Generalized entropy models

Fosgerau, Mogens and de Palma, André (2015): Generalized entropy models.

Abstract

We formulate a family of direct utility functions for the consumption of a differentiated good. The family is based on a generalization of the Shannon entropy. It includes dual representations of all additive random utility discrete choice models, as well as models in which goods are complements. Demand models for market shares can be estimated by plain regression, enabling the use of instrumental variables. Models for microdata can be estimated by maximum likelihood.

• Item Type: MPRA Paper
• Language: English
• Keywords: market shares; product differentiation; duality; discrete choice; entropy
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities; D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance

References

Anderson, S., de Palma, A. and Thisse, J. (1992) Discrete choice theory of product differentiation MIT Press Cambridge, MA.

Anderson, S. P., de Palma, A. and Thisse, J.-F. (1988) A Representative Consumer Theory of the Logit Model International Economic Review 29(3), 461.

Berry, S. (1994) Estimating discrete-choice models of market equilibrium The RAND Journal of Economics 25(2), 242–262.

Berry, S. and Haile, P. A. (2014) Identification in Differentiated Products Markets Using Market Level Data Econometrica 82(5), 1749–1797.

Berry, S., Levinsohn, J. and Pakes, A. (1995) Automobile Prices in Market Equilibrium Econometrica 63(4), 841–890.

Fosgerau, M., McFadden, D. and Bierlaire, M. (2013) Choice probability generating functions Journal of Choice Modelling 8, 1–18.

Fosgerau, M. and McFadden, D. L. (2012) A theory of the perturbed consumer with general budgets Working Paper 17953 National Bureau of Economic Research.

Fudenberg, D., Iijima, R. and Strzalecki, T. (2014) Stochastic Choice and Revealed Perturbed Utility Working Paper .

Goldberg, P. K. and Verboven, F. (2001) The Evolution of Price Dispersion in the European Car Market The Review of Economic Studies 68(4), 811–848.

Knittel, C. R. and Metaxoglou, K. (2014) Estimation of Random-Coefficient Demand Models: Two Empiricists’ Perspective Review of Economics and Statistics 96(1), 34–59.

Kullback, S. and Leibler, R. A. (1951) On Information and Sufficiency The Annals of Mathematical Statistics 22(1), 79–86.

Kuminoff, N. V., Smith, V. K. and Timmins, C. (2013) The New Economics of Equilibrium Sorting and Policy Evaluation Using Housing Markets Journal of Economic Literature 51(4), 1007–62.

Mattsson, L.-G. and Weibull, J. W. (2002) Probabilistic choice and procedurally bounded rationality Games and Economic Behavior 41(1), 61–78.

Matzkin, R. L. (2007) Chapter 73 Nonparametric identification in J. J. H. a. E. E.

Leamer (ed.), Handbook of Econometrics Vol. 6, Part B Elsevier pp. 5307– 5368.

McFadden, D. (1978) Modelling the choice of residential location in A. Karlquist, F. Snickars and J. W. Weibull (eds), Spatial Interaction Theory and Planning Models North Holland Amsterdam pp. 75 –96.

McFadden, D. (1981) Econometric Models of Probabilistic Choice in C. Manski and D. McFadden (eds), Structural Analysis of Discrete Data with Econometric Applications MIT Press Cambridge, MA, USA pp. 198–272.

McFadden, D. and Train, K. (2000) Mixed MNL Models for discrete response Journal of Applied Econometrics 15, 447–470.

Rockafellar, R. (1970) Convex analysis Princeton University Press Princeton, N.J.

Ruzhansky, M. and Sugimoto, M. (2014) On global inversion of homogeneous maps Bulletin of Mathematical Sciences pp. 1–6.

Shannon, C. E. (1948) A Mathematical Theory of Communication Bell System Technical Journal 27(3), 379–423.

Train, K. E. and Winston, C. (2007) Vehicle choice behavior and the declining market share of u.s. automakers International Economic Review 48(4), 1469– 1496.

Verboven, F. (1996) The nested logit model and representative consumer theory Economics Letters 50(1), 57–63.