Latent separability and price variation in the estimation of demand System

Cherif, Olfa and Ayadi, Mohamed (2010): Latent separability and price variation in the estimation of demand System.

Abstract

The aim of this paper is to overcome the problems caused by insufficient price variation in estimating a large demand system. For that, we propose a new form of Stone-Lewbel (SL) cross section prices developed under latent separability that explore individual specific variation in the composition of the bundles of exclusive goods. The estimation of demand system under latent separability needs the choice of at least one exclusive good per group. We estimate Quadratic Almost Ideal Demand System (QAIDS) under weak and latent separability using traditional aggregate price indices and SL prices. Our empirical analysis is based on fifteen non durable goods of a Tunisian Family Expenditure Survey Data. The results show greater differences among effects price and estimates of price elasticities obtained under weak separability and latent separability using both traditional price indices and SL prices. We obtain higher precision of estimates of own price elasticities using SL prices under latent separability.

• Item Type: MPRA Paper
• Language: English
• Keywords: Latent separability, Weak separability, Demand system, Exclusive goods, Price variation, SL prices
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory; D - Microeconomics > D1 - Household Behavior and Family Economics > D12 - Consumer Economics: Empirical Analysis

References

Blackorby, C., D. Primont, And R. R. Russell (1977): “On testing separability restrictions with flexible functional forms”, Journal of Econometrics, vol 5.

Blackorby, C., D. Primont, And R. R. Russell (1978): “ Duality, Separability and Functional Structure”, Theory and Economic Applications. New York: North Holland.

Blackorby, C., And A. Shorrocks, Eds. (1995): “Separability and Aggregation, Vol. 1, Collected Works of W.M. Gorman. Oxford : Claendon Press.

Banks, J., RW. Blundell et A. Lewbel(1997): Quadratique Engel Curves, Indirect Tax Reform and Welfare Measurement” Review of Economics and Statistics ,79 , 527-539.

Blundell, R. W., and J. M. Robin (1997): Estimation in large and disaggregated demand systems: An Estimator for Conditionally Linear Systems”, UCL Discussion paper 97-2, forthcoming in Journal of Applied Econometrics.

Blackorby, C., R. R. Russel (1997): “Two –stage Budgeting: An extension of Gorman’s Theorem”, Economic Theory, 9, 185-193.

Blundell, R. W., and J-M. Robin (2000) : Latent separability: Grouping goods without weak separability” Econometrica ,68 , 53-84.

Cragg, J., and S. Donald (1996): Inferring the Rank of a Matrix, Journal of Econometrics, 76, 223-250.

Chavas J.P, Dhar T and R-W Cotterill (2003): An Economic Analysis of Product Differentiation under Latent Separability. American Agricultural Economics Association

Cherif, O, Ayadi, M and Ben Ishak, A, 2009, “Séparabilité latente et estimation d’un long système de demande: Apports de la méthode de selection SVM”, 26èmes Journées de Microéconomie Appliquée

Deaton, A. S. (1975): “ The Structure of Demand” 1920-70, Vol 6, Section 2. The Fontana Economic History of Europe, Collins : Fontana.

Deaton, A. S. (1979): “ The Distance Function in Consumer Behavior with Applications to Index Numbers and optimal Taxation”, Review of Economic Studies, 46, 391-406.

Deaton, A. S., and J. Muellbauer (1980): An Almost Ideal Demand System”, American Economic Review, 70, 312-336.

Diewert , W. E., And T. J. Wales (1995): “ Flexible Functional Forms and Tests for Homogeneous Separability”, Journal of Econometrics, 67, 259-302.

Gorman, W. M. (1959): “Separable Utility and Aggregation “, Econometrica, 21, 63-80.

Gorman, W. M. (1981): Some Engel Curves, in Essays in the Theory and Measurement of Consumer Behavior in Honor of Richard Stone, ed.By Angus Deaton. Cambridge : Cambridge University Press.

S. Goldman and H. Uzawa (1964): “A note on separability in demand analysis”, Econometrica 32, 387-398.

Hoderlein, S. and A. Lewbel, 2007, Price Dimension Reduction in Demand Systems With Many Goods, Working Paper, Mannheim University.

Hoderlein, S. and S. Mihaleva (2008): Increasing the price variation in a repeated cross section, Journal of Econometrics vol 147, pp 316- 325.

INS : Institut National de la Statistique de la Tunisie (http//www.ins.nat.tn).

Kleinbergen, F. Paap, R. (2003): Generelized Reduced Rank Tests using the Singular Value Decomposition, Tinbergen Institute Discussion Paper TI 03-003/4.

Leontieff, W and Sono, (1947): Introduction to a theory of the internal structure of functional relationships, Econometrica, Vol 15, pp. 361-373.

Lewbel, A. (1996): “Aggregation Without Separability : A Generalized Composite Commodity Theorem”, American Economic Review, 86, 524-543.

Lewbel, A., (1989): Identification and Estimation of Equivalence Scales under Weak Separability, Review of Economic Studies 56, 311-16.

Lewbel, A., (1999): Consumer Demand Systems and Household Expenditure, in PE- SARAN, H. and M. WICKENS (Eds.), Handbook of Applied Econometrics, Blackwell Handbooks in economics.

Lewbel, A., (2001): Demand Systems With and Without Errors, American Eco-nomic Review, 611-18. Labeaga, J. M., and J. Puig (2004): Some Practical Implications of Latent Separability with Application to Spanish Data (mimeo, Departement of Economics, UNED).

Ronald W. Anderson (1979): Perfect price aggregation and empirical demand analysis, Econometrica vol 47.

Ruiz N. (2005): « Séparabilité homothétique, échelle d’équivalence généralisée et identification des effets prix dans les systèmes de demande. Communication pour le 45ème congrès annuel de la société canadienne de science économique.

Strotz, R. H. (1957): “The Empirical Implications of Utility Tree”, Econometrica, Vol 25, pp : 269-280.