Friday, December 4, 2015

Limit cycles versus avalanches

I'm not sure I understand the allure of Steve Keen. One of his papers came up in comments (from Steve Roth) here. One of the first comments on my blog was from someone who said I should check Keen out. His big thing is nonlinear differential equations; you get graphs like this in his papers:

One of Keen's claims to fame is that he "predicted" the global financial crisis. Of course, if you think everything happens in cycles, then a financial crisis is always just around the corner. However the business cycle isn't very cyclic -- in the sense of being periodic (see Noah Smith for a good overview). I have a view that would be more like avalanches or earthquakes. They will be spaced out because it takes time to build up mechanical energy or snow (or in the economics case, too much output), but the exact failure time isn't unpredictable.

One of the other problems with these limit cycles (as they're called in the biz) is that they aren't always terribly robust to noise. Here's a simple one with and without noise:

Anyway, Keen has a model in the paper Roth linked to that produces this graph of the real growth rate:

If we take this at its most charitable (i.e. best fit) of Keen's model (red) to some real data from the US, we see something like this:

It's not terrible, but it seems like it wouldn't really continue into the past or future and line up exactly. And with noise on this level, you'd actually expect those nice cycles at the top of the post to completely evaporate. 

What does the IT model have to say about this? Well the RGDP growth trend (brown) definitely looks less impressive:

The IT model story of the post-war era has been that of gradually falling RGDP growth. This is roughly what we'd expect if those nominal shocks (avalanches) were at their average level over the entire period. If we add the shocks in, we get this:

Note that this model comes from just M0 and the labor supply (equal to nominal shocks). Overall, instead of a story of cyclic booms and busts with one leading to another, we have a story of over-estimating future growth because it slows over time. These over-estimates lead to the Fed being unsustainably expansionary relative to the trend, eventually culminating in a recession. Strong enough recessions are usually accompanied by financial crises (because contracts become unsustainable, and panic leads to non-ideal information transfer and falls in prices).

That is to say recessions happen because of a backward-looking bias in growth expectations (similar to inflation). Previous growth will be higher than future growth, so estimating future growth from previous growth will be biased high -- leading to unsustainable Fed growth targets, business investment, and general over-optimism about the future.

I wouldn't say this is totally inconsistent with Keen's version (there's still over-investment that leads to recession), but here there is also a continuous fall in economic growth as the economy gets larger.

But I still don't get the desire to see the economy as a robust and well-defined cycle. The idea of aperiodic failures of the market due to a combination of an optimism bias and irrational panic is more appealing to my sensibilities. Maybe other people want economics to be as precise as a nonlinear circuit (sometimes even more precise than possible)? 


  1. A couple of comments.

    First, you may have the causation backwards in the combination of financial crisis and recession. Arguably, both our recent recession and the Great Depression were mainly caused by overindebtedness and leveraged financial speculation, instead of recessions causing financial crises.

    Second, as I have pointed out, sufficiently long cycles are in the short term indistinguishable from random walks, and their periods are variable. The variability of the periods shorter cycles (of less than a decade) does not mean that they do not exist, nor that their associated difference equations are unpredictive. Trying to fit something like the picture of Keen's model instead of using difference equations seems unfair, unless Keen's model really is that stupid. I kind of doubt that it is, given the century old analogy of the business cycle as a pendulum at which small boys are throwing rocks. You should not expect smoothness and regular periods. If modern economists expect well defined cycles instead, then they have forgotten that analogy.

    1. One more comment.

      I think that your reference to the effect of the Fed on the business "cycle" is entirely apropos. Post 1900, central banks have attempted to prevent or mitigate recessions and to "take away the punch bowl" when the economy overheats. Note that the analogy I cited between the business cycle and a pendulum comes from before the establishment of the Fed. It is quite possible that the actions of central banks have not eliminated the business cycle, but have FUBARed it through countercyclical policies, at least in the short term. :)

    2. This comment has been removed by the author.

    3. "overindebtedness and leveraged financial speculation"

      A bit of a chicken and egg problem there ... you only have too much debt or 'speculation' relative to future income/growth prospects. If growth had continued, the debts and speculation that went bad in 2008 wouldn't have gone bad. But there was a financial crisis and sound, liquid investments became speculative and illiquid.

      Financial panic can cause any level of debt to be unsustainable. The debt could have been sustainable without the financial panic.

      If you want to account for the possibility of financial crises -- debt that is appropriate even in the midst of recession, you must take the most pessimistic growth path possible ... which is zero growth, maybe less!

      Therefore there should be no debt as any level of debt can be unsustainable.

      I don't really believe there should be no debt. That's why I think it is fine for the government to step in during crises because that makes it possible for us to have debt.

    4. The question is not what level of debt is appropriate even in a recession, but what level of debt is inappropriate outside of a recession.

  2. "One of Keen's claims to fame is that he "predicted" the global financial crisis. Of course, if you think everything happens in cycles, then a financial crisis is always just around the corner."

    He also famously lost a bet about the crash of the Australian housing market after the financial crisis, and had to walk a long way in a T-shirt proclaiming so as a result.

  3. "Previous growth will be higher than future growth" ... I wonder if somebody like John Cochrane would blame that on the buildup of too many unwise regulations. Like the buildup of plaque in arteries maybe. You've no doubt seen his laundry list(s) of regulations he'd eliminate and/or simplify? Noah was critical of John on this... saying that would maybe amount to a one-time bump in economic output, but would do little in the long term.

    1. Probably yes -- Cochrane would probably see regulations as increasing drag on growth.

      However, it appears to be the same in several countries and characterized by k ~ log(NGDP)/log(M0).

      That means either regulations are an inevitable fundamental process, or it's not regulations.

  4. "Note that this model comes from just M0 and the labor supply (equal to nominal shocks)."


    Is this a curve fitting exercise?

    1. I'm not fitting polynomials if that is what you mean ... the dashed brown line is the solution to

      dN/dM = k(N, M) N/M

      for k slowly varying and the orange curves are the solution to

      dN/dM = k(N, M) N/M + d/dt log EMP

      The solution is just a function of M = M0 and employment = EMP.

      In terms of the differential equation (different error term in the above post, than at this link) it is here:

      In terms of a DSGE-style model it is here:

  5. The cartoonish non-linear attractor is hopefully used by Keen as a teaching prop, as professors are want to do, rather than some sort of profound statement on the economy. I fully adopt all of Jason Smith's statements (that sounds like something Milt Friedman might write, lol, giving his blessing) except any suggestion that monetarism works. The Fed is impotent, see here for a good opinion piece backed by evidence: or Google Bernanke's FAVAR 2002 paper (Fed has 3.2% to 13.2% control, out of 100%, on any real variable change says econometrics from 1959-2001). Fed power is a myth. Money is neutral long and short term, unless you are a day trader, and I would posit the day traders, having been taught in b-school "Don't Fight The Fed" are simply reacting to each others shared beliefs.

    1. Ray, you write:

      "...except any suggestion that monetarism works. The Fed is impotent..."

      I'm not saying there is or ever will be, but can you describe what the hypothetical evidence would look like that would make you doubt that statement?

  6. O/T: Jason, imagine you were forced to teach undergrad economics, intro through year four, but you were free to introduce the students to the information transfer model at anytime. What would your syllabus look like? I assume it would be a mix of interesting stuff from this blog and your papers and more traditional sources. The goal wouldn't necessarily be to prepare those students for traditional economics grad schools, nor to prepare them for the business world or jobs at government agencies. The goal would be to fill their vulnerable minds with whatever you thought was best for getting them on track to understand how things really are in the world.

    1. Noah's syllabus looks nice:

      Except I'd throw in the IT model as a big reveal at the end that describes the AD/AS model and Solow (and money, and most of the general behavior of macro). And show how it means that you shouldn't trust micro because of things like this:


    2. I asked Noah if there were particular texts and/or papers he'd include in that syllabus, but my comment went into moderation, and I'm not hopeful it will come back out. What about you Jason? Was there one/some you read that you liked?

    3. I liked Gary Becker's 1962 paper "Irrational Behavior and Economic Theory". I might refer to Irving Fisher's 1892 thesis "Mathematical Investigations in the Theory of Value and Prices".

    4. This comment has been removed by the author.

    5. Ah, some vintage pieces!... Lol. By chance, I tried leaving a link to the Becker one for commentator rsj at Rowe's blog yesterday, but it got stuck in the spam. Oh well... soon after Nick started quizzing us to see if we were worthy of commenting there... and now I'm doing that (clearly I'm NOT worthy, but I'm trying to fake it!) ;^D

  7. O/T: Jason, my question above is echoed a bit in Nick Rowe's latest post (where he describes the philosophy of the econ intro courses at Carleton). What do you think of this comment by Avon?

    1. I think I agree -- you need a framework (what Avon means by "laws" ... Newton's laws are a framework) to understand data. Just doing regressions without a framework is not really teaching anything besides regressions.

    2. Yes, that makes sense in relation to Noah's post. You've made a similar point about having a well defined and explicit framework. However there were a couple of sentences there that made me wonder. For example:

      "There is an awful lot of pseudo-science nonsense in the social sciences, but economics is not one of them."

      "Economics is a serious science precisely because it has laws to organize its structure."

      I would suppose that there may well be some "pseudo-science nonsense" in economics, and that the laws (framework) are far from settled. And even some of the things that are called frameworks, are not really frameworks or very good frameworks (which was the point of one of your posts).

      Also, when he writes:

      "Economics does have laws: 1) Humans are rationally self interested and organize their lives accordingly, 2) Prices adjust until the amount demanded equals the amount supplied. ... Students need to understand that organizing structure of these laws from day one, and that is the micro foundation of economics."

      I figured you might say that "micro foundations" are of debatable value.

      I get the impression that Avon thinks this is very much settled science at this point. That there's a solid framework in place. But I have the impression that the science is young and still searching for a good framework a consensus can be built around.

    3. FWIW, my impression is that economics is a nascent science, like astronomy at the time of Tycho Brahe.

    4. I followed Frances Wooley's link to this post from her in 2011, which was interesting. I'm not sure I quite understand her inductive vs deductive distinction here. I suppose she means economics is deductive in the sense of starting with some assumptions (a framework?). But economics can't be *entirely* deductive, ... else it'd be mathematics, right? It seems to me that at some point you have to test what you've deduced (thus testing your assumptions).

    5. Bill,

      Actually it's a bit weirder than that: astronomy was a nascent science when science itself was nascent! Economics is nascent, but it's happening after science has been well-established. I think that leads to a lot of "too much science" ... or "physics envy" (at least what I think "physics envy" is). Because science exists as an example, people who study economics can't seem to handle as much uncertainty as they should given the data.


      I'd say the real difference is that macroeconomics can't really run experiments. That makes it more deductive (deriving models from assumptions and comparing to data) than inductive (looking at data and pulling out regularities).

    6. Tom,

      I didn't really key in on the microfoundations piece -- that's just an example of a framework. The general sentiment is that you can't just look at regressions without a framework.

      That's because there isn't enough data to do that (it's 'uninformative'). That's another way to look at the deductive vs inductive. Looking at regressions without a framework is induction.

  8. Jason, I love your stuff.

    Your view that "a backward-looking bias in growth expectations" leads to "general over-optimism about the future" is a striking insight. I'll have to let it sit a while before I know whether I agree. Meanwhile, you give me things to think about. So, thank you.

    Since nobody appears to have brought this up:

    Your final graph above shows RGDP growth and a remarkable model of it, based on "just M0 and the labor supply". After I slept on it, though, it occurred to me that labor supply by itself should provide a remarkable model of RGDP growth, because ... Okun's law.

    1. Thanks.

      And yes, I completely agree ... it is just Okun's law. I actually noted it in a comment here.

      So in a sense M0 gives you the trend (because M0 determines trend NGDP and P) and Okun's law gives you the fluctuations.

      Basically, Okun's law is the information equilibrium relationship

      P : NGDP ⇄ L

      which is just a shorthand for the differential equation

      P = dN/dL = k (N/L)

      N ~ Lᵏ

      P ~ k Lᵏ⁻¹ = k N/L

      So L ~ k N/P = k R where R = RGDP ... therefore

      d/dt log L = d/dt log R

      Which is just one form of Okun's law. Basically, Okun's law is the information equilibrium relationship everyone already believes ... :)

    2. In "DSGE form", the result is just:

      ℓt = nt - πt + cℓ

      which allows us to figure out the "nominal shocks":


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