Three Dimensions of Economic Crisis:
Theoretical, Empirical, and Policy
Analysis in Business Cycles
Prepared for IDEAs Conference on
Re-regulating global finance
in the light of the global crisis
April 10, 2008
Ping Chen
China Center for Economic Research at
Peking University, Beijing, China
Center for New Political Economy at
Fudan University, Shanghai, China
pchen@ccer.edu.cn
Nature of Business Cycles and
Economic Crisis
•
•
•
•
•
Exogenous school
Frisch (1933), Friedman & Schwartz(1963),
Lucas (1972), RBC, Black & Scholes (1973)
Endogenous school
Marx, Schumpeter, Hayek, von Mises, Keynes, Minsky,
• Natural experiments 》The Great Depression (1929-41),
Stock Market Crash (1987), Sub-Prime Crisis (2008-)
• Computational experiment 》Discovery of deterministic
color chaos (Chen 1996) > Endogenous nature
Operational Implications of
Exogenous/Endogenous divide
• Exogenous forces 》events driven by random
walk or white noise 》time series uncorrelated
》history does not matter! 》no
internal/historical constraints to government
policy!
• Endogenous forces 》events driven by
wavelets 》time series highly correlated 》
history does matter! 》strong
internal/historical constraints to government
policy!
Auto-Correlation Function for
Deterministic & Stochastic Time Series
Different auto-correlations for
Competing detrended time series
1
AC(n)
0.5
0
HPc
LLc
FDs
-0.5
-1
0
10
20
30
40
50
Equilibrium Illusion created by First-Differencing
(High Frequency Noise Amplifier 》Whitening
Filter) in Econometric Analysis
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
• X(t) = FD[S(t)]=S(t+1)-S(t)
Evidence of Strange Attractor in Stock Market
Obtained by WGQ transform (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)
Fractal 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
Economic diagnosis:
Exogenous(1973) vs. Endogenous events
P c H is t o ry o f F S P C O M H P C y c le s
20
Pc
15
O ilS h o c k
Pc (yrs)
S t o c k C ra s h
10
5
0
1965
1970
1975
1980
1985
External shock: frequency moved AFTER the shock
Internal instability: frequency moved BEFORE the shock
1990
Noise-Driven Cycles（ Frisch 1933）vs.
Harmonic Brownian Motion
（Unlenbeck & Orstein, 1930）
• Wang & 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 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
More Micro Elements >
Less Macro Fluctuations
(Independent fluctuations may cancel out each other)
• SN=X1+X2+ . . . . . . +XN
• Relative Deviation (RD) =
Observed Relative Deviation 》 Implied Numbers
(Data Source: Fed. Reserve St. Louis)
Real Personal consumption：
• Real GDP:
0.15%
0.2 %
(800,000)
(500,000)
• Real Private Investment:
1.2%
(10,000)
• Dow Jones Industrial (1928-09)：
• S&P 500 Index (1947-2009)：
• NASDAQ (1971-2009):
1.4%
1.6%
2.0 %
(9000)
(5000)
(3000)
• Texas Crude Oil Price (1978-2008): 5.3 %
(400)
US Household & Firm Numbers in1980
and Their Capability in Generating RD
• 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.
Economic Implications from
Principle of Large Numbers
• Household fluctuations contribute less than
10% of GDP fluctuations 》weak “micro
foundations” in business cycles
• Small firm fluctuations contribute only about
a quarter of GDP fluctuations
• Only public companies and giant
organizations may generate large fluctuations
in investment, which is 6-10 times larger than
GDP fluctuations 》meso foundations of
business cycles
Why Lucas is wrong about microfoundations
and rational expectations?
• MISTAKE I. Lucas critique also applies to Lucas theory when
relative prices move in pairs 》creates arbitrage opportunity
• Under rational choice between leisure and work, there is arbitrage
opportunity among mass
• Example: shock > wage DOWN > many workers choose leisure >
leisure price UP > some workers choose work instead > cancel out
the rational mass effect under “rational expectations”
• MISTAKE II. Lucas model of island economy with N agents 》
disguised model of representative agent 》system degree of
freedom =3 》individual degree of freedom is 3/N ~ 0!
• Counter example: Ideal Gas in physics, each particle has 6 degree
of freedom 》system with N particle has 6N degree of freedom
• Conclusion: equilibrium illusion of self-stabilizing market is created
by representative agent model in macro + FD whitening filter in
econometrics
Dan Gilligan, President of the PMA(Petroleum Marketers
Association) on Oil Price Manipulated by Financial Giants
• Did Speculation Fuel Oil Price Swings?? (CBS 60 Minutes, 01/12/2009)
•
http://www.cwpma.org/Template.php?-p=HomeNewsPopup&-d=News&-r=52.0
•
in 2000, Congress deregulated the futures market, granting exemptions for complicated
derivative investments called oil swaps, as well as electronic trading on private exchanges.
•
Volatility in price of oil per barrel within one year： $67↑ $147↓ $45； even jump $25 in one day!
•
Changes in demand & supply less than 5% 》Changes in price of oil larger than
100%
In mid-June - end of Nov. 2008，Congress investigation started > $70 billion
speculative capital left future market 》demand of oil dropped 5％》Price of oil
dropped more than 75% to $100
•
•
•
•
•
60％-70％of oil contracts in future market controlled by speculative capital
In past 5 years，capital poured into oil market by Hedge Funds and Big Investment Banks:
$13 billion ↑ $300 billions
Large players：Morgan Stanley, Goldman Sachs, Barclays, J.P. Morgan put hundred of
billions of dollars in oil future market， California pension fund. Harvard Endowment,
and large institutional investors
Smith Theorem and
Market Share Regulation
• Adam Smith Theorem: Division of labor is
limited by market extent 》danger of
monopolistic competition
• Hidden hypothesis in efficient market (invisible
hand) 》unlimited market extent
• Real market 》Limitation of market extent and
players 》Necessary of International anti-trust
law not only for merge & acquisition but also for
trading in financial market
• Disclose market positions in trading for big
players
Policy Implications for
Crisis Policy
• Traditional policy with “too big to fail”
• Take over failed companies by a bigger firm, such as
Citigroup and Bank of America 》prediction: Citigroup
and Bank of America would become worse
• Better competition policy under Principle of Large
Numbers
• Breaking up AIG, Citigroup into competing firms 》
improve chances of innovation and competition +
diversify risk of wrong decision
• Examples: China broke up China Airline into several
companies, Oligarchs in Russia
RD Behavior for Stochastic Models
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 >
resilient market of endogenous fluctuations
Source of Financial Instability：Nonlinear Trend &
Higher Moments in Birth-Death Process
• Option pricing model based on nonlinear birth-death
process f

t

[(a1  a1 )  ( a2  a2 ) 2  (a3  a3 ) 3 ] f (  t )

2

[a1  (a2  a2 ) 2  (3a3  2a3 ) 3 ] f (  t )
2

3

[a2 2  (3a3  a3 ) 3 ] f (  t )
3

4
3

a

f (  t ) 
3
 4

[(a1  a1 )  (a2  a2 ) 2  (a3  a3 ) 3 ]  0,

• Stability condition：
• Under stability: finite first & second moment 》Ito 》
construct arbitrage portfolio 》Black-Scholes model
Crisis：Trend Collapse &
Divergence of Higher Moments
TED Spread(3个月欧洲美元与美国国债的息差)
基点
250
200
150
100
50
2008-4
2008-3
2008-2
2008-1
2007-12
2007-11
2007-10
2007-9
2007-8
2007-7
2007-6
2007-5
2007-4
2007-3
2007-2
2007-1
0
Dow Jones Industrial in Great Depression
Policy Constraints during Crisis
• International coordination
• Danger of trade protection, asymmetric investment, and
competitive devaluation
• Domestic constraints:
• Expansionary monetary policy 》danger of inflation,
devaluation, and capital flight
• Expansionary fiscal policy 》danger of new bad loans,
crowding out small & medium healthy firms
• Finding new source of growth 》structural adjustment 》
green economy
References
• Coase, R. H. The Firm, the market, and the Law, University
of Chicago Press, Chicago (1990), Coase, R. “Social Costs”
(1960).
• Frisch, R. "Propagation Problems and Impulse Problems in
Dynamic Economics," in Economic Essays in Honour of
Gustav Cassel, George Allen & Unwin, London (1933).
• Friedman, M. “The Case for Flexible Exchange Rates,” in M.
Friedman, Essays in Positive Economics, University of
Chicago Press, Chicago (1953).
• Friedman, M. and A.J. Schwartz, Monetary History of
United States, 1867-1960, Princeton University Press, NJ:
Princeton (1963).
• Lucas, R.E. Jr. "Expectations and the Neutrality of Money,"
Journal of Economic Theory, 4, 103-124 (1972).
• Minsky, H.P. Stabilizing an Unstable Economy, Yale
University Press, New Haven (1986).
References
• Chen, P. “Empirical and Theoretical Evidence of Economic Chaos,”
System Dynamics Review, Vol. 4, No. 1-2, 81-108 (1988).
• Chen, P. “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).
• Chen, P. “Microfoundations of Macroeconomic Fluctuations and the
Laws of Probability Theory: the Principle of Large Numbers vs.
Rational Expectations Arbitrage,” Journal of Economic Behavior &
Organization, 49, 327-344 (2002).
• Chen, P. “Evolutionary Economic Dynamics: Persistent Business
Cycles, Disruptive Technology, and the Trade-Off between Stability
and Complexity,” in Kurt Dopfer ed., The Evolutionary Foundations of
Economics, Chapter 15, pp.472-505, Cambridge University Press,
Cambridge (2005).
• Chen, P. “Complexity of Transaction Costs and Evolution of
Corporate Governance,” Kyoto Economic Review, 76(2), 139－153
(2007).
• Chen, P. “Equilibrium Illusion, Economic Complexity, and
Evolutionary Foundation of Economic Analysis,” Evolutionary and
Institutional Economics Review, 5(1), 81-127 (2008).
• Schrödinger, E. What is Life? Cambridge University Press,
Cambridge (1948).