@article{c2cab07d90854e55b500cd4a8c6039c5,
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",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "2",
}