Xu Cheng (UPenn): Optimal Estimation of Two-Way Effects under Limited Mobility
Abstract: We propose an empirical Bayes estimator for two-way effects in linked data sets
based on a novel prior that leverages patterns of assortative matching observed in
the data. To capture limited mobility we model the bipartite graph associated with
the matched data in an asymptotic framework where its Laplacian matrix has small
eigenvalues that converge to zero. The prior hyperparameters that control the shrinkage
are determined by minimizing an unbiased risk estimate. We show the proposed
empirical Bayes estimator is asymptotically optimal in compound loss, despite the weak
connectivity of the bipartite graph and the potential misspecification of the prior. We
estimate teacher values-added from a linked North Carolina Education Research Data
Center student-teacher data set.
Economics
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