Competing Models

Agents compete to acquire an asset whose value depends on how well they can predict an unknown variable. Agents are Bayesian, observe identical data, but have different models: they use different subsets of explanatory variables to make their predictions. The winning model crucially depends on the sample size. With small samples, we present a number of results suggesting it is an agent using a low-dimensional model, in the sense of using a smaller number of variables relative to the true data generating process. With large samples, we show that it is generally an agent with a high-dimensional model, possibly including irrelevant variables, but never excluding relevant ones.