Wage growth and tight labor markets

Ernie Tedeschi put up a version of a chart today I think I saw from Adam Ozimek about a year ago showing a linear relationship between 25-54 year-old employment population ratio (which I updated yesterday) and the employer cost index that's a measure of wage growth:

I have some issues with this being called a "wage Phillips curve" because what this really shows is just economic growth: as the economy grows, employment grows as well as wages. It's kind of just supply and demand here. As non-engaged labor becomes scarce, wage growth go up. The Phillips curve is a relationship between prices of goods and employment — lower unemployment causes some measure of the price of goods to increase. This requires an additional step beyond the labor market picture where e.g. higher wages chase scarce goods causing their prices to increase — the wage-price spiral.

But as I talked about last year, I don't think this simple linear relationship is the true relationship between these variables — it's actually somewhat spurious. Back then, I projected (based on the DIEM [1]) what continued economic growth would look like on this graph and the data would follow a line of much lower slope. And sure enough (click to enlarge) —

I used different data for wages (Atlanta Fed's Wage Growth Tracker) because it has a longer time series and is reported monthly (like EPOP) instead of ECI's quarterly frequency. The addition of the data from before 1994 (yellow) also helps show that this isn't just a simple line. The data since last year (black) have followed the expected non-recession trendline (gray). In fact, if you look at the last 3 years of data, it's even more clear that the lower slope from the dynamic equilibrium is correct, not the linear fit:

This supports the conclusion that what's being seen here is just a consequence of economic growth. Wages tend to grow and employment rate tends to rise (and unemployment tends to fall) between recessions [2]. 

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Footnotes:

[1] The graph is made from a parametric plot of the wage growth DIEM and the EPOP DIEM:

[2] The rates these change at are different — their units are different, so they're not really even commensurate! Wage growth (or ECI growth) is % change per year (therefore changes if you change the time scale) while EPOP or unemployment are just fractions (%, or pure numbers). 

Employment-population ratio and labor force participation rate

I haven't updated the forecasts of labor force participation for ages 25-54 or the employment population ratio by gender in awhile. I was prompted by this tweet from Ernie Tedeschi about how labor force participation hasn't abated — but it shouldn't show any signs until after a recession has already hit (here, here). Here are the updated models for labor force participation and women's employment-population ratio:

For some reason I don't fully understand, the code for men's employment-population ratio had the dynamic equilibrium hard coded to 0.007/year when the actual solution from the entropy minimization was 0.005/year. It's the latter value that matches the original fit while also fitting the post-forecast data, but I'll present both graphs — the 0.007/year value is the one that shows recent data lagging the forecast. My guess for the reason was that I was comparing the value for the fit for women in the graph above (which is 0.007/year) and forgot to change it back or document it. Anyway, here's the E-POP ratio for men with both dynamic equilibria:

Last but not least is the employment population ratio for everyone in the labor force — which has a forecast from the CBO to compare to (again, via Ernie Tedeschi) ...

... that's doing poorly.

I added the CBO's August 2018 projection from Ernie's graph. Here's the longer run (the graph above was made to match Ernie's tweet):

Core PCE inflation: three cheers for DSGE

Core PCE inflation data — the measure commonly believed to be the most closely watched by the Fed — was released today. To be a bit of a troll, my Twitter headline for this post is going to be that the NY FRB DSGE model is remarkably accurate (black is post-DIEM forecast data):

... at least in its forecast mean. Given that the error bands are smaller for the dynamic information equilibrium model (DIEM), we'd say it improves our Bayesian prior more than the DSGE model does despite the near zero deviation from the mean forecast. Here's the year-over-year measure for the monthly data:

Of course, I really dislike year-over-year measures. Sure, they help eliminate seasonal variations, but the introduce correlated errors ... i.e. the present value depends on the measured value — including its error — from a year ago. And since there are undoubtedly seasonal/annual/multi-annual fluctuations, year-over-year measures make an implicit assumption that your measurement error has no seasonal variation which is unlikely. This is why lots of year-over-year measures tend to increase the order of the AR processes that can be used to estimate them in the short run. Of course, the benefit is that overall error is usually smaller than when you take derivatives (which only impact the points right next to each other) because much of the uncorrelated error over the course of a year is averaged out.

Note: this should not in any way be read as disparaging the performance of the DSGE model above — it would likely be just as right about other measures. It's mostly about reading anything into the individual time series points (i.e. saying core PCE inflation has fallen over the past couple quarters).

Here's the continuously compounded annual rate of change (aka log-derivative) versions alongside some other forecasts from the FOMC (purple points with error bars representing the "central tendency") and Jan Hatzius (lavender dots):

This white dots with black outlines represent the annual averages. Here's the quarterly version:

Overall, the DIEM forecast is performing well — as well as a fancy DSGE model. However, the path — being relatively constant — isn't very challenging.

GDP data!

I have some NGDP and RGDP dynamic information equilibrium model forecasts I've been tracking the performance of. These, unfortunately, aren't very exciting because GDP data is (surprise) super noisy. Or at least it's noise in the DIEM view. Some people tend to think of the fluctuations of GDP from one quarter to another as somehow meaningful. I'll probably hear about it on APM/NPR's Marketplace tonight. At least it's working better than the NY Fed's DSGE model which predicts about the same average path but with much larger error bands.

Anyway, here's the latest:

Happy birthday to the blog!

I started this blog with its first post six years ago today. At the time, I had derived supply and demand diagrams from an information theoretic approach [1] that I thought might be publishable if it weren't for the institutional roadblocks. For one, I'm not an economist, and while I love the earnestness of "econophysicists" no one listens to them, nor do they (in general) provide a good reason for doing so. The work is sometimes referred to as "heterodox", a) I don't really think it is because that's its own thing (q.v. Carolina Alves) and b) I didn't really know about it at the time — therefore that community isn't/wasn't necessarily a viable alternative to mainstream publication.

I decided to just present the results on this blog — the draft paper I had written was presented in the first few posts here. Eventually those results would be incorporated and expanded on in my first econ pre-print, originally on the arXiv in q-fin.EC (there's a re-post of it at SSRN). That first pre-print contained the model in the forecast above that's been doing well for almost 4 years. Another pre-print followed a couple years later containing its own forecast (of unemployment and JOLTS data) that's also been doing well.

And here we are — six years later. To celebrate, I made an animation of one of the forecasts that I've been tracking the longest — more than half the time this blog has been in existence. The model itself was first written down in February of 2014, less than a year after the blog started — though there general concept was written down in August of 2013.

The interesting thing about this model is that it's a simple idea: the interest rate is the "price of money" and NGDP (~ aggregate demand) is the "demand for money" — with the monetary base being the "supply of money". (It's also a component of the information equilibrium IS/LM model.) It's possible it's not correct (or is only an "effective theory") and what we really have is a dynamic information equilibrium model. But it's still working for now!

Thanks everyone for reading! 

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Footnotes:

[1] And which Thomas Mikaelsen has recently been checking my math on!

Wage growth forecast continues to do well

The Atlanta Fed updated their wage growth tracker a few days ago while I was at Coachella, so I didn't have a chance to update it at the time. The post-forecast data continues to be pretty much in line with the original forecast from February 2018 (as always, click to enlarge):

Plus, despite being paid a fraction of what Jan Hatzius of Goldman Sachs is paid, my forecast for the same set of variables is looking a bit more informative than his:

That blue dashed line is the nominal GDP dynamic equilibrium and is part of my "limits to wage growth" hypothesis where nominal wage growth is halted by a recession if it starts to exceed nominal economic growth (and therefore eats into profits on average/in the aggregate). It's a speculative part of the information equilibrium "macro model". We did appear to skirt the edge of it towards the end of 2016 before the data dipped a bit. Given the noise in the data, it is difficult to tell if that was the fading "mini-boom" of 2014 or the beginnings of a genuine downturn that was averted. Job openings was showing a similar downturn at the time that was significant enough (alongside yield curve flattening) for me to posit a coming recession in late 2019 to early 2020 — but might have faded away in subsequent job openings data and revisions. However, the downturn is still present in quits and separations so basically we're still in a situation where only time will tell.

Median interest rate spread inverted

We're at edge of the two sigma band where a recession occurs after the monthly median interest rate data manifests a yield curve inversion. The median daily interest rate data showed a brief inversion at the end of March — about two weeks ago:

The 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.

Note that except for the 2001 recession, these median rate spreads started to head back up by this point over the past few recessions — reminding us that we will probably see the Fed lower rates (increasing the short-long rate spread) before a recession starts. Or maybe the yield curve will prove to be a false alarm — to be placed on the scrapheap of indicators that lose their predictive ability as soon as they're widely recognized.

CPI inflation forecast still holding up after 2 years (plus useless forecasts)

Here's the latest CPI data (all items, post-forecast data in black) and the dynamic information equilibrium model (DIEM) forecast from 2017:

Note that the dashed line is the revised parameters from this post (from one year ago) — but given the revised line falls entirely within the error band it's really a trivial correction (more on this below). Especially when we look at the inflation rate:

Useless forecasts from the Peterson Institute

When I saw a forecast from the Peterson Institute, I was initially excited to have another model with which I could compare the dynamic information equilibrium model. However, it turns out that not only was it for core CPI inflation (which is far less interesting than headline inflation shown above — it's constant, so I stopped tracking it), but it was also a useless forecast for core CPI inflation (clue and red dashed lines):

Going by a simple AR process around a constant value of inflation (a model that outperforms the most advanced DSGE models), we should expect an error band due to fluctuations in the data roughly comparable to the DIEM band shown above. That's because the DIEM is actually constant over the post-recession period and the error is estimated by taking the standard deviation of the model residuals — i.e. basically the process for AR process estimation [1].

So Collins and Gagnon (the authors) should have known that. They also should have known that the prior data looks like the data in the graph above — pretty much within half a percentage point of 2% over roughly the past decade. Which also means they should have known that their forecast (and in particular the difference between their forecasts which is the focus of the article) is basically within the noise of a model with a maximally uninformative prior — i.e. useless. 

True, this means the DIEM for core CPI data is also useless [2] — part of the reason I stopped tracking it. In fact, I note that the re-estimation of parameters in the all item CPI was also trivial and it generates an effect comparable to the difference between these Peterson Institute forecasts. But at least I've acknowledged that it's within the noise (and given an estimate of the model error).

But this Peterson Institute forecast? It's such a small deviation, I'd almost think that they made it knowing that it probably couldn't be rejected by the data. It's basically a non-forecast.

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Footnotes:

[1] Neglecting the little bit at the beginning that effectively tracks the expected mean reversion (as described in a footnote here).

[2] The all item CPI forecast actually showed a tiny improvement over a constant model — but was also related to a lot of other dynamic equilibrium models. But also, the various DIEM models show a great deal of improvement of the error bands (here, here) — bands this Peterson Institute forecast didn't even give us.

Dynamic equilibrium in population growth

I saw some data from Brookings today (via Noah Smith) about population growth that looked almost exactly like wage growth data — and it turns out it is well-described by a dynamic information equilibrium model (DIEM):

The 1991 recession and the 2008 recession are both followed (with a lag on the order of years) by a fall in the population growth rate. The 2001 recession basically coincides with the population growth decline. However, there is a drop in population growth not associated with a recession, but rather associated with the end of Obama's term as President and the beginning of the current administration's term:

Update: Forgot the labels — they show the shock centers for the unemployment rate (u), wage growth (W), and JOLTS hires (HIR). These labels are actually centered on the shock (including the text) so the actual center is a bit to the left of the arrow.

JOLTS day!

The Job Openings and Labor Turnover Survey (JOLTS) data released today continues the status quo of bending slightly below the dynamic information equilibrium model (except for hires):

Click to enlarge any of these images. I wanted to see if incorporating more data in the model for job openings (which showed its largest drop since 2015 today) could handle the deviation — and it can (you can cycle back and forth between these two images on a desktop/laptop):

However, this same trick does almost nothing to total separations:

And only nudges quits:

So, as with most macro data, there's some ambiguity here. Hires (the more robust leading indicator for non-equilibrium shocks — but also only by about 5 months) is showing no deviation, quits and separations (which lagged in the past) showing robust deviations, and openings being ambiguous (and also had the largest revisions last month). According to the hires data, we should continue to see the unemployment rate fall (stay on the DIEM path) through July of 2019 (5 months from February 2019, which is the data that was released this week).