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.         

The FTPL version of the Neo-Fisherian proposition

Probably for macroeconomists

The Neo-Fisherian doctrine is the idea that a permanent increase in a flat nominal interest rate path will (eventually) raise the inflation rate. It is then suggested that current below target inflation is a consequence of fixing rates at their lower bound, and rates should be raised to increase inflation. David Andolfatto says there are two versions of this doctrine. The first he associates with the work of Stephanie Schmitt-Grohe and Martin Uribe, which I discussed here. He like me is not sold on this interpretation, for I think much the same reason. (There is a closely related discussion of the Neo-Fisherian doctrine by John Cochrane, which I will refer to in a subsequent post on Woodford’s recent idea of reflective equilibrium.) But he favours a different interpretation, based on the Fiscal Theory of the Price Level (FTPL).

Let me first briefly outline my own interpretation of the FTPL. This looks at the possibility of a fiscal regime where there is no attempt to stabilise debt. Government spending and taxes are set independently of the level or sustainability of government debt. The conventional and quite natural response to the possibility of that regime is to say it is unstable. But there is another possibility, which is that monetary policy stabilises debt. Again a natural response would be to say that such a monetary policy regime is bound to be inconsistent with hitting an inflation target in the long run, but that is incorrect.

A simple example is a model without sticky prices where bonds are denominated in nominal terms, and a monetary policy that involves a constant nominal interest rate. A constant nominal interest rate policy is normally thought to be indeterminate because the price level is not pinned down, even though the expected level of inflation is. In the FTPL, the price level is pinned down by the need for the government budget to balance at arbitrary and constant levels for taxes and spending.

The idea still works even with sticky prices and indexed debt, as my EJ paper with Tatiana Kirsanova shows. Here the budget is balanced, after a positive shock to debt say, by a period of above target inflation which reduces real government debt through lower real interest rates. This raises a somewhat pedantic point about David’s post. I’m not sure the path he shows for inflation, with no inflation surprises and no period of lower real rates, would be sufficient to stabilise the government’s budget constraint. Unless I have missed something, a period of higher inflation is required to do this. 

However I have a much more serious problem with this FTPL interpretation in the current environment. The belief that people would need to have for the FTPL to be relevant - that the government would not react to higher deficits by reducing government spending or raising taxes - does not seem to be credible, given that austerity is all about them doing exactly this despite being in a recession. As a result, I still find the Neo-Fisherian proposition, with either interpretation, somewhat unrealistic.

Why Sen is right about what is being done to Greece

At first sight the negotiations between Greece and the Troika seem to be simply a battle about resources: how much of the pie that is Greek national income their creditors should receive. There have been many similar types of battle over the years - what makes this one unusual is that the creditors have a unique weapon on their side. With primary surplus approximately achieved, Greece’s bargaining position would normally be extremely strong. The Eurozone creditors would be desperate to salvage what they could from their foolish decision to effectively buy some privately owned Greek government debt. The only reason the Troika is able to call the shots is that it can threaten to eject Greece from the Eurozone. [1]

Part of the deliberate mystification that goes on here is to present Eurozone exit as if it somehow automatically follows if there is a Greek default. But of course Greece has already defaulted, and it remains in the Eurozone. Greece wants to remain in the Eurozone. What will stop them if they do default will be a run on their banks, and a refusal of the lender of last resort for their banks - the ECB - to act in that capacity. Again this will be presented by the ECB as inevitable given the ECB’s own rules. But as Karl Whelan points out, the ECB in reality has considerable discretion, and it has been using that discretion in its role as part of the Troika.

Still, even if the sides are a little unequal in their power, is it still just a battle over resources? One side advocates left wing/populist/humanitarian policies and the other side policies that are more of the consensus/neoliberal/tough variety. [2] One side has suffered a massive fall in GDP partly as a result of previously agreements, while the other is negotiating over what is to them peanuts. So there is plenty of opportunity to pick sides based on preferences. Both sides would almost certainly be better off with an agreement, so it also makes sense for people to appeal for flexibility, which is why I signed this letter.

But to pick sides, or to call for flexibility from both, misses the main point. Yes, this is a battle over resources, but it is a battle where one side is using its power to pursue a policy that is very short-sighted, involving incredible hubris, and which is ultimately self defeating. The Troika are not acting in the long term interests of those they represent. This is I believe what Amartya Sen was saying when he compared these negotiations to the Versailles agreement. 

The most obvious example of this are the Troika’s continuing demands for positive primary surpluses and the austerity measures required to achieve them. This is just stupid. It continues to waste large amounts of valuable resources, as well as inflicting real suffering. It certainly is not in the interests of Greece, but it is almost certainly not in the interests of the creditors either. If you shrink the pie, you are less likely to get the amount of pie you have a claim to. (Martin Sandbu goes through the maths here.) It is disgraceful that key parts of the IMF plays along (or worse) with this. In the past I have described how heterogeneous the IMF is, but taking absolutely no notice of what your own research department says about austerity is crazy. Ambrose Evans-Pritchard talks about the Fund's own credibility and long-term survival being at stake. Keynes, who helped found the organisation, would be turning in his grave.

What about all the reforms that the Troika is insisting on? It is tempting to look at each in turn, and apply our economics expertise to come to an evaluation. If a reform demanded by the Troika might tend to increase the long run pie, then perhaps they are right to insist on it. This neglects one small issue: democracy. The Greek people have elected a government with a mandate. The Troika appear to be acting as if this is neither here nor there, and that is deeply worrying, at least to those of us who are very weary of yet further economic and political integration. (For those who have that integration as their ultimate goal, Greece can be seen as an annoying obstacle that should be thrown aside. [3])  

The hubris of the Troika is incredible. They have convinced themselves that they must override the democratic wishes of the Greek people because the Troika have the wisdom about what is good for the Greek economy. This is the same body that with its superior wisdom prevented full default, and imposed ridiculously strong austerity on Greece and crashed the economy as a direct result. To cover up these errors they play to stories in the media about the lazy and privileged Greek people, stories that largely disintegrate when confronted with evidence. Now they shrug their shoulders and say I have to keep on the same disastrous path because my electorate gives me no choice!

Amartya Sen is right. This is our Versailles treaty moment. It could be so very different. No doubt some of Syriza’s mandate may be unwise, but their own economists may recognise that and welcome the excuse to shelve them. The Troika and Syriza’s negotiating team could be cooperating in that endeavour, but I’m pretty sure that is not what is happening. On austerity the priority of the Troika should be to eliminate the Greek output gap, which means in the short term less rather than more austerity. This would not just be in the interest of the Greek people but also the interests of the rest of the Eurozone.

[1] This is why I think these negotiations are less like bargaining over a mutually beneficial exchange (rolling over lending in exchange for reforms), and more like a discussion with a mugger over which of your personal possessions you hand over.

[2] Or add any other description you prefer - my point is that they differ and people have strong views about them both in principle and practice, and therefore pick sides accordingly.

[3, postscript] Karl Whelan shows here that Giavazzi’s piece is as grounded in facts as some other FT op-eds. 

How to be a New Keynesian and an Old Keynesian at the same time

A recurring theme in economics blogs, particularly those that tend to be disparaging of mainstream Keynesian theory, is that Keynesians like to be New Keynesian (NK) when talking about theory, but Old Keynesian (OK) when talking about policy. John Cochrane has recently made a similar observation, which is picked up by Megan McArdle. To take just one example of this alleged sin, in the basic New Keynesian theory Ricardian Equivalence holds (see below), so a tax financed stimulus should be as effective as a debt financed stimulus, yet Keynesians always seem to prefer debt financed stimulus.

The difference between Old and New that Cochrane focuses on relates to models of consumption. In the first year textbook OK model, consumption just depends on current income. The coefficient on current income is something like 0.7, which gives rise to a significant multiplier: give these consumers more to spend, and the additional spending will itself generate more output, which leads to yet more income, and so the impact of any stimulus gets multiplied up.

Basic NK models employ the construct of the (possibly infinitely lived) intertemporal consumer. To explain, these consumers look at the present value of their expected lifetime income, and the income of their descendents if they care about them (hence infinitely lived). This has two implications. First, temporary shocks to current income will have very little impact on NK consumption (it is a drop in the ocean of lifetime income). The marginal propensity to consume out of that temporary income (mpc) is near zero, so no multiplier on that account. Second, a tax cut today means tax increases tomorrow, leaving the present value of lifetime post-tax income unchanged, so NK consumers just save a tax cut (Ricardian Equivalence), whereas OK consumers spend most of it. However NK consumers are sensitive to the real interest rate, so if higher output today leads to higher inflation but the nominal interest rate remains unchanged, then you get a multiplier of sorts because NK consumers react to lower real interest rates by spending more.

So far, so different. But the NK consumption model assumes that agents can borrow whatever they need to borrow. There are good theoretical reasons why that is unlikely to be true (e.g. asymmetric information), and even better empirical evidence that it is not. Empirical studies that look for ‘natural experiments’, where agents obtain an unexpected increase in post-tax income which is likely to be temporary, typically find a mpc of around a third (even for non-durables), rather than almost zero as the basic intertemporal model would predict. (For just one recent example: Consumer Spending and the Economic Stimulus Payments of 2008, by Parker, Souleles, Johnson, and McClelland, American Economic Review 2013, 103(6): 2530–2553.)

So if mainstream Keynesian theory wants a more realistic model of consumption, it often uses the (admittedly crude) device of assuming the economy contains two types of consumer: the unconstrained intertemporal type and the credit constrained type. A credit constrained consumer that receives additional income could consume all of that additional income, so their mpc out of current income is one. [1] That credit constrained consumer is therefore rather Old Keynesian in character. But there are also plenty of unconstrained consumers around (e.g. savers) who are able to behave like intertemporal maximisers, so by including both types of consumer in one model you get a hybrid OK/NK economy.

So it is perfectly possible to be an Old Keynesian and a New Keynesian at the same time, using this hybrid model. It may not be a particularly elegant model, and the microfoundations can be a bit rough, but plenty of papers have been published along these lines. It is a lot more realistic than either the simple NK or OK alternatives. It explains why you might favour a bond financed stimulus over the tax financed alternative, because there are plenty of credit constrained consumers around who are the opposite of Ricardian.[2] 

You can make the same point about one of the other key differences between OK and NK: the Phillips curve. The New Keynesian Phillips curve relates inflation to expected inflation next period, and assumes rational expectations, while a more traditional Phillips curve combined with adaptive expectations relates current inflation to past inflation. While I do not think you will find many economists using the OK Phillips curve on its own nowadays, you will find many (including this lot) using a hybrid that combines the two. The theoretical reasons for doing so are not that clear, but there is plenty of evidence that seems to support this hybrid structure. So once again it makes sense to be both OK and NK when giving policy advice.

Neither story is as exciting as the idea that New Keynesians are really closet Old Keynesians, who only pay lip service to New Keynesian theory to gain academic respectability. Instead it’s a story of how mainstream Keynesian economists try to adapt their models to be more consistent with the real world. How dull, boring and inelegant is that!

[1] I say ‘could’ here, because if the increase in income lasts for less time than the expected credit constraint, then smoothing still applies, and the mpc will be less than one.

[2] My own view is that the mpc out of temporary income is also significant because of precautionary savings: see the paper by Carroll described here.

Expectations driven liquidity traps

For macroeconomists

This is my own take on the idea of expectations driven liquidity traps (as opposed to liquidity traps where the natural real interest rate is low and unobtainable). I note some of the literature that has promoted these thoughts at the end, but I am not trying to summarise what these papers actually say, but rather to give my own thinking on how such a trap could arise. The usual health warning on such occasions applies: if you think I have got something wrong, or missed something important from the literature, please let me know.

Consider the diagram below, which represents the simplest possible model. Real interest rates are always constant, which is the 45 degree line. Monetary policy follows the Taylor principle, but nominal rates cannot go below zero, so the bold monetary policy line kinks. There is one ‘locally stable’ equilibrium at the inflation target (let us call that the ‘intended’ equilibrium), and one ‘indeterminate’ equilibrium when we are at the ZLB (which involves negative inflation).

It is often said that the intended equilibrium is ‘globally unstable’. (Michael Woodford in Interest and Prices  - page 123 onwards - talks about global ‘multiplicity of equilibria’.) By this is meant that, in the absence of imposing an endpoint constraint that has to be met, there are infinitely many rational expectations solutions to the model, many of which involve inflation exploding. I trace one: if we start at A, the monetary authority raises nominal interest rates, but for constant real rates that must mean that expected inflation next period is even higher etc etc.

John Cochrane says: “Transversality conditions can rule out real explosions, but not nominal explosions.” As a result, he suggests, we cannot rule out travelling along this unstable path. After all, hyperinflations do occur. I am less worried about this. Hyperinflations occur when monetary policy makes no attempt to stabilise inflation. Here we have a model where everyone understands it does, so it makes sense to impose an endpoint on any dynamic path. 

For example, what happens when interest rates and inflation go up when we are at A. Do agents say to themselves ‘hyperinflation here we come’. Of course not. This is inconsistent with the model, which involves an inflation target. They say instead ‘that was unexpected - we must have got something wrong’. We only travel along the unstable path for as long as agents do not revise their ‘beliefs’ (in this case, expectations about the inflation target and the real interest rate). Once they revise their beliefs, whether it is their belief about the inflation target or the real interest rate, inflation is likely to fall towards the intended steady state. [1]

Note that we cannot just say - suppose we start at A, as if history put us there. History does not put us there: in this forward looking model history is irrelevant. Given the Taylor principle, there are only two reasons we could be at A within the context of this model: agents get the real interest rate wrong, or the inflation target wrong. Once we allow beliefs to be revised, it seems inconceivable that hyperinflations would occur within the context of this model.

In looking at how beliefs change we are applying a simple notion of learning. The fact that learning helps stabilise inflation around the intended steady state should not be surprising, because what we are in effect doing is adding some backward dynamics into the model. A locally stable steady state with forward looking dynamics will tend to flip to a stable steady state with backward dynamics. This property is helpful, because we probably do not know the mixture of backward and forward looking dynamics we have in the real world, so it is good that policies should be robust to this.

A consumer has to eventually get on to their stable saddlepath because it is stupid for them to accumulate infinite wealth and stupid for others to carry on lending them more and more (no Ponzi games). But things in this model are not so very different - all we are saying here is that we are working with a model in which we rule out hyperinflation because that is a stupid thing for central banks to allow. But unlike the consumer case, it is not impossible that central banks could allow it, which is why we sometimes see hyperinflation. [2]

If we start off with inflation below the inflation target, then we can apply a symmetrical argument. Nominal interest rates will fall. This is inconsistent with agents’ beliefs, so if they revise these beliefs it seems likely that inflation will rise rather than carry on falling. But suppose they do not revise their beliefs. In that case we do not shoot off to hyper negative inflation. This path will converge on the ZLB steady state. This steady state is not ‘locally stable’, but ‘indeterminate’.

Indeterminacy means that the model does nothing to tie down the initial point. We could start anywhere below the intended steady state, and a solution of the model would get us to the indeterminate steady state. While this may sound desirable, it is not, because we normally want the model to give us a unique dynamic path. With a forward looking model where history does not matter we need something to give us our starting point. Often indeterminate steady states flip to unstable points if we change from forward looking to backward looking dynamics.

This is where the desirability of the Taylor principle comes from. If we replace the Taylor rule plus the Taylor principle by a constant nominal interest rate that passes through the intended steady state, then the fact that this steady state would be indeterminate is conventionally seen as a very strong argument against constant nominal interest rate policies. The ZLB is just a particular constant interest rate policy.

To put this point another way, recall that in this purely forward looking model history is irrelevant. We cannot say ‘history means we start somewhere, and then we converge to the indeterminate steady state’. Now incorrect beliefs could start us anywhere, but beliefs are not completely independent of the model and subsequent dynamic paths. All along the approach to the ZLB equilibrium, events are contradicting those initial beliefs.

However, it may be as unrealistic to assume beliefs are continually revised as it is to assume they are never revised. Suppose beliefs are not revised for some time, and the initial belief involves an inflation target which is below the actual target. Inflation is below target, which leads to interest rates falling, which if real rates are constant implies still lower inflation next period. If beliefs do not get revised, we do not go to hyper disinflation, but to the ZLB steady state. Suppose agents only revise their beliefs once they get close to the ZLB steady state. What will happen then?

Recall that originally agents thought that the inflation target was a bit below the actual target (1% rather than 2%, say). Inflation has now fallen much further (to -3%, say). Is it possible that they might conclude that they originally overestimated the true inflation target? If they ignored the fact that the ZLB is a constraint, they might decide that current stability implied that the inflation target was -3%. The central bank cannot demonstrate that this is incorrect by lowering nominal rates, because of the ZLB. This is why this situation is very different from the hyperinflation case.

In a model this simple, we have stretched credibility a bit to get us to a point where we stay at the ZLB steady state. Agents ignore all the observations on the path towards that position, each of which was inconsistent with a -3% inflation target. But if you add in additional uncertainty, allowing the real interest rate to temporarily change for example, things get more complicated. Agents could interpret falling nominal rates when inflation was 1% as being due to temporarily lower real interest rates.

So for a time, at least, we could stay at the ZLB steady state because of ‘self-fulfilling’ but mistaken expectations. If we allow real interest rates to change, then at some point real interest rates will rise and agents will recognise this. Instead of nominal rates rising (as they should if the inflation target was -3%), they will stay at zero, which should make agents revise their belief about the inflation target. So the ZLB steady state remains transitory. But we could stay stuck in the ZLB steady state because of mistaken beliefs for some time: for as long as beliefs remain unchanged or no information arrives that makes them change.

Does this story of an expectation driven liquidity trap fit the evidence better than stories based on an unobtainable negative natural real rate? Or is it instead just a cute (‘liberating’) theoretical construct with zero application. I think it is difficult to argue that something like this applies today to countries like the US or UK. Expectations of inflation are still positive, and central bank inflation targets are clearly positive and pretty credible. (The concept of pessimistic beliefs, or animal spirits, might well be more applicable in the context of other models with different unobservable variables.)

However, if we take the idea seriously at all, it does suggest that one-sided inflation targets are dangerous. Central banks that have a target of 2% or less invite speculation that they would settle for zero inflation if that came around, which would make falling into an expectations driven liquidity trap that much easier. Perhaps the major economy where the central bank’s intentions towards inflation have been least clear, and therefore the potential for an expectations driven liquidity trap greatest, has been (until very recently) Japan.

Some literature:

Benhabib, J, and Farmer, R (2000) ‘Indeterminacy and Sunspots in Macroeconomics’ , in John

Taylor and Michael Woodford (eds.): Handbook of Macroeconomics, North Holland.

Benhabib, J, Schmitt-Grohe, S and Uribe, M (2002) ‘Avoiding Liquidity Traps’, Journal

of Political Economy 110(3), pp. 535–563. (pdf)

Cochrane, John, 2011, “Determinacy and Identification with Taylor Rules”, Journal of Political Economy 119(3), pp. 565–615. (pdf)

Farmer, R (2012a) “Confidence, Crashes and Animal Spirits,” Economic Journal, Vol. 122, No. 559, Pages, 155-172

Mertens, K and Ravn, M (2012) ‘Fiscal Policy in an expectations driven liquidity trap’ (pdf)

[1] With asset market bubbles, we can get the rather interesting possibility that we continue to travel along the explosive path, not because expectations of the fundamentals are wrong, but because agents think they can make money along that path but get out before the bubble bursts. However, this does not seem to apply to inflation and monetary policy.

[2] Of course it is not completely impossible that some people are misers or get away with Ponzi schemes, which illustrates the point that the difference in rationale for imposing end point conditions in each case is not that great.

Fiscal backing

In an earlier post I went through the logic of why we do not think higher government debt necessarily causes inflation, even if that debt is denominated in nominal terms, as long as the central bank does not monetise that debt. As I argued there, talk of monetisation is largely unnecessary: we just need to say that the central bank uses interest rates to control inflation, and can therefore offset the impact of any increase in government debt.

However, as Mervyn King said, central banks are obsessed with budget deficits. This seems to contradict the previous paragraph. Are there some ways in which central banks would either lose the power to control interest rates, or be forced to abandon any inflation targets, as a result of fiscal policy? 

In the previous post the thought experiment I considered was a sustainable increase in the level of government debt. By sustainable I mean that the fiscal authorities raise taxes (or cut spending) to service this higher level of debt. But suppose they do not: suppose the budget deficit increases because spending is higher, but there is no sign that the government is prepared either to cut future spending or raise taxes to a sustainable level.

In 1981 Sargent and Wallace published a well known paper which said that, in this situation, the central bank could in the short term control inflation, but in the longer term inflation would have to rise to create the seignorage to make the government budget constraint balance. In other words, to keep the economy stable the central bank would eventually be forced to monetise. This was later generalised by the Fiscal Theory of the Price Level (FTPL). If the government did not act to stabilise debt itself (which Eric Leeper called – a little oddly - an active fiscal policy, and which others - including Woodford, Cochrane and Sims - have called even more confusingly a non-Ricardian policy [1]), then the price level would adjust to reduce the real value of government debt. Fiscal policy determines inflation.

One of the critiques of this theory is that the government budget constraint appears not to hold at disequilibrium prices. See, for example, Buiter here, and a response from Cochrane. I do not want to go into that now. Let’s also concede that if the monetary authority does either follow a rule that allows the price level to rise (by fixing the nominal interest rate for example), or tries to move interest rates to both stabilise debt and inflation (as in my recent paper with Tatiana Kirsanova), then the FTPL is correct.

The case I want to focus on here is where the central bank refuses to do either of those things, but carries on controlling inflation and ignoring debt. Suppose the government is running a deficit which is only sustainable if we have a burst of inflation which devalues the existing stock of government debt, but the central bank refuses to allow inflation to rise. You can say it does this by fixing the stock of money, or by raising the rate of interest - I do not think it matters which. This is an unstable situation: interest payments on the stock of debt at the low price level can only be paid for by issuing more debt, so debt explodes. In this situation, we have a game of chicken between the government and central bank.

Now the game of chicken would probably end when the markets refused to buy the government’s debt. That would be the crunch moment: either the central bank would bail the government out by printing money, or the government would default, which forces it to change fiscal policy. But in Buiter there is an elegant equilibrium outcome: the market just discounts the value of debt by an amount that allows the central bank to set the price level, but for the government’s budget constraint to hold at that price level. We get partial default. This discount factor becomes the extra variable that solves for the tension that both fiscal and monetary policy are trying to determine the price level.

You could quite reasonably suggest that such a central bank could not exist, because the government has ultimate power. It can always instruct the central bank to monetise the debt. However suppose the central bank actually managed the currency for a whole group of nations, and could only be instructed to do anything if they all agreed to do so. Furthermore that central bank was located in the one country in that group that would never contemplate monetisation, so it would be immune to pressure ‘from the street’. That central bank should be pretty confident it could win any game of chicken. [1]

Has any of this any relevance to today’s advanced economies? It seems to me pretty clear that these governments are not playing any game of chicken. Quite the opposite in fact: they are being far too enthusiastic in doing what they can to stabilise debt, despite there being a recession. So we certainly do not seem to be in a FTPL type world. Instead monetary policy right now retains fiscal backing.

Yet in a way we are having the wrong conversation here. Rather than trying to convince central banks that their fears are groundless, we should be asking whether monetary policy should – of its own free will – raise inflation to help reduce high levels of debt. I agree with Ken Rogoff that it should, and have argued the case here. Yet however optimal such a policy might be, the chances of it happening in today’s environment are nil. It looks like we may have to go through a lost decade before we are allowed to contemplate such things. 

[1] I guess a rationale for calling this fiscal policy ‘active’ is that stable regimes in Leeper require one partner to be active and the other passive. So in the normal regime monetary policy is active and fiscal passive, and this flips in a FTPL regime. In a FTPL regime, Ricardian Equivalence no longer holds (because taxes are not raised following a tax cut) – hence the label non-Ricardian.

[2] In this situation, would buying that government’s debt ‘show weakness’ in the game? If we follow Corsetti and Dedola and treat reserves as default free debt issued by the central bank rather than money, then not at all. Instead the central bank is giving the fiscal authority the best chance it can to put its house in order, by removing any bad equilibrium, but it retains the power to force default at any point. We no longer have Buiter’s method of resolving that game, but only because the central bank has the means which could force a win. As long as the government believes that the central bank would prefer the government to default rather than see inflation rise, the government should back down.