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Semiparametric estimation of random coefficients in structural economic models

  • Stefan Hoderlein

    ()

    (Institute for Fiscal Studies and Boston College)

  • Lars Nesheim

    ()

    (Institute for Fiscal Studies and University College London)

  • Anna Simoni

    (Institute for Fiscal Studies and Bocconi)

In structural economic models, individuals are usually characterized as solving a decision problem that is governed by a finite set of parameters. This paper discusses the nonparametric estimation of the probability density function of these parameters if they are allowed to vary continuously across the population. We establish that the problem of recovering the probability density function of random parameters falls into the class of non-linear inverse problem. This framework helps us to answer the question whether there exist densities that satisfy this relationship. It also allows us to characterize the identified set of such densities. We obtain novel conditions for point identification, and establish that point identification is generically weak. Given this insight, we provide a consistent nonparametric estimator that accounts for this fact, and derive its asymptotic distribution. Our general framework allows us to deal with unobservable nuisance variables, e.g., measurement error, but also covers the case when there are no such nuisance variables. Finally, Monte Carlo experiments for several structural models are provided which illustrate the performance of our estimation procedure.

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File URL: http://cemmap.ifs.org.uk/wps/cwp091212.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP09/12.

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Date of creation: Apr 2012
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Handle: RePEc:ifs:cemmap:09/12
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  1. Hoderlein, Stefan & Klemelä, Jussi & Mammen, Enno, 2010. "Analyzing The Random Coefficient Model Nonparametrically," Econometric Theory, Cambridge University Press, vol. 26(03), pages 804-837, June.
  2. Carrasco, Marine & Florens, Jean-Pierre, 2002. "Spectral Method for Deconvolving a Density," IDEI Working Papers 138, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2009.
  3. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, 01.
  4. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(03), pages 472-496, June.
  5. 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.
  6. Darolles, Serge & Fan, Yanqin & Florens, Jean-Pierre & Renault, Eric, 2003. "Non Parametric Instrumental Regression," IDEI Working Papers 228, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2010.
  7. Eric Gautier & Yuichi Kitamura, 2008. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Working Papers 2008-15, Centre de Recherche en Economie et Statistique.
  8. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Marc Henry & Yuichi Kitamura & Bernard Salanie, 2010. "Identifying Finite Mixtures in Econometric Models," Cowles Foundation Discussion Papers 1767, Cowles Foundation for Research in Economics, Yale University, revised Jan 2013.
  10. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72 Elsevier.
  11. 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.
  12. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
  13. Michael P. Keane & Kenneth I. Wolpin, 1995. "The career decisions of young men," Working Papers 559, Federal Reserve Bank of Minneapolis.
  14. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
  15. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  16. Sandra Campo & Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2003. "Semiparametric Estimation of First-price Auctions with Risk Averse Bidders," Working Papers 2003-09, Centre de Recherche en Economie et Statistique.
  17. repec:bla:restud:v:77:y:2010:i:1:p:273-304 is not listed on IDEAS
  18. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
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