Quantifying Family, School, and Location Effects in the Presence of Complementarities and Sorting
扩展了控制函数方法以处理多个群体层次和互补性，为存在分类时的多水平混合效应模型提供因果解释基础，并估计了学校和通勤区投入对教育和工资的下界影响。
We extend Altonji and Mansfield’s control function approach to allow for multiple group levels and complementarities. Our analysis provides a foundation for a 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 high school graduation 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.