| Abstract: |
We propose a method for forecasting individual outcomes and estimating random
effects in linear panel data models and value-added models when the panel has
a short time dimension. The method is robust, trivial to implement and
requires minimal assumptions. The idea is to take a weighted average of time
series- and pooled forecasts/estimators, with individual weights that are
based on time series information. We show the forecast optimality of
individual weights, both in terms of minimax-regret and of mean squared
forecast error. We then provide feasible weights that ensure good performance
under weaker assumptions than those required by existing approaches. Unlike
existing shrinkage methods, our approach borrows the strength - but avoids the
tyranny - of the majority, by targeting individual (instead of group) accuracy
and letting the data decide how much strength each individual should borrow.
Unlike existing empirical Bayesian methods, our frequentist approach requires
no distributional assumptions, and, in fact, it is particularly advantageous
in the presence of features such as heavy tails that would make a fully
nonparametric procedure problematic. |