Prediction with Misspeci ed Models

Many decision-makers in the public and private sectors routinely consult the implications of formal economic and statistical models in their work. Especially in large organizations and for important decisions, there are often competing models. Of course no model under consideration is a literal representation of reality for the purposes at hand –more succinctly, no model is “true”–and di¤erent models focus on di¤erent aspects of the relevant environment. This fact can often be supported by formal econometric tests concluding that the models at hand are, indeed, misspeci…ed in various dimensions. There are well-developed practical Bayesian procedures, with solid theoretical foundations, for combining competing models in decision-making (Geweke, 2005, Section 1.5). But these procedures all condition on one of the models under consideration being true. Non-Bayesian model selection procedures may be less formal but proceed under the same maintained hypothesis. This leads to the common situation in which decision-makers are left to balance informally the various predictions and decisions that are formal consequences of competing economic and statistical models. In this circumstance serious attention is typically granted to the implications of models to which formal econometric procedures assign very little credence. The approach taken here draws on a literature long established in statistics and recently emerging in econometrics that dispenses with the condition that one of the