Stress Testing with Misspecified Models

Stress testing has become an important component of macroprudential regulation yet its goals and implementation are still being debated, reflecting the difficulty of designing such frameworks in the context of enormous model uncertainty. We illustrate methods for responding to possible misspecifications in models used for assessing bank vulnerabilities. We show how ‘exponential tilting’ allows the incorporation of external judgment, captured in moment conditions, into a forecasting model as a partial correction for misspecification. We also make use of methods from robust control to seek the most relevant dimensions in which a regulator’s forecasting model might be misspecified – a search for a ‘worst case’ model that is a ‘twisted’ version of the regulator’s initial forecasting model. Finally, we show how the two approaches can be blended so that one can search for a worst case model subject to restrictions on its properties, informed by the regulator’s judgment. We demonstrate the methods using the New York Fed’s CLASS model, a top-down capital stress testing framework that projects the effect of macroeconomic scenarios on U.S. banking firms.