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Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models

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Abstract

This paper studies the problem of nonparametric identification and estimation of binary threshold-crossing and binary choice models. First, conditions are given that guarantee the nonparametric identification of both the function of exogenous observable variables and the distribution of the random terms. Second, the identification results are employed to develop strongly consistent estimation methods that are nonparametric in both the function of observable exogenous variables and the distribution of the unobservable random variables. The estimators are obtained by maximizing a likelihood function over nonparametric sets of functions. A two- step constrained optimization procedure is devised to compute these estimators.

Suggested Citation

  • Rosa L. Matzkin, 1988. "Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models," Cowles Foundation Discussion Papers 889, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:889
    Note: CFP 809.
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d08/d0889.pdf
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    References listed on IDEAS

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    1. Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-1327, September.
    2. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    3. Rosa L. Matzkin, 1990. "Estimation of Multinomial Models Using Weak Monotonicity Assumptions," Cowles Foundation Discussion Papers 957, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Victor Aguirregabiria & Arvind Magesan, "undated". "Identification and Estimation of Dynamic Games when Players' Beliefs Are Not in Equilibrium," Working Papers 2012-03, Department of Economics, University of Calgary.
    2. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    3. Henderson, Daniel J. & Parmeter, Christopher F., 2009. "Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension," IZA Discussion Papers 4103, Institute for the Study of Labor (IZA).
    4. Juan Mora & Ana I. Moro, 2006. "Consistent Specification Test For Ordered Discrete Choice Models," Working Papers. Serie AD 2006-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    5. Volinskiy, Dmitriy & Bergstrom, John C. & Cornwell, Christopher M., 2005. "A Pseudo-Sequential Choice Model for Valuing Multiple Environmental Policy or Program Components in Contingent Valuation Applications," 2005 Annual meeting, July 24-27, Providence, RI 19109, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    6. 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.
    7. 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.
    8. 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.
    9. Joel L. Horowitz & N. E. Savin, 2001. "Binary Response Models: Logits, Probits and Semiparametrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 43-56, Fall.

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