Competing Models
This addresses model selection biases in economics and finance, such as in auctions and stock return factors, but is incremental in its theoretical analysis.
The paper tackles the problem of which predictive model agents believe is best based on subjective posterior mean squared error, showing that low-dimensional models are favored in small samples while high-dimensional models (including irrelevant variables but not excluding relevant ones) are preferred in large samples.
Different agents need to make a prediction. They observe identical data, but have different models: they predict using different explanatory variables. We study which agent believes they have the best predictive ability -- as measured by the smallest subjective posterior mean squared prediction error -- and show how it depends on the sample size. With small samples, we present results suggesting it is an agent using a low-dimensional model. With large samples, it is generally an agent with a high-dimensional model, possibly including irrelevant variables, but never excluding relevant ones. We apply our results to characterize the winning model in an auction of productive assets, to argue that entrepreneurs and investors with simple models will be over-represented in new sectors, and to understand the proliferation of "factors" that explain the cross-sectional variation of expected stock returns in the asset-pricing literature.