COMPLEX ECONOMICS

Current ecological crises are driven by excess consumption, which has been justified by neoclassical theories of unlimited growth. The theory of metabolic growth provides a better alternative to understand biophysical limits of economic growth and ecological constraints of the modern division of labor. It should be noted that among the founding tenets of classical economics is the Smith theorem that the division of labor is limited by market extent. Malthus, of course, whatever one thinks about the overall argument he provides, at least realized there could be competition between resources and population, and this issue subsequently influenced the works business cycle Furthermore, the nonlinear dynamics of the division of labor and the theory of metabolic growth reveal lifecycles (more exactly, wavelets) in the co-evolutionof ecology-technology-culture. This ecological systems or the trade-off between stability and complexity in which general equilibrium frameworks break down under increasing returns toscale. Clearly, given the predicaments of the modern period, coordination of nations is a more critical issue of the global division of labor than science philosophy should be brought to the fore in combination with complexity economics.

Biophysical limit and metabolic growth: New understanding of modern division of labor and sustainable economies

Abstract：An empirical and theoretical analysis of financial crises is conducted based on statistical mechanics in non-equilibrium physics. The transition probability provides a new tool for diagnosing a changing market. Both calm and turbulent markets can be described by the birth-death process for price movements driven by identical agents. The transition probability in a time window can be estimated from stock market indexes. Positive and negative feedback trading behaviors can be revealed by the upper and lower curves in transition probability. Three dynamic regimes are discovered from two time periods including linear, quasi-linear, and nonlinear patterns. There is a clear link between liberalization policy and market nonlinearity.Numerical estimation of a market turning point is close to the historical event of the U.S. 2008 financial crisis.

Tang, Yinan, Ping Chen. “Transition Probability, Dynamic Regimes, and the Critical Point of Financial Crisis,” Physica A, 430, 11-20 (2015). 

Abstract：The sub-prime crisis in the U.S. reveals the limitation of diversificationstrategy based on mean-variance analysis. A regime switch and a turning point can be observed using a high moment representation andtime-dependent transition probability. Up-down price movements are induced by interactions among agents, which can be described by thebirth-death (BD) process. Financial instability is visible by dramatically increasing 3rd to 5th moments one-quarter before and during the crisis.The sudden rising high moments provide effective warning signals of a regime-switch or a coming crisis. The critical condition of a marketbreakdown can be identified from nonlinear stochastic dynamics. The master equation approach of population dynamics provides a unified theory of a calm and turbulent market.

Key Words: high moments, birth-death process, transition probability,regime switch, crisis warning

PACS: 89.65.Gh, 05.45.Tp, 05.10.Gg, 89.75.-k

Tang, Yinan, Ping Chen. “Time varying moments regime switch and crisis warning The birth–death process with changing transition probability,” Physica A, 404, 56-64 (2014).

Abstract：Both exogenous and endogenous growth theories in neoclassical economics ignore the resource constraints and wavelike patterns in technology development. The logistic growth and species competition model in population dynamics provides an evolutionary framework of economic growth driven by technology wavelets in market-share competition. Learning by doing and knowledge accumulation ignores the interruptive nature of technology advancement. Creative destruction can be understood by using knowledge metabolism. Policies and institutions co-evolve during different stages of technology cycles. Division of labor is limited by the market extent, numbers of resources, and environment fluctuations. There is a trade-off between the stability and complexity of an ecological-industrial system. Diversified patterns in development strategy are shaped by culture and environment when facing learning uncertainty. The Western mode of division of labor is characterized by labor-saving and resource-intensive technology, while the Asian and Chinese modes feature resource-saving and labor-intensive technology. Nonlinear population dynamics provides a unified evolutionary theory from Smith, Malthus, to Schumpeter in economic growth and technology development.

Key words: growth theory, market-share competition, technology wavelet, learning uncertainty, knowledge metabolism.

EL Classification: C30, E37, D83, L50, O00

Chen, Ping. “Metabolic Growth Theory：Market-Share Competition, Learning Uncertainty, and Technology Wavelets” Journal of Evolutionary Economics, 24(2), 239-262 (2014).

This ongoing Grand Crisis originated in the United States, then transmogrified into an international crisis. It represents a natural experiment. The positive side of this crisis is its fundamental lesson. It is not a theoretical debate confined to ivory towers, but a historical event that has destroyed social confidence in the mainstream equilibrium theory of the so-called efficient market. This has accelerated the rise of the nonlinear evolutionary theory of the viable market.Three observations reveal where the equilibrium theory of asset pricing and business cycles went wrong: (1) the meso foundation of macro fluctuations; (2) the endogenous nature of persistent cycles in financial macro indexes;and (3) the trend of collapse and higher moment risk in the derivative market. The new perspective of nonlinear population dynamics in continuous time provides a better alternative to existing rational-actor/linear models of finance, not only for understanding the cause of the present situation, but to inform efforts related to redesignand reform. The systematic failure in the mortgage security market, unprecedented concentration in the international financial market, and unfettered speculation in the commodity and currency markets have all contributed to the current disaster. A new international financial order can be achieved if a robust and workable international antitrust law can be enacted and a Tobin tax on foreign exchange transactions can be established through global efforts. An overhaul of financial theory is needed to develop a viable market for sustainable economies.

Chen, Ping. “From an efficient to a viable international financial market,” in R. Garnaut, L. Song and W.T.Woo eds. China’s New Place in a World in Crisis: Economic, Geopolitical and the Environmental Dimensions, Chapter 3, pp.33-57, Australian National University E-Press and The Brookings Institution Press, Canberra (2009). Also, Chapter 16, pp. 301-319, in Chen (2010).

Abstract: Conflicting agendas in corporate governance show the limits of the transaction costs approach and property rights theory. A top-down approach of control and monitor may have negative effect on the competitiveness of the firm. The mechanic picture of transaction costs and agency costs is rooted in reductionism of firm theory. The Coase world of zero-transaction costs is contrary to the law of thermodynamics and historical trends of industrial economies. Diversified patterns in corporate governance and corporate culture can be better explained by the creative nature of the firm in evolutionary economics. China’s experiments under mixed property rights during economic transition shed new light on life cycles in changing ownership and corporate governance. The survival of a firm is more associated with the emergence of selective mechanisms and adapting ability.

Keywords: transaction costs, corporate governance, selective mechanism, life cycles,evolutionary thermodynamics.

*Chen, Ping. “Complexity of Transaction Costs and Evolution of Corporate Governance,” Kyoto Economic Review, 76(2), 139－153 (2008). Also, Chapter 14, pp.270-282, in Chen (2010).

Abstract：The principle of large numbers shows that the relative deviation for a macro system with independent elements is of the order of Lucas’ approach to a microfoundations for macroeconomic fluctuations is thus not capable of explaining the magnitude of observed macroeconomic fluctuations. Arbitrage activity would largely eliminate correlations created by rational expectations among economic agents when they face counter movements in relative prices. The complex nature of many-body problems and the statistical feature of aggregate indexes cannot be ignored in a micro–macro modeling. Intermediate structures, such as fifinancial markets and industrial organizations, are more important than households and fifirms in generating business cycles.

Keywords: Large numbers; Microfoundations; Arbitrage; Relative price movements; Rational expectations;Intermediate structure

Ping Chen,  “Microfoundations of Macroeconomic Fluctuations and the Laws of Probability Theory：the principle of large numbers versus rational expectations arbitrage,” Journal of Economic Behavior & Organization, 49, 327-344 (2002). Also, in Chen (2010), Chapter 13, pp. 251-269.

Introduction：A central issue in business-cycle theory is the nature and origin of persistent business cycles. There are mainly two lines of economic thinking: the endogenous school and the exogenous school (Zarnowitz 1992). Schumpeter considered business cycles as the life rhythm of an economic organism (1939).Goodwin introduced the nonlinear and chaotic oscillator to describe persistent business cycles (1951, 1990). However, early evidence of economic chaos has received little interest in mainstream economics, because the existence of economic chaos may imply serious challenges to the foundations of equilibrium theory and parametric econometrics (Barnett and Chen 1988; Chen 1988a, 1993a, 1996a, 1996b; Brock and Sayers 1988). In contrast, the exogenous school represents mainstream economics since the 1930s; whose founder was Ragnar Frisch (Kydland 1995).

Hayek realized that empirical features of business cycles were difficult to understand by equilibrium theory (Hayek 1933). However, Frisch suggested that a noise-driven damped oscillator might explain both market stability and persistent cycles, which he claimed in an informal paper in 1933 (Frisch 1933). Contrary to Frisch’s belief, physicists had known since 1930 that a harmonic oscillator under Brownian motion could not produce persistent oscillations (Uhlenbeck and Ornstein 1930; Wang and Uhlenbeck 1945). Today Frisch’s belief is still widely held among economists and econometricians. Indeed, it is a mystery as to why Frisch never published his promised paper, and why the first Nobel Prize in economics was awarded to an unproved and wrong idea. Reexamining the Frisch model will help us to understand the origin of equilibrium belief in economic thinking.

In this chapter, we will give a brief history of the Frisch model, and then discuss its theoretical and empirical implications. We will show that the linear deterministic model of business cycles has structural instability. The effect of external noise to a linear oscillator can be studied by the Langevin equation and the Fokker–Planck equation. We may obtain the analytical solution for a harmonic oscillator under Brownian motion. Its exponential decay in amplitude and autocorrelations indicate that white noise is not capable of producing persistent cycles. We can directly estimate the intrinsic frequency and friction coefficient from real US GDP data. We then will discuss the main implications from the Brownian motion of a harmonic oscillator, and basic problems of the linear model of business-cycle theory.

Chen, Ping. The Frisch Model of Business Cycles – a Spurious Doctrine, but a Mysterious Success (1999), Also, in Chen (2010), Chapter 12, pp.239-250.

Instability, Complexity, and Bounded Rationality in Economic Change

Ilya Prigogine, Ping Chen, and Kehong Wen

In Cooper, W.W., S.Thore, D.Gibson, and E.Phillips Eds. Impact: How IC2 Institute

Research Affects Public Policy and Business Practices, Quorum Books, Chapter 11,

pp.209-218, CT: Westport (1997).

Abstract：Economic order and structural change can be better understood from the perspective of self-organization under non-equilibrium constraints. The constructive role of instability, prevalence of complexity, and source of bounded rationality are demonstrated by examples of traffic flow, complex business cycles, economic crisis, division of labor, and economic development. The socioeconomic order can only be maintained by self-organization processes.

Abstract ：The random-walk (white-noise) model and the harmonic model are two polar models in linear systems. A model in between is color chaos which generates irregular oscillations with a narrow frequency (color) band. Time-frequency analysis is introduced for evolutionary time series analysis.The deterministic component from noisy data can be recovered by a time-variant filter in Gabor space. The characteristic frequency is calculated from the Wigner decomposed distribution series. It is found that about seventy percent of fluctuations in Standard & Poor stock price indexes, such as the FSPCOM and FSDXP monthly series, detrended by the Hodrick-Prescott (HP) filter, can be explained by deterministic color chaos. The characteristic period of persistent cycles is around three to four years. Their correlation dimension is about 2.5.

The existence of persistent chaotic cycles reveals new perspective of market resilience and new sources of economic uncertainties. The nonlinear pattern in the stock market may not be wiped out by market competition under nonequilibrium situations with trend evolution and frequency shifts. The color-chaos model of stock-market movements may establish a link between business-cycle theory and asset-pricing theory.

Ping Chen, “A Random Walk or Color Chaos on the Stock Market?Time Frequency Analysis of S&P Indexes,” Studies in Nonlinear Dynamics & Econometrics , 1(2), 87-103 (1996). Also, in Chen (2010), Chapter 6, pp.151-172.

A new analytical tool of time-frequency analysis, based on the symmetry principle in frequency and time, is introduced for studies of business cycles. The Wigner-Gabor-Qian (WGQ) spectrogram shows a strong capability in revealing complex cycles from noisy and nonstationary time series.

Competing detrending methods, including the first difference (FD) and Hodrick-Prescott (HP) filter, are tested with the mixed case of cycles and noise.FD filter does not produce a consistent picture of business cycles. HP filter provides a good window for pattern recognition of business cycles.

Existence of stable characteristic frequencies from economic aggregates provide strong evidence of endogenous cycles and valuable information about structural changes. Economic behavior is more like an organism instead of random walks. Remarkable stability and resilience of market economy can be seen from the insignificance of the oil price shocks and the stock market crash.Surprising pattern changes occurred during wars, arm races, and the Reagan administration. Like microscopy for biology, nonstationary time series analysis opens a new space for business cycle studies and policy diagnostics.

The role of time scale and preferred reference from economic observation is discussed. Fundamental constraints for Friedman’s rational arbitrageurs are eexamined from the view of information ambiguity and dynamic instability. Nonlinear economic dynamics offers a new perspective in empirical measurement and theoretical analysis.

Chen, Ping. “Trends, Shocks, Persistent Cycles in Evolving Economy: Business Cycle Measurement in Time-Frequency Representation,” in W. A. Barnett, A. P. Kirman, and M. Salmon eds., Nonlinear Dynamics and Economics,  Chapter 13, pp. 307-331, Cambridge University Press (1996). Also, in Chen (2010), Chapter 7, pp.173-197.

INTRODUCTION：Neoclassical models in microeconomics often describe an atomized society, in which every individual makes his or her own decision based on individual independent preference without the communication and interaction with the fellow members within the same community.1 Therefore, static economic theory cannot explain collective behavior and changes of social trends, such as fashion, popular name brand, political middling or polarization.

Physicists have been interested in collective phenomena caused by the success of ferromagnetic theory in explaining collective phenomena under thermodynamic equilibrium. The Ising fish model2 and the public opinion model3 represented the early efforts in developing complex dynamic theory of collective behavior. However, the human society is an open system, there is no ground to apply the technique of equilibrium statistical mechanics, especially, the Maxwell-type transition probability, to social behavior. Therefore, these pioneer models have been discussed in physics community, but received little attention among social scientists.

However, the development of nonequilibrium thermodynamics and theory of dissipative structure open new way to deal with complex dynamics in chemical systems and biological systems,4,5,6 that have many similarities with the behavior of social systems. In this short article, we will introduce new transition probability into master equation from the consideration of socio-psychological mechanism. The model may shed light on social behavior such as fashion, public choice and political campaign.

Chen, Ping. “Imitation, Learning, and Communication: Central or Polarized Patterns in Collective Actions,” in A. Babloyantz ed., Self-Organization, Emerging Properties and Learning,  pp. 279-286, Plenum, New York (1991). Also, in Chen (2010), Chapter 9, pp.210-216.

Chen, Ping. “The Aggregation-Theoretic Monetary Aggregates are Chaotic and Have Strange Attractors: An Econometric Application of Mathematical Chaos” (co-authored with William A. Barnett), in Dynamic Economic Modeling, W. A. Barnett, E. Berndt, and H. White eds., Chapter 11, pp.199-245, Cambridge University Press, Cambridge (1988 ).

Abstract：Empirical and theoretical investigations of chaotic phenomena in macroeconomic systems are presented. Basic issues and techniques in testing economic aggregate movements are discussed. Evidence of low dimensional strange attractors is found in several empirical monetary aggregates. A continuous time deterministic model with delayed feedback is proposed to describe the monetary growth. Phase transition from periodic to chaotic motion occurs in the model. The model offers an explanation of the multiperiodicity and irregularity in business cycles and of the low-dimensionality of chaotic monetary attractors. Implications in monetary control policy and a new approach to forecasting business cycles are suggested.

Chen, Ping. “Empirical and theoretical evidence of economic chaos,” System Dynamics Review,  Vol. 4, No. 1-2, 81-108 (1988). Also, in Chen (2010) Chapter 4, pp.85-113.

Abstract: Nonlinear models are introduced to describe the nonequilibrium dynamics of social evolution. The difference between Western and Oriental culture, and their roles in the origin in the division of labor, are described by a behavioral model in information diffusion and learning competition. It shows a trade-off between stability and diversity. The stochastic mechanism of social differentiation and the empirical evidence for this is discussed in a stochastic model of multistaged development. It shows that the break-down of the Gaussian distribution during a transition. Finally, an ideal model of social bifurcation is given.

Key Words: Information diffusion, learning, competition, behavior, division of labor, bifurcation

“Origin of Division of Labor and Stochastic Mechanism of Differentiation,” European Journal of Operational Research, Vol. 30, No. 3, pp. 246-250 (1987). Also, in Chen (2010), Chapter 8, pp.201-209.