RDP 2003-11: How Should Monetary Policy Respond to Asset-Price Bubbles? Appendix B: Comparison with Kent and Lowe (1997)

Kent and Lowe (1997) present a simple model of an asset-price bubble that has similarities with ours. They derive optimal activist policy in their model for two of the cases we have examined: when the probability of the bubble collapsing is exogenous, and when this probability rises with the previous period's policy interest rate.^[20]

Kent and Lowe show that, when policy cannot affect the bubble's probability of collapse, optimal activist policy generates average inflation in their period 2 equal to the central bank's target rate of inflation. When policy can affect the bubble's probability of collapse, however, optimal activist policy generates average inflation in period 2 less than the central bank's target rate of inflation (where the averages are calculated over all possible outcomes for the bubble).

The qualitative nature of these results carries over to our model set-up. When policy cannot affect the bubble, average inflation in every year of our model is also equal to the central bank's target. When policy can affect the bubble, however, either by affecting its probability of bursting or its rate of growth, average inflation from year 2 onward is always less than the central bank's target when activist policy is implemented.^[21]

Kent and Lowe use their model to make the case that, when policy can affect the bubble's probability of collapse, it may make sense for the policy-maker to raise interest rates early in the life of the bubble, even though this will increase the likelihood of inflation being below target in the near term. As we have seen, this general case – for tightening policy early in the life of the bubble – survives in our model. What our model adds to this story is that ‘early in the life of the bubble’ may not last very long. For many of our simulations, within a couple of years or so of the bubble's inception, it is no longer clear whether optimal activist policy should be tighter or looser than the policy chosen by a sceptic.

Footnotes

Theirs is a 3-period model in which the bubble, which has formed in period 1, can either grow or collapse back to zero in period 2, and if it has grown, can grow further or collapse in period 3. Their periods should, therefore, probably be thought of as spanning more than one year. [20]

Recall that it takes two years for policy changes to affect inflation in our model. As for the Kent and Lowe model, in each year the averages must be calculated over all possible outcomes for the bubble, weighted by their appropriate probabilities. Calculated in this way, the averages are therefore equivalent to period-0 expectations. [21]