Measurement Error Nonseparable

Measurement Error Nonseparable - Estimating Nonseparable...

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Unformatted text preview: Estimating Nonseparable Models with Mismeasured Endogenous Variables * Suyong Song UW-Milwaukee Susanne M. Schennach Brown University Halbert White UC San Diego October, 2011 Abstract We study the identification and estimation of covariate-conditioned average marginal effects of endogenous regressors in nonseparable structural systems when the regressors are mismea- sured. We control for the endogeneity by making use of covariates as conditioning instruments; this ensures conditional independence between the endogenous causes of interest and other unob- servable drivers of the dependent variable. Moreover, we recover distributions of the underlying true causes from their error-laden measurements. Our approach relies on a useful property of the Fourier transform, namely, its ability to convert complicated integral equations that re- late unobservables to observables into simple algebraic equations. Specifically, we show that two error-laden measurements of the unobserved true causes are sufficient to identify objects of inter- est and to deliver consistent estimators. We obtain uniform convergence rates and asymptotic normality for estimators of covariate-conditioned average marginal effects, faster convergence rates for estimators of their weighted averages over instruments, and root- n consistency and asymptotic normality for estimators of their weighted averages over instruments and regressors. We investigate their finite-sample behavior using Monte Carlo simulation and apply our new methods to study the impact of family income on child achievement. Our findings suggest that these effects are considerably larger than previously recognized. JEL Classification: C13, C14, C31 Key Words: causal effects; child development; endogeneity; measurement error; nonparametric estimation; nonseparable structural equation. * The authors would like to express their appreciation to Jin Seo Cho, Gordon Dahl, Graham Elliott, Anthony Gamst, Stephen Hoderlein, Joel Horowitz, Arthur Lewbel, Chuck Manski, Dimitris Politis, James Powell, Andres San- tos, Yixiao Sun, and Quang Vuong, as well as seminar audiences at various universities, at the Midwest Eonometrics Group 2010 and at the Economeric Society 2011 Winter Meetings for helpful comments and discussions. Department of Economics, University of Wisconsin-Milwaukee. E-mail: songs@uwm.edu Department of Economics, Brown University. E-mail: smschenn@brown.edu Department of Economics, University of California, San Diego. E-mail: hwhite@ucsd.edu 1 Introduction In this paper, we examine the identification and estimation of a variety of average marginal effects of mismeasured endogenous variables in nonseparable structural systems. We control for endogene- ity by making use of covariates as conditioning instruments; this ensures conditional independence between the endogenous causes of interest and other unobservable drivers of the dependent variable....
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Measurement Error Nonseparable - Estimating Nonseparable...

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