Quantitative Economics

Journal Of The Econometric Society

Edited by: StĆ©phane Bonhomme ā€¢ Print ISSN: 1759-7323 ā€¢ Online ISSN: 1759-7331

Quantitative Economics: Nov, 2015, Volume 6, Issue 3

Estimating nonseparable models with mismeasured endogenous variables

Suyong Song, Susanne M. Schennach, Halbert White

We study the identification and estimation of covariateā€conditioned average marginal effects of endogenous regressors in nonseparable structural systems when the regressors are mismeasured. We control for the endogeneity by making use of covariates as control variables; this ensures conditional independence between the endogenous causes of interest and other unobservable drivers of the dependent variable. Moreover, we recover distributions of the underlying true causes from their errorā€laden measurements to deliver consistent estimators. We obtain uniform convergence rates and asymptotic normality for estimators of covariateā€conditioned average marginal effects, faster convergence rates for estimators of their weighted averages over instruments, and rootā€n consistency and asymptotic normality for estimators of their weighted averages over control variables and regressors. We investigate their finiteā€sample behavior using Monte Carlo simulation and apply new methods to study the impact of family income on child achievement measured by math and reading scores, using a matched motherā€“child subsample of the National Longitudinal Survey of Youth. Our findings suggest that these effects are considerably larger than previously recognized, and depend on parental abilities and family income. This underscores the importance of measurement errors, endogeneity of family income, nonlinearity of income effects, and interactions between causes of child achievement.

Causal effects child development endogeneity measurement error nonparametric estimation nonseparable C13 C14 C31


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Supplement to "Estimating nonseparable models with mismeasured endogenous variables"

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Supplement to "Estimating nonseparable models with mismeasured endogenous variables"