Financial crisis, Omori’s law, and negative entropy flow
Jianbo Gao
PMB InTelliGence, LLC, West Lafayette, IN 47906
Mechanical and Materials Engineering, Wright State University
[email protected]://www.gao.ece.ufl.edu/
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 1 / 36
Outline
Background and significance
Exposure network preceding the crisisI Omori-like lawI Information flow
Forewarning crisis through distribution analysis
Forewarning crisis using entropy
Nonlinear dynamics associated with crisisI Recurrence plot analysisI Stability of Okun’s law
Concluding remarks
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 2 / 36
Background
In the past three decades, many countries have experienced financialcrises with different degrees of severity
Especially costly is the 2008 global financial crisis, which has affectedessentially all the industrialized countries, as well as a large number ofdeveloping economies
The 2008 global financial crisis has again pushed early warning system(EWS) models into the spotlight for reducing the risks of future crises
EWS models aim to anticipate whether and when individual countriesmay be affected by a financial crisis
I Types of crises: currency crises, banking crises, sovereign debt crises,private sector debt crises, and equity market crises
I Most EWS models focuses primarily on currency crises
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 3 / 36
Background (Cont’)
Existing EWS models are not very effective in forewarning crisesI Rose and Spiegel (2009) examined Multiple-Indicator Multiple Cause
(MIMIC) model of Goldberger (1972)I They found that few of the characteristics suggested as potential
causes of the crisis actually help predict the intensity and severity ofthe crisis across countries
The best indicators for the 2008 crisis include asset price inflation,rising leverage, large sustained current account deficits, and a slowingtrajectory of economic growth (Reinhart and Rogoff 2008)
Overall, economists have not had a particularly good track record atpredicting the timing of crises (Rose and Spiegel 2009)
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 4 / 36
Background (Cont’)
In economics, an important assumption is the economic equilibriumI economic forces are balancedI in the absence of external influences, the equilibrium values of
economic variables will not change
The assumption clearly is violated during a crisis
Existing EWS models employ aggregated variables that cannotexamine the nonlinear dynamics of participating players on scalessmaller than a country in unstable, non-equilibrium economies
Most desirable approach: Understand the large scale emergenteconomic behavior by studying the detailed interactions among theparticipating players of an unstable economy
We propose an anatomical approach toI analyze the exposure networks associated with Fannie Mae/Freddie
Mac, Lehman Brothers, and American International GroupI help understand the mechanisms of financial crisesI identify new robust indicators for financial crises and economic
recessions
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 5 / 36
Data used in this study
Two types of data were used for this study
One is the amount of investments exposed to FNM, FRE, LEH, andAIG, obtained by exhaustively searching the relevant files on theInternet, and then extracting the amount of investments
The other is income data of thousands of companies in 9 sectors ofUS economy, from 1990 - present
I 9 sectors: Financial, Consumer Goods, Consumer Services, BasicMaterials, Health Care, Industrials, Oil/Gas, Tech-Telecommunications,and Utilities
I Data were obtained from COMPUSTAT data base, by inputting stocksymbol lists for those 9 sectors
I Pretax income data were partitioned into 2 clusters, positive andnegative
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 6 / 36
Exposure network and Omori law
Exposure network: network nodes were the companies which investedin FNM, FRE, LEH, and/or AIG, and the strength of the links wascharacterized by the amount of the investment
The exposure networks we constructed contain 34, 151, and 146companies worldwide, exposed to AIG, LEH, and FNM/FRE,respectively
The complementary cumulative distribution function (CCDF)
P(X ≥ x) = Probability that X ≥ x million
is well fitted by an Omori-law-like distribution for earthquakeaftershocks:
P(X ≥ x) =(
1 +x
β
)−α, α > 0, β > 0
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 7 / 36
Exposure network and Omori law (Cont’)P(X ≥ x) =
(1 + x
β
)−α, (α, β) are (2, 118), (1.6, 116), and (0.5, 2), for
AIG, LEH, and FNM/FRE
10−2
100
102
104
10−2
10−1
100
Data x
CC
DF
P(X
≥ x
)
AIGLEHFNM/FRE
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 8 / 36
Properties of the Omori-like law
When x � β, Omori-like law becomes a power-law, P(X ≥ x) ∼ x−α
I When α < 2, the distribution is heavy-tailed having infinite varianceI When α ≤ 1, the mean also becomes infinite
If we introduce a new random variable, Y = X + β, then Y followsthe Pareto distribution,
P(Y ≥ y) = P(X ≥ y − β) =(
1 + y−ββ
)−α=(
βy
)α, y ≥ β
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 9 / 36
General considerations about business operation
How is a business operated?
I Suppose a company engages in a number of businessesI Different business areas make different profitsI The one with the highest profit will be privileged and expands rapidlyI While attracting large investments, it also requires larger liquidity and
costs to run itI In a profitable time, all parties will be happy, and investments will be
enhancedI In a troubled time, however, the dominant business area may bring
down the entire company — housing bubble
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 10 / 36
Stability of the Omori-like economy
From a mathematical modeling perspective, we may assume thatwhen a promising business area is just beginning, the situation isstable
The second law of thermodynamics states that entropy cannotdecrease
The most stable situation is the one with the highest entropyH(f ) = −
∫f (x) ln f (x)dx where f (x) is the PDF
When the mean investment x is given, exponential distributionF (X ≥ x) = e−λx , x ≥ 0maximizes entropy, where λ = 1/x
Entropies for exponential and Omori-like law:HExp(f ) = 1 + ln xHOmori(f ) = 1 + ln x + 1/α + ln[(α− 1)/α], when α > 1
Entropy difference: under the condition that mean is the same,x = β/(α− 1), entropy difference = 1/α + ln[(α− 1)/α] < 0— Less stable
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 11 / 36
Deriving the Omori-like law
Mathematically, treating λ as a random variable with a PDF f (λ) isequivalent to treating x = 1/λ as a random variable
Then the PDF for x becomes
f (x) =
∫ ∞0
λe−λx f (λ)dλ
and CCDF is
F (X ≥ x) =
∫ ∞x
f (x)dx =
∫ ∞x
∫ ∞0
λe−λx f (λ)dxdλ
Assuming uniform convergence and exchange order of integration, weobtain
F (X ≥ x) =
∫ ∞0
e−λx f (λ)dλ
— Laplace transform of f (λ)
Gamma distributed f (λ) yields Omori-like law !
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 12 / 36
Deriving the Omori-like law (Cont’)
Gamma distribution:f (λ) = 1
Γ(α)βαλα−1e−βλ, λ ≥ 0, α > 0, β > 0
I A special case: chi-square distribution of degree n,p(λ) = 1
2n/2Γ(n/2)λn/2−1e−λ/2I{λ≥0}
I chi-square distribution is the distribution for the summation of nindependent, standard normal random variables
Q =n∑
i=1
X 2i
I Except for a constant scaling coefficient, Q amounts to the totalenergy of a mechanical system
I chi-square distribution is the distribution that maximizes the entropy ofthe compound system (called variational principle by Chakraborti andPatriarca (2009))
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 13 / 36
100
102
10−2
10−1
100
P(X
≥ x
)
100
102
104
10−3
10−2
10−1
100
100
102
104
10−3
10−2
10−1
100
P(X
≥ x
)
100
102
104
10−3
10−2
10−1
100
100
102
104
10−3
10−2
10−1
100
Pretax income x
P(X
≥ x
)
100
102
104
10−3
10−2
10−1
100
Pretax income x
(b) Industrial sector 1992 Q1
(c) Technology sector 2001 Q2
(d) Technology sector 2001 Q4
(f) Financial sector 2008 Q2
(e) Financial sector 2007 Q4
α = 0.94 ± 0.13 α = 1.22 ± 0.16
α = 1.78 ± 0.27 α = 1.82 ± 0.40
α = 1.00 ± 0.05
(a) Industrial sector 1991 Q4
α = 0.91 ± 0.10
α = 0.97 ± 0.06
α = 0.91 ± 0.07
α = 1.23 ± 0.10
α = 0.63 ± 0.10α = 0.91 ± 0.08
α = 0.96 ± 0.04
Distribution of lossesaround recession times
CCDF (log-log scale) fornegative (red square) andpositive (black circle) pretaxincomes amongst U.S.companies
Omori-like law still applies !
During crises or recessions,the distribution for thenegative income cluster isheavier than that for thepositive income cluster
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 14 / 36
Health of US financial industry: far from recoveredRed: negative income; black: positive income
100
105
10−3
10−2
10−1
100
2008 Q1P
(X ≥
x)
100
105
10−3
10−2
10−1
100
2008 Q2
100
105
10−3
10−2
10−1
100
2008 Q3
100
105
10−3
10−2
10−1
100
2008 Q4
Pretax income x
P(X
≥ x
)
100
105
10−3
10−2
10−1
100
2009 Q1
Pretax income x10
010
510
−3
10−2
10−1
100
2009 Q2
Pretax income x
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 15 / 36
Health of US financial industry: far from recovered
100
105
10−3
10−2
10−1
100
2009 Q3
P(X
≥ x
)
100
105
10−3
10−2
10−1
100
2009 Q4
100
105
10−3
10−2
10−1
100
2010 Q1
100
105
10−3
10−2
10−1
100
2010 Q2
Pretax income x
P(X
≥ x
)
100
105
10−3
10−2
10−1
100
2010 Q3
Pretax income x10
010
510
−3
10−2
10−1
100
2010 Q4
Pretax income x
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 16 / 36
Health of US financial industry: far from recovered
100
105
10−3
10−2
10−1
100
2011 Q1
Pretax income x
P(X
≥ x
)
100
105
10−3
10−2
10−1
100
2011 Q2
Pretax income x
P(X
≥ x
)
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 17 / 36
2006_Q1 2006_Q4 2007_Q3 2008_Q20
2
4E
ntro
py
2006_Q1 2006_Q4 2007_Q3 2008_Q20
2
4
6
Ent
ropy
2006_Q1 2006_Q4 2007_Q3 2008_Q20
2
4
Ent
ropy
2006_Q1 2006_Q4 2007_Q3 2008_Q20
2
4
Ent
ropy
2006_Q1 2006_Q4 2007_Q3 2008_Q20
2
4
Ent
ropy
Time
(a) Financial
(b) Consumer goods
(c) Consumer services
(d) Technology
(e) Healthcare
Entropy for negative incomes:2008 crisis
H = −∑
Pi log Pi
Red: negative incomeblack: positive income
By the 2nd law ofthermodynamics, large entropy ismore stable
When entropy for negativeincomes exceeds that for positiveincomes, negative income clusteris even stronger than positiveincome cluster — very indicationof onset of crises
Crisis propagates
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 18 / 36
1999_Q1 2000_Q1 2001_Q1 2002_Q1 2003_Q10
2
4E
ntro
py
1999_Q1 2000_Q1 2001_Q1 2002_Q1 2003_Q10
2
4
Ent
ropy
1999_Q1 2000_Q1 2001_Q1 2002_Q1 2003_Q10
2
4
Ent
ropy
1999_Q1 2000_Q1 2001_Q1 2002_Q1 2003_Q11
2
3
4
Ent
ropy
1999_Q1 2000_Q1 2001_Q1 2002_Q1 2003_Q10
2
4
Ent
ropy
Time
(a) Financial
(b) Consumer goods
(c) Consumer services
(d) Technology
(e) Industrial
Entropy for negative incomes:2001 recession
Red: negative incomeblack: positive income
By the 2nd law ofthermodynamics, large entropy ismore stable
When entropy for negativeincomes exceeds that for positiveincomes, negative income clusteris even stronger than positiveincome cluster — very indicationof onset of crises
Crisis propagates
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 19 / 36
1990_Q1 1991_Q1 1992_Q1 1993_Q10
1
2
3E
ntro
py
1990_Q1 1991_Q1 1992_Q1 1993_Q10
1
2
3
Ent
ropy
1990_Q1 1991_Q1 1992_Q1 1993_Q10
1
2
3
Ent
ropy
1990_Q1 1991_Q1 1992_Q1 1993_Q10
1
2
3
Ent
ropy
1990_Q1 1991_Q1 1992_Q1 1993_Q10
1
2
3
Ent
ropy
Time
(b) Consumer goods
(c) Consumer services
(d) Technology
(e) Industrial
(a) Financial
Entropy for negative incomes:1991 recession
Red: negative incomeblack: positive income
By the 2nd law ofthermodynamics, large entropy ismore stable
When entropy for negativeincomes exceeds that for positiveincomes, negative income clusteris even stronger than positiveincome cluster — very indicationof onset of crises
Crisis propagates
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 20 / 36
Identification of crises/recessions using various metrics
1990 1993 1996 1999 2002 2005 2008
−2
0
2
Time
Ent
ropy
diff
eren
ce
Consumer ServicesIndustrialTechnologyFinancialTotal
1990 1993 1996 1999 2002 2005 2008−200
−100
0
100
Time
Tot
al in
com
e
Consumer ServicesIndustrialTechnologyFinancialTotal
1990 1993 1996 1999 2002 2005 2008−5
0
5
Time
I(i)/
|I(i−
1)|
Consumer ServicesIndustrialTechnologyFinancialTotal
(a)
(b)
(c)
Comparison of metrics: entropy difference,total income, and total income ratio
(a) variation of difference between entropy ofnegative and positive incomes with time
(b) variation in time of total income (wherethe income of the 1st quarter of 1990 is takenas 1 unit)
(c) variation in time of total income ratio(= IQj (i)/|IQj (i − 1)|
), where i denotes year
and j = 1, · · · , 4 denotes quarter, so IQ1 (1990)means 1st quarter income in 1990 (this ratiocrudely measures GDP contraction/expansion)
The grey and orange vertical dashed lines
indicate, respectively, the downturn onset
times determined by NBER and the dates the
NBER announced their onset identifications
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 21 / 36
When has the US financial crisis ended?
2008_Q1 2009_Q1 2010_Q1 2011_Q12
2.5
3
3.5
4E
ntro
py
Time
Financials
Positive incomeNegative income
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 22 / 36
On the meaning of negative entropy flow
Consider entropy change associated with the transition from anexponential to an Omori-like distribution
Denote the mean investment at t = 0 by x0.
At t = i , after weighing profits and losses, the mean investmentbecomes xi
The profit is given by ri − 1, where xi = rix0
Using the entropy formula for exponential and Omori distribution,∆Hi = ln ri + 1/α + ln[(α− 1)/α]
I ln ri is directly related to profits or lossesI 1/α + ln[(α− 1)/α < 0 is due to distributional changes of the
investments and may be termed entropy change due to structuralchanges in a business
Since 1/α + ln[(α− 1)/α < 0, to make total entropy changenon-negative, ln ri has to be large enough
I Take AIG and LEH for examples, where α = 2 and 1.6I Then 1/α + ln[(α− 1)/α = −0.19315 and −0.35583I When ∆Hi = 0, ri = 1.2131 and 1.4274, respectively — impossible
during crises
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 23 / 36
Summary of basic results
Losses in exposure networks can be modeled by a two-parameterOmori-law-like distribution for earthquake aftershocks
I Such a distribution suggests that losses will be widespread aroundcrises or recessions
Indeed during crises or recessions, the heavy-tailed distributions forthe negative income cluster are even heavier than those for thepositive income cluster
Consequently, the entropies associated with the distribution of thenegative income cluster exceed that of the positive income cluster
Distribution and entropy based indicators for crises are very accurate,and can monitor general economic recessions, besides financial crises
Moreover, instability propagates from the crisis initiating sector toother sectors, just as cancer spreads from one part of a body to otherparts
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 24 / 36
Stability of Okun’s law and economic recessions
Okun’s law: rising unemployment typically coincides with growthslowdowns
1950 1960 1970 1980 1990 2000 2010
−2
0
2
4
6
Time (year)
Diff
eenc
e si
gnal
∆ (unemployment)∆ (GNP)
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 25 / 36
Model specification of Okun’s law
There are two basic forms of Okun’s law. One is the first-differenceform, described byyt − yt−1 = α + β(ut − ut−1) + εtwhere yt is the natural log of observed real output, ut is the observed
unemployment rate, α is the intercept, β, which is negative, is Okun’s
coefficient measuring how much changes in the unemployment rate,
ut − ut−1, can cause changes in output, yt − yt−1, and εt is the disturbance
term
yt − yt−1 may be written as yt − yt−1 = ln Pt − ln Pt−1 =
ln Pt−1
(1 + Pt−Pt−1
Pt−1
)− ln Pt−1 = ln
(1 + Pt−Pt−1
Pt−1
)≈ Pt−Pt−1
Pt−1
Gap form of Okun’s lawyt − y∗t = α + β(ut − u∗t ) + εtwhere y∗t represents the log of potential output, u∗t is the natural rate of
unemployment, and y∗t and u∗t are complicated functions of time
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 26 / 36
Complicating factors of Okun’s law
Okun’s coefficient, originally thought to be close to 3, has been foundto be well below 3, and to vary substantially with time and withspatial samples under consideration
Okun’s coefficient depends on the model specification and themethod employed to estimate it
Using regional data, Okun’s coefficient has been found to vary fromregion to region
There appears to be an asymmetry in Okun’s law, i.e., cyclicalunemployment is more sensitive to negative than to positive cyclicaloutput
There is a time varying aspect of Okun’s law, as can be revealed byrolling regressions, or by explicitly allowing for time-varyingcoefficients
Violation of Okun’s law has also been observed
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 27 / 36
Cross recurrence plot (CRP) of ∆(GNP) and ∆(unemployment)
Construct vectors Xi = (xi , xi+L, · · · , xi+(m−1)L) and Yj
CRP: a dot is at (i , j) whenever ε2 ≤ ||Xi − Yj || ≤ ε1
where ε1 and ε2 are pre-specified scale parameters
1940 1960 1980 2000 20201940
1950
1960
1970
1980
1990
2000
2010
2020
∆ (Unemployment)
∆ (G
NP
)
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 28 / 36
Insights from the ratio time series
CRP suggests existence of an invariant aspect of the dynamics ofunemployment and production during recessions
Local extrema of the ratio time series coincides with economicrecessions
1950 1960 1970 1980 1990 2000 2010−10
−5
0
5
10
Time (year)
∆ (u
nem
ploy
)/ ∆
(G
NP
)
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 29 / 36
Partition data into cumulative normal and recessions timesRi =
∑11j=i rj , Ni =
∑12j=i nj
Name Dates Duration NotationRecession of 1949 Nov 1948 - Oct 1949 11 months r1
Recession of 1953 July 1953 - May 1954 10 months r2
Recession of 1958 Aug 1957 - April 1958 8 months r3
Recession of 1960 - 61 Apr 1960 - Feb 1961 10 months r4
Recession of 1969 - 70 Dec 1969 - Nov 1970 11 months r5
1973 - 75 recession Nov 1973 - Mar 1975 1 year 4 months r6
1980 recession Jan 1980 - July 1980 6 months r7
Early 1980s recession July 1981 - Nov 1982 1 year 4 months r8
Early 1990s recession July 1990 - Mar 1991 8 months r9
Early 2000s recession March 2001 - Nov 2001 8 months r10
Late-2000s recession Dec 2007-June 2009 1 year 6 months r11
Table: List of recessions from 1948 - present. Data from National Bureau ofEconomic Research, http://www.nber.org/cycles/cyclesmain.html
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 30 / 36
Okun’s law during 12 cumulative normal periods
−2 0 2−3
0
3
6 1N
−2 0 2−3
0
3
6 2N
−2 0 2−3
0
3
6 3N
−2 0 2−3
0
3
6 4N
∆ (G
NP
)
−2 0 2−3
0
3
6 5N
−2 0 2−3
0
3
6 6N
−2 0 2−3
0
3
6 7N
−2 0 2−3
0
3
6 8N
−2 0 2−3
0
3
6 9N
−2 0 2−3
0
3
6 10N
−2 0 2−3
0
3
6 11N
∆ (unemployment rate)−2 0 2
−3
0
3
6 12N
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 31 / 36
Okun’s law during 11 cumulative recession periods
−1 0 1 2−3
0
3
61R
−1 0 1 2−3
0
3
62R
−1 0 1 2−3
0
3
63R
−1 0 1 2−3
0
3
64R
∆ (G
NP
)
−1 0 1 2−3
0
3
65R
−1 0 1 2−3
0
3
66R
−1 0 1 2−3
0
3
67R
−1 0 1 2−3
0
3
68R
−1 0 1 2−3
0
3
69R
−1 0 1 2−3
0
3
610R
−1 0 1 2−3
0
3
611R
∆ (unemployment rate)
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 32 / 36
Variation of Okun’s coefficient with time
0 2 4 6 8 10 12−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
Cumulative period
Oku
n co
effic
ient
Recession
Normal period
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 33 / 36
Variation of coefficient of determination with time
0 2 4 6 8 10 120
0.1
0.2
0.3
0.4
0.5
Cumulative period
R2 (
coef
f of d
eter
min
atio
n)
Recession
Normal period
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 34 / 36
Partial summary
CRP allows for detecting general, non-local correlations betweenunemployment and production and suggests that Okun’s law duringeconomic recessions appears to have captured an invariant aspect ofthe dynamics of unemployment and production
Regression analysis based on data during recessions and normaleconomic times separately shows that Okun’s coefficient is remarkablystable during recessions
However, Okun’s law is continuously weakening during normaleconomic conditions, with the Okun’s coefficient continuouslydecreasing, and approaching 0 in the recent few years, suggestingalmost a total breakdown of Okun’s law after the recent giganticrecession
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 35 / 36
Concluding remarks
Distribution and entropy based indicators for crises are very accurate,and can monitor general economic recessions, besides financial crises
Moreover, instability propagates from the crisis initiating sector toother sectors, just as cancer spreads from one part of a body to otherparts
Economic crises/recessions are inevitable since Okun’s law duringeconomic recessions appears to have captured an invariant aspect ofthe dynamics of unemployment and production
Entropy flow is close to zero in Marxian economics; is not notconsidered in major economic growth models, including Nobel prizewinning neo-classical growth model, the Solow-Swan model
It is time to seriously consider entropy flow when designing economicpolicies
Gao, Jianbo (PMB InTelliGence) Financial crisis, Omori’s law, and negative entropy flow July 2013 36 / 36