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Identifying Heterogeneity in Economic Choice Models

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  • Jeremy T. Fox
  • Amit Gandhi

Abstract

We show how to nonparametrically identify the distribution that characterizes heterogeneity among agents in a general class of structural choice models. We introduce an axiom that we term separability and prove that separability of a structural model ensures identification. The main strength of separability is that it makes verifying the identification of nonadditive models a tractable task because it is a condition that is stated directly in terms of the choice behavior of agents in the model. We use separability to prove several new results. We prove the identification of the distribution of random functions and marginal effects in a nonadditive regression model. We also identify the distribution of utility functions in the multinomial choice model. Finally, we extend 2SLS to have random functions in both the first and second stages. This instrumental variables strategy applies equally to multinomial choice models with endogeneity.

Suggested Citation

  • Jeremy T. Fox & Amit Gandhi, 2009. "Identifying Heterogeneity in Economic Choice Models," NBER Working Papers 15147, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:15147
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    Cited by:

    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. Christoph Breunig & Stefan Hoderlein, 2018. "Specification testing in random coefficient models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1371-1417, November.
    3. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    4. Steven T. Berry & Philip A. Haile, 2009. "Identification of a Heterogeneous Generalized Regression Model with Group Effects," Cowles Foundation Discussion Papers 1732, Cowles Foundation for Research in Economics, Yale University.
    5. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    6. 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.
    7. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.
    8. Peter C. Reiss, 2011. "Structural Workshop Paper --Descriptive, Structural, and Experimental Empirical Methods in Marketing Research," Marketing Science, INFORMS, vol. 30(6), pages 950-964, November.
    9. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    10. Hongju Liu & Pradeep K. Chintagunta & Ting Zhu, 2010. "Complementarities and the Demand for Home Broadband Internet Services," Marketing Science, INFORMS, vol. 29(4), pages 701-720, 07-08.

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    More about this item

    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
    • L0 - Industrial Organization - - General

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