IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Nonparametric Estimation in Random Coefficients Binary Choice Models

  • Eric Gautier


  • Yuichi Kitamura


This paper considers nonparametric estimation of the joint density of the random coe±-cients in binary choice models. Nonparametric inference allows to be °exible about the treatment ofunobserved heterogeneity. This is an ill-posed inverse problem characterized by an integral transform,namely the hemispherical transform. The kernel is boxcar and the operator is a convolution operatoron the sphere. Utilizing Fourier-Laplace expansions o®ers a clear insight on the identi¯cation problem.We present a new class of density estimators for the random coe±cients relying on estimates for thechoice probability. Characterizing the degree of ill-posedness we are able to relate the rate of conver-gence of the estimation of the density of the random coe±cient with the rate of convergence of theestimation of the choice probability. We present a particular estimate for the choice probability and itsasymptotic properties. The corresponding estimate of the density of the random coe±cient takes a sim-ple closed form. It is easy to implement in empirical applications. We obtain rates of consistency in allLp spaces and prove asymptotic normality. Extensions including estimation of marginals, treatmentsof non-random coe±cients, models with endogeneity and multiple alternatives are discussed.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: Crest working paper version
Download Restriction: no

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2008-15.

in new window

Length: 51
Date of creation: 2008
Date of revision:
Handle: RePEc:crs:wpaper:2008-15
Contact details of provider: Postal:
15 Boulevard Gabriel Peri 92245 Malakoff Cedex

Phone: 01 41 17 60 81
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Andrew Chesher & J. M. C. Santos Silva, 2002. "Taste Variation in Discrete Choice Models," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 147-168.
  2. P. Groeneboom & G. Jongbloed, 2003. "Density estimation in the uniform deconvolution model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 136-157.
  3. 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.
  4. 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.
  5. Patrick Bajari & Jeremy T. Fox & Stephen P. Ryan, 2007. "Linear Regression Estimation of Discrete Choice Models with Nonparametric Distributions of Random Coefficients," American Economic Review, American Economic Association, vol. 97(2), pages 459-463, May.
  6. Stephane Hess & Denis Bolduc & John Polak, 2005. "Random Covariance Heterogeneity in Discrete Choice Models," ERSA conference papers ersa05p375, European Regional Science Association.
  7. Klemelä, Jussi, 2000. "Estimation of Densities and Derivatives of Densities with Directional Data," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 18-40, April.
  8. Susan Athey & Guido Imbens, 2006. "Discrete Choice Models with Multiple Unobserved Choice Characteristics," Levine's Bibliography 122247000000001040, UCLA Department of Economics.
  9. 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.
  10. 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.
  11. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt3tb6j874, University of California Transportation Center.
  12. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 403-409.
  13. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2008-15. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Florian Sallaberry)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.