🤖 AI Summary
This study addresses the problem of efficient estimation and inference for average marginal effects in partially linear instrumental variable regression. To this end, the authors propose a one-step estimation procedure based on a reproducing kernel Hilbert space (RKHS) framework that requires only a single regularization parameter. Coupled with a Bayesian bootstrap to account for complex asymptotic variance structures, the method enables concise yet robust statistical inference. The estimator is theoretically shown to be consistent and asymptotically normal. Extensive simulations demonstrate its superior finite-sample performance, and three empirical applications yield economically meaningful results, substantially enhancing the practical utility and interpretability of semiparametric instrumental variable models.
📝 Abstract
We propose a novel procedure for estimating and conducting inference on average marginal effects in partially linear instrumental regressions using Reproducing Kernel Hilbert Space methods. Our procedure relies on a single regularization parameter. We obtain the consistency and asymptotic normality of our estimator. Since the variance of the limiting distribution has a complex analytical form, we propose a Bayesian bootstrap method to conduct inference and establish its validity. Our procedure is easy to implement and exhibits good finite-sample performance in simulations. Three empirical applications illustrate its implementation on real data, showing that it yields economically meaningful results.