percentage change in the consumption of i? Commodities with income elasticity less than 1 are called necessities, while those with income elasticity greater than 1 are called luxuries. If the income elasticity is negative, then that commodity is said to be an inferior good as its consumption falls with increasing income. The coefficient r^ is the
35
Chapter 2 Consumer Demand Models
uncompensated price elasticity of commodity i with respect to the price of commodity j , defined as
dPj/pj
d(logpj)
This coefficient answers the question that, if the price of commodity j increases by 1 percent, with income and other prices held constant, what is the percentage change in the consumption of i? If i = j , riy is known as the own-price elasticity and if i^j, r|ij is known as the cross-price elasticity. The Marshallian (or money-income-constant) demand equation can be transformed into its Slutsky (or real-income-constant) counterpart by using the Slutsky decomposition for the uncompensated price elasticity,
•Hij = "njj - Wjtii,
(i.ii)
where r)^ is the (ij)* compensated price elasticity and Wj is the budget share of good j , the proportion of income spent on j . After some algebraic manipulation of model (1.8) and using (1.2), (1.3) and (1.11), we can derive the Slutsky demand equation for good i as: log # = a; + Tli log g + ZTU- logpj,
i=l,...,n,
(1.12)
where log Q = log M - log P, with log P - YJ)=\ wj log Pj. the Divisia price index. That is, log Q is money income (log M) deflated by the price index
International Consumption Comparisons
36
(log P), or a measure of the consumer's real income. Note that real income and the compensated price elasticities r\'tj appear on the right-hand side of (1.12), while money income and the uncompensated elasticities f]^ are in (1.8). Consider the multiplication of the budget share of commodity j by the corresponding income elasticity,
WjTlj
_ Pjlj
d(loggj)
_ pjqj
dqj/qj
~
d(logM)
~
dM/M
M
M
_ Pj
dqj^ _
d(pjqj)
dM
dM
~
The far right-hand term answers the question, if income increases by $1, how much of that will be spent on commodity j? This quantity is referred to as the marginal share, 0j, of commodity j . That is,
6j =
' J dM
,
j=l,...,n.
(1.13)
As with the budget shares, the marginal shares also sum to unity. That is,
£ 6 '" - 7=1 ??%* •-in—£
7=1
• >•
<«•">
If we divide the marginal share by the corresponding budget share, we obtain the corresponding income elasticity. That is,
37
Chapter 2 Consumer Demand Models 0d(pjqj) J —*- = — Wj dM
1
Bqj/qj = —dM/M
(Pjqj)/M
d(logqj) — = rij. d(logM)
=
(1.15)
Furthermore, the budget-share-weighted average of the income elasticities also sum to unity. That is, n E Wylly
=
7=1
n 0 .• n I W ; — = I Qj =1j=\
Wj
(1-16)
j=\
Equation (1.16) is also called Engle aggregation. The consumer's maximization problem implies two testable constraints on the demand equations. The first constraint on the demand equations is demand homogeneity, which states that if income and prices all increase proportionally, then the quantity demanded of each good will remain unchanged. For example, suppose that all prices and money income double, then demand homogeneity assures us that this change would have no effect on consumption [or, equivalently, the demand function (1.5) is homogenous of degree zero], that is, qiaM,apx,...,apn)
= a0qj(M,pu...,pn)
=
qi{M,pi,...,pn).
In the context of equation (1.8), demand homogeneity can be expressed as In,-, + r|,= 0, 7=1
i=l,...,n.
(1.17)
38
International Consumption Comparisons
That is, the sum of the own- and cross-price elasticities and the corresponding income elasticity for each good is zero. In the context of equation (1.12), demand homogeneity (1.17) can be expressed as
£
riij = 0,
i=l,...,/i,
(1.18)
where we have also used equations (1.3) and (1.11). The second constraint on the demand equations is symmetry of the substitution effects, or Slutsky symmetry. This states that, when real income is held constant, the effect of a $1 rise in the price of good j on the consumption of good i is equal to the effect of a $1 rise in the price of good i on the consumption of good j . Consider the price derivative (or equivalently, the slope of the demand equation), dqjdpj. Going back to equation (1.12), this slope can be written as
dqt dpj
=
qi d(log qt ) pj d(logpj)
=
qt Pj
iy
Symmetry states that, this slope is the same when we interchange the i and j subscripts, that is, dqjdpj = dq-Jdpt. This means that (q/Pj)viij = (#/Pi) ^ ;,•, or, multiplying both sides by p-p-JM, we have
wxViu = WjTl'-,.,
ij = 1
»•
(1.19)
Chapter 2 Consumer Demand Models
2.2
39
The Structure of Preferences
Consider demand equations (1.12) for i = l,...,n goods. In this system of n equations there are n intercepts, oci, ..., a„, n income elasticities, r\i, ..., r)„, and n2 price elasticities r)^, i,j = 1,...,«, so that the total number of coefficients is n + n + n2 = n(n + 2). For a moderate-sized system of n = 10 goods, this total equals 120, which is an impossibly large number of coefficients to be estimated in an unrestricted fashion. Even when we take account of the homogeneity, symmetry and adding-up restrictions, the number of coefficients is still in the order of n2. One way of reducing the number of coefficients to be estimated is to set to zero some of the cross-price elasticities (TU- for i ^ j) in equation (1.12), perhaps on the basis of the intrinsic nature of the commodities involved or on the basis of prior evidence. A more systematic approach is to pattern the n x n elasticity matrix [TU- ] by further structuring the nature of the consumer's utility function u(qu--;qn)- Important early contributions in this area include Barten and Turnovsky (1966), Goldman and Uzawa (1964), Gorman (1959, 1968), Leontief (1947), Pearce (1961, 1964), Sono (1961) and Strotz (1957). A number of publications in this area have also appeared recently (see, for example, Baccouche and Laisney, 1991; Driscoll and McGuirk, 1992; Edgerton, 1993; Lewbel, 1995, 1996; Moschini, 1992; and Moschini et al, 1994). Suppose the n goods are broad aggregates such as food, clothing, housing and so on. It is then not unreasonable to view the demand for each good as representing the desire for some characteristic(s) unique to each good: food provides nutrition and taste, clothing provides warmth and style, and housing provides shelter. These unique, or basic, characteristics represent fundamental desires which generate utility. Moreover, for them to be truly basic characteristics, it should be the case that there is little or no interaction between
40
International Consumption Comparisons
them in the utility function, so that utility is generated by the consumption of food and clothing and housing, with the emphasis on the 'ands' representing the notion of additivity. These ideas can be formalized by an additive utility function, whereby utility is the sum of n subutility functions, one for each good: u(qu...,qn)
n
= £ Ui(qi),
(2.1)
i=\
where u\(qd is the sub-utility function for good i. According to (2.1), each marginal utility is a function of only the good in question, du/dqt - 3w/3g„ and is independent of the consumption of all other goods, that is, d2u/dqidqj = 0, i * j . Accordingly, (2.1) is also known as the preference independence (PI) form of the utility function. An example of (2.1) is the well-known Klein-Rubin (1948) or Stone-Geary utility function, u(q) = £"=iPil°g(?i -Y;) which is additive in log(gi-Yi)."-.log(gB-Y„)To analyse the implications of preference independence, let 8y be the Kronecker delta (8y = 1 if i=j, 0 otherwise) and define § to be the reciprocal of the income elasticity of the marginal utility of income, =
f a(logX) |_3(logM)
< 0,
where X is the marginal utility of income, see the discussion below equation (1.7). For brevity, we shall refer to (() as the income flexibility. The income flexibility (> | is expected to be negative. If preferences are of the form (2.1), the (ij)* price elasticity then becomes (see, e.g., Clements et al, 1995):
41
Chapter 2 Consumer Demand Models Tly =
(2.2)
If we use (2.2) in demand equation (1.12), the substitution term then becomes £
Tly log p-} = (hidogpi-logP 1 ),
(2.3)
7=1
where log P' = 27J=j97logpy- is the Frisch price index. In contrast to the Divisia price index defined below (1.12), which uses budget shares as weights, the Frisch index uses marginal shares as weights. As luxuries (rjj > 1 or, equivalently, 0 ; > w;) have marginal shares in excess of their budget shares, it follows that luxurious goods are more heavily weighted in the Frisch index than in the Divisia index. Using (2.3) in (1.12), the i* demand equation under preference independence takes the form log q-, = <Xi + Tii log Q + <|nii log
i=l,...,/t.
(2.4)
This shows that preference independence implies that only the own-relative price appears in each demand equation and that the own-price elasticity is §r\i. Accordingly, under preference independence, there are no specific substitutes or complements (Houthakker, 1960). Additionally, as § and the own-price elasticity <pr|i are both negative, preference independence implies that each income elasticity r|j is positive, so that inferior goods are ruled out. A further implication of preference independence is that the own-price elasticities (<|>r)i) are proportional to the corresponding income elasticity (T);), with the
42
International Consumption Comparisons
income flexibility ((|)) the (negative) proportionality factor. In other words, luxuries are more price elastic than necessities. The final feature of preference independence to note is the reduction in the number of unknown parameters in the demand equations. As stated above, in the unrestricted demand equation (1.12) for i = l,...,n there are n2 unknown price elasticities. By contrast, in (2.4) for i = \,...,n there is only one free parameter in the substitution term, the income flexibility (j). Altogether, there are (2ra + 1) parameters, au oc2, ..., oc„; r|i, r)2, ..., t|„ and <|), in the system of demand equations (2.4), which is in the order of n rather than the previous system of equations (1.12) which is in the order of n2. A weaker version of preference independence is block independence whereby the consumer's utility function is additive in groups of goods, rather than individual goods. Let the n goods be divided into G (< n) groups, written Si, ..., SQ, such that each good belongs to only one group. Then, preferences are of the block independence form when the utility function is the sum of G group utility functions, each involving the quantities of only one group, G
u{qu...,qn)
=
X wg(9g),
(2.5)
8=1
where qs is the vector of the qfs that fall under group Sg. Thus, if, for example, alcoholic beverages (beer, wine and spirits) make up one block-independent group and all other goods another, the marginal utility of, say, beer would then be affected by the consumption of wine and spirits, but not by the consumption of any good outside the alcoholic beverages group. Demand equation (1.12) for good i e Sg implied by (2.5) is (see, e.g., Clements and Selvanathan, 1991):
Chapter 2 Consumer Demand Models log # = OCi + Tli log <2 + 2 jeSg
43
fi TU.log^-, P
(2.6)
where r)^ is the (ij)* price elasticity (strictly speaking, this is also a Frisch price elasticity which holds constant the marginal utility of income). The Frisch elasticities are subject to the restriction I
Viij
=
ieS g .
(2.7)
jeSg
Equation (2.6) is to be compared with (2.4), the corresponding demand equation under preference independence. The assumption of preference independence implies that only the own relative price affects consumption, while block independence means that only the relative prices of goods in the same group as the commodity in question play a role. If the alcoholic beverages group comprises beer, wine and spirits, and if these form a block-independent group, then only the relative prices of the three beverages affect the consumption of each beverage and the prices of other goods play no role. It can therefore be seen that there is an appealing unification between preferences and demand equations.
2.3
Differential Approach to Deriving Demand Equations
The double-log demand system (1.8) considered in Section 2.1 is directly specified without any reference to the utility function. In this section, we apply
International Consumption Comparisons
44
the method of comparative statistics to derive the demand equations (1.5) in the form of partial derivatives starting from a general form of the utility function. Divisia Indices in Differential form
The differential of the budget constraint (1.1) is n
n
I Ptdqi + I q-APi = dM i=l
i=i
Dividing both sides by M and using the identity that dx/x = d(log x) and (1.2), we obtain d(log Q) + d(log P) = d(log M) where d(logQ) = t
Wid{logqi)
i=l
and d(logP) = t
M>id(!ogPi)
i=l
are the Divisia volume index and Divisia price index, respectively. The above equation decomposes the change in income into a volume and price index.
45
Chapter 2 Consumer Demand Models Barten's Fundamental Matrix Equation
The derivation of the demand equations using the method of comparative statistics involves the use of the first-order conditions (1.1) and (1.6) of the consumer utility maximization problem (1.4). We treat p\, p2, •••, pn and M as exogenous. Differentiating the budget constraint (1.1) with respect to pj and M, we get L Pi^—
= -*.
I P / ^ 7
= 1-
j=l,...,n,
(3.1)
and ;=1
(3-2)
dM
Equations (3.1) and (3.2) can be written in matrix form as - dq PT7 dp
=
1
>
,,,,,, (3-3)
and P'^7 dM
= l>
(3 4)
-
where dq/dp' = [dqjdpj] is the n x n matrix of price derivatives of the demand functions and dq/dM = [dq\/dM] is the vector of n income slopes of the demand functions. Differentiating (1.6) with respect to/?j and M, we get
46
International Consumption Comparisons "
d u
dqk
k=l dqtdqk
=
dpj
, ,, dX h&ij + Pi dPj'
i,j=l,...,w,
(3.5)
i=l,...,n.
(3.6)
where 5;, is the Kronecker delta, and d2u
«
dqk
k=\ dqidqk
Pi
dM
dX dM'
We write (3.5) and (3.6) in matrix form as U
,_ dX XI + p——
dq dp'
(3.7)
and U
dX
dq dM
dM
(3.8)
P,
where U is the Hessian matrix defined below (1.7). I is the n x n identity matrix and dX/dp' = [dMdpfi. Combining (3.3), (3.4), (3.7) and (3.8), we get U
dq
dq
p
dM
dp'
O
dX
dX
dM
dp'
0
XI (3-9)
p'
1
-q
The above matrix equation is known as Barten's Fundamental matrix equation in consumption theory (Barren, 1964).
Chapter 2 Consumer Demand Models
Al
If we solve equation (3.9) with respect to the first-order derivatives, we obtain the solutions
dM
(3.10)
p'U~xp
—^-U-xp(V-1py--^-rV-lpq', p U p p U p
dp'
(3.11)
dA dM
(3.12) p'U^p'
and dA dp
A l
p'U p
U
. P
1 Tl T T T - ^ p'U p
(3.13)
where we have also used U
-l
1
(p'u-lP)U'1 -u-'pifj-'py
p'U'p
u'p
(u-'py
-l
Now, we return to equation (1.5), the Marshallian demand equation for good i. The differential of (1.5) is given by (e.g. Theil and Clements, 1987; and Selvanathan and Clements, 1995): dq,
a 8^ = ~^dM + £ 9iZ^-dp:, dM j=idpj
i=l,...,n.
48
International Consumption Comparisons
If we multiply both sides of the above equation by p-JM, it can be transformed into the form
wid(logqi) = Qid(logU) + i^p^d(logpj), 7=1 M
dpj
J
i=l,...,n.
(3.14)
Relative Price Version
Using equations (3.10)-(3.13) and (3.14), we can easily derive the following simplified demand equations in relative prices: wi d(log q-d = 6i d(log Q) + £ v dlog EL y=i F
i=l,...,n,
(3.15)
where 0j = w\f\t is the i* marginal share; d(log Q) = d(log M) - d(log P) = X"=i Wjd( log qt), is the Divisia volume index of the change in the consumer's real income; d[log (p/P')] is the change in the deflated price of j with d(log P') = X°=i#jd(log p.) is the Frish price index: and Vy = (k/M)piu''pj is the (ij)"1 price coefficient, with X the marginal utility of income and u'1 the (ij)* element of the inverse of the Hessian of the utility function, U = [d2u/dq,dqj\. Note that the coefficients 9j and Vy are not necessarily constant. The price coefficients, Vy, satisfy Z^i^y = <|>0i, i=l, ....,«, where <j) is the income flexibility, defined in Section 2.2. Equation (3.15) above is the i'h demand equation of the relative price version of Their s (1980) differential demand system. The first term on the right of (3.15) gives the effect of real income on the demand for goodi. This term is a multiple Q, of the Divisia volume index d(log g). As this volume index equals d(log M) - d(log P), where d(log P) is the Divisia price index, it follows that the Divisia price index transforms the change in money income into the change in real income. Furthermore, as the Divisia
49
Chapter 2 Consumer Demand Models
price index is budget-share-weighted, it follows that this index measures the income effect of the n price changes on the demand for the i* good. The second term on the right of (3.15), EjLiVjjdTlogCpj IF)], deals with the effects of relative prices. The Frisch price index acts as a deflator of each price change, so that we refer to d[log (p/P1)] as the change in the Frisch-deflated price of j . Using the fact that Z;=i v y =¥*i> it c a n be shown that the substitution term can be written as the difference between X"=i Vjjd(log Pj), which is the specific substitution effect of the n prices on the demand for good i, and
6id(log P') is the general substitution effect. Accordingly, the general substitution effect acts as the deflator of the specific effect by transforming absolute prices into Frisch-deflated prices. If Vy > 0, then an increase in the Frisch-deflated price of j causes consumption of i to increase. Consequently, we follow Houthakker (1960) and define goods i and j as specific substitutes (complements) if Vy > 0 (< 0). Absolute Price Version
Equation (3.15) is formulated in terms of relative (or deflated) prices. The corresponding absolute price version is
Wid(log^)
n = 9id(log<2) + X 7iijd(logpj),
i=l,...,n,
(3.16)
where 7ty = Vy - <|)9j0j is the (i,j)* Slutsky coefficient. Equation (3.16) is the absolute price version of the differential demand equation. These coefficients satisfy demand homogeneity £ 7=1
7Tij= 0,
i=l,...,«,
(3.17)
50
International Consumption Comparisons
and Slutsky symmetry 7tij =
7tji,
i,j = l, ...,«.
(3.18)
The n x n matrix [Tty] is negative semidefinite with rank (n-l). Dividing both sides of (3.16) by w\, we obtain 0/w, as the income elasticity of demand for i; and Tii/Wj as the (ij)* Slutsky price elasticity. Preference Independence Version The two versions of the demand model discussed above, the absolute price version and the relative price version, both have their own attractions. The absolute price version (3.16) and the constraints (3.17) and (3.18) are linear in the parameters, which makes estimation and testing straightforward. However, when n becomes larger, as discussed in Section 2.2, the number of Tty's grows rapidly, making the absolute price version of the model suitable for small systems only. For larger models, it is necessary to use the relative price version of the model (3.15) (which is non-linear in the parameters) with suitable constraints on the v^'s. These constraints take the form of postulating that certain goods do not interact in the utility function. One such form is the preference independence, discussed in Section 2.2, when no good interacts with any other. Under preference independence, we have Vy = 0 for i * j
and
VH
=
fyQ,,
i,j = 1, ..., n.
Then, under preference independence, the relative price version of the demand model, (3.15), becomes
51
Chapter 2 Consumer Demand Models Wj d(log qd = 8i d(log Q) + 00,.d log
F
i=l,...,n.
(3.19)
The number of unconstrained coefficients in (3.19) for i=l,...,/i is n, which is made up of n-\ unconstrained 6i's (1 is constrained by Z"=i#, = 1) and (j). The Rotterdam Model
The coefficients of the demand equations (3.15), (3.16) and (3.19) are functions of income and prices. In general, these coefficients need not be constants. The Rotterdam model, derived below, parameterizes these coefficients. Equations (3.15), (3.16) and (3.19) are formulated in terms of infinitesimal changes. The Rotterdam model, due to Barten (1964) and Theil (1965), are finite-change versions of these equations. We write, Dxt = log xt log xt.i for the finite log-change from period t-1 to t for any positive variable x. The variable d(log q{) on the left of (3.15) becomes Dqlt and d[log (p/P1)] becomes (Dpjt - DP't), where DP\ = J^^QiDpi,, is a finite-change version of the Frisch price index. As the budget share w\ on the left of (3.15) does not involve a change, we could use either Wj?t-i or Wj,t or a combination thereof which treats t and t-1 symmetrically. The natural choice is to use the arithmetic average of wiit.i and wiit, wit = V£(wijt.i + wiit), which is mid-way between the two extremities. The finite-change version of (3.15) is then witDqit = QiDQt + I
va(Dpjt - DFO,
i = 1,..., n,
(3.20)
where Dgt = Z?=i wu D
52
International Consumption Comparisons
known as the i'h demand equation of the relative price version of the Rotterdam model. The finite-change version of the absolute price version (3.16) is witDq,t = QiDQt+tniJDpjt,
i = 1,..., n.
(3.21)
When the coefficients 9j and 7iy are specified as constants, (3.21) is known as the i'h demand equation of the absolute price version of the Rotterdam model. It follows from the relationship, 7iy = Vy - 9j9j, that the constancy of the coefficients 9j, Vy and § in the relative price version of the Rotterdam model implies that the Slutsky coefficients 7iy are also constant in the absolute price version. The finite-change version of the Rotterdam model under preference independence, equation (3.19), becomes w„ Dqit = Gj D& +
i = 1,..., n.
(3.22)
where the coefficients (|) and 9j are specified as constants.
2.4
Other Popular Demand Systems
The differential demand system (3.15) in relative prices and (3.16) in absolute prices derived in the last section are completely general, as their coefficients are not necessarily constants. This is in contrast to most other approaches of generating systems of demand equations. The other approaches involve the algebraic specification of either the direct utility function, the indirect utility
53
Chapter 2 Consumer Demand Models
function or the cost function. Consequently, the coefficients of the resulting demand equations are constants. In this section, we introduce three such wellknown demand systems, namely, the linear expenditure system (LES), the Translog Demand System (TRANSLOG) and the Almost Ideal Demand System (AIDS). Linear Expenditure System (LES)
The linear expenditure system (LES) can be derived by directly specifying the utility function as U(q) = u(qu q2,...,q„)
=
£ P; log (q, -yt),
(4.1)
where Pi > 0, Yi < q, and Xf=iP< = 1- Th e utility function (4.1) is the well-known Stone-Geary utility function. This utility function has also been previously considered by Klein-Rubin (1948). Another point worth noting about the structure of U(q) is that this utility structure will fall under the preference independent type as U(q) can be written as the sum of n individual utility functions, n
u{q) = u{qh...,qn)
= £ «,•(
where Ui(^) = Pi log (qt - Yi )• If we apply the first-order condition (1.6) to the utility function (4.1) we obtain, PiGi = PiYi + Pi M-t
PjJj
i=l,...,n.
(4.2)
54
International Consumption Comparisons
This is the algebraic form of the demand equations (1.5) associated with the Stone-Geary utility function (4.1). As expenditure on good i is a linear function of the n prices and income, (4.2) is known as the linear expenditure system (LES). If the Yi's are all positive, then (4.2) has the following interpretation. The consumer first purchases Yi units of good i at a cost of p^; this can be termed subsistence consumption of that commodity. The total cost of subsistence is Y!)=\PjYj> which leaves M - YIj=\PjY j a s supernumerary income. A fixed fraction Pi of supernumerary income is then spent on good i. The linear expenditure system was first applied to data by Stone (1954b); for other applications, see Deaton (1975) and Lluch and Powell (1975). It follows from (4.2) that the marginal share 8j = dip, qi)/dM implied by the linear expenditure system is equal to the constant coefficient Pi. Consequently, the income elasticity of i takes the form r\> = —,
i=l,...,n.
(4.3)
A rise in income with prices held constant causes the budget shares of necessities to fall and those of luxuries to rise. It then follows from (4.3) that increasing affluence causes the income elasticities of necessities to rise, while those of luxuries fall; the elasticities of both types of goods become closer to unity. Take the case of food, a necessity. The linear expenditure system implies that as the consumer becomes richer, the income elasticity, r|j, for food increases, causing food to become less of a necessity or more of a luxury. This behaviour of the elasticity is implausible as food should be less of a luxury for a richer consumer.
55
Chapter 2 Consumer Demand Models
Recall that the coefficient Pi in the Klein-Rubin must be positive. As this coefficient is interpreted as the marginal share in (4.2), it follows that the LES does not admit inferior goods. The uncompensated price elasticities under LES are given by (liZiiis
-p.X^L,
a
i
i,j=l,2,...,«.
(4.4)
PiQi
Translog Demand System
Another way of deriving the demand equations is by specifying the form of the indirect utility function. By substituting the demand equations (1.5) into the utility function u = u(q), we can write the utility function as a function of income and prices, u = u[q(M,p)]=U1(M,p).
(4.5)
The function U] is called the indirect utility function and it gives the maximum utility attainable corresponding to given values of income and prices. Roy's (1942) theorem, duj /dp: %= , l . / ' ,
. , 1=1,...A
(4.6)
gives a way of generating a system of demand equations from a specified form of the indirect utility function. Christensen, Jorgenson and Lau (1975) applied Roy's theorem to the following translog indirect utility Junction,
56
International Consumption Comparisons U,(M,p) = I P,.to*- £ + Vz 11
Py log %-log ^-,
(4.7)
where Pi's and py's are constants. Application of (4.6) to (4.7) yields the following demand equations
ft + ipa-fo*-^ J
Wi =
—
n
n n
,
i=l,...,n.
(4.8)
V;
ZPt + I I P ^ ^ - J *=1
A=l;=l
M
This demand system is called the translog demand system. Almost Ideal Demand System (AIDS)
The consumer's cost function is dual to the (direct) utility function in that it gives the minimum expenditure needed to attain a specified level of utility, given the prices. The cost function is also referred to as the expenditure function. By specifying the form of the cost function and then applying the Shephard's lemma dC • — =
i=l,...,«,
(4.9)
we can derive the corresponding demand function. Deaton and Muellbauer (1980a, 1980b) specified the cost function as C(u,p) =
a(p) + ub(p) e
,
(4.10)
57
Chapter 2 Consumer Demand Models where a(p) = S a,- log Pi + Vi £ I Y«7 log pt log p • i=l
«=ly=l
and 1 KP) = Pon^ , 1=1
with otj's, Pi's and Yy's all being constants. Applying (4.9) to (4.10), the resulting demand system can be written in the form n M w-, = oil + ft log—-+ EYi/togPj,
i=l,...,n,
(4.11)
log P = a(p) = I or,, log p, + Vi I I r y log A log p , .
(4.12)
where
i=l
i=l y=l
Deaton and Muellbauer refer to (4.12) as the almost ideal demand system or AIDS for short. The income and uncompensated price elasticities implied by AIDS are i=l,...,n,
(4.13)
Wi
and Tlij = - 5y +
r0-PAwj-fijlog
'M^ \ r
, i,j=l,...,«.
(4.14)
j
The estimation of (4.11) is more complicated when we use log P defined by (4.12). A more simple variant form of (4.12) is known as Stone's index,
58
International Consumption Comparisons
logP = I wklogPk.
(4.15)
k
With (4.12) replaced by (4.15), the budget share equations (4.11) are linear in the parameters to be estimated, viz, o.\, PJ and the Yij's. Working's Model
If prices are constant, as is approximately the case for the household expenditure survey, and if we choose units such that the price of each good is unity, then the AIDS model (4.11) simplifies to w\ = oCj + PilogM,
i=l,...,«.
(4.16)
In words, the budget shares are linear functions of the logarithm of income, which was first proposed by Working (1943) to analyse the household budget data. As the sum of all budget shares is unity, it follows from (4.16) that £f=l a i = 1 and X?=iP; = 0. Choosing the income unit such that M=l for some household, 0Cj is then interpreted as the budget share of i for that household. The coefficient Pi gives us 100 times the change in the budget share of commodity i (AWJ x 100) resulting from a 1 percent increase in income. Under Working's model the marginal shares and the income elasticity are given by 6i = Wi+Ps
(4.17)
and Tii = 1 + i-i-. w
i
(4.18)
59
Chapter 2 Consumer Demand Models
Equation (4.18) shows that a good with positive (negative) Pi is a luxury (necessity). As the budget share of a luxury increases with income, prices remaining constant, it follows from (4.18) that increasing income causes the income elasticity r|j of such a good to fall towards 1. The income elasticity of a necessity also declines with increasing income under (4.18). Thus as the consumer becomes more affluent, all goods become less luxurious under Working's model, which is plausible. This behaviour of the income elasticities is the same as that under the AIDS model. By contrast, under the LES the income elasticities of necessities increase, which is implausible, as discussed previously.
2.5
More on the Differential Demand Equations
In this section, we derive the more simple demand systems developed by Keller (1984) and Selvanathan (1985). Taking the differential of wt = p\qJM, we obtain dw; = Wj d(log j d(log pi) - Wj d(log M).
(5.1)
Substituting for w\ d(log qi) from (3.16) into (5.1) gives, n
dwi = 6id(logQ)+ Y1nijd(logpj) +
wid(logpi)-wid(logM)
j=i
+ wi d(log P) - Wj f > • d(log p •), 7=1
60
International Consumption Comparisons
where we have added and subtracted the same term, Wj d(log P), on the right hand side and used d(log P) = £ w;d(log Pj). Recognising that d(log M) - d(log P) = d[log (M/P)] = d(log Q), we can simplify the right-hand side terms as n
dwi = (6i - Wi)d(log 0 + £ (7t,7 + w,-8(>- - w,-w,) d(log pj), 7=1
which can be written as dwi = pi d(log 0 + I Yyd(log /?;),
(5.2)
7=1
where Pi
= Gi-Wj
(5.3)
and yij=nu
+wiSij-wiwj.
(5.4)
Equation (5.2) is the differential version of the AIDS model (4.11). If we reparameterize (3.16) using (5.3) in the form fy = Pi + w;, we get
Wi[d(log qO - d(log 0 ] = ^ d(log 0 + 1 ^d(log Pj). 7=1
(5.5)
61
Chapter 2 Consumer Demand Models
Equation (5.5) is named by Keller and van Driel (1985) of the Dutch Central Bureau of Statistics (CBS) as the CBS demand system. This system has the AIDS income coefficients, (3;, and the Rotterdam price coefficients, Tty. After re-arranging, equation (5.2) can be written in the form dwi + Wi d(log 0 = 9i d(log Q) + tY«d(log Pj).
(5.6)
7=1
Equation (5.6) has the Rotterdam income coefficients and the AIDS price coefficients as constants. Equation (5.6) was considered by Neves (1987) and was called the NBR system. The restrictions on the new coefficients, Pi's and Yy's, are SP,=0;
lY(,-=0;
£ Y,>-=0;
/=i
(=i
j=\
Yy = Yji;
and [jy + WjWj - w ; 5 y ] is negative semi-definite. In order to reduce the number of parameters, fty's, which is in the order of n2, Keller (1984) proposed the following decomposition for ny, ny
=
X(\\fAj - \|Wj).
(5.7)
Under (5.7), equation (5.5) becomes Wi[d(log
q{) - d(log 0 ] = pi d(log Q) + >u|/i [d(log A ) - d(log PJ],
(5.8)
where d(log P^ = Z 7 ^ ; d(logp 7 ). Keller (1984) refers to equation (5.8) as the CBS substitution independence (CBS/SI) model.
62
International Consumption Comparisons With specification (5.3), the model under preference independence (3.20)
becomes Wi[d(log <7i)-d(log 0 ] = Pid(log Q) + (Kfr + wO[d(log Pi)-d(log P')l,
(5-9)
where d(log P') = Z / P 7 + Wj)d(log pj). Keller and van Driel (1985) refers to equation (5.9) as the CBS preference independence (CBS/PI) model. Note that if X|/i = Pi + w\ and X = <|>, then equation (5.8) becomes (5.9). If \|/i = W{, then equation (5.8) becomes Wi [d(log
?i)-d(log 2)] = Pid(log Q) + XwifdOog pO-dOog P)l
(5.10)
Selvanathan (1985) refers to equation (5.10) as an Even Simpler demand system. As most of the applications of these models are with finite-change data, we now present the finite-change versions of these models. The finite-change versions of the four demand systems, the CBS demand system (5.5), the NBR demand system (5.6), the CBS/SI demand system (5.8), the CBS/PI demand system (5.9) and Selvanathan's even simpler demand system (5.10) can be written as follows: CBS demand system: wit(Dqit
-DQt)
= ^DQt+
inijDpj,
(5.11)
NBR demand system: Aw, + wuDQ,
= 9iD<2t+ iVijDpj,
(5.12)
Chapter 2 Consumer Demand Models
63
CBS/SI demand system: wit(Dqit-DQt) where DP vt
= p i Dj2, + X\|/ i (Dp it -DP v )
=YJJ\fjDpjt.
CBS/PI demand system: wit(Dqu -DQt)
= (3iDQ, + (P, + wit)(Dpit -DPt)
(5.14)
Where DP/ =Z;(P;+W;,)Dp;,.
Selvanathan's even simpler demand system: wit {Dqit -DQt)
= Pi D(2, + Aw„(Dpft - DP,)
(5.15)
where £>F, = £,- wyrDp;-r.
2.6
Aggregation and Consumer Demand
Issues associated with the aggregation in consumer demand are considered as the most important theoretical as well as empirical problem by researchers working in the consumer demand area (eg, see Barnett, 1979a, 1979b, 1981; Blundell et al, 1993; Buse, 1992; Chavas, 1993; Heineke, 1993; Lewbel, 1996; Malinvaud, 1993; Selvanathan, 1995; Slesnik, 1998; and Theil, 1971). The term aggregation has two meanings in consumer demand analysis. One refers to aggregation over commodities and the other is the aggregation over consumers.
64
International Consumption Comparisons
Aggregation over commodities
The aggregation over commodities can be described as follows: Consider the situation where a consumer derives utility from the purchase of n commodities. In this situation the utility maximization problem will result in n basic demand equations; one for each commodity. However, in practice, it may not be possible to analyse the demand for each good for reasons such as limitations on data availability, the difficulties in estimating a large demand system etc. To overcome this problem it is essential to group the n commodities into a smaller number of groups, such as food, clothing, housing etc. This is termed 'aggregation over commodities'. We can show that the aggregate demand equation for a group reflects the basic properties of the individual demand equations. Aggregation over consumers
Now we consider aggregation over consumers. With the introduction of flexible functional forms such as translog and almost ideal demand systems (e.g. Deaton and Muellbauer, 1980b; Christensen, Jorgenson and Lau, 1973; Diewert, 1974), the differential demand systems came under severe criticism. One of the criticisms is based on the aggregation of these systems over consumers. As the differential demand equations we discussed previously are derived from the utility-maximizing theory of a single consumer, they are micro in nature. Usually since data are obtainable in some aggregate form (e.g. per capita), we estimate the aggregate (or macro) form of the micro demand system. The critics argue that the theoretical properties of the micro system (such as demand homogeneity and Slutsky symmetry) will not carry over to the macro system. Sonnenschein (1973) concluded that with respect to market demand functions, there is little left of demand theory beyond homogeneity. In a similar vein,
Chapter 2 Consumer Demand Models
65
Shafer and Sonnenschein (1982) consider the conditions under which a market demand function has the same characteristics as a demand function for an individual consumer. They conclude that the required conditions are strong. These conclusions are pessimistic indeed. The first response to these criticisms was offered by Barnett (1979a, 1979b, 1981). More recently Mountain (1988) and Selvanathan (1991) provided additional response. These authors use a completely different approach to tackle the problem, an approach which uses statistical tools of analysis (Theil, 1971). This yields much more encouraging results about the properties of the market demand function. Theil (1971) aggregates differential demand equations in relative prices under fairly strong assumptions about the macro parameters and variables. Barnett (1979a, 1979b) relaxes these assumptions but works with absolute (undeflated) prices. Selvanathan (1991) extended Theil's work under the weaker assumptions of Barnett and derived macro demand equations in relative prices. The results show that the properties of the macrocoefficients are analogous to those of the microcoefficients.
References Baccouche, R., and F. Laisney (1991). 'Describing the Separability Properties of Empirical Demand Systems,' Journal of Applied Econometrics 6: 181206. Barnett, W.A. (1979a). 'Theoretical Foundations for the Rotterdam Model,' The Review of Economic Studies 46: 109-130. Barnett, W.A. (1979b). 'The Joint Allocation of Leisure and Goods Expenditure,' Econometrica 47(3): 539-563.
66
International Consumption Comparisons
Barnett, W.A. (1981). Consumer Demand and Labour Supply. Amsterdam: North-Holland Publishing Company. Barten, A.P. (1964). 'Consumer Demand Functions Under Conditions of Almost Additive Preferences,' Econometrica 32: 1-38. Barten, A.P., and S.J. Turnovsky (1966). 'Some Aspects of the Aggregation Problem for Composite Demand Equations,' International Economic Review 7:231-259. Blundell, R., P.Pashardes and G. Weber (1993). 'What do we Learn About Consumer Demand Pattern from Micro Data,' American Economic Review 83: 570-597. Buse, A. (1992). 'Aggregation, Distribution and Dynamics in the Linear and Quadratic Expenditure Systems,' Review of Economics and Statistics 74: 45-53. Cassel, G. (1932) The Theory of Social Economy. Revised Edition. Translated from the 5th German Edition by S.L. Barrow. New York: Harcourt, Brace. Chavas, J.P. (1993). 'On Aggregation and its Implication for Aggregate Behaviour,' Ricerche Economiche 47': 201-214. Christensen, L.R., D.W. Jorgenson and L.J. Lau (1973). 'Transcendental Logarithmic Production Frontiers,' Review of Economics and Statistics 55: 28-45. Christensen, L.R., D.W. Jorgenson and L.J. Lau (1975). 'Transcendental Logarithmic Utility Functions,' American Economic Review 65: 367-383. Clements, K.W. and S. Selvanathan (1991). 'The Economic Determinants of Alcohol Consumption,' Australian Journal of Agricultural Economics 35: 209-231. Clements, K.W., E.A. Selvanathan and S. Selvanathan (1995). 'The Economic Theory of the Consumer,' Chapter 1 in E.A. Selvanathan and K.W. Clements (eds). Recent Developments in Applied Demand Analysis:
67
Chapter 2 Consumer Demand Models
Alcohol, Advertising and Global Consumption. Berlin: Springer Verlag, pp. 1-72. Deaton, A.S. (1975). Models and Projections of Demand in Post-War Britain. London: Chapman and Hall. Deaton, A.S., and J. Muellbauer (1980a). Economics and Consumer
Behaviour.
Cambridge: Cambridge University Press. Deaton, A.S., and J. Muellbauer (1980b). 'An Almost Ideal Demand System,' American Economic Review 70: 312-326. Diewert, W.E. (1974). 'The Application of Duality Theory,' in M. Intriligator and D.A Kendric (eds). Frontiers of Quantitative Economics,
Vol.2.
Amsterdam: North Holland. Driscoll, P.J., and A.M. McGuirk (1992). 'A Class of Separability Flexible Functional Forms,' Journal of Agricultural Economics 10: 13-22. Edgerton, D.L (1993). 'On the Estimation of Separable Demand Models,' Journal of Agricultural and Resources Economics 18: 141-146. Goldman, S.M., and H. Uzawa (1964). 'A Note on Separability in Demand Analysis,' Econometrica 32: 387-398. Gorman, W.M. (1959). 'Separable Utility and Aggregation,' Econometrica 27: 469-481. Gorman, W.M. (1968). 'Conditions for Additive Separability,' Econometrica 36: 605-609. Heineke, J.M. (1993). 'Exact Aggregation of Consumer Demand Systems,' Ricerche Economiche 47: 215-232. Houthakker, H.S. (1960). 'Additive Preferences,' Econometrica 28: 244-257. Keller, W J . (1984). 'Some Simple but Flexible Differential Consumer Demand Systems,' Economics Letters 16: 77-82. Keller, W.J., and J. van Driel (1985). Differential Consumer Demand Systems,' European Economic Review 27: 375-390.
68
International Consumption Comparisons
Klein, L.R., and H. Rubin (1948). 'A Constant-Utility Index of the Cost of Living,' The Review of Economic Studies 15: 84-87. Leontief, W.W. (1947). 'Introduction to a Theory of the Internal Structure of Functional Relationships,' Econometrica 15: 361-373. Lewbel, A. (1996). 'Aggregation without Separabilty: A Generalized Composite Commodity Theorem,' American Economic Review 86(3): 524-543. Lluch, C, and A.A. Powell (1975). 'International Comparisons of Expenditure Patterns,' European Economic Review 5: 275-303. Malinvaud, E. (1993). 'A Framework of Aggregation Theories,' Ricerche Economiche 47: 107-35. Moschini, G. (1992). 'A Non-nested Test of Separability for Flexible Functional Forms,' Review of Economics and Statistics 14: 365-369. Moschini, G., D. Moro and R.D. Green (1994). 'Maintaining and Testing Separability in Demand Systems,' American Journal of Agriculural Economics 76: 61-73. Mountain, D.C. (1988). "The Rotterdam Model: An Approximation in Variable Space,' Econometrica 56(2): 477-484. Neves, P. (1987) 'Analysis of Consumer Demand in Portugal, 1958-1981,' Memoire de Maitrise en Sciences Economiques, Universite Catholique de Louvain, Louvain-la-Neuve. Pearce, I.F. (1961). 'An Exact Method of Consumer Demand Analysis,' Econometrica 29: 499-516. Pearce, I.F. (1964). A Contribution to Demand Analysis. Oxford: Clarendon Press. Roy, R. (1942). De I' utilite. Paris: Hermann et Cie. Selvanathan, E.A. (1985). 'An Even Simpler Differential Demand System,' Economics Letters 19: 343-347.
Chapter 2 Consumer Demand Models
69
Selvanathan, E.A. (1987). Explorations in Consumer Demand. Ph.D. Thesis, Murdoch University. Selvanathan, E.A. (1991). 'Further Results on Aggregation of Differential Demand System,' The Review of Economic Studies 58, 799-805. Selvanathan E.A. (1995). 'Aggregation and Consumer Demand,' in E.A. Selvanathan and K.W. Clements (eds.). Recent Developments in Applied Demand Analysis: Alcohol, Advertising and Global Consumption. Spriger-Verlag, pp 359-90. Selvanathan, E.A., and K.W. Clements (1995) Recent Developments in Applied Demand Analysis: Alcohol, Advertising and Global Consumption. Berlin: Springer Verlag. Shafer, W., and H. Sonnenschein (1982). 'Market Demand and Excess C Demand Functions,' in K.J. Arrow and M.D. fntriligator (eds.). Handbook of Mathematical Economics, Vol.n. Amsterdam: North-Holland Publishing Company. Slesnik, D.T. (1998). 'Are our Data Relevant to the Theory? The Case of Aggregate Consumption,' Journal of Business and Economic Statistics 16: 52-61. Sonnenschein, H. (1973). 'The Utility Hypothesis and Market Demand Theory,' Western Economic Journal 11: 404-410. Sono, M. (1961). 'The Effect of Price Changes on the Demand and Supply of Separable Goods,' International Economic Review 2: 239-271. Stoker, T.M. (1993). 'Empirical Approaches to the Problem of Aggregation Over Individuals,' Journal of Economic Literature 31: 1827-1874. Stone, R. (1954a). The Measurement of Consumers' Expenditure and Behaviour in the United Kingdom, 1920-1938. Vol. 1, Cambridge: Cambridge University Press.
70
International Consumption Comparisons
Stone, R. (1954b). 'Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand,' Economic Journal 64: 511527. Strotz, R.H. (1957). 'The Empirical Implications of a Utility Tree,' Econometrica 25: 268-280. Theil, H. (1965). 'The Information Approach to Demand Analysis,' Econometrica 33: 67-87. Theil, H. (1980). The System-wide Approach to Microeconomics. Chicago: The University of Chicago Press. Theil, H., and K.W. Clements (1987). Applied Demand Analysis: Results from System-Wide Approaches. Cambridge, Mass.: Ballinger Publishing. Working, H. (1943). 'Statistical Laws of Family Expenditure,' Journal of the American Statistical Association 38: 43-56.
CHAPTER 3
Data Analysis: OECD Countries S. Selvanathan &E^4. Selvanathan
In this chapter, we provide a preliminary data analysis of the consumption patterns in the OECD countries. In Section 3.1, we present the details of the data source and its characteristics. In the following Section, we present a summary of the data in the form of Divisia indices. In Section 3.3, we verify one of the wellknown empirical regularities in consumption economics, the Engel's law, for the OECD data. Section 3.4 presents some preliminary estimates of income and price elasticities based on a double-log demand system. In Section 3.5, we derive some preliminary estimates of the income flexibility. In the last two sections, we verify the famous Frisch's (1959) conjecture and.the assumption of preference independence. The results presented in this and the next chapter are obtained using the Demand Analysis Package, 2000 (DAP2000). A shorter version of the User's Guide to DAP2000 by Yang et al (2000) is presented in the Appendix to this book.
3.1 Data Source The basic data, consisting of annual consumption expenditures (in current and constant prices) and the population for the 23 OECD countries considered in this book are compiled from the Yearbook of National Account Statistics (United
International Consumption Comparisons
72
Nations: New York, various issues); National Accounts of OECD Countries (OECD: Paris, various issues) and International Financial Statistics Yearbook (various issues). Even though currently there are 30 OECD member countries, 6 of them have not been included as they have only recently joined the OECD (Mexico, 1994; the Czech Republic, 1995; Hungary, 1996; Poland, 1996; Korea, 1996; and the Slovak Republic, 2000) and, another country, Turkey, is not included due to data unavailability. Two of the 6 new OECD member countries, Korea and Mexico are included with the less-developed (LD) countries discussed in Chapter 4. Consumption data prior to 1981 for 18 of the 23 countries considered in this book were first considered in a previous study by Selvanathan (1993) and also reported in Chen (2001). For most OECD countries, goods and services are classified into 9 commodity groups, which are listed in Table 3.1. Table 3.1 Details of the commodity groups Commodity 1. 2. 3. 4. 5. 6. 7. 8. 9.
Food Clothing Housing Durables Medical Transport Recreation Education Miscellaneous
Description Food, beverages and tobacco Clothing and footware Gross rent, fuel and power Furniture, furnishings and household equipment Medical care Transport and communications Recreation, entertainment and cultural services Education and research Miscellaneous goods and services
Table 3.2 summarizes the general characteristics of the database. Column 1 of the table lists the 23 OECD countries considered in this study. Column 2 gives the local currency unit of each country, column 3 gives the sample period for
Chapter 3 Data Analysis: OECD Countries
73
Table 3.2 Characteristics of the OECD database Country
d)
Currency
Sample period
Sample size
Number of commodities
Comments (6)
1. 2.
Australia
(2) Dollars (Aus)
(3) 1960-1996
(4) 37
(5) 9
Austria
Schillings
1964-1996
33
9
3.
Belgium
Francs
1960-1996
37
8
4.
Canada
Dollars (Can)
1960-1995
36
9
5.
Denmark
Kroner
1966-1995
30
9
6.
Finland
Markkaa
1960-1996
37
8
7.
France
Francs
1964-1996
33
9
8.
Germany
Deutsche Mark
1961-1994
34
8
9.
Greece
Education is included in recreation.
Education is included in recreation.
Education is included in recreation.
Drachmae
1961-1995
35
9
10. Iceland
Kronur
1977-1996
20
9
11. Ireland
Irish Pounds
1973-1996
24
9
12. Italy
Lire
1964-1996
33
9
13. Japan
Yen
1970-1996
27
8
Education is included in recreation.
1970-1991
22
8
Education is included in recreation.
1952-1996
45
8
1983-1995
13
8
14. Luxembourg Francs 15. Netherlands
Guilders
16. New Zealand Dollars (NZ)
Education is included in recreation.
17. Norway
Kroner
1964-1996
33
9
18. Portugal
Escudos
1986-1995
10
8
Education is included in recreation.
19. Spain
Pesetas
1964-1996
33
8
Education is included in recreation.
20. Sweden
Kroner
1963-1996
34
9
21. Switzerland
Francs
1961-1994
34
8
22. UK
Pounds
1961-1996
36
8
23. USA
Dollars
1961-1996
36
9
Education is included in recreation.
International Consumption Comparisons
74
each country and column 4 presents the sample size. The number of commodity groups considered for each country is given in column 5 with some comments in column 6.
3.2
Summary Measures
Let there be n commodities. Let p^ be the price and qit be the per capita quantity consumed of commodity i and Mt be the total expenditure on the n commodities during period t. Therefore, the total expenditure Mt =X"=1p(V^(.,.The proportion of total expenditure devoted to commodity i, called the budget share of i, is
wit
=
^ - , M,
t=l, ...,T,
(2.1)
where T is the sample size. Table 3.3 presents the budget shares at sample means for each commodity, _ wt
=
1T — Xw,-f. T t=\
i=l, ...,«,
(2.2)
for the 23 OECD countries. For each commodity, the last two rows of the table present the mean budget share of each commodity group averaged over the 23 countries, wt = (1 / 23) Y,Hi w,•, and the corresponding standard deviation. As can be seen from the food column, among the OECD countries, on average, the
Chapter 3 Data Analysis: OECD Countries
75
Table 3.3
Miscellaneous
Education
Recreation
Transport
Medical
Durables
Housing
Country
Food
Clothing
Budget shares of 9 commodities in 23 OECD countries (Means x 100)
(1) Australia
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
1.
25.47
7.79
17.71
7.62
6.43
14.59
6.57
1.32
12.49
0.40
16.60
2.
Austria
25.05
10.53
14.55
8.40
3.88
14.30
6.28
3. 4.
Belgium
25.65
7.54
16.76
12.60
8.49
11.48
5.02
Canada
19.95
7.23
20.80
9.23
4.09
14.90
6.93
2.64
5.
Denmark
25.42
6.33
23.65
7.90
2.03
15.68
8.07
1.27
6.
Finland
29.85
6.72
18.56
6.85
3.30
15.11
8.18
7.
France
22.93
7.39
16.66
9.22
10.06
13.95
6.39
8.
Germany
27.00
9.57
18.24
10.57
3.02
14.31
9.25
9.
Greece
41.18
9.86
12.86
8.15
3.47
11.06
3.97
10.
Iceland
25.19
8.83
18.00
10.26
1.67
15.98
8.58
1.15 0.75
11.
Ireland
38.93
6.98
13.09
6.87
2.94
12.92
7.25
2.98
8.04
12.
Italy
30.14
9.57
13.94
7.81
4.84
11.31
7.40
0.56
14.44
13. Japan
23.23
7.05
18.47
6.09
9.68
10.17
10.43
14.86
14.
Luxembourg
23.85
7.49
19.07
9.81
6.75
15.34
3.82
13.88
15.
Netherlands
26.04
10.94
14.33
10.09
9.29
9.33
8.09
11.89
16.
New Zealand
18.42
5.25
18.49
11.32
6.04
15.80
8.73
17.
Norway
27.27
8.71
18.32
7.96
3.09
14.63
8.27
18. Portugal
29.90
9.20
9.35
8.07
4.79
29.87
9.40
13.86
7.64
4.36
15.58 12.27
6.78
19. Spain Sweden
25.52
7.65
24.78
6.78
2.82
15.10
9.28
21.
Switzerland
30.43
5.85
18.85
6.74
7.90
11.32
9.66
22.
UK
24.43
7.69
18.30
7.28
1.13
14.69
23.
USA
15.80
7.17
19.12
6.72
12.18
27.08
8.07
17.21
8.51
5.64
1.49
3.48
1.68
Mean
14.24 9.65 11.43
0.39
13.01 8.05 8.29 10.73
15.94 0.52
11.24 16.32
6.55
20.
Standard deviation
12.47
16.04 0.12
7.95
8.42
1.21
16.84
15.38
6.86
1.97
14.80
5.00
13.63
7.45
1.11
12.44
3.02
2.01
1.69
0.88
3.00
9.24
International Consumption Comparisons
76
American consumers allocate only about 16 percent of their income on food while the Greek consumers allocate about 41 percent of their income on food. On average, the OECD consumers allocate about one-fourth of their income on food. The remaining income is spent on clothing (8 percent), housing (17 percent), durables (9 percent), medical care (5 percent), transport (14 percent) and recreation and education (combined 9 percent). The standard deviations presented in the last row of the table reveal that there is more variation in the budget shares for food, housing and medical care across the OECD countries. We define price and quantity log-changes as Dpit
=
log^it-logpit.i
(2.3)
Dqit
=
logfjrit-logcjit.i,
(2.4)
and
respectively, so that when multiplied by 100, these log-changes can be interpreted as percentage growth rates from year t-1 to t. Here and elsewhere log refers to the natural logarithm. Columns 2-10 of Table 3.4 present the mean log-changes in per capita consumption of each commodity Dqt
=
-i.Dqu, T t=\
i=l, ...,n,
(2.5)
for the 23 countries. The last row presents the mean quantity log-changes averaged over all countries. As can be seen, the average growth in per capita consumption of food varies between .3 percent (USA) per annum and 2.4
11
Chapter 3 Data Analysis: OECD Countries Table 3.4 Per capita quantity consumed of 9 commodities in 23 OECD countries
(D
Miscellaneous
Education
Recreation
Transport
Medical
Durables
Housing
Clothing
Country
Food
(Mean log-changes x 100)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0)
(10)
1.
Australia
0.78
0.24
3.14
3.47
2.01
2.70
3.45
4.64
3.21
2.
Austria
1.13
2.94
2.99
3.99
3.74
0.87
Belgium
1.07
1.81 2.01
3.02
3.
2.43
2.77
3.80
3.37
3.66
4.
Canada
0.36
1.71
2.90
2.45
0.26
2.90
5.12
4.05
5.
Denmark
0.86
0.99
2.19
-0.25
2.34
2.33
3.41
6.40
6.
Finland
1.37
1.05
3.39
2.80
3.31
3.82
4.00
7.
France
1.03
0.34
3.66
1.65
5.57
3.14
4.03
8.
Germany
1.56
1.95
2.94
2.82
2.82
3.97
2.87
9.
Greece
2.27
1.76
4.05
2.99
5.31
6.12
5.66
-0.69
4.28
10.
Iceland
1.09
0.00
1.33
0.62
2.63
1.97
3.23
4.63
2.84
11.
Ireland
0.97
1.38
1.92
1.43
0.30
1.94
4.09
2.05
2.89
12.
Italy
1.41
1.78
2.39
2.83
5.00
4.18
3.51
2.61
13.
Japan
0.74
0.81
4.08
2.54
4.31
4.70
4.37
3.16
14.
Luxembourg
0.90
0.73
2.83
4.36
4.02
5.75
3.98
2.17
15.
Netherlands
1.71
1.87
2.31
3.35
3.57
4.91
3.98
3.31
16.
New Zealand
0.42
-1.06
0.88
3.07
2.92
3.41
2.35
17.
Norway
1.08
1.23
2.58
2.28
5.13
2.95
4.68
18.
Portugal
2.35
1.42
7.74
3.69
3.09
5.49
7.00
19.
Spain
1.23
1.55
2.12
1.74
6.08
5.78
3.27
20.
Sweden
0.53
0.97
1.33
0.44
3.34
1.97
2.59
21.
Switzerland
0.97
-0.26
1.56
-0.08
2.75
2.19
1.84
2.01
22.
UK
0.38
2.97
1.60
1.98
3.38
3.52
3.73
2.52
23.
USA
0.31
2.55
2.01
2.31
3.51
2.50
4.83
2.61
1.93
1.07
1.21
2.71
2.27
3.41
3.63
3.89
2.64
2.59
Mean
1.63 2.94 2.15 1.65 3.67
2.63
1.94 3.17
3.39
0.65 0.74
3.04 2.97 4.01
1.19
0.07
International Consumption Comparisons
78
percent per annum (Portugal) with an average of 1.1 percent per annum among the OECD countries. The average OECD annual growth in consumption of clothing is 1.2 percent, housing 2.7 percent, durables 2.3 percent, medical care 3.4 percent, transport 3.6 percent, recreation 3.9 percent and education 2.6 percent. Columns 2-10 of Table 3.5 present the annual mean log-changes in prices of each commodity Dp,
=
^i-DPu.
i=l, ...,«,
(2.6)
for the 23 countries. The last row of the table presents the mean price logchanges averaged over all countries. As can be seen, in the OECD countries, the average growth in the price of food varies between 2.6 percent (Germany and Netherlands) to 22.4 percent (Iceland) with an average of 6.4 percent per annum among the OECD countries. The average OECD annual growth in the price of clothing is 6.3 percent, housing 7.9 percent, durables 6.1 percent, medical 7.6 percent, transport 6.8 percent, recreation 6.6 percent and education 9.7 percent. Table 3.6 presents the Divisia volume index, DQt, for the period t, DQt
=
t
witDqit,
t=l,...,T,
(2.7)
where wit= Yi(w\t + wit_i) is the arithmetic average of the budget shares of commodity i in periods t and t-1. The last row of this table gives the Divisia volume index averaged over the whole sample period for each country,
DQ =
±i.DQt1 i=i
79
Chapter 3 Data Analysis: OECD Countries Table 3.5 Prices of 9 commodities in 23 OECD countries
(D
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0)
Miscellaneous
Education
Recreation
Transport
Medical
Durables
Housing
Clothing
Country
Food
(Mean log-changes x 100)
(10)
1.
Australia
6.07
5.51
6.42
3.96
6.92
5.74
7.00
6.88
6.31
2.
Austria
3.06
3.33
5.96
3.28
5.97
4.22
3.79
5.66
5.28
3.
Belgium
3.59
4.20
5.01
3.25
5.72
4.51
4.48
4.
Canada
4.88
3.54
4.76
4.29
5.58
4.19
3.70
5.81
5.53
5.
Denmark
5.47
5.14
8.04
6.08 5.79
5.66
6.37
5.14
7.04
7.20
8.37
7.78
6.79
5.47
6.25
7.19
6.
Finland
5.62
5.73
7.
France
5.45
5.79
6.95 6.82
5.32
3.37
6.52 6.67
4.77
8.
Germany
2.58
2.82
4.71
2.17
4.15
3.64
4.16
9.
Greece
11.39
11.42
10.27
11.24
11.31
10.61
10.93
12.11
12.31
10.
Iceland
22.42
23.03
23.16
21.84
24.77
22.28
22.74
26.04
23.84
3.57
11.
Ireland
8.07
7.56
10.22
7.81
12.84
9.52
7.91
12.29
10.59
12.
Italy
8.05
9.83
10.62
10.03
9.44
9.13
8.55
10.67
10.10
13.
Japan
4.00
4.82
4.44
2.95
3.86
3.98
3.89
14.
Luxembourg
5.57
5.44
6.20
4.72
5.91
5.36
4.67
6.03
15.
Netherlands
2.58
2.40
5.87
2.38
6.12
4.00
4.11
5.03
16.
New Zealand
6.09
5.00
9.59
4.14
8.61
2.64
5.86
17.
Norway
5.76
5.22
7.33
5.32
2.29
6.74
4.86
18.
Portugal
7.79
8.91
10.34
7.52
10.21
8.23
10.23
9.72
19.
Spain
8.30
9.22
9.37
9.20
8.05
8.80
9.69
11.60
20.
Sweden
5.84
5.04
8.13
6.48
6.30
7.02
6.00
21.
3.56
3.23
5.67
3.90
7.31
4.53
4.63 8.30
3.29
22.
Switzerland UK
6.29
7.01
7.09
3.94 5.84
23.
USA
4.36
2.89
4.60
3.34
5.96
4.26
3.08
5.67
5.33
6.43
6.29
7.90
6.12
7.57
6.76
6.59
9.67
7.81
Mean
4.32
7.64 7.07
9.01
6.75
7.22 4.91 6.91
International Consumption Comparisons
80
Tcfcle3.6 DivisiavoliiTeindces in 23 OECD countries (x 100)
I I (1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
1953
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
649
1954
6.95
1955
4.87
1956
7.62
1957
-1.30
1958
-222
1959
4.47
1960
597
1961
0.64
1.21 -0.75
6.99
1962
299
3.38
5.56
5.19
359
386
5.18
347
0.58
3.03
1963
5.23
3.44
0.67
289
1.35
4.99
7.78
254
a73
241
1964
280
1.60
3.77
4.38
4.33
7.59
369
420
292
232
393
1965
0.94
4.05
321
4.06
4.73
526
7.18
295
5.74
3.14
2.15
0.56
4.27
1966
297
271
2.56
311
238
393
1.81
6.47
386
1967
4.19 203
2.28
393
3.46
1.85
4.01
086
4.38
1968
4.19
5.04
2.06
1.91
0.43 295
4.04 6.20
4.64 284
5.65
9.86
4.35
3.38
4.96
301
1.52
642
1.25
295
5.74
1.02
1.84
1.44
6.16
311
1.72
4.81
1.77
1.71
1.91
1.79
4.28
4.69
272
4.73
3.57
246
286
4.13
6.92
6.93
1969
4.35 2.73
5.46
696
5.63
329
4.07 027
243
1970
£73
231
7.42
356
605
8.01
6.39
6.41
0.15
3.05
0.58
4.25 251
0.96
1971
0.72 7.18
4.07 6.37 -0.04
1.96
5.10 385
5.95
224
4.81
397
2.12
4.13
3.81 -1.81
3.69 274
237
1972
1.50
6.28
547
5.13
312
6.26
261
7.87 3.76
247
1.99
6.84
1.84
2.72
5.84
4.86
1973
6.55
360
6.04
7.66
4.64
1.81
4.99
395
1974
1.61
0.43 271
1975
210
258
0.06
270
1976
1.29
353
4.59 4.40
5.77
0.99
5.98
6.29
5.71
5.97
1.47
7.52
5.42
5.66
5.50
4.63
1.31
7.48
3.39
312
4.96
6.61
1.77
4.07 -3.34
1.36
236
066 -1.06
-0.03 2.00 -1.68
4.21
1.63
2.56
4.07
3.64 -0.62 -0.97 -1.76
2.94 206
257
349
-5.47 -1.97 305
4.96 227
3.99
1.29
242 -240 -0.48
1.17
7.11
5.18
4.29 4.67
0.90 289
239
359
5.11
3.49
370
1.76
1.07
4.41
0.43
5.00
1977
0.18 4.12
2.19
1.97
025 -1.36 251
4.08 3.49
1978
2.06 -0.38
234
2.67
0.11
1979
4.16
538
1.85
293
3.06
3.91
5.92
1.44 -1.51
317
0.13
3.31
291
4.19
383
4.99
854
6.95
259
4.01 2.76
3.08
-224
0.44 -0.92
1.16
4.70
3.00
1.35
4.60 4.19 2.49 0.60 521
296
267
1.46 -1.64
1.83
500
527
2.41
246
3.66
0.12 223
0.85
4.03
1.19
1980
2.10
214
1.70
0.75 -3.63
1.47
1.00
1.47 -2.69 3.42 -0.91 4.06
0.76
295 -0.72
2.21
-0.49 -1.19 3.10 -1.82 -1.36
1981
230
0.42
0.16
1.00 -1.31
1.44
1.71 -0.21 0.37
1982
0.03
1.09
1.90 -307
1983
0.96
4.17 -0.79
1964
271 -0.79
0.90
1.59
2.09 2.19 -1.01 0.98
1.76
296
1.72
3.98
3.38 257
6.06
0.25
0.37
0.56 -0.99 -280
-0.07
-0.65 -0.71
564 -9.06
0.21
356
0.20
-0.10
0.82
-1.12 -1.10
1.16
3.80
370
295
0.14
1.19
1.71
399
1.67 -1.63
0.50 228
1.61 -9.70 -2.57 -0.92 241
1.51
0.71
1.81
0.67 -0.55
258
3.15 -0.93
1.96
0.48 284
1.52
1985
3.82
1.44
1.32
4.46 4.19 290
1.97
1.93
3.66
4.61
265
262
1.20
320
9.20
2.84
2.42
0.89
350
3.45
1986
-0.36
0.77
1.72
375
274
296
0.45
5.88 -0.44
328
269
212
2.01
311
4.16
3.34
4.19
229
5.76
300
1987
2.24
1.98 2.65 269 -1.99 4.70 234
4.83
1.14
9.11
3.64
3.78 351
4.24
1.72
1.73 -1.89 6.47
515
4.14
1.14
4.57
1.88
1988
233
355
0.29 2.56 -270
4.29
3.96
4.27
335
0.18 0.16 -232
7.31
4.19
1.86
1.32
6.35 3.0B
1969
2.36
4.32
1.51
3.31
4.14
0.53
1990
-0.37 3.20
3.98
325
2.92 -0.77 -1.09 4.52 2.55
5.20 -0.17
265
3.78 £75
1.93
0.24 -0.69 0.63
1.99 -0.82 0.67 -0.17
372
277
1.32 235 -254
7.59
3.12
4.16
3.25 -0.92 -O.10 -124
206
525
1.11 -0.05 2.43
215
4.08 3.90
4.47
1.03 -0.11
1991
1.56
2.27
230 -7.51
1.90 -3.85
0.72
1992
2.52
0.88
1.32 -0.03
1.17 -1.74
0.91 -0.14
1993
2.75
0.66 -1.93
1994
4.31 2.68
1995
294 -6.39
1996
0.81
5.53
3.02
Mean
226
235
245
2.97
0.37 -1.28
283
1.59
0.98
5.79 2.48 -1.56 0.73
024
0.65
221
3.79 239 -3.06
1.47
4.07
2.41
0.83
1.68
1.86
0.20
1.24
3.65
1.97 -213 -1.29 -1.66
1.87
0.71
1.X -218 -0.41 -1.48 0.09 -4.12 247 2.72
0.77
0.24
3.82
1.95 -0.56 -201 -204 -1.79 2.52
1.84
123
260
5.94
1.83
0.95 -Q44
1.73 -1.36
5.10
1.21
1.69
1.60 4.85
386
202
1.54
0.92 -0.69 230
214
0.63
0.44
0.70
353
1.01
0.65
4.93
3.84
1.49
1.57
1.24
3.02 2.35
1.35
1.74
0.55
1.26
1.55
5.58
6.01
0.81
248
251
4.13
203
0.83
3.06
214
1.60
1.72
264
297
2.38 3.71
267
1.19
203
222
1.49 -4.39 252
371 -0.90 221
1.62
270
252
260
2.00 4.22
1.49
365 -1.46
3.28
283
283
1.57
0.05
0.42 -1.68 -1.59
1.42
81
Chapter 3 Data Analysis: OECD Countries
As can be seen from the last row of the table, overall consumption growth in the OECD countries varies between 1.2 percent (Sweden) and 3.7 percent (Portugal) with an overall average of 2.3 percent per annum across all OECD countries. Table 3.7 presents the Divisia price index, DPt, for the period t,
DPt
=
£ witDpit,
t=l,...,T.
(2.8)
The last row of this table gives the Divisia price index averaged over the whole sample period for each country, 1 T
—
DP
=
-I.
DR.
Tt=i
As can be seen from the last row of Table 3.7, the overall annual price growth in the OECD countries varies between 3.4 percent (Germany) and 22.8 percent (Iceland) with an overall average of 6.9 percent per annum among all OECD countries. The Divisia quantity index (DQt) and the Divisia price index (DPt) are first-order moments. The second-order moments, the Divisia quantity and price variances that correspond to the Divisia volume and price indices are
Kt
=
iwit[Dqit-DQt]2, i=i
t=l, ...,T,
(2.9)
82
International Consumption Comparisons Table a 7 Divisia price indices in 23 OECO countries (Means x 100)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
1953 1954
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
1.41
-0.65 3.59
1955
1.23
1956
0.87
1957
5.57
1958
1.36
1959
Q67
1960
1.25
1961
0.42
280
0.68
1.60
1962
1.77
1.01 -1.27
3.07
314
1.25
1.59
4.91
4.38
1963
0.48
3.66
3.96
5.21
293
3.14
207
3.49
1.75
1.43
1964
312
4.07
1.28
7.95
236
209
615
3.25
4.05
3.50
1.46
1965
3.30
4.39
4.47
1.95
343
264
308
4.36
3.51
313
4.16
9.18
5.11
391
5.10
1.64
1966
296
250
4.08
331
270
317
371
3.39
282
5.61
3.34
695
6.15 4.65
3.82
273
1967
3.48
3.91
246
3.48
603
4.79
3.10
1.73
1.85
300
3.00
4.31
5.61
4.26 4.36 254
248
1968
3.18
248
273
3.99
663
9.66 4.94
1.68
069
1.42
266
3.14
5.02
1.33
2.57 4.39
399
1969
3.13
3.35
3.02
3.76 4.50
1.95
685
1.95
292
282
4.66
3.42
3.34
3.32
269
4.42
1970
5.45
3.85
252
3.44
698
253
4.85
364
3.11
4.88
1971
6.46
4.65
500
246
665
6.47
537
536
289
5.33
560 4.51
1972
7.46
5.95
5.39
4.08
7.63
809
5.71
538
3.57
620
4.91
4.69
840
649
1973
887
7.02
698
S14
9.14 11.15 661
635 14.03
11.77 9.11
656
866
4.42
1974
1622 9.86 11.77 10.10 14.10 17.64 1244
659 21.24
14.40 19.01 19.34 9.41
9.59
896
1611
1975
14.32 7.83 1202 1004
9.65 15.10 10.82 593 1210
2Q61 1630 1Q91 9.70 1009
11.18
14.54 1025
635 2128
1976
11.04 655
9.37 1264
1857 1659
S74
9.07
841
a06
15.52 1024
238 1429
575
1355 1674
7.08
5.61 1205
7.80
21.54 10.10
1.09 15.19
641
7.58 1213
4.63
3.53 4.37
7.30
17.61 10.69
1.16
9.15
677
5.00
4.41
15.17 7.63
4.18 1270
S74
5.60
1.53
7.84
7.35
9.37 4.23 1281
691
7.00 10.23 11.05 866
4.14
9.51
637
5.77
3.86 5.76
4.46
813
623
7.70
720
683
4.28
7.9B 556
7.43
5.79
340
10.88 10.83 895
7.09
7.85
S22
9.37 9.63 15.50 9.84 7.74
1977
9.20
1978
878
4.08
4.05
7.17
9.08
7.31
S43
270 11.60 35.83
1979
9.91
4.07
388
829
9.77
7.64
9.95
4.37 1624 37.92 13.93 13.85 346
1980
9.24
640
608
9.59
9.85 11.01 1227
672
7.20
656
9.36
1981
9.21
7.08
7.77 10.79 11.45 10.70 11.80 578 21.29 41.42 1873 17.59 4.23
S30
5.99
1283
1342 10.81 616 1093
889
1982
1064
5.74
7.16
9.96 9.30
9.54 11.22 4.70 19.04 41.28 14.98 15.77 251 1Q16 509
1Q64
1369
602
1983
7.57
3.68 646
5.42
664
812
4.93
210 15.60 6377 1Q08 27.68
11.88 11.02 261
5.45
386
1984
7.37
5.25
3.87 611
673
7.43
11.29 723
4.82
3.93
1985
5.91
3.17 4.84
3.66
4.31
5.45
561
886
3.47 5.30
3.59
1986
836
1.69
1.53
3.81
3.26
3.10 266 -Q60 19.95 19.05 14.26 607
1987
7.70
0.98
1.57
3.96 4.62
3.55
1988
7.28
1.53
1.54
3.95
1989
623
239
3.03
4.90 4.02
1990
4.92
3.07 3.33 4.22
1991
253
290
1992
1.85
1993
603
3.87 4.38
4.94 19.72 44.14 17.31 1836
397
1380 11.76 4.09 15.62 10.40 9.51
5.47 857
300
7.73
270
1394
278 1680 27.29
7.39 11.32 254
642
251
9.B2 602
1.37 1688 27.84
7.13
224
4.09
617 1366
5.56
7.10
674
Q86
1.34
Q23 1285
658
9.09
4.64 0.47
3.80
5.62
248
3.13 -1.54 14.72 15.76 249
5.28
Q56
1.62
025 1057
7.57
5.10
1.48
4.37
386
270
5.67
Q55
270
052
650
5.93 10.08 4.98 5.85
208
5.07
4.12
4.71 1208
322 1274 21.86 4.71
642
1.87
366
1.15
650
652
652
3.13
5.72
4.54
256 17.91 15.51
1.97
610
235
357
225
5.46 4.60 11.46 636
9.3B
5.34
5.38
5.16
4.80 213
5.33
316
362 1753
282
668
250
308
314
1.97
370 11.05 625 10.07 5.58 508
3.97
3.96 270
1.11
230
3.53
242
392 14.15 4.47 258
5.47
1.90
303
1.03
273
a92
635
218
394
5.81
3.04
1.49
3.29
289
1.41
0.35
3.89
227
357 1291 4.16
1.88
4.87
1.32
211
1.10
205
680
5.40 4.93
332
321
271
1994
1.25
3.61
273
0.56
204
1.54
213
276 1Q08
1.66
274
4.55
Q78
270
233
1.12
546
4.64
285
1.26
270
233
1995
264
1.64
1.61
1.55
251
0.37
1.54
896
1.61
201
5.58 -Q45
1.43
292
236
4.17 4.63
259
281
223
1996
1.65
246
203
1.27
1.82
221
1.33
4.22 -Q18
1.27
1.26
3.34
1.20
266
206
Maan
5.98 4.22
4.43
6.36
5.76
335 11.20 2275
8.91
9.28 4.12
9.31
677
4.06 698
4.51
324
4.65
639
3.46 278 1398 19.61 3.85
9.34
3.02
5.68 294
282
4.89
358 11.32
548
677
5.62
3.85
623
605
682
83
Chapter 3 Data Analysis: OECD Countries and
H
=
Iwft[Dpft-DP,]2,
t=l,...,T.
(2.10)
These two variances measure the degree to which the quantities and prices of the individual commodities change disproportionately. When all quantities and prices change proportionately, these two variances will vanish. Tables 3.8 and 3.9 present these two variances for the OECD countries over the sample period. As before, the last row of the table gives the mean variance for each country averaged over the whole sample period. A comparison of these two variances reveals that the Divisia quantity variances systematically exceed the corresponding Divisia price variances. To confirm this relationship, in Figure 3.1, we plot -JfCf against yrif fort=l,...,Tandc=l,...,23. As can be seen, most of the points lie above the 45° line indicating that, on average, -yjKf >-y/nj\ This pattern agrees well with the results of Clements (1982, 1983), Meisner (1979), Selvanathan (1987), Selvanathan (1993), Selvanathan and Selvanathan (1993), Selvanathan and Selvanathan (1994) and Theil and Suhm (1981). To measure the co-movement of prices and quantities, we define the Divisia price-quantity correlation as
Kt
—
i
>
t=l, ...,T,
(2.11)
VKJl7 where Tt = £"=1w;,[£>p,r -DPt][Dqit -DQt]
is the Divisia price-quantity
International Consumption Comparisons
84
(16)
N z (17)
(18)
(19)
(20)
(21)
(22)
*: D (23)
USA
(15)
Switzerland
(14)
Sweden
(13)
Spain
(12)
Portugal
(11)
Norway
(10)
Netherlands
(?)
Luxembourg
(8)
Italy
(7)
Japan
(6)
Ireland
(5)
Iceland
Finland
(4)
Greece
Denmark
(3)
France
Canada
(2)
Germany
Belgium
1 (1953 >
Austria
Year
Australia
Table 3.8 Divisia quantity variances in 23 OECD countries ( x 10000)
(24)
2072
1954
19.70
1955
20.17
1956
1841
1957
11.32
1958
2273
1959
11.72 14.11
1960
507
1961
4.55
14.X 85.18
14.21
1962
23.47
2.43 34.20
1281
814 14.32
614
581
7.83 642
1963
31.67
4.86 55.34
1600
510 7.43
387
1.55
9.33 4.08
1964
4.73
10.90 4.37
37.78
555 2224
3225
596
7.37 347
1965
1.63 8.32 4.80 5.32
4214
5.20 7.77 7.91
4.91
19.56
4.48
1680 622 277
501
1966
4.95
1662
205
41.71 622 299
1.29 4.51
1967
5.67 8.53 280 7.50 5.38 4.07 1.19 4.67 6.07 2.63 4.16 5.01 4.35 7.23 332 350 14.48
1968
8.05 3.04
578
1057
15.35
672
4.55 2040
0.69
13.18
3.44
10.87 5.49 4.63 340 1207 25.73 4.99 1610 11.12
7.77
5.92 a i 8
664 286
685
508
1653 11.71
149 303
7.26
2264
2322
9.03 366 200
2.57 14.65 206 1602
687 a31 566
7.11 5003
5.81
21.42
2620
379 376
1971
3.88 25.30 7.27 25.09 13.92 1221 624
274 1056
3.99 553 1390
1.05
9.52
1972
27.91 24.11
1973
64.48 6.83 30.42 22.19 13.36 2620 7.47 698 5022
1974
5.94 10.86 15.91 5.30 33.63 14.97 11.89 9.47 1559
1975 1976
5.71
605
9.17 1289
8.09 4.01 10.92 2252 9.86 3.90 14.49
7.34 1539 214
7.76
2564 346
1.24 1070 7.12
180.26
1Q91 392
693
17.25 558 41.22 7.40 8.90
541
878 1614 7.89 11.34 1230
31.99 9.54 2071 11.50 3208 43.05 3.16 10.35 19.75 099
666
4.44 254 17.26
1359
275 4.86 4.19 215 371
5.91 2210 11.86 4.59
7.78 659
1296
381
500 321
1978
7.70 2205 3.61
4.87 7.56 659 662
1.72 1253
57.15 15.51
1.18 11.85 1669 363
2567
1.84
534
1979
3.56
7.27 993
2.95 3.60 532 299
222 1062
29.96 14.84
592 11.51
1960
3.98 4.61 16.34 4.46 22.18 4.44 4.93 1282 4649
1023 3.60 308 15.22
1981
2.11
4022 37.63 676
1982
8.76 2.65
879
3.45 2383
1983
6.52 7.53 3.84 350 2046 5.93 7.84
4.13 2341
1984
4.51
595
5.08 7.99 10.86 3.39 868
233 1Q70
1985
4.49
1.52
1.15
1986
5.07 4.67 243
9.17 a60 4.11 4.17 21.78
5.78 23.32 382 10.14
819
11.19 248 3.67 656
9.94 15.27 4.02 250 1586 9.26 0.48 1.93
10.65 551
7.14
5.40 4.31 2.36 377 1279 4.38 244 39.23 7.00
1988
4.71
4.52 335
4.63 630 7.32
520
380
697
1.77 212 283
500
665
317
698 660 1210
1232
283
4.38 258 311
24.01 70.29 4.28 5.97 1Q36 4.31 65.03 1009 667 433 4.98 1.03
7.55
24.70 392 3.32 1680 17.94 3.79
588 1241 4.14 307 692
349
1.75 5208
63.75 11.18 508
558 11.85 302 1353
1.78 4.10
262
3645
344
666
1.38
17.98 346
1070
7.89 1526
4.05
1.26 287 1593 543 1.19 224 274 1.24
049 0.61
3553
a 91
1.82 626
517 1201
876
578 4.24 119.45 19.10 4.20 1Q83 1241 3.34 7.20
1987
7.14
9.62 604
ace
10.20 1260 7.22
1977
7.36 857 4.37 654 2536
1.80 4.90
1.08 374
5.63 536 1547 21.71
661 14.55 834 9.51 5.48 3.65 1381
11.67 3.54 20.52 4.19 17.39 30.67 7.41
1.64
1.45 312 4.77
1970
1969
281
0.61
4.42 7.01 4.94
7.66 384 293
1.26 1Q57 353
30.17
9.73 31.43 4.75 5.37 17.12 674 4.60 34.97 1.10 15359 20.38 511 11.04 7.17 4.64 2001
1395 1596 14.81 0.97 677 4.58 3506 221.85 7.94 516 1.64 23.84 1.77
1969
5.87 8.99 3.44 3.00 604 282 4.87 214 7.67 11276 1017 4.20 11.22 1347
1990
3.11
1.93 3.83 4.26 1.83 10.16 5.08 4.92 588 4.35
647
5.38 843
267
544
673
4.70 632
1.46 4.11 297
641
1248
10.73 4.20 571
371
504
4.81
5.14
9.84 317 11.67
aso
9.17 263
4.29 7.62 309 14.80
19.23 357
1.85 4.45
1993
1.82 3.77 6.57
1994
1.38 5.62 290 316 49.34 4.24 249
1995
1.X
6.77
1996
5.01
8.25 17.87
Mean
8.74 876 7.23 11.55 11.63 13.06 521 7.40 1611
1.05 10.41 211 3073
1.73 278 14.38 5.07 10.66 11.22
1.05 215
19.72
854
633
1.34
1.84
9.41
541 23.91 241
1991 1992
1.05
1.16
19.55 ia93 553 1024 11.62 323 9.82 3.01 264 4.51 lass 359
4.71 4.59
1.97
4.15 1295 14.45
7.31 266
276
547
1216 249 1097 4.91
243
869
1.04 9.44
1.93 1Q65
5.19
235 11.84 883
605
362 4.22
1.55
588
1.83 1307
7.55
1.06
1.95 375 a61
4.15 4.97
13.99 14.59 233
572
0.92 1Q09
546
0.65
576
1.99
7.61
359
1.71
215 672
9.47 9.37
13.12 2307 601 11.89
Q53
4289 17.94 513 9.98 10.84 1Q12 1324
17.75
ax
17.34 30.63 9.81 617 324 582 534
Chapter 3 Data Analysis: OECD Countries
85
Ireland
Italy
(9) (10)
(")
(12)
(13
1953
(14) (16)
N
(16) (17) 344
1954
11.84
1955
271
1953
902
1957
326
1953
7.16
1953
1.02
1960
845
(18) (19)
(20)
Switzerland
Iceland
Sweden
Greece
(7)
Spain
Germany
(6)
Portugal
France
(5>
Norway
Finland
(4)
Netherlands
Denmark
(3)
Luxembourg
Canada
(2)
Japan
Belgium
(1)
Austria
Yea-
Australia
Table 3L9 Ovisia price variances in 23 OBCD oartries ( x 1000(9
<
(21) (22)
(23) (24)
1961
563
iaoo 082
1.30
1962
945
551 3606
212
1.69 560
1.31
1.23
079 078
1933
871
933 41.66
291
1.82 291
1.70
1.49
7.22 026
1954
272
1.73 1.64
1329
121 1.06
674
396 Q55
1.66 047
1935
246 237
1515 1.80
aio
1.66
1.53 4.00
1.16
346
1.72
7.99
Q93 315
1.96 Q37
1966
126 220
653 296
316
1.43
240 293
Q72
4.11
1.89
1.87
1.53 1.54
1.42 1.91
1967
131
4.07
Q99 319 854
398
323
328 243
1.53
900
318
590
207 497
1.10 227
1966
221
4.87
1.33 1.69 4.45
3255
365
7.79 4.33
1.90
12887
080
866
1.57 413
1.83 1.10
1939
629
1.91
Q49 210 1.27
045
1.45
266 3C0
051
1.69
1.57
545
429 291
Q56 122
491 393 234 17684
1.09
090 583
1.12
4.37
227
879
1.82 246
1.59 055
293 336 562
437
Q71
265 4.15
217 349 293
7.04
1.41
ace an
4.75 224
090 1.56
1.07
1970
541 261
1971
4.91
536
1972
27.37
305
397 241 4.18
Q65
1.28
1.00 1.10
1.96 4.59 077
898
054
1973
1909 1499
1066 2523 31.80
876
222 23259 2273
503 31.41 7.91
351
161.36
1974
9 8 7 1Q3B
874 4.02 1274
1983
596
4.57 1556
1655
1346 31.48 315
9.73
368
7.51
2583 1.90
480 445
1975
63 355
920 395 1.51
27.38
1.07
067 550
S78
720 887 382
807
822
4.58
282 252
897 272
1.44 7.19
362 4.71
815 340
476 1.44
533 11806 568
5380 31.69
1976
4.76
520
400 a 93 4.06
1589
231
057 4.12
2478
7.39 342 927
394
536
839
1977
245 341
4,75 336 4.04
512
239
094 341
24.80
578 4.66 232
74.35
587
1506
1978
586
4.43
1.81 617 253
390
032
1.00 1.84 1Q20
27.89
423 7.00 336
4.70
582
270
4.63 379
383 296
1979
264 384
593 1.98 2253
1.82
224
7.52 4.62 2864
14.99
4.54 281 430
423
391
1222
7.19 852
474 478
4.23 Q15 35370 391
1930
1.54
521
11.34 257 11.08
4.17
7.40
326 503 378
11.72
994 540 11.15
4.40
338
597.00
1.95 1.54
937 1049
1961
358 653
1433 541 367
4.36
225
272 584 1Q19
2818
294 1.40 202
588
1294
1.58
392 241
1486 411
7.55 422 1.29
925
407
1982
595
1933
2 6 9 7383
4.29
Q74
1.48 1.47 1.96
226
aeo
227
1.40 7.55 1Q50
549
422 1.97 7.13
240
934
363
548 24.77 9916
527 167.56 1016 1.03
248
25396
567
31.95 Q74
1.14 1034
1.02
205 1229 2027
526
1.71 813
1.16
225
1.19 035
308 244
13641 506 Q59 8368 :36209
801 094 088
7.86 556
1934
6871
1935
505
1.43
054 051 Q42
1.57
1.85
250 467 656
5567
287 393 Q70 11533 5575
0.59
201
035 021
040 1.74
1966
Q66
4.60
11.76 280 1.53
369
332
581 706 8907
4221
1.30 089 1935
288 14.46
233
821
383 989
318 537
1987
212 059
255 089 601
362
1.27
3343 1519 1313
7.01
am
1.30
668 2031
210 66S
1.53
1.96 1.77
204 Q55
1933
284 Q63
059 Q71 1.81
214
240
44.44 893 27.96 12393
341 033 1.75
1.57 37.18
1.68 540
1.66
297 Q89
1.46 251
1939
1.71
1.55
Q74 042 227
1.70
1.41
1.79 11.59 21.66
046
1.19 072 293
067 1358
239 680
1.84
264 1.71
120 262
1.51
1990
1.3
1.75
073 Q76 353
120
1.95
029 368 648
046
1.37 1.35 Q75
1.52 1.50
322 216
1.77
11.00 1.88
827 289
1981
1.03
084
1.97 387 313
446
1.07
1.86 650 511
080
418 1.48 Q16
214 816
274 1Q43
318
44.47 094
727 093
1992
091
1.39
479 1.07 1.73
285
126
084 944 686
1.48
1.41 1.33
123 1.31
1.17 363
245
1932 261
836 1.94
1983
094
1.01
542 045 1.62
823
1.55
1.58 1050 670
1.07
354 075
083 216
1.16 4.82
383
937 337
1.67 227
1994
1.33
262
074 374 1.08
087
1.03
1.18 601 288
1.78
277 1.63
332 532
1.08 212
1.06
1.58 Q49
332 1.43
1995
211
4.96
097 098 093
994
Q48
490 053
211
295 254
370 879
1.13 1.09
Q67
1.07
200 204
1996
1.44
4.31
1.43
278
027
1.63
346
1.01 267
329
252
Q18
975
093 204
Mm
643 589
1325
1330
11.62 7.10 1633
1805
S87 543 512
872 524 415
1122 14.72
1595 4.80 2329
1Q52 269
1539 361
International Consumption Comparisons
86
1954
N
(17)
(18)
(19)
(20)
Switzerland
(16) -0.44
Spain
(15)
Sweden
(14)
Portugal
(13)
Norway
Netherlands
(11)
(12)
Luxembourg
(10)
Italy
Greece
(9)
Japan
Germany
(8)
Ireland
France
(6)
(7)
Iceland
Finland
(4)
(5)
Denmark
(3)
Canada
(2)
Belgium
(1) 1953
Austria
Year
Australia
Tablea-IO Divisia price-quantity correlations in 23 OECD countries
(21)
(22)
< ^
V)
(23) (24)
-0.89
1955
0.21
1956
-0.95
1957
0.20
1958
0.19
1959
-0.60 •0.32
1960 1961
0.10
-0.97 0.02
-0.24
1962
0.06
-0.43 -0.95
-0.09
-0.69 -0.60
-0.03
1963
-0.21
0.64 -0.97
0.33
0.74 -0.44
-0.83
-0.24 -0.52 0.18
1964
-0.87
0.28 •0.42
-0.72
-0.81 •0.25
-0.58
-0.46 -0.27 -0.64 -0.07
1965
0.35 -0.86 -0.03 -0.27
-0.55
0.42 -0.75 •0.27
0.14
-0.40
-0.06
-0.57 -0.31 -0.63 -0.X 0.05
1966
0.61
0.55 -0.32 -0.49
0.24
0.16
0.12 -0.57
-0.06
-0.26
-0.34
-0.60 -0.C9 0.13
1967
-0.32 O X -0.36 0.23
0.78
0.63
0.25 -0.74
-0.16
-0.13
-0.51
-0.09 -O.08 0.16
0.32 0.01
1968
0.05
Q25 -0.38 0.54 -0.52 0.25
0.12 -0.39
0.00
0.21
-0.70
-0.79 -0.X
0.39 -0.32
1969
-0.74 -0.24 -0.58 0.10 -0.67 -0.36
0.44 -Q72 •0.62
-0.66
-0.39
-0.67
0.47 -0.27 -0.07 -0.07 -0.24
1970
-0.35 -0.57 -0.24 -0.03 0.01 -0.07 0.44
-0.35
-0.18
-0.26
-0.32 -0.21 -0.47 0.03 055
1971
-0.44 -0.50
0.34
0.07 -0.24 0.05
-0.27
045 -0.74 -0.06 0.32 0.52
1972
-0.94 -0.43 -0.44 -0.67 -0.75 -0.32 -0.91 -0.77 -0.51
-0.59 -0.42 -0.69 0.30
-0.05
-0.62 -0.42
0.18 -0.29 -0.82
1973
-0.78 -0.32 -0.79 •0.17 -0.77 0.38 -0.85
0.23 -0.05
-0.57 -0.52 -0.69 -OX
-0.99
-0.77
0.44 -0.60 -0.62
1974
-0.35 -0.14 -0.52 -0.48 -0.28 -0.17 -0.71 -0.40 •0.15
-0.67 -0.55 -0.79 -0.04 -0.07
-0.05
-0.63 -0.X -0.13 -0.67 -0.59
0.71 -0.52 0.10
0.23
0.25 0.17
0.05
0.08
-0.60
0.54 -0.04
0.01 0.00 0.04 •0.83
0.11 -0.22
-0.65 -0.29 0.41
0.61
0.73
0.08 -0.X
1975
-0.63 0.52 -0.02 -0.67 0.22 -0.48 0.16
0.41 -0.24
-0.86
-0.34 -0.71 -0.11 -0.21 -0.53
1976
-0.23 0.27 -0.39 -0.03 -0.37 -0.86 -0.09 O X -0.53
-0.18 0.30 -0.76 -0.26 -0.34
0.06
0.61 -0.48 0.34 -OX 0.12
1977
0.68 -0.53 0.71
0.47 -0.31 -0.01 -0.78 -0.06
0.26
0.00 -0.51 -0.57 -0.40 -0.19
1978
-0.39 0.02
0.13 0.00 -0.34 -0.29 0.27 -0.30 -0.19 -0.32 0.02
-0.19
-0.79 Q22 -0.74 0.28 -0.X
0.00 -0.60 -0.65 -0.68 -0.78 -0.49
0.38 -0.80 -0.44 -0.45
1979
0.08
0.31 -0.13 -0.82 -0.03 0.47 -0.23 -0.26 0.11 -0.78 -0.22 0.02
0.45
0.28
-0.63 -0.67 -0.59 0.32 -0.81
1980
-0.57
0.20 -0.58 -0.71 -0.30 -0.33 -0.40 -0.80 0.55 -0.55 -0.52 0.42 -0.67 -018 -0.53
-0.16
-031 -0.15 -0.44 -0.03 -0.70
1981
0.28 -0.57
0.07 -0.18 0.33
0.24
-0.59
-015 -0.14 -0.73 0.20 -0.32
1962
0.30 -0.26 -0.22 -0.25 -0.80 -0.74 -0.90 0.18 -0.68 0.19 -0.14 0.16 -0.44 -Q06
0.65
-0.39
0.06 -0.44 0.24 -0.29 -0.11
1983
-0.30 -0.43
0.37 -0.37 -0.82 0.31 -0.46 0.20 -0.45 0.33 -0.61 -0.64 -0.32 0.26 0.30
0.62
Q49
1984
-0.01
1985
-0.94 0.00 -0.59 -0.66 0.06 -0.83 -0.47 0.75 -0.01 0.43 0.70 -0.03 -0.72 -0.41 0.19 -0.76 0.11
1986
-0.91
1987
-0.18 0.27
0.31 -0.50 0.02
0.34 -0.06 •0.96 -0.03 -0.54 -0.28 0.55
0.10 -0.40 0.08
0.34 0.07
1983
-0.53 -0.11
0.20 •0.49 -0.51
0.11 -0.59 -0.96 -0.35 -0.47 -0.57 0.07 -0.53 -0.19 -0.43 -0.40 0.29 -0.87 0.23 -0.06 0.17
0.10 -0.08
1969
-053
1990
0.73 -0.51 -0.56 -0.07 -0.03 0.27 -0.88 -0.77 0.00 -0.60 0.33
1991
0.01 -0.57
0.13 -0.34 •0.71
0.79
0.07
0.17 0.01
1992
-0.36 -0.07
0.51 0.02 -0.53 0.32
0.13
0.09 0.48 -0.54 •0.29 -0.40 0.06
0.51
1993
-0.18
0.10 -0.35 -0.36 0.31
0.05
0.55 -0.29 -0.17 -0.22 0.09
0.65 -0.17 -0.03 •0.43 -O50
1994
-0.14 0.29
0.31 0.19
1995
0.20 0.03
0.45 -0.59 -0.35
0.39
0.15
1996
-0.40
0.33
0.06
0.29
Mean
-0.21 -0.06 -0.05 -0.34 -0.31 -0.05 -0.18 -0.16 -0.30 -0.25 -0.16 - O X -025 -020 -0.10 -0.22 -0.23 -0.07 -0.21 -0.25 -0.06 -0.19 -023
0.19 -0.63 -0.66 0.00 -0.61 -0.50 -0.62 -0.56 -0.75
0.22 -0.51 -0.73 -0.77 -0.64 -0.56 -0.02 -0.69 -0.35 0.06 0.27
0.OB -0.42 -0.13 0.28 -0.32 -0.75 -0.65 -0.87
0.51
0.03
0.15
0.26 -0.66 -0.44 -0.26 -0.63 -0.68
0.16 -0.07 -0.72
0.28 -0.05 0.02 -0.15 -0.34
0.36 -0.18 -0.63 -0.60 0.41 -0.24 0.09
0.17 0.34 -0.71 -0.07
0.X -0.61
-Q41 -0.81 -0.12 -0.07 -0.37
0.56 0.06 -0.69 -0.94 -0.69
0.01 -0.14 0.59 -0.22 0.04 -0.69 -0.13 -0.63 -0.84 -0.68 -0.36 -0.19 -0.76 0.56 -0.90 -0.18 0.11 -0.59 -0.56 -0.05 -0.08 -0.17
0.31
0.51
0.29
0.29
0.04 -0.50 -0.50 -0.66 0.16 -0.61 0.46
0.17 0.28 0.24 0.82 0.41 0.31 -0.72 -0.28 0.46 -0.31 -0.42 -0.44 0.18
0.18
0.64 •0.78 0.06 -0.23
0.75
0.67
0.23 -0.48 0.25 -0.71
0.00 -0.58 -0.67 -0.47 -0.04 0.53 0.16 -0.16 0.X
0.00 •0.46 0.01
0.16
015
0.72 -0.11 0.58 0.37 -0.76 0.03
Q27 -0.11 -0.52 -0.51
0.65 -0.35 0.17 0.42 -002 -0.61 0.23 -0.84 - O X 0.28 -0.17 0.10
0.63 -0.X
0.11
-0.47 -0.81
-0.58
-0.63
0.10
-0.70 -0.69
0.54
Chapter 3 Data Analysis: OECD Countries
Quantity standard deviation vs price standard deviation in 23 OECD countries Figure 3.1
covariance between price and quantities. Table 3.10 presents these correlations for the OECD countries over the whole sample period. The last row of the table presents the mean correlation for each country averaged over the whole sample period. As can be seen, about two-thirds of the correlations presented in the table are negative. The last row of the table shows that, on average, the correlations are negative for all OECD countries. This reflects the tendency of the consumer to move away from those commodities having above average price increases. Table 3.11 presents the averages of the Divisia moments over the sample period for each country from the last row of Tables 3.6-3.10. Columns 26 of the table present the average quantity index, average price index, average quantity variance, average price variance and average price-quantity correlation,
87
88
International Consumption Comparisons Table 3.11 Divisia moments in 23 OECD countries
Country
Divisia quantity index
Divisia price index
Divisia quantity variance
Divisia price variance
DQ
K (4) 8.74
n
Divisia price-quantity correlation
1.
Australia
2.26
DP (3) 5.98
6.48
P (6) -0.21
2.
Austria
2.35
4.22
8.76
5.89
-0.06
3.
Belgium
2.45
4.43
7.23
8.87
-0.05
4.
Canada
2.21
4.65
11.55
5.43
-0.34
5.
Denmark
1.62
6.39
11.63
5.12
-0.31
6.
Finland
2.70
6.36
13.06
13.25
-0.05
7.
France
2.52
5.76
5.21
13.30
-0.18
8.
Germany
2.60
3.35
7.40
11.62
-0.16
9.
Greece
3.28
11.20
16.11
7.10
-0.30
10.
Iceland
1.60
22.75
42.89
16.38
-0.25
11. 12.
Ireland
8.91 9.28
17.94
18.05
-0.16
Italy
1.72 2.64
5.13
8.72
-0.08
13.
Japan
2.97
4.12
9.96
5.24
-0.25
14.
Luxembourg
2.83
5.62
10.84
4.15
-0.20
15.
Netherlands
2.83
3.85
10.12
11.22
-0.10
16.
New Zealand
1.57
6.23
13.24
14.72
-0.22
17.
Norway
2.38
6.05
17.34
15.95
-0.23
18.
Portugal
3.71
8.82
30.63
4.80
-0.07
19.
Spain
2.67
9.31
9.81
23.29
-0.21
20.
Sweden
1.19
6.77
6.17
10.52
-0.25
21.
Switzerland
1.42
4.06
3.24
2.69
-0.06
22.
UK
2.03
6.98
5.82
15.39
-0.19
23.
USA
2.22
4.51
5.34
3.61
-0.23
2.34
6.94
12.09
10.08
-0.18
(D
Mean
(2)
(5)
All entries in columns 2 and 3 are to be divided by 100 and columns 4 and 5 by 10000.
Chapter 3 Data Analysis: OECD Countries
89
respectively, for each country. The last row of the table gives the grand mean, over all sample periods and over all countries. Tables 3.12 and 3.13 present the mean relative quantity log-changes ( Dqt - DQ ) and the mean relative price log-changes ( Dpt - DP ) for the 9 commodity groups for the 23 OECD countries. The last row of both tables present the average for each commodity group over the 23 countries. As can be seen, a clear pattern emerges in terms of the relative growth in consumption of food, clothing, transport and recreation, and of the relative growth in price of housing. In all OECD countries, food and (except for the UK and USA) clothing have a negative relative per capita growth in consumption, while transport and recreation have a positive relative per capita growth in consumption. In all OECD countries (except for Greece), the average relative growth in prices of housing is positive. Table 3.14 presents a summary frequency distribution (in percentages) of joint signs of relative consumption and relative prices for the OECD data. The entries in the first quadrant of the table are the percentages of the total number of observations having a simultaneous increase in relative prices and consumption, disaggregated by commodity and country. The entries in the other quadrants have a similar interpretation. For example, for food in Australia, relative prices and consumption move in the same direction for 8 + 28 = 36% of the time, while they move in the opposite directions 25 + 39 = 64% of the time. As can be seen, from the "all countries" rows and the "all goods" columns, over all, 31 + 29 = 60% of the pairs of relative prices and consumption have opposite signs, while 19 + 20 = 39% have the same sign. These results clearly support the law of demand, i.e. other things being equal, an increase in the relative price of a commodity causes its consumption to fall. Table 3.15 presents the summary results from Table 3.14.
International Consumption Comparisons
90
poo
lothi
ousi
urab
edic
rans ort
ecre tion
dues on
isce aneous
Table 3.12 Relative quantity log-changes of 9 commodities in 23 OECD countries (x 100)
LL
O
X
Q
^
H
DC
LLI
s
(D
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
o>
Country
D)
CO
Q.
Australia
-1.49
-2.02
0.87
1.21
-0.25
0.44
1.19
2.38
0.95
Austria
-1.21
-0.54
0.67
0.59
0.64
1.64
1.40
-1.47
-0.71
Belgium
-1.38
-0.44
-0.01
0.32
1.35
0.92
1.21
Canada
-1.85
-0.50
0.69
0.24
-1.95
0.69
2.92
1.84
-0.06
Denmark
-0.76
-0.63
0.57
-1.87
0.73
0.72
1.79
4.78
0.03
Finland
-1.32
-1.65
0.69
0.10
0.61
1.12
1.30
France
-1.48
-2.17
1.15
-0.86
3.06
0.63
1.51
0.11
-0.57
Germany
-1.04
-0.65
0.34
0.22
0.22
1.37
0.27
Greece
-1.01
-1.51
0.77
-0.28
2.03
2.84
2.38
-3.96
1.00
10. Iceland
-0.51
-1.60
-0.27
-0.98
1.04
0.37
1.64
3.04
1.25
11. Ireland
-0.75
-0.34
0.20
-0.29
-1.42
0.22
2.37
0.33
1.17
12. Italy
-1.23
-0.87
-0.25
0.19
2.36
1.54
0.86
-0.03
0.75
0.49
0.97 0.57
13. Japan
-2.23
-2.16
1.12
-0.43
1.35
1.73
1.41
0.20
14. Luxembourg
-1.93
-2.11
0.00
1.53
1.19
2.92
1.15
-0.66
15. Netherlands
-1.12
-0.97
-0.52
0.51
0.74
2.07
1.14
0.47
16. New Zealand
-1.15
-2.63
-0.68
1.50
1.36
1.85
0.79
-0.92
17. Norway
-1.30
-1.15
0.21
-0.10
2.75
0.57
2.30
18. Portugal
-1.36
-2.29
4.03
-0.03
-0.62
1.77
3.29
19. Spain
-1.44
-1.12
-0.55
-0.93
3.41
3.11
0.60
20. Sweden
-0.66
-0.21
0.14
-0.75
2.16
0.78
1.41
-0.45
-1.68
0.14
-1.50
1.33
0.77
0.42
-1.65
0.94
-0.43
-0.04
1.35
1.49
1.70
-1.91
0.33
-0.21
0.09
1.29
0.28
2.61
-1.27
-1.13
0.38
-0.07
1.08
1.30
1.55
21. Switzerland 22. UK 23. USA Mean
-1.64
0.67 -0.74 1.34
0.00
-1.12 0.59 0.49
0.39
-0.29
0.48
0.26
91
Chapter 3 Data Analysis: OECD Countries
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. Mean
(1) Australia Austria Belgium
(2) 0.08 -1.16 -0.84
(3) -0.47
Canada Denmark Finland France Germany
0.22 -0.92 -0.75 -0.32 -0.77
Greece Iceland
0.18 -0.33
Ireland Italy Japan
-0.84 -1.23 -0.12
Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden
-0.05 -1.27 -0.14 -0.30 -1.03 -1.01 -0.93
Switzerland UK USA
-0.50 0.33 -0.16
-0.83 -2.44
-0.52
-0.89 -0.23 -1.11 -1.25 -0.63 0.03 -0.53 0.22 0.28 -1.35 0.55
(4) 0.43 1.74 0.58 0.11 1.64 0.59 1.06 1.35 -0.93 0.41
(5) -2.02 -0.93 -1.17 -0.36 -0.31 -0.57 -0.44 -1.18 0.04 -0.90
1.31 1.34 0.32
-1.10 0.75 -1.17
0.58 2.02 3.36 1.27 1.52 0.06 1.36 0.57
-0.90 -1.47 -2.09 -0.74 -1.30 -0.10 -0.29 -0.77
-1.63
1.32 0.09
-0.68 -1.18
-0.65
0.96
-0.82
0.70 -0.18 -1.45 -1.23 -0.83 0.09 -0.09 -1.73
(6) 0.94 1.75 1.30 0.93 -0.74 2.01 -2.40 0.80
(7) -0.24 0.00 0.09 -0.46 -0.02 0.15 0.90 0.29
(8) 1.02 -0.42 0.05 -0.95
0.11 2.02
-0.59 -0.46
-0.27 -0.01
3.93 0.16
0.61 -0.14 -0.14
-1.00 -0.73
-0.26 0.29 2.28 2.38 -3.77 1.39 -1.26 -0.47
-0.26 0.16 -3.59 0.69 -0.59 -0.51 0.25
-1.25 -0.12 -1.00 0.81
-0.23 -0.95 0.27 -0.37 -1.20 1.41 0.39 -0.78
Miscellaneous
Education
Recreation
Transport
Medical
Durables
Housing
Clothing
Country
Food
Table 3.13 Relative price log-changes of 9 commodities in 23 OECD countries (x 100)
(9) 0.90 1.44
(10)
1.16 0.65
0.88 0.80 0.83 1.03 0.22
2.01
0.33 1.06 1.04
0.91
1.11
3.29 3.37
1.10
1.39
1.68 0.83 0.20 0.41 1.18 1.41
1.02
-0.12
0.03 1.45
-0.16 0.11 -0.25
-1.13 -1.43
1.16
0.69 0.90 2.29 0.45 0.85 -0.07 0.82
0.63
-0.18
-0.35
1.63
0.87
1.61
2.24
92
International Consumption Comparisons Table 3.14 Frequency distributions of relative consumption and relative prices of 9 commodities in 23 OECD countries (percentages)
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Ireland Italy Japan Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
All countries
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Ireland Italy Japan Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
All countries
o O
(2)
(3)
3
£4
<)
1
(5)
1
re
(6)
f)
7
1 £
(8)
8 6 6 9 3 3 3 3 6 5 9 3 15 14 2 17 6 0 16 9 6 11 11
14 9 0 20 14 22 13 24 26 16 13 31 46 14 14 17 22 11 25 9 21 0 9
11 41 14 6 38 11 41 18 6 16 13 6 4 14 30 33 19 22 13 21 15 20 3
8 13 22 11 17 39 13 15 21 26 17 25 8 10 14 8 19 0 28 30 9 11 11
8 25 22 54 10 25 19 12 12 26 9 9 4 29 18 8 13 33 19 12 21 29 14
22 34 33 11 24 25 53 36 29 11 30 34 12 33 25 25 53 44 19 24 30 29 31
56 6 11 14 10 22 13 9 21 16 17 16 19 5 18 25 6 11 19 15 24 6 6
7
17
18
16
19
29
16
(9)
19 31 37 14 19 32 11 17 25
18 25
9
37 23
25 31 28 17 34 25 13 27 18 26 26 28 23 10 20 17 19 0 31 42 55 17 14
58 66 50 60 62 50 34 64 50 32 52 44 27 29 57 58 44 11 28 58 61 63 69
3 0 8 14 3 8 3 0 12 26 13 3 4 19 7 8 3 11 9 9 15 6 14
72 47 39 51 41 36 63 52 41 37 43 53 73 67 64 50 41 89 41 45 76 63 74
14 3 22 23 24 19 53 18 38 16 17 31 19 43 16 8 28 11 50 21 6 11 6
42 38 33 51 52 42 25 36 47 37 35 41 42 33 41 42 25 56 59 39 39 49 54
25 25 28 54 52 39 59 30 26 26 48 28 42 29 30 25 72 22 34 52 36 37 86
33 19
24
49
9
55
22
42
39
15
9 21 6 21 0 22 13
9
30
0
j
Tra/
(1)
o
Misi
Country
Clot
Negative relative consumption
Positive relative consumption
1 1
16
49
11
40
18
22
45
40
29
Negative relative prices 47 35 28 14 22 28 50 9 33 30 42 25 11 32 20 11 17 34 34 10 22 30 42 19 19 31 56 22 21 31 45 9 38 32 32 15 16 24 32 26 17 30 35 26 19 29 53 16 23 32 38 15 29 32 24 38 18 32 52 20 17 28 33 8 16 28 25 13 11 44 26 78 3 32 22 19 15 35 18 24 3 36 24 15 26 34 49 29 14 37 14 40
33 16 44 34 7 36 16 18 53 26 26 25 12 14 9 8 38 11 44 15 24 11 37
17 34 33 26 14 19 16 21 21 16 26 13 8 14 23 42 25 0 13 15 6 14 9
33 9 11 14 24 19 19 12 18 32 13 28 31 14 20 17 19 22 13 30 12 20 6
19 13 11 14 3 14 3 3 9 16 9 16 27 24 7 33 6 0 0 12 18 6 6
0 38 33 23 24 14 22 36 21 26 13 41 19 48 23 42 13 0 22 24 9 29 3
17 9
11
8 9 3 14 10 6 3 12 12 16 9 9 4 24 18 8 13 0 19 12 12 0 6
19 21 25 19 16 21 18 20 23 24 19 25 19 25 22 24 18 19 19 19 15 20 15
24
18
19
12
23
16
10
20
^ (")
1 8 1
^
§ (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) Positive relative prices 11 14 17 33 28 18 39 19 53 31 3 44 50 41 31 19 20 13 16 44 16 31 6 63 14 25 50 20 25 22 28 25 6 44 33 34 22 54 40 37 26 11 9 23 9 46 9 14 21 17 28 21 14 52 52 52 28 33 41 44 24 19 28 44 25 31 8 25 6 36 59 30 19 21 28 31 19 6 41 66 9 9 24 58 9 16 24 3 24 64 33 12 58 29 44 21 24 25 20 9 15 32 29 18 32 37 42 37 26 33 19 26 32 63 32 21 26 35 39 33 18 30 9 26 22 48 48 13 61 47 27 19 16 9 25 9 16 41 66 9 31 27 19 23 12 46 19 81 30 12 46 19 33 14 24 52 14 19 38 33 10 19 10 27 23 18 25 9 30 55 41 29 0 45 33 21 33 17 42 50 27 67 0 8 0 20 50 22 16 56 41 34 16 9 53 16 41 11 17 22 33 0 67 78 56 38 11 33 21 28 50 34 29 31 28 25 19 19 22 42 30 18 30 9 24 55 42 29 9 36 9 22 45 15 3 12 30 39 45 27 9 61 49 17 29 27 11 19 23 9 26 63 40 37 18 34 9 43 46 31 6 74 9 6 51
(10)
30
20
19
31
30
39
19
17 14 9 24 26 13 22
13
18
Chapter 3 Data Analysis:
93
OECD Countries
Table 3.15 Frequencies of joint signs of relative consumption and relative price changes in 23 OECD countries (in percentages) Country
1. 2. 3. 4.
(1) Australia Austria Belgium
Positive consumption
Negative consumption
Opposite signs
Positive price (2) 18
Negative price (3) 35
Positive price (4) 28
Negative price (5) 19
(3)+(4)
20 20 22
28 30 32
21 25 19 16
59 55 58 67
(6) 63
5.
Canada Denmark
17
34
31 25 26 33
6.
Finland
24
30
25
21
55
7.
21
31
8.
France Germany
16
18 20
61 64
9. 10. 11. 12. 13. 14. 15. 16.
Greece Iceland Ireland Italy Japan Luxembourg Netherlands New Zealand
20 19 18 19 19 19 18 21
31 32 24 30 29
30 33 25 33 33 27
57 57
32 32 32 28
30 24 29 27
23 24 19 25 19 25 22 24
17.
Norway
28
34
1.8.
Portugal Spain
20 17
26 32
38 29 29
19
61 64
27 27 31
15 20 15
63 61 68
29
20
61
21
19. 20.
Sweden
18
21. 22. 23.
Switzerland UK USA
22 19 18
35 36 34 37
19
31
Mean
18 19 19
63 56 62 56 61 55 62 64
International Consumption Comparisons
94
3.3
Engel's Law
One of the most important empirical regularities in consumption economics is the Engel's law. This law sates that the budget share for food (wFt) falls with increasing income (Mt). Working (1943) and then Leser (1963) modelled the Engel's law into a linear regression framework, which is known as the Working's model, wR
=
ocF + P F logM t .
(3.1)
Choosing Mt =1 for some year t in equation (3.1), a F can be interpreted as the budget share of food during that year t. The coefficient p F gives 100 times the change in the budget share of food resulting from a 1 percent increase in income. Figure 3.2 presents the plot of food budget share (wFt) against the logarithmic of the per capita real consumption expenditure (log Mt) for the 23 OECD countries. As can be seen, in all plots, the points are scattered around a negatively sloping line. This clearly shows that Engel's law is well supported by the data. Table 3.16 presents the estimates for the Working's model parameters, ccF and PF for food in each country. As can be seen from column 3, all the income coefficient estimates are statistically significant. The cross-country average, for the 23 OECD countries, p F = -.20 (standard error = 0.02), is close to the findings from a number of previous studies, see Table 3.17. In Figure 3.3a, we pool the data across the 23 countries and plot the adjusted budget shares (wFtc - aFc) against the logarithm of income (log Mtc) in one graph. However, the points on the far right, which corresponds to Iceland, appear to be extreme among the 23 countries. In Figure 3.3b, we present the same graph for 22 OECD countries (excluding Iceland). As can be seen, the
95
Chapter 3 Data Analysis: OECD Countries
Australia
Austria
0.4 y=-0.1846x+1.9621 Ff=0.9706
0.1 8.8
9
9.2 9.4 LogQncome)
10.5
9.6
10.7
10.9 11.1 LogQncome)
11.3
Canada
Belgium 0.5
y=-0.1261x+1.34e9
y = -0.2108x+a9139 Ff=0.9452
Ff=0.9513
1
0.14 0.1
12.2
12.4
12.6
128
13
8.6
9
8.8
Logflncome)
9.2
9.4
Log(lncome)
Denmark
Finland
y = -0.2822x+3.2525
0.45 y = -0.1984x+23747
ff = 0.9571
Ff=0.9539
m 0.2 0.15 10.3
0.15 10.5
10.7
10.9
LogQncome)
9.8
10
10.2
10.4
10.6 10.8
Logflncome)
Food budget shares against logarithm of per capita real consumption expenditures in OECD countries Figure 3.2
96
International Consumption Comparisons
Food budget shares against logarithm of per capita real consumption expenditures in OECD countries Figure 3.2 (continued)
Chapter 3 Data Analysis: OECD Countries
97
Luxembourg
Japan 0.35 £
y = -0.1826x+1.574B Rz = 0.9764
0.3 ?
7.1
7.3
7.5
12.3
7.7
125
r 1
129
NewZealand
Netherlands
•> 3
127 Logflncome)
Logflncome)
0.2 0.19
0.3 0.2
Z 0.18
^ y=-0.22x+23556 ^
^
R?=0.9371
^ H k ^ ***^fc
n-i . 8.7
m 0.17
y = -0.1361x+1.4778 R? = a7218
0.16 4 9.1
9.5
9.9
9.4
9.45
Logflncome)
9.5
9.55
9.6
Logflncome)
Portugal
Norway 0.35
0.3O)
•o 0.25
y = -0.2123x+1.6944 «0 0.27
10.6
R?=0.9228
0.25
0.2 10.8
11
11.2
11.4
11.6
6.35
6.45
6.55
6.65
Logflncome)
Log(lncome)
Food budget shares against logarithm of per capita real consumption expenditures in OECD countries Figure 3.2 (continued)
International Consumption Comparisons
98
Sweden
Spain 0.35 a
0 3
% 0.25 m 0.2
y=-0.294x+4.1663 Bf=0.8801 0.1 12.6
12.8
13 13.2 Log(lncome)
y=-0.313x+a7341 Ff = 0.8675
0.15 4 10.8
13.4
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10
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i
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9.1
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9.7
Log(lncome)
Food budget shares against logarithm of per capita real consumption expenditures in OECD countries Figure 3.2 (continued)
Chapter 3 Data Analysis: OECD Countries
99
Table 3.16 Estimates of Working's model for 23 OECD countries (Standard errors are in parentheses) Country
(D 1.
Australia
Intercept
Income coefficient
ctvxlOOO
PF
fl2
(2)
(3)
(4)
1.962 (0.050)
-0.185 (0.005)
0.97
Austria Belgium Canada Denmark Finland France 8. Germany 9. Greece 10. Iceland
2.867 2.914 1.347 3.253 2.375 1.667 1.968
-0.238 (0.005) -0.211 (0.009)
-0.152 (0.002) -0.177 (0.003) -0.097 (0.005)
0.98 0.95 0.95 0.96 0.95 0.99 0.99 0.92
11.
3.357 2.439 1.575 2.157 2.356 1.478 2.516 1.694
-0.064 (0.023) -0.355 (0.041)
0.31 0.77
-0.314 (0.016)
0.93 0.98 0.92 0.94 0.72 0.94 0.92
2. 3. 4. 5. 6. 7.
Ireland
12. Italy 13. 14. 15. 16. 17. 18.
Japan Luxembourg Netherlands New Zealand Norway Portugal
(0.060) (0.108) (0.045) (0.120) (0.077) (0.018) (0.027)
1.411 (0.052) 1.421 (0.417) (0.345) (0.108) (0.043) (0.126) (0.083) (0.242) (0.103) (0.143)
-0.126 (0.005) -0.282 (0.011) -0.198 (0.007)
-0.183 -0.152 -0.220 -0.136 -0.202 -0.212
(0.006) (0.010) (0.009) (0.025) (0.009) (0.022)
19. Spain 20. Sweden 21. Switzerland
4.166 (0.256) 3.734 (0.240) 2.062 (0.086)
-0.294 (0.019) -0.313 (0.022) -0.177 (0.009)
22. UK 23. USA
1.725 (0.138) 1.493 (0.039)
-0.138 (0.013) -0.142 (0.004)
Mean
2.258 (0.166)
-0.199 (0.015)
0.88 0.87 0.93 0.77 0.97 0.89
100
International Consumption
-0.5
!i
I
9 , s
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*» " »
17
13
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o> •o 3
n
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Food budget share vs Log(lncome) for pooled data from 23 OECD countries Figure 3.3a
10
12
0> 3 XI
1 3
-4
y = -0.2453x+0.4128 Log(lncome)
Food budget share vs Log(lncome) for pooled data from 22 OECD countries (excluding Iceland) Figure 3.3b
Comparisons
Chapter 3 Data Analysis:
101
OECD Countries
Table 3.17 Previous estimates of Working's income coefficient for food Authors) 1. Aasness and Rodseth (1983) 2. Adams et al (1988)
Country Norway
Estimates derived from Time series Cross-section -.174 (.008)
3. Barten(1993)
Australia Netherlands
-.121 (.033) -.121 (.023)
4. Barten(1993) 5. Blanciforti and Green (1983)
Netherlands USA
-.125 (.023) -.127 (.031)
6. Chen (2001)
Cross-country Spain
7. Chung and Lopez (1988) 8. Chung and Lopez (1988) 9. Deaton and Muelbauer (1980) 10. Rebigetal(1988) 11.Rnkeetal(1984) 12. Finkeetal(1984) 13. lmhoff(1984) 14. Izan and Clements (1979) 15. Musgrove(1985) 16. Rajapakse(1992) 17.Selvanathan,S.(1993) 18. Theil (1987)
Spain Great Britain Cross-country Japan Sweden Netherlands Cross-country Dominican Republic
-.140 (.008) -.153 (.013) -.106 (.027) -.127 (.033) -.104 (.007) -.139 (.003) -.139 -.128 (.014)
Cross-country Netherlands
20. Theil etal (1987)
China Cross-country
Mean Weighted mean*
-.156 (.017) -.160 (.026)
Sri Lanka Cross-country
19.TheilandBnke(1984) 21. Yuen (2001)
-.149 (.011) -.183 (.013)
-.154 (.020) -.130 (.016) -.134 (.020) -.118 (.006) -.130 (.017)
-.144 (.023)
-.136 (.013)
-.137 (.020)
Source: Chen (2001) and Chung and Lopez (1988). The weights are inversely proportional to the individual standard errors.
points are scattered around a downward sloping straight line with slope PF = -.25. This estimate is in line with the cross-country average of p F = -.20 from column 3 (last row) of Table 3.16.
102
3.4
International Consumption Comparisons
Preliminary Estimates of Income and Price Elasticities
In Chapter 2, we introduced the double-log demand equations as an example for the demand equations without specifying the form of the utility function. In this section, we use double-log demand equations to obtain preliminary estimates for the income and price elasticities. In Chapter 9, we use the differential demand systems to obtain final estimates for the demand elasticities and then compare the two sets of estimates. We consider the double-log demand equation (2.4) given in Chapter 2 for commodity i in finite-change form DqA = oCi + Tii DQt + Yi [Dp* - DPt] + eit,
i=l,...,«,
(4.1)
where oti is an autonomous trend term; r); is the income elasticity of commodity i; Yi is the Slutsky own-price elasticity; and eit is a disturbance term. It is worth noting that this double-log demand equation includes only the own-relative price and not other prices. We estimate (4.1) by least squares (LS) for each country separately. Tables 3.18-3.19 present the estimates for the income elasticity (T);) and own-price elasticity (Y), respectively, for each commodity for the 23 OECD countries. The last row of the table presents the elasticities for each commodity averaged over the 23 countries. As can be seen from Table 3.18, all the income elasticites, except the ones for education corresponding to Denmark and Iceland, are positive. However, the two negative elasticities are statistically insignificant. All the elasticities in column 2 for food are less than one indicating that food is a necessity in all OECD countries. The average value of the food elasticity for the OECD countries is .6. On average, the income elasticities for clothing, durables,
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Chapter 3 Data Analysis: OECD Countries
105
transport and recreation are larger than one indicating that these commodities are luxuries in the OECD countries, while the income elasticities for housing, medical care and education are less than one indicating that they are necessities. In Table 3.19, most of the own-price elasticities (164 out of 196) are negative as they should be. On average, all the price elasticities are negative and less than one in absolute value, indicating that demand for all 9 commodities in the OECD countries are price inelastic.
3.5
Preliminary Estimates of the Income Flexibility
In this section, we discuss various informal data analysis techniques to obtain estimates for the parameter, income flexibility. While the estimates we derive in this section have only a preliminary status, we formally estimate the income flexibility in Chapter 9. The estimate of income flexibility is exclusively used as an input for general equilibrium models, where the price elasticities are estimated based on the <j) value. The study of income flexibility is important for a number of reasons. One of them is to test the well-known Frisch's (1959) conjecture, which states that the income elasticity of the marginal utility of income (1/0) decreases in absolute value as the consumer (or country) becomes more affluent. Frisch (1959, p. 189) provides some numerical conjectures for the dependence of the elasticity on the level of real income. The value of the elasticity varies from -10 (for an extremely poor population), -2 (for the middle income bracket) to -. 1 (for the rich part of the population). Later in this section, we verify whether or not Frisch's conjecture is supported by the OECD data. In Chapter 2, we derived the finite-change version of the CBS/PI demand equation (5.14) under preference independence, which we reproduce here.
106
International Consumption
wit(Dqit-DQt)
= PlT>Q[ +
where DP, = X ; (/? ; +wjt)Dpjt. elasticity of commodity i, Tli =
1+=
Comparisons
i=l,...,n,
(5.1)
Under the assumption of unitary income
= 1-
That is, Pi = 0. Therefore, under the assumption of unitary income elasticity, equation (5.1) becomes (Dqit-DQt)
= ty(Dpit -DPt),
i=l,...,/i,
(5.2)
where DPt = ~£jWjtDpjt is the Divisia price index. For a given i, if we regress the growth in consumption of i relative to the overall growth in consumption, (Dqit - DQt), against the growth in relative price (Dpit - DPt) of i for t=l,...,T, the slope of the regression line can be interpreted as (|), the income flexibililty. For each country, we obtain the estimates of <>| for i=l,..,«, and calculate the average (j) over i=l,...,/i, which we refer to as an unrestricted average estimate of the income flexibility. These estimates § for the 23 countries are reported in column 2 of Table 3.20. In the above regression model (5.2), as <j) is the same for all i=l,...,n for each country, we can also perform a restricted pooled regression by considering (Dqit -DQt) against (Dpit - DPt) for all i=l,...,/i and t=l,...,T. Figure 3.4 gives the plots (Dqit - DQt) against (Dpit - DPt) for t=l,...,T and i=l,...,n for each country. As can be seen from the plots, for all countries (except Switzerland), the points are scattered around a negatively sloping line. The slope
Chapter 3 Data Analysis:
OECD Countries
107
Table 3.20 Four sets of estimates for income flexibility in 23 OECD countries (x100) Income flexibility Country (1) 1. Australia 2. Austria 3. Belgium 4. Canada 5. Denmark 6. Finland 7. France 8. Germany 9. Greece 10. Iceland 11. Ireland 12. Italy 13. Japan 14. Luxembourg 15. Netherlands 16. Norway 17. New Zealand 18. Portugal 19. Spain 20. Sweden 21. Switzerland 22. UK
Unrestricted
Restricted
Divisia
Divisia Average
(2) -0.43 -0.57
(3) -0.54
(4) -0.34
-0.16 -0.10
-0.15 -0.11
(5) -0.24 -0.07
-0.50 -0.30 -0.05 -0.16 -0.25 -0.34 -0.37 -0.24 -0.14 -0.51 -0.37 -0.12
-0.53 -0.61 -0.13 -0.25 -0.34
-0.59 -0.38
-0.13 -0.49 -0.64
-0.31 -0.27 -0.60 -0.10 -0.47 -0.48 -0.32 -0.62 -0.20 -0.22 -0.50 -0.33 -0.17 -0.42 -0.43 -1.31 -0.17 -0.21 -0.24
-0.98 -0.09 -0.21
23. USA
-0.11 -0.48
-0.01 -0.06 -0.39
Mean
-0.39
-0.30
-0.50 -0.50 -0.33 -0.15 -0.49 -0.38 -0.27
-0.36 -0.39 -0.14 -0.24 -0.25 -0.34
-0.05 -0.50 -0.47 -0.05 -0.12 -0.13 -0.45 -0.40 -0.16 -0.06 -0.34 -0.33 -0.10 -0.21 -0.24 -0.19 -0.14 -0.19 -0.07 -0.12 -0.28 -0.21
International Consumption Comparisons
108
Austria
Australia
Relative price
Relative price
Canada
Belgium y = -0.1025x +0.316
• IP
•5 -;o
*o
-io
10*
20
S3
-aeRelative price
Relative price
Finland
Denmark
Relative price
Relative price
Relative quantity against relative price in OECD countries Figure 3.4
Chapter 3 Data Analysis: OECD Countries Germany
France
!5
-35
Relative quantity
y=-0.2492x + 0.1947
-tS
•
« 0
-20
20-
J 3
,!/ -10 •
-20-
y=-0,1614x +0.1877 -46Relative price
Relative price
Greece
Iceland
Relative quant ty
y « -0,371 x t 0.6643 •
80 40 • : -.•••
& * . * * • •
-'
0
**"5 -10
W--
W*
2° "
SD
-86Relative price
Relative price
Italy
Ireland
y = -0.1403x+ 0.4147
Relative quantity
y = -0.2414x + 0.3436 •20-
8 * •••" •
* 1R
• I s ' . 'IIS. "'—*
0
-1
•
-20-
Relative price
Relative price
Relative quantity against relative price in OECD countries Figure 3.4 (continued)
110
International Consumption Comparisons
y = -0.5084x +0.0788
*
# y=-0.369x
* •1
0
-10
9 SK>
23
•
• -1°-
3
•
•
Relative price
-20
-10
Norway
y = -0.1162X + 0.3152
* 1 ^• 0
• •
4k*> " *^&*
-19*
•
Relative price
Netherlands ae-,
+ 0.213
>•
Relative quantity
•10.
*
Luxembourg
10
20
3
•
89Relative price
Relative price
Portugal
New Zealand
y=-0.9768x +0.7961 Relative quant ty
Relative quantity
Japan
•
I0" - •
Relative price
40 -
0
-5
J "
«
•' W 9 U ? • 1I • . 5 •~~" 1 3
Relative price
Relative quantity against relative price in OECD countries Figure 3.4 (continued)
111
Chapter 3 Data Analysis: OECD Countries
Spain
Sweden
48_. y = -0.0944X + 0.5498
Relative quantity
•
20»• •
0
-40
-20
20
'
e)
40
-20 <
*
*
y = - 0 . 2 1 0 2 x + 0.1966
10»
0 •
-20
J^*fr**^^
jjj
•
«Relative price
Relative price
UK
Switzerland
y = - 0 . 0 6 4 x + 0.684
-5 «9RH <: -8 4
Re ative quantity
Relative quantity
•
o
e)
40
-10 -
3
•
ir ^f l '«Mi|.ViC«*t 0
-5
*4^ -10
13
^ •
y = 0 . 0 1 1 7 x - 0.0494
Relative price
Relative price
USA
„.
i
" • ^ , : ^
• -8 -
•
•
Relative price
Relative quantity against relative price in OECD countries Figure 3.4 (continued)
.
International Consumption Comparisons
112
of the regression lines can also be interpreted as estimates for <)). These restricted estimates of (j) for each country are presented in column 3 of Table 3.20. Even though the values of the estimates given in columns 2 and 3 of Table 3.20 vary widely, all these values have the correct (negative) sign. The overall average of the income flexibility estimates is about -.4 (column 2) and -.3 (column 3), which agrees with the income flexibility estimates found in most of the previous empirical studies (e.g., see Theil and Clements, 1987; Theil and Suhm, 1981; and Selvanathan, 1993). Now, we consider another method of obtaining an estimate for <)>. First, multiply both sides of (5.2) by wit{Dpit -DPt) and then take the sum over i=l,...,n to give
t wit[Dpu -DP,][Dqu -DQt] 1=1
= 4 ± wit[Dpit -DP,]2.
(5.3)
i=i
Using (2.10) and (2.11), we can simplify (5.3) as r,
=
<»nt,
=
^-,
t=i,...,T.
(5.4)
Therefore, (f
t=l,...,T.
(5.5)
Column 4 of Table 3.20 gives the value of <> | , based on (5.5) and Tables 3.8, 3.9 and 3.10, and are averaged over t=l,...,T for each country. As can be seen, the
113
Chapter 3 Data Analysis: OECD Countries
average estimate of (() for the 23 countries is -0.34, which is very close to the averages in columns 2 and 3 of the same table. An alternative method of obtaining an estimate for the income flexibility <j) is to sum both sides of (5.4) over t=l,.. .,T to give
r
=
4>n,
where T=(l/T) X , r t and TT=(1/T) £ , I I t . Therefore, 4
=
=.
(5.6)
n Column 5 of Table 3.20 gives the value of (|) for each country based on (5.6) and Table 3.11. As expected, all the estimates of <|) are negative with an average of -.21, which is somewhat lower than the (average) estimates of (|) in columns 2, 3 and 4. Instead of pooling the data across commodities and time, alternatively, one could pool them over countries and time. In order to achieve this, for equation (5.2), we add a country subscript c (=1,.. .,23), to get (Dqcu-DQf)
=
HDp
i=l,...,n.
(5.7)
Summing both sides over t=l,...,T and dividing by T for each country, c=l,...,23, we get (Dq[-DQC)
=
$(Dpf-DPc),
i=l,...,n.
(5.8)
114
International Consumption Comparisons
The values of (Dq~? - DQc) and (Dp^ - DPc) are relative consumption and relative prices presented in Tables 3.12 and 3.13, respectively. Now, for each commodity i (=1,.. .,9), if we plot (Dqf - DQc) against (Dpi - DPC), c=l,...,23, the resulting slope of the regression line (5.8) is also an estimate for 0. Figure 3.5 gives the plots for the 9 commodity groups. As can be seen, in all plots (except for education and miscellaneous), all the points are scattered around a negatively sloping straight line. In Table 3.21, we present the resulting estimate of <|) for each commodity group. As can be seen, the overall average over the 9 commodities is <> j - -.26 and (j> = -.42 with the two outliers excluded, which is not far away from the mean values presented in the last row of Table 3.20.
Table 3.21 Another set of estimates for <)> for OECD countries Commodity 1. 2. 3. 4. 5. 6. 7. 8. 9.
Food Clothing Housing Durables Medical Transport Recreation Education Miscellaneous
Mean (all goods) Mean (excluding education and miscellaneous)
Income flexibility -.39 -.73 -.09 -.67 -.51 -.33 -.24 .25 .34 -.26 -.42
115
Chapter 3 Data Analysis: OECD Countries
Clothing
Food
Relative consumption
-1.0
05
00 -0.5
-0.5 • «
\*
y=-0.388a<-1.4716
Relative consumption
0
5
1 •
J
-3
$1 •
£***S»J^»"H
)
1
-v •
•
•
y=-0.7254x-1.6022
• Relaive price
Housing
Durables
*1
y=-o.o9eac+a4sa2 •
43 2•
1
n >
•
-1
1 •
t
* Relative consumption
I
Relalte price
•
2
• ****«^> J
-2
-2
•
1
»*-1 •
•
••"*-"•
•
-2
y=-0.667k-0.6154
3 •
*-
• 1
^^t**N^f
*
Relative price
Relative price
Transport
Med cal care
4-, •
O
UO|)C
3-
1
••#•
3
F
.
•
O .2 . 5
' -4
-2
«#.• •
<)
••
d)
y=-0.5142x+1.3969
k
2
^4
^ ^ . 2
^ ^^ H'
7. IE
» •' • •*
y=-0.3a83x+1.233
-2-
* ••
—i
0-
•• •
-1
3Relative price
Relative price
Relative consumption vs relative prices for 9 commodity groups Figure 3.5
International Consumption Comparisons
116
Rrtiirfim
RscrGdJcn
3-
fc • •
i h
•
•
at vec
2
*-rr-r^r
»
, * * -1.5
-1.0
-0.5
*
•
" •
• 00
•»-3 IT
: • . '• 05
1.0
•
1
o> C5
*••
»
•
O
onsumptlon
pti
•
»
CO
•
V==-02412x+1.466*
*
J.5
20
•
25
30
£5
y=Q253c+Q.0575
1.5
FHattve price
feiative price
Mscellaneous
9<S
«
^
15
20
J5
ysQ3416y-a04» Flsiative price
Relative consumption vs relative prices for 9 commodity groups Figure 3.5 (continued)
3.6
Testing the Frisch's Conjecture
In the introduction to Section 3.5, we pointed out that one of the reasons for studying income flexibility is to test the famous Frish's (1959) conjecture,
Chapter 3 Data Analysis: OECD Countries
117
which states that the income elasticity of the marginal utility of income (l/(j>) decreases in absolute value as the consumer (or country) becomes more affluent. Alternatively, <> | should increase in absolute value as the consumer (or country) becomes more affluent. In this chapter, we verify whether or not Frisch's conjecture is supported by data from 23 OECD countries. To do this, we use the estimates of <) presented in Table 3.20 together with the real GDP per capita (in US dollars) presented in Table 1.2. We estimate a relationship of the form, <])c
=
X + \iyc + ec,
where X and \i are parameters to be estimated; the superscript c denotes country c; yc is per capita real GDP (in international dollars) of country c; and ec is an independent disturbance term with zero mean. The F-test statistic value for the null hypothesis that, H0: ji = 0 and the corresponding p-value with respect to columns 2-5 of Table 3.20 are (F = 1.44; p-value = 0.24), (F = 0.18; p-value = 0.67), (F = 1.83; p-value = 0.19), and (F = 0.39; p-value = 0.54). As for all columns, the level of significance a = 0.05 < p-value, we are unable to reject the null hypothesis, HQ: (X = 0. As none of the F-values are significant, we conclude that <j) is independent of real income. The finding that <j) is unrelated to real income is, of course, at variance with Frisch's (1959) conjecture. However, our rejection of Frisch's conjecture is well in agreement with a number of previous studies (e.g. Clements and Theil, 1996; Theil, 1980; Theil, 1987; and Selvanathan, 1993). We shall further analyse Frisch's conjecture in Chapter 4 (with LDC data).
International Consumption Comparisons
118
3.7
The Validity of Preference Independence
In Chapter 2 we pointed out that the assumption of preference independence leads to an attractive simplification of demand equations. There are two distinct justifications for this assumption (Clements, 1987; Clements and Selvanathan, 1994): (i) The economic justification in terms of preference independence being plausible when the commodities in question are broad aggregates; and (ii) the statistical justification that the assumption reduces the number of unknown coefficients to be estimated from the order of n2 to n. However, whether it is truly legitimate to invoke the assumption of preference independence is largely an empirical question. In this section and in Chapter 9, we discuss some empirical evidence on this topic. From Section 2.2, under preference independence, the finite-change version of (2.4) can be written as Dqit = TliDQt + riiifDp, -DP;),
i=l,...,«,
(7.1)
where Tlii
=
(hi,
(7.2)
with T|i being the income elasticity and Tin being the own-price elasticity of i. As (7.2) holds for i=l,...,ra, it is clear that, under preference independence, ownprice elasticities are proportional to income elasticities with 0 being the factor of proportionality. In other words, luxuries are more price elastic than necessities (Deaton, 1974; Pigou, 1910). To analyse the evidence on the proportionality relationship (7.2), we use the income and price elasticity estimates presented in Tables 3.18 and 3.19.
119
Chapter 3 Data Analysis: OECD Countries
Figure 3.6 plots each pair of the own-price elasticity (r^) against the income elasticity (r|j) and the solid line is the LS line. The points are scattered around a negatively sloping line and the location of the points give evidence that luxuries tend to be more price elastic. The estimate of the factor of proportionality is -.26 with standard error .03, which is not far from the estimates of (j) presented in Table 3.20. The significance of the factor of proportionality gives indirect evidence to the preference independence hypothesis. Even though our findings are in contrast to Deaton's (1974) findings, however, acceptance of preference independence was supported by a number of other previous studies (e.g., Clements et al, 1984; Selvanathan, 1993). We shall formally test the hypothesis of preference independence in Chapter 9.
*
Price elasticity
1' •** •»*'»", **fiV T r _Sjt_r
•
i
i
>
.
•
••
*
•
^
• -3 y = -0.2601 x
* Income elasticity
Own-price elasticity against income elasticity Figure 3.6
120
International Consumption Comparisons
References Aasness, I., and A. Rodseth (1983). 'Engel Curves and Systems of Demand Functions,' European Economic Review 20: 95-121. Adams, P.D., C.F. Chung and A.A. Powell (1988). 'Australian Estimates of Working's Law under Additive Preferences: Revised Estimates of a Consumer Demand System for use by CGE Modellers and other Applied Economists,' Impact Project Working Paper No.0-61, University of Melbourne, Victoria, Australia. Barten, A.P. (1993). 'Consumer Allocation Models: Choice of Functional Form,' Empirical Economics 18: 129-158. Blanciforti, L., and R. Green (1983). 'An Almost Ideal Demand System Incorporating Habits: An Analysis of Expenditures on Food and Aggregate Commodity Groups,' Review of Economics and Statistics 65: 511-515. Chen, D.L (2001). World Consumption Economics. Singapore, London: World Scientific. Chung, C.F., and E. Lopez (1988). 'A Regional Analysis of Food Consumption in Spain,' Economics Letters 26: 209-213. Clements, K.W. (1982). Divisia Moments of Australian Consumption,' Economics Letters 9: 43-48. Clements, K.W. (1983). 'The Demand for Energy Used in Transport,' Australian Journal of Management 8: 27-56. Clements, K.W. (1987). 'Alternative Approaches to Consumption Theory,' Chapter 1 in H. Theil and K.W. Clements, Applied Demand Analysis: Results from System-Wide Approaches. Cambridge, Mass.: Ballinger Publishing Company.
Chapter 3 Data Analysis: OECD Countries
121
Clements, K.W., S. Kappelle and EJ. Roberts (1984). 'Are Luxuries More Price Elastic than Necessities?' McKethan-Matherly Discussion Paper MM6, Graduate School of Business, University of Florida, Gainesville. Clements, K.W. and S. Selvanathan (1994). 'Understanding Consumption Patterns,' Empirical Economics 19: 69-110. Clements, K.W., and H. Theil (1996). 'A Cross-Country Analysis of Consumption Patterns,' Chapter 7 in H. Theil (ed.), Studies in Global Economics. Advanced Studies in Theoretical and Applied Econometrics. Boston: Kluwer Academic Publishers, pp.95-108. Chung, C-F., and E. Lopez (1988). 'A Regional Analysis of Food Consumption in Spain,' Economics Letters 26: 209-213. Deaton, A.S. (1974). 'The Analysis of Consumer Demand in the United Kingdom, 1900-1970,' Econometrica 42: 341-367. Deaton, A.S., and J. Muellbauer. (1980). 'An Almost Ideal Demand System,' American Economic Review 70: 312-326. Fiebig, D.G., J.L. Seale, Jr., and H. Theil (1988). 'Cross-Country Demand Analysis Based on Three Phases of the International Comparisons Project,' in J. Salazar-Carillo and D.S. Prasada Rao (eds.), International Comparisons of Purchasing Power and Real Income. Amsterdam: NorthHolland, pp.225-235. Finke, R., L.R. Flood and H. Theil. (1984). 'Maximum Likelihood and Instrumental Variable Estimation of a Consumer Demand System for Japan and Sweden,' Economics Letters 15: 13-19. Frisch, R. (1959). 'A Complete Scheme for Computing All Direct and Cross Demand Elasticities in a Model with Many Sectors,' Econometrica 27: 177-196. Imhoff, E.V. (1984). 'Estimation of Demand Systems using Both Time Series and Cross-Sectional Data,' De Economist 132: 419-439.
122
International Consumption Comparisons
Izan, H.Y., and K.W. Clements. (1979). 'A Cross-Cross-Section Analysis of Consumption Patterns,' Economics Letters 4: 83-86. Leser, C.E.V. (1963). 'Forms of Engel Functions,' Econometrica 31: 694-703. Meisner, J.F. (1979). 'Divisia Moments of U.S. Industry, 1947-1978,' Economics Letters 4: 239-242. Musgrove, P. (1985). 'Household Food Consumption in the Dominican Republic: Effects of Income, Price and Family Size,' Economic Development and Cultural Change 34: 83-101. Pigou, A.C. (1910). 'A Method of Determining the Numerical Values of Elasticities of Demand,' Economic Journal 20: 636-640. Rajapakse, M.H.S. (1992). An Analysis of Consumer Behaviour: A Case Study of Sri Lanka. Ph.D. Thesis, La Trobe University, Victoria. Selvanathan, E.A. (1987). Explorations in Consumer Demand. Ph.D. Thesis, Murdoch University, Western Australia. Selvanathan, E.A., and K.W. Clements (1995). Recent Developments in Applied Demand Analysis. London: Springer. Selvanathan, E.A., and S. Selvanathan (1993). 'A Cross-Country Analysis of Consumption Patterns,' Applied Economics 25: 1245-1259. Selvanathan, S. (1993| A System-wide Analysis of International Consumption Patterns. Advanced Studies in Theoretical and Applied Econometrics. Boston: Kluwer Academic Publishers. Selvanathan, S., and E.A. Selvanathan (1994). Regional Consumption Patterns. London: Avebury. Theil, H. (1980). The System-Wide Approach to Microeconomics. Chicago: University of Chicago Press. Theil, H. (1987). 'The Economics of Demand Systems,' Chapter 3 in H. Theil and K.W. Clements (eds.), Applied Demand Analysis: Results from
Chapter 3 Data Analysis: OECD Countries
123
System-wide Approaches. Ballinger Publishing Company, Cambridge, MA. Theil, H., and K.W. Clements (1987). Applied Demand Analysis: Results from System-Wide Approaches. Cambridge, Mass.: Ballinger Publishing Company. Theil, H., and R. Finke (1984). 'A Time-Series Analysis of a Demand System Based on Cross-Country Coefficient Estimates,' Economics Letters 15: 245-250. Theil, H., J.L. Seale, Jr. and C.-F. Chung (1987). 'A Regional Analysis of Food Consumption in China,' Empirical Economics 12: 129-135. Theil, H., and F.E. Suhm (1981). International Consumption Comparisons: A System-wide Approach. Amsterdam: North-Holland Publishing Company. Working, H. (1943). 'Statistical Laws of Family Expenditure,' Journal of the American Statistical Association 38: 43-56. Yang, W., K.W. Clements, D.L. Chen (2000). 'A User's Guide to DAP 2000,' Discussion Paper 00.02, Department of Economics, The University of Western Australia. Yuen, W.-C. (2001). 'Food Consumption in Rich Countries,' Chapter 6 in D.L. Chen (ed.), World Consumption Economics. Singapore, London: World Scientific.
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CHAPTER 4 Data Analysis: Less Developed Countries E.A. Selvanathan & S. Selvanathan
In this chapter, we provide a preliminary data analysis of the consumption patterns of consumers in less-developed countries (LDC). This chapter is structured the same as Chapter 3, so that a systematic comparison can be made between the OECD and LDC consumption patterns in Chapter 5. In Section 4.1, we present the details of the data source and its characteristics. In the following Section, we present a summary of the data in the form of Divisia indices. In Section 4.3, we verify the Engel's law for the LDC data. Section 4.4 presents preliminary estimates of income and price elasticities based on a double-log demand system. In Section 4.5, we derive preliminary estimates of the income flexibility. In Sections 4.6 and 4.7, we verify the famous Frisch's (1959) conjecture and the assumption of preference independence. Based on the results from Chapter 3 for OECD and this chapter for LDC, in Chapter 5, we present a comparison of the consumption patterns of consumers in the LD and the OECD countries. As with Chapter 3, the results presented in this chapter are obtained using the Demand Analysis Package, DAP2000 (see the Appendix of this book for further details).
International Consumption
126
4.1
Comparisons
Data Source
The basic data, consisting of annual consumption expenditures (in current and constant prices) and the population for the 23 LD countries considered in this book are compiled from the Yearbook of National Account Statistics (United Nations: New York, various issues) and International Financial Statistics Yearbook (various issues). Even though Mexico and Korea were admitted to the OECD recently (in 1994 and 1996, respectively), we have included them with the LD countries as most of the data for these two countries relate to their preOECD years. Consumption data prior to 1984 for 15 of the 23 countries considered in this book were considered by Brozdin (1988) and also reported in Chen (2001). We have cross-checked our updated data with Brozdin's data prior to 1984 and have used the revised data wherever appropriate. As with the OECD countries in Chapter 3, for most LD countries, goods and services are classified into 9 commodity groups, which are again listed in Table 4.1 with their description. Table 4.2 summarizes the general characteristics of the LDC database. Column 1 lists the 23 LD countries, column 2 gives the local currency unit of each country, column 3 gives the sample period for each country and column 4 presents the sample size. The number of commodity groups considered for each country is given in column 5 with some comments in column 6. It should be noted that only 6 of the 23 LD countries have data for all 9 commodity groups.
4.2
Summary Measures
In this section we present the summary measures defined in Section 3.2 of Chapter 3 for the LDC data.
127
Chapter 4 Data Analysis: LD countries Table 4.1 Details of the commodity groups Commodity 1. 2. 3. 4. 5. 6. 7. 8. 9.
Food Clothing Housing Durables Medical Transport Recreation Education Miscellaneous
Description Food, beverages and tobacco Clothing and footware Gross rent, fuel and power Furniture, furnishings and household equipment Medical care Transport and communications Recreation, entertainment and cultural services Education and research Miscellaneous goods and services
The budget shares (at sample means) for each commodity i (wt), defined in equation (2.2) of Chapter 3, are presented in Table 4.3 for the 23 LD countries. For each commodity, the last two rows of the table present the mean budget share of each commodity averaged over the 23 countries (^) and the corresponding standard deviation. As can be seen from the food column, among the LD countries, on average, the Hong Kong (as well as Singapore) consumers allocate only about one-fourth of their income on food while the Indian, Sri Lankan and Philippines consumers allocate more than half of their income on food. On average, the LDC consumers allocate about 38 percent of their income on food. The remaining income is spent on clothing (9 percent), housing (12 percent), durables (8 percent), medical (4 percent), transport (10 percent), recreation and education (combined 7 percent), and all other goods (12 percent). The standard deviations presented in the last row of the table reveal that there is more variation in the budget shares for food, housing and transport across the LD countries.
International Consumption
128
Comparisons
Table 4.2 Characteristics of the LDC database
Sample period
Sample Number of size commodities
Comments
Country
Currency
1.
(1) Colombia
(2) Pesos
(3) 1972-1992
(4) 21
(5) 9
2.
Cyprus
Pounds
1980-1994
15
9
3.
Ecuador
Sucres
1973-1993
21
7
Recreation and education are included in niscellaneous.
4.
Fiji
Dollars
1977-1991
15
8
Education is included in recreation.
5.
Honduras
Lempiras
1970-1982
13
8
Education is included in recreation.
6.
Hong Kong
Dollars
1970-1995
26
9
7.
Hungary
Forint
1983-1994
12
8
8.
India
Rupees
1980-1995
16
9
9.
Iran
Rupees
1983-1995
13
8
10. Israel
NewSheqels
1970-1995
26
9
11. Jamaica
Dollars
1974-1988
15
9
12. Korea
Won
1974-1996
23
8
Education is included in recreation.
13. Malta
Ponds
1974-1993
20
8
Education is included in recreation.
14. Mexico
Pesos
1970-1998
29
8
Education is included in recreation.
15. Philippines
Pesos
1983-1995
13
6
16. Puerto Rico
US Dollars
1963-1994
32
8
Durables is included in housing, recreation and education a included in niscellaneous. Education is included in recreation.
17. Singapore
Dollars
1963-1995
33
8
Education is included in recreation.
1960-1995
36
8
Education is included in recreation.
18. South Africa Rand
(6)
Education is included in recreation.
Education is included in recreation.
19. Sri Lanka
Rupees
1974-1995
22
8
Education is included in recreation.
20. Taiwan
Dollars
1962-1997
36
8
Education is included in recreation.
21. Thailand
Baht
1976-1995
20
8
Education is included in recreation.
22. Venezuela
Bdivares
1984-1995
12
8
Education is included in recreation.
23. Zimbabwe
Dollars
1975-1987
13
8
Education is included in recreation.
129
Chapter 4 Data Analysis: ID countries
Housing
Durables
Medical
Transport
Miscellaneous
Clothing
Education
Food
Recreation
Table 4.3 Budget shares of 9 commodities in 23 LD countries (Means x 100)
(2) 37.75
(3) 6.77
(4)
(5)
(8)
(9)
(10)
11.90
5.80
(6) 5.82
(7)
1. Colombia
14.06
3.99
1.58
12.34
2. Cyprus
27.19
10.01
7.88
11.03
2.86
16.81
6.50
1.13
3. Ecuador
38.34
10.40
8.28
7.07
4.01
11.16
4. Fiji
37.81
7.60
15.78
9.81
2.23
14.40
4.84
5. Honduras
46.25
10.22
20.58
7.90
6.93
3.10
2.47
6. Hong Kong
25.54
18.40
14.56
11.17
5.75
8.21
7.14
7. Hungary
43.41
8.42
12.04
8.67
1.18
12.02
6.81
8. India
54.53
10.90
11.18
4.32
2.68
9.10
1.44
9. Iran
41.95
10.79
25.85
6.29
4.23
5.78
1.88
10. Israel
27.32
6.54
21.93
11.56
5.10
4.00
2.69
9.45
11. Jamaica
41.87
3.70
11.92
5.86
2.18
11.41 12.87
3.25
0.25
18.09
12. Korea
39.77
6.38
10.62
5.97
5.13
10.52
10.27
11.34
13. Malta
34.66
8.36
6.30
10.07
14.84
6.60
15.48
14. Mexico
35.05
8.54
10.73
11.46
3.69 3.83
10.81
5.50
14.07
15. Philippines
58.60
3.70
3.80
13.42
16. Puerto Rico
29.00
9.33
14.60
8.38
5.70
14.46
6.36
12.17
17. Singapore
26.24
8.23
10.33
8.43
3.13
13.41
11.94
18.29
18. South Africa
33.93
8.73
11.31
12.31
3.90
15.17
5.67
8.99
19. Sri Lanka 20. Taiwan
61.69 42.32
6.84
5.08
4.41
1.62
12.94
3.74
3.67
5.09
16.85
4.69
5.19
7.21
11.46
7.18
21. Thailand
39.02
10.71
9.31
7.93
5.76
11.49
4.49
11.28
22. Venezuela
37.87
8.61
4.06
2.47
7.22
2.78
26.05
23. Zimbabwe
33.99
12.18
10.93 15.24
10.29
4.78
2.20
4.86
16.45
Mean
38.21
8.57
12.26
8.16
3.94
10.42
5.43
1.45
11.57
9.65
3.08
5.29
2.81
1.57
4.03
2.90
0.80
6.10
Country
(D
Standard deviation
16.59 20.75 7.53 2.56
1.38
7.86 7.45
1.81
4.05 3.22
4.65
15.82
130
International Consumption Comparisons
Columns 2-10 of Table 4.4 present the mean log-changes in per capita consumption Dqt (defined in equation (2.5) of Chapter 3) of each commodity for the 23 countries. The last row presents their averages over all countries. As can be seen, the average growth in per capita consumption of food varies between -7.19 percent (Zimbabwe) per annum and 4.0 percent per annum (Cyprus and Taiwan) with an average of 0.7 percent per annum among the LD countries. The average LDC annual growth in consumption of clothing is 1.6 percent, housing 2.7 percent, durables 2.9 percent, medical care 3.3 percent, transport 3.1 percent, recreation 3.8 percent and education 2.9 percent. Columns 2-10 of Table 4.5 present the annual mean log-changes in prices of each commodity {Dpt), defined in equation (2.6) of Chapter 3, for each of the 23 countries. The last row of the table presents the mean price log-changes averaged over all countries. As can be seen, in the LD countries, the average growth in the price of food varies between 2.9 percent (Singapore) to 42 percent (Israel) with an average of 13.6 percent per annum. The average LDC annual growth in the price of clothing is 12.8 percent, housing 13.1 percent, durables 13.2 percent, medical 14.5 percent, transport 13.8 percent, recreation 12.3 percent and education 15.3 percent. Table 4.6 presents the Divisia volume index (DQt) for each country, defined in equation (2.7) of Chapter 3, over the corresponding sample period. The last row of this table gives the average of the Divisia volume index (DQ) averaged over the whole sample period for each country. As can be seen from the last row of the table, overall consumption growth in the LD countries varies between -4.3 percent (Zimbabwe) and 6.2 percent (Taiwan). The overall average growth in consumption is 2.1 percent per annum for all LD countries. Table 4.7 presents the Divisia price index (DPt) for each country, defined in equation (2.8) of Chapter 3, over the corresponding sample period. The last row of this table gives the Divisia price index averaged over the whole sample
Chapter 4 Data Analysis: LD countries
131
Table 4.4 Per capita quantity consumed of 9 commodities in 23 LD countries
Education
(6)
(7)
(8)
2.76
1.69
(9) 1.25
(10)
1.47
2. Cyprus
3.98
4.71
6.06
5.94
9.74
3.37
6.51
10.83
7.32
Transport
(5) 1.62
Medical
(4) 1.74
Durables
(3) -0.12
Housing
(2) 1.38
Clothing
(D 1. Colombia
Country
Food
Recreation
Miscellaneous
(Mean log-changes x 100)
2.42
3. Ecuador
0.04
1.92
2.18
0.57
1.56
4.17
4. Fiji
-0.73
-0.28
-1.14
0.45
-1.50
2.83
-1.09
0.25
-3.03
3.63
2.22
0.59
-0.56
1.80
2.15 -1.08
5.60
9.01
6.24
4.94
6.10
-4.30
5.86 2.19
-0.52
-1.18
4.01
1.75
8. India
0.96
2.35
1.31
4.66
-0.33
6.72
6.05
9. Iran
-1.20
-0.91
2.60
-1.96
3.39
4.70
3.56 2.37
-1.23
1.87
5.69
4.23
5.43
3.76
0.55
2.55
-1.47
0.20
1.74
-0.70
3.23
0.98
3.01
-2.67
0.10
12. Korea
3.40
2.78
4.90
8.53
10.82
10.16
7.79
7.95
13. Malta
3.50
4.24
5.28
4.33
3.69
4.18
5.08
8.18
14. Mexico
1.06
-1.00
1.99
1.12
2.15
1.91
0.84
15. Philippines 16. Puerto Rico
0.75
0.38
1.67
0.69
5. Honduras 6. Hong Kong 7. Hungary
10. Israel 11. Jamaica
2.51 0.04 3.84 0.05
6.56
2.19
1.61 5.42 -0.97
1.24
0.92
0.22
-0.22
3.77
3.04
3.12
4.35
3.82
4.75
5.02
17. Singapore
1.56
3.38
5.20
3.36
5.31
5.19
7.74
5.51
18. South Africa 19. Sri Lanka
0.40
1.79
0.42
0.42
1.48
1.41
1.19
0.30
0.68
4.21
2.08
1.23
-0.93
6.63
4.28
0.21
20. Taiwan
3.99
8.17
6.94
8.17
7.94
11.93
8.26
6.15
21. Thailand
2.54
3.17
8.06
7.84
7.67
5.41
6.48
22. Venezuela
0.40
5.59 -2.17
0.29
0.16
3.11
-0.44
1.68
-0.88
23. Zimbabwe
-7.19
-6.04
-2.20
-1.00
-0.09
-15.30
0.50
-2.54
Mean
0.74
1.56
2.71
2.87
3.29
3.08
3.83
2.88
2.92
132
International Consumption Comparisons Table 4.5 Prices of 9 commodities in 23 LD countries
(D 1. Colombia
0)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
21.56
20.56
20.79
21.62
22.61
23.47
21.10
22.35
4.94
4.05
Miscellaneous
Education
Recreation
Transport
Medical
Durables
Housing
Clothing
Country
Food
(Mean log-changes x 100)
(10) 23.48
2. Cyprus
5.37
5.59
3.77
4.19
6.26
3.91
3. Ecuador
27.53
25.86
23.17
27.11
26.83
26.19
4. Fiji
7.39
8.88
7.96
6.29
9.90
5.44
7.44
5. Honduras
7.29
7.80
8.22
8.10
7.90
8.13
6.12
9.52
7.45
8.88
8.31
5.39
7.64
8.33
7.75
11.57
9.38
14.09
15.68
19.60
14.23
25.44
15.09
15.07 9.06
16.93 7.22
6. Hong Kong 7. Hungary
5.86 26.64 8.65 7.65
8. India
8.46
7.90
6.57
7.41
8.45
9.23
5.39
9. Iran
19.93
21.02
17.04
20.70
19.13
22.02
21.95
10. Israel
42.03
38.75
43.95
38.74
43.23
41.23
42.72
46.84
42.96
11. Jamaica
13.65
15.24
19.39
15.44
14.91
13.20
14.85
14.81
13.67
7.17
12. Korea
8.82
8.75
12.77
8.12
8.34
7.89
10.47
13. Malta
3.79
1.28
1.65
2.85
3.65
5.32
11.13 3.33
14. Mexico
27.37
27.02
28.30
27.39
28.85
30.77
29.95
31.37
15. Philippines
11.38
11.03
11.98
12.19
16. Puerto Rico
5.45
1.94
4.39
2.85
5.55
3.79
2.96
4.16
17. Singapore
2.94
2.03
3.61
3.52
3.87
3.92
1.40
2.91
18. South Africa
9.70
7.34
9.17
8.15
10.20
9.84
9.09
9.42
11.40
9.79
9.82
14.56
15.68
10.59
9.36
14.46
20. Taiwan
5.02
2.83
5.00
5.15
4.90
5.15
6.25
5.43
21. Thailand
4.53
7.01
6.35
5.96
5.53
6.18
5.87
7.13
22. Venezuela
32.34
26.89
25.78
33.13
29.76
32.80
28.21
31.92
23. Zimbabwe
13.13
11.89
10.13
10.39
10.94
15.15
10.63
10.42
Mean
13.58
12.77
13.11
13.17
14.52
13.83
12.28
19. Sri Lanka
5.39
9.89
12.83
15.30
14.20
133
Chapter 4 Data Analysis: LD countries Table 46
(8)
C
(9)
(10)
(11)
t (12)
(13)
2 (14)
a) 2 (15)
0)
(16)
(17)
(18)
3 o (A (19)
w
Tai\
(6)
I
Slnj
(5)
Hon
(3)
o I (7)
Phil
(2)
3 UJ
(4)
Kon
(1) 1961
o
Fiji
Year
Cole
Divisia volute indces in 23 LD comtries (Means x 100)
(20)
(21)
CO .c 1-
(22)
c IS
>
(23)
E N (24)
-1.65 0.61
1962 1963
3.05
333
1964
573 4.44 4.53
9.59
1965
582
312 -3.30
631
1966
273
4.96
1.66
312
1967
4.62 4.63
1.60
649
1968
9.41
669
4.15
626
1969
542 673
3.55
510
1970
804 1Q51 3.97
573 674
1971
354
568
374
247
4.27 674
230
1972
-1.60 4.94
688
382
4.40 7.52
1.23
a 25
858 635
369
3.87
4.72 673
527
1012
1973
270
1974
asi
655
-295 -567
341
1.35
-326
378 276
280
1975
Q80
695
-004 -Q44
-1.66 -1.83 370 8C8
1.81
596
1.12 -0.02
-9.71 4.27
1976
4.56
518
274
355 -3.77 688 S22
1.10
536 4.12 0.25
200 522
1977
1.73
4.56
4.22 1Q94
244 -258
1.16
360 4.94 -274
9.48 4.96 604
-14.03
1978
594
285
245
a 83 14.29
598 -6.83 7.56 7.53 4.57
221
026 690 4.17
4.63
1979
211
270
3.86 -379
533
389 -5.01 631 1041 5.82
-Q43 7.83
1.40
829
7.92 364
9.29
1960
214
386 -11.47 282
563
-343 -5.58 -229
-327
699
624
504
355
280
-4.38
1961
0,76 -Q07
1.52
263 -5.50 522
270
7.16 -0.96
-1.27 605
4.02
204
1.74
0.X
1291
1962
-0.47 9.58 Q09
-4.76 -7.46 243
-302
7.11 0.98 4.93 -833 -328
1.87 256 -0.02
235
268
0.54
-655
1983
-1.75 1274 -517
260
-1.08 4.22 4.67
11.32
1984
Q63 4.74 -001
-1.33
374
1.31
1985
-Q14 321
Q27
Q17
265
129 Q63
694
212
610
535
554
1.93
1.22
571 -Q02
•4.65
1987
1.92
682 -0.14
-1.12
1968
1.89 1Q71 -0.33
7.X
7.65 -4.22 394
1969
1.20
9.42 Q16
252
273
226
231 1.82
1.66
1990
123 653 -011
204
4.41 -322
1991
Q 02 Q79 -Q47
-0.79
604 -660 -Q03
1992
243
1.74 -5.93 393
9.25 7.51 -214 -6.87
323 -8.39 647
315
-255
1.93
1.71 -1.04 1568
1.69
9.15 -065
1.55
7.81 -6.65
595 Q71 0.18 -216 4.02 223
-Q41 268 -1.27 4.94 662 0.71 -361 -872 7.59 a57
683 -0.41
7.47 7.14 -256
Q86 4.83 362 -295 1.56
335
7.25 1Q54 -0.95 365 -Q10 S43 7.08 4.80 255 S63 295
3.52
306 -380 -5.50 S72
1.62
1.88 293
Q61 554
3.55 299 -1.93 391
083
-364
045 -3.43
545 228
278
-3249
362 373 0.06 Q34
-9.45
272
-1.60
-Q56 641 272
232
9.54 7.55
355 11.42
ax
1.74 -1893 1.83
-062 11.26 891 -9.27
0.44 -1284
7.78 377 222 -1.31 207
691
-1.78
648 S99 -Q5B
-028 607 3.52 515
7.01 034
9.01
0.94 203
383
Q64 361
4.41 -4.18
691
7.53 672
Q47
671
1.27 273
•0.23 4.32
4.59 300 -Q45 Q50 314
615 -1.98
692
692
625 -267
Q51 568
620
259
1.22 249
1.54
643
7.32
5.64 -633
4.70
7.30
-7.25
1.38
569
-5.21
527
672
648
1993
-674
1994
378
1995
4.95 0.03 233 -4.04
363
1996 1997 1996 Mban
9.38 3.87
285 -1313 9.34 -1.35 7.85 326 4.3B
1966
11.14 521
363
500 1363
-393
618
233
1.15
-0,92 264
551
204 4.53 7.54 Q39
4.97 1.64 5 X
1.46 -0.04 Q78 513 0.04 205
043 322 -0.17 586 4.64 1.10 Q69 274 4.34 0.77
1.57 615 4.79 -011 -4.26
134
International Consumption Comparisons
(19)
Zimbabwe
(18)
Venezuela
( 17 )
Thailand
(16)
Sri Lanka
(14) (15)
Taiwan
South Africa
(13)
Singapore
(12)
Puerto Rico
(11)
Philippines
Korea
(10)
Mexico
Jamaica
(9)
Malta
Israel
I ) I8!
Iran
CB C
o X7
India
(6)
c o
Hungary
5 (4) ( I
Honduras
(3)
Fiji
Ecuador
1 (1961 ) PI
Cyprus
Year
Colombia
Table 4.7 Divisia price indices in 23 LD countries (Means x 100)
(20)
(21)
(22)
(23)
(24)
1.89
1962
1.53
1963
1.52
0.53 1.05
1964
1.61
1.15
232
1965
1.91
0.51
3.70
120
1966
4.89
1.93
3.79
0.87
1967
276
232
3.19
4.34
1968
4.28
1.36
253
6.39
1969
4.18 -0.14 343
379
1970
3.97
150
393
4.07 229
1971
0.49
325
11.55
652
4.23 3.37
7.54
1972
291
4.41
13.87
557
3.52
673
4.05
8.00 1864
18.13
11.90
11.61 14.74 6.75
11.02
33.10
20.95
1282 1278 11.09
3257
1973
17.72
260
1974 23.60
19.32
14.71 1503
1976 21.89
1352
7.0O 0.98
3375 14.39 24.50 4.25 1284
1891
10.14
4.14
355
24.65 9.55 1625
1.40 17.16
3.06
0.59
1977 24.03
11.91
5.62
4.73
30.09 11.21 14.28 6.97 24.12
4.86
2.15 10.61 609
7.90 6.64
1.10
4.99
4356 26.03 18.23 3.96 1551
560
281
9.49 1354
6.56 9.11
666
8.58 14.94 11.03
57.11 20.70 18.24 6.62 1621
10.97 3.67 11.90 1316 9.56 10.69
10.86
1976 1978
16.43
11.28 4.89 10.51
1979 23.08
6.43 276 1282 1279 5.64 8.66 222
1.60
9.55 11.00
13.24 18.53 7.68 2311 1981 2304 10.77 1574 10.49 13.94 11.21
8524 19.91 25.40 14.39 30.40
9.38
6.96 14.50 21.24 18.51 155B
14.51
9.12
7861 11.40 17.60 9.16 2350
5.79
527 14.99 1208 14.75 11.38
13.58
6.41 17.40 6.87 11.29 9.53
£55
77.38 8.22 4.60 5.19 44.33
273
1.67 13.31 1373 3.90 5.31
1283
4.13 37.78
888
92.45 1279 285 •0.75 64.60
1.31
0.32 13.55 17.45 2.27 396
11.24
1.71 10.12 1696 0.76 0.41
15.53
1980 2329
1982 21.91 1983
1843
3.90
8.67
1984
18.65 6.11 31.78 5.50
845
7.43
598
8.70 158.52 23.76
3.58 -0.48 50.55 41.94 1.52
1.55
279
6.37
553
5.90 135.76 2326
327
0.87 299 10.89 897
1986 2273
1.79 24.56 8.35
502
503
683 19.00
38.72 11.64
3.81 -1.26 4625 16.16 0.64 054 1365 1.70 1.00 59.72 999 0.99 -0.15 17.42
821
0.56 212 12.19 1207
1987 2360
2.58 29.25 4.59
4.84
7.83
7.64 22.57
18.24 5.13
3.19
3.20 2.21 13.77
350
1.47
3.13 24.85 1312
1988 2382
3.26 47.56 10.15
7.31 12.05 852 20.45
1539 6.72 5.47 -0.46 77.49 872
348 13.86 11.62
1.81
4.25 2321
1989 2206
3.63 55.15 4.22
7.12 14.55 7.02 18.09
17.73
5.23
1990 26.37
4.51 39.42 7.22
7.23 25.06
8.73
13.97
9.20 4.43 24.59 11.41 3.97
1991 2 M 2
4.11 3864
824 35.30 1285 16.87
16.48
863
4.31 2200 15.56
1.93
259 14.59 1580 4.03 5.63 28.12
1985 21.07
5.00 27.94
7.44
9.81
0.91 86.04 AZi 1.89 2218 10.14
3.85
3.50 4.38 14.11 11.57 4.35 4.98 56.49 350 14.51 3348
3.75 6.01 3451
1992 25.00 6.55 41.85
699 20.35
8.28 20.42
10.31
5.51
305 14.34 7.44
1.47
2.16 14.54 379
4.11
3.47 27.06
1993
4.48 36.28
584 19.31
897 20.19
10.31
4.64
6.00 1.42 6.68
1.50
3.56 9.67
568
3.45
3.18 31.44
1994
5.52
7.41 18.00 9.08 31.23
11.17
6.09
1566
7.81
2.25 4.14 833
7.68
381
5.06 47.82
5.51
4.57
29.41
7.73
1.25
827
3.52
5.55 4369
5.16
27.59
3.12
1997
14.76
1.41
1998
1844
7.67
1995
664 39.36
1996
Mean 2204
4.92 2666
7.31 7.65
7.92 15.57
an
19.29
42.05 14.62
9.49
3.72 2872 11.67 4.22
3.03
8.25
9.23 11.54
5.13 5.60 30.91 11.66
Chapter 4 Data Analysis: LD countries
135
period for each country. As can be seen from the last row of Table 4.7, the overall annual price growth in the LD countries varies between 3.0 percent (Singapore) and 42.1 percent (Israel). The overall average growth in prices is 13.5 percent per annum among all LD countries. Tables 4.8 and 4.9 present the second-order moments, the Divisia quantity variance (Kt) and the Divisia price variance (n t ), defined in equations (2.9) and (2.10) of Chapter 3, for the LD countries over the sample period. As before, the last row of the table gives the variances for each country averaged over the whole sample period. A comparison of these two variances reveals that the Divisia quantity variances systematically exceed the corresponding Divisia price variances. To confirm this relationship, in Figure 4.1, we plot ^Kct against yjn ct for t= 1,... ,T and c=1,..., 23. As can be seen, most of the points lie above the 45° line indicating that on average, ^jKf >-\/n,e- This pattern agrees well with the results of the OECD countries (Figure 3.1) and previous studies. The Divisia price-quantity correlations (defined in equation (2.11) of Chapter 3), which measure the co-movement of prices and quantities, for the LD countries over the whole sample period are presented in Table 4.10. The last row of the table presents the correlation for each country averaged over the whole sample period. As can be seen, about two-thirds of the correlations presented in the table are negative. The last row of the table shows that, on average, the correlations are negative for all LD countries (except for Cyprus). This reflects the tendency of the consumer to move away from those commodities having above average price increases. Table 4.11 presents the averages of the Divisia moments over the sample period for each country collected from the last row of Tables 4.6-4.10. Columns 2-6 of the table present the average quantity index, average price index, average quantity variance, average price variance and the average price-
International Consumption Comparisons
136
Table 4 8 • v i s a quantity variances in 23 LD oomtries ( x 10000)
Yar
,3
<5
S
if
x
i
I
2
=
S
(1)
(9
(3)
(4)
(5)
®
(7)
{8)
B
(10)
(11)
^ (12)
(13)
i
s (14)
S (15)
t (16)
1961
i
w
(17)
(18)
w (19)
A W
^ H
S B
R W
542
1982
246
1963
915
604
19B4
2841 11.56 1240
3831
1985
11.60 281 364
953
1986
8823 20.26 Q82
913
1967
11.72 3089 1.01
24.70
1963
4285 823 267
994
1989
17.61 2325 4.96
826
1971
29C9
1972 1973 1522
219
1Q10
1883
875
1570 529 606
806
7Z7.20
5819
19.70
376
34.73 1804 568
19.66
622
804
Q26 14884
1504
323
Q51
21.17
353B 47.17 519
ace
4357
920
7.02 4586
1978
2281
961 14.06
24.74
1975 1286 1977 1658
11.63 7.01 7.98 24.35 723 S59
14.00
1974 1564 1976
f M
1Q77
1985 5286 1Q41
21.82
2334 269
2S31 1276 606
6S23 297
27.37 4.11
21.72 211 7380
5896 351
721 147.54 1960 12341 337
2052 1291 1674
56.35 1129 1241
3306
14.92 1393 934 14721 19.54 1340
12352
965
Q32 133.76
27.89 7.47
77.87
27.93
Q97
94.53
1665
91.83 3041
3349 7.94
1979 1967
4.44 27.09
1258
47.76
4257 10258 2293
4971 7.59
17.46 1362 1.97
39.01 4691 597
44.34
1980
633 14258
016
9922
5381
2382 2722 131.06 309
6342 615 2582
94.46 424 9.82
36928
8554
060
1597
4.85
7.82 9.76
1573 652
2049 2278 609
83.81 332 1532
13996
1271 Q66 2668
056
874
11.80
89.03 21.X 5278
4532 3351
7.95 1Q70 7.10
4989 4.13 916
37.71
2550
1338
4306 11654 1994
4.05 31.86
39.78 11.31 659
5357 226 1293
231.68
8503 524 29.29
13349
673 1.42
1961
1.98 347.68 394
1962
879
1963
345 15666 51.64
874
16636
1934 14.17 41.92 7.61
1Q58
1550 S78 4.23
1934 20587
2357 3310
7.22 S51 1.18 2997 1324 1088
1965
6CB 14.06 544
4QX
586 509 1683
17.21 12926
39.14 41.48
71.28 893 Q92 1931 3808 2847
3Q91 1.97 2035 1019 22002
1965
1.49 2677 670
4022
14.00 823 17.25 124.00
8804
2516 7.51
5016 9.41 Q3S 2386 3910 1942
6Q46 14.49 7.50 369 249.69
1987
401
5303
37.00 1836 526 10284
2884
342 925
1969
241 29.54 537 179.82
3201 3880 626 144.65
1303
1836 7.11
4848 594 307 1Q63 2629 1Q45
17.55 3246 2527 Q85
1999
359 3Q14 332
1Q77
14.52 2558 1517
6591
20.39
1312
1941 319 Q72 1681 2485 282
8889 4923 1598 54.06
1990
1.57
14.56 402
3373
7.99 39.61 4.56
9329
890
1023
1981
242 2989 357
1831
5878 1282 1245 33270
1Q17
344
2816 1.59 027 2927 1Q17 390
1982
219
51.62 29.17
425
3563 1.44 Q71 3604 2204 990 10546 971 2269 1279
1853 357
2589 2329 1.17 1551 3652 1Q92 2529 2231 3889 20B 154.46
1824 Q99 Q85 1801 37.89 277 72283 19.63 27.18 1275 3559 27.07 576 17.71
17.80 271
44.48 610 4.27
1993
3336 Q27
2015 1690 514 114.86
1S56
523
2524 7.66 Q24 2358 1984 7.17
4233 317 14.92 2877
1994
1518
1887 11.20 1561
4673
11.80
4.76
675 Q05 3354 S32 641
1073 2421 333 3322
2508
2571
11.36
597
1995
7.63
1996
529 9.3B
571 27.06 4.34 263
531
646
1997
691
11.61
1993
1.82
f*m
7.32
5923 042
7.47 5670 983
5039
64.54
39.22 17.50 9.65
94.91
44.42
4949 1582
41.11 1004 Q83 2548 17.93 1Q15
89.59 15.14 1550 1571 15267
137
Chapter 4 Data Analysis: LD countries Tabe49 Ovisia price variances in 23 LD countries ( x 10000)
I I I II (1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
a
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
1951
067
1932
237
(20)
(21)
1953
203
1934
281 0.45 088
1.51
1966
227 1.09 319
1.35
1.32
1936
663 380 1.27
14.81
1967
4.45 7.04 1.14
1501
1968
4.48 120 338
558
1969
1.72 422 567
850
1970
1.76 251 380
2840
1971
19.06
3529
372
387
633 4.05 937
1.91
1972
028
4630
24.38
Q78
1.80 591 269
567
1973 2217
(22)
1088
8545
1508
4.93
2S99 4833 34.70
1508
986
1245
0.62
2673
1583
1681
24.37 1961 7.68
6377
1975 14.18
3000
0.78
2237
27.77
17.09 17.51 94.44
508
098 9.09 29.43
5950 876
1976 1093
7.08
024
860
2044
11.91 2063 2095
384
390 7.01 34.80
41.67 821
1977 17.17
653
0.55
1040
3682 117.10 1570 985
10.44
066 1.84 4.11
4338 688 282
3928
075 1.48 250
3312 4.55 361
201
1974
1978 3263
1282
1577 1.00
225
1979 1540
646
3967 1295
41.51
1960 1Q01
666 117.11 022 16010
555
9678 852 14.21
314
107.10 2505 1630 1Q41
542
1867 1.66 1387 10080 10.48 21.78
9.60
4247 1952 5959
5218
14.33 1963 1723 11814 2660 74.69
29.76
1211 34215
1981
261 11.84
2363
3092 Q80
630
353
204.90 2021 11.38 2546
870
341 1822 1317
29.69 1640 31.68
1982
4.41 324
335
6836 0.77
7.64
511
13519
1504 5240 67.23
1882
617 1507 263
6593 214 4.57
4.70
1983
549 a 96 18802
24.06
4.31
7.98
34.49
44.40 37.92 4.C6
3656
4.62 846 5283
3669 241 526
34.71
21.31
1984 1876 4.05
9594
618
677
4.67 520 277
71.60
2831 593 14.81
2218 385 205 420 211
17.35 695 1235
6583
1965
S97 270
5596
2684
a 33
819 1996 1285 107.72
2570 11.63 1672
691 394 7.29 4.44 2893
2690 638 14.04
11.99 5688
1966
802 540
2323
9987
11.35
1987 1268 1.43
3209
2510
4.88
1013 1.92 6Q73
1248
1938 11.31 1.95
2837 10360
501
61.02 9.14 97.78
1989 1370 264
3847
4015
7.87
19S0 2274 1.80
663
21.06
613
1565 11.37 2514 4Q72
9.45 570
1.20
1602
1991 2217
acs
1992
872 568
14.79
1993
376
1698
1994
084
11.36 697 672 353 607
833 322 605
362 29.97
67.24 076 366 388 4.03
1303 202 242
2899 4267
7.71
580 1.58 310 50980 536 608 1072 625
3804 385 390
17.88
10.96 SOS 31.04 3313
501 1211 12073 9.42 1349 387 7.59
646
1.62 333
4534 4.01
19.30
276 21.68
579 2515 1385 543 1362
64.95 665 258
17.09
367
14.16 263 4519
571
239 17.37
1250 855 9.18 329 2391
6919 543 4.39
4397
4.47
11.41 236 24.99
1552
095 667 27a06 563 7.37 4.49 464
5501 4.09 7.91
627
11.41
1237 830 5886
1851
7.88
287.59 333 884 11.27 7.06
7.3B 379 600
3044
459 8832 14287
233
2934 456
127 208
2356 0.39 521
4.64
1.94
3286
227
301
1.19
1997
3054
2065 1298 374 549 252 901.41 295 644
17.09
1996
Man 1360 4.46
61.38 361 690 16940
11.24 40323 11.08 3892
656
1995
4.91 11.43 6214 67.30 44.16 429 1537
21.96
5061 7.49 4573
6Q93
3575 11.71 2226
5588 7.52 7.16 758 1023
8650 863 11.72
3214 2877
138
International Consumption Comparisons Table 410 Divisia price-quantity correlations in 23 LD countries
Year (1)
o (2)
o (3)
i
i
(4)
i (5)
u
. (6)
i
i
(7)
i
£
(6)
£ (9)
«
-
(10)
? (11)
^
5
(12)
5 (13)
Q
.
(14)
Q (15)
.
c (16)
o
t
(17)
o (18)
o
) (19)
1961
0.18
1962
-0.56
K (20)
!
| (21)
1963
-0.76
0.77
1964
0.07 -0.41 -0.37
-0.44
1965
-0.13 -0.19 -0.79
-0.29
1963
-0.03 -0.71 -0.20
-0.51
1967
-0.14 -0.48 -0.28
-0.08
1968
-0.75 -0.71 -0.44
-0.42
1969
-0.44
0.38 -0.30
0.26
1970
-0.02
0.10 -0.65
-0.32
1971
-0.95
0.39
0.67
-0.06
-0.65 -0.27 -0.67
-056
1972
-0.42 -0.07
0.12
0.86
-0.53
-0.82
-0.17 -0.50
-0.08
-0.70
-0.55 -0.59 -0.04
-0.51
-0.80 -0.67
-0.44
-0.16
0.00 -0.63 -0.43
-0.82
0.63 -0.02
-
> (22)
i
v
(23)
l (24)
1973
-0.20
1974
-0.44
0.08
1975
0.34
-0.48
-0.89
0,61
-0.48 -0.47 -0.56 -0.03
1976
-0.3B
-0.05
-0.54
035
-0.21 -0.31 -0.62 -0.59 -0.23
-0.48 -0.33 -093 -0.50
0.64
-051
1977
-0.82
-0.21
-091 -0.73
-0.09 -0.93 -0.36 -0.26 -0.45
-0.52 -0.54 -0.02
0.01 -0.57
-0.92
0.23 -0.58 -0.72 -0.13 -046
-Q24
0.10
-0.58 -0.18 -0.63 -0.44 -0.51 0.25
1978
-0.09
0.39 -0.80 -Q99 -0.03
-0.03 -0.91 -0.69 -0.20 -010
-0.32
1979
-058
-0.78 -0.65 -1.00 -0.47
-0.49 -0.42 -0.17 -0.30
0.76
-0.85 -0.13 -0.58 -0.36
0.65 -0.55
-0.56
1980
-0.03
0.37 -0.89 -0.82 -0.61
-0.50 -0.80
0.10 -0.59 -0.25
0.47 -0.54 -0.13 -0.11
0.05
-0.42
0.74
1981
0.11 -0.62
0 2 2 -0.92 -0.98 -0.02
0.09
-0.60 -0.56 -0.28 -0.24 -0.74
-0.18 -0.69 -0.78 -0.35 -0.40 -0.66
-Q60
1982
-0.63 -0.06 -0.51 -0.69 -0.99 -0.05
-0.26
-0.92
-0.17 -0.65 -0.39 -0.63 -0.29
0.16
-0.68
1983
-0.43
0 3 0 -0.51 -0.82
-0.48
-0.38
0 4 6 -0.45
-0.78
1984
-0.76
0 2 2 -0.58 -0.69
-0.24 -0.80 -0.46
0.66
-0.40
1985
-0.58
0 2 3 -0.04 -0.92
0.22 -0.09 -0.33 -0.45 -0.78 -0.74 -0.45 -0.41 -040
0.05 -0.89
0.17 -0.27 -037 -0.64
-0.61 -0.27
0.15
0.08 -0.55
1986
-0.19 -0.31
1987
-0.07
1963
-006 -0.30 -0.56
0.71
-0.62 -0.08 -0.45 -0.72 -0.14 -0.46 -0.03 -0.80
1989
-0.78 -0.48 -035
0.40
-0.34 -0.39 -0.42 -0.62
0 4 0 -0.14 -0.63
-0.78 -0.71 -0.31 -0.48
0.24 -0.87 -0.43 -0.06 -0.63 -0.41 -0.67 -0.22 -0.04
Q26 -0.45
0.36 -0.63 -0.32 -0.88 0.64
0.48
0.18 -0.24 -0.77 -0.04
0.57 -0.47 -0.45 -0.45 -Q35 -0.73
0.11 -0.60 -0.49 -0.76 -072
0.43 -0.46
-0.49 -0.95 -0.06 -0.71 -0.32
0.32 -0.24 -0.37 -0.80
0.46
0.31 -0.70 -0.42 -0.70 -0.81
Q37 -0.70 -0.71
0.15 -0.65 -0.77 -0.24 -0.46
0.40
-0.29 -0.55 -0.58 -0.36 -0.44
0.59 -0.20 -0.44 -057 -0.35
0.14
0.62
0.43
0.09 -0.67 -0.30 -0.35 -Q04
1990
0.08
0 6 2 -0.25 -0.58
-0.14 -0.43
0.10 -0.18 -0.51
-0.19 -0.11 -0.49 -0.60 -0.77 -0.26 -0.24 -0.99
1991
0.CE
0.32 -0.50 -0.82
-0.81 -0.13
0.39 -0.52 -0.48
0.33 -0.87
1992
0.00
Q41 -0.56
-0.33 -0.35 -0.03 -0.75 -0.46
0.84 -0.21 -0.39 -0.60 -0.89
0.60 -0.78 -0.88 -0.56 -0.79
0 3 5 -0.57 -0.43 -0.76 -0.40
0.23 -0.42 -0.36 -0.57 -0.73
0.86 -0.47 -0.87 -0.23
1993
-0.40
1994
Q17
1995
0.39
-0.31 -0.32 -0.67 0.01 -0.75 0.07
-0.63
0.13 -0.09 -0.41
0.02 -0.33 -0.90 -011 -0.40 -0.44
-0.75 -0.41
007
-0.19
-0.10
1997
0.44
0.40
1998
-0.27
Maai
-0.27
0.01
0.07 -0.19
0.31 -0.50 -0.83 -0.09 -0.36 -0.03 -0.24 -0.50 -0.74
0.75
1996
0.41 -0.89 -0.22
0.15 -0.64 -0.57
0.06 -0.66
-0.53 -038
0.44 -0.05 -0.69
051
Q03 -0.20 -0.59 -0.79 -0.17 -Q42 -0.20 -0.48 -0.33 -0.46 -0.08 -0.39 -0.20 -0.52 -0.41 -0.15 -0.42 -0.38 -0.15 -0.31 -Q16 -0.49
Chapter 4 Data Analysis: LD countries
139
Quantity standard deviation vs price standard deviation in 23 LD countries Figure 4.1
quantity correlation, respectively, for each country. The last row of the table gives the grand mean, over all sample periods and over all countries. As can be seen, on average, consumption in the LD countries grew at a rate of 2.1 percent per annum, while prices grew at a rate of 13.5 percent per annum. Also, at sample means, the Divisia quantity variance exceeds the price variance. The average price-quantity correlation for the LD countries is -.3.
International Consumption Comparisons
140
Table 4.11 Divisia moments in 23 LD countries
Country
Divisia quantity index
Divisia price index
Divisia quantity variance
Divisia price variance
Divisia price-quantity correlation
DQ (2) 1.64
DP (3)
K (4)
n
(1) 1. Colombia
(5)
P (6)
22.04
7.47
13.60
2. Cyprus
5.30
4.92
56.70
4.46
0.03
3. Ecuador
1.46
26.66
9.83
30.54
-0.20
-0.04
7.31
50.39
45.34
-0.59
0.78
7.65
64.55
4.01
-0.79
4. Fiji 5. Honduras
-0.28
6. Hong Kong
5.13
7.92
39.22
21.96
-0.17
7. Hungary
0.04
15.57
17.50
50.61
-0.42
8. India
2.06
8.11
9.65
7.49
-0.20
9. Iran
0.43
19.29
94.91
45.73
-0.48
10. Israel
3.22
42.05
44.42
60.93
-0.33
11. Jamaica
-0.17
14.62
49.49
35.75
-0.46
12. Korea
5.86
9.49
15.82
11.71
-0.08
13. Malta
4.65
3.72
41.11
22.27
-0.39
14. Mexico
1.10
28.72
10.04
56.88
-0.20
15. Philippines
0.69
11.67
0.83
7.52
-0.52
16. Puerto Rico
2.74
4.22
25.48
7.16
-0.41
17. Singapore
4.34
3.03
17.98
7.58
-0.15
18. South Africa
0.77
9.23
10.15
10.23
-0.43
19. Sri Lanka
1.57
11.54
89.59
86.50
-0.38
20. Taiwan
6.15
5.13
15.14
8.63
-0.15
21. Thailand
4.79
5.60
15.50
11.72
-0.31
22. Venezuela
-0.11
30.91
16.71
32.14
-0.16
23. Zimbabwe
-4.25
11.66
152.67
28.77
-0.49
2.09
13.52
37.18
26.59
-0.33
Mean
Columns 2 and 3 are to be divided by 100, and columns 3 and 4 are to be divided by 10000.
Chapter 4 Data Analysis: LD countries
141
Tables 4.12 and 4.13 present the mean relative quantity log-changes ( Dqi - DQ ) and the mean relative price log-changes ( Dpt - DP ) for the 9 commodity groups for the 23 LD countries. The last row, of both tables, presents the average for each commodity group over the 23 countries. The per capita consumption growth in food and clothing are negative in most LD countries. As can be seen from the last row of the two tables, for most commodities, on average, the relative prices and the relative consumption have opposite signs. Table 4.14 presents a summary frequency distribution (in percentages) of joint signs of relative consumption and relative prices for the LDC data. The entries in the first quadrant of the table are the percentages of the total number of observations having a simultaneous increase in relative prices and consumption, disaggregated by commodity and country. The entries in the other quadrants have a similar interpretation. For example, for food in Colombia, relative prices and consumption move in the same direction for 5 + 30 = 35% of the time, while they move in the opposite directions 35 + 30 = 65% of the time. As can be seen, from the "all countries" rows and the "all goods" columns, overall, 31 + 3 1 = 62% of the pairs of relative prices and consumption have opposite signs, while 17 + 21 = 38% have the same sign. These results clearly support the law of demand, i.e. other things being equal, an increase in the relative price of a commodity causes its consumption to fall. Table 4.15 presents the summary results from Table 4.14.
4.3
Engel's Law
In this section, we investigate one of the most important empirical regularities in consumption economics, the Engel's law, that the budget share for food (wFt)
International Consumption Comparisons
142
Table 4.12 Relative quantity log-changes of 9 commodities
Durables
Medical
Transport
Recreation
Education
(6) -0.17
(7) 1.12
(8) 0.05
(9) -0.39
(10)
0.10
(5) -0.02
0.76
0.64
4.44
-1.93
1.20
5.52
2.01
0.46
0.72
-0.89
0.10
2.71
-0.69
-0.24
-1.10
-1.46
2.87
5. Honduras
-0.53
-3.81
2.84
0.49 1.44
-0.20
-1.35
1.02
6. Hong Kong
-2.98
0.46
0.72
3.87
1.11
-0.19
0.97
7. Hungary
-1.11
-4.34
2.16
-0.55
-1.21
3.98
1.72
8. India
-1.09
0.29
-0.75
2.61
-2.38
4.67
3.99
9. Iran
-1.63
-1.34
3.13
-1.66
2.18
-2.39
2.96
10. Israel
-1.35
1.48
-0.85
2.47
1.01
2.21
0.55
-2.67
-0.67
11. Jamaica
-1.31
0.37
1.91
-0.53
3.40
1.15
3.18
-2.50
0.27
12. Korea
-2.45
-3.08
-0.96
2.67
4.96
4.30
1.93
2.09
13. Malta
-1.14
-0.40
0.64
-0.31
-0.96
-0.47
0.43
3.53
14. Mexico
-0.04
-2.10
0.88
0.01
1.05
0.80
-0.27
15. Philippines
0.06
-0.31
0.98
0.00
16. Puerto Rico
-2.96
1.03
0.30
0.38
1.61
1.08
2.01
2.28
17. Singapore
-2.78
-0.96
0.86
-0.98
0.96
0.85
3.39
1.16
18. South Africa
-0.37
1.02
-0.35
-0.35
0.71
0.64
0.42
-0.47
19. Sri Lanka
-0.89
2.64
0.51
-0.33
-2.50
5.06
2.71
-1.36
20. Taiwan
-2.16
2.02
0.79
2.02
1.79
5.78
2.11
0.01
21. Thailand
-2.25
0.80
-1.61
3.27
3.06
2.88
0.62
1.70
22. Venezuela
0.51
-2.06
0.39
0.26
3.22
-0.33
1.78
-0.78
23. Zimbabwe
-2.94
-1.79
2.05
3.26
4.17
-11.05
4.75
1.71
Mean
-1.35
-0.53
0.61
0.77
1.13
0.98
1.64
Clothing
(4)
Food
Housing
Miscellaneous
in 23 LD countries (x 100)
1. Colombia
(2) -0.26
(3) -1.77
2. Cyprus
-1.32
-0.59
3. Ecuador
-1.42
4. Fiji
Country
(D
0.78 1.05
-1.05
0.08 3.06 -5.09
1.43 1.58
0.14
3.36 -1.39
0.14
0.23
-0.47
-0.83
0.92
143
Chapter 4 Data Analysis: LD countries Table 4.13 Relative price log-changes of 9 commodities
Country
Food
Clothing
Housing
Durables
Medical
Transport
Recreation
Education
Miscellaneous
in 23 LD countries (x 100)
(1) 1. Colombia
(2) -0.48
(3) -1.47
(4) -1.25
(5) -0.41
(6) 0.57
(7) 1.43
(8) -0.94
(9) 0.32
(10)
2. Cyprus
0.46
0.67
-1.14
-0.73
1.34
-1.01
0.02
-0.87
0.94
3. Ecuador
0.87
-0.81
-3.49
0.45
0.16
-0.47
4. Fiji
0.08
1.58
0.66
-1.01
2.60
-1.86
0.13
1.34
5. Honduras
-0.36
0.15
0.57
0.45
0.25
0.48
-1.53
1.87
6. Hong Kong
-0.47
0.96
0.39
-2.54
-0.28
0.40
-0.17
-0.49
-0.50
1.12
-2.73
7. Hungary 8. India
-1.48
0.10
4.03
-1.34
9.87
0.34
-0.21
-1.54
-0.71
0.33
1.45 -0.03
3.65
1.46
0.95
-0.89
1.36
0.63
1.72
-2.26
1.40
-0.16
2.72
2.66
-0.02
-3.30
1.89
-3.31
1.18
-0.83
0.67
4.79
0.90
0.82
0.29
-1.42
0.23
0.18
-0.95
-7.45
-0.97
0.62
12. Korea
-0.67
-0.74
3.28
-1.37
-1.15
-1.59
1.64
13. Malta
0.08
-2.44
-2.07
-0.86
-0.07
1.61
-0.38
1.68
14. Mexico
-1.35
-1.70
-0.42
-1.33
0.13
2.05
1.23
2.66
15. Philippines
-0.29
-0.63
0.31
0.52
16. Puerto Rico
1.23
-2.27
0.18
-1.36
-1.26
-0.05
-0.09
-1.00
0.57
0.49
0.83
0.89
-1.64
-0.12
0.47
-1.89
-0.06
-1.08
0.97
0.60
-0.14
0.19
19. Sri Lanka
-0.14
-1.75
-1.72
3.02
4.14
-0.95
-2.18
2.92
20. Taiwan
-0.11
-2.30
-0.13
0.02
-0.23
0.02
1.12
0.30
21. Thailand
-1.08
1.41
0.74
0.36
-0.07
0.58
0.27
1.53
-4.01
-5.12
2.23
-1.14
1.89
-2.69
1.01
23. Zimbabwe
1.43 1.47
0.23
-1.52
-1.27
-0.72
3.49
-1.03
-1.24
Mean
0.06
-0.76
-0.41
-0.35
0.91
0.30
-0.71
9. Iran 10. Israel 11. Jamaica
17. Singapore 18. South Africa
22. Venezuela
0.09
1.98
-1.78 1.33
-0.43
1.16
1.31
0.92
International Consumption Comparisons
144
Table 4.14 Frequency distributions of relative consumption and relative prices of 9 commodities in 23 LP countries (percentages) Positive relative consumpti
ton
Negative relativei consumption w
8
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
Country
1
O
(1)
(2)
(3)
Colombia Cyprus Ecuador Fiji Honduras Hong Kong Hungary India Iran Israel Jamaica Korea Malta Mexico Philippines Puerto Rico Singapore South Africa Sri Lanka Taiwan Thailand Venezuela Zimbabwe
All countries
1. 2 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
Colombia Cyprus Ecuador Fiji Honduras Hong Kong Hungary India Iran Israel Jamaica Korea Malta Mexico Philippines Puerto Rico Singapore South Africa Sri Lanka Taiwan Thailand Venezuela Zimbabwe
All countries
1I
<•>
(5)
I I (6)
I (7)
5 7 40 7 42 8 9 53 25 8 21 0 11 14 17 26 13 20 14 0 11 18 8
25 14 10 7 50 40 27 20 17 20 21 27 11 25 17 13 16 11 10 14 16 18 0
5 14 5 29 0 4 9 7 25 4 14 5 16 7 8 6 16 11 0 0 0 18 8
25 14 35 29 8 16 18 20 0 16 29 27 11 18 8 13 6 17 29 20 21 9 17
29 19 14 29 14 5 27 25
30 7 15 21 33 40 9 40 17 28 7 18 16 25 0 26 38 20 10 40 21 45 0
16
19
9
18
16
22
30 21 0 7 8 16 9 7 25 12 14 18 11 21
35 14 15 43 42 16 55 13 33 12 29 9 16 14 42 19 13 17 24 0 21 27 25
40 14 45 36 33 48 27 33 33 48 29 41 58 46 42 65 41 57 43 80 11 18 50
15 29 40 21 8 4 27 7 42 16 29 0 53 25 33 26 6 26 33 6 0 18 42
40 29 40 36 33 40 55 40 50 68 21 68 47 39 17 58 16 54 33 43 53 36 17
19 16 17 29 26 21 27 25
30 57 25 36 50 32 55 20 25 44 43 32 32 43 58 42 25 37 29 57 58 18 42
23
41
22
41
24
39
40 7 30 36 33 16 36 7 33 16 29 18 26 29
§
1 1 8
() 20 0 14 0 12 18 7 0 20 0 0 21 29
.S
1
Ul (9) 20 43
0 13 20 7
10 13 17 14 6 11 9 25 12
25 14 36 50 24 27 47 33 40 86 14 32 29
17
25 43
12 20 16 50
48 53 26 29 26 32 45 33 36
C
28
i
£
1
1
I
5 79 20 21 8 36 27 7 25 12 14 23 37 39 33 16 31 40 14 43 11 45 17
18 22 18 17 19 19 16 19 17 16 14 15 16 22 14 17 19 19 15 17 12 24 13
30 57 30 43 0 48 36 7 33 36 21 27 37 21 33 48 31 34 38 51 21 45 50
25 57 20 43 17 12 36 20 33 8 36 18 21 14 17 6 9 11 33 0 58 9 33
25 36 30 36 42 40 27 20 17 68 21 77 21 39 33 45 44 40 38 54 53 9 33
15 14 5 7 33 4 9 20 42 12 29 0 32 18 58 10 47 17 24 14 26 45 33
20 57 45 57 42 48 45 47 25 44 36 18 37 32
26
17
34
23
37
Negative relative prices 30 30 10 20 24 7 21 14 32 30 15 25 34 29 7 14 17 17 33 0 24 28 0 20 36 0 9 9 24 27 27 27 34 25 8 17 31 44 16 24 39 29 14 36 24 64 9 14 26 36 37 11 11 29 50 14 8 33 8 25 36 6 13 16 27 47 44 34 20 32 29 20 29 31 24 14 35 43 49 6 11 26 47 16 18 26 9 55 17 50 35 17 23
31
I
.8
1
^
u. is (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)
<m. Positive relt stive pric
(10)
I
27
17
48 34 49 33 31 47 9 25
30 14 25 14 17 12 18 27 50 16 29 27 53 32 25 16 25 29 24 0 16 18 58
23 9 26 24 63 37 9 25
22
38
25
31
55 21 25 14 50 52 36 67 17 12 36 18 11 29 25 23 34 23 29 40 47 55 17
20 43 20 29 25 40 18 20 8 4 21 5 11 25 17 19 31 11 14 23 0 9 33
10 14 25 0 17 20 9 40 17 28 21 45 26 18
30 36
3 31 20 10 29 26 36 25
10 21 35 29 0 16 18 13 8 12 21 23 0 0 17 16 13 14 38 3 5 18 0
19 25 31 33 6 21 36 17
32
19
21
14
22
25 50 36 33 32 36 20 67 20 7 55 21 29
14 17 32 18 27 0 20 7 32 26 14
60 7 40 36 50 28 55 20 17 44 36 45 26 39 42 39 6 23 38 11 42 27 33
29 33 28 34 29 34 33 26 35 33 27 34 31 28 35 29 26 29 32 28 38 22 36
42
33
31
25 7
15 7 10 14 25 16 9 47 33 28 14 23 11 11 17 32 16 17 19 3 37 9 0
23 21 22 15 19 24 15 31 14 20 20 28 16 20 18 17 29 21 23 20 25 28 16
18
21
30 7
SO 53 52 29
8 13 12 14
13
145
Chapter 4 Data Analysis: LD countries
Table 4.15 Frequencies of joint signs of relative consumption and relative price changes in 23 LD countries (in percentages) Positive consumption
Negative consumption
Positive price (2) 18
Negative price (3) 30
Positive price (4) 29
Negative price (5) 23
2. Cyprus
22
24
33
21
57
3. Ecuador 4. Fiji
18
32
28
22
60
17
34
34
15
68
5. Honduras
19
33
29
19
62
6. Hong Kong 7. Hungary
19
24
34
24
58
16
36
33
15
69
8. India
19
24
26
31
50
9. Iran
17
34
35
14
69
10. Israel
16
31
33
20
64
11. Jamaica
14
39
27
20
66
12. Korea
15
24
34
28
58
13. Malta
16
36
31
16
67
14. Mexico
22
29
28
20
57
15. Philippines
14
33
35
18
68
16. Puerto Rico
Country (1) 1. Colombia
Opposite signs (3)+(. (6) 59
17
36
29
17
65
17. Singapore
19
27
26
29
53
18. South Africa
19
32
29
21
61
19. Sri Lanka
15
31
32
23
63
20. Taiwan
17
35
28
20
63
21. Thailand
12
26
38
25
64
22. Venezuela
24
26
22
28
48
23. Zimbabwe
13
35
36
16
71
Mean
17
31
31
21
62
International Consumption Comparisons
146
falls with increasing income (Mt). This can be written in a linear regression framework as the Working's (1943) model (see equation (3.1) of Chapter 3), wFt = ocF + P F logM t
(3.1)
In Figure 4.2, we plot the of food budget share against the logarithmic of the per capita real consumption expenditure for the 23 LD countries. As can be seen, in all plots (except for Fiji, Hungary and Zimbabwe), the points are scattered around a negatively sloping straight line. Even though the slope for Honduras is negative, as can be seen from the plot, most of the points represent a constant budget share regardless of the income level, indicating that the published data may be unreliable. The overall conclusion of the graphs in Figure 4.2 is that Engel's law is well supported by the LDC data. Table 4.16 presents the estimates for the Working's model parameters ocF and PF for food in each country. As can be seen from column 3, for most countries, all the income coefficient estimates for food are negative and statistically significant. It can also be noted that the positive income coefficient estimates (Fiji, Hungary and Zimbabwe) are all insignificant. The cross-country average of the income coefficient for the LD countries is (3F = -.14 with a standard error of .04. Among the 23 values, Hungary can be considered as an outlier. The average income coefficient, excluding Hungary is -.17. This is very close to the average value of -.20 obtained in Table 3.16 for the OECD data and those from previous studies in Table 3.17. In Figure 4.3a, we pool the data across the 23 LD countries and plot the adjusted budget shares (wFtc - aFc) against the logarithm of income (log Mte) in one graph. However, the points corresponding to Hungary appear to be extreme among the 23 LD countries. In Figure 4.3b, we plot the same graph for 22 LD
147
Chapter 4 Data Analysis: LD countries
Cyprus
Colombia
**
*
0.4
y=-053x+25731 #=0.8176
y=--0.0399X+0.563* # =0.5811
a> Is 0.28 .e (A
"
^
^
•
? 0.26 m
0.36
• ••
nx> 9.4
9.5
6.8
9.6
7
7.2
7.4
7.6
7.8
Log(lncome)
LogQncome)
Ecuador
Fiji y=-0.197x+22256 #=0.6005
o
0.4
y=0.0502x+0.0599 #=0.0356 •
10
•S 0.38
O) "O 3 00
9.1
9.2
9.3
0.36
•
0.34 6.25
9.4
6.3
•
y=-0.1776x +1.9944 #=0.9833
y=-0219x+1.7689 #=0.4947
•
6.45
Hong Kong
Honduras 0.5
6.4
6.35 Log(lncome)
Logflntxme)
0.48 ?0.46 0.44 0.42 5.8
5.85
5.9
5.95 6 LogQncome)
6.05
6.1
9.1
9.3
9.5
9.7
9.9
10.1
10.3
10.5
LogOncome)
Food budget share against logarithm of per capita real consumption expenditure in LD countries
Figure 4.2
148
International Consumption Comparisons
India
Hungary
y=-0.1813x+2.9896 ff=0.8182
0.49 ^0.45 § 0.41 3
0.37
• ,
y=0.6231x-6.1691 rf=0.2409
** 10.54
10.68
10.62
10.66
13.4
13.5
Israel
Iran
y=-0.0988x+1.0016 Pp- 0.8461
" 0.42 Cl> OI •D
y=-0.3807x+1.3689 # = 0.7275
0.32 23
2.4
•
^ » %
2.5
S> 1
Budget shar
«
g
0.47
a 0.37
%u • ?*•
2.6
7.1
6.9
7.3
•
I
i
fe
•
*
•
6.46
7.9
6.56
r]
^ ^ » < #
y=-0£197x+3.4125 r f « 0.9514
#
•S 0.4
•
*
O 0.3 0.2
8
Budget share
*
y=-0.0734x+0,8Sj84 #=0.2001
7.7
Korea
Jamaica
•
7.5
Log(lncome)
Logglncome)
6.36
13.6
Lag(lncome)
Log(lncome)
6.66
13
Log(lncome)
13.5
14
14.5
Log(lncome)
Food budget share against logarithm of per capita real consumption expenditure in LD countries Figure 4.2 (continued)
149
Chapter 4 Data Analysis: LD countries
Mexico
Malta 0.4
1y=-0.1001x+0.6483 Fp=0.6122
y = -0.377x +1.1334
0.25
*
Pf = 0.4449 0.2
2.9
3.1
18
3.3
1.9
2
2.1
2.2
2.3
7.65
7.75
Log(lncome)
Logflncome)
Puerto Rico
Philippines 0.61
I"
y = -0.0959x+1.4513 Ff = 0.2449
•5 0.59 •
m 0.58 0.57
8.95
9
•
9.05
Log(lncome)
Singapore
South Africa
I 0.3
« 0.35
I03
y=-0.1332x+1.3428 R?=0.9376
y=-0.029x+0.5573 I f = 0.0451
0.25
7.2
7.6
8
8.4
8.8
7.25
7.35
7.45
7.55
Logflncome)
LogQncome)
Food budget share against logarithm of per capita real consumption expenditure in LD countries Figure 4.2 (continued)
International Consumption Comparisons
150
Taiwan
Sri Lanka 0.75 I
y = -0.1679x+2.2313 R2 = 0.9688
y = -0.35B8x +3.3603 ^=0.7612
0.7
I-
f" 0.55 0.57.3
7.4
7.5
7.6
7.7
7.8
10.1
7.9
10.6
Thailand
Venezuela y=-0.2877x+2.8429
/ • •
y = -0.3448x+3.6869
R ^ 0.8416
1
r
8.1
8.3
8.5
8.7
8.9
«• *
,
FT"=0.0941 * •
•
•
o
* ^ > v^*"*"<£* ^
m 0.3
11.6
0.45-1 Budget share o o o
• £ 0.5
11.1
Log(lncome)
Log(lncome)
0.3 J
9.1
9. 53
Logflncome)
9.57
9.61
9.65
Log(lncome)
Zimbabwe y = 0.0079)(+0.2903 R?=0.0029
5.4
•
5.6
5.8
Log(lncomB)
Food budget share against logarithm of per capita real consumption expenditure in LD countries Figure 4.2 (continued)
151
Chapter 4 Data Analysis: LD countries Table 4.16 Estimates of Working's model for 23 LD countries (Standard errors are in parentheses) Country
Intercept a x 1000
(D
(2)
1.
Colombia
2.
Cyprus
3. 4. 5. 6.
Ecuador Fiji Honduras Hong Kong
7. 8. 9.
Hungary India Iran
10. Israel 11. Jamaica 12. 13. 14. 15. 16.
Korea Malta Mexico Philippines Puerto Rico
17. Singapore 18. South Africa
2.573 (0.238) 0.563 (0.069) 2.226 (0.345) 0.060 (0.459) 1.769 (0.398) 1.994(0.046) -6.169 (3.706) 2.990 (0.308) 1.369 (0.175) 1.002 (0.063) 0.898 (0.266) 3.412 (0.149) 0.648 (0.057) 1.133(0.168) 1.451 (0.458) 1.290 (0.121) 1.343 0.557 3.360 2.231 2.843
(0.050) (0.172) (0.344) (0.056) (0.251)
Income coefficient P> (3) -0.230 (0.025) -0.040 (0.009) -0.197 (0.037) 0.050 (0.072) -0.219 (0.067) -0.178 (0.005) 0.623 (0.350) -0.181 (0.023) -0.381 (0.070) -0.099 -0.073 -0.220 -0.100 -0.377 -0.096 -0.142
(0.009) (0.041) (0.011) (0.019) (0.081) (0.051) (0.017)
-0.133 (0.006)
(4) 0.82 0.58 0.60 0.04 0.49 0.98 0.24 0.82 0.73 0.85 0.20 0.95 0.61 0.44 0.24 0.70 0.94
(0.023) (0.045) (0.005) (0.029)
0.84
23. Zimbabwe
3.687 (3.246) 0.290 (0.251)
-0.345 (0.338) 0.008 (0.044)
0.09 0.00
Mean
1.370 0.407
-0.138 (0.043)
0.56
19. 20. 21. 22.
Sri Lanka Taiwan Thailand Venezuela
-0.029 -0.359 -0.168 -0.288
R2
0.05 0.76 0.97
International Consumption Comparisons
152
y =-0.1482x +0.0722
I, -1 o £ -3
Log(lncome)
Food budget share vs Log(lncome) for pooled data from 23 LD countries Figure 4.3a
I 3 -3 y = -0.2155x +0.3956 -4
Log(lncome)
Adjusted food budget vs log(lncome) for pooled data from 22 LD countries (excluding Hungary) Figure 4.3b
153
Chapter 4 Data Analysis: LD Countries
countries (excluding Hungary). As can be seen, the points are scattered around a downward sloping straight line with slope |3F = -.22. This estimate is very close to the cross-country average (excluding Hungary) of (3F = -.17 discussed above.
4.4
Preliminary Estimates of Income and Price Elasticities
In this section, we use double-log demand equations to obtain preliminary estimates for the income and price elasticities for the LDC data. In Chapter 9, we use the differential demand systems, derived in Chapter 2, to obtain final estimates for the demand elasticities and then compare the two sets of estimates. We consider the double-log demand equation (2.4) given in Chapter 2 for commodity i in finite-change form Dqit = Oi + y], DQt+ydDpit-DPt]
+ek,
i=l,...,n,
(4.1)
where oc; is an autonomous trend term; r\\ is the income elasticity of commodity i; V; is the Slutsky own-price elasticity; and 6it is a disturbance term. It is worth noting that this double-log demand equation includes only the ownrelative price and not other prices. We estimate (4.1) by least squares (LS) for each country separately. Tables 4.17 and 4.18 present the estimates for the income elasticity (r|j) and own-price elasticity (y,), respectively, for each commodity for the 23 LD countries. The last row of the table presents the mean elasticities for each commodity averaged over the 23 countries. As can be seen from Table 4.17, all the income elasticites are positive. The elasticities in column 2 for food in all countries (except for Philippines and
154
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Chapter 4 Data Analysis: LD Countries
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156
International Consumption Comparisons
Zimbabwe) are less than one indicating that food is a necessity in the remaining 21 LD countries. The average value of the income elasticity for food in the LDC is .7. On average, the income elasticities for clothing, durables, transport, recreation and education are larger than one indicating that these commodities are luxuries in the LD countries, while the income elasticities for housing and medical care are less than one indicating that they are necessities. This result is in line with the known phenomenon that consumers in poor countries tend to spend most of their income on life's necessities for survival, food, shelter and health care. In Table 4.18, most of the own-price elasticities (170 out of 187) are negative as they should be. On average, all the price elasticities are negative and less than one in absolute value, indicating that demand for all 9 commodities in the LD countries are price inelastic.
4.5 Preliminary Estimates of the Income Flexibility In this section, we present five sets of estimates for the income flexibility. In Section 3.5, we derived the first four sets of estimates and presented the estimates for the OECD data. In Table 4.19, we present the estimates for the LDC data. The first set of estimates is based on the regression results from equation (5.2) of Chapter 3. For each country, we obtain the estimates of (> | for i=l,..,«, and calculate the average <j>, which we refer to as an unrestricted average estimate of the income flexibility. These estimates (<j)) for the 23 countries are reported in column 2 of Table 4.19. Figure 4.4 presents the plots for the pooled data for (Dqit - DQt) against (Dpit - DPt), t=l,...,T and i=l,...,n for each LD country. As can be
Chapter 4 Data Analysis: LD Countries
157
Table 4.19 Four sets of estimates for income flexibility in 23 LD countries (x100) Income flexibility Country (1) 1. Colombia 2. Cyprus 3. Ecuador 4. Fiji 5. Honduras 6. Hong Kong 7. Hungary 8. India 9. Iran 10. Israel 11. Jamaica 12. Korea 13. Malta 14. Mexico 15. Philippines 16. Puerto Rico 17. Singapore 18. South Africa 19. Sri Lanka 20. Taiwan 21. Thailand 22. Venezuela 23. Zimbabwe Mean
Unrestricted
Restricted
Divisia
Divisia Average
(2) -0.33
(3) -0.27
-0.59 -0.19 -0.59 -1.92
-0.88 -0.16 -0.68
(4) -0.25 -0.04 -0.13 -0.64
(5) -0.21 0.11 -0.11
-0.63 -0.33
-0.86 -0.44
-0.11
-0.51
-0.25
-0.43 -1.00 -0.41 -0.97 -0.22 -0.40 -0.10 -0.12 -0.65
-0.25 -0.67
-0.23 -0.69 -0.28 -0.54 -0.09
-0.23 -0.28 -0.17 -0.73 -0.38 -0.85 -0.22 -0.59 -0.14 -0.16 -0.66 -0.26 -0.51 -0.63
-0.25 -0.46 -0.65 -0.27
-0.29 -0.30 -0.23 -0.78
-0.29 -0.23 -1.32
-0.48
-0.38
-0.30 -0.54 -0.04 -0.69 -0.07 -0.22 -0.96 -0.20 -0.50 -0.44 -0.32 -0.60
-0.62 -3.17 -0.23
-0.53 -0.08 -0.17 -0.77 -0.23 -0.43 -0.39 -0.20 -0.36 -0.12
-0.23 -1.24
-1.13
-0.44
-0.47
International Consumption Comparisons
158
Colombia i
Cyprus |
ge-i
6^n
• MM 0
-15 • -10 •
**SJ JO
1/ f
10
t •
15
4
•
"9
oo-
I
-20
t **
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y = -0.1564x+0.3169
Fiji
F*^"*"^
-20' aa.
Relative quantity
0
J*
«
g^j Relative price
Ecuador
•
6
•
Relative price
1
"
-201
*
y = -0.8835x+1.1599
•
y =-0.2712x- 0.085
•
•
•
0
40
* ^ • * * ' Til
-20
-40H
y=-0.6766x+0.1611 Relative price
Relative price
Hong Kong
Honduras -88-
•£ -:o -40 y=-0.6273x +0.4572
y = -0.3341x+0.159
8S-
-39Relative price
Relative price
Relative quantity against relative price in LD countries Figure 4.4
•
i J •
'
}
159
Chapter 4 Data Analysis: LD Countries
India
Hungary
y = -0.4Z76x+1.046
Relative price
Israel
Iran y=-1.0048x + 0.84
!)
Rel itive quant ty
30
y=-0.4076x + 0.3315
• •
^
« V»
-40
»' "JtlBt* 3 i i B K A *40'
^•w*Jk 0
•
ii. 60
n
-20
» Relative price
Relative price
Korea
Jamaica
a&_ • *
0
-10 •
•
15«k*\
K$~
JW
-%-
•
•
y = -0.2229x+1.1942 4 asRelative price
Relative price
Relative quantity against relative price in LD countries Figure 4.4 (continued)
:3
160
International Consumption Comparisons
Mexico
Malta _
30y=-0.1031x+0.0759
quaritity
4
•
a> | - 0
- m
*
"i ' ^ M i i 1 * -20 # • ^ » 5 * > 20
*•
11 ** ' D
•-10'
CC
39Relative price
Relative price
Puerto Rico
Philippines y = -0.1221x+0.0709
Relative price
Relative price
South Africa
Singapore
y = -0.463x+0.1032
•
2*
-8
•
*-4^BP
fry ?_ wrst/*-
2
Relat ve quant ty
Relative quantity
y=-0.253x+0.3116 20*
•
so l 20-
• ^ ^ 1 * * ' 5
-15
•J
Relative price
Relative price
Relative quantity against relative price in LD countries Figure 4.4 (cont.)
*
l . C T ' V ^
!5
161
Chapter 4 Data Analysis: LD Countries
Taiwan
Sri Lanka
46 y=-ft2742x+!5009
y=-0.$485x+1.0031
30
•40-
5 -!0
-25 is
:5
Relative price
Venezuela
Thailand .
2S_
•
Rekitive quantity
y=-0.2S05x+1.1942 20-
A •
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0
- * < ^ -10-
•
5
w
-17
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• S ^ ' * ' 13 " ~ ' • - . •
-20 y=-0.2274x+0.1909 • 89Relative price
Relative price
Zimbabwe y=-1.3186x-0.0758
SS
-BBRelative price
Relative quantity against relative price in LD countries Figure 4.4 (continued)
••
• :
4 •
International Consumption Comparisons
162
seen from the plots, the points are scattered around a negatively sloping line. The slope of the regression lines can also be interpreted as (|). These restricted estimates of <)| for each country are presented in column 3 of Table 4.19. Even though the values of the estimates given in columns 2 and 3 vary widely, all these values have the correct (negative) sign. The overall average value of the income flexibility estimate is about -.5 (column 2) and -.4 (column 3), which agrees with the income flexibility estimates found in most of previous empirical studies. Another method of obtaining an estimate for <>| is using the relationship (5.5) of Chapter 3,
* = v Column 4 of Table 4.19 gives the value of these (J) values averaged over t=l,...,T for each country. The income flexibilities are all negative with an average of -0.44. The last set of estimates for the income flexibility <() are calculated using the relationship derived in equation (5.6) of Chapter 3,
•
.
I. n
Column 5 of Table 4.19 gives these (j) values for each country. As expected, all the estimates of (j> (except for Cyprus) are negative. Apart from Honduras and Zimbabwe, the income flexibilities are close to the average value of -.47. The average values of the four sets of estimates presented in the last row of Table 4.19 are consistent with the OECD results in Section 3.5 and previous findings.
163
Chapter 4 Data Analysis: LD Countries
Clothing
Food
>
*
•
• °
-1
•
•_,
•
• i
#
1
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• •
—
•
•
• (f
>
•
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-3 •
•
*
• »
•
y=-0.2257x-0.7022 6Relative Price
Housing •
Durables 4-
•
s
3- •
*
* 2 -
r*T^f*i« r 0
•
**~ -2 • • -4- •
••
• -3»y = -0.1357x-1.3443 Relative Price
-5
»•
• ^ '
y = -0.1042x +0.5708
'•
•
•
•
a
Relative consum
Relative consumption
. •
y =-0.5221 x + 0.5876
4*
»
3-
> • • t
-2 •
^
"^•^
•
. , ] . %
^
"
•
Relative price
Realtive price
Medical care
Transport
Relative price
Relative price
Relative consumption vs relative prices for 9 commodity groups Figure 4.5
^
•
International Consumption Comparisons
164 Recreation
Education •
8 |
*
y=J0.9492x+0.4134 4-
-4•
.^*»>«.' • •
1
_aJ Relative price
;
; — : — i —
Relative price
Miscellaneous
* •
y=*^.i952x+1.0968
3
•V".
2<
« •
i*
•
4*
»
•
2
3 •
Relative price
Relative consumption vs relative price for 9 commodity groups Figure 4.5 (continued)
Next, for each commodity i (=1,...,9), we plot the relative consumption (Dq[ -DQC) against the relative price (Dp- -DPC), c=l,...,23, using the relative consumption and relative price values from Tables 4.12 and 4.13. Figure 4.5 gives the plots for the 9 commodity groups. The resulting slope of the regression line is an estimate for <> | . As can be seen, in all plots, all the points are scattered around a downward sloping straight line. In Table 4.20, we present
165
Chapter 4 Data Analysis: LD Countries
Table 4.20 Another set of estimates of $ for the LD countries Commodity 1. 2. 3. 4. 5. 6. 7. 8. 9.
Food Clothing Housing Durables Medical care Transport Recreation Education Miscellaneous
Mean
Income flexibility -.14 -.23 -.10 -.52 -.46 -1.39 -.27 -.95 -.20 -.47
the resulting estimate of <> | for each commodity group. As can be seen, the overall average for the 9 commodity groups is
4.6
Testing the Frisch 's Conjecture
In Section 3.6, we used the data from the affluent countries, like the OECD countries, to test the validity of Frisch's conjecture. In this section, we use data from the poorer countries, like the LDC, to verify whether Frisch's conjecture is supported by the data. In a nutshell, Frisch (1959) states that the income flexibility (> | increases in absolute values as the consumer (or country) becomes more affluent.
International Consumption Comparisons
166
As in Section 3.6, we use the estimates of <>| presented in Table 4.20 together with the real GDP per capita (in US dollars) presented in Table 1.2. We estimate a relationship of the form, df
=
X + \iyc + ec,
where A, and n are parameters to be estimated; the superscript c denotes country c; yc is per capita real GDP (in international dollars) of country c; and ec is an independent disturbance term with zero mean. The F-test statistic value for the null hypothesis that, H0: u, = 0 and the corresponding p-value with respect to columns 2-5 of Table 4.19 are (F = 2.34; p-value = .14), (F = .64; p-value = .43), (F = 1.33; p-value = 0.26) and (F = 2.75; p-value = .11), respectively. As, for all columns, the level of significance a = 0.05 < p-value, we are unable to reject the null hypothesis, H<,: \i = 0. As none of the F-values are significant, we conclude thattyis independent of real income. The finding that <j) is unrelated to real income is, of course, at variance with Frisch's (1959) conjecture. However, our rejection of Frisch's conjecture is well in agreement with a number of previous studies (e.g. Clements and Theil, 1996; Selvanathan, 1993; Theil, 1980; andTheil, 1987).
4.7
The Validity of Preference Independence
In Chapter 2, we showed that the assumption of preference independence leads to an attractive simplification of demand equations and that under preference independence, own-price elasticities (riu) are proportional to income elasticities (r|i) with <j) being the factor of proportionality. In Chapter 3, we also used the OECD data to provide evidence of this proportionality relationship. In this
167
Chapter 4 Data Analysis: LD Countries
section, we use the LDC data to provide more evidence on the proportionality relationship of the two elasticities. To analyse the evidence on the proportionality relationship, r^ = (pr|i, we use the income and price elasticity estimates presented in Tables 4.17 and 4.18. Figure 4.6 plots the own-price elasticities (r|ii) against the corresponding income elasticities (r|i) and the solid line on the plot is the least-squares line. The points are scattered around a negatively sloping line and the location of the points give evidence that luxuries tend to be more price elastic. The estimate of the factor of proportionality is -.35, which is not far from the estimates of (j) presented in Table 4.19. The significance of the factor of proportionality provides indirect evidence to the preference independence hypothesis. This finding is in agreement with that for the OECD data in Section 3.7. We shall come back to formally testing the hypothesis of preference independence in Chapter 9.
y = -0.3494X
*
Price elasticity
1 •
•
.5
•
*
*
•
'
.
2S
•wv^r^fgaa^, -1-
-2
.
• *
• • * • * . * • • • »
i .
•
'' n • •
~.
3 5
• * ^ ^ ~ * " ~ « .
« • • Income elasticity
Own-price elasticity against income elasticity Figure 4.6
168
International Consumption Comparisons
References Brozdin, R. (1988). 'LDC's Consumption: A Database Update,' Unpublished manuscript, Department of Economics, The University of Western Australia. Chen, D.L (2001). World Consumption Economics. Singapore, London: World Scientific. Clements, K.W., and H. Theil (1996). 'A Cross-Country Analysis of Consumption Patterns,' Chapter 7 in H. Theil (ed.), Studies in Global Economics. Advanced Studies in Theoretical and Applied Econometrics. Boston: Kluwer Academic Publishers, pp.95-108. Frisch, R. (1959). 'A Complete Scheme for Computing All Direct and Cross Demand Elasticities in a Model with Many Sectors,' Econometrica 27: 177-196. Theil, H. (1980). The System-Wide Approach to Microeconomics. Chicago: University of Chicago Press. Theil, H. (1987). The Economics of Demand Systems,' Chapter 3 in H. Theil and K.W. Clements (eds.), Applied Demand Analysis: Results from System-wide Approaches. Cambridge, MA.: Ballinger Publishing Company. Selvanathan, S. (1993). A System-wide Analysis of International Consumption Patterns. Advanced Studies in Theoretical and Applied Econometrics. Boston: Kluwer Academic Publishers. Working, H. (1943). 'Statistical Laws of Family Expenditure,' Journal of the American Statistical Association 38: 43-56.
CHAPTER 5 A Comparison of Consumption Patterns in the OECD and LD Countries E.A.. Selvanathan & S. Selvanathan
In Chapters 3 and 4, we presented preliminary data analysis of the two groups of countries, the OECD and LDC, individually. In this chapter, we present a comparison of the results. The OECD consumers are from high-income, highly industrialized countries and the LD consumers are from low-income, developing countries. Therefore, a comparison of the results from the OECD data in Chapter 3 with those from the LDC data in Chapter 4 would be able to capture the similarity and contrast in the consumption patterns among the high-income and low-income consumers of the various commodity groups. The combined data consists of 46 countries with varying income levels, the results presented in this chapter will be applicable to the consumption patterns of a typical 'world' consumer. In Section 5.1, we present various summary measures for the OECD and LD countries individually as well as all 46 countries combined representing the world consumers. In Section 5.2, we revisit the empirical regularities in consumption patterns, such as the law of demand, Engel's law, preference independence etc using the combined 'world' consumption data. Finally, in Section 5.3, we present our concluding comments.
170
5.1
International Consumption Comparisons
Summary Measures
In Table 3.3 and Table 4.3, we presented the average budget shares of the 9 commodity groups for the 23 OECD and 23 LD countries, respectively. In columns 2 and 3 of Table 5.1, we reproduce the average budget shares of the 9 commodity groups (averaged over the OECD and LD countries, respectively) and the corresponding standard deviations from the last row of Tables 3.3 and 4.3, respectively. Column 3 gives the budget shares for all 46 countries combined (we label this column as 'World'). In Figure 5.1, we present these budget shares in a bar-graph form. As can be seen, the LDC consumers allocate about one and a half times that of the allocation of OECD consumers of their income on food. This observation on food budget share supports the Engel's law discussed in Sections 3.3 and 4.3 that the budget share for food is lower for the higher income group compared to the lower income group. Furthermore, the variability of food budget share among the LD countries is almost twice that of the OECD countries, reflecting the higher variability on the food consumption patterns among the LD countries compared to the OECD countries. Both OECD and LDC consumers allocate about the same proportion of their income on clothing and durables. OECD consumers allocate more of their income on goods such as housing, medical, transport and recreation than the LDC consumers. On average, the world consumers allocate about one-third of their income on food; 8 percent of their income on clothing, 15 percent of their income on housing, 8 percent on durables, 5 percent on medical, 12 percent on transport, 7 percent on recreation, 1 percent on education and the remaining 12 percent on all other things. Comparing the standard deviations across commodities, one could observe more variability among the food budget shares than any other commodity groups.
Chapter 5 A Comparison of Consumption Patterns
171
Table 5.1
8
1
38.21 (9.65)
8.07(1.49)
8.57 (3.08)
Durables Medical Transport Recreation Education
17.21 (3.48) 8.51 (1.68) 5.00 (3.02)
12.26(5.29) 8.16(2.81) 3.94(1.57)
13.63(2.01) 7.45(1.69) 1.11 (0.88)
10.42(4.03) 5.43 (2.90)
Miscellaneous
12.44(3.00)
32 7 3 ( 9 98) 8 3 7 ( 2 42) 14 8 9 ( 5 05) 8 3 7 ( 2 29) 4 6 8 ( 2 49) 12 15(3 52) 6 5 2 ( 2 51) 1 2 7 ( 0 85) 12 15(4 77)
1.45(0.80) 11.57(6.10)
HOBCD HLDC
"O
O)
LL
IE o
o
X
o o
O)
cs o
•t?
C3
0)
CO
Z5
«>
(/) Q
o c
2?
Com rnociity
c .2 CD Q
0)
c •S
15 o
w
iscella neou
8 7
m
27.08 (5.64)
Edu
3 4 5
Food Clothing Housing
Dusin
1 2
Average budget shares ©f 9 commodities: OECD and LD countries (at sample means x 100) Country OECD countries LD countries World (!) (2)
2:
Average budget shares of 9 commodities, OECD vs LDC Figure 5.1
172
International Consumption Comparisons
Columns 2 and 3 of Table 5.2 reproduces the average consumption growth for the OECD and LDC from Tables 3.4 and 4.4. As can be seen, the consumption of food, medical care and transport grew at a faster rate in the OECD compared to the LD countries. In contrast, the consumption of clothing, durables and education grew at a slower rate in the OECD countries compared to the LD countries. The growth in consumption of housing and recreation is very similar across the OECD and LD countries. Column 4 of Table 5.2 presents the average growth in consumption for all countries. As can be seen, in all countries, on average, the consumption growth is higher for medical care, transport (which includes communications) and recreation. In columns 2 and 3 of Table 5.3 we reproduce the average growth in prices from Tables 3.5 and 4.5 for the OECD and LDC, respectively, and in column 4 we present the corresponding growth in prices for all 46 countries combined. A comparison of the price increases in columns 2 and 3 reveals that the prices for all commodity groups in the LD countries grew at a rate twice that of the OECD countries. Figures 5.2 and 5.3 present these summary statistics for the growth rates in consumption and prices, respectively, for the OECD and LD countries. In Table 5.4, we reproduce the mean Divisia measures presented in the last row of Tables 3.11 and 4.11 for the OECD and LDC, respectively, and present the corresponding values for all 46 'world' countries combined. As indicated by rows 1 and 2, while overall consumption, on average, grew at a slightly higher rate in the OECD compared to the LD countries, prices in the LD countries grew at a faster rate (almost twice) than those in the OECD countries. The overall world consumption grew at a rate of 2.2 percent per annum and the overall world prices grew at a rate of 10 percent per annum. As observed with the individual countries and over time, the Divisia quantity variance exceeds that of the price variance for OECD, LDC and the world as a whole. The Divisia price-quantity correlation is also negative for both the OECD and the LDC with
173
Chapter 5 A Comparison of Consumption Patterns Table 5.2 Average per capita quantity consumed of 9 commodities in OECD and LD countries (Mean log-changes x 100) Country 1. 2. 3. 4. 5. 6. 7. 8. 9.
(1) Food Clothing Housing Durables Medical Transport Recreation Education Miscellaneous
OECD countries (2) 1.07 1.21 2.71 2.27 3.41 3.63 3.89 2.64 2.59
LD countries (3) 0.74 1.56 2.71 2.87 3.29 3.08 3.83 2.88 2.92
World (4) 0.90 1.39 2.71 2.57 3.35 3.36 3.86 2.73 2.76
Table 5.3 Average prices of 9 commodities in OECD and LD countries (Mean log-changes x 100) Country
(D
OECD countries
LD countries
World (4) 10.00
1. 2.
Food Clothing
(2) 6.43 6.29
(3) 13.58 12.77
3. 4.
Housing Durables
7.90 6.12
13.11 13.17
5. 6. 7. 8. 9.
Medical Transport Recreation Education Miscellaneous
7.57
14.52
6.76 6.59 9.67 7.81
13.83 12.28 15.30 14.20
9.53 10.51 9.64 10.97 10.29 9.31 11.92 11.01
a world average of -.3, reflecting the tendency of the consumer to move away from those commodities having above-average price increases.
International Consumption Comparisons
S &
5
£
4
£ 3 -f ~
| 2\
-^ •»-mm™~mmt~~mm—-^—
•«-,•-. i ^ Q B D I
^ ^ » B-H-JH~m4B IK
ULDC
I 1 1 S o
~Q
O)
O)
CO
_
*
„
a. -S
Commodity
Average quantity log-changes in OECD and LD countries Figure 5.2
I OECD 1LDC
Commodity
Average price log-changes In OECD and LD countries Figure 5.3
175
Chapter 5 A Comparison of Consumption Patterns Table 5.4 Divisia moments in OECD and LD countries (at sample means) Country
Divisia quantity index
Divisia price index
Divisia quantity variance
Divisia price variance
Divisia price-quantity correlation
DQ
DP
K
n
P
(2)
(3)
(4)
(5)
(6)
1. OECD countries
2.34
6.94
12.09
10.08
-0.18
2. LD countries
2.09
13.52
37.18
26.59
-0.33
3. World
2.22
10.23
24.64
18.33
-0.26
(1)
All entries in columns 2 and 3 are to be divided by 100 and columns 4 and 5 by 10000.
5.2
Empirical Regularities
In Chapters 3 and 4, we observed a number of empirical regularities in the consumption patterns using the OECD and LDC data individually. In this section, we investigate them by combining the OECD and LDC databases, giving 46 countries of the world with varying income levels. Price and Quantity Variances
In Figure 5.4, we plot the quantity standard deviation, yJKf, against the price standard deviation,-y/n^, for t=l,...,T and c=l,...,46. As can be seen, most of the points lie above the 45° line indicating that, on average, ^Kct >-y!I(c. This shows that the Divisia quantity variances generally exceed the Divisia price variances.
176
International Consumption Comparisons
Quantity vs price standard deviations, 46 countries Figure 5.4
Law of Demand
Table 5.5 summarizes the frequency distribution of the joint signs of relative prices and consumption. Both in the OECD and LDC, relative prices and consumption move in the opposite directions about 60 percent of the time. We investigate further, the movement of relative consumption (Dqf - DQc) and relative prices (Dpf - DPc), by plotting these two variables for each commodity group across the OECD and LD countries combined. In Figure 5.5, we plot the relative consumption (Dqf - DQc) against the relative price (Dpf -DPC) for each commodity i (=1,...,9), by pooling the data from the 46 (OECD and LDC) countries. As can be seen, in all plots, the points are scattered around a negatively sloping straight line. This clearly supports the law of demand. Furthermore, the slope of the regression line in each plot can be interpreted as an estimate for the own-price elasticity of that
111
Chapter 5 A Comparison of Consumption Patterns Table 5.5 Average frequencies of joint signs of relative consumption and relative price changes in OECD and LP countries (in percentages) Country
Positive consumption
Negative consumption
Opposite signs
Positive price Negative price
Positive price Negative price
(3)+(4)
_£D
m
(3)
(4)
(5)
(6)
1. OECD countries
19
31
29
20
60
2. LD countries
17
31
31
21
62
3. World
18
31
30
21
61
Relative consumption vs relative price in 46 countries Figure 5.5
International Consumption Comparisons
178
Transport
*
y = -0.4732x + 1.4659 Pt on
Relative consumption
Medical care
•
^ ^ ^ »
(A C
• i
-2
• -2-
i
O
•2. TVe
to
«4-
^^^^^•r * «3 •f
E
-2
•
Education
1
*~
y=-G.606x + 0.9661
•
* ••
4
4 •
•' 7,
Relative consumption
•
Relative price
y = -0.2644x+1.4562
-3
• 2 * " > ^
-8 y = -1.1058x + 1.2068
Recreation
-6
•
1 •
> O
Relative price
J
•
-4-
CC
•
», |
I1
* 1
• ' ''
(I
•
•
'
2
•>
•
-4-
•
3
• nj
:
Relative price
Relative price
Miscellaneous
*
y = -0»0777x + 0.6559
•
3-
*
• 2 -,
•
• ••*%.• .5
-0.5 • «.5 *#>* 1.5 -1 -
•
• 2.5
3
n Relative price
Relative consumption vs relative price in 46 countries Figure 5.5 (continued)
». •
••
Chapter 5 A Comparison of Consumption
Patterns
179
commodity group or as an estimate of income flexibility under the assumption of preference independence and unitary income elasticity. Table 5.6 presents the estimates of income flexibility for the pooled data based on the plots in Figure 5.5. As can be seen, the overall average for the 9 commodity groups is 0 = -.40, which very close to the values obtained in a number of previous studies as well as those obtained in Chapters 3 and 4. Engel's Law
One of the empirical regularities considered in Chapters 3 and 4 is the Engel's law, which states that the budget share for food falls with increasing income. In Figure 5.6, we plot the budget share for food (wFt) against the logarithmic of the per capita real consumption expenditure (log Mt) for 22 OECD and 22 LD countries. (As Iceland and Hungary were found to be outliers, we have excluded these countries.) As before, the points are scattered around a negatively sloping straight line. The slope of the least-squares regression line is -.248, which is very close to the individual group values of -.245 for OECD (Figure 3.3b) and -.216 for LDC (Figure 4.3b). Clearly, the overall conclusion of Figure 5.6 is that Engel's law is well supported by the data from the 44 countries.
Validity of Preference Independence
In Tables 5.7 and 5.8, we reproduce the average income and own-price elasticities from Chapters 3 and 4 obtained using a double-log demand system. In all countries, food, housing, medical care and education are necessities (that is, income elasticity less than one) while clothing, durables, transport and recreation are luxuries (that is, income elasticity greater than one). On average, all the own-price elasticities are negative as they should be and all of them are
International Consumption Comparisons
180
Table 5.6 Estimates for <> j for the 9 commodities in 46 countries Income flexibility
Commodity 1. 2. 3. 4. 5. 6. 7. 8. 9.
Food Clothing Housing Durables Medical care Transport Recreation Education Miscellaneous
-.20 -.34 -.11 -.44 -.47 -1.06 -.26 -.61 -.08
Mean
-.40
H!
-1
qpoo
O) •o 3
-2
1
-3
= V
-4
to y = -0.2475x +0.5214 -5
Log(lncome) Adjusted food budget share vs the logarithm of income Pooled data from 44 countries Figure 5.6
181
Chapter 5 A Comparison of Consumption Patterns
Table 5.7 Average income elasticities of 9 commodities in OECD and LD countries* LD countries OECD countries (3) (2) 0.72 0.60 1. Food 2. Clothing 1.41 1.51 0.62 3. Housing 0.50 4. Durables 1.59 1.44 0.77 5. Medical 0.67 1.90 1.43 6. Transport 7. Recreation 1.16 0.99 0.57 8. Education 1.01 9. Miscellaneous 1.36 1.15 * Based on double-log demand equation with no constant. Country
(D
World (4) 0.66 1.46 0.56 1.52 0.72 1.66 1.08 0.79 1.25
Table 5.8 Average own-price elasticities of 9 commodities in OECD and LD countries* Country
LD countries OECD countries (2) (3) (D -0.22 1. Food -0.36 2. Clothing -0.43 -0.79 -0.17 -0.35 3. Housing 4. Durables -0.24 -0.43 -0.27 5. Medical -0.40 -0.39 -0.41 6. Transport 7. Recreation -0.44 -0.65 -0.23 -0.64 8. Education -0.40 -0.31 9. Miscellaneous * Based on double-log demand equation with no constant.
World (4) -0.29 -0.61 -0.26 -0.33 -0.33 -0.40 -0.54 -0.43 -0.36
International Consumption Comparisons
182
also less than one in absolute value for both OECD and LD countries. This indicates that in all countries, demand for all consumer goods is price-inelastic. In Figures 5.7 and 5.8, we plot the income elasticities and price elasticities for the 9 commodities using the average OECD vs LDC estimates, respectively. As can be seen, the points are scattered very close to the 45° line for income elasticities with correlation coefficient r = 0.86, and the points are mostly away from the 45° line for own-price elasticities with correlation coefficient r = 0.44. This shows that the income elasticities in OECD and LDC are highly positively correlated while the own-price elasticities in OECD and LDC are also positively correlated but less strongly. In Chapters 3 and 4, we discussed an informal method of testing the validity of the preference independence of the utility structure using the plot of the income elasticities against the own-price elasticities. If preference independence holds, then the own-price elasticities will be proportional to the income elasticities, with the income flexibility <>| being the factor of proportionality. In Figure 5.9, we plot each pair of the income elasticities (r|j) against the own-price elasticities (r|ij) for the 46 countries combined from Tables 3.18, 3.19, 4.17 and 4.18 and the solid line is the least-squares line. The points are scattered around a negatively sloping line giving support to the validity of preference independence for the world consumption data. The estimate of the factor of proportionality <]) is -.31, which is very close to the previous estimates presented in Chapters 3 and 4.
5.3
Conclusion
In this chapter, we presented a comparison of the results of the preliminary data analysis presented in Chapters 3 and 4 for the OECD and LD countries,
Chapter 5 A Comparison of Consumption Patterns
183
1.6
g
1.2
^
^
•
y=x
•
0.8 •
0 4-
0.4
1.4
0.9 0 E C D
1.9 Correlation = 0.86
Income elasticities of 9 commodities: OECD vs LDC Figure 5.7
-( .5
-0.4
-0.3
-( '.1
-0^—
-0.3 -
•
LDC
y =x
•
•
•
• -0.5 -
•
•
-0.7 -
« OECD
Correlation = 0.44
Own-price elasticities of 9 commodities: OECD vs LDC Figure 5.8
International Consumption Comparisons
•price elasticities
184
% o
1
y = -0.3054x
•
•
.
-1 " ^ f ^ ^ ^ - ' •. •
-2 •
*
r
• •*
•
•i
Income elasticities Income elasticities vs own-price elasticities for 9 commodities in 46 countries Figure 5.9
respectively. A comparison between the results of Chapters 3 and 4 showed that, while some differences exist between the consumption patterns of the OECD and the LDC consumers, there are more similarities in the consumption patterns of the two groups of consumers. In terms of income allocation, compared to the LDC consumers, OECD consumers allocate a lesser proportion of their income on food and more on housing, medical care, transport and recreation. The higher allocation of income on food of the low-income LD consumers compared to the high-income OECD consumers supports the Engel's law. Overall prices of consumer goods in the LD countries have increased at a rate almost twice that of their OECD counterparts. A number of empirical regularities also emerge from the data analysis of the two groups of countries; namely,
Chapter 5 A Comparison of Consumption Patterns (i) (ii) (iii) (iv) (v)
(vi)
185
Consumption patterns of both groups of countries support the Law of Demand; Quantity variance systematically exceeds the price variance; Budget share for food decreases when the consumer becomes more affluent; Consumer behaviour in both groups of countries gives tentative support for a preference independent utility structure, Food, housing, medical care and education appear to be necessities, while clothing, durables, transport and recreation are luxuries in both groups of countries, The demand for all consumer goods is price inelastic in both OECD and LD countries.
This page is intentionally left blank
CHAPTER 6 Stochastic Price and Quantity Index Numbers E.A. Selvanathan & S. Selvanathan
In the previous chapters, we have concentrated on utility-based demand analysis. As is well-known, the utility function can also serve as the basis for true-cost-of-living indices. This is known as the functional approach to index number theory, whereby the form of the index is related to the underlying utility function (see Diewert, 1981, for a survey). An alternative to the functional approach is the stochastic approach, whereby the proportionate change in each individual price is taken to be equal to the underlying rate of inflation plus other components, which are random and non-random. If we have n prices, then the rate of inflation can be estimated by taking some form of average of the n price changes. The stochastic approach can be viewed as a signal extraction problem. To illustrate, consider the simplest case whereby each of the n proportionate price changes is the sum of the underlying rate of inflation and an independent random component. Here each observed price change is a reading on the rate of inflation 'contaminated' by the random term. The averaging of the price changes serves to eliminate as much as possible of the contamination and leaves an estimate of the underlying signal, the rate of inflation. Although the stochastic approach is less well known than the functional approach, it has a long history going back to Edgeworth (see Frisch, 1936, for
188
International Consumption Comparisons
references). In addition, this approach has recently attracted renewed attention (Balk, 1980; Clements and Izan, 1981, 1987; Crompton, 2000; Diewert, 1995; Rao and Selvanathan, 1991, 1992, 1996; Rao, Doran and Selvanathan, 2002; Rao, Selvanathan and Pilat, 1995; Selvanathan, 1989, 1991, 1993, 2002; Selvanathan and Rao, 1992a, 1992b, 1994; Selvanathan and Selvanathan, 2003; and Theil et al, 1981). The attraction of the stochastic approach is that it provides standard errors for the price indices. These standard errors increase with the degree of relative price variability. This agrees with the intuitive notion that when the individual prices move very disproportionately, the overall rate of inflation is less well defined. The availability of the standard errors allows us to construct confidence intervals for the true rate of inflation. These interval estimates can be used in practical situations (e.g., wage negotiations). Many of the results in this chapter are derived exclusively with prices. However, the methodology could equally well be applied to quantities and be used for the measurement of real income, total factor productivity, and so on. The framework could also be used to test the purchasing power parity hypothesis (see Miller, 1984) and to extend the analysis of Divisia monetary aggregates (Barnett, 1981, Section 7.11). In this chapter, we apply the stochastic index numbers to measure the price and quantity movements in the OECD and LD countries. The organisation of this chapter is as follows. In Section 6.1, we develop unweighted indices and in the following four sections, we develop weighted indices using the stochastic approach. In Section 6.6, we present an extension together with an empirical application. Then, in Section 6.7, we apply the stochastic approach to price and quantity data for the OECD and LD countries to measure the price and quantity movements in these countries. Finally, in Section 6.8, we present the concluding comments.
189
Chapter 6 Stochastic Index Numbers
6.1
An Unweighted Average of Prices
The material in this and the subsequent four sections are from Clements and Izan (1987). Let/?it be the price of commodity i (i=l,...,n) in period t (t=l,...,T) and Dpit = log /?it - log p-A.\ be the price log-change. For each period, let each price log-change be made up of a systematic part a, and a zero-mean random component eit; that is, Dplt =
oct+ eit,
i=l,...,n; t=l,...,T.
(1.1)
As E[Dpit] = oct, we interpret oc, as the common trend in all prices. The random term eit is assumed to be independent over commodities and have a common variance o\; that is, Cov[eit, ejt]
=
ofby,
i,j=l,...,n,
(1.2)
where 5y is the Kronecker delta. From (1.1) we can see that eit = Dpn - GCt is the change in the i* price deflated by the common trend in all prices; i.e., eit is the change in the i* relative price. Hence (1.2) is interpreted as saying that the relative prices are independent and have a common variance. Furthermore, the assumption that E[ejt] = 0 means that all relative price changes have an expected value of zero. Under these assumptions, the best linear unbiased estimator of a t is af =
1« - I DPil, n (=i
International Consumption Comparisons
190
which is just the unweighted average of the n price log-changes. Also we have var a, = — a2.
(1.3)
n The variance a^ can be estimated unbiasedly by
&?
= -^—i(DPil-at)2.
(1.4)
n - 1 i=i
From (1.3) and (1.4) we see that when there is substantial variation in relative prices, the sampling variance of d, will be higher. This agrees with the intuitive notion that the meaning of the overall rate of inflation becomes less well defined when there are large changes in relative prices. Given the above interpretations, assumption (1.2), together with E[eit] = 0, is obviously very stringent. We now extend the model to relax these assumptions.
6.2
A Budget-Share-Weighted Average of Prices
We continue to take the relative price changes as having expectation zero and being independent, but we now replace (1.2) with
Cov[eit)Ejt]
=
X2 r=-Sti,
i,j=l.-,«,
(2.1)
191
Chapter 6 Stochastic Index Numbers
where A] is a constant with respect to commodities; and wu is the arithmetic average of the budget share of i during the two periods t and t-1. That is, wit l
/2(wit + wit_i). Under this assumption, the variance of the change in the relative
price of i is inversely proportional to wit. This means that the variability of a relative price falls as the commodity becomes more important in the consumer's budget. We write (1.1) in vector form as Dpt
=
otti+ et,
t=l,...,T,
(2.2)
where Dpt = [Dpit\; I = [1 ... 1]'; and e t = [eit]. Under (2.1), the n x n covariance matrix of et is
Vare,
=
A] W~\
(2.3)
where Wt = diag[vv ]( ... wnt]. Application of GLS to (2.2) under (2.3) gives
a, =
Since i'Wti
a, =
(l'Wti)-li'WtDpt
= Z"=iWl7 = 1 and
I "it Dp it1=1
.
i'WtDpt
= Zf=i^~'itDP'it >
tms
simplifies to
192
International Consumption Comparisons
This expression is identical to the finite-change form of the Divisia price index, DPt, defined in equation (2.8) of Section 3.2. The sampling variance of 5 , is X2t(i'Wti)~1 = Xzt; that is, Var at = %
(2.4)
This variance can be estimated unbiasedly by 1 ,„ ~ .,.—,~. 1 A -_ ~, (Dpt - a, i)'Wt (DPt -ati) = - 1 w, {DPit-at2)\ n -1 n - 1 i=i so that I] = -!-iwit(Dpit-at)i. rc - 1 i=i
(2.5)
We write (2.5) as
I] = -^-nt,
(2.6)
n-\ where n t = £"=1 vv,7 /Dp,-, - DPt ]2 is the finite-change form of the Divisia variance of relative price changes defined in equation (2.10) of Section 3.2. This IT measures the degree to which prices move disproportionately; n = 0 only if all prices change proportionately, that is, if there are no changes in relative prices. From (2.4) and (2.6) again we see that the sampling variance of the estimator of inflation will be higher the larger the relative price movements.
193
Chapter 6 Stochastic Index Numbers
6.3
The Extended Model
We now write Dp,t as the sum of the common trend in all prices oct, a commodity-specific component Pi and a zero-mean random component £;t» Dpit = Ot + Pi + Cit.
i=l,...,n;t=l,...,T,
(3.1)
where T is the number of observations. We assume that the £it's are independent over commodities and time, and that their variances are inversely proportional to the corresponding arithmetic averages of the budget shares,
Covt^Cjt]
=
^ - 5 ^ ,
(3.2)
where rjt is a constant with respect to commodities. Rearranging equation (3.1) and taking the mathematical expectation, we obtain Pi = E[Dpn - otj. Thus Pi is interpreted as the expectation of the change in the i* relative price. Model (3.1) is not identified. This can be seen by noting that an increase in a t for each t by any number k and lowering of Pi for each i by the same k does not affect the right-hand side of (3.1). To identify the model we impose the constraint
twfit=0,
(3.3)
194 where
International Consumption Comparisons wi
is the sample mean of wit.
interpretation
that
a
Equation (3.3) has the simple
budget-share-weighted-average
of
the
systematic
components of the relative price changes is zero.
6.4
A Two-Step Estimation Procedure: Step 1
We now develop a procedure to estimate (3.1) in two steps. In the first step we ignore the time dependence of the variance given by (3.2) and obtain the leastsquares residuals. These residuals are then used in the second step to adjust for heteroscedasticity in obtaining the final estimators. For i = j and t = s, we obtain from (3.2)
VarCu = ^ - -
(4.1)
In the first step we replace this with the specification
Var^it = ^ ,
(4.2)
W:
where rf is a constant. Multiplying both sides of (3.1) by •yjw^, we obtain yit
= OtX i + (3iXi + £it,
(4.3)
Chapter 6 Stochastic Index Numbers
195
where yit = ^j^Dpit; x ; = ^ T ; and £it = V^TCir I{ follows from (4.2) that var [£it] = wt var [£it] = if, a constant, so that least squares can be applied to (4.3). It can be shown that the LS estimators of (4.3), constrained by (3.3), are a* = twtDpu, /=i
P* = ^-i(DPit-at).
(4.4)
T t=\
The only difference between a* and the Divisia price index DPt is that the former uses constant weights (w t ), while the weights of the latter vary with time (wit). In fact, this difference will have little practical importance as budget shares tend to change slowly over time. The estimator of Pi defined in (4.4) is the sample mean of the change in the i* relative price. Now we use the estimators defined in (4.4) together with price logchanges Dpit and the sample means of the budget shares w, to obtain an estimate of the variance of £it in (3.1). This estimate will be used in the second step. As the budget shares are fairly stable over time, as an approximation we replace wit in (4.1) with w; to give
VarCi, = ^ - -
(4.5)
w
i
It is to be noted that this variance is time-dependent because of the t subscript of r\f. By contrast, the variance defined in (4.2) is constant over time. Substituting the estimators of cct and Pi in (4.3), the residual from that model is
196
International Consumption Comparisons
£ = J^lDpu- a?-P?] =
V^Ti(Dpu- OL*)- {Dpl
-a*)],
where the second step is based on the second equation in (4.4); Dpi ={\IT)jJt=xDpit is the sample mean of Dpu and cc* = ( l / r > l L a t is the mean of a*. Thus the sum over i=l,...,n of squared residuals is 6? = 1 [&1 2 = X Wi(Dpu -a*? i=i
i=i
+ I w^Dpi - a * ) 2 i=i
-2iw,.(%-fl;)(Dprat). i=i
The first term on the far right of this equation is the Divisia price variance Il t with wit replaced by wt. This measures the variability of relative prices within period t. The second term measures the variability of relative prices over the whole period. The last term, minus twice a weighted covariance, measures the degree to which relative price changes in period t coincide with price changes over the whole period. It can be easily shown that Qj /(n -1) is an asymptotically unbiased estimator of r\j.
6.5
A Two-Step Estimation Procedure: Step 2
We divide both sides of (4.3) by 9t to give Pit
=
a x
t it
+
P i * i t + Cit.
(5.1)
197
Chapter 6 Stochastic Index Numbers
As where yit = Jw^Dph/et; xit = J^/Qt; and Cit = yf^^it/et2 9 /(« -1) is an asymptotically unbiased estimator of r\j, it follows from (4.5) that
VarC lt = - |2v a r C i t 9
^2 6 wt
' («-l)
a constant, so that least squares can now be applied to (5.1). It can be shown that the LS estimators, constrained by (3.3), are a?* = ±WiDpu,
pr = ^ £ f t ( 0 p a - a O ,
i=i
(5-2)
T «=i
where <j)t = (1 / 0 2 ) / 1 [ = 1 (1 / 9?). As can be seen, the estimator a** is identical to a* defined in (4.4). The reason is that the new weighting factor in (5.1), l/9t, is the same for all i within the period t. The estimator P** of the systematic component of the change in the i* relative price is now a weighted average of (Dpn - a**) over all T periods. By contrast, P*, defined in (4.4), is an unweighted average. The weights in (5.2), 0i, ..., (Jh-, are inversely proportional to Qj, which in turn is proportional to the error variance in period t; thus, less weight is accorded to those observations with a higher error variance. We can also show that the sampling variances of the estimators defined in (5.2) are 92 Var < * = —'—, n l ~
Var p** =
1 i (n-l)Z(l/e2) t=l
-1-1 W;
(5.3)
International Consumption Comparisons
198
As can be seen, the sampling variance of a** increases with 9 2 , which in turn rises with relative price variability. Therefore, the same general result as before emerges here: the sampling variance of the estimator of inflation will be higher the larger the relative price movements. The sampling variance of (3** is proportional to the difference between (l/vv ; ) and a constant term, so that this variance increases as wt falls. It can also be shown that
Cov [a**, or" ] = 0 for t *s;
Cov[P**, P** ] =
^ (n-l)S(l/9?)
for i * j ;
(5.4)
t=i
and C o v [ a p , P J * ] = 0,
t=l,...,T;i=l,...,n.
(5.5)
From (5.3) and (5.4), we obtain Corr[P**,P**] = -j^=,
fori*j,
where w* = ( 1 / wt) - 1 . This shows that the correlation between the i* and the j * systematic components of relative prices is always negative and it falls (in absolute value) with declining budget shares of both i and j . Finally, we define the mean of a** over all T periods as a** = (1/T) J^^a**•
Var a "
= - ^ £ Vara?* = - ^ - j l *l T 2 i=i ( n - l ) T 2 (=i
Hence we have
(5.6)
Chapter 6 Stochastic Index Numbers
199
where we have used (5.3) and (5.4). It is to be noted that all the sampling variances defined in this section have only an asymptotic justification. The reason is that they all involve Qf /(n -1) which is an asymptotically unbiased estimator of f]f.
6.6
An Extension
Under the error variance structure (4.1), it was assumed that the variance of the i* error term Qt is inversely proportional to the corresponding i* budget share, wjt. Clements and Izan (1987) used this assumption in their estimation of the rate of inflation and empirically analysed this assumption and concluded that, "the variances are not inversely proportional to the budget shares as required by the assumption" (see page 345, Clements and Izan, 1987). Selvanathan (1987) relaxed this assumption on the error terms by allowing the errors to be correlated over commodities and derived a new estimator for the rate of inflation. Diewert (1995) and Crompton (2000) both correctly criticised the assumption made in Clements and Izan (1987) and proposed an alternative specification for the error variance structure. Under this variance structure, Crompton showed that the new variance estimator of the rate of inflation is robust to unknown forms of heteroscedasticity. Under this specification, while the estimator of the rate of inflation oct remains as the budget share weighted sum of the n price changes as given in (4.4), the robust variance estimator is now a budget share weighted sum of the squared relative price changes instead of the variance given in (5.3). In this section we shall present the details of Crompton's work. Crompton (2000) replaced the specific variance structure given by (4.1) with an unknown form of heteroscedastic variance structure,
International Consumption Comparisons
200
Var^i,
=
4-
(6-1)
This differs from the variance structure given in (4.1) in the sense that now the error variance is an unknown form of heteroscedasticity. As in Clements and Izan (1987), to obtain an estimator for the rate of inflation as a budget-shareweighted average of the individual price changes, we multiply both sides of equation (4.1) by ^/w,- to give yit
= a t x; +piXi+ £it,
(6.2)
where yit = ^Dpit; Xj = ^ ; and £it = V^~Cir Under (6.1), we have Var (^t) = X2jt wt. Since heteroscedasticity in the error term does not effect the rate of inflation estimator, we can estimate (6.2) directly by using LS and correct for heteroscedasticity in £it using White (1980) heteroscedasticity - consistent covariance matrix estimator. As Crompton (2000) points out, the advantage of this approach is that we do not need to concern ourselves over the nature of the error variance. Crompton (2000) showed that the constrained LS estimators of equation (6.2) for the rate of inflation and its variance can be written in scalar form as 6c, = twiDpit, !=1
Var 6c, = £ w,|? r ,
(6.3)
1=1
where \it = ytt - 6c, x t - (3, xt are the LS residuals. Comparing the results given in (6.3) with the results of 6c, in (5.2) and (5.3), we see that the point estimates of the rate of inflation, 6c,, are identical. However, the variance of the estimate of inflation in (6.3) is now a weighted
Chapter 6 Stochastic Index Numbers
201
average of the sum of squared residuals over the n commodities for any given period. As an illustrative application, first we reproduce the application presented in Selvanathan (2003). In this application, we use the Australian quarterly price and CPI data for the period September 1972 to June 1996. There are eight subcomponents (n=8) to the CPI, namely, food, tobacco and alcohol, clothing, housing, durables, health care, transport and miscellaneous. The data were obtained from the Australian Bureau of Statistics and the same data were used in Crompton (2000). The estimate for the rate of inflation, the two sets of standard errors based on Clements and Izan (1987) and Crompton (2000) obtained by using equations (5.2), (5.3) and (6.3) are presented in Table 6.1. In column 2 of the table, we present the estimates of inflation for Australia. In column 3, we present the CPI log-change. Comparing the CPI log-changes in column 3 with the inflation estimates in column 2, we see that the inflation estimates are very close to the CPI log-change. As can also be seen from the last row of Table 6.1, the mean quarterly rate of inflation is estimated to be 1.78%, with a standard error of .52%. This mean point estimate is also close to the mean CPI log-change of 1.89% as expected. Column 4 presents Clements and Izan's (C&I) standard errors and column 5 presents the Crompton's robust standard errors. As expected, the robust standard errors are generally smaller than the C&I standard errors (in actual terms, more than 75% of the times column 5 standard errors are lower than those in column 6). We illustrate this in Figure 6.1. Figure 6.1 plots the C&I standard errors against the robust standard errors presented in Table 6.1. As can be seen, most of the points fall above the 45o line indicating that, in general, the robust standard errors are smaller than C&I standard errors. Clearly, the conclusion from Table 6.1 and Figure 6.1 is that
International Consumption Comparisons
202
Table 6.1 Estimates of price inflation and standard errors for Australia (December 1972-June 1996) Standard errors
Standard errors
Rate of inflation
CPI log-change
C&l
Crompton
Dec Mar
(2) 1.00
(3) 1.00
(4) 0.19
(5) 0.18
1.59
1.97
0.50
0.55
(1) 1984 Dec 1985 Mar
Jun Sep
2.45 2.88
3.36
0.59
0.61
Jun
3.25
0.68
0.64
Dec
3.06
3.59
0.46
Mar
2.18
2.61
Jun
3.46
Sep
Rate of Inflation
CPI log-change
(2) 1.32
(3)
1.42
Sep
0.41
0.37
4.20
4.71
Dec Mar
Year
C&l
Crompton
1.50
(4) 0.16
(5) 0.14
1.33
0.27
0.24
2.37 2.18
2.32
0.41
0.40
2.27
0.24
0.21
Dec
2.03
1.94
0.35
0.35
0.33
1986 Mar
2.25
2.31
0.31
0.28
0.57
0.48
Jun
1.63
1.60
0.65
4.82
0.82
0.82
Sep
2.55
2.61
0.47
0.61 0.46
3.54
3.47
0.91
0.92
2.80
0.54
3.72
0.97
0.78
Dec 1987 Mar
2.77
3.33
1.97
1.99
0.41
0.49 0.38
Jun
3.03
3.58
0.50
0.45
Jun
1.54
1.46
0.35
0.36
Sep
0.51
0.70
2.85
2.09
Sep
1.62
1.68
0.22
0.18
1.77
1.81
1.74
0.22 0.49
0.20
0.48
Dec 1988 Mar
1.69
Jun
2.26
2.61 2.55
1.88 0.47
1.41
Mar
4.78 2.62
5.44
0.61
0.58
Jun
1.74
1.71
0.45
0.45
Sep
1.99
2.48
0.38
0.34
Sep
1.92
6.37
5.66
5.50
3.97
Dec
2.08
1.90 1.98
0.41
Dec
0.39 0.74
2.29 2.24
0.31
0.29
1989 Mar
0.98
0.97
0.27
Jun
2.44
2.45
0.51 0.52
0.45
0.32
1.92 2.42
0.40 0.29
0.42 0.25
Sep Dec
2.25 1.84
2.28 1.83
0.52 0.44
0.51 0.44
Dec
Mar
1.93
Jun
2.08
Sep Dec
1.77 2.08
0.75
0.42
0.52
Mar
1.03
1.32
0.14
0.14
1990 Mar
1.71
1.70
0.40
0.39
Jun
1.97
2.07
0.49
0.40
Jun
1.60
1.57
0.26
0.27
Sep
1.70
1.78
0.31
0.28
Sep
0.76
0.78
0.32
0.34
Dec
1.51
2.24
2.77
1.97
2.61
2.58
0.73
0.77
Mar
Dec 1991 Mar
-0.17
-0.19
0.90
0.92 0.24
1.47
1.71
0.37
0.35
Jun
2.23
2.63
0.50
0.53
Jun
0.17
0.19
0.28
Sep
2.10
2.33
0.37
0.36
Sep
0.58
0.56
0.50
0.51
Dec
2.82
2.95
1.05
0.75
0.87
0.93
0.40
0.35
Mar
1.86
2.21
0.47
0.50
Dec 1992 Mar
0.01
0.00
0.57
0.50
Jun
2.48
2.80
0.40
0.39
Jun
-0.39
-0.28
0.56
0.48
Sep
1.78
1.69
0.42
0.45
Sep
0.11
0.09
0.51
0.49
Dec
1.92
2.07
0.28
Dec
0.49
0.46
0.34
0.31
Mar
2.15
2.43
0.30
0.24 0.28
1993 Mar
0.84
0.92
0.39
0.40
Jun
1.92
2.18
0.37
Jun
0.28
0.30
1.94
Sep
0.46
0.18
0.18
0.27 0.38
0.23
Dec
1.81 3.94
0.41 0.40
0.37
Sep
0.38 0.46
Mar Jun
1.56 2.43
0.36
2.32
Jun
0.38 0.65
0.28 0.27
0.23 0.28 0.17
Sep
4.14
1.86
0.48 1.36
1.82
0.29 0.26
0.30 0.28
Dec 1994 Mar
0.72
0.36
3.45
3.47
Sep
0.63
2.91
2.86
0.41
0.39
Dec
0.84
0.63 0.80
0.16
Dec
0.39
0.38
Mar
2.11
2.13
0.47
0.40
1995 Mar
1.68
1.67
0.65
0.66
Jun
1.99
2.09
0.54
0.57
Jun
1.22
1.30
0.27
0.24
Sep
1.69
1.73
0.34
0.33
Sep
1.20
1.20
0.35
0.30
Dec Mar
2.32 -0.32
2.32
0.42 2.22
Dec 1996 Mar
0.70 0.39
0.23 0.32
0.12
1.51
1.09
Jun
0.66
0.76 0.42 0.67
0.25 0.35
Jun
-0.46 0.31
0.36 1.60
0.14
0.12
Sep
1.32
1.22
0.26
0.23 1.78
1.89
0.59
0.52
0.47
0.42
Wean
Chapter 6 Stochastic Index Numbers
203
0.70
I
I
0.50
0.30
u n m 0.10
0.30
0.50
0.70
Robust standard errors
Standard errors of the inflation estimates Australia, December 1972-June 1996 Figure 6.1
the robust standard errors should be used when determining the precision oi ine rate of inflation estimates. In Table 6.2 we present the estimates and their standard errors for the commodity specific component (3j. As can be seen, the coefficients for food, clothing, housing and durables are statistically insignificant indicating that the relative prices of food, clothing and housing remain almost a constant during the sample period. The relative price of tobacco and alcohol, health care and transport are significant; the estimated relative price of these three commodities increased by .35%, .38% and .21% per quarter, respectively. Figure 6.2 presents a scatter plot of the standard error of the estimate of inflation V(var at ) against the estimate of inflation (dt ) and the solid line is the LS regression line. As can be seen, the slope of the LS regression line is less than 1, indicating that the estimate of inflation increases faster than the standard
International Consumption
204
Comparisons
Table 6.2 Estimates of relative price changes: Australia December 1972 - June 1996 Estimate of relative price change
Commodity
/?,. X100 1. 2. 3. 4. 5. 6. 7. 8.
.06 (.07) .35 (.12) -.13 (.14) .08 (.08) -.07 (.07) .38 (.13) .21 (.08) -.82 (.10)
Food Tobacco and Alcohol Clothing Housing Durables Health care Transport Miscellaneous
Note: Standard errors are in parentheses.
•
•
y = 0.1733x +0.2089
1.7 •
(X1
o
*
(A O
•
1.2•
h.
•
"g Stand
0.7• '•
1
m (i
•
•j^-*"*
• -^•"""•""""^ *
•
1
2
3
4
Inflation rates (x100)
Estimated inflation rates vs their standard errors Australia, December 1972-June 1996 Figure 6.2
Chapter 6 Stochastic Index Numbers
205
error. To investigate this further, in Figure 6.3, we plot the t-values against the estimated inflation rates (at) (again the solid line is the LS regression line). There is a distinct positive relationship between these two variables, which confirms the tendency for the standard error to increase less rapidly than inflation. Consequently, in a relative sense, higher inflation tends to be estimated more precisely. In Figure 6.4 we plot against time the estimated inflation and the 95% confidence bands constructed as & ± 1.96V(vara). The jump in inflation and the increase in the width of the confidence band in the mid 1970s is to be noted.
6.7 Application of Stochastic Index Numbers to OECD and LDC In this section we use the methodology we described in the previous sections to estimate the growth in prices (i.e. rate of inflation) and the growth in consumption (i.e. quantity index) in the OECD and LD countries. The material presented in this section draws on Selvanathan and Selvanathan (2003). Tables 6.3 and 6.4 present the rate of inflation and their standard errors for the 23 OECD and 23 LD countries, respectively. Tables 6.5 and 6.6 present the estimated relative price changes |3* for the OECD and LD countries, respectively. For each country, the first column presents the point estimates and the second column presents the standard errors. As can be seen, most of the point estimates are estimated precisely. A clear distinction between the two sets of tables is that the estimates for the rate of inflation in all OECD countries are in single-digit figures while they are in double-digit figures for most of the LD countries. It is also worth noting that the estimates for the inflation rates in Tables 6.3 and 6.4 are very close to the Divisia price indices presented in Tables 3.7 and 4.7, respectively, of Chapters 3 and 4. The reason for this
International Consumption Comparisons
206
44
1
~
*
g
*•
75
y=1.0189x + 2.5697 •
.•*.
^ •
^ X ^
• • **2.*~+>^ •
•
**&0^
31 >
I
fc
.f • " 0 f
A
2
4
6
g_
I
1 Inflation rates (x100)
Estimated inflation rates vs their t-values Australia, December 1972-June 1996 Figure 6.3
• Upper D friflation • Lower
Estimated inflation rates and their 95% confidence intervals Australia, December 1972-June 1996 Figure 6.4
207
Chapter 6 Stochastic Index Numbers
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Iceland
Ireland
(1) 1953
Austria
Year
Australia
Table 6.3 Rate of inflation estimates and their standard errors in 23 OECD countries
s
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
1954 1955 1956 1957 1958 1959 1960 0.85 1.00
3.25 1.61
0.72 0.27
1.78 0.31
1962 2.15 1.13
0.63 1.25
-0.73 1.39
3.28 0.45
3.09 0.57
1.48 0.71
1963
0.49 1.10
4.03 1.10
3.39 1.76
5.27 0.56
3.15 0.35
2.99 0.75
1964
3.18 0.42
4.20 0.51
1.29 0.45
7.32 1.64
2.51 0.25
2.06 0.33
1965
3.29 0.45
4.24 0.73
4.53 1.54
1.95 0.45
3.32 1.26
2.89 0.50
3.13 0.44
4.30 0.87
1966
3.13 0.31
2.90 0.33
4.39 0.73
3.24 0.64
2.87 0.61
3.33 0.45
3.92 0.32
3.26 0.50
2.90 0.29
1967
3.58 0.33
4.27 0.65
2.58 0.29
3.60 0.69
6.68 0.86
4.70 089
3.44 0.64
2.00 0.48
1.77 0.51
3.10 0.37
1968
3.35 0.54
2.83 0.45
2.76 0.46
4.01 0.31
7.14 0.48
10.00 2.44
5.25 0.54
2.01 0.89
0.63 0.76
1.59 0.29
1969
3.10 1.03
3.37 0.48
2.96 0.53
3.83 0.43
4.52 0.64
1.97 0.34
7.01 0.46
1.97 0.56
2.95 0.51
2.75 0.55
1970
1961
3.47 0.64
5.63 0.81
3.89 0.43
2.54 0.95
3.56 0.74
7.00 0.57
3.54 5.52
4.93 0.30
3.75 0.24
3.36 0.79
4.96 0.22
1971 6.57 0.74
4.93 0.50
5.05 0.70
2.48 0.65
6.96 0.73
6.64 0.54
5.46 0.26
5.44 0.52
2.90 0.90
5.46 0.30
1972
7.60 1.32
6.11 0.37
5.27 1.08
4.01 0.49
7.56 1.20
8.08 0.30
5.65 0.65
5.38 0.47
3.63 0.27
614 0.61
1973
8.68 1.70
7.19 0.65
6.71 1.63
8.24 1.65
9.34 1.51
11.29 0.90
6.56 0.66
6.57 4.53
14.01 2.03
11.73 0.84
1974 16.24 1.42
10.11 1.02
12.06 1.05
10.03 0.65
14.34 1.27
17.48 1.90
12.56 0.81
6.69 0.77
21.43 1.33
14.62 1.56
1975 14.42 0.87
7.97 0.35
12.29 0.88
10.05 0.42
9.67 0.43
15.30 2.53
10.79 0.61
5.97 0.24
12.14 0.82
20.63 1.36
16.40 0.96
1976 11.12 0.72
6.65 0.53
7.75 1.10
7.50 1.33
9.40 0.60
12.62 1.79
9.42 0.51
4.23 039
12.76 0.56
18.13 2.22
16.55 1.06
1977
9.23 0.46
5.68 0.39
7.05 0.61
7.06 0.72
10.21 1.04
11.03 1.21
8.68 0.72
3.62 0.72
11.32 0.48
14.18 2.01
16.72 0.67
1978
8.81 0.98
4.12 0.47
4.10 0.39
7.23 0.85
9.13 0.50
7.27 0.71
8.48 0.41
2.71 0.47
11.63 0.49
35.87 1.13
7.56 1.94
12.18 0.68
1979
9.92 0.52
4.04 0.52
3.91 0.89
8.31 0.57
9.74 1.75
7.62 0.44
10.01 0.37
4.34 0.88
16.19 0.74
37.86 2.16
14.11 1.46
13.86 057
1980 9.24 0.29
6.33 0.49
6.07 1.14
9.60 0.58
9.72 1.01
10.92 0.73
12.31 0.82
4.87 0.54
19.91 0.94
44.20 0.64
17.67 1.06
18.43 1.02
1981
17.64 0.43
19.26 1.09
9.13 0.56
6.90 0.77
7.73 1.17
10.81 0.83
11.44 056
10.63 0.67
11.84 0.45
5.74 0.53
20.76 0.70
41.64 1.17
19.03 1.03
1982 10.47 0.74
5.63 0.51
7.15 1.17
9.94 0.73
9.25 0.39
9.66 1.60
11.29 0.60
4.72 0.67
19.02 1.02
41.47 1.12
14.93 0.78
15.79 0.62
1983
3.75 2.64
5.69 4.16
5.35 0.61
665 0.59
8.34 2.26
4.85 5.78
1.95 0.59
16.15 1.49
63.45 3.08
10.06 0.68
27.55 4.73
7.48 0.54
1984
7.84 3.06
5.24 0.58
614 0.78
3.91 0.46
617 0.95
6.69 063
7.37 0.35
2.75 0.57
17.02 0.99
27.65 1.23
7.45 0.50
11.23 0.86
1985
6.00 0.89
3.06 0.28
4.82 0.32
3.66 018
4.32 0.44
552 0.76
5.50 0.40
1.21 0.36
16.81 0.62
27.92 1.20
7.50 2.62
8.81 0.55
1986
8.40 0.40
1.78 0.89
1.64 1.27
3.90 0.63
3.20 0.17
3.13 0.82
2.81 0.84
-0.39 1.15
19.81 1.07
19.10 2.97
14.29 2.49
6.01 0.40
1967
7.61 0.57
0.99 0.49
1.48 0.58
4.01 0.33
4.40 0.78
3.42 0.79
3.06 0.38
-1.43 1.69
14.71 1.50
15.81 1.11
2.46 0.45
5.18 0.22
1968
7.27 0.53
1.49 0.42
1.48 0.27
3.96 0.31
3.79 0.46
4.27 0.29
2.65 0.43
3.00 1.90
12.91 1.01
21.87 2.12
3.99 2.97
5.47 0.39
1989 6.24 0.40
2.29 0.49
3.03 0.33
4.89 0.08
3.91 030
4.75 0.29
3.42 0.27
2.66 0.38
14.06 1.13
19.72 1.92
3.82 0.50
639 0.32
1990
4.80 0.19
3.02 0.38
3.29 0.29
4.23 0.23
2.64 0.37
5.60 0.18
2.93 0.33
2.53 033
18.05 0.62
15.49 0.96
1.89 0.26
6.11 0.47
1991
2.47 0.22
2.98 0.71
3.05 0.28
4.90 0.65
1.97 0.43
5.21 0.69
3.11 0.22
3.47 0.40
17.63 1.01
6.79 0.81
2.73 0.30
6.63 0.66
1992
1.87 0.36
3.85 0.27
2.31 0.69
1.05 0.33
2.26 0.45
3.29 0.54
2.32 0.45
3.81 0.25
13.9B 1.11
4.39 0.91
2.53 0.69
5.43 0.42
1993
1.53 0.47
3.17 0.32
2.37 0.78
1.38 0.33
0.21 0.30
3.53 1.11
2.10 0.30
3.38 0.28
12.64 1.07
4.03 0.86
1.78 0.33
4.57 0.47
1994
1.33 0.53
3.34 0.33
2.59 0.23
0.30 0.99
1.90 0.29
1.40 0.16
2.01 0.33
2.55 0.20
10.14 0.68
1.58 0.64
2.82 0.98
4.44 0.46
1995
2.65 0.57
1.26 0.60
1.39 0.18
1.55 0.43
2.47 0.63
-0.28 1.49
1.52 0.40
1.61 0.38
2.05 0.89
5.65 0.67
1996
1.59 0.39
2.07 0.48
1.91 0.26
0.89 0.56
1.77 0.30
2.18 0.61
1.41 0.81
4.18 0.45
8.81 0.79
Table 6.3 ccntinued'on nextpage
208
International Consumption
Comparisons
0.12 0.52
1954
4.21 1.13
1955
1.60 0.58
1956
1.58 0.82
1957
6.18 0.38
1958
2.09 0.69
1959
0.64 0.75
1960
2.06 0.78
1961
1.68 0.53
Switzerland
=3
(18)
(19)
(20)
(21)
(22)
(23)
USA
1953
(17)
Sweden
(16)
Spain
(15)
Portugal
(14)
Norway
Netherlands
(1)
Luxembourg
Year
Japan
Table 6.3 (continued) Rate of inflation estimates and their standard errors in 23 OECD countries
(24)
1.55 0.28
1962
1.76 0.56
4.89 0.49
4.26 0.36
1963
2.04 0.68
3.66 0.31
1.75 0.98
1.48 0.28
1964
6.22 1.20
4.16 0.18
3.54 0.34
1.51 0.32
1965
3.29 0.77
4.20 0.60
8.26 1.64
5.11 0.46
4.15 0.61
5.08 0.28
1.67 0.28
1966
5.93 0.80
3.38 0.47
6.63 0.87
6.30 0.17
4.83 0.31
3.89 0.43
2.73 0.50
1967
3.41 0.89
4.40 0.51
6.14 0.79
4.27 0.72
4.66 0.76
2.65 0.46
2.68 0.51
1968
4.08 3.51
3.15 0.41
4.63 1.19
1.30 0.43
2.84 0.65
4.51 0.49
4.01 0.45
1969
4.64 0.73
3.44 0.53
3.62 0.62
3.46 0.50
2.89 0.41
5.46 0.35
4.47 0.39
1970
4.32 0.42
9.50 0.53
6.42 0.84
5.74 0.43
4.00 0.50
5.77 0.58
4.47 0.25
3.31 0.56
1971
5.62 0.61
4.56 0.53
8.24 0.87
6.16 0.58
7.62 0.78
7.01 1.34
6.96 0.29
8.29 0.28
4.39 0.41
1972
5.17 0.77
4.61 0.37
8.49 0.68
6.47 0.49
7.81 1.16
5.32 1.63
7.48 0.65
5.81 0.91
3.45 0.31
1973
8.68 1.55
6.29 1.26
8.71 0.38
5.32 1.85
10.52 1.12 11.21 3.22
9.05 0.87
6.98 2.29
7.89 1.80
1974 18.63 2.36
9.47 0.62
9.63 0.91
9.11 0.63
16.33 1.06
9.52 1.31
9.64 0.65 15.53 0.85
9.74 0.79
1975 11.10 0.93
9.89 0.68 10.02 0.67
10.95 1.25
14.54 0.71
10.21 0.84
6.36 0.39 21.47 0.81
7.80 0.41
1976
8.76 0.49
9.13 0.97
8.46 0.76
8.18 0.50
15.68 1.01
10.34 0.25
2.34 1.02 14.37 0.42
5.84 0.75
1977
7.18 0.72
5.58 0.50 11.53 3.09
7.91 0.36
21.84 1.31
10.08 1.18
1.09 0.19 14.06 0.75
6.46 0.67
1978
4.73 0.88
3.54 0.63
4.18 0.56
7.47 0.36
17.56 0.68
10.79 0.65
1.23 1.08
8.69 1.03
6.79 0.48
1979
3.51 0.61
5.00 0.83
3.76 0.49
4.48 0.43
15.55 1.25
7.68 0.95
4.04 1.03 12.74 1.01
8.69 0.67
1980
6.71 0.73
7.14 1.43
6.51 0.67
9.40 0.60
14.75 9.18 11.80 0.28
4.13 0.80 15.32 1.00 10.31 1.11
1981
4.25 0.44
8.25 0.42
5.80 0.68
12.79 1.30
13.35 0.57
10.77 0.68
6.19 0.95 10.86 1.18
8.83 0.57
1982
2.49 0.47
10.02 0.94
4.96 0.56
10.55 0.92
13.72 0.66
9.42 0.82
5.47 0.54
8.34 0.65
5.96 0.68
1983
3.06 1.15
7.78 0.36
2.39 0.32
12.88 6.56
11.83 0.73
11.26 1.97
2.61 0.28
6.68 8.43
3.71 0.93
1984
2.55 0.42
6.41 0.39
2.57 0.91 10.10 0.80
5.94 0.35
11.38 0.85
7.26 0.78
3.00 0.29
4.95 0.83
3.85 0.32
1985
2.19 0.63
4.11 0.23
4.43 4.31
14.21 2.20
5.58 0.42
7.20 0.68
6.74 0.50
3.44 0.17
5.32 0.31
3.51 0.38
1986
0.84 0.32
1.58 1.67
0.21 0.65 13.07 0.89
6.77 0.94
9.06 1.15
4.67 0.73
0.53 1.31
3.92 0.70
2.46 0.78
1987
0.51 0.34
1.59 0.40
0.15 1.07 10.72 1.01
7.52 0.63
9.32 0.74
5.55 0.50
5.08 0.20
1.42 0.46
4.36 0.57
3.82 0.18
1988
0.55 0.14
2.65 0.40
0.27 0.45
6.54 1.64
5.88 0.28
9.99 0.89
4.81 0.29
5.76 0.38
2.01 0.36
5.03 0.41
4.02 0.39
1989
1.86 0.17
3.64 0.44
1.01 0.48
6.50 1.28
4.57 0.43 12.11 0.94
6.42 0.63
6.51 0.33
3.08 0.41
5.70 0.33
4.38 0.30
1990
2.41 0.34
3.60 0.22
2.05 0.46
5.43 0.71
4.47 0.53 11.46 0.57
6.16 0.40
9.19 0.90
5.33 0.49
5.40 1.44
5.14 0.53
1991
2.60 0.46
3.09 0.31
2.92 0.53
1.89 0.91
3.62 0.52 11.03 0.91
5.81 0.54
9.54 2.67
5.47 0.22
6.18 0.92
3.85 0.20 2.82 0.25
1992
1.84 0.41
2.81 0.41
1.07 1.06
2.75 0.50
8.87 0.39
5.90 0.34
1.49 1.77
3.74 0.57
5.51 0.95
1993
1.27 0.24
1.87 0.31
1.02 0.68
1.94 0.52
6.69 0.76
4.94 0.72
4.48 0.82
3.11 0.71
3.12 0.37
2.48 0.27
1994
0.72 0.37
2.22 0.46
2.28 1.10
1.24 0.56
5.40 0.44
4.69 0.78
2.78 0.49
1.18 0.29
2.58 0.46
2.18 0.17
1995 -0.60 0.50
1.00 0.45
2.79 0.93
2.29 0.38
4.09 0.39
4.65 0.65
2.46 0.32
2.82 0.26
2.15 0.26
1996 -0.15 0.45
0.97 0.53
3.34 0.48
0.54 1.28
2.62 0.27
2.14 0.38
1.15 0.55
209
Chapter 6 Stochastic Index Numbers
(6)
(7)
a* o
Korea
(5)
Jamaica
Honduras
(4)
Israel
Fiji
(3)
Iran
Ecuador
(2)
India
Cyprus
(1) 19a
Colombia
Yaar
c
2
Hungary
Table &4 Rate of inflation estimates and their standard e r a s in 23 I D cartries
(8)
(9)
(10)
(U)
(12)
(13)
1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
L12 231
131 L63
1L71158
1972
291021
4.55 272
14.19 208
7.98 0.96 18.47 l a
1973
17.25 260
1974
21421.62
19.08 L34
14.73132
1975
22.191.50
11101-82
1976
19.130.91
10.09L35
1977
2196 L80
U73184
1978
16.612.61
1L45L28
4.84 L33
1979
2106 L53
10.49 a 7 0
860220
1980
23.32 0.93
1108 L57
18.644.05
1931
2106 0.68
9.97 L19
1582 L68
1932
2L93L13
6.16 (M0
17.50 0.60
1983
18.400.43
198127
33.23 635
1984
18721.03
5.710.45
1985
2L15 1.06
1986 1987
18.20 L17
14.83 L98
3293 L32
699027
L09L76
3186 247
14.54 L53
4.14 128
137 L47
2501222
9.60 L55
1601 L62
5H116
4.30 L67
3122101
1169229
14.44 L06
L06a41
4.99 0.51
4147 L37
2626122
1&35194
14.89156
10.99 212
57.16168
2163 L65
1&91L37
7.69132
2159452
85.41612
19.83 292
2599 L75
10.581.29
1194 026
1115130
9.22152
78504.89
1L45L44
17.18 L71
655292
1L27126
954 064
6.62176
77.51128
816 L75
4.67 204
1771.78
870172
884163
9248 L33
1282 242
123 253
3210113
545178
8480.74
7.20 L38
604189
875 L09
15867110
73.61 L10
155160
4.65 141
27.82 265
LSI 1.96
268 L05
6.59169
5.53 LOO
5.81 L66
13540115
2295 L64
3.70183
22.700.72
L67146
24.51 L6S
8853.33
4.89 132
4.96186
6.90163
18.78 228
3857119
1L763.00
L59171
2154 L l l
239131
28.88245
4.73 L99
4.97 084
7.66 L88
7.66123
2298 225
18.20 L19
4.96179
112149
655159
24.13 L32
1938
73.61 LIS
103 0.30
47.27 L53
9.62 276
7.38182
L236L68
852157
2193142
1544160
1969
21.83 0.98
137 a 4 5
55.13 258
4.79 LS9
7.37 0.95
14.48 L35
7.03164
17.97 275
17.86 L77
523165
1990
25.961.34
4.14 037
3930176
7.44216
7.180.60
24.99251
9.75156
873L91
13.82 237
9.14162
1991
24.851.30
4.01 L17
3858023
7.60 L31
S47L05
3187 7.93
1275 L20
17.13 213
1620 L35
assaa
1992
24.55 a 6 6
6.00 a59
41.72 1.28
7.07 052
2104157
816140
2169 L92
1122186
527147
1993
425 tt77
36.15L89
580141
19.43 L65
9.08153
2136 L17
9.83 L49
4.57144
1934
504131
7.11 L15
18.15 L79
9.19192
3L57 264
1196 L27
657 L87
663165
39.66191
594 273
4.19154
1995 1996
7.75171
550164
4.91149
1937 1998
TaUe&4ai1nEdn3t[Bge
International Consumption Comparisons
210
Table 6.4 (continued)
Zimbabwe
(18)
Venezuela
(17)
Thailand
(16)
Taiwan
Singapore
(15)
Sri Lanka
Puerto Rico
(14)
South Africa
Philippines
(1) 1961
Mexico
Year
Malta
Rate of inflation estimates and their standard errors in 23 LD countries
(19)
(20)
(21)
(22)
(23)
(24)
1.88 0.34 1.59 0.63
1962
1.45 0.60
0.49 0.57
1964
1.72 0.60
1.02 0.35
2.90 0.27
0.54 0.68
1965
1.98 0.83
0.46 0.30
3.74 0.41
1.04 0.50
1966
4.77 0.86
1.86 0.62
3.88 0.32
0.37 1.34
1967
2.70 0.72
2.110.80
3.21 0.21
4.23 1.11
1968
4.23 0.64
1.25 0.44
2.58 0.62
6.18 0.78
1969
4.19 0.51
0.02 0.72
3.48 1.04
4.18 1.01
1963
1970 1971
669 0.98
3.99 0.30
1.27 0.51
3.95 0.68
5.45 2.39
4.20 0.63
3.43 0.74
7.59 0.91
2.33 0.60
1972
565 0.44
3.57 0.51
2.64 0.92
6.66 0.58
3.69 1.24
1973
11.55 1.51
11.40 2.16
14.15 2.82
7.09 1.95
10.52 1.17
20.73 2.12
12.78 1.42
12.67 1.66
11.08 0.90
1975
6.16 3.57
13.19 0.48
650 0.62
2.79 0.90
12.95 1.43
11.02 3.87
5.57 0.96
1976
1.43 1.32
17.32 0.60
3.20 1.17
0.76 1.16
&701.70
1.31 2.29
2.13 1.42
1977
7.10 1.34
24.22 1.35
4.84 0.31
2.08 0.54
10.63 0.61
6.02 1.53
7.99 0.71
1978
4.19 1.01
15.52 0.76
5.53 0.25
2.83 0.59
9.51 0.67
12.54 3.13
6.54 0.71
8.83 1.03
6.63 0.64
1979
6.61 1.26
1635 0.78
10.73 1.61
3.65 0.53
11.77 1.12
13.35 2.96
9.69 1.44
11.31 1.67
10.94 1.67
1980
14.67 2.99
30.36 2.59
9.27 1.73
6.92 1.43
14.49 1.06
21.94 4.31
ia53 2.12
13.72 3.22
14.36 2.05
1981
9.06 1.34
23.76 1.13
5.74 0.43
5.16 1.72
15.23 1.32
11.94 1.99
14.79 0.96
11.67 1.99
13.52 1.24
1982
5.50 2.94
44.44 1.42
2.73 0.83
1.79 1.21
13.29 0.50
13.89 3.05
3.85 0.39
5.39 0.64
12.90 1.30
1983
-0.77 0.45
64.47 1.76
1.35 0.66
0.39 0.75
13.68 2.73
17.40 1.95
2.21 0.43
3.91 085
11.20 L71
1984
-0.37 1.28
50.32 2.61 41.911.02
1.53 0.67
1.74 0.62
10.15 0.57
16.86 1.77
0.53 1.22
0.51 1.22
1985
-1.31 1.23
46.05 1.47
16.18 0.50
0.63 0.83
0.21 0.72
13.43 1.91
3.28 1.96
0.55 0.99
2.98 1.35
11.37 1.21
8.92 2.73
1986
1.03 1.48
59.63 1.14
2.23 0.94
0.98 0.75
-0.27 0.87
17.56 1.08
8.24 0.63
0.60 0.62
2.04 0.58
12.38 0.64
12.15 1.87
1987
0.89 0.76
8525 2.96
4.20 0.33
3.07 0.65
2.19 0.69
13.86 0.86
3.43 1.04
1.57 0.40
3.16 1.04
25.12 1.11
13.55 Z23
1988
-0.39 0.98
77.02 522
8.71 1.23
3.69 0.85
3.46 1.06
13.75 0.91
12.08 2.27
1.79 0.44
4.44 1.46
23.30 1.04
1974
31.06 3.96 9.52 0.60 6.71 0.62
10.82 2.34
14.89 3.11
1989
1.63 1.28
22.53 3.77
10.07 1.39
3.39 1.00
4.09 0.72
13.97 0.92
12.00 3.37
4.62 0.55
4.83 0.70
56.28 5.34
1990
4.36 0.63
24.36 1.46
11.50 1.12
4.13 0.46
3.37 0.73
14.38 0.39
31.89 11.96
3.59 0.38
5.66 0.68
34.15 0.99
1991
3.91 1.36
21.75 0.75
15.52 1.80
1.96 0.91
2.45 0.54
14.39 1.48
1613 4.14
3.38 1.11
5.77 1.15
2527 1.57
1992
2.77 1.36
13.82 0.88
7.48 0.88
1.48 1.03
2.00 0.42
14.19 2.26
3.41 2.26
4.58 0.82
3.44 0.77
2697 2.49
1993
5.64 0.92
2.62 6.08
6.65 0.64
1.64 0.92
3.11 0.82
9.53 0.69
5.84 2.58
3.39 0.44
2.64 0.95
31.42 1.56
1994
13.56 5.56
7.79 0.41
2.32 0.85
3.66 1.00
8.12 1.08
7.87 0.85
4.18 0.70
5.16 0.94
47.48 1.82
1995
29.47 1.82
7.68 0.57
1.32 0.56
a 16 0.35
7.83 2.02
3.59 0.20
5.79 1.06
43.55 1.27
1996
27.44 2.66
3.18 0.40
1997
14.30 0.27
1.05 0.48
1998
17.50 0.91
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Chapter 6 Stochastic Index Numbers
213
observation is that the estimate for the rate of inflation derived in (5.2) is also a weighted sum with the weights being the mean budget shares (w(), whereas the Divisia indices use the time-varying budget shares (wit). In Figure 6.5, we present a scatter plot of the standard error of inflation against the estimated rate of inflation for all 23 OECD countries combined. As can be seen, most of the time, the standard error increases along with the inflation but at a slower rate. In Figure 6.6, we plot the estimated inflation rates against the corresponding t-values. There is a distinct positive relationship between these two variables, which confirms the tendency of the standard error to rise less rapidly than inflation. Figures 6.7-6.8 present the same plots for all the LD countries combined. As we pointed out in the introduction to this chapter, most of the results derived in the previous sections are exclusively with prices and they could well be applied to quantities. The results, applied to the quantity data of the 23 OECD countries and the 23 LD countries, are presented in Tables 6.7 and 6.8, respectively. For each country, the two columns present the quantity index estimates and their standard errors (in adjacent columns). As can be seen, most of the point estimates are estimated precisely. As for the prices, the quantity index estimates obtained in Tables 6.7 and 6.8 are very close to the Divisia quantity indices presented in Tables 3.6 and 4.6, respectively, of Chapters 3 and 4. The reason for this observation is the same as that pointed out for prices in the last paragraph. Tables 6.9 and 6.10 present the estimates of relative quantity changes for the OECD and LD countries, respectively. In Figures 6.9 and 6.10, we present the scatter plots of the estimates of the quantity index against the corresponding standard errors and the estimates of the quantity index against the corresponding t-values for all 23 OECD countries combined. There is a distinct positive relationship between the quantity index
International Consumption Comparisons
214
* o o ,x. *-
8 -
I
6-
y = 0.041 x + 0.5261
• • •*
p i_ o •s ro •B
• V
4
•
Star
• • * 2."
-20
• •
^ - - — *
;&sj-^~~^^
0
20
40
60
80
Inflation rates (x100)
OECD inflation rate estimates vs their standard errors Figure 6.5
y = 0.7277X + 5.3671
* Inflation rates (x100)
OECD inflation rate estimates vs their t-values Figure 6.6
215
Chapter 6 Stochastic Index Numbers
40-
| i
20
J.
d M E M t / * ?
•
•'
y = 6.1749x + 4.3894
0 -
()
1
2
3
4
5
6
Inflation rates (x100)
LDC inflation rate estimates vs their standard errors Figure 6.7
• #
at o 3
.
•
•
y = 0.3988x + 5.7119
40
~•
CD
:> *"
20 -
0
20
40
60
80
Inflation rates (x100)
LDC inflation rate estimates vs their t-values Figure 6.8
216
International Consumption Comparisons
0.90 1.63
0.14 1.65
7.38 1.40
1962
3.26 1.59
3.67 0.42
5.31 1.53
1963 5.82 1.80
3.69 0.68
1.56 1.84
1964 2.86 0.62
1.77 1.15
Italy
1961 0.81 0.85
Ireland
(7)
Iceland
Finland
(6)
Greece
Denmark
(5)
(2)
Germany
Canada
(4)
(1)
France
Belgium
(3)
Year
Australia
Austria
Table 6.7 Quantity index estimates and their standard errors in 23 OECD countries
(8)
(9)
(10)
(11)
(12)
(13)
5.90 1.21
4.08 1.00
4.22 1.20
3.47 1.10
1.77 0.71
5.53 0.59
3.99 0.60
5.46 2.36
4.31 0.99
8.07 1.65
1953 1954 1955 1956 1957 1958 1959 1960
1.11 0.52
4.40 0.92
3.62 0.51
4.22 0.73
5.55 2.09
3.52 0.39
5.46 1.03
7.27 0.91
3.10 0.70
1966 3.20 0.62
3.14 0.90
2.50 0.71
3.50 056
2.19 1.18
4.34 0.42
1.93 0.22
6.88 0.36
6.62 0.72
1967 4.35 0.68
2.09 0.69
2.26 0.91
4.13 0.57
3.86 0.51
1.80 1.15
4.34 0.30
0.84 0.98
4.65 0.86
6.60 1.01
1968 4.35 0.68
3.63 0.41
5.32 0.83
2.20 0.61
2.46 1.24
0.50 1.07
3.09 0.65
4.26 0.62
6.58 1.42
4.41 0.28
1969 4.58 1.12
2.84 0.91
4.75 0.62
2.86 0.56
6.11 1.30
9.80 2 0 8
5.72 0.54
7.21 1.44
6.16 0.78
6.14 0.67
1970 2.73 0.63
6.26 1.21
4.40 0.59
0.88 1.69
2.88 1.03
7.42 0.89
3.85 0.51
609 0.89
7.92 2.57
6.61 0.66
1971 0.76 0.67
7.23 1.70
4.09 0.8B
637 1.67
0.30 1.22
2.13 1.27
5.24 0.75
3.79 0.60
6.07 1.24
2.42 0.44
1972
1.42 1.35
6.40 1.56
5.82 0.89
6.11 1.12
1.72 1.28
7.60 0.98
5.28 0.72
3.15 0.72
6.31 1.10
2.89 0.60
1973 6.80 2.45
3.74 1.11
6.30 1.93
5.44 1.50
5.77 1.18
5.55 1.71
4.79 0.58
1.39 0.91
8.03 1.44
1.60 0.82
0.56 1.22
2.47 1.42
4.01 0.50
-3.25 2.24
1.42 1.79
2 2 4 1.25
0.60 1.33
-1.03 1.59
-0.16 211
1.97 1.11
1975 2.03 0.84
2.70 0.47
0.23 1.51
2.75 0.63
3.11 1.44
2.00 1.59
2 6 4 0.51
3.52 a s s
5.01 1.16
-5.46 2 1 6
-1.91 0.91
1965
1974
5.06 0.97
1.34 0.83
3.53 0.78
4.56 0.84
4.35 0.51
7.08 1.12
0.51 1.82
5.28 0.87
4.30 tt47
4.70 0.92
1.52 2 2 6
2.99 0.36
1977 027 0.98
4.02 1.36
2.28 1.05
2.01 0.55
0.36 0.60
-1.37 1.00
2.53 0.54
4.01 0.76
3.40 1.32
5.50 0.90
1.95 0.67
1978 Z06 0.76
-0.29 2.04
2.39 0.70
2.65 0.48
0.16 0.84
289 0.85
4.18 0.46
3.82 a 4 2
5.01 0.76
8.12 2.65
6691.22
2.62 0.35
1.31 0.62
4.51 0.89
4.23 1.08
2.44 0.32
0.60 0.68
5.10 0.68
2.88 0.18
268 a77
1.46 1.03
-1.58 2 4 3
1.92 1.25
5.02 0.66
1980 2.09 0.78
2.01 0.61
1.69 1.45
0.74 0.74
-3.71 2.02
1.52 0.72
0.90 0.61
1.63 1.35
-1.76 1.87
3.24 1.31
-0.98 0.80
4.03 0.50 0.32 0.69
1976
1979
1981 2.27 0.47
0.51 1.00
a n 0.57
0.97 0.50
-1.38 1.13
1.34 1.00
1.60 0.38
-0.20 1.05
1.33 1.08
5.89 2 4 9
-0.11 1.43
1982 -0.11 0.84
1.06 0.65
2 0 2 1.12
-3.13 2.01
1.65 0.72
1.85 1.00
2.08 0.81
-1.10 0.64
1.02 1.52
5.94 1.72
-9.10 3.69
0.15 0.78
1983 0.80 0.71
4.15 0.84
-0.90 0.76
1.73 0.48
3.07 1.81
1.75 0.94
0.43 0.81
2.16 0.52
-0.89 1.57
-9.53 3.32
-2.43 1.20
-0.85 1.21
1984 2.59 0.40
-0.85 0.99
0.64 0.71
3.91 0.81
3.34 1.19
262 0.55
0.85 0.86
2.46 0.40
1.59 0.64
3.16 1.80
-1.14 1.14
1.91 0.47
1985 3.72 0.60
1.40 0.37
1.22 0.50
4.39 0.93
4.06 1.20
2.65 1.37
2.00 0.48
1.82 0.48
3.41 1.11
4.79 1.42
4.07 1.52
2.58 0.47
1986 -0.55 1.02
0.74 0.62
1.72 0.53
3.62 0.74
3.90 1.02
3.22 0.42
2.71 0.20
282 0.67
0.62 0.97
5.88 4.27
-0.43 1.48
3.07 0.44
1987 2.10 0.70
1.92 0.60
2.51 0.33
2.53 0.52
-1.94 1.28
4.57 0 6 6
2.23 0.43
4.71 1.75
1.50 1.55
8.88 3.01
3.60 0.87
3.46 0.71
1988 2.01 0.92
3.50 1.53
2.72 0.57
-0.99 049
-1.02 1.65
4.28 0.83
2.64 0.56
0.43 1.74
2.34 0.56
-2.62 3.28
4.33 1.36
3.63 0.65
1989 2.10 0.47
4.22 0.79
2.27 0.51
5.06 0.59
-0.28 0.67
3.54 0.42
2.67 0.53
1.37 0.63
2.01 0.66
-2.76 4.65
7.73 0.90
2.80 0.48
1990 -0.56 0.68
3.08 0.42
3.13 0.56
-1.07 0.75
-0.16 0.32
-1.25 1.21
2.02 0.39
5.27 0.79
0.89 0.42
-0.27 1.42
2 1 8 1.14
1.80 0.48
1991
1.46 0.38
2.01 0.61
2.28 0.42
-7.70 1.30
1.96 0.62
-3.73 241
0.64 0.68
4.29 0.67
0.86 0.64
0.05 1.23
1.97 0.70
3.91 0.55
1992 2.33 0.30
0.70 0.81
1.17 0.41
-0.21 0.30
1.07 0.76
-4.95 207
0.75 0.23
-0.23 0.59
1.08 0.97
4.60 1.88
253 055
0.70 0.36
1993 2.62 0.45
0.52 0.78
-2.00 1.06
0.59 0.41
1.28 0.42
-2.66 1.44
-0.40 0.82
-1.58 1.25
0.38 1.49
-4.30 1.45
234 0.41
-2.57 l.SS
-0.74 0.71
1.60 1.48
-1.35 1.21
4.84 1.12
1.04 0.37
0.18 1.09
4.% 1.48
3.44 1.06
1.27 0.42
5.60 1.41
5.63 1.73
0.37 0.58
1994 4.23 0.53
-2.87 0.65
1.13 0.56
2.55 0.56
5.92 2.76
1.62 0.44
0.77 0.52
1995 2.81 0.55
-6.59 1.05
0.56 0.47
0.36 0.57
0.62 0.52
3.55 0.74
0.85 0.47
1996 0.43 0.53
5.19 0.71
2.35 1.56
3.26 0.84
-1.17 0.43
Table 6.7 continued on next page
111
Chapter 6 Stochastic Index Numbers
Switzerland
*:
(18)
(19)
(20)
(21)
(22)
(23)
1.78 0.66 3.13 0.41 1.59 1.10 2.79 0.72 7.21 1.83 0.06 2.12 4.40 0.98 2.06 0.44 4.17 1.99 2.61 0.60 4.20 0.75 5.28 1.23 5.91 1.23 -2.02 2.11 3.71 0.62 2.20 0.84 0.00 0.92 0.26 0.87 0.79 0.45 2.92 0.57 8.92 2.08 3.96 0.95 -1.45 2.10 6.48 1.42 -2.40 1.98 8.28 5.08 -1.46 1.57 3.35 1.15 0.99 0.82 5.84 1.24 1.43 1.38 4.09 1.15 1.21 0.56 3.60 0.70 1.82 0.70 -0.54 1.04 3.92 0.88 2.02 0.89 2.16 0.58 1.28 0.47 3.98 1.48
6.60 1.14 7.31 2.32 5.29 0.58 5.75 1.07 6.27 0.66 3.42 0.36 4.08 0.49 7.48 1.61 6.78 1.09 3.94 1.28 1.62 0.72 3.76 0.36 1.46 0.29 0.49 0.63 0.24 1.22 -0.52 1.55 -0.69 0.85 -0.21 0.50 -1.49 2.00 -0.20 0.95 2.60 1.21 3.13 0.66 4.52 0.96 3.78 0.64 3.86 0.54 2.60 0.88 2.40 0.79 1.87 0.40 -1.80 1.58 1.24 0.19 1.46 0.71 1.75 0.39
4.32 0.95 3.41 0.83 0.98 1.16 1.79 0.83 3.95 1.12 3.45 0.59 0.72 0.52 -1.61 1.07 1.94 0.50 1.87 0.50 3.42 1.62 2.41 0.39 3.65 0.62 -1.43 0.97 -0.86 0.92 2.21 0.62 -1.23 0.68 -0.73 0.53 2.00 0.70 -1.11 0.51 1.52 0.21 2.36 0.65 4.14 1.39 3.98 1.48 1.76 0.90 0.56 1.02 -1.38 1.07 0.03 0.75 -2.19 1.39 -2.24 1.25 0.86 0.65 0.46 0.43 0.67 0.47
3
USA
Sweden
(15)
Spain
3
(16) (17) 5.81 1.59 6.54 1.57 5.74 1.43 6.68 1.33 -1.10 1.29 -1.62 1.57 4.77 1.07 5.64 1.21 4.95 0.82 5.58 0.62 7.92 0.57 4.44 1.97 6.89 1.27 1.45 1.62 3.75 1.04 5.10 1.11 7.40 1.61 6.33 1.41 5.20 0.43 4.37 1.13 2.17 0.45 7.85 0.95 4.24 0.87 2.61 1.46 7.67 1.02 3.62 0.57 3.00 0.81 -0.91 1.82 4.14 1.02 1.48 0.68 3.16 1.45 5.18 0.92 2.01 1.60 2.49 1.05 3.82 1.19 4.18 0.37 3.12 0.65 3.09 0.95 3.71 0.59 4.17 1.11 2.84 1.25 2.83 0.47 5.31 1.12 2.43 1.03 2.36 0.89 0.85 1.25 2.93 0.96 -0.88 1.11 0.52 0.67 -1.04 0.85 -3.03 1.52 3.64 0.91 1.68 1.80 -1.92 0.91 2.41 0.37 1.48 1.37 0.36 0.59 1.% 0.62 0.71 1.25 -1.05 0.67 2.70 0.48 2.66 0.96 2.62 0.75 1.03 0.54 3.12 2.36 2.68 0.91 2.00 0.78 1.97 0.38 3.20 1.00 3.44 0.61 4.16 1.12 1.79 0.58 1.74 1.09 4.11 0.84 3.16 0.45 0.26 0.72 0.17 1.22 3.92 0.78 1.30 0.90 2.89 0.41 0.34 1.02 3.86 0.86 3.69 1.15 3.64 0.67 -1.55 1.51 2.07 0.60 3.29 1.10 2.25 0.85 -3.18 1.18 1.57 0.72 1.60 0.53 0.15 0.96 -0.12 0.54 3.88 0.90 0.52 0.51 1.35 0.45 5.02 1.26 1.40 0.54 1.16 0.47 3.04 1.10 1.34 0.79 2.31 0.29 1.86 1.00 (14)
Portugal
(1) 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
E
Norway
Year
Japan
2
Netherlands
Table 6.7 (continued) Quantity index estimates and their standard errors in 23 OECD countries
(24)
3.71 0.73 2.51 0.39 2.89 1.10 2.20 0.73 2.08 0.47 1.83 0.31 2.58 0.28 4.09 0.50 4.26 0.43 3.72 0.52 2.71 0.38 1.91 0.90 -0.56 0.82 -2.36 1.06 1.69 0.70 3.17 0.55 1.09 0.75 0.86 0.50 3.10 0.42 0.17 0.57 -0.89 0.16 1.10 0.40 1.16 0.36 0.86 0.33 2.28 0.34 1.07 0.20 1.27 0.39 1.35 0.40 0.61 0.25 0.25 0.59 -1.52 0.45 -2.09 0.71 -0.96 0.42
1.18 1.04 4.21 0.96 2.58 0.90 0.73 0.61 1.54 0.67 2.10 0.45 2.97 0.40 0.28 0.65 2.60 0.42 2.89 0.94 5.83 0.91 4.94 1.01 -1.01 1.61 -0.50 0.36 1.12 0.70 0.18 0.73 4.67 0.73 4.00 0.42 -1.88 0.71 -0.80 0.65 0.73 0.25 3.87 0.46 1.86 0.60 3.52 0.45 5.80 1.05 4.56 0.73 6.10 1.74 2.58 0.89 0.16 0.66 -1.61 1.01 -1.46 1.30 2.43 0.38 2.30 0.55 1.14 0.72 3.08 0.53
3.46 0.69 2.72 0.48 4.17 0.47 4.32 0.61 3.96 0.42 1.88 0.50 4.30 0.67 2.67 0.67 1.15 1.01 2.44 0.97 4.90 0.67 4.05 0.68 -1.58 1.29 1.23 0.70 4.38 0.77 3.29 0.57 3.03 0.72 1.26 0.71 -1.26 1.60 0.65 0.59 -0.21 0.58 3.75 0.96 3.98 0.86 3.38 0.58 2.96 0.46 1.71 0.55 2.95 0.25 1.55 0.31 0.46 0.60 -1.90 1.26 1.80 0.46 1.80 0.47 2.12 0.52 1.44 0.35 2.01 0.68
International Consumption
218
Comparisons
Ecuador
Fiji
Honduras
Hong Kong
Hungary
India
Iran
Israel
Jamaica
Korea
(1) 1961 1962
Cyprus
Year
Colombia
Table &8 Quantity index estimates and their standard errors in 23 I D oouitries
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
1963 1964 1965 1966 1967 1968 1969 1970 1971
284165
616 1.67
4.24 1.34
1972
-1.52 087
519 1.46
7.04096
1973 287 1.13 1974 4.11 1.19 1975 0.93 1.14 1976 4.67 0.91 1977 1.73 1.25
146 1.21
664 O90 7.15056 543 076 4.77 267
1060 1065 7.25 225 -297069 -6.35 562
1978
298143
1979 1980 1981 1982 1983 1984
606 Q65 220 1.14
1451.25 -185272 150 1.41
-002 083 -0421.89 274 076 6961.75 4.23 087 1293 516
260109 593 099
264150 aw aso 14.77196 3.99133 -175094 547 202
-1.77 1.68
4.25 039 7.32 087
4.02 1.20 -215177 -6.86103 4.93118
270045 173183 3.82 078 ###345 282 078 559 3.89 216 029 -162 253 -569144 297 041 074 036 -1.16 656 1.50073 250 220 -551073 519 090 7.73 4.19 -097 Q82 -053 076 9.07 1.00 005051 455177 -7.44083 2391.57 -275 1.11 694235 0911.36 553 1.19 -1.78 073 13.21 4.24 -556199 270110 5551.03 162193 9.56277 068 084 4.47 286 -012 103 -1.39088 168 073 1.68035 207 071 3.27102 -880 554 648121 1985 -017 090 110 082 036 064 023 202 257 082 1.45 Q80 082 1.05 -014105 111 3.17 -109 210 1986 1.21041 535 1.51 0.05 075 4.95 205 6741.06 228 065 100 097 ### 120 9.57 285 -155198 1987 1.85 068 6.201.24 -O11O70 -132 250 10441.76 546 138 169 030 4.22156 7.23153 a43100 1988 1.91 044 9.95 204 -034 095 669166 7.10 1.66 -3.91 188 193 057 -3.06 3.89 2001.24 1.77 1.50 235 1.17 236099 222 Q61 1.98 3.51 -1.14187 1989 1.31089 a58200 018 041 260 076 1990 1.20 045 5781.00 -010 031 1.92 221 4.52 1.40 -3.19 204 174 032 1627 291 1.82 076 1991 -0.15 051 103 213 -032 062 -OS 158 535 209 -6.54 209 -014146 aC8 8.81 -060086 7.73 202 091069 191029 147 233 592163 1992 246 059 6,291.05 024 072 6111.41 Q84119 263055 -035 278 4.56 1.35 1993 -6.53193 043 075 1994 S4S195 -0311.03 207 077 060 210 5701.08 3.21083 1995 1996 1997
-3.80 199
3.45058 4.14 111
4.77 093
6.02 1.16 a391.30 6731.34 -2.12 1.92 1.90 088 5.79 1.53 7.85065 614136 4.90146 7.84 081 7.30 048 695031 a00O44 a i£ 0 4 1 7.46047 507 066 4.13 078 564 032 6.71046 5.05 067
1998 TiUe6.8aTtin£dnetpag2
219
Chapter 6 Stochastic Index Numbers Table 6.8 (continued)
Zimbabwe
(18)
Venezuela
(17)
Thailand
(16)
Taiwan
Singapore
(15)
Sri Lanka
Puerto Rico
(14)
South Africa
Philippines
(1) 1961
Mexico
Year
Malta
Quantity index esJinubas and their standard errors in 23 LD countries
(19)
(20)
(21)
(22)
(23)
(24)
-1.83 1.27
1962
0.74 0.43 3.27 1.09
4.08 0.54
1964
635 1.80
-4.11 1.27
4.69 1.33
11.68 266
1965
5.96 1.27
3.21 0.97
-3.39 0.60
7.56 1.07
1966
3.09 3.18
5091.75
1.70 0.29
3.68 1.00
1967
4.75 1.57
5.08 1.61
1.65 0.26
a291.70
1968
9.29 1.83
6.97 0.71
4.13 0.58
7.19 0.66
1969
5.65 117
7.54 1.25
3.53 0.64
5.47 0.69
1970
a 17 1.75 10.82 0.72
3.96 0.74
5.90 1.17
4.10 1.49
6.96 0.84
213 1.07
7.111.25
1963
1971
233 0.92
1972
4.31 1.37
4.54 0.96
7.67 0.58
1.09 1.06
a89 0.47
1973
4.08 0.65
-4.45 202
7.09 1.10
5.16 0.79
10.98 121
1.72 1.04
-3.37 210
4.17 2.25
285 1.33
1975
8.13 1.71
1.85 0.45
5.61 289
1.08 1.38
-0.06 0.64
-a80 280
4.52 0.42
1976
7.59 Z30
1.22 0.59
5.52 1.57
4.111.28
0.26 237
3.84 298
5.49 0.42
1977 15.24 4.90
0.96 0.72
3.81 1.27
5.12 1.30
-259 1.83 10.01 1.85
5.41 0.51
1974
3.71 127 -1.92 3.01 670 0.97
-13.97 1.53 4.46 4.14
7.74 2.46
4.85 1.12
2.20 1.12
691 0.82
-0.46 105
268 5.39
7.21 0.82
5.20 0.85
1979 10.52 1.77
5.88 1.19
-0.33 209
7.75 0.96
145 0.68
834 1.66
828 207
3.69 1.43
a79 3.69
9.26 4.55
3.97 0.47
-281 269
6.91 0.97
601200
5.48 3.51
3.56 0.62
3.39 0.72
-3.79 637
1981 -5.92 2.00
3.89 1.09
-100 1.75
603 1.41
3.89 1.02
2061.84
1.72 0.74
0.55 1.49
1283 4.22
1962 -8.54 260
-3.03 2,07
1.88 1.20
261 0.82
0.04 1.02
214 1.82
264 0.90
0.78 0.74
-644 291
1983 -217 1.28
-6.76 202
3.04 206
7.76 0.68
-6.76 0.91
-1.00 3.08
4.15 0.67
4.96 0.69
1132 4.91
1984
0.74 0.78
0.32 1.04
-217 0.35
3.86 1.98
2281.48
3.44133
-4.04 3.41
673 0.77
3.02 129
1985
6.46 296
0.75 111
-3.61 0.36
3.18127
-3.84 2.67
-5.47 219
3.55 1.56
3.69 0.86
-0.04 1.49
0.09 1.90
-a78a44
1966
3.42 242
-4.32 1.06
0.86 0.27
4.86 1.54
3.31 1.52
-3.09 203
-0.57 1.64
600 0.70
225 0.56
275 107
-1.64 4.23
1967
7.01 1.29
-235 1.31
1.57 0.43
3.03 0.86
a411.89
153 1.18
287 1.87
a81 0.82
7.26 1.82
1.80 0.47 -20.59 3.35
1988 10.20 273
-0.90 0.85
3.65 0.46
-0.10 1.10
1.42 1.28
3.09 135
3.27 0.83
10.28 1.38
828105
1.90 0.29
7.05 1.49
4.62 0.53
255 0.27
0.50 1.07
4.91 1.49
0.90 0.72
-0.74 260
9.82 1.81
a74 0.86
-9.29 235
1990
3.20 1.82
3.48 0.43
296 0.44
-247 1.02
2941.89
0.44 0.62
# # # 1163 634 109
a70 1.31
-0.411.26
1991
4.15 232
207 0.53
-1.31 0.19
1.49 1.38
0.72 2.05
-3.46 0.54
-0.48 211
589 1.45
3.34 0.76
5211.41
1992
1.92 1.90
225 0.43
0.65 0.38
3.25 210
3.96 1.59
-4.09 1.24
7.14 261
670 0.67
642 1.28
5.42 0.99
1993 1994
3.23 206
-0.61 0.89
2.34 1.43 1.92 1.94
5.38 1.35
-1.84 0.76
685 294
647 0.53
5.84 0.96
-296 201
0.75 0.82
1.04 0.62
634 1.34
7.10 1.42
560 1.05
-6.31 1.85
-144 0.76
259 1.04
1.98 0.92
4.28 1.61
7.20 0.51
0.28 0.58
1978 I960
1989
229 0.65
0.50 0.14 1.22 0.08
1995
-7.80 266
1.36 0.28
1996
-4.83 0.85
5.25 109
1997
6541.03
632 1.17
1996
5.02 0.50
-3269 261
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.a n
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222
Standard errors (x100)
International Consumption
y= -0.0054X + 0.9469 *
•
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•
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OECD quantity index estimates vs their standard errors Figure 6.9
y=0.9279x +1.0852 15
-46Quantity index estimates (x100)
OECD quantity index estimates vs their t-values Figure 6.10
Comparisons
223
Chapter 6 Stochastic Index Numbers
y = -0.027x +1.5899 o
y
12
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LDC quantity index estimates vs their standard errors Figure 6.11
y = 0.6403x +1.1833
23
X -so
-eeQuantity index estimates (x100)
LDC quantity index estimates vs their t-values Figure 6.12
224
International Consumption Comparisons
estimates and the corresponding t-values (with a slope coefficient of .59, which is less than one), which confirms the tendency of the standard error to rise less rapidly than the quantity index. Figures 6.11-6.12 present the same plots for all the LD countries combined.
6.8 Conclusion In this chapter, we introduced the recent developments in index number measurements based on the stochastic approach. We showed how this renewed approach can be used to measure the movement in prices and consumption growth in the OECD and LD countries. The main attraction of the stochastic approach is that it provides the point estimates of growth as well as the corresponding standard errors.
References Balk, B.M. (1980). 'A Method for Constructing Price Indices for Seasonal Commodities,' Journal of the Royal Statistical Society, Series A, 142, Part I: 68-75. Clements, K.W. and H.Y Izan (1981). 'A Note on Estimating Divisia Index Numbers,' International Economic Review 22: 745-747. Clements, K.W., and H.Y Izan (1987). 'The Measurement of Inflation: A Stochastic Approach,' Journal of Business and Economic Statistics 5: 339-350. Crompton, P. (2000). 'Extending the Stochastic Approach to Index Numbers,' Applied Economics Letters 7: 367-371.
225
Chapter 6 Stochastic Index Numbers
Diewert, W.E. (1981). 'The Economic Theory of Index Numbers: A Survey,' in A Deaton (ed.), Essays in the Theory of Consumer Behaviour. Cambridge: Cambridge University Press. Diewert, W.E. (1995). 'On the Stochastic Approach to Index Numbers,' Discussion Paper No. 95-31, Department of Economics, University of British Columbia. Frisch, R. (1936). 'Annual Survey of General Theory: The Problem of Index Numbers,' Econometrica 4: 1-38. Rao, D.S.P., T. Doran and E.A. Selvanathan (2002). 'Estimation of General and Commodity-Specific
Inflation
Rates
Using
Linear
Time-Varying
Constraints,' Journal of Agricultural and Applied Economics 34: 61-1 A. Rao, D.S.P., and E.A. Selvanathan (1991). 'A Log-Change Index Number Formula for Multilateral Comparisons,' Economics Letters 35: 297-300. Rao, D.S.P., and E.A. Selvanathan (1992). 'Uniformly Minimum Variance Unbiased Estimators of Theil-Tornqvist Index Numbers,'
Economics
Letters 39: 123-127. Rao, D.S.P., and E.A. Selvanathan (1996). 'On the Stochastic Approach to International Comparisons of Prices, GDP and Productivity,' in D.S.P. Rao and J. Salazar-Carrillo (eds.), International Comparison of Prices, Output and Productivity. Elsevier North-Holland Publishing Company, pp. 195-216. Rao, D.S.P., E.A. Selvanathan and D. Pilat (1995). 'Generalized Theil-Tornqvist Indices with Applications to International Comparisons of Prices and Real Output,' Review of Economics and Statistics LXXVII: 352-360. Selvanathan, E.A. (1989). 'A Note on the Stochastic Approach to Index Numbers,' Journal of Business and Economic Statistics 7: 471-474. Selvanathan, E.A. (1991). 'Standard Errors for Laspeyres and Paasche Index Numbers,' Economics Letters 35: 35-38.
226
International Consumption Comparisons
Selvanathan, E.A. (1993). 'More on Laspeyres Index Numbers,'
Economics
Letters 43: 157-162. Selvanathan, E.A. (2002). 'Extending the Stochastic Index Numbers,' Applied Economics Letters, forthcomig. Selvanathan, E.A., and D.S.P. Rao (1992a). 'Computation of Standard Errors for Geary-Khamis Parities and International Prices,' Journal of Business and Economics Statistics 10(1): 109-115. Selvanathan, E.A., and D.S.P. Rao (1992b). 'An Econometrics Approach to the Construction of Generalized Theil-Tornqvist Indices for Multilateral Comparisons,' Journal of Econometrics 54: 335-346. Selvanathan, E.A,. and D.S.P. Rao (1994). Index Numbers: A
Stochastic
Approach. London: Macmillan Publishers. Selvanathan, E.A., and S. Selvanathan (2003). 'Modelling the Commodity Prices in the OECD Countries: A Stochastic Approach,'
Economic
Modelling, forthcoming. Theil, H., F.E. Suhm, and J.F. Meisner (1981). International
Consumption
Comparisons: A System-Wide Analysis. Amsterdam: North-Holland.
CHAPTER 7
Testing Demand Theory Hypotheses: O E C D and LD Countries S. Selvanathan &E.A. Selvanathan
In Chapter 2, we pointed out that estimating a system of demand equations in an unrestricted fashion requires the estimation of an impossibly large number of coefficients. In many demand analysis applications, a priori restrictions such as demand homogeneity and Slutsky symmetry are imposed, thus reducing the number of unknown parameters. In a review article on systems of consumer demand functions, Barten (1977) summarizes the results from various empirical applications, which test the validity of the hypotheses of homogeneity and symmetry. These results show that homogeneity is generally not acceptable, while symmetry is a bit more acceptable. Barten concludes that one reason for these negative results is that since the test procedures are usually based on the asymptotic distribution of the test statistic without correction for small-sample bias, the results are biased towards rejection. Simulations by Bera et al (1981), Bewley (1983). Laitinen (1978) and Meisner (1979) have confirmed this conclusion. In view of these difficulties, Laitinen (1978) developed a finitesample test for testing homogeneity and Theil (1987) developed alternative distribution-free testing procedures for testing homogeneity and symmetry. Various aspects of testing demand theory hypotheses have also been researched in recent times by many researchers (for example, see Attfield, 1997, 1998; Buse, 1988; Cribari and Zarkos, 1997; Deschamps, 2000; Karagiannis and Mergos,
International Consumption Comparisons
228
2002; Keuzenkamp, 2000; Keuzenkamp and Barten, 1995; Muellbauer and Peshardes, 1992; Ng, 1995; and Pollak and Wales, 1992). In Chapter 2, we presented the theoretical framework of consumer demand and, in Chapters 3 and 4, we presented preliminary data analysis for the OECD and LDC data based on some of the theoretical results presented in Chapter 2 and the data-analytic techniques introduced in Selvanathan (1995). In this chapter, we present a detailed account of the conventional tests used for testing the demand theory hypotheses, homogeneity and symmetry, and illustrate their application using the OECD and LDC data. In Chapter 8, we test these hypotheses using alternative demand systems such as the AIDS, CBS and NBR introduced in Chapter 2. In Chapter 9, we test the hypothesis of preference independent structures among goods. The organisation of this chapter is as follows. In Section 7.1, we present the demand model and in Sections 7.2 and 7.3, we discuss the conventional tests for the demand theory hypotheses, homogeneity and symmetry. In Section 7.4, we present the summary results and our concluding comments.
7.1
The Demand Model
For commodity i (=[,...,n, the number of goods) and period t (=1,...,T, the sample size after lagging), the absolute price version of the Rotterdam model (3.21) from Section 2.3 with an error term added can be written as wit Dq« = Gi DQt + £ KijDpjt + eit.
(1.1)
where 0j is the i* marginal share satisfying Z"=i0/ = 1; TCy is the (ij)* Slutsky coefficient satisfying Zf=17ty =0; and all other notations are as defined in
229
Chapter 7 Testing Demand Theory Hypotheses
Chapter 2. The error terms are assumed to be normally distributed with zero mean and are independent over time. Equation (1.1) for i=l,...,n is a fairly general demand system in the sense that it can be considered as a first-order approximation to the true demand equations. If we sum both sides of (1.1) over i=l,...,n, we get Z"=ie,i = 0 f° r t=l,...,T. Therefore, the eit's are linearly dependent and one of the equations is redundant and can be deleted (Barten, 1969). We delete the n-th equation. It can be shown that the best linear unbiased estimators of the parameters for the system of equations (1.1) for i=l,...,n are the same as those obtained by estimating each equation separately by least squares (LS). See Theil (1971) for details. Let 2 be the (n-l)x(n-l) contemporaneous covariance matrix of the disturbance term eit of (1.1) for i=l,...,n-l. In general, S is unknown. For estimation and hypothesis testing, it is common practice to approximate this matrix by its unbiased estimator S, the matrix of mean squares and cross products of the LS residuals. Denoting yit = wit Dqit, yi = [8j nn ... nm]' and xt = [DQt Dph ... Dpnt]', and deleting the n* equation, (1.1) can be written for t=l,...,T as y,
= Xyi + Ei,
i=l,...,n,
(1.2)
where jj = \ylt] is a T-vector; X is a T x (n+1) matrix whose t* row is x't; and Ei = [Eit] is a T-vector. We write (1.2) for i=l,...,«-l as y
=
( I „ . , ® X ) Y + E,
(1.3)
where I„_i is the identity matrix of order («-l); y = [VJ], y = fy] and E = [E(] are vectors consisting of (n-1) subvectors; and ® is the Kronecker product.
International Consumption Comparisons
230
7.2
Demand Homogeneity
Here we reproduce the demand homogeneity restriction (3.17) introduced in Section 2.3:
171, = 0,
i=l,...,n.
(2.1)
Let a = [0 1 ... 1]' be a (w+l)-vector. Then, demand homogeneity, (2.1), can be written in vector form as a'Yi= 0,
i=l,...,/i.
For i=l, ...,n-l, this can be expressed as RY = 0,
(2.2)
where R = I„_i ® a'.
The Asymptotic Test of Homogeneity
The test statistic for testing the homogeneity restriction (2.2) is
trZ - 1 S
(2.3)
Chapter 7 Testing Demand Theory Hypotheses
231
where y 1S the LS estimator of y, 2 is the error covariance matrix; and S is the LS residual moment matrix, an unbiased estimator of 2 (Theil, 1971). When E is known, under the null hypothesis, (2.3) is distributed as F with (n-l) and (n-l)(T-n-2) degrees of freedom. Usually, the error covariance matrix S is unknown and is replaced by its estimator S. The test statistic for homogeneity then becomes
(Ryys-(RV) H
a'CX'Xr'a
Under the null hypothesis, it can be easily shown that, T H has an asymptotic x2 distribution with (n-l) degrees of freedom. It is worth noting that as (2.4) involves S"\ S must be non-singular. The necessary condition for S to be non-singular is that T- 2ra > 1 (Laitinen, 1978). Laitinen's Exact Test for Homogeneity
Laitinen (1978) derived the exact finite-sample distribution of ^ H in (2.4) under the null hypothesis of demand homogeneity restriction. Laitinen showed that *FH is distributed as a Hotelling's T2, which itself is distributed as a constant multiple («-l)(T-n-2)/(T-2n) of F(«-l,T-2n). This exact test is very useful in applications where the sample size is relatively small. Application of the tests of homogeneity to the OECD data
Table 7.1 presents the sample size after lagging (T) and the number of commodities (n) in columns 2 and 3 for the 23 OECD countries. The last column presents the value of (T-2n) which is used to verify the necessary condition for
International Consumption Comparisons
232
Table 7.1 Further characteristics of the OECD database Country (1) 1. Australia
Sample size after lagging T (2) 36
Number of commodities n (3) 9
T-2n (4) 18
2.
Austria
32
9
14
3.
Belgium
36
4.
Canada
35
8 9
20 17
5.
Denmark
29
9
11
6.
Finland
36
8
20
7.
France
32
9
14
8.
Germany
33
8
17
9.
Greece
34
9
16
10. Iceland
19
9
1
11. Ireland
23
9
5
12. Italy
32
9
14
13. Japan
26
8
10
14. Luxembourg
21
8
5
15. Netherlands
44
8
28
16. New Zealand
12
5
2
17. Norway 18. Portugal
32
9
14
9
8
-7
19. Spain
32
8
16
20. Sweden
33
9
15
21. Switzerland
33
8
17
22. UK
35
8
23. USA
35
9
19 17
Chapter 7 Testing Demand Theory Hypotheses
233
the non-singularity of the error covariance matrix S. Among the 23 OECD countries considered, S is non-singular (i.e., T-2n > 1) for 21 countries and singular (i.e., T-2n < 1) for the remaining 2 countries, New Zealand and Portugal. In order to achieve non-singularity of S for New Zealand, we aggregate the commodities into n = 5 commodity groups so that T-2n = 2 > 1 (where the housing group includes housing and durables; and the miscellaneous group includes transport, recreation, education and miscellaneous). As the sample size for Portugal is only 8, we drop Portugal from our analysis. We now calculate the test statistic (2.4) to test homogeneity using the data from 22 OECD countries (after dropping Portugal and using only 5 commodity groups for New Zealand). The results from the homogeneity test for the OECD countries are shown in Table 7.2. The observed values of the test statistic (2.4) are presented in column 2 of the table. The critical values at the 5 percent level of significance for the asymptotic %2-test are presented in column 3. Comparing column 2 with column 3, we see that homogeneity is acceptable only for 9 of the 22 OECD countries. These results are consistent with the results from most previous studies where the asymptotic test was used to test homogeneity (e.g., Selvanathan, 1993; Theil and Clements, 1987; and Chen 2001). Now we employ Laitinen's exact test to test the hypothesis of demand homogeneity. For the 22 OECD countries, the observed and critical values based on exact distributions are presented in columns 5 and 6 of Table 7.2. Comparing the observed values of the test statistic in column 5 with the critical values in column 6, we can see that homogeneity is now acceptable for all countries except Greece and the USA. These results support the view of Barten (1977) that the rejection of homogeneity is due to the failure of the asymptotic test.
International Consumption Comparisons
234
Table 7.2 Testing homogeneity in 22 OECD countries Asymptotic x2 test
Laitinen's exact test
Country
(1) 1. Australia
Data-based Critical Conclusion Data-based Critical Conclusion ¥H x2("-1.-05) T2 F(n-1 ,T-2n,a) (2) (3) (4) (5) (6) (7) 2 Do not rej F(8,18)=2.51 Do not rej 12.24 X (8)=15.51 1.10
2. Austria
12.38
X2(8)=15.51
Do not rej
1.03
F(8,14)=2.70
3. Belgium
23.31
X2(7)=14.07
Reject
2.56
F(7,20)=3.70* Do not rej*
4. Canada
9.59
Z2(8)=15.51
Do not rej
0.85
F(8,17)=2.55
Do not rej
5. Denmark
22.27
X2(8)=15.51
Reject
1.70
F(8,11)=2.95
Do not rej
6. Finland
27.92
X2(7)=14.07
Reject
3.07
F(7,20)=3.70* Do not rej*
7. France
44.64
X2(8)=15.51
Reject
3.72
F(8,14)=4.14* Do not rej*
2
Do not rej
8. Germany
17.13
X (7)=18.48*
Do not rej*
1.81
F(7,17)=2.61
Do not rej
9. Greece
64.52
X2(8)=15.51
Reject
5.61
F(8,16)=2.59
Reject
10 Iceland
58.31
X2(8)=15.51
Reject
0.91
F(8,1)=238.9
Do not rej
11 Ireland
154.35
X2(8)=15.51
Reject
8.04
F(8,5)=10.29*
Do not rej*
12 Italy
15.81
X2(8)=20.09*
Do not rej*
1.32
F(8,14)=2.70
Do not rej
13 Japan
40.76
X2(7)=14.07
Reject
3.64
F(7,10)=5.20* Do not rej*
14 Luxembourg
19.31
X2(7)=14.07
Reject
1.25
F(7,5)=4.88
15 Netherlands
2
Do not rej
X {7)=14.07
Reject
2.98
F(7,28)=3.36* Do not rej*
X2(4)= 9.49
Reject
1.89
F(4,2)= 19.25
Do not rej
X2(8)=20.09*
Do not rej*
1.43
F(8,14)=2.70
Do not rej
18 Spain
17.18 14.79
X2(7)=18.48*
Do not rej*
1.54
F(7,16)=2.66
Do not rej
19 Sweden
24.65
X2(8)=15.51
Reject
2.10
F(8,15)=2.64
Do not rej
20 Switzerland
16.52
X2(7)=18.48*
Do not rej*
1.74
F(7,17)=2.61
Do not rej
8.17
X2(7)=14.07
Do not rej
0.89
F(7,19)=2.54
Do not rej
56.77
X2(8)=15.51
Reject
5.03
F(8,17)=2.55
Reject
16. New Zealand 17 Norway
21. UK 22. USA
25.32 18.89
The level of significance a = 0.05. A * denotes critical value and conclusion at a = 0.01.
Chapter 7 Testing Demand Theory Hypotheses
235
Application of the tests of homogeneity to the LDC data
Table 7.3 presents the sample size after lagging (T) and the number of commodities (n) in columns 2 and 3 for the 23 LD countries. The last column presents the value of (T-2«) which is used to verify the non-singularity condition (T-2n > 1). For the original data, S is non-singular for 17 LD countries and singular or near-singular for the remaining 6 countries, Honduras, Hungary, India, Iran, Jamaica and Philippines. In order to achieve non-singularity of S for these 6 countries, we aggregate some of the commodities to achieve nonsingularity. The number of commodity groups presented in column 3 for these countries reflect the number of combined commodity groups. Table 7.4 presents the results for testing homogeneity for the LD countries. Columns 2-4 of the table present the results based on the asymptotic test statistic. As can be seen, homogeneity is acceptable only for 11 of the 23 countries. This result is also consistent with the findings of the OECD results. Columns 5-7 of Table 7.4 present the exact homogeneity test results for the 23 LD countries. As with the results for the OECD countries, using the exact test, homogeneity is now acceptable for all LD countries. As pointed out in the introduction to this chapter, the reason for the universal rejection of homogeneity could be due to the test procedures that are based on asymptotic distribution without correction for small sample bias. The results in this chapter for testing the homogeneity restriction for the OECD and LD countries using asymptotic and exact tests support this.
7.3
Slutsky Symmetry
We now take homogeneity as given and consider symmetry. The homogeneityconstrained version of model (1.1) is obtained by imposing the homogeneity
International Consumption Comparisons
236
Table 7.3 Further characteristics of the LDC database Country
(D
Sample size after lagging T (2) 20
Number of commodities n (3) 9
T-2n (4) 2
1.
Colombia
2.
Cyprus
14
6
2
3.
Ecuador
20
7
6
4.
Fiji
14
6
2
5.
Honduras
12
5
2
6.
Hong Kong
25
9
7
7.
Hungary
11
5
1
8.
India
15
7
1
9.
Iran
12
5
2
10. Israel
25
9
7
11. Jamaica
14
6
2
12. Korea
22
8
6
13. Malta
20
8
4
14. Mexico
28
8
12
15. Philippines
12
5
2
16. Puerto Rico
31
8
15
17. Singapore
32
8
16
18. South Africa
35
8
19
19. Sri Lanka
21
8
5
20. Taiwan
35
8
19 3
21. Thailand
19
8
22. Venezuela
11
5
1
23. Zimbabwe
12
5
2
Chapter 7 Testing Demand Theory Hypotheses
237
Table 7.4 Testing homogeneity in 23 LD countries Asymptotic %2 test
Laitinen's exact test
Country
(D 1. Colombia 2. Cyprus
Data-based Critical Conclusion H»H X2("-1,.05) (3) (4) (2) 2 Reject 268.72 Z (8)=15.51 21.36
X2(5)=11.07 2
Data-based Critical Conclusion T2 F(n-1 ,T-2n,<x) (5) (6) (7) F(8,2)=19.37 Do not rej 7.46
Reject
1.42
F(5,2)=19.30
Do not rej
3. Ecuador
14.84
1.35
F(6,6)=4.28
Do not rej
15.80
X (6)=16.81* 3C2(5)=11.07
Do not rej*
4. Fiji
Reject
1.06
F(5,2)=19.30
Do not rej
5. Honduras
13.74
5C2(4)=9.49
Reject
1.37
F(4,2)=19.25
Do not rej
6. Hong Kong
13.40
Do not rej
0.84
Do not rej
0.29
F(8,7)= 3.73 F(4,1)=224.6
Do not rej
4.58
X2(8)=15.51 *2(4)=9.49
8. India
191.76
Z2(6)=12.59
Reject
3.33
F(6,1)=234
Do not rej
9. Iran
15.14
X2(4)=9.49
Reject
1.51
F(4,2)=19.25
Do not rej
7.57
X2(8)=15.51
Do not rej
0.47
F(8,7)=3.73
Do not rej
7. Hungary
10. Israel 11. Jamaica
2
Do not rej
139.32
X (5)=11.07
Reject
9.29
F(5,2)=19.30
Do not rej
12. Korea
8.79
X2(7)=14.07
Do not rej
0.63
F(7,6)=4.21
Do not rej
13. Malta
27.70
Reject
1.32
F(7,3)=8.89
Do not rej
14. Mexico
19.16
5C2(7)=14.07 X2(7)=14.07
Reject
1.83
F(7,12)=2.91
Do not rej
15. Philippines
72.83
JC2(4)=9.49
Reject
7.28
F(4,2)=19.25
Do not rej
16. Puerto Rico
10.32
X2(7)=14.07
Do not rej
1.05
F(7,15)=2.71
Do not rej
17. Singapore
14.96
5C2(7)=18.47*
Do not rej*
1.55
F(7,16)=2.66
Do not rej
2.94
5C2(7)=14.07
Do not rej
0.32
F(7,19)=2.54
Do not rej
19. Sri Lanka
27.01
X2(7)=14.07
Reject
1.75
F(7,5)=4.88
Do not rej
20. Taiwan
13.87
X2(7)=14.07
Do not rej
1.51
F(7,19)=2.54
Do not rej
21. Thailand
23.64
X2(7)=14.07
Reject
1.12
F(7,3)=8.89
Do not rej
22. Venezuela
1.91
X2(4)=9.49
Do not rej
0.12
F(4,1)=224.6
Do not rej
23. Zimbabwe
1.46
X2(4)=9.49
Do not rej
0.15
F(4,2)=19.25
Do not rej
18. South Africa
The level of significance a = 0.05. A * denotes critical value and conclusion at a = 0.01.
238
International Consumption
Comparisons
restriction (2.1) on (1.1), Jit = OiDgt + S1 7iu(Dpjt-Dpm)+ eit,
Let Y,H= [9i % ••• "in-il' a n d Then, (3.1) can be written as
ji
= X H Y r + 6i,
x
i=l,...,n; t=l,...,T.
(3.1)
? = [DQt (DPn - DPm) ••• (DPn-i,t - D/V>]'-
i=l,...,n,
(3.2)
where XH is a T x n matrix whose Ith row is xf1'; andji and £j are as before. As for the unconstrained case, it can be shown that the best linear unbiased estimators of the Yi 's in (3.2) are the single-equation LS estimators (Theil, 1971). As before, we delete the n*equation and write (3.2) in matrix form as
y
= (I®X H )Y H + e,
(3.3)
where I is the identity matrix of order (n-l); y^ = [ Yj ] is a vector consisting of (n-l) subvectors; and y and E are as before. Let Y; be the LS estimator of Yi for i=l,...,n; and Y = [ Yi ] be the vector consisting of (n-l) subvectors. Here, we reproduce the Slutsky symmetry restriction, given by (3.18) from Section 2.3: 7tjj = 7Iji,
i,j=l,...,7l.
(3.4)
Chapter 7 Testing Demand Theory Hypotheses
239
In vector form, for i,j=l,...,n-l, the symmetry restrictions (3.4) can be written as Rf
= 0,
(3.5)
where R is a q x n(n-\) matrix with q = }4(W-I)(AI-2) and each row of R consists of zeros except for a 1 and a -1 corresponding to 7iy and np for some i^j. The test statistic for symmetry is
;
,
(3-6)
[q/(n-l)]trTlS
where S is the error covariance matrix of model (3.1) for i=l,...,n-l (Theil, 1971). Under the null, (3.6) is distributed as F with q and («-l)(T-«) degrees of freedom. As before, we replace X by its estimator S (when S is non-singular) and the test statistic becomes vps = (Ry H )'{R[S®(X H 'X H )- 1 ]R'}" 1 (Ry H ),
(3.7)
which has an asymptotic %2 distribution with q degrees of freedom. Using simulation experiments, Meisner (1979) showed that the asymptotic test is biased against symmetry, particularly in large demand systems. Since (3.4) involves cross-equation restrictions, the exact distribution of Ts is complicated and has not yet been derived. Now we apply (3.7) to the data from the 22 OECD countries and the results are shown in Table 7.5. A comparison of the observed value of (3.7) in
240
International Consumption Comparisons Table 7.5 Testing symmetry in 22 OECD countries
Country
Data-based
Critical
Conclusion
(1) 1. Australia
(2) 66.10
(3) X2(28)=41.34
2. Austria 3. Belgium
36.98
X2(28)=41.34
Do not reject
18.00
X2(21)=32.67
Do not reject
4. Canada
38.50
X2(28)=41.34
Do not reject
5. Denmark
77.80
X2(28)=41.34
Reject
6. Finland
51.50
Reject
(4) Reject
7. France
71.00
X2(21)=32.67 X2(28)=41.34
8. Germany
86.20
X2(21)=32.67
Reject
9. Greece
33.50
X2(28)=41.34
Do not reject
10. Iceland
111.27
X2(28)=41.34
Reject
11. Ireland
49.40
X2(28)=41.34
Reject
12. Italy
36.80
X2(28)=41.34
Do not reject*
13. Japan
61.30
X2(21)=32.67
Reject
14. Luxembourg
35.30
X2(21)=38.93*
Do not reject
15. Netherlands
15.20
X2(21)=32.67
Do not reject
16. New Zealand
9.67
X2(6)=12.59
Do not reject
17. Norway
39.70
X2(28)=41.34
Do not reject
18. Spain
33.70
X2(21)=38.93*
Do not reject*
19. Sweden
39.20
X2(28)=41.34
Do not reject
2
Reject
20. Switzerland
38.70
X (21)=38.93*
21. UK
29.50
X2(21)=32.67
Do not reject
22. USA
29.50
X2(28)=41.34
Do not reject
Do not reject*
q = 14(0-1 )(n-2). The level of significance a = 0.05. A * denotes critical value and conclusion at a = 0.01.
Chapter 7 Testing Demand Theory Hypotheses
241
column 2 with the x2-critical values for the asymptotic test presented in column 3 shows that Slutsky symmetry is acceptable for 11 countries at the 5 percent level and acceptable for 14 countries at the 1 percent level. Table 7.6 presents the results for testing symmetry based on (3.7) using the data for the 23 LD countries. Symmetry is acceptable for 12 countries at the 5 percent level and acceptable for 13 countries at the 1 percent level.
7.4
Summary results
In this chapter, we tested the demand theory hypotheses, demand homogeneity and Slutsky symmetry. We used the asymptotic tests as well as the finite-sample exact tests (for homogeneity) to test these hypotheses. Tables 7.7 and 7.8 summarize our findings regarding the homogeneity and symmetry hypotheses tests for the OECD and LD countries, respectively. As can be seen, homogeneity is acceptable for all OECD countries (except Greece and the US) and all LD countries. That is, as a whole, demand homogeneity is acceptable for 43 out of 45 countries. Symmetry is acceptable for only 14 out of the 22 OECD countries and 13 out of the 23 LD countries. That is, as a whole, Slutsky symmetry is acceptable for only 27 out of the 45 countries. Table 7.9 presents a summary of the findings, in terms of the proportion of acceptances (in percentages) of each hypothesis in the 45 countries (22 OECD and 23 LD) considered in this study. As can be seen from the table, among all 45 countries, demand homogeneity is acceptable for 96 percent of the countries while Slutsky symmetry is acceptable for only about 60 percent of the countries. Consequently, an overall picture emerges that demand homogeneity is generally acceptable while Slutsky symmetry is also generally acceptable but to a lesser extent.
International Consumption Comparisons
242
Table 7.6 Testing symmetry in 23 LP countries Country
Data-based
Conclusion
1. Colombia
(2) 78.29
Critical x2(q) (3) X2(28)=41.34
2. Cyprus
29.68
X2(10)=18.31
Reject
3. Ecuador
15.28
X2(15)=25.00
Do not reject
4. Fiji
17.69
X2(10)=18.31
Do not reject
5. Honduras
24.98
X2(6)=12.59
Reject
6. Hong Kong
36.48
X2(28)=41.34
Do not reject
7. Hungary
22.68
X2(6)=12.59
Reject
(D
2
(4) Reject
8. India
23.03
X (15)=25.00
9. Iran
30.19
X2(6)=12.59
Reject
10. Israel
28.60
X2(28)=41.34
Do not reject
11. Jamaica
29.43
X2(10)=18.31
Reject
12. Korea
87.07
X2(21)=32.67
Reject
13. Malta
39.22
X2(21)=32.67
Reject
14. Mexico
43.06
X2(21)=32.67
Reject
4.88
X2(6)=12.59
Do not reject
15. Philippines
2
Do not reject
16. Puerto Rico
18.32
X (21)=32.67
Do not reject
17. Singapore
27.05
X2(21)=32.67
Do'not reject
18. South Africa
24.30
X2(21)=32.67
Do not reject
19. Sri Lanka
36.86
X2(21)=38.93*
Do not reject*
20. Taiwan
20.63
X2(21)=32.67
Do not reject
21. Thailand
42.30
X2(21)=32.67
Reject
22. Venezuela
5.12
X2(6)=12.59
Do not reject
23. Zimbabwe
11.04
X2(6)=12.59
Do not reject
q = '/2(n-1)(n-2). The level of significance a = 0.05. A * denotes critical value and conclusion at a = 0.01.
Chapter 7 Testing Demand Theory Hypotheses
243
Table 7.7 Summary results: Testing demand theory hypotheses 22 OECD countries Country (1) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Ireland Italy Japan Luxembourg
15. 16. 17. 18. 19. 20. 21.
Netherlands New Zealand Norway Spain Sweden Switzerland UK
22. USA
Demand homogeneity (2)
Slutsky symmetry (3)
Do not Do not Do not Do not Do not Do not Do not Do not Reject Do not Do not Do not Do not Do not Do not Do not Do not Do not Do not Do not Do not
reject reject reject* reject reject reject * reject * reject
Reject Do not reject Do not reject Do not reject Reject Reject Reject Reject
reject reject * reject reject * reject reject * reject reject reject reject reject reject
Do not Reject Reject Do not Reject Do not Do not Do not Do not Do not Do not Do not Do not
Reject
reject
reject* reject reject reject reject reject* reject reject* reject
Do not reject
The level of significance used is a = 0.05. A * denotes conclusion at a = 0.01.
244
International Consumption Comparisons Table 7.8 Summary results: Testing demand theory hypotheses 23 LD countries
Country (1) 1. Colombia 2. Cyprus 3. Ecuador 4. Fiji 5. Honduras 6. Hong Kong 7. Hungary 8. India 9. Iran 10. Israel 11. Jamaica 12. Korea 13. Malta 14. Mexico 15. Philippines 16. Puerto Rico 17. Singapore 18. South Africa 19. Sri Lanka 20. Taiwan 21. Thailand 22. Venezuela 23. Zimbabwe
Demand homogeneity (2) Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject Do not reject
Slutsky symmetry (3) Reject Reject Do not reject Do not reject Reject Do not reject Reject Do not reject Reject Do not reject Reject Reject Reject Reject Do not reject Do not reject Do not reject Do not reject Do not reject* Do not reject Reject Do not reject Do not reject
The level of significance used is a = 0.05. A * denotes conclusion at a = 0.01.
245
Chapter 7 Testing Demand Theory Hypotheses Table 7.9 Summary of percentage acceptance of the demand theory hypotheses: 22 OECD and 23 LD countries Percentage acceptance Hypothesis (1)
OECD countries (2)
LD countries (3)
All countries (4)
1. Demand homogeneity
91
100
96
2. Slutsky symmetry
64
57
60
References Attfield, C.L. (1997). 'Estimating a Cointegrating Demand System,' European Economic Review 41(1): 61-73. Attfield, C.L. (1998). 'Bartlett Adjustments of Linear Equations with Linear Restrictions,' Economics Letters 60(3): 277-283. Barnard, G.A. (1963). 'In discussion,' Journal of the Royal Statistical Society, Series B, 25: 294. Barten, A.P. (1969). 'Maximum Likelihood Estimation of a Complete System of Demand Equations,' European Economic Review 1: 7-73. Barten, A.P. (1977). 'The Systems of Consumer Demand Functions Approach: A Review,' Econometrica 45: 23-51. Bera, A.K., R.P. Byron and CM. Jarque (1981). 'Further Evidence on Asymptotic Tests for Homogeneity and Symmetry in Large Demand Systems,' Economics Letters 8: 101-105. Bewley, R.A. (1983). 'Tests of Restrictions in Large Demand Systems,' European Economic Review 20: 257-269.
246
International Consumption
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Buse, A. (1998). 'Testing Homogeneity in the Linearised Almost Ideal Demand System,' American Journal of Agricultural Economics 80(1): 208-220. Chen, D.L. (2001). World Consumption Economics. Singapore, London: World Scientific. Cribari, N.F., and S.G. Zarkos (1997). 'Finite-Sample Adjustments for Homogeneity and Symmetry Tests in Systems of Demand Equations: A Monte-Carlo Evaluation,' Computational Economics 10(4): 337-351. Deschamps, P.J. (2000). 'Exact Small-Sample Inference in Stationary, Full Regular Dynamic Demand Models,' Journal of Econometrics 97(1): 51-91. Karagiannis, G., and G.J. Mergos (2002). 'Estimating Theoretically Consistent Demand Systems using Cointegration Techniques with Application to Greek Food Data,' Economics Letters 1'4(2): 137-143. Keuzenkamp, H.A. (2000). Probability, Econometrics and Truth: The Methodology of Econometrics. Cambridge: Cambridge University Press. Keuzenkamp, H.A., and A.P. Barten (1995). 'Rejection without Falsification on the History of Testing of Homogeneity Condition in the Theory and Consumer Demand,' Journal of Econometrics 67: 103-128. Laitinen, K. (1978). "Why is Demand Homogeneity So Often Rejected?' Economics Letters 1: 187-191. Meisner, J.F. (1979). 'The Sad Fate of the Asymptotic Slutsky Symmetry Test for Large Systems,' Economics Letters 2: 231-233. Muellbauer, J., and P. Pashardes(1992). 'Test of Dynamic Specification and Homogeneity in a Demand System,' in L. Phlips and L.D. Taylor (eds.), Aggregation, Consumption and Trade: Essays in Honour of H.S. Houthakker. Dordrecht: Kluwer Academic Publishers, pp.55-98.
Chapter 7 Testing Demand Theory Hypotheses
247
Ng, S. (1995). 'Testing for Homogeneity in Demand Systems when the Regressors are Nonstationary,' Journal of Applied Econometrics 10: 147163. Pollak, R.A., and T.J. Wales (1992). 'Specification and Estimation of Dynamic Demand Systems,' in L. Phlips and L.D. Taylor (eds.), Aggregation, Consumption and Trade: Essays in Honour ofH.S. Houthakker. Dordrecht: Kluwer Academic Publishers, pp.99-119. Selvanathan, E.A. (1995). Data Analytic Techniques for Consumer Economics,' Chapter 3 in E.A. Selvanathan and K.W. Clements (eds), Recent Developments in Applied Demand Analysis. Berlin: Springer. Selvanathan, S. (1987). 'A Monte Carlo Test of Preference Independence,' Economics Letters 25: 259-261. Selvanathan, S. (1993). A System-wide Analysis of International Consumption Patterns. Boston: Kluwer Academic Publishers. Theil, H. (1971). Principles of Econometrics. New York: John Wiley and Sons. Theil, H. (1987). 'The Econometrics of Demand Systems,' Chapter 3 in H. Theil and K.W. Clements (eds.), Applied Demand Analysis: Results from System-wide Approaches. Cambridge, MA: Ballinger Publishing Company. Theil, H., and K.W. Clements (1987). Applied Demand Analysis: Results from System-wide Approaches. Cambridge, MA: Ballinger Publishing Company.
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CHAPTER 8
A Comparison of Alternative Demand Systems H~A. Selvanathan <& S. Selvanathan
In Chapters 1 and 2, we presented a review of the economic theory of the consumer and developed a number of differential demand systems. We also pointed out that there are a number of competing demand systems available which are commonly used in applied demand studies for estimating the demand elasticities and for testing various demand theory hypotheses. In this chapter, we consider four of the well-known demand systems introduced in Chapter 2, namely, (1) Rotterdam demand system; (2) Almost Ideal Demand System (AIDS); (3) CBS demand system; and (4) NBR demand system. Choosing between different demand model specifications is very complicated. There are no set criteria available for the choice of functional forms in demand analysis. Choice of functional form is considered by many researchers as one of the most important issues in any aspect of empirical analysis of consumer behaviour (see Blundell, 1988). Many recent research studies have considered the choice of functional forms (for example, see Barten, 1993; Chua et al, 2001; Clements et al, 2001; Fisher et al, 2001; Lee et al, 1994; Neves, 1994; Tridimas, 2000). In this chapter, we use the most popular measure, the information inaccuracy to select the preferred demand system among the four systems.
International Consumption Comparisons
250
In Section 8.1, we present the finite-change version of these demand systems and estimate them to test the demand theory hypotheses, demand homogeneity and Slutsky symmetry, and compare the results with those from Chapter 7. In the following section, we use a concept from information theory, called the 'information inaccuracy', to measure the goodness-of-fit of the demand systems. This measure has been extensively used by a number of researchers in applied demand analysis (see, for example, Theil, 1975/76, 1980, 1996) and is well suited to analyzing the fitness of allocation models such as those considered in this book. In Section 8.3, we compare the performances of the four demand systems based on the goodness-of-fit criterion, the information inaccuracy. In the final section, we present our conclusion.
8.1
Four Demand Systems
In this section, we first present the four demand systems introduced in Chapter 2. The estimating forms of the Rotterdam, AIDS, CBS and NBR demand systems given by equations (3.21), (4.11), (5.5) and (5.6), respectively, of Chapter 2, with a random error term added, are given below (see also Barren et al, 1989). Rotterdam demand System w.aDgit = cti + Q]PQt+ £ xgDpj,+ En,
i=l,...,n.
(1.1)
i=l,...,n.
(1.2)
7=1
AIDS model Awit
= Xi + PiDQ, + t ^ D p j , + E i t , 7=1
Chapter 8 A Comparison of Alternative Demand Systems
251
CBS demand system wi( (Dq« - DQO = 8i + VjDGt + £ WgDPjt + eit,
i=l,...,/i.
(1.3)
M?/? demand system Awit+witDQt
= Ki + \iiDQt+ Y.
i=l,...,n.
(1.4)
The random error term captures the effect of all the variables not explicitly included in the specified models. It is assumed that the errors are contemporaneously correlated and are normally distributed with zero mean. We now use the demand analysis package DEMMOD (Barten et al, 1989) to estimate the four demand systems (1.1)-(1.4) with data for the OECD and LD countries individually. For all countries, we also test the demand homogeneity and Slutsky symmetry hypotheses, which were tested in Chapter 7 using only the Rotterdam demand system. For the OECD countries, Table 8.1 presents the value of the test statistics for homogeneity (given by equation (2.4) of Section 7.2) and symmetry (given by equation (3.7) of Section 7.3) and Table 8.2 presents the outcomes of the hypotheses testing across the four demand systems. The hypotheses test results for the LD countries are presented in Tables 8.3 and 8.4. The results corresponding to the Rotterdam demand system columns are the same as those reported in Chapter 7. We also use the same critical values presented in columns 3 and 6 of Tables 7.2 and 7.4 for homogeneity and column 3 of Tables 7.5 and 7.6 for symmetry. A comparison of columns 2-5 with columns 6-9 of Tables 8.2 and 8.4 for the four demand systems confirms our conclusion in Chapter 7 that
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International Consumption Comparisons
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The reason for the rejection of homogeneity is the asymptotic nature of the distribution of the test statistic used in columns 2-5. Based on Laitinan's (1978) finite-sample test, homogeneity is acceptable for all OECD countries (except for Greece and the US) and for all LD countries, irrespective of the demand system used. Looking at columns 10-13 of Tables 8.2 and 8.4, we see that Slutsky symmetry is acceptable for 14 of the 22 OECD countries and 14 of the 23 LD countries. This result holds for at least two of the four demand systems. Therefore, we conclude that for a majority of the OECD and LD countries, the Slutsky symmetry hypothesis is also acceptable.
8.2
Measure of Goodness-of-fit
The standard measure of goodness-of-fit used in econometrics is the multiple correlation coefficient. Since this coefficient refers to a single equation, its use is unattractive when the objective is to measure the fit of several equations that are estimated simultaneously. It is possible, however, to introduce a generalized multiple correlation coefficient to measure the fitness of an equation system (for example, see McElroy, 1977). In this section, we use a measure of goodness-offit, the information inaccuracy, a concept from information theory. This measure has been widely used in allocation models such as ours (see, for example, Theil, 1980, 1996). For illustration, we use the CBS demand system given by (1.3). However, simple modifications can be made to accommodate the other three demand systems. In order to define the information inaccuracy, first we shall start with the budget share predictions implied by the demand system.
257
Chapter 8 A Comparison ofAlternative Demand Systems Budget Share Predictions from the Demand Equations
Let wit be the actual budget share of commodity i in year t and wit be the predicted budget share. As the model determines the change in the share, we write the prediction as wu
=
wit.i + prediction of Aw,„
i= 1,... ,n,
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^ ^
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+ wit(DQt + Dpit -DM,)+
03.
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As the expectation of the demand model (1.3) provides the prediction of wit (Dqit - DQt), we have
International Consumption Comparisons
258
Prediction of wu{Dqit -DQ,) = w„(Dqit -DQ,) - e„,
(2.5)
where eit is the residual of the i* demand equation. Using (2.4) and recognizing that the second term in that equation is given, we obtain Prediction of Aw,-, = Prediction of wit (Dqjt - DQ,) + wit (DQt + Dpit - DM,) = wit{Dqu-DQt)
- eit + wit{DQt+DPil
-DM,)
= ™i,D(lit + ™uDPi, - witDM,- £,,, where the remainder term 0 3 is ignored and the second step is based on (2.5). Using (2.3), the above equation becomes Prediction of Aw„ = Aw„ - sit.
(2.6)
Therefore, using (2.6) in (2.1) gives wit
= wit_, + Aw,-, - sit.
wit
=
That is, w« - e,7.
(2.7)
Thus, equation (2.7) gives the budget share predictions implied by the demand system.
Chapter 8 A Comparison of Alternative Demand Systems
259
The Information Inaccuracy
To measure the quality of the predictions, we use a concept from information theory, called the information inaccuracy. This measure has been extensively used by Theil (1975/76, 1980, 1996) and is well suited to analysing the fit of allocation models such as ours. In general, if we have n goods with budget share predictions wu,...,wnt, the information inaccuracy of these predictions is defined as 1=
n
w.
/=i
wu
I>„log^.
(2.8)
When predictions are perfect (i.e., wit= wit, i=l,... ,n), I, = 0; otherwise I, > 0. Therefore, the smaller the information inaccuracy, the better the predictions. Consequently, the preferred demand system would be the one with the lowest value of information inaccuracy. If we define e;t = log (wit I wit) as the relative error, then I, = X"=1w,7e,-r can be interpreted as the Divisia mean (i.e., the budgetshare-weigh ted mean) of the relative errors. Thus Ir x 100 is approximately equal to the weighted average percentage error.
8.3
The Preferred Demand System
In this section we shall choose between the four versions of the model on the basis of the goodness-of-fit criterion, the information inaccuracy. We start with the budget share predictions implied by the four versions. For a particular country, we use the residuals from each demand system to obtain the predicted budget shares given by (2.7). We then use equation (2.8) to calculate the information inaccuracies for each demand system for t=l,...,T
260
International Consumption Comparisons
(T=sample size after lagging). We then evaluate the mean information inaccuracy for each demand system as 1T T (=1
These mean information inaccuracies are presented in Table 8.5 (OECD) and Table 8.6 (LDC) for the four demand systems. In column 2 of each table, we present the constraint acceptable for each country based on our conclusion from Section 8.2. Now, we use the information inaccuracy presented in columns 3 to 6 to select the preferred model based on the lowest value of the mean information inaccuracy (I). For example, for Australia, across the four demand systems, we found that only homogeneity restriction is acceptable. The information inaccuracies obtained under the homogeneity restriction for the four demand systems, Rotterdam, AIDS, CBS and NBR, are 137.94, 147.62, 144.14 and 193.52, respectively. The lowest value among these is 137.94, which corresponds to the Rotterdam demand system. Therefore, for Australia, the preferred demand system is the Rotterdam model. For the USA, we found that symmetry is acceptable for all four demand systems. The information inaccuracies under the symmetry restriction for the four demand systems, Rotterdam, AIDS, CBS and NBR, are 84.39, 69.21, 84.32 and 86.47, respectively. Here, the lowest value is 69.21, which corresponds to the AIDS. Therefore, the preferred demand system for the US is the AIDS. Table 8.7 gives the preferred demand system for each country based on the minimum information inaccuracy. As can be seen from column 2, for the 22 OECD countries, the CBS is the preferred demand system for 12 countries; AIDS for 5 countries; Rotterdam for 3 countries; and NBR for 2 countries. As can be seen from column 5, for the 23 LD countries, the CBS is the preferred demand
Chapter 8 A Comparison ofAlternative Demand Systems
261
Table 8.5 Mean information inaccuracies, OECD countries Acceptable constraint Country
(D
(Based on Table 8.2)
Mean information inaccuracy Rotterdam
AIDS
CBS
NBR
1.
Australia
(2) Homogeneity
2.
Austria
Homogeneity
200.44
189.00
182.38
197.18
3. 4.
Symmetry Symmetry Homogeneity Homogeneity
252.77
245.72 252.47
241.26 257.06
261.18 178.22
5. 6.
Belgium Canada Denmark Finland
169.59 236.61
173.05 244.19
160.78 257.37
7. 8. 9. 10.
France Germany Greece Iceland
Homogeneity Homogeneity
64.81 87.05 465.83 477.77
63.71 79.76 442.23
63.36 77.71 415.93 473.30
87.58 468.91 493.47
11. Ireland 12. Italy 13. Japan 14. Luxembourg 15. Netherland 16. NewZealand 17. Norway 18. Spain 19. Sweden 20. Switzerland 21. UK 22. USA
Symmetry Homogeneity Symmetry Symmetry Homogeneity Symmetry Symmetry Symmetry Symmetry Symmetry Symmetry Symmetry Symmetry Symmetry
All entries in columns 3-6 are to be divided by 106.
(3) 137.94
282.85 163.82 262.97
500.11 151.13 150.80 291.68 384.89 125.49 330.13 264.54 158.80 74.34 130.16 84.39
(4) 147.62
487.08 486.32 123.83 139.45 291.69 326.00 129.24 259.09 236.62 152.06 80.86 131.67 69.21
(5) 144.14
475.89 118.78 143.72 291.00 311.73 129.43 313.33 229.95 152.36 77.45 126.15 84.32
(6) 193.52
64.33
515.95 156.30 158.04 299.54 394.67 118.83 266.90 260.10 165.16 81.46 134.05 86.47
262
International Consumption Comparisons
Table 8.6 Mean information inaccuracies, LD countries Acceptable constraint Country
(Based on Table 8.4)
Mean information inaccuracy Rotterdam
(D 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
AIDS
Colombia
Homogeneity
(2) 127.49
Cyprus Ecuador
Homogeneity
333.85
349.10
Symmetry Symmetry Homogeneity
206.36 984.11 397.98
230.89 1097.72
Symmetry Symmetry Symmetry Homogeneity
742.53 228.85 173.85 693.00 956.38 513.65 298.61 798.59 230.29
Fiji Honduras Hong Kong Hungary India Iran Israel Jamaica Korea Malta Mexico
Symmetry Homogeneity Homogeneity Homogeneity Homogeneity
15. Philippines 16. Puerto Rico
Symmetry
17. Singapore 18. South Africa 19. Sri Lanka 20. Taiwan
Symmetry Symmetry Symmetry Symmetry Homogeneity
21. Thailand 22. Venezuela 23. Zimbabwe
Symmetry
Symmetry Symmetry
All entries in columns 3-6 are to be divided by 106.
15.79 798.64 584.65 233.35 1926.03 573.95 206.76 187.17 2145.38
(3) 121.85
379.63 760.58 175.26 173.06 693.61 952.62 547.34 136.39 833.56 208.49 16.68 775.86 536.50 227.72 1866.86 409.72 191.01 205.93 2365.79
CBS
NBR
(4) 119.67 361.75
(5) 106.27 352.11
207.89
251.35 1143.18 396.12
939.26 366.45 759.33 219.52 158.37 706.96 938.81 523.53 132.77 848.70 198.15
742.61 171.59 183.07 681.81 1001.52 536.88 173.69 790.61 249.24
19.50 772.60
807.29
534.68 238.08 1929.78 400.47 177.79 177.74 2274.59
0.77 584.86 233.87 1857.92 539.27 173.24 222.19 2206.2
Chapter 8 A Comparison of Alternative Demand Systems
263
Table a 7 Preferred demand systems, OECD and LD countries Country
Demand Mxtel (2)
1.
(1) Australia
Ftotterdam
2.
Austria
3.
Belgium
4.
Canada
5. 6.
Country
Ftestriction
Demand Wbdel (5)
(4)
Restriction (6)
(3) Homogeneity
1.
Colombia
CBS
Homogeneity
CBS
Homogeneity
2
Cyprus
Ftotterdam
Homogeneity
CBS
Symmetry
3.
Ecuador
Ftotterdam
Homogeneity
NBR
Symmetry
4.
Fiji
CBS
Symmetry
Denmark
NBR
Homogeneity
5.
Honduras
CBS
(Homogeneity
Finland
AIDS
Homogeneity
6.
Hong Kong
Ftotterdam
Symmetry
7.
France
CBS
Homogeneity
7.
Hungary
NBR
Syrrmetry
8.
Germany
CBS
Homogeneity
8.
Inda
CBS
Symmetry
9.
Greece
CBS
Symmetry
9.
Iran
CBS
Homogeneity
10.
Iceland
CBS
Homogeneity
10.
Israel
NBR
Syrrmetry
11.
Ireland
C8S
Syrrmetry
11.
Jamaica
Rotterdam
Horrogeneity
12
Italy
CBS
Symmetry
12
Korea
CBS
Homogeneity
13. Japan
AIDS
Homogeneity
13.
Malta
NBR
Horrogeneity
14.
Luxembourg
CBS
Symmetry
14.
Mexico
CBS
Homogeneity
15.
Netherlands
CBS
Symmetry
15.
Philippines
NBR
Syrrmetry
16.
New Zealand
Ftotterdam
Syrrmetry
16.
Puerto FSco
CBS
Syrrmetry
17.
Norway
AIDS
Syrrmetry
17.
Sngapore
CBS
Syrrmetry
18.
Spain
CBS
Symmetry
18.
South Africa
AIDS
Syrrmetry
AIDS
Syrrmetry
19.
Sri Lanka
NBR
Syrrmetry Syrrmetry
19. Sweden 20.
Switzerland
Rotterdam
Symmetry
20.
Taiwan
CBS
21.
UK
CBS
Syrrmetry
21.
Thailand
NBR
Horrogeneity
22
USA
AIDS
Symmetry
22
Venezuela
CBS
Symmetry
23.
Zrrfoabws
Ftotterdam
Syrrmetry
International Consumption Comparisons
264
system for 11 countries; NBR for 6 countries; Rotterdam for 5 countries; and AIDS for only 1 country. In summary, the CBS is the preferred system for most OECD and LD countries. Table 8.8 presents the preferences in percentages. As can be seen, for the majority of OECD and LD countries, the CBS demand system performs well. Overall, the CBS performs the best followed by Rotterdam, NBR and AIDS, in that order.
Table 8.8 Preferred demand systems for 22 OECD and 23 LD countries (in percentages) Percentage preference Demand system
1. 2. 3. 4.
(1) Rotterdam AIDS CBS NBR
8.4
OECD countries (2) 14 23 55 9
LD countries (3) 22 4 48 26
All countries (4) 18 13 51 18
Conclusion
In this chapter, we tested the demand theory hypotheses, demand homogeneity and Slutsky symmetry, using four demand systems, Rotterdam, AIDS, CBS and NBR. Our results show that, across the four demand systems, the demand homogeneity restriction is generally acceptable while the Slutsky symmetry restriction is also acceptable, but to a lesser extent.
Chapter 8 A Comparison of Alternative Demand Systems We also compared the performance of four demand systems using a measure of goodness-of-fit, the information inaccuracy, and found that the CBS system performs better than the other three demand systems. In the next chapter, we shall investigate the implications of imposing a restriction on the utility function to further simplify the model estimation.
References Barten, A.P. (1993). 'Consumer Allocation Models: Choice of Functional Form,' Empirical Economics 18: 129-158. Barten, A.P., L. Bettendorf, E. Meyermans and P. Zonderman (1989). Users' Guide to DEMMOD-3. Kathlieke Universiteit Leuven, Belgium. Chua, C.L., W.E. Griffiths and C.J. O'Donnell (2001). 'Bayesian Model Averaging in Consumer Demand Systems with Inequality Constraints,' Canadian Journal of Agricultural Economics 49(3): 269-291. Clements, K.W., W. Yang and D.Chen (2001). 'The Matrix Approach to Evaluating Demand Equations,' Applied Economics 33: 957-967. Fisher, D., A.R. Fleissig and A. Serletis (2001). 'An Empirical Comparison of Flexible Demand Systems Functional Forms,' Journal of Applied Econometrics 16(1): 59-80. Laitinen, K. (1978). 'Why is Demand Homogeneity So Often Rejected?' Economics Letters 1: 187-191. Lee, J.Y., M.G. Brown and J.L. Seale Jr. (1994). 'Model Choice in Consumer Analysis: Taiwan 1970-89,' American Journal of Agricultural Economics 76: 504-512. McElroy, M.B. (1977). 'Goodness of Fit for Seemingly Unrelated Regressions,' Journal of Econometrics 6: 381-387.
265
International Consumption Comparisons
266
Neves, P.D. (1994). 'A Class of Differential Demand Systems,'
Economics
Letters 44: 83-86. Theil, H. (1975/76). Theory and Measurement of Consumer Demand. Two Volumes. Amsterdam: North-Holland Publishing Company. Theil, H. (1980). The System-Wide Approach to Microeconomics. Chicago: The University of Chicago Press. Theil, H. (1996). Studies in Global Economics. Boston: Kluwer Academic Publishers. Tridimas, G. (2000). 'The Analysis of Consumer Demand in Greece: Model Selection and Dynamic Specification,' Economic Modelling 17(4): 455471.
CHAPTER 9
The Structure of Preferences: O E C D and LD Countries S. Selvanathan & E.A. Selvanathan
Estimating a system of demand equations in an unrestricted fashion requires the estimation of an impossibly large number of coefficients, especially with large demand systems. As discussed in Chapter 7, one way of reducing the number of coefficients to be estimated is to impose a priori restrictions such as demand homogeneity and symmetry. In Chapters 7 and 8, we carried out tests of these two hypotheses for the OECD and LD countries and across a number of demand systems. In this chapter, we investigate the implications of imposing another a priori restriction by specifying a form of utility structure, known as strong additivity (or preference independence) discussed in Chapters 1 and 2. Selvanathan (1993), using 10 broad aggregate commodity classification of the OECD countries, and Clements et al (1997) using a narrowly defined alcohol commodity group consisting of beer, wine and spirits, found tentative support for the preference independence hypothesis. Moschini et al (1994) also looked at testing separability restrictions on the demand systems. As pointed out in Chapter 7, one problem associated with testing is the test procedure, which is usually based on the asymptotic distribution of the test statistic without correction for small-sample bias and, therefore, the results are biased towards rejection. In view of these difficulties, Selvanathan (1987)
International Consumption Comparisons
268
developed an alternative distribution-free testing procedure for preference independence based on Barnard's (1963) Monte Carlo simulation procedure. In Sections 3.7 and 4.7, we performed an informal test of preference independent utility structure using the data from OECD and LD countries, respectively, and found indirect support for the preference independence hypothesis for both groups of countries. In this chapter, we present a detailed account of the conventional tests used for testing the hypothesis of independent preference structures within goods, and the new Monte Carlo simulation procedure to test the hypotheses, and illustrate their application using the OECD and LDC data. In Chapter 8, we presented a comparison of the performances of four alternative demand models and found that the CBS demand system is the preferred demand model for a majority of countries. Therefore, we use the CBS demand system in this chapter. The organisation of this chapter is as follows. In Section 9.1, we present the demand model under preference independence and in Section 9.2, we present the estimation procedure. In the following section, we present the estimation results under preference independence. In Section 9.4, we present the test results for preference independence using the asymptotic test for OECD and LDC data and then introduce the Monte Carlo method and discuss its application to test the preference independence hypothesis for the same data. Finally, in Section 9.5, we present the implied income and price elasticities and in Section 9.6, we present our concluding comments.
9.1
The Demand Model
For commodity i (=l,...,n, the number of goods) and period t (=1,...,T, the sample size after lagging), the finite-change version of the absolute price version of the
269
Chapter 9 The Structure of Preferences
CBS model, given by (5.5) in Section 2.5, can be written as wit (Dqit - DQt) = Pi DQt + £ TiijDpj, + Eit,
(1.1)
7=1
where p\ is the i* income coefficient satisfying S"=iA = 0; Jty is the (ij)"1 Slutsky coefficient satisfying Y!i=\nij - 0; a n d all other notations are as defined in Chapter 2. If Pi < 0, then good i is a necessity and if Pi > 0, then good i is a luxury. The error terms are assumed to be normally distributed with zero mean and are independent over time. When consumer's tastes can be described by means of a utility function, which can be written as the sum of n sub-utility functions, each involving one good only, then tastes are said to exhibit preference independence or additive preferences. Preference independence also means that the marginal utility of good i is independent of the consumption of commodity j , i^j. If the commodities are fairly broad groups such as those considered in this study, then it may be possible that, for example, the marginal utility derived from food may be independent from the marginal utility derived from clothing and so on. Then the broad commodity groups can be interpreted as representing the "basic wants" of the consumer and if these are truly basic wants, they could be expected to exhibit little interaction in the utility function. In the next section, we outline the estimation procedure and, in the following section, we now formally test the preference independence hypothesis with consumption data from OECD and LD countries. Under preference independence, the Slutsky coefficients take the form (see, for example, Selvanathan and Selvanathan, 1994)
^(KA+^x^-A-w,,),
(1.2)
270
International Consumption Comparisons
where <{) is the income flexibility (the reciprocal of the income elasticity of the marginal utility of income) and 8y is the Kronecker delta. Substituting (1.2) for 7ijj in (1.1) and adding a constant term ai? the preference independent version of (1.1) can be written as
wit (DqirDQt) = ai + PiDQ. + HP, + wit) DPil-UJ3j+wJt)Dpjt
+eit. (1.3)
As can be seen, equation (1.3) is nonlinear in its parameters. Therefore, we apply the maximum likelihood estimation procedure, as described in the next section, for its estimation.
9.2
Model Estimation
We write equation (1.3) in the following form: yit = a, + PiDQt + (j)zit + eit where yit = wit (Dqa - DQt), n-\
Zit = {Pi +W„) Dpl-UPj+wjt)Dp)t
and Dp*t = Dpit - Dpm, where we have also used S"=i Pi =0. In vector form, (2.1) can be written as
(2.1)
271
Chapter 9 The Structure of Preferences
yt
= X, y+ et,
whereat = tVu]; Xt = [DQtI„.i zt I„.i] with I„_i being the identity matrix of order n-1; zt= [ZiJ; y= IP' <> t «']' = [Pi ••• Pn-i I <> t I Od ... a n 4 ]'; and £j = [eit]. Assuming that the £j's are independent normal errors with zero mean and non-singular covariance matrix X, the log-likelihood function of them's is given by *(y,Z;y) = C + ^ n l s " 1 ! ~ ^ ( y 2
'
*
t
- X ^ ' E ^ y , -Xj),
(2.2)
lt=\
where C is a constant and T is the sample size. The first-order conditions for a maximum of (2.2) are d£
T
I
T
—-=
T-=--Z(yt-xt7)(yt-xt7)' = 0
dS
2
dy
<=i
(2.3)
2 t=i
and (2.4) d y
where
d(X,y) By'
3z, DQ.I + 0—L
z, I
(2.5)
272
International Consumption Comparisons 3z t
dig
and dz.
^ = - ( A + w a ) ^ p ; , + ^ Dpl-Zifa+wJDpl dfi
From the first order condition (2.3), we have
i-^I(yt-Xty)(yt-XtY)'.
This is the usual ML estimator of Z. It follows from (2.4) that
l
dZ.~ dy'
3(X t y) = I (y t - X j ) dy' t=i
(2.6)
Since E[(y t - X ^ ) ] = E[£j] = 0, the expected value of the right-hand side of (2.6) vanishes, so that the information matrix of the ML procedure is blockdiagonal with respect to yand 2T1. From (2.4), we also have d2l _ T d(Xty)', dydy' t=\ dy
3(X t y) r a 2 (x (7 ) + i ( y t -Xt^ys-1 a , ay <=i
273
Chapter 9 The Structure of Preferences
The second term on the right-hand side has zero expectation. Therefore, the asymptotic covariance matrix of the ML estimator of y is
V =
d2l> dydy'
£ d(xtry^ d(xty)y t=i dy
dy'
The ML estimator of y is obtained by means of Newton's iterative scheme based on successive estimates of V and 2. The asymptotic standard errors are the square roots of the diagonal elements of V with ML-estimates substituted for the unknown parameters in V.
9.3
Estimation Results
In this section we present the estimation results of the demand system (1.3) based on the estimation procedure described in the previous section. Tables 9.1 and 9.2 present the estimation results for the OECD countries. Table 9.1 presents the estimates of the intercept terms. As can be seen, for most countries, the intercept terms for food, clothing, durables and transport are negative while the intercept terms for housing, medical care, education and recreation are positive. This indicates that, in most countries, there is an autonomous trend in consumption out of food, clothing, durables and transport into housing, medical care, education and recreation. Table 9.2 presents the estimates for the income coefficient, Pi, i=l,...,9, in columns 2-10 and the estimates for income flexibility in the last column. As can be seen, for most countries, the income coefficient estimates for food, housing, and medical care are negative, indicating that food, housing and medical care are
International Consumption Comparisons
274
Table 9.1 Estimates of the intercept terms of the model under preference independence for 9 commodities in 22 OECD countries (Standard errors are presented below the point estimates)
Country
o
O (5) -0.364 0.088
0.298
-0.028
0.043 0.090
-0.072
0.061 0.204
0.072 -0.198
0.061 -0.177
0.104 0.421
0.049 -0.021
0.035 -0.175 0.044
Finland
0.075 -0.097
France
0.100 -0.040
1.
(2) -0.040
2.
Austria
0.076 -0.152
Belgium
0.093 -0.003
4.
Canada
0.106 -0.211
5.
Denmark
6. 7.
3.
u (3)
X (4) 0.427 0.055
Li-
(1) Australia
-0.212 0.039 -0.201 0.058
-0.211 0.082
2 (6) 0.015
H <7) -0.007 0.099
a: (8) 0.002 0.049
•o
(9) 0.030 0.013 -0.004
z (10) 0.149 0.055
0.086
0.023 0.147
-0.079 0.096 0.003
0.101 •0.043
0.056 -0.086
0.072 -0.092
0.028 0.090
0.071
0.119 0.027
0.059 0.390
0.052 -0.224
0.072 0.037
0.066 -0.224
0.042 0.098
0.019 0.068
0.045 0.049
0.093 0.624
0.036 -0.114 0.041
0.017 0.067
0.097 -0.369
0.046 0.079 0.049
0.011
0.043 0.019 0.050 -0.174
0.056
0.049 0.093
0.005
-0.011 0.059 -0.173
-0.133 0.032
0.363 0.061
-0.322
0.020 0.503
0.134 -0.156
-0.044
C.001
0.063
0.053
0.090
0.025
0.005
-0.087 0.057
-0.187
0.442 0.060
0.04S 0.016
-0.141
0.032
-0.170 0.060
0.207 0.041
0.220
-0.504 0.112
0.266
-0.076
0.148
0.068
0.136
-0.012 0.109
-0.008 0.019
-0.001
0.050
-0.033 0.047
-0.290
0.155
0.042
0.121
1 1 . Ireland
0.090
-0.207
0.091 0.162
0.145 -0.140
0.034 0.019
-0.275
0.187
-0.160 0.066
0.240
-0.006
0.231 -0.076
0.098 0.051
0.033 0.036
0.109 0.090
0.176 -0.126
0.082 -0.268
0.059
0.073
0.074
0.166
-0.105
0.031 0.100
0.116
1 2. Italy
-0.015
0.089
0.033 0.007
0.072 0.152
0.076
0.046
0.029
0.043
0.038
0.081
0.042
0.006
1 3. Japan
-0.369
-0.279
0.605
-0.119
0.168
-0.091
0.222
0.078
0.062
0.067
0.090
0.073
0.088
0.089
0.130
14. L u x e m b o u r g
-0.063
-0.188 0.085
0.088 0.151
-0.089
-0.102 0.090
0.287
0.162
-0.095
0.192
0.066
0.168
-0.363 0.101 -0.359
0.157 0.054 0.459
-0.208 0.090
0.143
-0.004 0.080
0.105 0.047
0.105 0.049 0.377
0.082 -0.209
0.216 0.470
-0.134
-0.063
-0.227
0.097
0.001
0.144 0.183
0.047 -0.106
0.052 0.084
0.049
0.048 0.105
0.131 0.104
0.045
0.006
0.065
-0.093
0.061 -0.119
0.058
0.040
0.050
0.091
0.271
-0.107
0.082
-0.020
0.029 0.063
0.040 8.
Germany
9.
Greece
0.137 1 0. Iceland
0.133
0.194 1 5. Netherlands
0.065
1 6. New Zealand
0.099 -0.078 0.089
1 7. Norway
-0.119 0.065
1 8. Spain
-0.646 0.161
0.136
0.040 -0.399 0.295
0.085
0.042 -0.109 0.060 0.067
0.047 -0.137
0.035
0.517 0.099 -0.039
1 9. Sweden
-0.130 0.058
0.045
0.063
0.036
0.012
0.064
20. Switzerland
-0.195
-0.202
0.264
-0.227
0.038 0.025
0.029
0.054
0.026
0.208 0.023
0.003
0.046
0.054
0.022
0.023
-0.207
0.043
0.179
-0.112
0.020
-0.006
0.038
0.045
0.028
0.010
0.074
0.182 0.036
-0.099
0.065 -0.075
-0.078
0.174
-0.113
0.336
-0.415
0.127
0.016
0.028
0.051
0.038
0.044
0.033
0.045
0.080
0.039
0.009
0.047
2 1 . UK 22. USA
All entries are t o be divided by 100.
0.000 0.002
0.040 0.125
0.079
275
Chapter 9 The Structure of Preferences Table 9.2 Estimates of the income coefficients for 9 commodities and income flexibility under preference independence in 22 OECD countries (Standard errors are presented below the estimates)
Country 1.
(1) Australia
o •0.145
U (3) 0.021
0.028
0.013
LL.
(2)
-D UJ
s (10)
0.068
(9) 0.008
0.008
0.017
0.005
0.017
0.058
-0.001
-0.001
-0.024
-0.262
0.001
2 (6) 0.007
H (7)
(8)
-0.117
Q (5) 0.120
0.030
0.016
0.025
0.013
0.034
-0.074
0.026
-0.023
0.128
X (4)
_c -0.545
2.
Austria
-0.088
0.057
0.025
0.015
0.018
0.019
0.006
0.026
0.013
0.017
0.059
3.
Belgium
-0.146
0.015
-0.077
0.095
-0.016
0.037
-0.012
0.104
0.020 0.035
0.035
0.009 0.025
0.039
-0.068 0.037
-0.015
0.008
-0.119 0.016
0.024 0.067 0.017
-0.153
0.039
-0.015
0.231
0.006 -0.010
-0.606 0.047
0.039 0.013
0.011 -0.002
0.031 0.013
Denmark
0.013 -0.140
0.033 0.022 0.014
0.019
Canada
0.036 -0.057
0.029
0.010
0.029
0.012 0.014
-0.578 0.069
-0.176 0.014
0.043
0.013 0.007
0.003
0.032
0.003 -0.016
0.035
•0.109
0.005 -0.086
0.033 0.115
4. 5.
0.025 6.
Finland
7.
France
8.
Germany
-0.116 0.024 -0.134
0.020 -0.012
0.010 0.078
0.011 0.021
0.191
0.012
0.012
0.010
-0.061 0.022
0.019
0.009
0.027
0.035 0.007
-0.089 0.016
0.043 0.009
-0.136 0.019
0.053 0.016
-0.011 0.005
0.139 0.024
-0.068 0.006
Greece
-0.197
0.122
-0.057
0.016
0.031
0.034
0.029
0.032
0.026
0.011
-0.166
0.023
-0.180
0.015 0.103
0.010
10. Iceland
-0.006
0.030 0.191
0.038 -0.217
0.013
0.016
0.027
0.003
1 1 . Ireland
0.072
-0.076
-0.005
0.019
0.013 -0.071
0.006
12. Italy
0.039 -0.092
0.049 0.017 0.047
0.001
0.022
0.011
-0.130
0.012 0.017
9.
0.073
0.026
0.046
0.001
0.013 0.063
0.002
0.014
-0.405 0.041
0.070
-0.392
0.013 0.034
-0.256
-0.013 0.004
0.016
0.039 0.055 -0.324
-0.010
0.050
0.041
-0.005 0.017
0.005
0.025
0.076
0.076
0.054
O.OOS
0.042
0.02S
0.016
0.017
0.065
-0.011
0.008 -0.002
-0.232 0.047
-0.011
-0.090
0.023 0.085
0.012 -0.024
0.014 0.062
0.031 -0.397
0.002
1 3. japan
-0.048
0.013 0.057
0.020
0.019
0.019
0.020
-0.018 0.017
0.024
0.022
0.036
0.053
14. Luxembourg
-0.135
0.008
-0.01 5
0.062
0.070
0.041
-0.041
0.011
-0.477
0.057
0.025
0.046
0.036
0.028
0.055
0.018
0.054
0.081
1 5. Netherlands
-0.139
0.093
-0.064
0.091
-0.029
0.060
0.001
-0.013
-0.109
0.025
0.023
0.012
0.013 0.067
0.043 •1.384
0.016
0.007
0.028 0.032
0.011 -0.024
0.020
-0.103
0.026 0.032
0.014
16. New Zealand 1 7. Norway
-0.101 0.016
0.029 0.012
-0.189 0.011
0.040 0.012
0.208
0.016
-0.004
0.025 -0.021
-0.575
0.002
0.059
0.001
-0.057
0.008
0.010
0.009
0.011
0.021
0.008
19. Sweden
0.035 -0.067
0.009 0.011
0.036 0.074
0.011
18. Spain
-0.159
0.050
-0.021
0.143
0.039
0.001
0.024
0.049 0.017
0.024
0.027
0.016
0.000
0.013
0.046
0.053
-0.156
0.016 0.064
0.004
0.018
-0.044
0.066
0.018
-0.020
-0.560
0.020
0.012 0.000
0.010 0.048
0.011 -0.002
0.023 0.102
0.010
-0.127
0.013 0.091
-0.117
0.012 0.024
0.015 -0.091
0.009 0.040
0.003 -0.082
0.024 0.207
0.027 •0.007
0.031 -0.336
0.012
0.016
0.011
0.019
0.028
0.019
0.046
20. Switzerland 2 1 . UK 22. USA
-0.099 0.021 -0.100 0.018
0.009
0.022
0.023 0.021 0.007
0.006
-0.012 0.012 0.011 0.013
0.016 -0.100
-0.001 0.004
0.098 0.057 -0.284
0.015
0.035
-0.035
-0.268
0.052
276
International Consumption Comparisons
necessities for most of the OECD countries. On the other hand, for all countries, the income coefficients for clothing (except for France), durables and transport are positive, indicating that these three commodities are generally considered as luxuries by the OECD consumers. The income flexibility estimates presented in the last column of Table 9.2 are all negative as they should be with an average value of -0.38, which is close to the preliminary estimates presented in Chapter 3 (see Table 3.20). Tables 9.3 and 9.4 present the estimation results of model (1.3) for the LD countries. Table 9.3 presents the estimates of the intercept terms. As with the OECD countries, the observation is very similar for the LD countries. In most LD countries, there was an autonomous trend in consumption out of food and clothing into housing and medical care. Table 9.4 presents the estimates of the income coefficients Pi, i=l,...,9, in columns 2-10 and the estimate for income flexibility in the last column. As with the OECD results, in most countries, food, housing and medical care are necessities; and durables and transport are luxuries. But, in contrast to the OECD results, a majority of LDC consumers consider clothing as a necessity. As expected, all the estimates for income flexibility presented in the last column of the table (except for Cyprus and India) are negative, as they should be, with an average of-.46 (excluding Cyprus and India). This average is well in agreement with the preliminary estimates for the LD countries presented in Chapter 4 (see Table 4.19) and with the OECD estimates in Table 9.2. Two points are worth noting in Tables 9.2 and 9.4. First is that, in contrast to our expectation, the income coefficient for food is positive for some countries, implying that food is a luxury in these countries. Therefore, for these countries, we estimate the model by suppressing the intercept term and found that their food income coefficient estimates are now negative. We use these estimates to calculate the elasticities. For Hungary and the Philippines, no improvement in the
277
Chapter 9 The Structure of Preferences Table 9.3 Estimates of the intercept terms of the model under preference independence for 9 commodities in 23 LD countries (Standard errors are presented below the estimates)
Country
Ecuador Fiji
0.154 -0.230
1. 2.
Cyprus
3. 4. 5. 6.
o (2) •0.077 0.099 -0.333 0.413 -0.451
(1) Colombia
Honduras H o n g Kong
7.
Hungary
8.
India
9.
Iran
10. Israel 1 1 . Jamaica 12. Korea 1 3. Malta 14. Mexico I S . Philippines 16. Puerto Rico 17. Singapore 18. South Africa 19. Sri Lanka
0.146 -0.399 0.400 -0.072 0.255 -0.818 0.195 -0.814 0.195 -0.411 0.551 0.116 0.103 -0.277 0.279 -0.560 0.239 0.218 0.289 0.106 0.075 0.020 0.059 -0.571 0.205 -0.322 0.166 0.014 0.093 -0.614 0.364
-0.238 0.201 -1.053 2 1 . Thailand 0.238 0.221 22. Venezuela 0.218 -0.331 23. Zimbabwe 0.742 All entries are t o be divided by 1 0 0 . 20. Taiwan
U (3) -0.223 0.084 0.423 0.329 -0.053 0.093 0.057 0.350 -0.384 0.364 -1.168 0.251 -0.309 0.076 0.053 0.160 -0.132 0.404 -0.207 0.166 0.041 0.125 -0.260 0.132 -0.178 0.192 -0.228 0.057 -0.018 0.015 -0.171 0.163 -0.209 0.102 -0 045 0.044 0.084 0.146 -0.022 0.049 0.242 0.089 -0.179 0.103 -0.071 0.307
X (4) 0.182 0.033 0.431 0.241 0.106 0.040 -0.100 0.250 0.719 0.678 0.718 0.097 0.283 0.162 0.036 0.029 0.207 0.524 0.417 0.116 0.085 0.169 0.274 0.094 -0.176 0.118 0.170 0.059 0.057 0.045 0.170 0.059 0.336 0.106 0.019 0.025 0.098 0.049 0.720 0.166 0.222 0.065 0.006 0.062 0.411 0.799
a (5) -0.064 0.055
-0.136 0.090
0.272 0.226
-0.447 0.171
-0.618 0.122 -0.119 0.170 -0.050 0.046
-0.158 0.111 0.032 0.093 -0.134 0.051 0.025 0.116 0.028 0.072 0.104 0.078
s (6) -0.121 0.073 0.247 0.056 0.028 0.043 0.036 0.065 0.004 0.033 0.131 0.110 0.030 0.023 0.098 0.089 0.084 0.145 0.146 0.058 0.073 0.063 0.232 0.089 0.064 0.088 0.044 0.029 -0.005 0.020 0.213 0.060 0.088 0.045 0.061 0.022 -0.007 0.048 0.080 0088 0.309 0.154 0.078 0.012 0.227 0.226
H (7) 0.167 0.072 -0.668 0.383
Q£
XJ
(8) -0.015 0.049
(9) -0.005 0.016
2 (10) 0.156 0.067 -0.101 0.270 0.212
0.295 0.075 0.244 0.237
0.075 -0.007 0.182
-0.077 0.108
0.059 0.066 0.029 0.138
-0.108 0.129 0.059
0.184 0.086
-0.017 0.016
-0.030 0.008
0.382 0.071
-0.020 0.055
0.006 0.027
0.216 0.312 0.090 -0.100 0.165 -0.013 0.075
-0.059 0.037
0.016 0.156 0.035
0.040 0.062 0.145
0.136 0.107
0.148 0.020 0.049 0.094 0.111 0.120 0.151 0.023 0.047
0.065 0.342 0.262 -0.329 0.153 -0.274 0.177
0.332 0.086 0.072 0.108
0.814 0.155 0.275 0.087 0.252 0.345 0.097 0.085 0.018 0.178 0.289 0.165 0.220 0.284 0.031 0.066 -0.054 0.038 0.461 0.159 -0.104 0.157 -0.042 0.035 -0.022 0.128 -0.360 0.218 0.428 0.151 -0.126 0.172 -0.236 0.471
278
International Consumption Comparisons Table 9.4 Estimates of the income coefficients for 9 commodities and income flexibility under preference independence in 23 LD countries (Standard errors are presented below the estimates)
Country 1.
(1) Colombia
2.
Cyprus
3.
Ecuador
4.
Fiji
5.
Honduras
6.
Hong Kong
7.
Hungary
8. 9.
India Iran
10. Israel 1 1 . Jamaica 12. Korea 1 3. Malta 14. Mexico 15. Philippines 16. Puerto Rico 1 7. Singapore 18. South Africa 19. Sri Lanka 20. Taiwan 2 1 . Thailand 22. Venezuela 23. Zimbabwe
o (2) -0.044 0.036 •0.026 0.053 -0.048 0.047 -0.044 0.028 -0.038 0.019 -0.134 0.037 0.135 0.046 0.108 0.071 -0.142 0.029 -0.132 0.018 -0.109 0.037 -0.069 0.036 -0.132 0.038 -0.127 0.019 0.011 0.027 0.047 0.040 -0.079 0.030
U
(3) 0.039 0.027 -0.093 0.037 0.058 0.029 -0.030 0.006 -0.071 0.012 0.256 0.037 0.040 0.021 -0.010 0.058 -0.140 0.008 0.057 0.027 0.014 0.012 0.011 0.019 -0.003 0.019 0.062 0.015 0.009 0.007 0.017
-0.089 0.025 -0.042 0.054 -0.106 0.030 0.016 0.042 -0.156 0.052
0.030 0.026 0.018 0.035 0.012 0.007 0.016 0.015 0.007 -0.028 0.017 0.044 0.024
-0.013 0.054
0.005 0.019
o X (4) •0.104 0.013 -0.034 0.038 -0.044 0.014 •0.002 0.033 0.114 0.023 -0.119 0.014 -0.153 0.018 -0.058 0.011 0.091 0.023 -0.165 0.021 -0.031 0.019 -0.059 0.016 0.020 0.014 -0.079 0.016 -0.021 0.021 -0.040 0.012 -0.057 0.019 -0.077 0.006 -0.045 0.007 -0.096 0.025 •0.078 0.012 0.012 0.014 0.012 0.050
Q (5) 0.032 0.020
0.062 0.028
£ (7)
(8)
0.080
0.017 0.025 0.097
0.003 0.015
0.025 -0.025 0.007 •0.018 0.013 0.034 0.005 -0.008
0.015 0.031
0.003 -0.014 0.016
0.124 0.019 0.000 0.021 0.029 0.012
0.024 0.022 •0.024 0.017 0.033 0.013 0.036 0.012 0.008 0.011 0.034 0.014
0.032 0.028 0.006 -0.025 0.007 -0.022 0.009 -0.003 0.012 -0.020 0.008 -0.010 0.008 0.014 0.009 -0.015 0.016 -0.011 0.008 -0.011 0.005 -0.002 0.004 0.004 0.013 -0.034 0.028 -0.015 0.003 -0.024 0.012
(9) -0.001
5 (10) -0.022
c
01)
0.026 0.081
-0.256 0.037 0.855
0.059 -0.010 0.022 0.081
0.039 0.000 0.024 -0.039
0.265 -0.097 0.039 -0.427
0.012
0.013 0.003 0.004
0.035 -0.964 0.041
0.015 0.021 -0.017 0.032 -0.041
-0.262 0.061 -0.681
0.013 0.016
-0.006 0.001 0.007
0.153 0.027
•D
2
(6)
0.122 0.022 -0.007 0.018 0.014 0.014 0.038 0.023 0.088 0.019
0.030 0.029 0.030 0.024 0.078 0.018 0.050 0.034 0.099 0.023 0.138 0.031
0.005
•0.023 0.013
•0.009 0.002
•0.017 0.003
0.011 0.026
0.032 0.007
-0.009 0.003
-0.018 0.014 -0.014 0.013 0.035 0.010
0.006 0.011 0.042 0.025 0.006 0.010 -0.016 0.018 0.016 0.023 0.002 0.009
0,032 0.163
0.084 0.009 0.035 -0.789
0,019 -0.033 0.016 0.156
0.055 •0.412 0.033 -0.943
0.028 0.000 0.027 0.109 0.037 0.0O1 0.017 -0.012 0.018 -0.068
0.073 -0.256 0.040 -0.625 0.100 -0.025 0.019 -0.055 0.023 -0.879
0.032 0.073 0.029 0.024 0.012 0.014 0.013 0.060 0.033 -0.051 0.028 0.116
0.099 -0.286 0.059 -0.494 0.047 •0.512 0.066 -0.225 0.041 -0.245
0.040 0.020 0.038
0.052 -0.070 0.058 -1.096 0.249
Chapter 9 The Structure of Preferences
279
estimates were achieved even after suppressing the intercept term. Therefore, we report the elasticities based on the original model, (1.1), for the Philippines and the homogeneity constrained model for Hungary. The second point is that the income flexibility for Cyprus and India were positive contrary to its usual negative sign, however, with the suppression of the intercept term, the resulting income flexibility is negative, as it should be.
9.4
Testing Preference Independence
In this section, we test the hypothesis of preference independence, initially using a likelihood ratio test, which is an asymptotic test. We then check the validity of these results using Monte Carlo simulations proposed in Selvanathan (1987). Asymptotic test
We now test the preference independence hypothesis using the likelihood ratio test. The test statistic has an asymptotic %2 distribution with k = l/2n(n-l)-l degrees of freedom. The results for this test for the OECD and LD countries are presented in columns 2-4 of Tables 9.5 and 9.6, respectively. As can be seen, for most countries, preference independence is not supported by the data. This result is consistent with previous studies which use the asymptotic test (for example, see Barten, 1977). Below, we shall investigate this matter further. Monte Carlo test
It is now well accepted in the econometrics literature that the negative results of various hypothesis testing in demand systems are at least in part due to the failure
International Consumption Comparisons
280
Table 9.5 Testing preference independence in 22 OECD countries Asymptotic %2 test
Monte Carlo Simulations
Country
(D 1. Australia 2. Austria
Data-based Critical (2) (3) 96.18 X2(35)=49.80
Conclusion (4) Reject
Rank (5) 1000
Conclusion (6) Reject
58.54
Z2(35)=49.80
Reject
707
Do not reject
3. Belgium
50.42
X2(27)= 40.11
Reject
907
Do not reject
4. Canada
119.47
9C2(35)= 49.80
Reject
1000
Reject
5. Denmark
51.17
X2(35)= 57.34
Do not reject*
432
Do not reject
6. Finland
24.11
X2(27)= 40.11
Do not reject
93
Do not reject
7. France
99.85
3C2(35)= 49.80
Reject
998
Reject
1000
Reject
2
8. Germany
78.46
X (27)= 40.11
Reject
9. Greece
64.91
X2(35)= 49.80
Reject
879
Do not reject
10. Iceland
115.73
X2(35)= 49.80
Reject
11. Ireland
74.09
X2(35)= 49.80
Reject
770 652
Do not reject
12. Italy 13. Japan
47.98
X2(35)= 49.80
Do not reject
379
Do not reject
77.93
X2(27)= 40.11
Reject
996
Reject
14. Luxembourg
51.94
X2(27)= 40.11
Reject
594
Do not reject
15. Netherlands
51.21
Z
(27)= 40.11
Reject
946
Do not reject
16. New Zealand
50.98
2
X (9)= 16.92
Reject
982
Do not reject*
17. Norway
72.48
Z2(35)= 49.80
Reject
955
Do not reject*
18. Spain
62.51
X2(27)= 40.11
Reject
985
Do not reject*
19. Sweden
72.31
%2(35)= 49.80
Reject
954
Do not reject*
20. Switzerland
71.71
X2(27)= 40.11
Reject
998
Reject
21. UK
60.56
X2(27)= 40.11
Reject
972
Do not reject*
116.36
X2(35)= 49.80
Reject
1000
22. USA
2
Do not reject
Reject
k = Vi>n(n-1)-1. The level of significance a = 0.05. A * denotes critical value and conclusion at a = 0.01.
281
Chapter 9 The Structure of Preferences Table 9.6 Testing preference independence in 22 LD countries
Monte Carlo simulations
Asymptotic Xk test Country (1) 1. Colombia 2. Cyprus 3. Ecuador
Data-based Critical (2) (3) 109.07 X2(35)=49.80 41.17 86.55
%2(14)=23.68
Conclusion (4) Reject
Rank (5) 888
Conclusion (6) Do not reject
Reject
743
Do not reject
2
Reject
999
Reject
2
Do not reject*
X (20)=31.41
4. Fiji
67.08
X (14)=23.68
Reject
989
5. Honduras
34.79
X2(9)=16.92
Reject
919
Do not reject
6. Hong Kong
64.65
X2(35)=49.80
Reject
583
Do not reject
7. Hungary
42.57
X2(9)=16.92
Reject
899
Do not reject
8. India
65.23
Z2(20)=31.41
Reject
693
Do not reject
9. Iran
13.11
X2(9)=16.92
Do not reject
670
Do not reject
119.59
X2(35)=49.80
Reject
999
Reject
Do not reject
119
Do not reject Do not reject
10. Israel 11. Jamaica
15.90
2
X (14)=23.69 2
12. Korea
50.96
% (27)=40.11
Reject
621
13. Malta
61.70
X2(27)=40.11
Reject
609
Do not reject
14. Mexico
49.54
X2(27)=40.11
Reject
770
Do not reject
15. Philippines
21.69
X2(9)=16.92
Reject
510
Do not reject
16. Puerto Rico
57.63
X2(27)=40.11
Reject
962
Do not reject*
17. Singapore
35.76
X2(27)=40.11
Do not reject
420
Do not reject
65.63
X2(27)=40.11
Reject
989
Do not reject*
18. South Africa
2
19. Sri Lanka 20. Taiwan
70.38 37.07
Reject Do not reject
906
Do not reject
X2(27)=40.11
572
Do not reject
21. Thailand 22. Venezuela
30.01
X2(27)=40.11
Do not reject
35
Do not reject
20.85
Z
Do not reject*
437
Do not reject
23. Zimbabwe
33.55
X2(9)=16.92
Reject
875
Do nor reject
X (27)=40.11
2
(9)=21.67*
k = 14n(n-1)-1. The level of significance a = 0.05. A * denotes critical value and conclusion at a = 0.01.
International Consumption Comparisons
282
of asymptotic tests which use the moment matrix S that could be singular (or near-singular) with insufficient data (for a review, see Barten, 1977). To overcome the problems associated with the asymptotic tests, distribution-free tests based on Barnard's (1963) Monte Carlo simulation procedure have recently been developed for demand theory hypotheses, homogeneity, Slutsky symmetry (Theil, 1987) and preference independence (Selvanathan, 1987, 1993). The basic idea behind the Monte Carlo tests is to simulate a large number of values of the test statistic under the null hypothesis to construct its empirical distribution. The observed value of the test statistic is then compared to this distribution, rather than its asymptotic counterpart. Below, we set out this Monte Carlo procedure and then present its application to preference independence. Using the standard notation, consider the system of equations y = XP + e. Suppose we are interested in testing the null hypothesis RP = b using a test statistic x. Obviously x is a function of the estimate of the parameter vector p. In general, the Monte Carlo procedure can be summarized as follows: Step 1: Estimate the unrestricted model and obtain the data-based value Xi Of X.
Step 2: Estimate the model under the null hypothesis RP = b and obtain the estimate S of the covariance matrix £ of the disturbances. Step 3: Generate quasi-normal error terms with zero means and covariance matrix S and use these errors together with the observed value of X and the restricted estimates to generate a new data set for y under the null. Use the generated data to estimate the unrestricted model. Step 4: Repeat Step 3 a certain number of times, N say, and in each case calculate the simulated value of the test statistic x.
Chapter 9 The Structure of Preferences
283
Step 5: Let x2, x3 ... xM be the values of the test statistic x obtained from the simulated data, where M=N+1. For a one-tailed test, we reject the null hypothesis for the observed sample at the a percent significance level if Xi is among the M' largest values of the Xi's such that (M'/M)xl00 = cc. The number of replications (N) is usually chosen to be sufficiently large to reduce the 'blurring effect', which leads to loss of power (see Marriot, 1979). However, after a certain number of replications, the return for increased computing time diminishes. According to Besag and Diggle (1977), the suggested number of replications to reduce the "blurring effect' for a 5 percent significance test is 999. If we use a = 5 percent significance level and N = 999 simulations, for a one-tailed test, we reject the null hypothesis if the rank of X] is 951,....,999 or 1000. For a = 1 percent and N = 999 simulations, for a one-tailed test, we reject the null if the rank of Xi is 991, ...., 999 or 1000. We now apply this Monte Carlo simulation procedure to test the preference independence hypothesis using the data for the OECD and LD countries. The results for the OECD and LDC data are reported in columns 5 and 6 of Tables 9.5 and 9.6, respectively. As can be seen from Table 9.5, preference independence is now acceptable for 15 of the 22 OECD countries. The results are even more encouraging for the LD countries. As can be seen from Table 9.6, preference independence is now acceptable for 21 out of the 23 LD countries. Table 9.7 summarizes the hypothesis testing results for preference independence for the OECD and LD countries. As can be seen, all 45 countries taken together, preference independence of the utility structure is acceptable for 36 out of the 45 countries. Consequently, the overall picture which emerges from the table is that preference independence hypothesis is generally acceptable for the 9 broad commodity groups considered in this study.
International Consumption Comparisons
284
Table 9.7 Summary results: Testing preference independence 22 OECD countries and 23 LD countries LD countries
OECD countries
Country (3) Colombia Cyprus Ecuador Fiji Honduras Hong Kong Hungary India Iran
Conclusion (4) Do not reject Do not reject Reject Do not reject* Do not reject Do not reject Do not reject Do not reject Do not reject
Conclusion (2) Reject Do not reject Do not reject Reject Do not reject Do not reject Reject Reject Do not reject
1. 2. 3. 4. 5. 6. 7. 8. 9.
10. Iceland
Do not reject
10. Israel
Reject
11. Ireland 12. Italy 13. Japan 14. Luxembourg 15. Netherlands 16. New Zealand 17. Norway 18. Spain 19. Sweden 20. Switzerland 21. UK 22. USA
Do not Do not Reject Do not Do not Do not
reject reject
11. Jamaica 12. Korea 13. Malta
Do not reject Do not reject Do not reject
reject reject reject*
14. Mexico 15. Philippines 16. Puerto Rico
Do not reject Do not reject Do not reject Do not reject Do not reject* Do not reject Do not reject Do not reject Do not reject
Country
(D 1. 2. 3. 4. 5. 6. 7. 8. 9.
Australia Austria Belgium Canada Denmark Finland France Germany Greece
Do not reject* Do not reject* Do not reject* Reject Do not reject* Reject
17. 18. 19. 20.
Singapore South Africa Sri Lanka Taiwan
21. Thailand 22. Venezuela 23. Zimbabwe
The level of significance used is a = 0.05. A * denotes conclusion at a = 0.01.
Do not reject
285
Chapter 9 The Structure of Preferences
9.5
Implied Income and Price Elasticities
In Section 9.4, we found that the preference independence hypothesis is widely acceptable for the OECD and LD countries. In this section, we present the implied income and price elasticitiy estimates under preference independence. The income elasticity implied by model (1.3) can be calculated as ili = 1 + A ,
i=l,...,/L
(5.1)
When the budget shares are fairly stable over time, wit in (5.1) can be replaced by its sample mean wt = (1/T) X^i^r and the implied income elasticity can then be written as
ili = 1 + = S
i=l,...,n.
(5.2)
When Pi < 0, we can deduce from (5.2) that T|i will be less than one and good i will be a necessity. On the other hand, when Pi > 0, r|j will be greater than one and good i will be a luxury. Similarly, the Slutsky (or compensated) own-price elasticity of good i implied by model (1.3) at sample means is
Tin =
'-
'—
'•
'—,
1=1, ...,n.
(5.3)
286
International Consumption Comparisons
To calculate these elasticities, we use the ML estimates of the income coefficient (Pi) and income flexibility ((()) presented in Table 9.2 for the OECD countries and Table 9.4 for the LD countries and the budget shares presented in Table 3.3 (OECD) and Table 4.3 (LDC). We present these income and price elasticity estimates for the OECD countries in Tables 9.8 and 9.9 and for the LD countries in Tables 9.10 and 9.11. In general, all except four of the income elasticities presented in Table 9.8 are positive. As can be seen from column 2 of Table 9.8, the income elasticity estimates for food are all less than one and positive. This means that food is considered to be a necessity by consumers in the OECD countries. For consumers in most OECD countries, housing, medical care and education are also necessities as the income elasticity estimates are mostly less than one. Also, for consumers in most OECD countries, clothing, durables, transport and recreation are luxuries as their income elasticity estimates are mostly greater than one. The average OECD income elasticity is .58 for food, .44 for housing, .88 for medical care and .70 for education. Also, the OECD average income elasticity is 1.46 for clothing, 1.60 for durables, 1.79 for transport and 1.10 for recreation. All (except four) own-price elasticities are negative as they should be. Most of these own-price elasticities are less than one in absolute value, indicating that the demand for all goods is price inelastic. Looking at Table 9.10, we see that all but three of the income elasticities are positive. The average LDC income elasticity is .78 for food, 1.19 for clothing, .69 for housing, 1.52 for durables, .85 for medical care, 1.37 for transport, 1.20 for recreation and .66 for education. This means that, as in the case of the OECD consumers, the LD consumers also consider food, housing, medical care and education as necessities, and clothing, durables, transport and recreation as luxuries.
287
Chapter 9 The Structure of Preferences Table 9.8
0.716
1.482
5. 6. 7.
Denmark
0.449 0.612
1.613 1.474 0.834
8.
Finland France Germany
9. 10.
Greece
11. 12.
Ireland Italy
Iceland
13. Japan 14. Luxembourg
0.416 0.670 0.522 0.340 0.444 0.696 0.792
1.753
1.321
0.770
0.428 0.356
1.233
0.809 1.284
1.449
0.428
1.216 1.120
1.625 1.849
2.473 2.258 1.824
0.179
0.052
0.266 0.507
1.361 0.973 1.084 1.550
1.295
1.308 1.482 1.867
1.499
1.449
0.555 0.004
2.005
2.040
0.420 0.490
1.720 1.603
0.296
1.765 1.803 1.108 1.854
0.433 0.465 0.444
Norway
0.631
1.337
18.
Spain* Sweden
0.842
0.783
0.740
1.640
0.956
1.415 1.004 1.330
1.608
0.923 0.552 1.094 -0.029 0.692 0.358 0.404 0.304
1.498 1.199
0.148 0.632 0.616 0.826 1.011
1.576
1.282 1.632
0.809 2.034
1.829 1.264
1.895
0.691
1.497
0.845 1.680
0.923 1.729
(8) 2.038 0.990
(9) 1.615
(10) 1.064
0.825
0.855 1.834
0.272 1.752
-0.131
0.945
-0.393
1.413 1.464
1.739 0.849
1.168 0.676
0.926
1.524
0.770
1.416
1.647
-0.085 1.011
1.080 0.888
2.420
1.188
0.300
1.219 0.816
0.183
1.781 1.944
1.158 1.419
1.530
0.865 0.555
1.539 1.689 2.343
0.870 1.159
0.959
1.063 1.574 0.954
1.786
1.097
0.704
1.205
1.707
0.523
1.591
1.456 0.440 Mean 0.575 * Elasticities are from the no constant model.
1.595
0.880
0.609 0.365
1.967 1.309 2.200 1.584
1.437 1.662
1.892
0.789 0.798 0.325
21. 22.
Switzerland* UK USA
0.537
2.232 1.256
Netherlands New Zealand
20.
(7) 1.203 1.895
0.636 0.253
15. 16. 17. 19.
(6) 1.113 0.397
Miscel
Canada
0.494
(5) 2.567 1.304
Educat
4.
(4) 0.342
Recrea
1.204
Trans f
0.430
3.
Medic;
(3) 1.272 1.538
Durabl
(2) 0.428 0.647
Australia Austria Belgium
Housir
0) 1. 2.
Clothii
Country
Food
Estimates of the income elasticities under preference independence for 9 commodities in 22 OECD countries
1.228
288
International Consumption Comparisons Table 9.9
-0.372 -0.230
Finland France Germany
-0.055 -0.152
8. 9. Greece 10. Iceland 11. 12.
Ireland
-0.215 -0.105 -0.101 -0.085
(3) -0.624
(4) -0.175 -0.120
(5) -1.124
(6) -0.563
(7) -0.540
(9) -0.861
-0.304
-0.102
-0.361
(8) -0.961 -0.243
-0.033
-0.093 -0.662
-0.051
-0.076
-0.738 -0.153 -0.054
-0.688 -0.876 -0.162
-0.059 -0.243 -0.452
-0.550 -0.554
-0.337 -0.074 -0.802 -0.838 -0.145 -0.317 -0.490 -0.445 -0.362 -0.407
-0.006 -0.230
-0.764
-0.215
(10) -0.503 -0.192 -0.096
-0.256 -0.103
-0.610 -0.578 -0.121
-0.565 -0.104 -0.418
-0.521
-0.484 -0.623
0.034
-0.319
-0.282
0.128
-0.353 -0.071
-0.262
-0.400 -0.311
-0.060
-0.072
-0.518 -0.108
-0.095 -0.132
-0.158 -0.620 -0.495 -0.277
-0.001
-0.516
-0.198
-0.286 -0.463
-0.092 -0.041
-0.353
-0.187
-0.293
-0.126 -0.469
-0.086 -0.2%
-0.116 -0.590
-0.653 -0.167
-0.836 -0.070
-0.486 -0.152
-1.015 -0.915
-0.898
-0.615
-0.261
-0.201
-0.368 -0.632
-0.330
-0.368
Italy 13. Japan 14. Luxembourg
-0.049
15.
-0.045 -0.565 -0.300
-0.161
-0.055
-2.039 -0.679
-0.758
-0.118
-0.136
-1.019 0.017 -0.117 -0.088 -0.185
-0.409 -0.645
-0.034
-0.093
-0.148
-0.158
-0.171 -0.477
-0.538 -0.093
-0.105
-0.503
-0.358
-0.316
-0.275
-0.157
-0.448
-0.315
-0.429
-0.328
-0.251
-0.361
Netherlands New Zealand
16. 17.
Norway 18. Spain* 19. Sweden
-0.256 -0.185
-0.131 -0.624 -0.484
-0.236 -0.188
-0.050 -0.747
Miscellaneous
Education
Canada Denmark
Recreation
-0.026
Transport
5. 6. 7.
Austria Belgium
Medical care
3. 4.
(2) -0.208 -0.142
Durables
2.
(1) Australia
Housing
1.
Clothing
Country
Food
Estimates of the own-price elasticities under preference independence for 9 commodities in 22 OECD countries
20.
Switzerland*
-0.161 -0.337
21.
UK
-0.060
22.
USA
-0.115
-0.645 -0.109 -0.404
-0.176
-0.484
Mean
-0.385
-0.111 -0.362
* Elasticities are from the no constant model.
-0.161
-0.296 -0.049
-0.281 0.041
-0.443 -0.438 -0.087
-0.101
-1.057 -0.172
-0.426 -0.140
-0.410
-0.143 -0.477 -0.138
Chapter 9 The Structure of Preferences
289
Table 9.10
Taiwan Thailand* Venezuela
23. Zimbabwe
1.870
0.588 0.962
1.080 1.047
1.508 1.042
1.396 0.178 1.245 0.544 1.283 0.247 0.825 0.450 1.313 0.260 0.878 0.884 0.449 0.322 0.113 0.432 0.542
2.546 0.882 1.132
2.325 3.069 1.004 1.255 0.962 0.716 1.269 1.808 1.160 1.611
0.749 -2.164 1.790 1.669 0.508 -0.018 0.942 0.472 0.749 1.295 1.219 0.644 0.725 0.848 1.079 1.220 0.379 0.476
(7) 1.118 1.585 0.911 1.559
(8) 1.071
(9) 0.960
1.163
0.681
0.337
0.085
2.204
2.073 0.944
1.809
1.132
0.826 0.793
1.259 1.814
1.643
1.288 1.227 1.516 1.383
1.203 1.352 1.109 0.582
2.368 1.838
1.140 1.116
0.674
Miscellaneous
0.728 0.473 0.993
(6) 2.375 0.546 0.552
Education
(5) 1.549
Recreation
(4) 0.132
Medical care
(2) (3) 0.884 1.582 0.872 0.884 0.875 1.552 0.883 0.596 0.918 0.301 0.477 2.391 0.857 1.351 0.800 1.079 0.662 -0.298 0.516 1.869 0.740 1.376 0.827 1.169 0.620 0.967 0.637 1.725 1.234 1.018 0.951 0.902 0.698 1.319 0.737 1.401 0.931 1.096 0.749 1.290 1.094 0.625
Transport
Korea Malta Mexico Philippines Puerto Rico* Singapore South Africa Sri Lanka
Durables
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Housing
(1) Colombia 2. Cyprus 3. Ecuador 4. Fiji 5. Honduras 6. Hong Kong 7. Hungary** 8. India* 9. Iran 10. Israel 11. Jamaica 1.
Food
Country
Clothing
Estimates of the income elasticities under preference independence for 9 commodities in 23 LD countries
(10) 0.818 1.055 1.002 0.685 1.038 1.188 1.072 1.440 2.516 0.653 1.722 0.998 1.705 1.010 0.923 0.806 1.398 1.264 1.374 1.839 1.142 1.321 1.082
Mean 0.775 0.688 1.193 1.518 0.847 1.368 1.195 0.657 1.220 * Elasticities are from the no constant model. ** Elasticities are for homogeneity constrained model.
290
International Consumption Comparisons Table 9.11
Medical care
Transport
Recreation
Education
Miscellaneous
(8) -0.262
(9) -0.242
(10) -0.188
-1.183 -1.758 -1.558 -0.057 -0.126 -0.044 -0.158 -0.053
-1.416
1.035
-0.080
-0.077
-0.251
-0.515
-0.268
Housing
(7) -0.241
Clothing
3. 4.
(6) -0.524
Food
2.
(5) -0.361
(1) Colombia
(2) -0.151
(3) -0.361
(4) -0.033
Cyprus Ecuador
-0.323
Fiji
Country 1.
Durables
Estimates of the own-price elasticities under preference independence for 9 commodities in 23 LD countries
5.
Honduras
6.
Hong Kong
-0.243 -0.316 -0.510 -0.281 -0.807 -0.110 -0.350 -0.045
7.
Hungary**
-0.425
-0.720
0.392
-0.354
8.
India*
-0.029
-0.060 -0.032
-0.105
9.
Iran
-0.377
0.242 -0.593 -0.676 -0.096
11. Jamaica
-0.183 -0.482
12. Korea
-0.142
-0.277 -0.110
-0.642
-0.230 -0.255
-0.194
-0.227
13. Malta
-0.304
-0.556
-0.753
-0.564
-0.290 -0.640 -0.470
-0.784
14. Mexico
-0.013
-0.037 -0.006
-0.027 -0.019
15. Philippines
-0.023
-0.065
-0.041
-0.067
-0.044
16. Puerto Rico*
-0.526 -0.163
-0.631
-0.675
-0.336
-0.588 -0.122
-0.192
-0.800 -0.848 -0.180 -0.293 -0.324
-0.555 -0.297
18. South Africa 19. Sri Lanka
-0.273
-0.608
-0.154
-0.529
-0.348 -0.577 -0.514
-0.554
-0.203
-0.519 -0.057
-0.852
-0.428
-0.580 -0.291
-0.667
20. Taiwan
-0.115
-0.272
-0.090 -0.247 -0.229
-0.442
-0.223
-0.360
21. Thailand*
-0.104
-0.212
-0.113
-0.249 -0.318
-0.233
-0.218
22. Venezuela
-0.032
-0.091
23. Zimbabwe
-0.713
-0.998
-0.063 -0.846
Mean
-0.240
-0.442
-0.293
10. Israel
17. Singapore
-1.232
-1.026 -0.799 -0.259
-0.188
-0.916 -0.275
-0.170 -0.088
-0.282
-0.005
-0.112
-0.082
-0.652
-0.692
-0.007
-1.224 -0.701
-0.663
-0.309
-0.424
-0.204 0.017
-1.448 -0.273
-0.782
-0.252 -1.021
-0.037 -0.038
-0.022
-0.866
-0.026
-0.048
-0.510
-0.870
-0.395
-0.465
-0.336
-0.201
* Elasticities are from the no constant model. ** Elasticities are for homogeneity constrained model.
-0.354
291
Chapter 9 The Structure of Preferences
As can be seen from Table 9.11, almost all of the own-price elasticities are negative as they should be and most of them are less than one in absolute value, indicating that, in general, demand for all goods in the LD countries is also price inelastic. In contrast to the OECD results, demand for clothing in Cyprus and Jamaica, housing in Cyprus, medical care in Cyprus, Fiji and Iran, and transport in Cyprus are price inelastic. A comparison of the preliminary income and price elasticity estimates presented in Chapters 3 and 4 with the estimates presented in this section reveals that they are very similar.
9.6
Conclusion
In this chapter, we tested the well-known utility structure, preference independence among consumer goods. We used the asymptotic test as well as the Monte Carlo simulations to test this hypothesis. Table 9.12 presents a summary of the findings for the 45 countries (22 OECD and 23 LD countries) considered in this book. As can be seen from the table, among all 45 countries, preference independence among commodity groups is acceptable for 80 percent of the countries.
Table 9.12 Summary of acceptance of preference independence hypothesis: 22 OECD and 23 LD countries (D 1. Number of acceptance 2. Percentage acceptance
OECD countries (2) 15 68
LD countries (3) 21
All countries (4) 36
91
80
292
International Consumption Comparisons
We also presented the income and own-price elasticities under preference independence. The results show that, in general, for a typical 'world' consumer, food, housing, medical care and education are necessities while clothing, durables, transport and recreation are luxuries. Mostly, demand for all goods is price inelastic.
References Barnard, G.A. (1963). 'In discussion,' Journal of the Royal Statistical Society, Series B, 25: 294. Barten, A.P. (1969). 'Maximum Likelihood Estimation of a Complete System of Demand Equations,' European Economic Review 1: 7-73. Barten, A.P. (1977). 'The Systems of Consumer Demand Functions Approach: A Review,' Econometrica 45: 23-51. Bera, A.K., R.P. Byron and CM. Jarque (1981). 'Further Evidence on Asymptotic Tests for Homogeneity and Symmetry in Large Demand Systems,' Economics Letters 8: 101-105. Besag, J., and PJ. Diggle (1977). 'Simple Monte Carlo Tests for Spatial Patterns,' Applied Statistics 26: 327-333. Bewley, R.A. (1983). 'Tests of Restrictions in Large Demand Systems,' European Economic Review 20: 257-269. Chen, D.L. (2001). World Consumption Economics. Singapore, London: World Scientific. Clements, K.W., W. Yang and S.W. Zheng (1997). 'Is Utility Additive? The Case of Alcohol,' Applied Economics 29: 1163-1167. Laitinen, K. (1978). 'Why is Demand Homogeneity So Often Rejected?' Economics Letters 1: 187-191.
Chapter 9 The Structure of Preferences
293
Marriot, F.H.C. (1979). 'Barnard's Monte Carlo Tests: How Many Simulations?' Applied Statistics 28: 75-77. Meisner, J.F. (1979). 'The Sad Fate of the Asymptotic Slutsky Symmetry Test for Large Systems,' Economics Letters 2: 231-233. Moschini, G., D. Moro and R.D. Green (1994). 'Maintaining and Testing Separability in Demand Systems,' American Journal of Agricultural Economics 76: 61-73. Selvanathan, E.A. (1995). 'Data Analytic Techniques for Consumer Economics,' Chapter 3 in E.A. Selvanathan and K.W. Clements (eds), Recent Developments in Applied Demand Analysis. Berlin: Springer. Selvanathan, S. (1987). 'A Monte Carlo Test of Preference Independence,' Economics Letters 25: 259-261. Selvanathan, S. (1993). A System-wide Analysis of International Consumption Patterns. Boston: Kluwer Academic Publishers. Selvanathan, S., and E.A. Selvanathan (1994). Regional Consumption Patterns. London: Avebury Publishing Company. Theil, H. (1971). Principles of Econometrics. New York: John Wiley and Sons. Theil, H. (1980). The System-Wide Approach to Microeconomics. Chicago: University of Chicago Press. Theil, H. (1987). 'The Econometrics of Demand Systems,' Chapter 3 in H. Theil and K.W. Clements (eds.), Applied Demand Analysis: Results from Systemwide Approaches. Cambridge, MA: Ballinger Publishing Company. Theil, H., and R.B. Brooks (1970/71). 'How Does the Marginal Utility of Income Change When Real Income Changes?' European Economic Review 2: 218240. Theil, H., and K.W. Clements (1987). Applied Demand Analysis: Results from System-wide Approaches. Cambridge, MA: Ballinger Publishing Company.
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APPENDIX
The Demand Analysis Package 2000 (DAP2000) Wana Yang, Kenneth W Clements <& Dongling Chen
The Demand Analysis Package 2000 (DAP2000 for short) is a computer program written in the GAUSS matrix programming language for students and researchers working in applied demand analysis. It is an enhanced version of the Demand Analysis Package (DAP), which was written in FORTRAN and BASIC by Selvanathan et al (1989). Features of DAP2000 include: * Preliminary data analysis, which tabulates consumption data, computes a variety of Divisia index numbers and estimates demand elasticities based on double-log demand equations. * Hypotheses testing, using both conventional asymptotic procedures and the recently-developed Monte Carlo simulation approach. The hypotheses tested are homogeneity, symmetry and preference independence. * Estimation of demand systems. These demand systems include the Rotterdam model (Barten, 1964; Theil, 1965), Working's (1943) model, Working's model under substitution independence (Keller, 1984), Working's model under preference independence (Clements, 1987), Selvanathan's (1985) model, and the constant elasticity model. (The Rotterdam and Working's models are included in the hypothesis testing part of the package; the other models are included in the MAS part, mentioned below.)
International Consumption Comparisons
296
*
The matrix approach to simulation (MAS), which is a recently-developed technique to evaluate demand systems. Four demand systems are employed with MAS here, Working's model under substitution independence, Working's model under preference independence, Selvanathan's model, and the constant elasticity model. The GAUSS code for DAP2000 can be downloaded from the web site: http://www.econs.ecel.uwa.edu.au/erc/.
A.1
Using the Package
To use DAP2000, one needs a PC with GAUSS for DOS (version 3.01 or higher) installed under the subdirectory \gauss. Four steps should then be followed: 1. Set up a user-specified subdirectory. This step can be completed by using the md command under MS-DOS mode or by using Windows Explorer, File, New Folder under Windows. 2. Copy the program file, dap. run, and the input data file into the subdirectory defined in Step 1. 3. Switch to MS-DOS mode and then select the subdirectory defined in Step 1 by using the cd command. 4. Type \gauss\gaussi dap.run and press Enter. For GAUSS version 3.2.17 or higher, type \gauss\gauss dap2000r.run and press Enter. DAP2000 will then commence running and prompt for the name of the output file (no more than 8 characters). PLEASE NAME THE OUTPUT FILE>
The output file contains all the results and the interactive correspondence between the program and the user. It is located in the user-specified subdirectory, defined in Step 1 above, when no other path is given.
Appendix The Demand Analysis Package
A.2
297
Input Options
An ASCII file is needed for input data for running DAP2000. This can be created in EXCEL by saving the document as a text file, or as output from other programs. The construction of the data file is quite flexible in DAP2000, which provides seven options. This and the next section draws on Selvanathan et al (1989). Data File Options
The data file can be constructed using one of the following seven options according to the nature of the data. Option 1: (a) Consumption expenditures in current prices (in millions of currency units); (b) Consumption expenditures in constant prices (in millions of currency units); and (c) Population (in millions). Option 2: (a) Consumption expenditures in current prices (in millions of currency units); (b) Price indexes; and (c) Population (in millions). Option 3: (a) Per capita consumption expenditures in current prices (in currency units); and (b) Per capita consumption expenditures in constant prices (in currency units). Option 4: (a) Per capita consumption expenditures in current prices (in currency units); and (b) Price indexes. Option 5: (a) Volume of consumption of each commodity (in millions of units); (b) Prices per unit (in currency units); and (c) Population (in millions). Option 6: (a) Per capita volume of consumption of each commodity (in volume units); and (b) Prices per unit. Option 7: (a) Price log-changes of each commodity; (b) Quantity log-changes of each commodity; and (c) Average budget shares. Structure of Data File
For all options, the data should be arranged with each column indicating one commodity and each row indicating one observation. Let n be the number of
International Consumption Comparisons
298
commodities and T be the number of observations. The option-specified data files take the form as follows: Options 1. 2 and 5: Lines 1 to T (n+1 entries): Item (a) for the n commodities and item (c). Lines T+l to 2T (n+1 entries): Item (b) for the n commodities and zero. Options 3. 4 and 6: Lines 1 to T (n entries): Item (a) for the n commodities. Lines T+l to 2T (n entries): Item (b) for the n commodities. Option 7: Lines 1 to T (n entries): Item (a) for the n commodities. Lines T+l to 2T (n entries): Item (b) for the n commodities. Lines 2T+1 to 3T (n entries): Item (c) for the n commodities. Interactive Input The following interactive input is programmed in DAP2000. Data Description PLEASE INPUT THE NAME OF THE COUNTRY/REGION OF ANALYSIS> PLEASE INPUT THE NAME OF THE CURRENCY OF THE COUNTRY/REGION> PLEASE INPUT THE SAMPLE SIZE> PLEASE INPUT THE INITIAL YEAR (4 digits)> PLEASE INPUT THE NUMBER OF COMMODITIES> PLEASE INPUT THE NAMES OF THE COMMODITIES EACH COMMODITY NAME SHOULD BE LESS THAN 8 CHARACTERS (Press ENTER key after each commodity name) Commodity 1 > Commodity 2 > Commodity 3 > Commodity 4 > ENTER DATA INPUT OPTION 1: Consumption Expenditures in Current and Constant Prices for the Commodities; and Population 2: Consumption Expenditures in Current Prices and Price Indexes for the Commodities; and Population 3: Per Capita Consumption Expenditures in Current and Constant Prices for the Commodities 4: Per Capita Consumption Expenditures in Current Prices and Price Indexes for the Commodities 5: Volume of Consumption and Prices Per Unit for the Commodities; and Population 6: Per Capita Volume of Consumption and Prices Per Unit for the Commodities 7: Price and Quantity Log-Changes, and the Arithmetic Average Budget Shares for the Commodities
299
Appendix The Demand Analysis Package OPTION NUMBER>
(The message "PLEASE INPUT THE BASE YEAR (4 digits)>" follows when Options 1-4 are entered.) PLEASE ENTER THE INPUT FILENAME>
Task Selection The package performs three major tasks, (i) preliminary data analysis; (ii) hypothesis testing; and (iii) MAS. Users can perform these major tasks simultaneously or separately by selecting the corresponding options when the package prompts. Note that the preliminary data analysis procedure is not valid when data input option 7 is used. The messages prompted for task selection are as follows: IS PRELIMINARY DATA ANALYSIS REQUIRED? ( 0-No; 1-Yes ) > IS HYPOTHESES TESTING REQUIRED? ( 0-No; 1-Yes) >
When the "Hypotheses Testing" option is chosen, the following messages will appear: PLEASE SELECT DEMAND MODEL 1: Rotterdam Model 2: Working's Model OPTION NUMBER> DO YOU REQUIRE CONSTANT TERMS IN THE DEMAND EQUATIONS? (0-No,1-Yes)> PLEASE INDICATE THE SIMULATIONS 1: Normal Disturbances 2: Bootstrap Disturbances OPTION NUMBER>
METHOD TO
IS MAS REQUIRED? ( 0-No; 1-Yes) >
GENERATE
THE
DISTURBANCES
FOR
300
International Consumption Comparisons
When the "MAS" option is selected, the package asks about the number of trials for the simulations, and the format of simulation results (see Section A.5 for further information): PLEASE INDICATE THE NUMBER OF TRIALS FOR SIMILATIONS> WHAT FORM OF RESULTS DO YOU WANT PRESENTED? 1: Detailed Results 2: Summary of Results OPTION NUMBER>
A.3
Preliminary Data Analysis
The preliminary data analysis procedure computes a variety of Divisia index numbers, estimates demand elasticities based on double-log demand equations, and produces high-quality tables of the data. Depending on the input data option, the preliminary data analysis procedure produces some or all of the following items in the form of tables: [This does not apply to data Option 7 which produces no tables for this part of the package.] 1. Current price expenditure, total expenditure and population. 2. Consumption expenditure in constant prices. 3. Per capita expenditure in current prices. 4. Per capita expenditure in constant prices. 5. Prices (or price indexes). 6. Per capita volume of consumption. 7. Budget shares. 8. Price log-changes. 9. Per capita quantity log-changes. 10. Arithmetic average of budget shares. 11. Divisia moments. 12. Relative price log-changes. 13. Relative quantity log-changes. 14. Frequencies of relative price and quantity log-changes. 15. Frequency distributions of relative price and quantity log-changes. 16. Least-square estimates of double-log demand equations.
301
Appendix The Demand Analysis Package
17. Residuals from double-log demand equations. 18. Frequencies of joint signs of relative consumption (adjusted for autonomous trends) and relative price changes. Table A. 1 provides an overview of what is produced for each input option. An explanation of the terms used in the tables is provided in Chapter 2 of the book. Table A.1 Overview of output of preliminary data analysis Input option
Output item*
Total number of tables
1-2 1-5,7-18 18 3-4 3-5,7-18 16 5-6 5-18 15 7 None 0 * Note that when an item is not produced for a given input option, the program will automatically skip it and continuously count the next item. Note also that two tables are produced for item 17, one for residuals with constants, and one for residuals without constants.
A.4
Hypothesis Testing and Estimation
The hypotheses of demand homogeneity, Slutsky symmetry and preference independence are tested in this part of the package, using both conventional asymptotic procedures and a newer Monte Carlo simulation approach. Two popular differential demand systems are used here, viz., the Rotterdam model and Working's model. A brief introduction to differential demand systems is given in Chapter 2 of this book.
International Consumption Comparisons
302 Two Demand Systems
Let pit, qit be the price and quantity demanded for commodity i (i=l,...,n) at time t (t=l,...,T), M(=X"=iP„9,( be total expenditure ('income' for short), where n is the number of commodities. Let wit=pitqit/Mt be the share of 1 income devoted to commodity i at year t, or the i" budget share. Furthermore, let wit be the arithmetic average of the i* budget share in year t and t-1; Dpit = logpit - logpit_x and Dqu = logqit - logqit_x be the log-change in the price and quantity of i from t-1 to t. Finally, define DQ, =£"=1wir £>#,., as the Divisia volume index. The Rotterdam Model The i* equation of the absolute price version of the Rotterdam model (Barten, 1964; Theil, 1965) takes the form witDqit = a, +0,D<2, + 1 XijDpj, +eu ,
(A4.1)
where cij is the intercept for commodity i; &, is the marginal share of i;flyis the (ij)* Slutsky coefficient; and elt is a disturbance term. As there are n commodities, the Rotterdam model consists of equation (A4.1) for i=l,...,n. The adding-up conditions for equation (A4.1) for i=l,...,n are Z"=ia;',- = 0> Y!i=\9i =1 and X"=i fty - 0 . These constraints imply that one of the demand equations is redundant, so that only n-\ equations are estimated. As there are t=l,...,T observations, we can express equation (A4.1) in vector form as y,= x Y,+e,-.
(A4.2)
Appendix The Demand Analysis Package
303
where yl = [yn,...,yn.]' withyu = witDqu, t=l,...,T; X=[i,DQ,DP1,...,DPJ is a Tx(«+2) matrix with i = [1,...,1]' a Txl vector, DQ= [DQU...,DQT]', DPj = [Dpku...,DpkT]' (k=l,...,«); Yi is a vector of (n+2) elements, with yi=[ai,0i,na,...,7iin]'\ and £,• = [en,...,ein ] ' . We can write equation (A4.2)fori=l,...,«-las y = ( I ® X ) Y + E,
(A4.3)
where y = [ yi,--,yn-i ] ' ; I is an (rc-l)x(rc-l) identity matrix; ® denotes the Kronecker product; Y = tYi»—.Yn-J'! anc^ e ~ [ei»"-,e'„-i]' • Equation (A4.3) represents a system of equations that can be estimated jointly by using GLS. The same result is obtained by applying OLS to each equation separately as each equation has the same independent variable matrix, X. Working's Model The i* marginal share 0; in equation (A4.1) is specified as a constant in the Rotterdam model. Under Working's (1943) parameterization, this marginal share is variable and takes the form fit + wit, where (3; is the (constant) income coefficient for commodity i and wit is the arithmetic average of the i* budget share in year t and t-1. Accordingly, the i* equation of this model is wit(Dqit -DQ,) = a, +/3tDQ, + £ n Dpj, +eu.
(A4.4)
The adding-up conditions for (A4.4) are YH=ia, = 0. S"=i A = 0 and Y."=\ n$ = 0, again implying that the number of equations to be estimated is n-1. Equation (A4.4) can be also expressed in the vector form as (A4.2) and (A4.3) by defining the following: yit=wit{Dqit-DQt) and
International Consumption Comparisons
304
Y, = [ai,/3i,nn,...,Kjn]'. As Working's model and the Rotterdam model are so similar, the discussion that follows in the next four sections will be based on the Rotterdam model only. The modifications required for Working's model are entirely straightforward. DAP2000 provides results for both models. Homogeneity
The hypothesis of demand homogeneity states that an equi-proportional change in all prices has no effect on any quantity demanded, when real income is held constant. In other words, consumers do not suffer from money illusion. In the context of the Rotterdam model (A4.1), homogeneity takes the form lTtij-0,
i=l
n.
(A4.5)
j=i
That is, the Slutsky coefficients 7l,j sum to zero over the second subscript. The vector form of (A4.5) is V'YJ = 0,
i=l,...,n,
(A4.6)
where v ' = [ 0, 0, 1, ..., 1]. As one equation is redundant in estimation, (A4.6) for i=l,..., n-\ can be written as R y = 0 , where R = I ® v ' ,
(A4.7)
with I the (n-l)x(n-l) identity matrix. Let b be the OLS estimator of Y- b =[b'1,...,b'„_1]' with b.^CX'X^'X'y,, i=l,..., Ti-1. Let S = [S;J] be an (7I-1)X(TZ-1) matrix with st: = e't e • /(T-k), where e; =y{ - X b ; is the OLS residual vector of the
Appendix The Demand Analysis Package
305
i equation and k is the number of independent coefficients in each equation. In the case of equation (A4.1), we have k = n+2. We assume that the disturbances Eit are normally distributed with zero means and a constant contemporaneous covariance matrix 2 , so that S is an unbiased estimator of 2 . Then, under the null hypothesis (A4.7), the test statistic b'R'S^Rb
v'(X'X) _1 v has an exact distribution as Hotelling's T2 with (n-l) and (T-k) degrees of freedom. This can be expressed as a multiple (n-l)(T-k)/(T-k-n+2) of F with (n-l) and (T-k-n+2) degrees of freedom. For more details, see Laitinen (1978) and Theil (1987). When homogeneity is imposed, equation (A4.1) can be written as witDqit =a t +diDQl +"f * (Dpj, -Dpnt) +eu.
(A4.8)
As each equation in (A4.8) for i=l,...,n-l has the same variables on the righthand side, the homogeneity-constrained estimator is obtained by applying OLS to each equation separately. Symmetry
The hypothesis of Slutsky symmetry states that when real income remains unchanged, the effect of an increase in the price of commodity i on the quantity demanded of commodity j is exactly the same as the effect of an increase in the price of commodity j on the demand for i. This implies that the substitution
International Consumption Comparisons
306
effect is symmetric in i and j , dqi/dpJ = dqj/dpi, implies that the Slutsky coefficients are symmetric Kij=Kji,
i,j=l,...,n.
i,j=l,...,n. In turn, this
(A4.9)
The objective here is to test (A4.9) given homogeneity. The total number of symmetry relations in (A4.9) for i=l,...,«-/ is m = (n-l)(n-2)/2. Accordingly, the hypothesis of Slutsky symmetry can be written in vector form similar to (A4.7) with R now being an mxn(n-l) matrix. The nonzero elements of R take the form ry = 1 and rik = -1 for i=l,...,m, j = (c-l)(n+l)+d+2 and k = (d-l)(n+l)+c+2, where c =l,...,n-l and d = c+l,...,n-l. These non-zero elements correspond to 7itj and n^for i^j. Let b be the estimator of y in (A4.3) under homogeneity, and S be the corresponding unbiased estimator of the disturbance covariance matrix 2 . Under normality, the test statistic b'R'{R[S ® (X'X)"1]R'}"1Rb is asymptotically (T—> °°) distributed as x^ under the null hypothesis (A4.9). The symmetry-constrained estimator and its covariance matrix are (Theil, 1987, p. 116) b = b-CR / [RCR']" 1 Rb var(b) = C - CRlRCR']"1 RC , where C = S ® (X'X)" 1 .
Appendix The Demand Analysis Package
307
Preference Independence, Part I: An Asymptotic Test
Consider the situation when the consumer's tastes can be characterised by a utility function that is additive in the n commodities: n
u(ql,...,qn)
= 'Zui(qi),
(A4.10)
i=l
where q\ is the quantity consumed of commodity i and U\(-) is the i* sub-utility function. Here, as the marginal utility of i is independent of the consumption of j , i*j, the Hessian matrix of the utility function is diagonal and (A4.10) is known as preference independence. Under preference independence, the Slutsky coefficients satisfy (see, e.g., Clements et al, 1995) TCI:/ =- - e
y
),
(A4.ii)
where (() is the income flexibility; 9; is the marginal share of i in equation (A4.1); and 8y is the Kronecker delta which takes the value of one if i=j and zero otherwise. The objective here is to test constraint (A4.ll) for i,j=l,...,«-7, given homogeneity and symmetry. We impose the hypothesis of preference independence by substituting the right-hand side of (A4.ll) for TTy in (A4.1) to obtain witDqit = or. + OPQ, + 06, [DPit -DPt']+eit,
(A4.12)
where DP't=Y!i=\^iDpit is the Frisch price index. As the term Dpu-DPt' is interpreted as the change in the relative price of commodity i, the implication of (A4.12) is that under preference independence only the own-relative price
308
International Consumption Comparisons
appears in each demand equation, which greatly reduces the number of unknown coefficients to be estimated.1 Equation (A4.12) is non-linear in its parameters and can be estimated by using a maximum likelihood procedure. The hypothesis of preference independence can then be tested using the likelihood ratio statistic A = -2(L r - L u ), where L r is the log-likelihood value for the restricted model, equation (A4.12), and L u is the corresponding value for the unrestricted model, equation (A4.8) with n^ -njt (i,j=l,...,«-7) imposed. Under the null hypothesis (A4.ll), A, has an asymptotic %2 distribution with n +(n-l)(n-2)/2 - 2 degrees of freedom. Preference Independence, Part II: A Simulation-Based Test
The likelihood ratio test of preference independence discussed in the previous section has only asymptotic justification; i.e., it holds only when the number of observations is large. The asymptotic nature of the test can bias the results against the null in small samples. The same problem also applies to the standard asymptotic tests of homogeneity and symmetry (Theil, 1987). To avoid these problems, this section sets out a distribution-free test procedure based on Monte Carlo simulations, which was first introduced into demand analysis by Theil et al (1985). This procedure involves comparing the data-based value of the test statistic with its empirical distribution generated from a simulation, rather than its asymptotic counterpart.2 For testing preference independence, both the restricted model (A4.12) and the unrestricted model (A4.8) with symmetry imposed are estimated and their likelihood values are computed. The procedure is as follows:
1
2
Other implications of preference independence are that inferior goods are ruled out and all goods are Slutsky substitutes. See also Selvanathan (1987, 1993), Taylor et al (1986) and Theil et al (1985).
Appendix The Demand Analysis Package
309
Step 1: Generate disturbances from a multivariate normal distribution with zero mean vector and covariance matrix S, the mean squares and cross-products of the restricted residuals.3 Step 2: Generate simulated values of the dependent variable of the restricted model by using (a) the data-based estimates of its coefficients, (b) the observed values of the independent variables, and (c) the generated disturbances. Step 3: Estimate both the restricted and unrestricted models with the generated values of the dependent variable and the observed values of the independent variables, and compute their log-likelihood values Lsr and Lsu , respectively. Step 4: Compute the value of the likelihood ratio test statistic A? = -2(L s r - L s u ). Step 5: Repeat 1,000 times Steps 1-4 to generate the simulated distribution of the test statistic under the null hypothesis. Step 6: Reject the null at the 5 percent level if the observed value of the test statistic X is larger than 950 simulated values of Xs. The assumption of normality of the disturbances can be relaxed by using the bootstrap procedure (Efron, 1979) to generate disturbances in Step 1. The DAP Output
The hypotheses testing and estimation procedure in the package produces the following results in the form of tables: 1. 2. 3. 4.
Estimates of the unrestricted model. The observed value of Hotelling's T2 test statistic. Estimates of homogeneity-constrained model. The asymptotic %2 test statistic for symmetry given homogeneity, its critical value and the test result at the 5 percent level. 5. Estimates of symmetry-constrained model. 6. Estimates of preference independent version of the model. 7. The asymptotic %2 test statistic of preference independence (given symmetry and homogeneity), its critical value and the test result at the 5 percent level. 3
Let S = L L , where L is the Cholesky decomposition for S. The quasi-normal error vectors, e, with zero mean and covariance matrix S can be generated from the standard normal error vector e* ~ iVf0,I) by using the transformation e=Le*.
310
International Consumption Comparisons 8. The simulation-based test result of preference independence (given symmetry and homogeneity), using normal disturbances. 9. The simulation-based test result of preference independence (given symmetry and homogeneity), using bootstrap disturbances.
Whenever estimates are reported, there is an accompanying table of the corresponding elasticities. Note that items 8 and 9 above are mutually exclusive. Therefore, a total of 12 tables are produced by this procedure.
A.5
The Matrix Approach to Simulation
The matrix approach to simulation (MAS) is a new technique for evaluating demand systems, which was developed by Clements et al (1998).
For
convenience, some details are presented here.
Four Demand Equations Although MAS is a general methodology for evaluating a number of alternative demand models, we confine ourselves to four such models. Working's Model under Substitution Let
yit=wit{Dqit-DQt).
For
Independence
commodity
i,
Working's
model
under
substitution independence takes the form
yu=a,+PtDQ,+Mji,+-wu)
Dpu-'£(Mj+wJ,)DpJt
+£„,
(A5.1)
where (%,ft,jUi and A are coefficients. This model is due to Keller (1984) who calls it the CBS/SI model. As this equation is formulated in terms of changes,
311
Appendix The Demand Analysis Package
the intercept (% reflects the residual trend in consumption of commodity i. Note that as Z/C/Zj+w^ J = l, the second term in the square brackets, Y.j( Mj+Wjt )Dpjt, is a weighted-average of the n prices, or a price index. Accordingly, the whole term in the square brackets is interpreted as the change in the relative price of commodity i. Note also that only the own relative price appears in this equation. The coefficients satisfy the following adding-up restrictions: X"=i a ,- = 0. X?=i/?,=0, S"=iMi= 0 • Dividing both sides of equation (A5.1) by wit and rearranging yields the following income and Slutsky ownprice elasticities for commodity i at time t
'lit
~ * "•" — ' W,,
'Iiit ~
— W:,
Working's Model under Preference Independence Working's model under preference independence can be expressed as (see, e.g., Clements, 1987, Sec. 1.15)
yu=ai+PlDQ,
+ 0(/Bi + wlt) DPu-JKPj+njtiDpj,
+£it,
(A5.2)
7=1
where (|) is the income flexibility (the reciprocal of the income elasticity of the marginal utility of income). Keller and van Driel (1985) call equation (A5.2) the CBS/PI model. The term in the square brackets is again the change in the i* relative price, with a (slightly) different price index acting as the deflator. The income and Slutsky own-price elasticities are
312
International Consumption
Comparisons
«H#+w,)[l-(#-w,)] w,.
Note that if the coefficient jx, in equation (A5.1) equals p ; , then (A5.1) becomes (A5.2). Selvanathan's Model Selvanathan's (1985) model can be written as
y^a^ftDQ.
+ yw,
+£«>
(A5.3)
7 =1
where y is a new coefficient, interpreted as the (common) elasticity of substitution. The income and Slutsky own-price elasticities are Vu=l + -=-,
tim=r(l-wa).
If (Xj - 0 in equation (A5.1), then that model becomes (A5.3). The Constant Elasticity Model The constant elasticity model takes the form Dqa = a, + n,DQ,+Vf,DPit-Y.Wj,Dp.
+ £«>
(A5.4)
where T], is the income elasticity and \|/; is a new coefficient. The Slutsky own-price elasticity for commodity i is
Appendix The Demand Analysis Package
313
y\iit = V f U - W f r ) . As is well known, equation (A5.4) does not satisfy the budget constraint; but it is still used as a pragmatic model. Note that (A5.4) is not a special case of (A5.1). As equations (A5.1) and (A5.2) are nonlinear in the parameters, we use a maximum likelihood procedure to estimate all four models.
Simulation Procedures
This section sets out the methodology of the matrix approach to simulation. We use the observed data set to estimate model j and provisionally regard it as the "true" model. The implied income and own-price elasticities are calculated and regarded as the true elasticities. Artificial data for the dependent variable are then generated from model j , by using the estimated parameters, the observations of the independent variables and simulated disturbances. These artificial data are then used to estimate model k. For all possible pairs k,j=l,2,3,4, this procedure yields a 4x4 comparison matrix. To describe this procedure in more detail, we write M(k| j) to denote the situation when model k is estimated given that the true model is j . ThisM(klj) lies behind the (kj)"1 cell of the 4x4 comparison matrix, as shown in Table A.2. Table A.3 gives the detailed simulation procedures for M(k|j). By repeating Steps 1-9 of Table A.3, with appropriate modifications for the true and the estimated models, we obtain all entries of Table A.3. Note that the diagonal of Table A.2 contains cases when the true and the estimated models coincide. These diagonal cases provide a simulation-based evaluation of the quality of the ML estimates for each of the four models; see Theil et al (1983) for details. Note also that the evaluation procedures described
314
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1
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International Consumption Comparisons
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CO Gfc!^
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Appendix The Demand Analysis Package
il ! !
2 "o
*
'5 s : •a -3
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International Consumption Comparisons
•W5 -1 =
i
•ws -I =
• m -I =
>WI
s aa
11 * a s —
ii
<S 3 s 1
s z
317
Appendix The Demand Analysis Package
in this section are focused on the quality of the elasticity estimates. These procedures can be easily modified when the coefficients of the models are of major interest; see Clements and Chen (1999). The Loss Function To evaluate the performance of the models, a loss function is used in this section which combines the bias and the standard error into a scalar measure. Let the loss function take the general form /(B,S), where B is the bias and S the standard error. It seems reasonable to postulate /, ^ 0 for i = B, S (where /,• = df/di), and/,,>0 (where fu-d2f/di2). A simple functional form satisfying these properties is f{B,S) = jaB2+(l-a)S2,
(A5.6)
where 0 < « < 1 . According to (A5.6), the square of the loss is a weighted average of the squared bias and the variance. It has the attraction of involving only one unknown parameter, a. This function implies the following losses for various values of the weight parameter or. a
Loss
1
B
/2
(Jk)RMSE
0
s
1
The DAP Output
For each of the four demand systems (A5.1)-(A5.4), the following output is produced by the MAS procedure in DAP2000:
International Consumption Comparisons
318 1. 2. 3. 4.
The estimated coefficients of the true model. The estimated income elasticities of the true model. The estimated price elasticities of the true model. The biases, root-mean-square-errors and standard errors of the simulated income and price elasticities for each of the four estimated models, given the true model. 5. Values of the loss function when a is 1 (the bias), .75, .5, .25 and 0 (the standard error) for each of the four estimated models, given the true model. Two options are provided for item 4 above. Under the "detailed results" option, details of the biases, standard errors and root-mean-square-errors for both income and own-price elasticities are presented in six tables for each estimated model. Accordingly, 4 x ( 6 + l) + 3 = 31 tables are produced for each true model and a total of 123 tables for the four demand systems.4
Under the
"summary of results" option, sample means of the biases, standard errors and root-mean-square-errors for both income and own-price elasticities are given in one table for each estimated model. Consequently, 11 tables are produced for each true model and a total of 43 tables for the four models. Note that in some cases, the estimation procedure may not converge within 30 iterations. In such a case, a message is printed that "Model did not converge" and the MAS output is omitted when the model in question is the true model. Therefore the number of tables generated by the package may be less than the total number of tables mentioned above.
In the case when the constant elasticity model is the true model, as the estimated coefficients coincide with the income elasticities, the table for these elasticities is omitted. In this case, the total number of tables is 30.
319
Appendix The Demand Analysis Package
References Barten, A. P. (1964). 'Consumer Demand Functions Under Conditions of Almost Additive Preferences,' Econometrica 31: 1-38. Clements, K.W. (1987).
'Alternative Approaches to Consumption Theory,'
Chapter 1 in H. Theil and K.W. Clements Applied Demand
Analysis:
Results from System-Wide Approaches. Cambridge, Ma.: Ballinger, pp.l35. Clements, K.W. and D.L. Chen (1999). 'Simulating Demand Systems,' Chapter 8 in D.L. Chen (ed.) World Consumption Economics.
Singapore, London:
World Scientific, pp. 198-212. Clements, K.W., S. Selvanathan and E.A. Selvanathan (1995). 'The Economic Theory of the Consumer,' Clements (eds) Recent Alcohol,
Advertising
Chapter 1 in E.A. Selvanathan and K.W.
Developments
in Applied
and Global Consumption.
Demand
Analysis:
Berlin, Heidelberg:
Spring-Verlag, pp. 1-72. Clements, K.W., W. Yang and D.L. Chen (1998).
'The Matrix Approach to
Evaluating Demand Equations,' Applied Economics 33: 957-967. Efron, B. (1979). 'Bootstrap Methods: Another Look at the Jackknife,' Annals of Statistics 7: 1-26. Keller, W.J. (1984). 'Some Simple but Flexible Differential Consumer Demand Systems,' Economics Letters 16: 77-82. Laitinen, K. (1978).
'Why is Demand Homogeneity So Often Rejected?'
Economics Letters 1: 1987-91. Selvanathan, E.A. (1985).
'An Even Simpler Differential Demand System,'
Economics Letters 19: 343-47. Selvanathan, S. (1987). 'A Monte Carlo Test of Preference Independence,' Economics Letters 25: 259-61.
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INDEX
Subject Index Additive, 13,40,42,66,67,120, 269, 292,307,319 Aggregation, 17,30, 37,63, 64, 66,67, 68, 69, 246, 247 AIDS, 53, 56, 57, 58, 59, 60, 61, 228, 249,250, 260, 264 Alternative demand systems, 228 Annual growth, 78,130 Area, 4 Asymptotic test, 233, 235, 239, 241, 268,279,282,291,308 Australian states, 26 Average growth, 76, 78, 130, 135, 172 Block independence, 42,43 Blurring effect, 283 Budget constraint, 10, 11,13, 32, 33, 44,45, 313 Budget shares, 17,19,22,25,32, 36, 41, 54, 58,74,75,76,78, 94,95, 96, 97, 98, 127,129, 146, 170, 171,193,195,198,199,213,285, 286,297, 300 CBS, 30, 61, 62, 63, 105, 228, 249, 250, 251, 256, 260, 264, 265, 268, 269 CBS, 310, 311 CBS/PI, 62,63,105, 311 CBS/SI, 61,62,63,310 Compensated, 8, 10, 35, 36, 285 Complements, 41, 49
Consumer demand, 14,22, 30,63, 227, 228 Consumer preference, 2, 9, 31 Consumption comparisons, 14, 18 Consumption patterns, 1, 71,125,169, 170,175,184, 185 Contemporaneously correlated, 251 CPI, 201 Cross-equation restriction, 239 Cross-price elasticities, 9, 38, 39 Cross-sectional, 15 DAP2000,71, 125, 295,296,297, 298, 304, 317 Data analysis, 71,105,125,169,182, 184, 228, 295, 299, 300, 301 Demand analysis, 30, 34, 63, 187, 249, 250,251,227,295,308 Demand curves, 9 Demand homogeneity, 8, 37, 38,49, 64, 227, 230, 231, 233, 241, 245, 250,251,264,267,301,304 Demand theory hypotheses, 227,228, 241, 243, 244, 245, 249,250, 264, 282 DEMMOD,251,265 Differential demand equations, 30, 64, 65 Distribution-free, 227,268, 282, 308 Divisia price, 19,21,83 Divisia moments, 21, 87, 88,135,140, 175,300
322 Divisia price variance, 83,135,175, 196 Divisia price-quantity correlation, 83, 135, 172 Divisia quantity variance, 19, 21, 83, 88,135,139,172,175 Divisia volume, 18, 44, 48, 51, 78, 81, 130, 302 Double-log, 14, 34,43,71,102,125, 153,179,295, 300, 301 Economic indicators, 3 Elasticites, 102, 153 Empirical distribution, 282, 308 Empirical regularities, 71, 94,141,169, 175,179,184 Engel's law, 6,14,17,27,71,94,120, 122, 125, 141, 146, 169,170, 179, 184 Engle aggregation, 37 Estimation procedure, 268, 269, 270, 273,309,318 Exact test, 231, 233, 234, 235, 237, 241 Exports, 3 Finite-change version, 51, 52, 62, 105, 118,250,257 Functional approach, 187 GDP, 2,5,6,7, 117, 166,225 Goodness-of-fit, 24, 250, 256, 259, 265 Imports, 3 Income elasticity, 7, 9, 10, 22, 34, 36, 38,40,41,50,54,58,59,102, 105,106,117,118,119,153,156, 167,179, 270, 285,286, 311, 312 Income flexibility, 40,42,48,71,105, 106,107,112,113,114,116,125, 156,157,162, 165,179,180,182, 270,273,276, 279, 286,307, 311 Indirect utility, 52, 55 Industrialised countries, 1
International Consumption Comparisons Inferior good, 34,41, 55, 308 Inflation, 3, 5, 6,187,188,190,192, 198,199,200, 201,203,204,205, 206,213,214, 215,224,225 Information inaccuracies, 25,259, 260 Information matrix, 272 Klein-Rubin, 40, 53, 55 Lagrangian, 32, 33 Land size, 2 Language, 2,4,16, 27 Law of demand, 89,141,169,176 LES, 13, 22, 53, 54, 55, 59 Less developed countries, 1, 15 Likelihood ratio test, 16,279,308, 309 Low-income countries, 1 LPW database, 19 Luxury, 54, 59, 269, 276,285 Marginal share, 22, 36,41, 48, 54, 55, 58, 228, 302,303, 307 Marginal utility, 13, 33,40,42,43,48, 105,117,269,270,307,311 Marshallian, 33, 35,47 Matrix approach, 296, 310, 313 Maximum likelihood, 270, 308, 313 Microeconomic policy, 2 ML estimates, 286, 313 Model estimation, 265 Money illusion, 8, 304 Money income, 7, 8, 35, 37,48 Monte Carlo simulations, 279, 281, 291,308 NBR, 61,62, 228, 249,250,251, 260, 264 Necessary condition, 231 Necessity, 54, 59,102,156, 269,276, 285,286 Non-singularity, 233, 235 Organisation for Economic Cooperation and Development, 1
Index Own-price elasticity, 35,41,102, 118, 119,153,167,176,285,312 Population, 2,4,28,71,105,126,297, 298, 300 Predicted budget shares, 257, 259 Preference independence, 13, 40, 41, 42,43,50,52,62,71,105,118, 119,125,166,167,169,179,182, 267, 268, 269, 279, 280, 281, 282, 283, 284,285, 291, 292,295, 296, 301,307,308,309,310,311 Preferred demand system, 249, 259, 260, 264 Preliminary estimates, 71, 102, 125, 153, 276 Price index, 7, 8, 35, 41, 44, 48, 49, 51, 81, 87, 106, 130, 135, 192, 195, 297,300,307,311 Private consumption, 2 Quadratic expenditure system, 17 Quasi-normal error, 282, 309 Real income, 8, 12, 36, 38, 48,105, 117,166,188,304,305 Regional, 24,28, 120,121,122,123, 293 Relative consumption, 89, 93,114,115, 116, 141,145, 163, 164, 176, 177, 178,301 Relative price, 8, 41, 43, 48, 49, 50, 52, 65, 89, 91, 93, 102,106,108,109, 110,111,114,115,116,141,143, 145, 153, 158, 159, 160, 161, 163, 164,176,177, 178,188,189,190, 191,192,193, 194,195,196,197, 198, 199, 203, 204, 205, 300, 301, 307,311 Religion, 2, 4, 17 Revealed preference, 17 RMS, 24, 26
323 RMSE,317 Root-mean-squared, 25 Rotterdam model, 51, 52, 228,260, 295,299,301,302,303,304 Sampling variance, 190,192,197,198, 199 Separability restrictions, 267 Simulations, 239,268, 282, 283,295, 296, 300, 301, 308, 310,313, 320 Slutsky symmetry, 11, 12, 38, 50, 64, 227, 238, 241, 245,250,251, 256, 264,282,301,305,306 Small-sample bias, 227,267 Specific substitutes, 41,49 Standard errors, 99,151,188,201,203, 204, 205, 213, 214, 215, 222, 223, 224,273,318 Stochastic approach, 187, 188, 224 Stone-Geary, 40, 53, 54 Substitutes, 8, 308 Substitution effect, 8, 12, 38,49, 306 Summary measures, 126, 169 System-wide, 10, 14, 29, 70, 122, 123, 168,247,293 Total expenditure, 10, 32, 74, 300, 302 Trading partners, 3, 5 Translog, 53, 55 Unbiased estimator, 189, 196, 197, 199, 229,231,238,305,306 Uncompensated, 35, 36, 55, 57 Unemployment, 3, 7 Unweighted average, 190, 197 Weighted average, 37, 197, 200, 201, 259, 317 Working's model, 58, 59, 94, 99, 123, 146,151, 295, 299, 301,303, 304, 310,311
International Consumption Comparisons
324
Author Index Aasness, 120 Adams, 120 Attfield, 227, 245 Baccouche, 39, 65 Balk, 188,224 Barnard, 245,268,282, 292,293 Barnett, 63, 65, 66, 188 Barten, 28,39,45,46,51, 66,120,227, 229, 233, 245, 246,249,250,251, 265, 279, 282, 292, 295,302, 319 Becker, 15, 24, 29 Bera, 227,245,292 Bettendorf, 265 Bewley, 227, 245, 292 Blanciforti, 120 Blundell, 63, 66, 249 Brown, 265 Brozdin, 126, 168 Buse, 63, 66, 227, 246 Byron, 245, 292 Cassel, 34, 66 Chavas, 63, 66 Chen, 14, 26, 29, 72, 120, 123, 126, 168, 233, 246, 265, 292,295, 317, 319 Christensen, 55, 64, 66 Chua, 249, 265 Chung, 120,121,123 Clements, 14,24,26, 27,29,40,42, 47,66,69,70,83, 112,117,118, 119,120,121,122,123,166,168, 188,189,199, 200, 201,224,233, 247,249, 265, 267, 292,293,295, 307,310,311,317,319,320
Crompton, 188,199, 200,201,224 Deaton, 22, 27, 54, 56, 57, 64, 67, 118, 119,121,225 Deschamps, 227, 246 Diewert, 64, 67, 187,188, 199, 225 Driscoll, 39, 67 Edgerton, 39, 67 Efron, 309, 319 Fiebig, 121 Finke, 121, 123, 320 Fisher, 249, 265 Fleissig, 265 Flood, 121 Frisch, 41, 43, 49, 51, 71, 105,116, 117,121,125,165,166,168,187, 225, 307 Gamaletsos, 22, 28 Goldberger, 22, 28 Goldman, 39, 67 Gorman, 39, 67 Green, 68,120, 293 Griffiths, 265 Heineke, 63,67 Hessian, 33, 46,48, 307 Houthakker, 14,27,41,49, 67,246, 247 Imhoff, 121 Izan, 122,188,189,199,200,201,224 Jarque, 245, 292 Jorgenson, 55, 64, 66 Karagiannis, 227, 246 Keller, 30, 59, 61, 62, 67, 295, 310, 311,319 Keuzenkamp, 228, 246
Chapter 3 Data Analysis: OECD Countries Kravis, 15,16,22, 28 Laisney, 39,65 Laitinen, 227, 231,233, 234, 237, 246, 265,292, 305, 319 Lau, 55, 64, 66 Lee, 249, 265 Leontief, 39, 68 Leser, 94, 122 Lewbel, 39,63, 68 Lluch, 2,17,18,19,22,27, 28, 54,68 Lopez, 120, 121 Malinvaud, 63, 68 McElroy, 256, 265 McGuirk, 39, 67 Meisner, 83,122, 226, 227,239, 246, 293 Mergos, 227, 246 Meyermans, 265 Moschini, 39, 68, 267, 293 Mountain, 65, 68 Muellbauer, 56, 57, 64, 67,121, 228, 246 Neves, 61, 68, 249, 266 Ng, 228, 247 Parks, 22, 29 Pashardes, 66, 246 Pearce, 39, 68 Pollak, 16, 22, 26, 28, 228, 247 Powell, 2, 17, 22, 27, 54, 68, 120 Rao, 121,188,225,226 Rodseth, 120 Seale, 121,123,265 Selvanathan, 1, 2,14,16,17, 24,26, 28, 30,42,47, 59, 62, 63, 65, 66, 68,69,71,72,83, 112,117,118, 119,122, 125, 166, 168,169, 187, 188, 199, 201, 205, 225,226, 227, 228,233, 247, 249,267,269, 279,
325 282, 293,295, 296,297, 308,312, 319, 320 Serletis, 265 Shafer, 65, 69 Shonkwiler, 320 Slesnik, 63, 69 Sonnenschein, 64,69 Sono, 39, 69 Stigler, 15, 24, 29 Stone, 13, 21,28,34,40, 53,54, 57, 69,70 Strotz, 39,70 Suhm, 15, 29, 83,112,123,226 Taylor, 246,247, 308, 320 Theil, 10,14,15,16,27, 29,30,47,48, 51,63,65,70,83,112,117,120, 121, 122, 123, 166, 168,188, 225, 226,227,229, 231,233,238,239, 247, 250, 256, 259, 266,282, 293, 295, 302, 305, 306, 308, 313, 319, 320 Tridimas, 249, 266 Uzawa, 39, 67 Wales, 16, 22, 26, 28, 228, 247 Williams, 2, 17, 27, 29 Working, 58,70, 94,146,168,295, 303,320 Yang, 71,123, 265, 292, 295,319 Yoshihara, 22, 30 Yuen, 123 Zarkos, 227, 246 Zonderman, 265
International Consumption Comparisons OECO Versus LDC This book presents an analysis of consumption patterns in the OECD (rich) and LDC (poor) countries using recent data (1950-1998) and econometric methodology for a number of broadly aggregated consumer goods. The income elasticity estimates for the 46 countries and 9 commodity groups are tabulated. The reliability of these elasticity estimates, and also the demand theory hypotheses, are investigated using simulation techniques.
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