Generalized aggregation of misspecified models: With an application to asset pricing

We propose a generalized aggregation approach for model averaging. The entropy-based optimal criterion is a natural choice for aggregating information from many “globally” misspecified models as it adapts better to the underlying model uncertainty and obtains more robust approximations. Unlike almost all other approaches in the existing literature, we do not require a “reference model,” or a true data generation process contained in the set of models — neither implicitly nor in otherwise popular limiting forms. This shift in paradigm prioritizes stochastic optimization and aggregation of information about outcomes over parameter estimation of an optimally selected model. Stochastic optimization is based on a risk function of aggregators across models that satisfies oracle inequalities. Our generalized aggregators relax the common perfect substitutability of the candidate models, implicit in linear averaging and pooling. The aggregation weights are data-driven and obtained from a proper (Hellinger) distance measure. The empirical results illustrate the performance and economic significance of the aggregation approach in the context of stochastic discount factor models and inflation forecasting.