Journal of Econometrics 32 (1986) 127-141. North-Holland LINEAR INSTRUMENTAL VARIABLE ESTIMATION OF LIMITED DEPENDENT VARIABLE MODELS WITH ENDOGENOUS EXPLANATORY VARIABLES* Whitney K. NEWEY Princeton Untversit_v, Princeton, NJ 08544. USA Universrty of CuliJornia, Berkeley, CA 94720, USA 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. 1. Introduction Instrumental variable estimation provides a powerful and flexible method of correcting for sources of specification error, such as errors in variables and simultaneous equations bias, in econometric models. In limited dependent variable models, where bias can result from distributional misspecification, methods that rely on the multivariate normality assumption may not lead to entirely satisfactory corrections for specification error. 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 the disturbances. Recently, Ruud (1984) has shown that in many circumstances it is possible to obtain consistent estimators of parameters of a limited dependent variable model with exogenous explanatory variables by weighted M-estimation, where the weights depend on the explanatory variables. When some explanatory variables are endogenous it is no longer appropriate to weight by functions of the explanatory variables, but one can form weights using the instrumental variables. The estimators that we present are weighted instrumental variables estimators, with weights that are exactly like those of Ruud (1984). In section 2 the weighted instrumental variables estimator is presented, and consistency up to a scale term of the estimator of the slope parameters is *This research was suppbrted by National Science Foundation tirant SES 8410249. I am grateful for useful discussions with A.R. Gallant and P. Ruud. 0304-4076/86/$3.5001986. Elsevier Science Publishers B.V. (North-Holland)