Partially varying coefficient instrumental variables models

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.National Science Foundation of China [70871003, 70971113]; University of North Carolina at Charlotte; Chinese Government; Fujian Province; Xiamen City; Chinese Ministry of Education; Fujian Province, Chin

Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

“…Our findings are unambiguous: the returns to education do depend on both experience and the categorical variables we use, in a non-linear manner. Additionally, we find that the returns to education tend to be overestimated for all of the observed work experience when the categorical explanatory variables are not accounted for in functional coefficients as in CDXW (2006) and Cai and Xiong (2010). These results are also important since our proposed tests show the absence of the constancy of the return to education, which is often assumed in most of the parametric empirical studies in labor economics.…”

“…While we do not observe overly drastic distinctions in the results based on our approach and approaches by CDXW (2006) and Cai and Xiong (2010), we do see some notable differences across the three approaches. First, findings by Xiong's (2010) andCDXW (2006) indicate that the returns to education may vary from (roughly) 15 to 22% and 16.5 to 30%, respectively.…”

“…The main reason for our decision is that our sample contains only 8 observations (out of 2049 available) with experience being more or equal to 9 years. We also suspect that the sample used by CDXW (2006) and Cai and Xiong (2010) excludes observations at the high levels of the observed years of experience in our sample, as their sample contains 1996 observations only. Thus, for comparative purposes, we primarily focus on work experience being less than 9 years.…”

“…However, they use a three-step nonparametric method to estimate this model. We compare our estimates of the return to education with the estimates based on all there existing approaches -the ones from SCU (2009), CDXW (2006) and Cai and Xiong (2010). When doing so, we mainly concentrate on work experience below or equal to 8 years.…”

“…CDXW (2006) exploit a two-step nonparametric procedure to estimate the returns to education in the context of model (6.2). Cai and Xiong (2010) consider the same data set and model specification as in CDXW (2006). However, they use a three-step nonparametric method to estimate this model.…”