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

Hidehiko Ichimura; T. Scott Thompson

doi:10.1016/S0304-4076(97)00117-6

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

Hidehiko Ichimura
, T. Scott Thompson

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

We consider a binary response model y_i = 1{x′_iß_i + ε_i ≥ 0} with x_i independent of the unobservables (ß_i, ε_i). No finite-dimensional parametric restrictions are imposed on F₀, the joint distribution of (ß_i, ε_i). A nonparametric maximum likelihood estimator for F₀ is shown to be consistent. We analyze some conditions under which F₀ is or is not identified. In particular, we show that if the support of F₀ is a subset of any half of the unit hypersphere, then F₀ 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.

Original language	English (US)
Pages (from-to)	269-295
Number of pages	27
Journal	Journal of Econometrics
Volume	86
Issue number	2
DOIs	https://doi.org/10.1016/S0304-4076(97)00117-6
State	Published - Jun 16 1998
Externally published	Yes

Keywords

Binary response
Discrete choice
Identification
Nonparametric estimation
Random coefficients

ASJC Scopus subject areas

Economics and Econometrics

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10.1016/S0304-4076(97)00117-6

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title = "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution",

abstract = "We consider a binary response model yi = 1\{x′i{\ss}i + εi ≥ 0\} with xi independent of the unobservables ({\ss}i, εi). No finite-dimensional parametric restrictions are imposed on F0, the joint distribution of ({\ss}i, εi). A nonparametric maximum likelihood estimator for F0 is shown to be consistent. We analyze some conditions under which F0 is or is not identified. In particular, we show that if the support of F0 is a subset of any half of the unit hypersphere, then F0 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.",

keywords = "Binary response, Discrete choice, Identification, Nonparametric estimation, Random coefficients",

author = "Hidehiko Ichimura and Thompson, \{T. Scott\}",

note = "Funding Information: An earlier version of this paper was presented at the 1993 Midwestern Econometric Group conference, the 1994 annual meeting of the American Statistical Association, a 1994 conference at Northwestern University sponsored by the National Science Foundation, and the 1994 Latin America meeting of the Econometric Society. We have benefited from communications with A. Ron Gallant, two anonymous referees, and seminar participants in the economics or statistics departments of the following institutions: The University of Minnesota, The University of Chicago, The University of Rochester, North Carolina State University, The University of North Carolina, Queens University, and the University of British Columbia. We also thank Charles Geyer, John Geweke, Rosa Matzkin and Herman Rubin. We thank the Minnesota Supercomputer Institute for providing computer support. Thompson thanks the National Science Foundation for support provided by grant SES–9110419. The views expressed herein are not purported to reflect those of the US Department of Justice.",

year = "1998",

month = jun,

day = "16",

doi = "10.1016/S0304-4076(97)00117-6",

language = "English (US)",

volume = "86",

pages = "269--295",

journal = "Journal of Econometrics",

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T1 - Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution

AU - Ichimura, Hidehiko

AU - Thompson, T. Scott

N1 - Funding Information: An earlier version of this paper was presented at the 1993 Midwestern Econometric Group conference, the 1994 annual meeting of the American Statistical Association, a 1994 conference at Northwestern University sponsored by the National Science Foundation, and the 1994 Latin America meeting of the Econometric Society. We have benefited from communications with A. Ron Gallant, two anonymous referees, and seminar participants in the economics or statistics departments of the following institutions: The University of Minnesota, The University of Chicago, The University of Rochester, North Carolina State University, The University of North Carolina, Queens University, and the University of British Columbia. We also thank Charles Geyer, John Geweke, Rosa Matzkin and Herman Rubin. We thank the Minnesota Supercomputer Institute for providing computer support. Thompson thanks the National Science Foundation for support provided by grant SES–9110419. The views expressed herein are not purported to reflect those of the US Department of Justice.

PY - 1998/6/16

Y1 - 1998/6/16

N2 - We consider a binary response model yi = 1{x′ißi + εi ≥ 0} with xi independent of the unobservables (ßi, εi). No finite-dimensional parametric restrictions are imposed on F0, the joint distribution of (ßi, εi). A nonparametric maximum likelihood estimator for F0 is shown to be consistent. We analyze some conditions under which F0 is or is not identified. In particular, we show that if the support of F0 is a subset of any half of the unit hypersphere, then F0 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.

AB - We consider a binary response model yi = 1{x′ißi + εi ≥ 0} with xi independent of the unobservables (ßi, εi). No finite-dimensional parametric restrictions are imposed on F0, the joint distribution of (ßi, εi). A nonparametric maximum likelihood estimator for F0 is shown to be consistent. We analyze some conditions under which F0 is or is not identified. In particular, we show that if the support of F0 is a subset of any half of the unit hypersphere, then F0 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.

KW - Binary response

KW - Discrete choice

KW - Identification

KW - Nonparametric estimation

KW - Random coefficients

UR - https://www.scopus.com/pages/publications/0003972760

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U2 - 10.1016/S0304-4076(97)00117-6

DO - 10.1016/S0304-4076(97)00117-6

M3 - Article

SN - 0304-4076

VL - 86

SP - 269

EP - 295

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -

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

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Keywords

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