Cheating with (Recursive) Models

TL;DR

This paper investigates how agents using recursive linear regression models can predict false correlations, showing that with more variables, they can falsely predict correlations close to perfect, regardless of true relationships.

Contribution

It characterizes the maximum false correlation that recursive models can predict under mean-variance constraints, revealing potential for highly misleading inferences.

Findings

False correlations can approach one as model size increases.

Agents can predict near-perfect correlations despite true independence.

Model misspecification leads to significant overestimation of relationships.

Abstract

To what extent can agents with misspecified subjective models predict false correlations? We study an "analyst" who utilizes models that take the form of a recursive system of linear regression equations. The analyst fits each equation to minimize the sum of squared errors against an arbitrarily large sample. We characterize the maximal pairwise correlation that the analyst can predict given a generic objective covariance matrix, subject to the constraint that the estimated model does not distort the mean and variance of individual variables. We show that as the number of variables in the model grows, the false pairwise correlation can become arbitrarily close to one, regardless of the true correlation.