Iterative Least Squares Estimator of Binary Choice Models: a Semi-Parametric Approach

Most existing semi-parametric estimation procedures for binary choice models are based on the maximum score, maximum likelihood, or nonlinear least squares principles. These methods have two problems. They are difficult to compute and they may result in multiple local optima because they require optimizing nonlinear objective functions which may not be unimode. These problems are exacerbated when the number of explanatory variables increases or the sample size is large (Manski, 1975, 1985; Manski and Thompson, 1986; Cosslett, 1983; Ichimura, 1993; Horowitz, 1992; and Klein and Spady, 1993). In this paper, we propose an easy-to-compute semi-parametric estimator for binary choice models. The proposed method takes a completely different approach from the existing methods. The method is based on a semi-parametric interpretation of the Expectation and Maximization (EM) principle (Dempster et al, 1977) and the least squares approach. By using the least squares method, the proposed method computes quickly and is immune to the problem of multiple local maxima. Furthermore, the computing time is not dramatically affected by the number of explanatory variables. The method compares favorably with other existing semiparametric methods in our Monte Carlo studies. The simulation results indicate that the proposed estimator is, 1) easy-to-compute and fast, 2) insensitive to initial estimates, 3) appears to be root(n)-consistent and asymptotically normal, and, 4) better than other semi-parametric estimators in terms of finite sample performances. The distinct advantages of the proposed method offer good potential for practical applications of semi-parametric estimation of binary choice models.