SEMIPARAMETRIC ESTIMATION OF A LOCATION PARAMETER IN THE BINARY CHOICE MODEL

This paper considers the estimation of a location parameter in the binary choice model with some weak distributional assumptions imposed on the error term in the latent regression model. Two estimators are proposed here, both of which are twostep estimators; in the first step, the slope parameters are consistently estimated by existing methods; in the second step, the location parameter is consistently estimated based on a moment condition. The estimators are shown to be consistent and asymptotically normal. A small Monte Carlo study illustrates the usefulness of the estimators. We also point out that the location and slope parameters can be estimated simultaneously.