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```									   EARLY WARNING
SYSTEMS FOR BANKING
CRISES

Course on Financial Instability at the Estonian Central Bank,
9-11 December 2009 – Lecture 7

E Philip Davis
NIESR and Brunel University
West London
e_philip_davis@msn.com
www.ephilipdavis.com
groups.yahoo.com/group/financial_stability
Introduction
• 3 types of models for early warning, logit,
signal extraction and binary recursive tree
• We apply the models first to prediction of
crises in Asia
• And then outline a new logit approach
which predicts banking crises in OECD
countries
Early warning systems
• Multivariate logit model uses macroeconomic,
institutional and financial variables X as inputs to
calculate probability of a banking crisis Y as the
output via logistic function estimator. Suitable for
answering question “what is the likelihood of a
banking crisis occurring in the next t years?”
e  'Xit
Pr obYit  1  F X it  
1  e  'Xit
• Non-parametric signal extraction approach
tracks individual time series X prior to and
during crisis episodes to answer question “is
there a signal S of future crisis or not?” If an
input variable’s aberrant behaviour can be
quantitatively defined whenever that variable
moves from tranquil to abnormal activity, a crisis
is forewarned.
• { S ij = 1 } = { │ Xij │ > │ X*ij │ } or
• { S ij = 0 } = { │ Xij │ < │ X*ij │ }
• Binary Recursive Tree (BRT) can be used to
answer question “which non-linear variable
interactions make an economy more vulnerable to
crisis than others?” Argued that liquidity, credit
and market risks are all potentially non-linear.
Estimator identifies single most important
discriminator between crisis and non-crisis
episodes across the entire sample, thereby creating
two nodes. Nodes are further split into sub-nodes
based on the behaviour of splitter variables’ non-
linear interactions with previous splitter variables.
This generates nodal crisis probabilities and the
associated splitter threshold values.
Figure 4: Schematic Diagram                     Entire Sample: 72
of Binary Recursive Tree                        crises
(BRT)
PARENT NODE

X1≤ V1*                                      X1>V1*

Splitter Variable: X1

Child Node 1:                                                         Child Node 2:
52 crises                                                             20 crises

Splitter Variable: X2                                                     Splitter Variable: X3

X2≤ V2*
X2> V2*               X3≤ V3*                                X3≥ V3*

Terminal Node 3:                   Terminal Node 3:              Terminal Node 4:                            Terminal Node 5:
48 crises                          4 crises                      17 crises                                   3 crises
Advantages and disadvantages
• Logistic models are ideally suited to predicting a binary
outcome (1 = banking crisis, 0 = no banking crisis) using
multiple explanatory variables selected on the basis of their
theoretical or observed associations with banking crises.
• Logistic approach is also parametric, generating confidence
intervals attached to coefficient values and their
significance, but logit coefficients are not intuitive to
interpret and they do not reflect the threshold effects that
may be simultaneously exerted by other variables.
• Signal extraction non parametric and can use high
frequency data
• Logit approach is the most appropriate for use as a global
EWS, while signal extraction methods are more appropriate
for a country-specific EWS (Davis and Karim 2008).
• BRT is able to discover non-linear variable interactions,
making it especially applicable to large banking crises
datasets where many cross-sections are necessary to
generate enough banking crisis observations and
numerous factors determine the occurrence of systemic
failure.
• In BRT no specific statistical distribution needs be
imposed on the explanatory variables. Also not
necessary to assume all variables follow identical
distributions or that each variable adopts the same
distribution across cross-sections.
• Although logistic regression does not require variables
to follow any specific distribution, Davis and Karim
(2008) showed that standardising variables displaying
heterogeneity across countries improved the predictive
performance of logit models.
• Logistic regressions are also sensitive to outlier effects,
yet it is precisely the non-linear threshold effects exerted
by some variables that could generate anomalous values
in the data.
• In low risk, stable regimes, variables may conform to a
particular distribution which subsequently jumps to a
regime of financial instability. Non-parametric BRTs
should handle such data patterns better than logistic
regressions.
• BRT is extremely intuitive to interpret. The model
output is represented as a tree which is successively split
at the threshold values of variables that are deemed as
important contributors to banking crises.
• Signal extraction is also easier to interpret than logit, but
is vulnerable to ignoring multivariate patterns at core of
instability
Illustrative results – logit (Asia)
Variable              Coefficient        z-Statistic   Coefficient    z-Statistic
DCRED(-1)               -0.033902         -2.091298      -0.032416     -2.046609
GDPPC(-1)               -0.000246         -3.451172      -0.000235     -3.535303
FISCY(-1)                0.010451          0.153806
INFL(-1)               -0.037791         -1.212934
RIR(-1)                0.114829          2.528462      0.113567      2.612414
DEPREC(-1)                0.053493          2.724725      0.044323      2.712526
DCREDY(-1)                0.022844          2.971898      0.021231      2.959820
DTT(-1)                 0.007492          0.322193
DGDP(-1)                -0.261366         -3.853235      -0.276748     -4.192324
M2RES(-1)               -0.000549         -2.232728      -0.000536     -2.190088
Expectation-Prediction Evaluation for Binary
Specification
Equation: IND_STAND
Date: 12/03/09 Time: 19:46
Success cutoff: C = 0.25

Estimated Equation
Dep=0     Dep=1      Total

P(Dep=1)<=C             80          7         87
P(Dep=1)>C             34         41         75
Total              114         48        162
Correct              80         41        121
% Correct          70.18      85.42      74.69
% Incorrect         29.82      14.58      25.31
Total Gain*         70.18     -14.58      45.06
Percent Gain**       70.18        NA       64.04
Signal extraction - Asia
2
1.8
1.6
1.4
1.2
NTSR

1
0.8
0.6
0.4
0.2
0
0.5   1          2          3.5        4        4.5         6         8         10    20
Percentile Threshold

GDP grow th                  Change Terms of Trade       Depreciation
Real Interest Rate           Inflation                   Fiscal Surplus/ GDP
M2/Reserves                  GDP per Capita

Real GDP growth Fiscal surplus/GDP Depreciation
% crises correct         10                 8              6
% no crises correct       99                 98            98
% total correct          65                 64            62
BRT - Asia
Node 1
Class Cases %
0    120 71.4
1     48 28.6

FISCY > -1.14
FISCY <= -1.14
Terminal
Node 2
Node 4
Class Cases %
Class Cases %
0     41 51.3
0     79 89.8
1     39 48.8
1      9 10.2

DGDP <= 4.75
DGDP >   4.75
Terminal
Node 3
Node 1
Class Cases %
Class Cases %
0    34 73.9
0      7 20.6                                                                    Asia
1    12 26.1
1     27 79.4
% crises correct    46
% no crises correct 90
DCREDY <= 60.49         DCREDY > 60.49     % total correct     84
Terminal                Terminal
Node 2                 Node 3
Class Cases %           Class Cases %
0     18 100.0          0     16 57.1
1      0    0.0         1     12 42.9
Leading indicator selection
Asia
Signal
Logit   Extraction   Tree
Real GDP Growth                                   
Real Interest Rate
Inflation
Fiscal Surplus/ GDP                                 
M2/ Foreign Exchange
Reserves                          
Real Domestic Credit Growth       
Real GDP per capita               
Domestic credit/GDP                                 
Depreciation                            
Terms of Trade                          
Current account/GDP
External short term debt/GDP
A new model for the OECD
• Existing work on early warning systems (EWS)
for banking crises generally omits bank capital,
bank liquidity and property prices, despite their
relevance to the probability of crisis in the mind of
bankers, policymakers and the public. One reason
for this neglect is that most work on EWS to date
has been for heterogeneous global samples
dominated by emerging market crises. For such
countries, time series data on bank capital
adequacy and property prices are typically absent,
while other variables affecting crises may also
differ in OECD countries.
• We argue results are misspecified
• Triggers of crisis depend on the type of economy and
banking system. In OECD countries with high levels of
banking intermediation and developed financial markets,
shocks to terms of trade are less important crisis triggers
than, say, property price bubbles.
• Also developed economy banking systems are more
likely to be regulated in terms of capital adequacy and
liquidity ratios
• Accordingly, we estimate logit models of crisis for
OECD countries only and find strong effects of capital
adequacy, liquidity ratios and property prices, such as to
exclude most traditional variables. Our results imply that
higher unweighted capital adequacy as well as liquidity
ratios has a marked effect on the probability of a banking
crisis, implying long run benefits to offset some of the
costs that such regulations may impose (e.g. widening of
bank spreads).
Methodology and data
• Multivariate logit with dependent variable being crisis
probability
• Problems of crisis dummies
– Definition of banking crises
– Start and end dates ambiguous
– Focus on switch date in core results
• Data partitioned to 1980-2006 and 2007 to leave subprime
crisis for out-of-sample
• Variables for bank regulation:
– Unweighted capital adequacy ratio - ratio of capital and reserves
for all banks to the end of year total assets
– Liquidity - ratio of the sum of cash and balances with central
banks and securities for all banks over the end of year total assets
Table of crises in sample
BG   CN   DK   FN   FR   GE   IT   JP   NL   NW   SP   SD   UK   US

1980   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1981   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1982   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1983   0    1    0    0    0    0    0    0    0    0    0    0    0    0
1984   0    0    0    0    0    0    0    0    0    0    0    0    1    0
1985   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1986   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1987   0    0    1    0    0    0    0    0    0    0    0    0    0    0
1988   0    0    0    0    0    0    0    0    0    0    0    0    0    1
1989   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1990   0    0    0    0    0    0    1    0    0    1    0    0    0    0
1991   0    0    0    1    0    0    0    1    0    0    0    1    1    0
1992   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1993   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1994   0    0    0    0    1    0    0    0    0    0    0    0    0    0
1995   0    0    0    0    0    0    0    0    0    0    0    0    1    0
1996   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1997   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1998   0    0    0    0    0    0    0    0    0    0    0    0    0    0
1999   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2000   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2001   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2002   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2003   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2004   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2005   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2006   0    0    0    0    0    0    0    0    0    0    0    0    0    0
2007   0    0    0    0    0    0    0    0    0    0    0    0    1    1
Box 1: List of Variables (with variable key)

1. Real GDP Growth (%) (YG)
Variables used in
2. Real Interest Rate (%) (RIR)
previous studies:
3. Inflation (%) (INFL)
Demirguc-Kunt and
4. Fiscal Surplus/ GDP (%) (BB)
Detragiache (2005);
Davis and Karim (2008).    5. M2/ Foreign Exchange Reserves (%) (M2RES)
6. Real Domestic Credit Growth (%) (DCG)
7. Liquidity ratio (%) (LIQ)
Variables introduced in
8. Unweighted capital adequacy ratio (%) (LEV)
this study.
9. Real Property Price Growth (%) (RHPG)

e  'Xit
Pr obYit  1  F X it                        'Xit
1 e
n    T
Log e L   Yit log e F  ' X it   1  Yit  log e 1  F  ' X it 
i 1 t 1
Table 2: The General To Specific Approach

-0.118    -0.124 -0.137      -0.135    -0.135    -0.144    -0.147
LIQ(-1)
(-3.55)   (-3.55) (-3.64)    (-3.55)   (-3.45)   (-3.39)   (-3.25)
-0.333    -0.239 -0.315      -0.247    -0.271    -0.280    -0.273
LEV(-1)
(-2.85)   (-1.90) (-2.24)    (-1.64)   (-1.67)   (-1.72)   (-1.62)
0.113     0.113   0.104      0.100     0.104     0.108     0.110
RHPG(-3)
(2.8)    (2.87) (2.67)       (2.59)    (2.67)   (2.76)     (2.67)
-0.099 -0.10         -0.10    -0.10     -0.13     -0.13
DCG(-1)          -
(-1.82) (-1.97)    (-1.86)   (-1.99)   (-1.98)   (-1.98)
0.084      0.085     0.165     0.173     0.166
RIR(-1)          -          -
(1.37)     (1.40)    (1.41)   (1.46)     (1.30)
-0.00    -0.00     -0.00     -0.00
M2RES(-1)        -         -        -
(-1.0)    (-1.0)    (-1.1)    (-1.1)
-0.13     -0.14     -0.13
INFL(-1)         -         -        -         -
(-0.8)    (-0.8)    (-0.7)
0.116     0.125
YG(-1)           -         -        -         -         -
(0.65)     (0.66)
-0.013
BB(-1)           -         -        -         -         -         -
(-0.1)
Note: estimation period 1980-2006; t-statistics in parentheses; LIQ-liquidity ratio, LEV- unweighted capital
adequacy ratio, YG-real GDP growth, RPHG-real house price inflation, BB-budget balance to GDP ratio,
DCG-domestic credit growth, M2RES-M2 to reserves ratio, RIR-real interest rates, DEP-depreciation, INFL-
inflation.
Table 3: Comparing the Effects of Sample Period on Estimation Results
Estimation period
1980-2006 1980-2007

-0.118      -0.13
LIQ
(-3.55)     (-4.1)
-0.333     -0.261
LEV
(-2.85)    (-2.51)
0.113       0.106
PHG
(2.8)      (2.79)

 p(crisis) 
log 
1 - p(crisis) 
= - 0.333 LEV(-1) – 0.118 LIQ(-1) + 0.113 RHPG(-3)
               

(-2.85)         (-3.55)          (2.8)
Marginal effect of 1% rise in
variable on crisis probability
LIQ     LEV    RHPG
BG     -0.17   -0.49    0.17
CN     -0.22   -0.61    0.21
DK     -0.05   -0.14    0.05
FN     -0.23   -0.65    0.22
FR     -0.78   -2.17    0.74
GE     -0.23   -0.65    0.22
IT     -0.17   -0.46    0.16
JP     -0.38   -1.05    0.36
NL     -0.56   -1.57    0.53
NW     -0.33   -0.91    0.31
SD     -0.12   -0.34    0.12
SP     -0.08   -0.24    0.08
UK     -1.19   -3.32    1.13
US     -0.08   -0.22    0.07
BG
-

0.00
0.20
0.40
0.60
0.80
1.00
BG 80
-
BG 90
-
C 00
N
-
C 83
N
-
C 93
N
-
D 03
K
-
D 86
K
-
D 96
K
-
FN 06
-
FN 8 9
-
FR 9 9
-
FR 8 2
-
FR 9 2
-
G 02
E
-
G 85
E
-
G 95
E
-0
IT 5
-8
IT 8
-

Probability
J P 98
-
JP 81
-
JP 91
-
N 01
L
-

Crisis
N 84
L
-
N 94
L
N - 04
W
N - 87
W
-
SD 97
-
SD 80
-
Crisis probabilities

SD 90
-
SP 00
-
SP 83
-
SP 93
-
U 03
K
-
U 86
K
-
U 96
K
-
U 06
S
-
U 89
S
-9
9
In sample prediction
Aftermath
Total                        False
Crises    of the
Calls                        Calls
Crises             Timing of False Calls relative to Crisis Onset
BG       0        0         0         0
CN       6        1         1         4      next year
DK       0        0         0         0
FN       10       1         1         8      next year
FR       14       1         0         13
GE       4        0         0         4
IT       7        0         2         5      2nd and 3rd years
JP       15       1         6         8      Next 7 years, with a break on the 4th year
NL       18       0         0         18
NW       14       1         2         11     next 2 years
SD       6        1         1         4      next year
SP       2        0         0         2
UK       20       2         0         18
US       0        0         0         0
total   116       8         13        95
Out of sample predictions
2007   2008   definition1 definition2
BG     X      X          X           X
CN      -      -                     -
DK      -      -
FN      -     X
FR     X      X         X           X
GE      -      -        -           -
IT     X       -                    X
JP      -      -
NL     X       -        X           X
NW     X      X
SD      -      -                    -
SP     X      X                     X
UK     X      X         X           X
US      -      -        -           -
Country elimination tests
US and   Norway       Finland   Sweden
Final      UK not   US not Japan not
Japan not    not          not        not
panel     included included included
included included     included   included

-0.118    -0.143    -0.125    -0.111    -0.119    -0.124    -0.121     -0.115
LIQ(-1)
(-3.55)   (-2.99)   (-3.55)   (-3.28)   (-3.29)   (-3.59)    (-3.5)    (-3.41)
-0.333      -0.3    -0.339    -0.344    -0.349    -0.282    -0.293     -0.343
LEV(-1)
(-2.85)   (-1.78)   (-2.79)   (-2.94)   (-2.86)   (-2.38)   (-2.43)    (-2.87)
0.113     0.152     0.119     0.111     0.118     0.089     0.083      0.107
PHG(-3)
(2.8)     (3.44)    (2.82)    (2.74)    (2.76)    (2.04)    (1.84)     (2.58)
Alternative crisis dates
Japanese
Final               US crisis
crisis at
version              at 1984
1992

-0.118     -0.119       -0.12
LIQ(-1)
(-3.55)    (-3.56)    (-3.58)
-0.333     -0.332     -0.317
LEV(-1)
(-2.85)    (-2.85)    (-2.73)
0.113      0.113      0.104
PHG(-3)
(2.8)      (2.8)      (2.56)
Aftermath elimination and
subprime runup

Aftermath                Final
1980-2007
Final                                      estimation
of the                version
version                                     with break
Crisis
-0.118     -0.128
LIQ(-1)
-0.118     -0.111                 (-3.55)     (-3.4)
LIQ(-1)                                     -0.333     -0.241
(-3.55)    (-3.48)     LEV(-1)
(-2.85)    (-1.94)
-0.333     -0.329                  0.113      0.106
LEV(-1)                         RHPG(-3)
(-2.85)    (-2.91)                 (2.8)      (2.85)
0.113      0.111                            -0.029
PHG(-3)                          LIQ(-1)b      -
(2.8)      (2.74)                           (-0.34)
-0.045
LEV(-1)b       -
(-0.19)
0.006
RHPG(-3)b      -
(0.05)
Further lags and systemic crises

LIQ (-2)   -0.104    LIQ (-1)   -0.121
(-3.27)              (-2.49)
LEV (-2)   -0.385    LEV (-1)   -0.768
(-3.22)              (-3.59)
PHG (-3)    0.119    PHG (-3)    0.235
(3.00)               (3.71)
Conclusions
• 3 approaches complementary
• Traditional approaches fruitful for EMEs such as Asia but
not for OECD countries
• Found relevance of bank capital, liquidity and property
prices absent from traditional EWS, exclude traditional
variables
• Can predict crises out of sample and specification is robust
• Warrants policy focus on bank regulation – of
capital, liquidity but also of terms of mortgages loans
• Also supports measures to reduce procyclicality, adjusting
capital or provisions countercyclically – and use of simple
leverage ratio as well as risk weighted capital adequacy
References
• Davis, E P and D Karim (2008a), "Comparing early
warning systems for banking crises", Journal of Financial
Stability, 4, 89-120
• Davis E P and Karim D (2008b), "Could early warnings
systems have helped to predict the subprime crisis?",
National Institute Economic Review, 206, 25-37 and
Brunel University Economics and Finance Working
Paper No 08-27
• Barrell R, Davis E P, Karim D and Liadze I (2009),
"Bank Regulation, Property Prices And Early Warning
Systems For Banking Crises In OECD Countries",
NIESR Discussion Paper No. 330

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