Econophysics Research by Victor Yakovenko

Publication Profiles

Research Grants

Video Recordings of the Talks

Coverage in the Media


1. Statistical Mechanics of Money, Income, and Wealth

[1.1] "Statistical mechanics of money" by A. A. Dragulescu and V. M. Yakovenko

Published:  The European Physical Journal B, v. 17, pp. 723-729 (2000)PDFcond-mat/0001432RePEc
Computer Animation Video by Justin Chen
Computer Simulations in Mathematica by Ian Wright
Abstract:  In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Gibbs distribution emerges in computer simulations of economic models. Then we consider a thermal machine, in which the difference of temperatures allows one to extract a monetary profit. We also discuss the role of debt, and models with broken time-reversal symmetry for which the Gibbs law does not hold.

[1.2] "Evidence for the exponential distribution of income in the USA" by A. A. Dragulescu and V. M. Yakovenko

Published:  The European Physical Journal B, v. 20, pp. 585-589 (2001)PDFcond-mat/0008305RePEc
Abstract:  Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2=50% agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8=37.5% calculated for two-earners families.

[1.3] "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States" by A. A. Dragulescu and V. M. Yakovenko

Published:  Physica A, v. 299, pp. 213-221 (2001)PDFcond-mat/0103544RePEc
Abstract:  We present the data on wealth and income distributions in the United Kingdom, as well as on the income distributions in the individual states of the USA. In all of these data, we find that the great majority of population is described by an exponential distribution, whereas the high-end tail follows a power law. The distributions are characterized by a dimensional scale analogous to temperature. The values of temperature are determined for the UK and the USA, as well as for the individual states of the USA.

[1.4] "Statistical Mechanics of Money, Income, and Wealth: A Short Survey" by A. A. Dragulescu and V. M. Yakovenko

Published:  Modeling of Complex Systems: Seventh Granada Lectures, AIP Conference Proceedings 661, New York, 2003, pp. 180-183,  PDFcond-mat/0211175RePEc
Abstract:  In this short paper, we overview and extend the results of our papers cond-mat/0001432, cond-mat/0008305, and cond-mat/0103544, where we use an analogy with statistical physics to describe probability distributions of money, income, and wealth in society. By making a detailed quantitative comparison with the available statistical data, we show that these distributions are described by simple exponential and power-law functions.

[1.5] "Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983-2001" by A. C. Silva and V. M. Yakovenko

Published:  Europhysics Letters, v. 69, pp. 304-310 (2005)PDFcond-mat/0406385RePEc
Abstract:  Personal income distribution in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs ("thermal") distribution, whereas the upper class (1-3% of population) has a Pareto power-law ("superthermal") distribution. By analyzing income data for 1983-2001, we show that the "thermal" part is stationary in time, save for a gradual increase of the effective temperature, whereas the "superthermal" tail swells and shrinks following the stock market. We discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively show that it applies to the majority of population.

[1.6] "Two-class structure of income distribution in the USA: Exponential bulk and power-law tail" by V. M. Yakovenko and A. C. Silva

Published:  In the book "Econophysics of Wealth Distributions", edited by A. Chatterjee, S. Yarlagadda, and B. K. Chakrabarti (2005, Springer series "New Economic Windows", ISBN 88-470-0329-6), pp. 15-23
Abstract:  Conference proceedings paper based on [1.5].

[1.7] "A study of the personal income distribution in Australia" by A. Banerjee, V. M. Yakovenko, and T. Di Matteo

Published:  Physica A, v. 370, pp. 54-59 (2006)PDFphysics/0601176RePEc
Abstract:  We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution.

[1.8] "Universal patterns of inequality" by A. Banerjee and V. M. Yakovenko

Published:  New Journal of Physics 12, 075032 (2010)PDFarXiv:0912.4898RePEc
Abstract:  We study probability distributions of money, income, and energy consumption per capita for ensembles of economic agents. Following the principle of entropy maximization for partitioning of a limited resource, we find exponential distributions for the investigated variables. We also discuss fluxes of money and population between two systems with different money temperatures. For income distribution, we study a stochastic process with additive and multiplicative components. The resultant income distribution interpolates between exponential at the low end and power-law at the high end, in agreement with the empirical data for USA. We discuss how the increase of income inequality in USA in 1983-2007 results from dramatic increase of the income fraction going to the upper tail and exceeding 20% of the total income. Analyzing the data from the World Resources Institute, we find that the distribution of energy consumption per capita around the world is reasonably well described by the exponential function. Comparing the data for 1990, 2000, and 2005, we discuss the effects of globalization on the inequality of energy consumption.

[1.9] "Global inequality in energy consumption from 1980 to 2010" by S. Lawrence, Q. Liu, and V. M. Yakovenko

Published:  Entropy 15, 5565-5579 (2013)PDFarXiv:1312.6443RePEc
Abstract:  We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980-2010. We find that the Lorenz curves have moved up during this time period, and the Gini coefficient G has decreased from 0.66 in 1980 to 0.55 in 2010, indicating a decrease in inequality. The global probability distribution of energy consumption per capita in 2010 is close to the exponential distribution with G=0.5. We attribute this result to the globalization of the world economy, which mixes the world and brings it closer to the state of maximal entropy. We argue that global energy production is a limited resource that is partitioned among the world population. The most probable partition is the one that maximizes entropy, thus resulting in the exponential distribution function. A consequence of the latter is the law of 1/3: the top 1/3 of the world population consumes 2/3 of produced energy. We also find similar results for the global probability distribution of CO2 emissions per capita.

[1.10] "Monetary economics from econophysics perspective" by V. M. Yakovenko

Published:  The European Physical Journal Special Topics 225, 3313-3335 (2016), in the issue Discussion and Debate: Can Economics be a Physical Science?PDFarXiv:1608.04832RePEc
Abstract:  This is an invited article for the Discussion and Debate special issue of The European Physical Journal Special Topics on the subject "Can Economics Be a Physical Science?" The first part of the paper traces the personal path of the author from theoretical physics to economics. It briefly summarizes applications of statistical physics to monetary transactions in an ensemble of economic agents. It shows how a highly unequal probability distribution of money emerges due to irreversible increase of entropy in the system. The second part examines deep conceptual and controversial issues and fallacies in monetary economics from econophysics perspective. These issues include the nature of money, conservation (or not) of money, distinctions between money vs. wealth and money vs. debt, creation of money by the state and debt by the banks, the origins of monetary crises and capitalist profit. Presentation uses plain language understandable to laypeople and may be of interest to both specialists and general public.

[1.11] "Universal exponential structure of income inequality: Evidence from 60 countries" by Yong Tao, Xiangjun Wu, Tao Zhou, Weibo Yan, Yanyuxiang Huang, Han Yu, Benedict Mondal, and Victor M. Yakovenko

Submitted:  Journal of Economic Interaction and Coordination,  arXiv:1612.01624RePEc
Abstract:  Economic competition between humans leads to income inequality, but, so far, there has been little understanding of underlying quantitative mechanisms governing such a collective behavior. We analyze datasets of household income from 60 countries, ranging from Europe to Latin America, North America and Asia. For all of the countries, we find a surprisingly universal rule: Income distribution for the great majority of populations (low and middle income classes) follows an exponential law. To explain this empirical observation, we propose a theoretical model within the standard framework of modern economics and show that free competition and Rawls fairness are the underlying mechanisms producing the exponential pattern. The free parameters of the exponential distribution in our model have an explicit economic interpretation and direct relevance to policy measures intended to alleviate income inequality.

2. Stochastic Volatility Models for Stock-Price Fluctuations

[2.1] "Probability distribution of returns in the Heston model with stochastic volatility" by A. A. Dragulescu and V. M. Yakovenko

Published:  Quantitative Finance, v. 2, pp. 443-453 (2002)PDFErratum:  Quantitative Finance, v. 3, p. C15 (2003),  PDF
Preprint:  cond-mat/0203046, RePEc, PDFViewgraphs:  vertical.pdf, horizontal.pdf,
Abstract:  We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula is in excellent agreement with the Dow-Jones index for time lags from 1 to 250 trading days. For large returns, the distribution is exponential in log-returns with a time-dependent exponent, whereas for small returns it is Gaussian. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow-Jones data for 1982–2001 follow the scaling function for seven orders of magnitude.

[2.2] "Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes" by A. C. Silva and V. M. Yakovenko

Published:  Physica A 324, 303-310 (2003)PDFcond-mat/0211050
Abstract:  We compare the probability distribution of returns for the three major stock-market indexes (Nasdaq, S&P500, and Dow-Jones) with an analytical formula recently derived by Dragulescu and Yakovenko for the Heston model with stochastic variance. For the period of 1982-1999, we find a very good agreement between the theory and the data for a wide range of time lags from 1 to 250 days. On the other hand, deviations start to appear when the data for 2000-2002 are included. We interpret this as a statistical evidence of the major change in the market from a positive growth rate in 1980s and 1990s to a negative rate in 2000s.

[2.3] "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact" by A. C. Silva, R. E. Prange, and V. M. Yakovenko

Published:  Physica A 344, 227-235 (2004)PDF
Preprint:  cond-mat/0401225, RePEc, PDFPresentation:  PPT.
Abstract:  We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. The slope of the exponential function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the exponential law continuously evolves into Gaussian distribution. The exponential-to-Gaussian crossover is well described by the analytical solution of the Heston model with stochastic volatility.

[2.4] "Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study" by A. C. Silva, and V. M. Yakovenko

Published:  Physica A 382, 278–285 (2007)PDF
Preprint:  physics/0608299, PDFPresentation:  PPT.
Abstract:  We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Dt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval Dt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.

3. Reviews Papers and Books on Econophysics

[3.1] "Applications of physics to economics and finance: Money, income, wealth, and the stock market" by A. A. Dragulescu

Posted: (2003) cond-mat/0307341, PDF.
Abstract:  Ph.D. thesis in physics defended on May 15, 2002 at the University of Maryland.  It covers the papers [1.1-1.4, 2.1] listed above and contains extra material.  (30 pages, 30 figures)

[3.2] "Research in econophysics" by V. M. Yakovenko

Posted:  (2003) cond-mat/0302270, RePEc, PDF.
Abstract:  Review of econophysics research in the group of Victor Yakovenko written for the online newspaper published by the Department of Physics, University of Maryland: The Photon, Issue 24, January-February 2003

[3.3] "Applications of physics to finance and economics: returns, trading activity and income" by A. Christian Silva

Posted:  (2005) physics/0507022, PDF.
Abstract:  Ph.D. thesis in physics defended on May 10, 2005 at the University of Maryland. It covers the papers [2.2-2.3, 1.5] listed above and contains much additional material.  (24 pages, 45 figures)

[3.4] "Econophysics, Statistical Mechanics Approach to" by V. M. Yakovenko

Posted:  (2007) arXiv:0709.3662, RePEc, PDF.
Published:  in Encyclopedia of Complexity and System Science, edited by R. A. Meyers, ISBN 978-0-387-75888-6, Springer (2009)
Abstract:  This invited review article surveys statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.  (24 pages, 11 figures, 144 citations)

[3.5] Book "Classical Econophysics" by A. F. Cottrell, P. Cockshott, G. J. Michaelson, I. P. Wright, and V. M. Yakovenko

Published:  Routledge (2009), ISBN 978-0-415-47848-9, series Advances in Experimental and Computable Economics.
Abstract:  This monograph examines the domain of classical political economy using the methodologies developed in recent years both by the new discipline of econophysics and by computing science. This approach is used to re-examine the classical subdivisions of political economy: production, exchange, distribution and finance. Covering a combination of techniques drawn from three areas, classical political economy, theoretical computer science and econophysics, to produce models that deepen our understanding of economic reality, this new title will be of interest to higher level doctoral and research students, as well as scientists working in the field of econophysics.  (384 pages)

[3.6] "Colloquium: Statistical mechanics of money, wealth, and income" by V. M. Yakovenko and J. B. Rosser, Jr.

Published:  Reviews of Modern Physics 81, 1703 (2009)PDFarXiv:0905.1518RePEc
Abstract:  The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.

[3.7] "Statistical mechanics of money, debt, and energy consumption" by V. M. Yakovenko

Published: Science and Culture 76 (9-10), 430-436 (2010), invited paper to the Special Issue on EconophysicsarXiv:1008.2179RePEc
Abstract:  We briefly review statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents in payment for goods and services. We focus on conceptual foundations for this approach, on the issues of money conservation and debt, and present new results for the energy consumption distribution around the world.

[3.8] "Statistical mechanics approach to the probability distribution of money" by V. M. Yakovenko

Published: Chapter 7 in the book New Approaches to Monetary Theory: Interdisciplinary Perspectives, edited by Heiner Ganssmann, ISBN 978-0-415-59525-4, Routledge (2011), pages 104-123, Routledge series International Studies in Money and Banking, proceedings of the workshop Money - Interdisciplinary Perspectives, Department of Sociology, Free University of Berlin, 25-27 June 2009.  arXiv:1007.5074RePEc
Abstract:  This invited Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents in payment for goods and services. Starting from the initially equal distribution of money, the system spontaneously develops a highly unequal distribution of money analogous to the Boltzmann-Gibbs distribution of energy in physics. Boundary conditions are crucial for achieving a stationary distribution. When debt is permitted, it destabilizes the system, unless some sort of limit is imposed on maximal debt.

[3.9] "Applications of statistical mechanics to economics: Entropic origin of the probability distributions of money, income, and energy consumption" by V. M. Yakovenko

Published: Chapter 4 in the book Social Fairness and Economics: Economic essays in the spirit of Duncan Foley, edited by Lance Taylor, Armon Rezai, and Thomas Michl, ISBN 978-0-415-53819-0, Routledge (2013), pages 53-82, Routledge series Frontiers of Political Economy, proceedings of the symposium in honor of Duncan K. Foley on occasion of his 70th birthday at the Department of Economics, New School for Social Research, New York, 20-21 April 2012.   arXiv:1204.6483RePEc
Abstract:  This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods, such as the principle of entropy maximization, to the probability distributions of money, income, and global energy consumption per capita. The exponential probability distribution of wages, predicted by the statistical equilibrium theory of a labor market developed by Foley in 1996, is supported by empirical data on income distribution in the USA for the majority (about 97%) of population. In addition, the upper tail of income distribution (about 3% of population) follows a power law and expands dramatically during financial bubbles, which results in a significant increase of the overall income inequality. A mathematical analysis of the empirical data clearly demonstrates the two-class structure of a society. Empirical data for the energy consumption per capita around the world are close to an exponential distribution, which can be also explained by the entropy maximization principle.

[3.10] "Modeling sustainability: population, inequality, consumption, and bidirectional coupling of the Earth and Human Systems" by S. Motesharrei, J. Rivas, E. Kalnay, G. R. Asrar, A. J. Busalacchi, R. F. Cahalan, M. A. Cane, R. R. Colwell, K. Feng, R. S. Franklin, K. Hubacek, F. Miralles-Wilhelm, T. Miyoshi, M. Ruth, R. Sagdeev, A. Shirmohammadi, J. Shukla, J. Srebric, V. M. Yakovenko, and N. Zeng

Published: National Science Review 3, 470-494 (2016)PDF
Research Highlight: Bojie Fu and Yan Li, National Science Review 3, 397-398 (2016)
Media Releases: Oxford University Press and University of Maryland
Abstract:  Over the last two centuries, the impact of the Human System has grown dramatically, becoming strongly dominant within the Earth System in many different ways. Consumption, inequality, and population have increased extremely fast, especially since about 1950, threatening to overwhelm the many critical functions and ecosystems of the Earth System. Changes in the Earth System, in turn, have important feedback effects on the Human System, with costly and potentially serious consequences. However, current models do not incorporate these critical feedbacks. We argue that in order to understand the dynamics of either system, Earth System Models must be coupled with Human System Models through bidirectional couplings representing the positive, negative, and delayed feedbacks that exist in the real systems. In particular, key Human System variables, such as demographics, inequality, economic growth, and migration, are not coupled with the Earth System but are instead driven by exogenous estimates, such as United Nations population projections. is makes current models likely to miss important feedbacks in the real Earth-Human system, especially those that may result in unexpected or counterintuitive outcomes, and thus requiring different policy interventions from current models. e importance and imminence of sustainability challenges, the dominant role of the Human System in the Earth System, and the essential roles the Earth System plays for the Human System, all call for collaboration of natural scientists, social scientists, and engineers in multidisciplinary research and modeling to develop coupled Earth-Human system models for devising effective science-based policies and measures to bene t current and future generations.

4. Invited Book Reviews

[4.1] Review of the book The Physics of Wall Street: A Brief History of Predicting the Unpredictable (2013) by James Owen Weatherall

Published in Physics Today 66, August 2013, p. 50


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