Saturday, August 31, 2019

Personal consumption expenditures and other data

The various components of Personal Consumption Expenditure (PCE) data came out today (here it is on FRED). One thing that the data revisions have done is made the hypothesized shock at the end of 2017/beginning of 2018 due to the TCJA in the dynamic information equilibrium model (DIEM) narrower (i.e. shorter duration) — but integrated it is about the same, it's just a bit higher for a shorter period. Here are the graphs of the level and rate (click to enlarge):

PCE tracks GDP fairly closely (in fact, they're almost informationally equivalent), so this gives us a hint as to how Q3 GDP will come out. However, both are lagging indicators of recessions, so this doesn't shed any light on US economic weakness either way.

The rate of change of the price level of PCE excluding food and energy, aka core PCE inflation, also has been consistent with the DIEM forecast since I started tracking it over two years ago:

*  *  *

There's been a lot of new about bond yields and fluctuations in the stock market these past couple weeks, however the story remains for the most part the same. Here's the 10-year rate forecast from four years ago that's still doing well — the rate dove down close to the lower edge of the expected fluctuations but is still consistent with the information equilibrium (IE) forecast:

BCEI is the Blue Chip Economic Indicators forecast (in red) of the same vintage. It's done ... poorly.

The other interest rate I've been tracking is Moody's AAA rate, for which the daily observation is now at the lower edge of the fluctuations in the monthly average band:

That gray vertical band is the estimate from here of the recession onset relative to yield curve inversion (using the median of multiple spreads, which turns out to be remarkably close to the principal component [1]). I've added monthly averages to the figure (in orange) because the various indicators were computed using monthly averages, not the daily data (red) which is just for tracking purposes:

The daily data has entered the range of the lowest spread observed before a recession for the past three recessions, so the monthly average will probably be close. The recession onset once hitting this lowest point was between one and five quarters since the 90s in the US. Note that this is not a rigorous analysis, just a comparison of against the prior three recessions for context.

Speaking of comparisons against prior recessions that aren't rigorous but rather just context, here's the S&P 500 forecast from two and a half years ago overlaid with a counterfactual shock comparable to the 2000 recession shock:

The post-forecast data is in black. As we can see, the data is falling consistently below the center prediction, but is still within the error band (the errors tend to be correlated in the short run, but longer run are closer to normally distributed).

As a side note, I've often encountered detractors that say the error bands on these forecasts are quite  large. However, despite their considerable size, they represent separation between predictable trend and unpredictable human behavior. The probability that someone is selling you snake oil (or insider information) rapidly approaches 100% as the error bands tighten from roughly this size. There's only so much that is knowable about a complex adaptive system.



[1] Here's the average (blue), median (yellow) and principal component (green) [click to enlarge]:

Wednesday, August 28, 2019

Milton Friedman's Thermostat, redux

Ext. Dagobah — Swamp

Jason: It seems monetary policy and inflation are completely uncorrelated. It seems reasonable to believe monetary policy doesn't actually affect inflation.

[Milton Friedman appears as a force ghost dressed as a Jedi from behind some foliage.]

Milton: I see you haven't heard my thermostat argument! Imagine a car ...

Jason: Actually, I have but ...

Milton: [Undaunted] ... driving on a hilly road trying to keep the same speed. If the driver was really good, the speed on the speedometer would be constant and you'd see the gas pedal go down and up in perfect correlation with the hills. But what you wouldn't see is speed changing — it'd be uncorrelated with the hills and the gas pedal.

Jason: Wait, is this a speedometer or a thermostat?

Milton: Quiet, you! I'm not finished ... Now if the driver wasn't very good, you might think you could tease out the relationship by looking at the gas pedal and the hills. But no! All you'd see in the gas pedal data when compared to the hills are the driver's random errors. No information about the relationship between the gas pedal and speed is available.

Jason: Ok, but how did we figure out looking at the gas pedal was important?

Milton: This isn't about whether we know about the gas pedal. We could be ignorant of the gas pedal — the point is that the model could exist!

Jason: So assume a complex model relationship between gas and speed when there appears to be no correlation?

Milton: Yes!

Jason: Sounds kind of like the opposite of Occam's razor to me. I think I'll stick with Occam.

Milton: Wait, I mean no! Anyone can see monetary policy affects inflation.

Jason: How?

Milton: Look at hyperinflation!

Jason: Ok, but can we extrapolate from 100% inflation down to 2% inflation? That's equivalent to extrapolating processes that happen on a time scale of a year to a time scale of 50 years ...

Milton: Gah! Physicists!

Jason: In fact, data seems to show a definite change in behavior around 10% inflation, which is remarkably close to the time scale between recessions ... [trails off, staring up at the sky]

Milton: Look, you. We have lots of evidence that monetary policy affects inflation.

Jason: Awesome! Why didn't you just show me that evidence instead of basically telling me that Occam's razor isn't always right? I mean, Occam's razor is a heuristic, not a theorem ... of course it's not always right. So are the models built using this evidence pretty good at forecasting, then?

Milton: Well, not exactly ...

Jason: Hmm. Can I see your evidence monetary policy affects inflation?

Milton: Here you go! All the evidence that monetary policy affects inflation!

Jason: Thanks, wow! Why didn't you just show me this in the first place?

Milton: I wanted to teach you about the thermostat!

Jason: But the reason we don't go with Occam's razor in this case is that we have all this evidence you just showed me ... it has nothing to do with thermostats or speedometers ... that's just question begging ... assuming we already have all this evidence ...

Milton: You're welcome!

[The force ghost suddenly vanishes.]

But here's what really happened ...

Jason: Hmm. Can I see your evidence monetary policy affects inflation?

Milton: You see, you won't be able to tease it out of the data. Imagine the Fed is a thermostat keeping a constant temperature ... the turning on and off of the heater is going to be completely uncorrelated with the temperature inside the house.

Jason: That's the same argument as the speedometer. Are you just trying to get out of showing me evidence because you don't have any?

Milton: You see, what I said is true ... from a certain point of view.

Jason: Certain point of view!??

Milton: Bye!

[The force ghost suddenly vanishes.]

Monday, August 26, 2019

A Solow Paradox for the Industrial Revolution

I've been toying with the idea of applying the Workers' History methodology to the Industrial Revolution and the rise of "capitalism" for my next book. The recent 1619 project articles in the New York Times magazine set off a weird firestorm on the internet involving this very subject.

The underlying debate here appears to be a moral/ethical one — are capitalism and the industrial revolution (IR) the offspring of slavery (and therefore "tainted" morally), or did they help bring about slavery's demise (as a technocratic "white savior")? Was the wealth of the US (and/or the UK) built on slavery or was growth and industrialization in the Southern US hindered by it?

I'm not going to be the person who answers this moral question, but one thing that I do think I can contribute to is analysis of the time series data. If we can get the events in the time series straight, then it helps focus the discussion of moral questions.

In fact, I already have looked at this a bit, inspired by Dietrich Vollrath's great blog post on the question of when "sustained growth" started [0]. Recent analysis of the data seems to point to an earlier starting point around 1650:
"... the onset of sustained growth in annual earnings much earlier than the actual Industrial Revolution. Both the GDP per capita and the annual earnings series being to accelerate around 1650."
Emphasis in the original. When I looked at the UK annual income data index with the dynamic information equilibrium model [1], I came up with similar results — possibly even earlier due to an overlapping negative shock to income growth in the late 1500s. This earlier shock may be purely a nominal one due to the so-called price revolution.

Important observations in this framework are that:

  1. The growth shock to UK income matches up with the slave trade
  2. The IR comes along as surge in income growth fades (i.e. no income growth from the IR)
  3. It's not a permanent shock to sustained growth, but rather part of a series with the second shock coming in the 1830-40s possibly associated with the railroad boom in the UK

As an aside, I noted parallels between the IR the Solow paradox/IT revolution — both occurring as a growth shock fades (slavery, women entering the workforce), and neither showing up in macro growth metrics. This discussion brought up some additional questions about the causality — did the IR cause the decline in the slave trade? But the data on the number of African slaves trafficked shows the fading of the growth shock had already begun before the IR:

This graph shows that if we just look at data before 1780, we still see the same saturation (purple dashed curve). It also shows that abolition comes as a genuine surprise in this data at this resolution (25 years) — only appearing in the last data point.

A plausible interpretation of events here is that exploitation of slaves began to see diminishing returns so that investment was directed elsewhere (i.e. seeking "alpha") — in particular the rail boom (that took over transportation from the canal system). The products of the industrial revolution — specifically rail — were a plausible target [2]. Whether abolition forced this shift in attention or instead just came after slavery was no longer as lucrative (and rail became lucrative) is not definitively adjudicated in the data, but the latter proposition has slightly stronger evidence.

This doesn't really say whether slavery caused (e.g. funded) the IR, but it does say that the IR did not cause the decline in slavery — slavery might have just been limited by its own logistics. The Haitian revolution (1791-1804) might be seen in this light as evidence of the limits of controlling slaves. In the aftermath, white Southerners in the US moved toward tighter controls which may have impacted exploitative growth in slavery. It's also possible practical limits on the number of slave ships traversing the middle passage intervened. Whatever the reason, slavery's expansion slowed because of factors that would have been already apparent in the first half of the 18th century.

The other question is whether "investment" in exploiting slaves delay industrialization of the US South (or even more broadly in the British Empire). This counterfactual analysis is possibly unanswerable as it involves knowing what redirecting investment to other areas (like industrialization) would have accomplished. However, there's something that came up when I began reading about this aspect — a myth about Eli Whitney's cotton gin.

I was reading this Bloomberg article by Karl Smith summarizing one case that instead of being a source of growth, slavery held back growth in the US compared to a (dubious) counterfactuals. In it, Smith says that:
"In 1795, the year after the invention of the cotton gin, the U.S. produced 8 million pounds of cotton. Widespread adoption of the gin raised that to 40 million pounds by 1801."
The implication here is that the cotton gin had an impact on cotton production. However, the only apparent change in cotton production in the US is a surge that begins sometime before 1790, with the gin coming right in the middle of that surge in 1795:

I made the cheeky suggestion/hypothesis that the legal framework established by the adoption of the US Constitution was a more likely cause of that jump in cotton production. But it's also plausible that the end of the US Revolutionary War resulted in some "catch-up" growth along with opening up new markets besides Britain — remember that aim of the revolution? In any case, the data shows precious little else happened between 1790 and 1860 except for that 10 year growth spurt at the beginning. The war of 1812 is almost indistinguishable from a statistical fluctuation.

Likely because of my claim, Sri Thiruvadanthai sicced Pseudoerasmus on me who agreed with my point about the cotton gin but then said my interpretation of the time series was "silly and preposterous" [3] before sending me a time series that not only didn't support Pseudoerasmus' claims about it (there is no "surge" in British demand evident in the data) but in fact confirmed my claims that if anything happened, it happened before 1790. Pseudoerasmus' time series came without a source, but covered cotton imports to Britain from 1778 to 1819. As you can see there are very few features in the data besides a surge around the end of the US revolutionary war and a fluctuation around the war of 1812.

There's actually a bit of below trend imports right in the middle of the US production surge!

My claim that nothing happened after about 1790 holds up even if you look at that data with a pure logistic description (per discussion with Michael aka @profplum99 on Twitter):

You might ask what level of confidence we should have in using these simplistic models to describe the data. The truth is that there's so little data (~ 70 points for US production, ~ 41 points for UK imports), it cannot support a complex model. In fact, a heuristic estimate (1 parameter per 20 data points) says that anything beyond 2-3 parameters is probably over-fitting leaving us with log-linear models. With circumstantial evidence (independent measures of the timing of the wars), we can probably add a couple more.

Of course, Pseudoerasmus takes it a bit further (here, here) ...
England imported 7 million lbs of cotton in 1780 but 56 mn lbs in 1800. There was this thing called the Industrial Revolution going on, Jason might have heard of it. At the same time, there was a surge in cotton output not only in the USA, but also in the West Indies & Brazil. 
The USA just prior to the Louisiana Purchase in 1803. the southern states but especially Georgia opened up new (within-state) frontier lands, one major reason being to plant cotton to meet suddenly booming British demand. 
It's pretty simple: the extra 50 million pounds of cotton (esp long-lint cotton) England imported by 1800 (relative to 1780) could not be all met from traditional sources. Also states like Georgia only acquired its hinterland after 1776.
As we can see, these claims from Pseudoerasmus are not supported by the data. There was a surge around the US Revolutionary war and a statistically significant drop around the War of 1812. There is no signal from the industrial revolution, and growth proceeds at roughly a constant rate from 1800 to 1860 (US production data) or 1790 to 1820 (British import data). Any causal factor happens before 1790. It is possible these claims might be supported by evidence besides this data — however, that would mean his claims still had no impact on the recorded time series and historical estimates.

To a great degree, it seems there's a "Solow paradox" around the Industrial Revolution — it shows up everywhere except the macroeconomic statistics [3]. The primary effect is that the IR appears to have provided the technological substrate for the railroad boom in the UK that ended in the Panic of 1847. The IR might have had an effect on manufacturing and industrial processes, but many of those got their start in gun manufacture (which incidentally, was a "medium of exchange" for the slave market). Plus, any growth beyond the 1840s is more likely dwarfed by sanitation improvements and the resulting population growth. 

Where are the macro effects of the industrial revolution?



Also in Karl Smith's article, he makes a claim about growth in cotton production that is basically false — while the saturation level might have been higher (likely due to cotton being grown in more areas of the US without having to compete with slave labor), the growth rate was only 8.5% after the Civil War while being 9.0% before it:



[0] It also points to Malthus possibly being wrong even in the time he was speaking — or at least his mechanism had a smaller impact than is commonly assumed.

[1] Paper here. The model itself is a maximum entropy approach to complex systems where exponential growth is an equilibrium with sparse non-equilibrium "shocks" away from it. In a sense, we are making minimal assumptions about the underlying processes given the guiding assumption that growth rates are well-defined observables. If growth rates aren't well-defined observables, then pretty much any question about economic growth is actually moot.

[2] As a second parallel between the post-WWII period and the IR, we have a rail boom and bust coming after the growth surge of the 1700s fades while in the US we have a dot-com and a housing boom (and respective busts) after the growth surge of the 60s and 70s fades.

[3] It seems to show up in the micro statistics — in the productivity of individual laborers given industrial equipment to run. But it's a fallacy of composition to assume these micro impacts aggregate to a macro effect.

Sunday, August 11, 2019

The Phillips curve and The Narrative

Illustrious Harvard economics Professor N. Gregory Mankiw wrote something in the New York Times about the Phillips curve a couple days ago. I wish he had written it a couple months ago because I would have used it in my book as a wonderfully distilled example of the dominant — yet largely unfounded — narrative about inflation. It's the just-so story many economists and pundits tell about the 20th century. Instead, I started off with a different quote with a different story (click to enlarge):

I did think that Lyndon Johnson shoving the Fed chair and causing inflation was a nice encapsulation of both the just-so story and the focus on macho men distracting from the actual cause being women (more later). But here's Mankiw, explicitly mentioning Milton Friedman and adding the “oil shocks” (chef's kiss) to the Vietnam spending narrative:
Soon after the Phillips curve entered the debate, economists started to realize that this trade-off was not stable. In 1968, Milton Friedman, the economist and author, suggested that expectations of inflation could shift the Phillips curve. Once people became accustomed to high inflation, wages and prices would keep rising, even without low unemployment. Soon after Mr. Friedman hypothesized a shifting Phillips curve, his prediction came to pass, as spending on the Vietnam War stoked inflationary pressures. 
In the mid-1970s, the Phillips curve shifted again, this time in response to large increases in world oil prices engineered by the Organization of the Petroleum Exporting Countries — an example of a “supply shock” in economists’ parlance.
So much derp!

Here's a (color!) version of the economic seismogram (a more conservative and visual representation of Granger causality) I used in the first chapter of my book to explain how the causality just doesn't match up. The bands indicate positive and negative shocks to equilibrium growth or decline in the various measures (their width indicated the duration of the shock much like the standard deviation indicates the width of a normal distribution). But now, I've added the Vietnam war deployed troop strength (source) at the top ... (click to enlarge)

Yes, the Vietnam war not only precedes the long (and fluctuating “cyclical” component, denoted with “cyc”) shocks to CPI and PCE measures of the price level, but women's labor force participation (CLF W and EPOP W) — the major component of my hypothesis that labor force size is behind inflation. However, Vietnam precedes the center of the price level shock by almost 10 years. That's a long time between cause and effect. It's possible Vietnam might have had something to do with the cyclical rise around 1970, but what about all the others continuing through the 90s?

The oil price story also looks plausible — until you get to the larger oil price shocks in the 90s and 00s that are not causally associated with bursts of inflation (the 90s one comes late, and there's no 00s one at all). Additionally, the exact same pattern appears in both CPI (which includes energy) and core PCE (which doesn't). In fact, the business cycle fluctuations are almost identical in magnitude in the two measures.

So we already have two just-so stories to explain the first three “cyclical” shocks to inflation in the 60s and 70s. It's weird that Mankiw includes the monetary flex:
For centuries, economists have understood that inflation is ultimately a monetary phenomenon.
Sure you have! That's why macro forecasting works so well. Oh, wait. But then shocks to the monetary base follow the shocks to inflation, and the unprecedented rounds of QE result in “lowflation”. Guess we need another just-so story! And that can't be about inflation expectations, because the empirical data we have (e.g. the Michigan survey) appears to be entirely backward-looking — surges in expectations follow surges in actual inflation. Time for some time travel!

The most convincing evidence for me is that people (particularly women) entering the workforce in the 60s and 70s through the 80s and 90s explains several different parts of this story in the diagram above:
  • Inflation reaches its peak about 3.5 years after CLF growth does, and when CLF declines in the Great Recession, inflation reaches its nadir (“lowflation”) about 3.5 years later in 2013.
  • Those two changes are of comparable magnitude — the smaller CLF decline in the Great Recession results in a commensurately smaller decline in the price level.
  • The “Phillips curve” is strong when women's labor force participation is rising from the 60s until the 90s. You can see “cyclic” CPI and PCE inflation surging during the latter half of periods of growth between recessions and flagging when unemployment spikes in a recession.
  • The “Phillips curve” is weak to non-existent after women's employment population ratio stops increasing and becomes strongly correlated with men's starting in the 90s.
  • The curve in Phillips (1958) is based on data from the UK during a period including WWI and WWII where soldiers re-enter the workforce en masse. I've seen a similar Phillips curve effect during the immediate post WWII period in the US.
  • This picture doesn't require a “just so” story about Vietnam war spending and oil shocks.
  • The same mechanisms appear to be at work in more than just the US — including Japan.
  • Monetary base shocks follow inflation shocks. We could still have monetary “hyperinflation” because the data shows a definite break in the behavior between inflation below about 10% and above 10%.
Mankiw also give us an example of the quick elision between the empirically well-founded piece of the Phillips curve that was in Phillips original paper — the relationship between wage inflation and employment — and the completely speculative macro-relevant piece — the relationship between price level inflation and employment.
But when unemployment is low, employers have trouble attracting workers, so they raise wages faster. Inflation in wages soon turns into inflation in the prices of goods and services.
The "soon" is doing a lot of work here in that second sentence. And the empirical relationship, while tight in the 60s, 70s, and 80s, hasn't manifested in CPI or PCE inflation for decades. This is the vanishing macro-relevant Phillips curve. I have a lot more about both versions of the “Phillips curve” in my overview post from last month.

As I mentioned at the top of this post, the first chapter of my book is about pointing out the inconsistencies in the dominant “narrative” and proposing that the real reason was the surge of women entering the workforce (to a lesser extent, the baby boom contributed a small increase noticeable in men's labor force size but dwarfed by women's increasing participation). But that's just one “narrative” that's widely shared without a lot of evidence. I go after two more “narratives” in my book: 1) the fall of unionization is the reason behind the decline in labor share of income and slow wage growth, and 2) the housing bubble was brought about by financialization and deregulation. I argue that these are incorrect and in fact: 1) unions appear to only have an effect on inequality, not wages (which are slow growing because that surge of women entering the workforce has ended), and 2) the housing bubble wasn't so much of a bubble but rather a structural unaffordability baked in by “the little xenophobia” of Nimbyism and de facto segregation through housing prices.

If you're interested, check it out!


Update 12 August 2019

There's more in this post, in particular two graphics on the Phillips curve that show a different way to visualize the changes. The first one illustrates where the correlation with men's EPOP as well as the strength (i.e. slope) of the Phillips curve:

The second shows the dynamic information equilibrium model (DIEM) for the cyclical fluctuations PCE inflation alongside the DIEM for the unemployment rate. It makes the inverse relationship very clear in the 70s and 80s and shows how it faded away ...

Tuesday, August 6, 2019

JOLTS data and Korean unemployment

I had an early morning and all-day meeting at work today so didn't get to look at the JOLTS forecasts in the light of the latest data release. Again, we continue the status quo where openings, separations and quits are all showing deviations consistent with the leading edge of a recession ... and hires continues to show no signs of any changes (click to embiggen):

I'm still using the 2019.7 year to fix the recession shock to be consistent with the previous counterfactuals — though it's increasingly looking like the center will be later. (In fact, the 2019.7 date is actually the recession onset in the original determination.)

*  *  *

In addition to JOLTS data, John Handley on Twitter low-key challenged me to look at the unemployment rate data for South Korea:

There might be an additional recession in the 90s (it's within the noise), but otherwise it looks like a dynamic information equilibrium model with a bit of a step response (red dashed line is kind of a heuristic sinc function response) in the Asian financial crisis and a local version of the long, slow unofficial "recession" that appears in Australia in the last decade (see here, here) associated with the commodities slowdown. It's not necessarily the cause, but it looks related in terms of magnitude and duration.

Sunday, August 4, 2019

UK productivity back to the 1800s and the new normal

I'm in the process of reading Forecasting (2019) by Jennifer Castle, Michael Clements and David Hendry in part due to a review by Diane Coyle. It's actually due to a line Coyle wrote in the review that I disagree with:
It explains the inherent difficulties in trying to forecast the future of a complex non- linear, non-stationary system in which behaviour can be affected by forecasts themselves, all from a limited amount of past data.
I don't disagree with the inherent difficulties in macro forecasting, but rather the characterization of macro as a "complex, non- linear, non- stationary system" — we don't really know that. I'd rewrite it like this:
It explains the inherent difficulties in trying to forecast the future of a system we don't yet [fully] understand in which behaviour can be affected by forecasts themselves, all from a limited amount of past data.
You can take or leave the fully in there. But it was due to that characterization that I thought it would be great for me to read a book about forecasting written by forecasters to potentially understand the unwritten assumptions and frameworks.

And so far, it's quite good as an introduction to forecasting for a non-technical audience. One of the things they point out early on is the apparent divergence from the log-linear growth in labor productivity in the UK and later the "hedgehog" graphs that miss the mark (from the book):

I wrote a post about interpreting UK productivity growth a year ago — and how the log-linear extrapolation leads you astray. But reading the book made me look up the long run data sets and check out what the dynamic information equilibrium model (DIEM) says ...

It's a simple model with one shock — the 20th century demographic shock associated with women entering the workforce (data from here) ...

... as well as the spike in inflation and various other macro measures.

But one thing it's important to point out is that this view of the data sees UK productivity growth in the 2000s as largely a "bubble" that evaporated in the Great Recession with the recent data being the "new normal". Or a better way to put it — a return to equilibrium after the growth of the 20th century.

It looks roughly the same for the US — with the recent data being the "new normal" (though there might be some uncertainty).



Edited an awkward sentence in the paragraph beginning "You can take or leave ..." to be slightly less awkward. But only slightly.

Saturday, August 3, 2019

Nimbyism in the labor market, or static thinking?

I admit I'm a little puzzled by a what a trend in wage *growth* is supposed to represent. What's the story about the economy in which raises increase a little bit faster each year?
That was J. W. Mason on Twitter in response to Ernie Tedeschi showing a linear trend in wage growth in a graph. Of course, Ernie is correct about it's existence meaning this is a theoretical problem. In fact there's a (log-)linear trend interrupted by recessions as well as the 2014 "mini-boom" since the 80s:

Identifying that structure is essentially the core of the dynamic information equilibrium model of wage growth (DIEM, paper on SSRN here) that I've used to successfully forecast wage growth since February of 2018:

My suggestion on Twitter for a potential avenue to make sense of this trend was to look at a place where a similar mechanism appears to be at work over the same period of time — housing prices (and here):

In my book, I suggest that this is a result of a nexus between housing prices, wage growth, de facto segregation, and nimbyism that results in white people essentially pricing non-white people out of their neighborhoods — which ends up pricing themselves out of their neighborhoods (and subsequently gentrifying others). What if restrictions on employment — prior experience, degrees, non-competes, etc — were acting on wages in the same way that social segregation and restrictions on building affordable housing (or even housing in general) on housing prices?

It's a plausible hypothesis — companies artificially (or socially) creating a shortage of ("acceptable") labor would make labor markets tighter for the individuals who met the restrictive qualifications in the same way the artificial (or social) restrictions on where people can live make housing markets tighter. "Desirable" jobs become like "desirable" neighborhoods with accelerating prices.

I'm not 100% behind this hypothesis, however. For one, the pattern is largely the same across income quartiles (available in the same Atlanta Fed data set, and that I looked at thanks to a question on Twitter from Patrick) — if it's happening, all wage levels are being impacted by labor market "nimbyism" (click to enlarge) [1]:

If we turn back to the housing price analogy, this would be like San Francisco, CA and Peoria, IL both having the same level of  "nimbyism" and accelerating prices — in fact, it would be like Peoria having a stronger acceleration since it's the 1st quartile that shows the effect most strongly.

But for me, the stronger evidence is that wage growth shows the same structure as JOLTS hires and the unemployment rate — implying it's part of the deeper structure of the labor market. In fact, it's precisely analogous to the regular, steady rate of decline in the unemployment rate that seemed to surprise at least a couple of people in the audience at my talk at the UW econ department:

That change in perspective is directly behind the success of the unemployment rate DIEM in the face of the competition (and related to the success of the wage growth model at the top of this post):

This is to say that J. W. Mason's confusion about the reason behind accelerating wage growth is a result of the same static equilibrium picture of the economy behind models of unemployment that build in a "flattening out" despite it almost never happening in the historical data. I discuss this "steady state" (per Moretensen-Pissarides 1994) thinking more in this post in the context of matching theory. Mason appears to share mainstream consensus that the labor market conditions were different when unemployment was above 5% several years ago compared to today's levels — his main difference is in his estimation that the "full employment" rate is lower than currently observed. 

I'm not singling out Mason because he's particularly wrong — I'm singling him out because I'm trying to emphasize this is a general view held by the broader economic consensus that goes deeper than left-right, socialist-neoliberal, or even mainstream-heterodox divides.

Aside from a brief "mini economic boom" in 2014 [2], the US labor market was (and continues to be) in the same dynamic equilibrium from roughly 2010 to the present day. This dynamic equilibrium appears in the unemployment rate data, JOLTS data, and, as we started out with here, wage growth data. Aside from that mini-boom, nothing of macroeconomic significance has happened in the US labor market since the Great Recession [3].

Of course, "wage growth climbs because that's what we observe" is not really an explanation. But it's also not a "puzzle" specifically in the recent data. However, I don't think anyone has come up with an explanation — I think it's an unresolved problem in economics. I have been working on understanding these dynamic equilibria in terms of maximum entropy distributions of growth states. I call them k-states in reference to the information transfer index I typically represent with the letter k. These are effectively growth states (i.e. the growth rate of some observable is k r where r is some fundamental rate like population growth), and stable distributions of them appear to pop up in e.g. stock markets or profit rates. Stable distributions of k-states give rise to stable ensemble averages 〈k〉, which are observed as these "dynamic equilibria". There's a lot more mathematical detail in my SSRN paper, but you can also check this blog post. But again — I think this is an unresolved problem in economics.



I did want to note that in the housing prices case, the structural similarity to wage growth begins in the 70s, whereas e.g. the unemployment rate has the same structure going back as far as we have data (even including the Great Depression).



[1] The main differences lie in the overall rate of wage growth acceleration as well as the structure of the non-equilibrium shocks. The 2nd and 3rd quartiles have what looks like a step response (which can take the form of two simultaneous shocks in opposite directions), but the 1st quartile's rebound is so delayed that it's difficult to consider it anything other than an additional shock. That delayed shock lines up with positive shocks that look like part of the 2014 mini-boom in the 2nd and 4th quartiles — in fact, it would appear that the 1st quartile is responsible for most of the 2014 mini-boom signal in the aggregate data. You might squint and see a bit of the 2014 mini-boom in the 3rd quartile, but overall it's too uncertain to posit a shock.

What's interesting is that in the data by quartiles there appears to be a negative shock in mid-to-late 2017 in at least three of the series. In the aggregate data, the 1st quartile positive shock is much larger so we end up not seeing the smaller negative shock in the aggregate data with any certainty. I imagine it was what I was seeing in this post.

[2] Note that this boom appears to have happened in the EU as well, but about 2 years later. So it could in principle have been caused by US-specific policy that led to a world-wide economic boom (the US is a sizable fraction of the world economy) — but I think there could be an as-yet-unidentified common factor behind it. 

[3] In the EU, there was a double dip recession — a second rise in the unemployment rate (see [2]).