经济物理的基本问题

1、经济物理的基本问题陈平北京大学国家发展研究院 退休教授复旦大学新政治经济学中心 高级研究员/pchen清华大学高等研究院 讲座2013年11月21日“经济物理”的历史由来法国社会学家孔德 (Auguste Comte, 1798-1857 ): “social physics” 首次出书叫“社会物理”（1856）。陈平博士论文第一稿原名“社会物理引论”，描写具有文化因子（有别于蚂蚁）的劳动分工的演化（2012 改名“代谢增长论”），被导师 Ilya Prigogine 否定，改为“非线性经济动力学”（1987）。国际会议改名为“演化经济动力学”（1989，陈平 2004）美国波士顿大学的物理学

2、家H. Eugene Stanley (1995)为power law 的发现制造了一个新词：经济物理 econophysics，被物理学界接受，成为文献分类的新领域物理学家设想的理论模型或计算机模拟瑞士数学家与物理学家贝奴力（Daniel Bernoulli 1700-1782）：gambling and utility function(1738)John von Neumann (1903-1957 ): game theory, growth modelIlya Prigogine (1917-2003): Brussletor BZ reaction dissipative stru

3、cture, chemical reaction and population dynamics, self-organization(1971, 1977), complex systems (1987)Hermann Haken (1927- ): synergetics (1973), adiabatic approximation, laser Hamiltonian systemWolfgan Weidlich (1931- ) : Ising model for public opinion, social dynamicsSanta Fe Institute (SFI, 1984

4、-), Philip Anderson (spin glass model), Murray Gell-mann (complex adaptive system), edge of chaos, artificial life，automata system，interacting agents经济物理的基本问题经济复杂（非线性，非均衡，非稳态，多体，多层次，开放系统）现象能否简化为相对简单的科学模型？（1）能否找到相对优越参照系经济学的哥白尼问题（2）能否找到普适的基函数作为建模的基石经济学的开普勒问题（3）能否找到普遍的动力学方程，具有某种普适不变量牛顿-爱因斯坦-薛定谔问题【目标】：超

5、越简单的经验观察的统计描述耗散系统的哥白尼问题:经济指数的最佳趋势-波动分离问题保守系统的优化框架和耗散系统的演化框架非线性动力学与非平衡态统计力学在经济学的应用观察宏观与金融指数的非稳态运动 - - FD vs. HP (von Neumann) filter白噪声还是色混沌？ Louis Bachelier (1900) 的Brownian motion 还是 Schumpeter的生物钟？软边界振子与延时微分方程（类似神经元模型）基函数与经济波动的本质：外来噪声驱动vs. 内生（非线性）振子描写经济动力学的基函数白噪声，谐振波，与 wavelets Wigner transform, G

6、abor wavelet, and logistic wavelet经济波动 (business cycles) 的本质：内生震荡还是外来噪声驱动？Frisch model of noise driven harmonic cycles (1933), Harmonically bounded Brownian motion (Unlenbeck & Orstein 1930, Unlenbeck & Wang 王承书 1945)噪声与混沌的模式识别Math Representation in Frequency DomainFourier spectrum E(f) for color cy

7、cle and white noiseSpectrum E(f) of Harmonic Wave, White Noise, and Color Noise (Chaos)Wave NoiseStationary (Discrete Fourier Transform) vs.Non-Stationary (Joint-Time-Frequency Analysis)Time Series Analysis 钱世锷，陈大庞(1994)S&P500 Stock Price Index FSPCOM with log-linear (LL) and HP growth trendsDetrend

8、ed cycles with varying lengthsDifferent images of auto-correlationsUncertainty Principle in Signal ProcessingGabor (Gaussian) Wavelet with Minimum UncertaintyGabor Space (1946) in discrete time-frequency spaceMinimum uncertainty in time-frequency spaceUn-orthogonal base functionThe Coherent State (G

9、aussian Packet, Gabor Wavelet)The Uncertainty Principle in Quantum Mechanics & Information TheorySeparating noise and signal in Gabor spaceTime section in Gabor space (signal peak is far above the noise level)Time-dependent band filter in time-frequency spaceSeparating signals and noise in Gabor (ti

10、me-frequency) spacePhase portraits of HP cyclesWhite noise vs. color chaosStock Price Indexes (Standard & Poor 500)correlation dimension of color chaos in =2.5variance of color chaos = 69 %Structural instability of linear dynamical modelsStructural Stability (Resilience) and Regime Switch in Nonline

11、ar DynamicsLinear Demand-Supply Curves Unique Equilibrium 均衡幻象：“看不见的手”的自稳定市场为什么经济学家不能接受混沌？经济学自由主义的自稳定的理想市场=均衡态+白噪声Frisch 噪声驱动谐振子模型（1933）Friedman 外生货币论Lucas 理性预期模型真实经济周期(RBC)模型Bernanke 金融加速器模型 宏观经济学+金融经济学+计量经济学全是噪声驱动（永动机）模型非线性供求曲线 多均衡态 经济复杂性+市场内生不稳定性的起源Noise-Driven Cycles（ Frisch 1933）vs. Harmonic Br

12、ownian Motion（Unlenbeck & Orstein, 1930）Wang 王承书 & Unlenbeck (1945)Frisch model for American business cycles，which would be damped in 5-20 years（Chen 1999,2004)!Frisch model：Perpetual Motion Machine of Second Type？Frisch was not the FIRST: G.E.Uhlenbeck and L.S. Ornstein, On the Theory of Brownian M

13、otion, Physical Review, 36(3), 823-841 (1930). Frischs Informal conference paper: R. Frisch, “Propagation Problems and Impulse Problems in Dynamic Economics”, in Economic Essays in Honour of Gustav Cassel, George Allen & Unwin, London (1933). Frischs promised paper, Changing harmonics studied from t

14、he point of view of linear operators and erratic shocks, was advertised three times under the category papers to appear in early issues in Econometrica, including Issue No. 2, 3, and 4 of Volume I (April, July, and October 1933) but never appeared in Econometrica since 1934.Frisch never mentioned a

15、word about his prize-winning model in his Nobel speech in 1969 (Frisch 1981).Equilibrium Illusion through First-Differencing (High Frequency Noise Amplifier = Whitening Filter) in Econometric Analysis经济学滤波器=高频噪声放大器制造均衡幻象Frequency response for the FD filterX(t) = FDS(t)=S(t+1)-S(t)经济学的基本方程力学系统：波动方程与扩

16、散方程化学，人口，与生态系统：化学反应方程和人口动力学方程（Lotka-Volterra 模型）经济学的统一基础: 生态人口动力学市场份额竞争为主（策略定价）压倒价格竞争（只是策略竞争的一种手段）三层次论：微观-中观（金融与产业）-宏观经济学薛定谔的启示：如何同时理解基因（金融市场）的稳定性和变异性？Principle of Large Numbers如何理解金融市场在危机冲击下的柔韧性 (resilience) ？经济增长与波动过程中的不变量与普适方程：relative deviation （RD） 和birth and death processPrinciple of Large Num

17、bers for Positive Variables SN=X1+X2+ . . . . . . +XN Observed relative deviation of US real GDP is 20 times larger than Lucas model（Chen 2002)！Relative Deviation (RD) and the Implied Number (N*) from Empirical ObservationRelative deviationImplied numberLarge Numbers in US EconomyWeak microfoundatio

18、ns in labor and producer marketThe observed implied numbers predicted by the Lucas model is 400 500 times smaller (RD is 20 times larger ) than in US real economy.Possible microfoundations in financial markets and industrial organizationnot in labor or producer marketImplication Three layer structur

19、e (micro, meso, macro) rather than two layer structure (micro, macro) in economies Implications from the Failure of Lucas Model of MicrofoundationsRoots of persistent business cycles:Financial intermediates and industrial organizationFrom two layer model (micro-macro) Three layer model (micro-meso-m

20、acro)Nature of macro fluctuations social movementsStable RD in US Macro Indexesobserved under HP filter RD Behavior for Stochastic Models Random walk is damping over timeBrownian motion is exploding over timeOnly the Birth-death process is stable in time, which is a statistical model of endogenous f

21、luctuationsEconomic diagnosis经济危机的诊断和预警生灭过程的含时转移概率理解危机的不同途径：Fat tail distribution (Levy, fractal Brownian motion, power law), regime switch between calm and turbulent market高阶矩，生灭过程的主方程，与时间变化的转移概率Linear (BS) & Empirical (S&P 500) Transition Probability in Birth-Death Process from S&P data (Tang & Ch

22、en 2010)Higher Moment Deviations (=System Risk) during Crisis (4-5th Moments are 1000 times larger than 2nd Moment Failure of Portforlio Diversification)Source of Financial Instability：Nonlinear Trend & Higher Moments in Birth-Death ProcessOption pricing model based on nonlinear birth-death processS

23、tability condition：Under stability: finite first & second moment Ito construct arbitrage portfolio Black-Scholes modelCorrections of Option Pricing Model for Interacting Trend & DiffusionNo such thing as risk-free interest rate only exist moving trend in interest rateMultiple frequency co-exist in f

24、inancial market interacting between market trend & group players complex dynamics逻辑斯蒂增长，市场份额竞争，与知识的新陈代谢李约瑟问题, Wallerstein paradox, 和东西方文明的分岔Lotka-Volterra model with culture factorLogistic wavelets 和产业、文明的兴衰复杂性与稳定性的trade-off: 理论生物学与演化经济学一般斯密原理：劳动分工受市场规模、资源种类、和环境涨落的限制Metabolic Growth (Life Cycles): 知

25、识的代谢增长和技术发展的逻辑斯蒂小波Physics Foundation of BiologySchrdinger (1948): What is life? (Quantum biology)Large molecule, meta-stable state, non-periodic structure, information as negative entropyPrigogine (1972): Thermodynamics of evolutionDissipative structure with matter flow, energy flow, and information flow in open systemConstructive role of positive feedback (catalytic reaction) Self-organization (order out of chaos)非平衡物理与经济复杂系统：Haken vs. PrigogineHaken synergetics 协同学Laser Hamiltonian systemAdiabetic approximation take out slo