Competing Models

Different agents compete to predict a variable of interest related to a set of covariates via an unknown data generating process. All agents are Bayesian, but may consider different subsets of covariates 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 size of the dataset. With small data, typically it is an agent using a model that is `small-dimensional,' in the sense of considering fewer covariates than the true data generating process. With big data, it is instead typically `large-dimensional,' possibly using more variables than the true model. These features are reminiscent of model selection techniques used in statistics and machine learning. However, here model selection does not emerge normatively, but positively as the outcome of competition between standard Bayesian decision makers. The theory is applied to auctions of assets where bidders observe the same information but hold different priors.