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Optimal Estimation of Two-Way Effects under Limited Mobility

Author

Listed:
  • Xu Cheng

    (University of Pennsylvania)

  • Sheng Chao Ho

    (Singapore Management University)

  • Frank Schorfheide

    (University of Pennsylvania)

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

Suggested Citation

  • Xu Cheng & Sheng Chao Ho & Frank Schorfheide, 2025. "Optimal Estimation of Two-Way Effects under Limited Mobility," PIER Working Paper Archive 25-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:25-013
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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