Friday, June 19, 2015

This analysis is so bad

Scott Sumner and/or Mark Sadowski.
There are so many issues with the presentation in Sumner's post that it's hard to know where to begin.

I've already gone through the basic logic that the set of countries that should show austerity has an impact in the Keynesian case are those at the ZLB [1] -- call this set ZLB. The countries that should show monetary offset are those with independent central banks -- call this set ICB.

Sumner effectively tests the Keynesian austerity on the set ICB, and ICB ≠ ZLB. Now he could correct this and test austerity on ICB ∩ ZLB (the intersection -- the countries in the middle of the Venn diagram with circles labeled ICB and ZLB), but there are only a few countries in that set (basically only the Eurozone, the US and Japan are in this situation). And there weren't enough points to be conclusive anyway.

I'd like to summarize the many, many issues:

Issue 1: Data manipulation. Throwing out some of the relevant data to the Keynesian hypothesis and keeping some data irrelevant to the Keynesian hypothesis. This will not test the Keynesian hypothesis. Mentioned in previous blog posts. The way to fix this is to include the correct sets of points (ICB and ZLB) and test each hypothesis separately.

Issue 2: Dependent variable bad. Dependent variable includes a large irrelevant signal -- high trend growth countries will appear at higher y-values for reasons that have nothing to do with austerity during a recession. The ∆NGDP (or ∆RGDP) has two components:

 ∆NGDP =  ∆NGDPtrend + Austerity + Recession

For Singapore, South Korea and Israel ∆NGDPtrend compounded over 5 years will lead to a much larger value: 28% rise over 5 years for 5% growth in Israel and a 5% rise over 5 years for 1% growth in Japan. Even if these two countries engaged in the same amount of austerity (as they apparently did on the graph) the ∆NGDPtrend  would put Japan at the bottom and Israel at the top. So two countries -- even with the same amount of austerity -- appear at two different places on the y-axis for reasons that have nothing to do with austerity (trend growth). You could correct for this by subtracting trend growth.

Issue 3: Independent variable bad. At least Israel didn't really have a recession (I am too lazy to look up the other countries, but Israel's NGDP growth barely registers the global recession; see Evan Soltas). Now Israel wasn't in a liquidity trap, so monetary offset works according to both models. Nearly half of Iceland's so-called austerity happens after the country exits the recession and real interest rates rise above zero. So the amount of austerity these countries engaged in listed in the data is suspect. The only way to fix this is to go get the data oneself.

Issue 4: Inconclusive result treated as conclusive. The given data is actually inconclusive (R² is roughly zero, from the comments on the post -- H/T Tom Brown -- the p-value is greater than 0.9). After throwing out the Eurozone countries (or more accurately summing them together, giving them a weight of ~ 0.05), there is insufficient data to show anything at all. Yet Sumner decides that it shows the Keynesian picture is wrong and/or the results are consistent with monetarism. What he should have said was nothing. Sumner could fix this by deleting the post or posting  a retraction.

Issue 5: Lack of counterfactuals. You need a model to understand the counterfactual situation in order to understand what austerity is and what growth is in the cases with and without austerity. Market monetarism cannot produce a counterfactual at all because there is no way of knowing how the market would have behaved with and without austerity. Even with prediction markets you can't know what people would have predicted given different a situation. Because of the dependence on expectations (which we only see because of existing markets according to the market monetarist model), we'd have to read human's counterfactual minds somehow. Markets (purportedly) read their real world minds, but how do you read the counterfactual state of a human mind? There is actually no way to fix this.


So both axes, the data points, the method and the fit are completely wrong. Did I miss anything? This is just garbage analysis. Either Sumner and Sadowski don't know what they are doing or are deliberately trying to mislead their audience. I generally go with ignorance rather than conspiracy since that's nearly always more likely.

My question is: how did Sumner and Sadowski end up so ignorant of the basics of hypothesis testing and "experimental" set-up? 
  • Maintain consistent treatment of your data. These are issues 1 and 3. Make sure the data you use to test a hypothesis actually satisfies the conditions of the hypothesis. Don't throw out data that tests one hypothesis and keep data that tests another.
  • Make sure your data tests your hypothesis. These are issues 2, 4 and 5. At best, Sumner came up with an inconclusive result about whether austerity turns your country into a low trend growth country or not. That should be inconclusive. No one ever said that -- Keynesians think austerity affects growth while it is in place -- it doesn't permanently impact the trend; monetarists think there is monetary offset so austerity has no impact -- it definitely shouldn't turn your country into a low growth country or a high growth country.

I'm just baffled.

Update 6/20/2015:

This blog being the farthest from the bright center of the econoblogosphere it might take me awhile to get to all the comments resulting from being linked by a real blog, but I will do my best (accounting for the fact that I have just returned from a two week work trip, so spending some time with my wife on a rather beautiful day in Seattle is a bit higher priority). In the meantime, I responded to one "comment" i.e. Sumner's counter-criticism here. Feel free to hit that post up with criticism as well. Maybe it answers some of your comments below.


[1] In the information transfer model, these countries are the one with IT index ~ 1 (the zero lower bound isn't relevant). My problems here are with the methodology -- I am actually advocating a different model from Krugman or Sumner so I don't really have a horse in this race. My model also works better than either of these models.


  1. Jason, I don't understand the problem with Israel. If it never was in a liquidity trap (or at the ZLB?), then why isn't that an "Issue #1" problem instead of an "Issue #3" problem?

    1. BTW, I saved a copy of that meme... I have other uses for it! Lol.

    2. It never engaged in austerity and never had a recession. It shouldn't be considered at all.

      However it also has high NGDP trend growth meaning the y-axis value for it doesn't show what it purports to show.

    3. Basically Israel has three issues:

      1. Inclusion
      2. Y-axis value
      3. X-axis value

    4. Ah, OK. However not engaging in austerity in and of itself is not a problem is it, since covering a range of austerities is what the x-axis is all about, right? So you're saying the x-axis value is a problem because it shows up too far on the austerity side (right side) of 0, when it really should be closer to 0 (or perhaps to the left)?

      Also, now that I think about it, that meme is pretty appropriate for me most of the time! I just might adopt that as my avatar.

    5. It should show zero austerity. And from my earlier post, Iceland should show about 1/3rd as much as it does.

      And sometimes I feel that way too! Ha!

  2. Thanks Jason. I assume you've seen this?

  3. I'm not particularly baffled, for two reasons.

    1) Macroeconomics is pretty much pre-scientific, in the modern sense of science.

    2) Testing the theories against each other does not involve the usual tools. Regression is irrelevant. I had to work through the logic to see the right tests. (BTW, it would not surprise me if both theories are false. ;))


    Oh, I just submitted a note about how to test the theories against each other to Sumner's site, as Billikin. We shall see what happens. :)

    1. @Bill, where did you submit that? I searched for "Billikin" here and here but I didn't see that.

    2. My note is awaiting moderation. As I expected. ;)

    3. Bill,

      I agree. And it wouldn't surprise me either -- actually in my model, both are right in different regimes, which also means both are wrong in different regimes.

  4. Jason, I asked Mark about weighting points in his regression. I think he interpreted my question to be an implication that his "Euro Area" point in plot #3 should be weighted by 19. That wasn't my intended implication and it wasn't necessarily the only weighting I was asking about either. I was hoping he'd give me his thoughts on the pros and cons of weighting each point with the size of the economy it represents (or, for that matter, any other candidate weighting scheme).

    It sounds like you (in a previous comment somewhere) thought that weighting points (say according to economy size or population size) isn't necessarily a good idea either. Why is that?

    Overall, do you think it's possible to salvage some kind of regression analysis here? Given your issue #5, it sounds like you think that's not really possible for the MM model. How about for the Keynesian model?

    1. Tom! I haven't heard from you in ages. Did I say something to offend? LOL. So you're hero Sadowski has finally been humbled.

    2. Hi Mike. No, you didn't say anything to offend. Lol. I've just cut back on my blog comments for the past several months. Maybe a year. I just had a flurry of activity recently.

  5. I maintain you are still wrong about the zero lower bound in the Keynesian's just the most obvious case that the interest rate isn't square with its natural rate...

    now does Scott Sumner believe this ?I'm not sure....but if you equate Keynesianism with Krugmanism and assume that Krugman claiming that the eurozone should not have undergone austerity is somehow related to Keynesianism...and you pay attention to the dozen times or so Krugman has cited these graphs in support of the argument against is suddenly admissible evidence against Krugman 's argument....

    Is it science ?....probably not...but why get bent out of shape over an argument custom made to respond to the low bar Krugman has been making (especially for someone like you, who approves of that empirically challenged Nobel laureate)

    1. You're totally right LAL -- I think the "natural rate of interest" is the issue. The zero bound is more about e.g. an admittedly imperfect Taylor rule going negative than it is about zero nominal rates. In fact, that is one of the major points in my response to Sumner.

      I realized that I kind of assumed what everyone meant by "the zero lower bound" was that your real rate couldn't get negative enough because nominal rates were near zero and inflation was low. Not literally nominal interest rates at zero.

    2. I see, thanks for writing the articles, even though we get caught up in it all, getting everything we assume stated clearly helps everyone in the long run...

  6. Thanks Jason for your ongoing war against the forces of bad data manipulation, against which apparently the gods themselves labor in vain. Keep up the good work!

  7. Jason, my name is Ken Duda. I'm a computer programmer who supports Sumner's program at Mercatus.

    I am not going to defend Sumner's specific analysis. However I would ask you to think carefully about whether it's possible for a central bank to increase economic activity when there's rising unemployment, falling NGDP (or at least falling NGDP growth), low inflation, and the short-term risk-free nominal interest rate is zero. Krugman, Delong, and Wren-Lewis basically say no, or probably not, maybe the central bank should try, but there's not much it can do. I think they're wrong and the market monetarists are right. The idea that the monopoly issuer of a fiat currency can't induce more nominal spending seems nuts. Sure, the interest rate channel may be dead, but what about the expectations channel? If the central bank tells the market that it will hit its NGDP target come hell or high water, it's just a matter of time, and by the way, the target is rising constantly at say 5% a year, and all this money we're creating will absolutely not be sucked right back out of the economy until NGDP hits that target (or, more precisely, until a prediction market tells us that we'll overshoot our target if we fail to suck the money back out of the economy), then people expect more spending in the future, and that expectation of future spending stimulates spending today, either investment spending to build in anticipation of the future spending, or simply "getting while the getting is good", i.e., buying before prices rise significantly (inflation).

    Again, I am not here to defend Sumner and Sadowski's analysis in this case. However, it breaks my heart to see good intelligent people arguing about style or argument types etc when we just went through 8 years of 10 million people needlessly unemployed, lives shattered, savings lost, when the whole thing could have been averted with better monetary policy. Why can't you, me, Scott, Paul, Simon, Brad all get together, set aside the debate over fiscal stimulus, and demand better monetary policy? Market-guided NGDPLT seems like such a dramatic improvement over high-priest-guided inflation targeting, let's make it happen.


    Kenneth Duda
    Menlo Park, CA

    1. Ken, is there not already general agreement that fiscal stimulus would work if the central bank did not actively impede it?

    2. It may be that at the ZLB central banks don't do enough to offset fiscal austerity. In other words, it's politics not economics. They could offset it but in reality they don't.

      Therefore fiscal stimulus works "better" at the ZLB, because the central banks don't offset. They appreciate the help because they don't want the political heat from doing the heavy lifting like raising the inflation target.

      Krugman pushed raising the inflation target (which NGDPLT does) but then considered it too politically controversial.

      Why did the central banks advise fiscal stimulus during the crisis? Because it works not because they wanted window dressing. I think many on the left believe fiscal stimulus and government spending and investment work "better" and more directly especially in the context of deregulated financial markets. Of course some sorts of government spending is wasteful, think of military spending and unproductive, but then so is some private investment pushed by lower interest rates: think of the epic housing bubble/ponzi scheme.

      I'm in favor of market-guided NGDPLT, but think it would behove Scott and Mark to be more diplomatic to those who prefer government-directed investment and spending. It does work well and will ease the political load the central bank has to take on when maintaining NGDP levels. Just some thoughts. I do agree that K, D and W-L could do more to encourage switching to an NGDP target, but I don't think they are opposed.

    3. See Ken, you have I have spoken about this before and this is my trouble. I can agree intelligent people shouldn't fight rather than keep up solutions but Mark Sadowski's post was about fighting rather than coming to any consensus.

      It was about "Na-na, we're right and the Keynesians are wrong.' it would help if he and Scott could back off on making these kinds of categorical claims with such noisy data.

      Again, my first impulse was to give the MMers their shot at NGDP as long as they don't try to hamstring fiscal policy. They simply are not having it.

      Scott seems intent in winning a Holy War against Keynesianism

    4. Folks, thanks for the responses. I think I pretty much agree with all of them, and I feel like this Holy War is entirely unnecessary. I think we, and basically all economists, would agree that:

      1. in a depressed economy, fiscal stimulus can increase output if the monetary policy at the time is to ignore any effect of the fiscal stimulus (and the markets expect that monetary authority will ignore fiscal stimulus);

      2. the monetary authority, if it wants, can always offset positive fiscal stimulus by tightening as much as the fiscal stimulus stimulates;

      3. monetary policy alone is sufficient to restore aggregate demand as long as monetary policy is not paralyzed;

      4. monetary policy can become paralyzed if the policy instrument is the nominal short-term risk-free interest rate, and that rate is at zero.

      So why are we arguing? I just don't get it. Let's demand better monetary policy now. I think almost everyone here would agree that if the choices were (A) current policy, or (B) market-forecast-driven NGDP level targeting, B would be better. Fiscal stimulus is impossible thanks to braindead Republican deficit-obsessed obstructionism, so while I would love to see more fiscal stimulus, it's just not going to happen. Instead, let's focus on what we can do, which is better monetary policy, where no congressional cooperation is required.

      The Federal Reserve has the wrong target. Let's fix that, and, while we're at it, put an end to the tea-leaf reading and drive policy with market forecasts. You just know it's wrong when volumes of articles are written parsing ever last word of an FOMC statement. It shouldn't matter whether Janet Yellen says "patient" or not. And with NGDPLT, it wouldn't.

      I'm sorry that Scott and Mark are annoying everyone, but let's please keep our eye on the prize.


      Kenneth Duda
      Menlo Park, CA

    5. Why are we arguing, Ken? Burden of proof.

      Sumner's ideas may be the best ever, but he bears the burden of proof to get them accepted. Empirical proof is not easy to come by in macroeconomics, especially as it is not a particularly empirical discipline. It is these attempted proofs that the current arguments are about. They are necessary for improving empirical research in macroeconomics.

    6. But Bill, it's the wrong argument. We don't need to compare NGDPLT versus fiscal stimulus. We need to compare NGDPLT against current policy. Current policy to me appears to be inflation targeting, but also watching unemployment, and maybe other things, and chasing that unclear set of goals mainly by targeting the fed funds rate, but then offsetting that by paying IOR, i.e., working against itself, oh and "forward guidance", and with occasional rounds of QE, etc etc.

      So the burden of proof here should be to convince people that NGDPLT is better than that.

      I lack the expertise to understand how to accomplish that. Can you help? What would proof that NGDPLT is better than current Fed policy look like?


      Kenneth Duda
      Menlo Park, CA

    7. @Ken 3:44pm

      So interestingly the ITM says that Fiscal and Monetary policy can be *orthogonal* - see graph on ( If that's true, then a *lot* of interesting things pop out - chief among them being that monetary policy does not offset fiscal policy and fiscal policy might be better...

    8. Hello Ken,

      I am not as much of a true believer in the efficacy of monetary policy or even the desirability of effective monetary policy. In fact, unemployment (at least in the US) does not appear to be affected by any kind of policy (see e.g. here)

      You said:

      "The idea that the monopoly issuer of a fiat currency can't induce more nominal spending seems nuts."

      There are lots of things that seemed nuts but turned out to be true (quantum mechanics comes to mind). But I'm not sure it really is that much of a stretch in this case. As an economy becomes larger, the most likely place to find a given dollar is in a transaction in a low growth market -- there are simply more ways an economy can be organized where this is true. It is the same process where there are more ways for a given amount of energy can be allocated among low energy red photons than a few high energy blue photons.

      In general, where most of economics sees rational actions by forward looking agents, I see randomness. It is interesting (to me at least) that randomness can lead to utility optimization (for example) or the asset pricing equation.

      I've managed to turn myself into a true believer of my own theory -- or at least my own framework since several theories exist in it -- although I do my best to maintain some skepticism. In that theory NGDPLT is the flip-side of price level targeting.

      However, I may well be wrong and NGDPLT may be right. Knowledge advances both when new ideas are created, but also when there is criticism of those ideas.

      Good luck in your ventures.

    9. Ken,

      Wrong argument? Tell that to Sumner. He's the one who framed and posed it. Tell that to Sadowski. (BTW, Sadowski's research does not exactly fit Sumner's framing, which is part of the problem with the blog post.)

    10. Jason, thanks for taking the time to go through my comments.

      I tried to go through your post that "NGDPLT is the flip-side of price level targeting", i.e., "Expectations (rational or otherwise) and information loss", but I didn't get very far, because I wasn't sure what you meant by "actual distribution of NGDP". At the end of the day, NGDP will have one value (not much of a "distribution", unless one likes Dirac deltas). Today, we have whatever information we have, and based on that information, we can forecast NGDP and generate some probability distribution. Is the result of that effort A or B? If it's B, then I have no idea what you mean by A. If it's A, and B is just what the market thinks but you can calculate A if you try, then I'd say anyone who could calculate A can make a lot of money in the NGDP futures market, if such a market ever comes to exist. But I'm not sure I'm following.

      I am also puzzled by what you conclude from the "remarkable recovery regularity". I have also noticed the regularity in recovery patterns, and find it interesting/puzzling. But I don't get from there to monetary policy does not matter. Do you have another explanation for 10 million people being unemployed between 2008 and 2014? I guess the RBC people think they all simultaneously decided they preferred leisure over paychecks. Bad monetary policy is the only explanation I've been able to find --- a collapse in future spending expectations leads people to save and not spend, the paradox of thrift kicks in, and blammo. The Fed can save us from this self-fulfilling doom prophecy by saying there will be spending, inflation and unemployment be damned, and then acting accordingly, ideally guided by an NGDP futures market that would tell us in real time if the market believed the Fed or not. I don't see any other credible path.

      That's why this is so important. It's not just a theoretical debate. Millions of livelihoods hang in the balance. That's why I'm so keen to get reasonable-minded people, like Scott and Simon Wren Lewis and you and Mike Sax and so on, to stop quarreling over who called whom a liar and start pushing for better monetary policy. Unless you truly believe monetary policy doesn't matter, in which case I guess there's no reason to push for improvements.

      For what it's worth, I like the idea of modeling Homo Economicus as random rather than precisely utility maximizing. And I think that (strict) price level targeting would also be a big improvement over today's monetary policy, just that NGDPLT is better because it responds differently (and better) to positive supply shocks than PLT.


    11. Hi Ken,

      Regarding the distributions: the result of 'that effort' is the distribution B.

      For concreteness, lets take the variable to be 2015 Q1 NGDP growth. There is a market prediction of that value that has distribution B. Then there is a distribution A that we'd get from e.g. looking at the many worlds of quantum mechanics. If we had a thousand "identically prepared" Earths, 2015 Q1 NGDP growth would also have distribution A. Since we can neither calculate A from quantum mechanics nor set up the ensemble of Earths experimentally, the distribution A is completely inaccessible for now. [Maybe we could derive it from a fundamental theory of economics, but that doesn't exist.] The best we have (from markets, from macro models, from individual's intuition, from all of those together) is B.

      Since B is different from A, we have information loss (in the sense of decoding a signal when B is used to approximate distribution A, see e.g. here).

      Someone who could calculate A would definitely clean up in an NGDP futures market.

      Sumner essentially has the piece that comes from the difference between B and A showing up as the unforeseeable error term "et" here:

      Regarding the unemployment questions: the idea is that policy regimes were different over the period 1949-2014 (as well as technology, demographics, etc); there was a more Keynesian view up until the 1970s and a more monetarist view afterwards. However the unemployment recovery from recessions is pretty much the same across that entire period. If I keep changing the macro policy background, but the unemployment recovery has the same general behavior it seems like the macro policy doesn't make much a difference with regard to unemployment. Unemployment falls at a roughly constant rate from 1949 to 2014.

      Macro policy may change the height of the unemployment peaks, and it likely affects other variables -- it just doesn't (surprisingly!) have much of an impact on the rate at which unemployment declines after a shock.

    12. Hi Jason,

      I wrote out a response to Ken yesterday regarding the A and B NGDP distributions using a Kalman filter as an analogy, but then I erased it because I realized I didn't understand what you were saying as well as I initially thought.

      My analogy went like this: say X is a Gaussian random scaler and a-priori we know it's initial distribution (say it initially has mean m0 and variance v0, or it's N0 = N(m0,v0)). If we then obtain a measurement of X (call it y) and we know our measurement variance is r (again, unbiased & Gaussian) then we can combine N0 with y and r to produce a new estimate with distribution N1 = N(m1,v1) and it will be optimal in the sense that it's unbiased and that v1 is minimum. In other words the distribution of the estimation error is N(0,v1), with v1 at a minimum. If we performed this test over an ensemble of identically prepared experiments we could verify this. In this analogy N0 is like A. Now if we didn't know N0 precisely, but instead had an estimated initial normal distribution B (with B =/= N0), then our filter would no longer optimally process the measurement (assume we continue to know r exactly), and we could verify this over an ensemble of identically prepared experiments.

      Where I ran into trouble was your statement that N* >= N. Maybe my analogy was flawed from the start, but I couldn't square that with my analogy, since N is analogous to the measurement y and it's not clear what N* is in the analogy.

      Perhaps a better analogy is a linear feedback control system where the Kalman filter is used to estimate the current state, but there's a separate control law that attempts to optimally minimize some cost function on each iteration. Here again, we can prove that this cost function is minimized with perfect information (A) (assuming we've solved for the optimal control) rather than flawed information (B), but only in a statistical sense. I still have trouble seeing what's analogous to your N* in that analogy.

      Is that line of analogies fundamentally flawed, or am I just missing something obvious?

      It's almost as if the ensemble (or some ensemble) is built into the information transfer framework in some sense and thus we're guaranteed (with very high probability) that N* >= N.

    13. Hi Tom,

      One way to look at it is in terms of cumulative success in recovering the signal with a Kalman filter (which as you say is used to estimate the current state). If I know A, my cumulative success will give me N*, but if my best estimate of A is B, then my cumulative success will be N < N*.

    14. Thanks Jason. Yes, maybe that works.

  8. I don't know where this comment belongs but I'll post it here anyway...

    I don't get what the point of engaging with Sumner and crew ends up doing. At this point, having read a large chunk of your work, you're playing chess while the rest of the blogosphere is playing checkers (or rather, posting long winded logically inconsistent screeds about checkers). Sumner and everyone in his orbit (e.g. Nunes, Sadowski) can't even formulate a god-damn model of what they're doing (well, if you don't consider Central Bank = awesome to be a viable, testable model - and I love that you can use the IT framework their to build an MM model for them). His readership probably wouldn't know a differential equation if it bit them in the rear, and nobody is going to change their minds about their beliefs/derp.

    Your framework is powerful, extensible, predictive and at the limits reducible to previously established economics (like S/D curves and QTM). That's fan-effing-tastic and you should be publishing! I know it's currently cool to say that blogs are where the conversation "happens" but you're honestly not going to get the level, quality, or feedback of an interested academic community - and I don't mean the economics community. The natural home for further research is probably within the econophysics community, many of whom are floundering around working on ABMs and other more dead-end lines of research. I think it'd be super effective to get a working group of some kind started to get the ball rolling. You're never going to get economists on board to a large extent, there is just way too much entrenchment. But if econophysicists can coalesce around the ITM, I think huge strides can be made into challenging orthodoxy (without the general craziness that usually comes with heterodox research)

    Anyway, those were just my 2 cents...

    1. Thanks for the vote of confidence.

      The main reason I engage with other economists is that I find it fun to argue about this stuff. It also helps show by example just how useful the ITM can be in simplifying the discussion.

      By the way, I did try to construct a market monetarist model way back when:

      It's not as empirically accurate.

      There is also this piece:

  9. "I'm sorry that Scott and Mark are annoying everyone, but let's please keep our eye on the prize."

    Ken, you're such a nice, reasonable guy part of me would like to follow you here. But Scott and Mark are not keeping their eye on the prize. Both are doubling down on their Holy War against Keynesianism.

    It's not going to work to ask one side for a cease-fire while the other side-the MMers-are launching cruise missiles as we speak. Maybe you should suggest this to them too. As long as they do this there will be civil war

  10. Jason, it seems Nick Rowe is taking another look at Sadowski's plots today.

    Also, if we imagine that a Keynesian (or some other economist capable of doing counterfactuals) was presenting this data. Can you describe how he might factor in the counterfactual? Thanks.

    1. Hi Tom,

      I noticed that briefly this morning and was going to look at it further later today.

      The counterfactuals would be the path of government spending without austerity (so you know how much austerity happens and when) and the path of NGDP without austerity (so you know what NGDP would look like in the absence of an effect due to austerity).

  11. David Comerford takes a look at Sadowski's regressions. You might be interested.

    1. I should mention he makes three of his own regressions: folding in exchange rates. Nick Rowe had kind words.


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