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Journal of Economic Interaction and Coordination

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01.04.2015 | Regular Article

Microeconomic structure determines macroeconomic dynamics: Aoki defeats the representative agent

verfasst von: Sorin Solomon, Nataša Golo

Erschienen in: Journal of Economic Interaction and Coordination | Ausgabe 1/2015

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Abstract

Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fractal/intermittent fluctuations of macroeconomic quantities from the granularity of the mezo-economic collective objects (large individual wealth, highly productive geographical locations, emergent technologies, emergent economic sectors) in which the micro-economic agents self-organize. In particular, we present some theoretical predictions, which also met extensive validation from empirical data in a wide range of systems:

The fractal Levy exponent of the stock market index fluctuations equals the Pareto exponent of the investors wealth distribution. The origin of the macroeconomic dynamics is therefore found in the granularity induced by the wealth/capital of the wealthiest investors.
Economic cycles consist of a Schumpeter ‘creative destruction’ pattern whereby the maxima are \(\varLambda \)-shaped cusps. In between the \(\varLambda \)-cusps, the cycle consists of the sum of 2 ‘crossing exponentials’: one increasing (corresponding to the creation of the ‘new’) and the other one decaying (corresponding to destruction of the ‘old’).

This unification within the same theoretical framework of short term market fluctuations and long term economic cycles offers the perspective of a genuine conceptual synthesis between micro- and macroeconomics. Joining another giant of contemporary science—Phil Anderson 1972—Aoki emphasized the role of rare, large fluctuations in the emergence of macroeconomic phenomena out of microscopic interactions and in particular their non self-averaging, in the language of statistical physics. In this light, we present a simple stochastic multi-sector growth model.

Vorheriger Artikel Special Issue in Honor of Masanao Aoki

Nächster Artikel Stochastic macro-equilibrium: a microfoundation for the Keynesian economics

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In this paper we use for fractal fluctuations the definition of Mandelbrot for Lévy flights (Mandelbrot 1982): a random walk in which the step-lengths have a power law (Pareto) probability distribution. For intermittency we use the definition of Zel’dovich (1987): “Some specific structures in which a growing quantity reaches record high values typically arise for instabilities in random media. Despite the rarity of these concentrations, they dominate the integral characteristics of the growing quantity (the mean value, the mean square value, etc.). The appearance of such structures is called ‘intermittency’.” Thus we reserve the term ‘intermittent’ for random processes totally dominated by their largest collective objects and rarest events while for processes that are merely outside the basin of attraction of the normal distribution we use the term fractal.

We shall call occasionally \(A(x,t)\) and \(K(x,t)\) ‘densities’ when discussing them in the macro- approximation where \(A(x,t)\) and \(K(x,t)\) are considered as functions defined on a space where the locations \(x\) are real numbers. However one should not forget that the main point of this paper is that the macro/continuum approximation has severe limitations and the correct and binding formulation is the discrete one, where \(A(x,t)\) and \(K(x,t)\) are just the number of agents \(a\) and \(k\) at the discrete location \(x\) at time \(t\).

The notations \(K\), \(s\), \(A\), \(\delta \) are not the standard ones in the Malthus context. We use them here to facilitate the contact with the economist readership: with the present notations, Eq. 3 becomes identical with the familiar AK model Eq. 19 (Philippe 1997).

A few decades after Malthus, Verhulst (1838) included in Eq. 3 a non-linear term \(-K^2\) corresponding to \(k\)’s competition, confrontation, limited resources and called the new equation ‘the logistic equation’. In terms of the agents, the competition between \(k\)’s is expressed by the reaction: \( k+k \rightarrow k; \; c. \) The Verhulst non-linear term has the effect of diminishing the \(K(t)\) growth, \({dK}/{dt}\), as \(K(t)\) increases and in fact eventually leads to the saturation of the \(K\) population growth. Thus, the solution of the logistic equation starts increasing in time with the same exponential growth rate \(g\) as the Malthus solution Eq. 5, but eventually it curbs down and saturates. In the current discussion we will not discuss the effects of the Verhulst term.

We will use occasionally the integral \(\int _x \) and differential \(\varDelta \) notations when discussing the continuum approximation (Eqs. 8, 10) . However, one should remember that it is one of the main claims of the present paper that this approximation fails in crucial ways and that the correct formulation is the discrete one. In particular using discrete sum instead of the integral.

In higher dimensions \(d\), the condition for the \(k\) population to survive and proliferate is \(s/D_A > 1-P_d\). Where the Polya constant \(P_d\) is the probability that an \(a\) will eventually return to its site of origin (at least once) if one waits an indefinitely long time. In \(d=1\) and \(d=2\) dimenstions \(P_d=1\).

In fact one can compute it using the Poisson formula \(P(A(x,0)) = A^{A(x,0)} e^{-A} / A(x,0)!\)

Of course, while the exponent \(\alpha \) in the distribution (14) is stationary, the actual order of the individual \(K_i (t)\)’s changes in time. In fact we will see that in the regime \(\alpha < 1\) the events by which the largest agent \(K_1 (t)\) changes place with another \(K_i(t)\) correspond to very important global changes in the system.

Actually due to the finite number of components \(i=1,...,N\), the Levy distribution is truncated for very large values of \(S\). For such extreme values the distribution decays much faster (Huang and Solomon 2001; Mantegna and Stanley 1999). In order to avoid these complications, we express here the fractal properties of the \(K(t)\) evolution in terms of the central peak corresponding to very small fluctuations \(\varDelta K(t) =0\).

This is not a necessary assumption. Smaller shocks like the ones in Finland and Britain discussed in the Sect. 5.3 do not lead to negative \(g_{11}\) but only to an exchange in the relation between the intrinsic growth rates of different parts of the economy: from \(g_{11} > g_{22}\) to \(g_{11} < g_{22}\). To detect with precision such shocks one needed finer GDP time resolution (Challet et al. 2009): quarterly rather than annually.

Anderson PW (1972) More is different. Science 177(4047):393–396CrossRef

Aoki M (2004) New frameworks for macroeconomic modelling: some illustrative examples. UCLA Economics Online Papers

Aoki M (1968) Control of large-scale dynamic systems by aggregation. Autom IEEE Trans Autom Control AC–13(3):246–253CrossRef

Aoki M, Hawkins RJ (2010) Non-self-averaging and the statistical mechanics of endogenous macroeconomic fluctuations. Econ Model 27:1543–1546CrossRef

Aoki M, Yoshikawa H (1999) Demand creation and economic growth. University of Tokio, Tokio

Aoki M, Yoshikawa H (2009) The nature of equilibrium in macroeconomics: a critique of equilibrium search theory. Econ Open-Access Open Assess E J 3(2009–37):1–9

Aoki M, Yoshikawa H (2012) Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics. J Econ Interact Coord 7:1–22CrossRef

Barro RJ, Xavier S-M (1991) Convergence across states and regions. Econ Growth Center Papers Econ Activ 1:107–158

Biham O, Malcai O, Levy M, Solomon S (1998) Generic emergence of power law distributions and Lévy-Stable intermittent fluctuations in discrete logistic systems. Phys Rev E 58(2):1352CrossRef

Blank A, Solomon S (2000) Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components). Phys A Stat Mech Appl 287(1):279–288CrossRef

Bouchaud J-P, Mézard M (2000) Wealth condensation in a simple model of economy. Phys A Stat Mech Appl 282(3):536–545CrossRef

Cantono S, Solomon S (2010) When the collective acts on its components: economic crisis autocatalytic percolation. N J Phys 12(7):075038CrossRef

Challet D, Solomon S, Yaari G (2009) The universal shape of eco-nomic recession and recovery after a shock. Econ Open-Access Open Assess E J 3 (2009-36). http://www.economics-ejournal.org/economics/journalarticles/2009-36

Delli G, Gaffeo E, Gallegati M, Giulioni G, Palestrini A (2008) Emergent macroeconomics: an agent-based approach to business fluctuations. Springer, New York

Dosi G (2011) Economic coordination and dynamics: some elements of an alternative ‘Evolutionary’ Paradigm. Institute for New Economic Thinking (downloaded from http://ineteconomics.org/blog/inet/giovanni-dosi-response-john-kay-elements-evolutionary-paradigm on 3 Feb 2012

Dover Y, Moulet S, Solomon S, Yaari G (2009) Do all economies grow equally fast? Risk Decis Anal 1(3):171–185

Gabaix X (2011) The granular origins of aggregate fluctuations. Econometrica 79:733–772

Haim L, Levy M, Solomon S (2000) Microscopic simulation of financial markets: from investor behavior to market phenomena. Academic Press, London

Hidalgo CA, Bailey K, Barabási A-L, Hausmann R (2007) The product space conditions the development of nations. Science 317(5837):482–487

Huang Z-F, Solomon S (2001) Finite market size as a source of extreme wealth inequality and market instability. Phys A Stat Mech Appl 294(3):503–513CrossRef

Huang Z-F, Solomon S (2001) Power, Levy, exponential and Gaussian-like regimes in autocatalytic financial systems. Eur Phys J B Condens Matter Complex Syst 20(4):601–607CrossRef

Karl P (1976) Unended quest: an intellectual autobiography. Open Court, LaSalle

Kesten H, Sidoravicius V (2003) Branching random walk with catalysts. Electron J Probab 8:1–51

Kirman AP (1992) Whom or what does the representative individual represent? J Econ Perspect 6(2): 117–136

Klass OS, Biham O, Levy M, Malcai O, Solomon S (2006) The Forbes 400 and the Pareto wealth distribution. Econ Lett 90(2):290–295CrossRef

Klass OS, Biham O, Levy M, Malcai O, Solomon S (2007) The Forbes 400, the Pareto power-law and efficient markets. Eur Phys J B 55(2):143–147

Lee K, Hashem PM, Smith RP (1997) Growth and convergence in a multi-country empirical stochastic Solow model. J Appl Econ 12(4):357–392

Leontief W (1947) Introduction to a theory of the internal structure of functional relationships. Econ J Econ Soc 15(4):361–373

Louzoun Y, Solomon S, Goldenberg J, Mazursky D (2003) World-size global markets lead to economic instability. Artif Life 9(4):357–370CrossRef

Louzoun Y, Shnerb NM, Solomon S (2007) Microscopic noise, adaptation and survival in hostile environments. Eur Phys J B 56(2):141–148CrossRef

Malcai O, Biham O, Solomon S (1999) Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements. Phys Rev E 60(2):1299CrossRef

Malthus T (1798) An essay on the principle of population as it affects the future improvement of society, with remarks on the apeculations of Mr. Godwin, M. Condorcet, and Other Writers 1798. J. Johnson, in St. Paul’s Church-yard, London

Mandelbrot BB (1982) The fractal geometry of nature. W. H. Freeman, New York

Mankiw GN (2006) Principles of economics, 4th edn. South-Western College Pub. ISBN 0-324-22472-9

Mantegna RN, Stanley EH (1999) Introduction to econophysics: correlations and complexity in finance. Cambridge University Press, CambridgeCrossRef

Marsili M, Maslov S, Zhang Y-C (1998) Dynamical optimization theory of a diversified portfolio. Phys A Stat Mech Appl 253(1):403–418CrossRef

Montroll EW (1978) Social dynamics and the quantifying of social forces. Proc Natl Acad Sci 75(10):4633–4637CrossRef

Pammolli F (2013) On innovation, instability, and growth. A review and an interpretative framework economia Politica, n. 1. In: Originally presented at the Fondazione Centesimus Annus—Pro Pontifice, 20th Anniversary international conference: rethinking solidarity for employment: the challenges of the twenty-first century, Rome and The Vatican, May 23–25

Philippe A, Howitt PW (1997) The economics of growth The MIT Press, Cambridge

Romer PM (1968) Increasing returns and long-run growth. IEEE Trans J Polit Control 13(3):246–253 (Economy 1986:1002–1037)

Romer PM (1989) Endogenous technological change. No. w3210. National Bureau of Economic Research, working paper

Romer PM (1990) Endogenous technological change. J Polit Econ 98(5):S71–S102CrossRef

Schumpeter JA (1936) The theory of economic development. Harvard University Press, Cambridge

Shnerb NM, Louzoun Y, Bettelheim E, Solomon S (2000) The importance of being discrete: life always wins on the surface. Proc Natl Acad Sci 97(19):10322–10324CrossRef

Solomon S (1998) Stochastic Lotka-Volterra systems of competing auto-catalytic agents lead generically to truncated pareto power wealth distribution, Truncated Levy-Stable Intermittent market returns, clustered volatility, booms and crashes. In Decision Technologies for Computational Finance. Springer, USA, pp 73–86

Solomon S, Golo N (2013) Minsky financial instability, interscale feedback, percolation and Marshall-Walras disequilibrium. Acc Econ Law 3(3):167–260

Solomon S, Levy M (1996) Spontaneous scaling emergence in generic stochastic systems. Int J Modern Phys C 7(05):745–751

Solomon S, Levy M (2003) Pioneers on a new continent: on physics and economics. Quant Financ 3(1):c12–c15CrossRef

Solomon S, Richmond P (2001) Power laws of wealth, market order volumes and market returns. Phys A Stat Mech Appl 299(1):188–197CrossRef

Solow RM (1956) A contribution to the theory of economic growth. Quart J Econ 70(1):65–94CrossRef

Verhulst P-F (1838) Notice sur la loi que la population poursuit dans son accroissement. Correspondance mathématique et physique 10:113–121

Von Hayek, Friedrich A (1937) Economics and knowledge. Economica 4(13):33–54

Yaari G, Nowak A, Rakocy K, Solomon S (2008) Microscopic study reveals the singular origins of growth. Eur Phys J B Condens Matter Complex Syst 62(4):505–513CrossRef

Zel’Dovich YAB, Molchanov SA, Ruzmaĭkin AA, Dmitrii D. Sokolov ((1987)) Intermittency in random media. Soviet Phys Uspekhi 30(5):353

Titel: Microeconomic structure determines macroeconomic dynamics: Aoki defeats the representative agent
verfasst von: Sorin Solomon
Nataša Golo
Publikationsdatum: 01.04.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Economic Interaction and Coordination / Ausgabe 1/2015
Print ISSN: 1860-711X
Elektronische ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-014-0135-3

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