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A Note on Nonparametric Identification of Distributions of Random Coefficients in Multinomial Choice Models

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  • Jeremy T. Fox

Abstract

I prove that the joint distribution of random coefficients and additive errors is identified in a mulltinomial choice model. No restrictions are imposed on the support of the random coefficients and additive errors. The proof uses large support variation in choice-specific explanatory variables following Lewbel (2000) but does not rely on an identification at infinity technique where the payoffs of all but two choices are set to minus infinity.

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  • Jeremy T. Fox, 2017. "A Note on Nonparametric Identification of Distributions of Random Coefficients in Multinomial Choice Models," NBER Working Papers 23621, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:23621
    Note: IO TWP
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    References listed on IDEAS

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    1. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    2. Matthew A Masten, 2018. "Random Coefficients on Endogenous Variables in Simultaneous Equations Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 1193-1250.
    3. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    4. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
    5. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," Cowles Foundation Discussion Papers 1718, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
    6. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    7. Jeremy T. Fox & Amit Gandhi, 2016. "Nonparametric identification and estimation of random coefficients in multinomial choice models," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 118-139, February.
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    Cited by:

    1. Gaillac, Christophe & Gautier, Eric, 2021. "Non Parametric Classes for Identification in Random Coefficients Models when Regressors have Limited Variation," TSE Working Papers 21-1218, Toulouse School of Economics (TSE).
    2. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    3. Wang, Ao, 2023. "Sieve BLP: A semi-nonparametric model of demand for differentiated products," Journal of Econometrics, Elsevier, vol. 235(2), pages 325-351.
    4. Roy Allen & John Rehbeck, 2023. "Obstacles to redistribution through markets and one solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 235-242, October.

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    More about this item

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • L0 - Industrial Organization - - General

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