Misclassification in Binary Choice Models

59 Pages Posted: 22 Sep 2014

See all articles by Bruce D. Meyer

Bruce D. Meyer

University of Chicago - Irving B. Harris Graduate School of Public Policy Studies; National Bureau of Economic Research (NBER)

Nikolas Mittag

University of Chicago - Irving B. Harris Graduate School of Public Policy Studies

Multiple version iconThere are 2 versions of this paper

Date Written: September 2014

Abstract

While measurement error in the dependent variable does not lead to bias in some well-known cases, with a binary dependent variable the bias can be pronounced. In binary choice, Hausman, Abrevaya and Scott-Morton (1998) show that the marginal effects in the observed data differ from the true ones in proportion to the sum of the misclassification probabilities when the errors are unrelated to covariates. We provide two sets of results that extend this analysis. First, we derive the asymptotic bias in parametric models allowing for correlation of the errors with both observables and unobservables. Second, we examine the bias in a prototypical application in two different datasets, using a variety of methods that differ in the amount of knowledge that is assumed about the error process. Our application is receipt of food stamps, the largest and most widely received welfare program in the U.S. Monte Carlo results and our empirical application show that the bias formulas accurately describe the bias in finite samples. Our results indicate that the robustness of signs and relative magnitudes of coefficients implied by the earlier proportionality results does not necessarily extend to estimated Probit coefficients, and does not apply when errors are correlated with covariates. Using administrative records linked to survey data as validation data, we evaluate estimators that are consistent under misclassification. Estimators based on the assumption that misclassification is independent of the covariates are sensitive to their functional form assumptions and aggravate the bias if the conditional independence assumption is invalid in all cases we examine. On the other hand, estimators that allow misreporting to be correlated with the covariates perform well if an accurate model of misreporting or validation data are available. Estimators that incorporate more information about the errors, such as aggregate underreporting rates, tend to be more robust to misspecification of the misreporting model.

Suggested Citation

Meyer, Bruce D. and Mittag, Nikolas, Misclassification in Binary Choice Models (September 2014). NBER Working Paper No. w20509. Available at SSRN: https://ssrn.com/abstract=2499371

Bruce D. Meyer (Contact Author)

University of Chicago - Irving B. Harris Graduate School of Public Policy Studies ( email )

1155 East 60th Street
Chicago, IL 60637
United States
(773) 702-2712 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Nikolas Mittag

University of Chicago - Irving B. Harris Graduate School of Public Policy Studies ( email )

1155 East 60th Street
Chicago, IL 60637
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
8
Abstract Views
171
PlumX Metrics