The Zero Lower Bound and Output Gap Uncertainty

            There is currently a great deal of uncertainty about the size of the output gap in the US, UK and elsewhere. Given the significant lags between fiscal policy decisions and their impact, does that mean we should be especially cautious in setting policy? This might seem like a rather academic question at present, because policymakers are not even trying to use fiscal policy to close the output gap, as this crystal clear post from Jonathan Portes shows. (The charts and arguments are for the UK, but you could write something similar for the US or elsewhere.) However, uncertainty about the output gap is often used as a justification for maintaining current policies, so it is a relevant question in that sense.

             I believe that there is a strong argument that goes in exactly the opposite direction. Uncertainty about the output gap should make us less cautious. This argument rests on two very reasonable assumptions: that monetary policy can impact on the economy more rapidly than fiscal policy, and that the Zero Lower Bound (ZLB) for nominal interest rates means that there is an asymmetry in what monetary policy can do. Let me try and illustrate the point with some stylised numbers.

            Imagine we are trying to set fiscal policy today with the aim of producing an outcome for the output gap and excess inflation in 2/3 years time. Interest rates are stuck at the ZLB, so as this outcome requires expansionary policy, we cannot use conventional monetary policy today. However we have the option of raising interest rates at any time.

Suppose our best guess is that output today is x% below the natural (constant inflation) rate, but we could easily be wrong. Suppose we set policy today to aim to eliminate that gap in 2/3 years: call this Policy A. Let us also assume for simplicity that if we are right about the output gap our policy succeeds. Call this scenario M. However, we think an equally likely case is that natural output today is 2% higher (scenario H), or 2% lower (scenario L). For simplicity those are the three possible states of the world, and they are all equally likely. In other words we are uncertain about the size of the output gap, but we want to close it and we have complete control over actual output.

 What is the expected outcome of this policy? In all three scenarios output is the same. However inflation will be below our target in scenario H, because we underestimated the size of the output gap. Again for simplicity, assume that for every 1% that output is below the natural rate, inflation is below its target by 1%. So in scenario H, where the natural level of output is higher than we thought inflation will be 2% below target. Assume symmetry: in scenario L, where we overestimate today’s output gap, inflation would be 2% above target, if interest rates stay at the ZLB.

However that is not the complete story, because in scenario L monetary policy can raise interest rates. It will do so, but assume that because of lags it only manages to cut excess inflation and the output gap by half. So with endogenous monetary policy, excess output and inflation will only be 1% in scenario L.

What are the expected costs of this policy? If our estimate of the output gap was right (scenario M), zero. But the other two scenarios are equally likely. If our loss function is quadratic in inflation and the output gap, then the social loss in scenario H is 4, but thanks to raising interest rates only 1 in scenario L. As all three scenarios are equally likely, the average loss is 5/3.

            Now consider Policy B where we aim to produce 1% more output in 2/3 years time. Call this the 'overshooting' policy. This might seem an odd thing to try and do, because under scenario M, where our estimate of the output gap is correct, we produce excess output and inflation. Once again conventional monetary policy rescues us to some extent, so in fact both inflation and output would be half a percent above target. But is it still an odd thing to do? No, because we should allow for uncertainty. The outcomes under the other two scenarios are shown in the table below. The average loss is 3.5/3.

		Excess inflation/output for unchanged interest rates	Excess inflation/output with endogenous interest rates	Loss
Policy A
	Scenario M	0	0	0
	Scenario L	2	1	1
	Scenario H	-2	-2	4
Policy B
	Scenario M	1	0.5	0.25
	Scenario L	3	1.5	2.25
	Scenario H	-1	-1	1

            

            In turns out we do better under the overshooting policy, Policy B. If this result seems paradoxical, think of it this way. In scenario H, where the current output gap is higher than we think it is, we can do nothing to correct our error. We suffer the full consequences of our mistake: higher unemployment. However in the opposite case, scenario L where the output gap is lower than we think, we have an insurance policy that can cover our mistake to some extent, because we can raise interest rates to moderate inflation. Because of the ZLB, this insurance policy only operates one way.

            Now of course these numbers are arbitrary, but the principle holds: with a one way insurance policy, its best to go for an overshooting policy to some degree.

            The only uncertainty in this story was the size of the output gap. We could achieve, using fiscal policy, exactly the level of output we wanted in 2/3 years time. In reality we cannot, of course. However exactly the same principle operates if the uncertainty is about the output forecast rather than (or as well as) the output gap. It is best to aim too high, because we have a one-way insurance policy. This is why a government that undertook austerity based on the assumption that, if everything went as expected, things would turn out OK was making an obvious mistake – the ZLB meant it had no option if things turned out worse.

So, the next time someone argues that we need austerity because we are uncertain about how large the output gap is, ask them why they are ignoring the option of raising interest rates if core inflation starts to rise.