Shrinkage methods are frequently used to estimate fixed effects. However, the risk properties of existing estimators are fragile to violations of the underlying distributional assumptions. I develop an estimator for the fixed effects that obtains the best possible mean squared error (MSE) within a class of shrinkage estimators. This class includes conventional estimators, and the optimality does not require distributional assumptions. Importantly, 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. A simulation study shows that the proposed estimator substantially reduces the MSE relative to conventional methods when the distributional assumptions of the conventional methods are violated, and loses very little when the assumptions are met. Using administrative data on the public schools of New York City, I estimate a teacher value-added model and show that the proposed estimator makes an empirically relevant difference. An optimized R package, FEShR, to implement the proposed method is provided.