Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables

We develop a novel identification method for a partially linear model with multiple endogenous variables of interest but a single instrumental variable, which could even be binary. We present an easy-to-implement consistent estimator for the parametric part. This estimator retains n-convergence rate and asymptotic normality even though we have a generated regressor in our setup. The nonparametric part of the model is also identified. We also outline how our identification strategy can be extended to a fully non-parametric model. Finally, we use our methods to assess the impact of smoking during pregnancy on birth weight.