Optimal Shrinkage Estimation of Fixed Effects in Linear Panel Data Models

Shrinkage methods are frequently used to estimate fixed effects to reduce the noisiness of the least square estimators. However, widely used shrinkage estimators guarantee such noise reduction only under strong distributional assumptions. I develop an estimator for the fixed effects that obtains the best possible mean squared error within a class of shrinkage estimators. This class includes conventional shrinkage estimators and the optimality does not require distributional assumptions. The estimator has an intuitive form and is easy to implement. Moreover, the fixed effects are allowed to vary with time and to be serially correlated, and the shrinkage optimally incorporates the underlying correlation structure in this case. In such a context, I also provide a method to forecast fixed effects one period ahead.