Wednesday, December 23, 2015

Summers in Winter

Larry Summers has a post in the Financial Times about - you guessed it - secular stagnation, and what he doesn't like about current monetary policy. In case you are looking for clarification on what Summers's theory of secular stagnation is all about, you won't find it here. He observes, as is well-known, that real rates of interest are low and expected (based on current asset prices) to remain so for some time. Why are real interest rates low? According to Summers, because of secular stagnation. And...
...secular stagnation is the hypothesis that the IS curve has shifted back and down so that the real interest rate consistent with full employment has declined.
Which does not tell me much. Maybe I can find the answer in this transcript of a Summers conference talk, which he references. Here's the relevant passage:
...broad technological features of the economy have changed that should not have been expected to be constant. That there are a variety of trends that are evolving that have led to lower real rates with the right presumption being that that will continue to be the case for quite some time to come.
What exactly are these "broad technological features" that changed? Apparently we should have expected them to change, whatever they are. What is the "variety of trends" and how are they evolving? Suffice to say that the broad technological features have changed in a persistent way, and along with the variety of evolving trends will cause low real rates of interest to continue to be low indefinitely. If you're enlightened by this, you'll have to explain it to me.

Now, on to Summers's policy critique. He has four complaints.
First, the Fed assigns a much greater chance that we will reach 2 per cent core inflation than is suggested by most available data. Inflation swaps suggest inflation on the Fed’s preferred PCE deflator measure will average only 1 per cent over the next 3 years, 1.2 per cent over the next 5 years and 1.5 per cent over the next 10 years. Survey measures of expected inflation are falling not rising. Moreover, if account is taken of quality change inflation measures would have to be further reduced.
There are many ways to measure anticipated inflation. We can use inflation swaps data, as Summers does; we can look at the breakeven rates implied by the yields on nominal Treasury securities and TIPS; and we can look at survey measures. What do people who do forecasting for a living, and who have access to all of that data, say? The Philly Fed's most recent Survey of Professional Forecasters has predictions of PCE headline inflation for 2016 and 2017, respectively, of 1.8% and 1.9%, which is pretty close to the 2% PCE inflation target. A Wall Street Journal survey shows a CPI inflation forecast that seems roughly consistent with the December FOMC projections for PCE inflation. So, it seems that "most available data," filtered through the minds and models of professional forecasters, suggests no less optimism than the FOMC is expressing in its projections, about achieving 2% inflation in the future.

Second, the Fed seems to mistakenly regard 2 per cent inflation as a ceiling not a target. One can reasonably argue that after years of below target inflation, it is appropriate to have a period of above target inflation. This is implied by arguments for price level targeting. Alternatively, it seems reasonable to simply suggest that the Fed should run equal risks of over and under shooting its inflation target. I would actually argue given the observed costs of deflation that the costs of under shooting the target exceed the costs of overshooting it.
In its updated "Statement of Longer-Run Goals and Policy Strategy," the FOMC tells us, with respect to its inflation target,
The Committee reaffirms its judgment that inflation at the rate of 2 percent, as measured by the annual change in the price index for personal consumption expenditures, is most consistent over the longer run with the Federal Reserve’s statutory mandate.
So, the goal is clearly 2 percent inflation, as measured using the headline PCE deflator. Is this a "ceiling," as Summers states? Later in the document, the FOMC states:
In setting monetary policy, the Committee seeks to mitigate deviations of inflation from its longer-run goal and deviations of employment from the Committee’s assessments of its maximum level.
So, deviations of inflation from 2%, on both the high and low sides, are considered by the FOMC to be undesirable. Why does it look to Summers as if 2% is a ceiling? He doesn't give us much to go on.

Third, the Fed seems to be in the thrall of notions that might be right but do not to my knowledge have analytic support premised on the idea that the rate of change of interest rates as distinct from their level influences aggregate demand. It is suggested that by raising rates the Fed gives itself room to lower them. This is tautologically true but I know of no model in which demand will be stronger in say 2018 if rates rise and then fall than if they are kept constant at zero. Nor conditional on their reaching say 3 per cent at the end of 2017 do I know of a reason why recession is more likely if the changes are backloaded. I would say the argument that the Fed should raise rates so as to have room to lower them is in the category with the argument that I should starve myself in order to have the pleasure of relieving my hunger pangs.
Unlike Summers, I do know of a model in which "...demand will be stronger in say 2018 if rates rise and then fall than if they are kept constant at zero." It's a model that Summers should like - a plain vanilla reduced-form New Keynesian model. This comes from Jim Bullard's "Permazero" speech, with reference to work by John Cochrane. Here, I'll extract Jim's Figure 2 from his talk:
Here, i is the nominal interest rate, Greek pi is the inflation rate, and x is the output gap. The figure shows the results of a reduction in the nominal interest rate to zero, followed, after a period of time, by a gradual increase in the nominal interest rate so as to achieve the inflation target. You can see that the sharp drop to zero in the nominal rate also gives a sharp - but temporary - increase in output. With a gradual increase in nominal interest rates, the corresponding drop in output is smaller, but persists for a longer time. So, if the nominal interest rate stayed at zero instead of increasing, then the output gap would stay at zero. But, suppose that we do Summers's "2018" experiment, i.e. return to zero somewhere in the right-hand side of the figure. Then the output gap will indeed be positive for a period of time. So, Summers is incorrect. Indeed, I think it would be difficult to find a model with a non-neutrality of money where this is not the case. Typically, a change in the nominal interest rate produces a short-run nonneutrality. That is, there are temporary real effects, and if the nominal interest rate persists at this different level, the real effects disappear. Fundamentally, it is true that the central bank can't go down unless it goes up. Whatever the benefits of stabilization by way of monetary policy are, the central bank cannot exploit them unless it sometimes chooses to have market nominal interest rates go up.

Fourth, the Fed is likely underestimating secular stagnation. It is failing to recognise its transmission from the rest of the world and it is overestimating the degree of monetary accommodation now present and likely to be present in the future by overestimating the neutral rate. I suspect that if nominal interest rates were 3 per cent and inflation were far below target there would be much less pressure to raise them than there has been of late. The desire to raise rates reflects less some rigorous Philips curve analysis than a sense that zero rates are a sign of pathology and an economy creating 200,000 jobs a month is not diseased. The complexity is that zero rates may be less abnormal than is supposed because of fundamental shifts in the saving investment balance.
For this, it helps to focus on a three key sentences in this paragraph:

1. "...the Fed is likely underestimating secular stagnation." Since Summers has not defined the concept clearly, it's hard to see how anyone could pay too little attention to it. But economists - both inside the Fed and outside - certainly are not ignoring the phenomenon of low real interest rates and the implications. Far from it.
2. "I suspect that if nominal interest rates were 3 per cent and inflation were far below target there would be much less pressure to raise them than there has been of late." Here's the time series for the fed funds rate and PCE inflation since 1960:
If we take "inflation far below target" to mean zero or lower, say, then a 3% fed funds rate and and inflation far below target has never occurred in the time series since 1960. If it did occur, then I think people would be scratching their heads about it. Would the Fed be talking about raising rates? Who knows? Seems like asking what you would do if you came around a bend in the road and encountered a two-headed goat.
3. "The desire to raise rates reflects less some rigorous Philips curve analysis than a sense that zero rates are a sign of pathology and an economy creating 200,000 jobs a month is not diseased." First, I'm not a big fan of using "rigorous" and "Phillips curve" in the same sentence. Second, it is true that a standard argument for liftoff is that that the current level of the policy rate is not consistent with: (i) past Fed behavior and (ii) the proximity of inflation and unemployment to the Fed's goals. So, to justify continued zero interest rate policy, one would have to make a case that there is something wrong with the way policy was conducted in the past, or something different about current circumstances. Summers might say that the different circumstance is secular stagnation. If so, he needs to be more explicit about what this is about.


  1. "Then the output gap will indeed be positive for a period of time. So, Summers is incorrect. Indeed, I think it would be difficult to find a model with a non-neutrality of money where this is not the case."

    I think this depends on what you assume about fiscal policy. If you assume that it acts to prevent higher debt service raising the level of debt above its opening level (but not preventing debt going below this level), then I think you can get the result where a temporary rise in rates does not result in any positive output gap.

    1. "Positive output gap" in this case means output higher than it would have been if prices were flexible. That is, if the nominal interest rate stays at zero, output stays the same. If interest rates go up gradually, and then go back down, then output goes down temporarily, and at the time interest rates go down again, output goes up.

    2. I understand what it means.

      I was thinking in terms of something like John Cochrane's model. We have a standard NK IS curve and Phillips curve, but we replace the central bank reaction function with an interest rate peg. We also have single period government bonds. I'm then suggesting a fiscal policy rule whereby lump sum taxes are the sum of: a) a fixed real amount; and b) any additional amount required to ensure that the real value of debt does not exceed a specified level (which we can take as the opening level).

      We can then consider what happens when rates are raised and then lowered again, on the assumption that this whole path of rates going up then down is announced at the time that rates start going up.

      In that scenario, I believe that you can get an immediate negative output gap which then reduces over time but never goes positive. Inflation follows a similar path. Critically, inflation only falls by surprise in response to the announcement - a fall in expected inflation being only possible in the event of a positive output gap.

      This scenario requires that deviations in inflation are strictly negative, which is possible here because the fiscal policy rule results in a drain of nominal bonds giving a permanent reduction in the equilibrium price level (determined here by the FTPL). Without this, a period of reduced inflation has to be followed by a period of higher inflation which then implies a positive output gap when the period of higher inflation ends.

      I'm not saying you're wrong to pick Summers up on this because I'd agree that many models will do exactly what he says they won't. I'm just suggesting one way that a model might do what he says.

    3. The underlying model - i.e. Woodford's - that Cochrane is working with, is Ricardian. So, the timing of taxes is irrelevant, and you cannot get the kinds of effects you mention. You could of course write down a model where tax policy matters, and work it out. But you seem to be suggesting that, if you are out at period 35 on the chart, and the nominal interest rate goes back to zero, that output will go down. Is that correct?

    4. If we are out at period 35, everyone expects interest rates to stay up, but it is then announced that interest rates will be cut to zero, then no - that is not what I am saying. In that case, the surprise cut must lead to a period of expected declining inflation which implies a positive GDP gap.

      I was thinking of a scenario where the cut in rates is announced at the time that rates rise in the first place (probably not what Summers had in mind admittedly). The only time that output goes down in my scenario is when the announcement is made. From then it continually rises, back to its original level, even when the expected rate cut takes place.

      The problem here with the 35 period horizon is having output rising continually from the time of the announcement through the time of the actual change. Furthermore because inflation is also rising from an initial downwards shock, so is the real interest rate. This means that when we have 35 periods until the actual rate changes are complete, the initial drop in output and inflation has to be implausibly large. (I would probably interpret this as implying that my supposed fiscal policy rule is unrealistic in this case.)

      As to Ricardian Equivalence, it's not really that the timing of tax matters. It's rather that the total amount of tax is increased, but driven by a real time rule that looks at the debt level in each period.

      Incidentally, I'm basing all this on looking at data sets that I find using iteration algorithms and that conform to the model equations (including the forward looking aspects) and converge to long term steady states. I know this does not amount to a rigorous proof, but it helps me get a sense of what solutions might look like under assumptions (like my fiscal rule) which are difficult to solve analytically.

    5. "I was thinking of a scenario where the cut in rates is announced at the time that rates rise in the first place ..."

      Me too. I'm basing this on the fact that, in the first chart, you can see that the nonneutrality dies out quickly. Probably better to choose 40 rather than 35. At 40 you can see that you're roughly back to where you are in period -10. So if we announce a policy in period -10 under which the nominal interest rate goes back to zero at period 40 (everything else the same), output should increase in period 40, with response that looks pretty much like period 0. Cochrane gives you the solution, so it would be straightforward to compute.

      "As to Ricardian Equivalence, it's not really that the timing of tax matters. It's rather that the total amount of tax is increased, but driven by a real time rule that looks at the debt level in each period."

      If you increase taxes in present value terms, then government spending has to go up. That's something different altogether. Now we're not talking about monetary policy.

    6. I agree that it would look as you describe, but only if we assume the fiscal policy rule is to keep lump sum taxes constant (and I'm assuming no government expenditure here).

      However, what is happening between periods -10 and 0 in that chart is that the real value of outstanding government bonds is rising. This is easy to see. The change in debt is equal to the actual real interest on outstanding debt less taxes. The real interest rate is rising between periods -10 and 0 and we're assuming taxes are constant.

      I am talking about a fiscal policy rule that would not allow this. Under my rule, the government has to raise lump sum taxes at this point to prevent the real debt rising. The impact of this is to cause a shock fall in both GDP and inflation at period -10, when the announcement is made. But the shock fall in inflation itself increases the real value of debt, so the tax increase needs to be even higher to compensate. It turns out the (only?) way to resolve this for all future periods is when both output and inflation fall by enough on the announcement that they then strictly only rise to reach their long-term equilibrium levels.

      This does not violate the inter-temporal government budget constraint. The absolute amount of future taxes goes up, but the present value stays the same, because future real rates have also increased.

    7. In the reduced form that Cochrane writes down, note that taxes do not appear anywhere. That's because, in the underlying model, government finance is irrelevant. As I mentioned above, it's a Ricardian world. Government spending on goods and services of course matters, in ways that people have studied in this class of NK models. What you're talking about is another - seemingly non-Ricardian - model. I can't tell from your description whether or not you have the ideas right.

    8. Fiscal policy comes into Cochrane's model when he talks about selecting between multiple equilbria. He has real primary surpluses, which I'm just equating to real taxes, because I'm assuming no government expenditure. This is pretty relevant to what I'm saying, because I'm suggesting a fiscal policy rule that forces us onto an equilibrium path that starts from a low point (post-announcement). It looks a bit like his paths D or E in Fig 15 (even though we're talking about a reduction of rates here.)

      It's pretty difficult to describe what I mean without charts, so I've set it out in more detail here:

      Feel free to tell me what you think, but likewise don't feel obliged to humour me.

    9. The way you've written it down, (1) and (2) solve for inflation and output given the nominal interest rate, which is determined by policy. Then (3) is just the tail on the dog, essentially. There's no effect of the stock of bonds or taxes on output and inflation.

    10. I disagree. There are multiple equilibria which meet (1) and (2), provided we allow for unexpected changes in output and inflation immediately following an announcement. However, if we consider equation (3), all but one of these equilibria result in the real stock of bonds rising or falling indefinitely, implying either that households are not maximising or they are engaging in a Ponzi-game. Exactly which equilibrium path avoids this depends on taxation policy.

      I'm grateful to you for engaging on this, but maybe we're never going to agree here?

    11. This isn't a disagreement, as we're just discussing mathematics. In an actual disagreement, there is no right and wrong. Yes, there are multiple dynamic solutions to (1) and (2), but (3) is irrelevant to those solutions.

    12. OK. Well, I’m happy to carry on. It’s an interesting discussion (for me at least).

      So, yes, this is about mathematics. But it’s not just about the solution to equations. It’s also about the choice of what problem we specify. And that’s where I think we may be differing.

      Take my equations (1), (2) and (3) together with the boundary conditions on b, and consider an announcement of a change in future taxes. It’s also useful to think of actual inflation, that appears in (2) and (3), as made up of expected inflation and unexpected inflation.

      The normal way to specify this problem is to take unexpected inflation as zero (or at least a random exogenous shock), even following an announcement. This means that (3) and the boundary condition do not give us complete freedom to set taxes. Taxation in at least one period must be set at a level which ensures the boundary condition is met.

      In this case, equation (3) has no bearing on output or inflation. This is the way the problem is usually specified, because when we have a central bank reaction function, it generally has to be done this way. And this is what I think you have in mind.

      However, I’m talking about a different problem (one that works fine here where we have an interest rate peg). I’m saying that we set taxes for all periods, but let unexpected inflation for the period of the announcement be determined endogenously. So I’ve simply swapped the status of a couple of variables. I’ve changed the nth tax charge from endogenous to exogenous and done the reverse for the announcement-period unexpected inflation.

      Given this, it should be fairly clear that equation (3) determines the level of unexpected inflation and since unexpected inflation also appears in equation (2), then we can conclude that tax policy will impact the solutions to (2) and (3). (Incidentally, the inflation tax due to unexpected inflation here is an exact substitute for the “missing” nth tax payment).

      Now, as you say, the maths part of this is not in question. What is perhaps at issue is whether this is a reasonable problem to specify. But, I’m pretty sure that this is equivalent to what Cochrane is doing in using the government budget constraint to choose between equilibria.

  2. Humm, sorry nut why would Cochrane model work in the first place? If indeed there is a relation between interest rate (expected and real) and output, we wouldn't be living in this conditions in the first place, would we?

    We have to account to the liquidity trap conditions, that due to the changes in liquidity preferences, monetary stimulus alone doesn't work since all liquidity will be absorbed and interest rates will remain at the zero lower bound.

    Actually if you think about it, the ZLB can only be explained by an horizontal LM...

    Ergo, it doesn't matter what the Monetary Authority does, rates will remain at zero, and if they move its not because the Monetary policy is successful, its because they lost the riskless character.

    All and all, why wouldn't monetary authorities raise rates when facing liquidity trap conditions? At least they would be giving themselves room to lower them after regaining monetary traction

    1. "...why would Cochrane model work in the first place?"

      I'm not endorsing the model, and I don't think Cochrane is either. It's just a baseline New Keynesian model.

    2. OK I understand. But IMHO this is all but a Keynesian model, since it fails to understand what Keynes saw in the first place.

      There is a tendency to see aggregated Demand and Supply like normal Supply and Demand curves, which they aren't and Keynes was very conscious of that, that leads models to have a huge "neo-classic" behaviors, namely the equilibrium adjustments, which Keynes firmly disbelieved , and its IMHO the fulcrum of his General theory.

      IMHO, any model that ignores the effect of the increased risk aversion in a depression, cannot be called Keynesian, and the "ZLB" can only be achieved in liquidity trap conditions, i.e. once you reach zero you will stay at zero, the model doesn't go back to equilibrium by itself.

    3. I certainly agree that NK models have much more to do with Prescott's work that Keynes's, but this is the state of the art now among people who call themselves Keynesians.

    4. Jose seems not to understand what equilibrium means, and also seems to think that "what Keynes meant" is somehow important.

    5. Hopefully Jose is in a mood to learn something. But learning usually happens in small steps. I don't want to overwhelm him with too much information.

    6. Always in the mood to learn Stephen...

      If you call yourself a New Keynesian (not me by the way), then yes its important to know what Keynes meant, if not you better call yourself a new something else.