Friday, January 22, 2016

Is CPI an information-theoretic measure of labor force size?

Update 25 Jan 2016: This model gets much better: 
Update 23 Jan 2016: Since this post is getting a lot more traffic than I expected, I'm adding a direct link to what is meant by information equilibrium and to my paper:
I noticed something today while randomly plotting various macroeconomic indicators, and so built an information equilibrium model to quantify it. The civilian labor force (CLF) looks a bit like core CPI, so I put together the information equilibrium model


So that

log CPI = a log CLF + b


(d/dt) log CPI = a (d/dt) log CLF

which means that the inflation rate is a times the labor force growth rate. This gives us a decent model (after adding a lag and smoothing the CLF -- a surprisingly noisy measure):

Here's a version you can play with yourself at FRED where I fit a = 2.67. This model means CPI and CLF are in information equilibrium -- that fluctuations in CLF result in informationally equivalent fluctuations in CPI (plus noise).

This tells a different story of inflation in the US than exists in the mainstream, especially if you compare the CLF growth rate with the population growth rate:

During the 1960s and 70s, we had a labor force growing faster than population -- typically associated with people other than white males entering the labor force (women, African Americans). This coincided with the period of high inflation in the US. As always, there is a question of causality -- the fit at the top of the post chose a lag of y₀ = 0.33 years with CLF increases causing inflation about 4 months later.

The usual story of the end of the so-called great inflation of the 1970s was that the Volcker Fed managed to credibly rein in monetary policy, reducing inflation.

The new story is that either 1) the Fed was superfluous, or 2) the Fed's impact came through a different channel. In 1), the labor force had reached its new equilibrium participation rate, so it stopped growing as fast, lowering inflation. In 2), the Fed-caused recessions of the 1980s killed the rise in labor force participation (setting up the new equilibrium).

Similarly, the recent lack of inflation may have nothing to do with the Fed. We can see in the figure above the changes in the CLF roughly match the population growth rate. The recent lack of inflation is simply due to slow population growth in the US. It is quite a coincidence that as our population growth rate fell below 0.75% per year, it became hard for the Fed to maintain 2% inflation (given a = 2.67).

The lowflation in Europe, the US and Japan may simply be low population growth -- and independent of the ECB, Fed. and BoJ. This would also mean inflation targeting by the central bank is a case of Feynman's cargo cult science -- they literally had zero control except to cause recessions by creating a coordinating signal for sunspots [1].

Increasing labor force participation just leads to a spike in inflation that can last several years (as the US saw in the 60s and 70s). To generate sustainable inflation, governments would need to increase the population growth rate.


Update #1

With the relationship between the growth rates being a ~ 3, we can take population growth to be the growth in radius r and inflation to be the growth in volume V ~ r³ of a sphere. While the volume numbers differ from the radius numbers, any signal in the change of the radius can be read off the change in volume.

Update #2

Also works for Japan

Update #3

And Canada

Update #4

Switched from LOESS smoothing to moving average for the US and Canada model since I used a moving average in the model for Japan.

Update #5

These posts on the "miracle" of a 2% inflation target ("magic number") alongside 2% inflation are relevant as well:


[1] In Farmer's paper Global Sunspots and Asset Prices in a Monetary Economy, the Fed is Mr. W (the coordinating source of "sunspots"):
What coordinates beliefs on a sunspot equilibrium? Suppose that Mr. A and Mr. B believe the writing of an influential financial journalist, Mr. W. Mr. W writes a weekly column for the fictitious Lombard Street Journal and his writing is known to be an uncannily accurate prediction of asset prices. Mr. W only ever writes two types of article; one of them, his optimistic piece, has historically been associated with a 10% increase in the price of trees. His second, pessimistic piece, is always associated with a 10% fall in the price of trees. 
Mr. A and Mr. B are both aware that Mr. W makes accurate predictions and, wishing to insure against wealth fluctuations, they use the articles of Mr. W to write a contract. In the event that Mr. W writes an optimistic piece, Mr. A agrees, in advance, that he will transfer wealth to Mr. B. In the event that Mr. W writes a pessimistic piece, the transfer is in the other direction. These contracts have the effect of ensuring that Mr. W’s predictions are self-fulfilling.


  1. Is there a way to relate this to your previous p-as-detector expression with p = dD/dS = k*D/S with a time-varying k? The expression governing how k varies with time seems like it should be related now to the CLF.

    1. Not really; this is in terms of a completely different (single) variable. You have

      f(CLF) = CPI = g(NGDP, M0)

      If you could write

      g(NGDP, M0) = g(NGDP/M0)


      g(NGDP, M0) = h1(NGDP) h2(M0)

      then there would be a sporting chance. But alas, you cannot.

      Note that the detector in p:CPI⇄CLF is not relevant here, but is it is given by

      p ~ a (CLF/c0)^(a - 1)

    2. From your post we have:

      CPI = exp(b)*(CFL^a)
      (CPI/exp(b))^(1/a) = CFL

      Now combined with your expression for p above, we have:

      p ~ c*(CPI)^(1-1/a)

      with c a constant.

      Did I do that right? I guess I would have figured we'd have

      p ~ CPI

    3. That p in p:CPI⇄CLF wasn't the price level, but rather an arbitrary (abstract) price.

    4. In my first comment above I probably should have referred to your macro section (in your draft paper for the Summer post) rather than to the "micro" p in p:D⇄S.

      Looking back at that macro section now I see:

      "...and define the abstract price to be the price level P"

      Eventually coming up with:

      "log P ~ (k – 1) log M"

      The P in this expression I've been associating with CPI. In other words, I've been thinking:

      P ~ CPI

      I figured P was abstract in the sense that it needs an arbitrary scale factor to align it with CPI, which is one of the calibrating parameters for the model.

      I'm tempted to conclude:

      (1-k) log M ~ a log CFL + b

      But I'm not sure.

      If you were going to incorporate this post into your Summer talk draft paper, would you explain the how the abstract P in the macro section relates to CPI here?

    5. Hi Tom,

      It's usually just a choice to assign some macro aggregate to be the "detector" measuring information transfer in the market. In the interest rate market, the detector is the interest rate. In several macro models, the detector is the price level (measured by CPI, PCE, GDP deflator or whatever).

      But in the ITM-QTM equation where I say

      log P ~ (k - 1) log M

      P can be CPI (you can't really empirically tell the difference from PCE). And yes:

      a log CLF ~ (k - 1) log M

      so that for large k (just to simplify at present)

      k ~ a log CLF/log M

      which is not too different from

      k ~ log NGDP/log M

      Which implies a relationship between NGDP and CLF much like the relationship between CLF and CPI ...

    6. "Which implies a relationship between NGDP and CLF much like the relationship between CLF and CPI ..."

      Interesting! Thanks for the chart and the feedback.

      The above comment where you wrote:

      "That p in p:CPI⇄CLF wasn't the price level, but rather an arbitrary (abstract) price."

      left me scratching my Bart-Simpson-esque head for a bit again, but I think I've got it now. Let me run it past you to be sure: p here is an "abstract price" in the sense that

      p = dCPI/dCLF

      where '=' should really be 'is defined as.' Is that it? It's telling you the "price" (or exchange rate) of units of CPI in terms of units of CLF.

    7. ... and thus p (in your comment) doesn't really correspond to any usual macro measures in the sense that

      p ~ X

      Where X is some customary macro measure (like CPI, NGDP etc)

    8. "Since this post is getting a lot more traffic than I expected"

      How much traffic has it had so far, and how much does a typical post get? Why do you think this one is above average? I wonder if there are any widgets that automatically display a statistic about that (to us readers) on a post by post basis.

    9. It's more that we don't know yet if dCPI/dCLF corresponds to anything (maybe, maybe not), but yes, that's it.

      Regarding the traffic, it had gotten about 5x the median post traffic (integrated over a whole week) even though it was posted on a Friday night at around 6pm PST and it has only been two days.

      Maybe it is due to the East Coast winter storm.

    10. Thanks.

      Traffic: so you don't think it's due to its content combined with people linking to it out there somewhere (in blogs, Twitter or whatnot?). I guess you could tell. I was hoping for a more exciting story. :D

    11. ... like it showing up in Woodford's, Krugman's or Bernanke's Twitter feeds (if such things exist).

    12. Cullen Roche once did a post on my old blog, which was very exciting! My coworker beat me there though: he had a blog post get linked to by Brad DeLong (some kind of model he did for fun on the local housing market: sorry I don't have a link). I'm sure you've had similar... it's amazing to see a huge explosion of hits, and then look to see what the heck is going on.

    13. Sometimes it is easy to tell where the traffic is coming from (e.g. the links from Scott Sumner and Mark Thoma), but while this one has an abnormally large contribution from twitter (re-tweeted by Eric Lonergan), it doesn't account for it completely. Most is coming from feedly and google, like normal, but with above average traffic. Hence, the East Coast storm theory ...

  2. "no control" ... perhaps this should be the new Fed insignia?

  3. This is really an interesting finding. While playing around in your FRED model , I noticed that the labor force curve looked similar to curves of annual % debt changes , particularly private debt. Messing with it a bit , I found that % change in private debt per capita matches pretty well with % change in labor force , so this is something that you might want to consider as a possible mechanism or , at least , an interaction in the labor force/inflation relationship.

    Of course , there's the chicken/egg problem. Labor force spikes would likely go along with income gains that could cause new borrowing , or inflation itself might stimulate borrowing as people try to keep up with rising costs , while some might borrow more as their old debt burdens are deflated away. I don't presume to know what the specific interactions might be , but I thought it might be worth considering. Here's a graph to show you what I mean :

    ( I applied a fudge-factor to the labor force curve to roughly align the peaks. )


    1. Interesting -- all of those mechanisms seem plausible.

  4. Awesome stuff, Jason- I think you are well on your way to the Grand Unified Theory of inflation with this analysis. However, I believe that money printing and government spending, if done on a sustained basis, can also produce sustained inflation. As I recall, Argentina currently does not have a super fast growth in labor supply, yet has had near hyperinflation due to money printing. Also, not to forget the Weimar Republic's hyperinflation episode. So a GUT of inflation will also have to include a measure of change in monetary base, no?

    1. Todd, Jason does have a hyperinflation model. Type "hyperinflation" into the search box in the right hand column.

    2. I do, but I do not pretend to really understand it. There are lots of possibilities. It does seem associated with pegged interest rates, however.

      And that may represent the issue I am having with getting the UK data to work in the model above (aside from a massive gap in the data on FRED -- where I am even unsure if the measure corresponds to CLF). Rates have been pegged since 2009.

      So maybe you need pegged rates and money printing?

      Even mainstream economists think hyperinflation is something completely different ...

    3. I forgot about Jason's hyperinflation posts. In any case, I just meant that not all inflation is caused by labor market growth. Clearly some can be due to money printing/spending. I think this is an important point for situations such as Japan, which desperately needs inflation to reduce the value of its long-term debt, but has no reasonable way to increase labor market participation.

    4. That brings up a very profound issue: does market macroeconomics require high labor force growth in order for it to work? Most of our institutions seem built around the concept of inflation, but if that goes away in wealthy societies because labor force growth falls to zero, we're going to need a bigger boat, I mean, new institutions.

      Aside: I am looking at population growth figures and the Great Depression corresponds to a fall in population growth after the 1920s (the US seriously limited immigration with the immigration act of 1921) and the high inflation of the 1970s corresponds to about 20 years after the post-WWII baby boom.

    5. For the 1970s don't forget the women's movement. A lot of young women then opted for paid employment over unpaid labor (housewife). That was a big difference from the 1960s and 1950s. (In the 1940s a lot of women went to work while the men were at war. BTW, my mother knows Rosie the Riveter. :))

    6. I think I included that in the discussion in the post when I talked about women and African Americans being allowed into more of the labor force after discrimination lessened a bit over the 1950s-1970s.

  5. This paper on Japan comes with a model for why inflation falls with labor force.


    1. Thanks for the reference! Interesting!

      The linked model also has the benefit of explaining the path of the unemployment rate.

  6. I wonder if we can construct an upper bound on the CPI by folding in the the size of the military and a hypothetical ending of the drug war? The CLF already includes the unemployed (as I understand it). I say "ending the drug war" as a stand-in for dramatically reducing the incarceration rate. Emptying the prisons (and mental institutions) would be a more clear cut notion I guess. We could toss ending child labor laws in as well I suppose. Lol.

    1. The total population includes everyone:

      Since the employment population ratio is on the order of 50-60%, this would put a bound of about a factor of 2 on CPI and 1200% on the inflation rate (100% increase in 1 month, annualized).

    2. Yes, that would be a loose bound on CPI, assuming no net immigration.

  7. 1) Do you think the model can be adapted to model NGDP in terms of CLF?

    2) Did you find any counter examples: i.e. countries for which CLF did not model CPI very well?

    1. 2) Not yet. One issue with UK: there seems to be a giant gap in the labor force data in every version on FRED. It's right where it would get interesting and makes the model into two trivial fits.

      1) Boom:

    2. Ha!... thanks. I'll check it out.

      BTW, I asked David Beckworth for his opinion of your post here. This was his response:

      "I see it as correlation not causality. Recall that in the Postbellum period of US history that there was rapid population growth and yet there was mild deflation for almost 30 years."

      Here's my follow up question:

      "Was the United states on the gold standard at that time? Do you suppose that could have affected the mechanism?"

    3. The US was not only on the gold standard, except for greenbacks still in circulation, in 1872 or 3 it went off of the double standard of silver and gold, which meant than to new silver coins were being minted. Furthermore, until the 1890s new mining of gold did not keep up with population growth. A lot of people in the US called for a return to the free coinage of silver. Bryan's Cross of Gold speech in 1896 was about the free coinage of silver. It was a popular speech, and Bryan performed it at Chatauquas well into the 20th century.

    4. That's "no new silver coins", not "to new silver coins". ;)

    5. Thanks Bill. That's interesting. I'd love to hear one of the presidential candidates bring up an impassioned plea for bimetalism again... purely for the comedic value (I'd love to see the audience's confused reaction).

    6. Tom, I think that the equivalent today would be a call for the repeal of the debt ceiling, for starters. Then maybe a proposal to fund, say, Medicare for all by printing money instead of borrowing it. Or minting a few trillion dollar coins. :)

    7. For this thread, RE: Tom's question and Beckworth's quote.

      It is a good point, but population growth is not labor force growth and it is possible to have had an increase in subsistence farming (not "labor" per se) during the settling/displacement of Native population in the Western US. Also note that there was hyperinflation during the Civil War, and the long deflation was mostly a long adjustment back to the ante bellum price level.

      But it is an interesting issue and I'll be interested in looking into it. It is possible there are other factors.

      I am not saying the model above constitutes "the truth". It is just a simple model that can act as a first order approximation or a null hypothesis.

    8. "subsistence farming" ... I was thinking the same thing this afternoon (mostly because you'd mentioned it someplace else)


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