36 Econophysics
Jovanovic
Although financial economics and mathematical finance still largely dominate modern financial theory, in the past few years a new player has increasingly been making itself felt, and could lead to a rethinking of some of the theoretical foundations of modern financial theory. This new player is econophysics.
This article makes three contributions to the history of modern financial theory: an analysis of the theoretical foundations of econophysics (and their connections with the history of financial economics); a study of the reasons underlying the emergence of econophysics; and a presentation of the manner in which econophysics has become the third component of modern financial theory.
Econophysics’ major distinguishing feature is the use of pure Lévy processes.
Jovanovic (2013) History of Econophysics’ Emergence (pdf)
Blair Fix
Econophysics is an attempt to understand economic phenomena (like the distribution of income) using the tools of statistical mechanics.
The particle model of physics demonstrates how a seemingly equal process (the random exchange of energy) can give rise to wide inequalities. If econophycisists are correct, this model tells us why human societies are mired by inequality. It’s just basic thermodynamics.
The idea required a leap of faith: treat humans like gas particles. Econophysicists highlighted an interesting parallel. When humans exchange money, it is similar to when gas particles exchange energy. One party leaves with more money/energy, the other party leaves with less.
With the parallel between energy and money, ecophysicists arrived at a startling conclusion. Their models showed that when humans exchange money, inequality is inevitable.
When econophysicists use ‘random exchange’ to explain income, many people are horrified by the lack of causality. To understand the behavior of large groups of particles, Boltzmann was forced to use the mathematics of probability. The resulting uncertainty in cause and effect made him uneasy.
Quantum mechanics would later show that at the deepest level, nature is uncertain. But this quantum surprise does not mean that probability and determinism are always incompatible. In many cases, the use of probability is just a ‘hack’. It is a way to simplify a deterministic system that is otherwise too difficult to model. Like a coin toss, econophysicists think we can treat monetary exchange in probabilistic terms.
Econophysicists think we can model the exchange of money without understanding property transactions.
Garrett Abstract
Climate change is a two-way street during the Anthropocene: civilization depends upon a favorable climate at the same time that it modifies it. Yet studies that forecast economic growth employ fundamentally different equations and assumptions than those used to model Earth’s physical, chemical, and biological processes. In the interest of establishing a common theoretical framework, this article treats humanity like any other physical process; that is, as an open, nonequilibrium thermodynamic system that sustains existing circulations and furthers its material growth through the consumption and dissipation of energy. The link of physical to economic quantities comes from a prior result that establishes a fixed rela- tionship between rates of global energy consumption and a historical accumulation of global economic wealth. What follows are nonequilibrium prognostic expressions for how wealth, energy consumption, and the Gross World Product (GWP) grow with time. This paper shows that the key components that determine whether civilization “innovates” itself toward faster economic growth include energy reserve discovery, improvements to human and infrastructure longevity, and reductions in the amount of energy required to extract raw materials. Growth slows due to a combination of prior growth, energy reserve depletion, and a “fraying” of civilization networks due to natural disasters. Theoretical and numerical argu- ments suggest that when growth rates approach zero, civilization becomes fragile to such externalities as natural disasters, and is at risk is for an accelerating collapse.
Linking physical to economic quantities comes from a fixed relationship between rates of global energy consumption and historical accumulation of global economic wealth. When growth rates approach zero, civilization becomes fragile to externalities, such as natural disasters, and is at risk for accel- erating collapse.
Garrett Memo
As with any other natural system, civilization is composed of matter. Internal circulations are maintained by a dissipation of potential energy. Oil, coal, and other fuels “heat” civilization to raise the potential of its internal components. Dissipative frictional, resistive, radiative, and viscous forces return the potential of civilization to its initial state, ready for the next cycle of energy consumption.
The material growth and decay of civilization networks is driven by a long-run imbalance between energy consumption and dissipation.
Treating civilization as a dissipative physical system like any other on our planet.
Garrett Summary
This paper has presented a physical basis for interpreting and forecasting global civilization growth, with the intent that it might be used to develop a consistent theoretical basis for forecasting interactions between humanity and climate during the Anthropocene. The perspective is that, like a living organism [Vermeij, 2009], energy consumption and dissipation drives material flows to civilization. If there is a net convergence of matter within civilization, then civilization grows. Growth increases the availability of new and existing reserves of matter and energy, and this leads to a positive feedback loop that allows growth to persist or even accelerate. These rather general thermodynamic results can be expressed in purely economic terms because there appears to be a fixed link between global rates of primary energy consumption and a very general expres- sion of human wealth: 𝜆 = 7.1 ± 0.1 Watts of primary energy consumption is required to sustain each $1000 of civilization value, adjusting for inflation to the year 2005 (see supporting information and Garrett [2012a]). It was argued that wealth does not rest in inert “physical capital”, as in traditional treatments. Rather, wealth can be interpreted to include all aspects of civilization, even the purely social. Value lies in the density of a network of connections between civilization elements, insofar as this network contributes to a global scale consumption and dissipation of energy (equation (41)). Global economic production Y is positive when consumption exceeds dissipation, and there is a net diffusion of matter to civilization that grows its size. This leads to an economic growth model for wealth C and economic production Y that is more simple, physical, and dimensionally self-consistent than mainstream models: dC = Y dt (70) Y = 𝜂C (71) where Y is directly proportional to a lengthening of civilization’s networks and growth of its energy reserves. The real rate of return on wealth 𝜂 is somewhat analogous to the total factor productivity in traditional models. Prognostic expressions for 𝜂 presented here show that its value is determined by a combination of rates of civilization decay, the quantity of available energy reserves, the amount of energy required to incorporate raw materials into civilization’s structure, and the accumulated size of civilization due to past raw material flux convergence. Current values of the rate of return can be inferred from equation (71). For example, current global rates of return are about 2.2% per year [Garrett, 2012a]. Trends in 𝜂 can be forecast based on estimates of future decay and rates of raw material and energy reserve discovery (equation (56)). Thus, this paper offers a set of prognostic expressions for the growth of civilization, expressible in economic and energetic terms that can be linked to physically measurable quantities. The implications that have been described are summarized as follows: - Civilization inflation-adjusted wealth is sustained by global energy consumption and grows only as fast. - Some combination of price inflation and unemployment is related to rates of civilization decay. - Rates of return on wealth decline in response to accelerated decay or increased resource scarcity. - Rapid rates of current growth act as a drag on future rates of growth. - Rates of return grow when there is “innovation” through technological change. - The GWP grows when energy consumption grows super-exponentially (at an accelerating rate), or when global energy reserve discovery exceeds depletion. - If growth rates of wealth approach zero, civilization becomes fragile with respect to externally forced decay. This appears to be particularly true if prior growth was super-exponential.
Many of these conclusions might seem intuitive, or as if they have been expressed already by others within more traditional economic perspectives. What is novel in this study is the expression of the eco- nomic system within a deterministic thermodynamic framework where a very wide variety of economic behaviors are derived from only a bare minimum of first principles. More importantly, a sufficient set of statistics exists for global economic productivity, inflation, energy consumption, raw material extraction and energy reserve discovery that the nonequilibrium solutions presented here can be evaluated and falsified with no requirement for any a priori tuning or fitting to historical data. Such evaluation will be addressed in Part II. Specifically, it will be shown that the logistic equation given by equation (64) closely matches the evolution of global economic rates of return since 1950, allowing for observed rates of technological change defined by equation (56). Logistic behavior has been recognized in the evolution of human empires throughout history. It will be shown to be evident in global rates of economic growth as well. Global civilization has enjoyed explosive growth since the industrial revolution, but it is unclear how long this can be sustained when it is facing ongoing resource depletion, pollution, and climate change. Global economic wealth is tied to energy consumption, and energy consumption through combustion is tied to carbon dioxide emissions. Without a sufficiently rapid switch to noncarbon sources of energy, growing wealth is necessarily linked to growing emissions.
Yet accumulating carbon dioxide in the atmosphere is also likely to drive accelerating civilization decay through amplified hydrological extremes, storm intensification, sea level rise, and mammalian heat stress. The prognostic expressions that have been derived here might be useful to help guide a physically plausible range of future timelines for civilization growth and decay, particularly in models that couple human and climate systems during the Anthropocene.
Garrett (2014) Long-run evolution of the global economy:1. Physical basis (pdf)
36.1 Economy as dissipative system
Ayres
In a closed Walrasian model resources are assumed t o be generated by labor and capital. The neo-classical (Walrasian) equilibrium system does not qualify as a dissipative structure. The neoclassical system is, in effect, a per- petual motion machine. This fact was emphatically pointed out by the Nobel prize-winning chemist F. Soddy in 1922 (Daly, 1980), but Soddy’s work was vir- tually ignored by economists. The first economists to stress the dissipative nature of the economic system were Boulding (1966) and Georgescu-Roegen (1971). The relevance of mass and energy conservation to environmental- resource economics was first emphasized by Kneese et al. (1970).
In reality, resource inputs originate outside the economic system per se: they include air, water, sunlight and material substances, fuels, food, and fiber crops, all of which embody free energy or available work.
The economic system, in reality, is absolutely dependent on a continu- ing flow of free energy from the environment.
Evidently, the real economic system looks very much like a self-organizing dissipative structure in Prigogine’s sense: it is dependent on a continuous flow of free energy (the sun or fossil fuels), and it exhibits coherent, orderly behavior. Moreover, like living organisms, it embodies structural information as morpho- logical differentiation and functional specialization.
Since the economy is, by assumption, a dissipative structure, it depends on a continuous flow of free energy and materials from and to the environ- ment. Such links are precluded by closed neoclassical general equilibrium models, either static or quasi-static.
The energy and physical materials inputs to the economy have shifted over the past two centuries from mainly renewable to mainly nonrenewable sources.
Dynamic economic growth is driven by technological change (generated, in turn, by economic forces), which also results in continuous structural change in the economic system. For instance, so-called Leontief input- output coefficients do not remain constant.
It follows, incidentally, that a long-term survival path must sooner or later reverse the historical shift away from renewable resources. This will only be feasible if human technological capabilities continue to rise to levels much higher than current ones [8]. But, since technological capability is itself an output of the economic system, it will continue to increase if, and only if, deliberate investment in R&D is continued or even increased.
In short, the role of knowledge-generating activity in retarding global entropy seems to be growing in importance.
The economic system is not necessarily stable against all pertur- bations, and the more it is intentionally managed to optimize growth, the more it becomes vulnerable to the consequences of human error.
Ayres (1988) Self-organisation in Biology and Economics (pdf)
Shiozawa
Many protests and contestations have been voiced out against equilibrium theory. Some argued that it neglects the increasing returns to scale which underlies in the development of modern industries. Others contested the maximizing principle which is always supposed in the formulation of economic behaviors, both for consumers and producers. In 1970’s, many eminent economists criticized the state of the art of economic science and proposed to abandon a equilibrium analysis. But, this has not been done, partly for lack of new framework and partly for fear of us loosing ready made formulae for economic behaviors.
New image of systems theory is requested and I think this new image should be the notion of “dissipative structure”. Professor Prigogine, in his early days of his research, was interested in non-equilibrium phenomena and remarked to the dissipative structure, which appears both in space and time. The importance of dissipative structure is evident, if one once knows that any living systems and subsystems are far from equilibrium but that they are all dissipative structure.
Most simple example of dissipative structure is given as the flame of a candle. Once lid, a candle continues to burn unless all wax is consumed or the oxygen is exhausted.
Dissipative structure sometimes takes the form of stationary state but it is very different from equilibrium. The latter is sensitive to boundary conditions.
The concept of dissipative structure is important for economics, because it makes possible to have new idea how economic system works. In the equilibrium framework, boundary conditions are imposed as constraints of the system. In the dissipative framework, boundary conditions are not directly relected to the speed of the consumptions or the extent of employment. It is instead the internal structure which determines volumes and speeds of economic quantities.
Most simple example is the extent of cultivated field. When there is a large surface of cultivable field and there is relatively small population, it is easy to see that whole surface is not necessarily cultivated. Some part which can be cultivated by the population will be cultivated effectively.
Keynes was the first person to realize that, in economy, it is not the boundary condition or the amount of resources which determines how much of the resources are used.
50 years have passed after Keynes went to other world. During these years, many efforts had been made, in vain, to harmonize Keynesian macroeconomic theory with the neo-classical micro-economics. This is a natural outcome. The micro-economics, which is based on equilibrium framework, denies the existence of internal structure such as dissipative structure. Unless we are emancipated from the framework of general equilibrium, there will be no breakthrough for a new economics.
If the problem is only the existence of internal structure, the economics system can be characterized as self-organizing system. But, the economy is not only a self-organizing system. Viewed as an ecological system, it is a system which constantly brings resources in and cast waste off. Economic activities are based on the constant flow of energy and materials. So the economy is also a dissipative structure.
The proper difficulty of the economics is that the complexity is the real condition for the economic agents. This is not true for physical and chemical sciences.
If we consider the boundednes of our rationality, it becomes rather evident that our behavior is not directed by a decision made once for all. It is a continuous sequence of adaptive adjustments, which will be organized according to rough program of purpose pursuit. Consequently, the theoretical framework of the economics should be reorganized as process analysis. Equilibrium analysis has been the obstruction for the economics to proceed to this old but still new direction.
Shiozawa (1996) Economy as a Dissipative Structure (pdf)
Caballero
Some of the motivations for the econophysics literature do strike a chord with the task ahead for macroeconomists. For example, Albert and Barabási (2002), in advocating for the use of statistical mechanics tools for complex networks, write:
Physics, a major beneficiary of reductionism, has developed an arsenal of successful tools for predicting the behavior of a system as a whole from the properties of its constituents. We now understand how magnetism emerges from the collective behavior of millions of spins . . . The success of these modeling efforts is based on the simplicity of the interactions between the elements: there is no ambiguity as to what interacts with what, and the interaction strength is uniquely determined by the physical distance. We are at a loss, however, to describe systems for which physical distance is irrelevant or for which there is ambiguity as to whether two components interact . . . there is an increasingly voiced need to move beyond reductionist approaches and try to understand the behavior of the system as a whole. Along this route, understanding the topology of the interactions between the components, i.e., networks, is unavoidable . . .
The complex-systems literature itself offers fascinating examples of the power of interconnectedness. Bak, Chen, Scheinkman, and Woodford. (1992) and Sheinkman and Woodford (1994) bring methods and metaphors from statistical mechanics to macroeconomics. They argue that local, nonlinear interactions can allow small idiosyncratic shocks to generate large aggregate fluctuations, rather than washing out via the law of large numbers. They discuss a kind of macroeconomic instability called “self-organized criticality,” comparing the economy to a sand hill: at first, a tiny grain of sand dropped on the hill causes no aggregate effect, but as the slope of the hill increases, eventually one grain of sand can be sufficient to cause an avalanche. In the limit, aggregate fluctuations may emerge from hard-to-detect and purely idiosyncratic shocks.
Put differently, a complex environment has an enormous potential to generate truly confusing surprises. This fact of life needs to be made an integral part of macroeconomic modeling and policymaking. Reality is immensely more complex than models, with millions of potential weak links. After a crisis has occurred, it is relatively easy to highlight the link that blew up, but before the crisis, it is a different matter. All market participants and policymakers know their own local world, but understanding all the possible linkages across these different worlds is too complex. The extent to which the lack of understanding of the full network matters to economic agents varies over the cycle. The importance of this lack of understanding is at its most extreme level during financial crises, when seemingly irrelevant and distant linkages are perceived to be relevant. Moreover, this change in paradigm, from irrelevant to critical linkages, can trigger massive uncertainty, which can unleash destructive flights to quality.
Mandelbrot (2008, in a PBS NewsHour interview with Paul Solman on October 21, 2008) said: “[T]he basis of weather forecasting is looking from a satellite and seeing a storm coming, but not predicting that the storm will form. The behavior of economic phenomena is far more complicated than the behavior of liquids or gases.”
When acute financial distress emerges in parts of the financial network, it is not enough to be informed about these direct trading partners, but it also becomes important for the banks to learn about the health of the partners of their trading partners to assess the chances of an indirect hit. As conditions continue to deteriorate, banks must learn about the health of the trading partners of the trading partners of their trading partners, and so on. At some point, the cost of information gathering becomes too large and the banks, now facing enormous uncertainty, choose to withdraw from loan commitments and illiquid positions. A flight-to-quality ensues, and the financial crisis spreads. The common aspects of investor behavior across these episodes―re-evaluation of models, conservatism, and disengagement from risky activities―indicate that these episodes involved Knightian uncertainty and not merely an increase in risk exposure. The extreme emphasis on tail outcomes and worst- case scenarios in agents’ decision rules suggests aversion to this kind of uncertainty. …conflated the possibility of catastrophe with catastrophe itself.
The very acceptance of the key role played by complexity in significant macroeconomic events should be enough to point us in the direction of the kind of policies that can help to limit macroeconomic turbulence.
Durlauf Abstract
This article explores the state of interplay between recent efforts to introduce complex systems methods into economics and the understanding of empirical phenomena. The empirical side of economic complexity may be divided into three general branches: historical studies, the iden- tification of power and scaling laws, and analyses of social interactions. I argue that, while providing useful ‘stylised facts’, none of these empirical approaches has produced compelling evidence that economic contexts exhibit the substantive microstructure or properties of com- plex systems. This failure reflects inadequate attention to identification problems. Identification analysis should therefore be at the centre of future work on the empirics of complexity.
Durlauf Memo
There are three main areas of work on the complexity/empirics interface. The first consists of historical studies. The study of economic complexity was in fact originally championed to a large extent by economic historians in the context of empirical studies of path dependence in economic activity. The second consists of the identification of data patterns that are consistent with some of the features of complex environments. A major feature of this work has been the effort to identify where power laws, which represent a particular class of probability distributions, and scaling laws, which describe relationships between variables that appear to be independent of the scale of measurement, occur in various economic data series. This search has to a substantial extent been led by physicists as there are a number of physical systems in which such laws are present. A third area of work has focused on the study of social interactions. To a large extent, this work has eschewed an explicit connection to complexity; nevertheless a number of social interactions models, e.g. Brock and Durlauf (2001a,b; 2003) and Glaeser et al. (1996), possess structures mathematically equivalent to certain complex systems. More important for the purposes of this article, empirical work on social interactions has focused on the analysis of precisely the type of interdependences between individual actors that lie at the heart of the microstructure of complexity-based models. My overall assessment of the empirical complexity literature is critical. The lit- erature has succeeded in describing interesting historical episodes and performing original statistical calculations that are consistent with complex systems models as well as presenting a body of regression evidence that suggests the presence of the sorts of interdependences across individuals that are a hallmark of complexity. However, this evidence is far from decisive and is amenable to alternative inter- pretations. It is therefore unclear whether this work has provided evidence in support of economic complexity per se.
Following Durlauf (2001), four properties seem particularly relevant to social science contexts
Nonergodicity. A system is nonergodic if the conditional probability state- ments that describe the system do not uniquely characterise the average or long-run behaviour of the system. A standard example of a nonergodic system is one where a shock at one point in time affects the long-run state of the system.
Phase transition. A system exhibits a phase transition if it can undergo a qualitative change in its aggregate properties for a small change in its parameters. Phase transitions are commonplace in physical contexts. Water experiences a phase transition when its temperature moves below 0 degrees centigrade. Similarly, if one heats a magnetised piece of iron, there is a temperature above which magnetisation disappears.
Emergent properties. Following ideas well described in Anderson (1972) and Crutchfield (1994), emergent properties are properties of a system that exist at a higher level of aggregation than the original description of a system. By this definition, ice is an emergent property of water. While the property of being ice describes how water molecules are collectively aligned, not of one molecule in isolation, the properties by which one molecule aligns with its neighbours are described at the level of the molecule. Similarly, magnetisation is an emergent property as it derives from the alignment of spins of individual atoms in a common piece of iron.
Universality. A property is universal if its presence is robust to alternative specifications of the microstructure of the system. In physics, magnetisation is universal in the sense that its presence in iron occurs for a range of different specifications of the interdependence of spins between individual atoms.
Power Laws and Scaling Laws
A second area of empirical work on economic complexity has attempted to identify the presence in economic data of certain statistical properties that are associated with complex systems. In particular, this work has attempted to identify power and scaling laws.
Recent research has focused on the identification of Zipf-type properties in a range of socioeconomic data. Important examples include Axtell (2001) on firm sizes and Gabaix (1999) on city sizes.
Durlauf (2004) Durlauf 2004 Complexity and Empirical Economics