Average Marginal Effects in One-Step Partially Linear Instrumental Regressions

TL;DR

This paper introduces a new kernel-based method for estimating average marginal effects in partially linear instrumental regressions, providing valid inference via a Bayesian bootstrap, with demonstrated good finite-sample performance and real-data applications.

Contribution

It presents a novel single-parameter regularized approach using RKHS for inference on marginal effects in instrumental regressions, with a valid Bayesian bootstrap inference method.

Findings

Estimator is consistent and asymptotically normal.

Bayesian bootstrap provides valid inference despite complex variance.

Method performs well in finite samples and real data applications.

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.