Measuring Uncertainty of Optimal Simple Monetary Policy Rules in DSGE models

This paper presents a new approach to measure the parameter uncertainty for optimal simple monetary policy rules in the New Keynesian dynamic stochastic general equilibrium models. More precisely, we propose a new algorithm which enables to directly introduce parameter uncertainty into the optimal simple precommitment rule problem. As a result we find distributions of the optimal monetary policy reactions and the minimized welfare losses. To compare the distributions of the monetary policy parameters and the welfare losses we apply the first order stochastic dominance ordering (SD1). The SD1 inequality between the probability distribution is verified by means of the Kolmogorov-Smirnov test. The proposed algorithms are applied to the Erceg, Henderson and Levine (2000) small-scale closed economy model estimated for the Polish economy. For the welfare-loss-minimizing central bank, we examine three types of the dynamic specification of its policy rule: backward-, current- and forward-looking. Finally, for a given set of optimal and implementable monetary policy rules, we show that the fully specified forward-looking monetary policy rule with interest rate smoothing mechanism minimizes the welfare-loss in the sense of the stochastic ordering SD1.