Title

Competing Models

Author(s)

José Luis Montiel Olea José Luis Olea (Columbia University)

Pietro Ortoleva Pietro Ortoleva (Princeton University)

Mallesh Pai Mallesh Pai (Rice University)

Andrea Prat Andrea Prat (Columbia University)

Abstract

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.

Creation Date

2021-11

Section URL ID

Paper Number

2021-89

URL

https://arxiv.org/pdf/1907.03809.pdf

File Function

Jel

C20, C30

Keyword(s)

Models. Low-dimensional Model, High-dimensional Model

Suppress

false

Series

13