Identification and Sensitivity Analysis for Teacher Bias Designs Based on Administrative Data

A series of papers uses administrative data on school students’ grades to assess whether teachers discriminate against certain demographic groups. Often, differences in teacher and test grades are regressed on student-level variables. However, it is unclear under what circumstances such an estimation strategy is valid. We conceptualize teacher bias as a direct causal effect of student-level attributes on teacher grades, fixing student ability. Standardized tests merely proxy for student ability; additionally, there may be confounders of ability and teacher grade. Accordingly, teacher bias is nonparametrically unidentified. However, we suggest substantive and parametric assumptions that ensure identification using difference-in-grades estimators. Estimators based on regression control for test grades are shown to be inconsistent even under these strong assumptions. We then develop a parametric sensitivity analysis that allows researchers to investigate the consequences of departures from critical assumptions. We illustrate our methodology using administrative data from Denmark.