Steve Williamson and the sign of the effect of interest rates on inflation

This is prompted by the latest post by Steve Williamson, where he reiterates a view he's expressed a few times, that the Fed's [and other central banks'] efforts to keep interest rates pinned at the zero bound, in an effort to push inflation back up to its presumed target, is self-defeating, since low interest rates are typically associated with low inflation.  If they want inflation to rise, he argues, the Fed should tighten policy.  To illustrate his point, he imagines a hypothetical alien econometrician trying to figure out what happened when Volcker tamed inflation in the early 1980s in the US.  Interest rates fell.  Ergo, lower interest rates caused lower inflation.

What central banks are doing is very well explained by modern New Keynesian theory.  In that theory, the nominal rate that the central bank controls has to fall if the natural real rate - the rate associated with stable prices - falls.  A central bank that sees inflation falling below its desired target would need to lower interest rates to correct the problem, or see inflation fall further below the target.  Lower rates would lower real rates, which would increase demand relative to potential supply, putting upward pressure on prices, bringing about the desired correction in inflation.

Through the lens of this New Keynesian theory, the fact that lower nominal rates are happening at the same time as low inflation does not mean that low nominal rates are causing low inflation.  On the contrary, higher rates would imply still lower inflation.  If the central bank wanted lower inflation in the long run, nominal rates would initially be raised, contracting the economy, putting downward pressure on prices, and soon after rates would be lowered in line with the new lower inflation target.

Now Steve might well say that the fact that low nominal rates are happening at the same time is circumstantial evidence that the NK model is wrong, and that on the contrary, the relationship is causal.  That's true.  But this circumstantial evidence is a very loose test of the theory.  A sterner test might be how well the theory does at matching the response of the economy to  a surprise increase in nominal rates as identified in VARs.  Such surprises are widely taken to induce falls in inflation (and falls in output).  Sims got his Nobel partly for helping us see this.  This stock-taking survey by Christiano, Eichenbaum and Evans explains 'what we have learned and to what end' [sic - I rejigged the title].  The NK model matches this empirical regularity quite well.  And, with some effort, building in mechanisms to slow the response of consumption and investment in the model, it can match the fact that these responses tend to be hump-shaped too.  Steve's alien econometrician, confronted with just interest rate and inflation data, is going to have a tough time distinguishing between the 'mistakenly chose lower inflation by keeping rates low' theory from the sticky price theory.  But if we gave her a computer, taught her the method of undetermined coefficients, and data on the output gap, I think she would reject Steve's theory.  (Because she would see the negative output gap, and be able to compute the low natural real rate warranting low nominal rates).

With flexible prices, the need for interest rates to fall to combat a fall in inflation vanishes.  The inflation-control problem becomes one simply of adjusting the money supply to offset changes in velocity.  Steve's fretting in such a world about central bank choices would be highly germane.  So this could boil down to whether you are happy to believe that prices are sticky.  And if you aren't you had better explain to us why VARs imply real effects from monetary policy shocks.

Later in his post, Steve criticises central banks for worrying about deflation.  He says:  "As far as I know, there is no sound theory that actually delivers such a phenomenon. We certainly have multiple equilibrium models in which the economy can be stuck forever in a Pareto-dominated equilibrium, but I don't know of a model like that in which a bad equilibrium is associated with deflation (maybe you do?). Indeed, in a wide class of models, deflation can be associated with Pareto optima - that's the logic of the Friedman rule (not that I'm endorsing that)."

Well, this same New Keynesian theory delivers this phenomenon exactly.  The model was shown by Benhabib, Schmitt-Grohe and Uribe to have two steady states.  One involves inflation fluctuating around the central bank's inflation target.  The other is a liquidity trap with nominal interest rates trapped at zero.  In this model, if prices are sticky, the Friedman Rule is not optimal.   Falling prices generates deviations of actual prices from desired prices which hurts firms.  In this steady-state, further contractionary shocks cannot be responded to and the lack of response (again, because of sticky prices) would generate welfare costs.  Moreover, the inability of central banks to move interest rates around allows new sources of fluctuations arising from self-fulfilling changes in views about the future.  In a model of flexible prices, where there is no motive for central bank stabilisation policy, the unattractive features of this steady state would disappear.

Recall that Steve says he knows of no 'sound' theory which has the property described above (and which would therefore cause central banks to worry so much).  So Steve may be omitting to mention this sticky price theory because he doesn't think that theory is 'sound'.  In fairness, there are lots of ways to shoot the theory down.  Even without letting the anti-macro blog-trollers in on this act, there are plenty of criticisms of the sticky price model from within macro.  Steve and his collaborators in the New Monetarist school don't like that people just assume prices are sticky because they see that they move infrequently.   They want people to try to figure out why they are sticky.  And many, like Lucas, Golosov, Midrigan, Karadi, Gertler, Leahy and others are doing just this, digging deeper.  The models they come up with are, currently, too tricky to handle to do the equivalent of the monetary policy analysis so far done in the 'let's just assume prices are sticky and be done with it' models.  [More importantly for their focus, they are also - think justifiably - pissed at the superficial way in which money is dealt with, if it is at all.  But no time to go into that here.]

However, for me, if this is what Steve is doing, he is raising the bar for 'sound' very high.  I know of no 'sound' theory that can explain the response of economies to identified monetary policy shocks, in that case, or, if such a test should not be met, contains within it an explanation of why.  And in the absence of it, if I were a policymaker, I would be happy to follow the lead of Blanchard and Kiyotaki who told us we should assume prices are sticky and be done with it (for now).  And, to recap, if you do, you will find that deviations of inflation below your intended target warrant temporarily lower interest rates;  and that if you wind up with interest rates stuck at the zero bound, and prices falling, the electorate in your economy will not thank you for it.

[Updates:  This version includes two corrections:  a link to the right Benhabib et al paper;  and revisions to clarify that the second liquidity trap steady state exists even with flexible prices.  Though I think it's correct that the costs of negative inflation in this steady state disappear with flexible prices.

Note also Steve Williamson's reply in the comments section, clarifying where he thought the gap in the theory was.  Ie not just liquidity trap steady states, but ever declining output and inflation dynamics, which he dubs the 'black hole theory'.]