Competing Models

TL;DR

This paper analyzes how different agents with varying models predict outcomes and which model they believe is best, depending on sample size, with implications for auctions, market sectors, and asset pricing.

Contribution

It characterizes the conditions under which low-dimensional versus high-dimensional models outperform others in predictive accuracy as sample size varies.

Findings

Small samples favor low-dimensional models.

Large samples favor high-dimensional models, including irrelevant variables.

Implications for auctions, sector entry, and asset pricing factors.

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 over-represented 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.