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Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution

Authors
Journal
Journal of Econometrics
0304-4076
Publisher
Elsevier
Publication Date
Volume
86
Issue
2
Identifiers
DOI: 10.1016/s0304-4076(97)00117-6
Keywords
  • Binary Response
  • Discrete Choice
  • Random Coefficients
  • Nonparametric Estimation
  • Identification
Disciplines
  • Mathematics

Abstract

Abstract We consider a binary response model y i =1{ x i ′ β i + ε i ⩾0} with x i independent of the unobservables (β i, ε i) . No finite-dimensional parametric restrictions are imposed on F 0, the joint distribution of (β i, ε i) . A nonparametric maximum likelihood estimator for F 0 is shown to be consistent. We analyze some conditions under which F 0 is or is not identified. In particular, we show that if the support of F 0 is a subset of any half of the unit hypersphere, then F 0 is identified relative to all distributions on the unit hypersphere. We also provide some Monte Carlo evidence on the small sample performance of our estimator.

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