Instrumental Variable Estimation of Nonparametric Models

TLDR

In econometrics, understanding the structural relationship among dependent variables is essential for answering many research questions. This study seeks to provide identification and estimation results for nonparametric conditional moment restrictions. The authors characterize identification as completeness of certain conditional distributions, establish sufficient conditions for exponential families and discrete variables, and propose a consistent, nonparametric two‑stage least‑squares estimator based on series approximation that mitigates an ill‑posed inverse problem by bounding integrals of higher‑order derivatives. The paper demonstrates that identification and estimation of nonparametric structural functions are achievable under the proposed conditions.

Abstract

In econometrics there are many occasions where knowledge of the structural relationship among dependent variables is required to answer questions of interest. This paper gives identification and estimation results for nonparametric conditional moment restrictions. We characterize identification of structural functions as completeness of certain conditional distributions, and give sufficient identification conditions for exponential families and discrete variables. We also give a consistent, nonparametric estimator of the structural function. The estimator is nonparametric two-stage least squares based on series approximation, which overcomes an ill-posed inverse problem by placing bounds on integrals of higher-order derivatives.