Monetary Policy, Asset-Price Bubbles and the Zero Lower Bound

We use a simple model of a closed economy to study the recommendations of monetary policy-makers, attempting to respond optimally to an asset-price bubble whose stochastic properties they understand. We focus on the impact which the zero lower bound (ZLB) on nominal interest rates has on the recommendations of such policy-makers. For a given target inflation rate, we identify several different forms of `insurance' which policy-makers could potentially take out against encountering the ZLB due to the future bursting of a bubble. Even with perfect knowledge of the bubble process, however, which of these will be optimal varies from one type of bubble to another and, for certain bubbles, from one period to the next. It is therefore difficult to say whether the ZLB should cause policy-makers to operate policy more tightly or loosely than they would otherwise do, while a bubble is growing -- even after abstracting from the informational difficulties they face in practice. We also examine the implications of the ZLB for policy-makers' preferences as to their inflation target. Policy-makers who wish to avoid concerns about the ZLB should take care not to set too low a target -- especially if the neutral real interest rate is low.