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. (shrink)

Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement (...) calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use. (shrink)

In his doctor's thesis [1], Henkin has shown that if a formal logic is consistent, and sufficiently complex, then it must admit a non-standard model. In particular, he showed that there must be a model in which that portion of the model which is supposed to represent the positive integers of the formal logic is not in fact isomorphic to the positive integers; indeed it is not even well ordered by what is supposed to be the relation of ≦.For the (...) purposes of the present paper, we do not need a precise definition of what is meant by a standard model of a formal logic. The non-standard models which we shall discuss will be flagrantly non-standard, as for instance a model of the sort whose existence is proved by Henkin. It will suffice if we and our readers are in agreement that a model of a formal logic is not a standard model if either: The relation in the model which represents the equality relation in the formal logic is not the equality relation for objects of the model. That portion of the model which is supposed to represent the positive integers of the formal logic is not well ordered by the relation ≦. That portion of the model which is supposed to represent the ordinal numbers of the formal logic is not well ordered by the relation ≦. (shrink)

A deep theme of Austrian economics has been that of spontaneous order or selforganization of the economy. The origin of this theme dates to the putative founder of the Austrian School, Carl Menger, with his theory of the spontaneous emergence of money for transactions purposes in primitive economies being archetypal example (Menger, 1892). Menger drew this approach from the Scottish Enlightenment figures David Hume, Adam Ferguson, and Adam Smith, with the latter’s Wealth of Nations (1776) particularly important. The most important (...) developer of this idea within the tradition after Menger was F.A. Hayek (1948), who would identify this self-organization phenomenon with emergence, later expanding upon this into the broader concept of complexity (Hayek, 1952, 1967). Caldwell (2004) argues that this became an increasingly important focus of Hayek’s thought in the later years of his life. Among those examining this development in more detail besides Caldwell have been Koppl (2006, 2009), Rosser (2010a),1 and Lewis (2010). This essay will consider more thoroughly the relationship between the concepts of emergence and complexity and the roles that they have played in Austrian economics as well as more broadly in philosophy and science. An important point is that both of these concepts do not possess precise meanings; they are “terms of art” within philosophy. However, while closely linked through the general idea of a whole being “greater than.. (shrink)

According to Bikas Chakrabarti (2005, p. 225), the term econophysics was neologized in 1995 at the second Statphys-Kolkata conference in Kolkata (formerly Calcutta), India by the physicist H. Eugene Stanley, who was also the first to use it in print (Stanley, 1996). Mantegna and Stanley (2000, pp. viii-ix) define “the multidisciplinary field of econophysics” as “a neologism that denotes the activities of physicists who are working on economics problems to test a variety of new conceptual approaches deriving from the physical (...) sciences.” The list of such problems has included distributions of returns in financial markets (Mantegna, 1991; Levy and Solomon, 1997; Bouchaud and Cont, 1998; Gopakrishnan, Plerou, Amaral, Meyer, and Stanley, 1999; Sornette and Johansen, 2001; Farmer and Joshi, 2004) the distribution of income and wealth (Drăgulescu and Yakovenko, 2001; Bouchaud and Mézard, 2000; Chatterjee, Yarlagadda, and Charkrabarti, 2005), the distribution of economic shocks and growth rate variations (Bak, Chen, Scheinkman, and Woodford, 1993; Canning, Amaral, Lee, Meyer, and Stanley, 1998), the distribution of firm sizes and growth rates (Stanley, Amaral, Buldyrev, Havlin, Leschhorn, Maass, Salinger, and Stanley, 1996; Takayasu and Okuyama, 1998; Botazzi and Secchi, 2003), the distribution of city sizes (Rosser, 1994; Gabaix, 1999), and the distribution of scientific discoveries (Plerou, Amaral, Gopakrishnan, Meyer, and Stanley, 1999; Sornette 1 and Zajdenweber, 1999), among other problems, all of which are seen at times not to follow normal or Gaussian patterns that can be described fully by mean and variance. The main sources of conceptual approaches from physics used by the econophysicists have been from models of statistical mechanics (Spitzer, 1971), geophysical models of earthquakes (Sornette, 2003), and “sandpile” models of avalanches, the latter involving self-organized criticality (Bak, 1996). An early physicist to assert the essential identity of statistical methods used in physics and the social sciences was Majorana (1942). A common theme among those who identify themselves as econophysicists is that standard economic theory has been inadequate or insufficient to explain the non-Gaussian distributions empirically observed for various of these phenomena, such as “excessive” skewness and leptokurtotic “fat tails” (McCauley, 2004).. (shrink)

We use NF to designate the system known as Quine's New Foundations, and NF + AF to designate the same system with a suitable axiom of infinity adjoined. We use ML to designate the revised system appearing in the third printing of Quine's “Mathematical Logic”. This system ML is just the systemPproposed by Wang in [4], and essentially includes NF as a part.The pripcipal results of the present paper are:A. In NF the axiom of infinity is equivalent to the definability (...) of an ordered pair having the same type as its constituents.B. Considering the formulas of NF as having translations in the formalism of ML in the sense defined in [4], we find that a formula of NF is provable in NF if and only if its translation is provable in ML. From the fact that the axiom of infinity is provable in ML, one might be tempted to conclude that the axiom of infinity is provable in NF. It is explained why this is not a valid inference. Consequently, it would appear that there is a sense in which NF + AF is stronger than ML. (shrink)

distraction that leads innocent Post Keynesians into “classical sin.” Davidson (1994, 1996) argues that core Post Keynesian (PK) ideas such as that insufficient aggregate demand arise from fundamental uncertainty in a monetary economy do not depend on nonlinearity or complexity, that these core concepts are axiomatically and ontologically true, and that the inability of agents to forecast well in dynamically complex situations reflects mere epistemological problems of insufficient computational abilities. Thus complex dynamics is merely a classical stalking horse. This writer (...) (Rosser, 1990, 1998, 2001) disagrees with the argument presented above and its relatives (Mirowski, 1990; Carrier, 1993). Dynamic complexity provides a foundation for fundamental uncertainty in Keynesian and PK models, and this applies to most of the various sub-branches of PKE besides Davidson’s “fundamentalist” or “Keynes-Post Keynesian”2 approach. The argument will be considered regarding three subdivisions of Post Keynesianism as identified by Hamouda and Harcourt (1988): the aforementioned fundamentalist Keynesianism, Sraffian (or neo-Ricardian), and Kaleckian (or Kaleckian- Robinsonian).3 Following King (2002, chap. 10), I admit to being more in sympathy with those he describes as “synthesizers” than with the more partisan sectarians of these approaches.4 I shall describe how each sub-branch has been analyzed using ideas of.. (shrink)

Kumaraswamy Vela Velupillai [74] presents a constructivist perspective on the foundations of mathematical economics, praising the views of Feynman in developing path integrals and Dirac in developing the delta function. He sees their approach as consistent with the Bishop constructive mathematics and considers its view on the Bolzano-Weierstrass, Hahn-Banach, and intermediate value theorems, and then the implications of these arguments for such “crown jewels” of mathematical economics as the existence of general equilibrium and the second welfare theorem. He also relates (...) these ideas to the weakening of certain assumptions to allow for more general results as shown by Rosser [51] in his extension of Gödel’s incompleteness theorem in his opening section. This paper considers these arguments in reverse order, moving from the matters of economics applications to the broader issue of constructivist mathematics, concluding by considering the views of Rosser on these matters, drawing both on his writings and on personal conversations with him. (shrink)

In 1991 this author published a book entitled, From Catastrophe to Chaos: A General Theory of Economic Discontinuities with Kluwer Academic Publishers. Due to the con troversial and unusual nature of this book’s content, there was considerable difficulty in getting publishers to agree to publish it prior to its being accepted by Kluwer. Initially conceived as a heterodox challenge to established economic thinking, this book became viewed by many readers as a reference volume on applications of nonlinear dynamics in general (...) to many fields of economics. Now, in 2000 Volume 1 of the second edition has appeared from Kluwer also, subtitled, Mathematics, Microeconomics, Macroeconomics, and Finance. It covers in expanded form the material contained in the first eight chapters of the first edition. What is this book about and how does the new edition differ from the first one? The underlying philosophy presented is that discontinuities are important objects of study in economics, indeed in many disciplines beyond economics as well. Although discontinuities may arise dynamically due to random exogenous shocks, the more truly interesting ones are those that arise endogenously from dynamical economic systems. In dynamical systems discontinuities can arise endogenously in the presence of nonlinearities in the systems. Thus, the more general topic of nonlinear dynamics in.. (shrink)

This essay reviews the arguments made for a New Austrian theory of business cycles by Tyler Cowen, based on risk analysis and assuming rational expectations. This contrasts with the Old Austrian view that questions measurable risk in economic analysis. The way risk is applied to analyze business cycles suffers from serious inconsistencies. The use of rational expectations is mistaken in the face of economic complexity as understood by the traditional Austrians. However, Cowen is commended for his open-mindedness, even as this (...) leads him away from a strictly Austrian perspective. (shrink)

This paper presents a view of the process of transition from planned command socialism to mixed market capitalism involving nonlinear complex dynamical phenomena. After the former institutional structure disappears a coordination failure can bring about macroeconomic collapse as in almost all of the former Soviet bloc or macroeconomic boom as in China. A closely linked phenomenon is the rise of the underground economy as inflation and income inequality increase. This can lead to a jump from one equilibrium to a very (...) different one as nonlinear social feedback processes operate in the transition. (shrink)

Various complex dynamics in ecologic-economic systems are presented with an emphasis upon models of global warming dynamics and fishery dynamics. Chaotic and catastrophic dynamic patterns are shown to be possible, along with other complex dynamics arising from nonlinearities in such combined systems. Problems associated with amplified oscillations due to these nonlinear interactions in the combined interactions of human economic decisionmaking with ecological dynamics are identified and discussed. Implications for policy are examined with strong recommendations for greater emphasis in particular upon (...) the precautionary principle to avoid catastrophic collapses beyond critical thresholds and the scale-matching principle to ensure that efforts to manage complex nonlinear dynamics are directed at the appropriate levels of ecologiceconomic interaction. Key Words: complex dynamics, chaos, catastrophe, fisheries, global warming.. (shrink)

Economies making a transition from centrally planned socialism to market capitalism can experience chaotic hysteresis. This can arise from elements of the previous system persisting even as institutions are transformed with the system possibly experiencing chaos during this conflict. A model of investment cycles accompanied by technological stagnation shows this phenomenon which can be viewed from a cusp catastrophe perspective. Empirical tests of Soviet investment and construction data provide incomplete support for the cusp structure with chaos. Nonlinear structures are found (...) with bifurcation effects for all cases and possibly chaotic dynamics for five-year lagged construction data. (shrink)

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. (shrink)

September 2008 Abstract: We consider the precursors to the discovery of sensitive dependence on initial conditions by Edward Lorenz (1963) in his model of climatic fluid dynamics. This will focus on work in various disciplines that imply either such sensitivity, irregular endogenous dynamic patterns, or fractal nature of an attractor, as is also found in the attractor underlying the model Lorenz studied. Going from ancient hints in Anaxagoras through nineteenth century mathematics and physics, the main areas of such development will (...) be argued to have been in celestial mechanics, oscillators, and economics. (shrink)

“A Public Domain, once a velvet carpet of rich buffalo-grass and grama, now an illimitable waste of rattlesnake-bush and tumbleweed, too impoverished to be accepted as a gift by the states within which it lies. Why? Because the ecology of the Southwest happened to be set on a hair trigger.”.

Daily returns of stock markets in 27 emerging markets in Asia, Africa, South America, and Eastern Europe from the early 1990s through 2006 are analyzed for the possible presence of nonlinear speculative bubbles. The absence of these is tested for by studying residuals of VAR-based fundamentals, using the Hamilton regime-switching model and the rescaled range analysis of Hurst. For the first test absence of bubbles is rejected for 24 countries (except Mexico, Sri Lanka, and Taiwan), and for the second it (...) is rejected for 26 (except Malaysia). BDS testing on residuals after ARCH effects are removed fails to reject further nonlinearity in the residual series for all countries. (shrink)

Speculative bubbles present a problem for the development of sophisticated financial markets in developing economies. This paper discusses the evolution of regulatory institutions in Pakistan pertaining to the Karachi stock exchange and empirically tests for the presence of stock market bubbles in that stock market in recent years. A fundamental is estimated using a VAR approach, and residuals of this fundamental are tested for trends using Hamilton regime switching and Hurst rescaled range methods. Nonlinearities beyond ARCH are also tested for (...) using the BDS test. We are unable to reject the hypothesis of no bubbles or non nonlinearities during the period studied, indicating that Pakistan faces this difficult problem in developing appropriate regulations and institutions for the oversight of its financial markets. (shrink)

James Madison University Harrisonburg, VA 22807 Tel: 540-568-3212 Fax: 540-568-3010 Email: [email protected].

Roger Koppl (2009, p. 1) argues that “Austrian economics is a school of thought within the broader complexity movement in economics.” Is he correct? While there are many who have argued for some overlapping between the two, I shall argue that this is probably an overly strong statement. The main reason is that there are substantial elements and strands within Austrian economics that do not fit in with any of the multiple varieties of complexity theory, even though there are some (...) that clearly do. While I have some disagreements with Koppl’s argument, I think that he does a good job of identifying some of the main strands of Austrian economics that are consistent with complexity thought. The most important of these are associated with the work of Friedrich A. Hayek, who.. (shrink)

A time series of the Shanghai stock index in China for the 1990s is studied for the possible existence of nonlinear speculative bubbles. Three alternative specifications of fundamentals are estimated using VAR models of domestic and international variables. These are subjected to regime switching tests and rescaled range analysis tests. Nulls of no persistence were mostly rejected, suggesting the strong possibility of bubbles. Nonlinearities beyond ARCH effects using the BDS test could not be rejected. The paper also discusses the special (...) circumstances of the stock market in an emerging transition economy. (shrink)

We present three arguments regarding the limits to rationality, prediction, and control in economics, based on Morgenstern's analysis of the Holmes-Moriarty problem. The first uses a standard metamathematical theorem on computability to indicate logical limits to forecasting the future. The second provides possible nonconvergence for Bayesian forecasting in infinite dimensional space. The third shows the impossibility of a computer perfectly forecasting an economy with agents knowing its forecasting program. Thus, economic order is partly the product of something other than calculative (...) rationality. The joint presentation of these existing results should introduce the reader to implications of these concepts for certain shared concerns of Keynes and Hayek. (shrink)

This paper examines how institutions for managing environmental resources change over time with economic development and the seriousness of environmental problems. Different problems tend to be more serious at different levels of development requiring different approaches. A major point is that traditional systems of management in poorer countries were often effective at managing common good resources, and institutions that replicate their advantages should be encouraged at higher levels of economic development as well.

Large increases unofficial economies in many transition economies arise from a dynamic interaction with rising income inequality and public sector changes in multiple equilibria system. Returns to unofficial activity are first increasing and then decreasing, implying two distinct stable equilibria, with changes in inequality possibly causing a jump from one to the other. Multiple regressions of data from 18 transition economies find income inequality significantly correlated with the size of the unofficial economy, with the maximum annual rate of inflation also (...) significantly correlated. The latter appears to be the only significant correlate with the increase in the size of the unofficial economy. (shrink)

James Madison University Harrisonburg, VA 22807 USA Tel: 540-568-3212 Fax: 540-568-3010 Email: [email protected].

I am writing this in December, 2010, the final month that I am Editor of the Journal of Economic Behavior and Organization (JEBO), having first assumed this position effectively in August, 2001.1 It has mostly been a rewarding, if increasingly time-consuming, experience, as submissions have approximately doubled over this period. I have gotten better at doing things more quickly, and the switch from snail mail to electronic handling of matters has speeded things up, but the workload has increased substantially. In (...) any case, t has been fascinating to see what people submit to the journal and to have an influence on the direction of the profession of economics, however marginal. I have also gotten to know many interesting people that I would not have if I had not been Editor, both members of my editorial board, as well as authors, submitters, and referees. While it will be a relief not to have all this constant responsibility and work, I confess that I shall miss it. However, as other editors can attest, there are many things that are not so pleasant that accompany the job of journal editor aside from the simple workload. A well-known one is the complaining by authors who have had their papers rejected for publication. This is par for the course and goes with the territory. There are also all the hassles with getting referee reports back and being able to make decisions without making authors wait too long. This also goes with the territory, although many editors have tried many methods to get reports back sooner. While these are common to pretty much all editors, other problems can be more unusual. One of the most challenging problems I have dealt with is one that other editors.. (shrink)

abstract Cowen and I agree that rational‐expectations theory is unrealistic and that risk is difficult to quantify. However, we continue to disagree about the riskiness of consumption as opposed to investment. Since more investment might lead to a recession if investment is relatively risky, Cowen's use of rational‐expectations theory to buttress the Austrian school's claim that market economies can shift toward relatively more investment without experiencing macroeconomic disruption remains suspect.

The literature on speculative bubbles in foreign exchange rates is voluminous, with much of it failing to reject the presence of bubbles in many exchange markets.1 Serious testing of this issue began with the work of Meese (1986), Evans (1986), and Woo (1987). Each used a different approach, and each found evidence failing to reject the presence of bubbles in at least some exchange markets.

Ecologic-economic systems tend to exhibit greater complexity than systems that are purely ecological or economic. The interactions between the two types often generates nonlinear relations that lead to various kinds of complex dynamics that complicate management and decisionmaking regarding them. Of these, forests have characteristics that lead them to have special problems not usually encountered in the management of such systems. A central one is the long time periods involved managing forests compared to most other such systems. This means that (...) the issues regarding determination of discount rates for valuing future outcomes are more important for forestry management than for many other systems. Also, forests generate a wider range of externalities than do most other ecologic-economic systems, with implications for various hierarchical levels of management. This paper considers the array of these problems as they appear for a variety of forestry management issues. (shrink)