Competing Models

Different agents compete to predict a variable of interest. All agents are Bayesian, but may have `misspecified models' of the world, i.e., they consider different subsets of explanatory variables to make their prediction. After observing a common dataset, who has the highest confidence in her predictive ability? We characterize it and show that it crucially depends on the sample size. With small samples, it is an agent using a small-dimensional model, in the sense of using a smaller number of variables relative to the true data generating process. With large samples, it is typically an agent with a large-dimensional model, possibly including irrelevant variables, but never excluding relevant ones. Applications include auctions of assets where bidders observe the same information but hold different priors.