Woodford’s reflexive equilibrium

 For macroeconomists

Karl Whelan recently tweeted: “Read Cochrane and Woodford on neo-Fisherism today. Cochrane - clear and thought provoking. Woodford - unclear and rambling.” I agree about the clarity of John Cochrane’s writing, both in absolute terms and relative to Michael Woodford. But on this occasion I think Woodford has a more realistic approach. So here is my attempt to explain the issue that both are addressing, and Woodford’s version of learning. The two papers Karl is referring to can be found here and here.

The ‘problem’ that both address is that in the standard New Keynesian model a fixed interest rate policy involves an infinite number of rational expectations equilibrium paths. Another way of saying the same thing is that the initial jump in prices is not tied down, but if you choose to select a starting point the subsequent path would preserve rational expectations. This multiple equilibrium result typically means that macroeconomists would regard this monetary policy regime as problematic, but Cochrane says that there is no logical reason to reject these paths, and Woodford agrees. However Woodford argues that this policy is problematic, because if you choose some particular way of selecting a particular equilibrium (and Cochrane does suggest one), it will not be learnable in the sense Woodford describes. (The idea that indeterminate rational expectations solutions are not learnable is not new, as I note below.)

What is Woodford’s reflexive approach to learning? For me the most intuitive way to describe it is that it is very similar to Fair and Taylor’s method of finding the solution to a dynamic economic model involving rational expectations, although it may be that this just reflects my background. (Woodford’s discussion of how his idea relates to the literature, which opens with this analogy, is very readable and can be found in section 2.4.) The method starts by assuming some arbitrary values for expectations variables in the model, and solves it. This gives a solution to the model conditional on those arbitrary expectations. Now take that solution, and recompute using these solution values as expectations. Iterate until the solution hardly changes, and take that solution as the rational expectations equilibrium. The logic is that if some set of expectations (almost) reproduce themselves in this way, they are (almost) model consistent.

Woodford’s reflexive learning is very similar, although he would impose some arbitrary, and small, cut off for the number of iterations (=n). This has various interpretations, but the one I like is that each period a proportion of the population fully recomputes their expectations assuming rationality (or iterates a large number of times), while others stick to their previous expectations. Another interpretation (which could also have diversity) is to appeal to ‘level k thinking’, which has been observed in experiments. The reflexive learning idea is based on work by Evans and Ramey, and is closely related to the E-stability concept developed by Evans and Honkapohja: Woodford explains why he prefers his approach. Evans and Honkapohja have also applied their learning technique to this very issue, with similar results: see George Evans here for example.

Woodford shows, both analytically and with numerical examples, how the reflexive equilibrium converges to the rational expectations equilibrium as the number of iterations n increases if monetary policy is described by a Taylor rule that obeys the Taylor principle, but does not for a fixed nominal interest rate policy. To quote:

“It is true that under the assumption of a permanent interest-rate peg, the only forward-stable PFE are ones that converge asymptotically to an inflation rate determined by the Fisher equation and the interest-rate target (and thus, lower by one percentage point for every one percent reduction in the interest rate). But for most possible initial conjectures (as starting points for the process of belief revision proposed above), none of these perfect foresight equilibria correspond, even approximately, to reflective equilibria — even to reflective equilibria for some very high degree of reflection n.”

There is much more in the paper, but on the issue of reflective equilibrium a natural conjecture (mine not Woodford) is whether all indeterminate solution paths fail to be a reflexive equilibrium. In other words is this a rationale for ignoring indeterminate solutions, or perhaps more appropriately, designing policy to avoid them? Using the analogy with the Fair-Taylor algorithm, it may depend on the relationship between iterative stability and dynamic stability. When there was much more use of iterative methods for model solution I think there was a literature on this (and it may still be alive), and I seem to remember both similarities but also differences, but beyond that I have no idea.

I am not qualified to address the extent to which Woodford’s idea of a reflexive equilibrium adds to the learning literature, but it is now beginning to look as if the result that a fixed interest rate policy is not stable under learning is robust. As James Bullard says in a recent presentation (HT ‘acorn’ in comments), this may be “a sort of “victory” for the learning literature”. 

Postscript (31/12) See this note from Evans and McGough (in a Mark Thoma post) which I think is consistent with what I say here.         

One reason why monetary policy is preferred by New Keynesians

I promised to write something on this some time ago, so this post is overdue. It was inspired by markets in Provence, where I have been for the last week. (hence lack of posts, and delay in publishing comments).

There are practical reasons for preferring interest rate changes (when possible) to changes in government spending as the stabilisation tool of choice, although the extent to which these are inevitable or just conditional on current institutional arrangements is an interesting question. Here I want to give an economic reason for this preference.

Imagine a monetary economy made up of independent producers, each of whom produces a unique good, where these goods are exchanged in a market. The government can be a buyer in this market, and transforms the goods it buys into useful public goods. Total consumption is what each producer chooses to buy from other producers in the market, plus the public goods they receive. Producers have preferences over private and public goods which are independent of income, and let’s initially assume that the government provides just the right amount of public goods so as to achieve the optimum balance between private and public consumption. Because people can choose to use their income to buy goods or hold money, there is potentially an aggregate demand problem.

Suppose, for example, individuals decide for some reason that they want to hold more money. They expect to sell their output, but plan to buy less. If everyone does this, aggregate demand will fall, and producers will not sell all their output. If goods cannot be stored, and if producers cannot consume their own good, this could lead to pure waste: some goods remain unsold and rot away. (If all producers immediately cut their prices, then a new equilibrium is possible where producers’ desire to hold more real money balances is achieved by a fall in prices. So we need to rule this possibility out by having some form of price rigidity.)

The government could prevent waste in two ways. It could persuade consumers to hold less money and buy more goods, which we can call monetary policy. Or it could buy up all the surplus production and produce more public goods, which we could call fiscal policy. Both solutions eliminate waste, but monetary policy is preferable to fiscal policy because the public/private good mix remains optimal.

Three comments on this reason for preferring monetary policy. First, if for some reason monetary policy cannot do this job, clearly using fiscal policy is better than doing nothing. It is better to produce something useful with goods rather than letting them rot. We could extend this further. If for some reason the impact of monetary policy was uncertain, then that could also be a reason to prefer fiscal policy, which in this example is sure to eliminate waste. Second, the cost of using fiscal rather than monetary policy obviously depends on the form of public spending. If the public good was repairing the streets the market was held in one year earlier than originally planned the 'distortion' involved is pretty small. Third, another means of achieving the optimal solution, besides monetary policy, is for the government to give everyone the extra money they desire.

Eurozone delusions

I have already had a number of interesting comments on my previous post which illustrate how confused the Eurozone macroeconomic debate has become. The confusion arises because talk of fiscal policy reminds people of Greece, the bailout and all that. That is not what we are talking about here. We are talking about what happens when the Eurozone’s monetary policy stops working.

If Eurozone monetary policy was working, the Eurozone would be experiencing additional (monetary) stimulus everywhere, and average inflation would be 2%. Because Germany through 2000 to 2007 had an inflation rate below that in France and Italy, it now has to have an inflation rate above these countries. Something like 3% in Germany and 1% in countries like France and Italy for a number of years. If ECB monetary policy was working, Germany would get no choice in this, because it is part of what they signed up to when joining the Euro.

Monetary policy is not working because of the liquidity trap, so we instead have average Eurozone inflation at about 0.5%, with Germany at 1% and France/Italy at nearer zero. That implies a huge waste of Eurozone resources. That waste can be avoided, in a standard textbook manner, by at least suspending the Stability and Growth Pact (SGP), and preferably by a coordinated fiscal stimulus.

Why is this not happening? There are two explanations: ignorance or greed. Ignorance is a non-scientific belief that fiscal stimulus cannot or should not substitute for monetary policy in a liquidity trap. Greed is that Germany wants to avoid having 3% inflation, because it controls fiscal policy.

Those that say that Germany would be ‘helping out’ France and Italy by agreeing to suspend the SGP and enact a stimulus therefore have it completely wrong. If things were working normally, Germany would be getting a (monetary) stimulus, whether it liked it or not. What Germany is doing is taking advantage of the fact that monetary policy is broken, at the rest of the Eurozone’s expense. Germany gains a small advantage (lower inflation), but the Eurozone as a whole suffers a much larger cost.

Often greed fosters ignorance. It is unfortunate but not surprising that many in Germany think this is all about Greece and transfers and structural reform, because that is what they keep being told. How many of its leaders and opinion makers understand what is going on but want to disguise the fact that Germany is taking advantage of other Eurozone members I cannot say. What is far more inexplicable is that the rest of the Eurozone is allowing Germany to get away with it.

       

The risks to the UK recovery are fiscal not monetary

So this is how it is going to go. As the UK recovery proceeds, and rapid employment growth continues, at some point firms will begin to find it difficult to fill jobs. There are few signs (pdf, section 3) of that yet, but it is likely to happen sometime in 2015 or 2016. At that point, real wages will start to rise. Labour scarcity, and the recovery in investment that has already begun, will mean that at some point in the next year or two UK productivity growth will also recover to more normal levels.

What happens to interest rates will depend crucially on the relative timing of these two changes. If productivity increases when real wage growth resumes, wise heads on the MPC will note that cost pressures remain weak. If there are no other inflationary pressures, the case for raising interest rates also remains weak. However if real wages start rising before productivity growth picks up, such that unit labour costs rise, then the MPC will raise rates.

Which will happen is I think anyone’s guess, given the uncertainties associated with the UK productivity puzzle. It may come down to measurement errors in the data. However I also suspect it will not matter a great deal either way. This is because I take the MPC seriously when they say rate increases, when they come, will be small and gradual.

We can speculate about the impact of one or two quarter point increases in interest rates, but I think this would be ignoring the elephant in the room. That is fiscal policy, where its 2010 all over again. We have two austerity programmes: for simplicity call them Labour and Conservative. One is tough, the other is - well let’s just say very tough. Here is a picture.

Alternative Austerity Paths for cyclically adjusted net borrowing (excluding Royal Mail and APF transfers): source OBR and my estimates for Labour

We see the sharp fiscal contraction in 2010 and 2011. Thereafter it eases off. (If we look at the primary balance, which excludes interest payments, the easing off is even more noticeable - see here). Under the current government’s plans, fiscal tightening resumes again in earnest after the election. My guesses for what would happen under Labour are based on their (somewhat vague) statements so far.

In the past I have been a bit dismissive of these government plans, saying they represent a political gambit by Osborne to make Labour look relatively profligate. However that may have been politically naive. After all if the Conservatives win the 2015 election (or are part of a new governing coalition) this will have been achieved having followed a strategy of frontloading austerity. So why change a winning strategy? They might therefore keep to these plans, cut spending and welfare sharply in the first two or three years (more hits on the poor and disabled), and then again ease off, perhaps with tax cuts in the second half of the five year term.

Maybe the UK economy will be luckier than it was after 2010. Perhaps the recovery will be strong enough to shrug off this fiscal contraction, as the US economy has been able to. (Although many will correctly claim that the US recovery has been slower than it might have been as a result.) But the key similarity with 2010 is that UK interest rates will be at or close to their lower bound, so there is no insurance policy if things do go wrong. Just as in 2010, the government will be taking a huge gamble by embarking on a sharp fiscal contraction. The one difference from 2010 is that this time there is no pretext to take such a risk.  

The US and the Eurozone 2012-3

If fiscal policy is important at the zero lower bound, why did the US recovery continue in 2012 and 2013 despite a large fiscal contraction? Or to put the same question in a comparative way, why was the Eurozone’s fiscal contraction in 2012/3 associated with a recession, but not in the case of the US?

GDP growth had been reasonable in both the US and the EZ in 2010 and 2011. While US growth continued into 2012/3, EZ growth collapsed. Yet as the chart above shows, fiscal tightening was only slightly greater in the EZ in 2012, and became considerably tighter in the US in 2013.

Before discussing this, it is important to make two important points. The first is that the macroeconomy is complex, involving important lags in behaviour and expectations of future events. For that reason alone, you will not get precise matches between causes and consequences by just eyeballing the data. Second, different fiscal measures have different effects, and trying to express the fiscal stance in one simple measure will always be a crude approximation. However, despite these qualifications, I think we can provide something of an answer to this question by just looking at the numbers. 

In comparative terms, there are two obvious answers looking at 2012. The first is the EZ crisis. Although this began in 2010, it reached a critical position in 2012, when Greece was almost forced out. It is hardly surprising in these uncertain circumstances that EZ investment fell by nearly 4% in 2012. The second is monetary policy. The ECB raised rates from 1% to 1.5% in 2011, and compared to the US there was no Quantitative Easing. Combining the two, monetary conditions tightened considerably in the periphery as a result of the crisis. There was no comparable crisis in the US, which allowed investment to increase by 5.5%.

Explaining 2013 seems more difficult. Monetary policy had eased in the EZ (although of course not by as much as it should have), and OMT had brought the crisis to an end. In the US there was considerable fiscal tightening. So why did the US continue to grow and EZ GDP continue to fall?

For the EZ one proximate cause was a sharp decline in the contribution of net exports. Net exports added 1.5% to GDP in 2012, but only 0.5% in 2013. If this contribution had been more even at 1% in each year, GDP would have fallen by over 1% in 2012, and stayed roughly flat in 2013. Fiscal policy continued to tighten, which also would have reduced growth.

In the US something else happened: the savings ratio, which had been elevated at 5.5% or above since 2009, fell to 4.5%. This could have been a result of fiscal tightening, but it seems more probable that it represented the end of a prolonged balance sheet correction. (The US savings ratio averaged 4.5% between 1996 and 2007 and the OECD’s forecasters expect it to fall further this year and next.) The OECD estimates that the US output gap in 2013 was -3.5%, which was much the same as their estimate for 2012. So growth of 2% did nothing to close the output gap in 2013. This was despite a large fall in the savings ratio, perhaps bringing to an end the balance sheet correction that began with the Great Recession. So US growth in 2013 should have been very strong, and the obvious explanation for why it was not is very restrictive fiscal policy.

Price level targeting intuition

For students and maybe teachers of macroeconomics. The analysis here is standard: a more general discussion can be found in Woodford's Interest and Prices for example (see pages 497-501 in particular). All this adds is a bit of intuition which I at least found helpful. If there are any mistakes in the algebra or numbers below, please let me know and I will correct them 

When monetary policy can commit (i.e. follow a time inconsistent policy), why does the optimal response to an anticipated cost-push shock involve bringing the price level back to its original value? I do not think it is obvious why it should, yet the result is an important part of the justification for price level or nominal income targeting, so here is my attempt at some intuition.

To make things simple, ignore discounting in both the monetary policymakers objectives and the New Keynesian Phillips curve (NKPC). For notational clarity, assume perfect foresight. So the monetary policymaker tries to minimise the weighted sum of the output gap (y) and inflation (π), both squared (the inflation target is zero), from period zero onwards, subject to a series of NKPC constraints. The shock is a cost-push shock (u) in period zero, which is observed at the beginning of period zero.

To start us off, assume that the policymaker can only set period zero output and inflation. Expected inflation in period 1 is zero (the shock is not persistent, and the central bank is credible.) So the problem can be expressed as choosing output and inflation to minimise the Lagrangian:

This gives us two first order conditions:

which can be combined as

Equation (1) can be thought of as a policy rule: the combination of the output gap and inflation that optimal monetary policy would select if it cannot achieve zero for both. So, for example, if output has a large impact on inflation, then (1) gives a larger ‘weight’ to inflation. If people like diagrams, we can represent the loss function by indifference curves around the ‘bliss point’ zero, which are circles if β is one. The monetary rule (1) is the line joining the points where these indifference curves are tangent to the Phillips curves.

To take a concrete example, let the cost push shock be 10, and set α=β=1. Adding (1) to the Phillips curve implies that the central bank creates a negative output gap of 5, which gives an inflation rate of 5. The optimal policy involves one of intratemporal smoothing, balancing the costs of inflation against the costs of lower output. The welfare cost is 50, compared to a cost of 100 if the policymaker allowed no fall in output.

Suppose now that the policymaker can make promises about period 1 only. The Lagrangian then becomes

The first order conditions always imply that the Lagrange multiplier for any time period is equal to the output gap for that period divided by α. In addition to the first order condition (1) for period zero inflation, we also obtain

We can add (1) to this, to get

Equation (2) gives us the key intuition behind the price targeting result. Suppose αβ is large, so the final term is small. In this case (2) tells us that the sum of inflation in the two periods will be close to zero. Higher inflation in period zero will be almost balanced by negative inflation in period one. A moment’s thought implies that this must mean the price level at the end of period one will be close to its original value.

Inflation in period zero will be positive as a result of the cost push shock. We can reduce its size by creating negative inflation in period 1. By creating negative inflation of x in period 1, we reduce inflation in period zero by x. With a cost push shock of 10, creating negative inflation of 5 in period 1 balances positive inflation of 5 in period zero, which is the optimum combination. Creating less negative inflation in period 1 will lead to a greater welfare loss, but so will reducing inflation by more than 5 in period 1.

However, what if αβ is not large? Specifically, suppose we return to the example where α=β=1. Combining this with the NKPC for each period implies the optimal policy is

The optimal policy creates negative inflation in period one, but not by enough to keep the price level unchanged. Prices end up higher by 2, compared to 5 when we could only change period zero values. The welfare cost is now 40, which is an improvement on 50.

Why does the case non-negligible αβ stop approximate price level targeting in this two period case? Think about what exact price level targeting would imply. It would involve inflation of 5 in period zero and -5 in period one. This could be achieved with an output gap of -5 in period one, but no output gap in period zero. So although inflation would be balanced, output gaps would not be. A more balanced output combination involves a higher final price level.

(The policy is now time inconsistent: at t=1 there is an incentive for the policymaker to not carry through and reduce output, but instead set the output gap to zero. Unfortunately if this change in policy is anticipated in period 0, inflation will be 6 rather than 4 in period 0, and the overall welfare cost will be 52 (36+16), which is worse than the case where policy only operated in period zero.)

Suppose we now allow the policymaker to make promises in period 0 about the output gap in period 1 and 2. Instead of just reducing output in period one, we can spread lower output over periods one and two. The output costs become more balanced, which reduces the extent to which we fail to achieve a balanced inflation profile. We can then derive the following policy rule

                                                                  

As the fall in output in period 2 is likely to be lower than the previous fall in output in period 1, the deviation from price level targeting is reduced.

If we allow the policymaker to make commitments T periods ahead, then we can derive the following first order condition:

                                                  

High inflation in period 0 can now be balanced by negative inflation in many later periods. Intuitively the output gap in period T will become very small as T becomes large. This implies that the sum of inflation over all periods is almost zero. That means that the price level in period T is almost the same as the original price level. Thus the optimal policy in effect involves a long term price target, although that target is approached gradually.

Bullard on the 'Death of a Theory'

Following this post, James Bullard (President of the St. Louis Fed, and member of the FOMC - the US equivalent of the Monetary Policy Committee) kindly sent me his article (pdf) entitled ‘Death of a Theory’. As the theory he is referring to is the idea of fiscal stimulus at the Zero Lower Bound (ZLB), the title tells you that the article comes to the opposite conclusion to my post. His article is clearly written, and works with the New Keynesian framework which I also use. So we do not need to worry about those who practice the demand denial that Paul Krugman talks about here. I also think the article reflects the views of many economists. For these reasons, I thought it would be useful to say why I disagree with it.

Bullard gives three reasons why “Fiscal policy should return to being set for the medium and longer run.” They are that

(i) actual political systems are ill-suited to implement the advice from the theory

(ii) monetary stabilization policy has been quite effective [at the ZLB], making fiscal experiments redundant 

(iii) governments pushed distortionary taxes into the future, which in the theory reduces or eliminates the desired effects.

Let me take each in reverse order.

The standard textbook countercyclical fiscal policy involves increasing government spending now, and financing this by raising taxes once the recession is over. I have argued before that this framing is unfortunate, because it is unnecessarily complex. We need to worry about the impact of future distortionary taxes on future output, and then compare these to the output gains during the recession. Instead I have argued that we should focus on what I call a ‘pure’ countercyclical increase in government spending, where the additional current spending today is financed by reduced spending (not higher taxes) in the future. Bringing forward public investment is the exemplar of such a policy, which is perhaps one reason why it commands such widespread support.

So criticism (iii) is specific to one particular form of countercyclical fiscal policy. Point (ii) is generic. However we need to be careful about what is being claimed here. Does ‘quite effective’ mean has some effect, or does it mean as effective as conventional policy? I agree with the former, but not the latter. Nor do not think Bullard tries to claim the latter. Yet the latter is what you need if you want to assert that fiscal policy is unnecessary, because fiscal policy is unnecessary only when it is dominated by monetary action. By dominated I mean that monetary policy can do everything that fiscal policy can do, but with more certainty and at less cost. I know of no reason why this should be true for unconventional monetary policy. As an example, in the Werning paper I discussed here, forward commitment monetary policy works best when it works with changes in government spending - it does not make fiscal action unnecessary.

But we do not need to get into theory here. We just need to look at what has happened since 2008, and what is still happening in the Eurozone. There are three possible explanations for the deep and prolonged recession:

a) Monetary policymakers have been particularly inept

b) Monetary policy makers have succeeded in finding the optimal combination of inflation and output, so the recession was just an unfortunate consequence of an inflationary shock

c) The ZLB has created limitations to what monetary policymakers can do

I do not agree with (a). I suspect the only people who believe (b) are central bankers.

I find the first of Bullard’s criticisms the most perplexing. There is a perfectly sensible argument which says that for fine tuning demand, monetary policy is more flexible than fiscal policy. I have no problem with this. However what we are talking about today is a very large and prolonged recession. The fiscal actions that are required are not fine tuning. Furthermore, in both the US and the UK we had in 2009 governments acting to implement countercyclical fiscal policies, and by most accounts these did indeed stimulate demand, although not by enough to end the recession. Now perhaps ‘ill-suited’ is code for ‘many politicians dislike this policy’. But if it is, then you do not talk about the ‘death of a theory’, but instead you discuss the political problems of implementing a theory.

To see why this distinction is so important, consider what has happened since 2010. We have had cuts in government spending in varying degrees across countries, and where the cuts have been largest, the recession has been more severe. That is the ‘dying theory’ working, and politicians for whatever reason choosing to go against it. What worries me about the ‘monetary policy is still all you need’ line is that (to put it most politely) it encourages these misguided policy actions. That is not good for most people in the economy, but it also does monetary policymakers no good either, because they promise too much.

Monetary versus Fiscal: an odd debate

A long time ago, the debate between monetarists and Keynesians was the debate in macro. But it was a rather limited debate: both sides generally used the same model (IS-LM), and so it was all about parameter values. It was also, dare I say, a little dull. More recently, but before the recession, that debate had largely gone away, but since then it seems to have come back. This post asks why that is.

Before the recession, what I have called the consensus view was this. Under flexible exchange rates, monetary policy was the instrument of choice for demand stabilisation. Textbooks tend to give you a list of reasons why this is, but as I and colleagues argue here, it follows naturally in a New Keynesian model. It is not because fiscal policy cannot stabilise demand, but because (in fairly simple cases) monetary policy is better at doing so. From a welfare point of view, it dominates.

Does that mean, when monetary policy is unconstrained, it is all you ever need in a New Keynesian framework? In theory no. To take just one example, in a model with wage and price stickiness, real wages will deviate from their natural level following shocks, and in principle changes in income taxes or sales taxes could correct this. Even more obviously, these same taxes can in principle offset cost-push shocks. However you might describe this as a niche role for fiscal policy: the basic and fundamentally necessary task of stabilising demand is best handled by changing interest rates.

The qualification that monetary policy is unconstrained is critical, of course. If you are a member of a monetary union, it is a completely different game, and now fiscal policy’s ability to influence demand makes it useful, although perhaps not essential. I have argued that a failure to understand this was a major factor behind the Eurozone crisis.

The other example of a constrained monetary policy is of course the Zero Lower Bound. At the ZLB we have fiscal policy versus unconventional monetary policy. There are good reasons for thinking that unconventional monetary policy will not dominate fiscal policy as a stabilisation tool. Analysis of one particular unconventional policy, forward commitment (which is not the same as forward guidance), shows fiscal policy is not dominated in this case.

So which is better comes down to parameter values and the details of the model used. Given the uncertainties here, the only reasonable approach to take in advising policymakers is to use a combination of both policies. If you are thinking that concerns about debt might rule out using fiscal policy, you are wrong: temporary balanced budget changes in government spending can still be a useful tool.

This eclectic approach seems to me to be the one taken by, say, Paul Krugman or Brad DeLong. What I do not understand is why there are others who take a different view, and want to argue that monetary policy is still all you need. Where does this certainty about the powers of unconventional monetary policy come from? As I have already noted, it does not come from the theory that I know. So maybe it comes from a belief about parameter values, but given how untried this policy is, how can you be so certain as to not want to hedge your bets with fiscal action?

But perhaps it’s not the effectiveness of unconventional monetary policy that is crucial here, but a profound mistrust concerning the effectiveness of fiscal actions. Yet I cannot see the macroeconomics behind that either. In its purest form, all fiscal stimulus involves is bringing forward public spending, just as monetary easing encourages the private sector to bring forward their spending. That is bound to be effective in combating demand deficiency. Is the fact that the spending takes place this year rather than in five years time that costly, particularly if the spending is investment like in character?

So I remain mystified where this desire to downgrade the usefulness of fiscal policy at the ZLB comes from. I suspect I am missing something, and would like to know what that is.

Bold macroeconomic policy changes for a new government

One of the features of the incoming 1997 Labour government was that it undertook significant and progressive changes in macroeconomic policy. Not only was it right to give independence to the Bank of England [1], but the institutional framework they created for this was innovative and effective. As I have written recently, the fiscal framework established a year later was also clear and progressive compared to past practice and what was being done elsewhere.

So could the government that gets elected in 2015 be equally bold? I think it could be. Furthermore, the suggestions I make below apply to many advanced economies. Yet why look two years ahead now, when recovery from recession is either far from complete, or for many countries has not begun? One reason is that the lags in policy making can be quite long. A new government will not have spent the year before an election working out its policies - it will have been too busy campaigning. Policies get decided much earlier. To have a chance in that decision making process, ideas need to be bounced around earlier still.

On monetary policy, the new government needs to acknowledge that the recession has indicated clear problems with the inflation targeting regime. Three things need to change. First, the medium term inflation objective should be accompanied by an objective of minimising the output gap - in other words the UK should have a dual mandate like the US. Second, nominal GDP should be adopted as an intermediate target, to guide the MPC as to how best achieve these two objectives. Third, the inflation target of 2% is too low, because it increases the risk that we will soon suffer another Zero Lower Bound (ZLB) recession. In the UK the government fixes this target (which is one reason why the 1997 decision was progressive), and it should raise it. All of these changes will assist the process of recovery as well as help in the longer term.

On fiscal policy, we have to distinguish between policies pre and post recovery. If the government inherits an economy where the interest rate set by the Monetary Policy Committee is still at 0.5%, then its priority should be fiscal policies that promote recovery. I agree 100% with Paul Krugman that governments around the world have needlessly confused long term issues involving debt with this short run priority: here is one of many posts I have written arguing this. Yet the incoming government should also have a fiscal strategy post recovery.

This should involve both rules and institutions. Whatever fiscal rule is adopted, it should make three things clear. First, it does not apply at the ZLB. [2] Second, it should focus on a long term objective of reducing the debt to GDP ratio. Third, deficits have to be flexible in response to shocks in the short term. Now how you square these three things is tricky, and I still have an open mind on this, but for the moment you should read this very interesting proposal from Tony Dolphin at the IPPR as to how it might be done. That proposal utilises an enhanced UK fiscal council (OBR), which is the institutional leg of the reform.

Before discussing that, however, I want to say a bit more about why the policy goal should be to gradually reduce debt to GDP. I would give four main reasons. First, it allows room for fiscal policy to support monetary policy if it again hits the ZLB, without worrying about the bond markets. Second, it reduces real interest rates, which should encourage private investment (although the more open the economy the smaller this effect will be). Third, it reduces future distortionary taxation. Finally, future generations will need all the resources we can give them to help cope with their inheritance of hugely disruptive climate change.[3]

In the context of similar proposals from Hopi Sen [4], Chris Dillow recently raised some doubts. Some of these relate to the short term position: yes, investment probably responds more to expected future growth than the cost of capital, but with an active monetary policy, reducing debt to GDP should not inhibit growth. A more serious concern is that reducing real interest rates might increase the risk of hitting the ZLB, which is one reason why I propose raising the inflation target. [5]

The current government should be credited with setting up the OBR, but it did so with a very restricted remit. The OBR is not allowed to crunch the numbers on alternative policies, so it cannot even produce the raw material on which others can propose advice. Perhaps this made sense to avoid throwing a new institution into the middle of a fierce political debate in 2010, but it does not make sense in the longer term. At the very least the OBR should be given the freedom to look at alternative fiscal policies, but its role could go further still, as the IPPR proposal suggests.

[1] I should confess that before 1997 I was very dubious about central bank independence. In retrospect that was because I did not have the imagination to see how that the institutional set-up could be crucial. Despite my recent criticisms, I think the MPC has done much better than elected governments would have done. However my fears were that we would get something more like the ECB, so they were not groundless. I also worried that an independent central bank might be too conservative in the Rogoff sense, and that concern has also been realised. 

[2] Or equivalently, there should be a rule that directs policy in very different ways at the ZLB.

[3] In an ideal world, we would be dealing with climate change now, and perhaps - as I discussed here - using higher government debt to help pay for it. However we are not, and it does not look like this is going to change any time soon.
Postscript 24/6/13: As well as leaving capacity for fiscal stimulus after a large negative demand shock, Obstfeld argues that we need low debt to leave capacity for a (partial) bail out of the financial sector.

[4] I obviously disagree with Hopi on how the Labour party should respond to the myth that their fiscal mismanagement was responsible for the UK’s current plight. If you want to get into the apology idea, then it seems reasonable that governments should only apologise for major errors rather than every particular thing they could have done better. As I have argued before, there is no comparison between Labour’s fiscal errors and the current government’s mistakes. Governments that commit errors that go against expert opinion at the time bear a particular responsibility. Few (myself included) raised objections to the constant 40% debt to GDP ratio when it was adopted in 1998.

[5] In the UK I suspect that the main short term impact of a tighter fiscal regime will be a depreciation in the exchange rate rather than lower interest rates. In the context of the last Labour government, I think that would have been helpful.

My verdict on NGDP Targets

At the beginning of the year I decided I needed to firm up my views on nominal GDP (NGDP) targets, and when I thought it was interesting track that process through blog posts. I think I have now done enough to reach a tentative conclusion. I also gave a policy talk at the Bank of England yesterday, which was a useful incentive to get my thoughts in order.

Here is a link to the slides from my presentation. What I first do is compare targeting the level of NGDP to an ideal discretionary monetary policy. That is a demanding standard of comparison, but I argue that NGDP targets have the potential advantage over discretion that they may allow central banks to pursue a time inconsistent policy after inflation shocks that would otherwise be politically difficult (see this post). More speculatively, the uncertainty for borrowers of NGDP variation may be more costly than uncertainty over inflation, as Sheedy argues (see this post).

Against these advantages, I see two major negatives. First, following a shock to inflation, I think NGDP targets would hit output more than is optimal (see here and here). Second, if there is inflation inertia (inflation depends on past inflation rather than expected inflation), then targeting the level of NGDP is welfare reducing, because it is better in that case to let bygones be bygones. (There is a related point about ignoring welfare irrelevant movements in non-core inflation, but that probably needs an additional post to develop.)

So far, so typical two handed economist. But now let’s shift the comparison to actual monetary policy, rather than some ideal. Or in other words, how does actual policy as practiced in the UK, US and Eurozone compare to an ideal policy? While NGDP targets may well hit output too hard following inflation shocks (and more generally gets the short run output inflation trade off wrong), current policy seems even worse. One interpretation of this is that policymakers are obsessed with fighting what they see as the last war. Outside the US this is often institutionalised by having inflation targets (even if they are flexible) rather than a dual mandate, locking in the error Friedman complained of during the Great Depression.  As attitudes or institutional frameworks are unlikely to change soon, moving to NGDP targets represent a move towards optimality.

This bias in policy is particularly unfortunate when we are at the zero lower bound (ZLB), because unconventional monetary policy is far less predictable and efficient. Although fiscal stimulus is likely to be less costly as a way of raising output at the ZLB than committing to higher future inflation, monetary policy has to work with fiscal policy as it is. (However policymakers have a responsibility to let the public know when inappropriate fiscal policy is making it difficult for monetary policy to meet its objectives, as Bernanke is now doing, but the Bank of England has not. As for the actions of the ECB in encouraging austerity at the ZLB, I have described the gravest macroeconomic policy errors as those that are both wrong and contradict the textbooks.)

With perverse fiscal policy and uncertain unconventional monetary policy, we need to raise inflation expectations as a means of overcoming the ZLB and raising demand. Here I agree with Christina Romer: we need to indicate something rather more fundamental than the kind of marginal change implied by the forward guidance we currently have in the US and are likely to have soon in the UK. My proposal is therefore the adoption of a target path for the level of NGDP that monetary policy can use as a guide to efficiently achieving either the dual mandate, or the inflation target if we are stuck with that. NGDP would not replace the ultimate objectives of monetary policy, and policymakers would not be obliged to try and hit that reference path come what may, but this path for NGDP would become their starting point for judging policy, and if policy did not move in the way indicated by that path they would have to explain why.

To some supporters of NGDP targets this advocacy may seem a little wimpish. Why limit NGDP to an intermediate target that can be overridden? Given the problems with NGDP targets that I mention above, it would I believe be foolish to force monetary policymakers to follow them regardless. In general I think intermediate targets should never supplant ultimate objectives, and NGDP is an intermediate target. The analogy I would draw is with monetary targets as adopted by the Bundesbank, and as briefly adopted in the UK. As I wrote here, most readings of Bundesbank policy suggest that they treated money targets pretty flexibly. Following the oil price shocks of the mid 70s and early 80s, inflation did rise substantially, but the target ensured that inflation came back down again. In contrast the UK adoption of money targets was far less flexible, so we had inflation overkill in the early 80s, and these targets were quickly dropped.

How was this proposal received by my audience at the Bank? Did my reasoning stand up to their criticism? Well at least one of the slides I would change in hindsight, but perhaps all that is best left for a separate post tomorrow.

Sheedy on NGDP targeting and debt contracts

An argument that is sometimes made for a monetary policy that targets a path for nominal GDP (NGDP) is that it reduces risk for most borrowers who take out debt contracts with repayments fixed in nominal terms (see, for example, Nick Rowe here). However, as far as I am aware, this argument has not been quantified in a way that allows it to be compared with the more familiar benefits of inflation targeting. A recent paper by Kevin Sheedy does just that.

Before getting to the punchline, it is worth setting out the argument more precisely. A good deal of the borrowing that goes on in the economy is to smooth consumption over the life cycle. We borrow when young and incomes are low, and pay back that borrowing in middle age when incomes are high. To do this, we almost certainly have to borrow using a contract that specifies a fixed nominal repayment. The problem with this is that our future nominal incomes are uncertain - partly for individual reasons, but also because we have little idea how the economy as a whole is going to perform in the future. If the real economy grows strongly, and our real incomes grow with it, repaying the debt will be much easier than if the economy grows slowly.

As most individuals are risk averse, this is a problem. In an ‘ideal’ world this could be overcome by issuing what economists call state contingent contracts, which would be a bit like a personal version of equities issued by firms. If economic growth is weak, I have a contract that allows me to reduce the payments on my debt. However most people cannot take out debt contracts of that kind, or insure against the aggregate risk involved in nominal debt contracts. We have what economists call an incomplete market, which imposes costs.

Monetary policy can reduce these costs by trying to stabilise the path of nominal GDP, because it reduces the risks faced by borrowers. Of course monetary policy cannot remove the uncertainty about real GDP growth, but if periods of weak growth are accompanied by periods of moderately higher inflation, then this is not a problem from the borrower’s point of view. (Koenig discusses this in detail in a paper here.)

How do we quantify this benefit of NGDP targeting, and compare it to the benefits of inflation targets? Sheedy defines a ‘natural’ debt to GDP ratio, which is the private debt to GDP ratio that would prevail if financial markets were complete. Under certain conditions the natural debt to GDP ratio is likely to be constant, and Sheedy suggests that departures from this benchmark are unlikely to be great. So a goal for monetary policy could be to close as far as possible the gap between the actual and natural debt to GDP ratio, in an analogous way to policy trying to close the output gap. To do this it would target the path of NGDP.

The current standard way of modelling the welfare costs of inflation, due to Woodford, is to measure the cost of the distortion in relative prices caused by prices changing at different times to keep up with aggregate inflation. This suggests monetary policy should have an inflation target rather than a NGDP target. (I note here that typically in the literature these costs are far greater than costs associated with output gaps.) What Sheedy does is set up a model which has these costs of inflation present, but also has the costs of nominal debt contracts discussed earlier. With these two different goals, an optimal monetary policy will go for some combination of inflation targeting and NGDP targeting. The key question is which kind of costs are more important. [1]

Sheedy’s answer is that the costs of nominal debt contracts are more important. The optimal monetary policy gives a 95% weight to the NGDP target, and just 5% to the inflation target. Now of course this is just one result from a highly stylised model, and Sheedy shows that it is sensitive to assumptions about the duration of debt contracts and the degree of risk aversion. Nevertheless it is very interesting result.

A very simplistic way of describing why this may be very important is as follows. If the focus of monetary policy is always on the cost of inflation, NGDP targets will appear to non-economists at least (e.g. politicians) to be second best. They are a nominal anchor, so we will not get runaway inflation or deflation by adopting them, but why not just target inflation directly? Who cares about nominal GDP anyway? This paper suggests a simple answer - borrowers care. If we see monetary policy has being important to the proper functioning of financial markets, as we now do, then reducing the risk faced by borrowers is a legitimate goal for policy. It may make sense for inflation to be high when real growth is low, and vice versa, because this reduces the risks faced by borrowers. I think a politician that was not beholden to creditors could sell that.

[1] For those interested in government debt, there is an interesting parallel in the literature. Some authors (e.g. Chari, V. V. and Kehoe, P. J. (1999), “Optimal fiscal and monetary policy", in J. B. Taylor and M. Woodford (eds.), Handbook of Monetary Economics, vol. 1C, Elsevier, chap. 26, pp.1671-1745.) developed the idea that nominal government debt contracts could be a useful way of avoiding costly changes in distortionary taxes following fiscal shocks, because inflation could change real debt. However Schmitt-Grohe and Uribe (Schmitt-Grohe, S. and Uribe, M.  (2004), “Optimal fiscal and monetary policy under sticky prices", Journal of Economic Theory, 114(2):198-230) showed that once you added in nominal rigidity to the model so that inflation was costly, inflation costs dwarfed any gains. This example makes the fact that we get the opposite result with private debt contracts particularly interesting, although as Sheedy and others have noted, this may be partly because this earlier literature assumed short maturity government debt.

 

Leading Macroeconomist Leaves Central Bank

Maybe not the most compelling title for a post, but the news that Lars Svensson is not renewing his term as Deputy Governor of Sweden’s central bank (HT Saroj Bhattarai) will be of great interest to academic macroeconomists. What I want to suggest here is that it should also be of wider interest.

Apart from making major contributions to the discipline, Svensson has also been extremely influential among policymakers, and is often associated with the idea of flexible inflation targeting. (Here is just one example.) It is interesting news because of why he is leaving. He says: "I have failed to find support for a monetary policy that I believe would lead to better performance, with both a higher inflation rate closer to the target of two percent and a lower unemployment rate." He has for some time been fighting a losing battle to persuade his colleagues that current Swedish monetary policy is too deflationary (see for example Britmouse), and he has decided to give up the fight.

Interest rates in Sweden are low, at 1%, but according to Svensson they should have got there faster and should now be even lower. Here is a plot of inflation (blue, left hand scale) and unemployment.

Inflation is currently zero, so well below the 2% target. GDP growth was 1.2% last year. Unemployment rose in the recession, came down a bit, but has begun to rise again. The case for lower interest rates over the last two or more years looks pretty clear.

So why have most of Svensson’s colleagues not been following his advice? Their concern is that low interest rates are encouraging Swedes to borrow too much. Now of course one of the ways monetary stimulus is supposed to work is that it encourages more borrowing, but the worry is that borrowing in Sweden is dangerously high, and could threaten financial stability. There are echoes here of doubts expressed by some members of the Fed (see here and here) and international organisations (Tim Taylor here). However so far these have been just concerns, which do not seem to have had a major impact in preventing expansionary policy. Except in Sweden.

Svensson’s arguments against such concerns are persuasive (pdf), and I find the argument that there are better financial instruments available to deal with these problems particularly strong. However I want to draw a slightly different parallel, with policy at the ECB. At first sight similarities appear slight: although both central banks are resisting a cut in interest rates from low to very low levels, in the Eurozone growth is negative rather than just slow, and inflation is currently only a little below target rather than zero (although the ECB itself expects it to fall to nearly 1%). In addition, the ECB has not focused on financial stability as a reason for not cutting rates. Yet the parallel is this. In both cases we have central banks making decisions that appear to contradict the wisdom of mainstream macroeconomics. So what, you may say, but in both cases the cost is being measured in unnecessary unemployment, and below target inflation. Compute the cost in terms of lost output, and they are the kind of losses that could cost a politician their job. The cost in terms of human misery is greater still. You may be pretty skeptical of the wisdom of macroeconomists, but do you really think that these central bankers know better?