That referendum was fun. Shall we do it again?

Whether the UK as a whole gets to choose whether to have a referendum on continuing membership of the European Union depends on the result of the general election in 2015. Given that we have this choice, it is worth thinking about similarities and differences between the EU referendum and the referendum on Scottish independence.

The key similarity is that the immediate economic consequences of independence in both cases are negative: according to John Van Reenen, even more so with the UK leaving the EU. In both cases nationalism will play an important role. I would argue that in both cases independence is seen by many as a means to a particular end. With Scotland, it was a way of ensuring that Scotland would not be governed by a right wing Conservative party. With the EU, it is a way of stopping large scale migration into the UK.

Is another similarity that the established parties are likely to be united in arguing against independence? There must be serious doubt about this. I suspect that Cameron has a strong preference for continued membership, and even that in his eyes the referendum is largely a political ploy to stop Conservative voters moving to UKIP in 2015. However Cameron also has a preference for remaining the leader of his party. He is very unlikely to get significant changes to the terms of EU membership before the referendum, including the free movement of labour. There are said to be between 50 and 100 Conservative MPs who will argue for leaving the EU whatever the outcome of Cameron’s negotiations. There are about 300 Conservative MPs at present. It is therefore possible that, once the negotiations have ended with little gained, a majority of Tory MPs will want to exit from the EU.

This leads to one clear difference between the two referendums. I think it is fair to say that outside Scotland few took the chances of a Yes vote seriously until the final weeks of the campaign. There are three reasons for thinking that will not happen with the EU referendum. First, UK public opinion has until quite recently shown a majority in favour of leaving the EU. Here are the polls conducted by YouGov.

Second, unlike Scottish independence, a majority of the UK press will be arguing for exit from the EU. Third, to make his negotiating stance credible, Cameron will have to at least give the impression that he might decide to recommend leaving the EU if he does not get significant concessions. As I note above, he will not have to try very hard.

This has an important implication which I think has been underestimated by many. Once the election result is known in 2015, if the Conservatives win there is a distinct possibility that the UK may vote to leave the EU. That kind of uncertainty is likely to be bad for non-residential investment, during a period in which we might hope that investment demand takes over from consumption as a primary driver of growth. We also know that, if the Conservatives win the next election, there will be a renewed fiscal contraction. With interest rates likely to be close to their lower bound, there remains limited scope for monetary stimulus to counter these influences.

So this is one important difference between the two referendums. Because most people were assuming a No vote until the last few weeks of the Scottish campaign, it seems unlikely there was sufficient uncertainty for a long enough period to have damaged the Scottish economy, and as far as I know there is no evidence that it did. In contrast, the two years of uncertainty from 2015 and 2017 is almost bound to be damaging for the UK economy.

Inflation risks

When it comes to the issue of when interest rates should start rising, one of the points I and others have often made is that the risks are not symmetric. If inflation starts rising faster than we expect monetary policy can quickly respond. Alternatively if we actually have more ‘spare capacity’ than we currently believe, it may take some time for this to become apparent (inflation is more sticky when it gets low), and the zero lower bound limits what monetary policy can do.

In this light, the following table from the Bank of England’s inflation report issued today is rather interesting. 

In scenario 1, there is more slack in the labour market than the Bank currently thinks. In scenario 2, firms are currently working at a higher rate of capacity utilisation than the Bank estimates. In both scenarios monetary policy is endogenous. Inflation is higher in scenario 2, but monetary policy succeeds in getting it back to target by the middle of 2017. In scenario 1, inflation remains below target throughout the period.

Now as a macroeconomist I really want to know more. These are different shocks, so they are not a pure test of asymmetry. The path of interest rates is not shown, so we do not know how much of a constraint the zero lower bound is (if at all) in scenario 1. In scenario 1 unemployment falls quite a lot more than in the central projection, but the additional GDP growth seems small by comparison. The opposite is true in scenario 2. This is undoubtedly a result of different shocks being applied, but all the report tells us is that judgement was used in deciding how to shock the model to best capture each scenario. As I am sure Tony Yates would say, it would be nice for those who are interested in this detail to know a bit more.

However, putting all these qualifications aside, these simulations are welcome given all the discussion underway. They suggest that the upside risks to inflation are small, because monetary policy is capable of responding quickly. Overestimating the degree of current slack does not lead to inflation ‘taking off’. Perhaps this helps to explain why the Bank appears to some to be rather relaxed about the need to raise rates.     

Humility and Chameleons

Macroeconomics tells you to (temporarily) raise, not cut, government spending when we have a recession caused by deficient demand and interest rates are at their lower bound. That is the claim that some of us make. Others say we are being far too sure of ourselves and our subject, in part because there exist models where this is not true. As a result, we should not loudly complain when politicians do not follow this advice. A bit more humility please.

If you think we should have more humility, imagine the following. The UK or US government tomorrow abolishes their independent central bank, and immediately raises rates to 5%, saying it was about time savers had a better deal. Well macroeconomists generally think that independent central banks are a good idea, and we nearly all believe that raising interest rates when inflation is below target and unemployment is high is crazy. But wait a minute. There are models that suggest keeping interest rates low is causing low inflation, and that raising rates could stimulate the economy - I discuss one here. So perhaps we should not be critical of a government that did this. We should be humble, and leave the politicians to do as they please while we get on with our research. Let us make sure we are absolutely sure before shouting too loud.

Why is that wrong? Two reasons. First, the existence of a model that says higher interest rates could stimulate the economy is not in itself evidence that it might. In an interesting paper, Paul Pfleiderer talks about Chameleon models. He defines a chameleon model as “built on assumptions with dubious connections to the real world but nevertheless has conclusions that are uncritically (or not critically enough) applied to understanding our economy.” The model that I discussed where higher rates could stimulate the economy assumes (among other things) agents believe the inflation target is negative, and that raising rates will show them they are wrong. Possible, but highly improbable.

Second, economic policy always takes place in an uncertain environment. Raising interest rates might have reduced inflation in the past, but maybe this time is different? If we wait until we are all absolutely sure about the impact of a policy change, we will wait forever. However, if we are more than 90% certain that raising interest rates, or cutting government spending, will make the recession worse, we should say so. If politicians ignore this advice, we should make sure everyone knows. This is no intellectual game - people’s welfare is at stake.

The two arguments why the Zero Lower Bound matters

I think it is important to distinguish between two arguments why the Zero Lower Bound (ZLB) for nominal interest rates matters. I will label these the first and second, and economists and statisticians will soon [1] see why these labels have some significance. The first argument is debatable, but the second is I believe very difficult to argue against.

The first argument why the ZLB matters is that unconventional monetary policy either does not work, or hits limits on what it can do, and these constraints bite. In short, monetary policy at the ZLB cannot fully achieve monetary policy goals. The second argument about why the ZLB matters is that the impact of monetary policy becomes more uncertain. Under the second argument, it is possible for some particular dose of unconventional monetary policy to duplicate what interest rate policy might otherwise achieve, but there is more uncertainty about what that appropriate dose is. The impact of any unconventional monetary policy action is therefore more unpredictable than the impact of conventional policy.

Much of the discussion of unconventional monetary policy involves the first argument. An important feature of Quantitative Easing (QE) is that its size is potentially unbounded - the central bank can create as many reserves as it likes. So if the impact of each unit of QE on the economy is constant, even if this constant is small, if we knew what that constant was we just scale up the programme so it has the desired effect. However, it seems to be much more likely that the policy involves diminishing returns, but to be honest I have no idea whether that means there are limits to what the policy can currently do. There are also some who worry that unconventional monetary policy has dangerous side effects on financial stability if it becomes too large. As I said, the first argument is debatable.

What seems clear to me is that we know much less about the impact of QE, or other kinds of unconventional monetary policy, than we do about conventional monetary policy. This almost follows by definition: we have well established models for conventional policy, and much more data to check these models against. What data we have also suggests the impact of unconventional monetary policy is more uncertain. (This is the conclusion drawn by John Williams, who has done a good deal of work on their impact, and I have never heard anyone argue against this view.) That is why I think it is very difficult to deny that the impact of monetary policy at the ZLB is much more uncertain compared to monetary policy outside the ZLB. [2]

Why do I make this distinction? Good policy tries not only to achieve the best outcome for the economy, but it also tries to reduce the uncertainty associated with that outcome. Indeed, we might well be prepared to sacrifice some of the former for some of the latter: uncertainty is in general undesirable. A standard way to judge the merits of a particular rule for macro policy, for example, is to ask whether it reduces the variance of output or inflation when the economy is hit by a standard set of shocks.

Let me return to an old friend. Suppose you are a doctor, and you have two medicines to treat a disease. One is reliable, but the other requires trial and error to get the correct dose, and occasionally has nasty side effects. In these circumstances, you would rather not run out of the reliable medicine. Indeed, you would want to go out of your way to avoid running out of the reliable medicine.

Seen from this perspective, it becomes almost undeniable that fiscal austerity at or near the ZLB is a dangerous policy. By making us more reliant on unconventional monetary policy it increases macroeconomic uncertainty. It makes it more likely that we will have to resort to the unreliable medicine. I think too much of the argument over whether monetary policy is all you need focuses on the first reason why the ZLB may be important, and ignores the second. [3]

[1] I was tempted to write ‘in a moment’ rather than ‘soon’, but decided a bad pun might detract from the main text.

[2] The Williams paper also elaborates on a well known idea that uncertainty about the impact of policy instruments should make policy makers cautious in using those instruments. I think this is an additional consideration, which would reinforce the point I’m making here. I also agree that good policy should take into account the characteristics of uncertainties arising from the economy, and have used this to argue - for example - that policymakers should over rather than under estimate the size of the output gap at the ZLB.

[3] This is not an argument about whether fiscal stimulus is more or less reliable than monetary stimulus, interesting though that question is. All I require is that an austerity policy reduces short run aggregate demand, which it clearly does. It also does not say that there are no circumstances in which we should undertake austerity at or near the ZLB - in theory the benefits of austerity could be so great that they outweigh the costs of putting us in a dangerous place. In the absence of a significant and rising default premium on debt, I do not think those benefits exist, but that is a separate argument.

The danger of self-fulfilling output gap pessimism

The debate about the size of the output gap (the difference between what output is now and what it could be without generating accelerating inflation) is taking place in most countries as we struggle to emerge from the Great Recession. This post is about how policy makers handle that uncertainty. If you think you are pretty sure what the size of the output gap is, you need read no further.

Let me try and crystallise this uncertainty in a simple binary fashion. One possibility is that since the recession innovation and technical progress (lets call this ‘underlying productivity’) has not grown as fast as we might have expected based on pre-recession trends. We have two major pieces of evidence for this. The first is survey data where firms are asked how much spare capacity they have. If underlying productivity had continued at pre-recession pace, we would expect them to be reporting more spare capacity than they currently are. The second is the behaviour of inflation: if the output gap was large and negative we would expect inflation to be falling faster than it is. (A nice summary is provided by Greg Ip.)

The other possibility is that supply is somehow following demand. Now the concept that economists normally have of supply does not do this: we think of production functions with capital, labour and technologically determined productivity. There may be some endogeneity here: less demand leads to less investment, which reduces capital a bit, and if innovation has to be embodied in new capital this can slow technical progress. Perhaps in recessions where wages are low, people want to work less. But the evidence from previous business cycles is that this endogeneity is not large enough to make supply largely follow demand. In normal business cycle downturns, firms report that they have plenty of spare capacity and inflation falls.

Although the traditional ‘production function’ notion of supply has served us reasonably well in the past, today it gives us a serious puzzle - why has underlying productivity slowed so much following this particular recession? Now the extent of this puzzle varies from country to country. The productivity puzzle is particularly acute in the UK, and much less in the US [For an analysis of the US position, see here (HT Econbrowser).] . In the UK, if actual productivity really does tell us how underlying productivity has behaved since the recession (as the survey evidence and perhaps inflation suggests), it would be a slowdown that is almost unprecedented in UK history. (For some international examples of previous finance led recessions, see Mark Thoma here.)

Keeping things simple, we can think of two policy responses. The ‘pessimistic’ response is to assume that underlying productivity growth really has slowed, while an ‘optimistic’ response would hope that once demand gets going, supply will follow. Although this issue is normally discussed in the context of monetary policy, long term fiscal plans also depend (in a rational world) on estimates of long term output (i.e. on supply) rather than short term movements in demand. In the UK there is a target for the future cyclically adjusted budget deficit. Last year we saw the OBR revise down its estimate for underlying supply, and future fiscal plans were tightened as a result. They could well do the same again quite soon (see this recent study from the Social Market Foundation).

Which response we choose (or more realistically, lean towards) depends in part on which view about supply we think is more probable. But it should also depend on the size of the mistake that will be made if this belief is wrong. The mistake we make if we adopt the optimistic view and go for expansionary policy but it turns out supply has indeed fallen is straightforward: we get inflation without any additional growth. The mistake we make if we are pessimistic and pursue a more contractionary policy is more unusual. If supply follows demand, and yet we adjust demand to match supply, we run the danger of self-fulfilling pessimism. In monetary policy we focus on inflation rather than the output gap, and because inflation is sticky, the output gap steadily falls away without any above trend growth, and inflation stays near target. With fiscal policy we cut future spending to match lower expectations about supply, but expectations about future government spending influence spending decisions today, reducing demand and therefore supply.

So how costly is each mistake? Higher inflation without higher growth is not good, but fortunately we will see it when it happens, and we have a well tested tool with which to deal with it - raising interest rates. So we will get a year or two of above target inflation. The mistake on the other side is potentially much larger, for two reasons. One I have talked about before: at the zero lower bound, it is more difficult to raise demand once we realise the mistake. The other is the more worrying. It may take some time before we see the mistake. At some point we will realise that we could have had GDP a good few percentages points higher than we did for a good few years, without a significant increase in inflation. But it might take some time for that realisation to occur. (For example, an unexpected positive demand shock that does not raise inflation.) That could lead to a cumulated percentage output loss in double figures. These are lost resources that we will never get back. There is an even worse outcome, which is that although supply might be elastic to demand in the short term, it becomes less so as demand stays low. In this case the cost in terms of lost GDP might continue forever.

In these circumstances, it seems to me that policy should lean towards being optimistic about supply, even if we are somewhat sceptical that it is really following demand - because the costs of self-fulfilling output gap pessimism could be so high.

This has some similarities with the position policymakers found themselves in during 2010. Although the chances that markets would suddenly stop buying government debt in countries outside the Eurozone seemed small even then, the scale of the damage if they had done so was thought sufficiently large that it justified switching to austerity. I have always thought that this reaction was quite understandable, and my main quarrel has been that positions were not changed when it became clear during 2011 that this risk was negligible. If policymakers were highly risk averse then, a similar attitude should make them very worried about self-fulfilling output gap pessimism today.  

One more time – good policy takes account of risks, and what happens if they materialise

From the Guardian's report of Mervyn King’s press conference today, where the Bank of England lowers forecast UK growth this year to zero.

Paul Mason of Newsnight suggests that the Bank of England should stop trying to use monetary policy to offset the impact of chancellor George Osborne's fiscal tightening, and call for a Plan B instead.

King rejects the idea, saying that Osborne's plan looked "pretty sensible" back in 2010. Overseas factors have undermined it, he argues.

Now Mervyn King had little choice but to say this, but he is wrong (and probably knows he is wrong) for a simple reason. Even if the post-2010 Budget forecast of 2.8% growth in 2012 had been pretty sensible, there were risks either side. There always are, although the nature of the recession probably made these risks greater than normal. It is what you can do if those risks materialise that matters.

Now if growth had appeared to be stronger than 2.8%, and inflation becomes excessive, the solution is obvious, well tested and effective – the Bank of England raises interest rates. But if growth looked like falling well short of 2.8%, the solution – more Quantitative Easing - is untested and very unclear in its effectiveness. (And before anyone comments, the government knows it has no intention of telling the Bank to abandon inflation targets.) With this basic asymmetry, you do not cross your fingers and hope your forecasts are correct. Instead you bias policy towards trying as far as possible to avoid the bad outcome. You go for 3.5% or 4% growth, knowing that if this produced undesirable inflation you could do something about it. That in turn meant not undertaking the Plan A of severe austerity.

So all the talk about how much austerity, or the Eurozone, or anything else, caused the current UK recession is beside the point when it comes to assessing the wisdom of 2010 austerity. Criticising the Bank of England for underestimating inflation in the past is even more pointless – do those making the criticism really think interest rates should have been higher two or three years ago? Even if the Euro crisis has been unforeseeable bad luck for the government (although I think excessive austerity is having its predictable effect there to), the government should not have put us in a position where we seem powerless to do anything about it.

If you are sailing a ship near land, you keep well clear of the coast, even if it means the journey may take longer.  So the fact that the economy has run aground does not mean the government was just unlucky. You do not embark on austerity when interest rates are near zero. Keynes taught us that, it is in all the textbooks, and a government bears responsibility when it ignores this wisdom. To the extent that the government was encouraged to pursue this course by the Governor of the Bank of England, that responsibility is shared.

Consumption and Complexity – limits to microfoundations?

One of my favourite papers is by Christopher D. Carroll: "A Theory of the Consumption Function, with and without Liquidity Constraints." Journal of Economic Perspectives, 15(3): 23–45. This post will mainly be a brief summary of the paper, but I want to raise two methodological questions at the end. One is his, and the other is mine.

Here are some quotes from the introduction which present the basic idea:

“Fifteen years ago, Milton Friedman’s 1957 treatise A Theory of the Consumption Function seemed badly dated. Dynamic optimization theory had not been employed much in economics when Friedman wrote, and utility theory was still comparatively primitive, so his statement of the “permanent income hypothesis” never actually specified a formal mathematical model of behavior derived explicitly from utility maximization. Instead, Friedman relied at crucial points on intuition and verbal descriptions of behavior. Although these descriptions sounded plausible, when other economists subsequently found multiperiod maximizing models that could be solved explicitly, the implications of those models differed sharply from Friedman’s intuitive description of his ‘model.’...”

“Today, with the benefit of a further round of mathematical (and computational) advances, Friedman’s (1957) original analysis looks more prescient than primitive. It turns out that when there is meaningful uncertainty in future labor income, the optimal behavior of moderately impatient consumers is much better described by Friedman’s original statement of the permanent income hypothesis than by the later explicit maximizing versions.”

The basic point is this. Our workhorse intertemporal consumption (IC) model has two features that appear to contradict Friedman’s theory:

1)      The marginal propensity to consume (mpc) out of transitory income is a lot smaller than the ‘about one third’ suggested by Friedman.

2)      Friedman suggested that permanent income was discounted at a much higher rate than the real rate of interest

However Friedman stressed the role of precautionary savings, which are ruled out by assumption in the IC model. Within the intertemporal optimisation framework, it is almost impossible to derive analytical results, let alone a nice simple consumption function, if you allow for labour income uncertainty and also a reasonable utility function.

What you can now do is run lots of computer simulations where you search for the optimal consumption plan, which is exactly what the papers Carroll discusses have done. The consumer has the usual set of characteristics, but with the important addition that there are no bequests, and no support from children. This means that in the last period of their life agents consume all their remaining resources. But what if, through bad luck, income is zero in that year. As death is imminent, there is no one to borrow money from. So it therefore makes sense to hold some precautionary savings to cover this eventuality. Basically death is like an unavoidable liquidity constraint. If we simulate this problem using trial and error with a computer, what does the implied ‘consumption function’ look like?

To cut a long (and interesting) story short, it looks much more like Friedman’s model. In effect, future labour income is discounted at a rate much greater than the real interest rate, and the mpc from transitory income is more like a third than almost zero. The intuition for the latter result is as follows. If your current income changes, you can either adjust consumption or your wealth. In the intertemporal model you smooth the utility gain as much as you can, so consumption hardly adjusts and wealth takes nearly all the hit. But if, in contrast, what you really cared about was wealth, you would do the opposite, implying an mpc near one. With precautionary saving, you do care about your wealth, but you also want to consumption smooth. The balance between these two motives gives you the mpc.

There is a fascinating methodological issue that Carroll raises following all this. As we have only just got the hardware to do these kinds of calculation, we cannot even pretend that consumers do the same when making choices. More critically, the famous Freidman analogy about pool players and the laws of physics will not work here, because you only get to play one game of life. Now perhaps, as Akerlof suggests, social norms might embody the results of historical trial and error across society. But what then happens when the social environment suddenly changes? In particular, what happens if credit suddenly becomes much easier to get?

The question I want to raise is rather different, and I’m afraid a bit more nerdy. Suppose we put learning issues aside, and assume these computer simulations do give us a better guide to consumption behaviour than the perfect foresight model. After all, the basics of the problem are not mysterious, and holding some level of precautionary saving does make sense. My point is that the resulting consumption function (i.e. something like Friedman’s) is not microfounded in the conventional sense. We cannot derive it analytically.

I think the implications of this for microfounded macro are profound. The whole point about a microfounded model is that you can mathematically check that one relationship is consistent with another. To take a very simple example, we can check that the consumption function is consistent with the labour supply equation. But if the former comes from thousands of computer simulations, how can we do this?

Note that this problem is not due to two of the usual suspects used to criticise microfounded models: aggregation or immeasurable uncertainty. We are talking about deriving the optimal consumption plan for a single agent here, and the probability distributions of the uncertainty involved are known. Instead the source of the problem is simply complexity. I will discuss how you might handle this problem, including a solution proposed by Carroll, in a later post.

Is monetary policy taking Euro uncertainty seriously?

                There is a wonderful scene is the film Being There, where the innocent gardener played by Peter Sellers is asked by the President whether he should stimulate the economy. I thought of this while wondering why central banks seem to be gripped by inactivity as the global economy looks more perilous by the day (see R.A. here). I remembered being equally puzzled by the actions of the UK’s Monetary Policy Committee at a similar time last year, when they almost voted to raise interest rates, and by the ECB that did raise rates. On both occasions spring was in the air, and when much of the natural world is coming back to life, perhaps central bankers are filled with undue optimism about economic growth. This led me to think of Being There.

                I doubt, however, if this hypothesis would survive econometric testing.  A better hypothesis, which I talked about here, is that central banks take inflation targeting rather more literally than economists thought they did.  Actually, we probably suspected this of the ECB, but I really did believe that both the Fed and MPC saw themselves as pursuing ‘flexible inflation targeting’, which meant also being strongly influenced by the output gap. Perhaps I was naive, but in the case of the MPC I know these people, and they are all really good economists who know what optimal policy is all about.

                Perhaps my naivety partly comes from underestimating the influence of public accountability. With an explicit inflation target, the performance of the MPC is judged by most of the media as success in meeting that target. Very few non-economists blame the continuing recession on monetary policy, but the MPC has had a really hard time as a result of underestimating inflation. As I said here, forecast errors are generally down to bad luck rather than incompetence, but that is not widely recognised.

                It is true that knowing what the output gap is at the moment is very difficult, but that should not mean that you ignore it. As I argued here, at the Zero Lower Bound (ZLB) output gap uncertainty should make you more inclined to pursue an expansionary policy. Another factor I suspect is having to rely on Quantitative Easing to stimulate the economy. The impact of QE is very uncertain, the numbers involved are very large, and we should not discount the influence of those who look at these numbers and say hyperinflation is nigh. Other possible factors were mentioned in that earlier post.

                But these are explanations, not excuses. In that earlier post I talked about central projections. However the MPC prides itself (and quite rightly) on stressing the uncertainty of forecasts by using its famous fan charts. It was therefore with some surprise to read, via Britmouse, that one member of the MPC thought that “The forecasts in May were consistent, two years out, with roughly balanced risks on either side of the (inflation) target.” To which I immediately thought: balanced risks, what about the Euro?

                So I went to the Inflation Report, and sure enough the fan chart shows the forecasts for inflation pretty evenly distributed around 2%. I then read the section on uncertainty. I’ll be honest here – this is normally part of the report where I tend to skip. It is full of platitudes like ‘Inflation depends on X, and X could be higher, but then again it might be lower’. I found “..the biggest risks stem from developments in the Euro area..” which is consistent with Mervyn King's recent remarks. But then I read this “As was the case in past Reports, the MPC sees no meaningful way to quantify the size and likelihood of the most extreme outcomes associated with developments in the euro area and they are therefore excluded from the fan charts.”

                This is something I should have picked up before, but as I said that is my fault. As a principle it strikes me as a little odd – we try and quantify uncertainty, unless it’s really important! But it also raises an immediate question. If the forecast probabilities are evenly distributed around 2% without allowing for a really bad Euro outcome, what allowance was the MPC making for this bad outcome when deciding not to undertake further QE?  I would have thought that, as the Inflation Report says that a bad Euro outcome would reduce output, the MPC also believes this bad outcome would reduce inflation. So, making some allowance for this would reduce expected inflation below the 2% target. So what happened to this downside risk?

                I cannot think of an answer. Perhaps there is some equally large but imponderable uncertainty on the positive side, which can be set against a bad Euro outcome. If there is, I think we should know about it, if only to cheer everyone up. But maybe it’s just that spring air.

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.