Wednesday, July 1, 2015

The Sadowski Theory of Money

Tom Brown mentioned Mark Sadowski has another post over at Marcus Nunes' blog; it includes what might be the most hilarious monetarist volley yet. But intriguingly it points to an opening for full scale acceptance of the information transfer model. I'll call it the Sadowski Theory of Money (STM). Mark first shows us a plot of the monetary base (SBASENS) and CPI. I have no idea what happens next or in the follow up post because this is effectively what he shows:

When I was back in college in the 1990s, I once was watching some local cable access program late at night. In it there was some suited presenter -- likely at one of the Helium wells out near Amarillo -- going through a model of how Helium escapes from underground traps. It was quite detailed. In the end, he came out with the result that the measured levels of Helium meant that the Earth couldn't be older than 6000 years old. I started weeping.

Regardless of how adept people are at mathematics or statistics, it does not indicate of how good they are at the pursuit of knowledge. The reasons range from being blinded by ideology or religion to a lack of curiosity about the results they produce. I think Mark is part of the former.

I'm not quite as emo as I was back in college, so the reason I couldn't get past the first graph in Mark's post was that I busted out laughing. If you zoom out from the graph, you can see why:

Over the course of the history of economic thought (starting from Hume and continuing through Milton Friedman and beyond), there was a theory that was called the Quantity Theory of Money. In its most rudimentary form, it said that increases in the amount of money (say, the monetary base MB) led to an increase in the price level (P),

P ~ MB

or, taking the log of both sides (to compare growth rates):

log P ~ log MB

This is actually somewhat successful as an initial stab at a macroeconomic model that persists to this day as at least a starting point. Mark says, "Balderdash! The QTM is so Eighteenth century." He says we really need a new model. His model is this:

log P ~ k log MB

And we are living in a new modern era of monetary policy effectiveness, so only data since 2009 is relevant! So Mark studies the correlation between log P and log MB, scaling the variables and the axes in order to derive a value for k. An excellent fit is given by [1]

log P ~ 0.125 log MB

"Monetary policy is (a tiny bit) effective!" Mark shouts from the hilltops (after doing some rather unnecessary math I guess so he doesn't have to come out and state the equation above), "We are governed by the Sadowski Theory of Money!"  We can see how Mark has thrown hundreds of years of economic thought out the window by putting the STM on this graph of the QTM from David Romer's Advanced Macroeconomics (along with a point representing the US from 2009 to 2015):

Ok, enough with the yuks. Because in truth Mark Sadowski might be my first monetarist convert. That's because the model

log P ~ k log MB

is effectively an information transfer model (I had the codes ready to fit that data above) ... but just locally fit to a single region of data. You could even find support to change the value of k, allowing k to change from about 0.763 to about 0.125 [2] going through the financial crisis. Here is the fit to 1960-2008:

You're allowed to do what Mark did in his graph in the information transfer model. But then you have to ride the trolley all the way to the end. That change in k from 0.763 to 0.125 over the course of the financial crisis  would be interpreted as a monetary regime change. Let's explore what happened to the relationship bewtween a variation in P and MB:

δ (log P) ~ δ (k log MB)

δP/P ~ k δMB/MB

So the fractional change in P (inflation) is k time the fractional change in MB (monetary base growth rate). Between 2008 and 2010, according to the STM, that dropped by a factor of about 0.763/0.125 ~ 6. That is to say monetary policy suddenly became six times less effective than it was before the financial crisis.

Before 2008, a 100% increase (a doubling) of the monetary base would have lead to a 70% increase in the price level. After 2008, it leads to a 9% increase in the price level.

Monetary policy suddenly becoming far less effective ... sounds exactly like a liquidity trap to me.

The Sadowski Theory of Money is an information transfer model with a sudden onset of a liquidity trap during the financial crisis [3].


[1] There is a constant scale factor for the price level of about 84.1 for the CPI given in units of 1984 = 100; I will call it a "Sadowski" in honor of the new theory and its discoverer. The equation is shown in the graphs.

[2] Note that k = (1/κ - 1) so k = 0.763 is κ = 0.57 (near the QTM limit of 1/2) and k = 0.125 is κ = 0.89 (near the IS-LM limit of 1).

[3] Of course, 'M0' (MB minus reserves) works best empirically and has no sudden onset of the liquidity trap, but rather a gradual change from the 1960s to today.


  1. Jason, thanks for doing this post. I think I get your point here, and again you answered my only question (so far) in your footnote [3].

    Next time please remember to turn your camera on BEFORE clicking on the link so we can all enjoy seeing a video clip of your response as you first start reading.

  2. "I have no idea what happens next or in the follow up post..."

    That is evident.

    1. Hi Mark,

      VARs are still at their heart linear models.

      I'm still impressed with the audacity of graphing the price level scaled to follow the post-crisis monetary base. It's a masterstroke!

  3. All these "theories" ignore the actual mechanism of money creation: banks create the medium of exchange by crediting bank accounts out of thin air and then borrowing reserves in the interbank market. Which indeed ties the monetary base to NGDP or whatnot, but the causality is reversed: more credit means more sales and/or higher prices and ultimately more monetary base. But not the other way round. So it is a relationship that cannot be used to steer the economy and it duly broke down immediately the moment QE was enacted. So looking at this stuff is like estimating properties of ether or phlogiston. 100% useless.

    Here Scott Sumner and his acolytes get shredded on not knowing the basics of the monetary system:
    (4 years on and they are as clueless)

    1. Hi Peter,

      None of those links provide any mechanisms that when put into models empirically match data. Show me a model based on M2 that makes a line that goes through some data points and I will totally listen.

      However, one of the main reasons for this blog and why I put together the information equilibrium model is to get away from data-free theorizing about how things "really work".

      Like this

    2. Hmm, the monetary system is a manmade system, like the postal system. To find out how a parcel gets from A to B will you run regressions or simply ask people who run the system? The monetary base causes nothing, say bankers and central bankers.

    3. PeterP, "The monetary base causes nothing" ... can you describe specifically some examples of what evidence would convince you to change your mind about that?

    4. Peter,

      Let's rephrase [1] your quesiton:

      "Hmm, the monetary system is a manmade system, like the internet. To find out how a data packet gets from A to B will you run regressions or simply ask people who run the system?"

      It ranges from hard to impossible to predict how a packet makes it from point A to point B -- even by the people who run the servers. Here's a typical Google search done by me in Seattle:

      Even though it is a man-made system, it obeys mathematical laws -- in particular, queueing theory:

      The internet can be modeled as a traffic queues on a quasi-scale free random network pretty well, in which case it doesn't really matter which companies own which servers or who makes the rules or builds capacity. Or how a packet makes it from point A to point B.

      One of the most awesome things about large systems is that they start to behave in easily quantifiable ways -- because of central limit theorems and the law of large numbers.

      In any case, if it really is as complicated as you say, then it is likely impossible to understand at all.

      [1] Although, I'm pretty sure the post office obeys queueing theory as well.

    5. Also, my prediction (in the link above) based on information theory and the law of large numbers is outperforming the NY Fed -- the people who run the system.

      If you can show me data where the people who run the system can predict things better than I can with some basic assumptions, I am interested in hearing about it!

  4. here is a writing tip for you: that whole thing about He is a distraction; if you had just shown graph one, and then said, lets zoom out, and show graph two , then this whole blog post would have been a lot better

    don't show off with anecdotes; that if only for really good writers

    in the math, your text is in the order MB, P
    in the subsequent equation, it is in the order P, MB
    don't confuse your readers like that

    1. Personally, I liked the anecdotes.

    2. You are right that brevity is the soul of wit.

      Mathematics is often written backwards from the way it would be said in causal language in English ... we write y = f(x), not f(x) = y when x causes y to change. That is really just notational convention; it means the same thing either way. But then if that confuses readers, the asymptotic notation y ~ f(x) is really going to throw them.

      Cheers, Tom.


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