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Endogeneity and measurement error in nonparametric and semiparametric models

Abstract

It has long been an area of interest to consider a consistent estimation of nonlinear models with measurement error or endogeneity in the explanatory variables. Contrast to linear parametric models, both topics in nonlinear models are difficult to correct for. As a result, many of studies have addressed only one of them in nonlinear models, although controlling for only one mostly fails to identify economically meaningful structural parameters. Thus, this dissertation presents solutions to simultaneously control for both endogeneity and measurement error in general nonlinear regression models. Chapter one of this dissertation studies the identification and estimation of covariate-conditioned average marginal effects of endogenous regressors in nonseparable models when the regressors are mismeasured. Endogeneity is controlled for by making use of covariates as conditioning instruments; this ensures independence between the endogenous causes and other unobservable drivers of the dependent variable. Moreover, distributions of the underlying true causes from their error-laden measurements are recovered. Specifically, it is shown that two error-laden measurements of the unobserved true causes are sufficient to identify objects of interest and to deliver consistent estimators. Chapter two develops semiparametric estimation of models defined by conditional moment restrictions, where the unknown functions depend on endogenous variables which are contaminated by nonclassical measurement errors. A two-stage estimation procedure is proposed to recover the true conditional density of endogenous variables given conditioning variables masked by measurement errors, and to rectify the difficulty associated with endogeneity of the unknown functions. Chapter three investigates empirical importance of endogeneity and measurement error in economic examples. The proposed methods in chapter one and two are applied to topics of interest, the impact of family income on children's achievement and the estimation of Engel curves, respectively. The first application finds that the effects of family income on both math and reading scores from the proposed estimator are positive and that the magnitudes of the income effects are substantially larger than previously recognized. From the second application, findings indicate that correcting for both endogeneity and measurement error obtains significantly different shapes of Engel curves, compared to the method which ignores measurement error on total expenditure

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