Inferences for a Partially Varying Coefficient Model With Endogenous Regressors

ABSTRACT

In this article, we propose a new class of semiparametric instrumental variable models with partially varying coefficients, in which the structural function has a partially linear form and the impact of endogenous structural variables can vary over different levels of some exogenous variables. We propose a three-step estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic normality of these proposed estimators are established. Moreover, a generalized F-test is developed to test whether the functional coefficients are of particular parametric forms with some underlying economic intuitions, and furthermore, the limiting distribution of the proposed generalized F-test statistic under the null hypothesis is established. Finally, we illustrate the finite sample performance of our approach with simulations and two real data examples in economics.

KEY WORDS:

• Endogeneity
• Functional coefficients
• Generalized F-test
• Instrumental variables models
• Nonparametric test
• Profile least squares

ACKNOWLEDGMENTS

The authors thank the Editor, the Associate Editor, and two anonymous referees for their helpful and constructive comments and suggestions that improved significantly the article. In particular, the authors are indebted to one of the reviewers who initiated the idea of using the conditional linear projection in Section 3.1. Finally, the authors also acknowledge the financial supports from NSFC with grants #71271179, #11101341, #71131008 (Key Project), #71631004 (Key Project), and the National Science Fund for Distinguished Young Scholars (#71625001).