Transcript Frisch model

Division of Labor, Technology
Metabolism, and Business Cycles
- A Constructive Criticism of
Mainstream Economic Principles
• Ping Chen
• China Center for Economic Research, Peking University
• [email protected]
Center for New Political Economy, Fudan University
http://www.cnpe.org.cn/
• Ilya Prigogine Center for Studies in
• Statistical Mechanics and Complex Systems, University of Texas at Austin
• [email protected]
•
Nov.11, 2004 at China People’s University
参考书: 陈平,文明分岔、经济混沌、和演化经
济动力学，北京大学出版社 (2004)。
• 正象达尔文发现有机界的发展规律一样，马克思发现了人类历史的发
展规律，即历来为繁茂芜杂的意识形态所掩盖着的一个简单事实：人
们必须首先吃，喝，住，穿，然后才能从事政治，科学，艺术，宗教
等等；所以，直接的物质的生活资料的生产，因而一个民族或一个时
代的一定的经济发展阶段，便构成为基础，人们的国家制度，法的观
念，艺术以至宗教观念，就是从这个基础上发展起来的，因而，也必
须由这个基础来解释，而不是象过去那样做得相反。
•
• - 恩格斯， “在马克思墓前的讲话“
•
马克思恩格斯选集，第3卷，574页， 人民出版社，北京1972年版
Is Economics a Science?
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Conflicting doctrines:
Man’s nature is selfish and greedy (classical)
Man’s nature is free and social animal (Marx)
Bounded rationality (behavioral economics)
• Conflicting Nobel prizes:
• 1974 Gunnar Myrdal, Friedrich August von
Hayek
From Ilya Prigogine:
Order Out of Chaos (1984)
• Whitehead wrote that a “clash of doctrines is
not a disaster, it is an opportunity.” If this
statement is true, few opportunities in the
history of science have been so promising: two
worlds have come face to face, the world of
dynamics and the world of thermodynamics.
• Where classical science used to emphasize
permanence, we now find change and
evolution.
Observation, Question, Theories, Evidence
• How to start from an observation of “real
world”?
• Any observation implies an implicit theory,
the question is judging competing theories
• Pay equal attention to supporting evidence
and counter examples
• Find hidden assumption in existing theory
and alternative perspective
A Good Question Is Half-Done
• [Observation No.1] at Taiyuan Heavy Machine
Co.:
• After more than 10 years, worker’s number
multiplied three times, but production output is
only about one third of design capacity, WHY?
• Economy of scale, market extent, and diversified
pattern in division of labor
From Cybernetics to Complex Systems
Wiener (cybernetics) – negative feedback mechanism
for dynamical stability;
Schrödinger (quantum biology) – meta-stable state,
non-periodic crystal, and negative entropy flow;
Prigogine (non-equilibrium physics) – positive feedback,
catalytic reaction, and order out of chaos.
Question #1: Why China’s history favors selfsufficiency while West prefers division of labor?
• [Classical economics]
• Rational choice under scarcity (What shapes people’s
preference?)
• Optimal equilibrium under non-scale economy
• Wallerstein Paradox and Needham’s Question:
China lacks man while Europe needs space?
• Marthus: ecology (resource limitation)
• Max Weber: culture (Protestant/Confucius)
• Marx/Mao: class struggle is the driving force of
production?
• New classical/anthropology: irrationality?
Quantitative Counter Evidence and
Historical Puzzle
• [Question 1a] Is there any empirical evidence than
landlord system and small-farming is more
productive in history? (Answer: No).
• [Question 1b] Why China’s policy based on
agriculture (grain production) while Europe based
on commerce?
• [Question 1c] Why spice trade in the West had
different impact than silk/tea/china trade in China?
Equilibrium & Non-equilibrium Order in
Evolutionary Thermodynamics
From Non-equilibrium Thermodynamics
to Cultural Anthropology
• Why spice trade? Animal husbandry vs.
grain production
• Why China developed labor-intensive but
resource-saving technology while Europe
developed labor-saving but resourceintensive technology?
• Geography and climate shaped the initial
condition of technology and culture
Individualism (Risk-Taking) &
Collectivism (Risk-Aversion) Behavior
Challenge to Microeconomics
• What is the nature of competition?
• Price competition vs. market-share competition
• What is the ideal state of competition?
• Perfect/monopoly/proper competition?
• What is the social outcome of competition?
• Positive or reverse selection?
• Increasing/decreasing division of labor?
Smith Dilemma (Stigler 1951) and TradeOff between Stability & Complexity
(Chen 2002)
• Adam Smith Theory: “Invisible hand” > perfect
competition > many small firms
• Smith Theorem: Division of labor is limited by
market extent > monopoly > few large firms
• How small and large firms could coexist?
• [中国国企的改革战略]抓大放小，与集团作大？
Re-Understanding Chinese Society
• Ecological crisis and peasant wars
• Small-scale farming and population mechanism: 按效分配，
按劳分配，与按势分配。
• [中国问题应用]：
• 三农问题与乡镇机构的过度扩张
• 奖励生育，粮食自给，过度恳荒，与生态危机
• 趋同教育，恶性（完全）竞争，与就业危机
• [中国前途]：
• 保护生态（小康社会），发展劳动分工与规模范围经济，
鼓励创新（适度竞争），可持续协调发展
• 质疑过度个人主义（过度消费，福利社会，大政府，过度
法制），均衡陷阱，过度/垄断竞争
Specie Competition, Technology Metabolism,
Product Cycles, and Growth Wavelets
L o g is t ic C o m p e t it io n
2.5
population
2
1.5
1
0.5
0
0
100
200
300
t im e
400
500
Challenge to Growth Theory and
Transaction Cost School
• Convergence (Solow)?
• South-North Gap (Endogenous growth, Romer,
Lucas)?
• Decreasing transaction cost (Coase)?
• Independent of initial condition (Coase Theorem)?
• Convergence equilibrium (Stalin/Coase) vs.
Diversity development (Schumpeter’s
Constructive destruction)?
Question #2: Market Economy Is Inherently
Stable? (macro-finance- micro-econometrics)
• Equilibrium thinking in economics:
• Negative-sloped demand curve (Marshall) > convex
function > fixed point theorem in Arrow-Debreu model in
microeconomics
• Econometrics: Frisch model of noise-driven harmonic
oscillator
• Friedman’s monetary shocks
• Real Business Cycle School (Prescott & Kydland):
technology shocks
• Fama’s efficient market hypothesis and Brownian motion
model in finance theory
• Friedman spirit and arbitrage-free theory in asset pricing
Historical Events: Great
Depression and Financial Crises
• Keynesian Revolution: Insufficient macro demand
• Austrian school: internal instability in financial
market
• Neo-classical synthesis: a compromise to classical
economics
• Lucas: New classical counter-revolution: micro
foundations and rational expectations
Question 2a: Can We Test Competing
Economic Theories by Quantitative Analysis?
(Testing noise versus chaos from macro &
financial time series)
• Equilibrium model:
• Steady state + random noise
• Keynesian school: damped oscillation
• Schumpeter (evolutionary) school: persistent cycles
(limit cycle or deterministic chaos)
Test #1: Monetary and Macro Chaos or Noise?
Economic Chaos: Copernicus Problem in
Macroeconomics (1984-1996)
• Discovery of monetary chaos (1985) >
implication for Austrian school
• HP filter and time-frequency analysis (1994)
> wide evidence of color chaos in macro
and stock indexes
Re-Examine Empirical and Theoretical
Foundations of Equilibrium Economics (1999-2002)
• Reject Frisch model (1999- ) > perpetual motion
machine of the second kind
• Reject Lucas model (1999-2002) > against the law
of large numbers
• Find better measurement > relative deviation >
meso economy, trivial result of consumption
smooth
• Reject random walk and Brownian motion model
> fever birth-death process
Re-Examining Empirical and Theoretical
Foundations of Equilibrium Economics
• Econometrics – Frisch model of noise-driven
damped harmonic oscillator (1933)
• Macroeconomics – Lucas model of microfoundations
and rational expectations (1972)
• Finance –geometric Brownian motion (diffusion
model) (Osborne 1959, Black & Scholes 1973)
• Microeconomics – Friedman’s thought experiment
of arbitrager against speculator in an efficient market
(1953)
> Equilibrium illusions through a short-time window
and representative agent
Physics Selects Better Alternatives
• Frisch model – against the second law of
thermodynamics (Unlenbeck & Orstein 1930, Chen
1999,2003) > nonlinear oscillator (color chaos)
• Lucas model = disguised representative model –
against the law of large numbers (Schrödinger 1940,
Chen 2002) > statistical mechanics
• Brownian motion – explosive in time (against
economic coherence) (Chen 1999, 2003) > birth-death
process
• Friedman argument = Maxwell demon – perfect
information against the uncertainty principle in
information theory (Brillouin 1951, Chen 1999, 2003)
> economic complexity
Why Strong Resistance to Economic Chaos
• Logistic curve and multi-humped function is
excluded by utility theory in microeconomics
(multiple equilibrium against unique equilibrium)
• Non-integrable system implies the failure of
regression approach in econometrics
• Chaotic pattern against the belief of efficient market
in finance theory, rational expectations and finetune by government interference in macroeconomics
• Difficulties in empirical tests: non-stationarity,
strong noise, short time series
Equilibrium Illusion through
a Whitening Looking Glass (FD)
X(t) = FD[S(t)]=S(t+1)-S(t)
F D W h it e n in g F ilt e r
0.4
0.35
Freq Response R(f)
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
f
• Frequency response for the FD filter
S&P500 Stock Price Index
with log-linear (LL) and HP growth trends
(VHP filter for von Neumann-Hodrick-Prescott)
8
X(t) = Ln SPX
7
X
LL
HP
6
5
4
3
2
1950
1960
1970
1980
1990
2000
Detrended Cycles with Different Images
0.6
0.4
Cycles
0.2
0
-0.2
FD
HPc
LLc
-0.4
-0.6
-0.8
1950
1960
1970
1980
1990
2000
Different Images of Auto-Correlations
1
AC(n)
0.5
0
HPc
LLc
FDs
-0.5
-1
0
10
20
30
40
50
Copernicus Problem in Choosing
Proper Observation Reference
FD (First-Differencing) – Observing rate of changes in
a time unit – ignoring (low-frequency) long-term
growth trend + amplifying high-frequency noise
• Gaussian random noise for monthly to annual
macro data (mainstream econometrics)
• Fractal Brownian motion for high frequency
(minutes) financial data (econophysics)
HP (von Neumann-Hodrick-Prescott) filter for weekly
to quarterly data– Observing business cycles around
a smooth trend in a medium time window (~ years)
– mainly (continuous-time) color chaos (strange
attractor) + some white noise
Uncertainty Principle in Signal Processing
Gabor (Gaussian) Wavelet
with Minimum Uncertainty
1
4
t2
h(t )  (
) exp( 
) exp( i t )
2
2

2
1
The Coherent State (Gaussian Packet, Gabor
Wavelet)
WDb (t, ) = 2 exp{- [ (t/)2 + ()2 ] }
The Uncertainty Principle in
Quantum Mechanics & Information Theory
Gabor Space (1946) in
discrete time-frequency space
• Minimum
uncertainty in
timefrequency
space
• Unorthogonal
base function
Wigner Distribution (1932)
• Probability representation in quantum optics
• Fourier transform of autocorrelation in a
symmetric time window


WD (t ,  )   s (t  ) s(t  ) * exp( i  ) d
2
2
Stationary (Discrete Fourier Transform) vs.
Non-Stationary (Joint-Time-Frequency Analysis)
Time Series Analysis
Separating signals and noise in
Gabor (time-frequency) space
U
n
f
i
l
t
e
r
e
d
&
F
Evidence of Strange Attractor in Stock Market
Obtained by WGQ (Wigner transform + Gabor
space + Qian algorithm) Time-Varying Filter
FSPCOM Filter ed HP Cycles
0.3
0.2
0.2
0.1
0.1
X(t+T)
X(t+T)
FSPCOM Raw HP Cycl es
0.3
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
-0.3
-0.3
-0.2
-0.1
0
X(t)
0.1
0.2
0.3
-0.3
-0.2
-0.1
0
X(t)
0.1
0.2
0.3
Stock Price Indexes (Standard & Poor 500)
Correlation dimension = 2.5
Variance of color chaos = 69 %
F
S
P
C
O
M
S
S
t
)
4
r
i
g
o
g
(
2
O
S
0
-
2
-
4
1
9
41
59
51
59
61
t
59
71
59
81
59
9
5
Structural Stability in Parameter Space:
Linear vs.nonlinear models
Stability pattern of Samuelson model in parameter space. Here, ST denotes the steady
state; DO, damped oscillation; EO, explosive oscillation; EP, explosive solution; PO,
linear periodic oscillation.
Test #2: Frisch Model Failed to Generate
Persistent Business Cycles (Chen 1999)
• The observed auto-correlation will be damped
exponentially (Wang and G. E. Unlenbeck 1945);

Tr
2 
2 
 ( )  exp( )[cos(
)
sin(
)]
T
Tr
2 T
Tr
• For the Frisch model of the U.S.business cycles,
American business cycles would be ceased
within 4~10 years!
Nature of the Frisch Fantasy:
A Perpetual Motion Machine of Second-Type
Table I. The Frisch Model for US Real GDP Cycles (time unit is year)
Detrending
T1 T
g
1

 T

FD
1.02
1.79 1.86 3.4 3.5 2.0 0.010 0.57
HP
0.41
1.30 1.32 4.7 4.8 4.9 0.018 2.8
LL
0.055 0.11 .015 42 57 36 0.021 1600
where, g is the variance ratio of the observed residual to the external noise.
• The relaxation time T is 2 yrs for FD, 5 yrs for HP, 36 yrs
for LL. No persistent cycles in Frisch model of US GDP.
• The variance of external shocks should be 75% larger than that of
US real GDP for FD!
• HD is better than FD and LL in applying Frisch model to GDP
series.
Myth about the Frisch Model
• Frisch was not the FIRST: G.E.Uhlenbeck and L.S. Ornstein,
"On the Theory of Brownian Motion," Physical Review, 36(3),
823-841 (1930).
• Frisch’s 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).
• Frisch's promised paper, "Changing harmonics studied from the
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 word about his prize-winning model
in his Nobel speech in 1969 (Frisch 1981).
The Principle of Large Numbers
for Positive Variables
• SN=X1+X2+ . . . . . . +XN
Relative Fluctuation (RD) and the Implied
Number from Empirical Observation
• Relative fluctuation
ST 

N
N

• Implied number
N* 
1
macro
2
 macro 2

 macro 2

N
~
1
N
Relative Deviation (RD)
Under Different References
•
•
•
•
Data
GDPQLn(HP) GDPQLn(LL)
GDPQLn(ST)
GDPQLn(FD)
 (%)
0.2
0.4
1.2
140
N*
200,000
70,000
7,000
0.5
HP – upper bound for the number of micro agents
ST – Static time window of 10 years, lower bound
LL – middle range figure
FD – useless in studying micro–macro relation caused
by negative mean.
The Relative Deviation and Implicit Number
For Macro Indexes under ST and HP Methods
•
•
•
•
 (%) [N*]
GDPQLn
GCQLn
GPIQLn
LBMNULn
ST
1.2 [7,000]
1.4 [6,000]
2.2 [2,000]
1.1 [8,000]
HP
0.22 [200,000]
0.16 [400,000]
1.3 [6,000]
0.43[50,000]
GDPQ – US Real GDP quarterly
GCQ – US Real Consumption quarterly
GPIQ – US Real Investment quarterly
LBMNU – US Non-Farm Business Hours quarterly
Numbers of Households and Firms
in 1980 of the US Economy
• Realistic Number and Potential Relative Deviations
Micro-Agents
Households
Corporations*
Public Companies
N
80.7(million)
2.9(million)
20,000
 (%)
0.01
0.05
0.7
*Here, we count only those corporations with more than $100,000 in assets.
Test #3: Weak microfoundations in
labor and producer market
The 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 organization
not in labor or producer market
Implication >
Three layer structure (micro, meso, macro)
rather than two layer structure (micro, macro)
in economies
Failure of the Lucas Model of Rational
Expectations and Inter-temporal Substitutions
• Relative prices move in opposite directions: Rising
demand of leisure will raise leisure prices, which would
induce arbitrage activities
• Arbitrage activities by rational agents would cancel out
inter-temporal substitution.
• Rational expectations hypotheses is a self-defeating
mechanism as Lucas critique in forecasting market
movements.
• Lucas model of island economy (1972) is a disguised
model of representative agent, which ignored statistical
effect under the Principle of Large Numbers.
Stable RD in US Macro Indexes
observed under VHP filter
re l d e v (% )
8
gdpc1
6
g p d ic 1
pcecc96
4
2
0
1950
1960
1970
1980
1990
2000
Test #3: Persistent Fluctuations in
Financial Market
Order
Mean
Variance
Brownian motion
Birth-Death
~ exp( rt )
~ exp( rt )
~ exp( 2rt ){e
RD
~e
2
t
2
 2t
(1  e
 1}
 t 2
)
Random-Walk
t
t
~ e rt (e rt  1)
~
1
1
N0
t
• Random walk is damping over time
• Brownian motion is exploding over time
• Only the Birth-death process is stable in time, which is a
statistical model of endogenous fluctuations
Test #4: Failure of Friedman Spirits (~
Maxwell Demon) for Efficient Market
• Arbitrage risk (De Long et al 1990)
• Information cost (Grossman and Stiglitz 1980)
• Information ambiguity (limited data, time delays,
dynamical uncertainty)
• Limited replication of winner’s strategy under
complex dynamics
• Complex patterns in resilient market
Understanding Resilient Market (Order &
Changes) by Economic Biophysics
• Viability (survival zone) at micro: Non-convex
utility of individual behavior
• Diversity at meso (finance and industrial
organization): Lotka-Volterra competition for
market niches
• Persistent cycles at macro: Birth-death process
(economic metabolism) in growth fluctuation and
nonlinear oscillator (biological clock) in business
cycles
Policy Implications
• Source of innovation & crises: Meso
economy in three layers of economic
organism (Schumpeter, Keynes, Minsky):
micro - financial intermediates – macro
• Policy change: from demand side to
supply side, from managing monetary
shocks to technology waves (Rostow)
中国问题的新思考：非均衡的现
实与多样的发展
•
•
•
•
如何解决就业问题？
宏观调控的措施？
房地产泡沫与金融改革
效率与公平的悖论：土地，教育，医疗，
社保
• 世界工厂与外向政策
Toward a General Synthesis of Smith,
Schumpeter, Keynes, and von Neumann
• Keynes’s Goal of his General Theory
(disequilibrium framework) and Einstein’s
General Relativity
• Retreat of neo-classical synthesis (equilibrium
framework) by Hicks and Samuelson
• Construct a general framework based on
evolutionary (non-equilibrium) perspective
从均衡经济学到复杂经济科学
• 老子，道德经：“道生一，一生二，二生三，
三生万物。”
• 市场-政府-与社会的互动
• 微观-中观-宏观的结构演化
• 演化经济学的兴起
• 新政治经济学的整合：可持续协调发展与效率，
公平，创造的兼顾
• 看不见的手，帮助的手，掠夺的手，还是规制
的手？
• 保护产权还是保护创新？