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’.]

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14 Responses to Steve Williamson and the sign of the effect of interest rates on inflation

  1. Steve Williamson says:

    The “no sound theory” comment I made had to do with what I think of as the black hole theory of deflation, often articulated, but never written down formally. That “theory” says that deflation is a trap – deflation causes postponement of expenditures, demand and output fall, this makes inflation lower, and we spiral into oblivion. That’s not NK at all. BSG give two examples of models in which the Taylor rule has the bad properties you describe. In one of those models, a Friedman rule (deflation forever) is in fact optimal, i.e. the “bad” steady state is actually the good steady state. In the other one – Rotemberg’s model – there are quadratic costs to changing prices, so when there is deflation, there are welfare losses for changing prices constantly. In Rotemberg’s model, deflation is also optimal, but the optimal inflation rate is somewhere between zero and the Friedman rule inflation rate.

    An interesting question here is: What’s the optimal inflation rate? Central banks are fixated on 2%, for no good reason apparently. Some versions of NK say optimal inflation is 0%, but of course those models make a point of leaving standard long-run monetary distortions out of the model.

    • Tony Yates says:

      Thanks for these points.
      For others – there are a few papers trying to figure out where between 0 and the FR is optimal policy with sticky prices. This one, by Schmitt-Grohe and Uribe [a different paper from the one linked to in the main post, so do click through if you don’t know it] gets the answer that at the central calibrated value of price stickiness the optimal interest rate is 3.8%. This calibration [taken from a Sbordonne paper] implies firms change prices on average every 9 months. Maybe a shade too sticky?
      Another factor is that inflation is systematically overstated, perhaps by as much as 0.5-0.75 percentage points, though it’s a while since I looked at these papers.
      [Update: if you look at figure 3, page 18, of SGU, then even if you cut price stickiness in half [which i think would be a tad on the side of thinking prices too flexible] the optimal nominal rate falls only to 3.8 per cent.]

  2. I’m interested in the Concept of “Written Down Formally.” In my view, Formalizing involves Making Something Clearer or Easier to Understand. It is not necessary for Proof, for example. So, Fisher’s Theory of Debt-Deflation does not need to be Formalized to be Useful or True. Are we on the same page?’s-more-to-mathematics-than-rigour-and-proofs/

    • Tony Yates says:

      Written down formally involves verifying mathematically. Lots of results we think we can get intuition for using verbal reasoning, or having a hunch about how results would change based on knowing some other formal model, don’t turn out to be true, in my experience.

  3. Diego Espinosa says:

    Saying, “see, there’s an output gap, so there must be sticky prices” seems to assume what you are trying to prove.

    The concept “output gap” is derived from the concept “sticky prices”. One cannot “see”, or observe, the phenomena. One can observe higher long term unemployment. Short term unemployment seems close to its historical average. Some other observations: profits to gdp are at peak; asset prices are booming; ex-structures, business investment staged a robust recovery; inflation has been relatively stable. Which of these observations support the “sticky price” theory?

    • Tony Yates says:

      I’m not saying ‘there’s an output gap therefore prices are sticky’. I’m saying: there’s a theoretically coherent explanation for why central banks are keeping interest rates low to try to raise inflation: which is, that they think the natural real rate has fallen a lot, and they think prices are sticky [presumably by inspecting evidence on prices themselves].
      Unemployment is another indicator of the output gap, but you face the same problem trying to distinguish between the natural rate of unemployment [the counterpart to the flexible price level of output] and the actual rate.

      • Diego Espinosa says:

        Perhaps I misunderstood, but I thought you were treating the output gap as an observed phenomenon. For instance, you talk of the econometrician being given “data on the output gap”, and “seeing” it. Without that observed data, it is not clear how your econometrician will support the NK model over Williamson’s.

        If you meant, instead, that the output gap data was derived from your theory, then, as I argued, this is akin to assuming what you are trying to prove.

      • Tony Yates says:

        I’m not getting through to you. I’m not trying to prove anything. I’m trying to point out that there is a theoretically consistent explanation for what central banks are doing. Namely, that they think prices are sticky; from which the policy responses to deviations of inflation from target, and the existence and trajectory of the output gap would follow.
        It was loose of me to speak of ‘data on the output gap’. Given data on interest rates, inflation and output, the hypothetical econometrician would reject flexible prices, which cannot explain the apparent real effects of monetary policy shocks.

  4. daniels says:

    Tony, the question one has to ask (and I think you yourself asked in a previous blog post in 2013) is how persistent are the effects of sticky prices in response to shocks? At what does prolonged economic performance stop being due to sticky prices and wages and starts being mostly about more structural issues (not just demographics, can be a long run increase in tightness of collateral constraints after a financial crisis for example, the point is these things would affect the steady state of a flex price economy; or a persistent increase in search and matching frictions in labour and product markets when a financial crisis requires a significant change in the structure of the economy).
    At that point, looking at flexible price perspective to dynamics may become more relevant. And from that perspective current baseline forecasts are that real equilibrium interest rates should start rising over the medium run unless we’re really heading towards some new secular stagnation episode (for which monetary policy isn’t the useful tool anyways). If the equilibrium interest rates start rising earlier than imagined by the central bank but the central bank still thinks it needs to keep interest rates close to zero, then it is possible that this ends up making lower inflation expectations a stable outcome (in the sense that these expectations wouldn’t be contradicted by rational expectations). It is quite conceivable that an institution one of whose key raisons d’etre is its ability to influence the economy due to sticky prices and wages (though recent research has reemphasized that credit easing/lender of last resort central bank policies are important even without nominal rigidities) and a flock of private sector economists and financial journalists schooled heavily in IS/LM style thinking will tend to exaggerate the importance of negative output gaps and find the current situation in which both in the US and the Eurozone we see mostly positive quantity signals (e.g from PMI’s and other quantity indicators of economic activity levels).acompanied by low inflation. They would also be puzzled by the rather good performance of the Japanese economy in 2000-2007 in an environment with very low inflation. I think this is what Steve Williamson is getting at.

    • Tony Yates says:

      These are good challenges.
      But I don’t think you need to maintain that prices don’t change for 6 years to argue that there is a justification for low interest rates now. If you compare sticky price models with and without propagation in consumption and investment, for example, you can see quite different dynamics in the output gap. That is to say the output gap can be propagated out by these other sources of persistence. Monetary policy itself, perhaps initially slow to respond, and then constrained from responding, can serve to propagate too.
      Despite that I agree that much of the fall in output probably is supply side related. In the UK, for example, inflation never fell below target, which is one way of inferring just this. Things are more concerning in the US and EA though with inflation sliding.

      • daniels says:

        Aha, but that gets to the issue of real rigidities and there’s a host of reasons why real rigidities aren’t as strong as those embedded in many keynesian models (recent paper by Klenow et al on reset price inflation being much more flexible than assumed by keynesian models comes to mind). There is a precautionnary argument to be made for low interest rate policies on one hand. On the other hand, the Keynesian mindset on this is partially self fulfilling, in that the more we’re concerned about this the bigger the pessimism and uncertainty shock hitting the economy (Even in flex price models with multiple equilibria or with sentiment shocks talk of deflation could serve as a coordinating device towards a lower output equilibrium). So maybe Draghi’s attitude of trying to not make this low inflation too big a deal is reasonable after all? For another perspective on this, think of deflation fear as a form of anxiety and typical central bank responses as the opposite of classic cognitive behavioural therapy anxiety treatment recommendations,
        Ok, maybe that’s a stretch…
        On the other hand, if we’re really worried about the zero lower bound then maybe we should contemplate moving to an inflation target of 4-5% (payments systems have improved and will keep on improving, and the costs of long run inflation of that magnitude have been elusive to show- unless you really are a strong believer in the price dispersion effect emerging with Calvo pricing as a realistic feature and not just a “bug” of a non microfounded model of price rigidity). In which case, central banks would need to accept setting on average higher nominal interest rates going forward as part of the move.

      • Tony Yates says:

        I like it when comments begin ‘Aha’!
        I accept there’s a controversy about how sticky prices are. I don’t think that Bils and Klenow have the final word. See, for instance, the debate about whether sales price changes should count as price changes or not, or only changes in the ‘reference’ price. I think you can find your way to this literature by googling Kevin Sheedy.
        Speaking rather loosely, personally I would prefer policymakers to tell the truth about the risks they face, rather than try to pump up confidence by hiding them. But I can see that there’s a case for doing it.
        Agree that long run higher inflation and nominal interest rates might be warranted on account of the ZLB. But achieving it now would require lower rates for longer, paradoxically, before they would eventually be higher.
        Thanks for your contributions to my site. It’s good to have high quality vetting like this.

  5. minglingmike says:

    I hope you or someone else has the mercy to answer my stupid question: why are rising stock prices not counted as inflation? thanks

    • Tony Yates says:

      It’s not a stupid question. Whether you want to ‘count’ it in an inflation measure is up to you. It depends on what you want to achieve with the inflation measure. Economists often want to distinguish between changes in the relative price of money and final goods [what you are calling inflation] and asset prices, so there is no point in counting one in the other. Institutionally, governments have been mandated to try to preserve the purchasing power of benefits in terms of goods, which is why for them measures of inflation that exclude asset prices are appropriate.

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