Monday, June 30, 2014

Hard core information transfer economics

Noah Smith had a link that reminded me of something from the philosophy of science in his post from yesterday. It inspired me to lay out the "hard core" of the information transfer economics research program since it is fairly simple:

1. Demand is a source of information that is transferred to the supply, and a price is a detector of information transfer.

2. The dynamics of supply, demand and the price are governed by the differential equation (and definition):

$$ p \equiv \frac{dD}{dS} = \frac{1}{\kappa} \; \frac{D}{S} $$

There are two approaches to macroeconomics I've been taking. One is that macro is just like micro: you can write down aggregate demand and aggregate supply functions just like you'd do for a single good market. The second is that macro is the sum of micro: i.e. macroeconomic observables are expectation values of microeconomic observables in an ensemble of micro markets. The former may be a good approximation to the latter within some realm of validity. The first approach is an "auxiliary hypothesis" in the Lakatosian sense. The second adds some assumptions around the partition function as auxiliary hypotheses.

The idea of a changing $\kappa$ in the price level is another "auxiliary hypothesis"  (this has some support from the sum of micro approach). The idea that the "price" of a treasury bond with interest rate $r$ is $r^{c}$ is another auxiliary hypothesis.


  1. Where does the exogenous solution fit in here? Another "auxiliary hypothesis" or something else?

    1. It's a solution to the differential equation above where the economy is in the presence of a "monetary base bath" such that S = S0 is held constant as discussed in this post:

      It is a possible solution, so it's part of the "hard core"; an auxiliary hypothesis would be required to ignore the solution. For example, electromagnetic waves have advanced and retarded solutions and the retarded ones are selected via causality (the auxiliary hypothesis in that case).

    2. Thanks Jason. I came to the same conclusion while trying to explain it to someone else. I guess I understood more than I thought. Although your final paragraph adds something I wouldn't have thought of.

  2. Ram asks if your theory is "amenable to statistical learning.":

    1. I don't know enough about statistical learning to make an informed comment. I will say that the number of parameters is much less than the number of data points, though.

    2. Jason, to play devil's advocate, I can look at your latest post and guess that I could get a reasonably good fit to the data you plotted with a quadratic. Perhaps with a couple of other normalizing constants. Now getting a result for the standard deviation at each M might be a bit more difficult, but could probably be worked out. I realize that such a procedure would not have the benefit of any theoretical underpinnings (purely ad hoc?), however:

      1. In your opinion, can I arrive at curves like you have w/o any theory, but still maintaining just as low of a parameter to data point ratio that you have?

      2. If "yes" to 1., what's the strongest recommendation to prefer your model over a purely ad hoc model with a comparable parameter to data point ratio? Is it the theoretical underpinning? More than that?

    3. The key thing is that the constant "M00" which I've referred to as MB0 before is fixed by fitting the price level model to the data of each individual country. That bit of theory puts the data in the right location along the horizontal axis. The vertical location is arbitrary in both graphs (price level is arbitrary and so are the relative scales of the economies -- you could set NGDP in Yen to Dollars, Pounds or Euros, etc and even change billions of Yen to trillions of Yen).

      Without the correct theory, you wouldn't know where to put the data in two dimensions. In fact, this is what the price level curve looks like if you don't use the theory:

      (And even that has one adjustment -- Japan is in trillions of Yen while the others are in billions of their national currency.)

      The strongest recommendations would be the simplicity of the underlying theoretical framework, empirical success across a variety of markets, and the generality with which the model can be applied, e.g. across different countries.

      However, I don't think there is another model out there that has anywhere near as few parameters. In the two sets of curves in this post:

      there is literally one parameter per country, i.e. M00, the scale of the monetary base (the unit of currency and the price level are arbitrary numbers already). The US is broken up into two pieces, so maybe that's a slight cheat.

      I'm not even aware of a model out there of any kind at all. I did a couple of Google image searches on "price level model", "price level fit", etc, but all I seem to come up with are my own graphs and vague supply and demand diagrams. There is this, which is from 1983 (Thomas Sargeant "End of Four Big Inflations") and it is the closest thing to a model of empirical data I've ever seen:

      It basically says P is proportional to M ... during hyperinflation.

      I'd pose this as a challenge to the entire discipline of macroeconomics. Is there a graph out there with a theoretical price level and an empirical one?

      There is Barro's graph on which the graph at the link below is based, but it doesn't have a theory model except money growth = inflation, which is shown to be wrong in the graph because inflation is low for developed countries.

  3. Jason, is it the case that targeting price levels, inflation rates, or NGDPLT would all be described by the endogenous solution to the above DE? I think the answer is "yes." Now supposing your theory is true, and Sumner is given dictatorial powers at the Fed or BoJ and he tries NGDPLT and discovers that it's harder than he first imagined to hit his target. Suppose for example he sets up his NGDP futures market, but it's a failure. BTW, would it be a failure? It seems to me he would repeatedly think to himself "Money is still tight, thus I must be more aggressive." At some point won't he become so aggressive that he'll actually start to cross into the realm of the exogenous solution, at which point prices do start to move? Then what happens?

    Is money "tightness" one of those non-explanatory concepts you've taught me to be cautious about?

    Scott was sounding a bit self congratulatory today about having won the big debates, but commentator dtoh (an MM fan, mind you) was having none of it:

    You haven’t won the debate at all. You haven’t even answered the simple question of

    “How can you monetary policy be effective when the CB triples the money supply and still seven years later we haven’t had a full recovery.”

    And you still haven’t presented a coherent theory on how the transmission mechanism works. How do you expect to change conventional wisdom if you respond to people who ask how it works by saying, “Oh.. the Hot Potato Effect… but you won’t be able to understand it because it’s very complex and not at all intuitive.”"

    1. BTW, I think dtoh might be even less happy with your explanations if he's worried the HPE is too complex and counter-intuitive. :D

    2. I think this gets at why I don't feel all that great about expectations and reside on the concrete steppes. What would Sumner actually do?

      The key to the difference between the two paths is a "market oriented" vs an "at all costs" approach. During WWII, the Fed subordinated its independence to the Treasury department, keeping interest rates pegged at 2.5% by (I assume) only issuing repurchase agreements at a fixed repo rate and then dutifully passing on the inevitable requests for printed cash from banks to the Treasury.

      Would Sumner say inflation shall be 5% and just start crediting banks with reserves? That won't work because banks just won't request to have those reserves as cash (because the markets don't want it) so the Treasury won't step up the printing presses.

      Sumner could even say NGDP shall be $X and that won't do much of anything as long as printed cash is still determined by market based requests from banks. It's the market-based injection of cash that needs to break to get inflation at high kappa (at least in this model).

      The Sumner Fed could say that all requests for printed cash from the Treasury will be honored from any bank and the Sumner Treasury could honor all those requests regardless of collateral from the Sumner Fed -- at that point you'd probably switch over to the hyperinflation solution.

    3. Thanks Jason. Is it just me, or does the confidence level of professional macro practitioners (who have a public presence) seem way higher than the results they obtain can justify?

    4. Jason, you write:

      "The Sumner Fed could say that all requests for printed cash from the Treasury will be honored from any bank and the Sumner Treasury could honor all those requests regardless of collateral from the Sumner Fed -- at that point you'd probably switch over to the hyperinflation solution."

      How about instead we stick with the paradigm of the Fed purchasing stuff on the open market. And for fun, lets say they use electronic money (i.e. send a check, or directly credit a Fed deposit holder, depending on who's selling: of course sending a check eventually results in a direct Fed deposit credit for some bank, so it's all kind of the same). Now I realize that's leaving the confines of your model (with M0 used for M), but let me press on.

      It seems logical to me that somewhere between the two extremes of

      1. The Fed making moderate sized purchases of traditional assets (Treasury debt) as they do now and

      2. The Fed purchasing the entire world (as Sumner has mentioned on occasion)

      Prices have got to rise, don't they? But as long as the Fed is negotiating on the open market to buy all things for sale on Earth, then does that still qualify as "endogenous?"

    5. I have the suspicion that a switch to using exclusively electronic money in the economy would change inflation from depending on "M0" to depending on MB (the full base including reserves).

      In this case, crediting banks with reserves with a few key strokes would be very much like printing money and handing it out. A bank wouldn't have to go back to the Fed to request cash (from the Treasury) to support its money creation through fractional reserve banking.

      I'm still trying to think through this one ... there are a couple of possibilities

      1. After removing physical currency from the economy, you end up with the "exogenous solution" no matter what since physical currency was the anchor that prevented electronic credits to banks from the Fed from generating inflation. It doesn't matter if the Fed buys a little or a lot.

      2. The "endogenous" solution applies if the Fed is buying assets (including Treasuries) on the open market; the "exogenous" solution applies if the Fed buys e.g. Treasury debt at some fixed interest rate (monetizing the debt) like in WWII. The only way the Fed could "buy the world", i.e. other assets, in this manner (i.e. outside a fair market value) is with the backing of the FBI/DoD since people likely won't sell their businesses for Fed credits based on the Fed's valuation (outside the market).

      3. Maybe the electronic money is a bit like bitcoin, except it is controlled by the Treasury, which can mine it at will. These bitbills become M0. However, in this scenario, it doesn't seem necessary for transactions to happen with "bitbills" (they'd happen with debit cards using M1, i.e. money created via fractional reserve banking), so banks wouldn't need to request bitbills except via some sort of reserve requirements. Therefore I'm not sure if this really is different from 1. or 2.

    6. Jason, thanks... that's interesting. I didn't mean to suggest though that I was banning physical currency... just to suggest that in practice when the Fed buys stuff it probably initially uses electronic money (if they buy from a Fed deposit holder they credit the Fed deposit holder's Fed balance, and if they buy from a non-Fed deposit holder (e.g. with a check), then when the non-Fed deposit holder deposits his check, the Fed pays by crediting the depositor's bank's Fed deposit electronically). I'm assuming the Fed will order the BEP to print up whatever paper currency is required down the road to meet demand. I.e. basically, exactly what they do right now. I don't know if that clarification has any bearing on your answer.

    7. Yeah, the Fed electronically credits banks' accounts. Banks then request cash from the Fed to keep their business running. The Fed reviews these requests and sends them off to Treasury for printing.

      I was in a discussion with one commenter who said that the Fed can't foist currency on banks when I said that "printing M0" generates inflation when the base is small -- the above is what he meant: the banks request cash to meet their needs. That's why M0 controls inflation and not reserves -- the latter just sit there somewhat idle. Reserves do seem to affect short term interest rates, though.

      In the "buy the world" scenario banks still wouldn't necessarily request additional M0 be printed, so it won't necessarily generate inflation. This is still basically the #2 situation in my answer above.

      Basically, if we're not talking about paper currency being eliminated, then only the #2 situation in my answer above applies.


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