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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. 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.
    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. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," NBER Working Papers 15276, National Bureau of Economic Research, Inc.
    4. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    5. 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.
    6. 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.
    7. 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.
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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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