Fosgerau, Mogens and Ranjan, Abhishek (2017): A note on identification in discrete choice models with partial observability. Forthcoming in: Theory and decision

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Abstract
This note establishes a new identification result for additive random utility discrete choice models (ARUM). A decisionmaker associates a random utility U_{j}+m_{j} to each alternative in a finite set j∈{1,...,J}, where U={U₁,...,U_{J}} is unobserved by the researcher and random with an unknown joint distribution, while the perturbation m=(m₁,...,m_{J}) is observed. The decisionmaker chooses the alternative that yields the maximum random utility, which leads to a choice probability system m→(Pr(1m),...,Pr(Jm)). Previous research has shown that the choice probability system is identified from the observation of the relationship m→Pr(1m). We show that the complete choice probability system is identified from observation of a relationship m→∑_{j=1}^{s}Pr(jm), for any s<J. That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on m. This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.
Item Type:  MPRA Paper 

Original Title:  A note on identification in discrete choice models with partial observability 
Language:  English 
Keywords:  ARUM; random utility discrete choice; identification 
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 > D1  Household Behavior and Family Economics > D11  Consumer Economics: Theory 
Item ID:  76800 
Depositing User:  Prof. Mogens Fosgerau 
Date Deposited:  15 Feb 2017 16:59 
Last Modified:  01 Oct 2019 20:11 
References:  Amemiya, T. (1981) Qualitative Response Models: A Survey Journal of Economic Literature 19(4), 14831536. Berry, S. and Haile, P. (2016) Identification in Differentiated Products Markets Annual Review of Economics 8(1), 2752. Fosgerau, M., McFadden, D. and Bierlaire, M. (2013) Choice probability generating functions Journal of Choice Modelling 8, 118. Maddala, G. (1983) LimitedDependent and Qualitative Variables in Econometrics Cambridge University Press Cambridge. Mattsson, L.G., Weibull, J. W. and Lindberg, P. O. (2014) Extreme values, invariance and choice probabilities Transportation Research Part B: Methodological 59, 8195. Matzkin, R. L. (1993) Nonparametric identification and estimation of polychotomous choice models Journal of Econometrics 58(12), 137168. 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. 53075368. McFadden, D. (1974) Conditional Logit Analysis of Qualitative Choice Behaviour Frontiers in Econometrics Academic Press New York pp. 105142. 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. 198272. McFadden, D. (1989) A method of simulated moments for estimation of the multinomial Probit without numerical integration Econometrica 57(5), 9951026. McFadden, D. L. (2014) CPGF construction: A refinement of Fosgerau, McFadden, and Bierlaire (2013) "Choice Probability Generating Functions", Journal of Choice Modeling, 8, 118. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/76800 