Linear instrumental variable estimation of limited dependent variable models with endogenous explanatory variables

The purpose of this paper is to present and analyze an instrumental variables estimator for limited dependent variable models that does not require functional form assumptions for the distribution of disturbances. This estimator is a weighted instrumental variables estimator, where the weight is the ratio of a multivariate normal density to the actual density of the instrumental variables. A semi-non-parametric estimator of the weights is presented and some conjectures concerning the asymptotic distribution of the estimator are discussed.