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A Simple Nonparametric Approach to Estimating the Distribution of Random Coefficients in Structural Models

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  • Jeremy T. Fox
  • Kyoo il Kim

Abstract

We explore a nonparametric mixtures estimator for recovering the joint distribution of random coefficients in economic models. The estimator is based on linear regression subject to linear inequality constraints and is computationally attractive compared to alternative, nonparametric estimators. We provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions. We verify the consistency conditions for discrete choice, continuous outcome and selection models.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 17283.

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Date of creation: Aug 2011
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Handle: RePEc:nbr:nberwo:17283

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  1. Wilfried Seidel & Karl Mosler & Manfred Alker, 2000. "A Cautionary Note on Likelihood Ratio Tests in Mixture Models," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 52(3), pages 481-487, September.
  2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, Econometric Society, vol. 71(5), pages 1591-1608, 09.
  3. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 41(3-4), pages 561-575, January.
  4. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 41(3-4), pages 577-590, January.
  5. Ichimura, H. & Thompson, S., 1993. "Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distributions," Papers, Minnesota - Center for Economic Research 268, Minnesota - Center for Economic Research.
  6. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1001-1028, September.
  7. Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan & Patrick Bajari, 2011. "A simple estimator for the distribution of random coefficients," Quantitative Economics, Econometric Society, Econometric Society, vol. 2(3), pages 381-418, November.
  8. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics, Springer, Springer, vol. 7(4), pages 343-376, December.
  9. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, Econometric Society, vol. 55(5), pages 999-1033, September.
  10. Andrews, Donald W K, 2002. "Generalized Method of Moments Estimation When a Parameter Is on a Boundary," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(4), pages 530-44, October.
  11. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
  12. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, Elsevier, vol. 166(2), pages 204-212.
  13. Wagner Kamakura, 1991. "Estimating flexible distributions of ideal-points with external analysis of preferences," Psychometrika, Springer, Springer, vol. 56(3), pages 419-431, September.
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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, Elsevier, vol. 166(2), pages 204-212.

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