Measuring the 'Dark Matter' in Asset Pricing Models

Abstract

We propose a new quantitative measure of model fragility, based on the tendency of a model to over-fit the data in sample with poor out-of-sample performance. We formally show that structural economic models are fragile when the cross-equation restrictions they impose on the baseline statistical model appear excessively informative about combinations of model parameters that are otherwise difficult to estimate. We develop an analytically tractable asymptotic approximation to our fragility measure which we use to identify the problematic parameter combinations. Using these asymptotic results, we diagnose fragility in asset pricing models with rare disasters and long-run consumption risk.

Keywords: Cross-equation restriction; Information theory; Limited information likelihood; Model fragility and complexity; Robustness; Disaster risk; Long-run risk

JEL Classification: C1, D83, E44, G12