Continuous Consumer Equivalence Scales: Item-specific effects of age and sex of household members in the budget allocation model PDF
Preview Continuous Consumer Equivalence Scales: Item-specific effects of age and sex of household members in the budget allocation model
CONTINUOUS CONSUMER EQUIVALENCE SCALES Aan Welmoet aan Elise, Rutger en Helmerik voor wie geen schaal toereikend is CONTINUOUS CONSUMER EQUIV ALENCE SCALES Item-specific effects of age and sex of household members in the budget allocation model J. BLOKLAND Foreword by W.H. SOMERMEYER Professor of Economics, Erasmus University Rotterdam Director, Econometric Institute 8JartinustJViihoff CJhe Hague 1976 ISBN-I3: 978-90-247-1847-4 c-ISBN-I3: 978-1-4613-4381-3 001: 10.1007/978-1-4613-4381-3 C 1976 by H.E. Stenfert Kroese B.V. No part of this book may be reproduced in any form by print. photoprint. microfilm or any other means. without written permission from the publisher. FOREWORD Costs of children as consumers is an issue as interesting and intriguing as it is intricate and tricky. It is interesting particularly because costs of children are often obscured, hence underestimated ('cheaper by the dozen'); more enlightened considerations may have an impact on family planning and population policy at a micro and macro level of living, respectively. From a methodological point of view, the topic is intriguing since consumption by individual members of a family cannot be measured directly, but can only be inferred to in an indirect way. Consequently, attempts at solving the children's cost problem were as frequent and diversified as they have been unsatisfactory or unsuccessful. One (older) approach to establishing costs of consumption by children compared with (male) adults was based on physiological considerations, viz. with respect to calorie requirements, and of a normative rather than an empirical nature: an international (League of Nations) consumer equivalence scale as well as our national (Amsterdam) scale were the results of these efforts. Unfortunately, this physiological myopia grossly underrates (young) children's consumption: the calories they use up may be small in number, but they are high in price. Moreover, not only their bodies, but also their gradually developing minds need (reading and other) matter, involving costs. A fortiori, this applies to women, who - as the biologically stronger sex - have been deemed to need less calories than men, disregarding their mental and other needs (after all, it is all a matter of mind over matter). These (literally) shortcomings of the purely physiological slant, gave ris.e to a second, more general approach. In essence, it tries to estimate costs of a(n additional) child of a certain age and sex by comparing consumption between families with and without such a child. The trouble with this method, however, is to assess the extra amount of money needed for compensating the additional costs of that supernumerary member of the family. This brings back the problem at the back-door after having thrown it out at the front door. The former methods' main deficiency, viz. the lack of a sound underlying theory, logically led to the construction of a model, explaining family composition in terms of both size and composition as well as incomes (and prices) of the families. In this respect, pioneering work has been performed by S.J. Prais, later in collaboration with H.S. Houthakker. Still, these studies resemble the former, 'comparative' ones in the sense that for typifying the families their members are classified into broad age-sex groups. Consequently, the resulting consumer scales are discrete rather continuous; moreover, they show occasional leaps and bounds between adjacent age classes. Therefore, the last, logical step, was, of course, to estimate continuous consumer scales, again by means of a model. This arduous task was undertaken by Dr. Blokland. In order to reach meaningful results he had to cope with serious restrictions inherent to the data and severe conditions imposed by the model. Neither was he spared the econometrician's nightmare of multicollinearity. Thanks to Dr. Blokland' s efforts, however, the results of his research seem to be as reasonable as might be expected under the circumstances. All in all, the author appears to have made a jolly good job of it. W.H. Somermeyer ACKNOWLEDGEMENTS The research reported on in this book was started in 1971 as the follow-up to a paper I presented together with Professor W.H. Somermeyer at the Second World Congress of the Econometric Society in Cambridge (1970). In the course of several years a number of problems suggested a different approach, and that led to a new study on the same theoretical basis, but with different empirical results. I was fortunate in finding Professor W.H. Somermeyer, director of the Econometric Institute of the Erasmus University Rotterdam, who was one of the authors of the budget allocation model, willing to discuss the study with me, and I feel greatly indebted to him for his stimulating and helpful comments, without which I could not have finished this study so successfully. Professor J.H.P. Paelinck, director of the Netherlands Economic Institute, read all the chapters, and I am indebted to him for his valuable remarks. Words of special appreciation go to Mr. L. Hordijk, who assisted me not only with the technical details of the computer programming, but also with some model-building problems. I also wish to thank Messrs F. van Doeland and A.S. Louter for their computer help. The difficult task of transforming the manuscript into a first English typescript version was undertaken by Mrs. A.C.A. E1derson. Mrs. K. Boet corrected the English of a second version, and Mrs. A.H. van Doeland typed this book perfectly. I wish to thank them all here. Although I thus received much help from many persons, I am alone responsible for any remaining errors. CONTENTS 1. Scope and method of the study 2. Earlier contributions to the estimation of family-size effects on expenditure 4 2.1. Possible contributions of survey data 4 2.2. Normative approach 5 2.3. Empirical approach 8 2.3.1. Subsampling households by size scales 8 2.3.2. Discontinuous scales 13 2.3.3. Continuous scales 16 2.4. Concluding remarks 20 3. The expenditure allocation model 23 3.1. Model without family size effects 23 3.1.1. Derivation 23 3.1.2. Some properties 26 3.2. Model incorporating family size effects 29 3.2.1. Derivation 29 3.2.2. Some properties 31 3.2.3. Specification of the ~tandard consumer function 32 3.2.4. Specification of the equivalence function 33 3.2.5. Some properties of the equivalence function 36 Appendix 3.A. Derivation of homogeneous demand functions from the Slutsky conditions imposed on the expenditure allocation model 43 Appendix 3.B. Conditions for a budget constrained utility maximum imposed on the expenditure allocation model without family size effects 44 Appendix 3.C. Conditions for a contrained utility maximum imposed on the expenditure allocation model incorporating family size effects 49 Appendix 3.D. Derivation of parameter equations for the standard consumer functions 52 4. Estimation of family size effects in the expenditure allocation model 56 4.1. Model with direct identification of the parameters 56 4.1.1. Specification of the model 56 4.1.2. Disturbances of the model 62 4.2. Model with indirect identification of the parameters 71 4.2.1. Specification of the model 71 4.2.2. Identification of the parameters 74 4.2.3. Application of the model 77 5. Results of the indirect estimation procedure 81 5.1. Survey 81 5.2. Allocation of the total budgets to three large categories 82 5.3. Allocation of the food budget to seven categories 85 5.3.1. Four specifications of the cubic equivalence function 85 5.3.2. Two subsamples: small and large families 98 5.3.3. Two subsamples: high and low total expenditure 102 5.3.4. The effect of enlarging the admitted range of the equivalence coefficients 107 5.4. Comparison between the present results and those of Prais and Houthakker 111 5.5. Comparison between the present results and the results obtained with some 'naive' models 116 5.5.1. Introduction 116 5.5.2. First naive model: without family size effects 116 5.5.3. Second naive model: number of family members 118 5.5.4. Third naive model: number of standard consumers 120 6. Summary 123 Annexes 129 Selected Bibliography 158 Subject Index 166 1. SCOPE AND METHOD OF THE STUDY In every family sooner or later the question arises: what exactly does each member - or, as the case may be, an additional member - of the family cost. In any family decisions are made with respect to purchases for the benefit of the members of the family, individually or collectively. How and by whom such decisions are made may vary from one family to another and according to the consumption category the purchases relate to, but there are certain decisions which are made by or for the family as a whole. How families arrive at their decisions is no doubt a highly interesting aspect of the sociology of the family, but is one on which we have no information and which we do not propose to discuss in this book. Instead, we concentrate on the question how each family member adds to the cost of living of the family, depending upon certain characteristics, such as age and sex, relevant to his or her consumptive needs. In other words, as the book's sub-title clearly states, we intend to analyse the effects of family size and family composition on family expenditure. We were motivated to undertake this analysis by the dissatisfaction we felt with regard to the results of former studies. Although quite a number of studies have been published on our subject, we found them deficient in some respects. Still, they enabled us to draw
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