Teachers and Inequality in Student Performance - Estimating Value Added and Sorting Under Endogenous Mobility

This paper deals with issues related to estimating the causal impact of teachers on student test scores. The central challenge is that students and teachers are matched non-randomly. To deal with this, we propose an extension of the standard teacher value-added model that is more robust to such endogenous mobility bias than conventional models. We then apply and extend recent innovations in bias correction of variance components to quantify the overall importance of teachers and estimate patterns of sorting and segregation. We find that teachers in Denmark are more important for student inequality than the conventional approaches would suggest. Further, we document a novel pattern of negative sorting that is driven by compensatory school investments through the within-school matching of high-value-added teachers to low-ability students. We also show that high-value-added teachers tend to be more experienced and educated and that they are particularly skilled at classroom management. Finally, we present suggestive evidence that these teachers also promote student non-cognitive skills and well-being.