Shrinkage estimation of fixed effects with matched data

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This paper develops an empirical Bayes estimator for a panel data model with two-way fixed effects, with a focus on matched data with limited mobility.  The hyperparameters that control the variance (degree of shrinkage) and the location of the prior are determined by minimizing an unbiased risk estimate. We established the optimality of the proposed estimator by showing that it asymptotically attains the same loss as an oracle estimator with a hyperparameter that is chosen based on the knowledge of the fixed effects. In a Monte Carlo study we show that the proposed estimator outperforms a number of competitors, including the least squares estimator. The method will be applied to the estimation of teacher values-added from a linked student teacher data set obtained from the North Carolina Education Research Data Center.