Bounding mean regressions when a binary regressor is mismeasured

Match Bias in Wage Gap Estimates Due to Earnings Imputation

“…As shown by Aigner (1973) and u* p 0 others, the binary errors-in-variables case results in least squares coefficient estimates that are biased toward zero, but with the precise bias difficult to specify absent additional assumptions. Bollinger (1996) has established bounds for the true coefficient, with the least squares estimate providing the lower bound and a variant of reverse regression providing an upper bound. Card (1996, pp.…”

“…In order to focus on imputation match bias, we ignore the standard form of measurement error, which is not so large in wage level analysis. Measurement error has been a focus in longitudinal studies (Freeman 1984;Bollinger 1996;Card 1996). Farber and Western (2002) note that, as union density falls below .50, random reporting error biases density upward, substantially so as density becomes very small (when true density is zero, all bias is positive).…”

“…3 There has been considerable attention given to mismeasurement in reported earnings in the CPS (Mellow and Sider 1983;Bound and Krueger 1991;Bollinger 1998). These authors have been careful to delete allocated earners from their analysis.…”

Bounding Parameter Estimates with Nonclassical Measurement Error

“…In addition to the Ashenfelter and Kreuger (1994) twins data, replicates have been given by Barron, Berger, and Black (1997a), Card (1996), Freeman (1984, Kaestner, Joyce, and Wehbeh (1996), Loewenstein and Spletzer (1998), Mellow and Sider (1983), Romeo (1997), and Romeo and Sun (1996). Alternatively, other studies have examined the accuracy of data by comparing questionnaire responses to administrative data (Bollinger 1998;Bollinger and David 1997;Bound, Brown, Duncan, andRodgers 1990,1994;Bound and Krueger 1991;Duncan and Hill 1985;Marquis, Marquis, and Polich 1986;Rodgers, Brown, and Duncan 1993). Taken together, these studies offer little support for the classic EVM; measurement error often exhibits a covariance with the true value.…”

“…With a single report on a binary variable, Bollinger (1996) showed that the reverse regression bound can be improved.…”