Partially Linear Models with Endogeneity: a conditional moment based approach

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 (Robinson (1988)), to partial out the non-linear part of the model, with a smooth minimum distance approach (Lavergne and Patilea (2013)), to exploit all the information of the conditional mean independence restriction. Our estimator is easy to compute, consistent and √n-asymptotically normal under standard regularity conditions. Simulations show that our estimator is competitive with GMM-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 (2011) 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.