The History of Economics and the Pre-History of Econophysics: Boltzmann versus the Marginalists ASSA Annual Meetings: Jan. 7, 2018 Geoffrey Poitras, Simon Fraser University 1 Economics vs. Econophysics Is the emergence of the new subject of Econophysics incongruent with the adoption of mathematical, theoretical and empirical methods from physics in neoclassical and modern economics? What is Econophysics? Is this a separate subject or a sub-discipline of Economics or a sub-discipline of Physics?

Intellectual history can provide insights needed to answer such questions Mathematical Marginalists, such as Edgeworth, responsible for adopting methods from classical physics The prehistory of Econophysics commences with the contemporaneous beginning of statistical mechanics by Ludwig Boltzmann ASSA Annual Meetings: Jan. 7, 2018 2 What is Econophysics? Term initially coined by Eugene Stanley (1995) Econophysics is a pure subject in statistical mechanics Jovanovic and Schinckus (2013, p.465): econophysicists have positioned themselves in theoretical niches that mathematicians and economists have barely investigated, or not investigated at all, because of the constraints of the theoretical framework.

Roehner (2002, p.3): the term econophysics designates the investigation of economic problems by physicists. Consistent with the usage of astrophysics, geophysics, neurophysics and biophysics and with the appearance of econophysics articles in physics journals Is this too narrow as it restricts the econophysics community only to physicists and physics journals? ASSA Annual Meetings: Jan. 7, 2018 3 Essentials of Econophysics Schinckus (2010, p.3816) accurately recognizes that econophysics depends fundamentally on empirical observation: The empiricist dimension is probably the first positivist feature of econophysics Phenomenology characterizes the conventional experimental methodology and philosophical basis of econophysics

Roehner (2002, p.21): experimental research is an essential part of physics Economics is characterized by the prevalence of nonexperimental data Many studies in econophysics examine financial variables where large data sets are available, though the data is still nonexperimental ASSA Annual Meetings: Jan. 7, 2018 4 The Prehistory of Econophysics The history of econophysics begins in 1995 when physicists and physics journals, such as Physica A, began systematically considering economic problems The prehistory of econophysics is concerned with the development of theoretical and empirical methods used in statistical mechanics The origins of statistical mechanics can be traced to the 2 nd half of the 19th century

Not all key contributions to statistical mechanics are used in econophysics Ising models Quantum mechanics, fractal geometry and chaos theory get almost no attention ASSA Annual Meetings: Jan. 7, 2018 5 Early Statistical Physicists Rudolf Clausius (1822-1888) The second law of thermodynamics Josiah Gibbs

(1839-1903) Gibbs ensembles ASSA Annual Meetings: Jan. 7, 2018 James Maxwell (1831-1879) Maxwell Distribution 6 Ludwig E. Boltzmann (1844-1906) Founding father of the Second Scientific Revolution and intellectual giant in the kinetic theory of gases Important influence on Einstein (Brownian motion) and Planck

(theory of black matter) First to demonstrate that time irreversible processes explain second law of thermodynamics Originator of the ergodicity hypothesis ASSA Annual Meetings: Jan. 7, 2018 7 Origins of Ergodicity The etymology for ergodic begins with an 1884 paper by Boltzmann The ergodic property was initially associated with the kinetic theory of gases where the unobservable properties of the velocity of gas molecules can be macroscopically measured, esp. using temperature Other macroscopic measures include density, pressure,

viscosity, stresses and heat flow. The ergodic hypothesis maintains that a dynamical system samples all points in the dynamical space Ergodicity is a long run property ASSA Annual Meetings: Jan. 7, 2018 8 The Ergodic Property Boltzmann was concerned with demonstrating the dynamic properties of the Maxwell distribution (the velocity distribution of gas molecules in thermal equilibrium) that the distribution would emerge whatever the initial condition of the system ASSA Annual Meetings: Jan. 7, 2018

9 Irreversibility, Entropy and Cosmology Heat can never pass from a colder to a warmer body without some other change occurring at the same time (Clausius) For Boltzmann, time was irreversible, i.e., could only move in one direction Coffee cup example This observation was a direct result of the second law of thermodynamics, the universal law of increasing entropy a measure of the randomness of molecular motion and the loss of energy to do work. First recognized by Clausius in the early 19th century, the second law maintains that the entropy of an isolated system, not in equilibrium, will necessarily tend to increase over time. Entropy approaches a maximum value at thermal equilibrium. The second law is of central importance to the big bang theory in

cosmology ASSA Annual Meetings: Jan. 7, 2018 10 The History for Economics: Was there a Marginal Revolution? Around the time Boltzmann introduced the ergodicity hypothesis, the history of economics is undergoing the Marginal Revolution marking the transition from classical political economy to neoclassical economics It is the use of mathematics, and the associated connection to the developed mathematical theories of classical physics, that is the defining characteristic of the new theories of economics introduced by those the marginalists that adopted the mathematical approach to study economic phenomena, e.g., Fisher (1892). ASSA Annual Meetings: Jan. 7, 2018

11 Early Mathematical Economists Augustin Cournot (1801-1877) Cournot Equilibrium Vilfredo Pareto (1848-1923) Pareto wealth distribution ASSA Annual Meetings: Jan. 7, 2018 Stanley Jevons (1835-1882) Sunspot theory

12 Classical Physics and the Marginalists Mirowskis thesis recognizes that important theoretical elements of neoclassical economics were adapted by the mathematical marginalists from concepts developed in 19th century classical physics Just as the gravitating force of a material body depends not alone upon the mass of that body, but upon the masses and relative positions and distances of the surrounding material bodies, so utility is an attraction between a wanting being and what is wanted. Jevons, Mathematical Theory of Political Economy (1874, p.482) ASSA Annual Meetings: Jan. 7, 2018 13

Cournot and the Marginalists Irving Fisher, a student of Gibbs, observed (1898, p.119) : Sixty years ago the mathematical treatise of Cournot was passed over in silence, if not contempt. To-day the equally mathematical work of Pareto is received with almost universal praise. In Cournot's time mathematical economists could be counted on one's fingers, or even thumbs. Subsequent influence on the early mathematical marginalists: Cournot was closely studied by both Jevons and Walras; Marshall makes reference to Cournots genius and exploits the marginal cost analysis developed by Cournot in extending the marginalist contribution beyond utility. Edgeworth makes abundant references to Cournot in Mathematical Psychics. ASSA Annual Meetings: Jan. 7, 2018 14

Edgeworth and Mathematical Psychics (1881) Chap. II of the Principes Mathmatiques makes an explicit reference to Newtons Principia and the use of relative vs. absolute space in pricing commodities Cournot did not consider utility, but did have a demand function The unifying concept of the marginal revolution is the use of (unobservable) utility function: An analogy is suggested between the Principles of Greatest Happiness, Utilitarian or Egoistic, which constitute the first principles of Ethics and Economics, and those Principles of Maximum Energy which are among the highest generalisations of Physics, and in virtue of which mathematical reasoning is applicable to physical phenomena quite as complex as human life. (p.v, Mathematical Psychics) ASSA Annual Meetings: Jan. 7, 2018

15 Pareto and Rational Mechanics Rational mechanics gives us a first approximation to theory of the equilibrium and of the movements of bodies. In the same way the theories of Jevons, Walras, Marshall, Irving Fisher, and others present us with a first approximation to the full theory of economic phenomena. It must be clearly understood that it is only an approximation; it is similar to that just made in the case of the heavy body supposed to fall in a vacuum. Pure economics has no better way of expressing the concrete economic phenomenon than rational mechanics has for representing the concrete mechanical one. It is at this point that there is a place for mathematics. Pareto (1897, p.499) ASSA Annual Meetings: Jan. 7, 2018

16 Rational versus Statistical Mechanics Brush (1979) sees the evolution from rational to statistical mechanics as part of a Second Scientific Revolution [The Second] Scientific Revolution, associated with the theories of Darwin, Maxwell, Planck, Einstein, Heisenberg and Schrdinger, substituted a world of process and chance whose ultimate philosophical meaning still remains obscure (Brush 1983, p.79). This Second Revolution superceded the: First Scientific Revolution, dominated by the physical astronomy of Copernicus, Kepler, Galileo, and Newton, ... in which all changes are cyclic and all motions are in principle determined by causal laws. The irreversibility and indeterminism of the Second Scientific Revolution replaces the reversibility and determinism of the First. Mirowskis thesis places the rational mechanics underlying neoclassical economic theory with the First Scientific Revolution ASSA Annual Meetings: Jan. 7, 2018

17 Jevons and Laplacian Determinism Jevons (1877, p.738-9) reflects the Laplacian determinism of the marginalists: We may safely accept as a satisfactory scientific hypothesis the doctrine so grandly put forth by Laplace, who asserted that a perfect knowledge of the universe, as it existed at any given moment, would give a perfect knowledge of what was to happen thenceforth and for ever after. Scientific inference is impossible, unless we may regard the present as the outcome of what is past, and the cause of what is to come. To the view of perfect intelligence nothing is uncertain. With Boltzmann, the philosophical view that for perfect intelligence nothing is uncertain is replaced by the view that perfect intelligence has created order from infinite uncertainty

ASSA Annual Meetings: Jan. 7, 2018 18 Frank Knight on the Marginalists The utility theory should be seen as the culmination, historically and logically, of the rationalistic and individualistic intellectual movement of which the competitive economic system itself is one aspect and modern science and technology are others. To its admirers it comes near to being the fulfilment of the eighteenth-century craving for a principle which would do for human conduct and society what Newtonian mechanics had done for the solar system. (Knight 1931) Neoclassical economics is the culmination of a Darwinian transition from classical political economy to neoclassical economics ASSA Annual Meetings: Jan. 7, 2018

19 From the Marginalism to Neoclassical Economics Following Colander (2000) and many others, there is considerable confusion and debate about the time line and historical content of neoclassical economics. Aspromourgos (1986) traces the etymology of the term to Veblen (1900) where it is used to characterize the Marshallian version of marginalism. Veblen employed a Darwinian interpretation for the emergence of neo-classical political economy, this etymology is consistent with neoclassical economics having: a positive, basic relationship to the earlier classical theory and some development beyond it because Marshall, more than any of the other marginalist founders, sought to present his theory as having a substantial continuity with classical economics. ASSA Annual Meetings: Jan. 7, 2018

20 What is Neoclassical Economics? Stigler (1941) popularized the extension of neoclassical economics to include all the marginalist founders. Colander (2000, p.133): In many ways, the two books that tied up the loose ends and captured the essence of neoclassical economics, Hickss Value and Capital (1939) and Samuelsons Foundations (1947), were culminating works they put all the pieces of marginalism together. Important work thereafter was modern. This approach permits the emergence of modern economics from neoclassical economics being connected to the transition from deterministic to stochastic models. ASSA Annual Meetings: Jan. 7, 2018

21 From Neoclassical to Modern Economics Samuelson (1947) extended the static neoclassical approach to include both static and dynamic theories. Static analysis described equilibrium as resulting from economic agents solving maximization problems taking prices as parameters ... Samuelsons analysis of dynamics rested on the concept of stationary equilibrium, which holds that equilibrium constitutes a state of rest (De Vroey and Duarte 2013, p.979). Lucas (1980, p.278) provides further elaboration of this point: The underlying idea seems to be taken from physics, as referring to a system at rest. In economics, I suppose such a static equilibrium corresponds to a prediction as to how an economy would behave should external shocks remain fixed over a long period, so that households and firms would adjust to facing the same set of prices over and over again and attune their behavior accordingly.

How to translate deterministic neoclassical theories into empirically testable stochastic models? ASSA Annual Meetings: Jan. 7, 2018 22 Ergodicity and Econometrics For Economics, Ergodicity is the property that permits a single ex post time series sample path to be used to estimate the parameters for the distribution of the ex ante ensemble of future time paths In the limit for time, an ergodic process will possess a steady state distribution that is independent of initial conditions. Ergodic processes can have non-linearity in the mean providing a wider class of theoretical processes for modeling economic variables than the reversible stationary unimodal processes which are conventional in econometric work Stationary processes are also reversible, only the distance

between observations matter, not where in the process the observation occurs (no impact from initial or boundary conditions) ASSA Annual Meetings: Jan. 7, 2018 23 Founders of Econometrics Ragnar Frisch (1895-1973) 1st Nobel Mem.Pr. 1969 (with Tinbergen) Jan Tinbergen (1903-1994) 1st Nobel Mem.Pr. 1969 (with Frisch)

ASSA Annual Meetings: Jan. 7, 2018 Herman Wold (1908-1992) Wold Decomposition Theorem 24 Estimating empirical relationships for non-experimental data R.G.D. Allen (1934): The future progress of economic science depends largely upon the work of investigators, like Professor Frisch, who realise the importance of subjecting the concepts and conclusions of abstract economic theory to the test of statistical determination and verification.

Wold (1969) recognized that: experimental versus nonexperimental model building is a dualism that goes to the core of the scientific method. Recognition is due -- and perhaps overdue -- for nonexperimental analysis as an active partner to the method of controlled experiments, and for the integration of both experimental and non-experimental approaches in the scientific method. ASSA Annual Meetings: Jan. 7, 2018 25 Developments in Statistical Mechanics: 1920s Around the time that the transition from deterministic neoclassical economic theories to the stochastic empirically testable models of modern economics, Physics, in general, and statistical mechanics, in particular, was undergoing dramatic changes

Quantum mechanics developed by the likes of Max Born, Wolfgang Pauli, Werner Heisenberg and Erwin Schrdinger in a remarkable period from 1924-8 Ernst Ising introduced the one dimensional Ising model of ferromagnetism in 1925, a model ultimately solved in the important two-dimensional phase transition case by Lars Onsager in 1944 Empirical limitations of ergodic processes in physics identified at the same time such notions were entering economics ASSA Annual Meetings: Jan. 7, 2018 26 Whither Goes Modern Economics? Modern Economics is a many-headed monster that now encompasses distinctly different epistemological and

methodological approaches ergodicity is essential to both the traditional Lucas approach and the inductive Granger causality, ARCH/GARCH approach Robert Lucas attacked the idea that an economic system is in any sense at rest [as] simply an anachronism Lucas represents a continuation in the evolution of economics stretching back to the marginalists advancing a modern system that relies on the equilibrium discipline, rational expectations and Walrasian microfoundations ASSA Annual Meetings: Jan. 7, 2018 27 Modern Economics and Epistemology The epistemology of an alternative camp is set out by Keynes (1939, p.559):

Prof. Tinbergen is obviously anxious not to claim too much. If only he is allowed to carry on, he is quite ready and happy at the end of it to go a long way towards admitting, with an engaging modesty, that the results probably have no value. The worst of him is that he is much more interested in getting on with the job than in spending time in deciding whether the job is worth getting on with. He so clearly prefers the mazes of arithmetic to the mazes of logic, that I must ask him to forgive the criticisms of one whose tastes in statistical theory have been, beginning many years ago, the other way round. Striking at fundamental assumptions underpinning the use of time reversible (stationary) ergodic processes, Keynes questioned the validity of passing from statistical description to inductive generalisation ASSA Annual Meetings: Jan. 7, 2018 28

Induction and Causality Using combinations of stationary, i.e., independently, identically distributed (iid), error term distributions ensured the early econometric models implicitly assumed a restricted form of ergodicity. The generalization of this discrete time estimation approach to the class of ARCH and GARCH error term models by Engle and Granger, e.g., Engle and Granger (1987), was of such significance that a Nobel memorial prize in economics was awarded for this contribution in 2003. By modeling the evolution of stationary error term volatility, this approach permitted a limited degree of non-linearity to be modeled providing a typically better ex ante fit to observed economic time series. ARCH, GARCH and related time series models are systemically dependent on the assumption of Ergodicity ASSA Annual Meetings: Jan. 7, 2018

29 Phenomenology in Physics An excellent example of phenomenology in physics is provided by the close collaboration between the theoretician Max Born and the experimentalist James Franck at Gttingen, starting in 1921, that led to important breakthroughs in quantum mechanics. Im (1996) observes: Born's close collaboration with Franck was well suited to his research style: a formal and mathematical description of nature based upon plentiful observational data. Can non-experimental data provide a foundation for a phenomenological approach to economic phenomena? ASSA Annual Meetings: Jan. 7, 2018 30

Irreversibility and Economic Phenomena Reversible processes originate when equilibrium states are compared irreversibility arises from the presence of initial conditions and the associated path to equilibrium Suggests important stochastic differences between properties of static equilibria and the dynamic paths taken to achieve equilibrium from some initial starting point Unlike Boltzmann where irreversibility is a consequence of the second law, in economics statistical processes are reversible as a consequence of employing stationary distributions to test theories of static equilibrium. Irreversibility can be obtained as a consequence of the nonlinear dynamics associated with using diffusion processes with non-linear drift terms Consider the case of the quartic density examined Poitras and Heaney (2015) ASSA Annual Meetings: Jan. 7, 2018

31 The Quartic Ex Ante Forecasting Distribution ASSA Annual Meetings: Jan. 7, 2018 32 Implications of the Quartic for Economic Models Bimodal ex ante forecasting distributions are inconsistent with the use of risk and return as measures of security performance The use of a single observed ex post sample path will not provide necessarily produce informative forecast estimates Bimodal ex ante densities requires both modes to be identified leading to the use of range estimates where

the spread between modes is combined with information about distance between modes and location of the modes relative to the current price as risk measures The empirical basis for range estimates could be complex or intuitive ASSA Annual Meetings: Jan. 7, 2018 33 Modern Econophysicists? Benoit Mandelbrot (1924-2010) (many contributions prior to mid-1990s ) ASSA Annual Meetings: Jan. 7, 2018

Maurice Allais (1911-2010) Economist with physics training 34 ASSA Annual Meetings: Jan. 7, 2018 35