Coal production 1905-1939 and the Great Depression

I saw this tweet from Beatrice Cherrier that contained an interesting example of NBER data from the 1940s — a time series of coal production in tons:

I noticed that it had the form of a dynamic information equilibrium model:

Whereas the original graph sees 9 business cycles (which corresponds to the NBER recession bands in light orange), the DIEM only sees about 4 (the first one could be two that are unresolved) given the noise in the data. There is the recession associated with WWI (the "post WWI recession" and the depression of 1920) — this is the one that isn't resolved. There's a shock in 1926 which is followed by the shock in 1929 and the Great Depression. Finally, there's the 1937 recession. Often, that last one is blamed on monetary policy or fiscal policy, but the monetary shocks and fiscal shocks both come after this shock to coal production in late 1936/early 1937. The cuts in government spending impact WPA employment in mid-to-late 1937:

The unemployment rate shock is centered in 1938:

The 1937 shock also appears to his several countries (e.g. France), making it unlikely that it was some US-specific policy.

Also as a side note the WPA expansion in 1935 doesn't seem to have a visible impact on the unemployment rate in 1935. Another thing to note is that the market crash in 1929 comes much closer to the middle of the Great Depression shock — coal production was already falling so the market crash can't really be considered a cause. Note also that the unemployment shock comes in 1930 (per the graph above).

Maybe I'll have to do this for the Great Depression!

Data revisions (inflation and rgdp forecasts)

Revised real GDP and quarterly PCE inflation data came out today, so here are how the dynamic information equilibrium model (DIEM) forecasts are doing (versus the FRB NY DSGE model forecast):

The PCE inflation forecast from the FRB NY is doing remarkably well — if not for those almost 300 basis point error bands (compared to half the size for the DIEM).

Here's the monthly PCE forecast compared to a Fed forecast and one from Jan Hatzius:

The beginnings of an information equilibrium macro model

I've been trying to put together a summary of the information equilibrium/dynamic information equilibrium models that comprise a single (still preliminary) macro model. It's mostly for my own notes. At the top of this post is a graphical representation (click the graphic enlarge) of several posts. This recent post explains the relationship between information equilibrium and dynamic information equilibrium (there is also this "tour of information equilibrium" presentation) — these are represented by blue double arrows and purple single arrows, respectively. The gray dashed lines represent vague "links" (obviously NGDP is related to NGDP/L, it being in the numerator, but the "limits to wage growth" connection is more speculative). The black line relates NGDP with its growth rate by a mathematical operation (log-derivative a.k.a. the continuously compounded annual rate of change). There are two "exogenous shock" inputs — one is the business cycle (which is behind recessions, possibly based on the "limits to wage growth"), and the other are social factors (women entering the workforce, Baby Boomers retiring after the Great Recession).

We have:

• Matching theory and dynamic equilibrium (relating JOR, HIR, and u)
• Okun's law (quantity theory of labor)
• Nominal Solow model (part of this is related to Okun's law)
• Labor shocks and the business cycle (HIR leads u and wage growth shocks)
• Demographic shocks and trend growth (CLF, CPI, and NGDP/L)
• Limits to wage growth (speculative explanation of when business cycle shocks occur)
• Labor share (relating W and NGDP)
• Equivalence of PCE, PI, and NGDP

I left out the interest rate models because they're not terribly relevant at this level. Not that interest rate signals are irrelevant — it's entirely possible the limit to wage growth mechanism functions because the Fed raises rates until wage growth stagnates at a level at or below NGDP growth, so then starts to lower rates which sends a signal to markets that a bear market is approaching creating a self-fulfilling prophesy. I'm still agnostic on that.

However, all the IE and DIEM  relationships (blue double and purple single lines) above are empirically valid. It's essentially the connection between the top half and the bottom half of the graphic that is speculative.

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Update 27 March 2019

If you were wondering where we are regarding that "limits to wage growth" picture:

The Hatzius band is from this post. The dashed line is the mean NGDP growth rate from a dynamic information equilibrium model.

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The various abbreviations:

HIR = JOLTS hires rate
JOR = JOLTS job openings rate
u = unemployment rate (UNRATE on FRED)
U = unemployment level
L = employment level (PAYEMS on FRED)
NGDP = nominal gross domestic product
K = "capital"
PCE = personal consumption expenditures
PI = personal income
CLF = civilian labor force (CLF16OV on FRED)
W = wages (wage growth is Atlanta Fed wage growth tracker)

Beveridge curve update (and labor force participation)

I don't think I've updated the (traditional) Beveridge curve for almost a year, so here you go:

The details behind this plot (in terms of the dynamic information equilibrium model, DIEM) are actually in my paper (it's Figure 3.6). It's first appearance on this blog was in October of 2017. A couple of weeks later I speculated about the existence of another Beveridge-like curve relating labor force participation (ages 25-54) and unemployment which also seems to be working out well:

Due to women entering the workforce affecting the data before the 1990s and the mis-match between the non-equilibrium shock timing in the recessions since then, it might never have been observed without the DIEM. Here's the labor force participation forecast on its own:

Declining employment rate for 15-24 year olds in the US

I can't seem to find the original forecast (maybe I never published it?), but I did look at the employment rate for 15-24 year olds with the dynamic information equilibrium model some time in late 2017. In any case, it's not the forecast that's interesting but rather the deviation from it:

This metric is showing some deviations that could be indicative of a potential recession in the 2020 time frame (in line with other indicators such as the yield curve). However, it also showed a false positive in the mid-90s:

The unemployment rate in the same age group might help explain the false positive as we can see a dramatic dip in the rate at the same time indicating that people 15-24 were leaving the labor force (potentially going to college through newly expanded student loan programs).

However the more recent downturn in the employment rate doesn't have an immediate corollary in the unemployment rate.

In any case, it will be useful to watch these employment metrics.

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Update 22 May 2019

Here's the latest data update from earlier today ...

Market updates 2k19! And an old forecast ...

Well, first, the 3-sigma deviation in the interest rate model is apparently over (for now), meaning that the 10-year interest rate is back to where information equilibrium predicted it would be in August of 2015 (almost 4 years ago):

That model is an information equilibrium model in the more traditional sense on this blog where [1] we have p : NGDP ⇄ M0 and r ⇄ p in the shorthand notation which tells us that

log r = k₁ log(NGDP/M0) - k₂

with

k₁ = 2.8

k₂ = 6.4

once we solve the differential equations and fit the parameters (k₁ and k₂ were estimated in August 2015). The projection was based on log-linear extrapolation of NGDP and M0 and an AR process. The second piece of the model tells us that the exchange rate for a bit of GDP and a dollar of physical currency (i.e. dNGDP/dM0, which you can call "the price of money") is in information equilibrium with the 10-year interest rate. Note that this model also yields a kind of "quantity theory of money" where NGDP ~ M0^β where but really the "quantity theory of labor" q : NGDP ⇄ L with PCE ⇄ q is a much better model of inflation than the quantity theory of money.

The latest data for the dynamic equilibrium version (based on Moody's corporate AAA rate) is also in line with the forecast:

The relationship between a dynamic information equilibrium model and plain information equilibrium (IE) is that the DIEM is agnostic about the information transfer and we have something like p : A ⇄ B (which is IE) but we don't know/care what A or B is (or we only look at A/B) but rather assume A ~ exp(a t) and B ~ exp(b t) so that (d/dt) log p ~ a − b + Σᵢ σᵢ which is a constant (the "dynamic equilibrium") plus shocks (σᵢ). These different models all derive from the same central relationship [2].

That gray band is where the interest rate spread indicator points to a recession based on a simple linear extrapolation (blue)/AR process (red) based on median (which in this case is basically equal to the principal component) of multiple spreads:

And finally, here's the dynamic equilibrium S&P 500 forecast that's been ongoing since January of 2017 (two years now):

I show a counterfactual recession with the parameters of the 2001 recession shifted over to the 2020 time frame.

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Update 23 March 2019

I have been so focused on my own median spread metric that I failed to note that the yield curve actually inverted yesterday for the 3m-10y spread. Lots of people (e.g. here) have brought up the fact that yield curve inversion is not a panacea in terms of leading indicators. And it's not — there was a false positive as recently as the late 90s. But according to the median metric (which still hasn't inverted), not only is actual inversion unnecessary, but the hazard function shows a wide spread for the probability of observing inversion in the median spread:

Additionally, we can see in the median rate spread data above, for the previous three recessions the median spread started to increase just before the recession onset in the final quarter before an NBER recession would be determined to begin. This can be viewed as the Fed beginning to notice signs of weakness and lowering rates (thereby increasing the spread) in that final quarter:

We can also see that late 90s inversion false positive being undone by the Fed lowering rates in the midst of a series of financial crises around the world (Asia, Russia) and the bailout of LTCM.

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Footnotes:

[1] This is for IE noobs who have only seen the blog after I pieced together the DIEM model and this blog became in John Handley's words "all dynamic equilibrium".

[2] Here's a kind of mental map relating the various pieces (from my tour of information equilibrium presentation):

MASSIVE revisions to the JOLTS series!

There were massive revisions to the Job Openings and Labor Turnover Survey time series in the last release — going all the way back to the start in December of 2000. These were more extensive than the revisions last year. However, the old model fit is consistent with the new data, and the forecasts are pretty much unchanged (this is actually pretty astounding). Here is the data release from February (blue) and the new one from March (red) for hires and job openings:

And here are the models (JOLTS openings continues to fall a bit below the expected trend):

Actually, the revision made the hires model slightly better. If you look back to the previous post on JOLTS data, you can see the latest points are now completely in line with the forecast compared to being a bit above.

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Update

Per anonymous comment below, the counterfactual has gotten a bit smaller over the past several months because the counterfactual recession date was fixed to 2019.7 based on the yield curve data. If we push the date out further — say, to 2022 — the counterfactual shock size gets bigger (and more uncertain):

Policy in information equilibrium: job guarantee

One of the things I've found about the information equilibrium approach is that the results are remarkably stubborn in showing any effect of any government policy whatsoever on things like inflation, unemployment, or output. However, there is one kind of policy that does seem like it would have an effect: a job guarantee or some WPA-style government employment scheme. That's because the size of the labor force directly impacts inflation and output (here, or here, with shocks to labor happening before changes to inflation and output). To that end, I assembled a model like this one where the relevant variables are the labor force size (CLF16OV), GDP per employed person (GDP/PAYEMS), headline CPI inflation (CPIAUCSL). I also included working age population and the unemployment rate to look at labor force participation rates (it's not exactly the traditional EPOP measures, but it gives an idea).

Now there are far fewer shocks than in that model, so the relationships are somewhat uncertain (the most uncertain is the relationship between inflation and labor force because the Great Recession shock is buried in the noise of the inflation rate, effectively leaving only one shock to estimate the relative sizes). But overall, it gives us a way to estimate the effects of a policy like the Job Guarantee.

First, we assume the policy is implemented in the next administration and employs about 20 million more people than otherwise (without the policy) in 2030. That (along with normal growth) brings us up to something over 90% labor force participation. Most of the effect takes place during the next administration (2021-2025) but it's a logistic function that's asymptotic so effects continue for a few years after. We also assume there aren't any recessions between now and 2030. (Ha! I mean, I could add one, which would create a Phillips curve like fluctuation in inflation but that's for another time.)

The dynamic information equilibrium model (DIEM) seems to say that CPI lags CLF increases by about 3.5 years and are a bit narrower, and somewhat larger. GDP/PAYEMS also lags CLF increases (by roughly the same length of time) and are about the same width as the CLF change but are bigger in magnitude. In this logistic function page on Wikipedia, the magnitude is L, the width is 1/k, and the delay goes into x₀. For more on the DIEM, see my paper. This means if we know what the shock looks like to CLF, then we know what it looks like to CPI and GDP/PAYEMS. Here's the forecast with and without the JG policy:

Since the inflation effect was a bit more uncertain, I included both the average and worst case effect. Here's the effect on labor force participation (note the lack of recessions, one — implausible —assumption):

The purple curves are the size of the labor force as a fraction of the working age population. Note that 100% of the working age population in the labor force is not necessarily a successful policy since it means e.g. students working.

Now for the funny bit: here's the effect on (year over year, or YoY) inflation (I went back to the 1960s just to give you a flavor):

I cracked a smile when that came out of the models. We'd be looking at 70s-style inflation which people were not happy about at the time. What about growth? Here's the effect on nominal GDP per employed person:

Unfortunately, the CPI-deflated real GDP per employee in 2019 dollars is uncertain precisely because the inflation effect is uncertain (in general RGDP is a much more uncertain measure because it combines errors in NGDP and in CPI or other price level measurement):

So there you have it: the effects of a Job Guarantee. It definitely seems more like a policy you'd want to implement during a recession (a la WPA) rather than one that's permanent.

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PS Does this make Job Guarantee now an information equilibrium policy? I mean MMT now claims it as if it made it up when it is kind of the whole point of Marxism and Roosevelt included it in his "Second Bill of Rights".

MMT cannot produce forecasts nor accurately fit data

FRBNY DSGE inflation forecast, January 2019. Objectively better than MMT, even if it's wrong.

Over the weekend, I wrote up a bit on my views of MMT including my critiques of it. I got some comments that it was too long or that it wasn't clear what my critique was. Let me try again with a different — and more practical — take.

Modern Monetary Theory (MMT) cannot produce forecasts nor accurately fit data and is therefore far inferior to even the most objectively inaccurate Dynamic Stochastic General Equilibrium (DSGE) model.

Two phases of the 2008 housing crisis

I revisited an old post randomly, and it had a picture of housing starts that I realized had a connection to the more recent post on the housing crisis in terms of the Case-Shiller Housing Price Index. Recall that I showed the CS index as having a dynamic equilibrium in its growth rate remarkably similar to wage growth, but there were two shocks to the level of the CS index (that show up as spikes in the growth rate). First, here's the CS level:

And here's the CS growth rate:

I color coded the extra shocks red. The dashed green path in the first graph shows effectively the counterfactual without the global financial crisis. These two extra shocks bookend the "unexplained" bit of housing starts in the old post I revisited:

This all shows the 2008 housing crisis in the US as really a two-phase event. There's the large but relatively ordinary housing bust (the bust in housing starts in the mid-70s was actually bigger especially given the lower population at the time) that is followed up (and made worse) by the global financial crisis that starts around the Lehman bankruptcy.