Direct Semiparametric Estimation of Single-index Models with Discrete Covariates

Ha .. rdle and Stoker (1989), Powell, et al. (1989), and Stoker (1991) have developed average derivative estimators of the parameter in the singleindex model E(Y X=x) = G(x ), where G is an unknown function and X is a random vector. These estimators are non-iterative and, therefore, easy to compute. However, they require X to be continuously distributed, which precludes their use in many applications. This paper develops a noniterative, easily computed estimator of for models in which some components of X are discrete. Coefficients of continuous components of X are obtained using average derivative techniques. Coefficients of discrete components are obtained from differences between certain integrals of G. The estimator is n-consistent and asymptotically normal. An application to data on product innovation by German manufacturers illustrates the estimator's usefulness.