Abstract
In this paper, nonlinear least squares (NLLS) estimators are proposed for semiparametric binary response models under conditional median restrictions. The estimators can be identical to NLLS procedures for parametric binary response models (e.g. Probit), and consequently have the advantage of being easily implementable using standard software packages such as Stata. This is in contrast to existing estimators for the model, such as the maximum score estimator (Manski, 1975, 1985) and the smoothed maximum score (SMS) estimator (Horowitz, 1992). Two simple bias correction methods—a proposed jackknife method and an alternative nonlinear regression function—result in the same rate of convergence as SMS. The results from a Monte Carlo study show that the new estimators perform well in finite samples.
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