Monday, December 2, 2013

Taking the Model to the Data

Stephen Williamson has generated something of a firestorm by arguing the Fed's QE programs have actually been lowering inflation over the past three years. His argument is based on a new paper of his that builds upon the monetary search framework of Lagos-Wright (2005). I actually like this approach to modeling money-like assets, but the implications Williamson draws about QE has Nick Rowe, Brad DeLong, Paul Krugman, and Scott Sumner up in arms. David Andolfatto valiantly rides to Williamson's defense (update: so does Noah Smith) only to be rebuffed again by Nick Rowe.

I do not want to rehash their arguments here, but I do want to respond to a challenged made by David Andolfatto:
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?).
Okay, David wants us to take Stephen Williamson's model to the data. Stephen probably thinks he has already done so with this figure of PCE inflation. However, one cannot really draw any conclusion using headline PCE inflation because it has embedded in it supply shocks and other temporary perturbations completely unrelated to monetary policy. This is why the Fed and others look at core PCE inflation. For these reasons, I too will use the core PCE inflation measure here as we empirically examine Williamson's claims.

Below is the figure for core PCE inflation. Williamson's argument is premised on inflation falling over the past three years. This figure suggests something else has been happening: it has been bouncing between 1% and 2%. Ryan Avent argues this is intentional. The Fed's 2% inflation target is actually an upper bound. According to this view, the Fed is more concerned about preserving its inflation-fighting credibility than it lets on in public and effectively is keeping one foot on the brake and one on the gas pedal so that inflation stays in the 1%-2% range. In any event, the point here is it is not clear that inflation has been trending down for the past three years.

Williamson's bigger claim, though, is that the Fed's purchases of treasuries are actually driving down the inflation rate. If this is the case, then we would expect to see a negative relationship between the growth in its holdings of treasuries and the inflation rate. The data, though, suggest otherwise. The figure below shows the year-on-year growth rate of treasuries held by the Fed plotted against the core PCE inflation rate. It appears that Fed's purchases of treasuries leads core inflation by about six to nine months. [Update: here is the figure for longer-term treasuries--it is even stronger.]

To verify this 'eye-ball test', I put the two series in a vector autoregression (VAR) and estimated it once with 6 lags and once with 12 lags. The data was monthly and I estimated the model for the 12/2007-9/2013 period. Below is the Core PCE inflation impulse response function (i.e. typical response) to a positive standard deviation shock to the year-on-year growth rate of the Fed's treasury holdings.The first figure shows the response for the 6-month lag VAR and the second figure for the 12-month lag VAR. In both cases core PCE inflation responds in the same direction as the shock with a lag.

Now these effects are modest, but they go in the opposite direction of that predicted by Williamson. So the data seem to be telling a different story. The Fed's treasury purchases do lead to modestly higher inflation. It is nothing to write home about, but it is definitely not disinflationary.

Again, I like the Lagos-Wright (2005) approach promoted by Williamson. In fact, Josh Hendrickson and I have a paper built on it. In our extension of the model, QE programs can pack a real economic punch if the monetary base injections are expected to be permanent. This is because a permanent injection is expected to permanently raise future nominal income which in turn relaxes current borrowing constraints. The implications of our model, then, is that the Fed's QE programs have not been as effective as they otherwise could be, because all along the Fed has signaled its asset purchases are temporary (though QE3 has added some permanence with its conditional nature). This point about permanent monetary injections is not novel. It has been made many times before by Paul Krugman, Michael Woodfod, Scott Sumner, Bill Woolsey, and others. It is also a point I repeatedly make on this blog. Finally, it is why so many of us are big supporters of level targeting.

P.S. The success of monetary policy in Japan under Abenomics is also hard to reconcile with Williamson's model. Here too, I believe the results are due to the expected permanence of the monetary base expansion.

Update: Mark A. Sadowski provides further empirical evidence that runs contrary to Williamson's claims.


  1. Excellent blogging. So often economic models are fragile, resting upon dubious premises. Wiggle some of the premises---in Williamson's case change headline PCE to core---and the model collapses.
    If the economy could be modelled, I suspect Wall Street, soaked in money and talent, would have done so.
    And are economic forecasts better today than a generation ago, despite computing power everywhere?

  2. David,
    I have very similar empirical results to you, something which I had brought up in the comment section of Nick Rowe's original post on this subject.

    I've run VAR Granger causality tests using the Toda and Yamamato technique on the US monetary base since December 2008, and find the monetary base Granger causes the PCEPI and the impulse responses are *positive*. Furthermore, I've estimated a four variable VAR (similar to Honda et al below) over the period since December 2008 using industrial production, the PCEPI, the monetary base and the 10-year T-Note as variables, and find the impulse response of PCEPI to changes in the monetary base to be significantly *positive*.

    Williamson's model also predicts that QE reduces long-maturity bond yields.

    I also have VAR Granger causality tests that show that the monetary base Granger causes nominal 10-year T-Note yields and that the impulse response is *positive*.My 4-variable VAR mentioned above also shows that the impulse response of 10-year T-Note yields to changes in the monetary base to be significantly *positive*.

    In “An Injection of Base Money at Zero Interest Rates: Empirical Evidence from the Japanese Experience 2001–2006" by Yuzo Honda, Yoshihiro Kuroki, and Minoru Tachibana (March 2007):

    Figure 3 shows that Honda et al finds the effect of the original Japanese QE on the yields of 5, 7 and 10 year bonds was significantly *positive*. Table 2 shows that reserve balances Granger caused core CPI (and to be clear, the effect is *positive*).

    P.S. Something else worth noting is that Williamson's model shows that permanent increases in the monetary base permanently *reduce* the inflation rate.

    1. Mark, both your results and the BoJ paper are very interesting. Thanks for alerting me to it. It will be interesting to see how Williamson will respond to these results. If nothing else, it should give him pause. You should write this up as a guest post for me or Scott Sumner (or research note we could link to).

  3. Professor Beckworth,

    Nice post. But what you have said here suggests to me QEs and monetary policy have only temporary and modest effects on economy- just look at the fluctuations in your diagrams. Actually Williamson had argued QEs have no effect on economy several times. It's interesting that he changed his mind.

    "The success of monetary policy in Japan under Abenomics is also hard to reconcile with Williamson's model. Here too, I believe the results are due to the expected permanence of the monetary base expansion'. Permanet injection means fiscal policy. You actually have the same conclusion as Williamson does in his paper. Both Keyens and Friedman recommended similar policy decades ago: Using newly-created money to do fiscal stimulus. Friedman changed his position latter on because of his ideology. You have been more open to fiscal (helicopter money) than other so-called Market Monetarists. Experience in the last 5 years strongly suggests that fiscal policy is more powerful than monetary. It's time to admitt it.

    1. I think we all agree there is a shortage of money and money-like assets. Let's say we all agreed to a helicopter drop to address this shortfall. Even here, though, the effects could be limited if the Fed tightened (because it was concerned about inflation) to offset the helicopter drop. This is just another way of saying the monetary injection would not be permanent, even though it is fiscal policy. So even Williamson's call for fiscal policy may not work. What is needed is a commitment that the monetary injection-however it is delivered--will be permanent. That is why Market Monetarist have pushed so hard for nominal GDP leveltarget.

    2. Reply to David Beckworth.

      “Even here, though, the effects could be limited if the Fed tightened (because it was concerned about inflation) to offset the helicopter drop.” That’s the problem with having two bodies or systems for imparting stimulus: monetary and fiscal. If they disagree on how much stimulus is needed, they fight against each other. That makes as much sense as a car with two steering wheels, each controlled by a different person. And that is why MMTers (amongst other groups) tend to advocate combining monetary and fiscal stimulus.

      “What is needed is a commitment that the monetary injection-however it is delivered--will be permanent.” Don’t agree. What is needed is a commitment that the monetary injection will remain in place as long as it is needed.

      I.e. for example, if the private sector has an excessive bout of irrational exuberance, the injection would need to be withdrawn (as pointed out by MMTers). But the only effect would basically be to dampen inflation: there’d be little by way of a GDP reducing effect.

  4. David,
    "In our extension of the model, QE programs can pack a real economic punch if the monetary base injections are expected to be permanent. This is because a permanent injection is expected to permanently raise future nominal income which in turn relaxes current borrowing constraints"

    This is not entirely true. If monetary injections are expected to be permanently held as ER by the banking sector, they will have no effect on nominal income.

    1. Yes, but this would only occur if the Fed chose to raise IOR enough to effectively sterilize any monetary base injection. This effectively is the same thing and implies a choice by policymakers. Again, a commitment by policymakers to a higher level target would solve this problem. I have written about his here:

    2. I agree, and...
      1. The Fed could also do this by changing the reserve requirement.
      2. A policy choice implies some sort of conscious decision and it's not at all clear that ER levels meet this criterion.... especially when you consider that the "policy choice" on ER directly counteracts the policy choice on QE.
      3. The Fed could rely on ER as their sole policy tool and entirely abandon QE/OMP for the next decade.

  5. As a trader- a currency trader for the past 30 years (and an economics degree from decades ago).. a helicopter drop would be almost useless. The market would see it as a once off and adjust by looking beyond the drop, figuring out what happens next. The most likely scenario would be that the central bank would go back to its previous policy, therefore a permanent adjustment would not occur.

  6. David, to be completely fair to Steve, you should have included only long-term treasuries, as the composition of the Fed's portfolio does matter. I am not sure the results would be different, but still...

    1. Okay, here is the FRED chart for Treasury securities 5 years and longer that are held by the Fed:

      I haven't run a VAR on it, but it appears to be an even stronger positive relationship!

  7. As a natural scientist, the question all this brings up for me is: how people can publish models without showing that they are consistent with relevant data?

  8. David, have you looked at the effect of QE purchases of MBS and how it might have affected house prices?
    In any case, it is welcome to see empirical work rather than an endless multiplication of theories with no attempt to test them as is the wont of too much modern macro

  9. David,
    It seems critical here to define Williamson's relationship as being "stock" or "flow". I'm not sure which it is, but your chart implies flow is that matters (i.e. % change in Treasuries purchased). Does flow also matter to the portfolio balances effect?

  10. I have a working paper up, which shows, while applying a VAR model, that for the US QE is raising core inflation. But this is the only clear example, despite Denmark in the 1990s, showing a positive response! The paper can be accessed here:

    1. Prior to your comment, I was only aware of a about dozen VAR studies that use either reserve balances or the monetary base as a variable. Of those, only two focus on a period of time when the policy rate was at the ZLB. One is Honda et al (2007) which I mentioned in my above comment. The other study is "Quantitative easing works: Lessons from the unique experience in Japan 2001-2006 by Eric Girardin and Zakaria Moussa (January 2010). (I honestly can't remember if Girardin and Moussa found anything contrary to Williamson's model's predictions.)

      Your literature review mentions another paper I was not aware of, namely "The Effectiveness of
      Unconventional Monetary Policy at the Zero Lower Bound: A Cross-Country Analysis by Leonardo Gambacorta, Boris Hofmann and Gert Peersman (2012). And then there is of course your paper.

      I'm still in the early stages of reading your paper, and Gambacorta et al, but your paper, and apparently Gambacorta et al, provide evidence inconsistent with the predictions of Williamson's model.

    2. So Mark, you need to write all of this up--the literature review and your own findings into a paper. It is sorely needed.

  11. A commenter at Stephen Williamson's blog named "Anonymous" pointed out that there is empirical evidence that QE increases inflation, namely, he referred to this post.

    (By the way, has anyone noticed the large number of commenters named "Anonymous" at Williamson's blog? I know there's more than one because they have to keep identifying themself by when they last commented, or what their previous point was. What on earth is that all about?!?)

    Here is Stephen Williamson's response:

    "In order to properly confront the data, we need a model of how QE works, and then we have to argue that the data is somehow consistent with that. I don't think we would call that serious empirical work in that sense."

    Of course the implication is that David doesn't have a model of how QE works (and evidently nor do I). Now, this is of course completely untrue. In fact David discusses and links to the paper he cowrote with Joshua Hendrickson ("The Supply of Transaction Assets, Nominal Income, and Monetary Policy Transmission") in which he extends the very same monetary search framework of Lagos-Wright that Williamson uses in order to show the effects of QE.

    But more importantly, the main subject of David's post isn't his own model, but Williamson's model, which as David demonstrates (and as I further demonstrate in my comment above) is inconsistent with the empirical evidence. So rather than a dearth of economic models, we have a surplus, and the model which is the subject of David's post seems to be failing the test.

    At this point, it's taking every ounce of energy I can muster to keep being as civil as possible. But frankly Williamson keeps making factual, empirical and theoretical claims which range from being demonstrably false to being utterly ridiculous. Aren't there any real world repurcussions for this kind of behavior?

  12. That is disappointing. Sounds like we need to send SW this t-shirt.

    1. But what kind of relation does SW model predict? I don't think it is between percentage changes. It seems to be between inflation and the stock of bonds (perhaps adjusted relative to the size of the economy). Serious empirical work must pay attention to these things.

    2. You seem to be missing the whole point.

      The mere fact that it can be shown that the two time series are positively correlated is sufficient to call into question the theoretical claims of Williamson's model. And the "kind of relation" is not at all an issue when establishing whether two time series are positively correlated.

      To see why, consider the fact that Granger causality tests should always be done on level data otherwise the results will be inconsistent. This is discussed in detail by James Hamilton in “Time Series” on pages 651-3. In particular, all of my Granger causality tests are done in levels using a VAR technique developed by Toda and Yamamato that addresses the issue of nonstationarity by adding additional lagged terms as exogenous variables.

      So, as it turns out, the "kind of relation" is completely irrelevant to the question at hand.

      P.S. My 4-variable VARs are estimated using level data.

  13. Another commenter named "Anonymous" said the following in Stephen Williamson's latest post:

    "David Beckworth empirical results reject your hypothesis."

    And Stephen Williamson responded:

    "That's not serious empirical work."

    Recall that so far the only empirical evidence that Stephen Williamson has offered in support of his model is a graph of year on year PCEPI inflation which he claims shows inflation has been falling for three years (actually, it's more like two).

    In contrast David estimates a two variable VAR with 6 and 12 lags in which the impulse response of core PCEPI to the Fed's Treasury holdings is the opposite of what is consistent with Williamson's model.

    In addition, in comments I describe my own VAR Granger causality test results, and my own 4-variable VAR estimates which are contrary to the predictions of Williamson's model. And by my count so far we have found three (maybe four) research papers with VAR estimates contrary to the predictions of Williamson's model.

    I wonder what qualifies as "serious empirical work" in Williamson's estimation?

  14. "Williamson's bigger claim, though, is that the Fed's purchases of treasuries are actually driving down the inflation rate."

    Actually, not. The idea behind looking at the drop in inflation over the last 3 years was to argue, first, that it's puzzling, at least for some people. Then, I argued that it's possible that part of what is going on here is a drop in the liquidity premium. What could cause that: (i) an increase in private sources of safe collateral; (ii) QE. Working against that is that the Treasury has actually lengthened the average duration of the debt held by both the public and the Fed. Not sure what the net effect is, as I haven't seen the data. As well, obviously there are a pile of things going on. You're not going to conclude much of anything from your 2-variable VAR. How can you argue that you've even identified a "shock to the Fed's Treasury holdings." Like I said: not serious empirical work.

    1. Stephen:

      Thanks for dropping by, but you missed what I said.

      First, I noted inflation has NOT been trending down over the past three years as you claim. You arbitrarily picked headline inflation which has many problems--it has supply shocks and other temporary perturbations embeded in it that are unrelated to monetary policy. A better measure, core inflation, shows no sign of decline. So despite your snarkiness ("...puzzling for some people"), the motivation for your argument is suspect at best.

      Second, you're missing the point of the two variable VAR. All one has to do with it is show that treasury purchases are positively correlated with inflation to show your theoretical claims are suspect too. You set this simple test up with your claims, not me. Recall that you declared "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)" or "QE actually pushes the Fed further from its inflation goal." This simply is not supported in the data. Trying to avoid this fact by saying "not serious empirical work" doesn't help your case.

      Third, your lack of humility in this whole conversation is a little surprising since you admit you "haven't seen the data." Please tell me New Monetarism isn't going all calibration, no empirics on us.

    2. 1. Here's what I actually said. Read the part after the chart in the first post in the sequence:

      You'll notice I said very little about the effects of QE, and discussed mostly a set of other factors. So QE is not the only thing driving inflation, by any means, and it may not be quantitatively important. The fact that you find some correlation in the data says next to nothing - you need to do the work properly.

      2. You can make good arguments that core inflation is NOT a better measure of inflation. Why do you think the Fed uses headline PCE?

      3. I haven't seen the data on the average duration of outstanding Treasury debt, though it exists somewhere. As for lack of humility, a guy with only a VAR in his pocket doesn't have a leg to stand on.

    3. No, you did say something about QE and I quoted it above. Can't get away from it. Again, I was testing your narrow claim you made. If you want a more complicated VAR along these lines--though not directly examining QE--go read my paper with Josh Hendrickson linked above. It too is a Lagos-Wright model with very different implications than yours. Unlike some, we put our model to the data.

      Yes, the Fed uses headline PCE inflation, but it also uses core PCE inflation. And many Fed officials prefer core as noted by your buddy James Ballard

    4. Look at what you're reporting. What I'm thinking about is a change in the composition of the maturity structure of the outstanding debt, not a change in the size of the balance sheet. You're reporting the quantity of Treasury securities of all maturities. In fact, in my model, at the zero lower bound (and indeed with excess reserves outstanding and interest on reserves, for any nominal interest rate), swaps of reserves for T-bills that increase the size of the balance sheet are irrelevant - that's what a liquidity trap is about. So, you're looking at the wrong data. Note that you need to be thinking about the whole maturity structure of the outstanding debt (held by the public). That's affected both by what the Fed is doing, and what the Treasury is doing. If you read this:

      (or some more recent version), you'll see that the average duration of debt outstanding has been increasing and is expected to. Thus, the Fed and the Treasury are working at cross purposes.

    5. Addendum: In the second to last line in the comment, "debt outstanding" in that instance means held by the Fed and the public.

    6. I agree that the Fed and Treasury are working at cross purposes and did a post on it here (using the same treasury report you link to above):

  15. David,

    Just to be clear, I my post was a defense of Williamson as an academic; it was not an endorsement of any personal view I have on the effects of QE on inflation. Williamson's model identifies a particular effect (the prediction rests strongly on how the fiscal authority behaves). As I said in my blog, "how quantitatively important these effects are relative to others remains an open question."

    As for predictions, I am not entirely sure, but I believe that the experiment considered by Williamson in his model would also lead to permanently lower inflation expectations. Market-based measures of inflation expectations have remained relatively stable in the data.

    1. Thanks David. I also believe--but don't have chart right in front of me to be sure--that inflation expectations have tended be higher during QE programs than outside of them.

    2. David and David,
      I find the US monetary base Granger causes (at the 1% significance level) 5-year inflation expectations as measured by TIPS over the period since December 2008 and the impulse response is positive. I also find that the UK monetary base Granger causes (at the 1% significance level) 5-year inflation expectations as measured by inflation-linked gilts over the period since April 2009 and the impulse response is positive.

  16. Dear fellow Market Monetarists,

    TravisV here. Isn’t this data a huge problem for our worldview?

    The main source of demand for government bonds is…..central banks??????

  17. David B: did you know Austin Community College is cutting hours of some faculty and staff due to Obamacare ?
    I think you wrote something about the employment effects of the ACA.

  18. David,
    Tony Yates commented on this post and I wrote a comment at the Economist's View links in reply (I also left it at Tony Yates site although I'm not sure if he accepts comments). Here is my reply.

    December 5, 2013

    Empirical verification of QE's impact on inflation
    By Tony Yates

    "Matt O Brien tweeted round an interesting piece by David Beckworth, which estimated a VAR to try to resolve a debate between Steve Williamson on the one hand, and Brad deLong, Paul Krugman, Noah Smith and others about whether QE was deflationary or inflationary...We have to look for ‘QE shocks’, which are changes in QE not prompted by changes in the economy, in order to measure the effects of QE on the economy. Why? Because if we don’t, we might conflate the effect on the economy of what policymakers are responding to (the terror at the great contraction turning into a depression) with the effects of QE itself..."

    But this problem of endogeneity bias actually would serve to *underestimate* the impact of QE on inflation. And Beckworth's results, as well as mine, and the four papers mentioned in Beckworth's comment thread, nevertheless show that QE has a *significantly positive* effect on inflation.

    "...The basic problem with trying to recover QE shocks is that QE hasn’t been going on for long enough to make a credible enough stab at disentangling QE shocks from QE prompted by the Fed following through on how it thinks it should be doing its job. The sample time series is too small..."

    This I would argue is false. The US has now been doing QE for just over five years. Thus there are now 60 monthly observations. And there are a number of VAR studies of monetary policy in which the size of the time series is this size or smaller.

    "...To cut a long story short then, you can’t hope to do this at all well with a two variable VAR. People often found three or four variable VARs were inadequate when they tried to identify interest rate shocks..."

    But once again, Beckworth managed to show that QE has a significantly positive effect on inflation despite this handicap. Moreover, my estimated VARs use four variables, and similarly the four papers mentioned in Beckworth's comment thread all used three or four variables (if memory serves me correctly).

    So yes, it would be nicer if we had a longer time series (or more even incidents to study). But that's true of almost anything isn't it?

      Yuzo Honda, Yoshihiro Kuroki, and Minoru Tachibana
      March 2007

      "Many macroeconomists and policymakers have debated the effectiveness of the quantitative monetary-easing policy (QMEP) that was introduced in Japan in 2001. This paper measures the effect of the QMEP on aggregate output and prices, and examines its transmission mechanism, based on the vector autoregressive (VAR) methodology. To ascertain the transmission mechanism, we include several financial market variables in the VAR system. The results show that the QMEP increased aggregate output through the stock price channel. This evidence suggests that further injection of base money is effective even when short-term nominal interest rates are at zero."

    2. Quantitative easing works: Lessons from the unique experience in Japan 2001-2006
      Eric Girardin and Zakaria Moussa
      February 2010

      "The current financial crisis has now led most major central banks to rely covertly or overtly on quantitative easing. The unique Japanese experience of quantitative easing is the only experience which enables us to judge this therapy's effectiveness and the timing of the exit strategy. This paper provides a new empirical framework to examine the effectiveness of Japanese monetary policy during the "lost" decade and quantify the effect of quantitative easing on Japan's activity and prices. We combine advantages of Markov-Switching VAR methodology with those of factor analysis to establish two major findings. First, we show that the decisive change in regime occurred in two steps: it crept out from late 1995 and established itself durably in February 1999. Second, we show for the first time that quantitative easing was able not only to prevent further recession and deflation but also to provide considerable stimulation to both output and prices. If Japanese experience is any guide the quantitative easing policy must be seen as a symptomatic treatment; it must be accompanied with a dramatic restructuring in the financial framework. The exit from quantitative easing must be postponed and decided within a clear program and according to clear numerical objectives."

    3. The Effectiveness of Unconventional Monetary Policy at the Zero Lower Bound: A Cross-Country Analysis
      Leonardo Gambacorta, Boris Hofmann and Gert Peersman
      August 2012

      "This paper assesses the macroeconomic effects of unconventional monetary policies by estimating a panel VAR with monthly data from eight advanced economies over a sample spanning the period since the onset of the global financial crisis. It finds that an exogenous increase in central bank balance sheets at the zero lower bound leads to a temporary rise in economic activity and consumer prices. The estimated output effects turn out to be qualitatively similar to the ones found in the literature on the effects of conventional monetary policy, while the impact on the price level is weaker and less persistent. Individual country results suggest that there are no major differences in the macroeconomic effects of unconventional monetary policies across countries, despite the heterogeneity of the measures that were taken."

    4. This paper shows that the US QE raises core inflation:

      Monetary Transmission via the Central Bank Balance Sheet
      Stefan Behrendt
      November 2013

      "This paper estimates the effects of unconventional monetary policies on consumer as well as asset price inflation, economic activity and bank lending at the hand of a VAR analysis, covering episodes of balance sheet policies of 9 countries over the last 20 years. While recent episodes of unconventional monetary policies have been extensively analysed, this paper reduces deficiencies about long-run implications following central bank balance sheet policies in Scandinavian countries, Australia in the 1990s and Japan in the early 2000s. Results of this study are that balance sheet policies, in response to a collapse of asset price bubbles, can ensure a short run stabilisation of economic activity but are not able to lift the economy out of the ensuing deflationary slump alone. Additionally, they do not pose severe problems associated with inflation, as laid out in several theories such as the static monetarist interpretation of the quantity theory of money, or towards newly created asset price bubbles."

    5. Thanks Mark. I tweeted a link of your comment to Yates.

  19. David,
    Tyler Cowen has a post in which he responds to Williamson's claims concerning the evidence on QE. In particular he cites Girardin and Moussa (2010):