Monday, November 17, 2014

Because empirical success

I've occasionally had discussions with some commenters, most recently Philippe on this thread, that such and such explanatory variable can't possibly be used to explain what I'm trying to explain because it doesn't make sense to that commenter. In the recent case, Philippe suggested that it didn't make sense that physical currency (the currency component of the monetary base, which I call M0) was an explanatory variable for inflation. Philippe suggested other forms of money that should matter for inflation, like M1 or central bank reserves.

You could probably put the brief back and forth between Nick Rowe and myself in the previous few posts into this framework, except in that case I'm disagreeing with Nick by saying expectations (the explanatory variable) can't explain the price level or inflation. Nick suggests that expectations (and central bank targets or guidance) are an explanatory variable, while I'm saying expectations do not explain much more than the most recent NGDP and M0 numbers.

Maybe the information transfer model is wrong and expectations and M1 matter for inflation. Whatever model you have, though, it can't be too different from the ITM. Why? Because empirical success. Here are the information transfer model results for the price level and inflation. First, here they are for the core PCE measure:

And here are the results for core CPI:

This is more empirically successful than any economic model of inflation that has ever been published. The P* model from the Federal Reserve was comparable in the 1990s, but choked on new data. Maybe the ITM will choke on new data, too. However, time and data will tell, not theoretical arguments. The details of the model are all written down in the "for beginners" posts linked on the sidebar of this blog. Have a go yourself! All of the data I've used is from FRED (except the Japanese monetary base data, which is from here).

Also note that the fact that both fits are good means that core PCE and core CPI inflation are not independent measures. The information transfer model describes them both equally well given the data we have, so there is no telling which is the "real" measure of inflation. What is interesting is that this observation follows regardless of whether you believe the information transfer model or not. The ITM fit to each measure implicitly defines a global transformation you can perform to turn CPI data into PCE data meaning that PCE = f(CPI) so that any property of CPI can be mapped to a property of PCE. The next time you see an economist chide someone for confusing the two measures, you can come to the rescue with the retort: there is no economically meaningful difference in PCE or CPI inflation. It's like the fact that there is no physically meaningful difference in measuring distances in kilometers or miles.

And it's not like the model for the US is a fluke; here is Japan:

The empirical accuracy doesn't mean various theoretical criticisms of the information transfer model are prima facie wrong; it just means they should be discounted (i.e. given a low prior probability of being correct) unless they are accompanied by a model of comparable empirical success. Or as I said to Philippe:
The benefit of using M0 as the explanatory variable for inflation is that it gives an incredibly accurate model. If you have done [sic] better model that uses M1 or MB that explains the price level, I'm interested in hearing about it! But if you're just making hand waving arguments without any empirical evidence, that seems like a step backwards from the ITM.
The ITM doesn't just do inflation -- the interest rate model is pretty good too:

If you're of the opinion that the Fed's expansion of reserves will result in inflation, that people's expectations matter, or even that human decisions and behavior matter in a macroeconomic system at all, I'd first like to see some lines going through some data points.

Update 7:30pm MST, for Nick's comment below: 

Both of the error results for the PCE and CPI inflation models above have approximately zero mean. First, PCE inflation error:

Second, CPI inflation error:


  1. Here are two models of the price level:

    1. P(t) = M(t) + e(t)

    2. P(t) = P(t-1) + e(t)

    The second model will win empirically (the variance of e(t) will be smaller). But it is useless for policy.

    1. Nick,

      Your comment implies weird definitions of "explain" and "empirical success" -- the "error" terms e(t) are from undefined distributions that do not have zero mean. And in the second model, all of the "empirical success" is contained in the undefined biased error function and an undefined constant. The (non-recursive definition of the) model is:

      P(t) = P0 + Σ_t' e(t')

      where Σ_t' is the sum from t' = 0 to t' = t.

      This is a bit like saying the empirical success of the "standard model" of physics is irrelevant because there exists a model of the electron's gyromagnetic constant where g = g0 + ε where g0 = 2 and ε is an unexplained error term that is more precise than the current measurement of g - 2 but you're not telling me what it is.


      1. success = model + magic
      2. more success = less model + more magic

      is not a starting point to prove anything (to me at least). I guess at this point this gets into the philosophy of whether or not something "explains" something else.

      Anyway, I added the graphs of the inflation error to the post above. They have zero mean (within the accuracy of the data) implying that the error term in the ITM has zero bias

      P(t) = k(t) M(t)^k(t) + ε(t)

      where < ε(t) > = 0.

      For your models above, < e(t) > = f(t) for case 1 and < e(t) > = g(t) for case 2 ... and you haven't told me what f(t) or g(t) are (angle brackets are time averages). And in the second model, g(t) is the entire explanation of P(t)!!!

    2. Jason: I don't have a clue what you are saying. And I think you don't have a clue what I'm saying either.

      Let me try one last time:

      Suppose we need a theory of what determines the speed of the car.

      Theory A says that speed is determined by the rpm of the wheels.

      Theory B says that speed is determines by the position of the gas pedal.

      Theory A will work very well indeed (except on ice, or with badly worn tires).

      But theory B will be much more useful for someone driving the car and trying to keep to the speed limit.

    3. I agree with what you are saying here -- I'm guessing theory A is supposed to be theory 2 and B is 1 in your comment above.

      However the best representation in terms of 1 and 2 above would be:

      1. Speed(t) = gas(t-1) + e(t)
      2. Speed(t) = speed(t-1) + e(t)

      Yes, 2 would be more accurate and less useful (it's effectively the EMH).

      However the theory I'm working on is more like this

      3. Speed(t) = f(gas(t), mass(t), k(gas, mass))

      Where f is an explicit function and k is another explicit function representing the "fuel efficiency" (the mass of the car changes as you burn fuel or add passengers).

      Theory 3 is not only more empirically accurate than 1 or 2; it explains more than 1 or 2.

      For reference:

      Speed = price level
      Gas = base money
      Mass = NGDP
      k = information transfer index

  2. Nick is right in that your model doesn't really explain anything. It comes down to what your objectives are - if we study economics in order to guide policy, with the objective of influencing the world around us, then I'm not sure how helpful your model really is.

    One reason I can think of for that is that it uses only the currency component of the monetary base, yet this is not determined by the central bank, but rather determined endogenously. Your model doesn't actually tell the CB what it should do if it wants to increase inflation, (or NGDP). Ostensibly it looks like it should print hard currency (buy bonds with physical cash?), but I would be very willing to bet that if it did that, the empirical relationship you found that caused you to select this model would break down. So great, you've got an empirically well-fitting model, but it doesn't give us any extra insight we can translate into action.

    That is, the increase in currency that we see linked to inflation is an effect, not a cause.

    We care about finding the causes, not just the relationships/correlations.

    Given that it is based on a very simple principle, I don't think the ITM actually gets us very much new knowledge.

    1. Hi Ben,

      I'm a bit confused by this because you commented on this post:

      Where I wrote that the model is approximated by the AD-AS model with monetary offset for high inflation (low kappa) and the IS-LM model for low inflation. Scott Sumner and Paul Krugman use those models for policy advice all the time.

      The model does depend on M0, but during times when AD-AS model is accurate, M0 follows MB, which is directly related to short term interest rates. More about that here:

      Inflation targets do appear to set M0 endogenously, but the maximum inflation rate falls as a country grows meaning at some point the max will fall below 2% and the CB won't be able to hit it. I've made some predictions that the U.S. will continue to undershoot inflation and that Canada is near the cusp where they will start to undershoot in the next couple years. You can search on " prediction" in the Search bar on this blog and pull these predictions up ... If predicting macro variables is not useful for policy, I'm not sure what is!

      M0 is not the only policy lever -- the other is NGDP, which can be steered by fiscal policy when inflation is low; when inflation is high fiscal policy is useless because of monetary offset.

      There are useful policy applications!

      [however I'd really prefer the theory be studied by some real economists before anyone makes any policy recommendations from it anywhere besides a low-traffic blog]

  3. Very strong work, Jason! This is the sort of thing you need to hammer over and over again if you want to make a splash. Come to think of it, you should publish. If not in an econ journal, I'm sure you could get it published in something like PLOS. Would also be very interesting to apply ITM to developing countries and see how it works.

    1. Thanks Todd.

      PLOS is a good idea ... I've been (ver slowly) working on a submission to the economics e-journal, but the day job has been taking up a lot of time lately.

      I have applied the ITM to China and Russia on this blog -- probably the closest to developing counties; the impasse is good quality data for P, NGDP (importantly in the local currency) and M0 -- simultaneously.

  4. Jason, two of your figures are not showing up for me. The 1st one (top left) and next to last from the bottom.

    1. Hi Tom ... I'm not sure why ... They're showing for me on multiple devices.


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