Sunday, December 01, 2013

Does QE cause deflation?

Oh my gosh. I am really excited. For years, I've been waiting for a chance to disagree with Brad DeLong about something econ-related, and the day has finally come!! It's enough to make me break my blogging hiatus a few days early.

Remember back in 2011 when Narayana Kocherlakota theorized that low interest rates cause deflation? Well, on Wednesday, Steve Williamson made a similar claim, writing that in a liquidity trap, QE will cause long-term deflation. Williamson based his post on this paper.

In a testy response, Nick Rowe called Williamson's post "horribly wrong," lamenting: "What the hell has gone wrong with some of the best and brightest in economics?" Brad DeLong then jumped in, accusing Williamson of mistaking an unstable equilibrium for a stable one. Paul Krugman echoed that accusation.

But David Andolfatto, in this excellent post, showed that DeLong and Krugman's criticisms are misplaced. In a typical New Keynesian model - the kind that now mostly dominates business-cycle theory, and the kind preferred by Rowe and Krugman - it's true that Williamson would be picking an unstable equilibrium. But Williamson is not using a New Keynesian model! Williamson's model is actually quite different. And as Andolfatto points out, there are macro models out there that are very similar to New Keynesian models, but have one small twist that makes the "QE-causes-deflation" equilibrium the stable one!

So DeLong and Krugman have gone too far. They are arguing from their preferred model, and that's fine. But to say - as Brad does - that Williamson doesn't deserve a "union card as an economist" is wrong. And to say - as Krugman does - that Williamson has made a simple "misconception" by forgetting about stability is wrong. Williamson is simply using a different model than the standard model, and DeLong and Krugman have not yet examined that model carefully.

What's more, Andolfatto points out that Williamson's critics should be more empirical and less theoretical in their arguments:
The fact that Japan has spent decades [with deflation despite zero nominal interest rates and periodic bursts of QE] suggests that [such an equilibrium] may in fact be stable... 
It seems to me that the critics should have instead attacked his results and interpretations with empirical facts (or am I too old-fashioned in this regard?). After all, Williamson at least motivated his post with some data (the diagram at the top of this post). And he makes what is potentially a testable prediction (notice the if-then structure of the statement):
In general, if we think that inflation is being driven by the liquidity premium on government debt at the zero lower bound, then if the Fed keeps the interest rate on reserves where it is for an extended period of time, we should expect less inflation rather than more.
Yes. Although macro data is not generally very conclusive, it's important to look at it anyway. Williamson's model, if I'm not mistaken, predicts that QE will cause a short burst of slightly higher inflation, followed by a long period of lower inflation disinflation in the long-term. That seems consistent with what happened after Japan's QE during the Koizumi years. It also seems consistent with what the U.S. is experiencing now. (As for Japan's new Abenomics QE, it is too early to tell.)

Of course, Krugman, DeLong et al. have their own explanation for Japan' s ongoing deflation (and the U.S.' ongoing inflation) - the "secular stagnation" hypothesis. And that's fine. To determine whether QE's failure to cause inflation is caused by a Williamson model, secular stagnation, or some third phenomenon is far beyond the scope of this blog post.

My point is to say that neither theory nor data tell us that Williamson's model is obviously wrong.

(Well, OK, actually, that's not quite true. As Nick Rowe points out, Williamson's model implies that QE will cause a never-ending deflationary spiral. Obviously that's not realistic. But that kind of infinite spiral exists in most New Keynesian models too, if a central bank keeps interest rates too high. Generally, none of these models makes any sense in extreme cases.)

Now, on plausibility grounds, Williamson's model is suspect - he assumes that Congress follows a certain policy rule, and in fact his results depend on Congress acting in that one simple predictable way. That's almost certainly not very realistic. So don't read this post as me endorsing the Williamson model! Then again, New Keynesian models - and indeed, all of modern macro models - contain huge lists of equally unrealistic (and empirically falsifiable) assumptions about the behavior of economic agents. So don't get me started down that road...

But anyway, I completely disagree with DeLong's and Krugman's criticisms of Williamson. They shouldn't have pounced on the stability thing. And as for Nick Rowe, as nearly as I can tell, he's just angry that anyone in the world could have anything other than a monetarist/New Keynesian view of how the economy works. And instead of getting mad, I think he should be engaging with alternative models. (Update: Rowe has a response.)

OK, so now let me move on (as Andolfatto also does) to giving Steve Williamson a hard time. 

In his new 2013 paper, Williamson says that:

1. QE causes low interest rates and deflation,

2. That's a good thing, because deflation is good, and

3. Fiscal stimulus (i.e. having the Treasury issue more debt) would be effective in getting us out of a depression.

Fine. Good. These things flow right out of Williamson's model. Paul Krugman would actually seem to have a lot to agree with in #3! 

BUT, a year and a half ago, Williamson wrote this:
I think some serious inflation is coming, maybe sooner than later. The Fed thinks it can control this with reverse repos and term deposits at the Fed. No way. When will the inflation happen? In line with this post, look out for increases in house prices. The higher house prices will support more credit, both at the consumer level, and in higher-level financial arrangements. The "bubble" will grow, and support the creation of more private liquid assets, which will in turn substitute for publicly-issued liquid assets, causing the price level to rise.
His prediction was based on this 2012 paper.

These two predictions are exactly opposite!!!

(Oh, and to round out the set of predictions, here Williamson argued that because of Wallace Neutrality, QE can't affect inflation one way or the other!)

Maybe Williamson changed his mind about how the world works between 2012 and 2013. Great! Fine! He should write a post about what made him change his mind. 

BUT, what Steve and I usually argue about is the general state of macro - he says macro is in fine shape, I say it hasn't discovered much. I think this reversal supports my thesis. If a top-flight macroeconomist, who knows the whole literature backwards and forwards, can so easily change his workhorse model in one year, and reverse all of his main predictions and policy prescriptions, then good for him, but it means that macroeconomics isn't producing a lot of reliable results.

Sure, I know that Williamson (2012) and Williamson (2013) have different sets of assumptions, and that's why their conclusions are so opposite. But how does Williamson expect us to tell which set of assumptions corresponds to the real world, and which is just fantasy-fun-land? The papers, of course, offer no guidance, which is utterly normal for macroeconomics. A million thought experiments, and no way to tell which one to use. Is this science, or is this math-assisted daydreaming?

Anyway, to sum up, the only person I really agree with in this whole debate is Andolfatto. Which is totally unrelated to him buying me a beer at the St. Louis Fed conference earlier this year. 


Brad DeLong responds to me in the comments. Steve Williamson joins in. I'm relieved to find I still disagree with Brad!

Steve Williamson responds to DeLong/Krugman/Rowe on his blog.

Steve Williamson responds to me on his blog. Key quote:
Back in days of yore, my concern was that we could indeed get higher inflation. How? I had thought that the Fed had the ability to control inflation, but when push came to shove, they wouldn't do it. Once people caught on to that idea, we could get on a high-inflation path that was self-sustaining. Of course, since I said that, I've continued to work on these problems, and stuff has been happening. In particular, we're not seeing that high-inflation path. 
So a year of low inflation made Steve go looking for an alternative model to explain the fact that QE wasn't causing inflation. And the feature of the model that Steve changed was his assumption about the behavior of policymakers. That clears things up a bit. And Krugman will be happy to know that Williamson updated his priors. But I think my criticism stands. If one year of data and one change in assumptions can utterly reverse both the prediction ("QE causes inflation" --> "QE causes deflation") and the policy recommendation ("less QE" --> "more QE, and maybe more fiscal stimulus"), I still think this is a teachable moment about the limitations of modern macro. If we have to change our working model of the macroeconomy to fit the most recent macroeconomic event, that demonstrates how silly the whole endeavor is, right?

Scott Sumner chimes in, agreeing with Nick Rowe. So does David Beckworth, who does some quick-and-dirty data analysis. Beckworth and Williamson argue in the comment section.

Tyler Cowen chimes in, agreeing with me.

Krugman has a response. He says that the basic problem with Williamson's model is that there's no explanation for why firms have an incentive to change their prices in response to QE - and hence, no micro-level explanation for why QE causes deflation. That's a legit question, of course. I think that in Williamson's model, QE just lowers aggregate demand by depriving banks of usable collateral (long-maturity govt. bonds), so that they need to hold more cash. That's like a liquidity preference shock, which causes cash hoarding and lowers AD, causing firms to lower their prices. I'm not 100% sure, and it doesn't seem particularly realistic, but that's how I think the model works. It turns out that in Williamson's model, things that increase output decrease inflation. So there is sort of a reverse Phillips Curve, at least when the interest rate is at the ZLB.

Scott Sumner gets increasingly annoyed at Williamson.

More discussion with Brad in the comments.

Brad DeLong responds on his blog. Key excerpt:
[One story of how QE causes deflation] is: (i) people think “there is going to be a deflation; I need to hold more currency”; (ii) people sell their assets to the Federal Reserve, and so the Federal Reserve injects more currency into the economy; (iii) people notice that they have more currency, and think “it would not be rational for me to hold this much currency unless there were a deflation going on”; (iv) people think “if there is a deflation going on, I need to cut my prices in order not to lose my customers”; (v) people start cutting their prices, and the deflation begins. 
This is also a fine story. But it is not a story of the Federal Reserve undertaking Quantitative Easing. It is a story of a self-fulfilling deflationary-expectations panic.
This is true, but I'm not sure that this is what is going on in Williamson's model; in his model, I think the QE (and the weird fiscal policy response that it induces) actually starves banks of collateral, which reduces aggregate demand and causes deflation that way. It all hinges on the way Williamson models the behavior of banks. I'd definitely like to see Williamson explain this part better, but I have kind of run out of time to pay attention to this issue at the moment...

Steve Williamson responds to Krugman. This response is pretty interesting, as you can really see the differences in philosophies of how macro itself should be done.

Karl Smith comes out of blogging retirement to enter the debate on the DeLong side.

Williamson writes a second, longer response to Krugman, trying to explain his intuition. He says that his results come from financial markets, not from goods markets. What's kind of interesting here is that Krugman/DeLong are basically saying that Williamson's model isn't microfounded enough, or at least the microfoundations of firm behavior aren't made explicit enough. Usually, Williamson would tend to be the guy saying "But how does it work?" while Krugman would be the guy saying "IS-LM works, just use it." 

And here is the second part of Williamson's explanation of his intuition.

Bob Murphy chimes in, on the side of DeLong and Rowe. It's kind of neat how this debate has totally shuffled the usual "opinion coalitions".

Nick Rowe has one more response to Williamson, and still thinks Williamson is nuts. Key line: "[Williamson's model] explains why Zimbabwe had hyperdeflation." *ZING*

Yichuan Wang, Scott Sumner, and Tyler Cowen have more. The econ-blogger field continues to be mostly anti-Williamson. 

Iza Kaminska jumps into the debate, endorsing Williamson's ideas and providing her own intuition for why QE is deflationary. 

Ryan Avent enters the debate, taking a rather nuanced position. He presents some quick-and-dirty evidence in favor of Williamson's assertion. 

Tony Yates says who cares if QE is deflationary or not, the point is that it didn't do what we wanted it to do.

Nick Rowe continues to say not-very-nice-things about the "QE causes deflation" supporters.

Tyler Cowen has a great roundup of evidence that QE is, in fact, inflationary. The evidence is not conclusive - evidence in macro almost never is - but it definitely puts Steve Williamson's story on the back foot.

Steve Williamson attempts to explain his "QE causes deflation" idea with a Socratic dialogue of sorts.

John Cochrane is interested in the question. He writes down a simple model with a Fisher equation and a Taylor rule, and finds that "higher interest rates cause inflation" (which is similar to "QE causes deflation") is a stable equilibrium in that model, which has multiple equilibria. Williamson says Cochrane "gets it." Nick Rowe and Scott Sumner respond to Cochrane.


  1. Pretty easy: if the credit channel is shot, eg. because the household balance sheets are underwater then what remains is the interest income channel: lower rates mean lower income paid by the govt to treasuries' holders. It can easily overwhelm everything else if debt/GDP is large enough and then lower rates are deflationary.

  2. Krugman and deLong went ballistic because reputation of the former rests on QE being expansionary: it was his silver bullet for Japan which failed to achieve anything.

    1. Anonymous6:19 AM

      Hardly. I suggest you read Krugman before "refuting" him. No sign of a silver bullet here.

      "What Abenomics seems to be is an attempt, finally, to do what should have been done long ago: combine temporary fiscal stimulus with a real effort to move inflation up."

    2. Read his 1998 Japan paper, not his rewriting of history now. Then he said QE was thew way to go and downplayed fiscal policy because japan has "large debt". That was before MMT taught him that sovereign currency issuers control their rates and can have as large deficits as necessary.

      Now he knows QE is mostly ineffective hence his attempts to rewrite.

    3. Anonymous10:02 AM

      So now Krugman's a bad guy because he learns from his mistakes?

      You surely pooped enough diapers when you were little; will you forever be the pants-pooper?

      Not trolling: You are clearly not responsive to learning or chronology, so I'll find someone more amenable to reason. Have a nice life.

    4. Learning from mistakes is one thing, rewriting of history is another. He has a lot of reputation attached to QE being expansionary, if it is deflationary it would be very embarrassing for him. Apparently neither he nor DeLong are willing to debate the issue, hence threats and emotional responses. Like yours.

    5. Anonymous7:07 PM

      No, he doesn't.

  3. I agree David's post is very good. It forced me to think. It forced me to write this post in response. I think David is wrong.

    1. Noted!

      But I still think that the evidence, crappy as it is, needs to come first, rather than our intuition about which modeling assumptions make sense.

    2. If I were convinced that the evidence supported Steve's theory, I would reluctantly believe that the inflation rate was in fact chosen by a benevolent deity who was determined to ensure full employment, despite what central bankers did.

    3. Because it is not in the interests of any individual agent to create the socially optimal rate of inflation to ensure full employment. If it isn't a benevolent deity determining inflation, it must be determined by some secret collusive group that wants full employment. Throw methodological individualism right out the window! Bring on the Functionalist Theory of inflation!

    4. Har har.

      OK, YOU write down a DSGE model, and then I'll make fun of its assumptions. ;-)

    5. Hey Noah! I *did* write down my very own DSGE model, and it only has one equation (because my math is so bad), but I'm very proud of it nevertheless.

  4. Steve Williamson wasn't the first to produce a model saying that raising rates would cause inflation--Andolfatto mentioned an earlier paper here: From what I can tell by skimming, that is the same New Keynesian model as Krugman, except for where the authors alter an implicit assumption regarding the direction of causality in the Taylor rule.

    To be clear, I think the notion that raising the interest rate right now would increase inflation is phony baloney. But, as far as the NK model goes, this looks pretty ambiguous. I don't really believe the quantity theory either, but it offers a good intuition as to why: we can in principle achieve a higher nominal interest rate by either printing money or destroying it. In the former case, prices rise, lifting the nominal rate; in the latter, prices fall lowering the interest rate. I think this is what Friedman meant when he said that low interest rates were a sign that money was too tight, not too loose.

    1. Ok, something got garbled in that comment. What I meant was that increasing the money supply could raise the nominal interest rate via inflation, or lower it via the money demand curve. New Keynesians always assume the latter, but in principle the former is always possible, even in their own models. Thus we can't be sure whether raising the interest rate is associated with a larger or smaller money supply, inflation or deflation.

    2. Yep. Which is why using interest rates as a way to communicate the stance of monetary policy is such a very bad idea. The Wicksellian indeterminacy problem keeps rearing its ugly head, one way or another. Interest rates don't even have the right units. Their units are 1/years, whereas what the central bank ultimately controls, and seeks to control, has $ in the units.

    3. "Their units are 1/years, whereas what the central bank ultimately controls, and seeks to control, has $ in the units."

      This is some serious pseudophilosophy. A car gas pedal moves in inches and yet we can use it to control a variable with units of mph. Or are you suggesting the driver should be in some kind of a hamster wheel and control velocity with velocity?

    4. PeterP: good point re gas pedal. I would need to rephrase what I'm saying to avoid your objection.

  5. For an explanation about why QE causes deflation we need to begin with Marshall's example of a housewife debating about how to divide a given quantity of wool among various uses: socks, cardigans etc.

    Money is fungible. It can be used either as a medium of exchange (to buy goods and services) or to buy financial assets. QE results in very low interest rates. This favours the use of money as a financial asset; hedge funds and the like can borrow at negligible interest rates and parlay tiny mispricings of financial assets into large profits. Similarly individuals are tempted to use their accumulated savings to buy financial assets. This means less money available for lending to firms, which means smaller income flows available for spending, which means low inflation or deflation.

    I have written about this in my book "The General Theory of Money" at

    1. "This means less money available for lending to firms"

      Why? Does the money spontaneously combust and vanish from the face of the earth?

    2. If money were simultaneously available for multiple purposes, there would never be a shortage of money.

    3. Ah I see. You think there is a fixed amount of money in a big pot somewhere. When people borrow money they take it out of the pot and there is then less money available for other people to borrow.

      Clearly you have absolutely no understanding of money or banking. You should probably do some basic research into those areas.

    4. "This favours the use of money as a financial asset; hedge funds and the like can borrow at negligible interest rates and parlay tiny mispricings of financial assets into large profits."

      That has nothing to do with low interest rates. You can arbitrage no matter what the rate is.

      "Similarly individuals are tempted to use their accumulated savings to buy financial assets. This means less money available for lending to firms, which means smaller income flows available for spending, which means low inflation or deflation."

      You are confusing wealth/capital with money.

  6. To continue with my previous post I have also commented on inflation and low interest rates in two blogs in 2011.

    Why Banks Do Not Lend at Near-Zero Interest Rates
    Low Interest Rates: A Policy with No Rationale

  7. "And as Andolfatto points out, there are macro models out there that are very similar to New Keynesian models, but have one small twist that makes the "QE-causes-deflation" equilibrium the stable one!"

    Krugman was not just arguing that Williamson's equilibrium was unstable; he was also arguing that raising interest rates would not get us to that equilibrium. As I put it, he was arguing against the concept of immaculate equilibrium. That if you find an equilibrium, we will get there, even if it takes a miracle; or that just achieving one factor in the equilibrium will automatically make us achieve all of the others.

    An analogy is, suppose it's an equilibrium for a man to be at 240 lbs. and have blood pressure of 160/100. And it's also an equilibrium for him to be 170 lbs. and 130/80. That doesn't mean that if he takes powerful blood pressure medication to bring him to 130/80, that will also make his weight drop to 170. Nor will it give him many of the other benefits of eating healthy and dropping to 170.

    Williamson seems to say that there's an equilibrium (in a model that really excludes a lot that matters) where interest rates are a lot higher than they are now and inflation is a lot higher than it is now. So, if we raise interest rates we will get to that equilibrium. He seems to be saying that raising interest rates will also raise inflation, just like taking blood pressure medicine to lower our blood pressure, will also lower our weight.

    But the causation is not there. That will not get us to that equilibrium. Other measures must be taken, including measures outside of the model, like eating healthy foods and exercising.

    1. QE is criminal who cares what excuse is used to justify it, it steals from anyone not receiving the proceeds of same. Anyone involved with QE FED Governments should be in jail. If everyone was QEing printing money you would get inflation end of story. Inflation is more of something in this case money. It is possible in it's current form that the economy as a hole is deflating this is probably by design. If I had a QE printing press I would be quite happy if everything I was buying with QE money was at a deflated price.

    2. "Inflation is more of something in this case money"

      So an increase in the supply of potatoes is "potato inflation"?

  8. Anonymous6:22 AM

    A little note: quite some large and small companies in at least the UK and the Netherlands are in trouble because, once, before 2008, they bought all kind of derivatives which turned sour when interest rates declined. Do not underestimate the magnitude of this (google 'RBS scandal'. Oops - you will have to refine this search!). These companies actually have to pay loads of additional money because of low interest rates which will prevent them from borrowing money to invest this in whatever. In this case, though for reasons not related to what the models say, lower interest rates do depress the economy.

  9. "Williamson's model, if I'm not mistaken, predicts that QE will cause a short burst of slightly higher inflation, followed by a long period of lower inflation."

    Alas, I believe you are mistaken.

    On page 14 of Stephen Williamson's paper, equation 40 states that the gross inflation rate is given by:


    Where Mu is the gross inflation rate, Beta is the discount factor bound between 0 and 1, x1 is the amount of currency and u is a a strictly increasing, strictly concave, and twice continuously differentiable function.

    Thus an increase in the amount of currency strictly decreases the inflation rate. In my reading of his paper this appears to be true regardless of whether the central bank is operating a channel or a floor system, regardless of the maturity of the debt it purchases, and whether it is at or away from the zero lower bound.

    On page 16, in the section on conventional open market operations in short-maturity debt, he notes:

    "Some of the effects here are unconventional. While the decline in nominal
    bond yields looks like the “monetary easing” associated with an open market
    purchase, the reduction in real bond yields that comes with this is permanent,
    and the infl‡ation rate declines permanently. Conventionally-studied channels
    for monetary easing typically work through temporary declines in real interest
    rates and increases in the in‡flation rate. What is going on here? The change
    in monetary policy that occurs here is a permanent increase in the size of the
    central bank’s holdings of short-maturity government debt – in real terms –
    which must be …nanced by an increase in the real quantity of currency held
    by the public. To induce people to hold more currency, its return must rise,
    so the in‡flation rate must fall..."

    1. You never know with these things until you calculate the impulse responses...and sadly Steve didn't publish those yet.

    2. I agree that we can't really be sure what the impulse response might be of the model once it is moved from a stationary to a stochastic environment.

      Consequently what makes you so confident that this model predicts QE will cause a "short burst of slightly higher inflation"?

      I see absolutely nothing in this model which suggests that might happen.

    3. I agree that we can't really be sure what the impulse response might be of the model once it is moved from a stationary to a stochastic environment.

      Correct. I was wrong to assume what I assumed.

      I see absolutely nothing in this model which suggests that might happen.

      If the long-run equilibrium price level is higher - as one might expect it to be if the monetary base rises - then the impulse response would have to be hump-shaped in order to have long-term deflation. But I now see that that's not what's happening in this model. What I think is happening is that permanent one-time Fed policy changes cause permanent one-time fiscal policy changes that permanently alter banks' need for collateral, and hence permanently increase the demand for cash, thus decreasing AD and causing deflation now and forever.

    4. permanent one-time Fed policy changes cause permanent one-time fiscal policy changes

      But fiscal policy is a function of which politicians we've elected, I get a distinct queasy feeling when any model suggests they are an "effect" -- a Tea Party government is obviously going to make different decisions than a Chavista under basically all circumstances. And QE isn't really a meaningful policy change -- the inflation target basically guarantees it won't be.

  10. Noah, here is my reply:

    1. Thanks, David!

      Realize, though, that Williamson's model might have inflation going up for a short while and then down even farther for a long while in response to a QE shock. I'm not sure because he didn't publish the impulse response graphs.

    2. Noah, then he is not being very clear. In his blog post he says the following:

      "...the rate of inflation is being determined primarily by the liquidity premium on government debt. Once we recognize that, it's not surprising that the inflation rate has been falling for the last three years (see the chart)"

      It seems clear to me in this passage that he is claiming (1) inflation has been falling over the past three years and (2) that it is because of his proposed theory. I provide empirical evidence on these claims.

  11. Could someone maybe explain what is that 'one small twist that makes the "QE-causes-deflation" equilibrium the stable one!' ... and how that equilibrium is reached and maintained?

    Then we could think about whether it is more plausible, in addition to maybe fitting data from Japan showing long term coexistence of QE and deflation pressure.

    1. Could someone maybe explain what is that 'one small twist that makes the "QE-causes-deflation" equilibrium the stable one!'

      A different type of expectation formation.

    2. The Federal Reserve offers to buy bonds via QE at a higher-than-previous market price, and so the price of bonds goes up. People look at this hi her price and conclude: at this high price these bonds wouldn't be good investments unless we expected faster deflation; but because we are holding them they must be good investments; so we must expect faster deflation--and so we are going to start lowering our prices faster then we previously planned.

      That's not "a different type of expectation formation". That's simply not thinking about the disequilibrium foundations of equilibrium economics at all...

    3. Oh of course, the confidence fairy.

      QE doesn't work because everybody says OMG if the Fed thinks it's that bad then I won't consume and invest.

      [slaps head] Of course, the more money you print, the more it's worth in goods and services (deflation).

      Just like fiscal policy doesn't work because everybody says OMG the debt, my future taxes etc., things are going to get worse so I won't spend and invest.

      The dismal science, indeed.

  12. I think Noah Smiths critique--Not Quite Noahpinion: Does QE cause deflation?:

    "DeLong and Krugman have gone too far. They are arguing from their preferred model.... Williamson is simply using a different model than the standard model, and DeLong and Krugman have not yet examined that model carefully..."

    is simply wrong.

    Look: Williamson claims that his own model says:

    1. The real interest rate on bonds is (a) the rate of time preference, plus (b) the derivative of the marginal utility of consumption, minus (c) the liquidity premium on bonds K.
    2. Set the derivative of the marginal utility of consumption to zero...
    3. From (1) and (2), the real interest rate on bonds is (a) the rate of time preference, minus (c) the liquidity premium on bonds K.
    4. Assume we are at the zero lower bound...
    5. At the zero lower bound, the liquidity premium on bonds K must be equal to the liquidity premium on cash L.
    6. The real interest rate on bonds is then (a) the rate of time preference, minus (d) the liquidity premium K=L.
    7. So if you lower (d) the liquidity premium L=K, you will raise the real interest rate on bonds, and so raise the rate of deflation.
    8. Expanded QE policies lower the liquidity premium L=K.
    9. Hence expanded QE policies increase the rate of deflation, Q.E.D.

    And because Williamson has not paid enough attention to Frank Fisher and company, he is simply wrong in his own model.

    In his model, at the ZLB with stable consumption, a reduction in the liquidity premium L=K produces:

    * first, an immediate upward climb in the price level as people who no longer value cash and bonds so highly dump it for currently-produced goods and services;
    * second, increasing expectations of higher deflation as people regard the now-elevated price level; and,
    * third, a new steady-state equilibrium with people comfortable holding the stock of bonds even though the liquidity premium K is less because of the higher expected rate of deflation.

    Williamson's isn't a model in which expanded QE produces faster deflation. It's a model in which expanded QE bumps the price level up, and after that price-level bump-up is completed people then expect deflation and a return to normal...

    1. Wrong. I'm looking at an equilibrium where the price level at the first date is tied down by fiscal policy. Then, monetary policy determines the inflation rate. The experiment I'm thinking about is a once-and-for-all change in policy at the first date. Then I determine the implications for the inflation rate. You're thinking about something different.

    2. Steve, questions:

      1. Is the impulse response to that policy change hump-shaped?

      2. Is the long-term equilibrium price level lower after the policy change?

    3. 1. Haven't worked that out. I'm just looking at a stationary equilibrium where everything is constant forever. I'm not sure we even want to think about the policy experiment in the way you have in mind. If you take it to a stochastic environment, we would want to define QE in terms of a policy rule, and then ask how this changes the operating characteristics of the economy.

      2. In the experiment I did, the price level at the first date is fixed by the fiscal authority. But it doesn't actually matter what it is - note that you never see the price level in any of the equations. What matters is the inflation rate.

    4. Right, so this definitely doesn't correspond to the situation Brad was talking about, where there's a hump-shaped inflation response, and the long-term equilibrium price level is higher.

      So back in the real world, we seem to be seeing some slight inflationary effects from Abenomics QE. And we've seen some slight increases in inflation expectations every time Bernanke announces new QE...but inflation doesn't really rise. And when Koizumi's BOJ did QE in the early 2000s, there was a slight bump in inflation...but after that bump, deflation set back in. So I think it is worth asking if we're seeing hump-shaped impulse responses to policy shocks, where QE causes a small short-lived burst of inflation and then a longer, larger spell of disinflation afterwards. It's an interesting hypothesis.

    5. BOJ had a 1% target, though. Was there any reason to doubt them?

      It always amazes me that there is surprise at the lack of inflation when the CB credibly promised there wouldn't be inflation. The only thing more amazing is the belief that CBs can't inflate if they decide to (given that they can buy every asset in existence).

    6. Anonymous1:48 PM

      Responding to Noah Smith's 2:36 pm post...

      It's important to clarify that the bump in inflation expectations that has happened after QE policy announcements would only occur because (so far) the market believes that QE should cause inflation.

      But the market just learned something, here. That EXPECTATIONS HUMP will now fade and eventually disappear in any future QE (increase) announcements.

      Someone should make a bet that if the FED will stop QE, the dollar will suddenly inflate. I would, but I'm liquidity constrained....

      Note: I was on team-Krugman. I'm not an "inflationista" at all - I've been pro-QE all along. But the more I consider why the market would behave this way, the more it agrees with everything else I think I know.

  13. "Sure, I know that Williamson (2012) and Williamson (2013) have different sets of assumptions, and that's why their conclusions are so opposite."

    That's not correct. There are some different things going on, for example with fiscal policy and collateral, but there's nothing contradictory about the results. Who said there was?

  14. Count me among those agreeing with you on this one, Noah. Good return.

    Barkley Rosser

  15. Whether anyone agrees or disagrees with Stephen, I think he started a very fruitful discussion.

    1. Perhaps...let's see how the fruit tastes!

  16. Noah,

    Sometimes we discard models just because the assumptions are stupid. If I tell you that under my theory of perfect ballspectations it is "efficient" for the 10 ball bearings in my box to be stacked exactly on top of each other, then in the absence of experimental evidence would you really consider my "theory" equal to the theory that the balls are all lying on the bottom of the box? Or would you tell me I'm balls-out stupid and maybe direct me to the chapter on perturbation analysis?

    Honestly, no self-respecting physicist would *ever* postulate an unstable equilibrium. Williamson refuses to consider perturbations from perfect ratex. David Andolfatto once tried to explain it to Stephen with reference to Howitt '82 as such:

    "The point of his paper is this. Interest rate pegging is perfectly feasible, if one assumes rational expectations. But if we depart from the rational expectations solution concept, even just marginally, and (I think) in a perfectly reasonable way (he studies a class of learning rules with very weak restrictions), then interest rate pegging will lead to the familiar Wicksellian "cumulative process." Pegging it too high will lead to a deflationary spiral, pegging too low will lead to the opposite. "

    Here was Stephen's response:


    Things are confusing enough without "disequilibrium" and ad-hoc expectations, and Wicksellian cumulative processes coming into the mix. You're free to do that, if you want, but it doesn't help me understand anything."

    Note the scare quotes and that nobody said anything about "ad-hoc" expectations. Howitt was considering fairly general perturbations from ratex, no matter how small.

    Like Krugman says, "Nice day for weather" and "Mary had a little lamb." It's ball bearings all the way down in fresh water macro.

    1. Agreed...if your model's equilibrium isn't stable with respect to epsilon departures from rationality, you have a big problem.

    2. An "epsilon departure from rationality?" What do you mean? Be precise.

      K: You shouldn't quote me out of context. I'm was just telling Andolfatto that he was getting way too complicated. If you still think rational expectations is a big deal, you're fighting the battle on the wrong front. There are plenty of other interesting things to worry about - more frictions than you can shake a stick at.

    3. Suppose fraction 1-epsilon of agents form expectations by rational expectations and fraction epsilon don't.

    4. Steve,

      "You shouldn't quote me out of context."

      I didn't mean to.

      "If you still think rational expectations is a big deal, you're fighting the battle on the wrong front. There are plenty of other interesting things to worry about - more frictions than you can shake a stick at."

      You misunderstood me. I don't want you to consider deviations from ratex because I think they are important frictions. I want you to consider whether your solution, if perturbed from the ratex equilibrium, would converge back to it. Every solution, ratex or otherwise needs to pass this test, or like our stack of ball bearings, it doesn't qualify for consideration. Every physics student has this drilled into their head in their junior and senior years. If you think that ratex is an absolute rather than approximate solution and therefore not in need of stability analysis then you've transitioned from science to religion.

      A bit of price stickiness plus a Taylor rule does the trick of stabilizing the solution. It also implies that expected inflation goes down with surprise hikes in the short rate, and therefore that the CB has direct control over the real short rate. The new Keynesian liquidity trap follows.

    5. This comment has been removed by the author.

    6. Noah,

      "if your model's equilibrium isn't stable with respect to epsilon departures from rationality, you have a big problem."

      I didn't necessarily mean departures from "rationality". Ratex is much stronger than rationality. The most obvious departure from ratex, IMO, is that we have absolutely no idea what the true dynamic of the economy and no way of finding out. And markets aren't even remotely complete, so there is nothing to save us from our ignorance. But anyways, you do in fact have a big problem.

    7. Yeah, there are lots of meanings of "rationality".

  17. Anonymous6:05 PM

    Great conversation. The argument is over whether Fed policy can cause deflation? Whether Fed policy is inflationary or deflationary depends on the condition of the labor market. Where is the analysis of labor policy or labor contribution?

    Wage inflation is the inflation the Fed most worries about especially upward wage-price spirals. An upward wage price spiral requires that labor have a strong bargaining position that can tie wage inflation to price inflation. This condition has been so not-the-case since 1980. Pile on with a global labor force, communication ability that improves outsourcing, too high unemployment and increasing wage inflation. Wage inflation becomes a daunting task not easily created by policy of any sort let alone policy blunder.

    The ability of the Fed is asymmetric. The Fed has infinite ability to smash labor and wage inflation, but is limited in ability to stimulate wage inflation by the ZLB. There is no way that the Fed acting without help from fiscal policy can set off a wage-price spiral under current conditions. The labor market would first need to recover before Fed policy gains traction. The deep recession, drop in GDP, the collapse of collateral in the housing bust, the almost 10% drop in inflation adjusted median wage from 2007-2011 mean that there is nor enough income at the bottom to bid up prices.

    The Fed cannot by law conduct fiscal policy and until they can there are few ways that the Fed can act independent of fiscal policy to change wealth distribution or increase employment at the ZLB. Fed policy is impotent under current conditions.

    -jonny bakho

  18. Bill Ellis7:43 PM

    Noah, Do I get this right ? Your defence of Williamson is based on something that "doesn't seem particularly realistic" ? Have you surrendered ?

    1. Now you see the true meaning of the picture. His "little friend" is Stephen Williamson! Buhahahahaha!

  19. Noah, I think you have the most rational take on the whole affair. But I'm sympathetic to deflationary monetary expansion ...

  20. "QE just lowers aggregate demand by depriving banks of usable collateral (long-maturity govt. bonds"

    But the banks lose their long-maturity government bonds, but get in return an equal amount in cash. Isn't $X in cash just as good collateral as $X in long-maturity government bonds? Actually better? As $X in long-maturity bonds gives you the ability to borrow only less than $X in cash.

    1. I realize I have just about zero expertise in these models, but a question like this, which seems obvious, should be answerable to non-experts, but I'm not holding my breath, here or at Stephen's site, where I also asked it. This stuff is almost never made accessible to people who don't spend a billion hours reading all the super mathematical papers in this area. You gotta give one thing to Krugman, he usually makes his economics understandable to non-experts in the area -- even to just well educated laypeople with no more than micro and macro econ I.

  21. This comment has been removed by the author.

  22. I'm not sure how useful these models are. The real game is expectations -- as Fisher predicted long ago and Friedman recapped somewhat later, decades of successful tight money policy have created long-term expectations of low inflation, leading to ever-falling nominal rates. QE doesn't change long-term expectations much, so it doesn't do much to the trend (remember, the Fed target is a continual promise QE won't be inflationary!). At the same time, relatively small surprises have large effects, because money is still tight (so markets care about money, which correlation began in 2008) and surprises DO change expectations.

    Imagine Yellen comes in drunk on her first day and says something like "Welcome back to the 1970s folks, we're targeting unemployment and don't care much about inflation!" Or something more sane, like NDGPLT. I think the Fed target matters a lot more than anything else (the Chuck Norris effect), and empirical support for that notion will continue to grow...

    1. Sorry, I should clarify -- the first use of "tight" is simply the Fed's inflation targeting regime that started with Volcker. The second (referring to the current situation) should really be "too tight" i.e. tighter than optimal.

      The Fed's policy is a bit schizophrenic, they're so married to the <2% target they want to push on the gas (QE) but not let up on the brake (the target).

  23. Anonymous10:33 PM

    I really do not think that any of you know what on earth you're talking about.

  24. Anonymous10:35 PM

    QE is irrelevant. With the US economy accelerating, the recession is over. QE is done and Zirp is nearing its final year imo.

  25. Anonymous10:58 PM

    I think that was the main argument of the post.

  26. Re: Noah Smith: "I think that in Williamson's model, QE just lowers aggregate demand by depriving banks of usable collateral (long-maturity govt. bonds), so that they need to hold more cash. That's like a liquidity preference shock..."

    Except that in a liquidity preference shock that makes people want to hold more cash, the liquidity premium goes up (i.e., cash becomes more valuable). But in Williamson's shock, the liquidity premium goes down. So you have the sign wrong...

    1. Anonymous1:47 PM

      No, in SW the swapping of long-term bonds (LTB) with reserves increases liquidity, as currency is more liquid than LTB. The idea is that an increase in the demand for liquid assets reduces their real rate of interest. At the zero lower bound this can only be achieved with an increase in the rate of inflation. An increase in the supply of liquid assets must be followed by an increase in the rate of interest to get people to hold them. Hence, the swap of less liquid assets with more liquid assets (QE) reduces inflation, given the nominal rate targeted by the Fed. This is all about arbitrage. You can't explain the model using AD analogies.

  27. That's a legit question, of course. I think that in Williamson's model, QE just lowers aggregate demand by depriving banks of usable collateral (long-maturity govt. bonds), so that they need to hold more cash.

    I think this is wrong. I think SW has talked about a model like this before, but I don't think that is in the model. I think short term bonds have more liquidity than long term bonds in this model, and QE does not cause liquidity hoarding.

  28. Anonymous12:38 PM

    Forgive me, I'm just an armchair economist. But let me get this straight: the thinking here is that QE causes deflation, or that printing money makes money worth....more?

    If so, seems we don't have a debt problem after all, do we?

  29. "This is true, but I'm not sure that this is what is going on in Williamson's model; in his model, I think the QE (and the weird fiscal policy response that it induces) actually starves banks of collateral, which reduces aggregate demand and causes deflation that way. "

    Doesn't this call for MORE deficit spending, so as to increase the supply of quality collateral (in the form of government bonds), and prevent the type of safe asset shortage plaguing the repo market for quite some time? I've actually been expecting to read this for quite some time (but have not).

  30. Anonymous11:25 PM

    Oh what a dis-functional family the profession of academic economics is - so very good that it's now 'out there' for all the world - particularly policy-makers - to see. There are two incredibly valuable 'take-aways' from this episode of internecine bloodletting -

    First, it's pretty obvious that none of the many sides in the debate actually know what the hell they're talking about, or what the IRL-impact of their advice would be if anyone were foolish enough to act in reliance on it. These clowns are just mouthing whatever wild and fanciful notions happen to pop into the brains from moment-to-moment.

    Second, it's ethically indefensible for any of them to give advice - and just as unethical for policy-makers to listen to such advice. 'First, do no harm' - none of them can clear that essential prerequisite to ethical advice-giving. Other professions know enough to keep their mouths shut until they can conclusively demonstrate that what they are proposing won't make matter worse than they already are - academic economists aren't capable of grasping even that.

    But cheer up, lads - you're not alone. Witch doctors, Tarot Card readers and professional astrologers have the same kinds family feuds. It's all harmless and entertaining fun - 'long as we all remember to take none of them seriously. Roger Fox

  31. Noah,
    It seems to me you forgot Delong's rules:
    1. Paul Krugman's analysis is correct
    2. If you think that Paul Krugman's analysis is incorrect, see rule number 1.

    This thing is huge, so maybe I missed it, but I think the notion of stability that Delong/Rowe/Krugman front are getting at is the idea that if expectations turn out to be slightly different from the presumed equilibrium, there are clear incentives, arbitrage possibilities perhaps, that push behavior toward said equilibrium and not away from it. If my memory serves me correctly, in game theory this is considered "robustness." But I may be wrong about that.

    Stephen Williams doesn't go there. He doesn't have an intuition for how this works. He worked backwards from equilibrium conditions he assumed to be true to a mathematical construction that gets you there. To me that seems like bad science. But others have probably made these points better than I ever could...

  32. Another way in which QE could be deflationary is due to its effect on expectations of interest rates in the future. QE implies lower interest rates for an extended period of time which is also emphasised by forward guidance. Because households and firms expect interest rates to stay low, there is no rush to borrow as cheap loans will also be possible in the future (in the same way that falling prices is assumed to make consumers hold off spending). Borrowing costs will only rise when the economy picks up so it would be best to wait until the economy shows signs of improvement to take out a loan. Therefore, if we are at a point where interest rates are low but the economy is expected to remain weak, low interest rates do not have the effect that they should do and the weaker demand could be deflationary. For more on why monetary policy has not provided much of a boost, see

  33. I'm astounded that you think Ryan Avent agrees with Williamson. I agree with Avent but not Williamson.

    1. Agreed. Avent: "Is QE deflationary? Yes, quite obviously so. Consider: ... Prolonged QE is effectively a signal that the central bank is unwilling commit to higher inflation... QE therefore reinforces expectations that economic activity will run below potential and demand shocks will not be completely offset....QE will be associated with a general disinflationary trend.
      Now, do I actually think QE is deflationary? No, I don't. My read of available evidence leads me to believe that, other things equal, QE increases demand and inflation. The problem is that in macroeconomics other things are never equal. In particular, a central bank may deploy QE at two different times with two different intentions. And the intentions make all the difference."

  34. Anonymous7:18 PM

    QE has had two main goals: keep mortgage rates low and long term gov debt rates low. The first is the bigger issue because it more quickly translates to the broader economy via home sales & construction. I would focus on this because of Williamson's statement:

    "To keep things simple, we assume there is no privately produced collateralizable wealth."

    Has he been asleep for the past 10 years? The biggest collateralizable asset class is not gov't debt, but real estate. Real estate collateralizes all mortgages, and it was the degradation of the value of this collateral that accelerated the financial crisis.

    Consider just the mortgage market. MBSs make up roughly a third of the Fed's balance sheet, so they are a critical component. Where would it be without any QE? Where would rates, home sales, and home prices be? How would that propagate through the broader economy?

    Also, conventional wisdom says QE increases the inflation rate (does not ensure high inflation, just a higher rate than without). If the math really says it will yield deflation, there should be a huge investment opportunity, Williamson should open a hedge fund a la Scholes. If the math is not worth investing on, then it's not worth basing policy decisions on.

  35. Wonks Anonymous2:12 PM

    You can add another update, Williamson has a Socratic dialogue with a visitor from the moon who hasn't yet been blinded by Michael Woodford.