  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.
