Yes, I've read Duncan Foley. Have you?

I am not as familiar with the works of Pablo Neruda.

One of the most common comments I get asks (in varying degrees of stridency) whether I am aware of the work of Duncan Foley. Have you read Foley? or This has already been done by Foley. It seems people equate any reference to entropy and thermodynamics in economics with Foley.

The most time I've spent on this was answering an email from someone who read my book. In that context, it was completely understandable since I did not reference Foley in the book (for reasons described below). My recent paper directly cites Foley and even includes a footnote about the differences, and in that context I tend to be less charitable.

I am reproducing my email below (with some minor edits). However let me give a TL;DR

• Foley and I may both use partition functions, but these are very general things in mathematics and the Lagrange multipliers and constraints are different — which are the only real properties of a partition function, meaning it's completely different. (I also construct the partition function from an ensemble of markets in my recent paper.)
• Foley asserts prices are Lagrange multipliers (analogous to inverse temperature); in my work prices are measures of information flow and the Lagrange multipliers are related to the size of the economic state space. For Foley, prices determine whether an economy is "hot" or "cold"; for me, a "cold" economy would be large low-growth economy, and a "hot" economy would be a small, emerging one.
• Foley's approach is so analogous to thermodynamics that you'd even have a second law. One of the most important properties of the information transfer approach is that it explicitly allows second law violations from the beginning (and they seem to be key to understanding disequilibrium scenarios like recessions).
• Foley uses utility. I think utility is at worst garbage, at best an unobservable effective field.
• Foley doesn't ever use his theory to describe empirical data, while I do. There are papers where Foley is a co-author that have empirical data in them, but any theoretical description of or lines through the data do not depend on the Foley's thermodynamic theory of economics (and are often just regressions). n.b. Happy to be corrected if I'm wrong about this.
• It is my opinion (!) that Foley's approach isn't the best, but I don't think Foley is prima facie misguided or his approach will never lead to a successful theory. It could! It doesn't seem to have yielded any major empirical successes yet, however.

Anyway, here's (most of) my response to that email from a reader regarding Foley:

...

I am aware of Foley's work. One of the first things I did when I started applying communication/information theory to prediction markets and thought I had something new was a big literature search — and any search on entropy and economics brings up Foley. The strongest connection between my work and Foley's work is "statistical equilibrium" (whose terminology I've adopted) that I've talked about on my ... blog where I've also made several other references to Foley and Smith.

However there are also strong differences — in particular the constraint in the partition function and its "temperature" variable [Lagrange multiplier]. For example, in Foley (1996), prices are [analogous] to inverse temperature and the partition function defines an economic state with a well-defined maximum entropy "offer" (i.e. constraint).

The partition function I've looked at uses factors of production as the inverse temperature, and looks at an economy as a maximum entropy state with a well-defined growth rate. This "growth rate" is actually understood in terms of underlying information theory (matching demand "events" with supply "events" which we can think of as messages in communication theory).

There is a similarity in the discussion of entropy (I've made several references to Foley's statement that physics and econ are different because the formalism was set up to study irreversible processes in the latter — no one voluntarily undoes their utility gains — as opposed to reversible processes in the former). However, the information theory treatment tells us not to expect the second law of thermodynamics to hold because the conditions that make it hold are not met. A good example is that traders can all panic and try to sell causing a correlation that would violate the 2nd law; in contrast, atoms don't panic. This makes economics very different from thermodynamics. But I think a consequence of this is that Foley's thermodynamics can reproduce Walrasian/classical economics pretty well because there shouldn't be big market failures in classical economics.

That's just a couple of examples. There are others (e.g. I avoid most discussions of utility, but also show it is probably only a useful concept near equilibrium).

However since I didn't get that deep into statistical equilibrium in the book, and decided to base the book on economist Gary Becker's model (based on the suggestion from economist David Glasner that Becker's approach would be more persuasive/intuitive than my physics jargon), references to Foley fell by the wayside (as a side note, I also edited out a reference to Philip Mirowski because I thought it detracted from the narrative). In general, these references were too technical (I only touch on the 2nd law violation because you can illustrate it with Gary Becker's model) for what was supposed to be a book for a general audience. (I also think the physics jargon and direct analogies with thermodynamics are at least one barrier to traction for Foley and others [in mainstream economics].)

But you are right that I'm mostly focused on understanding empirical problems, partially because that's what I've always done as a physicist (I was technically a nuclear and particle theorist, but most of what I did was build models to explain data) and partially because economics lacks models with anything approaching what scientists would call "empirical accuracy" (and Foley's work doesn't seem to address empirical data much either).

...

Econophysics for fun and profit

If you are a physicist planning on revolutionizing economics with your bold new theory, I highly recommend reading Cosma Shalizi's very excellent rant [1] "Why oh why can't we have better econophysics?". For a short version, check out the entry on "scientists" at Noah Smith's Econo-troll bestiary. In [1] Shalizi says:

Let me also complain that there isn't enough physics: the repertoire of ideas taken from physics is very impoverished. Basically, we see random walks, power laws, and spin systems over and over again. These are important ideas, but they're just a small part of theoretical physics! To give an example, Eric Smith and Duncan Foley have a fun paper working through detailed mathematical analogies between the axiomatic versions of utility theory and thermodynamics, leading to a reversible "engine" that runs on credit.

The link is broken and should actually point to this working paper [2] Is utility theory so different from thermodynamics? which has subsequently been published. What follows is kind of an unstructured comment on that paper and borrows liberally from it and other related materials by the authors.

It turns out attempting to find analogies between physics and economics has a long history, including Walras (1909) and Fisher (1926) among others. Eventually, economists got fed up with this. Paul Samuelson has a fit in 1960:

The formal mathematical analogy between classical thermodynamics and mathematical economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes -- such as entropy or energy -- in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should ``utility'' be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?

Oh snap. Anyway, some of the basic ideas that came out of the thermodynamic analogy seem to be that goods are extensive measures like energy or volume and prices are intensive measures like pressure or temperature. Hey, that's what I found! Prices are like pressure, the quantity supplied is like volume and the quantity demanded is like energy in the information transfer model.

Foley and Smith [2] make a really interesting point about the thermodynamic analogy: economists tend to study what seem to be irreversible processes (people will not make exchanges to undo their utility gains) and physicists tended to study reversible processes (at least when they started coming up with thermodynamic laws). This difference changes the whole approach to problem solving, leaving the fields looking completely different. However, this is the point where I think [2] goes down a rabbit hole the information transfer model avoids. The authors make the mistake that Samuelson derides above: they make a homological association (in order to avoid the word "analogy") of utility with entropy.

The idea of utility maximization is pervasive in economics and inextricably links it with the normative ethical theory with the same concept. "Rational" expectations has economic agents out there maximizing individual utility. Cue Shalizi: "Alas, experimental psychology, and still more experimental economics, amply demonstrate that empirically [the neoclassical framework is] just wrong." If your economic framework has utility maximization as a fundamental theorem in the same way that thermodynamics has a second law, then the framework itself really is just a (likely normative) description of a particular class of states (since utility maximization is not generally true in the real world) and your entire mode of study as a would be econophysicist is to calculate expansions around your theory. This is perverse. It would be like building a particle theory in a quantum field framework, finding the vacuum state and then making up an entirely new theory to study deviations from that vacuum. That is to say the framework should ideally describe the fluctuations around the equilibria. Barring that, the framework should at least allow the kinds of fluctuations you see. If some of your fluctuations are meaningful and actually, whoops, violate fundamental theorems in your framework, then what good are your equilibria? 

My personal feeling is that the normative stuff got economics in trouble in a lot more ways than physicists trying to make analogies with thermodynamics. Homo economicus is an alien. If your models require humans to behave like this in order to be solvable then there is something seriously wrong. (For another interesting take, check out this great article on Nietzsche and Austrian economics -- the successful capitalist as Übermensch, rather than, as most economics research shows, mostly just lucky or sitting on economic rent. I mean, basic analysis shows that without barriers to entry prices should become the marginal unit cost of production and profit should go to zero, no?)

The information transfer model avoids this morass the same way Shannon made information theory into a field in its own right: not caring about the content of the message. Information content is maximized in a random string! I don't care what the signal being sent from the demand to the supply actually is. This is not to say the information transfer model is right; it's just not normative. For example, diminishing marginal utility sounds pretty dumb if you try and ascribe it to the thermodynamic analogy in the information transfer model (weirdly quoting myself):

Translating [diminishing marginal utility] to the thermodynamic analogy the ridiculousness becomes obvious: it says "when undergoing an isothermal expansion, the pressure an atom is willing to exert falls because of the diminishing marginal utility of extra volume". Diminishing marginal utility for goods is actually a sign choice and is due to choosing demand as the information source rather than destination.

I precede that statement by noting the fact that in the information transfer model, diminishing marginal utility is not even a property of an economic agent (which aren't even defined), but rather an ensemble of economic agents.

I think if you are a physicist with an eye to revolutionize economics, you should keep a few things in mind. Theorems and fundamental laws that always apply don't translate well to the human domain. Be cautious when making normative claims and be aware of normative assumptions that are baked into your model. This is especially dangerous in economics due to its closeness to normative ethics and due to the moral gut feelings humans have about e.g. debt. And be nice: make sure your model reduces to stuff economists already know (for some reason people get angry when you declare their entire grad school education was all for naught).

PS What is it with Smiths and economics? Noah Smith, Eric Smith, Adam Smith. My last name is Smith, too.

Causal entropic forces as economic forces

Fig. 1 from Causal entropic forces (2013).

Recent advances in fields ranging from cosmology to computer science have hinted at a possible deep connection between intelligence and entropy maximization, but no formal physical relationship between them has yet been established. Here, we explicitly propose a first step toward such a relationship in the form of a causal generalization of entropic forces that we find can cause two defining behaviors of the human "cognitive niche" — tool use and social cooperation — to spontaneously emerge in simple physical systems. Our results suggest a potentially general thermodynamic model of adaptive behavior as a nonequilibrium process in open systems.

That's the abstract to Causal entropic forces [pdf] (2013) by Wissner-Gross and Freer (WGF) appearing Physical Review Letters. Adding causality to the description of entropic forces (entropy maximizing forces) creates systems of mindless atoms that can perform tasks that look like the actions of intelligent agents. I have previously speculated that entropy maximization can lead to emergent rational (i.e. "intelligent") economic agents and organized several posts for a future draft paper.

I suggest you read the paper, but there are a few points made in it that I'd like to emphasize. First, WGF point out entropic forces are the results of restrictions on the state space:

... an environmentally imposed excluded path-space volume ... breaks translational symmetry, resulting in a causal entropic force ... directed away from the excluded volume.

 This isn't specific to 'causal' entropic forces (plain entropic forces have this same underlying reason -- something has to exclude state space volume [or more generally make it less likely] in order for you to have an entropy gradient in a specific direction). When I speculated economic forces are entropic forces dependent on the properties of the state space, that is what I had in mind. Budget constraints are constraints on the economic state space (or in e.g. Gary Becker's 1962 paper Irrational Behavior and Economic Theory, the opportunity set).

Second, WGF's causal entropic forces don't really require strict causality, just a tendency not to immediately undo a state change. The reluctance of economic agents to undo exchanges was identified by Foley and Smith as one of the differences between thermodynamics and economics. We could also potentially interpret the endowment effect as a manifestation of causal entropy.

Third, causal entropic forces acting on macroeconomic states would behave like a restorative force (rather than simply wandering around the state space if all states are equally likely). Measures like unemployment would generally return to some level determined by the state space. We'd likely find the economy near the point expected given the least informative prior, which for a high dimensional system is near the surface and in the center of the budget constraint hyperplane, not just over a long period of time, but regularly -- even after displacement from equilibrium.

This is a bit of a subtle point. If we place the economy in some state at time t where all states are equally likely, that point represents a local entropy maximum just as much as say the centroid of a high dimensional opportunity set bounded by a budget constraint hyperplane:

Budget constraint plane for consumption goods 1, 2, and 3 bounded by money M.

However, causal entropic forces will make our state evolve towards the centroid (which is near the center of the budget constraint hyperplane of a high dimensional opportunity set) over time, instead of randomly moving through the state space (so that only on average it is near the center of the hyperplane). In a sense, this is the difference between a random walk and a random walk with drift.

Fourth, there was one aspect of List (2004) I wasn't able to reproduce with purely random transactions (entropic forces). Over time, the standard deviation of the market price fell monotonically:

As mentioned above, causal entropic forces would act like a restoring force pushing the price towards the "equilibrium" (i.e. the information equilibrium), damping deviations from it, over time.

I would also like to point out that WGF's paper is a tremendous blow to those who think humans as rational utility maximizers (or even boundedly rational, or adaptive agents) are a prerequisite for economic theory. Whatever puzzle you might think is too hard for random particles to solve, causal entropic forces are something you will have to consider.

Update 24 April 2017: In a subsequent post, I used causal entropy to simulate a demand curve:

Ecological fallacy and emergent dynamics

Diane Coyle has a review of a new book on statistics for a general audience. It's Truth or Truthiness: Distinguishing Fact From Fiction By Learning to Think Like a Data Scientist by Howard Wainer. It sounds fun and is definitely seems like the kind of book needed in today's data environment.

One of the things Diane writes about in the review is the ecological fallacy:

I also discovered that one aspect of something that’s bugged me since my thesis days – when I started disaggregating macro data – namely the pitfalls of aggregation, has a name elsewhere in the scholarly forest: “The ecological fallacy, in which apparent structure exists in grouped (eg average) data that disappears or even reverses on the individual level.” It seems it’s a commonplace in statistics ... Actually, I think the aggregation issues are more extensive in economics; for example I once heard Dave Giles do a brilliant lecture on how time aggregation can lead to spurious autocorrelation results.

Now I am not 100% sure I read this correctly, so I'm not going to attribute this interpretation to Diane. However, the way this is written could be taken to impugn the macro structure: this is not the meaning of the ecological fallacy.

The ecological fallacy states that observed macro structures do no imply anything about the micro agents. It does not say that the converse is true, i.e. the lack of agents behaving consistently with the macro structure implies the macro structure is spurious (it may or may not be).

I think a good example here is diffusion. The macro structure (an entropic force pushing density to become e.g. a uniform distribution) does not imply that individual molecules are seeking out areas of low density. Individual molecules are just moving randomly. A graphic from the Wikipedia article on diffusion illustrates this nicely:

However, the random motion of individual molecules does not make us question the validity of the macro observable diffusion. In a sense, all emergent properties would be suspect if this were true.

But Diane also said she noticed that macro structures tend to fall apart when disaggregated; this is exactly what we'd expect if macro and economic forces are entropic forces like diffusion. I've already noted that nominal rigidity (sticky prices and wages) appears to be the result of entropic force [1] (nominal rigidity appears in aggregate data, but isn't true for individual prices). We can see e.g. Calvo pricing as a "microfoundation" for something that doesn't exist at the micro level ‒ much like (erroneously) creating a density depended force for individual molecules in diffusion. I also showed how consumption smoothing, transitive preferences, and rational agents can arise from agents that fail to meet any of those properties.

Essentially, the issues with the ecological fallacy should be ubiquitous in economics if it really is about entropic forces and macro is different from aggregated micro.

...

Footnotes:

[1] Possibly even more interesting are causal entropic forces; this formulation can make inanimate objects appear to do intelligent things. I constructed a demand curve from them here. As I noted in the first link in this footnote, the causality may be deeply related to Duncan Foley and Eric Smith's observation that the real difference between economics and the physics of thermodynamics is the former's focus on irreversible transformations (agents don't willingly undo gains) and the latter's focus on reversible ones (for e.g. experiments).

Economics is neither physics nor computer science

I was a bystander in a crash of paradigms recently -- Eric Weinstein joined a discussion prompted by Chris House when House asked the question: Why are physicists drawn to economics? House seemed to think it was out of mathematical hubris physicists felt they could jump right in. Weinstein, in comments at Orderstatistic (House's blog) and Noahpinion, pushed for an interpretation of economics in terms of gauge theory.

Now there is nothing incorrect about Weinstein's reformulation of economics in the language of fiber bundles with ordinal utility behaving like a connection (gauge field).  As a physicist, I actually enjoyed the mathematics involved in reformulating gauge theory in the language of fiber bundles (and differential forms). I gave seminars on both as a grad student. Similarly there is nothing incorrect about Eric Smith and Duncan Foley's reformulation of economics as thermodynamics. Actually, the existence of both reformulations is a little unsurprising -- the partition functions found in quantum field theory and thermodynamics are closely related.

However, Steve Ellis, one of the professors on my thesis committee, asked me a question at one of those seminars that has stuck with me. What is it good for? (He would disparagingly pronounce the word JAR-GON as if it was the name of a villain from Krypton.) Paul Samuelson answered in 1960 in the case of thermodynamics with absolutely nothing ...

The formal mathematical analogy between classical thermodynamics and mathematical economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes -- such as entropy or energy -- in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should 'utility' be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?

If he was alive today, Samuelson would probably throw in gauge theory. The thing is, thermodynamics was the big thing in physics at the time of Walras (1870s), and statistical mechanics was fully developed by the time of Fisher (late 1800s to early 1900s). Both of those economists used analogies that used the big new physics at the time. Today theoretical physics is dominated by quantum field theories, so Weinstein is in good company. 

Utility as gauge field, utility as thermodynamic potential: what are they good for? If it is nothing more than a re-labeling, a translation into a new language, then I submit it's not really good for anything practical. It is analogous to translating the English "person" into Japanese -- 人 -- look at the beautiful simplicity of the representation! Of course, it doesn't help you do anything that you couldn't do with the English word besides save space or enable elegant graphic design (think Maxwell's equations on a t-shirt which uses modern mathematical notations, not Maxwell's [1], and definitely not the even more elegant version reformulated as differential forms). And to use it you need to learn Japanese (to use the gauge representation of utility, you need to learn gauge theory).

Maybe these reformulations help in the way most analogies help -- helping thinking and intuition?

To that end let me introduce two other (related) reformulations of economics as computer science. Cosma Shalizi wrote what is my favorite blog post ever -- ostensibly a book review, it becomes a coherent framework for thinking about markets. If running an economy is an optimization problem (allocating raw materials, goods and services), then the top-down communist model where every allocation is centrally planned is akin to trying to solve the linear programming problem directly. Shalizi demonstrates that this is beyond the capabilities of computers for thousands of years, given the size of modern economies. Instead, the market and the price mechanism are remarkably more effective for such an easy system to use.

Nick Hanauer and Eric Beinhocker seemingly independently took this idea up earlier this year, saying that capitalism is an algorithm that solves problems. Economics must therefore be the study of that algorithm. Arguing against the market as a force of nature, they argue the market as algorithm is supposed to function in the service of humanity. These top-level interpretations are the flip-side of the reformulations in mathematics. The former give purpose of the machine while the latter fiddle with the gears.

We return to Steve Ellis's question: Other than giving a general motivation for capitalism and a framework for interpreting the value of the results of capitalism, what are these reformulations as computer science good for? I mean, as far as the science of economics goes? I can see that if you believe capitalism is an algorithm, it e.g. forestalls moralizing in favor of the market distribution of resources. But it doesn't help figure out how the Phillips curve works. (I'm definitely not saying these ideas are wrong!)

What is the impact on the everyday work of particle physics if it is seen as quantum field theory as fiber bundles? I will tell you as a particle physicist: very little. Physics at least has topological solutions that are illuminated by a fiber bundle approach (instantons, Aharonov-Bohm effect, etc). I will make the bold claim that economics has no such topological solutions.

I'd venture to say that recasting economics in this or that mathematical framework or coming up with a new analogy doesn't really add new capabilities to the science of economics that didn't exist before. This pessimism may seem weird coming from a blog that's all about reformulating economics as information theory.

But!

There are quantitative results that come from this particular reformulation -- a quantitative treatment of money as the unit of account and medium of exchange, an excellent model of the price level (including Japan and the general trend towards disinflation), and a reason for the evolution of the Phillips curve, among others.

At least, that's the answer to Steve Ellis's question [2].

[1] See this link to Einstein's special theory of relativity for a hint of how Maxwell wrote them down.

[2] This post can be seen as a sequel to this older post that references some of the same material.

The entropy term and the unreasonable effectiveness of NGDP

I realize I've now said this at least twice in comments, but I think it deserves a post on its own. Awhile ago, I used an elaborate analogy to write nominal output the sum of the output in several markets, plus a money market, plus an entropy term. Each term in that sum represents an economic (entropic) force -- microeconomic forces for the individual markets and a macroeconomic force for the entropy term.

NGDP* = TS + k P M + k₁ P₁ X₁ + k₂ P₂ X₂ + ...

I labeled this NGDP* for reasons that will be clear later. In the individual markets, the microeconomic forces represent supply and demand for the individual products. But what about the purely macroeconomic entropic force arising from the entropy term? Functioning much like the arrow of time, this represents the macroeconomic resistance agents collectively have to undoing their economic gains. Without coordination, it is unlikely that agents will undo a large portion of their aggregate gains. Unfortunately, the coordination usually comes in the form of panics and recessions.

That entropy term represents an economic force acting against agents undoing their gains. And that's great! Because in my version of the model, agents are random (or so complex/dependent on unknown initial conditions -- i.e. financial histories -- that they appear random). Real individual humans don't make random transactions (at least most of the time), so the random agent model needs way for agents to not on average sell their house at a loss if they don't have to. Voilà: the entropy term.

Many people on first coming to my blog ask if I've heard of Duncan Foley (because he's also applied thermodynamics to economics). I have checked out his work, but his approach is much different than mine. However, I am indebted to him (and his co-author Eric Smith) for this idea about entropy (coming from this paper). They couched it in terms of reversible versus irreversible processes, but irreversible processes are exactly entropy producing processes. In economics using the potential above, that entropy producing process would be economic growth. Economic growth is exploration of the state space along with an aggregate tendency not to undo the gains in output (i.e. entropy).

One more thing: if you were to just sum up the output in the individual markets, you'd technically miss out on the entropy term. You ask: But isn't that how NGDP is calculated ... just adding up all the (final) purchases of goods and services? So isn't NGDP missing that entropy term?

Technically, yes. But since the entropy term is (for a large economy) proportional to the sum of all final purchases of goods and services in the individual markets, NGDP plus the entropy term will be proportional to NGDP. So

k₁ P₁ X₁ + k₂ P₂ X₂ + TS = NGDP + TS ~ (1 + α) NGDP ≡ NGDP*

This clears up a minor mystery (at least for me). Everyone is so down on NGDP (except Scott Sumner); they (e.g. Diane Coyle) say it misses a lot of things that happen in a real economy. And according to what I just said, it does! How in the 1930s did we come up with a measure that happens to capture the aggregate economy in a theory developed 80 years later?

Apparently Simon Kuznets stumbled upon a measure that just happens to be proportional to the true measure in the information transfer model. And since economics has a scale invariance (e.g. add zeros to everything denominated in money an there's no change), and NGDP is measured in money, we lucked out. NGDP turns out to be a measurement of the entropy term.

Eight years of blogging

I spent the past week on Twitter putting up a list of my favorite posts on the blog as a kind of Irish wake for the form for the blog's 8th anniversary. As is typical on these anniversaries, a bit of statistical analysis or visualization — this time, the years of the selected favorites:

Looks like 2016-2017 was my peak by the number in my own opinion. It's not just bias by the quantity of posts, either. The most prolific year was 2015 with an average rate of a post per day. Favorites per total number has been increasing steadily — at least in terms of my own opinion, quality has been rising:

Here's the list (not in order) for posterity:

"It's people. The economy is made out of people."

"Solow has science backward"

"Good ideas do not need lots of invalid arguments in order to gain public acceptance"

"Maximum entropy better than game theory"

"Lazy econ critique critiques"

"Can a macro model be good for policy, but not for forecasting?"

"Remarkable recovery regularity and other observations"

"A Solow Paradox for the Industrial Revolution"

"Macro criticism, but not that kind"

"Ceteris paribus and method of nascent science"

"Things that changed in the 90s"

"The economic state space: a mini-seminar"

"Stocks and k-states"

"The ISLM model (reference post)"

"An information transfer traffic model"

"My introductory chapter on economics"

"Keen, chaos, and equilibrium"

"What mathematical theory is for"

"The Phillips curve and The Narrative"

"UK productivity and data interpretation"

"Qualitative economics done right, part 1"

"Goldilocks complexity"

"Neo-Fisherism and causality"

"Resolving the Cambridge capital controversy with MaxEnt"

"The irony of Paul Romer's mathiness"

"More like stock-flow inconsistent"

"Stock-flow consistency is tangential to stock-flow consistent model claims"

"Should the left engage with neoclassical economics?"

"Milton Friedman's Thermostat, redux"

"Efficient markets and the Challenger disaster"

"The irony of microfoundations fundamentalism"

"What if money was made of vinegar?"

"The 'quantity theory of labor' and dynamic equilibrium"

"No one saw this coming: Bezemer's misleading paper" ("Letter to Dirk Bezemer")

"Keen"

"DSGE, part 5 (summary)"

"Yes, I've read Duncan Foley. *Have you?*"

"Utility maximization and entropy maximization"

"Is the market intelligent?"

"DSGE Battle Royale: Christiano v. Stiglitz"

"The philosophical motivations"

"Wage growth in NY and PA" 

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

"Thought experiment"

"Dynamic equilibrium: unemployment rate"

"Labor market update: external validity edition"

"Efficient markets and the Challenger disaster"

II. Entropy and microfoundations

In Part I, we started with an empirical macro observation: the long run neutrality of money. There are many macro relationships that have followed from empirical study like the Phillips curve and Okun's law. But, asked e.g. Lucas, were these relationships consistent with microeconomics?

Lucas suggested based on the Phillips curve changes that previously observed macro relationships could change whenever policy changed [1]. A microfounded theory purportedly avoids this by determining how people respond to changes in policy (hence the reason that the Lucas critique tends to be interpreted as saying you must have microfoundations). That is a potential solution.

There is another way: assume ignorance. That is assume the principle of indifference: given the macrostate information you know  (NGDP, price level, MB, unemployment, etc), assume the system could be in any microstate consistent with that information with equal probability [2]. In Bayesian language, this is the simplest non-informative prior. This way lies statistical mechanics, thermodynamics and information theory.

We can see these two paths: assume ignorance about the microfoundations and derive what conclusions that will hold under most microfoundations, or assume particular microfoundations and see what macrostates result.

However we can also see the Sisyphean aspect of the microfoundations program. Since the macrostate represents a loss of information relative to the microstates, many different microfoundations will lead to the same macrostate ... or another way, the details of even the correct microfoundations are lost.

How do we know the details of the microfoundations are lost? The efficient markets hypothesis. At least in the sense that I rationalize both Fama and Shiller winning Nobel prizes in economics. The EMH (put one way) is the idea that price data is maximally uninformative. Note: that is maximally uninformative, not completely uninformative. How else could there be things Shiller found like long run trends, mean reversion and momentum? 

Equilibrium in thermodynamics represents a state of maximum entropy (ignorance) about initial conditions of the system: all we know are "conserved quantities" i.e. properties of the macrostate. Well, we could know more ... and knowing more would theoretically allow you to extract useful work from that knowledge. Consider Bennett's information powered engine [3].

Imagine a tape of double-sided pistons with a separating wall and a single atom (green) on one side (see top of the diagram). One side of the wall is labelled 0 and the other 1. Knowledge of which side the atom is on can be converted into work by performing the compression cycle given in the bottom of the diagram. This work could theoretically be used to power a vehicle (I changed the vehicle from Sethna's [3] train in the picture below):

How does an information powered warp drive engine relate to the EMH? Supposedly if you knew the series of price movements, you could beat the market by using that information (which becomes useless after you used it). However, this is about as likely as turning knowledge of all the positions of all the gas molecules in a room into useful work.

One more analogy before we get back to microfoundations. One way to see biology is as a process by which living things intercept entropy (free energy) flows. An autotroph converts low entropy high energy photons into high entropy waste (heat, low energy photons); a heterotroph converts low entropy organisms into high entropy waste (heat, poop). Economic agents intercept entropy (information) flows: they convert low entropy money into high entropy goods and services.

In living things, the free energy in the photons or sugars is converted into lower free energy products and the information in their original structure is lost. The information in the market (e.g. prices of goods) is converted in to quantities of goods where the prices they were bought at no longer matter (according to the EMH). This information is consumed by the market in the same way free energy is consumed by organisms.

So take the principle of indifference and posit that information flows from the demand to the supply the way the entropy flows through the conversion of high energy photons into low energy photons that is transferred to the environment.

We have the information source (demand) $I_{D} = K_{D} n_{D}$ and information destination (supply) $I_{S} = K_{S} n_{S}$ (here the Hartley information $I = n \log k \equiv K n$ corresponds to the Shannon information when all the states $k$ are equally probable, i.e. indifference). Define an information flow detector (a price) that measures the transfer of information from D to S

$$
\text{(1) } \frac{dD}{dS} \equiv p
$$

Take a small demand signal $dD \ll 1$ and a small supply signal $dS \ll 1$ so that $D/dD = n_{D}$ and $S/dS = n_{S}$ with $n \gg 1$ and assume $I_{D} = I_{S}$ (define $\kappa \equiv K_{S}/K_{D}$). So that now we have

$$
\text{(2) } p = \frac{dD}{dS} = \frac{1}{\kappa}\; \frac{D}{S}
$$

Which is the minimal equation we came up with that satisfied homogeneity of degree zero which guarantees the long run neutrality of money in Part I. This derivation is basically a simplified presentation of one of the first posts on this blog [3].

Returning to the microfoundations of macroeconomics, we can say that observed relationships that follow from equations of the form (2) represent microfoundation-independent macroeconomic results. They represent what we know given the greatest amount of ignorance about the microfoundations. Additionally, these macroeconomic relationships will be consistent with microeconomics.

I've used the notation p:D→S as a shorthand for these relationships There are a few of these we've mentioned on the blog (of varying degrees of accuracy):

P:NGDP→MB 

Price level (quantity theory of money, liquidity traps and hyperinflation)

r:NGDP→MB 

Interest rates (part of the IS-LM model)

P:NGDP→L 

Labor market (leads to Okun's law)

P:NGDP→U 

Unemployment (less accurate than the labor market version, but gives an interesting interpretation of the natural rate of unemployment)

Note that the Phillips curve follows from looking at the price level market and the labor market, and you can see the changes over time (the gradual flattening) is predicted by the theory.

[1] We found a way to predict these changes based on the unemployment market mentioned at the end the post.

[2] Under e.g. different assignments of initial endowments. In this earlier post I discuss the idea from Foley and Smith that economics grew up with special consideration for initial endowments and thus a predilection for studying irreversible processes rather than reversible ones that dominated physics.

[3] Citations: I borrowed the nice pictures from Entropy, Order Parameters, and Complexity by James P. Sethna (2006), which are based on pictures in the Feynman Lectures on Computation (which is based on work by Charles Bennett). Some of the discussion is based on those works as well. The derivation of the equations follows from work by Fielitz and Borchardt who developed the the original information transfer model of physical processes.

Information transfer economics FAQ (reference post)

FAQ (Frequently Asked Question) pages used to be a more prevalent aspect of the internet, but seem to be fading ‒ probably due to being able to ask those questions directly in a Google search or on Quora or similar sites. Anyway, this will be a reference post that will be occasionally updated with some of the questions and misunderstandings I frequently run across from readers. Here's a link to some basic definitions that I'll assume readers have read.

Don't economists already study information in economics?

The "information" in information transfer economics is from information theory and the study of communication channels. It has a technical definition more directly related to probability than to e.g. knowledge of how the monetary system works or whether a company is about to announce disappointing earnings. The key insight from Shannon in his seminal paper on the subject was that the meaning of messages sent through a communication channel is not as important as the number of possible messages (which determines the information content of each message). It's that state space that matters here.

That being said, the work of Christopher Sims comes closest to treating information in a similar way. (And he finds the message doesn't seem matter!)

Why do you treat economic agents as mindless atoms?

This is a bit of a mischaracterization of how the information equilibrium/dynamic equilibrium framework treats economic agents. The best way to put it is that the framework treats humans as so complex their decisions appears to be algorithmically random (i.e. indistinguishable from a computer program with random outputs for a given set of inputs). The main assumption however is that an ensemble of economic agents will fully explore the possible options available to them in the presence of constraints. The net result is a model that looks like "mindless atoms", but it isn't the whole story. 

This approach is somewhat different from traditional economics where agents are usually assumed to choose the best option available to them. However, economist Gary Becker had a paper from 1962 that also looked at this "random" approach (thanks to economist David Glasner to pointing it out to me). He [Becker] referred to it as "irrational", but I am agnostic as to the motivations of the agents. Even a rational decision can look like an irrational one if you are missing some knowledge of the agent (e.g. selling a stock at a loss in recession looks irrational, but it is possible the person had medical bills to pay).

But mindless atoms don't panic ...

While information equilibrium treats agents effectively as random "mindless atoms" (but really treats them as so complex they look random), the information transfer framework is more general. If agents didn't spontaneously correlate in state space due to human behavior (e.g. panic, groupthink), then the information transfer framework reduces to something that looks like boring standard thermodynamics. However, they do in fact panic. In terms of thermodynamics, this means that the information transfer framework is like thermodynamic, but missing a second law of thermodynamics. The "mindless atoms" will occasionally panic and huddle in a corner of the room and you have non-ideal information transfer as opposed to information equilibrium.

There is less the information transfer framework can say about scenarios where we have non-ideal information transfer, but it still could be used to put bounds on economic variables.

Wait. Isn't this just saying sometimes your theory applies and sometimes it doesn't?

Yes, but in a particular way. For example, the effect of correlations (panic, groupthink) is generally negative on prices.

Additionally, empirical data appears to show that information equilibrium is a decent description of macroeconomic variables except for a sparse subset (i.e. most of the time). That sparse subset seems to correspond to recessions. Since human behavior is one of the ways the system can fail to be in information equilibrium, this is good evidence that information equilibrium fails in exactly the way the more general information transfer framework says it should.

In a very deep way, one can think of information equilibrium being a good approximation in the same way the Efficient Market Hypothesis (EMH) is sometimes a good approximation. Failures of the EMH seem to be correlations due to human behavior.

If your theory is so awesome, why aren't you well known in economics circles?

The short answer is: I don't know. You'd think forecasting better than macro institutions would somehow get out there more. But I think the bulk of  econ twitter and the dwindling econoblogosphere is more interested in how they think the economy works than how it actually works.

That said, I was invited to give a talk at my local university's (and alma mater's) economics department — so I'm guessing like most things in academic research it's more of a long slog than becoming a rock star overnight.

Well, why haven't you at least been published then?

It's apparently really hard to be published in an econ journal even if you're a famous professor, with revisions often taking years. If you don't have an econ degree, you're almost certainly going to get desk rejections (as I have).

I have two papers (so far) available as pre-prints (here and here) and at least in physics and machine learning these are basically the only things people read these days because publishing is so slow. Even economics does basically the same thing, except their pre-print server is closed off to everyone except insiders.

Why don't you get rich using your theory?

In a way, I am because my 401(k) is invested in index funds. The theory says that unless you can predict human behavior, you cannot predict episodes of non-ideal information transfer. Therefore the optimal portfolio choice is to diversify and hold for a long period of time. This is what most financial advisers say anyway (and the reason is effectively the same: because the EMH is a good starting approximation).

Some individual people might well be good at predicting human behavior and therefore could potentially outperform the diversified index fund investor, but I am not one of those people. Individual human behaviors frequently baffle me.

I have put together some speculative research about stock markets, but again the results are broadly similar to already known investment strategies.

So you have economics all figured out?

No, not in the slightest. This is all research. I am currently testing the models using empirical data and forecasts. Readers should not confuse my excitement and interest for certainty.

Are you a heterodox economist?

Not really because heterodox econ is its own thing. Though I have no issues with any approach that is honest in its representation — especially because economics is at best a nascent science.

But you're definitely saying mainstream economics is wrong?

Not really. I do believe there are some assumptions made in many (mainstream and heterodox) approaches in economics about the impact of human decision-making, human behavior, and complexity of the macroeconomic system that are unfounded from an empirical perspective. A simpler approach like information equilibrium avoids making strong assumptions about human behavior (we only assume agents explore opportunities most of the time) and uses information theory as a shortcut to understanding complex systems (per the abstract of Fielitz and Borchardt's original paper on information equilibrium for natural systems).

That being said, information equilibrium can be used to formulate many mainstream economic models. Several of these information equilibrium versions of mainstream models tend to be less empirically accurate than information equilibrium models constructed from observed empirical regularities directly (a good example is the New Keynesian DSGE model versus the monetary information equilibrium model).

In the sense that modern economics grew out of the principles of supply and demand and marginalism, one can think of information equilibrium/information transfer as a generalization of those principles. It therefore has some overlap with mainstream economics.

Have you heard of Duncan Foley?

Yes.

Have you heard of Steve Keen?

Unfortunately, yes.

What about MMT?

*sigh*

But how could you possibly find anything wrong with MMT?

*eyes roll back in head*

But what about X?

Over the past six years (as of 2019), I have written over a million words on information equilibrium, dynamic equilibrium, information transfer, and the applications to economics. I probably have written about X, so have a look via the search bar (or better yet a Google site search like this for "scope" which will search comments as well). I try to use mainstream economics terminology where I can, so you can use phrases like nominal rigidity or tâtonnement. Comments are open on all of the older posts if you have questions.

If you're looking for a good place to start, I put together a "tour of information equilibrium" chart package.