Balanced variable addition in linear models

Abstract

This paper studies what happens when we move from a short regression to a long regression in a setting where both regressions are subject to misspecification. In this setup, the least-squares estimator in the long regression may have larger inconsistency than the least-squares estimator in the short regression. We provide a simple interpretation for the comparison of the inconsistencies and study under which conditions the additional regressors in the long regression represent a ‘balanced addition’ to the short regression.