The fundamental equation of economics

It is every physicist's dream to find a formula so powerful that it can explain everything (and carry the inventor's name). Such hopes are not as prevalent in Economics, first as we realize that we cannot find such a fundamental equation (we are just not smart enough), second because an economy is so complex that it defies any attempts to reduce it to one equation.

This does not stop James Wayne, who as a physicist is still pursuing his dream. And he claims to have found the Fundamental Equation Of Economics (FEOE), thereby finally proving that Economics is truly part of Physics. What a relief. And what is this equation that can, as the author forcefully argues, explain all observed economic phenomena and solve all economic problems, without exception? What is this formula that shows that equilibrium, the laws of supply and demand, DSGE and SL/ML (whatever that is) models are all deeply flawed? Here it is: The change in time of the joint probability distribution of future valuation of assets and liabilities is a function of its current distribution. We do not know yet what this function is, because it is currently too difficult to figure it out at the atomic level, but we know it exists. Now we can go revolutionize Economics and solve the world's problems.

Long live the Wayne Equation!

Five universal laws for economics

Physicists believe that social sciences can only be described as true sciences if on can figure out some laws that always apply, without exceptions, and if there some invariant constants that would be good, too. Social scientists do not believe this is the right approach, foremost as one has to deal with individuals and societies that make choices.

James Wayne realizes that Physics lacks one ingredient that is essential in social sciences: choice. Fundamentally, I am not convinced that we actually choose, but that it only looks like it at the level of abstraction that we can master at this point and for the foreseeable future. Indeed, our decisions are the results of complex chemical reactions in our brains under the influence of complex environments and likely some randomness. But we have found a simpler abstraction with the framework of choices under constraints, and that is certainly missing in Physics.

Now Wayne adds the concept of choice to Physics, and then determines five new Physics laws: 1) the outcome of any future event is indeterministic; 2) there is a joint probability of future events that helps predicting them; 3) actions can be taken at any time to change this distribution; 4) we cannot retain complete information about past histories; 5) eventually, some equilibrium is reached. He can then use these new laws to re-understand natural and social sciences under a unified framework. All this in only 8 pages of text and not a single equation. True science at work.

homo socialis

Everyone is familiar with homo œconomicus, the greedy economic agent that brings an economy to its most efficient allocation under perfect circumstances. But circumstances are less than perfect (externalities, imperfect competition, lack of commitment, asymmetric information, etc.) and Adam Smith's invisible hand needs a little help from some authority. Through regulation, taxation, subsidies and punishment, that authority can try to get closer to the first-best allocation, but at a cost.

According to Dirk Helbing, this cost is now overwhelming, because in current societies top-down management of an economy is not computable anymore. One should rather find a bottom-up approach, following the craze about Web2.0 and social media. Thus enters homo socialis, an economic agent who is very aware of all the ills of unfettered markets. If this sounds like one of those revolutionary solutions that would end world hunger, it is. It even comes with a new type of money, a must for these types of exercises.

So, how does this work? Homo socialis is an economic agent with other-regarding preferences. He needs institutions that allow him to express such preferences instead for reverting to the greedy homo œconomicus. Hence the institution of "qualified money" that rewards good behavior by this friendly and altruistic market participant by giving him "reputation." But if he is that altruistic, why does he needs such rewards? That is not clear. And who gives them? Is there any budget constraint here? It would really help to formalize a little bit all the author's ideas, but it is quite confusing. For example, the value of qualified money depends on its history. In other words, every single banknote may have a different value, depending on the context in which it was used. How is that simplifying the problem of complexity?

Helbling gives as as example the management of traffic lights in a city, a rather bizarre example. In the homo œconomicus scenario, an authority sets traffic light patterns and does not adapt them when lines become too long somewhere. In the homo socialis, this adaptation happens, presumably from a feedback coming from car drivers. Why the restriction in the first scenario? In fact cities do have feedback rules in place (notice the cameras along the roads?) without the drivers needing to do anything. But foremost, why such an example? It is unrelated to the question at hand. The argument that the computation would be too complex for a central planner fails because at least he has a complete picture. Individual car drivers suffer from a lot of asymmetric information when taking decisions, even altruistic ones. Note also that the example does not use the crazy qualified money scheme.

What a confusing and confused paper. You would think this would be a first draft for someone who works for the first time in the area. But no, except for the methodological silliness and conceptual errors, this paper is actually quite well written and the literature well researched, including 22 self-citations.

How econophysics describes the income distribution

It has been a while since I last discussed a paper from econophysics, where it appears there is a substantial literature trying to describe the distribution of income. It turns out to be quite difficult, because the goal is to do this with a single equation. What one would want to do with that equation is not clear to me, but anyway.

Maciej Jagielski and Ryszard Kutner claim success with this endeavor by essentially dividing up the distribution in three parts, fitting each to a different distribution function, and then rejoining them into a single equation. But what income are they taking about, you may ask? They look at European income in 2006 and 2008, and take the data from the SILC EU project. That still does not determine what income they are considering, as the dataset allows multiple different ways to define income. It is not even clear whether this is income before or after taxes and whether it includes capital gains.

One problem the authors realized is that they need oversampling for to incomes. To take care of this, they look at the European billionaires on the Forbes list of the richest people over several years, conclude that changes in wealth must be "income" and take that, dropping all negative incomes along the way. Then they notice a large discontinuity from merging the two dataset and decide to divide the top incomes by 100 to make the joint distribution continuous. Oh boy. And this is the dataset they used for their study, believe it or not.

Quantum money

It has been a while since we last discussed then latest developments in econophysics, the field trying to blend the methods of Physics (and sometimes its lessons) into Economics. The most mysterious and often counter-intuitive field of Physics is Quantum Physics. The same could be say of Monetary Economics within Economics. So why not study the Quantum Physics of Money?

Stephen Ternyik does this for us, and the result is expectedly disturbing and unintelligible. I spent more time than I should on trying to understand the abstract, and the paper itself was not too helpful. SO here is the abstract, and maybe a reader can translate this into something that makes sense to me:

The marginal minimization of the reserve requirement on demand deposits is the single cyclical cause behind the long-term crises of the monetary production economies and progressively decreases the time value of money on economic productivity. The total economic cost of this monetary and banking system (fiat credit a priori via private commercial banks; fiat money a posteriori via public monetary police) is the loss of dynamic efficiency in the space-time production structure, i.e. the quantitative increase of entropic volatility in the
monetary production economy equals the quantitative increase of the fiat credit quantum (mechanically and thermodynamically). A radical maximization of the reserve requirement on demand deposits is the basic economic remedy for the temporal monetary stabilization of the space-time production structure, according to the natural/physical laws of human economic productivity.

Econophysics of growth

It is sometimes saddening to see how Economics is currently being criticized for its failure to predict this and that. While at least economists realize that things are not that simple, non-economists have been really silent in offering concrete alternatives, or at least some that would be workable within a decade. Except for the econophysicists, who have no shortage of wacky ideas. They are always good to brighten your days, making you realize that Economics is after all in much better shape than we think.

My latest read was a paper by Hans Danielmeyer and Thomas Martinetz who have come to the realization that Robert Solow's 1956 growth theory is missing leisure and Economics has been in dire straights ever since. Because, you know, there are only 24 hours in a day. How could Macroeconomics have done without labor demand and supply? How could we have missed that long-term per-capita growth depends primarily on labor hours? Actually it does not. Growth accounting reveals that the labor input plays only third fiddle to total factor productivity, physical capital and possibly even human capital. But wait, Danielmeyer and Martinetz are even more innovative than I thought. They discover human capacity, which is general knowledge embodied through education. Quick, someone call Paul Romer.

This is truly path-breaking work we have here. The consequences are immense. As human capacity is limited, after all we are not omnipotent, growth will come to a halt. I eagerly await the authors' discovery of computers and technical progress. There is even a quantitative evaluation of the theory, which has much broader scope than you would expect. Indeed, it can explain the over-valuation of real estate in Japan, the 2008 banking crash can be traced back to policy makers neglecting the trade-off between growth and national wealth, and we face a "convergence crisis" in the 2040's because of stagnant human capacity. Fascinating.

Two millenia of growth in a couple of equations

Many scientists dream of finding a unified theory of something, a theory that would encompass others and explain, with a few equations, a large number of observations. Physicists in particular have been looking for fundamental equations. In economics, there is currently a drive among growth theorists to find a unified growth theory, although here the focus is not on a single equation, but rather a model. Indeed, one has to realize that explaining several thousand years of economic growth involves some complexity.

And now the physicists get interested in the topic. Andrey Korotayev and Artemy Malkov actually go beyond a simple one equation model and use some theory, linking surplus output to population growth à la Malthus. Up to 1970, population is hyperbolic, while GDP is quadratic-hyperbolic (in both cases levels, and not growth as the authors assert). They conclude from this that technological progress is expanding because of the larger number of inventors as population grows. That seems a bit simplistic, as one should also bear in mind that there are decreasing returns to inventing, as documented by rather constant long-run growth rates for total factor productivity in modern history despite an increasing share of a growing population dedicated to research and development. But one can get misled when one looks only at few indicators.

Compared to other physicists, Korotayev and Malkov are careful to use real numbers for output and draw on growth theory a little bit. However, they tout a bit too much high correlation coefficients between data and their forecast. Indeed, when both have a trend, the R2 will always be very high (not counting the fact that for some data points, the uncertainty about their measurement is considerable). And using a logarithmic scale for the graphs would also give a fairer visual assessment of the fit.

PS: I am rather surprised to see that physicists have such difficulties formatting correctly their equations.

Econochemistry?

I have highlighted in the past some exceptionally bad examples of forays of physicists into Economics (search for "Econophysics"). Not all are that bad, but they generally have in common that they portray the economy just as exogenous stochastic processes where no economic agents take decisions. That can make sense in some contexts, but these are rare cases. Now it seems chemists are venturing into Economics, what good could that bring?

Yochanan Shachmurove and Reuel Shinnar are an economist and a chemist who managed to get a paper into the working paper series of the department of Economics at the University of Pennsylvania. So it must be a serious piece. Their point is that is Chemistry, they have to deal with chemical reactors that depend on many variables and are very difficult to predict. This is not unlike an economy, where a multitude of factors may matter in ways so complex with some randomness thrown in that forecasting is very difficult as well. The authors suggest to use partial control, which involves identifying a few crucial variables and monitor those for forecasting. That does not look like much of an innovation to economists, as we are used to abstract modeling, factor analysis, econometrics and simple rules like the Phillips Curve or the Taylor Rule.

The methodology of partial control they are trying to push, though, hits a few roadblocks when applied to Economics. The first is that it needs an objective, which is easy to set in a chemical plant (it is the choice of the plant manager) but not so easy for an economy as a whole. The second is that it needs to separate the problem into independent units. They suggest, for example, to treat the United States as independent from the rest of the world. That may work for some questions, but many it does not, especially when the point is to summarize complex interactions. Third, the procedure requires a hierarchy of reactions. Much of our understanding of general equilibrium would not be captured by such constraints. Fourth, the method relies a lot on the ability to manipulate controls. That is easy in a chemical plant, but an entirely different problem in an economy. The authors take the example of the Fed and interest rates. Well, the Fed has a target on one very special interest rate, all others are market driven.

While Shachmurove and Shinnar offer scattered examples of how to apply partial control, there is no sense of how a complete model would look like. I would wait to see a model in operation before calling this an interesting modeling strategy for Economics.

An economist's foray into econophysics

I have described here some of the outlandish forays of physicists into Economics, where they try to use concepts from their discipline with disastrous results (last post here). But economists themselves may borrow concepts from physics. One that stuck was sunspots, from some chance correlation between sunspot activity and stock market performance, and made popular by David Cass and Karl Shell. But there were very little physics in this.

Martin Evans ventures deeper, using the concept of dark matter to understand exchange rate movements. It is well known that it is very difficult to understand what moves exchange rates. Dark matter is something that we cannot observe, but we see its impact. In this case, Evans builds a model where dark matter has an impact on nominal exchange rates, and then on other variables. This is based on the empirical observation that something like dark matter has an impact on expectations on long-run exchange rates, but not on recent and future interest rate differentials. This is achieved in the model by introducing shocks to household risk aversion. Why? Well, it is dark matter (or animal spirits). But all that matters is that it explains a large share of exchange rate fluctuations, in a rather consistent way for the other variables. Physicists would be happy with that. Economists would want to understand why.

The Econophysics of migration

Sorry to report a second time in the same week about Econophysics (previous one here), but this paper is just too bizarre for me not to mention it. Physicists have the reputation, maybe wrongly, to be very bright, methodical and keen on logic. Hence it surprises me very much when I see this papers were completely senseless arguments are made and empirical evidence is tortured in utmost comical ways. I sincerely hope only the worst physicists make it to Econophysics and my view of the profession is thus biased.

Today's paper is by Anca Gheorghiu and Ion Spanulescu. It starts with a paragraph that has nothing to do with the topic, migration, that should from the onset get a failing grade from any teacher beyond elementary school:

Physics, is the most suitable for modelling the economic phenomena and structures or financial-banking operations, because it takes into consideration the process variables characteristics and permits to use some procedures – including the mathematical one – especially probability theory for minimizing or eliminating such influences depending on human factor and unexpected phenomena also, which cannot be predicted by direct methods.

I think was is meant here is that physics bring statistics to the table when analyzing economic phenomena. Color me shocked. After some generic rambling about what causes migration, the authors come up with an "improved model" (their words) for migration: the net present value of migrating equals the benefits of migrating less the costs of migrating. We are making significant progress here.

But there is more. Gheorghiu and Spanulescu then think of various countries as attractors, and that various forces pull people towards the respective countries. This is of course the well-known gravitational model of migration. Hey, we are using Physics concepts in Economics already! Of course, these economic attractors must be defined, and they come up with gold reserves, computers per capita and the proportion of Internet users. Why is a bit a mystery to me. The empirical evidence is presented in the form of histograms, which are apparently at the forefront of statistical techniques.

For some reason, the authors then compare countries to positive and negative electric charges and try to somehow fit migration into the Coulomb's law of electrostatic interaction. I was hoping the electro-magnetic properties of gold, the use of electrons in computers and the Internet would justify the previous empirical analysis, but no, it is entirely forgotten. Indeed, there is no attempt to somehow link all this to any measurement.

I have already spent too much time on this.

The econophysics of religion

Other social scientists do not like when economists venture into their turf and challenge established methodology. We economists, of course, welcome these instances of Economics imperialism because we believe our methods are superior. But other scientists also venture into Economics, and the most brazen are the physicists. They created a new field, Econophysics, that has been met with bewilderment or amusement by economists, including myself (Exhibits A and B). Economics and Econophysics largely ignore each other. Here is now the paper that will be with upmost bewilderment in social sciences, Econophysics applied to religion.

Marcel Ausloos studies a religious sect, the Antoinists, over 80 years. Lacking information about membership, attention is turned towards income and expense reports. Ausloos tries to find patterns and regimes in the data in order to understand the growth and decay of the cult. While there is some discussion of GDP and demographics, the exercise is all about fitting the evolution of expenses with a mixture of geometric growth and a sine wave in three different regimes. Why is not clear. And I also do not think the data has been adjusted for inflation. A really bizarre study, I doubt scholars in religion will learn much from it, and economists certainly nothing except to view this field even more with suspicion.

Econophysics: an introduction

I have criticized a number of times Econophysics as a rather naive venture of physicists into Economics, where there is too much focus on "automatic" data exploration and too little use of theory and understanding of what the data measure. But may it is just my prejudice against and my ignorance of Econophysics.

B. G. Sharma, Sadhana Agrawal, Malti Sharma, D. P. Bisen and Ravi Sharma offer in six pages an account of what Econophysics is, what its goals are, what it can contribute and where it is headed. The basic idea is that economic agents are like particles in that they are in large numbers and interact in complex ways. The dynamics of such complex processes are studied with powerful statistical tools in Physics, and physicists think that this should also apply to Economics. The focus is very much on the stock market, probably because physicists have realized where money can be made. There is no sense that there would be an attempt to improve welfare. They are also much more likely to completely discard a model in one set of observations does not corroborate it. Physicists are especially critical of how economists stick to rejected dogmas and of their inability to explain how small shocks can pan out into large crises.

The focus is really on the description of data process and documenting there statistical properties. In particular, econophysicists want to find ways to exploit even the smallest opportunities for arbitrage by finding, often through obscure and complex black box processes, the right price of an asset at any moment in time. However, there is no attempt at understanding why these arbitrage opportunities arise, say because of some form of irrationality, asymmetric information or perverse interactions in the price mechanism. From this I conclude that Econophysics can be interesting to make money on the stock market, but at least at this point, does not help us in any way in understanding why the world is like it is. Which I find rather ironic for Physics.