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The random coefficients logit model is identified

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  • Fox, Jeremy T.
  • Kim, Kyoo il
  • Ryan, Stephen P.
  • Bajari, Patrick

Abstract

The random coefficients multinomial choice logit model, also known as the mixed logit, has been widely used in empirical choice analysis for the last thirty years. We prove that the distribution of random coefficients in the multinomial logit model is nonparametrically identified. Our approach requires variation in product characteristics only locally and does not rely on the special regressors with large supports used in related papers. One of our two identification arguments is constructive. Both approaches may be applied to other choice models with random coefficients.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 166 (2012)
Issue (Month): 2 ()
Pages: 204-212

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Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:204-212

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Jeremy T. Fox & Kyoo il Kim, 2011. "A Simple Nonparametric Approach to Estimating the Distribution of Random Coefficients in Structural Models," NBER Working Papers 17283, National Bureau of Economic Research, Inc.
  2. Andrews, Donald W K & Schafgans, Marcia M A, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 497-517, July.
  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. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
  5. J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers 173, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Heckman, James J & Willis, Robert J, 1977. "A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 27-58, February.
  7. Briesch, Richard A. & Chintagunta, Pradeep K. & Matzkin, Rosa L., 2010. "Nonparametric Discrete Choice Models With Unobserved Heterogeneity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 291-307.
  8. Eric Gautier & Yuichi Kitamura, 2011. "Nonparamatric estimation in random coefficients binary choice models," Working Papers hal-00403939, HAL.
  9. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
  10. Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients," NBER Working Papers 15210, National Bureau of Economic Research, Inc.
  11. repec:cdl:compol:217 is not listed on IDEAS
  12. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
  13. Ichimura, H. & Thompson, S., 1993. "Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distributions," Papers 268, Minnesota - Center for Economic Research.
  14. Amit Gandhi & Jeremy T. Fox, 2009. "Identifying Heterogeneity in Economic Choice and Selection Models Using Mixtures," 2009 Meeting Papers 165, Society for Economic Dynamics.
  15. Magnac, Thierry & Maurin, Eric, 2003. "Identification and Information in Monotone Binary Models," IDEI Working Papers 180, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2004.
  16. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  17. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
  18. Jeremy T. Fox & Amit Gandhi, 2009. "Identifying Heterogeneity in Economic Choice Models," NBER Working Papers 15147, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. 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.
  2. Steven T. Berry & Philip A. Haile, 2010. "Identification in Differentiated Products Markets Using Market Level Data," NBER Working Papers 15641, National Bureau of Economic Research, Inc.
  3. Elena Krasnokutskaya, 2012. "Multi-Attribute Auctions with Unobserved Heterogeneity in Supplier Qualities and Buyers Tastes," 2012 Meeting Papers 283, Society for Economic Dynamics.
  4. Hyungsik Roger Moon & Matthew Shum & Martin Weidner, 2012. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers CWP08/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Olivier Allais & Fabrice Etilé & Sébastien Lecocq, 2012. "Mandatory labels, taxes and market forces: An empirical evaluation of fat policies," PSE Working Papers halshs-00736556, HAL.
  6. Mathias REYNAERT & Frank VERBOVEN, 2012. "Improving the performance of random coefficients demand models: the role of optimal instruments," Center for Economic Studies - Discussion papers ces12.07, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  7. Jean-Pierre H. Dube & Günter J. Hitsch & Pranav Jindal, 2012. "The Joint Identification of Utility and Discount Functions From Stated Choice Data: An Application to Durable Goods Adoption," NBER Working Papers 18393, National Bureau of Economic Research, Inc.
  8. Cerquera Dussán, Daniel & Ullrich, Hannes, 2010. "Consumer welfare and unobserved heterogeneity in discrete choice models: The value of alpine road tunnels," ZEW Discussion Papers 10-095, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  9. Olivier Allais; & Fabrice Etile; & Sebastien Lecocq, 2012. "Mandatory labelling, nutritional taxes and market forces: An empirical evaluation of fat policies in the French fromage blanc and yogurt market," Health, Econometrics and Data Group (HEDG) Working Papers 12/14, HEDG, c/o Department of Economics, University of York.
  10. Wakamori, Naoki & Welte, Angelika, 2013. "Why Do Shoppers Use Cash? Evidence from Shopping Diary Data," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 431, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  11. Hyungsik Roger Moon & Matthew Shum & Martin Weidner, 2014. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers CWP20/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. repec:hal:wpaper:halshs-00736556 is not listed on IDEAS
  13. Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients," NBER Working Papers 15210, National Bureau of Economic Research, Inc.
  14. Jeremy T. Fox & Kyoo il Kim, 2011. "A Simple Nonparametric Approach to Estimating the Distribution of Random Coefficients in Structural Models," NBER Working Papers 17283, National Bureau of Economic Research, Inc.
  15. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2012. "A Poisson mixture model of discrete choice," Journal of Econometrics, Elsevier, vol. 166(2), pages 184-203.
  16. Andrew Chesher & Adam Rosen, 2012. "An instrumental variable random coefficients model for binary outcomes," CeMMAP working papers CWP34/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  17. Stefan Hoderlein & Lars Nesheim & Anna Simoni, 2012. "Semiparametric estimation of random coefficients in structural economic models," CeMMAP working papers CWP09/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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