Quantifying Family, School, and Location Effects in the Presence of Complementarities and Sorting

We extend the control function approach of Altonji and Mansfield (2018) to allow for multiple group levels and complementarities. Our analysis provides a foundation for causal interpretation of multilevel mixed effects models in the presence of sorting. In our empirical application, we obtain lower bound estimates of the importance of school and commuting zone inputs for education and wages. A school/location combination at the 90th versus 10th percentile of the school/location quality distribution increases the high school graduation probability and college enrollment probability by at least .06 and .17, respectively. Treatment effects are heterogeneous across subgroups, primarily due to nonlinearity in the educational attainment model.