Designing Optimal Policy Rules Under Parameter Uncertainty: A Stochastic Dominance Approach

Abstract This paper proposes a novel Bayesian decision-theoretic framework for ranking and selecting simple macroeconomic policy rules in linear rational expectations models under structural parameter uncertainty. Unlike standard approaches that rely on point estimates, expected welfare losses, or worst-case scenarios, our framework utilizes stochastic dominance (SD) orderings of finite or infinite degree to account for the entire posterior distribution of welfare losses. This approach allows a policymaker – without a predetermined attitude toward random loss – to identify efficient sets of policy rules that are robust to all monotonic transformations of the underlying loss distributions. We introduce the Optimal Policy Feedback Coefficient and Minimized Welfare Loss functions to provide a feasible numerical algorithm for identifying SD-optimal rules. We apply this framework to the debate on price-level targeting versus inflation targeting within a richly specified DSGE model of the U.S. economy featuring financial frictions on both sides of the bank’s balance sheet. Our empirical results demonstrate that while the Taylor rule may achieve lower welfare losses than price-level rules, the result is highly dependent on the specific source of parameter uncertainty. Furthermore, our framework yields distinct policy recommendations compared to the standard Bayesian robust approach, suggesting more aggressive policy responses to supply, demand, and financial shocks.