More thoughts on ‘expectations driven’ liquidity traps

Warning - this is technical, so really just for macroeconomists.

The idea that we could get stuck in a steady state with nominal interest rates at zero and negative inflation has been dismissed by some because it has been associated with the policy proposal to raise nominal interest rates to avoid that outcome. Here I want to explore an alternative interpretation that disconnects the theory from the policy.

First, a recap on the theory. Take a really simple model, where the real interest rate is positive and constant. The central bank sets the nominal rate according to a Taylor rule that obeys the Taylor principle. The rule is calibrated such that there is a steady state at which nominal interest rates are positive and inflation is at target. Furthermore under rational expectations/perfect foresight, if agents know the inflation target, the real rate and the rule, we immediately go to that steady state. In more complex and realistic models it may take time to get to this ‘intended’ steady state, but it is ‘locally’ or ‘saddlepath’ stable.

However there is another steady state, because nominal interest rates cannot go below zero. For given real interest rates, this Zero Lower Bound (ZLB) steady state must involve negative inflation. This steady state is ‘indeterminate’, which means that we can describe dynamic perfect foresight paths that start at some arbitrary level of inflation below the central bank’s target, but end up at the ZLB steady state. To see this diagrammatically, look at this earlier post, or (plus algebra) this from David Andolfatto, or pages 123 to 135 in Woodford’s Interest and Prices. [1]

Stephanie Schmitt-Grohe and Martın Uribe have a paper which embeds this logic in a more elaborate model of involuntary unemployment based on nominal wage rigidity. They suggest that it tells a better story about the US recession than the New Keynesian idea involving a downward shift in the natural real interest rate. It is a story of a jobless recovery: growth resumes at the ZLB steady state, but involuntary unemployment is also positive at that steady state, because inflation is negative and nominal wages are downward rigid.

The paper interprets the ZLB steady state as one where agents have the wrong expectations about the central bank target. Call this the ‘mistaken beliefs’ story. With that story, raising rates could reveal or signal the authority’s true inflation target. In Stephanie and Martin’s paper, because raising nominal rates leads to an immediate change in beliefs and therefore a rise in expected inflation, we see an immediate jump to output growth above trend, which allows unemployment to fall. Many will just think this idea is incredible, but as Paul Krugman keeps emphasising, ZLB economics often turns things upside down.

In an earlier post I suggested that this story could possibly be plausible for (pre Abe?) Japan or the Euro area, because their inflation targets are one-sided: they seem content if inflation is below target, so in principle it might be possible to believe they might be content to end up at the ZLB steady state. In addition there is no QE in the Eurozone, and was only briefly in Japan. I suggested, I hope correctly, that the situation is different in the US, and it clearly is in principle in the UK. For that reason alone, I thought the mistaken beliefs story unlikely for these two countries.

However, after seeing Stephanie present her paper last week and thinking more about it, I wondered whether we could give the ZLB steady state a different interpretation? Suppose agents believe that is where inflation is heading because they do not think monetary (or any other) policy is capable of achieving the inflation target. Given current attitudes to fiscal policy, and a pessimistic view of the power of QE, this interpretation does not seem so farfetched for the US or UK. Economists sometimes worry about a deflationary spiral, where inflation just keeps falling into a bottomless pit. But maybe the ZLB steady state is like a ledge that can stop this descent. [2]

Under this interpretation, the policy of raising interest rates could be a disaster. There is no boost from any increase in expected inflation, because beliefs do not change. We lose the negative inflation equilibrium, but what seems likely in that situation is that we just get a negative deflationary spiral. The ledge preventing descent into the deflationary pit crumbles away. [3] If this interpretation is tenable, then it means that the possibility of becoming stuck in a ZLB steady state is not necessarily linked to the policy proposal of raising rates to get out of it.

My own view of the evidence is that the ‘balance sheet recession/natural rate too low’ story is still the more convincing, and that we are currently seeing in the US and UK a very slow return to the inflation target equilibrium. However that story is not without its problems: with a simple New Keynesian Phillips curve, a gradual reduction in the output gap should be associated with inflation gradually rising towards target, which is not what we are seeing at the moment. So I am not so confident that I can dismiss the ZLB steady state story out of hand. The message I draw from that possibility is that inflation targets need to be two sided and clear, and that policy (monetary and fiscal) at the ZLB should do everything it can to try and achieve that target. Assuming that below target inflation must eventually rise because nominal rates are zero could turn out to be a big mistake. [4]

[1] At the intended steady state, where inflation is at target, the target fixes the end-point of any dynamic process, and this (rather than history) then determines the initial level of inflation. At the ZLB steady state, there are multiple dynamic paths that lead there, so something else (‘confidence’) fixes the initial point. It cannot be history, because the model is forward looking and history does not matter. This may be a little too arbitrary or extreme for some tastes.

It is also controversial whether an inflation target is sufficient to fix an end-point for any dynamic inflation process, rather than allowing dynamic processes that explode. As I note in my earlier post, John Cochrane says: “Transversality conditions can rule out real explosions, but not nominal explosions.” I have less of a problem than he does with this. 

[2] A third interpretation might be that agents revise down their beliefs as inflation falls. The problem there is that this involves learning, which may make the stability of the ZLB steady state problematic. Jess Benhabib, George Evans, and Seppo Honkapohja have modelled learning when there are the same two steady states, and what they find is that the ZLB steady state is unstable: inflation keeps on falling. (It is a deflationary spiral.) My intuitive explanation for their result is that learning is equivalent to introducing backward looking expectations dynamics, and typically an indeterminate equilibrium with rational expectations dynamics (which the ZLB steady state is) becomes unstable with backward looking dynamics. Equally a ‘saddlepoint’ perfect foresight equilibrium (which the intended steady state is) becomes stable when expectations are backward looking, so they find that the inflation target steady state is stable under learning.

[3] Following on from footnote [1], you might ask why agents in this case will not select the only steady state left, and therefore raise their expectations. Why can I imagine agents assuming a deflationary spiral, but I want to rule out inflationary spirals? The answer is because the ZLB provides asymmetry. If it looks like an inflationary spiral is developing, the central bank can depart from its Taylor rule and raise rates substantially. That should change beliefs. They cannot do the same for a deflationary spiral.

[4] In an early draft of this post I had a different introduction, based on Narayana Kocherlakota’s recent dissent. Some may recall that Kocherlakota originally put forward the mistaken beliefs ZLB steady state idea, but then seemingly recanted. So my idea was that perhaps what had changed was not his view about the theory, but his interpretation of it. However having read some more about his current views, I don’t think this stands up, but it was such a neat idea I cannot resist mentioning it as a footnote. 

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.

Getting unhinged by ‘unhinged’: macroeconomic trade-offs and taboos

Central bankers, and even some of the best economists, sometimes talk about inflation expectations becoming ‘unhinged’. I do not like this term, and have been known to react quite badly to it. Some might say overreact. Let me say why.

But before doing so, I want to make three things clear, lest I be misunderstood. First, I think inflation expectations are really important. Second, I largely believe the great moderation story. As a result of setting inflation targets (explicitly or implicitly), and acting to achieve them, central banks did succeed in stabilising inflation expectations at low levels, and this has made the job of stabilising the economy as a whole rather easier. I may be wrong about this, but that is what I currently think. (I chose this as an example of the achievements of the microfoundations revolution in macro in my mild disagreement with Paul Krugman on this issue.) Third, I think it is more than likely that if inflation stays above/below target for some time, inflation expectations will adjust. 

But I would not call this expectations becoming unhinged. It is all about language. I would have no problem if another term was used. I used the term ‘adjust’ above, but we could also say ‘increase’, or ‘become less predictable’, or even ‘shift’. In fact any of the other words we normally use for macroeconomic variables. When discussing consumption, we do not talk about expectations of future income becoming unhinged. When discussing exchange rates and UIP, we do not obsess about expectations of future rates being unhinged. Whether intentional or not, the use of the term unhinged is designed to create an impression. The impression is of disastrous uncontrollability. If we talked about a person become unhinged, we indicate madness.

It is as if inflation expectations can be in one of two states: either low variance with mean reversion to the inflation target (or something close to it), or as highly volatile and could go anywhere. In this second imagined state, as expectations of inflation drive actual inflation, we could have ‘inflation bubbles’, which would become very costly for the central bank to prick. As we really do not want to go to that second state, we have to do everything we can to stay in the first state.

It is this view of the world that I find very difficult to believe - in fact I find it absurd. Why would inflation expectations become so unanchored from a central bank’s inflation target? They would do so if people thought the central bank had no intention of trying to achieve that target. So the only circumstances in which inflation expectations might become unhinged are when the central bank itself became unhinged. That could happen if the central bank was ordered to permanently monetise growing budget deficits, but that is not the world we are currently in.

When central bankers talk about unhinged expectations, they nearly always mention the 1970s and early 1980s. Do we really want to go through that again, they ask? Yet that was a period, in the US and UK, when it was very unclear what the central bank’s inflation target was, or indeed whether it had one. (This was not the case for Germany, as I note here.) So the lesson of that time is that inflation targets are important, but not that they should never be changed or missed.

I would draw a very different lesson from that period. It is important not to have taboos in macro. If there was a taboo at that time, it was that rising unemployment would mean a return to the 1930s. This prevented many seeing variations in unemployment as a means of stabilising inflation.

Could it be that we have a similar problem today, except roles have become reversed? With nominal rates at the zero lower bound, and doubts over unconventional monetary policy, we could use higher inflation (raised in a premeditated and controlled way) as a means of getting unemployment down. Of course that entails costs, and so we need to do the cost benefit analysis, and look at alternatives (like fiscal policy) that may be less costly. But if raising inflation is taboo we will not have that discussion. In this context, talk of expectations becoming unhinged reinforces that taboo.

In memory of Mel, who showed even as a teenager an appreciation for the absurd by helping me found the LUWS.