Macro Prediction with Micro Models: A New Model Selection Paradigm

The idea of using the accumulated prediction error, or APE, as a model selection criterion was originally proposed in the time series context. This article attempts to extend the use of APE to the comparison of linear models for panel data. We propose a generalized APE, or GAPE, assuming that the goal of modeling is to predict an aggregate statistic. We argue that in panel data analysis, it is more relevant to predict an aggregate statistic rather than individual future values. This gives rise to a new model selection paradigm, namely that the merit of a model should be evaluated in terms of the speciic objective of modeling. Our main result shows that GAPE in the current context can be decomposed into the summation of a goodness-of-t term and two penalty terms. In addition to penalizing model dimension, as most model selection methods do, GAPE also places penalty on the complexity of the prediction target. Comparisons between GAPE and the closely related BIC criterion are made both from an asymptotic perspective and through simulation.