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Mapping the State of Financial Stability
14th Annual DNB Research Conference
3rd November 2011
DNB, Amsterdam
Peter Sarlin (Åbo Akademi / TUCS) &
Tuomas Peltonen (European Central Bank)
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An example of a SOM output at certain time
Mexico ArgentinaTaiwan Malaysia
Singapore
Turkey Brazil
Philippines South Africa
India
Tranquil
Pre crisis
Post crisis
Crisis
UK Indonesia
Thailand
Japan
Canada
Czech Republic China
Poland
Hong Kong
Switzerland
Norway
Denmark
Euro area
US
Korea
Sweden
Russia
Australia
New Zealand
Hungary
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1. Introduction - What do we do in the paper?
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Create the Self-Organizing Financial Stability Map (SOFSM)
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A model that can visualize multidimensional macro-financial
vulnerabilities and the state of financial stability across
countries and over time
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A model that has good out-of-sample predictive capabilities
of future systemic events / financial crises
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2. Self-Organizing Financial Stability Map (SOFSM)
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Building blocks for creating the SOFSM:
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Self-Organizing Maps
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Identifying systemic events
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Vulnerability indicators
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Model training
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Model evaluation
Mapping the State of Financial Stability
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2.1 Self-Organizing Maps (SOMs) – what are they?
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SOM is an Exploratory Data Analysis (EDA) technique by
Kohonen (1981) ➨ Viscovery SOMine
It is a clustering and projection technique:
–
–
–
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•
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Spatially constrained form of k-means clustering
Preserves the neighbourhood relations of the data (instead of trying to
preserve the distances between data)
Projects data onto a grid of nodes (rather than projecting data into a
continuous space)
Enables visualization of high-D data ➨ 2D grid of nodes without
losing the topological relationships of data and sight of individual
indicators.
Enables a flexible distribution and interactions.
Kohonen’s group has continuously reviewed the SOM literature
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The SOM has been used in approx. 10 000 works
Applied to currency and debt crises: Arciniegas and Arciniegas Rueda
(2009), Resta (2009), Sarlin (2011) and Sarlin and Marghescu (2011)
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2.1 Self-Organizing Maps (SOMs) – training algorithm
xj
mb
Radius of the
neighborhood σ
1.
2.
3.
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Compare all data points xj with all nodes mi to find for each data point the
nearest node mb (i.e., best-matching unit, BMU)
Update each node mi to averages of the attracted data, including data
located in a specified neighbourhood σ
Repeat steps 1 and 2 a specified number of times.
The SOM parameters are radius of the neighbourhood σ, number of nodes
M, map format (ratio of X and Y dimensions), and number of training
iterations t.
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2.1 Self-Organizing Maps (SOMs) – interpreting the output
Indicator 1
Indicator 2
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This is a 2D map that represents
multi-D data with a 2-level
clustering
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For each indicator, we create a
„feature plane“ where the color
coding represents the distribution
of its values on the 2D map.
Indicator 3
Indicator 4
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2.2 Identifying systemic events and creating financial stability cycle
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Use the data set from Lo Duca and Peltonen (2011): 28 countries (18
EMEs & 10 AEs), Quarterly data 1990Q1-2010Q3
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Identification of systemic events:
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The Financial Stress Index (FSI) includes 5 components for each
country, measuring volatilities and sharp declines in key market
segments (stock, foreign exchange and money markets)
A systemic event occurs when the FSI is above the 90th percentile of the
country-specific distribution (on average, negative real consequences)
Using the FSI, we identify four classes to describe the financial
stability cycle:
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Pre-crisis periods (18 months before the systemic event)
Crisis periods (systemic events defined by a financial stress index)
Post-crisis periods (18 months after the systemic event)
Tranquil periods (all other periods)
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2.3 Vulnerability indicators
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14 indicators of country-level macro-financial vulnerabilities:
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Domestic = inflation, GDP growth, CA deficit, budget balance,
credit growth, leverage, equity price growth, equity valuation
Global = inflation, GDP growth, credit growth, leverage, equity
price growth, equity valuation
Test several transformations of the indicators (over 200
transformations of the indicators tested).
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Select
best-performing
(as
a
leading
indicator)
transformations of the variables
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2.4 Model training
Tranquil
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Pre crisis
Euro
area
„Static“ model, i.e. model is not re-estimated
recursively:
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Post crisis
Crisis
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C18
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Pre crisis
Tranquil
Euro
area
Post crisis
Data as an input to the SOFSM
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Class variables + vulnerabilities for training
Only vulnerabilities for mapping and evaluating
Crisis probabilities as an output of the SOFSM
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Crisis
Training set (estimation sample): 1990Q4 - 2005Q1
Test set (out-of-sample): 2005Q2 - 2009Q2
In the benchmark, we use 18 months as a forecast
horizon
Account for policymakers’ preferences when
evaluating the performance as in Alessi and Detken
(2011) (benchmark μ=0.5)
Map data onto SOFSM and retrieve a crisis
probability
0.01 0.10 0.19 0.28 0.38 0.47 0.56 0.65
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2.5 Model evaluation
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Defining early warning nodes
• When calibrating the policymakers’ preferences, we vary the
thresholds.This changes the number of “early warning nodes”.
µ =0.4
µ =0.5
µ =0.6
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2.5 Model evaluation
• Training the SOM:
• While a higher number of nodes M improves in-sample performance, it
decreases generalization, i.e. out-of-sample performance.
• We increase M and find the first model with Usefulness ≥ 0.25 (logit model).
• In terms of “Usefulness”, when µ=0.5, the models are by definition very similar
on in-sample data, while the SOM performs better on out-of-sample data
• Robustness is tested with respect to three aspects
• SOM parameters: radius of neighborhood and number of nodes
• Policymakers’ preferences
• Forecast horizon
Crash periods
Precision
Recall
Tranquil periods
Precision
Recall
Model Data set μ
Logit T rain 0.5
SOM T rain 0.5
TP
FP
TN
FN
162
190
190
314
830
706
73
45
0.46
0.38
0.69
0.81
0.92
0.94
Logit
SOM
77
112
57
89
249
217
93
58
0.57
0.56
0.45
0.66
0.73
0.79
T est
T est
0.5
0.5
Accuracy
U
AUC
0.81
0.69
0.79
0.71
0.25
0.25
0.81
0.83
0.81
0.71
0.68
0.69
0.13
0.18
0.72
0.75
Reminder:
Recall positives = TP/(TP+FN), Recall negatives = TN/(TN+FP), Precision positives = TP/(TP+FP), Precision negatives = TN/(TN+FN), FP rate =
FP/(FP+TN), TP rate = TP/(FN+ TP), Accuracy=(TP+TN)/(FN+FP+TN+ TP).
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3. Mapping the State of Financial Stability – The two dimensional
SOFSM
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This is the 2D SOFSM that represents multi-D data.
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The stages of the financial stability cycle are derived using only
the class variables (pre-crisis, crisis, post-crisis and tranquil
periods)
Tranquil
Pre crisis
Post crisis
Crisis
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3. Mapping the State of Financial Stability – Constructing the four
clusters according to the financial stability cycle
C24
C18
Tranquil
Pre crisis
Tranquil
Pre crisis
Post crisis
0.50
0.75
0.01
0.22
0.44
Tranquil
0.47
0.70
0.00
•
0.33
Tranquil
0.01
0.02
0.29
Tranquil
Post crisis
Crisis
0.18
0.35
0.52
0.06
0.25
0.44
0.63
Tranquil
Pre crisis
Post crisis
0.68
0.32
Pre crisis
Tranquil
Post crisis
Crisis
0.50
0.21
PPC0
Pre crisis
Crisis
0.11
Post crisis
0.22
Tranquil
0.00
P18
Crisis
0.11
Post crisis
0.53
Pre crisis
T0
Pre crisis
0.35
Tranquil
P24
0.32
0.18
P12
Crisis
0.23
0.00
Post crisis
Crisis
0.13
0.65
Pre crisis
Post crisis
Post crisis
Crisis
P6
Pre crisis
Tranquil
Pre crisis
Crisis
C0
0.00
Tranquil
Post crisis
Crisis
0.26
C6
Pre crisis
Post crisis
Crisis
0.01
C12
Crisis
0.55
0.82
0.00
0.09
0.18
0.27
Clustering is performed using hierarchical clustering based on class
variables. The map is partitioned into four clusters according to the financial
stability cycle: a pre-crisis, crisis, post-crisis and tranquil cluster.
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3. Mapping the State of Financial Stability – The distribution of 14
indicators across the 4 clusters
0.17
0.41
0.29
0.52
0.64
0.76
0.14
0.27
0.41
0.55
0.68
0.80
0.19
0.32
0.46
0.59
0.86
0.08
0.61
0.76
0.25
0.14
0.30
0.60
0.75
0.57
0.73
0.90
0.13
0.28
0.14
0.85
0.18
0.52
0.14
0.83
0.17
0.57
0.71
0.86
0.15
0.31
0.56
0.46
0.61
0.76
0.92
0.11
0.25
0.39
0.52
0.80
Tranquil
Pre crisis
Post crisis
Post crisis
0.18
0.66
Tranquil periods
Tranquil
0.06
0.81
Crisis
Post-crisis periods
0.70
0.68
Tranquil
Crisis
Crisis
0.42
0.55
Post crisis
Pre crisis
0.28
0.43
Global real equity growth
Crisis
0.42
0.30
Pre crisis
Tranquil
0.00
0.70
Tranquil
Post crisis
0.65
0.57
Global real credit growth
Crisis
0.39
0.44
Post crisis
Pre crisis
0.27
0.31
Pre crisis
Tranquil
0.01
0.71
Crisis periods
Post crisis
0.91
0.57
Crisis
0.41
Crisis
Tranquil
Crisis
0.45
0.43
Post crisis
Pre crisis
Post crisis
0.91
0.30
Global real GDP growth
Pre-crisis periods
Crisis
0.46
0.16
Pre crisis
Tranquil
Crisis
0.31
0.72
Pre crisis
Post crisis
0.85
Crisis
Tranquil
Pre crisis
0.71
Post crisis
Global equity valuation
Global leverage
0.58
Tranquil
Crisis
0.55
0.45
Pre crisis
Post crisis
Crisis
0.43
0.32
Global inflation
Pre crisis
Post crisis
0.16
0.18
Tranquil
Tranquil
Pre crisis
0.31
0.83
Government deficit
CA deficit
0.19
0.69
Post crisis
Crisis
Crisis
Crisis
Crisis
Crisis
Pre crisis
Post crisis
Post crisis
Post crisis
Post crisis
Post crisis
Tranquil
Tranquil
Pre crisis
Pre crisis
Pre crisis
Pre crisis
Tranquil
Tranquil
Tranquil
Tranquil
Pre crisis
Equity valuation
Leverage
Real equity growth
Real credit growth
Real GDP growth
Inflation
0.29
0.40
0.52
0.63
0.02
0.18
0.34
0.50
0.66
0.82
• Domestic: early signs of crisis - equity growth and valuation, budget deficit, followed by real
GDP and credit growth, leverage, budget surplus, and CA deficit.
•Global: early signs of crisis - equity growth and level, followed by real GDP growth, while
global credit growth and leverage are more concurrent with crises.
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3. Mapping the State of Financial Stability – Temporal dimension
Evolution of macro-financial conditions (all 14 indicators) for
the United States and the Euro area (2002-10, first quarter)
US
2006
Pre crisis
US
2002
2010
US
2007
Euro
2006
Euro
2007
Tranquil
US
2008–09
Euro
2008
Crisis
Euro
2002
US
2004–05 Euro area
aggregate,
did not
Euro reflect the
2004–05 crisis in GR,
IE, PT.
Euro
2010
Post crisis
US
2003
Euro
2003
Financial
Stress Index
also
decreased
for the euro
area
aggregate
Euro
2009
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3. Mapping the State of Financial Stability – Cross section
Visualizing current macro-financial vulnerabilities in
key advanced and emerging economies (2010Q3)
Mexico ArgentinaTaiwan Malaysia
Singapore
Turkey Brazil
Philippines South Africa
India
Contagion
through
similarities in
macro-financial
vulnerabilities
SOFSM enables
identifying
events surpassing
historical
experience
Tranquil
Pre crisis
Post crisis
Crisis
UK Indonesia
Thailand
Japan
Canada
Czech Republic China
Poland
Hong Kong
Switzerland
Norway
Denmark
Euro area
US
Korea
Sweden
Russia
Australia
New Zealand
Hungary
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3. Mapping the State of Financial Stability – Regional evolution
Evolution of the macro-financial conditions in Emerging Market
Economies and Advanced Economies (2002-10 , first quarter)
EME
2005
Tranquil
Pre-crisis
Tranquil
AE
2004
Pre crisis
EME
2004
AE
2005
Post-crisis
EME AE
2006 2006
2007
AE
2007
AE
2008
EME
Crisis
2008
Post crisis
EME
2010
AE
2010
AE
2002
EME
2002
AE
2009
Crisis
EME
2009
AE
2003
EME
2003
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4. Conclusions
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Self-Organizing Financial Stability Map is a useful model for
financial stability surveillance:
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mapping the state of financial stability and visualizing
multidimensional macro-financial vulnerabilities
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has good out-of-sample predictive capabilities of future
systemic events / financial crises (EWS)
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the SOFSM is flexible with respect to, e.g., events of
interest, vulnerability indicators, forecast horizons,
policymaker‘s preferences
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Thank you for your attention!
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