Friday, June 12, 2015

Counterfactuals and the second derivative

Scott Sumner put up on his blog what I called a derp Rorschach test on teh twitters -- since no counterfactual was presented in the picture, you can invent whatever counterfactual you want to confirm your priors. However, I'd like to point out that it is far from obvious that you can draw Sumner's preferred conclusion for a simple reason: the second derivative.

See, the curvature of total employment in the graph on Sumner's blog is far sharper at the beginning of the dip than at the end -- something consistent with an inertial picture of the economy where "forces" act on employment much like forces act on objects. In that case, we can have an acceleration that is more than normal for awhile (normal is just trend growth) and then becomes less than normal afterwards. Stimulus and austerity. It looks something like this:

Of course, this is perfectly consistent with the picture Sumner shows (I added the line from the graph above):

Basically, the idea that this picture "obviously" shows anything is just confirmation bias. We need to know your counterfactual! And I can show you the counterfactual for the model above ... it looks like this:

Sumner can't show you a counterfactual. In fact, no market monetarist can ever show a counterfactual -- no market monetarist is the market. What the market would have done in an alternate world is completely unobservable. That's probably why Britmouse and Sumner think the graph shows something obvious. Whatever happened is the only thing that could have been observed to have happened!


One thing I wanted to note, but forgot, is that ordinary automatic stabilizers have roughly the same effect of "stimulus + austerity". When a recession hits, a lot of money goes out as unemployment insurance -- but it slows over time.


  1. Hi Jason, can you explain what you mean by the phrase "no market monetarist is the market?" Also, in the second plot, is the solid blue line supposed to be the same solid blue line in your first plot (i.e. a curve fit to the actual data)? In other words, does it represent fiscal stimulus followed immediately by austerity?

    How did you come up with the dashed blue, solid black and solid red curves in the last plot? Were you assuming the "Growth Force" from the 1st plot determined the magnitude of the 2nd derivative?

    Also, in your 1st sentence, did you mean to write "on teh twitters?"

    1. I sort of answered this one down below. Yes, it's "fiscal stimulus" followed by "fiscal austerity" and the solid blue curve is the same in both diagrams -- the scales are different to allow you to see the other ones (they would have gone off the graph on the first scales.

      An the phrase "no market monetarist is the market" means that no one person can say what the market would have done -- they can only say what they would have done. But if the market followed any individual, it'd be a representative agent model.

      Only the market can say what it would have done, but the only market we have is the actual market -- we don't have counterfactual markets to query.

      And yes, I did do that one on purpose ... I think I picked it up from Duncan Black.

  2. Also, how did you determine the magnitudes of the "Growth 'Force'" in the 1st plot?

    1. Hi Tom,

      I didn't do much rigorous analysis here -- it's a plausibility argument, not a definitive model. I put together a model of a particle where acceleration is one value in the "stimulus" period and another value in the "austerity" period, with the second one lower. The actual values for the accelerations were:

      13 and 1 : the original model
      13 and 6 : the stimulus only model
      6 : nothing
      6 and 1 : austerity only model

      It was basically fit by eye ... not a rigorous analysis.

  3. Thanks Jason. BTW, Scott has a follow up question for you.

  4. I feel like whenever I see you do counterfactual you aren't quite fleshing it out enough, you have to make a model of the central banks behavior's at the heart of monetary offset and kind of makes your counterfactual irrelevant to Scott...since his central bank completely offsets austerity in all imaginable universes with the same regime

    1. Yes, that is true -- if Scott tries to analyze my counterfactual with his model, it's not going to make sense. But that's the key point: it's a different model.

      Let's say I come up with a counterfactual where the planet Jupiter doesn't exist. I have a Newtonian model of the solar system, so removing Jupiter perturbs the orbits of the other planets resulting in a new configuration.

      A person, let's call him Steve, comes along with an Ptolemaic model of the universe and says that my model neglects the crystal spheres the planets are attached to -- removing Jupiter doesn't do anything. Steve says there is just an empty spot where Jupiter's crystal sphere was.

      What we have is a disagreement about the model. But on the face of it I would say Steve is correct about his counterfactual given his model (prior) and Steve should agree that my counterfactual is correct given my model.

      Now the Ptolemaic model and the Newtonian model can be made to agree to a given level of accuracy with empirical observations (sufficient epicycles can be added).

      Now what we have a case of here is Steve not only refusing to accept my counterfactual is correct in my own model but somehow saying only his model is obvious given the empirical data. It's sheer bloody-mindedness.

      If I don't believe if monetary offset works in a liquidity trap you can't say to me "you forgot monetary offset". That is equivalent to saying "you forgot to use my model". This is a recurring theme on Scott's blog. The latest is his link to Sadowski's post -- Iceland was never in a liquidity trap or even remotely close to zero interest rates. That it offset fiscal consolidation says nothing about the argument for or against fiscal austerity in a liquidity trap!

      Scott's problem with Paul Krugman is that Krugman doesn't use Scott's model. He needs to get over it. Paul is not going to use Scott's model and Scott isn't going to use Paul's. It's going to come down to which one makes better predictions and/or which one has better internal logic -- that is assuming market monetarism is right, what results ... and better yet, what doesn't result?

      I've basically come to the conclusion that the market monetarist model isn't falsifiable (if you know of a way that it is, let me know!):

      Which makes any time Scott presents data even more maddening! His model isn't falsifiable with data! It doesn't matter what the data is! Gah!

    2. "bloody-mindedness"... had to look that one up; I wasn't sure if you'd just coined that one or not. It says chiefly British. Did you spend some time in the UK?

      BTW, I asked Sadowski about how confident he was in monetary offset (in any country) and what would falsify his belief in it. He gave me an answer, and said he was as close to 100% confident in it as an inductive reasoner could claim to be. I should have asked him about it in liquidity traps (which I take it the UK was in).

    3. I think I can still say you forgot monetary offset so long as the central bank believes they can do something about it...the central bank will do something in all the counterfactuals...does the bank exactly accommodate or try to over/under shoot? Are all actions going to have the same result?....when pressed Scott has given hypothetical scenarios in the past in which central bank decisions can make fiscal stimulus effective...any model completely agnostic to the central bank seems suspect to the information model with the liquidity trap specification, are you telling me the central bank can't harm the economy? ... I don't think that is anyone's model...and I think that is at one half of the monetary offset story...but is it falsifiable....maybe not in the market monetarist got me there..

    4. Hi LAL,

      If markets worked perfectly, then when the IT index ~ 1 the central bank can't really hurt the economy either (unless it does drastic things like cut the monetary base in half). When IT index ~ 1, then dP/dM ~ 0 for both directions of M.

      But in our imperfect world, the central bank can cause markets to panic resulting in non-ideal information transfer.

      If kappa < 1, then the monetarist view holds and the economy is basically described by a quantity theory of money. So the ITM isn't completely agnostic about the central bank.

      The basic idea is that in the limit as the size of the economy goes to infinity, monetary policy becomes mostly irrelevant and inflation goes to zero.


      Nah -- I've just watched a lot of British comedies. And Sadowski's answer seems about right.

  5. BTW, I Googled "Duncan Black." His twitter account was not what I was expecting: it seems quite uh... explicit ... that he's not who you had in mind. Lol. There's a Scottish economist by that name too.... but he died in 1991. I doubt the latter ever wrote "on teh twitters."

    OK, this must be the one:

    But he uses "on the twitter" not "on teh twitters." Just so you know. (c:

    1. Yeah, it was the second one. I only thought that was the likely source ... it was probably just osmosis from teh intertubes.

    2. You mean the 3rd one I think. The 2nd was the Scottish economist who died before twitter was invented. The 1st is the gay porn star / male escort, who (in contrast to #2) is apparently a frequent twitterer. Which reminds me of my colleague at work who reads "Zero Hedge." He said reading ZH is a guilty pleasure: he refers to it as "bear porn." Don't Google that phrase though! Lol.

    3. Ha! That is pretty funny. I'm sure 'atrios' aka Duncan Black has already been informed about this other Duncan Black, but I think I might remind him if he ever talks about gold or zero hedge.


Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.