Identification of Regression Models with a Misclassified and Endogenous Binary Regressor
Hiroyuki Kasahara () and
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We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate that satisfy the following conditions are present. The instrumental variable (IV) corrects endogeneity; the IV must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, and is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.
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