Abstract
In this paper two demand models with general household equivalence scales (GES) are estimated. These GES are identifiable, since they have the independence of base utility (IB) or equivalence scales exactness (ESE) property. Estimates of household characteristics adjusted income can then be calculated relative to a specific household type. This “individual equivalent income (IEI) is then used to calculate measures of inequality in the distribution of welfare. As more than one model is estimated, the sensitivity of these estimates to model specification changes can be considered. Comparisons are also made to estimates of inequality based on household income.
It is found that absolute inequality is sensitive to model specification, but relative inequality is not. This is true using indices of inequality of the Atkinson (1970), Kolm (1976a,b) and Sen (1973) type, or more general measures of inequality based on estimates of Lorenz curve decile ordinates, constructed using methods introduced by Beach and Davidson (1983). Thus, if absolute measures of inequality are required, these results suggest some further research is required to determine a class of models which is less sensitive to model specification error. However, if only relative measures of inequality are needed, then estimates of inequality appear to be very robust to the choice of model specification.
Similar content being viewed by others
References
Atkinson A (1970) On the measurement of inequality. Journal of Economic Theory 2:244–263
Banks J, Blundell R, Lewbel A (1994) Quadratic Engel curves, indirect tax reform and welfare measurement. University College London, Department of Economics Working Paper No. 94-04
Barnes R, Gillingham R (1984) Demographic effects in demand analysis: Estimation of the quadratic expenditure system. Review of Economics and Statistics 66:591–601
Beach CM, Davidson R (1983) Distribution-free statistical inference with Lorenz curve and income shares. Review of Economic Studies 50:723–735
Blackorby C, Donaldson D (1982) Ratio-scale and translation-scale full interpersonal comparability without domain restrictions: Admissible social evaluation functions. International Economic Review 23:249–268
Blackorby C, Donaldson D (1993a) Adult-equivalence scales and the economic implementation of interpersonal comparisons of well-being. Social Choice and Welfare 10:335–361
Blackorby C, Donaldson D (1993b) Household equivalence scales and welfare comparisons: A comment. Journal of Public Economics 50:143–146
Blundell R, Pashardes P, Weber G (1993) What do we learn about consumer demand patterns from micro data. American Economic Review 83:570–597
Bollino CA, Violi R (1990) GAITL: A Generalised version of the almost ideal demand system. Economics Letters 33:127–129
Davies J, Hoy M (1995) Making inequality comparisons when Lorenz curves intersect. American Economic Review 85:980–986
Deaton A, Muellbauer J (1980) An almost ideal demand system. American Economic Review 70:312–326
Härdle W (1990) Applied nonparametric regression. Cambridge University Press
Jorgenson DW, Lau LJ, Stoker TM (1982) The transcendental logarithmic model of aggregate consumer behavior. In: Basmann RL, Rhodes GF (eds) Advances in Econometrics (Vol. 1), JAI Press, Greenwich, CT, pp. 97–238
Jorgenson DW, Slesnick DT (1984) Aggregate consumer behavior and the measurement of inequality. Review of Economic Studies 51:369–392
Jorgenson DW, Slesnick DT (1987) Aggregate consumer behavior and household equivalence scales. Journal of Business and Economic Statistics 5:219–232
Keuzenkamp HA, Barten AP (1991) Rejection without falsification: On the history of testing the homogeneity condition in the theory of consumer demand. Unpublished paper, presented at the European Meetings of the Econometric Society, Cambridge, England
Kolm S (1976a) Unequal inequalities I. Journal of Economic Theory 12:416–442
Kolm S (1976b) Unequal inequalities II. Journal of Economic Theory 13:82–111
Kwong K-S (1987) The distributive impact of price changes in Canada. Unpublished mimeo
Lewbel A (1985) A unified approach to incorporating demographic effects into demand systems. Review of Economics Studies 52:1–18
Lewbel A (1989a) Household equivalence scales and welfare comparisons. Journal of Public Economics 39:377–391
Lewbel A (1989b) Nesting the AIDS and translog demand systems. International Economic Review 30:349–356
Lewbel A (1991) The rank of demand systems: Theory and nonparametric estimation. Econometrica 59:711–730
Lewbel A (1993) Household equivalence scales and welfare comparisons: Reply. Journal of Public Economics 50:147–148
Nicol CJ (1989a) Testing a theory of exact aggregation. Journal of Business and Economic Statistics 7:259–265
Nicol CJ (1989b) A reinterpretation of the almost ideal demand system. In: Raj B (ed) Advances in econometrics and modelling, Kluwer Academic Publishers, Amsterdam, pp. 117–129
Nicol CJ (1991) Aggregate consumer behaviour without exact aggregation. Canadian Journal of Economics 24:578–594
Nicol CJ (1995a) Model specification and estimation effects in applied demand analysis using microdata. Department of Economics Working Paper No. 57, University of Regina
Nicol CJ (1995b) Model specification issues in consumer demand systems using United States microdata. Department of Economics Working Paper No. 56, University of Regina
Nicol CJ (1996) A comparison of demand specifications estimated using Canadian and United States microdata. Unpublished mimeo, University of Regina
Nicol CJ (1994) Identifiability of household equivalence scales through exact aggregation: Some empirical results. Canadian Journal of Economics 27:307–328
Ramezani A, Rose D, Murphy S (1995) Aggregation, flexible forms and estimation of food consumption parameters. American Journal of Agricultural Economics 77:525–532
Sen AK (1973) On economic inequality. Clarendon Press, Oxford
Survey of Family Expenditures Microdata Files (1978, 1982, 1984 and 1986) Family expenditure surveys section. Statistics Canada, Ottawa, Canada
Thistle PD (1990) Large sample properties of two inequality indices. Econometrica 58:725–728
Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57:307–333
Wang Q, Halbrendt C, Johnson SR (1996) A non-nested test of the AIDS vs. the translog demand system. Economics Letters 51:139–143
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nicol, C.J. Estimating inequality in the distribution of welfare using demand models. Empirical Economics 22, 365–392 (1997). https://doi.org/10.1007/BF01208829
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01208829