The Econophysics of Income Distribution as Economics

Transcription

1 The Econophysics of Income Distribution as Economics by John Angle Inequality Process Institute Post Office Box 429 Cabin John, Maryland October, 2007

2 The Econophysics of Income Distribution as Economics Summary Econophysics is the extension of the field of statistical mechanics into economics. Statistical mechanics is micro-macro theory: the derivation of the properties of a population of particles [in econophysics, economic agents], from a simple model of the particles and their interaction. Unlike particle systems of physical particles, e.g., molecules, the particles of the particle systems of econophysics are taggable, i.e., identifiable through time. Consequently, the particle systems of econophysics can be tested against data at the micro as well as the macro level. Econophysics was largely about price movements in financial markets, a subject opened by Louis Bachelier s dissertation, supervised by Henri Poincare at the University of Paris, in A few attempts were made by econophysicists beginning in the late 1990's to model personal income and wealth distribution. These attempts however were more than anticipated by John Angle s particle system model, the Inequality Process, published in 1983 as a model of personal income, and developed in a chain of papers between then and now. Thomas Lux, chair of the Economics Department of the University of Kiel, surprised a worldwide gathering at the Saha Institute of Nuclear Physics called in 2005 to celebrate five years of progress on a model almost isomorphic to the Inequality Process, by telling attendees that all the findings in that literature - including those presented at that conference - had been anticipated by Angle s papers on the Inequality Process. The latest paper Lux cited was published in However, Lux was no fan of the Inequality Process (IP) as economics. In fall 2005, after establishing the IP as one of the few successes of econophysics beyond the study of price movements in financial markets, Lux joined with three others (Mauro Gallegati, Steven Keen, and Paul Ormerod, (2005, 2006)) to reject particle system models such as the IP and its similar, more recent replications by econophysicists, not as science but as economics. Gallegati et al. give four criticisms of econophysics, four worrying trends. The first is the rediscovery of known economics. They cite Lux March 2005 paper upbraiding econophysicists for wasting time rediscovering the IP. Gallegati et al. s criticisms #2 and #3 are not substantial. Most of their paper is about criticism #4 of particle system models with a micro level, and consequently a macro level, equality constraint. They claim that such models cannot be dynamic in the sense that the equality constraint on aggregate wealth or income cannot change (criticism#4a). There is an implied but not well thought out second component to their criticism, (criticism #4b), that such particle system models that just move a fixed positive quantity around between particles cannot explain the creation of that positive quantity. Criticism #4a is easily shown to be a misapprehension, and, in fact, bypassed by the macro model of the IP in the same way it is bypassed in similar physical models. The second part of criticism 4 (#4b) is more interesting. There is an answer to it for the IP. Gallegati et al. conclude by conceding that there is no mathematical model in economics that competes with the particle system models of the econophysics of wealth and income distributions for explaining empirical phenomena quantitatively. Gallegati et al. was covered in a colorful four page spread, entitled Culture

3 Crash, in the June 8, 2006 issue of Nature. Ormerod and an econophysicist appear in close-ups, grimacing, each photo atop an aggressive criticism of the other side. No mention of the IP in the Nature article; the IP was not directly criticized in Gallegati et al. They gave it via indirect citation as the example of economics ignored by physicists. Had I been contacted by the reporter for Nature I would have said that I see the IP as underpinning, not undermining, accepted verbal principles of economics. The IP explains a wider set of economic principles and empirical phenomena than either Gallegati et al. or their physicist antagonist in the Nature article knew of.

4 The Econophysics of Income Distribution as Economics The Brouhaha Mauro Gallegati, Steven Keen, Thomas Lux, and Paul Ormerod are four economists who have committed their careers to econophysics, working with physicists to create a science of economics modeled after the field of statistical mechanics in physics. These four, Gallegati et al., jointly offer four criticisms of a new subfield of econophysics, particle system models of income and wealth distributions. Gallegati et al. offered their criticisms informally at an unscheduled session at the Econophysics Colloquium, in Canberra, Australia in November 2005 [ ], later wrote them up as Worrying Trends in Econophysics and published the paper the following spring in Physica A [1], an econophysics journal, in the issue of papers from the Canberra conference. Gallegati et al. is the first article in that issue. Gallegati et al. attracted its own critical comment from an econophysicist who has been broadly critical of economics as science, Joseph McCauley [2]. Gallegati et al. s broad and acerbic dismissal of an entire research frontier of econophysics and McCauley s response attracted the attention of Nature, as prominent a venue in the science as there is. Gallegati et al. and McCauley s response were covered by an article by Philip Ball in the June 8, 2006 issue of Nature [3] magazine, headlined Culture Crash, a feature article. It has large color photographs, a feature news article in Nature s format. The Nature article emphasized conflict between the views of Gallegati et al. and McCauley and contributed to the impression of conflict between the econophysics of income and wealth distribution and economics, and prompting the present paper which addresses the question of whether there is inconsistency between mainstream economics and the frontier field of the econophysics of income and wealth distribution. Interacting Particle System Models The criticisms of Gallegati et al. are directed toward the use of particle system models of income and wealth distributions. Particle system models are perhaps the best known tool of statistical mechanics. A particle system model is a micro-macro theory. It explains the properties 2

5 of a population of particles [in econophysics, economic agents], from a radically simplified model of the particles and their interactions. Most economists encountered the first and best known particle system, the Kinetic Theory of Gases (KTG) in high school physics. The KTG explains the thermodynamics of a volume of gas in terms of the mechanics of gas molecules as elastic spheres in collision. Parsimonious Micro Hypothesis Explains Observed Macro Phenomenon The KTG reduces the macro-level phenomenon of heat, not well understood in the 18 th th and early 19 century, to the micro-level: gas molecules behaving like elastic spheres in collision and exchanging their kinetic energy according to Newtonian mechanics which was well th th understood in the 18 and early 19 century. At that time atoms and molecules were entities in a speculative theory of matter that gained plausibility from the practical success of the KTG, not vice versa. The KTG did not have model verismilitude when it was proposed since atoms and molecules were not familiar or plausible at the time. Rather the KTG was recommended by its parsimony, how simple and well understood it was as a model, and how easily it implied the macro level phenomenon such as Boyle s Law, for example. The KTG s success created its verisimilitude. Verisimilitude is a trailing aspect of a successful model, not a criterion to judge a new model on. Unfortunately, Gallegati et al. judge the particle system models of the econophysics of income distributions on their verisimilitude as economics, ignoring their parsimony and explanatory scope. Gallegati et al. s Four Criticisms Gallegati et al. (2005) have four criticisms of econophysicists involved with the econophysics of income and wealth distribution. These are: Our concerns about developments in econophysics arise in four ways: a lack of awareness of work that has been done in economics itself a resistance to more rigorous and robust statistical methodology the belief that universal empirical regularities can be found in many areas of economic activity 3

6 the theoretical models that are being used to explain empirical phenomena. Criticism #1: Wasting Time Re-Discovering the Inequality Process Their first criticism is based on one citation, Thomas Lux [4] paper, Emergent Statistical Wealth Distributions in Simple Monetary Exchange Models: A Critical Review, presented to The International Workshop on the Econophysics of Wealth Distributions, a March 2005 conference at the Saha Institute of Nuclear Physics in Kolkata, India. This conference was called to celebrate five years of progress in creating an econophysics of income and wealth distribution, Emergent statistical wealth distributions in simple monetary exchange models: a critical review. Lux is chair of the Economics Department, Kiel University in Germany and an authority on financial markets. Lux s paper at this meeting chastised the attendees for not reading the economics literature. He gave only one example of the cost of not doing so: the waste of five years of work and many publications re-discovering part of the findings about the Inequality Process (IP) [Angle, 5-27], a particle system model of income and wealth distribution. Lux spoke at Econophys-Kolkata, a conference called to celebrate five years and a great many papers, eight prominent ones of which are [28-35], and the creation of an econophysics of income and wealth distribution via a particle system model almost identical to the Inequality Process. Lux made the jarring announcement that Angle s findings about the Inequality Process (IP) had anticipated them all. The latest Angle paper Lux cited was from All those anticipated econophysics papers had just scratched the surface of the explanandum of the Inequality Process (IP). However, while Lux praised the IP to make his point that one economist can be worth a many physicists when it comes to doing econophysics, he didn t think much of the IP as economics, referring to it as a toy model. Criticisms #2 and #3: Do As I Say Now, Not As I Did Six Months Ago Gallegati et al. s criticisms #2 is and #3 are mixed together in their presentation. They are not substantial and, oddly, are inconsistent with the published research of the first author of Gallegati et al., Mauro Gallegati. In May 2005 Gallegati and a co-author published a paper [36], Power Tails in the Italian Income Distribution but Gallegati et al. denounce a) the search for 4

7 universal statistical laws like the Pareto pdf (the power tail function Clementi and Gallegati fit in [36]), but apparently grandfathering in as exceptions statistical laws well known to economists today such as the Pareto Law (and the Pareto pdf) [37], Gibrat s Law (whose most general form is that randomness in the achievement of income and wealth assures inequality) [38], and the Kuznets Pattern, and b) assert that data on income distribution are so poor it is impossible to find universal statistical laws of income distribution. Oddly Clementi and Gallegati [36] fit a function to the far right tail of the Italian income distribution, perhaps the most dubiously measured part of the most dubious of such data from an OECD country. The U.S. Bureau of the Census evaluation of its data on large incomes asserts that these income data contain more non-sampling error than its data on incomes nearer the median and that its estimates of the relative frequency of large incomes have a serious downward bias [39, pp ]. Noncompliance with the Italian income tax is legendary. One might guess that taxpayers who have concealed income on their tax returns will also do so when when asked by a government interviewer what their income is. Gallegati et al. do not cite, discuss, or renounce Clementi and Gallegati [36] published four months before the Econophysics Colloquium in Canberra. Bah humbug! captures the spirit if not the details of criticisms #2 and #3. While Gallegati et al. correctly point out that in many cases the fits of pdfs to income distributions by econophysicists contradict each other, their criticism of the methods used in fitting pdfs to income and wealth distributions betray their ignorance of the importance of parsimony. They huffily advocate fitting pdfs with more degrees of freedom because they offer closer fits, unaware of the cost in lost parsimony. A closer fit is a better fit in the view of Gallegati et al. regardless of how many degrees of freedom used up. Gallegati et al. do not discuss the literature on nonsampling errors in large household sample surveys of income and wealth. Rather they compare these data unfavorably to high frequency stock and option market price and volume data, data that econophysicsts might work with. The study of price movements in financial markets was pioneered by Louis Bachelier [40] in his 1900 dissertation. It has been the main subject of econophysics since the renewal of interest in the subject decades ago. Gallegati et al. advocate that econophysicists confine themselves to data from financial markets. Nothing Gallegati et al. present in support of their criticisms #2 and #3 5

8 invalidates in any way the econophysics of income and wealth distribution as an exciting new area for scientific investigation. One might be forgiven for taking criticisms #2 and #3 as lightly as the first author of Gallegati et al. himself takes them. But Gallegati et al. make it clear that criticisms #1 to #3 are merely a grumpy preamble to their criticism #4. Criticism #4 of Gallegati et al.: Conservative Particle System Models Have No Dynamics The fourth, last, and most emphatically made criticism of Gallegati et al. s Worrying Trends in Econophysics is of the particle system models of the econophysics of income distributions as economic models for not being dynamic. They express themselves vigorously on this point, which they summarize in their article s abstract as: Fourth, the theoretical models which are being used to explain empirical phenomena. The latter point is of particular concern. Essentially, the models are based upon models of statistical physics in which energy is conserved in exchange processes. There are examples in economics where the principle of conservation may be a reasonable approximation to reality, such as primitive hunter-gatherer societies. But in the industrialised capitalist economies, income is most definitely not conserved. The process of production and not exchange is responsible for this. Models which focus purely on exchange and not on production cannot by definition offer a realistic description of the generation of income in the capitalist, industrialised economies. Gallegati et al. conclude their paper with a one sentence paragraph [2, pp. 6]: But econophysicists will not offer any real way forward for economics if they restrict their attention to exchange-only models.. What Gallegati et al. mean by exchange-only models are particle system models with zero-sum exchanges of a positive quantity between particles in an isolated population of particles that persist indefinitely through time. Thus these particle system models have an equality constraint on 6

9 that positive quantity at the population level. The well known kinetic theory of gases (KTG) is a particle system model with a macro level equality constraint. In the KTG particles are gas molecules and the positive quantity exchanged is kinetic energy. In the Inequality Process and the similar models proposed in the year 2000 and later - the ones that Lux referred to when he chided the econophysicists at the International Workshop on the Econophysics of Wealth Distributions for re-inventing - the particles are people and the positive quantity wealth in either its stock or flow form. It is the equality constraint of these particles systems that induces the high dudgeon in Gallegati et al. They project into this feature of particle system models the point often made in the first class meeting of Econ 101 that economics is less concerned with how wealth is distributed (how the pie is sliced up) than how to increase the size of the pie, and later in the course, that the way the pie is sliced up has to support its production and expansion. But Gallegati et al. appear to have difficulty making this latter objection succinctly - call it criticism #4b, because they think that the equality constraint prevents particle system models with equality constraints from having macro level dynamics. Criticism #4a Applies To the KTG Too And Is Known To Be Invalid For It Let s address Gallegati et al. criticism #4a, that particle system models with an equality constraint are incapable of macro level dynamics, then deal with the more interesting point they only hint at (criticism #4b) because they incorrectly think criticism #4a is valid. Responding to criticism #4b requires showing how the distribution of the positive quantity in the particle system models of interest might optimize the production of that quantity. Criticism #4a can be dismissed by pointing to the well known properties of the kinetic theory of gases (KTG), a particle system model similar to those of the econophysics of income and wealth distributions. As anyone who has taken a course in statistical mechanics knows, the equality constraint on particle kinetic energy in the kinetic theory of gases model need only last as long as it takes the distribution of particle kinetic energy to converge, which it does momentarily in the case of the subject matter of the KTG. The KTG handles change in the equality constraint as an exogenously determined 7

10 variable, for example, heat applied to the vessel in which the volume of gas molecules is isolated. Angle [6] figured out the analogous dynamics of the Inequality Process in the late 1980's and these have been restated in [25, 26]. The Key Point Is Whether the Process Converges More Quickly Than the Equality Constraint on the Quantity Distributed Changes Angle found papers on the evidence of whether an egalitarian revolution actually changed the distribution of wealth and income in a country. That is a separate issue from whether it had reshuffled the occupants of that distribution. The evidence is that no substantial change to the distribution occurred. That evidence puts limits on the time to convergence of the empirical process determining the distribution. It is quick converging by comparison to the time it takes the economic product and the share of it going to labor to change substantially. Also the difficulty of even the most violent of egalitarian revolutions to eliminate the right tail of the wealth and income distribution - the distribution of great wealth or income - implies a quick converging process. So the Inequality Process satisfies the condition to have valid exogenously driven dynamics like the KTG. Gallegati et al. s criticism #4a is thus invalid for the Inequality Process as it is for the KTG. The Inequality Process Response to Gallegati et al. s Criticism #4b: It s an Evolutionary Process Gallegati et al. do not clearly state criticism #4b but they hint at it. Criticism #4b is that they do not see how a model that merely circulates a fixed positive quantity among members of a population in a way that neither consumes nor creates that quantity - what the Inequality Process and its imitations do - can model an economy in which wealth is created and consumed. The question of how the Inequality Process perform this feat with what it has is important. The Inequality Process Figures Individual Productivity Without Knowing Anything About the Technology of Wealth Production Despite the origin of the Inequality Process as a particular social science theory of a particular statistical pattern in inequality of wealth, the Inequality Process is a general evolutionary process. Think of a population of particles, each a solution to the problem of how to generate wealth. Assume that nothing is known about each particle except its current wealth and 8

11 its recent history of wealth. Since, on average, each particle has as many losses as wins, it only takes a short history of a particle s wealth to estimate the proportion of wealth lost in a loss for each particle. That proportion,, is the particle s parameter. (1 - ) measures the particle s productivity. The more robust loser, the particle with smaller, is more losses away from death (Gambler s Ruin) at any given amount of wealth than others. The Inequality Process solves the problem of how to allocate wealth to individual particles to maximize aggregate wealth production by the population, while minimizing extinction risk for the population, and consequently, for the Inequality Process itself. The Inequality Process solves this problem despite changing conditions. The Inequality Process moves fluidly from one particular solution to another with changing conditions, using very little information, just knowledge of current particle wealth and particle wealth in the recent past. The Inequality Process does not need to measure individual particle productivity directly. In industrial economies there is a great diversity and complexity of ways of producing wealth. It is evident that this diversity and complexity has grown with techno-cultural evolution and is increasing. The Inequality Process does not have to know about the diversity and complexity of producing wealth. In the Inequality Process, competition between particles for wealth measures particle productivity using the inference rule that the more productive particle loses a smaller proportion of its wealth when it loses. Thus the Inequality Process operates homogeneously up and down the scale of technocultural evolution inferring wealth productivity from zero-sum competition for wealth alone without a) direct knowledge of individual particle productivity, or b) modeling the wealth production process. The Inequality Process is a competition process in a population of particles that transfers wealth (or energy, fuel, or food, or any positive quantity useful for its own production) via randomly decided competitions between randomly paired particles. While, short term, wealth goes to winners of these encounters since the chance of winning is 50%, in the long term wealth flows to the robust losers. If the level of productivity rises in the Inequality Process population of particles, holding the global mean of wealth constant, expected particle wealth falls in every 9

12 productivity equivalence class of particles. In the Inequality Process the penalty for being a productivity laggard grows as productivity rises in the population incentivizing particles to become more productive. Further, as the level of productivity rises in the Inequality Process population of particles, the variance of wealth in each equivalence class decreases, i.e., the transfer of wealth from the less to the more productive occurs more efficiently making wealth a better indicator of productivity. So, as the productivity of a population rises, the Inequality Process works more efficiently to transfer wealth to the more productive. That s why the Inequality Process is a functional attractor. Once a process of competition in a population of particles chances into the Inequality Process, the Inequality Process increases wealth, reduces extinction risk for the whole population, particularly the more productive particles, and creates incentives for further productivity gains. The Inequality Process adapts fluidly to productivity increase or decrease in the population of particles, to change in constraints on wealth production, and to change in global mean wealth. While incentivizing productivity increase, the Inequality Process requires no schedule of productivity increase be met. Thus, once a competition process within a population chances into the form of the Inequality Process, the Inequality Process tends to become self-perpetuating with increasing stability as the population of particles prospers and grows (assuming greater wealth and smaller risk of individual loss of wealth contribute to population growth). The Inequality Process moves the population in which it has become established and itself into the future with increasing assurance. The Inequality Process is an evolutionary optimizing process in an interacting population, a market economy, in which the wealth each actor creates depends on the product of the whole population. As an evolutionary process, the Inequality Process models selection rather than search, the groping process by which each economic actor explores how to become more productive. The Inequality Process Uses Zero-Sum Competition to Assess Particle Wealth Productivity The mechanism with which the Inequality Process transfers wealth to the more productive is the asymmetry of gain and loss. If the more productive lose less when they lose - because they 10

13 rebound faster, or are treated more gently, or have more leverage - then the Inequality Process, if it is the empirical process of wealth distribution, will transfer wealth to the more productive, nourishing their more efficient production, and causing upward drift in aggregate wealth production. The Inequality Process implies faster upward drift in aggregate wealth production, the higher the level of productivity in a labor force, since its mechanism of wealth transfer to the more productive works more efficiently in a more productive labor force, i.e., an IP-like empirical process becomes an attractor over time [26]. Zero-sum competition is the perturbing mechanism that transfers wealth from the less productive to the more productive in the Inequality Process via the asymmetry of loss and gain of wealth. Zero-sum competition is how the Inequality Process learns about particle productivity. Zero-sum competition between particles is thus the Inequality Process explanation of aggregate wealth production. If nature chose extreme parsimony for its algorithm to maximize wealth production, it may have chosen zero-sum competition as in the Inequality Process. The Inequality Process as Mainstream Economics Gallegati et al. write that they... are economists who are critical of much of... mainstream work in economics.. The Inequality Process lets Gallegati et al. rejoin the mainstream while doing econophysics. The Inequality Process is transaction-oriented, i.e., market-oriented, and dynamic. It turns out that not getting bogged down in the representation of how wealth is produced, a large number of ways, allows the Inequality Process, and the empirical process actually distributing wealth to individuals, to operate in an extremely efficient way in terms of its information needs. The Inequality Process implies - simultaneously and parsimoniously - a number of propositions, some paradigmatic, some theoretical, others empirical regularities, stylized facts, long relied on in economics: 11

14 Proposition 1) All distributions of income and wealth are right skewed with tapering right tails; hence the impossibility of a radically egalitarian distribution of labor income (the Pareto Law in a general, qualitative statement). Implication of the Inequality Process The Inequality Process generates right skewed distributions. 2) The far right tails of income and wealth distributions are fitted by a Pareto pdf. 3) Differences of wealth and income arise easily, naturally, and inevitably via an ubiquitous stochastic process, even in the comparison between individual workers with identical productivity; hence the impossibility of radically egalitarian distribution of labor income ( Gibrat s Law in a general qualitative statement). The far right tails of the Inequality Process stationary distribution approximate that of a Pareto pdf. In the Inequality Process, differences of wealth arise easily, naturally, and inevitably, via an ubiquitous stochastic process. In the Inequality Process each particle has a parameter representing its productivity of wealth. The parameter determines mean wealth of the particles in the equivalence class of each value of the parameter but there is a distribution of wealth around the mean. Interestingly, the shape of these distributions are those of the distribution of labor income conditioned on education. The shapes of the distribution of wealth in an equivalence class of the Inequality Process parameter differ in the same way the distribution of labor income differs between workers with different educations. 12

15 4) Each worker s earnings are closely tied to each worker s productivity; [part of economics since Aesop s fable of the ant and the grasshopper was the whole of economics], yet there is dispersion of wage among workers with identical productivity. 5) The ratio of mean wages in two occupations remains constant, given no change in the productivity of labor in either occupation, despite fluctuation in the mean wage in the labor force as a whole. 6) Labor incomes small and large benefit from a business expansion strong enough to increase mean labor income; A rising tide lifts all boats ; there is a community of interest between rich and poor in prosperity; in radical egalitarianism - Gallegati et al. s misconception of the Inequality Process, these interests are opposed. 7) Competition in the market creates wealth and transfers wealth to the more productive of wealth via transactions without central direction. In the Inequality Process, a particle s expected wealth is the product of the ratio of its productivity to the population harmonic mean of productivity multiplied by the unconditional mean of wealth. Higher productivity -> higher mean wealth; also higher productivity -> greater stability of wealth. The wealth of particles in a higher productivity equivalence class stochastically dominates the wealth of particles in a lower productivity equivalence class. But regardless of which productivity equivalence class a particle is in, there is a distribution around mean of that equivalence class and any wealth amount is possible. In the gamma pdf macro model of the Inequality Process, the ratio of the expected wealth of two particles remains constant despite changes in the unconditional mean of wealth. In the Inequality Process, an increase in unconditional wealth increases all percentiles of the stationary distribution of wealth by an equal factor, i.e., a rising tide lifts all wage incomes equally in the logarithm, the only way it could occur without altering the ratio of wage incomes between occupations whose marginal product ratio remains constant. In the Inequality Process, competition between particles causes wealth to flow via transactions from particles that are by hypothesis and empirical analogue less productive of wealth to those that are more productive, nourishing wealth production, and explaining the upward drift in mean wealth without the process a) requiring knowledge of how wealth is produced, or b) central direction [i.e., with extreme information efficiency ]. Thus this process can operate homogeneously over the entire course of techno-cultural evolution. 13

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