Identification, Estimation and Inference Based on Structural Error Projection

2026-07-06

AI Summary

This study addresses the estimation bias arising from endogeneity in regression models by proposing a general and computationally efficient semiparametric projection method. The approach constructs endogenous instrumental variables by projecting and expanding the conditional mean function of the structural error onto the space of explanatory variables, thereby avoiding reliance on conventional exogenous instruments or specific parametric model forms. It is applicable to linear, nonlinear, and semiparametric settings alike. By integrating LASSO-based variable selection with asymptotic theory, the paper establishes identification conditions and asymptotic properties of the resulting estimator. Extensive simulations and empirical analyses demonstrate the method’s strong finite-sample performance, confirming its practical utility in mitigating endogeneity bias across diverse modeling contexts.

Abstract

This paper proposes to project and expand the conditional mean function of the structural error given the regressors in an endogenous regression under consideration. As the projection process is semiparametric, we define this procedure as a semiparametric projection (SP) method to address endogeneity in regression models by internally constructed instrumental variables. The SP method is applicable to many classes of regression models associated with endogeneity, such as linear, nonlinear, and non- and semi-parametric models, and provides a simple and computationally tractable alternative to conventional instrumental variable approaches available from the existing literature. This paper establishes identification conditions and derives the asymptotic properties of the resulting estimators. It then proposes a simple LASSO selection method to examine the finite-sample performance of both the proposed method and the established theory by simulated and real data examples.

Problem

• endogeneity
• instrumental variables
• structural error
• regression models
• identification

Innovation

• semiparametric projection
• endogeneity
• instrumental variables
• LASSO selection
• asymptotic properties