## Monday, December 2, 2019

### Information Transfer Economics: Year in Review 2019

It's the Information Transfer Economics Year in Review for 2019!

It's my annual meta-post where I try in vain to understand exactly how social media works. But most of all, it's a way to say thank you to everyone for reading. Perhaps there's a post that you missed. Personally, I'd forgotten that one of the top five below was written this year.

As the years go by (now well into the 7th year of the blog), the blog's name seems to be more and more of a relic. I do find it a helpful reminder of where I started each time I open up an editor or do a site search. Nowadays, I seem to talk much more about "dynamic information equilibrium" than "information transfer". In the general context, the former is a kind of subset of the latter:

All of the aspects have applications, it's just that the DIEM for the labor market measures a) gives different results from traditional econ, b) outperforms traditional econ models, and c) has been remarkably accurate for nearly the past three years.

Most shared
The post notes an interesting empirical correlation between the fluctuations in the JOLTS job openings rate (and even other JOLTS measures) around the dynamic equilibrium (i.e. mean log-linear path) with the fluctuations in the S&P 500 around the dynamic equilibrium. It's a kind of 2nd order effect beyond the 1st order DIEM description.
Feedly's algorithm for determining shares is strange, however. I'm not sure what counts as a share (since it's not tweets/retweets). Adding to the confusion as to what a share means, it didn't make the top 5 in terms of page views (per Blogger). Like most years, the top posts are mostly criticism. Those were:

Top 5 posts of the year

#1: MMT = Keynes + Monetary kookiness
I wrote this soon after Doug Henwood's Jacobin piece that Noah Smith recently re-tweeted. Pretty much for me, the whole "MMT" thing is not really theory because it doesn't produce any models with any kind of empirical accuracy. I actually have a long thread I'm still building where I'm reading the first few chapters of Mitchell and Wray's MMT macro textbook. Their entire approach to empirical science is misguided — it'd pretty much have to be because otherwise the MMT would've been discarded long ago. It's also politically misguided in the sense that it does not understand US politics. And as Doug Henwood points out, the US is probably the only country that meets MMT's criteria of being a sovereign nation issuing it's own currency because of the role of the US dollar in the world. But this blog post points out another way MMT bothers me: it's just weird. MMT acolytes talk about national accounting identities like how socially stunted gamers talk about their waifu.
#2: Resolving the Cambridge capital controversy with MaxEnt
This started out as a tongue in cheek sequel to my earlier post "Resolving the Cambridge capital controversy with abstract algebra". Here I showed that the re-switching argument that eventually convinced Paul Samuleson that Joan Robinson was right turns out to have a giant hole in it if your economy is bigger than, say, two firms. This sucked me into a massive argument on Twitter about Cobb-Douglas production functions where people brought up Anwar Shaikh's "Humbug" production function — which I found to be a serious case of academic dishonesty.
#3: JOLTS day: January 2019
No idea why this became so popular, but it was an update of the JOLTS data. It turns out the "prediction" was likely wrong (and even if it turns out there is a recession in the next year, it would still be right for the wrong reasons). I go into detail about what I learned from that failed prediction in this post.
#4: Milton Friedman's Thermostat, redux
This is one of my fun (as in fun to write) "Socratic dialogs" where I try to explain why Milton Friedman's thermostat argument is actually just question begging.
#5: Market updates, Fair's model, and Sahm's rule
This is another post that consists mostly of updates (including the inaccurate model from Ray Fair, who is possibly more well known for his inaccurate models of US presidential elections). But it's also where I talk about Claudia Sahm's "rule" that was designed to be a way for automatic stabilizers to kick in in a more timely fashion based on the unemployment rate. There's a direct connection between her economic implementation of a CFAR detector (a threshold above a local average) and my (simpler) dynamic equilibrium threshold recession detector.

The top 3 of 2019 made it into the top 10 of all time, which had been relatively stable for the past couple years. Overall, I'm posting less (I've been exceedingly busy at my real job this past year), but it seems that ones I do post are having more of an impact. Nothing will likely ever dislodge my 2016 post comparing "stock-flow consistency" to Kirchhoff's laws (in the sense that both are relatively contentless without additional models) with tens of thousands of pageviews for reasons that are still baffling to me.

New book!

I also wrote my second short book and released it in June — A Workers' History of the United States 1948-2020. As you can tell from the title, it's a direct response to Friedman and Schwartz's Monetary History and essentially says the popular narratives of the US post-war economy are basically all wrong. Inflation, unionization, and the housing bubble are manifestations of social phenomena — but especially sexism and racism. Check it out if you haven't already.

Thank you!

Thank you again to everyone for your interest in my decidedly non-mainstream approach to economics. Thank you for reading, commenting, and tweeting. I think the ideas have started to gain some recognition — a little bit more each year.

(Here are the 2018, 2017, and 2016 years in review.)

## Thursday, November 28, 2019

### Average weekly hours in the UK

I came across this chart (via a re-tweet from Ian Wright) where Alfie Sterling extrapolated the 1946-1980 trend in average hours worked in the UK alongside an extrapolation from data post-1980:

There seems to be an entire industry in the UK built out of extrapolations like this (here's productivity). I've reproduced a version of this — it uses data for all employees, not just full time employees, so the level is a bit higher [click to enlarge]:

But the story is roughly the same — the trend was a steeper decline before 1980 and shallower after. However, plotting the graph on this scale (as well as cutting off the data at 1946) obscures some of the issues with extrapolating linearly willy-nilly. Zooming in a bit and taking that linear fit back to 1900 shows the 1946-1980 trend is unique to the period 1946-1980:

In fact, as I looked at a couple of years ago, this data is pretty well described by a dynamic information equilibrium model (DIEM):

The trend from World War II (WWII) to 1980 is almost certainly part of the demographic shift of women into the workforce in Anglophone countries that seems to govern so many things. The other major effects seem to be WWI and WWII ending in 1918 and 1945, respectively. Aside from those three events, average weekly hours is on a steady decline of 0.13% (consistent with what I found earlier for US data [1]).

This perspective is a lot less policy (or productivity, or wage) dependent, depending more on major social changes (war, women entering the workforce) — a recurring theme in my book. The trends differ across countries (with e.g. France and Germany's annual labor hours falling at closer to a 1% rate) implying that they may be set more by social norms.

...

Footnotes:

[1] Here's the figure showing the -0.13% trend and the same 60s-70s demographic shock:

## Saturday, November 23, 2019

### The S&P 500 since 2017

One of the forecasts I made when I first worked out the theory behind the dynamic information equilibrium model (DIEM) besides the unemployment rate was for the S&P 500. This forecast has worked out remarkably well — though one might ask how could it not with error bands on the order of 20%? I changed the color scheme a bit since the original forecast, but here's where we are (note that it's a log plot):

The black line is post-forecast data. The vertical blue bands are NBER recessions. The vertical red/pink bands are the non-equilibrium shocks to the S&P 500. The green error bands are the 90% confidence bands for the entire data series since the 1950s and the blue error band over the forecast data was the 90% confidence projection from estimating an AR process on the deviations from the dynamic equilibrium starting from the forecast date. That AR process was trained on the data since 2010.

The AR process error gets fairly close to the error bands for the whole series. My interpretation of this is that the AR process model has captured pretty much nearly the entire range of error except for recessions — that is to say the data from 2010 to 2017 gave us a decent estimate of non-recessionary deviations from the dynamic equilibrium due to news shocks, policy, foreign affairs, et cetera.

I think the past couple years has given us some additional evidence that hypothesis is correct as the current administration has effectively conducted some "natural experiments". I estimated a couple of non-equilibrium shocks to the post-forecast data — we can zoom in to see them better:

The first shock is a positive one taking place at the end of 2017 and the beginning of 2018 — almost certainly due to the TCJA (which incidentally appears to have had other effects). If that had been the only thing that happened since 2017, everyone with a 401(k) account invested in an S&P index fund (full disclosure: that's what I do) would have had 17% more in it today even without contributions.

Instead of being around 3650, we're closer to 3100 today. Why? It appears to be due to the "trade war" with China. The major announcements are shown with black arrows (). The first round of tariffs began before the ink on the TCJA had dried (green arrow) and basically cut what was estimated to be a sizable 20% gain back to zero. A second round of tariffs comes in August and September of 2018, accompanied by a subsequent shock.

The Fed's rate increase in December 2018 did produce a rapid drop in the S&P 500, but the effect seems to have since evaporated. I estimated the tariff shock with and without the data from from December 2018 and January 2019 and got nearly the exact same result in terms of the longer run level in both cases. It's of course not impossible that the effect of tariffs is what evaporated and what we're seeing is purely the effect of the Fed — but this is inconsistent with a) the fact that the tariffs seem to have had a lasting effect in 2018 and b) the December 2015 rate increase also largely evaporated [1].

So it seems that mismanagement of government policy does have sizable & quantifiable effects on the stock market. However, the key conclusion here is that these policy decisions appear to be within the range of the overall 20% error since the 1950s — and that policy changes are basically a 2nd order effect on the stock market after recessions with deviations on the order of δ log SP500 ~ 0.1 with recessions having an effect δ log SP500 ~ 0.6-0.8 or more [2].

...

Footnotes:

[1] The December 2015 rate increase was a shock on the order of δ log SP500 ~ 0.15, but in less than a quarter was only δ log SP500 ~ 0.05 and consistent with zero by 2017. The December 2018 rate increase has almost exactly the same structure: an initial drop by δ log SP500 ~ 0.15 and a quarter later the level was back up to within δ log SP500 ~ 0.05 of the pre-hike level.

[2] And per [1], Fed decisions having an effect on the order of δ log SP500 ~ 0.15 that quickly evaporate over the next quarter.

## Monday, November 18, 2019

### Projections, predictions, accountability, and accuracy

John Quiggin has an entertaining article up at The Conversation that looks at the persistently undershooting IEA "projections" of renewable energy production as a case study in the lack of accountability for statements about the future. This particular case comes up every two years because the IEA updates their "projections" every two years (Quiggin cites a 2017 critique from Paul Mainwood and David Roberts talked about it at Vox two years prior in 2015). It's 2019, so time for another look!

I personally have a soft spot in my heart for these "hedgehog" graphs where the future lines keep missing the data — I keep a gallery of macroeconomic "projections" (predictions? forecasts?) here. Often, the dynamic information equilibrium model (DIEM) is a much better model (such as for the unemployment rate), so I wanted to try it on this data.

Why should the DIEM be an appropriate model? Well, for one thing we can view the generation and consumption of electricity as a matching model — a megawatt-hour of production is matched with a megawatt-hour of consumption. Renewable energy is then like a manufacturing sector job or a retail sector job (... or an unemployment sector job a.k.a. being unemployed). But a more visually compelling reason is that technology adoption tends to follow (sums of) logistic curves per Dave Roberts' article at Vox:

These are the same logistic curves the DIEM's non-equilibrium component is built from. Logistic curves are also seriously problematic for "center predictions" — you really need to understand the error bands. The initial take-off is exponential, resulting in enormous error bands. The center is approximately linear, and only once you have reached that point do the error bands begin to calm down (see here for an explicit example of the unemployment rate during the Great Recession).

One issue was that I had the hardest time finding corroborating data that went back further than the "actual" data in Mainwood's graph. I eventually found this which is claimed to come from the IEA (via the World Bank). It largely matches up except for a single point in the 90s, allowing for error in digitizing the data from the plot. (Be careful about production versus consumption and world versus OECD if you try to find some data yourself.) That point in the 90s is inexplicably near zero in Mainwood's "actual" data. It's possible there are some definition issues (it's non-hydro renewables, which may or may not include biomass). But as this isn't a formal paper, the recent data seems fine, and the details of the fit aren't the main focus here we can just proceed.

I ran the DIEM model for the IEA data from 1971 to 2015, and this was the result:

Overall, the DIEM forecast is highly uncertain, but encompasses the 2012 and 2016 IEA forecasts for the near future. Mainwood's "corrected" forecast (not shown here) is well above any of these — it represents a typical problem with forecasts of logistic processes where people first see a lot of under-estimation, over-correct, and seriously over-estimate the result.

The best way to see the DIEM forecast is on a log scale:

There are three major events in this data — one centered in the early 80s (possibly to due to oil shocks and changes in energy policy such as the Carter administration), a sharp change in the late 80s, and then finally the current renewable revolution with wind and solar power generation due to a combination of policy and technology. The equilibrium growth rate (the "dynamic equilibrium") is consistent with zero — i.e. without policy or technology changes, renewables don't grow very fast if at all.

You can also see that it's likely we have seen the turnaround point in the data around 2010 — but it is also possible the global recession affected the data (causing renewables to fall as a fraction of global energy production). The global recession may be making it look like the turnaround has passed.

Quiggin's larger point, however, is something I've never really even considered. Do people really see projections as different from predictions or forecasts? If someone tried to hide and say their lines going into the future were "projections" and therefore not meant to be "predictions", I would just laugh. Does this really fool anyone?

I cannot come up with a serious rational argument that projections are different from predictions. We sometimes call predictions forecasts because that seems to move a step away from oracles and goat entrails. But any statement about the value of a variable in the future is a prediction. Sure, you can say "this line is just linear extrapolation" (a particular model of expected future data) and that it most certainly won't be right (a particular confidence interval). But it's still a prediction.

That's why the error bands (or fan charts, or whatever) are important! If you draw a line and say that we shouldn't take it seriously when we discover it's wrong, that just means the ex ante error bands were effectively infinite (or at least the range of the dependent variable). As such, there's literally zero information in the "projection" compared to a maximally uninformative prior — i.e. a uniform distribution over the range of the data. You can show that with information theory. Any claim that a projection that shouldn't be compared to future data yet has some kind of value is an informational paradox. It represents information and yet it doesn't!

Is this why a lot of economic and public policy forecasts leave off error bands? Is somehow not explicitly putting the bands down believed to keep the confidence in some kind of unmeasured quantum state such that it can't be wrong?

But as Quiggin mentions, this has ramifications for accountability. People year after year cite the IEA "projections" that continue to be wrong year after year. And year after year (or at least every two years) some rando on the internet takes them to task for getting it wrong, and the cycle begins again.

The thing is that it's not that difficult to explain why the IEA projections are wrong. Forecasting the course of a non-equilibrium shock (in the DIEM picture) is nigh impossible without accepting a great deal of uncertainty. Even if you don't believe the DIEM, a logistic picture of technology adoption is sufficient to understand the data. The only problem is that they'd have to show those enormous error bands.

...

PS I am almost certain those error bands exist in their models; they just don't make it into the reports or executive summaries.

PPS The existence and form of "executive summaries" should be all the evidence we need that CEOs and other "executives" aren't super-genius Übermenschen.

## Friday, November 8, 2019

### World GDP growth and silly models

In my travels on the internet, I came across this paper (Koppl et al [1]) from almost exactly a year ago. It has the silliest model of the world economy I've ever seen. Here's the abstract:
We use a simple combinatorial model of technological change to explain the Industrial Revolution. The Industrial Revolution was a sudden large improvement in technology, which resulted in significant increases in human wealth and life spans. In our model, technological change is combining or modifying earlier goods to produce new goods. The underlying process, which has been the same for at least 200,000 years, was sure to produce a very long period of relatively slow change followed with probability one by a combinatorial explosion and sudden takeoff. Thus, in our model, after many millennia of relative quiescence in wealth and technology, a combinatorial explosion created the sudden takeoff of the Industrial Revolution.
Caveats about extrapolating that far back notwithstanding, the problem isn’t so much what is written in the abstract but rather that the model cannot support any of the statements in it. Overall, it’s a good lesson (cautionary tale?) in how to go about mathematical modeling.

Just so there are no complaints that I "didn't understand the model", I went and reproduced the results. There's something they kind of gloss over in their paper that I'll come back to later that accounts for the small discrepancies.

First, the population data is basically exactly their graph (I have two different sources that largely match up):

The black dashed line at the end will come back later. Constructing their recursive M function (that represents the combinatorial explosion) and putting it together with the Solow model/Cobb-Douglas production function in the paper allows us to reproduce their graph of world output (GDP in Geary–Khamis international dollars) since the dawn of the Common Era (CE):

Like the population graph above and the M-function graph below, it is also graphed on a linear axis for some reason. They zoom in to 1800-2000 because they want to talk about the Industrial Revolution:

We reproduce this down to the segmented lines drawn between points in the time steps. Although you can't really see it in this graph, this is really part of a continuous curve in the model that goes back to at least the 1600s — it's not the Industrial Revolution (for more on take-off growth, see here or here). A log-log graph helps illustrate it a bit better:

The authors then show their output points alongside a measure of GDP in international dollars. For some reason it’s now points instead of line segments. But at least we’re on a log scale!

I didn’t use the exact same time series for comparison; instead, I used GDP estimates from Brad Delong here [pdf] that I had on hand. However, they're reasonably close to the data they present in their paper. In fact, it’s a bit better fit! I'm doing my best to be charitable. There is an almost exact factor of 4 difference in the level of their data and Delong's, which I think is accounting for “seasonally adjusted annual rate” for quarterly data. Koppl et al actually have two other model fits in their paper with different parameters. I just reproduced the yellow one that was closest to the data  (see the others at the end of this post).

The one graph I’m not reproducing exactly here is their M function. I think they just plotted a version with different parameters than for their yellow model result. As I didn’t care that much, I just did the M function from the yellow model result since that’ll be most germane to our discussion. Like most combinatorial functions, it goes along fairly flat (in linear space) and then jumps up suddenly (again, in linear space):

It starts at M₀, which is 50 in the parameters for their yellow result. The last several numbers in the series are 117.1, 125.3, 136.1, 151.0, 173.7, 213.2, 303.1, 668.8, 9323.4, 326360625.7. The next number is 4.9 × 10^26. Five hundred octillion.

What is supposedly happening in this model is that a current inventory of products (stick, flint, feathers) are at random brought together to produce a new product (an arrow for a bow) with some probability. That new inventory then has elements brought together to craft a new output good. It's basically a Minecraft crafting economy with the number of products you discover increasing combinatorially (roughly on the order of e.g. the gamma function or factorial). The factorials enter through a binomial coefficient.

Combinatorial explosion is building all along, but it really doesn't explain the Industrial Revolution. In fact, you can’t really say this “starts” anywhere with any kind of objective criteria. It starts at M₀, if anything, which is assigned to “year 1” (t = 0) — the beginning of the CE. The location of the super-exponential “take off” point (viewed on a linear scale) is then 60 or so time steps from year 1. But what is a time step? That’s what the authors gloss over. The time is just “scaled” so that the combinatorial series fits in the period from about “year 1” to about the present year.

The time steps turn out to be about 31 years (at least that's what I used), which is remarkably close to a “generation”. But this time scale is a fundamental parameter of their model — telling us where and when the combinatorial explosion occurs. If it had instead been on the order of a quarter, we could go from subsistence to the modern age in about 16 years. Instead whatever combination of current output goods that produces a new product with some probability happens only once every 30 years. You could of course adjust the probability to compensate a change in the time scale — making the probability parameters smaller increases the number of time steps it takes to cover the dynamic range of GDP values. However, since none of these parameters are estimated from some underlying data, the exact location and span of the model result in time is completely arbitrary.

I will pause to note that leaving out time scales like this is a general failing in economics (see here or here), making it impossible to understand the scope of their theoretical models.

The real  problem is when you go to the next time steps (I've also started adding graph labels to the graphs themselves). Combinatorial explosion doesn’t stop once you’ve explained as much of the data you want to explain. It keeps going, and going, and going, and going ...

Of course the GDP data ends so we can't see just how realistic this model is. Remember — their M function is heading towards 10^26 when it's about 600 around the year 2000.

This made me want to use the  the dynamic equilibrium model to extrapolate the data a bit further. In it, we have general exponential growth interrupted by periods of much higher (or lower) growth (“shocks”).

I wrote about population growth and how you might go about modeling it with the dynamic equilibrium model about two years ago with a follow up referencing the well-known 1970s report titled Limits To Growth. The general result there is that the recent population data is consistent with a saturation level of about 12-13 billion people by 2300. That most recent surge in population growth is associated with the advent of modern medicine (others seem to be associated with e.g. the Neolithic revolution in farming or sanitation). Maybe that’s right, maybe that’s wrong. But at least it’s a realistic extrapolation based on a slow decline in world population growth.

I used the world GDP data and population data to create a GDP per capita measure. I then extrapolated that data using another dynamic equilibrium model — one that’s remarkably consistent with the widespread phenomenon of women entering the workforce in larger numbers in the 1950s, 60s and 70s in the world’s largest economies. Again, it’s possible GDP per capita will continue to expand at its current rate for much longer than the next 25 to 50 years, but with growth slowing in most Western countries and even China, it’s entirely possible we’ll see a decline to a rate of growth more consistent with the 1800s than the 1900s.

We can combine our extrapolation of GDP per capita with population to form an extrapolation of world GDP over the next hundred years. The new picture of the longer term output growth shows how silly the combinatorial model is unless we arbitrarily restrict it to the most recent 2000 years.

In 2077 [2], world GDP by this extrapolation is about 513 trillion 1990 Geary–Khamis international dollars instead of the combinatorial version which gives 8.2 duodecillion (10^39) international dollars. We can compare this to world GDP in 2000 which was about 96 trillion international dollars in this data.

An increase by a factor of 5 from the year 2000 is not entirely unreasonable given slowing global growth, but an increase by a factor of a duodecillion (which I had to look up) [3] seems ... um, improbable.

US real GDP grew by a factor of about 10 over 70 years from 1950 to today, but that also includes the period in the middle of the last century where growth was much higher. Plus, the data in the GDP extrapolation also grows by a factor of about 10 over 70 years from 1950 to 2020.

The main take away is that this combinatorial model is both arbitrary in its timing — it's set up to have growth explode after the industrial revolution — but also its scope, being limited to the period from about 1 CE to about 2000 CE [4]. Going a single time step too far gives not just unrealistic but absolutely silly results. The model seems very much like someone (maybe Koppl) had this combinatorial idea (maybe after someone mentioned Minecraft to him) and it was given to a bunch of grad students to figure out how to make it fit the data. Odd parameters, large time steps that result in segmented data graphs, arbitrarily setting terms in sums to zero — it's not a natural evolution of a model towards the data. I saw this in their figure 4 and laughed:

Of course, the default color scheme for Mathematica is instantly recognizable to me (and in part why I tried to reproduce the figures exactly down to the dotted grid lines). But these line segments are all supposed to be aiming for that blue line. None of them are remotely close to even qualitatively explaining the data.

It's not an a priori bad insight for a model — it makes sense! It's kind of a Gary Becker irrational agents meets a Minecraft opportunity set. But combinatorial explosion is just too big to explain GDP, which is much more in the realm of the exponential with varying growth rates. So instead of mathematical modeling, you start building a Rube Goldberg device to make the model output kind of look like the data ... if you squint ... from across the room.

And yet instead of languishing on a grad student's file share or hard drive where it should be, this model ended up LaTeX'd up on the arXiv.

...

Footnotes

[1] It should be noted that Roger Koppl, the lead author, is associated with Mercatus and George Mason University (like one of the other co-authors) with lots of references to Hayek and Austrian economic in any description. Additionally, the paper came up on Marginal Revolution this past week. It should be a huge grain of salt, and in fact this paper is pretty typical of the quality of the work product from GMU-related activities [5].

[2] Chosen due to the time step scale.

[3] This made me think of Graham's number — for a time the largest number that has ever been used for anything practical (in this case it's an upper bound for a graph coloring problem). In part because the Koppl et al GDP is so high itself, but also because like the suspicion of mathematicians that the real answer for Graham's number is about 20, a more realistic estimate of GDP is much, much lower.

[4] There are other choices, such as limiting ourselves to only about 4 items in the combinations that I believe was more a computational limit (my computer has overflow problems if you increase that number or add too many time steps), that basically turn this "model" into a ~10 parameter fit.

[5] The paper goes on a tangent about "grabbing" which is basically a right wing rant:
Our explanation might seem to neglect the important fact of predation, whereby some persons seize (perhaps violently) goods made by others without offering anything in exchange for them. Such “grabbing,” as we may call it, discourages technological change.
The model put forward has absolutely nothing to do with this and can't explain technological change well enough to warrant speculation about secondary effects like this.

In addition, this is completely ahistorical. Violently seizing others' goods is in fact a major driver of innovation in history — a huge amount of innovation comes in the form of weapons. The silicon chips you're using right now to read this? Needed to make the computations fast enough to accurately guide a nuclear weapon to its target. The basics of computers with vacuum tubes were built to better aim artillery — even physics itself came from this.

### Wage growth and belated GDP updates

Wage growth data from the Atlanta Fed came out yesterday and the dynamic information equilibrium model (DIEM) has been doing fairly well for awhile — coming up on two years in a couple months!

J.W. Mason will have to continue to be puzzled. Black is post-forecast data, and click to enlarge. We can also say the DIEM forecast was better than Jan Hatzius' (Goldman Sachs) forecast from this same week one year ago. Orange is the actual average over that time period with one standard deviation errors, compared with Hatzius' range in purple:

Other forecasts where the DIEM is outperforming are RGDP growth and PCE inflation (those belated GDP updates). These cases aren't so much about the center of the prediction, but rather the error band being smaller for the DIEM model and still being accurate.

There's also the FOMC forecast, which is fine but claims a lot more precision in their "central tendency" that must be reflecting something other than RMS error [1]:

And here's the forecast of nominal GDP (NGDP) over employment (PAYEMS or here L) that forms the basis of (the information equilibrium view of) Okun's law and the "quantity theory of labor":

...

Footnotes:

[1] A "central tendency" in the opinions of a group of people is sometimes called "groupthink".

## Friday, November 1, 2019

### Jobs day: October 2019

The Employment Situation data from BLS was released on FRED today (a.k.a. "Jobs Day") which includes the latest  unemployment rate and the "prime age" (25-54) labor force participation rate data among many other measures. I've emphasized those two particular measures since I've been tracking the performance of the Dynamic Information Equilibrium Model forecast since 2017. And now, almost three years later, they're as accurate as ever (black is the post-forecast data):

For a bit of context, here's a rogues' gallery of forecasts from the Federal Reserve Board of San Francisco (FRBSF), Ray Fair, Nobel laureate Paul Romer (a prediction from 2017 [1]), and Jan Hatzius (Goldman-Sachs) [click to enlarge]:

Additionally, PCE inflation data came out yesterday — it was also in line with the (very boring) DIEM forecast:

...

Footnotes:

[1] Also in the tweet with the unemployment prediction is a horribly wrong labor force participation forecast (the DIEM model of CIVPART was based on the dynamic equilibrium for the prime age participation rate forecast above). Click to enlarge:

## Saturday, October 26, 2019

### Exploration of an abstract space: prices, money, and ... ships at sea?

 AIS data from ships at sea. Credit: Spire Maritime.

I was asked a question on Twitter that I think does help us understand how the information equilibrium framework views prices and money. Of course, it being Twitter, this wasn't exactly asked as a question but rather offered as a condescending retort:
"That guy [i.e. me] is just confused. He doesn't even acknowledge that the price has to be paid. In his model, there is no difference between a price that has to be paid and one that doesn't have to be paid. → there is no concept of truthful revelation."
I do appreciate the fact that he must have read the material because he came away with a conclusion that is in fact true. The implied question is how do I reconcile using information equilibrium to describe not just prices, but also things that have nothing to do with prices as we traditionally think of them.

What follows is an edited and expanded version of my response on Twitter with links.

The issue is that there is absolutely no way, mathematically speaking, for that "truthful revelation" message of paying a price in a single transaction to be communicated through the network. The set of prices simply does not contain the "bandwidth" to carry that information. In mathematical terms, the dimension of the space of price messages is so much smaller than the dimension of the space of information about the transaction. So therefore, neither that "truthful revelation" information nor paying the price could be critical to the functioning of a market. More likely (but still speculative), the price mechanism is destroying huge quantities of irrelevant information via what is called an "information bottleneck" in machine learning.

In fact, what's more important is when a transaction cannot happen. That non-transaction carries so much more information about macro constraints (buyers cannot afford it, do not want it, have a substitution, sellers do not have enough, or it cost more than the current price to manufacture) — mapping out the opportunity set. (Again, maybe the information bottleneck is singling out the lower-dimensional subset of transactions that map the opportunity set.)

A good analogy of what those abstract "tokens" we call money are doing is that it's the same thing ships do in the ocean — they both mediate a transaction and explore an abstract space. In the picture below, we have a bunch of AIS data from ships near the port of Galveston/Houston Ship Canal. Ships generally try to take the shortest, most efficient path between their origin and destinations, but can also travel anywhere the water is deep enough. Sometimes they have to avoid storms, and sometimes they have to follow specific paths — like the well-defined Houston Ship Canal in Galveston Bay.

No one journey maps the world, but a collection of their paths creates an (albeit incomplete) picture of the world. That's the graphic at the top of the post — it's AIS data alone, yet it develops a strikingly good map of the continents. The ships exploring the "opportunity set" of the ocean collectively map out the complex set defined by macro constraints (i.e. continents). That's what money is doing, except it's a more abstract space we can't see.

Or at least that's what money is doing if the information equilibrium picture of economics is correct! Information equilibrium follows from agents fully exploring (i.e. MaxEnt) the the available opportunity set — or as I sometimes put it "state space". Random agents do that, but to a good approximation so do complex intelligent agents where you don't necessarily understand how they make their decisions — the limit of algorithmic complexity is algorithmic randomness. Often people will say that I treat people like mindless atoms, but that's just a useful approximation — and humility! I don't pretend to know how people make complex decisions, so I effectively treat them as so complex as to be random.

We can see that the AIS picture of the continents is incomplete. That's what the framework calls "non-ideal information transfer". It's non-ideal information transfer from the information defining the shape of the continents to the information in the AIS tracking data. I talk about that in more detail in my Evonomics article (which brought me into that Twitter thread) as well as in my talk at UW econ. The key takeaway is that the information transfer framework (which is both information equilibrium and non-ideal information transfer) assumes markets are not necessarily ideal — that the AIS map of the continents is imperfect.

In addition to non-ideal information transfer, there are also non-equilibrium shocks. In the AIS picture, that would be things like embargoes against certain countries or major storms that disrupt shipping. The dynamic information equilibrium model (DIEM) — information equilibrium plus a model of non-equilibrium shocks — is one way to try and model these effects that's remarkably successful in describing e.g. the unemployment rate (tracking it for over two years, and outperforming several other models):

Speaking of the unemployment rate and getting back to the original "question" at the top of the post, what's interesting to me is that the process of exploring the opportunity set is what happens in every "market" even if there aren't "prices" in the usual sense. Or at least where "prices" aren't always the observable data. An example is the job market. The observable "prices" in that case are hires or unemployment — salaries are often not as easily measured as stock market prices. Human agents explore the abstract space of employment opportunities that are in aggregate bounded by macro constraints — even if you can manage to talk your way into an employer hiring you against their initial objections (i.e. influence the local shape of the opportunity set) there are still constraints in the aggregate.

That's why it's more useful to think of prices more abstractly — they represent a transaction where an some amount of A is exchanged for some amount of B. That A can be a job, money, blueberries, or your free time. Mapping the abstract constrained opportunity set with transactions is about information and doesn't care what's doing the mapping or the content of the message — the key insight of information theory. When those things matter, we're back to non-ideal information transfer [1].

That's why "there is no difference between a price that has to be paid and one that doesn't have to be paid" — if an observable represents information about a change in the information content of an opportunity set (a hire, a market price change), then there's economics happening there. Information is flowing — from person to person at the individual level — but the price (even an abstract one like the unemployment rate) is really only seeing changes in information flow.

...

Footnotes:

[1] There's a neat mathematical illustration of this using the chain rule — in fact, we can think of money (or ships!) as a real-world manifestation of a chain rule for an economic derivative. If we exchange A for B, we have an exchange rate "small amount of A" ($dA$) to "small amount of B" ($dB$) or:

$$\frac{dA}{dB}$$

... a derivative in calculus. Of course you could exchange A for a small amount of money ($dM$) and money for B:

$$\frac{dA}{dB} = \frac{dA}{dM} \frac{dM}{dB}$$

That's just the chain rule in calculus. As long as we maintain information equilibrium between A, B and M, then money doesn't really matter.

As a side note: ships are an example of tokens that go with the flow of the transaction, as opposed to money going in the opposite direction. It's interesting as the direction of exchange for money is basically a sign convention in information equilibrium as I mention in a footnote here that also gets into the discussion of the direction of information flow that came up in some of my earliest posts.

## Thursday, October 10, 2019

### Wage growth in NY and PA

Without meaning to start an argument, I concurred with Steve Roth and @Promethus_Fire that a minimum wage study by the NY Fed might not have taken into account factors that may have confounded the study in contradiction to J. W. Mason's assertions without evidence that a) border discontinuity automatically controls for them (it does not), and b) economic data is continuous across the NY-PA border (it is not, and I provide several examples that by inspection should give us pause in making that assumption).

Even otherwise arbitrary political boundaries that you might think were transparent to the people living there create weird effects. One example I remember vividly on my many drives between UT Austin and the suburbs of Houston (where I grew up) on US 290 while I was a student was the border between Washington county and Waller county whereupon crossing the Brazos river the road suddenly became terrible. There's no particular reason for this in terms of demographics or geography, but the political boundary meant some completely different funding formula or crony capitalist network at the county level. Something similar happens at the NY-PA border:

On the NY side we have shoulder markings and shoulders that vanish right when you cross the border into PA. It's a tiny difference, but it means more materials and hundreds more labor hours of public spending on the NY side of what is basically the same road. And it's not like people travel into PA never to be heard from again — on this stretch of road traffic is likely balanced in either direction and most certainly isn't discontinuous at this specific point.

Anyway, that was the point I was trying to make. Other things like level of education also vary across this border as well as the PA side being much more likely to have an old-fashioned male breadwinner model of household income. My most recent piece of evidence was that the rate of foreign born residents was higher on the NY side (which looks like New England) than the PA side (which looks like West Virginia).

But then J. W. Mason expressed incredulity at my claim that the wage growth data was relatively smooth. This led me down a rabbit hole where I put together a dynamic information equilibrium model (DIEM) of wage growth on both sides of the border based on the NY Fed data. This data was restricted to leisure and hospitality sectors, but it turns out to be interesting nonetheless. Here's the NY Fed's graphic:

Now I put together the wage growth model at the national level about two years ago. And one of the reasons I went down this rabbit hole was that the Atlanta Fed just released data for September in their wage growth tracker today and I had just compared that data with the forecast:

Pretty good! And it's definitely better than any other forecast of wage growth in the US that's available. If we use this model to describe the NY and PA data, we get a pretty good fit:

There's a single non-equilibrium shock that slows growth that comes right at the beginning of 2012 — coincidentally right when the ARRA deficit spending dries up. There are no other effects and the rest of the path — including all the data through the NY minimum wage increases — is a single smooth growth equilibrium.

How smooth? The smooth model fits the data to within about 2%. It's quantitative evidence J. W. Mason's incredulity was completely unfounded. If we look at these residuals (that are less than 2%), there is a noticeable correlated deviation right during the NY minimum wage increases:

However, this correlated deviation is mirrored in the PA data which means that PA and NY saw the same deviation from smooth growth. There's no meaningful difference between the two that's correlated with the NY minimum wage increases: both saw the same correlated deviation, but more importantly both saw basically wages grow as expected with the deviation from trend growth being less than about 2%. If you forecast in 2010 that average wages would be 10 dollars per hour in 2016, they'd be 10 dollars ± 20 cents.

[Update 13 November 2019] Additionally, that correlated deviation in wage growth matches up the the national level surge in wage growth in 2014-2015 (two figures above). [End update]

It's important to emphasize the part about the lack of differences correlated with the minimum wage hikes — over the entire period, wage growth is not just higher but it increases faster on the NY side. But that's a difference between the NY and PA sides of the border that's persistent through the period 2010-2019.

Does this mean minimum wages are bad? No! In fact, since wages are largely a good proxy for economic output, it means that this shows minimum wages likely have no effect on economic growth. Unlike the naysayers who say minimum wage hikes slow growth or cause unemployment, this aggregate data shows they have no real effect.

Wait, no effect? How can that be good?

Because it's no effect at the aggregate level. At the individual level, earning more money for an hour of minimum wage work is a great benefit since one earns the money faster while allocating a given amount of one's limited time to work. If you don't see any aggregate effects, it basically means minimum wage workers effectively have more free time since they're ostensibly producing the same output for the same total compensation (which they arrive at faster because of the higher wage) — otherwise, there'd be aggregate effects!

If your car gets a boost and now travels 100 mph instead of 70 mph, but you still get from Seattle to Portland in three hours, you must have had spent more time stopped at a rest stop or eating at a restaurant — increased leisure time.

Of course, this is assuming the data is measured properly and these conclusions are correct about no aggregate effects — some studies see net gains from minimum wage increases (i.e. we get from Seattle to Portland in two and a half hours).

## Wednesday, October 9, 2019

### Calling a recession too early (and incorrectly)

A little over a year ago, I said that the JOLTS Job Openings Rate (JOR) data was indicating a possible recession in the 2019-2020 time frame based on the dynamic information equilibrium model (DIEM). It appears that even if there is a recession in 2020, this "forecast" will not have been accurate. This post is a "post mortem" for that failed forecast looking at various factors that I think provides some interesting insights.

Data revisions

As noted in the forecast itself, there was always the possibility of data revisions — especially in the March data release around the Fed March meeting. The March 2019 revision was actually massive, and affected every single data point in the JOLTS time series ... in particular JOR. It made the previous dip around the time the forecast was made largely vanish.

The original reason to look to JOLTS data as a leading indicator was based on the fact that the JOLTS measures seemed to precede the unemployment rate in terms of the non-equilibrium shock locations. In 2008, the hires rate (HIR) seemed to lead with JOR closely following. Closer analysis shows that HIR falls early in part due to construction in the housing bust (which also affected JOR). Now I speculated at the time that the ordering probably changed depending on the details of the recession. In the more recent data, it looks like the quits rate (QUR) might be the actual leader. This would make more sense in terms of a demand driven and uncertainty-based recession where people cut back on spending or future investments (or having children) and so seeing a rough patch ahead might be less inclined to quit a job.

Second order effects!

Recently I noticed a correlation in the fluctuations around the dynamic equilibrium for JOR and the S&P 500. A rising market seems to causes a rise in JOR about a year later. When the forecast was made in 2018, the market rise of 2017 had yet to manifest itself in the JOR data. The "mini-boom" of 2014 along with the precipitous drop of 2016 made it look more like a negative shock was underway.

I should note that these fluctuations are on the order of 10% relative to the original model (i.e. less than a percentage point in estimating the rate), so represent a 10% effect on top of the dynamic equilibrium.

Mis-estimating the dynamic equilibrium

These various factors combined into a bad estimate of the JOR dynamic equilibrium that was much larger (i.e. higher rate) than it appears today. The rate was estimated to be about 25% higher (10.7% versus 8.7%), which meant a persistent fall in JOR relative to the forecast:

I should also note that the entropy minimization procedure (described here as well as in my talk at UW econ) has a much better result (i.e. well-defined minimum) with the additional data:

This did not affect the other JOLTS measures as strongly — and in fact the HIR data has shown little evidence of a "recession", especially since I discovered the longer HIR data series a couple months after the original forecast. The quits data has only recently been showing the beginnings of a deviation from the original 2017 forecast:

While all this is bad for my 2018 recession prediction, it actually means the dynamic equilibrium model was really good at forecasting the data over the past two years.