Tuesday, July 1, 2014

A challenge to macroeconomists

In light of my comments on this post by Scott Sumner who declares victory without having specified anything quantitative at all, and pursuant to a discussion with Tom Brown on this post where I brought up something I have noticed in my efforts to build up a macroeconomic model, I'd like to make a point. It appears no economist has ever actually compared a theoretical model of inflation to empirical data. I've tried to find other cases with which to compare my efforts (my efforts are here, here and here, for example), and the best I've come up with is this analysis from 1983:

It's from Principles of Economics, Volume 1 by Mankiw. Even this is taking "theoretical model" fairly loosely. First off, these graphs don't even appear in the original paper by Sargent. Second, the graphs only loosely imply that P = k M, however economists don't actually believe the k in that equation is constant. Third, this only covers a four years of the post WWI hyperinflation.

This puts not just DSGE fans in the realm of being like string theorists [1] in physics (theoretical models with no contact to data), but in fact all macroeconomists since, well, Walras.

My challenge/request/bleg is simple:
Produce a graph with an empirical measure of the price level (or inflation rate*) and a theoretical curve.
It can be any measure of the price level (here is an example from FRED). Just give me some data points with a line near it (it doesn't even have to go through the data points).

Maybe there are a bunch of such graphs in gated economics journals. I highly doubt it. I don't believe they exist. Why? Because when I do a Google image search on "price level model" (without the quotes, even) I get back my own #$%@ graphs!!!

You might want to send me this graph from Nick Rowe:

I see your ad hoc monetary-policy-can-hit-any-inflation-target-it-likes model (that isn't even accurate) and raise you the interest rate (link):

I'd really prefer something that isn't a straight line. Actually, I'd really like to see results for Japan. Here are mine (oh, with an interest rate model of course):

Did I mention that it's the same model as the one used for the Canadian graphs above? [2]

[1] Don't get me wrong. I love string theory.

[2] Hopefully this post is taken as good-natured ribbing, or at least good-natured snark.

*Update 7/3/2014. Nick Edmonds makes a good point (H/T Tom Brown) that economists tend to look at the inflation rate rather than the price level. To that end, I'll expand the challenge to price level or inflation rate. Here is one for the US from me:

Here are results for Japan. Here are some "out of sample" results for the US (predicting today's low inflation from data in the 1970s). Here are some more general considerations, extracting the general trend towards lower inflation.

Macroeconomists, you're "On Notice" :)

Update 7/3/2014 This one (on inflation) is pretty good from the NY Fed:

Update 7/3/2014 Not for nothing, the NY Fed model has 42 (!) parameters. The information transfer model (ITM) has 3. Additionally, the NY Fed results were "smoothed", whereas the ITM results were not.


  1. This comment has been removed by the author.

  2. Jason, I posted a link to your challenge on a number of blogs. I hope you get a response or two. The only one I've seen so far is from Mike Freimuth, who had this to say (I don't know how to get a link to an individual comment there, but it's the first one from "Free Radical."):


    1. Thanks Tom.

      I kind of gathered from various blog posts out there on methodology that the qualitative analysis of the impacts of various effects was the way things are done, which doesn't lend itself to direct comparisons with time series data.

      I've seen the results of the e.g. CBO's models, but they're pretty empirical (linear extrapolations and so forth). The search goes on!

  3. But, I have seen economists challenge the public to believe that dillution of money and rising prices do not matter.

    Your challing the their challange, I like that.

    My favorite is the x small amount of rise in the prices you pay is good along with the implication that that the price rise is only x.

    Did you measure the data you are using? Can you measure the price rise and check the data? I asked the person at the grocery store about what he thought was the price rise rate. He said he did not know but the official data was wrong. After asking him to think about it he came to a number that was closer to what I was figuring than the data.

    Prices for diferent things change at different rates durring time of large price changes.

    I observed in your data and other hyper dilution graphs, the log graphs even seem to be exponential for periods! Also, more often the price level is greater than the money level when high dilution rates are going on. I watched a video where people in Zimbabwe were paying $10 worth of gold nugit or powder for a loaf of imported bread. They were getting gouged in a better currency.

    You might like the following findings on velocity of money measure (or non measure) discussed on Professor Keens page.

    They measure meaure vleocity by solving for,v , in gdp=v*M. They do it for different money supplies an get a v for that money supply. They do it for M1,MZM, and M2 simultaniously.

    Start at the snake comment: or the Just Bouncing Ideas Arround comment.


    Your stuff looks interesting.

    Definately dilution of money has an effect.

    Are non economists getting paid to do economics?

    1. Thanks. Have a look around the blog.

      I didn't measure the price level data myself, but I'm using data from several governments which should mitigate some of the "concerns" (I personally haven't noticed any inflation, and the grocery store is a bad place to look because food prices are volatile, which lends itself to a ratchet -- you notice more when prices go up but not when they go back down).

      Here is the model across several countries:


  4. GDP and M2 money level:


    1. Thanks. However, the implied theory there is PY = MV, but V is not constant (M2 velocity):


      Now if there was a model for velocity with a curve going through that velocity data, that would certainly fit the bill.

    2. To be explicit:

      PY and M enourmously vary over time more than V. Because P, Y (or PY), and M generally grow exponentially but V does not in the US data. (If one were to accept the v=PY/M calculation as being close to reality.) So, compared to PY and M over decades V is dancing in one place. So for prices over time M is much more significant than V.

      Since this is a log plot and V is the ratio of PY:M the distance between PY and M is V. See V on the bottom?
      This has ln(V) on the right scale. See while the exponentially growing terms move about e^4.5=33.1 or 3200% times V only moves e^0.33=1.39 or 39%.

      But remember V is not directly measured. It is calculated. from the other terms. So, the V "indirect" measure (calculation) is debatable in it self.

      This is totally visible in the levels but not so clear if one plots changes.

    3. My approximate theory would be a strait line of slope 1 in a log-log plot, starting at (M2(t0)*MONEYTURNOVER(T0),PRICE_agregatedoutput(t0)). If one drew diagonal lines of slope 1 at differernt Y hights I think that would represet computed V, "indirect measure of V". One would be tempted to consider variation in V as a less important factor over long periods of time.


      The theoretical green line is off by less than about 20% from exponentially varying quantities that vary about 3200%. Not to bad.

      There is the data.

    4. I'll bet the correlation coefficeint is greater than 0.95 or 0.98.

    5. For Australia:


    6. Thanks for the graphs.

      The question that remains: what is the underlying theory? M2 ~ NGDP ... does M2 create NGDP or NGDP create M2? Let me submit that this quantity theory is actually the theory I'm trying to put forward. I could write down a version of the information transfer model where:

      dNGDP/dM2 = k NGDP/M2

      (we've only assumed long run neutrality of money in writing this equation) and solve it to obtain

      log NGDP = k log M2

      This is effectively the quantity theory of money and would be interpreted as an information transfer system from aggregate demand (NGDP) to the money supply (M2). However a changing coefficient k and using currency-only ("M0") works better:


      As an aside the model k log M2 = log NGDP fails for Japan since the 1990s and fails for the US since the 2008 financial crisis:



    7. Japan:

      There is probably a lot more to Japan. Japan has been a major exporter so their production is consumed by others too. They also have demegraphic changes. There might be other variables too. They have been a merchant with and manufacturer to the world. They were manufacturing in China before the west was.

      So there is an international component, not fully in the equation. One can trade with the rest of the world with out very much money by using bills of exchange (temporary credit extiquishable with goods). This was done in the past when gold was used so a lot less money did not have to transported, the concentration of shipment being goods and bills. Goods are effectively traded for goods only the difference is settled with money or tradable bills.

      They also had a huge debt driven problem. Professor Keen relates GDP to changes in debt and maybe even the second derivative of debt, by data. He is working on an equation where debt is in the quantity theory. M2 includes bank money or check money which is generated by bank loans and extinguished by payment.

      Japan might emphasize the problem with the practice of aggregates, not counting international trade, and debt dynamics, and other unknowns variables not in the models.

      Japan negates the models with the few variables we are using. That is it.

      Doesn't Japan falsify these theories when other significant variables are not included in the model.

    8. "The question that remains: what is the underlying theory?"

      Accurate data trumps theory.

      I think there are a lot of folks trying to convince us that money dillution does not cost us. Often it does.

      If you look at that theory if production goes up and money doesn't we should be getting more for our money. Or if we produce more we should be able to get more, after all we produced it.

    9. Anonymous, you write "Accurate data trumps theory." I think both are valuable. Tycho Brahe obtained lots of great data, but if it weren't for the theories of Kepler and Newton, there would be (at best) only an outdated and inadequate explanation for it. If we had to cross our fingers with Ptolemy's explanations, it might be tough getting satellites into useful orbits.

      I think good theories can be very useful in a practical sense. How do we know if they're good or not? That's where the data comes in.

    10. I I am terribly sorry if I have been gruff. My detailed responses have been clobered so often by the comment system and me not using a proper editor, I no longer have time to go into detail.
      Mr. Smith can figure out my model that was a strait line fit of the parametric plot of two time series each approximately growing in time exponentially at the same rate. (All variables ploted in log scale except for the independent variable time.) You fit the time series and the parametric plot. He is using that type of math. Having a V term that is not growing exponentially but dancing around a value does not change the long term dynamic much. He asked me what the theory was. I gave data and a strait line fit for the US data. The math is the model.
      The data is in the plots. If it is accurate what are the relationships? I give level data because it is often ignored but has higher correlations and less subject to certain types of errors of analysis.
      What I was getting at is that good real accurate data can falsify a good theory but not visa versa. A good theory usually cannot falsify good real accurate data.

    11. Noting , ln(a/b) = ln a –ln b
      Noting , ln(ab) = ln a +ln b

      Strait line fits are rise/run = slope

      Theoretical variables in lower case:
      Strait line fit for gdp(t), m(t), when t-t0>>1 (slope r)
      If gdp(t)=gdp(t0)exp(rt) or equivalently ln(gdp(t))=rt + ln(gdp(t0) ,
      ln(m(t))=rt + ln(m(t0))
      ln(m(t)v(t))=rt ln(m(t0)v(t0)) exponential stait line fit.

      For long periods, t>>t0 , v(t)/v(t0)<max(v)/min(v)<<exp(rt)

      Or plug in the strait line fit equations for gdp(t), m(t) above.
      ( ln gdp(t) – ln gdp(t0) ) / (ln v(t)m(t) – ln v(t0)m(t0)) aproxamately =
      ( ln gdp(t) – ln gdp(t0) ) / (ln m(t) – ln m(t0)) aproxamately = 1

      aproximately = rt/rt =1

      Shows exponential growth rates are about the same in the long run for the model strait line slope 1, and individual time series log same slope in time.


    12. Yes, I believe that for high inflation countries, the inflation rate is equal to the money supply growth rate. However for low inflation countries, there is a statistically significant deviation from that slope = 1 line. See for example here:


      or here:



    13. "The question that remains: what is the underlying theory? M2 ~ NGDP ... does M2 create NGDP or NGDP create M2?"

      Causiality is the clasic question that equation hardly ever indicates. As, equations often only indicate quantitative relationships. Or, I did not learn how to figure causiality from equations. Please let me know how to do that, if you know how.

      But, in this case I think it is not a model of casiality but of defined equal and oposite value flow. The defition of value being, accounting historical cost, what was paid for each and every item. I think the quantity theory of money, PY=MV, is refering to aproximately the same (historical cost) money flowing in the oposite direction of goods. (Oh money supply changes. That screws up value, historical costs, the unit of account, accounting and falsifies money myths.)

      In a purchase often what we think is one transaction is actually to. From purchasers point of view: 1. Receive the goods. 2. Pay for them or pay the credit supplier.

    14. Here is a graph of yours that is practically identical to two I sent you, ln(GDP vs M2):

      The NGDP time series is almost identical to GDP for the U.S. And you have red lines that look like slope one like I told you about the graph I sent you. As I discribed, the different parellel slope lines represent different velocities. In linear-linear graphs the slope would be affected by “velocity”.

      Do/did you have a thoery on that graph and the aproximate slope 1 of the line?


      It is the second to the last graph on:


    15. My personal thoughts on causality are here:


      And yes! I do in fact have a theory behind the straight lines on that graph. I'm glad you asked. They are lines of constant interest rate, related to the graph at the top of this blog on the right side with the red 3D surface. There is more here:



  5. Nick Edmonds responded too:


    After a quick look around today it looks like nobody else did.

    1. Thanks Tom!

      I responded and did and update to the post.

  6. David Andolfatto too:


    1. Thanks Tom!

      There's another update as I found an example (!); it's pretty good. It's a complicated DSGE model, but it fits the challenge.

    2. Do you think you can make a side by side comparison with it?

    3. I have a graph-digitizing program that should allow me to do that. I would also like to understand the model a bit before I say anything about it :)

    4. I just realized the NY Fed model has 42 parameters compared to the ITM model that has 3. By the AIC (which incidentally, Noah Smith just referred to a few minuted ago), that means the likelihood function for the Fed model would have to be 4.3 x 10^18 % in order to select it over the ITM if the likelihood of the ITM model was 50%. Or the other way ... if the Fed model had a likelihood of 99%, then the ITM would have to have a likelihood of 1.1 x 10^-15 % to lose to it.

      Now I'm not sure all of those parameters are necessary to describe inflation and there are other things described by the Fed model like the capital stock, but as we say in engineering, there's a lot of margin.


    5. Jason, that's awesome!... thanks for pointing that out to me, and for diving into the AIC analysis so quicklly... I'm going to have to read up to get the full gist of it. Had you heard of the AIC or those other ICs before?

    6. Yes I had ... I was actually in the middle of looking at it when Noah put up his post. The AIC sort of quantifies the chi^2 per degree of freedom metric.

      I was shocked at how many parameters the DSGE model had ... And the fact that one with 'only' about 30 gets inflation so wrong (the purple line in the graph at the bottom of the post).

  7. my model is the wisdom of the herd:


    1. That's probably a better one than most! But it's pretty nihilistic from a theory point of view (the theory is that there is no theory, only expectations).

      However -- the simple martingale of past inflation is an excellent guide to future inflation; expectations of future inflation (survey data) are skewed high (biased errors):


  8. I wanna know the best way to protect from the loss of purchasing power often caused by dilliution of money. That is a better question.


    First graph.

    1. The first graph shows 0% inflation at about 7% money growth ... which is a bit odd.

      Here's my version of that graph using data from Barro's textbook:


      "Dilution" as you say appears to have two components: one is as the medium of exchange, which is what you are referring to, and a second is as a unit of account (information carrying capacity). When money is at its most "dilute" it can carry very little information, so it doesn't have to cause a lot of inflation.

    2. OK, remember your first year college cost? If it was 10 to 20 years ago since you started, look up the current price for the first year. If your adventurous you can do food, housing, etc. Rate of change (Pnow/Pthen) raised to (1/(Years since first year of college))-1. Then multiply that by 100.

      That is interesting about 7% is what the grocery store said. And at that time the offical cpi chang was about 0. 8b

      Levels over a longer period of time are a better changes measure. Why is that? There are several reasons.

      (But, you are probably too young for this to work since you said you did not notice food prices going up.)

    3. Let me intercept your intercept. In that graph the prices aways go up by more than 3% annually.

      In 24 years every ones prices will have more than doubled.

      Again using levels over a longer time is much more accurate.

  9. Jason, some questions on the Fed model:

    1. Are you comparing against the SWFF model (solid blue) or the SW model (dashed purple)?

    2. Are both the SWFF and SW models benefiting from "smoothing?"

    3. Why does the true inflation look so different in your plot vs the Fed plot? You have true inflation rates approaching 15% (1980) while the Fed plot doesn't have anything above 3 (whatever units that's in). Does the Fed "smooth" the truth data too? What are the units?

    1. I was looking at the SWFF model primarily. And the Fed is using the GDP deflator that may not be annualized rate. Both of the model results are smoothed, but I don't know about the deflator.


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