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 [Jason Smith] 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, focusing on the elements that map the coastlines rather than the bulk.)

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.

Update 1 Feb 2022

I wanted to add that the price having to be paid does help motivate people to explore that state space (either providing things to exchange for money, or using that money to purchase things). But that motivation exists as an underlying factor for most economic observables. Employment is motivated by needing money, and therefore a job, to live, while employers need employees to make money. Therefore the unemployment rate acting like a measurement of a different kind of price level is not that wild of an idea.

...

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.

As another side note, this is where you end up with if you were to write an introductory chapter in an economics book from this viewpoint.

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).

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.

Leading indicators?

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.