## Thursday, October 18, 2018

### Limits to wage growth

It started off with a simple observation prompted by a Twitter thread: since wage growth tends to increase between recessions (i.e. wages accelerate) in the dynamic information equilibrium model (DIEM) while NGDP growth appears to be roughly constant in the absence of an asset bubble or major demographic shift (and especially in the post-Great Recession period), at some point wage growth would exceed NGDP growth. What happens then?

There are a couple of things that could happen:
1. Additional consumption by people with higher wages can spur nominal growth (due to wage-led real growth or wage-price spiral)
2. Investment declines as wages eat into profits (e.g. the Marxist view), prompting a recession
There are other theoretical treatments of this scenario, and all of them seem plausible. My question was more about what the data says. I set about combining the wage growth DIEM (green) and the NGDP DIEM (blue) [1] onto a single graph. The result shows that since the 1980s, when wage growth hit NGDP growth, we got a recession. There's even a hint that the same thing happened in the 1980s based on other data (FRED, larger green dots). Click to enlarge:

The wage growth data from the Atlanta Fed is in green (small green dots), while the NGDP growth data from the BEA is in blue (blue dots). The asset bubbles and crashes (dot-com, housing) are shown as dotted blue lines, but the main trend of NGDP during the fading demographic growth surge is shown as the thick blue line. The former don't show up very strongly in the labor force, while the latter does — that's why I think the trend is more relevant.

It is possible that rising wages in the 1990s led to the increased NGDP growth (wage-led growth). However, it is also possible that the asset bubble (dot-com) allowed wages to rise a bit more above the NGDP trend than they would have otherwise. What is interesting is that the "housing bust" happens a bit earlier than the 2008 recession — which doesn't actually happen until wage growth reaches NGDP growth.

If we project wage growth and NGDP growth using the models, we find that they cross-over in the 2019-2020 time frame. Actually, the exact cross-over is 2019.8 (October 2019) which not only eerily puts it in October (when a lot of market crashes happen in the US) but also is close to the 2019.7 value estimated for yield curve inversion based on extrapolating the path of interest rates. I put in a counterfactual recession in wage growth to show what it might look like.

In any case, this provides a test: will NGDP growth increase (wage-led growth), or will we get a recession due to limits to wage growth? Or will neither of these happen — and the models turn out to be wrong?

One other thing to note: this would be almost completely unobservable without the dynamic information equilibrium model and the low noise wage growth data from the Atlanta Fed. NGDP growth is extremely noisy, and other measures of wage growth are much more uncertain (ECI, or the aforementioned national income). However, extracting the trends of the data using the DIEM allows this pattern to emerge.

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Footnotes:

[1] Here are the wage growth and NGDP DIEMs compared to data:

### The CBO forecasts unemployment (and so do I)

The Congressional Budget Office (CBO) forecast the unemployment rate over the next ten years back in April 2018. Their model (blue dashed line segments) is a pretty standard "natural rate"-like (equilibrium rate) model where unemployment has some non-zero equilibrium level (here, about 4.8%) it would eventually reach (shown in the graph above). However, nothing analogous to the path they propose nor the equilibrium level it sustains has ever been observed in US unemployment data over any 10-year period.

Of course, the path from the dynamic information equilibrium model (DIEM, gray bands) over the same period (conditional on no recession) has also never been observed — at least for that length of time. It has been observed over e.g. the past 10 years, but the additional 10 years would make it a twenty year continuous decline in unemployment. This seems unlikely, but then Australia has done it with only a few blips — all much smaller than US recessions (unemployment rose about 1.5 percentage points during the Global Financial Crisis).

However, that unbroken decline would also make it a 20-year period without a recession, only seen in a couple countries (like the aforementioned Australia). Therefore I added a few possible counterfactual recession scenarios (gray dashed lines) to compare to the CBO forecast. Two of the scenarios have a height (severity) and width (measuring the steepness of the unemployment increase) taken from the average of the post-war recessions (7.9%, and rising over ~ 4 months, respectively). These two have different onsets: the first turns around during 2019 just like the CBO forecast, and the second takes off when the CBO forecast rises above the DIEM forecast. A third counterfactual matches the rise of the unemployment rate in the CBO forecast along with the height. This third counterfactual is effectively the recession that the CBO is forecasting from the standpoint of the DIEM.

One benefit of the DIEM is that it forecasts paths of unemployment that have observational precedent. A drawback to this is that if unemployment begins to exhibit behavior that has never been seen (like remaining constant for almost 8 years), it is unlikely the DIEM will be able to follow along. This makes the DIEM falsifiable, unlike the equilibrium rate models. Equilibrium rate models only have to claim that a recession intervened, and that unemployment will reach its equilibrium in another 10 years. But then, what's the use of an equilibrium rate that is never observed?

...

PS I'm not impugning the work of the CBO, which is tasked to forecast based on traditional understanding of the macroeconomy. However, most economists seem to only forecast a few quarters into the future (understandable) and the oddity of the traditional understanding (especially its lack of precedent in empirical data) only comes out over longer horizons. The Fed typically puts this as a vague "longer run" column in their projection materials [pdf]. The CBO forecast is one of the few to show what this looks like explicitly — in a sense, it's more honest.

## Wednesday, October 17, 2018

### Labor force participation and unemployment

I think sufficient evidence has accumulated to say that there was likely a positive shock to prime age labor force participation rate (LFPR) in 2016 associated with the shock lowering the unemployment rate (U) in 2014. I posited the existence of this shock based on the observed relationship between LFPR and the unemployment rate despite the limited evidence in the LFPR data itself. Much like how the similar shock structure of JOLTS hires, wage growth, and the unemployment rate imply a relationship that could be used for forecasting, the downward shift in unemployment in 2014 forecast such an upward shift in labor force participation some time later.

As we can see by comparing the models with and without the shock, it's definitely an improvement [1] (click to enlarge):

The relationship between LFPR and U implies a Beveridge-like curve — however it would be one that is completely obscured by the long duration of shocks to LFPR (it reacts slowly, while U reacts quickly with greater magnitude). The recent data remains consistent with the predicted relationship:

...

Footnotes:

[1] Of course, the data is still consistent with a somewhat higher value for the dynamic information equilibrium slope:

The next few months should allow us to distinguish between these models (as data will being to fall below the forecast relatively soon if the actual slope is lower).

## Tuesday, October 16, 2018

### Are consumption, income, and GDP different measures?

I read this great blog post by Beatrice Cherrier on macro modeling, and I plan on having more to say about it in the future. However, there was an example of discourse on modeling consumption and income that made me wonder: What is the relationship between consumption and income? Does income drive consumption? I used the idea here — that dynamic information equilibrium models (DIEMs) with comparable shock structure are related — to take a look at Personal Income, Personal Consumption Expenditures, and Nominal GDP (FRED series PI, PCE, and GDP, respectively). But the best I can conclude is that these data series represent the same information, and it is likely the differences are entirely measurement errors (questions of e.g. what is treated as income versus what agents think of as income). It's either that, or there's no fixed relationship — sometimes increased income drives consumption, sometimes increased consumption drives income.

Here are the DIEMs for the three data series — they consist of the demographic shock (increasing labor force participation by women) of the 60s and 70s and the boom-bust-boom-bust cycle of the dot-com and housing bubbles. There is a residual "business cycle" element on top of the demographic shift that I will discuss later. PCE is red, PI is purple, and GDP is turquoise (click to enlarge).

As far as can be gleaned from the data, the demographic shock as well as the 2001 and 2008 recessions are effectively simultaneous (the "asset bubble era"). The dot com asset bubble has income precede consumption and the housing asset bubble has consumption precede income (they both look statistically significant based on the errors estimates of the shock centers). If we look at the residual "business cycle" (the "Phillips curve era") after extracting the demographic shock, the measures are all over the place in terms of causality (aside from simultaneously falling during recessions):

The bottom line is that it seems more likely that the various discrepancies could be accounted for by measurement differences than, say, a nonlinear and complex relationship between consumption and income that fails to be measurable at this level of fidelity. True, it's Occam's razor, but the idea that to a good approximation consumption is 68% of NGDP [1] and 78% of income seems both useful and reasonable. Especially given the alternative is an armchair behavioral relationship that couldn't be rejected by data for at least another 100 years.

...

Footnotes:

[1] Actually, consumption is about 60% of NGDP before the demographic shift and rises to 68% after. A similar story is told using wages.

### JOLTS day (October 2018)

The Job Openings and Labor Turnover Survey (JOLTS) data for August 2018 was released today (available on FRED), and there aren't a lot of surprises from the dynamic information equilibrium model viewpoint (DIEM, described in detail in my working paper). Even the uptick in JOLTS openings doesn't entirely change the fact that most of the data since 2016 is part of a correlated deviation that could represent the beginnings of a recession at the end of 2019 or beginning of 2020. We'd really need to be seeing an openings rate of 4.9% and higher to discount that possibility. Recession counterfactuals shown as gray bands. As always, click to enlarge.

I'll also be monitoring the "alternate" model of hires (with a lower dynamic equilibrium rate and additional positive shock in 2014) based on a longer time series (discussed here).

Regardless of which model you use, the hires data continued the status quo implying (based on this model of combined DIEMs) that we should continue to see the unemployment rate fall through January of 2019 (5 months from August 2018) and wage growth continue through July 2019 (11 months from August 2018).

### Building "models"

Fabio Ghironi asked me about the dynamic information equilibrium models (DIEMs) as models in the economics sense (causal relationships between variables) rather than the physics sense (mathematical descriptions of data) at my talk for the workshop he organized. Much of the work I have been doing is in the latter sense, but I've also put together a few models in the former sense (e.g. a monetary one and an information equilibrium version of the 3-equation New Keynesian DSGE model).

I've been steadily working toward building some models based on the dynamic information equilibrium descriptions of data — I've been collecting useful descriptions of data in "macroeconomic seismographs" as a first step. With the longer hires series and similar shock structure to wage growth, I can show in principle how this kind of model building would progress.

First, one identifies multiple DIEMs with similar shock structure — the one that comes to mind most readily is wage growth, JOLTS hires, and unemployment:

We can perform a log-linear transformation (scaling) along with a temporal translation on each series to map them to each other. I chose to map wage growth and unemployment to the hires DIEM:

This tells us that e.g. the log-amplitude of the shocks to hires are about 0.3 times the size of the log-amplitude shocks to wages and unemployment, but more importantly that hires lead wages by 0.9 year and unemployment by 0.4 year. Basically:

UNRATE(t) = f(HIRES(t − 0.4))
WAGE(t) = g(HIRES(t − 0.9))

where f(.) and g(.) are log-linear transformations of the HIRES data. We could add e.g. Okun's law (see here) and labor-driven inflation (here) and get a description of RGDP, inflation, wage growth, and unemployment rate based on a single input (JOLTS hires). This model is effectively a "quantity theory of labor" model where the economy is driven by hiring.

One thing this model implies that given the hires data that came in last month (data for July), we should expect the unemployment rate to fall for at least another 5 months (from July, so until December) and wage growth to increase for another 11 months (from July, so until June 2019). What's interesting is that this suggests we should start seeing some kind of decline in the hires rate late this year or early next year if the yield curve inversion estimate is accurate. Of course, all of these estimates have an error on the order of 1-2 months.

## Monday, October 15, 2018

### Wage growth data from the Atlanta Fed

The Atlanta Fed released the latest data in its wage growth tracker, and it's consistent with the dynamic information equilibrium model:

### Interest rates and model scope

Along with the market slump last week, long term interest rates fell a bit resulting in a smaller spread. However, the data didn't fall even remotely enough to bring it back in line with the monetary information equilibrium interest rate model:

This model r10y = f(NGDP, M0) essentially says long term (10-year) interest rates are related to nominal output (NGDP) and the monetary base (minus reserves), and it's failing fairly badly as the Fed has increased short term rates (as I've mentioned earlier). In fact, most of the monetary models constructed with the information equilibrium framework have not performed very well.

There's a great story here about a naive scientist — trusting the zeitgeist and the public face of academic economics — building models where output, money, and interest rates were strongly connected, but that failed when compared to data.

However, there might be knowledge to glean from how this model is failing (which may be a failure of scope, not of the underlying principles). Don't read this as a defense of a model that isn't working (trust me, I actually relish the idea of more evidence that money is irrelevant to macroeconomics), but rather a post-mortem on a model that basically has the scope conditions of a DSGE model, as eloquently described by Keynes:
In the long run we are all dead. Economists set themselves too easy, too useless a task, if in tempestuous seasons they can only tell us, that when the storm is long past, the ocean is flat again.
That last bit about the flat ocean is the scope condition: an economy nowhere near a recession. Let me explain ...

I was looking at the model in the first graph above and noticed something in the data. The long rate seems to respond to the short rate — it seems almost repelled by the short rate as it approaches. Where that happens the model error increases. Here's the long rate model (gray) with the long rate data (blue) and short rate data (yellow dashed):

The strongest episodes are the 1970s, the 80s and the 2000s recession. Sure enough, if you plot the model error versus the interest rate spread the error increases as the 10-year rate and the 3-month rate approach each other:

As a spread decline (and eventual yield curve inversion) is indicative of a recession, this makes a pretty good case for limiting the model scope of r10y = f(NGDP, M0) to cases where the 10 year rate is higher than the 3-month rate (r3m). When it is out of scope, the model r10y ~ r3m ~ EFFR is a much better model [1]. That is to say: long term interest rates are the free market price of "money" unless the Fed is rapidly raising short rates (in which case it's a fixed price set by the Fed). This view makes sense intuitively, but also turns forecasting long term interest rates into an occasional game of "guess what the Fed is going to do" with short term interest rates.

...

PS

Here are the latest views of the rate spread (estimated recession onset in late 2019 to early 2020) and the dynamic equilibrium model of the interest rate (using Moody's AAA rate). Click to enlarge.

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Footnotes:

[1] In fact, it reduces the error by about 10%.

## Thursday, October 11, 2018

### Consumer Price Index (CPI) forecast performance

The latest CPI data was released today, and is basically in line with the dynamic information equilibrium forecast of inflation I've been tracking since 2017 (click to enlarge):

The dashed line shows a later estimate of the 2014 shock parameters from March of 2018. It has negligible effect on the rate of inflation, but did impact the price level (i.e. the integrated effect on the rate of inflation):

Basically, the shock was a bit smaller than the estimate from early 2017 (which was made while the shock was still underway).

## Tuesday, October 9, 2018

### Unemployment continues to decline — why?

The unemployment data came out the morning of the workshop at the UW economics department I participated in, so my plot of the unemployment rate in my presentation was out of date by a month's worth of data. Here's the updated plot — the 3.7% unemployment rate falls a bit below the forecast (and there appears to be a general positive bias to the model [1]):

Some of the questions I got at my talk were about the process behind the observation of the constant negative (logarithmic) slope of the unemployment rate outside of a recession. Overall, this seemed to be the empirical observation that contrasted most with the typical view in economics (either some equilibrium rate or something like a natural rate). I knew that it was, and it was part of the reason I chose the labor market as the primary focus of my talk [2]. My answer was some vague hand-waving about the matching function. However, I'll try to answer it a bit more coherently here.

I'll begin with the information equilibrium Cobb-Douglas matching function $M$

$$H = M(U, V) = c U^{a} V^{b}$$

where $H$ is JOLTS hires, $V$ is JOLTS vacancies (openings), and $U$ is the level of unemployment (number of unemployed people). Taking the logarithm, we obtain:

$$\log H = a \log U + b \log V + \log c$$

Now let's subtract $(a+b) \log L$ (the size of the labor force) from both sides. After some re-arranging, we get:

$$\frac{1}{a} \log H - \log L - \frac{b}{a} \log V - \log c = \log \frac{U}{L}$$

The right hand side is the unemployment rate $u$ (ratio of unemployed to the labor force). Taking the time derivative, we get:

$$\frac{1}{a} \frac{d}{dt} \log H - \frac{d}{dt} \log L - \frac{b}{a} \frac{d}{dt} \log V = \frac{d}{dt} \log u \equiv \alpha$$

The right hand side is the empirically observed to be a constant rate of decline of the unemployment rate (outside a recession). Since the terms on the left hand side [3] are all positive (increasing total number of job openings, increasing population, increasing total number of hires), we can see that the reason the slope is negative is because of labor force growth and job openings growth — and labor force growth is fairly tightly correlated with economic growth. As I put it in the talk, economic growth and the matching function eat away at the stock of unemployed people over time.

Now $\alpha$ being negative is not a foregone conclusion — the parameters of the matching function and the rate of population growth could be such that the unemployment rate increases (or stays flat) over time. So overall, the  slope of the unemployment rate outside of recessions is a measure of matching efficiency (high (absolute value) slope = efficient, low slope = not efficient).

Interestingly, a look at the data for the unemployment rate by education level finds that the efficiency is highest (and about equal) for people with college degrees or higher as well as high school degrees. It is lower for people with "less than high school", but is lowest for people with "some college". One way to interpret this is that having completed college or high school improves matching (completion serves as an indicator), while not finishing high school or not finishing college makes job matching more difficult (e.g. harder to evaluate than someone who is a high school graduate or a college graduate).

Additionally, matching efficiency by race is actually comparable for black and white people. This does not mean discrimination doesn't exist — just like how companies can heuristically evaluate college graduates with the same "efficiency" as high school graduates doesn't mean high school graduates are paid the same or treated with the same respect in the workforce as college graduates. It'd be better interpreted as companies having a better idea how to match high school graduates with high school graduate jobs — and, in the case of race, black people with "black" jobs. By efficiency, we don't mean an objective "good"; making prejudiced choices is likely faster and cheaper than striving to be unbiased despite being wrong. Higher "efficiency" could mean more discrimination.

...

Footnotes:

[1] This is likely due to beginning the forecast not just soon after a shock, but also at a point when the data was undergoing a positive fluctuation. Re-fitting the parameters, makes everything fit a bit better — but the recent data is still a bit low:

[2] Not only was this the most empirically successful aspect, but also one that showed a significant contrast with the traditional approaches.

[3] Also, if we assume the matching function has constant returns to scale (i.e. $a + b = 1$, as is empirically plausible per Petrongolo and Pissarides (2001)), we can simplify a bit (where $h$ is the hires rate, and $v$ is the vacancy rate):

$$\begin{eqnarray} \frac{1}{a} \frac{d}{dt} \log h - \frac{1-a}{a} \frac{d}{dt} \log v & = & \frac{d}{dt} \log u \equiv \alpha \\ \frac{1}{a} \frac{d}{dt} \log \frac{h}{v} + \frac{d}{dt} \log v & = & \alpha \end{eqnarray}$$