03548cam a22003257 4500001000700000003000500007005001700012006001900029007001500048008004100063100001800104245007800122260006600200300005700266490004200323500002000365520202700385530006002412538007202472538003602544588002502580690016602605690014202771690009402913700002103007710004203028830007703070856003803147856003703185w20509NBER20200926014525.0m o d cr cnu||||||||200926s2014 mau fo 000 0 eng d1 aMeyer, Bruce.10aMisclassification in Binary Choice Models /cBruce Meyer, Nikolas Mittag. aCambridge, Mass.bNational Bureau of Economic Researchc2014. a1 online resource:billustrations (black and white);1 aNBER working paper seriesvno. w20509 aSeptember 2014.3 aWhile 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. aHardcopy version available to institutional subscribers aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.0 aPrint version record 7aC25 - Discrete Regression and Qualitative Choice Models • Discrete Regressors • Proportions • Probabilities2Journal of Economic Literature class. 7aC81 - Methodology for Collecting, Estimating, and Organizing Microeconomic Data • Data Access2Journal of Economic Literature class. 7aH53 - Government Expenditures and Welfare Programs2Journal of Economic Literature class.1 aMittag, Nikolas.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w20509.40uhttp://www.nber.org/papers/w2050940uhttp://dx.doi.org/10.3386/w20509