Partially varying coefficient instrumental variables models |
| |
Authors: | Zongwu Cai Huaiyu Xiong |
| |
Institution: | 1. Department of Mathematics & Statistics, University of North Carolina at Charlotte, NC 28223, USA. Wang Yanan Institute for Studies in Economics, MOE Key Laboratory of Econometrics, and Fujian Key Laboratory of Statistical Sciences, Xiamen University, Xiamen, Fujian 361005, China.;2. Wells Fargo Bank, 550 California Street, San Francisco, CA 94102, USA. |
| |
Abstract: | In this article, we study a new class of semiparametric instrumental variables models, in which the structural function has a partially varying coefficient functional form. Under this specification, the model is linear in the endogenous/exogenous components with unknown constant or functional coefficients. As a result, the ill‐posed inverse problem in a general non‐parametric model with continuous endogenous variables can be avoided. We propose a three‐step estimation procedure for estimating both constant and functional coefficients and establish their asymptotic properties such as consistency and asymptotic normality. We develop consistent estimators for their error variances. We demonstrate that the constant coefficient estimators achieve the optimal ‐convergence rate, and the functional coefficient estimators are oracle. In addition, efficiency issue of the parameter estimation is discussed and a simple efficient estimator is proposed. The proposed procedure is illustrated via a Monte Carlo simulation and an application to returns to education. |
| |
Keywords: | efficiency endogenous variables functional‐coefficient models instrumental variables local linear fitting non‐parametric smoothing simultaneous equations |
|
|