Misclassification in Binary Choice Models

Bruce Meyer, Nikolas Mittag

NBER Working Paper No. 20509
Issued in September 2014
NBER Program(s):Economics of Aging, Children, Health Care, Health Economics, Labor Studies, Public Economics

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.

download in pdf format
   (282 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/w20509

Published: Bruce D. Meyer & Nikolas Mittag, 2017. "Misclassification in binary choice models," Journal of Econometrics, vol 200(2), pages 295-311.

Users who downloaded this paper also downloaded* these:
Arbatlı, Ashraf, Galor, and Klemp w21079 Diversity and Conflict
Rose w20494 The Bond Market: An Inflation-Targeter's Best Friend
Aizenman, Jinjarak, and Park w20917 Financial Development and Output Growth in Developing Asia and Latin America: A Comparative Sectoral Analysis
Rodrik w20935 Premature Deindustrialization
Michalopoulos and Papaioannou w20513 On the Ethnic Origins of African Development Chiefs and Pre-colonial Political Centralization
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us