On Neo Fisherianism and adaptive learning.

There is continuing debate on the blogosphere about whether, contrary to common monetary economics parlance, interest rates are not low because inflation is low, but low interest rates are actually causing low inflation, with more contributions from John Cochrane, Noah Smith and David Andolfatto.

A few thoughts.

1 I wonder if the debate isn’t gettting too hung up on models using rational expectations.  RE is just a convenient tool, probably a not very realistic one.  If we drop RE and use a version of the New Keynesian model with adaptive learning instead, we would arrive at answers that sound pretty much like what central banks already say.  And nothing like neo-Fisherianism.   Note ‘rational expectations’ refers to when agents in the model have forecasting rules for inflation that are the same as the rules you would have if you knew exactly how the model worked.  ‘Adaptive learning’ means here:  behaving like an econometrician, basing forecasts of the future on how inflation (and other things) have depended on past values of things you can see, and updating your forecasting rules as new data comes in, either validating or flouting the rule you used last time.

2 Relative to historically followed policy rules, a policy that cut rates to the zero bound and held them there, in the absence of any other shocks hitting the economy, would cause explosive upward movements in inflation.  The explosions would come from the initial upward movements in inflation causing private agents’ extrapolative forecasting rules to change, which would amplify the past movement, causing more forecast rule revisions, and so on.

3 The coincidence/comovment of falling interest rates and inflation could only come from policy responding to an inflation-depressing shock, and incompletely stabilising it.

4 If the Fed had shifted its preferences privately to deliver very low inflation, that would eventually deliver low interest rates and low inflation.  But, initially, it would have required an interest rate increase.  This seems a pretty implausible account of what happened recently.  For starters, interest rates did not increase since the onset of the crisis.  Second, FOMC members did not lower their inflation targets, or, at least if they did, they did it privately [and it didn’t even make the transcripts released] and contradicting what they had told us about their long term view of inflation.

5 In this model, although the Fisher equation will prevail in the long run, one can’t deliver a particular level of inflation with an interest rate peg worked out from this equation, unless one starts from steady state and there are no shocks.  In an economy buffeted with shocks, a fixed interest rate will cause explosive movements in inflation one way or the other, depending on the luck of the draw.

Bringing this together.  If you believe in a more realistic version of the popular New Keynesian model modified so that we have inflation expectations formed by adaptive learning, rather than rational expectations, then you can’t believe that low infaltion was caused by lowering nominal interest rates.  You’d believe things that sound pretty much like the received wisdom, the words coming out of the mouths of central bankers.

[Added later]

Making this small step on the road to realism helps simplify the problem too.  With RE we have to figure out the subleties involved with what happens when agents project out for the future fixed interest rates [if they are fixed for long enough, it can mean there are infinitely many paths for inflation] and for future fiscal policy.  With this model of learning, none of that is relevant.  Agents don’t form views about monetary or fiscal policy.  They aren’t aware that there are rules guiding policy instruments.  They simply run regressions of the things they need to care about on the things they see.

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3 Responses to On Neo Fisherianism and adaptive learning.

  1. Nick Rowe says:

    Belatedly (I only just saw this post from e-axes): good post.

    And even if we do have (strong form) rational expectations, what happens in equilibrium depends on agents’ beliefs about what the central bank would do counterfactually at points off the equilibrium path. Is the Neo-Fisherite equilibrium a Perfect Equilibrium in any meaningful sense? And if the central bank announces a new inflation target, and at the same time announces a new policy for the nominal interest rate including what it would do at points off the equilibrium path, and if that announcement is credible, we might see something like the Neo-Fisherite result.

    • Tony Yates says:

      Thanks Nick.
      My post was my conclusions after reading the brilliant but very hard Cochrane JPE. My get out clause was: I don’t think I really deeply understand this, but, since for purposes of realism RE is a step too far, I’m going to claim that we don’t need to understand it, and we can reason using the much simpler, recursive dynamic methods that learning models allow.

      • Nick Rowe says:

        I found that paper hard too!

        Most of the time, I think you are right on this. But sometimes, like when a central bank does a currency reform (the clearest case), or like when Roosevelt raised the price of gold in 1934(?), I think people set aside their learning rules. What happens next won’t be exactly strong rational expectations, but more like a new Schelling focal point, except messier coordination during the transition. How to model that…..

        The standard NK model is very reasonable on this for the interaction between the Phillips curve and the Taylor Rule. But I think it sweeps a similar problem for the Euler-IS curve under the rug. It just assumes that people expect that Y will eventually converge to Y*, provided the central bank sets the real rate respond correctly. If r = the natural rate for all t, then one equilibrium is that Y=Y* for all t. But another equilibrium is that Y=0.5Y* for all t (assuming a log utility function). Old Keynesians would (justifiably) be very upset at this assumption of (expected long run) full employment. But this problem would go away if they put M back in the model.

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