Competing Models

We develop a model in which different agents compete to predict a variable of interest. This variable is related to observables via an unknown data generating process. All agents are Bayesian, but may have ‘misspecified models’ of the world, i.e., they consider different subsets of observables 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 big data, we show it is typically ‘large dimensional,’ possibly using more variables than the true model. With small data, we show (under additional assumptions) that it is an agent using a model that is ‘small-dimensional,’ in the sense of considering fewer covariates than the true data generating process. The theory is applied to auctions of assets where bidders observe the same information but hold different priors.