Monday, September 21, 2015

The classical mechanics of Wicksell

Simon Wren-Lewis quotes Andrew Haldane (chief economist at the Bank of England):
QE’s effectiveness as a monetary instrument seems likely to be highly state-contingent, and hence uncertain, at least relative to interest rates. This uncertainty is not just the result of the more limited evidence base on QE than on interest rates. Rather, it is an intrinsic feature of the transmission mechanism of QE.

Haldane continues at the link on Wren-Lewis's blog:
All monetary interventions rely for their efficacy on market imperfections. The non-neutrality of interest rates relies on imperfections in goods and labour markets. Stickiness in goods prices and wages ... allow shifts in nominal interest rates to influence real activity. The effectiveness of QE relies on these goods and labour market frictions too. But it relies, in addition, on imperfections in asset markets.
Also at the link, Haldane says:
All of which has direct implications for the transmission mechanism for QE. If asset frictions are highly state-dependent and volatile, so too will be the efficacy of QE. Estimates of the impact of QE during periods of high risk premia and disturbed financial conditions may be very different than when asset markets are tranquil and risk premia low.
Let me see if I can sum up here. The effect of QE on interest rates depends on:
  • Price stickiness in goods and labor markets
  • Frictions in goods and labor markets
  • Imperfections in asset markets
  • Risk premia in asset markets
  • State-dependent asset frictions
  • ... etc (more at the link)
The more obvious conclusion, Mr. Haldane, is that QE doesn't work the way you thought ... like, at all. I'm going to put out a bold claim here that adding effect X isn't going to suddenly take you from not being able to describe the data at all to describing it really well.

Imagine if Davisson and Germer upon discovering scattering peaks from their nickel-oxide crystal target had said that "electron scattering seems likely to be highly state-contingent"? And imagine if they started to add a bunch of very complicated electromagnetic effects coupling electrons to light waves in order to reproduce the diffraction pattern?

Lucky for us, they didn't and instead used their experiment to back up de Broglie's wave-particle theory. [FYI, the data from that experiment is shown in the picture at the top of the post.]

QE doesn't seem that complicated to me. And it even works for the UK:

The macroeconomic theory everyone seems to be working with (still) is the Wicksellian natural rate of interest. Paul Krugman mentioned it today. It really does create a unifying picture the various views of quantitative easing. Imagine it as the last common ancestor of Austrian, Keynesian and monetarist theories of economics. It proposes the existence of a (not directly observable) natural rate of interest where if rates are below it, inflation accelerates and if rates are above it, inflation decelerates.

Everyone seemed to be operating under the assumption that QE would, ceteris paribus, lower interest rates below the natural rate, causing inflation to accelerate. The failure of inflation to accelerate has been rationalized in several ways (not all mutually exclusive):
  1. Not enough QE
  2. It will: next month, next year, ...
  3. Going below the natural rate requires negative nominal rates
  4. QE is expected to be taken away
  5. QE depends on conditions
  6. QE has nonlinear effects on the natural rate
There are more (including Mark Sadowski's theory that QE has actually has lead to inflation at a tiny fraction of the rate predicted by the quantity theory of money), including a #7 that I'll get to later.

No one seems to be arguing for number 1; (almost) everyone thinks the trillions of dollars (in the US) and billions of pounds (in the UK) should have shown something if they were going to.

Number 2 includes the permahawks, the inflationistas, the Austrians and people at Zero Hedge. This view is not irrefutable per se, but it's been almost a decade. Long and variable lags, indeed.

Number 3 is the liquidity trap argument.

Number 4 is part of the thinking in a version of the liquidity trap argument (Krugman's 'credible promise of irresponsibility'), but is also the monetarist view.

Number 5 is Haldane's view above, but is not limited to him.

Number 6 can be included in 5, but is also implicit in the calls for a more complicated macroeconomic theory that takes into account financial markets, behavioral factors and non-linear models.

All this leaves out the idea:
7. The Wicksellian view is wrong.
This might be hard to take. Paul Krugman says at the link above: 
As I’ve been trying to point out – and as others, notably Ben Bernanke, have also tried to point out – such monetary wisdom as we possess starts with Knut Wicksell’s concept of the natural interest rate.
Emphasis mine [3]. But it's been around for over a hundred years. It wasn't really based on data (I checked Wicksell's Interest and Prices).  Actually, you could easily make this theory fit any data you'd like. Look at interest rates set by the central bank. If there is (accelerating) inflation, interest rates are below the "natural rate" and if there isn't, rates are above the "natural rate". Since there's no indicator of what the natural rate is besides its supposed effect on inflation [1].

That is of course unless interest rates head down to zero (or very low values) and you still get disinflation. In that case the Wicksellian rate has to be very negative today and in the US we've been above it since the 1980s (hence the constantly falling inflation). With QE, we've kind of pushed the Wicksellian rate off the bottom of the graph [2].

Maybe it's time to stop coming up with new frictions or expectations and just give up on the idea of a natural rate of interest. 

PS I just found out Knut Wicksell and I have the same birthday.


[1] It's similar to the market monetarist view where the indicator of the stance of monetary policy is determined by the variable it's supposed to affect ... NGDP.

[2] Interestingly, that's also a problem with market monetarism ... the economy has grown, requiring a larger monetary base, so no one can expect the central bank to take back all of the QE, hence some of the QE should have produced inflation. If the inflation rate is falling, it must mean that the inflation rate without the QE would have fallen a lot more.

[3] And after writing this, I saw that Mark Thoma put out a bunch of tweets (including a link to Krugman) making references to the natural rate. E.g. this one.


  1. I still do not understand why QE gets a special name. It's essentially asset purchases. All central banks ever do is asset purchases.

    That aside, it doesn't seem like the 'neo-wicksellian' view is really even part of any macro theory; just rationalizations of the way monetary policy works. In the basic two equation New Keynesian models (I don't know if they should really be called that, but for sake of a better term... Also, I'm assuming the CB follows a Taylor Rule that follows the Taylor Principle), for example, permanently reducing the nominal interest rate, which is the same as reducing the inflation target increasing the nominal interest rate for a given inflation rate, will result in lower inflation. Also, inflation only accelerates/decelerates under certain monetary-fiscal policy combinations that have nothing to do with the wicksellian logic at all.

    So, yeah, I guess I agree with number seven, but I don't really think that conclusion should be all to unconventional.

    1. Hi John,

      I tend to think of QE as a policy of asset purchases that raises reserves above reserve requirements (i.e. excess reserves). These are asset purchases don't result in additional physical cash in the economy. However, that just seems like a logical interpretation of the data -- which in no way indicates whether it is right.

      I think the Wicksellian view is always somewhere behind the use of monetary policy to guide the economy ... whether through interest rates (in which case it is direct; central banks make interest rates fall until inflation pressures appear and raise them to remove inflation pressures) ... or through monetary expansion (more money reduces the price of money measured by the interest rate).

      I agree that fiscal policy can be viewed independently of the natural rate of interest -- for example, in a pure Phillips curve economy fiscal policy can raise inflation and lower unemployment. Or, using the concept of NAIRU (which seems like the same Wicksell logic just transferred over to wage-price spirals instead of investment-price spirals in Wicksell).

      However, in most mainstream views the reason fiscal policy works is that the mechanism of monetary offset is cancelled out by e.g. the liquidity trap argument (#3 above).

      Mark Thoma links to a paper (I linked to the tweet in footnote 3 above) that begins:

      The natural rate of interest is a key concept in monetary economics because its level relative to the real rate of interest allows economists to assess the stance of monetary policy. However, the natural rate cannot be observed; it must be calculated using identifying assumptions. ... [Two different] approaches indicate that the natural rate has been above the real rate for a long time.

      So I think it is widely viewed as central to ... um ... central banking.

    2. Hi Jason,

      To clarify, when I mentioned fiscal policy I was talking more in line with the fiscal theory of the price level (see here:, here:, and here:

      With regard to the natural rate of interest, I don't deny that it's a part of NK theory, it is just different in NK models than how it is presented by people. The natural rate of interest in an NK model is just the real interest rate at which output is at its flexible price level. Inflation determination works completely independently of the natural rate of interest (which is why all you need to have a working NK model is a Taylor Rule and a Fisher relation). The Phillips curve only relates output to inflation rather than actually causing inflation - that's what the CB does.

      P.S. I don't know if it's strictly legal, but I found a chapter of Michael Woodford and Benjamin Friedman's that proved to be really informative and gives a nice overview of the price-determination literature:

    3. I agree -- as I mention below, I was taking Wicksell as the last common ancestor of modern economic theories. It helps organize the reasoning for why QE did or didn't have an effect. It's not exactly what e.g. market monetarists or Keynesians think, but it does represent a core nugget in the connection between monetary policy, inflation and output.

      I'm not as familiar with the fiscal theory of the price level, but I didn't mean to preclude its existence when I mentioned the Phillips curve and NAIRU. This was mostly about monetary policy and the effects of QE.

      And thanks for the links!

  2. No one seems to be arguing for number 1; (almost) everyone thinks the trillions of dollars (in the US) and billions of pounds (in the UK) should have shown something if they were going to.

    I think some of the sec-staggers have been arguing for 1. They are convinced that the Wicksellian natural rate is seriously negative, and that inflation needs to be raised so that the real rate can be pushed down further. How to increase inflation, they are vague about, but I gather they think more QE will do it via the same-old, same-old money multiplier + quantity theory thinking that never dies.

    1. Additionally, Nick Rowe seems to believe that the central bank should just buy up everything on Earth until it raises the inflation rate -- that's QE-infinity.

      Matt Yglesias also seems to think you can do some more QE if things get bad ...

      But yes, I put the "(almost)" in there because there are some who think even more QE at some point just has to raise inflation.

  3. "PS I just found out Knut Wicksell and I have the same birthday."

    You don't look a day over 160.

  4. "Actually, you could easily make this theory fit any data you'd like."

    A similar pattern that we've seen before:

    X causes Y but the only way to tell if X is present is to observe Y. If Y then there must have been X. If not Y, then X was insufficiently present.

    We could create such a theory that blames particular people using that pattern. NGDP is caused by Scott Sumner's attitude. If NGDP is too low, it means Scott is putting out negative NGDP vibes and he needs to improve his attitude. If it's too high, then he should probably back off a bit and take a chill pill.

    1. What to call that school of thought... hmmm. Perhaps "Sumnerian Monetarist." Maybe I should adopt that handle and start pestering Scott everyday about it (along with the rest of the ...uh... 'persistent' critics he attracts):

      "Scott, is see that NGDP is still lagging... You're clearly not trying hard enough!"

    2. I wonder if there's some connection between the MMist conception of expectations and Newcomb's paradox?

    3. It's also behind the "confidence fairy" and pretty much anything that has to do with expectations.

  5. Don't you think calling it "The classical mechanics of Wicksell" is a bit too flattering? After all, classical mechanics is actually useful under many circumstances, and was sufficiently accurate to get us to the moon (I think!... let me know if I'm wrong about that).

    I get what you mean in this context.. with respect to the Davisson and Germer experiment. But still!

    Also, reaching back a bit further in time, I have the impression that the QTM actually originated with David Hume. Do you know if that's true? The market monetarists are really working from that model (more or less) aren't they? I don't recall them focusing too much attention on Wicksellian natural rates. They're all about expectations.

    1. Regarding my 2nd paragraph, I just read your reply to John. So you think the MM guys are also worried about the natural rate?

    2. I know your question was intended for Jason, but I can't help jumping in here.

      It seems to me from how Sumner and monetarists in general is that they try their best to ignore the natural rate by claiming that the ZLB is irrelevant. If there is a natural rate and it is strictly negative so that the ZLB binds, then monetarists should agree that monetary offset no longer occurs, but they seem to just believe that central banks are omnipotent and can cause the price level to go up by sheer force of will (much like a lot of people think politicians can make job growth increase for no apparent reason, for example)

    3. first part continued:

      Nick Rowe wrote a post that sort of explains the monetarist view of interest rates (here: Nick's view of Neo-Fisherism seems to suggest that he thinks natural rate logic is flawed because the interest rate is a bad indicator of the stance of monetary policy (i.e. high interest rates mean tight monetary policy in some circumstances but not others).

    4. I would say Sumner and Rowe represent "market monetarist" rather than simple "monetarist" views ... the difference -- as you point out John -- is that they don't think interest rates are a good indicator of the stance of policy. Rowe still says macro policy can be done via inflation targeting by changes in interest rates (essentially as Canada does now), which is more traditional monetarist.

      The traditional monetarist view did think in terms of interest rates (Volcker, Greenspan), but more in terms of targeting (expected) inflation via changing interest rates (which utilizes the Wicksellian mechanism).

      As I mention above, I don't necessarily think the different theories are exactly Wicksell -- Wicksell is the last common ancestor.

      I didn't mean to say that the theories are exactly Wicksell (evolution can produce feathers and fur from scales). It's just that Wicksell can be used to understand each of the different theories.

    5. People do attribute the quantity theory to Hume (as well as many others in more ancient history as Wicksell notes in Interest and Prices). Wicksell believed (if I understand it correctly) the quantity theory was best understood in terms of interest rates ... but I don't think that makes him any less of a 'monetarist'.

      Interest rates reflect the "price" of money, which is affected by supply and demand shocks -- not just supply shocks.

  6. Cochrane derives a nice analysis of QE using a present value equation for an economy when mv=py doesn't hold.

    1. Thanks LAL, I'll have to check that out.

    2. ...or rather the monetarist interpretation...I think there is a YouTube video ...and some papers...most if it reveals no effect

  7. Some stuff that might interest you:
    (The second and third section concern the natural rate of interest)

    Observations that suggest that there is no natural rate of interest:

    1. Thanks for the links. Although I actually agree with Krugman's quote about "Talmudic scholars" of Keynes, Wicksell, etc ...

      And there is a natural rate of interest! It's the information equilibrium value of the price in the market

      (r ⇄ p) : NGDP ⇄ MB


  8. Jason, you are among the few that distinguishes between reserves and currency 's effect on inflation. I tend to view reserves simply as being permanent bank capital -- it supports leverage and drives interest rates. In short, reserves set the price of riskless-to-risky debt.

    Reserves are all about debt, not NGDP. QE 1 was mostly about improving information transfer in the banking system (which was overleveraged and facing possible default), and returning banks back to an equilibrium. Post-QE, the demand for debt correspondingly went up, the debt supply remained slow, and so the price of income rose, and rates fell.

    Reserve-generating QE has been highly effective at stabilizing debt markets, but little else. This should be one of your QE-effectiveness options.

    Re Wiksell, I can buy the idea of a natural rate of RGDP growth and therefore much of NGDP (demand). Under the gold standard of Wicksell's time, money was fixed -- hence a possible natural rate (supply). As far as I can tell, rates are only the interaction of CB supplied MB (supply) and NGDP (demand).

    When debt markets presume that the CB will provide elastic supplies of MB on demand, there is no fixed rate of interest for NGDP. Or rather, there could be a Wiksell-ian natural rate to keep the debt markets kicking along, but nobody should say that this has anything to do with NGDP.

  9. I think the thing that most people are missing is that the interest rate and inflation rate determine the velocity of money. If the interest rate goes down the velocity of money goes down. So while the equation of exchange still works, the simplified idea of a constant velocity of money and prices changing with the quantity of money is just no correct except in the very long term.

    1. Hi, Vincent,

      What is the long term velocity of money? There must be enough data to make a good estimate, no? Thanks. :)

    2. John hussman has looked at velocity of money. I include one of his graphs and link to him.