Saturday, August 5, 2017

Dynamic equilibrium in average hourly wages

Another piece of data FRED updated on Friday was average hourly earnings. Being a price (and a ratio), the dynamic equilibrium model should be applicable. Sure enough it is (and it works really well):

What is interesting to me is the "Phillips curve" behavior ‒ the bursts of wage increases prior to recessions (and reductions in the civilian labor force):

The large, broad increase in wages is associated with the broad increase in the labor force. The Great Recession is associated with a decrease in wages and a negative shock to the labor force. The other four smaller wage increases occur just before recessions in a similar fashion to the smaller shocks impacting PCE inflation:

Essentially, this creates a picture where there are two kinds of shocks to wages: demographic and post-recovery/pre-recession shocks that occur just before recessions. There was a broad demographic increase in wages associated with women entering the workforce, and a smaller one associated with the Great Recession (I imagine early/forced retirements of some "Baby Boomers" [1]). The smaller and narrower positive shocks occur between recessions (centered in 1980 ‒ i.e. between the 1974 and 1981 recessions ‒ as well as 1989, 1997, and 2007). These match up with shocks to PCE inflation. This is not to say the post-recovery/pre-recession shocks cause recessions. They likely don't; what happens is that wages start to rise and a recession intervenes cutting the improvement short.

This would tell a story of why wages are stagnant: wages haven't increased because there haven't been any demographic increases in the labor force and because too many recessions have cut wage growth short. According to the model, wages grow at an average rate of 2.3%. However rising wages between recessions are a significant component of higher wages.



[1] This creates an interesting hypothesis: was the Great Recession bad simply because it occurred when Baby Boomers started to reach retirement age? The baby boom is generally associated with beginning in the 1940s, and the 2008 recession was the first one after 1940 + 65 years = 2005. Forget the Fed's missteps or over-leveraged banks ‒ was the Great Recession inevitable after the post WWII baby boom?

Friday, August 4, 2017

Labor market model updates

There were some labor market data releases today, including the civilian labor force ("prime age") and the unemployment rate. So I've updated the graphs (including the one in this discussion of forecast stability). The black points are the new data. I added the RMS error to the unemployment rate change graph as well.

Thursday, August 3, 2017

More updates to the python IEtools

I added some more functionality to the package (on GitHub) for working with information equilibrium. There's now a fitting function for the parameters in an information equilibrium relationship as well as better file readers (FRED xls and csv), and the imported data structures now include growth rates and interpolating functions.

There's also a little demo of Okun's law.

Comparing recoveries

One of the points I try to stress on this blog is that models can be used to frame data. The tweet above shows one particular framing of investment data that shows the post-Great Recession recovery has been lackluster compared to other recoveries.

I used the same framing for nominal GDP data (which is roughly proportional to investment):

Included alongside the data is the dynamic equilibrium model of GDP (that I previously used in two discussions of data framing) shown with dotted lines. They follow the data fairly closely. In fact using this framing, the issue with the present recovery is that it's normalized to the housing bubble peak, but is otherwise right on track:

However, the dynamic equilibrium model essentially says there are few long-run features of the NGDP data. In a sense there are only three between 1948 and the present:

  • The Korean war and the permanent build-up of the Department of Defense (the military-industrial complex)
  • Women entering the workforce
  • The housing bubble

This means that, using this frame, the gradual fall in recovery performance is really about the gradual fading of the burst of nominal growth that came with women entering the workforce and has little to do with policy choices of the present compared to policy choices of the past [1]. Other recoveries were stronger because they were riding a wave where half the population was moving into GDP-measured work.



[1] I want to stress that this doesn't mean policy couldn't change the situation. They would just have to be policy choices on the scale of the social change involved when women entered the workforce, or generating the military-industrial complex. For example, there is some evidence that the Affordable Care Act (Obamacare) may have generated a small economic boom in terms of employment. It does not appear to be large enough to show up in the NGDP data, though.

Wednesday, August 2, 2017

Great Recession timing by state

Using the dynamic equilibrium model with state-level (not seasonally adjusted) unemployment data, I put together a collection of the centroids of the Great Recession shock by state. Here are all the fits on a single graph:

And here is a histogram of the start dates:

I was testing to see if any pattern could be discerned (e.g. did the Great Recession start somewhere specific and spread?), but the result looks pretty random (blue late, red early):

The unchallenged assumption of human agency in economics

One of the things I read in multiple places is that economics is different because its subject is human beings who can reflect on the findings of economics and change their behavior. And while I do think this is possible for some economic observables, I do not think it is inevitable for every economic observable. Part of the reason is that I do not think humans are "really thinking" about many of their economic choices. Additionally, there's actually some evidence that humans aren't really thinking about interest rates for example.

Despite the sometimes convoluted rationales one hears about investment decisions from co-workers, I am under the impression that many of those decisions are made for reasons not known to the decider.

This is one step beyond what I usually assume as a basis for the information equilibrium approach -- instead of the the rationales being inscrutable to the economic theorist, they are in addition inscrutable to the economic agent.

Today, Sean Carroll linked to a piece about a philosophical discussion about comprehension and consciousness, and the Daniel Dennett's ideas could form a philisophical basis for the even stronger assumption. The introduction to the debate states:
On comprehension, [Daniel] Dennett maintains that much animal and indeed human behaviour displays “competence without comprehension”, achieving ends without the subject’s understanding why. In a similar vein, he holds that human cultures can develop blindly, due to the natural selection of the “informational viruses” that Richard Dawkins has labelled “memes”, including some of the greatest products of human culture ... 
When we get down the the debate itself, Dennett says:
I am claiming – and it seems quite obvious to me, not in the least “peculiar” – that we must break our habit of assuming “thinking” whenever we see cleverness.

As Dennett points out, we are uncomfortable with this idea:
People are generally comfortable with the discovery that they have no direct knowledge “from the inside” of the properties of the blood-purifying events in their kidneys, or of the properties of the peripheral events in the eyeball and optic nerve that subserve vision, but the idea that this ignorance of internal properties of the relevant events in the brain carries “all the way up” is deeply counterintuitive. 
Of course it's not an absolute, but as Dennett says human ingenuity may have less of a role than we think:
Yes, some of the marvels of culture can be attributed to the genius of their inventors, but much less than is commonly imagined, and all of it rests on the foundations of good design built up over millennia by uncomprehending hosts of memes competing with each other for rehearsal time in brains ...
So when economists start with rational agents, or even agents that have "agency", we have to understand this is actually a philosophical assumption turned modeling assumption and not necessarily obvious.  And may in fact be behind some of the problems of economic theory.

If correct, this will probably be the hardest idea to convince people of ...


Update 7 August 2017

Thanks to Chris Dillow for linking to this post. You should read his ‒ he gives more practical reasons instead of "high-falutin’ grand theory".

One thing I did want to emphasize is that regardless of whether humans really are thinking about economic choices, it is effectively a model assumption to start your economic model with agents thinking about their choices. Like all assumptions, this may or may not be a good model choice. You can start modeling an ideal gas by first figuring out the quark states in atomic nuclei and then build up atoms and molecules, finally doing a vast simulation using individual atoms figuring out that the pressure is inversely proportional to the volume. An easier way is to start from simply the idea that an ideal gas is made of a lot of something.

The issue is that no one has yet built up an empirically accurate model of the macroeconomy starting from the idea that humans are thinking about their decisions (or from agents at all). For specific assumptions about how humans think, there are even theoretical results that show those assumptions have no consequences (the famous SMD theorem). And for microeconomics, it's actually not necessary for agents to think about their decisions to obtain some standard economic results (for example, there is Gary Becker's paper about "irrational" agents, or see here where I reproduced the results of John List's experiments using random agents).

It seems like the natural starting point to think about economics is human decisions ‒ and even our own experience, attempting to probe our own minds for insight. But maybe this is just a bias because we ourselves are humans. When dealing with animal ecosystems, biologists don't usually start from their intuition of what the animals are thinking. In fact, there exist examples where the animals are treated pretty much like molecules in a chemical reaction.

In fact, one of the best economic models treats humans as not fully thinking about their decisions (random utility discrete choice models). Maybe we should open up the field to a less human decision based, more pluralistic approach where the primary metric is empirical (external) validity ‒ not whether the model satisfies our biases about how an economic model should work.

Tuesday, August 1, 2017

Economics criticism as art criticism

“To justify its existence, criticism must be partial, passionate, and political, that is to say, written from an exclusive view that opens the widest horizons.”
In reference to an article about economics education, Steve Keen said [1]:
... they use the word "complex" while clearly not understanding its modern meaning
The word "complex" does not have a specific modern meaning. Saying an economist misunderstands the modern meaning complexity is about as meaningful as writing an art review stating an artist misunderstands the modern meaning of complexity, which is to say: not.

In reference to Tony Yates saying Keen was policing heterodox semantics in the use of "complex", Keen goes on to say:
 ... And it's maths semantics by the way, not economics. Look it up.
I have no idea what Keen means here, because while there are different definitions of "complex" used in mathematics they are either nonsensical in this context or undermine Keen's own work ...

Complex numbers? Obviously not.

Group complexity? Ha ha. No.

Computational complexity? Pretty sure Keen doesn't mean the economy is NP-hard.

Complex dynamics? Does he mean this? Because this is the mathematics definition. What Keen does is actually just dynamical systems (which includes Lorenz attractors) as opposed to complex dynamical systems. Basically, if this is what he means, Keen should leave off the "complex" adjective. However that makes his comment about "complex" self-refuting, and its inclusion a meaningless affectation. Yes, I include complexity. How? By calling them complex dynamical systems instead of just dynamical systems.

Kolmogorov complexityThe definition here is the length of the shortest computer program that reproduces the output. In the context of economics this means that a Kolmogorov complex economy would essentially require simulating the entire economy down to every agent, every firm. In contrast, Keen's approach that says a system of dozens of nonlinear differential equations that can be written down on a few pages can capture the main behaviors of an economy unequivocally demonstrates that by this definition economies are not complex. [As an aside, this is what I mean when I say economic agents are complex.]

Complex adaptive systems? This is not really mathematics, but rather a general collection of ideas. One of those ideas is this:
Complex systems consist of a large number of elements. When the number is relatively small, the behaviour of the elements can often be given a formal description in conventional terms. However, when the number becomes sufficiently large, conventional means (e.g. a system of differential equations) not only become impractical, they also cease to assist in any understanding of the system.
Emphasis in the original. This is a quote from leading complexity theorist Paul Cilliers' Complexity and Postmodernism: Understanding Complex Systems [pdf], and it basically refutes Keen's approach to economics with his Minksy software which consists of differential equations.

*  *  *

Maybe by the modern definition of complex, Keen just means something like the Facebook setting for relationship status "It's Complicated" (which I used as a title for my piece on exactly this problem, and see also here). Similarly, Keen also appears in the documentary Boom Bust Boom for a few seconds, mentioning money and debt. However, later on the film had someone else say that economics shouldn't be approached like a branch of theoretical physics. If I had to pick an economist who used the most inappropriate physics models, it would be Keen who treats the economy like it's a nonlinear electronic circuit with his Minksy software. It's a very odd juxtaposition. Additionally, like asserting complexity, decrying economics as too physics-like [2] is another buzzphrase in economics similar to juxtaposition in art (at least in the 90s and 00s).

However with the last complexity definition, you may have noticed the rather jarring appearance of the word "postmodernism" ‒ or at least it might have been more jarring if I hadn't sprinkled this post with references to art criticism, Baudelaire, and juxtaposition.

In reading recent economic criticism, it seems like more and more art criticism ‒ art criticism of a movement falling out of fashion. Noah Smith writes that even the art criticism is becoming predictable:
At this point, blanket critiques of the economics discipline have been standardized to the point where it’s pretty easy to predict how they’ll proceed. Economists will be castigated for their failure to foresee the Great Recession. Some unrealistic assumptions in mainstream macroeconomic models will be mentioned. Economists will be cast as priests of free-market ideology, whose shortcomings will be vigorously asserted. We will be told that economics moves in cycles of fad and fashion. Readers will be reminded that economics deals with humans instead of atoms, making scientific certainty impossible. The piece will end with a call for humility on the part of economists, a more serious consideration of unconventional ideas and reduced prestige for the economics profession.
I had fun reconstructing a loose facsimile of this generic critique out of Baudelaire quotes about art and other things:
In order for the artist to have a world to express he must first be situated in this world ... In art, there is one thing which does not receive sufficient attention. The element which is left to the human will is not nearly so large as people think. ... The priest is an immense being because he makes the crowd believe astonishing things. ... That which is not slightly distorted lacks sensible appeal; from which it follows that irregularity – that is to say, the unexpected, surprise and astonishment, are a essential part and characteristic of beauty. ... An artist is only an artist on condition that he neglects no aspect of his dual nature. ... What is art? Prostitution.
You really only have to read "human will" as "rational agents" and "astonishing" with a negative connotation to pretty much capture it. But the real point here is that these critiques are not scientific ones based on technical arguments and empirical testing. They are critiques of "realism" or the "use of math". Realism is subjective -- it depends on scope and scale of the theory. Math is a tool. The critiques of mathematics in economics play out like critiques of a photographer's use of light, or an artist's use of mixed media. There's something wrong with it in an aesthetic sense, not a technical one (see more here and here).

The terms used in economics critiques take on lives of their own much like how the terms in art criticism take on lives of their own. "Complexity" means something different in economic criticism than it does in science (or even in economic theory). Phrases like "physics envy" and calling for "pluralism" just mean "wrong using math" and "listen to me".

And like many art critics, economics critics don't produce a lot of successful results themselves.



[1] Each of these quotes can be obtained from Twitter at this link.

[2] Ironically, the foremost research institute for complex adaptive systems (Santa Fe) was founded by (and is staffed by) several physicists so the the complaint that economics is too physics-like yet doesn't properly understand complexity is ... an odd juxtaposition.

Bootstrapping measurements

First, this isn't about bootstrapping in stats. It's about something more fundamental to the scientific method.

I've been seeing an idea crop up again ‒ in a recent comment that I can't seem to find right now, on Twitter, and in a blog post from Roger Farmer:
My talk was predicated on the fact that there can be no measurement without theory ...
This is one of those ideas that seems to have morphed from something insightful into something that very serious people say [1].

Yes, in some sense any "measurement" is going to be made inside some paradigm that is going to influence the measurement process (what to measure, how to measure, or whether a measurement is showing a "change"). It's the subject of James Burke's great documentary series The Day the Universe Changed where he explores how conceptual frameworks (theory) influence how the universe is perceived (measurement).

What is forgotten is that there are different degrees of influence. Sure, using an HP filter with GDP data leaves the idea of a recession defined by GDP shocks entirely up to the theorist. Your "theory" of how smooth GDP "should be" determines whether or not you see recessions in the GDP data. Even more theory goes into whether or not you think GDP is above or below potential.

In contrast, unemployment rates are pretty straightforward measurements that don't involve a lot of macroeconomic theory to interpret. Sure, there are theories involved in turning responses to the surveys (you might use an optical transfer function of a telescope as an analogy for the corrections to survey data) into unemployment rate data and different definitions of "unemployed" (for which data are also available). However, none of those caveats depend strongly on your macroeconomic theory. Whether unemployment is "high" or "low" depends on your theory (i.e. the counterfactual), but the time series is just an (imperfect) empirical measurement of the number of people without jobs who want one.

In macroeconomics (or economics in general) there exists a hierarchy of empirical measurements that depend more or less strongly on your theoretical framework. Here's a heuristic hierarchy starting from least theory dependent to most theory dependent with some examples:

S&P 500 (least)
Unemployment rate
Non-accelerating rate of unemployment
Natural rate of interest (most)

It is important to note that the S&P 500 measurement itself is not theory dependent. It is the weighted sum of some stock values. The S&P 500 is not "really" some other value in the sense that GDP could "really" be much higher because of stuff that isn't included. Whether or not this measurement is important to the economy is theory dependent, however.

The same kind of thing exists in physics. The QCD scale is theory dependent (and even regulator scheme dependent). The temperature outside is less theory dependent. The mass of an object is even less theory dependent.

And it's a good thing this hierarchy exists! Because otherwise science would never work. If all observations were strongly theory dependent, you'd never have a set of observations you could use to get started theorizing. Any observation would've come via some other implicit theory, so you couldn't use it to motivate your own theory. (I guess there's the outside chance you just happened to stumble upon the theory that explains everything at once right out of the gate.) You need a set of measurements that enables you to bootstrap into the push and pull of theory and evidence that we call science.

Physics started with falling objects. Evolutionary biology started with counting different creatures. Prices and counting seem like a good start for economics [2]. In any case, the idea that there can be no measurement without theory should be a qualified statement.



[1] I think another case of very serious people discussing economic methodology comes in the form of "complexity".

[2] I mentioned this before here, but counting and motion represent the two big paradigms of mathematics: algebra and calculus. And instead of the diagram from XKCD, I actually see two pyramids with physics at the top of one and economics at the top of the other with mathematics in the intersection. Money and physical reality (geometry, motion) are the two major drivers of mathematics and the mathematics that is actually developed tends to be constrained by this. In the 1200s Fibonnacci introduces algebra and "Arabic" (Indian) numerals in Italy for merchants' accounting an interest computations. Adelard is involved int he reintroduction of geometry and astronomy to Western Europe a bit before. You can also see the difference in that algebra was for business, but geometry and motion were more heavily involved with astronomy and time (and hence religion). Consider this a more social view of mathematics as a human institution instead of a philosophical view from Plato's cave.

The unrealistic assumptions of information equilibrium

The title is a bit of a joke as information equilibrium basically assumes humans are pretty ignorant about the details of economic processes ‒ a manifestly realistic assumption in my opinion. Anyway, I was reading Brad DeLong's blog post of contrition; it includes a lot of assumptions that he came to re-think after the financial crisis. This inspired me to write down the assumptions that go into the information equilibrium approach generally, but specifically because a particular point DeLong makes that I will use below.

Information equilibrium

First, information equilibrium between observable process variables A and B  (e.g. GDP and total employment, supply of toilet paper and demand for toilet paper) is not just assumed. It is first shown to be an empirically accurate description in the past and present, and assumed to hold in the future based on what is essentially Hume's uniformity of nature assumption [1]. The Lucas critique is frequently brought up in this context, essentially asserting the opposite. However, the uniformity of nature assumption is bolstered by the generality of the assumptions underlying an information equilibrium relationship.

These assumptions are:

  1. We are generally ignorant of the micro processes behind the two observable process variables A and B that are in information equilibrium. We only assume that the micro processes fully explore their respective micro process state spaces, are uncorrelated, and represent a large number of selections from those state spaces.
  2. We are completely ignorant of the micro processes behind the transfer system of information from one process variable to the other.

The first assumption says that if rolling 6-sided dice generates the process variable A, then those 6-sided dice will land on each side and there are lots of dice.

The first assumption is also what I mean when I sometimes say I assume humans are so complex, they can be treated as random. Randomly selecting states in a state space is not functionally different from complex agents that fully explore the state space through some unknown algorithm or algorithms that are algorithmically complex.

The piece about being uncorrelated will raise some eyebrows for lots of reasons, but it really isn't as unrealistic of an assumption as it seems. First, because it really isn't assumed -- it just separates information equilibrium from non-ideal information transfer (below). And second, because what really matters is temporary correlation. A large fraction of people in the US go through a generally correlated lifestyle where they are born, go to school, get a job, and work for some period of time. Many schools in the US are on a schedule with summers off. This causes some of us to be correlated in our graduation dates (high school in May or June year x, college in May or June of year x + 4). This is not the important correlation in the assumption above. The state space for the micro process is in a sense inaccessible.

The important (and regime-switching between ideal and non-ideal information transfer) uncorrelated behavior is that you and I don't buy toilet paper or sell a stock at the same time. If we do, that's important -- in the case of a stock, it can trigger a sell-off. Generally in equilibrium there are buyers and sellers of both toilet paper and stocks.

When I say uncorrelated, I mean agents (micro processes) are going about their business without regard to what a majority of other agents are doing. If they correlate, then we're in "information disequilibrium" (discussed below).

Dynamic equilibrium

This is a special case of information equilibrium where the large number of micro processes and selections from the state space is growing exponentially in the long run, except for a finite number of disequilibrium shocks. It is not so much assumed as empirically tested. The same assumptions as information equilibrium apply; their generality lends weight to the uniformity of nature assumption underlying the approach to forecasts.

Information disequilibrium (non-ideal information transfer)

Regarding that DeLong post, here is his point that inspired me to write down these assumptions:
... the discovery that the rating agencies had failed in their assessment of lower-tail risk to make the standard analytical judgment: that when things get really bad all correlations go to one.
In a sense, the information transfer framework operationalizes this assumption into a "founding principle": when things get "bad", those micro processes correlate and information equilibrium fails. Generally speaking, there should be only a finite number of discrete "bad" periods. The "bad" periods will show up as deviations from information equilibrium [2].

Again, it is not so much of an assumption but rather a usefulness criteria: if things are persistently "bad", then information equilibrium isn't a useful framework.



[1] I would like to point out that the general uniformity of nature assumption is essentially empty. If nature fails to be uniform in the particular way you thought it was uniform (i.e. your model fails), this does not in any sense disprove that some uniformity no one has thought of exists. That is to say the lack of observation of a particular uniformity does not prove some uniformity does not exist. Therefore assuming uniformity exists cannot be disproved except via an exhaustive search over all possible uniformities.

[2] Non-ideal information transfer lets us say a few things about these "bad" periods ‒ and they will be bounded by the equilibrium solution.

Friday, July 28, 2017

Dynamic equilibrium and ensembles (and collected results)

I previously worked out that ensembles of information equilibrium relationships have a formal resemblance to a single aggregate information equilibrium relationship involving the ensemble averages:

\frac{d \langle A \rangle}{dB} = \langle k \rangle \frac{\langle A \rangle}{B}

I wanted to point out that this means ensemble ratios and abstract prices will exhibit a dynamic equilibrium just like individual information equilibrium relationships if $\langle k \rangle$ changes slowly (with respect to both $B$ and now time $t$):

\frac{d}{dt} \log  \frac{\langle A \rangle}{B} \approx (\langle k \rangle - 1) \beta

plus terms $\sim d\langle k \rangle /dt$ where we assume (really, empirically observe) $B \sim e^{\beta t}$ with growth rate $\beta$. The ensemble average version allows for the possibility that $\langle k \rangle$ can change over time (if it changes too quickly, additional terms become important in the solution to the differential equation as well as the last dynamic equilibrium equation).

Generally, considering the first equation above with a slowly changing $\langle k \rangle$, we can apply nearly all of the results collected in the tour of information equilibrium chart package to ensembles of information equilibrium relationships. These have been described in three blog posts:
1. Self-similarity of macro and micro 
Derives the original ensemble information equilibrium relationship 
2. Macro ensembles and factors of production 
Lists the result for two or more factors of production (same result gives matching models) 
3. Dynamic equilibrium and ensembles 
The present post arguing the extension of the dynamic equilibrium approach to ensemble averages

Thursday, July 27, 2017

Adding race and gender to macroeconomics

Narayana Kocherlakota has an article at Bloomberg View about how macroeconomists can't keep ignoring race and gender ‒ something I agree with. In fact, I believe that ignoring race and gender has lead to two major misunderstandings in macroeconomics ... two misunderstandings that can be clarified by use of the dynamic equilibrium model.

Women entering the workforce

There are a variety of explanations of the so-called "Great Inflation" of the 60s and 70s, some monetary, some focused on government spending. However, due to the strong connection between labor force growth and inflation (see also the piece on demographic inflation by Steve Randy Waldman aka Interfluidity), it seems likely that the long non-equilibrium process of women entering the workforce in the 1960s and 70s is the causal factor. The main shock to the civilian labor force participation is dominated by the effect of women getting jobs and the employment-population ratios for men and women show different general structures in terms of dynamic equilibrium:

In fact, using the charts from here to display the shocks (shown as vertical lines in the graphs above) and their width (duration), we can see that the shocks to the labor force participation and to the employment population ratio for women precede the shocks to inflation using various measures:

[added in update] Positive shocks to the measure in blue, negative shocks in red. (Note that the increase in labor force participation for women consists of a long positive shock with a few negative shocks corresponding to recessions that aren't shown.)

Racial disparities in unemployment

Another area where macro without race and gender leads to misunderstanding is in unemployment rate dynamics. Ordinary observation of unemployment statistics leads Kocherlakota to write:
Arguably the most important is that blacks ‒ especially black men ‒ are much more likely to lose their jobs. This risk of job loss is highly cyclical, which is why blacks fare so much worse than whites during recessions. For example, the black unemployment rate peaked at nearly 17 percent after the Great Recession, compared with just over 9 percent for whites.
The wrong framework (and general lack of including race and gender) leads Kocherlakota to the wrong diagnosis in this case. The problem is not necessarily a dynamic one (i.e. due to black losing jobs more than whites), but rather one of hysteresis [1]. The overall dynamics for black and white unemployment are approximately the same (with this model indicating a similar matching function).

In the graph above, the black dynamic equilibrium is applied to white unemployment with the only difference being the starting value (about 5% instead of 10%). The model describes both sets of data roughly equally well indicating that the issue is initial conditions (slavery, Jim Crow), not present day dynamics. This hysteresis is caused by the fact that unemployment declines at the same relative rate for both black and white workers and both are subjected to the same shocks to the macroeconomy.

One way to imagine this is as two airplanes flying from Seattle to Chicago, with one taking off about an hour later than the other. Since both planes are subjected to the same wind conditions (macro shocks), the plane taking off later never catches up. In this case, the solution required is different from the solution to the problem as diagnosed by Kocherlakota: one would need to either make macro shocks affect black workers less, or increase employment through increased hiring. We are talking about something akin to reparations: Black Americans need to be compensated for being kept out of jobs by racist policies of the past.

Just two examples

Those are just two examples I've seen in my work with the dynamic equilibrium model, but they're definitely not the only ones. The "Great Inflation" sent macroeconomics off on a wild goose chase ending in DSGE models that can't forecast, attributing the inflation to central bank policy (which continues to this day). If it had been understood at the time that a certain amount of inflation would be inevitable because of women entering the workforce, the history of past 40 years of macroeconomics might have been different.


Update: changed EPOP graphs to have the same x- and y-axis. The original graph is here:



[1] When I say hysteresis, I am in no way saying discrimination has ended. For example, being employed does not tell us whether someone is underemployed or paid less for the same job.

Macro ensembles and factors of production

I was inspired by Dietrich Vollrath's latest blog post to work out the generalization of the macro ensemble version of the information equilibrium condition [1] to more than one factor of production. However, as it was my lunch break, I didn't have time to LaTeX up all the steps so I'm just going to post the starting place and the result (for now).

We have two ensembles of information equilibrium relationships $A_{i} \rightleftarrows B$ and $A_{j} \rightleftarrows C$ (with two factors of production $B$ and $C$), and we generalize the partition function analogously to multiple thermodynamic potentials (see also here):

Z = \sum_{i j} e^{-k_{i}^{(1)} \log B/B_{0} -k_{j}^{(2)} \log C/C_{0}}

Playing the same game as worked out in [1], except with partial derivatives, you obtain:

\frac{\partial \langle A \rangle}{\partial B} = & \; \langle k^{(1)} \rangle \frac{\langle A \rangle}{B}\\
\frac{\partial \langle A \rangle}{\partial C} = & \; \langle k^{(2)} \rangle \frac{\langle A \rangle}{C}

This is the same as before, except now the values of $k$ can change. If the $\langle k \rangle$ change slowly (i.e. treated as almost constant), the solution can be approximated by a Cobb-Douglas production function:

\langle A \rangle = a \; B^{\langle k^{(1)} \rangle} C^{\langle k^{(2)} \rangle}

And now you can read Vollrath's piece keeping in mind that using an ensemble of information equilibrium relationships implies $\beta$ (e.g. $\langle k^{(1)} \rangle$) can change and we aren't required to maintain $\langle k^{(1)} \rangle + \langle k^{(2)} \rangle = 1$.


Update 28 July 2017

I'm sure it was obvious to readers, but this generalizes to any number of factors of production using the partition function

Z = \sum_{i_{n}} \exp \left( - \sum_{n} k_{i_{n}}^{(n)} \log B^{(n)}/B_{0}^{(n)} \right)
where instead of $B$ and $C$ (or $D$), we'd have $B^{(1)}$ and $B^{(2)}$ (or $B^{(3)}$). You'd obtain:

\frac{\partial \langle A \rangle}{\partial B^{(n)}} = \; \langle k^{(n)} \rangle \frac{\langle A \rangle}{B^{(n)}}

Gross National Product

I looked at NGDP data in the past with the dynamic equilibrium model (see here [1], and here [2]), however the annual time series on GNP data at FRED goes back a bit further in time and includes the onset of the Great Depression. Here are the results, first using the housing and stock market "bubble" frame for 1990s-2000s, and then the "no knowledge" frame (discussed in [1]):

Here are the GNP growth rates:

It will be interesting to see which one is the better model. The latter suggests a potential "demographic" shift of e.g. baby boomers leaving the workforce over a ten year period centered around 2014.

Self-similarity in dynamic equilibrium

Let me say up front I am not saying the idea that stock market price time series are self-similar is new. What's new is that a specific structure (i.e. the dynamic equilibrium + shocks) appears at different scales. Here we steadily zoom in on the S&P 500 from a multi-year timescale, to a few years, to on the order of a year, down to months (discovering new shocks at smaller and smaller scales):

Wednesday, July 26, 2017

Updating Samuelson's family tree ...

PS This was a bit tongue in cheek.

A dynamic equilibrium history of the United States

In writing the previous post, I got the idea of collecting all of the dynamic equilibrium results for the US into a single "infographic". It was also inspired by the recently scanned 75 Years of American Finance: A Graphic Presentation, 1861-1935, the 85-foot long detailed timeline compiled by Merle Hostetler in 1936 available at FRASER.

Hopefully the chart is fairly self-explanatory: positive shocks in blue, negative shocks in red, recessions in beige. The "tapes" indicate the range of data analyzed with the dynamic equilibrium model. The widths of the bars are proportional to the widths of the shock (roughly, the 1-sigma width).

U is the unemployment rate. CLF is the civilian labor force (participation rate). EPOP is the employment-population ratio (for men and women). PCE is the personal consumption expenditures price index. CPI is the consumer price index (all items), and C-S is the version available with the Case-Shiller data (see here). The Case-Shiller housing price index itself is included along with the S&P 500. AMB stands for adjusted monetary base.

The arrow indicates the non-equilibrium process of women entering the workforce (where I didn't try to decouple the recession shocks from the broad positive shock).

Here is a zoomed-in version of the post-war period:

I'll leave the possible narratives to comments.


Update 4pm

I added the multiple shock version of the PCE dynamic equilibrium discussed in this post on the Phillips Curve. We can resolve the main shock of the 1970s into several shocks; these are shown in purple:

Additionally, we can see the "vanishing" Phillips Curve:

Unemployment shocks are preceded by PCE inflation shocks such that as unemployment recovers from the previous shock, inflation rises (unemployment goes down, inflation goes up, and because an inflation shock is ending when unemployment rises, inflation is going down when unemployment is going up). That goes for the recessions of the 70s, 80s and 90s. However, the early 2000s recession doesn't have a distinct shock (at least one that the algorithm can find in the data), and the Great Recession is preceded by a fairly small shock relative to the previous ones.

And even if it wasn't fading away, the causality is uncertain here. It could well be from unemployment to inflation and not the other way around (i.e. low unemployment causes inflation, but inflation doesn't cause unemployment).


Update 27 July 2017

I updated all the figures with more accurate versions of the widths and years (I had read some of them off the relevant graphs). I also increased the font size a bit and the image sizes because some of the lines are too narrow to show up except on a big image.

Tuesday, July 25, 2017

Causality in money and inflation ... plus some big questions

I noticed that the monetary base had what looks like a series of stepped transitions, so I tried the dynamic equilibrium model out on the data. The description is decent:

I am showing the results assuming a dynamic equilibrium growth rate μ of zero, but I also tried the entropy minimization and found that μ ~ 1.6%. It doesn't strongly change the results either way, so we can reasonably say that monetary base growth dynamic equilibrium is close to zero.

I imagine many readers of econ blogs out there spitting out their coffee and saying: "Close to zero?!!" Yes, the monetary base in the absence of shocks grows about as fast as PCE inflation in the absence of shocks (π ~ 1.7%).

Aha! So, that's basically the quantity theory of money, right?

Well, no.

The interesting piece comes from the big shock in the middle part of the twentieth century. I've looked at several models of several macroeconomic observables that have this major shock, and we can play a game of "one of these things is not like the others":

NGDP [added in update]

1977.5 ± 0.1

1977.7 ± 0.1

1978.3 ± 0.1

(Prime age) CLF
1978.4 ± 0.1

AMB [this post]
1985.2 ± 0.1

The center of the monetary base shock comes well after the inflation, labor force participation, and output per employee. So while the PCE inflation rate and the monetary base growth rate match up in equilibrium (both ~ 1.6-1.7%), shocks to inflation are *followed* by shocks to the monetary base. Causality appears to go from inflation to "money printing", not the other way around.

As a side note, the slowdown in monetary base growth preceding the Great Recession that is used as part of the case for the claim that the Fed caused the recession (by e.g. Scott Sumner) is actually just the end of this large transition/shock in the monetary base.

I have an hypothesis that instead of Fed policy, the labor force growth slowdown might be behind the various bubbles (dot-com, housing) and financial crises of the past few decades. Much of the growth people were accustomed to in the 60s, 70s, and 80s was due to women entering the workforce (enhanced by more minorities in the workforce due to Civil Rights legislation, and by the post WWII baby boom). As this surge in labor force participation faded in the 1990s reaching its new equilibrium, investors looked for new (and potentially risky) sources of growth. This lead to bubbles and crashes as investors sought to maintain the rates of asset growth once supported by a growing labor force.

I am also working on an hypothesis that the Great Depression was caused by similar factors, except in that case it was the agriculture-industry transition that was ending. There was a analogous surge in labor force participation (including a surge in women entering the workforce) in the 1910s and 20s that is apparent in census data (see e.g. here or here).

The question arises: what does a "normal" economy look like? How does an economy that isn't undergoing some major shock (demographic or otherwise) function? I wrote about this before, and I think the answer is that we don't really know as there's no data. More and more I'm convinced we're flying blind here.