Measuring 'Dark Matter' in Asset Pricing Models

Abstract

We formalize the concept of ``dark matter'' in asset pricing models by quantifying the additional informativeness of cross-equation restrictions about fundamental dynamics. The dark matter measure captures the degree of fragility for models that are potentially misspecified and unstable: a large dark matter measure signifies that the model lacks internal refutability (weak power of optimal specification tests) and external validity (high overfitting tendency and poor out-of-sample fit). The measure can be computed at low cost even for complex dynamic structural models. To illustrate its applications, we provide quantitative examples applying the measure to (time-varying) rare-disaster risk and long-run risk models.

Keywords: Fragile beliefs, Unstable models, Misspecification and robustness, Out-of-sample fit, Semiparametric information bounds.

JEL Classification: C52, G12, D81, E32