Misspecified Model Estimation and Its Impact on Predictions

TL;DR

This paper examines how misspecification of population coefficients in a linear model affects prediction accuracy, especially under certain conditions like residual information and alignment with latent factors.

Contribution

It provides a theoretical analysis of prediction distortions caused by coefficient misspecification in a linear model with applications to bias and consumer research.

Findings

Misspecification leads to systematic prediction errors.

Residual information influences the extent of prediction distortion.

Alignment between misspecification and latent-to-coefficient mapping affects bias.

Abstract

We study a linear statistical model where outcomes depend on regressors with fixed population coefficients and observation-specific latent coefficients, along with measurement errors. A decision-maker estimates population coefficients and uses the estimates to predict the latent coefficients for a given observation. We analyze how misspecification of some population coefficients distorts predictions, investigating comparative statics with respect to: (1) residual information in regressors associated with misspecified coefficients after projecting out those associated with free coefficients, (2) alignment between misspecification vector and latent-to-coefficient mapping. Applications include employee rating with unconscious bias and LLM-mediated consumer research.