Efficient estimation of binary choice models under symmetry

This paper proposes a semiparametric maximum likelihood estimator for both the intercept and slope parameters in a binary choice model under symmetry and index restrictions. The estimator attains the semiparametric efficiency bound in Cosslett (1987) under the symmetry and independence restrictions. Compared with the estimator of Klein and Spady (1993) which attains the semiparametric efficiency bound in Chamberlain (1986) and Cosslett (1987) under the independence restriction, we show that there are possible efficiency gains in estimating the slope parameters by imposing the additional symmetry restriction. A small Monte Carlo study is carried out to illustrate the usefulness of our estimator.