RDP 2005-04: Monetary Policy, Asset-Price Bubbles and the Zero Lower Bound 5. Conclusions

In this paper we have used a simple model of a closed economy to investigate what impact the ZLB on nominal interest rates has on the recommendations of an activist policy-maker attempting to respond optimally to an asset-price bubble. In assessing our results, it should be remembered that this framework almost certainly magnifies the impact of the ZLB, most notably because it does not allow for other arms of policy (or unconventional monetary policy operations) to help extricate the economy from a situation in which policy has become constrained by the ZLB.

For example, the possibility of encountering the ZLB in the future would clearly hold fewer fears for monetary policy-makers in an economy with sound public finances than in one burdened with high net public debt and persistent deficits. In the former, policy-makers would be aware that fiscal policy could be called upon, if necessary, to aid in stimulating the economy and forestalling any risk of deflation becoming entrenched. Likewise, our closed-economy setting precludes the use – as advocated for Japan by numerous authors, such as Svensson (2001) and McCallum (2000) – of exchange rate policy as a tool to help rescue an economy suffering from the effects of a severe asset-price bubble collapse.

Notwithstanding these caveats, our framework has the twin advantages of simplicity and transparency, while at the same time capturing the key stylised features of the interaction between output, inflation and real interest rates. It thus allows us to analyse at least the direction in which the presence of the ZLB might influence the recommendations of an activist policy-maker trying to respond optimally to a bubble. It also allows us to understand intuitively the mechanisms driving the results of such analysis, and how the relative importance of these mechanisms might vary as we alter either the stochastic properties of the bubble or the parameters which characterise the economy.

Table 1 summarises the results from our various numerical simulations for the case of an economy with a steady-state neutral nominal interest rate of i* = 3 per cent. For each scenario, the table shows, as time proceeds and the bubble grows, whether the impact of the ZLB on an activist's recommendations would be to make to make them tighter (+), looser (−) or little different (=) than otherwise (where ‘little different’ here denotes an impact of less than 25 basis points).

Table 1: Impact of the ZLB on an Activist's Recommendations
Tighter (+), looser (−), or little different (=) than otherwise, i* = 3.0
Scenario Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Policy can't affect bubble
pt = 0.2, baseline model = = =
pt = 0.4, baseline model = = = = =
pt = 0.4, β = 0.5 = =
pt = 0.4, λ = 0.6 = = = = = =
pt = 0.4, λ = 1.0 = = = =
Policy affects bubble growth = = = =
Policy affects probability of bursting
p* = 0.4, δ = 0.2 = = + +

There are two broad sets of lessons worth highlighting. The first concerns the appropriate level of the steady-state neutral nominal interest rate – the sum of the economy's neutral real interest rate and policy-makers' choice of target inflation rate. From Table 1 we see that, even for a very low neutral nominal interest rate of i* = 3 per cent, in most scenarios the ZLB has relatively little effect on an activist policy-maker until the bubble has become quite large.[20] Moreover, as Figures 3, 6 and 8 confirm, even those ‘ZLB effects’ in Table 1 which are not negligible dissipate rapidly for neutral nominal interest rates above 3 per cent.

These observations suggest that fears of encountering the ZLB should not be overstated, unless the neutral nominal interest rate in the economy is very low. They thus have an obvious implication for policy-makers who wish to avoid having to worry about the ZLB when trying to cope with an asset-price bubble. Such policy-makers should simply avoid targeting too low an inflation rate, so as to ensure that the economy's neutral nominal interest rate is in turn not too low.

The results in Table 1 also shed light on how the ZLB might affect the recommendations of an activist policy-maker, facing an asset-price bubble, for a given target inflation rate. We may interpret these results through our ‘insurance’ framework for analysing the impact of the ZLB on an activist's thinking.

Recall that there are three forms of ‘insurance’ which a policy-maker can take out against the risk of encountering the ZLB due to the future bursting of an asset-price bubble. Two of these – to attempt to deflate the bubble before it can grow further, or to restrain its future growth – are available only if policy-makers can influence the future behaviour of the bubble. The third, to build a buffer of extra inflation and output against its future collapse, is always available to policy-makers in our model.

The particular scenarios and choices of parameter values we have considered in this paper, as summarised in Table 1, might suggest that this third form of insurance tends to be the most cost-effective.[21] The key point, however, is that this is not uniformly so – and, for different scenarios, the form of insurance which is most cost-effective seems to depend delicately upon the parameters describing both the economy and the stochastic properties of the bubble. Indeed, in some instances, such as when policy-makers can influence a bubble's probability of bursting, it appears that the most effective form of insurance for an activist can even switch suddenly and decisively from one period to the next. Overall, therefore, whether the ZLB should cause policy to be tighter or looser than otherwise, while a bubble is growing, would seem to be a subtle question – even after abstracting from the significant informational difficulties facing policy-makers in practice.


The two exceptions are: when the bubble's probability of bursting may be influenced by policy; and when the bubble is exogenous but the economy is relatively unresponsive to policy-makers' actions. In these two cases a sizeable ‘ZLB effect’ arises when the bubble is still only of a moderate size. [20]

It is worth recalling, however, the caveat noted in Section 3.1 that the cost of this third policy option would be higher, per unit of insurance against encountering the ZLB, were inflation expectations in our model economy not assumed to be purely backward-looking. That said, this would likely only serve to further complicate the issue of which form of insurance would be judged by policy-makers to be most cost-effective for different bubbles at different times, and therefore reinforce the conclusions which follow. [21]