GDP data and a Beveridge (not Phillips) curve

Roger Farmer and Olivier Blanchard have been in a mini-debate about the Phillips curve on Twitter, and David Andolfatto has a nice overview. My thoughts on the Phillips curve are in a post from a couple weeks ago. But generally without a big upswing in labor force participation, price level (e.g. CPI) inflation and unemployment won't have a relationship. The only relationship will be between unemployment and wage growth — with unemployment shocks in recessions causing wage growth shocks six months later. If we take the models of wage growth and unemployment (click to embiggen):

... and combine them into a parametric plot, we get a Beveridge-like curve (though not as clean as the one between unemployment and vacancies described in more detail in my paper because wage growth fluctuations are smaller and the data noisier):

The black points [were supposed to be] the last 24 months of data [but I realized just now that I think I left off the last two years of data (it's using only the pre-forecast unemployment rate data which starts in January 2017) ... I will have to fix it. Update 9pm: Fixed.]. The light gray lines are the "equilibrium" paths in the absence of shocks (which move the path from one equilibrium to another) — data travels up these curves in equilibrium. Of course, this relationship between wages and unemployment was the one Phillips was originally talking about — not the macro-relevant Phillips curve relating price level inflation (e.g. CPI inflation) to unemployment.

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Added 31 July 2019

The ECI measure of wages also came out and the latest data is exactly where this forecast from a year ago said it would be:

Of course the "Ozimek curve", plotted versus prime age 'non-employment' (i.e. one minus employment) is effectively showing the exact same behavior as the "Beveridge curve" above. However since a) ECI is much noisier than ATL Fed data, b) ECI is only quarterly, c) ECI is a shorter time series, and d) 'non-employment' moves in a smaller range than the unemployment rate the actual result is less illustrative of the structure:

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[Back to the original post.] In other news, last week 2019 Q2 GDP data came out (along with some data revisions) which is basically in line with the dynamic information equilibrium model (DIEM) forecasts. Here's NGDP:

You can see the TCJA effect a bit more clearly, but it's still within the error bands of the model.

The FRB DSGE model forecast of RGDP has been as accurate as the DIEM in its mean forecast, but given its wider error bands we can say that the DIEM forecast is more informative:

Update 31 July 2019 

Thought I'd add PCE inflation as well ... same story as RGDP:

Continuing decline in the median house price

Every decline of the same (log) scale in the median house price (FRED) as the current one has been associated with a recession. Of course, there have only been three times in the data since 1963 — the 1970 recession, the 1990 recession, and the 2008 recession.

As I have noted previously on twitter (and in my book), the Case-Shiller housing price index and wage growth have similar structure since the 70s (click to enlarge):

My hypothesis here is that "white flight" and de facto segregation has set up a dynamic where white people essentially drive up housing prices so much that they price themselves out of housing — requiring a crash of some kind. This dynamic is not entirely dissimilar to the hypothesized "limits to wage growth", where nominal wage growth between recessions climbs until it exceeds nominal GDP growth and triggers a recession. Which of these mechanisms is the more fundamental is not clear, but there was a recession without a (significant) decline in housing prices (Case-Shiller or median) in 2001. However the 2008 and 2018-9 (i.e. recent) declines in housing prices seem to have preceded (be preceding) declines in labor market metrics.

In any case, this looks like it could be a leading indicator — and some proposed mechanisms of recessions involve people thinking they're poorer than they used to be (e.g. their house isn't worth as much) and cut back on spending. As a side note, in the once hot housing market in Seattle where I live the "For Sale" signs seem to be sticking around for a lot longer than they used to [1].

The latest data came out this week and we're still seeing the non-equilibrium shock (per the Dynamic Information Equilibrium Model or DIEM) we saw in the last update:

Also, rental vacancy data came out today and depending on whether the DIEM has a slightly negative dynamic equilibrium rate (−0.5%) or a 0% rate is still undetermined:

I've been following this for over two years now. However — no non-equilibrium shock to rental vacancies.

Footnotes:

[1] Actually true! (Especially accounting for the seasonal cycles).

Unemployment Rate: Backstroke of the West

I've been interested in labor market data for Washington state — a) because I live there, and b) because there was a natural experiment where the minimum wage was raised to $15 — as well as the West Census Region (WSR). It seems that the region might be showing some economic weakness, and possibly showing signs of recession earlier than the rest of the US. See here and here for some earlier looks.

First, it still looks like a deviation in the unemployment rate for Washington state:

But compared to earlier pictures, the error bands have tightened quite a bit in the counterfactual (purple). This doesn't mean they won't expand again (see e.g. here, going into the Great Recession) — in fact, it means there's more certainty we're seeing a shock.

The same shock appears in the WCR unemployment rate (which population-wise is dominated by California):

Little blips like this have happened before (in particular in the 90s), so this is not proof positive a recession is beginning. However, like the broader US, we are seeing a deviation indicative of a non-equilibrium shock in several of the JOLTS measures for the WCR (click to enlarge):

And also like the broader US, the hires measure is showing a lot less of a deviation than quits or openings. But WCR JOLTS hires are showing more of a deviation than the US JOLTS hires, possibly helping us understand how the blips above show up in Washington state and WCR unemployment rate data while being absent from the US unemployment rate data.

Mis-measurement of the unemployment rate?

A recent NBER working paper [pdf] has called into question the BLS measurement of the unemployment rate, concluding that the metric is actually a couple of percentage points higher than reported. The paper is "Measuring Labor-Force Participation and the Incidence and Duration of Unemployment" by Hie Joo Ahn and James D. Hamilton (2019) — and a H/T to Ernie Tedeschi and Ben Casselman for it appearing in my twitter feed. The overall difference appears to be that it's almost a uniform shift to a higher rate, but my question was whether/how this impacts the dynamic information equilibrium model (DIEM).

Here's their result for the unemployment rate (they actually look at multiple measures) and the DIEM fit to their adjusted data:

This adjusted unemployment rate is pretty much as well described by a DIEM as the BLS number. In fact, you have to dive down into the shock parameters to notice anything besides the uniform shift.

The data only contains two complete shocks (Great Recession/2008, mini-boom/2014), so I'm only looking at those parameters. Overall, the only real difference is that the 2014 "mini-boom" for the unemployment rate is smaller and narrower — possibly shedding some light on why it seems to have gone largely unnoticed.

But overall, this mis-measurement doesn't have any impacts on the DIEM's ability to describe the data — and the adjusted data tells essentially the same story of the BLS data for the past couple decades.

PS We could potentially conclude that the fraction of unemployment that is long term (>27 weeks) might be lower because the average duration of unemployment has fallen in the paper's analysis. This might explain something puzzling about the elevated rate of long term unemployment — but the paper's analysis doesn't go back far enough to see if there's a change in the 90s (when long term unemployment started to stay elevated relative to headline unemployment).

Getting one wrong: EU unemployment ... plus a mini-boom?

One of the major tenets of science is being as honest as possible, and showing e.g. bad forecasts. Back when I first put the Dynamic Information Equilibrium Model (DIEM) together, I quickly looked at other countries including the European Union. However, I hadn't checked back in on that forecast in the intervening two years. Unfortunately for the forecast, but fortunately for people in the EU, the unemployment rate dropped much faster than the DIEM expected right after the forecast ...

The gray bands are the non-equilibrium shock centers and widths (shock duration). The discrepancy can easily be understood as a positive shock to employment, and fitting the parameters means this shock began in January of 2017 — coincidentally (and aggravatingly) exactly when the original forecast was made. But still, this shows a shortcoming of the model. If you make a forecast right before a non-equilibrium shock hits, it's going to be wrong.

What's interesting is that this means the 2014 mini-boom in the US may not have been unique to the US — the same drop in the unemployment rate of comparable size appears in the EU starting in January of 2017 [1]. It's possible this EU mini-boom could have been caused by the US mini-boom, but there could be other causes as well. It's not entirely certain what caused the mini-boom in the US.

There is another possibility — since the EU time series is much shorter than the US version, we might have underestimated the dynamic equilibrium slope. However, even if I re-estimate it using all the available data, there's still a slight shock in the same place:

This gives us some confidence that the non-equilibrium shock hypothesis might be the better one. However, the only real way to tell will be to continue to follow forecasts. Hopefully I won't wait another two years before checking in on it this time!

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Footnotes:

[1] Here's a side by side comparison of the EU and US unemployment rates showing the mini-booms:

The Phillips Curve: An Overview

Noah Smith has an article in Bloomberg today about the Phillips curve — the relationship between employment and inflation where "employment" and "inflation" can mean a couple of different things. Phillips' original paper talked about wage inflation (wage growth) and unemployment, but sometimes these can refer to inflation the price level in general (e.g. CPI inflation) or even expected inflation (in the New Keynesian Phillips Curves [NKPC] in DSGE models). I realized I don't have a good one-stop post for discussion of the Phillips curve, so this is going to be that post.

Noah's frame is the recent congressional hearings with Fed Chair Powell, and in particular the pointed questioning from Alexandria Ocasio-Cortez about whether the Phillips curve is "no longer describing what is happening in today’s economy." He continues to discuss the research finding a 'fading Phillips curve' and mentioned Adam Ozimek's claim that the Phillips curve is alive and well — all things I have discussed on this blog in the context of the Dynamic Information Equilibrium Model [DIEM]. Let's begin!

1. There is a direct relationship between wage growth and the unemployment rate

The structure of wage growth and the unemployment rate over the past few decades shows a remarkable similarity (as always, click to enlarge):

The wage growth model has continued to forecast well for a year and a half so far, while the unemployment rate model not only has done well for over two years now (I started it earlier) but has outperformed forecasts from the Fed as well as Ray Fair's model. Regardless of whether the models are correct (but seriously, that forecasting performance should weigh pretty heavily), they are still excellent fits to the prior data and describe the time series' structure accurately. There's actually another series with this exact shock pattern ('economic seismogram') match — JOLTS hires. The hires measure confirms the 2014 mini-boom appearing in wage growth and unemployment so we're not just matching negative recession shocks, but positive booms. We can put the models together on the same graph to highlight the similarity ... and we can basically transform them to fall on top of each other by simply scaling and lagging:

This find that shocks to JOLTS hires lead unemployment by about 5 months, and shocks to wages by 11 months — with first two leading NBER recessions and the last one happening after a recession is over. We can be pretty confident that changes in hires cause changes in unemployment which in turn cause changes in wage growth. Between shocks, the normal pattern is that unemployment falls and wage growth rises (accelerates). The rate of the latter is slow, but consistent (and forecast correctly by the DIEM):

2. Adam Ozimek's graph is more like a Beveridge curve and isn't quite as clean as presented

I used the wage growth model above and a similar model of prime age employment to reproduce a version of Ozimek's graph in an earlier post. Ozimek uses the Employers Cost Index (ECI), but I use the Atlanta Fed wage growth tracker data because it is monthly and goes back a bit farther in time [3]. However, this pretty much produces an identical graph to Ozimek's when we plot the same time period:

The DIEMs for wage growth and prime age employment population ratio [EPOP] also have some similar structure — however the 2014 mini-boom is not as obvious in EPOP if it appears at all ...

This indicates that these two series might have a more complex relationship than unemployment and wage growth. In fact, if you plot them on Ozimek's axes highlighting the temporal path through the data points in green (and yellow) as well as some additional earlier data in yellow (and highlighting the recent data in black) you see how the nice straight line above is somewhat spurious and the real slope is actually a bit lower:

The green dashed line shows where the data is headed (in the absence of a recession), and the light gray lines show the "dynamic equilibria" — the periods between shocks when wage growth and employment steadily grow. When a recession shock hits, we move from one "equilibrium" to another, much like the Beveridge curve (as I discuss in this blog post and in my paper).

3. The macro-relevant Phillips curve has faded away

The Phillips curves above talk about wage inflation, but in macro models the relationship is between unemployment and the price level (e.g. CPI or PCE inflation) — the NKPC. Now it's true that wages are a "price" and a lot of macro models don't distinguish between the price of labor and the price of goods. But it appears empirically we cannot just ignore this distinction because there does not appear to be any signal in price level data today ... but there used to be!

Much like in the first part of this post, we can look at DIEMs for (in this case) core PCE inflation and unemployment, and note that they really do seem to be related in the 60s through the 80s:

We see spikes of inflation cut off by spikes in unemployment, which fade out in the 90s. This is where a visualization of these "shocks" I've called "economic seismograms" is helpful — the following is a chart in a presentation from last year (this time its the GDP deflator):

Spikes in inflation are "cut-off" by recessions during the 60s and 70s, but that effect begins to fade out over time. What's interesting is that the period of a "strong Phillips curve" pretty much matches up with the long demographic shift of women entering the workforce in the 60s, 70s, and 80s. The Phillips curve vanishes when women's labor force participation becomes highly correlated with men's (i.e. only really showing signs of recession shocks). This is among several things that seem to change after the 1990s.

Why does this happen? I have some speculation (a metaphor I use is that mass labor force entry is like a "gravity wave" for macro) that I most concisely wrote up in a comment about my new book:

My thinking behind it is that high rates of labor force expansion (high compared to population growth) are more susceptible to the business cycle. Unlike adding people at the population growth rate, adding people at an accelerated rate because of something else happening — women entering the workforce — is more easily affected by macro conditions. Population grows and people have to find jobs, but women don't have to go against existing social norms and enter the workforce in a downturn, but are more likely to do so during an upturn (i.e. breaking social norms gets easier if it pays better than if it doesn't). 

This would cause the business cycle to pro-cyclically amplify and modulate the rate of women entering the workforce, which gives rise to bigger cyclical fluctuations and also the Phillips curve. 

As a side note: I think a similar mechanism played out during industrialization, when people were being drawn from rural agriculture into urban industry. And also a similar mechanism plays out when soldiers return from war (post-war inflation and recession cycles).

That new book's first chapter is largely about how this effect is generally behind the "Great Inflation" — and that it has nothing to do with monetary policy. Which brings us back to the beginning of this post: the Fed can't produce inflation because it never really could [1].

Update 13 July 2019: I wanted to add that this relationship between inflation and unemployment and the fading of it isn't about "expected" inflation (the expectations augmented Phillips curve), but observed inflation. It remains entirely possible that the "Lucas critique" is behind the fading — that agents learned how the Fed exploits the Phillips curve and so the relationship began to break down. Of course, the direct consequence is that apparently the Fed became a master of shaping expectations ... only to result in sub-target inflation after the Great Recession. It would also mean that the apparent match between rising labor force participation and the magnitude of the Phillips curve is purely a coincidence. I personally would go with Occam's razor here [2] — generally expectations-based theories verge on the unfalsifiable.

Summary

So 1. yes, wage growth and unemployment appear to be directly causally related; 2. wage growth and EPOP are not as closely or causally related; and 3. yes, the Phillips curve relationship between unemployment and the macro-relevant price level inflation has faded away as the surge of women entering the workforce ended.

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Footnotes:

[1] This is not to say a central bank can never create inflation — it could easily create hyperinflation, which is more a political problem than a macroeconomic mechanism. The cut-off between the "hyperinflation" effective theory and the "monetary policy is irrelevant" effective theory seems to be on the order of sustained 10% inflation. (Ina side note mentioned at that link, that might also be where MMT — or really any one-dimensional theory of how an economy works — is a good effective theory. Your economy simplifies to a single dimension when money printing, inflation and government spending all far outpace population and labor force growth.)

[2] Is granting the Fed and monetary policy control of inflation so important that we must come up with whatever theory allows it no matter how contrived?

[3] Update 14 July 2019: Here's the ECI version alongside the Atlanta Fed wage growth tracker data — graph originally from here. ECI's a bit too uncertain to see the positive shock in the 2014 mini-boom.

Wage growth, inflation, interest rates, and employment

With the Fed hearings in Congress this week and some new data releases this week, I thought it'd be good to get a dynamic information equilibrium model (DIEM) snapshot just before the end of the month and what many people are thinking is going to be the first Fed rate cut since the Great Recession. The Atlanta Fed's Wage growth tracker was updated today and the latest results are in line with the DIEM forecast from a year and a half ago:

We're pretty much at the point where wage growth has reached the NGDP growth dynamic equilibrium, which I've speculated is the point where a recession is triggered (by e.g. wages eating into profits, resulting in falling investment). Of course, the NGDP series is noisy, but this is what the "limits to wage growth" picture looks like with an average-sized shock (in the wage growth time series):

Inflation (CPI all items, seasonally adjusted) came in today lower than the 2.5% dynamic equilibrium this month but well within the error bands. This is year-over-year and continuously compounded annual rate of change (i.e. log derivative):

But inflation doesn't give us much of a sign of a recession (it can react after the fact, but isn't a leading indicator).

A metric many people look at is the yield curve — I've been tracking the median of a collection of rate spreads (which basically matches the principal component). This is only loosely based on dynamic information equilibrium (i.e. there's a long-term tendency for interest rates to decline), but is really more a linear model of the interest rate data before the last three recessions (so caveat emptor) coupled with an AR process forecast:

That linear model gives us an estimate of when the yield curve should invert as an indication of a recession. One thing to note is that with the Fed potentially lowering interest rates at the end of the month, the path of the interest rate spread will likely "turnaround" and start climbing — it's done so in the past three recessions. That turnaround point has been between one and five quarters before the recession onset, but then the turnaround has also usually been at about -50 bp — these are indicated with the gray box on the next graph:

As a side note: when people say AR processes outperform DSGE models, this is an example of one of those AR processes.

If the fed lowers rates this month, then the turnaround will be 20-30 bp higher than the past three recessions — is this an indication of looser policy than in the past? Political pressure? This is not necessarily to say the Fed's rate decisions will have an impact. It's just a representation of how the Fed changes policy in the face of economic weakness. Much like how a person who sees themselves about to get in a car accident might tense up, tensing up does not do anything to mitigate or prevent the accident.

Earlier this week, JOLTS data came out. I've speculated that these measures are leading indicators, and it appears that shocks to JOLTS hires appear at around 5 months before shocks to the unemployment rate and around 11 months before shocks to wage growth (the model above) — the latter coming after the recession has begun. In any case, JOLTS quits appears to be showing a flattening indicating a turnaround:

I talked about this on Twitter a bit. In the last recession, hires led the pack but that might have been a result of the housing bubble where construction hires started falling nearly 2 years before the recession onset. If that was a one-off, then quits and openings look like the better indicators. Here's openings:

As a side note, I talk about that atypical early lead for hires in my book as an indication that potentially the big xenophobic outbreak around the 2006 election might have had an impact on the housing bubble (an earlier draft version appears here as a blog post).

Again, a lot of this is speculative — I'm trying to put out clear tests of the usefulness of the dynamic information equilibrium model for forecasting and understanding data. But the series that seem to lag recessions (wage growth, inflation) are right in line with the DIEMs, while the series that seem to lead recessions (JOLTS) are showing the signs of deviations.

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Update 4:30pm PDT

Here's the 10-year-rate forecast from 2015 still doing much better than the BCEI forecast of roughly the same vintage ...