Income Elasticity and Economic Development

Advanced Studies in Theoretical and Applied Econometrics

VoVV lume 42

Managing Editor:J. Marquez, The Federal Reserve Board, Washington, D.C., U.S.A.

Editorial Board:F.G. AdamsFF , University of Pennsylvania, Philadelphia, U.S.A.P. BalestraPP , University of Geneva, SwitzerlandM.G. Dagenais, University of Montreal, CanadaD. Kendrick, University of Texas, Austin, U.S.A.J.H.P. Paelinck, Netherlands Economic Institute, Rotterdam, The NetherlandsR.S. Pindyck, Sloane School of Management, M.I.T., U.S.A.W. Welfe, University of Lodz, Poland

The titles published in this series are listed at the end of this volume.

Income Elasticity andEconomic DevelopmentMethods and Applications

by

M. Ohidul HaqueVictoria University,Footscray, Australia

A C.I.P. Catalogue record for this book is available from the Library of Congress.

Published by Springer,P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

Printed on acid-free paper

All Rights Reserved© 2005 SpringerNo part of this work may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, microfilming, recordingor otherwise, without written permission from the Publisher, with the exceptionof any material supplied specifically for the purpose of being enteredand executed on a computer system, for exclusive use by the purchaser of the work.

Printed in the Netherlands.

ISBN-10 0-387-24292-9 (HB) Springer Dordrecht, Berlin, Heidelberg, New YorkISBN-10 0-387-24344-5 (e-book) Springer Dordrecht, Berlin, Heidelberg, New YorkISBN-13 978 0-387-24292-7 (HB) Springer Dordrecht, Berlin, Heidelberg, New York ISBN-13 978 0-387-24344-3 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York

TO MY PARENTS

CONTENTS

PREFACE XIII

ACKNOWLEDGEMENT XV

CHAPTER 1: INTRODUCTION 1

1 Introduction 12. A Brief Discussion on Demand Analysis 12.1 Literature on Applied Engel Curve Analysis 22.2 Properties of Demand Functions 43. Engel Curve Analysis and Its Uses 7 4. Outline and Contributions of This Book 10f5. Limitations and Conclusions 13

CHAPTER 2: AUSTRALIAN HOUSEHOLD

EXPENDITURE SURVEYS 15

1. Introduction 152. Changes in Data Collection Procedures for Various Versions 173. Validity of the HES Data 204. Other Observations on the HES Data 235. Recommendation and Concluding Remarks. 27

CHAPTER 3: FUNCTIONAL FORMS FOR ENGEL CURVES 31

1. Introduction 312. The Model 322.1 Specification of Functional Forms 332.2 Complete Systems of Consumer Demand Equation 343. Data 344. The Choice of Functional Form 354.1 Non-nested Hypothesis Testinyy g 365. Empmm irical Application 385.1 Computation of Engel Elasticityt 425.2 Classification of Items 446. Limitation and Conclusions 457. Appendix 3A: Approximate Standard Errors of Elasticity Estimates 47

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CHAPTER 4: PROBLEMS IN NON-LINEAR

ENGEL FUNCTIONS 49

1. Introduction 492. Methodological Issues 502.1 Estimation of Engel Functions from Grouped Means 502.2 Estimation of Within Group Geometric and Harmonic Means from Concentration Curves 522.3 Average Elasticity of a Variable Elasticity Engel Curve 53 2.3.1 Definition. 543. Numerical Illustrations 563.1 Compmm arisons of Elasticities 614. Conclusions 64

CHAPTER 5: THE BOX-COX ENGEL FUNCTION 65

1. Introduction 652. The Model Specification of the Engel Functions 662.1 Specification of Functional Forms 663. The Box-Cox Engel Function 674. Estimation of Elasticityt from the Box-Cox Engel Function 68 4.1 Elasticity of the Box-Cox Functional Form 684.2 Estimation of the Box-Cox Engel Function 69 5. Empirical Illustrations 71 5.1 Elasticity Estimates 736. Statistical Tests for Special Engel Functions 757. Conclusions 77

CHAPTER 6: A REVIEW OF PERSONAL

INCOME DISTRIBUTION 79

1. Introduction 792. Survey of Literature on Personal Income Distribution 802.1 Income Distribution Function 802.1.1 The Normal Distribution 812.1.2 Pareto’s Law 822.1.3 Mandelbrot’s Model 852.1.4 Champmm ernowne’s Mode1 85 2.1.5 The Lognormal Distribution 882.1.6 Gamma Density Function 893. Further Discussion on the Measurement of Income Inequalities 894. Conclusions 91

viii CONTENTS

CHAPTER 7: ELASTICITY FROM

CONCENTRATION CURVES 93

1. Introduction 932. Definitions and Specification of the Concentration Curves 942.1 Lorenz Curve 94 2.1.1 Mathematical Definition of the Lorenz Curve 942.2 Concentration Curves 962.2.1 Properties of the Concentration Curve 963. Estimation of Engel Elasticity from

Concentration Curves: A New Formulation 97 4. Specification of the Concentration Curve 985. Empirical Illustrations 996. Indication foff r Further Research 1057. Conclusions and Limitations 106 8. Appendix-7A: The Method of Obtaining Weighted Elasticity 108

CHAPTER 8: ESTIMATING INCREASE IN

CONSUMER DEMAND 111

1. Introduction 1112. Method of Estimation of Increase in Consumer Demand From the Equation of the Lorenz Curve 1123. Numerical Illustrations on Demand Projo ections 116 4. Conclusions and Limitations 122

CHAPTER 9: FOOD DEMAND ANALYSIS IN AUSTRALIA 125

1. Introduction 1252. Food Expenditures by Various Socio-economic and Demographic Characteristics 126 3. Patterns of Food Expenditures Classified by Various

Household Compositions, Income Levels and Ethnicitytt 1273.1 Protective Effecff ts of Plant Foods 1383.2 Expenditure on Diary Products and Fats 1383.3 Expenditure on Meat and Fish: 1384. Estimation of Total Expenditure Elasticity

for Various Food Items 1395. Estimation of Elasticity Index for Food Items 1475.1 Computation of Elasticitytt Index 1496. Estimating Change in Consumer Demand Due

to Changes in Income and Income Inequality 1507. Limitations and Conclusions 152

ixCONTENTS

CHAPTER 10: DEMAND FOR TRANSPORT

AND COMMUNICATION 157

1. Introduction 1572. Expenditure Pattern of ‘Transport and Communication’ by City, Household Composition, Income Level and Ethnicity 1583. Estimation of Income Elasticity for Transport and Communication Item 162 3.1 Data 1623.2 Choice of Functional Form 1633.3 Estimation of Engel elasticity 1654. Further Evidence from Income Distribution 1695. Implication of the research on transport planning 1696. Problems and Future Options 1707. Conclusions 171

CHAPTER 11: DEMAND FOR ALCOHOL IN AUSTRALIA 173

1. Introduction 1732. Expenditure Patterns of Alcohol Items 1743. Models of Engel Function 1773.1 Choice of Best Functional Form Among Various Alternatives 1784. Estimation of Elasticity 179 4.1 Consistent Estimates of Engel Elasticity 1815. Estimation of the Elasticity Index 1836. Estimating the Change in Consumer Demand 1857. Discussion 187

CHAPTER 12: CONSUMERS’ EQUIVALENCE SCALES

: A REVIEW 189

1. Introduction 1892. Theory of Consumer Equivalence Scales Based on Observed Household Expenditure Survey Data. 1922.1 The Engle Model 1922.2 The Rothbarth Model 1942.3 The Prais and Hd outhakker Model 1952.3.1 A Proposed Solution of the Forsyth’s Problem 1972.3.2 Illustrations with Linear Functions 1983. Utility Theory and Consumers’ Equivalence Scales 200 3.1 The Barten Model 2023.1.1 Barten’s Solution to Forsyth’s Problem 2033.1.2 Extension of Barten’s Procedure foff r a solution of Forsyth’s Problem 2064. The Translation Model 2095. The Extended Linear Expenditure System (ELES) 2116. Functional Forms 2126.1 The Extended Working-Leser Function 212

CONTENTSx

6.1.1 The PIGL Demand System 214 6.1.2 The PIGLOG Function 2156.2 The Bojer Demand Function 2156.3 The Pollak-Wales Demand Functions 2166.4 The Linear Demand System 2166.5 Further Considerations on Functional Forms 2187. Conclusion 219

CHAPTER 13: CONCLUSIONS 221

1. Introduction 2212. Methods of Computing Engel Elasticity 2213. Uses of Income Elasticity 224 4. Concluding Remarks 225

REFERENCES 227

INDEX 251

xiCONTENTS

PREFACE

Consumer demand analysis attempts to explain variations in consumers’expenditure, using time-series and cross-sectional data on income, price, the distribution of income, the effects of the introduction of new commodities andfchanges in tastes and preferences. In most planning and forecasting situations, theerror in forecasting of real income is likely to be less than that associated withrelative prices. As a result, interest centres on the relationship between expenditureon a particular item and income, treating prices as fixed. Hence, it is of greatinterest to estimate income elasticity for various household expenditure items. This is because it gives the percentage change in expenditure on a commodity due to 1% rise in household income, which is very helpful for planning and forecastingrpurposes.

Any planned governmental investment would lead to economic growth, which ismainly measured by income elasticity, but the methods of estimating incomeelasticity is quite large, varying from traditional methods to sophisticated methodbased on concentration curves. The method of estimating income elasticity byvarious alternative methods is the subject matter of this book. The present book ismainly concerned with cross-sectional data in estimating income elasticity forvarious household expenditure items. It provides a number of new techniques forestimating income elasticity, which have distinct advantages over the traditionalmethods. For example, estimating income elasticity from the Box-Cox Engelfuff nction based on a non-linear mumm lti-dimensional search technique is a new addition to our knowledge. A new method of computing Engel elasticity based onconcentration curves is also presented in this book. Furthermore, a new method of estimating the change in consumer demand with respect to an increase in incomeand a change in income inequality from household expenditure survey data is alsoprovided. Empirical illustrations are given with reference to Australian HouseholdExpenditure Survey (HES) data.

The present book constitutes an investigation into the principles underlying the formulation and estimation of income elasticity by various techniques for theAustralian HES data. Some basic observations on the Australian HES data collectedby the Australian Bureau of Statistics (ABS) are provided in Chapter 2. The discrimination among the various forms of Engel curves has been made in Chapter3, while various problems in computing Engel elasticity by the traditional WeightedLeast Squares (WLS) method are dealt with in Chapa ter 4. Estimation of incomeelasticity based on the Box-Cox general Engel function is presented in chapter 5. A review of income distribution, and estimation of income elasticity based onconcentration curves are presented in chapters 6 and 7 respectively. Chapter 8 isconcerned with the estimation of increased consumer demand fd off r various householdconsumption items with respect to changes in income and income inequality. Demands for some specific household consumption items such as food, transport

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and communication, and alcohol are presented in chapters 9, 10 and 11 respectively. Chapter 12 deals with a review of consumers’ equivalence scales, which areimportant for an accurate estimation of income elasticity, while the final chapterprovides some concluding remarks about the studies presented in this book.

This book provides good examples showing how to calculate income elasticityusing a number of methods from widely available published grouped data. Some of the techniques presented here can be used in a wide range of policy areas in all developed, under developed and developing countries. Policy analysts, economists, business analysts and market researchers can find this book very useful.

M. O. HAQUE

xiv PREFACE

ACKNOWLEDGMENTS

I wish to express my gratitude to Victoria University, where I spent more than sevenyears writing this book, which is heavily drawn from a number of published andforthcoming papers. Most importantly, I am grateful to an unknown referee, whoread the entire manuscript several times and provided valuable comments toimprove the manuscript. My appreciation is extended to Mr Li Weidong of BeijingJiaotong University, who assisted me in typing a large portion of the book. I am alsovery grateful to Associate Professor Alan Morris, and Mr. Jesse Singh, who helped me to put the entire book into the publisher’s prescribed formate. Of course, I gratefully acknowledge Mrs Herma Drees and Ms Deborah of Springer, whoprovided constant advice and help in preparing to the manuscript. Indeed Iacknowledge Ms Margarita Kumnick of CSES of Victoria Universitytt who editedand proofread the final manuscript for publication.

At this stage, I gratefully acknowledge the publishers of MetroeconomicaMM ,

Journal of Economic Development, Sankhya, Indian journal of Quantitativekhhk

economics, Drug and Alcohol Review, Transportation and Journal of Applied Statistics, for permission to use my articles and notes already published in thesejournals.

Finally, I wish to express my appreciation to my wife, Nargis and my threechildren, Tariq, Sadira and Mahera. I missed many enjn oyable moments with themdue to my heavy workload in preparing this book.

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