Growth-at-risk and macroprudential policy design

Abstract

This paper explores the foundations for the application of the empirical growth-at-risk (GaR) approach to the assessment and design of macroprudential policies. It starts considering a stylized benchmark linear specification of the empirical GaR approach in combination with a linear–quadratic social welfare criterion that rewards expected GDP growth and penalizes the gap between expected GDP growth and GaR. If the growth rate follows a normal distribution, this welfare criterion can be microfounded as consistent with expected utility maximization under preferences for GDP levels exhibiting constant absolute risk aversion. The benchmark formulation implies an optimal policy rule linear in the risk indicator and an optimal gap between expected growth and GaR that does not depend on the time-varying risk indicator and is inversely related to the cost-effectiveness of macroprudential policy and the risk preference parameter. Extensions of the benchmark formulation show the potential to adapt the analysis and its insights to the richer specifications typically considered in empirical work.