Partially linear models with endogeneity: a conditional moment-based approach

Abstract

Summary In a partially linear conditional moment model we propose a new estimator for the slope parameter of the endogenous variable of interest, which combines a Robinson’s transformation to partial out the nonlinear part of the model, with a smooth minimum distance approach to exploit all the information of the conditional mean independence restriction. Our estimator only depends on one tuning parameter, is easy to compute, consistent and $\sqrt{n}$-asymptotically normal under standard regularity conditions. Simulations show that our estimator is competitive with the generalised method of moments-type estimators and often displays a smaller bias and variance as well as better coverage rates for confidence intervals. We revisit and extend some of the empirical results in Dinkelman (2011b) who estimates the impact of electrification on employment growth in South Africa. Overall, we obtain estimates that are smaller in magnitude, more precise, and still economically relevant.