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Mapping the State of Financial Stability

14th Annual DNB Research Conference3rd November 2011DNB, Amsterdam

Peter Sarlin (Åbo Akademi / TUCS) &Tuomas Peltonen (European Central Bank)

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An example of a SOM output at certain timeAn example of a SOM output at certain time

Taiwan

India

UK Indonesia

Japan Thailand

Canada

Russia Czech Republic

Poland Norway

Hungary

China Hong Kong Switzerland

Australia New Zealand

US

Denmark Euro area

Korea Sweden

Argentina Brazil

Mexico Turkey

Malaysia Philippines

Singapore South Africa

Crisis

Post crisis

Tranquil

Pre crisis

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1. Introduction - 1. Introduction - What do we do in the paper?What do we do in the paper?

• Create the Create the Self-Organizing Financial Stability Map Self-Organizing Financial Stability Map (SOFSM)(SOFSM)

• A model that can A model that can visualize multidimensional visualize multidimensional macro-financial vulnerabilities and the state of macro-financial vulnerabilities and the state of financial stability financial stability across countries and over across countries and over timetime

• A model that has A model that has good out-of-sample predictive good out-of-sample predictive capabilities of future capabilities of future systemic events systemic events / financial / financial crisescrises

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2. Self-Organizing Financial Stability Map (SOFSM)2. Self-Organizing Financial Stability Map (SOFSM)

• Building blocks for creating the SOFSM:Building blocks for creating the SOFSM:• Self-Organizing MapsSelf-Organizing Maps• Identifying systemic eventsIdentifying systemic events• Vulnerability indicatorsVulnerability indicators• Model training Model training • Model evaluationModel evaluation

• Mapping the State of Financial StabilityMapping the State of Financial Stability

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2.1 Self-Organizing Maps (SOMs)2.1 Self-Organizing Maps (SOMs) – – what are they? what are they?

• SOMSOM is an is an Exploratory Data AnalysisExploratory Data Analysis (EDA) technique (EDA) technique

by Kohonen (1981) ➨ Viscovery SOMineby Kohonen (1981) ➨ Viscovery SOMine• It is a It is a clusteringclustering and and projectionprojection technique: technique:

– Spatially constrained form of Spatially constrained form of kk-means clustering-means clustering– Preserves the Preserves the neighbourhood relations of the data neighbourhood relations of the data

(instead of trying to preserve the distances between data)(instead of trying to preserve the distances between data)– Projects data onto a grid of nodesProjects data onto a grid of nodes (rather than projecting (rather than projecting

data into a continuous space)data into a continuous space)

• Enables visualization of Enables visualization of high-D datahigh-D data ➨ ➨ 2D grid2D grid of of nodes without losing the topological relationships of nodes without losing the topological relationships of data and sight of individual indicators. data and sight of individual indicators.

• Enables a Enables a flexible distribution and interactions.flexible distribution and interactions.• Kohonen’s group has continuously reviewed the SOM Kohonen’s group has continuously reviewed the SOM

literatureliterature• The SOM has been used in approx. 10 000 worksThe SOM has been used in approx. 10 000 works• Applied to currency and debt crises: Arciniegas and Applied to currency and debt crises: Arciniegas and

Arciniegas Rueda (2009), Resta (2009), Sarlin (2011) and Arciniegas Rueda (2009), Resta (2009), Sarlin (2011) and Sarlin and Marghescu (2011)Sarlin and Marghescu (2011)

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2.1 Self-Organizing Maps (SOMs)2.1 Self-Organizing Maps (SOMs) – – training algorithm training algorithm

mb

xj

Radius of the neighborhood σ

1. 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)

2. Update each node mi to averages of the attracted data, including data located in a specified neighbourhood σ

3. 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) –2.1 Self-Organizing Maps (SOMs) – interpreting the interpreting the outputoutput

• This is a This is a 2D map 2D map that that represents multi-D data with represents multi-D data with a 2-level clusteringa 2-level clustering

• For each indicator, we For each indicator, we create a create a „feature plane“ „feature plane“ where the color coding where the color coding represents the represents the distributiondistribution of its values on the 2D mapof its values on the 2D map..

Indicator 1Indicator 1 Indicator 2 Indicator 3 Indicator 2 Indicator 3 Indicator 4 Indicator 4

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2.2 Identifying systemic events and creating financial 2.2 Identifying systemic events and creating financial stability cyclestability cycle

• Use the data set from Use the data set from Lo Duca and Peltonen (2011)Lo Duca and Peltonen (2011): : 28 28

countries (18 EMEs & 10 AEs), Quarterly data 1990Q1-countries (18 EMEs & 10 AEs), Quarterly data 1990Q1-2010Q32010Q3

• Identification of Identification of systemic eventssystemic events::• The The Financial Stress Index (FSI)Financial Stress Index (FSI) includes 5 components for includes 5 components for

each country, measuring volatilities and sharp declines in each country, measuring volatilities and sharp declines in key market segments (stock, foreign exchange and money key market segments (stock, foreign exchange and money markets)markets)

• A systemic event occurs when the FSI is above the 90A systemic event occurs when the FSI is above the 90thth percentile of the country-specific distribution (on average, percentile of the country-specific distribution (on average, negative real consequences)negative real consequences)

• Using the FSI, we identify four classes to describe the Using the FSI, we identify four classes to describe the financial stability cyclefinancial stability cycle::

• Pre-crisisPre-crisis periods (18 months before the systemic event) periods (18 months before the systemic event)• CrisisCrisis periods (systemic events defined by a financial periods (systemic events defined by a financial

stress index)stress index)• Post-crisisPost-crisis periods (18 months after the systemic event) periods (18 months after the systemic event)• Tranquil Tranquil periods (all other periods)periods (all other periods)

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2.3 Vulnerability indicators2.3 Vulnerability indicators

• 14 indicators of country-level 14 indicators of country-level macro-financial macro-financial vulnerabilitiesvulnerabilities::

• DomesticDomestic = inflation, GDP growth, CA deficit, budget = inflation, GDP growth, CA deficit, budget balance, credit growth, leverage, equity price growth, balance, credit growth, leverage, equity price growth, equity valuationequity valuation

• GlobalGlobal = = inflation, GDP growth, credit growth, inflation, GDP growth, credit growth, leverage, equity price growth, equity valuationleverage, equity price growth, equity valuation

• Test several Test several transformationstransformations of the indicators (over 200 of the indicators (over 200 transformations of the indicators tested). transformations of the indicators tested).

• Select best-performing (as a leading indicator) Select best-performing (as a leading indicator) transformations of the variablestransformations of the variables

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2.4 Model training2.4 Model training

• „„Static“ modelStatic“ model, i.e. model is not re-, i.e. model is not re-

estimated recursively:estimated recursively:• Training set (estimation sample): 1990Q4 - Training set (estimation sample): 1990Q4 -

2005Q12005Q1• Test set (out-of-sample): 2005Q2 - 2009Q2Test set (out-of-sample): 2005Q2 - 2009Q2• In the benchmark, we use 18 months as a In the benchmark, we use 18 months as a

forecast horizonforecast horizon• Account for policymakers’ preferences Account for policymakers’ preferences

when evaluating the performance as in when evaluating the performance as in Alessi and Detken (2011) (benchmark Alessi and Detken (2011) (benchmark μμ=0.5=0.5) )

• Data as anData as an input to the SOFSMinput to the SOFSM• Class variables + vulnerabilities for Class variables + vulnerabilities for

trainingtraining• Only vulnerabilities for mapping and Only vulnerabilities for mapping and

evaluatingevaluating

• Crisis probabilities as an output of Crisis probabilities as an output of the SOFSMthe SOFSM

• Map data onto SOFSM and retrieve a crisis Map data onto SOFSM and retrieve a crisis probabilityprobability

Crisis

TranquilPre crisis

Post crisis

Euro area

C18

Crisis

TranquilPre crisis

Post crisis

Euro area

0.01 0.10 0.19 0.28 0.38 0.47 0.56 0.65

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2.5 Model evaluation2.5 Model evaluation

• Defining early warning nodesDefining early warning nodes• When calibrating the policymakers’ preferences, we When calibrating the policymakers’ preferences, we

vary the thresholds. This changes the number of “early vary the thresholds. This changes the number of “early warning nodes”.warning nodes”.

µ µ =0.4=0.4 µ µ =0.5=0.5 µ µ =0.6=0.6

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Data set μ Precision Recall Precision Recall AUCLogit Train 0.5 162 190 830 73 0.46 0.69 0.92 0.81 0.79 0.25 0.81SOM Train 0.5 190 314 706 45 0.38 0.81 0.94 0.69 0.71 0.25 0.83

Logit Test 0.5 77 57 249 93 0.57 0.45 0.73 0.81 0.68 0.13 0.72SOM Test 0.5 112 89 217 58 0.56 0.66 0.79 0.71 0.69 0.18 0.75

Tranquil periods

Accuracy UModel TP FP TN FN

Crash periods

2.5 Model evaluation2.5 Model evaluation

• Training the SOM:Training the SOM:• While a higher number of nodes While a higher number of nodes M M improves in-sample improves in-sample performance, it decreases generalization, i.e. out-of-sample performance, it decreases generalization, i.e. out-of-sample performance.performance.• We increase We increase MM and find and find the first model with Usefulness ≥ 0.25 the first model with Usefulness ≥ 0.25 (logit model).(logit model).

• In terms of “In terms of “UsefulnessUsefulness”, when ”, when µµ=0.5, the models are by =0.5, the models are by definition very similar on in-sample data, while the SOM performs definition very similar on in-sample data, while the SOM performs better on out-of-sample data better on out-of-sample data • Robustness is tested with respect to three aspectsRobustness is tested with respect to three aspects

• SOM parameters: radius of neighborhood and number of SOM parameters: radius of neighborhood and number of nodesnodes• Policymakers’ preferencesPolicymakers’ preferences• Forecast horizonForecast horizon

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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Crisis

TranquilPre crisis

Post crisis

3. Mapping the State of Financial Stability – The two 3. Mapping the State of Financial Stability – The two dimensional SOFSMdimensional SOFSM

• This is the 2D SOFSM that represents multi-D data.This is the 2D SOFSM that represents multi-D data.• The stages of the financial stability cycle are derived The stages of the financial stability cycle are derived

using only the class variables (pre-crisis, crisis, post-using only the class variables (pre-crisis, crisis, post-crisis and tranquil periods)crisis and tranquil periods)

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C24

Pre crisisTranquil

Crisis

Post crisis

0.01 0.26 0.50 0.75

C18

Pre crisisTranquil

Crisis

Post crisis

0.01 0.22 0.44 0.65

C12

Pre crisisTranquil

Crisis

Post crisis

0.00 0.18 0.35 0.53

C6

Pre crisisTranquil

Crisis

Post crisis

0.00 0.11 0.21 0.32

C0

Pre crisisTranquil

Crisis

Post crisis

0.00 0.23 0.47 0.70

P6

Pre crisisTranquil

Crisis

Post crisis

0.00 0.11 0.22 0.33

P12

Pre crisisTranquil

Crisis

Post crisis

0.01 0.18 0.35 0.52

P18

Pre crisisTranquil

Crisis

Post crisis

0.06 0.25 0.44 0.63

P24

Pre crisisTranquil

Crisis

Post crisis

0.13 0.32 0.50 0.68

T0

Pre crisisTranquil

Crisis

Post crisis

0.02 0.29 0.55 0.82

PPC0

Pre crisisTranquil

Crisis

Post crisis

0.00 0.09 0.18 0.27

3. Mapping the State of Financial Stability – Constructing 3. Mapping the State of Financial Stability – Constructing the four clusters according to the financial stability cyclethe four clusters according to the financial stability cycle

• Clustering is performed using hierarchical clustering based on Clustering is performed using hierarchical clustering based on class variables. class variables. The map is partitioned into four clusters The map is partitioned into four clusters according to the according to the financial stability cycle:financial stability cycle: a pre-crisis, crisis, a pre-crisis, crisis, post-crisis and tranquil cluster.post-crisis and tranquil cluster.

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Inflation

Pre crisis

Crisis

Post crisis

Tranquil

0.17 0.29 0.41 0.52 0.64 0.76

Real GDP growth

Pre crisis

Crisis

Post crisis

Tranquil

0.14 0.27 0.41 0.55 0.69 0.83

Real credit growth

Pre crisis

Crisis

Post crisis

Tranquil

0.18 0.32 0.45 0.58 0.71 0.85

CA deficit

Pre crisis

Crisis

Post crisis

Tranquil

0.19 0.31 0.43 0.55 0.68 0.80

Government deficit

Pre crisis

Crisis

Post crisis

Tranquil

0.19 0.32 0.46 0.59 0.72 0.86

Global inflation

Pre crisis

Crisis

Post crisis

Tranquil

0.08 0.25 0.41 0.57 0.73 0.90

Global leverage

Pre crisis

Crisis

Post crisis

Tranquil

0.16 0.31 0.46 0.61 0.76 0.91

Global equity valuation

Pre crisis

Crisis

Post crisis

Tranquil

0.14 0.30 0.45 0.60 0.75 0.91

Pre-crisis periods

Pre crisis

Crisis

Post crisis

Tranquil

0.01 0.14 0.27 0.39 0.52 0.65

Real equity growth

Pre crisis

Crisis

Post crisis

Tranquil

0.16 0.30 0.43 0.57 0.71 0.85

Leverage

Pre crisis

Crisis

Post crisis

Tranquil

0.18 0.31 0.44 0.57 0.70 0.83

Equity valuation

Pre crisis

Crisis

Post crisis

Tranquil

0.17 0.30 0.43 0.55 0.68 0.81

Global real GDP growth

Pre crisis

Crisis

Post crisis

Tranquil

0.13 0.28 0.42 0.57 0.71 0.86

Global real credit growth

Pre crisis

Crisis

Post crisis

Tranquil

0.15 0.31 0.46 0.61 0.76 0.92

Global real equity growth

Pre crisis

Crisis

Post crisis

Tranquil

0.11 0.25 0.39 0.52 0.66 0.80

Crisis periods

Pre crisis

Crisis

Post crisis

Tranquil

0.00 0.14 0.28 0.42 0.56 0.70

Post-crisis periods

Pre crisis

Crisis

Post crisis

Tranquil

0.06 0.18 0.29 0.40 0.52 0.63

Tranquil periods

Pre crisis

Crisis

Post crisis

Tranquil

0.02 0.18 0.34 0.50 0.66 0.82

3. Mapping the State of Financial Stability – The 3. Mapping the State of Financial Stability – The distribution of 14 indicators across the 4 clustersdistribution of 14 indicators across the 4 clusters

• Domestic:Domestic: early signs of crisis - early signs of crisis - equity growth and valuation, budget deficitequity growth and valuation, budget deficit, , followed by followed by real GDP and credit growth, leverage, budget surplus, and CA real GDP and credit growth, leverage, budget surplus, and CA deficitdeficit. . •Global:Global: early signs of crisis - early signs of crisis - equity growth and levelequity growth and level, followed by , followed by real GDPreal GDP growthgrowth, while , while global credit growth and leverage global credit growth and leverage are more concurrent with are more concurrent with crises.crises.

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3. Mapping the State of Financial Stability – Temporal 3. Mapping the State of Financial Stability – Temporal dimensiondimension

Evolution of macro-financial conditions (all 14 indicators) for the United States and the Euro area (2002-10, first quarter)

Euro area aggregate, did not reflect the crisis in GR, IE, PT.

Financial Stress Index also decreased for the euro area aggregateCrisis

TranquilPre crisis

Post crisis

US20022010

US2008–09

US2007

US2006

US2004–05

US2003

Euro2002

Euro2003

Euro2004–05

Euro2006

Euro2007

Euro2008

Euro2009

Euro2010

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Taiwan

India

UK Indonesia

Japan Thailand

Canada

Russia Czech Republic

Poland Norway

Hungary

China Hong Kong Switzerland

Australia New Zealand

US

Denmark Euro area

Korea Sweden

Argentina Brazil

Mexico Turkey

Malaysia Philippines

Singapore South Africa

Crisis

Post crisis

Tranquil

Pre crisis

3. Mapping the State of Financial Stability – Cross 3. Mapping the State of Financial Stability – Cross sectionsection

Visualizing current macro-financial vulnerabilities in key advanced and emerging economies (2010Q3)

Contagion through similarities in macro-financial vulnerabilities

SOFSM enables identifying events surpassing historical experience

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3. Mapping the State of Financial Stability – Regional 3. Mapping the State of Financial Stability – Regional evolutionevolution

Evolution of the macro-financial conditions in Emerging Market Economies and Advanced Economies (2002-10 , first quarter)

Pre-crisis

Crisis

Post-crisis

Tranquil

Crisis

Pre crisis

Post crisis

EME 2005

AE 2004

EME 2004 AE

2005

AE 2006

AE 2010

AE 2007

EME 2010

AE 2002

EME 2002

EME 2008

AE 2008

AE 2003

EME 2003

EME 2006 2007

Tranquil

AE 2009

EME 2009

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4. Conclusions4. Conclusions

• Self-Organizing Financial Stability Map Self-Organizing Financial Stability Map is a useful is a useful model for financial stability surveillance:model for financial stability surveillance:

• mapping the state of financial stability mapping the state of financial stability and and visualizing multidimensional macro-financial visualizing multidimensional macro-financial vulnerabilitiesvulnerabilities

• has has good out-of-sample predictive good out-of-sample predictive capabilities capabilities of future of future systemic events systemic events / financial crises / financial crises (EWS)(EWS)

• the SOFSM is flexible with respect to, e.g., the SOFSM is flexible with respect to, e.g., events of interest, vulnerability indicators, events of interest, vulnerability indicators, forecast horizons, policymaker‘s preferencesforecast horizons, policymaker‘s preferences

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Thank you for your attention!Thank you for your attention!