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)

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can (...) only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies “free enterprise” with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it. (shrink)

This article argues that the neoclassical era in economics has ended and is being replaced by a new era. What best characterizes the new era is its acceptance that the economy is complex, and thus that it might be called the complexity era. The complexity era has not arrived through a revolution. Instead, it has evolved out of the many strains of neoclassical work, along with work done by less orthodox mainstream and heterodox economists. It is only in its beginning (...) stages. The article discusses the work that is forming the foundation of the complexity era, and how that work will likely change the way in which we understand economic phenomena and the economics profession. (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)

This book is about the economics profession, or more precisely, the process by which economic thinking changes. We believe that this process is important because economics is currently at a turning point; it is changing from a static approach to understanding, in which deductive reasoning is the key method used, to a complexity approach to understanding, in which inductive and deductive methods are used simultaneously, and the full complexity of the system is acknowledged and dealt with. The change is ongoing (...) and has many levels and dimensions, most of which have not coalesced to the degree that they have reached the lay public. But anyone involved in economic research recognizes the changes, although they do not necessarily understand how they all fit together. (shrink)

The first is that we are wrong to suggest that the mainstream is no longer limited to a restrictive orthodoxy of beliefs and assumptions that discourages dissenting voices. In developing his argument, Vernengo claims that our characterization of a cutting edge branch of the mainstream that does not hold to a neoclassical orthodoxy is misleading. Although he states that he accepts our characterization of the economics profession as a complex adaptive system, with many competing views, he sees the cutting edge (...) as a sham. He argues that the true role of the cutting edge is to allow the mainstream to “sound reasonable when talking about reality, while orthodoxy provides authority to the cutting edge.” He calls this an “organized hypocrisy” and calls us naive about the sociology of the economics profession. Because of this naiveté on our part he believes that we are giving bad advice to advocate that heterodox economists should think of themselves as economists first and heterodox economists second. (shrink)

We attempt to clarify divisions made by us in previous work (Colander et al., 2004a,b) between “orthodox, mainstream, and heterodox” in economics, following very useful remarks in Dequech (2007-08), whom we thank. We also provide specific advice for heterodox economists, namely: worry less about methodology, focus on being economists first and heterodox economists second, and prepare ideas to leave the incubator of heterodoxy to enter the mainstream economic debate.

This book is about the economics profession, or more precisely, the cutting edge of the economics profession. Economics is currently at a turning point; it is changing from a static approach to understanding, in which deductive reasoning is the key method used, to a complexity approach to understanding, in which inductive and deductive methods are used simultaneously, and the full complexity of the system is acknowledged and dealt with. The change is just beginning, but the groundwork is currently being laid. (...) This book is about that groundwork and those economists who are developing it. They are the cutting edge of economics. Those who are doing cutting edge work are researchers who are pushing and testing the boundaries of the profession in such a way that it draws the attention of the elite in the profession. The cutting edge has the potential of changing mainstream economics and ultimately what is considered the orthodoxy. (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)