Zur korrekten Interpretation der Ergebnisse einer log-linearen Regression bei Heteroskedastie. Eine methodische Untersuchung mit einer Anwendung auf die relativen Löhne von Ausländern / Correctly Interpreting the Results from a Log-linear Regression under Heteroskedasticity. Methods and an Application to the Relative Wages of Immigrants

Summary The common estimator for relative adjusted wage differentials based on dummy variables in loglinear regressions is inconsistent in the presence of group-specific heteroskedasticity. The direction and magnitude of the bias are derived. At the same time, a heteroskedasticity-consistent estimator is proposed. The formulas are exact for normally distributed errors and approximations otherwise. An example on the wage determination in the German labor market shows that ignoring the problem of heteroskedasticity will lead to an underestimation of the relative wage gap between Germans and Immigrants, since the wages of immigrants are relatively less dispersed. Evidence from the literature as well as an independent analysis using data from the German Socio-Economic Panel for 1996 yield a downward bias of up to 25 percent. The importance of these results extend beyond the case of dummy variables to the general problem of Computing expectations of retransformed variables.