Monday, December 10, 2018


Checking in on the dynamic information equilibrium model forecasts, and everything is pretty much status quo. Job openings are still on a biased deviation. Click to enlarge.

Based on this model which puts hires as a leading indicator, we should continue to see the unemployment rate fall through March of 2019 (5 months from October 2018):

The dashed line shows a possible recession counterfactual (with average magnitude and width, i.e. steepness) constrained by the fact that the JOLTS hires data is not showing any sign of a shock.

Here's the previous update from November (with September 2018 JOLTS data).

Friday, December 7, 2018

The last employment situation report of 2018

Next month, this dynamic information equilibrium model (DIEM) forecast will be 2 years old [1]. It's been pretty much spot on (shown alongside some of the forecasts published by the FRBSF's FedViews):

It's biased a little high with today's 3.7% number, but compared to the competition — the FRBSF forecast had us at 4.7% compared to the DIEM's 3.9 ± 0.2% — the miss distance is 5 times smaller (1.0 pp vs 0.2 pp):

The FOMC forecast a 4.5% unemployment rate average for 2018. With almost all the data (which is why the average point is gray inside a black circle instead of white), it's looking closer to 3.9% — a 0.6 pp difference. The DIEM annual average is 4.1% — a 0.2 pp difference (3 times smaller).  

I'm also tracking a couple of forecasts (versus the FOMC and the CBO) based on forecasts made this year. The DIEM is a little lower because the data from 2017 gives us a better indication of the size of the 2014 shock to unemployment (the "mini-boom"). I show some possible counterfactual recessions in the DIEM consistent with the CBO's forecast (i.e. if the CBO forecast is accurate through 2022, then there'd be a recession shock in the DIEM)


As of writing this, the S&P 500 was down almost 2%. I thought I'd update the S&P 500 forecast (also from almost two years ago [2], and also pretty spot on) to show some more of the recent volatility. The last update was here. We're skirting the edge of the AR process band, but we're still inside the 60-year volatility band of the DIEM model, the lower edge of which (marked by a red dashed line) indicates the need to posit another shock to the DIEM.

The median interest rate spread (which is about the same as the average or the principal component per the original model description) continues to trend downward. Note: this isn't a DIEM model, but rather a simple linear model of yield curve inversion as a leading indicator of recession.



[1] The model itself was born in a January 10, 2017 blog post when I derived it from an information equilibrium relationship for JOLTS data similar to a matching model.

[2] I feel like I just have to show the S&P 500 forecast before all those points:

Wednesday, December 5, 2018

Imagine there's no bubble

It's easy if you try.

I've been writing my forthcoming book — trying to dot all the i's and cross all the t's with the data analysis — and I came across something that was a bit shocking. There seemed to be some trouble in the Case-Shiller housing price index model which had some ambiguity with the shocks. While there was a decent fit to the CS index level, the growth rate was not well-described. This is not a good qualitative fit to this growth rate data:

But if you squint at that data, you see a pattern that looks a bit more like the pattern in wage growth — see the dynamic information equilibrium model (DIEM) described here. So I went to Shiller's (continuously updated) data directly to get a longer term time series, and sure enough a DIEM describes CS index (i.e. housing price) growth pretty well:

The dashed line shows a fit to the small fluctuations in the aftermath of the Great Recession (possible step response to the recession shock) that aren't that big in the growth rate, but create a noticeable effect in the level.

You can then integrate and exponentiate to recover the index level:

Here, you can see the large effect on the level of those two post-recession fluctuations in the growth rate (difference between the dashed and solid green curves). Overall, this is a great description of both the level and the growth rate of housing prices. But it raises a big question:

Where's the housing "bubble"? 

In the aftermath of the S&L crisis of the late 80s, the growth rate for housing prices in equilibrium increases steadily — much like wages. But there's no positive shock sending prices higher, no event between 1990 and 2006, just steady acceleration. Sure, the growth rate becomes insane at the end of that trajectory (> 10%), but that's the result of the equilibrium process. There's no "bubble" unless there's always a bubble.

Did new ways of financing allow this acceleration to increase for a longer time? There's some evidence that wage growth is cut off by recessions (i.e. when wage growth reaches NGDP growth, it triggers a recession). What is the corresponding housing price growth limit? The pattern of debt growth roughly matches the housing price growth starting in the late 80s, but the shock to debt growth in the Great Recession comes well after the shock to housing prices.

However, this improved interpretation of the housing price data puts the negative shock right when the immigration freak-out was happening and the shock to construction hires (not construction openings, but hires). This would raise a question as to why a shock to the supply of new housing would cause prices to fall. I've previously discussed how increasing the supply of housing should actually increase prices because it should be considered more as general equilibrium (supply doesn't increase much faster than demand). But also the dynamic information equilibrium model that produces this kind of accelerating growth rate is (d/dt) log CSCS (just like the wage growth model). This has the interpretation that the demand for housing is related to the growth rate of housing prices (since the left side is demand). 

It's important to note that the shock to housing price growth rate comes before any decline in housing prices. The decline in growth rate would only have become noticeable in early 2006, but whatever the shock was that triggered it could have come as early as mid-2005 — which points to another possibility: hurricane Katrina. Or maybe simply housing prices themselves were the cause. Eventually, regardless of creative financing options, people become unable to afford prices that grow faster than income. It's not so much of a bubble, but supply and demand for a scarce resource. Maybe demand for housing really was that great. Judging by the increase in homelessness in the aftermath (e.g. Seattle), that is a plausible explanation. If it was truly a bubble, then there'd be a glut of housing, but prices seem to have continued on their previous path [1].


Update 5 December 2018 

See Kenneth Duda's comment below and my response for a bit more on possible causes, including the OTS decision to loosen requirements set by the CRA. I would like to point out that the difference between the dashed green curve and the solid one in the CS-level diagram above could be interpreted as a result of mis-management by the Fed and the government in 2008. However, it could also be interpreted as a measure of the general level of panic and overreaction (the downturn appears to overshoot the price level path resulting in a deeper dive than indicated by later prices).


Update 9 December 2018

Per Todd Zorick's comment below and expanding on footnote [1], here are the housing price indices for Seattle:

And for Dallas:

As you can tell, the shocks are quite different. Dallas doesn't have much of a housing collapse, but seems to be undergoing a fairly large shock over the past couple years. Do note that the time periods are different (since the 90s for Seattle, since 2000 for Dallas) because that was the data on FRED.



[1] I will note that recent data from Seattle shows a decline (a similar turnaround might be visible in the Shiller data as a downward deviation at the end of the graph above):

You can also see the tail end of the drop in 1990 associated with the birth of grunge.

It is possible this is part of the early signs of the hypothetical upcoming recession.

Thursday, November 29, 2018

Ambiguous histories: productivity

Productivity came up on Twitter yesterday, and I put together a quick dynamic information equilibrium model (DIEM) of the utilization-adjusted Total Factor Productivity (TFP) data curated by John Fernald at the FRBSF. First, let me note that I generally think of TFP as phlogiston. However, this case is a good example of potential ambiguity in finding the dynamic equilibrium.

The TFP data is actually pretty well described by the DIEM, but its possible to effectively exchange the regions of the data that are "shocks" and the regions of the data that are "equilibrium". In this first graph, equilibrium is from the start of the data series until the 70s and 80s (a negative shock) and then in equilibrium again until the 2000s, followed by another negative shock after the Great Recession.

This data actually fits pretty well to Verdoorn's law that says (d/dt) log P ~ 0.5 (d/dt) log RGDP, and the shocks are deviations away from Verdoorn that just change the level. Additionally, this version has most of the data as equilibrium data (an underlying assumption of the DIEM approach). The fit is just slightly worse than this other fit (in terms of AIC, BIC, errors, etc) that sees the 80s and the present as equilibrium with positive shocks in the 50s & 60s as well as during the 2000s (i.e. where the previous fit was "in equilibrium"). This version says Verdoorn's law was just a coincidence during the 1940s & 50s (when it was hypothesized).

Of course, there are other reasons to prefer the second fit — e.g. it matches better with the UK data, it has recognizable events (post-war growth, the financial bubbles). But the best way to show which one is right will be data. The first fit predicts a return to increased productivity growth soon. If higher growth doesn't return soon, it means each new data point requires re-estimating the fit parameters for events in the past — a sign your model is wrong. The second predicts continued productivity growth at the lower rate with any major deviations implying a new shock (not re-estimating parameters for old shocks).

But still, the math on its own is ambiguous. The difference in AIC isn't enough to definitively select one mode over another. Circumstantial evidence can help, but what's really needed is more time for data to accrue.

Wednesday, November 28, 2018

Third quarter GDP numbers

No lunch break today, so I'm late with these updates. The Q3 GDP numbers and related metrics are out. No surprises, but here are the various forecasts and head-to-heads I'm tracking.

First, here's RGDP growth and inflation from the FRBNY DSGE model and the dynamic information equilibrium model (DIEM) (click to enlarge):

The post-FRBNY forecast data is in black there. Here's RGDP growth over the entire DIEM forecast period (black is post-DIEM forecast data) alongside the FOMC forecast (annual averages):

Tuesday, November 27, 2018

I don't trust Granger causality

In my travels through the econoblogosphere and econ Twitter, I've come across mentions of Granger causality from time to time. I do not trust it as a method for determining causality between time series.

If you need to know what it is, the wikipedia article on it is terrible, and basically you should just refer to either Toda and Yamamoto (1995) or Dave Giles excellent description of what the process actually involves whenever you have co-integrated series which is pretty much all the time in macro.

However, Granger causality was developed before the idea of cointegration. From Granger's Nobel lecture [pdf]:
When the idea of cointegration was developed, over a decade later, it became clear immediately that if a pair of series was cointegrated then at least one of them must cause the other. 
Or as Dave Giles put it:
Both of these ... time-series have a unit root, and are cointegrated ..., we know that there must be Granger causality in one direction or the other (or both) between these two variables.
Since almost every macro time series is cointegrated, you can always find Granger causality one way or another (or both). Since almost every macro time series is cointegrated, you really have to work (basically follow the entire process Giles describes). There are lots of interim results that are needed to judge whether or not you can trust the results from determining cointegration to the number of lags to the results of the test in both directions.

Even then, there are things that will pass Granger causality tests that represent logical fallacies or bend our notion of what we mean by causality. I give some examples, using the dynamic information equilibrium approach — which turns out to provide a much better metric for causality.

Let's say we have two ideal cointegrated series where the noise is much much smaller than the measurement. The only thing adding noise does is make the p-values worse.

The way these two series are set up, only the first (blue) could potentially Granger-cause the second (yellow) because the second is effectively constant (after first differences or subtracting out the linear trend to remove the cointegration) for all times t < 0. Therefore, by construction, we'd only have to test that yellow depends on a possible linear combination of its own lagged values and the lagged values of the blue series since blue cannot depend on lagged values of yellow (they're all approximately constants after first differences or zero after subtracting the linear trend). And depending on the temporal resolution, the yellow curve does not strongly depend on lagged values of itself. This sets up a scenario where Granger causality is effectively satisfied if we can represent the yellow curve in terms of lagged values of the blue curve.

Here are the derivatives after subtracting the linear trend; the green curve is the blue curve shifted to the center of the yellow (it's still a bit wider). A representation in terms of an "economic seismogram" appears above the curves.

Except in cases where there is too much noise, too little temporal resolution or the blue shock is much wider than the yellow one, the yellow shock can nearly always be reconstructed  in terms of a linear combination of the lagged values of the blue curve (the logistic shocks have approximately Gaussian derivatives, which are used in linear combination in e.g. smooth kernel estimation). E.g. for integer lags (p < 0.01 for lag 7) (green curve is the linear combination of the lagged blue curve):

This is great, because it means that — except in extreme cases — an economic seismogram where shocks precede each other is sufficient to satisfy Granger causality. But this is also problematic for Granger causality for exactly the same reason I wouldn't use a single shock preceding another as the sole basis for causality because of the post hoc ergo propter hoc fallacy. Granger causality is effectively a test of whether changes in one series precede changes in another, and calling it "causality" is problematic for me. A better wording for a successful test in my opinion would be "Granger comes before" rather than "Granger causes". However, a failure of the test (i.e. the yellow curve does not 'Granger cause' the blue one) is a more robust causality result because it is based on physical causality — it is literally impossible for an event outside another event's past light cone to have caused that event. As Dave Giles puts it, it's a better test of Granger non-causality: affirming that the yellow curve did not cause the blue one more than affirming the blue one caused the yellow one.

But it gets weirder if we give the earlier shock a different shape than the later one (the darker bands are negative in the economic seismogram, green is simply the shifted version of the blue function again [update: replaced with correct figure]):

It is actually possible to fit the lagged blue function to the yellow one well enough to achieve p < 0.01 for the coefficients:

You can do even better at higher temporal resolution (which also allows more lags):

This different-shaped shock also satisfies Granger causality (the blue series Granger-causes the yellow series), but I would say that we should definitely have less confidence in the causality here — it really is more of a case that the blue shock just "Granger comes before" the yellow one. I would have more confidence if there e.g. two shocks in this case:

What is also strange is that you can also have a single shock Granger cause a pair of later shocks:

Again, I'd really just say that the blue shock "Granger comes before" the yellow ones (despite the green fit being almost perfect).

Anyway, those are some of the reasons why I don't really trust Granger causality as a method especially when there are limited numbers of events (common in macro) — unless it's Granger non-causality, which is fine! 

If I was up on my real analysis, I'd probably try to prove a theorem that says the economic seismograms satisfy Granger causality and under which conditions. The temporal resolution needs to be high enough, noise needs to be low enough, and the earlier shocks need to be sufficiently narrow but I don't have specific relationships. The last one is actually temporal resolution dependent (i.e. increasing the number of samples and the number of lags eventually allows a wide shock to Granger cause a narrow one). But I think a good take away here is that reasoning with these diagrams using multiple shocks is actually better than Granger causality.

Wednesday, November 14, 2018

Data dump: JOLTS, CPI

Checking in on the dynamic information equilibrium model forecasts, and everything is pretty much status quo. The JOLTS hires data [1] is showing even fewer signs of a recession than before, but job openings is still on a biased deviation. Based on this model which puts hires as a leading indicator, we should continue to see the unemployment rate fall through February of 2019 (5 months from September 2018), at which point it will be 3.8 ± 0.2 % (90% CL) [2]. Additionally, CPI inflation is well within expected values. And finally, the S&P 500 forecast is still on a negative deviation, but within the norms of market fluctuations. As always, click to enlarge.


CPI inflation (all items)

S&P 500


[1] The old hires without the 2014 mini-boom is here:

[2] October's 3.7% was on the low end of the CL — it was expected to be 3.9 ± 0.2 % (90% CL), so there might be a bit of mean reversion between now and March (when the February numbers come out).

Unions, inequality, and labor share

I've started writing the first draft of my next book, so I've been trying to gather up all the dynamic information equilibrium model results into economic seismograms [1] to try to provide a complete picture. In the gathering, there have been some unexpected insights — this time about unions and their effect on inequality. Here's the seismogram in the new style that can be displayed on a Kindle [2] (click to enlarge):

This shows the civilian labor force (women), wages, manufacturing employment (as a fraction of total employment), the labor share of output (nominal wages/NGDP), unionization, and income inequality (using Emmanuel Saez's data).

One of the interesting things I noticed was that unionization and inequality show almost exactly the same pattern: each bump up in unionization sees a bump down in inequality a few years later, and the decline of unionization in the 80s is followed by rising inequality in the 90s.

What's also interesting is that the decline in the labor share of output starts happening before unionization declines — i.e. a decline in unions wasn't the predominant way labor lost its share of output. I've talked about my hypothesis for a more likely causal factor before: labor share declined as women entered the workforce because the US pays women less than men. A rough order of magnitude calculation where capital just pockets the extra 30 cents on the dollar they save by hiring a woman gets the expected decline in labor share about right.



The unionization model is discussed here:

And here are the models of inequality and labor share (also here for the latter):



[1] One of the other things I realized in the process was that it's not seismograph, which is the machine, but seismogram. I went back on the blog and corrected all the references in the posts.

[2] Comments are welcome, but be sure to click to see the higher resolution version. Dark bands are negative shocks (or "bad" shocks), while the lighter bands are positive (or "good" shocks).

Tuesday, November 6, 2018

A workers' history of the United States 1948-2020

On my book blog, I'm starting up the next book tentatively titled A workers' history of the United States 1948-2020 based on some of the dynamic information equilibrium model results and macroeconomic seismograms. Take a look ...

I'll say similar things for half the salary

Jan Hatzius made some macro projections about wages, unemployment, and inflation:
Goldman’s Jan Hatzius wrote Sunday that unemployment should continue to decline to 3% by early 2020, noting the labor market also has room to accommodate more wage growth. Hatzius predicted that average hourly earnings would likely grow in the 3.25% to 3.50% range over the next year. ... For now, Goldman has a baseline forecast of 2.3% for core PCE ...
Well, these are all roughly consistent with Dynamic Information Equilibrium Model (DIEM) forecasts from almost two years ago (early 2017, except for the wage growth which is from the beginning of this year). Hatzius' unemployment forecast is a bit lower (I'm currently guessing there will be a recession that will begin the raise unemployment in the 2020 time frame based on JOLTS data making both of these forecasts effectively "counterfactuals"). His wage forecast is consistent but biased low compared to the DIEM, while his inflation forecast is consistent but biased high compared to the DIEM. 

Of course, there's a hedge:
Hatzius said that the economic outlook is still subject to change from a number of geopolitical factors, such as the U.S. midterm elections on Tuesday [today] ...
The DIEM forecasts will generally only change if there is a recession, but as we haven't seen any real impact on JOLTS hires (see here) we should continue to see the unemployment rate fall through January of 2019 (5 months from August 2018) and wage growth increasing through July 2019 (11 months from August 2018).

Here are the graphs — click to enlarge: