Regression with a Misclassified Binary Regressor: Correcting for the Hidden Bias
Presented by:
Pierre Nguimkeu
Department of Economics
Georgia State University
Thursday, October 22, 2020
3:45 pm-5:00 pm
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We address the estimation of linear regression models with a misclassified binary regressor that is potentially correlated with the other regressors. We show this correlation creates a bias that has been overlooked by existing solutions. This bias arises because the misclassification error is necessarily correlated with the other regressors in the model if the misclassified binary regressor is. It has not shown up in earlier work because it has assumed (explicitly or implicitly) that the misclassified binary variable is orthogonal to other regressors in the model. We show that this `hidden' bias can be substantial and could result in existing estimators taking the wrong sign. We propose two classes of corrections: (i) a bias-adjusted least squares estimator that either takes misclassification probabilities as given (e.g. through validation studies) or estimates these probabilities as a first step when a distribution for the true binary regressor is assumed; (ii) parameter bounds that are identified under relatively weak conditions and do not require any of the above information or assumptions. We prove the consistency and asymptotic normality of the proposed estimators. The finite sample performances of the proposed methods are provided through Monte Carlo simulations, and are compared with existing methods to demonstrate superiority. An empirical application on the effect of food stamp participation on obesity is provided to illustrate the usefulness of the proposed methods in practice.
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