Optimal monetary policy in a regime-switching economy

This paper is of interest for two reasons. First, it provides a simple algorithm for solving an optimal control problem in which the law of motion of the economy is a Markov regime-switching vector autoregression. Second, it applies this algorithm to study optimal monetary policy in a stylised small open economy model, which alternates randomly between two states: a `no-bubble' regime, in which the exchange rate fluctuates, in a stationary way, around its long-run equilibrium; and a `bubble' regime, in which the exchange rate (absent any offsetting impact of policy or exogenous shocks) increasingly deviates from it. We compute the optimal policy rule for this economy, as opposed to an optimised reaction function. This rule is regime-contingent in that policy response varies according to whether the economy is experiencing a bubble or not. The main results are as follows. First, while the optimal weights on output and inflation do not vary much between regimes, the optimal reaction to the asset price is highly dependent on the regime as well as the stochastic properties of the bubble. Second, uncertainty about the regime makes policy more cautious. Third, a policymaker uncertain about the true stochastic properties of the asset price tends to obtain a `robust' performance (i.e. minmax outcome) by responding little to the asset price. Finally, over-estimating the probability of an incipient bubble is generally more costly than under-estimating it