Financial vulnerability and monetary policy

We present a microfounded New Keynesian model that features financial vulnerabilities. Financial intermediaries' occasionally binding value-at-risk constraints give rise to variation in the pricing of risk that generates time-varying risk in the conditional mean and volatility of the output gap. The conditional mean and volatility are negatively related: during times of easy financial conditions, growth tends to be high, and risk tends to be low. Monetary policy affects output directly through the investment-savings curve, and indirectly through the pricing of risk that relates to the tightness of the value-at-risk constraint. The optimal monetary policy rule always depends on financial vulnerabilities in addition to the output gap, inflation, and the natural rate of interest. We show that a classic Taylor rule exacerbates deviations of the output gap from its target value of zero relative to an optimal interest rate rule that includes vulnerability. Simulations show that optimal policy significantly increases welfare relative to a classic Taylor rule. Alternative policy paths using historical examples illustrate the usefulness of the proposed policy rule.