Measuring “Dark Matter” in Asset Pricing Models

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 indicates 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.