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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d08b/d0889.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 889.

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Length: 53 pages
Date of creation: Sep 1988
Date of revision:
Publication status: Published in Econometrica (March 1992), 60(2): 239-270
Handle: RePEc:cwl:cwldpp:889

Note: CFP 809.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Nonparametric models; identification; likelihood function; consistency;

References

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  1. 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.
  2. Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-27, September.
  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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Citations

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Cited by:
  1. Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc.
  2. Steven T. Berry & Philip Haile, 2010. "Identification in Differentiated Products Markets Using Market Level Data," Cowles Foundation Discussion Papers 1744, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
  3. 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).
  4. 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.
  5. Victor Aguirregabiria & Arvind Magesan, 2012. "Identification and estimation of dynamic games when players' beliefs are not in equilibrium," Working Papers tecipa-449, University of Toronto, Department of Economics.
  6. 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.
  7. 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).
  8. 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).
  9. 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.

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