Essays on Nonparametric Estimation of Partially Linear Models Under Endogeneity

Geng, Xin

Graduate Thesis Or Dissertation

Essays on Nonparametric Estimation of Partially Linear Models Under Endogeneity Public Deposited

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/db78tc124

Abstract

We propose a kernel based estimator for a partially linear model in triangular systems where endogenous variables appear both in the nonparametric and linear component functions. This model has a wide range of applications in many fields of economics. Compared with the two alternative estimators currently available in the literature for such model, this estimator has an explicit functional form, is much easier to implement, and may significantly outperform theirs in finite sample simulation. Our estimator is inspired by the control function approach of Newey (1999) and was initially proposed by Martins-Filho and Yao (2012). It builds on the additive regression estimation by Kim et al. (1999). In the first chapter, we fully describe the model and estimators, give the finite sample performance via a Monte Carlo study, and establish: (i) square root n asymptotic normality of the estimator for the parametric component, and (ii) consistency and the uniform convergence rate of the estimator for the nonparametric component. In addition, for statistical inference, a consistent estimator for the covariance of the limiting distribution of the parametric estimator is also provided. Various intermediate results will also be of use to theorists. In the second chapter, we study the effects of foreign aid and policy on economic growth. This aid-policy-growth relationship has been a popular topic and quite controversial in the past decade. We use the same data sets of Burnside and Dollar (2000) and Easterly et al. (2004) but implement the estimator derived earlier in the semiparametric model rather than a linear specification. We find that good policy significantly promotes growth, irrespective of aid; aid effect on growth in general is not obvious, but with good policies, aid is growth enhancing at high levels.

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