One-step smoothing splines instrumental regression

TL;DR

This paper introduces a one-step nonparametric regression estimator using smoothing splines for models with endogeneity and instrumental variables, providing convergence rates and practical advantages over existing methods.

Contribution

It develops a novel one-step smoothing spline estimator for endogenous models with instrumental variables, including monotonicity constraints and extensions to partly linear models.

Findings

Estimator achieves favorable convergence rates.

Simulation studies show superior performance over two-step methods.

Economically meaningful results in Engel curve estimation.

Abstract

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique regularization parameter. We derive rates of the convergence for the estimator and its first derivative, which are uniform in the support of the endogenous variable. We also address the issue of imposing monotonicity in estimation and extend the approach to a partly linear model. Simulations confirm the good performances of our estimator compared to two-step procedures. Our method yields economically sensible results when used to estimate Engel curves.