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Partially varying coefficient instrumental variables models
Author(s) -
Cai Zongwu,
Xiong Huaiyu
Publication year - 2012
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2011.00497.x
Subject(s) - estimator , mathematics , asymptotic distribution , instrumental variable , consistency (knowledge bases) , constant (computer programming) , rate of convergence , parametric statistics , asymptotic analysis , mathematical optimization , econometrics , statistics , computer science , computer network , channel (broadcasting) , geometry , programming language
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.