Monday, 14 May 2012

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.     

4 comments:

  1. Interesting post, Ryan Avent over at Free Exchange has been desperately making this point for some time.

    Does the existence of unconventional monetary policy change the policy choices?

    For instance, Mr Osborne* could argue that he does have an insurance policy in the form of further increases in QE.

    Does your argument still hold without assuming that monetary policy is ineffective or the monetary policymakers are inept? I believe DeLong and Summers make this assumption in their recent working paper?

    Do you have any thoughts on today's twitter debate between Mr Hancock, Mr Smith and Mr Portes?

    Mr Hancock appears to believe that low interest rates are an indication of the success of the coalition's spending plans. I was under the impression that low interest rates on government debt indicate an economy locked in depression, and rates are likely to rise when/if the economy recovers? For example, Friedman (1968) argued that low interest rates were an indication that monetary policy had been too tight.

    Mr Smith appears to be unaware that net present value used in cost-benefit calculations for public sector investment use a real discount rate, and not a nominal discount rate. I find the fact that a well respected commentator on the economy, who writes for The Times, does not understand such a basic idea in public finance quite disturbing.

    *Of course this would require Mr Osborne to have some understanding of macroeconomics, a hypothesis which is rapidly being falsified by reality.

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  2. Panicy Finalist15 May 2012 04:33

    Thanks Simon,

    PPE finalist here revising for Monday. I think I understand the take home message from this post: That in a ZLB its better to err on the side of over stimulation via fiscal policy. Because if the stimulation in fact turns out to be too much we always have monetary policy to help out(unlike if we under stimulate, because of ZLB).

    I'm trying to show this in the 3 equation model, by shifting the IS curve (though fiscal policy) but having an uncertain Yn, and thus uncertain PCs. I think I've just about got it.

    However, normally when we compute the loss function we don't just take into account the distance of inflation from target but also the distance of output from the natural rate. Am I right to think that in H output will be below its natural rate while in L it will be above (but less above the better monetary policy responds)? If so, I don't think this changes the result as it's still better to err on the side of over stimulation (esp if we say we dislike yYn).

    Another effect which I think might also strengthen the result is that if we err on the side of over stimulation and 'the market' thinks that we have overestimated Yn, then it will expect higher inflation once the fiscal policy has fed through (Though I admit this effect may well be small). But higher inflation expectations would lower the ZLB intrest rate today, allowing output to improve today and not just tomorrow.

    One problem with this arguement is that it is better the worse monetary policy is in reacting to the over stimulation [at least in expectation] while your arguement is better the better monetary policy reacts. But we can have both so long as monetary policy isn't [expected to be] perfect.

    I hope you find the time to respond to this and let me know if any of what I've said is just plain wrong so I don't repeat the same mistakes on Monday!

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    Replies
    1. Don't panic! You are right that we would normally look at both excess inflation and the output gap in computing loss. However as (by construction) they are always the same here, we can just look at one. Best of luck for Monday!

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  3. Regulating an economy via interest rate adjustments in effect means regulating them by regulating capital spending or investment spending. Strikes me that makes as much sense as doing the regulation by adjusting spending on just say cars, roads, baked beans and massage parlours.

    As to the idea that interest rate adjustments influence credit card spending, there is one study which shows there is no such effect.

    Thoughts?

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