Underspecification of the Empirical Return-Factor Model and a Factor Analytic Augmentation as a Solution to Factor Omission

Abstract

This empirical paper comprehensively sets out the impact of underspecification on a key foundational concept in empirical finance, the linear factor model. It places emphasis on the extensive consequences of factor omission for model estimation and interpretation. Factor omission in time-series models that relate asset returns to pre-specified factor sets is a common problem. A proposed standard and widely-used solution is the inclusion of a residual market factor which is assumed to be a catch-all proxy for omitted factors. This study shows that a specification that incorporates a set of carefully selected macroeconomic factors will be underspecified. The inclusion of residual market factors will alleviate but not eliminate the consequences of underspecification. Although the early use of factor analytically derived factor scores in factor models has been criticized, augmenting a model comprising pre-specified factors with statistical factors derived from the residuals results in an accurately specified model for which the diagonality assumption holds. Consequently, this paper shows that a factor analytic augmentation is an effective and readily implementable solution to the factor omission problem.

Keywords: linear factor model, underspecification, Arbitrage Pricing Theory, asset pricing

JEL Classification: C01, C22, C58, G12