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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 the point identfication of the joint distribution of the vector of random coefficients and additive, good-specific errors in a multinomial choice model. The identification theorem extends the binary choice results of Ichimura and Thompson (1998) as well as Gautier and Kitamura (2013) from two to two or more choices.

Suggested Citation

  • Jeremy T. Fox, 2021. "A Note on Nonparametric Identification of Distributions of Random Coefficients in Multinomial Choice Models," Annals of Economics and Statistics, GENES, issue 142, pages 305-310.
    • Handle: RePEc:adr:anecst:y:2021:i:142:p:305-310
    DOI: https://doi.org/10.15609/annaeconstat2009.142.0305
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    6. 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.
    7. 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.
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    Cited by:

    1. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    2. Roy Allen & John Rehbeck, 2021. "Obstacles to Redistribution Through Markets and One Solution," Papers 2111.09910, arXiv.org.
    3. 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.
    4. Christophe Gaillac & Eric Gautier, 2021. "Nonparametric classes for identification in random coefficients models when regressors have limited variation," Working Papers hal-03231392, HAL.
    5. Wang, Ao, 2023. "Sieve BLP: A semi-nonparametric model of demand for differentiated products," Journal of Econometrics, Elsevier, vol. 235(2), pages 325-351.

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    More about this item

    Keywords

    Discrete Choice; Multinomial Choice; Random Coefficients; Demand.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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