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On the limited applicability of statistical physics to economics

from Lars Syll

Statistical mechanics reasoning may be applicable in the economic and social sciences, but only if adequate consideration is paid to the specific contexts and conditions of its application. This requires attention to “non-mechanical” processes of interaction, inflected by power, culture, institutions etc., and therefore of specific histories which gives rise to these factors …

you shall not pass statistical physics - You shall not pass | Meme GeneratorOutside of very specific cases, statistical physics is more likely to provide useful metaphors and ways of thinking than computational techniques and definite answers. Although statistical mechanical explanation can shed light on particular mechanisms that may be at play (e.g. explaining how distributions are shaped by the differences between the ways in which wages and profits may respectively evolve) these must be interpreted in a specific causal context … In the context of the human sciences, agency – not merely the exercise of individual choice but the shaping of the circumstances of collective life – is the central factor both in determining the properties of a system and in shaping individual choices. The exercise of human agency may bring a social system closer to an “equilibrium” in some circumstances, and disrupt it in others. It is among the specifically social factors that must be taken note of in the dialogue between statistical physics and the social sciences.

Sanjay Reddy

  1. yoshinorishiozawa
    December 21, 2021 at 3:52 am

    Generally speaking, economists know too little about physics, biology, meteorology and their scientific methods. Based on their very poor knowledge, economists often argue that we should reject to learn from natural sciences on the basis that natural and social sciences are fundamentally different. Of course, it is not wise blindly to imitate natural sciences. Also, it is true that there are so many such silly imitations, but it does not imply that we cannot or should not learn from experiences of natural sciences. The paper of Sanjay G. Reddt’s paper argues some concrete cases of successful (and failed) attempts from which we economists may learn. He teaches us kinds and aspects in which economics can learn from physics and in particular from statistical physics. Among these possibilities of learning, we have some negative ones, i.e. to learn how we should not learn from some past experiences.

    These are some excerpts from Section 1, which are noteworthy for further arguments:

    Explanation is therefore treated here as a distinct concept from both description and prediction.

    Explanation is important for science because it is required if we are to make sense of why things are the way they are.

    The concept of natural selection provides an apposite example. It provides a method of explanation insofar as it helps us to understand the process by which specific organisms came into existence.

    Obversely, a framework that has predictive power may not provide very much by way of an explanation.

    While both prediction and explanation may be desirable, they are not always jointly attained, as the example of natural selection illustrates.

    A scientific theory ought to possess some power of explanation, whether or not it possesses power of prediction.

    Some of the conclusions are also notable:

    Statistical mechanics reasoning may be applicable in the economic and social sciences, but only if adequate consideration is paid to the specific contexts and conditions of its application.

    History, context and collective agency are all factors which must be taken note of in the dialogue between statistical physics and the social sciences, if it is to progress.

    Although I do not deny the possibility to learn from statistical physics successfully (e.g. the entropy maximization), I believe we should pay more attention to new approaches that do not draw on statistics. See for example, two of my papers:

    A new framework for analyzing technological change, Journal of Evolutionary Economics, 2020.

    The principle of effective demand: a new formulation (open source) Review of Keynesian Studies, 2021.

    The two papers are neither predictive or descriptive (in a narrow sense), they give a good explanation on what is happening in particular aspects of the economy. None of them assume equilibrium, perfect rationality, nor representative agent, but provides history-friendly microfoundations to Post Keynesian and evolutionary economics based on a totally different understanding on how market economy works.

    • yoshinorishiozawa
      December 21, 2021 at 6:23 am

      The paper I read is the draft version of the published paper. I suppose there is no big difference between them.

  2. December 21, 2021 at 7:08 am

    In short you have to treat economy as a complex
    system, just like climate.

    • yoshinorishiozawa
      December 21, 2021 at 12:37 pm

      Dear reallifeeconomics. You have a good vision of the economy. But, having a good vision does imply that we can easily obtain a good theory. Do you have any idea?

      • Meta Capitalism
        December 21, 2021 at 2:39 pm

        They can start by being useful economists rather than an idler, hobbiest, or literature-only armchair economist blinded by conceit and the false premise that for economics to be “a science” it must be about the dispassionate search for timeless truth which is for the sake of mathematical tractability reducible to simple “if-then” rules that tell us what even the “dimmest observer of real-existing capitalism already” knows from experience.

        Economic research as it should be, is therefore a matter of trying to understand how the particular complex system in which we happen to live functions – or malfunctions – at any particular time, and to what sort of forces, pressures and policies it responds. (Post-Neoliberal Economics by Edward Fullbrook, Jamie Morgan – https://a.co/aoFhlto)

      • December 22, 2021 at 11:33 am

        Thanks. I do not think that a good vision of economy requires theory, as it does for math or physics. There can not be (politics or value) neutral economics. May be that is the reason why classics called it political economy and objected to its being concieved as a theoretical science. We live in the age of much more advanced science, compared to the times of A. Marshall. Furthermore, we have computers that dramatically changed scientific methodology. So, the stubborn objection of the classics can be somewhat relaxed: In addition to political economy, these days we can also practice economics as a computational social science. This means model building. They may be closed and/or ad hoc (in economical sense) mathematical models or computational simulations. Such models are useful to represent relevant aspects of our economical lives. I believe that political economy must inform the theories behind these models, which are useful only if they are good surrogates of the economical reality in question.

      • yoshinorishiozawa
        March 4, 2022 at 9:19 am

        In my above reply, I wrote

        But, having a good vision does imply that we can easily obtain a good theory.

        It seems that I missed to add the important word “not”, although it seems there were no big confusions. The above sentence must be read as

        But, having a good vision does not imply that we can easily obtain a good theory.

      • March 5, 2022 at 10:06 am

        Yes.. It is a necessary but not a sufficient condition..

  3. C-Rene Dominique
    December 21, 2021 at 3:51 pm

    I agree almost completely with Yoshinori”s comments.The modern economy, being a complex multifractal system with a Feigenbaoum attractor, needs statistical physics more than ever; otherwise we will be asking What is wrong with economics? for the next hundred years. Moreover,statistical physics is applicable to the whole Universe. Those interested should google the conclusions of Mohamed El Naschie in E-infinity Cantorian space-time.

  4. Gerald Holtham
    December 21, 2021 at 6:23 pm

    Any understanding of an economic system will have to rely on the law of large numbers, I believe. Individuals are not automata and will be unpredictable without detailed knowledge of each one (which Amazon tries to obtain!). But group behaviour can be more predictable. That is why representative agent theorising and phoney “microfoundations” are such a waste of time. The analogy of brownian motion at the molecular level or even indeterminacy at the quantum level giving rise to deterministic physical laws is interesting. But it is only an analogy. It is not clear to me how far there is a formal equivalence with economic systems. I would be interested in hearing from C-ReneDominique why he is so confident about that.

    • December 22, 2021 at 10:25 am

      Statistical physiscs works with particles that interact according to laws of physics. Wheras, in economy there are no such laws. Agents have variable behaviours, which may change during interaction with other agents or with the environment.

    • yoshinorishiozawa
      December 22, 2021 at 11:27 pm

      Any understanding of an economic system will have to rely on the law of large numbers.

      Gerald, you are generalizing too much. I agree with you if you say “some understanding of an economic system will have to rely on the law of large numbers.”

      New technologies (new product and production techniques) comes quite “randomly” if we observe an economy from the outside. However randomly they may come, the real wage will generally go up if mangers of firms choose more profitable techniques and if wage and markup rates remain constant, See my paper on the new framework for analyzing technological change. To obtain this result, I use the law of large numbers nowhere.

      • Meta Capitalism
        December 24, 2021 at 5:00 am

        Any understanding of an economic system will have to rely on the law of large numbers. ~ Gerald Holtham

        Gerald, you are generalizing too much. I agree with you if you say “some understanding of an economic system will have to rely on the law of large numbers.”

        [T]he real wage will generally go up if mangers of firms choose more profitable techniques and if wage and markup rates remain constant. ~ Shiozawa Yoshinori

        The historical evidence shows Gerald, in his comments, has indeed frequently “generalized too much” the power of statistics and “the law of large numbers.” Everything is relative.

        Real Wages: Economic jargon uses the term “real” in an idiosyncratic way. It refers only to a price adjustment, often applied to concepts that are somewhat unreal to start with. “Real wages” refer to money wages adjusted for the erosion of purchasing power as measured by the rise in the consumer price index (CPI). The adjustment is supposed to reflect the decline in purchasing power of nominal wages when the cost of living rises. This measure shows that there has not been a real gain of annual wages since the 1970s. If annual wages rise by a nominal amount (say, 2% a year), but consumer prices also rise by this much, there has been no real gain. And if the CPI rises faster than wages, wage-earners “really” receive less.

        But even this measure fails to reflect the erosion of labor’s real living standards. In recent years wage earners have suffered from an much more unpleasant reality. They are not able to consume anywhere near what they are paid, because a rising proportion of their household budget must now be paid to the FIRE sector as debt service, rent and other housing costs and insurance, as well as steeper FICA wage withholding. (The “Hudson Bubble Model” later in this book explains the accounting.) So what really is “real” is substantially less than what is reported as real wages. The CPI refers to the shrinking proportion of household budgets (perhaps as little as one third) that is spent on commodities. What is missing is the rising carve-out for debt, rent, and other FIRE-sector rake-offs.

        (J IS FOR JUNK ECONOMICS: A Guide To Reality In An Age Of Deception” by Michael Hudson – https://a.co/1wqdM9P )

        Real Wealth: The market price of assets deflated by the rise in the consumer price index (CPI) or a Gross Domestic Product (GDP) price deflator for goods and services. The implication is that wealth is eroded when wages or prices rise. But the wealthy do not spend much of their income on consumption, so this adjustment seems irrelevant.

        The way that most of the One Percent makes its fortunes is not “real” in the sense of producing value in the form of goods and services. “Wealth” today refers not only to tangible means of production, but to any bankable asset. A “wealth” fund consists of financial claims on society’s means of production (in the form of mortgages and other bank loans, stocks and bonds) – what Frederick Soddy called virtual wealth, which rightly should appear on the liabilities side of the economy’s balance sheet.

        The problem with confusing real wealth with financial claims is that rising access prices for housing and other basic needs is treated as a gain for “the economy” as a whole. The middle class imagines itself to be growing wealthier as the price of its housing rises – on credit – causing debt deflation for the overall economy and thus slowing real wealth creation.

        (J IS FOR JUNK ECONOMICS: A Guide To Reality In An Age Of Deception” by Michael Hudson – https://a.co/67hd3UO )

      • Meta Capitalism
        December 24, 2021 at 8:58 am

        [T]he real wage will generally go up if mangers of firms choose more profitable techniques and if wage and markup rates remain constant. ~ Shiozawa & Economic Myth Making

        It is economic myth making to claim _real wages_ are determined by new technology and that this new technology leads to higher _real wages_. The devil is in the details. Only the few who are highly skilled benefit from these higher _real wages_ (~10% or less) while the lion’s share of these gains to to the .01% who own the monopoly capital. It is a myth that higher productivity leads to higher wages when reality shows real wages have become detached from productivity growth.

    • Meta Capitalism
      December 27, 2021 at 12:37 am

      Any understanding of an economic system will have to rely on the law of large numbers, I believe. ~ Gerald Holtham

      I have come to think that macroeconomics must be seen as the study of emergent phenomena based on the behaviour of a large number of disparate individuals. Individual behaviour can only be understood probabilistically and macroeconomic phenomena are often the convolution of a large number of probability distributions. We can observe empirical regularities and the hope must be that we can find a combination of widespread behavioural tendencies (confirmed by observation at micro level) and statistical mechanics that will “explain” those regularities. ~ Gerald Holtham

      The most useful work done in economics has been qualitative and produced generalisations that have proved true and useful up to a point. To get past that and identify the limits of the generalisations and the qualifications to which they would be subject – to promote them to something nearer to law-like statements – would require much more data and statistical testing. But I acknowledge that in very many cases that is not possible. The theory may not be specifiable with the necessary precision and we just don’t have the data. And perhaps no valid law-like statements exist in economics. ~ Gerald Holtham

  5. C-Rene Dominique
    December 22, 2021 at 3:00 pm

    To Gerald and Reallifeec: Ask yourself Why income distribution, firms’ size,, returns, language ecology, stars’ sizes distribution, etc.follow a power law? Or why is economics a non ergodic construct?(contrarily to what we would wish). The power law can be broken by policy changes but it is an emergent universal law. Statistical physics allows us to figure out that the modern market lives in dimension between 2 and 3.

    • December 22, 2021 at 5:01 pm

      Power law is not universal, but it is true that quite a few economic phenomena follow power law distribution. You have to be careful though, because there are continous distributions that can be taken for a power law, like log-normal for example. It is also true that economic processes are not ergodic, or anything like it. These are all well known features of complex systems.

    • yoshinorishiozawa
      December 23, 2021 at 12:23 am

      We should ask why various phenomena obey the power law. Many of power law distributions (fat or long tailed distributions) have a specific characteristics named stable distribution. (See “Stable distribution” in Wikipedia. Do not misunderstand that an phenomenon is stable in an ordinary sense of the word). French mathematician Paul Lévy investigated this type of distributions and determined the general form of stable distributions. Except the normal distribution that has a finite variance, all other stable distributions have no variance (or have unbounded variance). Physical systems normally obey the normal distribution, probably because aberrations are bounded within a certain energy level. In financial markets and others, we observe many distributions that are not bounded in the similar way. Many of them obey a stable distribution (at least asymptotically), probably because some “universality” like central limiting law works. (Do not confuse with “universal” laws like Newton’s law of universal gravitation.)

      Stable distributions except the normal distribution have no simple algebraic formula, but they are expressed as a Fourier transform. It is known that these distributions are asymptotically proportional to a power of the random variable. Quite different from normal distributions, they exhibit an extremely fat density at points far from the “mean”. (Nota bene: If the index is smaller than 1, theoretically there are no means.)

      • yoshinorishiozawa
        December 23, 2021 at 12:49 am

        Error: central limiting law -> central limit theorem (law of large numbers)

  6. Meta Capitalism
    December 23, 2021 at 5:09 am

    Class distribution of revenues

    In chapters 7 and 8 we explain the path-breaking work on the statistical mechanics of money by Dragulescu and Yakovenko (2002) and how, assuming the conservation of money, a highly unequal Gibbs–Boltzman distribution of wealth will arise in a simple exchange economy. In chapter 13 we move on to an economy in which the buying and selling of labour is allowed. We show that in such an economy the distribution of income becomes even more unequal, characterized by what is termed a power law distribution. We generate these results with very simple assumptions about the nature of production relations. In chapter 14 we look at the laws governing the level of profits in a capitalist economy, focusing in turn on input–output, monetary and demographic constraints. The background to this is the concern of the classical economists with an apparent tendency for profit rates to decline with the passage of time. We confirm that this tendency is real, and explain why the criticisms of it by Okishio were ill founded. (Cockshott et. al. 2009, 4)

    (….) 8.1 Introduction

    The application of statistical physics methods to economics promises fresh insights into problems traditionally not associated with physics (see, for example, Farmer et al. (2005)). Both statistical mechanics and economics study big ensembles: collections of atoms or economic agents, respectively. The fundamental law of equilibrium statistical mechanics is the Boltzmann–Gibbs law, which states that the probability distribution of energy e is P(e) = Ce-e/T , where T is the temperature, and C is a normalizing constant (Wannier, 1966). The main ingredient that is essential for the textbook derivation of the Boltzmann–Gibbs law is the conservation of energy. Thus, one may generalize that any conserved quantity in a big statistical system should have an exponential probability distribution in equilibrium (Cockshott et. al. 2009, 148)

    An example of such an unconventional Boltzmann–Gibbs law is the probability distribution of forces experienced by the beads in a cylinder pressed with an external force (Mueth et al., 1998). Because the system is at rest, the total force along the cylinder axis experienced by each layer of granules is constant and is randomly distributed among the individual beads. Thus the conditions are satisfied for the applicability of the Boltzmann–Gibbs law to the force, rather than energy, and it was indeed found experimentally (Mueth et al., 1998). (Cockshott et. al. 2009, 148)

    We claim that, in a closed economic system, the total amount of money is conserved. Thus the equilibrium probability distribution of money P(m) should follow the Boltzmann–Gibbs law P(m) = Ce-m/T . Here m is money, and T is an effective temperature equal to the average amount of money per economic agent. The conservation law of money (Shubik, 1997) reflects their fundamental property that, unlike material wealth, money (more precisely the fiat, ‘paper’ money) is not allowed to be manufactured by regular economic agents, but can only be transferred between agents. (Cockshott et. al. 2009, 148-149)

    It is tempting to identify the money distribution P(m) with the distribution of wealth (Ispolatov et al., 1998). However, money is only one part of wealth, the other part being material wealth. Material products have no conservation law: They can be manufactured, destroyed, consumed, etc. Moreover, the monetary value of a material product (the price) is not constant. The same applies to stocks, which economics textbooks explicitly exclude from the definition of money (McConnell and Brue, 1996). So, in general, we do not expect the Boltzmann–Gibbs law for the distribution of wealth. Some authors believe that wealth is distributed according to a power law (Pareto-Zipf), which originates from a multiplicative random process (Montrell and Shlesinger, 1982). Such a process may reflect, among other things, the fluctuations of prices needed to evaluate the monetary value of material wealth. (Cockshott et. al. 2009, 149)
    Cockshott, W. Paul et. al., ed. et. al. Classical Econophysics. New York: Routledge; 2009; p. 4; 148-149. (Routledge advances in experimental and computable economics; v. 12).

    What assumptions underlie these claims that the “statistical mechanics of money” and do they hold in the real-world?

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