Competing Models

Abstract

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 overrepresented 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.

Narratives About the Macroeconomy

“…This approach is in line with a broad theoretical literature on causality and causal inference (Ellis and Thysen, 2021;Olea et al, 2021;Pearl, 2009;Spiegler, 2020aSpiegler, ,b, 2021.…”

Pathwise concentration bounds for Bayesian beliefs

“…In settings where multiple agents choose their actions based on the same observables, our concentration results can be used to quantify the minimal extent of the differences in their prior beliefs needed to rationalize different choices. For example, Olea, Luis, Ortoleva, Pai, and Prat (2021) showed that when observing signals of an object's value, misspecified agents with lower‐dimensional models have a higher willingness to pay after the first few observations, while correctly specified agents have a higher willingness to pay in the long‐run; our result on the speed of convergence may help to better identify the switching time.…”

Competitive Model Selection in Algorithmic Targeting

“…Liang (2020) considers games of incomplete information in which the players have data and use algorithms to derive their beliefs. Olea et al (2022) study a game between agents competing to predict a common variable, and where agents obtain the same data but differ in the algorithms they utilize for prediction. In all these papers, the algorithms under consideration are fixed exogenously.…”