Tuesday, April 30, 2019

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]. 



[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). 

Monday, April 29, 2019

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.

Friday, April 26, 2019

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:

Wednesday, April 24, 2019

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 yearsAnother 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! 



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

Friday, April 19, 2019

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.

Thursday, April 11, 2019

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.

Wednesday, April 10, 2019

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.



[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.

Tuesday, April 9, 2019

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).

Sunday, April 7, 2019

Things that changed in the 90s

Welcome back the 90s. Did you miss us?

It's my understanding that the fashion today among the millennial generation (1980-2000) is to call yourself a 90s kid if you were born in the 90s, but the reality is that the people born in the latter half of the 90s would have no real memories of the time [1]. It's all pretty funny as I see the kids today on my lawn sporting 90s fashions. I gave the kid my old box of round sunglasses in every color. As a 70s kid by the millennial metric, I spent my formative years in the 90s. This makes any assertions I have about the period immediately suspect — both being prone to being overly nostalgic for or traumatized by events of the era. For example, the baby boomer economic pundit class of today can be seen as being traumatized by the high inflation of the 70s and so remain oddly preoccupied with it even in an environment of sub-2% inflation.

With that caveat, I wanted to collect in one place several economic trends that changed in the 90s that I've noticed or blogged about. I am exploring as a major theme of my forthcoming book what happened. My thesis is that that there was a major social change underway in the US in the 70s that effectively comes to an end by the 90s — women entering the workforce peaks in the 70s and reaches a new equilibrium by the 90s, which is closely matched by white flight that emerges with the civil rights movement. I believe that these trends had observable effects in many economic time series. Also, this list is intended to be updated — leave a comment if you find some data where the trend changes in or around the 1990s. 

What changed: Phillips curve, women's employment-population ratio, men's self-citations

This post (and this follow up) lays out my hypothesis that the Phillips curve was an epiphenomenon of the rise in women's labor force participation. However, it also touches on one social change — men's self-citation in academic literature — that might have been caused by the increasing number of women in academia. By the 90s, women's employment-population ratio, the Phillips curve, and self-citations reach new equilibria (correlated with men's at a lower level, zero slope, and ~1.6 times the level of self-citations by women, respectively).

What changed: Recessions (?)

Related to the fading of the Phillips curve, the 90s sees the beginning of what I call the "asset bubble era" where recessions seem to be governed by the rise and fall of asset bubbles ("dot-com", and the housing bubble) as opposed to the more cyclic fluctuations of inflation and employment of the "Phillips curve era".

What changed: Long term unemployment

Until the 1990s, the fraction of the unemployed that have been unemployed for 27 weeks or longer ("long term unemployment", here) basically followed the unemployment rate with a surge during a recession and catch-up decline through the recovery. After the 90s, recessions start causing cumulative increases in the long term unemployed as the catch-up decline in the faction faded away. I don't have any hypothesis as to the cause here, except to say that it's undoubtedly related to the overall change in the 90s.

What changed: Unionization, inequality, labor share, manufacturing employment

In this post, I try my hand at divining causality among women entering the workforce, manufacturing declining, labor share declining, unionization declining, and inequality rising. They happen basically in that order and have mostly completed their transitions to their new equilibria by the end of the 90s.

What changed: The dynamics of consumption relative to investment

In this post, I noticed that while the ratio of consumption to investment follows a pretty normal cycle well-described by a dynamic information equilibrium model starting the late 80s and early 90s, the period before appears to be just noise with a slight downward trend (which is similar to housing prices discussed below). 

What changed: Immigration

In this post that's mostly about the Great Recession, I point out that immigration from Mexico changes from increasing during the 90s to declining after the 90s. My speculation was that increasing xenophobia might have caused a slowdown in economic growth contributing to the Great Recession.

What changed: Housing price dynamics

Although I don't show it in the post [2], the longer term Case-Shiller index is relatively flat (or at least averages to flat) before the 70s. And much like consumption-to-investment ratio above, the dynamic equilibrium process doesn't become really clear until the 80s and 90s. But one of the other things that happens is that until the 90s, this pattern follows the business cycle — falling with recessions. However, while e.g. wage growth takes a dive in the 2000s recession, housing prices don't which contributes to the housing affordability crisis we're experiencing today. My hypothesis is that this has something to do with white flight fading out and the gentrification process kicking in — the new segregation after de jure segregation and redlining.

Women's employment in manufacturing
What changed: Fraction of women employed in manufacturing

In researching my upcoming book, I found a striking statistic. In the 90s, the fraction of women in manufacturing employment — which had been increasing since the 1960s — started declining precipitously. It returned a level not seen since the 1960s after the Great Recession. Now at less than 30%, it is one of the most gender-asymmetric sectors.


Updates 24 June 2020

Violent crime
What changed: Violent crime in general fell after peaking in the early 90s

One of my favorite explanations for the drastic rise and fall of violent crime in the US after peaking in the early 90s is the lead-crime hypothesis, but I'm open to other possibilities.

What changed: People claiming the invented "American" ancestry on the US census

In researching my now released book, I found another striking statistic. Sometime between 1990 and 2000 the number of "Americans" doubled. I don't mean the population of the United States, but rather the number of people claiming the newly invented "American" ancestry (and I don't mean Native Americans). Apparently there was an additional 20% surge in "Americans" right after Obama was elected who have subsequently died off.

Police murdering people
What changed: The share of violent deaths in the US caused by the police

The share of all violent deaths in the US has gone from about 5% to about 10% — and this took off sometime after the 90s after being flat at about 5% for decades (even including decades where overall violent crime was increasing per above). Possibly 9/11 related. Possibly due to military equipment being sold to police in the wake of the wars in Iraq and Afghanistan. But as I describe in more detail in my book, this might be part of the growing cultural division in white people. This rise in violent death could be effectively interpreted as ethnic violence committed by white police against Black people as well as the violent patrolling of de facto segregation based on housing prices mentioned above.



[1] Actually, what we think of as "the 90s" is really a period from 1988 to 1998, much like how "the 80s" is really a period from 1977 (or this) to 1987. At least in the US. By video game consoles, we also have the 90s being 1988 to 1997 and the 80s being 1977 to 1986. There's really no arguing against it.

[2] It's here (blue) along with the model (green) for the period from the 70s to the present (click to enlarge). Aside from the spike right after WWII, there's really just noise.

Friday, April 5, 2019

Interest rates and inflation

Apparently Randall Wray has set off the econ twitters with a pull quote captured here:
"There is no empirical evidence to support the belief that raising interest rates fights inflation."
It was pretty funny seeing the flurry of "obviously it does" countered with another flurry of studies of the lack of a connection or just various models (including DSGE models which are bad at forecasting) showing different results. I just found myself in a rare agreement with Wray. My own heterodox take — inflation is always and everywhere a labor force phenomenon — would probably be met with equivalent derision if anyone was paying attention.

My working hypothesis is two-fold:

  1. When labor force participation is increasing faster than equilibrium (when women are entering the workforce in a demographic change or men entering the workforce after a war), we get a surge of inflation. When labor force participation declines, inflation flags.
  2. When recessions happen during the a surge in labor force participation, it modulates that increase in participation causing oscillations — the Phillips curve. I have speculated that it is possible these processes are connected and that you always get "gravity waves" of inflation when labor force participation is increasing faster than equilibrium.
It is possible that the Fed triggers the recessions in the second part by raising rates instead of the oscillations being endogenous (i.e. generated by the surge process itself). In that sense, it is possible the Fed causes the recessions which cut off inflation. This would create a pattern of a series of Fed hikes before a recession which cuts off the inflation (and occurs near, but just after the peak). We'll call this A. However, if the Fed raising rates fights inflation, that should create a different pattern in the data: a surge in inflation should have started before the Fed starts hiking rates, and subsequently turnaround and end after or while the Fed is hiking rates — independent of a recession. This could also manifest as a fall in inflation. We'll call this B. Of course, there is also the possibility that Fed rates have nothing to do with the pattern of inflation (which is closer to my working hypothesis where the Phillips curve is endogenous). We'll call this C.

I will look at this through one of my "economic seismograms" that basically are a visual form of Granger causality (but a bit more conservative). I drew the changes in the time series with increases and decreases shown in red and blue (red is associated with economic growth, blue with decline/recession) and layered the Fed rate changes in yellow (raising rates) and green (lowering rates) as lines on top (click to enlarge):

What do we have? Well, in the period around 1960, we have a B — the Fed raised rates and what followed was a decline in inflation. You could possibly say that the '71, '74, and 80s recessions are A's.

In nearly every case though, the Fed's rate increases begin before the surges in inflation and end randomly relative to the turnaround point (the midpoint). It's almost the neo-Fisher hypothesis that Fed rate increases cause inflation! Recessions come at the tail end of these inflation surges as they're cut off by unemployment spikes, but sometimes we have no inflation surge (through most of the 90s and 00s). The Fed is always dutifully raising and lowering rates in sync with recessions. We even have an anti-B during the period of "lowflation" following the Great Recession — the Fed had lowered rates. That is to say most of the time we have C.

In fact, the single best explanation (we'll call it D) is that inflation and interest rates are unrelated but the Fed thinks it controls inflation and mitigates recessions with them, so it raises rates during economic expansion and lowers them after economic indicators turnaround before an oncoming recession. This has the benefit of the premise being incontrovertibly true — the FOMC does believe it can affect inflation or recessions with its rate choices.

I should always bring up Milton Friedman's thermostat here: if the Fed really did control inflation with policy, then it would look like there's no specific relationship between rates and inflation if they were doing it right. Of course this view is both question begging and unscientific in the sense that it shuts down inquiry. But a really good counter is that Fed policy is obviously correlated with recessions, so Occam's razor is that we should assume D until convincing evidence comes along to change our minds.

What is Okun's law about, anyway?

In my iconoclastic way, I've referred to any relationship between employment and output as "Okun's law" (e.g. here and here). In the first of those links, I noted that "Okun's law" understood that way was at best an approximation. However, a few weeks ago Britonomist on Twitter piqued my interest in the original form by saying:
I don’t remember being taught any explanation of why c in Okum’s law was 2 for instance, but I would have found the subject very dull if it was just memorising various estimated parameters without any deeper explanation.
I set off to try and show why c = 2 using the dynamic information equilibrium model. What I learned was that the interesting part of Okun's law is almost entirely about the one or two quarters spent in recession. If we take the form ΔY/Y = k − c Δu where the change is over a year, and the typical coefficients where k = 3% and c = 2, we can show a pretty good "explanation" of k

k ≈ (eγ − 1)   c (eα − 1) ū

where γ ≈  2.4% is the dynamic equilibrium for RGDP growth (i.e. the difference between the dynamic equilibria for NGDP = 3.8% and the GDP deflator = 1.4%), α ≈ − 8.3% is the dynamic equilibrium for the unemployment rate, and ū is the average unemployment rate over the period (~ 5.9%). This gives us

k ≈ 2.4% − 2 − 8.3%) × 5.9% = 3.4%
k ≈ 2.4% 2 0.5%) = 3.4%

That ū shows up because the RHS of Okun's law is in terms of the change in the unemployment rate Δu rather than Δu/u ≈ Δu/ū (otherwise, we'd have a direct relationship between dynamic equilibria). The exponentials convert a logarithmic growth rate (dynamic equilibria) to a yearly change.

The truth is that we get k approximately right for c = 1, 2, or 1.4 (per the best fit later, and these values give 2.9%, 3.4% and 3.1%, respectively) as that term is about a 10-20% correction. The main driver behind the value of c is the recessions:

In the figure, I show year over year RGDP growth (gray) along with the DIEM model for the unemployment rate (purple). Okun's law is a transformation of the latter, and I show both the traditional coefficients (red) and the best fit over the data shown (dashed red). I also show the dynamic equilibria (dashed purple for the unemployment rate and dashed gray for RGDP). You can see that the k-value is mostly about the constant levels between non-equilibrium shocks (vertical lines) — it turns out the c-value is mostly about the shocks themselves.

The peak of shock n in (d/dt) log u(t) is aₙ/(4 bₙ) above the dynamic equilibrium α using the logistic function ansatz of step height aₙ and width bₙ. But again, we have that factor of ū to account for in relating Δu rather than Δu/u ≈ Δu/ū, which means that the shocks to unemployment are about 1/ū = 16.9 times bigger than the shocks to real GDP if c = 1. If c = 2, we have about a factor of 8.4. This turns out to be a better empirical fit (at least for more recent years):

So we end up with c = 2 because the shocks to the unemployment rate are about 8 times bigger than the shocks to real GDP and the average unemployment rate is about 5-6%. This is all to say that c = 2 is essentially a fluke of scaling two correlated relative rates of change. If we use that scaling factor of 8.4 to try and match (the log of) the unemployment rate and RGDP with a dynamic equilibrium subtracted (the correct frame), we can match the size of the steps without changing the scaling factor, but we have to move around the dynamic equilibrium and the offset (click to enlarge):

I had to change the dynamic equilibrium for Y = RGDP (γ) from 5% to 4% and eventually down to 2.4% to get these to line up (this is due to the demographic shift of the 1960s and 70s). Taking the rates of change ΔY and Δu removes the offset, but leaves the changing dynamic equilibrium which shows up in the graphic above as the size of the shocks not exactly matching.

Again, this makes Okun's law seem more like scaling two correlated series to match each other than any structural relationship between variables. Effectively, big recessions have big drops in RGDP and big spikes in unemployment while small recessions have small drops in RGDP and small spikes in unemployment. The fact that c = 2 means this proportional relationship hasn't changed very much over the past few decades (it's actually risen from about 1 in the 50s and 60s to about 2 in the 90s), but the actual value of c is an empirical point estimate. Mainly, c is based on the relative size of recession shocks to real output compared to recession shocks to the unemployment rate.

Unemployment rate holds steady at 3.8%

The unemployment rate reported today held steady at 3.8%, which continues to show that the dynamic information equilibrium model is better than forecasts from FRBSF, the FOMC, the CBO, and Paul Romer (click to enlarge):

I would like to give plaudits to Tim Duy and his observation about the Fed's reaction function:
It’s something I have been blind to - as long as inflation is not a problem, the Fed doesn’t hike rates when unemployment is flat (which is their forecast). This even held as recently as 2016.

The recent flattening of the unemployment rate data and the Fed's lack of hikes bears this out.


As a side note, it was probably a bit brash to put a forecast in my paper — but it has turned out pretty well (click to enlarge):