II. THE EMERGENCE OF ECONOPHYSICS AS A RESEARCH FIELD

According to Kutner and Grech (Reference Kutner and Grech2008), econophysics as a field of research dates back to 1991, when Mantegna published a paper about Lévy processes in finance. However, Jovanovic and Schinckus (Reference Jovanovic and Schinckus2010a) trace the roots of the basic ideas of econophysics to papers by Benoît Mandelbrot (Reference Mandelbrot1963, 1965), who saw an analogy between the evolution of financial markets and the phenomenon of turbulence. In the 1960s, Samuelson (Reference Samuelson1965) evoked the possibility of using Lévy processes in finance but the first authors to make use of these processes in finance were Mandelbrot (1962, 1963, 1965) and especially Fama (Reference Fama1963, Reference Fama1965), who tried to study financial markets using a non-Gaussian statistical framework directly inspired by Lévy’s work (1924) on the stability of probability distributions,Footnote ⁴ and the generalization of the central-limit theorem proposed by Gnedenko and Kolmogorov (Reference Gnedenko and Kolmogorov1954).Footnote ⁵ According to these works, Lévy processes, in their Paretian form, provide a better description of the evolution of financial markets, and they take into account price variations that are very large in relation to average variations, allowing, therefore, the possibility of price “jumps.” However, the stability of the Paretian distribution means that the variance depends on the size of the sample and the observation scale, and does not tend towards a limit value. The variation is said, therefore, to be infinite because it does not have a limit-value.Footnote ⁶ This infinite variance appears to be the cause of the abandonment of Lévy processes in financial economics (see Jovanovic and Schinckus Reference Jovanovic and Schinckus2010a).

The infinite variance hypothesis was unacceptable because it is meaningless in the framework of financial economics. Variance and the expected mean are the two main variables of theoretical significance. In the 1960s, the period in which financial economics was constituted as a scientific discipline, the relationship between risk and return was taken from Markowitz’ work (1952, 1959). Markowitz associated risk with variance and return with the mean. In this perspective, if variance were infinite (as it is in a Lévy process), it became impossible to understand and to compute the notion of risk as defined by Markowitz.

The use of Lévy in finance, then, has been progressively abandoned, and this point has not been discussed in the literature, since it implied a new measure of risk (Fama Reference Fama1965). Ten years after his 1965 article, Fama (Reference Fama1976) himself preferred to use normal distribution to describe monthly variations, thereby abandoning α-stable distributions. In his extension of modern portfolio theory to the Paretian framework, Fama (Reference Fama1965, p. 416) deplored the fact that no computational definition yet existed for evaluating this parameter. This led him to conclude: “Although the model discussed in the previous sections provides a complete theoretical structure for a portfolio model in a stable Paretian market, there are several difficulties involved in applying the model in practical situations” (Fama Reference Fama1965, p. 414).

Although “[a]t the moment [1963] very little is known about the sampling behavior of procedures for estimating the parameters of these distributions,” Fama (Reference Fama1963, p. 429) explained that the next step in the acceptability of Levy processes in economics would be “to develop more adequate statistical tools for dealing with stable Paretian distributions” (1963, p. 429).

It was only about thirty years later that these discussions re-emerged under the label “econophysics.” As a specific label defining a conceptual practice, it was first coined by the physicist H. Eugene Stanley in 1996 in a paper published in Physica A (Stanley et al. Reference Stanley, Afanasyev, Aamaral, Buldyrev, Goldberger, Havlin, Leschhorn, Maass, Mantegna, Peng, Prince, Salinger, Stanley and Viswanathan1996) As the name suggests, econophysics presents itself as a hybrid discipline that can be defined in methodological terms as “a quantitative approach using ideas, models, conceptual and computational methods of statistical physics” applied to economic and financial phenomena (Burda, Jurkiewicz, and Nowak Reference Burda, Jukiewicz and Nowak2003, p. 1). A similar definition of econophysics is found in Mantegna and Stanley (Reference Mantegna and Stanley2000, p. 355).

Econophysics presents itself as a new way of thinking about the economic and financial systems through the “lenses” of physics. As much as neoclassical economics imported models from classical physics as formulated by Lagrange (Mirowski Reference Mirowski1989), and financial economics built on the model of Brownian motion also imported from physics, so too econophysics tries to model economic phenomena using analogies taken from modern condensed matter physics and its associated mathematical tools and concepts. And, whereas mainstream microeconomics is based on the rational behavior of individuals, econophysics focuses on interactions between actors that lead to the emergence of statistical macro-laws, which are typically power laws instead of Gaussian ones as expected in neoclassical economics.Footnote ⁷ This approach is directly in line with the development of so-called “complexity science” during the 1990s (Rickles Reference Rickles2007), for which economic systems are obvious candidates for a treatment in terms of “complexity” because they are composed of multiple components (agents) interacting in such a way as to generate the macro-properties of economic systems and subsystems (Rickles Reference Rickles, Collier and Hooker2008, p. 4).

Though economists and econophysists have in common their focus on mathematical modeling, there is a deep difference in the way they model economic behaviour. Economics tends to be based on methodological individualism and focused on individuals’ characteristics, analyzing their behaviour in terms of given personal elements (utility function, risk aversion, etc.). Beyond that, all psychological and emotional factors are excluded from the economic analysis, the mainstream being based on the notion of perfectly rational agents (Mongin 2002; Lallement 2000), a notion that supposes a specific modeling of individual behavior. In neoclassical economics, rationality explains the (microscopic) behavior of each individualFootnote ⁸ without taking into account the result of their interactions with the economic system.Footnote ⁹

In opposition to this view, econophysics provides no specific model of the rational individual’s behavior. Econophysicists avoid the difficult task of theorizing about the individual psychology of investors (Brandouy Reference Brandouy, Bourghelle, Brandouy, Gillet and Orléan2005), and they do not care about rational agent theory. In that sense, there is no real micro-econophysics, and that discipline does not take into account the personal characteristics (utility, etc.) of individuals. Econophysicists do not focus on the interactive abilities of agents but, rather, on the macro-result of their interactions. Financial systems consist, then, of a large number of components whose interactions generate observable properties. The heterogeneity of the components (agents) is supposed to be captured in the macro-result of the system. Few works in econophysics are dedicated to the analysis of the heterogeneity and interaction of agents, which is an approach that refers to a larger field including experimental psychology and artificial intelligence.

Using the standard tools of statistical mechanics, such as microscopic models, the Ising model, and scaling laws, econophysicists aim at explaining how emergenceFootnote ¹⁰ appears at the macro-level of complex economic systems. Epistemologically, econophysics is founded on the belief in the universality of some general statistical properties that reappear across many and diverse phenomena (McCauley Reference McCauley2004). This statistical universality can be characterized by scaling laws considered to be at the heart of econophysicsFootnote ¹¹ (Bouchaud Reference Bouchaud2002; or Stanley et al. Reference Stanley, Gabaix, Gopikrishnan and Plerou2007, p. 288). These scaling laws can take a variety of forms and, according to most econophysicists (Mandelbrot 2004; McCauley, Reference McCauley2004), economic complex systemsFootnote ¹² obey a specific kind of invariance that can be characterized by power lawFootnote ¹³ distributions of the form: p(x) ∼ x^-α, where p(x) is the probability of there being an event of magnitude x, and the scaling exponent α is a constant whose value is set either by the empirically observed behavior of the system, by a theory, or by simulations.

III. THE POSITION OF ECONOPHYSICS IN THE DISCIPLINARY SPACE

Given that econophysics is based on different fundamental assumptions from those of mainstream economics, an analysis of the publication venues should give us a good idea of the position of that new field in the space of scientific disciplines. From what we have already said about econophysics being promoted by “outsiders” to the discipline of economics, and given that this discipline is very autonomous and has a strong tendency to refer essentially to itself,Footnote ¹⁴ we should expect econophysicists to have difficulty publishing their results in the major economics journals.

In order to reconstruct the subfield of econophysics, we started with the group of the most influential authors in econophysics, and tracked their papers in the literature using the Web of Science database of Thomson-Reuters.Footnote ¹⁵ We identified a group of 242 source papers covering the domain of econophysics, and the papers that cite them over the period 1980 to 2008, to analyze the evolution of the field. Starting with these core papers, which serve to construct the population of researchers, we then identified 1817 other papers that cited the source articles. The core papers being central to econophysics, we estimated that papers citing them would, in all probability, also be discussing econophysics. Analyzing all the cited authors in those papers shows that, indeed, all the usual figures associated with econophysics are well cited.Footnote ¹⁶

As shown in Table 1, more than 70% of the key papers that have been published since 1996 appear in physics journals, while only 21.6% found their place in either economics or finance journals. For the previous period (1980 to 1995), there were very few papers written by the source authors. They were written mainly by economists, and were not based on a physics approach.Footnote ¹⁷ However, economists who are interested in econophysics (Lux or Gallegati, for example) do not write only papers about econophysics. They have been trained as economists, and they also write papers about economics (mainly macroeconomics). This shows that the papers of Mandelbrot and Fama in the 1960s are not the only connection between economics and econophysics. There are also contemporary economists who make connections between these two fields.

The data shown in Table 1 point to a specific trend: papers promoting a physics approach to economics did not find a place in the mainstream of the discipline, and moved in the shadow of physics. A reliable measure of rejected submissions is difficult to obtain, but, as we show in the conclusion, the main actors of econophysics did try to publish in those mainstream economics journals, although without much success. So, the trend is not simply the effect of self-exclusion but also reflects a resistance on the part of mainstream economics.

Table 1.

Disciplines in which the source papers have been published (Web of Science)

Table 2 shows that one single physics journal, Physica A, devoted to “statistical mechanics and its applications,” published by far the largest number of econophysics papers, with 41% of the total of the second period (1996 to 2008). It has, thus, become the leading journal of this new field, the second being another physics journal, the European Physical Journal B, devoted to Condensed Matter and Complex Systems. Moreover, one of the four editors of Physica A is the inventor of the term “econophysics”: H. Eugene Stanley. Note that whereas one can consider that mainstream economics is centered in the USA, it seems that the center of econophysics is in Europe, where Physica A and the European Physical Journal are edited. An analysis of the institutional affiliations of the authors shows a real geographical divide, since 72% of our source papers are from European institutions, while only 16% are from American institutions.Footnote ¹⁸

Table 2.

Journals where the source papers have been published (Web of Science)

In Table 2, we see that only 4% of the key papers were published in Physica A between 1980 and 1996, when a majority of the papers still were published in economics. Taken together, tables 1 and 2 suggest that the resistance to the ideas of ecconophysics was such that after 1995, the promoters of econophysics created their own niche outside economics and finance in order to publish their results. This is consistent with Whitley’s observation that “research which ignores current priorities and approaches and challenges current standards and ideals is unlikely to be published in academic journals” of the discipline (Whitley Reference Withley1986, p. 192).

Since the appointment of J.B. RosserFootnote ¹⁹ as editor-in-chief in 2002, the Journal of Economic Behavior & Organization has begun publishing regular articles on the issue of complexity in economics, allowing econophysicists to publish their work in that journal. The fourth journal on the list, Quantitative Finance, is a relatively new one. As we will see below, it was created in 2001, and can be considered one of the first non-physics journals specifically devoted to the new field, as its editorial board includes many econophysicists and the two editors are an econophysicist (Jean-Philippe Bouchaud) and a mathematician (Micheal Dempster).

The centrality of physics for econophysics is clearly visible in Figure 1, which maps the network of co-citations between journals cited in papers citing our 242 source papers in econophysics. The dense core of the network is composed of physics journals, while economics and finance journals are peripheral (north-west on the map) and Quantitative Finance is in-between.

Figure 1.

Most co-cited journals (and manuals) in papers citing our 242 source articles in econophysics (100 co-citations +), 1980-2008.

Another way to look at the centrality of physics journals is provided in Table 3, which shows that between 1996 and 2008, only 12% of the citations came from economics or finance journals, even if the explicit topic of econophysics papers were economic and financial phenomena. Interestingly, this trend was similar in the previous period (1980 to 1995), even as more than half the papers had been published in economics and finance journals. Econophysics, thus, essentially is discussed in physics journals, a result confirmed by Table 4, which shows that, for both periods, about three-quarters of the citations come from papers published in physics journals usually devoted to condensed matter and statistical mechanics.

Table 3.

Disciplines citing the source papers (Web of Science)

Table 4.

Main journals citing the source papers (Web of Science)

In addition to the two journals already identified as the “core” of econophysics, we find Physical Review E, the major American physics journal devoted to research on “statistical, nonlinear and soft-matter physics.” The only economics-related journals citing econophysics are Quantitative Finance, Journal of Economic Dynamics and Control, Journal of Economic Behavior & Organization, and Macroeconomic Dynamics. While the first is managed by econophysicists, the macro-dimension of the latter leads its editors to be more open to an econophysics perspective. A recent special issue entitled “Applications of Statistical Physics in Economics and Finance,” published in 2008 by the Journal of Economic Dynamics and Control, explicitly proposed to “overcome the lack of communication between economists and econophysicists” (Farmer and Lux Reference Farmer and Lux2008, p. 3). Doyne Farmer and Thomas LuxFootnote ²⁰ were the guest editors for this special issue, whose articles have been written by economists and physicists. As these authors noted in their editorial, physicists “are perhaps the only group of scientific professionals who are even more arrogant than economists, and in many cases the arrogance and emotions of both sides have been strongly on display” (Framer and Lux Reference Farmer and Lux2008, p. 3). In order to overcome the gap between the two camps, this special issue offered twelve articles dedicated to econophysics, written by authors coming from economics as well as from physics.

Another journal, Quantitative Finance, appears to be the main economics journal to publish many papers devoted to econophysics. Interestingly, in 2008 the most-cited journal in this publication is Physica A, followed by Quantitative Finance itself, the Journal of Economic Dynamics and Control, and then by two physics journals (European Physical Journal B and Physical Review E).Footnote ²¹ We should emphasize that economic-related journals citing econophysics cannot really be considered as mainstream journals in economics but, rather, as what Backhouse (2004, p. 265) called “orthodox dissenter” journals; that is, journals that are still rooted in mainstream theory but are open to other approaches.Footnote ²² All this suggests that the “mainstream” journals are not very open nor interested in publishing papers dedicated to econophysics.

The complete absence of mainstream economic journals from Table 4 again confirms that, between 1996 and 2008, this discipline was not influenced much by econophysics, and does not really acknowledge its existence. By contrast, Table 5 shows that econophysics does depend on economic and finance journals, since nearly half the total of its citations (46.5%) goes to these disciplines, though physics still remains an important reference, with about a third of the citations going to papers published in physics journals, followed by mathematics journals for about 7% and a tail of many different science journals (13%). During the first period (1980 to 1995), more than 56% of the references cited were to economics or finance journals. Thus, we observe a decreasing dependence of econophysics on the economics literature and a growing presence of physics journals as a source of knowledge for econophysics, up from 19.2% to 32.6%, which again is consistent with a development of that field essentially outside the field of economics.

Table 5.

Disciplines cited in the source papers (two citations or more) (Web of Science)

This trend can be observed also in Table 6, which lists the main journals cited in the source papers. While economics journals (American Economic Review) often were cited in the key papers written between 1980 and 1995, physics journals became the main source of knowledge for the papers published after 1996.

Table 6.

Main journals cited in the source papers (two citations or more) (Web of Science)

Taken together, these data confirm that as a field, econophysics is building on the existing institutional structures of physics instead of trying to impose itself inside the existing field of economics. A measure of the rapid growth of that field within physics is provided by Table 7, showing the evolution of the annual number and proportion of papers devoted to that topic in Physica A since 1996.

Table 7.

Number of papers dedicated to econophysics published in the Physica A journal (Web of Science)

The trend is clear despite an exceptional year in 2007 when two special issues of the journal were devoted to econophysics. A similar trend (not shown here) is observed in the European Journal of Physics B. The growing presence of econophysics in the pages of physics journals probably has contributed to the official recognition of the field by the Physics and Astrophysics Classification Scheme (PACS), and econophysics has been, since 2003, an official subcategory of physics under the code 89.65 Gh .

The openness of physics journals to topics such as econophysics contrasts strongly with the closure of mainstream economics journals to that topic. Though more research will have to be done on that question, it is probable that this openness of physics to non-physical topics is related to the fact that model building has become a self-conscious and important part of the practice of physics as compared with the search for new laws. As a consequence, there may have been more sensitivity on the part of physicists to search for new phenomena to be modeled using their tools. In addition, such a wide view of their field could open up new job avenues for physicists at a time when the job market was difficult. While many physicists turned toward biology, some, especially statistical and condensed matter physicists, turned to social phenomena under the rubric of “sociophysics” and “econophysics,” either as full-time or part-time research programs, as many were working in physics-related departments. It was easier to present their work to physics journals as example of modeling exercises analogous to those found in physics than to try to pass through the gatekeepers of economic and financial journals. The difficulty was compounded by the fact, already mentioned, that the conceptual foundations behind the mathematical techniques are very different from those found in mainstream economics. In fact, the conceptual and methodological specificity of econophysics is closely linked to the different disciplinary origins of the authors who promote that research program, as most have been trained as physicists and not as economists. Econophysics is, therefore, a field developed mainly by authors who have been trained as physicists and who work now in a physics department. That is the case for eight of our key authors. Of course, some economists are interested in econophysics: Thomas Lux and Mauro Gallegati, for example, are leading authors in econophysics, and both have been trained as economists.

IV. THE INSTITUTIONALIZATION OF ECONOPHYSICS

If the 1990s saw the emergence and growth of econophysics as a research program, the next decade witnessed the growing institutionalization of this field. Though papers could be published in existing physics outlets, the specialty could develop further by having its own specialized conferences, journals, textbooks, and training programs.

A simple and practical way to spread knowledge relating to econophysics as a new paradigm is to organize workshops and colloquia. The first conference devoted to econophysics took place in Budapest in 1997. Unsurprisingly, it was organized by the department of physics of the university. Two years later, the European Association of Physicists officially endorsed the first conference on Application of Physics in Financial Analysis (APFA), which was organized in Dublin. The APFA colloquium was entirely dedicated to econophysics, and it was organized annually until 2007. There now exist several annual conferences dedicated to econophysics, such as the Nikkei Econophysics Research workshop and symposium, and the Econophysics Colloquium. Combined with publications of papers through specialized journals devoted to the field, and textbooks, these events contribute to the stabilization and spread of a common scientific culture among econophysicists. As for scientific societies, one can point to the creation in 2006 of the Society for Economic Science with Heterogeneous Interacting Agents (ESHIA), which aims at promoting interdisciplinary exchanges among economists, physicists, and computer scientists (essentially in artificial intelligence), an objective consistent with econophysics. The absence of the label in the name of the organization may be a way to bring more economists on board by letting their discipline keep its own name instead of being swallowed by the new term, a gesture that would surely be perceived as hostile and imperialistic.

One can consider Quantitative Finance, created in 2001, to be a journal essentially devoted to questions of econophysics (their editorial boards include many econophysicists), followed by the Journal of Economic Interaction and Coordination (JEIC), which started in 2005. As mentioned above, the Journal of Economic Dynamics and Control is also open to papers related to econophysics, since this journal published recently a special issue devoted to this theme.

The first textbook, entitled Introduction to Econophysics, was published in 2000 by Mantegna and Stanley. Though several have appeared since (Roehner Reference Roehner2002, and McCauley Reference McCauley2004, for example). As Figure 1 shows, this first textbook remains the most central to the field. The aim of such textbooks is to define and stabilize the contour of the field as well as its methods, thus helping to create a shared culture uniting the members of the new specialty. As such, they constitute an important step in the process of institutionalization of the field. As Jovanovic notes (2008, p. 219), “Given that collections of articles are published before textbooks, the interval between the moment when the former were published and the moment when the textbooks were published gives an indication about the evolution of the discipline.” The swiftness of the development of econophysics can be gauged by noting that it took twice as long (that is, two decades) to have the first textbooks devoted to another recent specialty: behavioral finance (Schinckus Reference Schinckus2009b).

A last important component of a truly institutionalized research field is the creation of new academic courses, and the organization of training MA and PhD programs uniquely devoted to that field. Here again, the physics discipline served as the institutional basis, and several physics departments have offered courses in econophysics since 2002 (universities of Ulm in Sweden, Fribourg in Switzerland, Munster in Germany, Wrolcaw in Poland, and Dublin in Ireland). Usually, these courses are framed for physicists, and focus on statistical physics applied to finance. An additional step in the institutionalization of econophysics has been the creation of full academic programs totally dedicated to econophysics. The first universities to offer complete programs leading to a diploma were Polish, where Warsaw proposed a Bachelor and Wrolcaw a Master. In 2006, the university of Houston (USA) was the first to coordinate a PhD in econophysics,Footnote ²³ and in 2009, the university of Melbourne (Australia) planned to launch a similar program.Footnote ²⁴ All are part of physics departments and, therefore, physics-oriented. In order to familiarize students with the economic reality they are supposed to describe, these programs do provide some courses on the financial and macroeconomic reality, but they are not based on the theoretical basis of finance and macroeconomics.Footnote ²⁵

All these new academic programs show that econophysics is developing outside the social sciences and the discipline of economics, as a new scientific community with its own journals, conferences, and training programs. Since the middle of the 2000s, the conditions for the production of knowledge and the long-term reproduction of the group of econophysicists are now in place, and provide the basis for a sustained growth in the annual number of publications.