Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Saturday, October 31, 2015

NeoFisherism without rational expectations

Is the Fed's "zero-interest-rate policy" (ZIRP) inflationary or deflationary? You'd think that macroeconomists would have a straight answer for such a simple question. But we don't. As usual, the answer seems to depend on things.

Someone once joked that an economist is someone who sees something work in practice and then asks whether it might work in theory. Well, appealing to the evidence is not much help here either. We have examples like that of Volcker temporarily raising rates (by lowering the money supply growth rate) to lower inflation in the early 1980s. But then we have the present counterexample of ZIRP, which seems to be having little effect in raising inflation. Indeed, the Fed has consistently missed its 2% inflation target from below for years now (see Understanding Lowflation).

Some economists suggest that there are theoretical reasons to support the notion that ZIRP is deflationary. The proposition that targeting a nominal interest rate at a low (high) level results in low (high) inflation is known as "NeoFisherism." The idea goes back at least to Benhabib, Schmitt-Grohe and Uribe (2001) in their The Perils of Taylor Rules. The idea has been taken seriously in policy circles. My boss, St. Louis Fed president Jim Bullard wrote about it here in 2010. You can read all about the recent controversy here: Understanding the NeoFisherite Rebellion.

The basic idea behind NeoFisherism is the Fisher equation:

FE1: Nominal interest rate = real interest rate + expected inflation.

One interpretation of the Fisher equation is that it is a no-arbitrage-condition that equates the real rate of return on a nominal bond with the real rate of return on a real (e.g., TIPS) bond. FE1 implicitly assumes that the risk and liquidity characteristics of the nominal and real bond are identical. Steve Williamson and I consider a model where the nominal bond (potentially) carries a liquidity premium, in which case FE1 becomes:

FE2: Nominal interest rate + liquidity premium = real interest rate + expected inflation.

I'm not aware of any economist that disputes the logic underlying (some version of) the Fisher equation. The controversy lies elsewhere. But before going there, let me describe the way things are supposed to work in neoclassical theory.

Start in a steady-state equilibrium where FE1 holds. Now consider a surprise permanent increase in the nominal interest rate. What happens? Well, a higher nominal interest rate increases the opportunity cost of holding money, so people want to economize on their money balances. However, because someone must hold the outstanding stock of money, a "hot potato effect" implies that the equilibrium inflation rate must rise (the real rate of return on money must fall). In the new steady-state equilibrium, real money balances are lower (the price-level and the inflation rate are higher than they would have been prior to the policy shock). If people have rational expectations, then absent any friction, inflation expectations jump up along with actual inflation. If there are nominal rigidities, then inflation may (or may not) decline for a while following the shock, but in the long-run, higher interest rate policy leads to higher inflation. [Aside: my own view is that a supporting fiscal policy is needed for this result to transpire; see here: A Dirty Little Secret.]

The conventional wisdom, however, is that pegging the nominal interest rate is unstable. Suppose we begin, by some fluke, in a steady-state where FE1 holds. Now consider the same experiment but assume that people form their expectations of inflation through some adaptive process; see Howitt (1992). For example, suppose that today's inflation expectation is simply yesterday's inflation rate. Then an increase in the nominal rate must, by FE1, lead to an increase in the real interest rate. An increase in the real interest rate depresses aggregate demand today (consumer and investment goods). The surprise drop in demand leads to a surprise decline in the price-level--the inflation rate turns out to be lower than expected. Going forward, people adapt their inflation forecasts downward. But given FE1, this implies yet another increase in the real interest rate. And so on. A deflationary spiral ensues.

For those interested, refer to this more detailed discussion by John Cochrane: The Neo-Fisherian Question.

Now, the thought occurred to me: what if we replace the assumption of rational expectations in my model with Williamson (cited above) with a form of adaptive expectations? What would happen if we performed the same experiment but, beginning in a steady-state where there is an "asset shortage" so that the FE2 version of the Fisher equation holds. My back-of-the-envelope calculations suggest the following.

First, because expected inflation is fixed in the period the nominal interest rate is raised, FE2 suggests that either the real interest rate rises, or the liquidity premium falls, or both. In our model, there is substitution out of the cash good into the credit good. But because there is a cash-in-advance constraint on the cash good, i.e., p(t)c(t) = M(t), it follows that a decline in the demand for c(t) corresponds to a decline in the demand for real money balances--that is, the price-level p(t) must jump up unexpectedly (for a given money supply M(t)).

Now, given the surprise jump in the price-level, an adaptive expectations rule will adjust the expected rate of inflation upward. What happens next depends critically on the properties of the assumed learning rule, the policy rule, etc. For my purpose here, I make the following assumptions. Suppose that the economy remains in the "asset shortage" scenario and assume that the government fixes the money growth rate at exactly the new, higher, adaptively-formed, inflation expectation. In this case, the economy reaches a new steady-state with a higher interest rate, an arbitrarily higher inflation rate, and an arbitrarily lower liquidity premium (conditional on the liquidity premium remaining strictly positive). [Note: by arbitrary what I mean is that the new inflation rate is determined, under my maintained assumptions, by the initial surprise increase in inflation, which may lie anywhere within a range such that the liquidity premium remains positive. In the absence of a liquidity premium, the inflation rate would rise one-for-one with the nominal interest rate.]

I hope I made my point clear enough. The claim that increasing the nominal interest rate leads to higher inflation does not depend on rational expectations as is commonly claimed. A simple adaptive rule could lead to higher inflation expectations. The key is whether the price-level impact of increasing the nominal interest rate is positive or negative. If it's positive, then people will revise their adaptive expectations upward and, depending on the learning rule and policy reaction, the ensuing inflation dynamic could play itself out in the form of permanently higher inflation. The NeoFisherite proposition is possible even if people do not have rational expectations.

Postscript Nov. 01, 2015
Tony Yates suggests the cost channel in Ravenna and Walsh (2006)  together with least-squares learning might deliver the same result. It's a good idea. Somebody should try to work it out! 


  1. Sure it doesn't depend on RE, but it does depend on the expectation that the interest rate increase is permanent, yes?

    1. In general, the result depends on all sorts of things: the learning mechanism, the policy reaction function, the direction of the initial price move, etc. For the restrictions I had in mind for my particular example, I think the answer is yes, the interest rate must stay elevated (since if the shock is temporary, the process would work in reverse).

  2. Prof. Andolfatto,

    Thanks for this. I would need a clarification, though.
    You set as just an aside (but in fact it is anything but an aside) that a supporting fiscal policy is needed for the Neo-Fisherian result to hold, as you explained in your "A Dirty Little Secret" of a while ago.

    This means that when Neo-Fisherites claim that increasing the nominal interest rate leads to higher inflation, the fiscal authority is also implicitly assumed to increase the rate of growth of its nominal debt (for a strictly positive nominal interest rate and a constant money-to-bond ratio, so as to finance a higher primary budget deficit (for instance, in the form of helicopter drops).

    In other words: the monetary authority has to print more money, and the fiscal authority has to spend it, for the Neo-Fisherian result to yield. Is that correct?

    Yet this implies that, for an increasing nominal interest rate policy to deliver higher inflation (in the Neo-Fisherian spirit), the monetary authority has to raise the rate of money supply growth. In other words, it is not really that the monetary authority has to raise the nominal interest rate; on the contrary, it needs manage (viz, increase) money supply today so that spending increases, inflation rises, and eventually the nominal interest rate reflects the rise in inflation.

    If that is the case (and unless I am missing somethjng), it seems that we are back to the traditional chain of causation, while simply raising the nominal interest rate today would not set in motion the same chain of causation and would not end up in higher inflation.

    Where am I wrong?

    1. I don't think you are wrong. See the following links.

    2. Thanks. But if you think I am not wrong, then it is not true that increasing the nominal interest rate leas to higher inflation, and Neo-Fisherism is simply a case of taking the wrong nexus of causation. Isn't that so? I am bit confused...

    3. Neo-Fisherism implicitly assumes that the monetary authority is dominant over the fiscal authority. There is usually an equivalence between the policy rate and some quantity variables (like the money/bond ratio). Under this scenario, the central bank "causes" the interest rate to go up, either directly (with the quantity variables adjusting passively) or indirectly through direct manipulation of the quantity variables. Implicit in all of this is an accommodating fiscal authority.

  3. This argument deeply frustrates me because of the implication that it has some bearing on Fed policy, when it doesn't. There are two reasons.

    1. The analysis generally assumes that the Fed's interest rate target is pegged. It's not. The Fed can move it anywhere it wants anytime it wants, and the markets know it. Plus, the Fed has repeated over and over that its "nominal anchor" of a 2% inflation target (or ceiling?) is sacrosanct. No serious observer thinks that the Fed Funds target will stay at zero if there's even a whiff of inflation.

    John Cochrane acknowledged this error here:

    2. The argument is cast in exactly the wrong terms: "Is the Fed's "zero-interest-rate policy" (ZIRP) inflationary or deflationary?" is exactly the wrong way to frame the question. Whether ZIRP is inflationary or deflationary depends entirely on the rest of monetary policy and also the market's expectations of future monetary policy.

    Nick Rowe has a very good post explaining this error:

    So please, stop asking this question, because it's the wrong question. The Fed's interest rate target could be inflationary or deflationary. Raising the target could be expansionary or contractionary. It depends on the rest of policy. Suppose the Fed said to the markets, "guess what, we're setting the Fed Funds target to 5%, and we want to see how long the US economy can remain in deflation, regardless of unemployment. We'll be satisfied after a year of -2% inflation." Or, suppose the Fed said to the markets, "guess what, we're setting the Fed Funds target to 5%, and changing our inflation target to 4%, and guess what, it's not a ceiling any more, we'll actually tolerate inflation of up to 10% if we are at less than full employment, which we're redefining as U-6 of less than 3%."

    Same interest rate target. Different effect.

    The question I wish people would ask is, how do we get the Fed to support aggregate demand properly, rather than allowing the AD disaster of 2009 and then acting like it had done everything it could?

    Kenneth Duda
    Menlo Park, CA

    1. Ken,

      I agree with you and thought about mentioning the fact that "ZIRP forever" may not be a very good approximation for Fed policy. I agree with your point 2 as well.

      Nevertheless, I thought it would be a useful thought experiment to frame the question the way I did. First, we know since at least Benhabib, et. al. (2001) that a Taylor rule based on the Howitt/Taylor principle and a ZLB constraint can give rise to ZIRP as a global long run equilibrium. Jim Bullard worries that these dynamics are in play right now. This is one reason why he favors some form of lift off now.

      Now, of course, the proper policy experiment is not to consider a once and for all increase in the policy rate; rather, it would be to consider a shift in the entire policy function--a shift that would entail, among other things, an increase in the current policy rate (together with a path for the rate to its new long run equilibrium). I talk about this here:

      But in that post, the NF argument would seem to depend critically on RE. The point of my post here is to suggest that RE is not necessary to deliver a NF-like result. I think my argument would survive even in a more carefully specified Fed/Treasury policy functions.

      Thanks for your comment!

  4. you say : "because someone must hold the outstanding stock of money, a 'hot potato effect' implies that the equilibrium inflation rate must rise"--but why is this true? Doesn't the fed raise interest rates by selling Treasuries, which then reduces the amount of cash in the economy?
    We only talk about the fed "raising the rate," but really what's happening is the fed sells assets to soak up cash such that the rate raises, and it's not at all clear to me how this would imply increasing asset prices, commodity prices, or wages.
    Do you have a formal model for this step? I think that might clarify things a lot!

    1. Tyler, yes, we usually think of the Fed raising rates by selling treasuries. Here is a model that formalizes this conventional view:

      My post here, however, is based on this model here:

      In that model, the Fed raises the policy rate but the money-to-bond ratio adjusts endogenously. I think there is a corresponding change in open market operations that entail fewer swaps of money for bonds. Still, the existing stock of money must be held by somebody in the economy. And the price-level, in these models, must adjust to ensure that the quantity of *real* money balances is willingly held.

      Let me know if this doesn't fully answer your question. I have to run off now. Back in a bit.

  5. > Start in a steady-state equilibrium where FE1 holds. Now consider a surprise permanent increase in the nominal interest rate. What happens? Well, a higher nominal interest rate increases the opportunity cost of holding money, so people want to economize on their money balances. However, because someone must hold the outstanding stock of money, a "hot potato effect" implies that the equilibrium inflation rate must rise.

    Is it an increase in rate because the economy is suddenly expected to perform better or because central banks tightened? Wouldn't that make all the difference?

    If it's central bank action, no one should need to hold the outstanding stock, it will simply be removed from the economy.

    1. Ah yes, I think you could be correct. Perhaps I should not have assumed that M(t) remained fixed in the experiment (with other policy variables adjusting implicitly to make the interest rate rise). But even if M(t) fell, the question would be how much does it fall relative to the decline in the demand for M(t).

      Thanks, Benoit.

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  7. Yes, this is the preferred view of the Fisher Effect. What happens to Inflation depends on many factors. Basically, inflation begins to float away from nominal rates that sit there like a couch potato. But where does inflation float to? Well, that depends on labor share movements, money streams through the economy, which sectors see inflation and which don't, and just like you say, people form their expectations around reactions and constraints beyond movements in the nominal rate.
    here is my post of the conclusion that I came to...

    1. Ed, personally, I am skeptical of the NF proposition. My own view is that supply/demand factors (with emphasis on fiscal policy) are important; see here:

    2. David, In your paper you say that long-run inflation is ultimately determined by the fiscal authority. I see your point in the model, yet the dynamics of wage increases also affect long-run inflation. It seems now that wage dynamics is the over-riding factor. Does your model speak to this?

    3. No, it doesn't. I don't even have labor in that model, there is just an endowment and a storage technology. But if I added labor in, its price would be determined competitively. It would be of some interest to model the labor market as a search market where firms and workers bargain over wages. In that sort of set up, the wage dynamics may play a more interesting role.

      I'm curious, however, what you mean by the fact that wage dynamics are presently the over-riding factor. Do you mean real or nominal wages? And do you mean wage dynamics irrespective of how labor productivity is evolving?

  8. David: If I understand you correctly, the Central Bank in your thought-experiment increases the nominal rate of interest at time t while holding M(t) constant. In effect, it is announcing that bonds will pay higher coupons than originally promised, while keeping M(t) exogenously fixed.

    But that is not how the Fed (or BoC) operates. By announcing a higher nominal interest rate, the Fed is announcing that it will freely trade money for bonds at a higher nominal interest rate. So M(t) falls if there is an excess supply of money/excess demand for bonds in the market where money is traded for bonds.

    In your thought-experiment, if the government (or CB) announces higher coupons on bonds, while holding M(t) fixed, wouldn't bond prices immediately jump up to restore the original nominal interest rate?

    1. Let me try a slightly different thought-experiment: suppose the rate of interest (on bonds) increased because of (say) and increased desire to invest or a reduced desire to save. Assume adaptive expectations on inflation, so that is both an increased real and nominal rate. And suppose the central bank holds M(t) constant. If M pays 0% interest, that increase in i and r increases the opportunity cost of holding money, and causes an excess supply of money, which causes P(t) to rise.

      That is the standard result in a flexible-price version of the ISLM model. I shifted the IS curve to the right, which shifts AD curve right, which causes P to jump up, to reduce M/P and shift the LM curve left.

      But that is very different to how the central bank raises i. The central bank raises i by shifting the LM curve right/down, in a model where P cannot jump.

    2. Curses: I meant to say:

      "But that is very different to how the central bank raises i. The central bank raises i by shifting the LM curve LEFT/UP, in a model where P cannot jump

    3. Nick, another person commented that I might not have my thought experiment quite right. This is entirely possible, as I have not worked it out formally.

      In the context of the experiment I was thinking about, I suppose we could think of a decrease in the money-to-bond ratio. This is possible with a fixed money supply if the supply of bonds is increased. In this case, there is a supporting fiscal action to my story (but I think such fiscal support is necessary for any "monetary policy" thought experiment).

      In any case, I was just thinking of any way in which a policy change that involved a higher nominal interest rate might also, on impact, cause the price level to rise. Tony Yates suggested the Ravenna and Walsh cost channel story. I think I've seen Christiano et al use similar set ups where firms need to borrow to finance operating costs or part of the wage bill. In such a set up, an increase in the nominal interest rate will increase costs, which may be passed onto consumers. From there, all we need is to let adaptive expectations do the rest of the work. It's an interesting possibility, I think--one I've never heard discussed before.


    4. David: Suppose the government does a helicopter bonds operation (bond-financed transfer payments). And suppose some people are borrowing-constrained Hand-To-Mouth types, so Ricardian Equivalence fails. For a given M(t), that would raise (real and nominal) interest rates, increase the opportunity cost of holding M(t), cause an excess supply of M, and put upward pressure on P. In ISLM terms, the fiscal loosening shifts the IS curve right, which shifts the AD curve right.

      "Tony Yates suggested the Ravenna and Walsh cost channel story."

      Puts on Grandpa Simpson voice. You and Tony Yates are far too young. Back in the late 1970's, we used to hear that argument all the time. From crazed Post Keynesians, and cranky amateurs writing letters to the editor. They said that the Bank of Canada's raising interest rates would raise firms' costs, and so cause inflation to increase further. They were wrong in theory and wrong in practice. They were wrong then and are wrong now. They failed to distinguish between a one-off increase in the price level (that the cost-push argument might or might not cause, if nominal wages are sticky), from a permanent ongoing downward pressure on inflation, that would only accelerate as expectations adjusted, due to the reduction in aggregate demand. We defeated those people thoroughly, back in the days of 'trench warfare monetarism', as they called it.

    5. Nick, I read your first paragraph above as supporting my thought-experiment (though you may not agree that this is what monetary policy is about). Am I correct?

      In terms of whether higher interest rates "cause" inflation or not, I don't know, I remain somewhat agnostic. As you know, what's important is how an entire policy regime changes, not just the contemporaneous change in a policy variable.

      Having said this, there is the "price puzzle" in the VAR literature which shows that inflation tends to rise in the short-run following a (temporary) increase in the policy rate.

      In terms of theory and evidence, I found this paper very interesting (about the Brazilian hyperinflation):

    6. David: On my first paragraph: yes, it supports your "raising interest rates causes a higher price level". But I would call that (expansionary) fiscal policy, not monetary policy.

    7. I always thought, and I am not an economist, that more lending could lead to higher inflation, not some artificial peg. And also, demand for bonds as an asset causes an asset shortage of bonds. That pushes yield down.

  9. Prof Andolfatto, you say:

    "Neo-Fisherism implicitly assumes that the monetary authority is dominant over the fiscal authority. There is usually an equivalence between the policy rate and some quantity variables (like the money/bond ratio). Under this scenario, the central bank "causes" the interest rate to go up, either directly (with the quantity variables adjusting passively) or indirectly through direct manipulation of the quantity variables. Implicit in all of this is an accommodating fiscal authority."

    Forgive me, I am still not clear: if, as you say, the central bank "causes" the interest rate to go up, either directly (with the quantity variables adjusting passively) or indirectly through direct manipulation of the quantity variables, in all cases it is restricting the money supply. How is this possibly leading to higher (expected) inflation?

    Ok, you also say that implicit in all of this is an "accommodating" fiscal authority, and you are actually stating this point more precisely in replying to Nick Rowe, by assuming that as the central bank raises the nominal interest rate, the fiscal authority increases its rate of growth of its nominal debt. But it seems to me that rather than accommodating, the fiscal authority would then have to lean against the central bank wind by contrasting the increase in the cost of money with larger public deficits. In the end, then, if inflation is ever to rise in this model, it would be the result of the greater impact, on balance, of larger deficits on aggregate demand.

    Unless, of course, higher nominal interest rates are assumed to stimulate demand, through, for instance, the future consumption channel via the Euler equation. But even in this case, the higher nominal interest rates have to "financed" by larger public indebtedness. Is this what the Neo-Fisherites are saying? In other words, what is the transmission channel from higher nominal interest rates to higher inflation?

    1. I do not wish to speak for all who hold the Neofisherite banner. I share the view state in your concluding paragraph. You may also want to read this:

      Having said this, there are Neofisherites who state their propositions in the context of "cashless" economies. I am not entirely clear what the role of fiscal support is in those models. They seem to rely very heavily on rational expectations and not on balance sheet effects.

  10. I'd certainly agree that you don't need RE to get a neo-fisherite effect, but the reason I don't draw too much from neo-fisherism is that permanently raising the interest rate is just not an available tool for the monetary authority. All they can do is raise the rate currently and tell people what they intend to do in the future. This is consistent with a model in which the rate is raised permanently. But it is also consistent with different models.

    For example, it might be consistent with a model in which the interest rate is increased, the economy dives and the monetary authority is forced under political pressure to reduce rates again. And there's no reason why such a model should not be RE consistent, if we want that to be a criterion.

    Of course, we can look at models where the interest rate is raised permanently and the results may be interesting and useful. But it doesn't mean that raising the rate now in the real world and intending to keep it raised will actually mean that the best model is one where the rate stays raised. I find the alternative model much more plausible.

    1. Nick,
      If you agree that you don't need RE to get an NF result, then you've made me happy! I don't think the result is obvious a priori, however. And I still haven't a proof of the proposition.

    2. Nick Rowe:
      "... "raising interest rates causes a higher price level". But I would call that (expansionary) fiscal policy, not monetary policy...."


      Yet, as regards causation, the impact on inflation would derive from the fiscal stimulus financed via larger public debt. And, to the extent that the central bank keeps M(t) constant, debt financing results in a higher real and nominal interest rate: no NF causation, here.

      Moreover, if the central bank were to accommodate the fiscal stimulus by increasing M(t) so as to keep M(t)/D(t) constant, the real rate would stay constant, the impact on inflation would be larger than under no monetary accommodation, and the nominal interest rate would rise one-to-one to incorporate higher inflation. Again, no special NF causation here.

      In the end, I fail to see how one can obtain NF results (either with or without RE).

  11. David: You start with a "Neoclassical" model with money (I assume something like MIU/CIA/CGCG), and then work out the consequence of an increase in the nominal interest rate.

    I think this approach is misleading, because in these models the policy instrument is the money growth rate, *not* the nominal interest rate. Since the response of the nominal interest rate to changes in the money growth rate has the opposite sign when prices are sticky, this is an important distinction.

    Take your experiment of an increase in nominal interest rates. In the flexible price model, this corresponds to an increase in the money growth rate (which raises inflation, and thus nominal interest rates). This is expansionary monetary policy.

    I would argue that the proper analog of this policy in a NK model is *not* a policy of setting the same path of nominal interest rates, but replicating the path of money growth. In other words, the analog of "raise the money growth rate" in the flexible price model, is "shift the Taylor rule towards looser monetary policy" in the NK model, which lowers interest rates in the short run, but raises them in the long run.

  12. To add to my comment above:

    My hypothesis is that when Neofisherians say, "we should raise nominal interest rates to raise inflation", they mean what New Keynesians mean when they say "we should raise the inflation target."

    The disagreement is that NFs seem to think that such a policy would be implemented by the Fed announcing that it is raising interest rates tomorrow, while NKs think it would be implemented by credibly announcing a higher inflation target (and then raising interest rates when inflation starts to rise).