Predicting vulnerabilities in the EU banking sector : the role of global and domestic factors. No 29 / November 2016.
Date: 2016-12-15
Institutions: European Systemic Risk Board
Subjects: bank, credit policy, economic model, macroeconomics, monetary crisis, public policy

Working Paper Series 

No 29 / November 2016 

Predicting vulnerabilities 
in the EU banking sector: 
the role of global and 
domestic factors 

by 
Markus Behn 
Carsten Detken 
Tuomas Peltonen 
Willem Schudel 

 
Abstract

We estimate a multivariate early-warning model to assess the usefulness of private credit and
other macro-ﬁnancial variables in predicting banking sector vulnerabilities. Using data for 23
European countries, we ﬁnd that global variables and in particular global credit growth are
strong predictors of domestic vulnerabilities. Moreover, domestic credit variables also have
high predictive power, but should be complemented by other macro-ﬁnancial indicators like
house price growth and banking sector capitalization that play a salient role in predicting
vulnerabilities. Our ﬁndings can inform decisions on the activation of macroprudential policy
measures and suggest that policy makers should take a broad approach in the analytical
models that support risk identiﬁcation and calibration of tools.
Keywords: early-warning model; banking crises; signalling approach; systemic risk
JEL classiﬁcation: G01, G21, G28

Non-technical summary

In this paper, we assess the usefulness of credit and other macro-ﬁnancial variables for the
prediction of banking sector vulnerabilities in a multivariate framework. Using data for 23
European countries, we ﬁnd that global variables and in particular global credit variables are
strong predictors of macro-ﬁnancial vulnerabilities, providing good signals when used as single
indicators and demonstrating consistent and signiﬁcant eﬀects in multivariate logit models. This
concurs with the view that excessive global liquidity was one of the factors that contributed to the
accumulation of ﬁnancial vulnerabilities ahead of the global ﬁnancial crisis (see, e.g., Committee
on the Global Financial System 2011, International Monetary Fund 2013). The domestic credit-
to-GDP also predicts vulnerabilities, although the eﬀect is smaller than for the global credit
variables.

Despite the importance of credit variables, we also ﬁnd evidence suggesting that other vari-
ables play a salient role in predicting vulnerable states of the economy. For example, domestic
house price growth and global equity growth are positively associated with macro-ﬁnancial vul-
nerabilities. Moreover, banking sector variables exert signiﬁcant eﬀects: Strong banking sector
proﬁtability may incur excessive risk-taking, leading to increased vulnerability, while a high
banking sector capitalisation decreases the probability of entering a vulnerable state. This re-
sult is important for policy makers involved in setting the CCB, as it reinforces the notion that
higher bank capital ratios reduce the likelihood of ﬁnancial vulnerability.

The results illustrate that even though credit variables are essential ingredients of early
warning models, other macro-ﬁnancial and banking sector variables are important covariates to
control for and to improve the predictive power of these models. Moreover, in an increasingly
integrated economy, vulnerabilities that develop at a global level potentially transmit to countries
around the world and should hence be taken into account by policy makers. Overall, policy
makers should take a broad approach in the analytical models that support decisions on the
activation of tools instead of focusing only on the domestic credit-to-GDP gap to assess the level
of cyclical systemic risk.

1

1

Introduction

Being faced with the longest and most severe ﬁnancial crisis in decades, policy makers around the
globe have actively searched for tools which could help to prevent or at least reduce the intensity
of future ﬁnancial crises. One such tool is the countercyclical capital buﬀer (CCB), which aims
to address cyclical systemic risk and is an integral part of the Basel III regulations and the EU
Capital Requirements Directive (CRD IV). To measure the level of cyclical systemic risk, the
Basel III framework promotes a methodology based on the ratio of aggregate credit to GDP
(Basel Committee on Banking Supervision 2010), which has consequently featured prominently
in policy decisions around the globe. However, while credit growth and the credit-to-GDP ratio
are clearly important determinants of cyclical systemic risk, there are a number of other factors
that can also indicate a build-up of vulnerabilities, which provides the motivation for this paper.

We assess the usefulness of credit and other macro-ﬁnancial variables for the prediction of
banking sector vulnerabilities in a multivariate framework, hence enabling a more informed
decision on the activation of the CCB. The Basel Committee on Banking Supervision (BCBS)
guidelines are based on an analysis that uses a sample of 26 countries from all over the world, for
which the credit-to-GDP gap (deﬁned as the deviation of the credit-to-GDP ratio from its long-
term trend) performs as the best single indicator in terms of signalling a coming ﬁnancial crisis.
However, the guidelines (or the underlying work by Drehmann et al. 2011) rely on individual
indicators and do not compare the predictive power of the credit-to-GDP gap to that of other
potentially relevant variables related to risks to ﬁnancial stability in a multivariate framework.1
Acknowledging the potentially very large implications that this policy has for the international
banking sector, our paper aims to ﬁll this gap by estimating a multivariate early-warning model
that includes private credit and other macro-ﬁnancial and banking sector variables.

Our ﬁndings suggest that global variables and in particular global credit variables are strong
predictors of macro-ﬁnancial vulnerabilities, providing good signals when used as single indi-
cators and demonstrating consistent and signiﬁcant eﬀects in multivariate logit models. This
concurs with the view that excessive global liquidity was one of the factors that contributed
to the accumulation of ﬁnancial vulnerabilities ahead of the global ﬁnancial crisis (see, e.g.,
Committee on the Global Financial System 2011, International Monetary Fund 2013). The
domestic credit-to-GDP also predicts vulnerabilities, although the eﬀect is smaller than for the
global credit variables. Despite the importance of credit variables, we also ﬁnd evidence sug-
gesting that other variables play a salient role in predicting vulnerable states of the economy.

1Several other potential shortcomings of the credit-to-GDP gap have been discussed in the literature. For
example, Edge and Meisenzahl (2011) argue that gap measures are sensitive to the exact speciﬁcation of the
trending variable, in particular with regards to end-of-sample estimates of the credit-to-GDP ratio. For other
critical views on the reliability or suitability of the credit-to-GDP gap in the context of the CCB, see for example
Repullo and Saurina (2011) and Seidler and Gersl (2011).

2

For example, domestic house price growth and global equity growth are positively associated
with macro-ﬁnancial vulnerabilities. Moreover, banking sector variables exert signiﬁcant eﬀects:
Strong banking sector proﬁtability may incur excessive risk-taking, leading to increased vulnera-
bility, while a high banking sector capitalisation decreases the probability of entering a vulnerable
state. This result is important for policy makers involved in setting the CCB, as it reinforces
the notion that higher bank capital ratios reduce the likelihood of ﬁnancial vulnerability.

The results illustrate that even though credit variables are essential ingredients of early
warning models, other macro-ﬁnancial and banking sector variables are important covariates to
control for and to improve the predictive power of these models. Moreover, in an increasingly
integrated economy, vulnerabilities that develop at a global level potentially transmit to countries
around the world and should hence be taken into account when determining CCB rates. The
Basel III/CRD IV framework accounts for this by ensuring that the institution-speciﬁc CCB rate
is calculated as a weighted average of CCB rates in countries to which the bank has exposures.
Overall, policy makers should take a broad approach in the analytical models that support
decisions on the activation of tools instead of focusing only on the domestic credit-to-GDP gap.

Our paper adds to the literature on early-warning models for ﬁnancial and banking crises
(see Alessi et al. 2015 and Holopainen and Sarlin 2016 for recent papers conducting horse races
among existing methods). It builds on the so-called ‘signalling approach’, originally developed
by Kaminsky et al. (1998), and extended by Demirg¨u¸c-Kunt and Detragiache (2000), Alessi and
Detken (2011), Lo Duca and Peltonen (2013), Sarlin (2013), and features a multivariate logit
model to identify vulnerabilities in the banking system (see, e.g., Barrell et al. 2010, Babecky
et al. 2014, Karim et al. 2013). As a traditional early-warning model, our approach rests on the
translation of predicted crisis probabilities from the logit model into binary signals that can then
be evaluated given policy maker’s preferences between type I (missing a crisis) and type II errors
(false alarms of crises). Other recent contributions to the early-warning literature have focused
on exploiting diﬀerent methodologies to extract warning signals (Alessi and Detken 2014, Ferrari
and Pirovano 2015), characterisations of the ﬁnancial cycle (Drehmann et al. 2012, Sch¨uler
et al. 2015, Galati et al. 2016), or machine learning approaches (Lin et al. 2008, Holopainen
and Sarlin 2016). While previous studies using multivariate early-warning models often focused
on emerging markets (e.g., Frankel and Rose 1996, Demirg¨u¸c-Kunt and Detragiache 1998, 2000,
Manasse et al. 2016) or a few large economies or individual countries (e.g., Hanschel and Monnin
2005, Ito et al. 2014, Castro et al. 2016) our analysis is conducted for a sample of 23 EU Member
States spanning over the period from 1982 to 2012, hence informing possible decisions on CCB
rates in EU countries.

The remainder of the paper is organised as follows: We present our data set in Section 2 and
introduce the methodology in Section 3. Estimation results and robustness checks are presented
in Section 4, while Section 5 is reserved for our concluding remarks.

3

2 Data

This section introduces the data used for our study. We begin with the identiﬁcation of vulner-
able states, i.e., the dependent variable in the study, based on banking crises in the European
Union. We then proceed by introducing the independent variables used in the empirical analy-
sis. Finally, we present some descriptive statistics on the development of key variables around
banking sector crises in the sample countries.

2.1 Deﬁnition of vulnerable states

The paper develops an early warning model that attempts to predict vulnerable states of the
economy from which—given a suitable trigger—banking crises could emerge. Thus, we are not
trying to predict banking crises per se, even though we need to identify these crises in order to
determine the vulnerable states. Speciﬁcally, we deﬁne a vulnerable state as the period twelve
to seven quarters before the onset of a banking crisis. The time horizon accounts for the CCB
announcement period of twelve months that is speciﬁed in Art. 126(6) of the CRD IV, and for
a time lag required to impose such a policy. At the same time, extending the horizon too far
into the past may weaken the link between observed variation in the independent variables and
the onset of banking crises. To analyse this, we provide a number of alternative time horizons
in the robustness section.

In order to identify banking crises, we use the dataset which has been compiled by Babecky
et al. (2014) as part of a data collection exercise by the European System of Central Banks
(ESCB) Heads of Research Group (labeled as HoR database hereafter). This quarterly database
contains information on banking crises in EU countries (except Croatia) between 1970Q1 and
2012Q4. The crisis index takes a value of 1 when a banking crisis occurred in a given quarter
(and a value of 0 when no crisis occurred). The HoR database aggregates information on banking
crises from “several inﬂuential papers”, including (in alphabetical order): Caprio and Klingebiel
(2003); Detragiache and Spilimbergo (2001); Kaminsky (2006); Kaminsky and Reinhart (1999);
Laeven and Valencia (2008, 2010, 2012); Reinhart and Rogoﬀ (2011, 2013); and Yeyati and
Panizza (2011). The crisis indices from these papers have subsequently been cross-checked with
the ESCB Heads of Research before inclusion into the database. A list of the banking crisis
dates for our sample countries based on this dataset is provided in Table 1. In the robustness
section, we test the robustness of the results by regressing the benchmark model on banking
crisis data provided by Reinhart and Rogoﬀ (2011) and Laeven and Valencia (2012).

We set the dependent variable to 1 between (and including) twelve to seven quarters prior to
a banking crisis as identiﬁed by the ESCB HoR database and to 0 for all other quarters in the

4

data. In order to overcome crisis and post-crisis bias (see e.g. Bussi`ere and Fratzscher 2006),
we omit all country quarters which either witnessed a banking crisis or which fall within six
quarters after a banking crisis.

2.2 Macro-ﬁnancial and banking sector variables

The panel dataset used in the analysis contains quarterly macro-ﬁnancial and banking sector
data spanning over 1982Q2-2012Q3 for 23 EU member states. The data is sourced through Haver
Analytics and originally comes from the BIS, Eurostat, IMF, ECB, and OECD (see Appendix 1
for a detailed description). Table 1 provides an overview of the data availability for our main
variables, while Table 2 gives descriptive statistics for the variables included in our study.

Accelerated credit growth is one of the key variables in the Basel III/CRD IV framework, as
it is seen as a sign of overheating that may be associated with systemic events in the banking
sector (see also, e.g., Schularick and Taylor 2012, Drehmann and Juselius 2014, or L´opez-Salido
et al. 2016). To measure credit growth and levels, we follow Drehmann et al. (2011) and use the
long series on total credit and domestic bank credit to the private non-ﬁnancial sector compiled
by the BIS. This data includes borrowing from non-ﬁnancial corporations, households and non-
proﬁt institutions serving households. It aims to capture all sources of lending, independent of
the country of origin or type of lender, and includes loans and debt securities such as bonds
and securitised loans (see Dembiermont et al. 2013 for a description of the database). To our
knowledge, the BIS credit series oﬀers the broadest deﬁnition of credit provision to the private
sector, while having been adjusted for data gaps and structural breaks. Our models account
for credit growth and leverage, both at the domestic and at the global level. Credit growth is
measured as a percentage (annual growth), while leverage is measured by the deviation of the
credit-to-GDP ratio (using nominal GDP data) from its long-term backward-looking trend (see
Appendix 1 for details on the calculation). Global credit variables have been computed using
a GDP-weighted average of the variable in question for several countries, including the United
States, Japan, Canada, and all European countries which are in this study (see also Alessi and
Detken 2011).

In order to test the importance of credit variables in a comparative fashion as well as to
analyse the potential importance of other factors, we include a number of additional variables in
our study. These variables are available for fewer observations than the credit variables, which
is why the number of observations in the full model diﬀers from the number of observations in
models that include only credit variables (estimating credit models on the reduced sample yields
results that are very similar to the ones for the full sample). To account for the macroeconomic
environment and monetary stance, we include nominal GDP growth (domestic and global) and
CPI inﬂation rates. Furthermore, we use data on annual equity and residential house price

5

growth, both domestically and globally, to account for the common view that asset price booms
can be associated with a build-up of vulnerabilities in the banking sector (see, e.g., Allen and
Gale 2009, Brunnermeier and Oehmke 2013, or Jord`a et al. 2015). Finally, to control for
banking sector proﬁtability and solvency, we include aggregate bank capitalisation (calculated
by the ratio of equity over total assets) and aggregate banking sector proﬁtability (deﬁned as
net income before tax as a percentage of total assets).

As we are estimating binary choice models using panel data, non-stationarity of independent
variables could be an issue (Park and Phillips 2000). We perform panel unit root tests suggested
by Im et al. (2003) as well as univariate unit root tests developed by Dickey and Fuller (1979)
in order to analyse the time series properties of the variables of interest. In the panel unit root
test, the null hypothesis that all cross-sections contain unit roots can be rejected at least at the
10 percent level for all series except for the credit-to-GDP gap and global credit growth. We
complement the panel unit root analysis by using the Dickey and Fuller (1979) test country-by-
country, and can reject the null hypothesis of a unit root for the credit-to-GDP gap at least at
the 10 percent level for all countries except for Estonia, Lithuania and Greece. Furthermore, in
the country-by-country unit root tests, we can reject the null hypothesis for the global credit-
to-GDP gap at least at the 10 percent level for all countries except for Estonia and Lithuania,
while for global credit growth the null hypothesis can be rejected for all countries. This implies
that sample periods for individual countries seem to aﬀect unit root test results. Overall, the
transformations done to the original variables, the results from the unit root tests and general
economic theory make us conﬁdent that we have addressed potential non-stationarity concerns
for the variables of interest.

2.3 Development of the key variables

Before entering the discussion of the main results, we shortly present some descriptive statistics,
which provide the context of our main argument of moving beyond credit variables when predict-
ing macro-ﬁnancial vulnerabilities. Figure 1 presents the average development of the six main
variables of interest over time before and after the onset of a banking crisis. For the purpose
of predicting crises, one would hope to ﬁnd an indicator variable that (on average) peaks (or
bottoms out, or at least changes direction) a number of quarters before a crisis, so that it can
be used as a signal. In the current case of predicting a vulnerable state of the economy which
precedes a potential banking crisis, we would be interested in variables that change direction a
bit earlier before the onset of a crisis (i.e., two to three years before the crisis), so that policy
makers can use this time to increase the resilience of banks.

In this context, we observe that among the six variables depicted here, the credit-to-GDP
gap shows one of the least clear pictures in terms of signalling a coming crisis. On average,

6

the credit gap increases slowly prior to a banking crisis and only starts falling about one year
into the crisis. Yet, this does not need to be a very surprising development, as this variable
is a ratio and therefore requires the numerator to grow more slowly (or decrease faster) than
the denominator in order for the variable to decrease in value. The BCBS itself concedes that
the credit-to-GDP trend may not capture turning points well (Basel Committee on Banking
Supervision 2010). Consequently, the ratio will not fall unless credit falls faster than GDP,
something which is not at all certain during banking crises. Still, it shows that purely from a
descriptive perspective, any signal derived from the credit gap needs to come from the level of
this variable (i.e., a threshold value), not from changes in its development.

Unlike the credit gap, credit growth (as depicted in % year-on-year growth) does appear to
hit a peak about two years before the onset of a banking crisis, even though its fall only becomes
clear during the last pre-crisis year. A similar development can be observed in nominal GDP
growth and equity price growth ﬁgures. These variables do peak before a crisis (on average),
but the signal that a crisis is coming only becomes evident shortly before the crisis happens.
This makes it diﬃcult, at least from a descriptive point of view, to extract any strong signal
from these variables. By some margin, residential house price growth outperforms the other
domestic variables in terms of signalling ‘power’ in this descriptive exercise. In our sample, the
growth rate of residential house prices tends to peak about 3 years before a crisis happens on
average, starting a clear descent (although prices are still rising) that lasts into the crisis where
growth stalls. Based on this evidence, we would conclude that residential house prices would be
a useful tool (at least much more useful than the other variables shown here) for decisions on
the CCB, as it passes the early warning requirement (one year of implementation plus one or
two quarters of publication lag) with verve. So, at least from a descriptive standpoint, it is clear
that it makes sense to gauge the developments of diﬀerent macro-ﬁnancial variables to predict
or signal coming crises. Whether this result holds in a more rigorous comparative (multivariate)
framework, will be discussed in the subsequent analysis.

3 Methodology

In this section we introduce the methodology used in the empirical analysis. We start by
introducing the logistic regressions used in our multivariate framework. Thereafter, we explain
how we evaluate individual indicators’ and model predictions’ usefulness for policy makers.

7

3.1 Multivariate models

In order to assess the predictive abilities of credit, macro-ﬁnancial and banking sector variables
in a multivariate framework, we estimate logistic regressions of the following form:

P rob(yit = 1) =

eαi+X (cid:48)
itβ
1 + eαi+X (cid:48)

itβ

(1)

where P rob(yit = 1) denotes the probability that country i is in a vulnerable state, where a
banking crisis could occur seven to twelve quarters ahead of quarter t. As independent variables,
the vector Xit includes credit and macro-ﬁnancial variables on the domestic and on the global
level as well as domestic banking sector variables (see Section 2.2). The estimations also include
country ﬁxed eﬀects, αi, in order to account for unobserved heterogeneity at the country level.2
Finally, we use robust standard errors clustered at the quarterly level in order to account for
potential correlation in the error terms that might arise from the fact that global variables are
identical across countries in a given quarter.3

The analysis is conducted as much as possible in a real-time fashion, meaning that only
information that is available at a particular point in time is used. Therefore, all de-trended
variables have been calculated using backward-looking trends, and all explanatory variables
have been lagged by one quarter, also to account for possible endogeneity. We are well aware
that this simple procedure cannot crowd out all endogeneity-related bias, but we note that the
dependent variable itself is an early warning variable. The time horizon for which this variable
is equal to 1 has been chosen in the context of our exercise and has not been exogenously
determined. Therefore, we consider endogeneity to be a somewhat smaller problem in this
study. Nevertheless, we have tested our models for diﬀerent speciﬁcations of the dependent
variable, both in terms of the pre-crisis period chosen (12-1/20-13 quarters before the onset of
a crisis) and the deﬁnition and data source of banking crises in the robustness section.

3.2 Model evaluation

Banking crises are (thankfully) rare events in the sense that most EU countries have encountered
none or only one over the past two decades. Still, when they occur, banking crises tend to be
very costly, both directly through bailouts and ﬁscal interventions and indirectly through the

2We do not include time dummies for two reasons: First, only quarters where at least one country experiences
a banking crisis could be used for identiﬁcation in such a speciﬁcation. As our sample includes many quarters
where none of the countries experienced a crisis the inclusion of time dummies would signiﬁcantly reduce the
sample size. Second, the focus in our paper is on the prediction of future banking crises. While time dummies
might improve the ex post ﬁt of a model, they are of little use for out-of-sample forecasting since they are not
known ex ante.

3Clustering at the country level yields smaller standard errors, in particular for the global variables.

8

loss of economic output that often tends to follow these crises (in particular for systemic banking
crises). Thus, policy makers have a clear incentive to be able to detect early enough potential
signs of vulnerabilities that might precede banking crises in order to take measures to prevent
further building up of vulnerabilities or to strengthen the resilience of the banking sector. Yet,
at the same time, policy makers may not want to be signalling crises when in fact they do not
happen afterwards. Doing so may (a) reduce the credibility of their signals, weakening decision-
making and damaging their reputation, and (b) needlessly incur costs on the banking sector,
endangering credit supply. As a consequence, policy makers also have an incentive to avoid false
alarms, i.e., they do not want to issue warnings when a crisis is not imminent. As pointed out
by Alessi and Detken (2011), an evaluation framework for an early warning model needs to take
into account policy makers’ relative aversion with respect to type I errors (not issuing a signal
when a crisis is imminent) and type II errors (issuing a signal when no crisis is imminent).

The evaluation approach in this paper is based on the so-called ‘signalling approach’ that
was originally developed by Kaminsky et al. (1998), and extended by Demirg¨u¸c-Kunt and Detra-
giache (2000), Alessi and Detken (2011), Lo Duca and Peltonen (2013) and Sarlin (2013). In this
framework, an indicator issues a warning signal whenever its value in a certain period exceeds a
threshold τ , deﬁned by a percentile of the indicator’s country-speciﬁc distribution. Similarly, a
multivariate probability model issues a warning signal whenever the predicted probability from
this model exceeds a threshold τ ∈ [0, 1], again deﬁned as a percentile of the country-speciﬁc
distribution of predicted probabilities. In this way, individual variables and model predictions
for each observation j are transformed into binary predictions Pj that are equal to 1 if the
respective thresholds are exceeded for this observation and 0 otherwise. Predictive abilities
can then be evaluated by comparing the signals issued by the respective variable or model to
the actual outcome Cj for each observation. Each observation can be allocated to one of the
quadrants in the contingency matrix depicted in Figure 2: A period with a signal by a speciﬁc
indicator can either be followed by a banking crisis twelve to seven quarters ahead (TP) or not
(FP). Similarly, a period without a signal can be followed by a banking crisis twelve to seven
quarters ahead (FN) or not (TN). Importantly, the number of observations classiﬁed into each
category depends on the threshold τ .

In order to obtain the optimal threshold τ one needs to take the policy maker’s preferences
vis-`a-vis type I errors (missing a crisis, T1(τ ) = F N/(T P + F N ) ∈ [0, 1]) and type II errors
(issuing a false alarm, T2(τ ) = F P/(F P + T N ) ∈ [0, 1]) into account. This can be done by
deﬁning a loss function that depends on the two types of errors as well as the policy maker’s
relative preference for either type. The optimal threshold is then the one that minimizes the
loss function. Taking into account the relative frequencies of crises P1 = P (Cj = 1) and tranquil
periods P2 = P (Cj = 0), the loss function is deﬁned as follows:

L(µ, τ ) = µP1T1(τ ) + (1 − µ)P2T2(τ ),

(2)

9

where µ ∈ [0, 1] denotes the policy makers’ relative preference between type I and type II errors.
A µ larger than 0.5 indicates that the policy maker is more averse against missing a crisis than
against issuing a false alarm, which—in particular following the recent ﬁnancial crisis—is a
realistic assumption in our view.

Using the loss function L(µ, τ ), the usefulness of a model can be deﬁned in two ways. First,
following the idea of Alessi and Detken (2011) and as in Sarlin (2013), the absolute usefulness
is deﬁned as:

Ua = min(µP1, (1 − µ)P2) − L(µ, τ ).

(3)

Note that Ua computes the extent to which having the model is better than having no model.
This is because a policy maker can always achieve a loss of min(µP1, (1 − µ)P2) by either always
issuing a signal (in which case T1(τ ) = 0) or never issuing a signal (in which case T2(τ ) = 0).
The fact that P1 is signiﬁcantly smaller than P2 in our sample (the share of observations that
is followed by a banking crisis twelve to seven quarters ahead is approximately 10 percent)
implies that, in order to achieve a high usefulness of the model, a policy maker needs to be
more concerned about the detection of vulnerable states potentially preceding banking crises in
comparison to the avoidance of false alarms. Otherwise, with a suboptimal performing model,
it would easily pay oﬀ for the policy maker to never issue a signal given the distribution of
vulnerable states and tranquil periods (see Sarlin 2013 for a detailed discussion of this issue).

A second measure, the relative usefulness Ur, is computed as follows (see Sarlin 2013):

Ur =

Ua
min(µP1, (1 − µ)P2)

(4)

The relative usefulness Ur reports Ua as a percentage of the usefulness that a policy maker would
gain from a perfectly performing model.4 The relative usefulness is our preferred performance
indicator as it allows the comparison of models for policy makers with diﬀerent values for the
preference parameter µ.5

4 Empirical results

In this section we present the empirical results. We ﬁrst explore the usefulness of credit variables
for the identiﬁcation of vulnerable states of the banking sector, and proceed by extending the
framework to a multivariate model including other macro-ﬁnancial and banking sector indicators.
Thereafter, we evaluate the out-of-sample performance of the estimated models and—ﬁnally—
present some robustness checks.

4A perfectly performing indicator would have T1 = T2 = 0, implying L = 0 and Ua = min(µP1, (1 − µ)P2).
5We also employ receiver operating characteristics (ROC) curves and the area under the ROC curve (AUROC)

for comparing performance of the early warning models (see Appendix 1 for details).

10

4.1 Estimation and evaluation

As the CRD IV regulations emphasise the role of credit variables for setting the countercyclical
capital buﬀer rate—in particular the role of credit growth and the credit-to-GDP gap—we start
by evaluating the usefulness of these variables for the identiﬁcation of vulnerable states within
the EU banking sector.

4.1.1

Individual indicators based on credit growth and credit-to-GDP ratios

First, we evaluate the usefulness of domestic credit variables by using a simple signalling ap-
proach. Using a preference parameter of µ equal to 0.9, Panel A of Table 3 reports the optimal
threshold for several credit variable indicators.6 Given the optimal threshold, the table also
shows the number of observations in each quadrant of the matrix depicted in Figure 2, the
percentage of type 1 and type 2 errors, as well as several performance measures, such as the
absolute and the relative usefulness, the adjusted noise-to-signal (aNtS) ratio7, the percentage
of vulnerable states correctly predicted by the indicator (% Predicted), the probability of a vul-
nerable state conditional on a signal being issued (Cond Prob) and the diﬀerence between the
conditional and the unconditional probability of a vulnerable state (Diﬀ Prob).

Among the domestic indicators, indeed, the credit-to-GDP gap performs best in the sense
that it generates the highest relative usefulness. This is consistent with ﬁndings by Drehmann
et al. (2011) for a diﬀerent set of countries and in line with the approach taken in the Basel III/
CRD IV framework. The credit-to-GDP gap issues a warning signal whenever it is above the
40th percentile of its country-speciﬁc distribution and achieves 25.6 percent of the usefulness a
policy maker would gain from a perfectly performing model. Other transformations of the credit
variables that perform relatively well are annual credit growth, the credit-to-GDP ratio and the
credit gap (deﬁned as the deviation of the stock of credit from its long term trend).

Interestingly, global credit variables seem to outperform domestic credit variables in terms
of usefulness for predicting vulnerabilities in the domestic banking sector. Panel B of Table 3
shows that these indicators usually exert a higher relative usefulness, a lower adjusted noise-

6A preference parameter of µ equal to 0.9 indicates a strong preference for the detection of crises by the policy
maker.
In our view this is a reasonable assumption as the current crisis illustrated once more that ﬁnancial
crises often translate into large costs for the economy. As Sarlin (2013) points out, using a µ equal to 0.9 and
simultaneously taking into account the unconditional probability of a crisis (which is about 10 % in our sample) is
equivalent to using a µ equal to 0.5 without adjusting for the unconditional probabilities (as in Alessi and Detken
2011 or Lo Duca and Peltonen 2013). Results for diﬀerent values of µ are available upon request.

7The aNtS ratio is the ratio of false signals measured as a proportion of quarters where false signals could
have been issued to good signals as a proportion of quarters where good signals could have been issued, or
(F P/(F P + T N ))/(T P/(T P + F N )). A lower aNtS ratio indicates better predictive abilities of the model.

11

to-signal ratio, and are able to predict a larger share of the vulnerable states in our sample.
In an increasingly integrated economy, vulnerabilities that develop at a global level potentially
transmit to countries around the world. Hence, focusing on the development of domestic credit
variables might not be suﬃcient, and the calibration of CCB rates should also account for global
developments. This reasoning is, to some extent, already reﬂected in the Basel III/CRD IV
framework, as the institution-speciﬁc CCB rate is calculated as a weighted average of CCB
rates in countries to which the bank has exposures.

The evaluation of the predictive abilities of global variables is subject to a caveat: As these
variables do not vary across countries, and as most countries had a crisis starting in 2008, the
good performance of these variables can in part be explained by a clustering of crisis episodes
within the same year. That is, indicators based on global credit variables correctly predicted
the current crisis in several of our sample countries, which puts the higher usefulness of global
as compared to domestic variables in a perspective. However, the current crisis is certainly one
of the best examples for a non-domestic vulnerability that spread to banking systems around
the world. Thus, if the aim of the CCB is to increase the resilience of the banking system, it
appears to be beneﬁcial to take into account both domestic and global developments.

4.1.2 Multivariate models including other macro-ﬁnancial indicators

While the signalling approach is a simple and useful way to assess the predictive abilities of
individual indicators, a multivariate framework has the advantage of being able to assess the
joint performance of several indicators. We therefore estimate simple logit models including
several of the individual credit variables as well as other macro-ﬁnancial indicators and assess
their performance and usefulness.

Results for these models are presented in Table 4. Again, we start by considering only the
domestic variables and focus on credit growth and the credit-to-GDP gap, as these variables
performed well in Section 4.1.1 and play a prominent role in the Basel III / CRD IV framework.
Credit growth seems to dominate the credit-to-GDP gap, which is statistically not signiﬁcant, in
this simple model. Next, we gradually include the global credit variables, interactions between
growth and leverage on the domestic and the global level as well as interactions between the

12

domestic and the global variables.8 The predictive power of the model improves with each step.9

In order to compare the models’ predictive abilities with those of the individual indicators we
once more apply the signalling approach by translating the predicted probabilities into country
speciﬁc percentiles and determining the optimal threshold for the issuance of warnings as the
one that maximizes the relative usefulness of the model (see Section 3.2). Table 5 shows that
the relative usefulness of the domestic model is 0.236, which is lower than the one of the best
individual indicators. However, the stepwise inclusion of the remaining variables improves the
usefulness, so that Model 3 surpasses the best domestic as well as the best global indicators in
terms of relative usefulness. This indicates the beneﬁts of a multivariate framework as compared
to single indicators. We will elaborate more on these beneﬁts by taking into account not only
credit variables, but also other variables that might aﬀect the stability of the banking sector.

Models 4-7 provide the estimation results for the extended models. The sample size is
somewhat smaller than in the Models 1-3, as the data is not available for all variables across
In order to make results comparable, Model 4 re-estimates
the whole period (see Table 1).
Model 3 on the reduced sample. The most striking diﬀerence between the two regressions is the
coeﬃcient for the domestic credit-to-GDP gap, which turns signiﬁcant in the reduced sample.
This indicates that any evaluation depends on the respective sample and should make policy
makers cautious when generalizing ﬁndings from a particular sample of countries. However,
the predictive abilities of the models are quite impressive. For example, Model 5, to which we
refer as our benchmark model, achieves 60.3 percent of the usefulness of a perfectly performing
model and thus outperforms any individual indicator. The area under the ROC curve for this
model is equal to 0.865, indicating a good predictive ability of the model for a wide range of
policy maker’s preference parameters (see Figure 3 for an illustration of the ROC curve for our
benchmark model).10

8We orthogonalise interaction terms with ﬁrst-order predictors in order to avoid problems of multicollinearity
(see e.g. Little et al. 2006). In particular, when interacting two variables X and Y , we ﬁrst form the simple
product X × Y and then regress it on the original variables: X × Y = α + β1 × X + β2 × Y + (cid:15). We then take the
residual from this regression—(cid:15), which is orthogonal to X and Y —to represent the interaction between the two
original variables. Variance inﬂation factors (VIF) smaller than ten for all variables indicate that we are able to
get rid of multicollinearity problems in this way.

9Note that the interpretation of interaction eﬀects in logit models is cumbersome. As pointed out by Ai and
Norton (2003), the interaction eﬀect is conditional on the independent variables (unlike interaction eﬀects in linear
models) and may have diﬀerent signs for diﬀerent values of the covariates. Moreover, the statistical signiﬁcance
of these eﬀects cannot be evaluated with a simple t-test, but should be evaluated for each observation separately.
Doing so allows us to conclude that for most observations only the Interaction(GC1×GC2) is signiﬁcantly positive,
while the other interactions are insigniﬁcant (although e.g. the Interaction(DC2×GC2) has a signiﬁcantly negative
sign in the regression itself).

10In contrast to the individual indicators and most of the credit models, the extended models perform well also
for lower values of the preference parameter µ, which we see as another advantage of these models. Results for
other values of µ are available upon request.

13

Overall, we ﬁnd that the credit variables are indeed among the most important predictors
of vulnerable states of the economy. However, both model ﬁt and model performance increase
signiﬁcantly when we include other macro-ﬁnancial indicators. For example, the consistently
positive coeﬃcient for house price growth indicates that asset price booms promote the build-up
of vulnerabilities in the ﬁnancial sector. This suggests that regulators should keep an eye on these
developments instead of focusing exclusively on the development of credit variables. Moreover,
Model 7 shows that banking sector variables exert a signiﬁcant inﬂuence on the build-up of
ﬁnancial vulnerabilities. We make the following observations: First, a country is more likely to
be in a vulnerable state, when aggregate bank capitalisation within the country is relatively low.
This is a particularly important ﬁnding in the context of countercyclical capital buﬀers as it
indicates that indeed regulators could improve the resilience of the banking system by requiring
banks to hold more capital when vulnerabilities build up. Second, we ﬁnd that future banking
crises are more likely when proﬁts in the banking sector are relatively high. As Borio et al.
(2010) point out, periods of high bank proﬁtability are typically associated with rapid credit
growth, increased risk-taking and building up of vulnerabilities, which could explain the positive
coeﬃcient for the proﬁtability variable preceding banking crises.

Figure 4 illustrates the relationship between predicted crisis probabilities from our bench-
mark model (Model 5) and actual banking sector capitalisation in the countries that had a
banking crisis in 2007/2008. Most countries exerted declining or constantly low levels of bank
capitalisation prior to the crisis, which is consistent with the evidence from Model 7. A notable
exception is Austria (and to some extent Denmark), where aggregate banking sector capitali-
sation actually increased prior to the crisis. At the same time, the benchmark model issues a
warning already in late-2004/early-2005 in most cases. Hence, if they had relied on this signal,
regulators would have had enough time for the activation of the CCB prior to the crisis—even
if we account for an announcement period of twelve months for the CCB.

4.2 Out-of-sample performance of the models

Given the objective of the early warning systems, any assessment should focus on the out-
of-sample performance. Moreover, as shown by e.g. Berg et al. (2005), successful in-sample
predictions are much easier to achieve than successful out-of-sample predictions. In order to
assess the out-of-sample usefulness of the models we proceed as follows: First, we consecutively
exclude countries that had a banking crisis prior to 2007 from the estimation of the benchmark
model. Then, we test whether the model based on the remaining countries is able to predict the

14

crises in the excluded ones.11

The results of this exercise are presented in Figure 5. The benchmark model signals the
banking crises in the Nordic countries well before their onset in the early 1990s. In both Finland
and Sweden, the indicator is consistently above the threshold from 1988Q2 onwards, which is
11 quarters ahead of the crisis for Finland and 9 quarters ahead for Sweden. In both cases,
banks would have had enough time to build up capital before the crisis if the countercyclical
capital buﬀer had been activated. Similarly, the model issues a warning signal for Italy from
1991Q2 onwards, 11 quarters ahead of the crisis in 1994. In the United Kingdom, the crisis is
relatively close to the beginning of the sample period. Yet, in those quarters preceding the crisis
of 1991, the benchmark model consistently issues a warning signal. Overall, the benchmark
model exhibits strong out-of-sample properties. Information from the current crisis seems to be
useful for the prediction of other systemic banking crises in the European Union.

4.3 Robustness checks

In this section we modify the benchmark model (Model 5 of Table 4) in several ways in order
to further assess the robustness of our results. The results from the robustness analysis are
presented in Tables 6 and 7.

First, we check whether our results depend on the deﬁnition of the dependent variable. Apart
from the ESCB Heads of Research database used in our analysis, the most common deﬁnitions
of systemic banking crises are provided by Reinhart and Rogoﬀ (2011) and Laeven and Valencia
(2012). Although the various databases are broadly consistent with each other, there are some
deviations in the timing of crises as the deﬁnition of a systemic event in the banking sector
requires a considerable amount of judgment. Columns 2 and 3 show that overall results are
relatively similar for all three crisis deﬁnitions. Moreover, the area under the ROC curve is also
greater than 0.8 for the other two models with the alternative crisis deﬁnitions, indicating good
predictive abilities of the models.

Second, we include a dummy variable that is equal to one for each quarter in which the
respective country is a member of the European Monetary Union (EMU). As expected, the
coeﬃcient for this dummy variable is positive and signiﬁcant as most crises in our sample occur
after the establishment of the EMU in 1999 (see column 4). However, the coeﬃcients of the other
variables remain largely unaﬀected by the inclusion of this dummy variable. Furthermore, the

11In principle we could have tried to ﬁt a model to the observations prior to 2007 in order to see whether this
model would be able to predict the current crisis. However, as most of the crisis episodes in our sample occur
after 2007, and as we particularly want to learn something from these episodes, we prefer the approach described
above, i.e., we use the information from the current crisis and check whether it would have been useful for the
prediction of past crises.

15

results are robust if we restrict the sample to include only countries from the EU-15 (column 5)
or only countries that are part of the EMU (column 6).

Third, we augment the model with a money market rate (column 7). The estimated negative
coeﬃcient is potentially related to the ’great moderation’, i.e., the general decline of inﬂation
and money market rates over the sample period. The high R-squared and AUROC indicate
that the ﬁt of the model is superior compared to the other models. Despite this, we do not
select this model as our benchmark model as its out-of-sample forecast abilities are inferior to
the benchmark model, potentially due to an overﬁtting problem.

Fourth, following Lo Duca and Peltonen (2013), we transform all variables into country-
speciﬁc percentiles before using them in the regression. This method can be seen as an alternative
way to account for heterogeneity across countries as diﬀerences in levels of indicators between
countries vanish for the transformed variables. Columns 8 and 9 show that most of the estimated
coeﬃcients have the same sign as in the benchmark model if we use this alternative method.

Finally, we analyse model performance across diﬀerent forecast horizons (see also Schudel
2015). Speciﬁcally, we check how the performance of the benchmark model and the indicator
properties of variables change if the time window of the vulnerable state preceding a systemic
banking crisis is altered from the twelve to seven quarters used in the standard speciﬁcations.
Results in Table 7 show that although the benchmark model is broadly robust to an alteration of
the forecast horizon, the relative importance and the estimated signs of the coeﬃcients tend to
vary a bit. Particularly important are the reversed signs for domestic and global credit growth
in the model with the twenty to thirteen quarters ahead deﬁnition of a vulnerable state and
the strong inﬂuence of global asset prices in this model (Model R3). As shown in Table 5, the
benchmark model with a forecast horizon of twelve to seven quarters (Model 5) provides the
highest absolute and relative usefulness measures, followed by the model with a forecast horizon
of twelve to one quarter (Model R2). The performances of the models with the early (six to one
quarter) and late (twenty to thirteen quarters) pre-crisis time horizons in terms of absolute and
relative usefulness are broadly similar, but markedly lower than that of the benchmark model.

5 Conclusion

As a response to recent ﬁnancial crises, the Basel III/CRD IV regulatory framework includes
a countercyclical capital buﬀer (CCB) to increase the resilience of the banking sector and its
ability to absorb shocks arising from ﬁnancial and economic stress. In this context, this paper
seeks to provide an early warning model, which can be used to guide the build-up and release
of capital in the banking sector. Given the prominence of private credit variables in the Basel
III/CRD IV framework, the paper ﬁrst examines the evolution of credit variables preceding

16

banking crises in the EU Member States, and assesses their usefulness in guiding the setting
of the CCB. Furthermore, the paper examines the potential beneﬁts of complementing private
credit variables with other macro-ﬁnancial and banking sector indicators in a multivariate logit
framework. The evaluation of the policy usefulness of the credit indicators and models follows
the methodology applied in Alessi and Detken (2011), Lo Duca and Peltonen (2013) and Sarlin
(2013).

The paper ﬁnds that, in addition to credit variables, other domestic and global ﬁnancial
factors such as equity and house prices and banking sector variables help to predict macro-
ﬁnancial vulnerabilities in EU Member States. The importance of global variables in our models
concurs with the view that excessive global liquidity is a key driver of ﬁnancial vulnerabilities
and highlights the importance of consistent cross-border and reciprocity arrangements, as in
the European macroprudential framework. Furthermore, higher banking sector capitalisation
decreases the probability of entering a vulnerable state which provides a rationale for the im-
plementation of countercylical measures like the CCB. Moreover, future banking crises tend to
be more likely when proﬁts in the banking sector are relatively high, concurrent with the view
that high bank proﬁtability could be associated with rapid credit growth, increased risk-taking
and building up of vulnerabilities. Overall, our ﬁndings suggest that policy makers should take
a broad approach in their analytical models supporting CCB policy measures.

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21

a)

c)

e)

b)

d)

f)

Figure 1: Development of key variables around banking crises

The ﬁgure depicts the development of selected key variables around banking crises within the sample countries.
The start date of a banking crisis is indicated by the vertical line, while the solid line shows the development in
the median country and the dashed lines represent the countries at the 25th and the 75th percentile, respectively.

22

Figure 2: Contingency matrix

The ﬁgure shows the relationship between model prediction and actual outcomes. Observations are classiﬁed into
those where the indicator issues a warning that is indeed followed by a banking crises twelve to seven quarters
ahead (TP), those where the indicator issues a warning that is not followed by a crisis (FP), those where the
indicator issues no warning and there is no crises seven to twelve quarters ahead (TN), and those where the
indicator issues no warning although there is a crisis coming (FN).

Figure 3: ROC Curve for benchmark model (Model 5)

The ﬁgure shows the Receiver Operating Characteristic (ROC) curve for our benchmark model. The area under
the ROC curve (AUROC) is equal to 0.8645.

23

a)

c)

e)

b)

d)

f)

Figure 4: Predicted crisis probabilities and banking sector capitalisation

24

a)

c)

e)

b)

d)

f)

Figure 4 continued...

The ﬁgure plots the predicted probabilities (grey bars) from our benchmark model (Model 5 in Table 4) around
the crises of 2008 in our sample countries (depicted by the dashed vertical lines). The optimal threshold for each
country is depicted by the dashed horizontal line. The model issues a warning whenever the predicted probability
is above this threshold. The black line shows the development of aggregate capitalisation in the banking sector
deﬁned as total banking sector equity over total banking sector assets.

25

a)

c)

b)

d)

Figure 5: Out-of-sample performance of the model

The ﬁgure shows results for an out-of-sample evaluation of our benchmark model (Model 5 in Table 4). We exclude
the respective country from the estimation and depict the predicted probabilities (grey bars) from a model based
on the remaining countries around the crisis in the excluded country (dashed vertical line). The model issues
a warning whenever the predicted probability is higher than the optimal threshold within the country (dashed
horizontal line).

26

Table 1: Data availability and crisis dates

Credit Variables

Other Variables

HoR Banking Crises

Austria
Belgium
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Ireland
Italy
Lithuania
Luxembourg
Malta
Netherlands
Poland
Portugal
Slovakia
Slovenia
Spain
Sweden
United Kingdom

1982Q1-2012Q3
1982Q2-2012Q3
1994q2-2012Q2
1982Q2-2012Q3
2005Q1-2012Q2
1982Q2-2012Q3
1982Q2-2012Q3
1982Q2-2012Q2
2003Q1-2012Q2
1997Q1-2012Q3
1999Q1-2012Q3
1982Q2-2012Q3
2005Q1-2012Q2
2004Q2-2012Q3
2006Q2-2012Q2
1982Q2-2012Q2
1997Q1-2012Q3
1982Q2-2011Q4
2005Q2-2012Q2
2005Q3-2012Q2
1982Q2-2012Q3
1982Q2-2012Q3
1982Q2-2012Q3

1986Q4-2012Q3
1982Q1-2012Q3
—
1992Q2-2012Q3
2005Q2-2012Q2
1987Q2-2012Q3
1992Q2-2012Q3
1991Q2-2011Q4
2003Q1-2012Q2
2002Q1-2012Q2
1999Q1-2010Q4
1990Q3-2012Q2
2005Q1-2012Q2
2004Q2-2010Q4
—
1982Q1-2011Q4
2003Q1-2012Q3
1998Q2-2011Q4
—
—
1995Q2-2012Q3
1986Q2-2012Q3
1988Q2-2012Q2

2008Q4
2008Q3-2008Q4
1998Q1-2002Q2
1987Q1-1993Q4, 2008Q3-end of sample
–
1991Q1-1995Q4
1994Q1-1995Q4, 2008Q1-2009Q4
2008Q1-2008Q4
2008Q1-end of sample
2008Q3-2009Q2
2008Q1-end of sample
1994Q1-1995Q4
2009Q1-2009Q4
2008Q2-end of sample
–
2008Q1-2008Q4
–
–
–
–
1982Q2-1985Q3
1990Q3-1993Q4, 2008Q3-2008Q4
1991Q1-1995Q2, 2007Q1-2007Q4

The table shows the availability of credit and other variables as well as the crisis dates for the 23 countries in
our sample. Credit variables are obtained from the BIS database for total credit to the private non-ﬁnancial
sector (see Dembiermont et al. 2013) and from Eurostat for those countries where the BIS data is not available.
Other macro-ﬁnancial and banking sector variables are obtained from various sources, including the BIS, IMF,
and OECD. The crisis deﬁnitions are from the ESCB Heads of Research database described in Babecky et al.
2014.

27

Table 2: Descriptive statistics

Dom. Credit Growth (qoq)
Dom. Credit Growth (yoy)
Dom. Credit Gap
Dom. Credit Growth (4q MA)
Dom. Credit Growth (6q MA)
Dom. Credit Growth (8q MA)
Dom. Credit to GDP Ratio
Dom. Credit to GDP Gap
Dom. Credit Growth - GDP Growth

Glo. Credit Growth (qoq)
Glo. Credit Growth (yoy)
Glo. Credit Gap
Glo. Credit Growth (4q MA)
Glo. Credit Growth (6q MA)
Glo. Credit Growth (8q MA)
Glo. Credit to GDP Ratio
Glo. Credit to GDP Gap
Glo. Credit Growth - Glo. GDP Growth

GDP Growth
Inﬂation
Equity Price Growth
House Price Growth
Banking Sector Capitalization
Banking Sector Proﬁtability
Gov. Bond Yield
Money Market Rate

Global GDP Growth
Global Equity Price Growth
Global House Price Growth

Obs.

1220
1220
1220
1220
1220
1220
1220
1220
1220

1220
1220
1220
1220
1220
1220
1220
1220
1220

919
919
919
919
756
756
862
862

919
919
919

Mean

Std. Dev.

Min

Max

0.0228
0.0926
0.1149
0.0232
0.0232
0.0233
1.2756
0.0346
0.0081

0.0152
0.0614
0.0597
0.0154
0.0156
0.0158
0.7557
0.0158
0.0022

0.0123
0.0242
0.0240
0.0172
0.0507
0.0066
0.0575
0.0460

0.0117
0.0135
0.0066

0.0196
0.0662
0.1186
0.0166
0.0154
0.0150
0.4259
0.0796
0.0171

0.0086
0.0289
0.0431
0.0071
0.0069
0.0065
0.1193
0.0285
0.0235

0.0088
0.0166
0.1199
0.0289
0.0161
0.0040
0.0237
0.0292

0.0229
0.0675
0.0162

-0.0318
-0.0690
-0.1570
-0.0173
-0.0122
-0.0099
0.4426
-0.1788
-0.0508

-0.0048
-0.0113
-0.0101
-0.0028
-0.0021
0.0005
0.5778
-0.0420
-0.0492

-0.0232
-0.0108
-0.3759
-0.0735
0.0238
-0.0142
0.0220
0.0010

-0.0585
-0.3344
-0.0389

0.0989
0.3579
0.4550
0.0897
0.0813
0.0805
2.4829
0.3249
0.0715

0.0335
0.1095
0.1593
0.0274
0.0280
0.0274
0.9933
0.0676
0.0671

0.0437
0.1078
0.3051
0.1204
0.1088
0.0292
0.1385
0.1643

0.0616
0.1122
0.0539

The table shows descriptive statistics for the credit variables and the other macro-ﬁnancial indicators used in the
empirical analysis. Credit variables are available for a longer period of time in most countries, which is why the
number of observations is larger for them.

28

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Table 4: Multivariate models

(1)
Model 1

(2)
Model 2

(3)
Model 3

(4)
Model 4

(5)
Model 5

(6)
Model 6

(7)
Model 7

Dom. Credit Growth (DC1)

Dom. Credit to GDP Gap (DC2)

6.38**
(2.59)
3.01
(1.93)

2.66
(2.95)
2.71
(2.80)

16.71***
(4.26)
1.96
(7.67)

Interaction(DC1 × DC2)

Glo. Credit Growth (GC1)

Glo. Credit to GDP Gap (GC2)

Interaction(GC1 × GC2)

Interaction(DC1 × GC1)

Interaction(DC2 × GC2)

GDP Growth

Inﬂation

Equity Price Growth

House Price Growth

Global GDP Growth

Global Equity Price Growth

Global House Price Growth

Banking Sector Capitalization

Banking Sector Proﬁtability

1.61
(2.75)
3.70
(2.66)
26.42
(21.83)
16.07***
(4.80)
-2.74
(6.57)
391.54**
(188.05)
45.98
(75.98)
-239.65***
(49.73)

3.93
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8.55***
(2.27)
55.68**
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29.01***
(5.61)
6.74
(6.67)
-486.53*
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-56.67
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-417.35***
(67.99)

1.54
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12.98***
(2.27)
55.12**
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25.99***
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12.19
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-324.72
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-28.48
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(91.07)
19.64
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-1.01
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16.73***
(5.40)
-10.24
(12.62)
7.39
(4.80)
16.29
(18.34)

-0.16
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13.24***
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83.05**
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19.72*
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26.84**
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-472.64
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-129.64
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7.61
(5.42)
14.97
(20.67)

Country dummies
Observations
Pseudo R-Squared
AUROC
Standard error

YES
1,220
0.0894
0.710
0.0266

YES
1,220
0.108
0.733
0.0232

YES
1,220
0.133
0.780
0.0185

YES
919
0.210
0.824
0.0195

YES
919
0.278
0.865
0.0160

YES
756
0.272
0.846
0.0165

0.70
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20.04***
(2.68)
53.94
(35.03)
6.72
(12.82)
41.15***
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-973.05***
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34.59
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-582.20***
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30.80
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14.19
(12.18)
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-9.88
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7.78
(6.12)
30.09
(22.55)
-136.85***
(39.63)
324.89***
(76.45)

YES
756
0.336
0.892
0.0157

The table shows estimation results for multivariate logit models, where the dependent variable is set to 1, twelve
to seven quarters preceding a banking crisis in a respective country. Observations for banking crises and six
quarters following banking crises are omitted, while other dependent variable observations are set to 0. All
regressions include country-speciﬁc dummy variables to account for unobserved heterogeneity across countries.
Robust standard errors adjusted for clustering at the quarterly level are reported in parentheses. * indicates
statistical signiﬁcance at the 10 %-level, ** at the 5 %-level, and *** at the 1 %-level.

30

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Table 6: Robustness checks

(1)
Benchmark

(2)
RR

(3)
LV

(4)
EMU

(5)
EU-15

(6)
Euro

(7)

(8)

(9)

Interest Rates Percentiles Percentiles

Dom. Credit Growth (DC1)

Dom. Credit to GDP Gap (DC2)

Interaction(DC1 × DC2)

Glo. Credit Growth (GC1)

Glo. Credit to GDP Gap (GC2)

Interaction(GC1 × GC2)

Interaction(DC1 × GC1)

Interaction(DC2 × GC2)

GDP Growth

Inﬂation

Equity Price Growth

House Price Growth

Global GDP Growth

Global Equity Price Growth

Global House Price Growth

D(EMU)

Gov. Bond Yield

Money Market Rate

Country dummies
Observations
Pseudo R-Squared
AUROC
Standard error

1.54
(3.73)
12.98***
(2.27)
55.12**
(22.35)
25.99***
(8.88)
12.19
(8.89)
-324.72
(305.59)
-28.48
(68.99)

-10.01**
(4.71)
23.91***
(4.32)
35.24
(36.30)
32.12***
(10.77)
-8.68
(10.83)
-255.97
(320.49)
77.07
(88.37)

-0.58
(3.28)
4.09
(2.60)
26.75
(26.96)
39.40***
(15.26)
42.49***
(15.62)

-1.08
(4.29)
15.68***
(2.51)
57.40**
(26.67)
49.67***
(10.14)
-4.67
(12.87)

1.01
(4.57)
12.46***
(2.64)
55.10*
(31.69)
18.57**
(9.42)
20.22*
(11.24)
-390.66
(296.43)
-240.77**
(102.03)

-4.23
(6.77)
14.70***
(4.73)
138.12*
(71.79)
13.00
(10.23)
18.52*
(10.52)
-121.35
(301.21)
-134.60
(101.30)

2.83
(5.86)
37.86***
(4.67)
83.42*
(46.34)
108.66***
(16.80)
-37.62**
(17.82)
-1,941.20***
(527.98)
208.01
(139.13)

(587.11)
12.25
(104.67)

1,718.19*** -806.86**
(345.60)
-17.42
(89.52)
-472.20*** -754.19*** -339.87*** -617.47*** -436.37*** -276.74** -1,466.07***
(133.84)
12.95
(20.57)
-29.70**
(12.35)
-1.57
(1.16)
21.02***
(6.20)
-8.78
(12.60)
6.86
(4.99)
11.56
(20.00)
2.83***
(0.62)

(102.92)
2.67
(20.61)
-3.98
(11.60)
-0.20
(1.49)
14.03***
(4.81)
-4.87
(12.25)
7.11
(4.56)
8.29
(17.54)

(91.07)
19.64
(18.97)
-29.04**
(11.73)
-1.01
(1.10)
16.73***
(5.40)
-10.24
(12.62)
7.39
(4.80)
16.29
(18.34)

(96.37)
18.29
(20.65)
-3.65
(10.79)
-0.43
(1.26)
23.45***
(5.33)
-7.63
(12.95)
8.58*
(5.07)
20.92
(18.53)

(182.09)
35.04
(24.89)
68.72***
(20.10)
-1.77
(1.91)
20.73**
(9.37)
0.08
(11.66)
6.47
(4.61)
27.49
(19.84)

(109.19)
14.00
(21.40)
15.29
(10.41)
-0.14
(1.51)
20.71***
(5.50)
-10.67
(15.21)
10.72*
(6.14)
27.87
(21.34)

(66.07)
11.35
(25.41)
-25.31*
(15.21)
-1.46
(2.11)
6.73
(8.52)
-40.28*
(20.80)
21.31***
(7.62)
51.73**
(23.01)

-0.009
(0.008)
0.039***
(0.007)
0.018***
(0.005)
0.024**
(0.010)
-0.033***
(0.008)
0.011
(0.009)
-0.001
(0.005)
-0.042***
(0.006)
0.003
(0.006)
-0.001
(0.005)
-0.008
(0.006)
0.019***
(0.005)
-0.004
(0.009)
0.016
(0.010)
0.046***
(0.014)

-0.000
(0.010)
0.050***
(0.009)
0.026***
(0.005)
0.018
(0.011)
0.004
(0.013)
-0.005
(0.010)
-0.004
(0.006)
-0.062***
(0.010)
0.001
(0.006)
-0.004
(0.006)
-0.009
(0.006)
0.015**
(0.006)
-0.004
(0.009)
0.018*
(0.010)
0.054***
(0.013)

-28.69
(45.08)
-125.08***
(38.55)

YES
919
0.278
0.865
0.0160

YES
835
0.286
0.827
0.0207

YES
893
0.442
0.807
0.0223

YES
919
0.314
0.887
0.0136

YES
869
0.269
0.847
0.0172

YES
664
0.270
0.836
0.0184

YES
862
0.477
0.942
0.0091

NO
919
0.324
0.892
0.0126

YES
919
0.372
0.909
0.0117

The table shows robustness checks for our benchmark model (Model 5 in Table 4).
In column 2 and 3, the
dependent variable is based on the crisis deﬁnition by Reinhart and Rogoﬀ (2013) and Laeven and Valencia
(2008), respectively. Column 4 includes a dummy that is equal to one for each quarter in which the respective
country is a member of the European Monetary Union (EMU) and column 5 restricts the sample to include only
EU-15 countries for which data availability is better than for the rest of our sample countries. Column 6 restricts
the sample to include only the countries that are a part of the EMU. In column 7 we include two interest rate
variables, the 10-year government bond yield and the 3-months interbank lending rate. In columns 8 and 9 we
transform all variables into country-speciﬁc percentiles before using them in the regression. Robust standard
errors adjusted for clustering at the quarterly level are reported in parantheses. * indicates statistical signiﬁcance
at the 10 %-level, ** at the 5 %-level, and *** at the 1 %-level.

32

Table 7: Robustness—Forecast horizon

(1)
Benchmark
7-12 quarters

1.54
(3.73)
12.98***
(2.27)
55.12**
(22.35)
25.99***
(8.88)
12.19
(8.89)
-324.72
(305.59)
-28.48
(68.99)
-472.20***
(91.07)
19.64
(18.97)
-29.04**
(11.73)
-1.01
(1.10)
16.73***
(5.40)
-10.24
(12.62)
7.39
(4.80)
16.29
(18.34)

919
0.278
0.865
0.0160

(2)
Model R1
1-6 quarters

-11.63
(8.06)
61.69***
(20.72)
-18.61
(82.99)
113.85***
(18.75)
17.90
(21.61)
6,895.95***
(1,067.10)
453.38
(322.98)
-1,947.93***
(565.00)
-28.92
(48.51)
77.15***
(24.02)
2.14
(2.34)
-22.60**
(9.98)
-0.39
(12.63)
14.15***
(5.08)
-60.67**
(30.62)

919
0.781
0.726
0.0179

(3)
Model R2
1-12 quarters

(4)
Model R3
13-20 quarters

-3.06
(4.28)
33.92***
(3.91)
139.78***
(36.95)
93.09***
(12.10)
2.08
(10.95)
2,763.43***
(502.18)
223.97**
(99.32)
-1,193.54***
(151.01)
-14.58
(20.64)
22.54*
(13.25)
-0.45
(1.40)
7.29
(6.19)
-2.07
(13.10)
15.06***
(4.91)
-32.74
(23.07)

919
0.617
0.960
0.0063

-11.77***
(4.07)
16.03***
(4.08)
-1.36
(32.76)
-50.73***
(14.10)
28.57**
(13.06)
-52.28
(449.06)
-606.47***
(111.78)
-458.57***
(79.88)
35.03
(40.03)
24.42**
(10.59)
-1.14
(1.98)
8.62
(5.91)
12.86
(9.72)
12.53***
(4.76)
116.13***
(21.94)

919
0.340
0.895
0.0134

Dom. Credit Growth (DC1)

Dom. Credit to GDP Gap (DC2)

Interaction(DC1 × DC2)

Glo. Credit Growth (GC1)

Glo. Credit to GDP Gap (GC2)

Interaction(GC1 × GC2)

Interaction(DC1 × GC1)

Interaction(DC2 × GC2)

GDP Growth

Inﬂation

Equity Price Growth

House Price Growth

Global GDP Growth

Global Equity Price Growth

Global House Price Growth

Observations
Pseudo R-Squared
AUROC
Standard error

The table shows the results of robustness analysis with respect to the forecast horizon. Column 1 re-estimates
Model 5 from Table 4, which is referred as the benchmark model. The dependent variable in this regression is
set to one twelve to seven quarters preceding a banking crisis in a respective country. In column 2, we replace
the dependent variable with a dummy that is equal to one, six to one quarter before a banking crisis. Similarly,
the dependent variable in column 3 equals one twelve to one quarter before a banking crisis in the respective
country. Finally, the dependent variable in column 4 is equal to one twenty to thirteen quarters before the onset
of a banking crisis in a respective country. Robust standard errors adjusted for clustering at the quarterly level
are reported in parentheses. * indicates statistical signiﬁcance at the 10 %-level, ** at the 5 %-level, and *** at
the 1 %-level.

33

Appendix 1: Data sources and technical estimation matters

(a) Data sources

The individual series used in our paper stem from the following original sources: Data on total
credit to the private non-ﬁnancial sector is obtained from the BIS and—for those countries where
BIS data is not available—from Eurostat. Information on nominal GDP growth and inﬂation
rates comes from the IMF’s International Financial Statistics (IFS). Data on stock prices is
obtained from the OECD, while data on house prices is provided by the BIS. Banking sector
variables are obtained from two sources: The OECD provides relatively long series on banking
sector capitalisation and proﬁtability on an annual basis that we use in the empirical analysis.
Additionally, for illustrative purposes, we use a shorter series of banking sector capitalisation in
Figure 4 that is available on a quarterly basis and which is obtained from the ECB’s Balance
Sheet Items (BSI) statistics. Finally, quarterly data on the 10-year government bond yield and
the 3-months interbank lending rate (money market rate) are obtained from the OECD.

(b) Calculation of the credit-to-GDP gap

Following the Basel Committee on Banking Supervision (2010), we use a backward-looking
Hodrick-Prescott ﬁlter with a smoothing parameter λ of 400,000 to calculate the credit-to-GDP
gap. Recommendations in the BCBS Consultive Document are based on a paper by Borio et al.
(2010), who ﬁnd that trends calculated with a λ of 400,000 perform well in picking up the
In particular, a λ of 400,000 is consistent with the
long-term development of private credit.
assumption of credit cycles being four times longer than business cycles if one follows a rule
developed by Ravn and Uhlig (2002), which states that the optimal λ of 1,600 for quarterly data
should be adjusted by the fourth power of the observation frequency ratio (i.e., if credit cycles
are four times longer than business cycles, λ should be equal to 44 × 1, 600 ≈ 400, 000).

(c) Receiver operating characteristics (ROC) curves

In addition to assessing the relative and absolute usefulness of a model, we also employ
receiver operating characteristics (ROC) curves and the area under the ROC curve (AUROC)
for comparing performance of the early warning models. The ROC curve shows the trade-oﬀ
between the beneﬁts and costs of a certain threshold τ . When two models are compared, the
better model has a higher beneﬁt (TP rate (T P R) on the vertical axis) at the same cost (FP
rate (F P R) on the horizontal axis).12 Thus, as each FP rate is associated with a threshold, the

12The TPR (also called sensitivity) gives the ratio of periods where the model correctly issues a warning to
all periods where a warning should have been issued, formally T P R = T P/(T P + F N ). The FPR (also called
speciﬁcity) gives the ratio of periods where the model wrongly issues a signal to all periods where no signal should
have been issued, formally F P R = F P/(F P + T N ). An ideal model would achieve a T P R of one (no missed
crises) and a F P R of zero (no false alarms).

34

measure shows performance over all thresholds or, equivalently, over all preference parameters µ
of the policy maker. The AUROC is computed using trapezoidal approximations and measures
the probability that a randomly chosen vulnerable state receives a higher predicted probability
than a tranquil period. A perfect ranking has an AUROC equal to 1, whereas a coin toss has
an expected AUROC of 0.5.

35

Imprint and acknowledgments 

Note 
This paper is forthcoming in the International Journal of Central Banking. 

Acknowledgements 
A previous version of the paper was titled "Setting Countercyclical Capital Buffers Based on Early-Warning 
Models – Would It Work?" (Behn et al. 2013). We would like to thank members of the ESRB Expert Group on 
Countercyclical Capital Buers, as well as seminar participants at the European Central Bank, European 
Systemic Risk Board, the Banque de France Workshop on Countercyclical Capital Buffers on 7 June 2013 in 
Paris and the 12th International Conference on Credit Risk Evaluation on 26-27 September 2013 in Venice for 
valuable comments and useful discussions. This paper is related to the comprehensive analysis conducted by 
the ESRB Expert Group on Countercyclical Capital Buffers. The views expressed are those of the authors and 
do not necessarily reflect those of the European Central Bank, the Eurosystem, De Nederlandsche Bank, or the 
European Systemic Risk Board. The usual disclaimer on errors applies here as well. 

Markus Behn 
European Central Bank, Frankfurt am Main, Germany; email: markus.behn@ecb.europa.eu 

Carsten Detken 
European Central Bank, Frankfurt am Main, Germany; email: carsten.detken@ecb.europa.eu 

Tuomas Peltonen 
European Systemic Risk Board, Frankfurt am Main, Germany; email: tuomas.peltonen@esrb.europa.eu 

Willem Schudel 
De Nederlandsche Bank, Amsterdam, Netherlands; email: c.j.w.schudel@dnb.nl 

© European Systemic Risk Board, 2016 

Postal address 
Telephone 
Website 

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+49 69 1344 0 
www.esrb.europa.eu  

All rights reserved. Reproduction for educational and non-commercial purposes is permitted provided that the 
source is acknowledged. 

Note: The views expressed in ESRB Working Papers are those of the authors and do not necessarily 
reflect the official stance of the ESRB, its member institutions, or the institutions to which the authors 
are affiliated. 

ISSN 
ISBN 
DOI 
EU catalogue No 

2467-0677 (online) 
978-92-95081-59-8 (online) 
10.2849/84807 (online) 
DT-AD-16-029-EN-N (online)