Identification and Estimation of Triangular Simultaneous Equations Models without Additivity

This paper is about identification and estimation in a triangular nonparametric structural model with instrumental variables and non-additive errors. Identification and estimation is based on a control function consisting of the conditional distribution function of the endogenous variable given the instruments. We allow for a structural disturbance of arbitrary, unknown dimension while identifying interesting structural effects, such as quantile and average effects. We consider a two-step approach to estimation. We find that the convergence rate for the second-step structural estimator depends on the strength of the instrument.