The time dimension of the links between loss given default and the macroeconomy.
Date: 2017-04-20
Institutions: European Central Bank
Subjects: Czechia, bankruptcy, corporate finance, financial market, macroeconomics

Tomáš Konečný, Jakub Seidler, 
Aelita Belyaeva, Konstantin Belyaev 

Working Paper Series 

The time dimension of the links 
between loss given default and 
the macroeconomy 

No 2037 / March 2017 

Disclaimer: This paper should not be reported as representing the views of the European Central Bank 
(ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. 

 
 
Abstract 

Most studies focusing on the determinants of loss given default (LGD) have largely ignored 
possible lagged effects of the macroeconomy on LGD. We fill this gap by employing a wide 
set  of  macroeconomic  covariates  on  a  retail  portfolio  that  represents  15%  of  the  Czech 
consumer  credit  market  over  the  period  2002–2012.  We  find  an  important  time  dimension 
to  the  links  between  LGD  and  the  aggregate  economy  in  the  Czech  Republic.  The  model 
that  allows 
a  number  of 
significant  macroeconomic  variables,  some  of  which  have  non-intuitive 
signs. 
Nonetheless,  a  more  general 
the  LGD  model  makes  current 
macroeconomic  variables  largely  irrelevant  and  highlights  the  importance  of  delayed 
responses of LGD to the macroeconomic environment. 

time  structure  of 

contemporaneous 

exclusively 

includes 

effects 

for 

JEL classification: C02, G13, G33. 

Keywords: Credit losses, loss given default, recovery rates, workout LGD. 

ECB Working Paper 2037, March 2017 1Non-technical summary 

Most  studies  focusing  on  the  determinants  of  loss  given  default  (LGD)  have  largely 

ignored possible lagged effects of the macroeconomy on LGD. We fill this gap by employing 

a wide set of macroeconomic covariates on a unique retail portfolio that represents 15% of the 

Czech  consumer  credit  market  over  the  period  2002–2012.    Using  data  on  consumer  credit 

(i.e.,  personal  loans),  credit  card  credit  and  overdrafts,  the  study  explicitly  models  delayed 

time effects of the macroeconomy on the final LGD value. To the best of our knowledge, the 

only study explicitly considering possible time effects of macroeconomic variables within the 

context  of  LGD  modeling  is  Bellotti  and  Crook  (2012).  The  present  study  differs  in  its 

explicit focus on potential lagged time effects, considering in particular a notably wider set of 

variables and lags of up to eight quarters within a simple and coherent estimation framework.  

The  study  uses  a  unique  comprehensive  dataset  on  loan  losses  corresponding  to 

approximately  15%  of  the  retail  consumer  credit  market  in  the  Czech  Republic  and  thus 

complements the rare evidence on the links between consumer LGD and the macroeconomy 

(e.g., Caselli  et  al. 2008; Bellotti and  Crook 2012;  and Calabrese 2012).  Besides discussing 

the results for a whole sample covering all three portfolios, we analyze each portfolio in more 

detail to explore possible subsegment-specific macroeconomic effects.  

Our findings suggest that one should be careful when considering possible links between 

the macroeconomy and  LGD,  given that macroeconomic time series data tend to be heavily 

correlated  and 

identification  of  size  effects  and 

their  direction  can  suffer  from 

multicollinearity issues. Nonetheless, by employingthe elastic net regularization that tends to 

perform well in similar settings we have been able to stress the importance of lagged macro 

effects in  addition  to  the  commonly  employed  contemporaneous  effects.  Furthermore,  the 

socio-demographic  background  of  the  clients  in  our  portfolio  plays  a  lesser  role  than  that 

indicated  by  exclusively  client-level  data  or  the  model  with  contemporaneous  values.  Our 

results should thus have profound implications for the modeling of retail LGD for regulatory 

purposes,  given  that  overly  focusing  on  contemporaneous  links  between  the  macroeconomy 

and LGD might lead to misperception of the risks in banks’ portfolios.  

ECB Working Paper 2037, March 2017 21.

Introduction

The  amount  of  research  on  loss  given  default  (LGD)  has  increased  substantially  since  the

adoption  of  the  Basel  II  Capital  Accord  and  its  successor  Basel  III.  Part  of  this  research 

interest  has  focused  on  the  macroeconomic  determinants5  of  LGD,  as  the  different 

characteristics influencing the recovery process can be determined by the current stage of the 

economy.  These  efforts  have  been  justified  by  regulators’  need  to  gauge  potential  losses  in 

banks’  loan  portfolios and to forecast the  credit  losses of  the  banking  sector with respect to 

macroeconomic developments, as well as by banks’ need to estimate their credit losses more 

accurately.  

The  present  study  focuses  on  the  link  between  the  LGD  and  macroeconomic  factors  using 

data  on  consumer  credit  (i.e.,  personal  loans),  credit  card  credit  and  overdrafts  in  a  sample 

representing approximately 15% of the Czech retail consumer credit market. The contribution 

of the paper is threefold. First, the study explicitly models potential delayed time effects of the 

macroeconomy  on  the  final  LGD  value.  Changes  in  macroeconomic  conditions  proxied  by 

key  macroeconomic  indicators  might  have  a  postponed  impact  on  various  dimensions 

important  for  the  recovery  of  defaulted  loans.  In  the  retail  segment,  clients’  willingness  to 

cooperate  probably  depends  both  on  their  current  situation  (e.g.,  unemployment  status  or 

earnings)  and  on  long-term  aspects  such  as  unemployment  spells  or  declining  savings.  The 

success of the recovery process might likewise depend on prevailing conditions in collateral 

markets, including real estate prices, though this effect might be limited in the case of retail 

loans, which are rarely hedged by real estate. To the best of the authors’ knowledge, the only 

5 In the following text we will use the term “macroeconomic” both for variables relating to the overall state of 
the  economy  (such  as  real  GDP  growth  and  inflation)  and  for  aggregates  in  the  retail  credit  segment  (such  as 

default rates and loan growth). 

ECB Working Paper 2037, March 2017 3study  explicitly  considering  possible  time  effects  of  macroeconomic  variables  within  the 

context of LGD modeling is Bellotti and Crook (2012). The authors use leads and lags of up 

to  six months  and conclude  that  using macroeconomic variables  generates inferior forecasts 

against benchmarks both without the macroeconomy and with the macroeconomic variables at 

the  time  of  default.  The  present  study  differs  in  its  explicit  focus  on  potential  lagged  time 

effects,  considering  in  particular  a  notably  wider  set  of  variables  and  lags  of  up  to  eight 

quarters within a simple and coherent estimation framework.  

The second contribution of the study is the selection of macroeconomic variables in our LGD 

models via elastic net regularization, which is an extension of the lasso regression (Tibshirani, 

1996).  The  elastic  net  is  a  convenient  tool  for  selecting  from  among  many,  possibly  highly 

correlated,  variables,  as  is  often  the  case  with  macroeconomic  time  series.  While  the  lasso 

tends to generate parsimonious models with only one variable from a set of highly correlated 

covariates,  the  elastic  net  provides  for  multicollinearity  by  choosing  a  group  rather  than  a 

single  representative  candidate.  The  multicollinearity  problem  within  the  context  of  ratings 

migration has been addressed by Figlewski et al. (2012). In their study of the U.S. corporate 

bond  market,  the  authors  find  that  the  direction  and  significance  of  the  links  between  U.S. 

corporate defaults  and  ratings  transitions  on the  one  hand,  and macroeconomic variables on 

the  other  hand,  depend  heavily  on  the  selection  of  the  remaining  (highly  correlated)  macro 

covariates.  

Finally,  the  study  uses  a  unique  comprehensive  dataset  on  loan  losses  corresponding  to 

approximately  15%  of  the  retail  consumer  credit  market  in  the  Czech  Republic  and  thus 

complements the rare evidence on the links between consumer LGD and the macroeconomy 

ECB Working Paper 2037, March 2017 4(e.g., Caselli  et al.  2008;  Bellotti  and  Crook 2012;  and  Calabrese  2012).  Besides discussing 

the results for a whole sample covering all three portfolios, we analyze each portfolio in more 

detail  to  explore  possible  subsegment-specific  macroeconomic  effects.  Our  focus  is  on  the 

“workout LGD” resulting from the collection of defaulted debt obligations and we leave out 

the market LGD observed from the market price shortly after the default event. We are aware 

that the scope of this study might be limited given its reliance on a limited sample of the retail 

consumer  portfolio  rather  than  on  the  whole  retail  credit  market.  However,  we  believe  our 

study still offers valuable information due to the scarce and comparatively rich data source in 

the context of evaluating  LGD determinants as  well as  the  straightforward transferability of 

our methodology to other institutions.  

Section  2  presents  in  more  detail  still  scant  evidence  on  the  links  between  LGD  and  the 

macroeconomy.  The  following  section  describes  the  data  on  LGD,  client-level  information, 

and  macroeconomic  variables  employed  in  the  study.  Section  4  outlines  the  overall 

methodology  and  the  mechanics  of  the  elastic  net  approach.  The  results  are  presented  and 

discussed in Section 5. The final section concludes. 

2. Empirical literature

A  few  studies  have  explicitly  addressed  the  corporate  recovery  rate  (i.e.,  1-LGD)  and  its

relationship to the state of the economic cycle (Altman et al., 2005a, 2005b, Frye 2002, 2005) 

by employing publicly traded defaulted bonds.6 Similarly, Acharya et al. (2007) used data on 

observed  prices  of  defaulted  securities  in  the  United  States  over  the  period  1982–1999  and 

concluded that the recovery rates in distressed industries are, on average, lower than those in 

6 A   number  of  studies  on  workout  LGD  focus  exclusively  on  firm-specific  factors  or  details  of  the  recovery 
process and avoid the potential influence of the macroeconomic environment (e.g., Bastos, 2010; Calabrese and 
Zenga, 2010; Emery et al., 2004; Grippa et al., 2005; Grunert and Weber, 2009). Witzany et al. (2010) employed 
survival analysis methods for LGD modeling, leaving macroeconomic factors unexplored. 

ECB Working Paper 2037, March 2017 5healthy industrial sectors. Nonetheless, the characteristics of defaulted corporate bonds differ 

significantly  from  workout  LGDs  on  defaulted  bank  loans,  as  the  post-default  price  is 

available only for the fraction of the debt that is traded and for which an after-default market 

exists, i.e., very often for corporate bonds issued by large companies only.  

Focusing on bank loans instead of corporate bonds, the empirical results by Dermine and Neto 

de Carvalho (2006) examine the timing of recoveries of bad and doubtful bank loans and the 

distribution of cumulative recovery rates. The authors estimate models on a European bank’s 

portfolio  of  loans  to  small  and  medium-sized  enterprises  and  do  not  find  any  support  for  a 

significant role of macroeconomic variables, including GDP growth, frequency of default in 

the industry sector, and the interest rate. This fact was explained by the absence of a sufficient 

recession during the period under consideration. 

Much less attention has been devoted to retail portfolios in the current literature. Bellotti and 

Crook (2009) found a significant relationship between LGD and retail interest rates, the level 

of unemployment, and earnings growth in their analysis of credit card LGDs at the transaction 

level.  Employing  aggregated  data,  Caselli  et  al.  (2008)  examined  the  sensitivity  of  LGD  to 

systematic  risk  and  found  a  relationship  between  LGD  and  the  development  of  the 

macroeconomy.  The  authors  employed  separate  multivariate  models  for  two  customer 

segments—SMEs  and  households.  For  SMEs  the  best  model  incorporated  the  aggregate 

number of employees and the GDP growth rate; for households the relevant macroeconomic 

variables  included  the  default  rate  (approximated  by  the  change  in  defaulted  loans  to  total 

loans),  the  unemployment  rate,  and  household  consumption.  The  authors  furthermore 

demonstrated a positive relationship between LGD and recovery collection length, but did not 

ECB Working Paper 2037, March 2017 6model  the  above-mentioned  link  in  their  multivariate  models.  Another  study  using  data  on 

individual  loans  (including  the  consumer  segment)  in  Italy  is  Calabrese  (2012).  The  author 

estimates  a  mixed  continuous-discrete  model  of  recovery  rates  and  finds  systematic  links 

between  recovery  rates  and  the  macroeconomy  proxied  by  the  interest  rate,  GDP  growth, 

unemployment, and the aggregate default rate. Finally, a top-down stress test on the Finnish 

economy  by  Jokivuolle  and  Virén  (2011)  included  a  system  of  equations  on  the  economy-

wide  probability  of  default  (PD),  LGD,  and  macroeconomic  variables.  It  estimated  a 

significantly negative relationship between the aggregate LGD and the gross profit rate. 

3. Data

The  retail  loan  and  consumer  credit  market  in  the  Czech  economy  was  significantly

underdeveloped at the beginning of the transformation process to market economy compared 

with western EU countries. However, financial deepening has caused a rapid credit expansion 

in  most  European  emerging  economies,  leading  to  considerable  accumulation  of  both  retail 

and corporate credit in the last twenty years. As such, the ratio of consumer credit to GDP in 

the  Czech  Republic  has converged  to a similar  level as  in  Western  European  countries  (see 

Table A1 for averages for selected EU countries). 

For  this  study  we  employ  a  dataset  consisting  of  over  18,500  defaulted  accounts  over  the 

period January 2003 to June 2010 provided by a large Czech bank. Using regulatory reporting 

data,  this sample  represents more than  15% of the Czech  retail consumer  credit  market  and 

consists of  consumer  loans  (credit  provided to  an  individual —or  family—on an  unsecured 

basis, also known  as personal loans), overdrafts (a type of revolving loan where a client—a 

natural pe rson—gets  additional  credit  through  a  current  account  up  to  a  limit  agreed  in 

advance), and credit card credit. It does not include loans for housing purchases or mortgages. 

ECB Working Paper 2037, March 2017 7The  bank  switched  to  the IRB  foundation  approach  at  the  beginning  of  2007,  and  data  for 

creating the LGD model for this transition were collected from 2002 onwards (five years for 

the retail portfolio, in accordance with the Basel requirement). Consumer loans account more 

than half of the sample, overdrafts for roughly 30%, and the credit card sub-portfolio for the 

rest.  

3.1. Definition of LGD 

The  Basel  Accord  defines  a  default  event  as  a  realization  of  one  or  more  of  the  following 

circumstances: the credit obligor i) is unlikely to pay, ii) is more than 90 days past due, or iii) 

is declared bankrupt. For retail clients only, the second and/or third condition has to be met. 

The default rate is defined as the ratio of the number of clients that defaulted during a given 

time period to the number of all observed clients at the beginning of the period concerned. As 

we focus only on standard bank loans excluding marketable instruments, our measure of LGD 

is derived as the ratio of losses to exposure at default (EAD). In order to measure LGD in this 

way,  recovery  cash  flows  from  defaulted  loans,  as  well  as  the  costs  of  the  bank’s  workout 

process,  must  be  observed.  The  loss  experienced  by  a  bank  is  understood  to  mean  the 

economic  loss,  i.e.,  the  loss  adjusted  for  discount  effects,  funding  costs,  and  direct  and 

indirect costs associated with collection of the instrument (BCBS, 2006). As the final amount 

collected from a defaulted loan can exceed the EAD, the real range of observed  LGDs may 

vary  from  negative  numbers  to  positive  numbers  higher  than  one.  We  truncate  the  LGD  at 

zero and one in order to make it comparable with the market LGD (obtained after the sale of 

defaulted market instruments).7 In  order  to  unify  the calculation procedure for either closed 

7 The choice to truncate LGD by zero and one is driven by a presumption that LGD behavior out of range [0,1] 
cannot be explained just by consumer’s characteristics (covariates) used in the regression procedure, but would 
require  to  incorporate  a  bank’s  collection  policy   in  terms  of  applied   interests,  fees  and  costs.  Due  to 
commercial 

ECB Working Paper 2037, March 2017 8loans or still open loans, we have chosen time horizon of one  year for observed LGD to be 

recorded.  Belotti  and  Crook  (2012)  are  also  have  used  period  of  one  year  in  the  collection 

process for LGD calculation. 

Table 1: LGD summary statistics for the whole sample and sub-portfolios, 2003q1-2010q2

Variable

Total

Consumer loans
Overdrafts
Credit cards

Obs

% of total

18,698
10,287
5,627
2,784

100
55.0
30.1
14.9

Mean

0.58
0.59
0.46
0.77

Median

Std. Dev.

0.79
0.78
0.46
0.90

0.40
0.42
0.30
0.30

Table 1 presents summary statistics of the LGD values for the  whole sample and individual 

sub-portfolios.  The  whole sample  average  LGD  of 0.58  is  very  close  to  the  value  of  0.54 

reported for the SME and household portfolio by Caselli et al. (2008) and to the value of 0.62 

reported for the Italian resident portfolio by Calabrese (2012). The value is nonetheless larger 

than the LGDs reported for corporates (e.g., Acharya et al., 2007). The highest average LGD 

is reported for the credit card portfolio (0.77) and the lowest is reported for overdrafts (0.46).  

Figure 1 presents the histogram of the LGD for the retail lending segment. 

confidentiality of data, the exact figures of due interests, fees and costs cannot be provided. Nonetheless, while 
the  issue  of  truncation  might  be generally  relevant,  it  is   likely  to  matter  more  for  the  evaluation  of  LGD 
determinants at the client and bank level, rather than at the macro-level, which is the main focus of the present 
study. 

ECB Working Paper 2037, March 2017 9Figure 1: Distribution of LGD in the sample, counts on the y-axis  

3.2 Transaction-level data 

We used historical observations from transactional systems on a monthly basis. Although our 

original  data  covers  the  period  from  January  2003  through June  2012,  i n  order  to  avoid 

possible estimation bias due to defaults with unfinished workout processes, we exclude cases 

after  June  2010.  Apart  from  the  information  on  LGDs,  the  data  contain  the  standard  socio-

demographic characteristics of retail clients usually collected by banks when a credit account 

is  opened.  These  include  the  client’s  age,  gender,  number  of  children,  education,  family, 

employment  status,  and  phone  ownership.  All  retail  loans  were  provided  in  Czech  crowns 

(CZK).  

The  retail  portfolio  offers  information  on  the  duration  of  the client’s  relationship  with  the 

bank in years and the exposure at default. Both variables are transformed logarithms. These 

client-related variables were used in prior studies, for example in Bellotti and Crook (2012). 

Table  2  contains  the  full  list  of  transaction-level  (henceforth  microeconomic)  variables 

employed.  

ECB Working Paper 2037, March 2017 10Table 2: Summary statistics of micro-variables employed, total sample 2003q1-2010q2

Variable
LGD
Relationship with bank*
Exposure at default*
Children
Education
Employment
Age
Female
Phone ownership
Family status
Note: The variables have been transformed into logarithm for the reasons of confidentiality as required by the data owner. Education 
=0 if Primary, =1 if Secondary, =2 if Graduate; Employment =0 if Unemployed, =1 if Student, pensioner, or house wife, =2 if employee 
or entrepreneur; Family status =1 if married or registered partnership.

Std. Dev.
0.4
0.7
1
0.7
0.6
0.3
11.7
0.5
0.5
0.3

Obs
18,698
18,698
18,698
18,698
18,698
18,698
18,698
18,698
18,698
18,698

Mean
0.6
2.9
9.9
0.3
0.5
1.6
37.9
0.3
0.5
0.6

Max
1
4.6
13.6
13
2
2
71.2
1
1
1

Min
0
1.1
4.7
0
0
0
18.4
0
0
0

3.3 Macroeconomic data 

The  macroeconomic data  we use reflect  the  choices  made  in  the  existing  literature on  LGD 

modeling.  These  data  will  serve  as  the  starting  point  for  our  estimations,  and  variable 

selection techniques will be applied for the ultimate model specifications. 

Table 3: Studies on LGD employing macro variables 

Author(s) and year of 
publication 

Acharya et al. (2007) 

Altman et al. (2005a) 

Sample 
coverage 

Corporate 
bonds 

Corporate 
bonds 

Altman et al. (2005b) 

Corporate 
bonds 

Macro variables employed by the 
study 

Did the study use lags or 
leads of macro variables? 

Default rate, volume of defaulted 
bonds, GDP growth, S&P stock 
index 
Default rate, Δdefault rate, total 
volume of (high yield) 
bonds,volume of defaulted bonds, 
GDP growth (y-o-y), ΔGDP 
growth (y-o-y), GDP indicator, 
S&P 500 index, ΔS&P 500 index, 
U.S. Treasury rate 
GDP growth (y-o-y), ΔGDP 
growth (y-o-y) 

no 

no 

ECB Working Paper 2037, March 2017 11Belotti and Crook (2012) 

Credit cards 

Retail interest rates, unemployment 
level, earnings growth 

yes,              

0-6months leads and lags

Bruche and Gonzalez-
Aguado (2008) 

Calabrese (2012) 

Corporate loans 

Caselli et al. (2008) 

Households and 
SMEs 

Dermine and Neto de 
Carvalho (2006) 

SMEs 

Jokivuolle and Viren (2011)  Corporate bank 

loans 

GDP growth (y-o-y), 
unemployment, investment growth 
(y-o-y), S&P 500 return 

Interest rate on delayed payment, 
GDP growth (y-o-y), 
unemployment, default rate 

ΔDefault-to-loan ratio (ΔD/L, y-o-
y), volume of bank loans, GDP 
growth (y-o-y), employment, 
Δunemployment, household 
consumption, total gross 
investment, total production, gross 
annual available income 
GDP growth (y-o-y), industry 
default rates 

Output gap, gross profit rate, 
interest rate, indebtness, stock 
market index and a housing price 
index, real house prices, real stock 
index, real interest rate 

no 

no 

no 

no 

no 

Table 3 lists the empirical studies on LGD that have considered macroeconomic effects, their 

portfolio of interest, a full list of the macroeconomic variables employed, and an indication of 

whether  they  allowed  for  time  effects.  We  focus  in  particular  on  those  candidate  variables 

which are potentially relevant to the retail segment and either take their exact counterparts or 

construct the closest possible approximation. Given the boundedness of our loss-given-default 

measure,  we  furthermore  transform  level  variables  with  a  clear  growing  trend  into  yearly 

growth rates.  

The indicators of retail credit risk we use include the amount of retail loans defaulting, the 3-

month  retail  default  rate,  and  the  first  difference  of  the  retail  default  rate  (e.g.,  Calabrese, 

2012; Caselli et al., 2008; Dermine and Neto de Carvalho, 2006). In addition, the ratio of the 

ECB Working Paper 2037, March 2017 12amount of retail loans classified as non-performing to the total retail credit portfolio (the NPL 

ratio)  proxies  for  materialized  credit  risk  in  banks’  balance  sheets.  The  retail  credit  growth 

variable  aims  to  approximate  demand  for  retail  credit  (Caselli  et  al.,  2008).  Labor  market 

developments are captured by the unemployment rate, change in the unemployment rate, and 

total employment (Caselli et al., 2008). Instead of the earnings index, as employed by Bellotti 

and  Crook  (2012),8  we  use  real  wage  growth  to  approximate  the  evolution  of  household 

earnings. The indicators referring to aggregate supply and demand are real GDP growth and 

change in real GDP growth (Altman et al., 2005a; Altman and Brady, 2002), growth in real 

industrial  production,  real  consumption  growth,  and  real  investment  growth  (Caselli  et  al., 

2008). Apart from the real 3-month Pribor as a measure of the monetary policy rate, we use 

average  retail  credit  rates and  the  retail credit  spread, defined as  the difference  between the 

average rates on retail loans and deposits (e.g., Bellotti and Crook, 2012). The inflation in the 

economy is approximated by CPI index growth, while real estate price index growth reflects 

the  situation  on  the  real  estate  market.  Growth  in  the  PX-50  stock  market  index  tracks 

developments in stock markets (e.g., Jokivuolle and Virén, 2011). 

All growth variables are expressed in  year-on-year terms, while level variables  are logged.9 

We  generate  leads  and  lags  of  the  macroeconomic  variables  of  up  to  eight  periods.  Some 

aggregates relating to the retail loan segment are available only from the beginning of 2002 or 

later. These include the amount of retail loans and defaults, retail credit rates and spreads, and 

the default rate and the NPL ratio. As a consequence, we had to shift the initial sample date in 

order to obtain the desired number of lags. The most restricted sample, allowing for eight lags 

8 The authors used an economy-wide earnings index, including bonuses as a ratio of the retail price 
index. 
9 Interest rates are not considered as level variables. 

ECB Working Paper 2037, March 2017 13of  all  the  macroeconomic  variables  considered,  was  limited  to  defaults  that  occurred  after 

2005q1.10  Instead  of  interpolating  the  quarterly  macroeconomic  covariates  to  monthly 

frequency,  we  mapped  the  same  quarterly  values  to  all  defaults in  the  relevant  quarter.  The 

sources of macroeconomic data are the Czech National Bank (CNB) and the Czech Statistical 

Office (CZSO). A statistical summary of the macroeconomic variables in the current study is 

presented in Table 4. These will be accounted for within the elastic net framework, which is 

described in more detail in the following section.11  

10 The estimation results presented in the following sections use the sample starting in 2003q1, i.e., the sample 
only includes contemporaneous values of the yearly growth rates of total and defaulted retail loans, retail rates 
and spreads, and default rates and the NPL ratio. Our results from the most restricted sample (2005q1–2010q2) 
are  qualitatively  very  similar  to  the  reported  output.  Similarly,  earlier  cutoff  dates  before  2003q1,  which 
effectively dropped some of the above-mentioned variables, left our results practically unchanged. These results 
are available upon request. 
11  Table  A2  in  the  Appendix  presents  the  correlation  table  of  the  macroeconomic  variables  employed.  The 
shaded areas highlight correlation coefficients in excess of 0.6, indicating a high degree of collinearity. 

ECB Working Paper 2037, March 2017 14Table 4: Summary statistics of macroeconomic variables, whole sample 2003q1-2010q2

Variable

Defaulted loans growth (y-o-y)
Default rate (3 months)
ΔDefault rate (3 months)
NPL ratio
Retail loans growth (y-o-y)
Unemployment rate
ΔUnemployment rate
Total employment (in thds)*
Real wage growth (y-o-y)
Real GDP growth (y-o-y)
ΔReal GDP growth (y-o-y)
Real ind. production growth  (y-o-y)
Real consumption growth (y-o-y)
Real investment growth (y-o-y)

bo 3
Rate on retail loans
Retail rate spread
CPI(y-o-y)
Property price index (y-o-y)
Stock market index (PX-50) (y-o-y)

ea  

Obs

18,698
18,698
18,698
18,698
18,698
18,698
18,698

18,698
18,698
18,698
18,698
18,698
18,698
18,698
8,698
18,698
18,698
18,698
18,698
18,698

Mean

Std. Dev.

0.3
1.7
0.0
8.0
20.3
7.0
0.2

3875.9
3.4
1.3
-0.1
0.5
2.2
-4.8
0.9
14.0
12.6
2.0
1.0
19.5

0.2
0.6
0.2
0.8
7.0
1.2
0.5

88.0
1.2
4.9
1.6
2.7
2.1
13.9
0.8
0.5
0.6
1.9
0.2
33.6

Min

-0.1
0.6
-0.3
6.4
9.3
4.3
-0.7

3780.1
1.5
-5.5
-3.8
-6.5
-1.1
-23.0
.
13.0
11.5
-0.3
0.8
-52.7

Max

0.6
3.2
0.3
9.4
31.4
8.5
1.3

4058.2
6.1
7.6
2.3
6.0
5.9
25.1

15.0
13.7
7.4
1.4
67.2

Note: *The variable is expressed in absolute value.

4. Methodology

We estimate the generalized-linear model (GLM) regressions with logit transformation of the

LGD parameter (Hastie and Tibshirani, 1990). The GLM framework is a standard benchmark 

that has been used in a number of existing studies on LGD determinants and forecasting (e.g., 

Altman et al., 2005b; Caselli et al., 2008; Grunert and Weber, 2009). In fact, other parametric 

approaches,  such  as  inverse-Gaussian,  Tobit,  and beta 

transformation,  do  not  seem  to 

outperform the standard approaches (Qui and Zhao, 2011; Bellotti and Crook, 2012). 

We run our estimations on the dataset described in Section 2, which aimed to match or at least 

approximate all the macro variables used in existing studies using macroeconomic variables 

(see  Table  3).  For  the  results  presented  in  later  sections  we  select  variables  (and  their   

ECB Working Paper 2037, March 2017 15respective  time  effects  where  applicable)  using  elastic  net  regularization  (Friedman  et  al., 

2010).  Elastic  net  regularization  is  an  extension  of  the  lasso  regression  developed  by 

Tibshirani  (1996).  The  lasso  regression  reduces  the  variability  of  the  estimates  through 

coefficient shrinkage. Given that some coefficients are set to zero, the procedure generates a 

sparser model and can serve as a variable selection tool at the cost of only moderate bias.12 

While the advantage of the lasso regression over other selection procedures, such as stepwise 

regression, is its lack of path dependency (some of the coefficients set to zero might change 

again  over  the  iteration  process),  the  lasso  applies  only  to  cases  of  more  observations  than 

variables. Furthermore, in the case of multicollinearity typical of macroeconomic time series 

data,  the  procedure  tends  to  select  only  one  variable  in  the  group.  Elastic  net  regularization 

aims  to  overcome  the  above-mentioned  limitations.  The  elastic  net  derives  from  the  lasso 

regression,  yet it allows for cases of more  variables than observations and  selects groups of 

highly correlated variables  instead of  a single  group representative  as  is  typical  of the lasso 

(Zhou and Hastie, 2005). Empirical studies suggest that the elastic net tends to outperform the 

lasso  in  settings  with  highly  correlated  groups  of  variables  (e.g.,  Zhou  and  Hastie,  2005; 

Friedman et al., 2010). The elastic net regularization problem for generalized linear models is 

defined as 

1
𝑁𝑁 𝐷𝐷𝐷𝐷𝐷𝐷𝑚𝑚𝐷𝐷𝑚𝑚𝐷𝐷𝐷𝐷(𝛽𝛽0, 𝛽𝛽) + 𝜆𝜆𝑃𝑃𝛼𝛼(𝛽𝛽)�

𝑚𝑚𝑚𝑚𝑚𝑚𝛽𝛽0,𝛽𝛽 �
where N is the sample size, 

 stands for the intercept and 

 are the estimated 

 regression 

, 

parameters. The penalty term 

𝛽𝛽0

 corresponds to 

𝛽𝛽

𝑝𝑝

𝑃𝑃𝛼𝛼(𝛽𝛽)

 for 

 and 

. 

(1−𝛼𝛼)

2
2 ‖𝛽𝛽‖2

𝑝𝑝
𝑗𝑗=1

(1−𝛼𝛼)

2
2 𝛽𝛽𝑗𝑗

𝑃𝑃𝛼𝛼(𝛽𝛽) =
12 The ridge regression—an alternative shrinkage method—shrinks yet keeps all the coefficients in the model. 

+ 𝛼𝛼‖𝛽𝛽‖1 = ∑

+ 𝛼𝛼�𝛽𝛽𝑗𝑗��

0 < 𝛼𝛼 < 1

𝜆𝜆 ≥ 0

�

ECB Working Paper 2037, March 2017 16The elastic net converges to the lasso as 

1 and to the ridge regression as 

0. 

We  obtain  our  final  model  specification  by  the  following  procedure.  First,  we  employ  the 

𝛼𝛼 →

𝛼𝛼 →

default  ten-fold  cross  validation  and  calculate  the  cross-validated  mean  squared  error 

(CVMSE)  for  all  values  of  lambda  and  alpha.13  Then  we  locate  a  value  of  lambda  over  all 

alphas with the minimum CVMSE. Finally, to obtain a more parsimonious specification, we 

select  a  model  corresponding  to  a  lambda  value  within  one  standard  error  of  the  minimum 

CVMSE.14 

Our  benchmark  specification  contains  exclusively  client-level  information.  In  the  following 

models,  we 

first  estimate 

the 

specification  using  client-level 

information  and 

contemporaneous macroeconomic variables, that is, we do not allow for time effects. Finally, 

we  present  a  full  model  including  client-level  and  macroeconomic  data  with  time  effects 

(lagged and lead values).  

5. Results

5.1 Whole portfolio

We begin the analysis with an examination of the marginal contributions relating to each of 

the macroeconomic variables with respect to the loss given default (LGD). Table 5 presents 

the  condensed  output  from  the  OLS  regressions  of  the  logit  LGD  on  a  particular 

contemporaneous macro variable (i.e., no time effects, ‘no lags’ column), and on its lags from 

t  to  t-8.  Values  listed  in  the  second  column  represent  the  sum  of  beta  coefficients  and  thus 

13 We considered a sequence of alpha values ranging from 0 to 1 with increments of 0.1. 
14  More  details  on  the  selection  algorithm  for  the  glmnet  package  in  R  can  be  found  at  http://cran.r-
project.org/web/packages/glmnet/glmnet.pdf. 

ECB Working Paper 2037, March 2017 17provide initial information on the long-term correlation between a macro variable of concern 

and the logit LGD.15  

Table 5: Marginal contributions of macroeconomic variables, whole sample 
2003q1-2010q2

(1)
no lags

(2)
lags t to (t-8)

Defaulted loans growth (y-o-y)
Default rate (3 months)
ΔDefault rate (3 months)
NPL ratio
Retail loans growth (y-o-y)
Unemployment rate
ΔUnemployment rate
Total employment (in thds)
Real wage growth (y-o-y)
Real GDP growth (y-o-y)
ΔReal GDP growth (y-o-y)
Real ind. production growth  (y-o-y)
Real consumption growth (y-o-y)

Real investment growth (y-o-y)
Real Pribor3m

Rate on retail loans

Retail rate spread

CPI(y-o-y)

Property price index (y-o-y)

Stock market index (PX-50) (y-o-y)

  Coefficient
0.25
0.05 ***
0.10
-0.02
-0.53
0.04 ***
0.16 ***
-3.11 ***
-0.03 *
-0.02 ***
0.03 *
0.06
-0.03 *
-0.01 ***
0.07 ***
0.04

0.04
-0.03 ***
-0.51 ***
0.18 *

SE
0.17
0.02
0.18
0.03
0.55
0.01
0.06
1.04
0.02
0.00
0.02
0.72
0.02

0.00
0.02

0.04

0.04

0.01

0.14

0.1

    Coefficient
-1.10
0.16 **
0.00 **
-0.12 *
-0.60
0.06 ***
0.30 **
2.36
-0.01 ***
-0.05 ***
-0.07 *
0.02
-0.02
-0.01 *
0.05
0.03

0.02

0.02

0.38
-0.05 **

SE
1.10
0.06
0.31
0.07
1.10
0.02
0.11
1.60
0.05
0.02
0.04
0.13
0.05

-0.01
0.10
0.15

0.12

0.02

0.47

0.02

Note: *, **, *** stand for 10 %, 5 %, and 1 % significance levels respectively.
The signs and standard errors in the specification with lags relate to the sum of coefficients 
on lagged values.
As the sample only includes contemporaneous values of the yearly growth rates of total and 
defaulted retail loans, retail rates and spreads, of default rates and the NPL ratio, results in 
Column 2 were obtained from the restricted sample covering 2005q1–2010q2.

15 Furthermore, a preliminary analysis from simple regressions of average LGD on individual lagged values of 
macroeconomic variables (see Figure A1 in the Appendix) reveals a temporal pattern of the correlations between 
periods t and t-8. The temporal patterns, as well as beta coefficients in the OLS regressions in Table 5 indicate 
smooth correction-style dynamics between the LGD and macro variables. Individual beta coefficients from the 
OLS regressions in Column (2) can be provided upon request.  

ECB Working Paper 2037, March 2017 18 
The preliminary evidence  is consistent with  the expected  significant link between  LGD and 

the macroeconomic environment. Most variables are significant and have the expected signs. 

The only counterintuitive and statistically significant signs are the coefficients for the yearly 

absolute change in the GDP growth rate and the growth rate of the stock market index in the 

specification  with  contemporaneous  values  (Column  1).  Other  cases  with  counterintuitive 

signs,  such  as  the  positive  correlation  of  LGD  with  growth  of  industrial  production  or  with 

growth in real estate prices in Column (2), are imprecise with large standard errors and hence 

not statistically significant. 

The  marginal  contributions  for  the  individual  sub-portfolios  in  Table  6  provide  a few  more 

detailed  insights.  First  of  all,  the  correlations  between  LGD  and  macroeconomic  covariates 

tend  to  be  weaker  for  overdrafts  and  credit  cards than  for  consumer  loans,  where  the 

coefficients  on  most  macro  variables  are  statistically  significant.  Secondly,  while  there  are 

fewer statistically significant coefficients in the overdraft portfolio as compared to consumer 

loans,  in  both  cases  the  coefficients  remain  intuitive.  This  is  less  so  for  the  credit  card 

portfolio—for example, the positive correlation between LGD and total employment, and the 

negative  correlation  between  the  LGD  and  the  unemployment  rate as  well  as   the  absolute 

change  in  the  unemployment  rate  in  Column  (6)  run  strongly  against  ex  ante  expectations. 

Finally, the credit card portfolio provides rather ambiguous information on the direction of the 

links  between  the  macroeconomic  variables  and  LGD,  as  in  most  cases  the  coefficient  sign 

varies 

depending 

on  whether 

or 

not 

time 

effects 

are 

allowed 

for.

ECB Working Paper 2037, March 2017 19s
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ECB Working Paper 2037, March 2017 20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The  output  from  whole  sample  logistic  regressions  of  LGD  on  client-specific  and 

macroeconomic variables in  Table  7 provides  a  somewhat  more complex picture.16 Column 

(1) presents the benchmark specification. The results highlight intuitive attributes that should,

on average, increase the chances of a successful workout process. The factors contributing to 

lower LGD include a longer relationship with the bank and smaller exposure at default. The 

positive  relationship  between  LGD  and  exposure  at  default  is  consistent  with  Calabrese 

(2012), Dermine and Neto de Carvalho (2006), and Grippa et al. (2005). On the other hand, 

Asarnow  and  Edwards  (1995)  do  not  find  a  significant  link  between  LGD  and  exposure  at 

default.  The  output  in  Column  (1)  furthermore  suggests  that  younger,  better  educated  male 

clients  with  children  and  phone  ownership  represent  the  most  promising  outcome  of  the 

workout  process.  The  only  counterintuitive  result  is  the  contribution  of  employment  or 

entrepreneurship status to higher LGD, i.e., a lower recovery rate. 

Column  (2)  represents  an  extended  model  with contemporaneous  macroeconomic  variables. 

The  coefficient  sign  and  size  of  the  client’s  most  robust  characteristics,  i.e.,  exposure  at 

default, length of relationship with the bank, and education, do not depart substantially from 

the benchmark specification in Column (1). Importantly, once the macroeconomic dimension 

is  included,  the  remaining  client-level  information  that  was  significant  in  the  benchmark 

specification does not pass the elastic net shrinkage procedure. These less-stable client factors 

16 We use variables identified by the elastic net regularization procedure and estimate the GLM with a logit link 
function for the LGD variable.  

ECB Working Paper 2037, March 2017 21Table 7: Logit estimates, whole sample 2003q1-2010q2

Explanatory variable logit LDG

Client- specific factors
Exposure at default
Relationship with bank
Age    
Children
Phone  
Employment  
Education
Female    
Macroeconomic variables, current values
Real GDP growth (y-o-y)
∆Real GDP growth (y-o-y)
Real Consumption Growth (y-o-y)  
Real Investment Growth (y-o-y)   
Real Pribor3m
Inflation rate (y-o-y)
Property prices (y-o-y)
Default rate   
Retail loan growth (y-o-y)
Macroeconomic variables, lagged and lead values
Real GDP growth (y-o-y) (t-1)
Real GDP growth (y-o-y) (t-2)
Real investment growth (y-o-y) (t-2)
Unemployment rate (t-8)        
Real wage growth (y-o-y) (t-3) 
Real wage growth (y-o-y) (t-4) 
Real wage growth (y-o-y) (t-5) 
Constant
Alpha
Observations
Adjusted R-squared
AIC

Client specific
(1)

All variables, no lags

(2)

All variables, lags included
(3)

Coefficient

SE

Coefficient

SE

Coefficient

SE

1.448***
-0.033***
0.397**
-1.046***
-0.498***
0.206***
-0.893***
0.362***

0.059
0.004
0.192
0.079
0.117
0.059
0.097
0.123

1.036***
-0.082***
0.815***
-0.059
0.388***

-0.631***
-0.000

0.023
0.284***
-0.398***
-0.056***
0.395**
-0.229***
-1.690**
-0.774***
-0.093***

0.909

-13.778***
0.9
18698
0.056
130270.953

-5.001***
0.9
18698
0.152
128276.671

0.058
0.004
0.183
0.087
0.113

0.093
0.116

0.094
0.080
0.090
0.019
0.165
0.064
0.745
0.126
0.027

1.235

1.044***
-0.080***
0.774***

0.057
0.004
0.181

-0.607***

0.093

-0.232***

0.070

-0.054**

0.021

0.063
0.063
0.013
0.225
0.109
0.106
0.088
1.563

-0.123*
-0.143**
-0.035***
0.315
-0.097
-0.444***
-0.161*
-7.704***
0.3
18698
0.152
128264.055

Note: *, **, *** stand for 10 %, 5 %, and 1 % significance levels respectively. Robust standard errors reported.
The values of Alpha stand for the elastic net weighting parameter with lowest residual mean-squared error.

include  gender,  number  of  children,  phone  ownership,  and  employment  status  with  a 

counterintuitive positive sign in the benchmark regression.  

The elastic net estimates in Column (2) put forward several macroeconomic factors consistent 

with previous findings. The negative association of LGD with real consumption growth is in 

line with the findings on households and SMEs by Caselli et al. (2008). A similar result holds 

for  real  investment  growth.  A negative  and  significant  relationship  between  investment  and 

LGD was reported  for  the retail  segment  by  Caselli  et  al.  (2008).  Bruche  and  Gonzalez-

ECB Working Paper 2037, March 2017 22 
Aguado (2008), on the other hand, do not find a significant link. Most of the other coefficient 

estimates likewise provide an  intuitive  interpretation.  This  concerns  the  positive  sign  on the 

interest rate  and real estate price  growth (e.g., Jokivuolle and Virén, 2011) and the inflation 

rate. Unlike Caselli et al. (2008), who used the total volume of retail loans, we find that the 

negative sign of the coefficient on retail loan growth is highly significant.17  

Inspection of the estimates of macro variables in Column (2) nonetheless indicates that some 

coefficients  have  counterintuitive  yet  significant  signs.  This  concerns  the  positive  sign 

(significant at a 1% level) of the change in the real GDP growth, and the negative sign of the 

default rate. 

Change in real GDP was used in the study of corporate bonds by Altman et al. (2005a). The 

authors found that while real GDP growth in their multivariate specification of the recovery 

rate model was insignificant and had the incorrect sign, change in real GDP growth improved 

the model performance markedly.18 In the present specification, the estimates do not conform 

to the results of Altman et al. (2005a). The signs on change in real GDP growth in Column (2) 

are in line with the variable’s marginal contribution in the contemporaneous specification in 

Table 5 (Column 1). The more  reasonable sign  estimates of the marginal contribution using 

lagged effects (Column 2) nonetheless suggest that the  model  specification  not allowing for 

time effects might be too restrictive.  

The  significant  positive  relationship  between  the  aggregate  default  rate  and  LGD,  as 

suggested by existing studies, is not supported by the counterintuitive results in Column (2) 

17 Altman et al. (2005a) likewise find a significantly negative sign for corporate bonds. 
18 Similarly, Calabrese (2012) reports a positive link between the LGD and real GDP growth. However, Caselli 
et al. (2008) and Acharya et al. (2007) found a negative link, though in the latter case only partly significant.   

ECB Working Paper 2037, March 2017 23(e.g.,  Altman  et  al.,  2005b;  Frye,  2005;  Düllmann  and  Trapp,  2005,  for  corporate  bonds; 

Altman  et  al.,  2005c,  for  corporate  loans; Caselli  et  al.,  2008,  for  SMEs  and  households). 

While  the  unconditional  contemporaneous  correlation  between  the  default  rate  and  LGD  is 

positive (see Table 5), the conditional correlation becomes negative once other variables have 

been  controlled  for.  The  above-mentioned  result  is  partly  consistent  with  the  ambiguous 

results by Caselli et al. (2008), who report an insignificant link for a pooled portfolio of SMEs 

and households, as well as by Calabrese (2012), who finds a negative link between the default 

rate and extreme values of the LGD. 

The  adjusted  R-squared  of  0.06  for  the  benchmark  client-specific  model  in  Column  (1) 

improves notably  to  approximately  0.15  for  specifications  including  macroeconomic 

determinants.  This  finding  is  consistent  with  Altman  (2005a),  who  reports  a  significant 

increase in the explained variation once change in GDP growth is included in the estimations. 

The same study, however, did not observe  an increase in R-squared  when real GDP growth 

was  included  instead  of  change  in  real  GDP  growth.  The  results  from  specifications  with 

contemporaneous  macroeconomic  variables  thus  partly  conform  to  the  extant  studies,  but 

should be evaluated carefully given the counterintuitive signs on key macro correlates such as 

change in real GDP growth or the default rate.  

The  results  listed  in  Column  (3)  point  to  the  importance  of  the  time  dimension  for  the 

evaluation  of  links  between  LGD  and  the  macroeconomy.  In  particular,  while  only  two 

contemporaneous  macroeconomic  indicators  from  Column  (2)  passed  the  elastic  net 

regularization  procedure  (real  consumption  growth  and  retail  loan  growth),  all  remaining 

variables enter the models with lags. Furthermore, the overall effect of each variable preserves 

ECB Working Paper 2037, March 2017 24an  intuitive  sign  and  is  significant  in  at  least  one  specification.  In  Column  (3),  LGD  is 

negatively linked to real GDP in the last two quarters and real investment growth in period t-

2. In  the  case  of  real  GDP  growth,  the  negative  coefficient  sign  conforms  to  the  results

reported  by  Bruche  and  Aguado  (2010)  and  Calabrese  (2012).  For  both  real  GDP  and  real 

investment  growth,  the  coefficient  furthermore  exceeds  the  marginal  contributions  from 

Table 5.  

A  number  of  existing  studies  have  found  a  significant  contribution  of  contemporaneous  or 

recent  unemployment  dynamics  for  LGD  modeling  (e.g.,  Acharya  et  al.,  2007;  Bellotti  and 

Crook,  2009;  Bruche  and  Aguado,  2008;  and  Caselli  et  al.,  2008).19  The  model  with  time 

effects  in  Column  (3)  points  to  unemployment  links  over  a  longer  time  horizon  of  eight 

quarters,  but  contrary  to  the  abovementioned  studies  statistically  insignificant.  .  The  final 

variable that passed the elastic net procedure in the specification with time effects in Column 

(3) is  real  wage  growth.  Unlike  the  estimates  for  real  GDP  growth  and  real  investment

growth, where the difference from the contemporaneous model was not substantial in terms of 

the  size  of  the  lag,  real  wage  growth  relates  to  LGD  with  a  lag  of  about  one  year. 

Furthermore,  wage  effects  did  not  appear  in  the  specification  without  time  effects,  which 

therefore  provided  imprecise  estimates  of  macroeconomic  links  to  LGD.  The  general 

evidence  for  a  negative  link  between  wages  and  LGD  is  consistent  with  the  findings  of 

Bellotti  and Crook (2012), who  found a significant link between  the recovery  rate  on  credit 

cards and earnings growth (though only at the 10% level).  

As  a  part  of  our  exercise  we  allowed  for  both  lead  and  lagged  interlinkages  between  the 

macroeconomy and LGD. While all the coefficient estimates kept their signs and remained of 

19 Interestingly, some studies report rather counterintuitive results for the unemployment rate (Calabrese, 2012). 

ECB Working Paper 2037, March 2017 25roughly  similar  size,  in  some  cases  they  became  smaller  or  even  non-significant.  Most 

importantly,  the  elastic  net  procedure  did  not  select  any  new  factor  that  is  consistently  and 

significantly  related  to  our  LGD  measure,  in  line  with  the  study  by  Bellotti  and  Crook 

(2012).20  

One  should  note  that  the  specification  allowing  for  time  effects  yielded  a  sparser  model  in 

terms of client-level information. The only dimensions that remained robust were the length 

of the relationship with the bank, the size of exposure at default, and education. This relates to 

the  explained  variation  of  the  flexible  specification  with  delayed  responses  of  LGD.  Given 

that the value added in terms of the adjusted R-squared is virtually zero (a stagnant 0.152 in 

Columns  2  and  3),  allowing  for  lagged  responses  of  LGD  should  provide  a  better 

understanding  of  the  interactions  with  the  macroeconomy  over  time,  rather  than  a  major 

improvement in the forecasting of LGD performance.  

The  results  presented  in  Columns  (2)  and  (3)  of  Table  7  represent  a  key  deliverable  of  our 

study.  We  distinguish  between  models  with  and  without  time  effects,  employ  variable 

selection  techniques,  and  see  how  they  differ  in  terms  of  the  final  specifications  and 

performance.  We  show  that  the  model  in  Column  (2),  which  selected  exclusively  from 

macroeconomic  variables  with  no  time  effects,  and  the  model  in  Column  (3),  which 

considered  both  contemporaneous  values  and  time  effects,  tend  to  differ  to  a  substantial 

degree.  This  outcome  points  strongly  in  favor  of  the  inclusion  of  time  effects  in  LGD 

estimations.  In  the  following section we  check  how this pattern is robust  at  the level  of  the 

individual portfolios. 

20  The  results  of  the  estimations  allowing  for  lagged  and  lead  effects  can  be  provided  by  the  authors  upon 
request. 

ECB Working Paper 2037, March 2017 265.2 Consumer loans and overdrafts 

The  logit  estimates  for  the  individual  portfolios  provide  more  detailed  information  on  the 

drivers  of  the  results  from  the  whole sample.  Table  8  provides  estimates  for  the  consumer 

loan and overdraft portfolios, while credit cards have been relegated to the Appendix (Table 

A3).  The  main  reason  in  the  case  of  credit  cards  was convergence  issues  arising  in  the 

estimations  using  the  elastic  net  algorithm,  as  the  large  variance  of  the  minimum  cross-

validated  mean  squared  error  (CVMSE) implied  that  only  a  constant  should  be  sel ected  for 

the lambda value within one standard error of the minimum CVMSE. As a result, we treat the 

results  for  credit  cards  with  some  caution and  report  the  output  for  a  lambda  value 

corresponding  to  the  minimum  CVMSE.  It  should  nonetheless  be  noted  that  the  results  for 

credit  cards  using  lambda  for  the minimum  RMSE  are  consistent  with  the  output  for  

consumer  loans  and  overdrafts.  Specifically,  the  overall  pattern  is  qualitatively  identical  for 

the whole sample and the individual sub-portfolios; while the coefficients on client-level and 

contemporaneous  macroeconomic  covariates  tend  to  be  significant  if  no  time  effects  have 

been  allowed  for,  they  become  largely  redundant  once  lagged  macroeconomic  effects  enter 

the model. The only client-level factors that pass the elastic-net regularization procedure once 

time effects are included are the size of exposure at default and the length of the relationship 

with 

the  bank.  This, 

again, 

is fully 

consistent  with 

the  whole 

sample. 

ECB Working Paper 2037, March 2017 27 
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ECB Working Paper 2037, March 2017 28 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The  benchmark  specifications  in  Columns  (1)  and  (4),  which  considered  exclusively  client-

level information, largely  conformed  to expectations,  but delivered strongly counterintuitive 

results  for  Education  in  the  former cas e and  Employment  in  the  latter.  These  irregularities 

nonetheless proved irrelevant in the extended specifications. In Columns (2) and (5) of Table 

8,  which  summarize the  es timates  accounting  for  contemporaneous  macro  links,  real 

consumption growth and investment growth proved to be statistically significant only in the 

case  of  consumption  loans,  which  ultimately  drove  the  results  for  the  whole sa mple.  The 

counterintuitive estimates for the default rate and absolute change in the GDP growth rate in 

Columns (2) and (5) replicate the output of the whole sample (Column (2), Table 7). Turning 

to  the  specifications  with  time  effects  in  Columns  (3)  and  (6),  one  can  observe  that  the 

statistically  significant  macroeconomic  effects  are  relevant  to  either  consumer  loans  or 

overdrafts only, the only exception being real wage growth. Nonetheless, even in the case of 

real wage growth the actual statistically significant lags between the two sub-portfolios differ. 

It is thus relatively straightforward to assign the drivers of the results for the whole sample to 

a particular sub-portfolio. While real  investment growth, unemployment rate-related  factors, 

and real wage growth seem to be key macroeconomic correlates for the consumer loan LGD, 

for overdrafts the relevant macroeconomic time effects are real GDP and real wage growth.  

6. Conclusion

Our approach allowed for investigation of the relevance of delayed macroeconomic effects to

the realized LGD on a sample representing 15% of the Czech retail credit market. One should 

be careful when considering possible links between the macroeconomy and LGD, given that 

macroeconomic time series data tend to be heavily correlated and identification of size effects 

and  their  direction can suffer  from  multicollinearity  issues.  By opting  for  explicit treatment 

of  

ECB Working Paper 2037, March 2017 29model  selection  through  elastic  net  regularization,  we  highlighted  the  importance  of  lagged 

macro effects other than the commonly employed contemporaneous effects. Furthermore, the 

socio-demographic  background  of  the  clients  in  our  portfolio  plays  a  lesser  role than  tha t 

indicated  by  exclusively  client-level  data  or  the  model  with  contemporaneous  values.  Our 

results should thus have profound implications for the modeling of retail LGD for regulatory 

purposes,  given  that  overly  focusing  on  contemporaneous  links  between  the  macroeconomy 

and LGD might lead to misperception of the risks in banks’ portfolios.  

This conclusion is important both from the perspective of commercial banks developing credit 

risk  models  for  estimating  losses  on their  retail  portfolios  and  to  regulators  assessing  the 

resilience  of  the  banking  sector  to  adverse  economic  developments.  This  is particularly 

relevant for stress-testing exercises and the need to correctly link the sensitivity of the LGD 

parameter to macroeconomic developments. In this respect, our results show that the lagged 

effect  of  the  macroeconomic  environment  must  be  taken  into  account  to  obtain  reliable 

predictions of potential losses in banks’ loan portfolios and correctly assess the robustness of 

the banking sector in the event of adverse macroeconomic developments.  

ECB Working Paper 2037, March 2017 30References 

Acharya  V,  Bharath  S,  Srinivasan  A  (2007)  Does  industry-wide  distress  affect  defaulted  firms? 
Evidence from creditor recoveries, Journal of Financial Economics, Vol. 85, No. 3, pp 787–821. 

Altman  E,  Brady  B,  Resti  A,  Sironi  A.  (2005a)  The  Link  between  Default  and  Recovery  Rates: 
Theory, Empirical Evidence, and Implications, Journal of Business, Vol. 78, No. 6, 2005, pp 2203–
2228. 

Altman E, Brady B, Resti A, Sironi A (2005b) The PD/LGD link: Empirical evidence from the bond 
market, In: Altman E, Resti A, Sironi A (eds) Recovery risk. Riskbooks, London, pp 217–233. 

Asarnow  E, Edwards D (1995)  Measuring loss  on default  bank loans:  A 24-year study, Journal  of 
Commercial Lending, Vol. 77, pp 11–23. 

Bastos J A (2010) Forecasting bank loans loss-given-default, Journal of Banking and Finance, Vol. 
34, No. 10, pp 2510–2517. 

Bellotti  T,  Crook  J  (2012)  Loss  given  default  models  incorporating  macroeconomic  variables  for 
credit cards, International Journal of Forecasting, Vol. 28, pp 171–182. 

Bruche  M,  González-Aguado  C  (2010)  Recovery  rates,  default  probabilities,  and  the  credit  cycle, 
Journal of Banking and Finance, Vol. 34, No. 4, pp 754–764. 

Calabrese  R,  Zenga  M  (2010)  Bank  loan  recovery  rates:  Measuring  and  nonparametric  density 
estimation, Journal of Banking and Finance, Vol. 34, pp 903–911. 

Calabrese,  R  (2012)  Predicting  bank  loan  recovery  rates  with  a  mixed  continuous-discrete  model, 
Applied Stochastic Models in Business and Industry. 

Caselli S, Gatti S, Querci F (2007) The Sensitivity of the Loss Given Default Rate to Systematic Risk: 
New Empirical Evidence, Journal of Financial Services Research, Vol. 34, pp 1–34. 

Chalupka  R,  Kopecsni,  J  (2009)  Modeling  Bank  Loan  LGD  of  Corporate  and  SME  Segments:  A 
Case Study, Czech Journal of Economics and Finance, Vol. 59, No. 4, pp 360–382. 

Dermine  J,  Neto  de  Carvalho  C  (2006)  Bank  loan  losses-given-default:  A  case  study,  Journal  of 
Banking and Finance, Vol. 30, No. 4, pp 1219–1243. 

Düllmann  K,  Trapp  M  (2004)  Systematic  risk  in  recovery  rates—an  empirical  analysis  of  US 
corporate credit exposures, Deutsche Bundesbank Discussion Paper, Issue 2. 

Emery  K,  Cantor  R,  Arner  R  (2004)  Recovery  rates  on  North  American  syndicated  bank  loans, 
1989–2003, Moody’s special comment. 

Figlewski  S,  Frydman  H,  Liang  W (2012)  Modeling  the  effect  of  macroeconomic  factors   on 
corporate default and credit rating transitions. International Review of Economics & Finance Vol. 21, 
No. 1, pp 87–105. 

Friedman J, Tibshirani R, Hastie T (2010) Regularization paths for generalized linear models via 
coordinate descent, Journal of Statistical Software, Vol. 33, No. 1, pp 1–22. 

Frye  J  (2000)  Depressing  recoveries,  Federal  Reserve  Bank  of  Chicago  Working  Paper,  Emerging 
Issues Series, 1–17 October. 

Frye J (2005) The effects of systematic credit risk: A false sense of security, In: Altman E, Resti A, 
Sironi A (eds) Recovery risk. Riskbooks, London, pp 187–200. 

ECB Working Paper 2037, March 2017 31Grigorian D A, Manole V (2006) Determinants of Commercial Bank Performance in Transition: An 
Application of Data Envelopment Analysis, Comparative Economic Studies, Vol. 48, No. 3, pp 497–
522. 

Grippa P, Iannotti S, Leandri F (2005) Recovery rates in the banking: stylised facts emerging from 
Italian experience, In: Altman E, Resti A, Sironi A (eds) Recovery risk, Riskbooks, London. 

Grunert J, Weber M (2009) Recovery rate of commercial lending: Empirical evidence for German 
companies, Journal of Banking and Finance, Vol. 33, pp 505–513. 

Han C H, Jang Y (2013) Effects of debt collection practices on loss given default, Journal of Banking 
and Finance, Vol. 37, pp 21–31. 

Hastie T J. Tibshirani R J (1990). Generalized Additive Models. Chapman & Hall/CRC. 

Jokivuolle E, Virén, M (2013), Cyclical default and recovery in stress testing loan losses, Journal of 
Financial Stability, Vol. 9, No. 1, pp 139–149.  

Pesola  J  (2007)  Financial  fragility,  macroeconomic  shocks  and  banks  loan  losses:  Evidence  from 
Europe, Bank of Finland Research Discussion Papers No. 15.  

Qi M, Zhao X (2011) Comparison of modeling methods for Loss Given Default, Journal of Banking 
and Finance, Vol. 35, pp 2842–2855. 

Tibshirani R (1996) Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical 
Society, Vol. 58, pp 267–288. 

Van  der  Kooij  A  (2007)  Prediction  accuracy  and  stability  of  regression  with  optimal  scaling 
transformations, Technical report, Dept. Data Theory, Leiden Univ. 

Witzany  J,  Rychnovský  M,  Charamza  P (2010)  Survival  Analysis  in  LGD  Modeling,  Working 
Papers  IES  2010/02,  Charles  University  Prague,  Faculty  of  Social  Sciences,  Institute  of  Economic 
Studies. 

Zhang J, Lyn C T (2012) Comparisons of linear regression and survival analysis using single and 
mixture distributions approaches in modelling LGD, International Journal of Forecasting, Vol. 28, Iss. 
1, January–March 2012,  pp 204–215. 

Zhou  H,  Hastie  T  (2005)  Regularization  and  variable  selection  via  the  elastic  net,  Journal  of  the 
Royal Statistical Society, vol. 67, pp 301–320. 

ECB Working Paper 2037, March 2017 32Appendix 

Table A1: Consumer credit in the Czech Republic and selected EU 
countries 

Consumer credit to GDP ratio (%)

2004
2008
2013

CZ EU25 EA12
7.1
2.3
7.3
5.2
6.8
6.1

6.5
7.3
6.7

SK
2.7
3.5
7.4

Average consumer annual credit growth (%)

2004–2014
2004–2008
2009–2013

CZ EU25 EA12
1.4
16.8
4.5
30.6
-1.7
3.1

1.7
5.3
-2.0

SK
15.6
12.0
19.2

PL
4.7
8.4
9.3

PL
13.8
22.1
5.5

DE
7.9
7.2
7.1

DE
0.1
-0.2
0.3

AT
10.3
9.8
8.0

AT
0.5
4.6
-3.6

BG
6.5
16.6
16.4

BG
19.2
38.9
-0.5

FR
7.9
8.7
8.1

FR
1.4
4.0
-1.3

GR
9.0
13.5
17.6

GR
9.8
18.6
1.0

ES
7.1
10.4
6.7

ES
1.9
13.3
-9.5

Note: Average growth rates computed from EUR-denominated values of the outstanding credit at the end of the particular year.

Source: ECB, Eurostat

ECB Working Paper 2037, March 2017 33Table  A2:  Correlation  plot  of  macroeconomic  variables  and  LGD,  whole  sample  2003q1-
2010q2

Defaulted 
loans 
growth         
(y-o-y)

ΔDefault 

Default rate                                                         
NPL ratio Cons. 
loans 
(3 months)
growth             
(y-o-y)

rate                      

(3 months)

Unempl. 
rate

ΔUnempl. 
rate

Total 
empl.

Real 
wage 
growth              
(y-o-y)

Real 
GDP 
growth              
(y-o-y)

Defaulted loans growth (y-o-y)
Default rate (3 months)
ΔDefault rate (3 months)
NPL ratio
Retail loans growth (y-o-y)
Unemployment rate
ΔUnemployment rate
Total employment
Real wage growth (y-o-y)
Real GDP growth (y-o-y)
ΔReal GDP growth (y-o-y)
Real consumption growth (y-o-y)
Real investment growth (y-o-y)
Real Pribor3m
Rate on retail loans
Retail rate spread
CPI(y-o-y)
Property price index (y-o-y)
Stock market index (PX-50) (y-o-y)
Real ind. production growth  (y-o-y)

1

0.51

0.04

0.51

-0.52

0.40

0.24

-0.59

-0.46

-0.34

0.25

-0.57

-0.27

0.02

0.44

0.45

-0.25

-0.54

0.23

0.33

1

-0.30

0.51

-0.07

0.79

0.34

-0.66

-0.24

-0.12

0.32

-0.32

-0.26

0.23

0.92

0.88

-0.33

-0.73

0.56

0.18

1

-0.35

-0.35

-0.60

0.48

0.17

-0.42

-0.68

-0.30

-0.50

-0.53

0.09

-0.34

-0.42

0.22

0.06

-0.58

-0.37

1

-0.44

0.63

-0.07

-0.70

-0.21

0.03

0.42

-0.37

0.18

0.14

0.70

0.77

-0.45

-0.49

0.15

0.31

1

-0.03

-0.35

0.61

0.51

0.67

-0.22

0.78

0.36

-0.40

-0.20

-0.20

0.39

0.43

0.31

-0.03

1

0.09

-0.75

0.03

0.13

0.51

-0.14

-0.04

0.27

0.81

0.88

-0.67

-0.70

0.70

0.51

1

-0.44

-0.66

-0.83

-0.30

-0.59

-0.85

0.28

0.24

0.18

-0.25

-0.59

-0.32

-0.42

1

0.36

0.44

-0.45

0.61

0.39

-0.49

-0.74

-0.78

0.74

0.84

-0.19

-0.28

1

0.68

0.16

0.72

0.67

0.18

-0.24

-0.16

-0.10

0.58

0.51

0.30

1

0.20

0.79

0.84

-0.42

-0.10

-0.03

0.23

0.51

0.52

0.37

ΔReal 
GDP 
growth          
(y-o-y)

Real cons. 

growth             
(y-o-y)

Real inv. 
Real 
growth                    
Pribor3m
(y-o-y)

Rate on 
retail 
loans

Retail 
rate 
spread

CPI                  

Prop. pr. 

(y-o-y)

Index                 
(y-o-y)

Real ind. 
Stock 
prod. 
market 
growth  
index            
(y-o-y)
(PX-50)                
(y-o-y)

Defaulted loans growth (y-o-y)
Default rate (3 months)
ΔDefault rate (3 months)
NPL ratio
Retail loans growth (y-o-y)
Unemployment rate
ΔUnemployment rate
Total employment
Real wage growth (y-o-y)
Real GDP growth (y-o-y)
ΔReal GDP growth (y-o-y)
Real consumption growth (y-o-y)
Real investment growth (y-o-y)
Real Pribor3m
Rate on retail loans
Retail rate spread
CPI(y-o-y)
Property price index (y-o-y)
Stock market index (PX-50) (y-o-y)
Real ind. production growth  (y-o-y)

1.00

-0.20

0.06

0.23

0.34

0.39

-0.36

-0.32

0.63

0.48

1.00

0.69

-0.26

-0.33

-0.29

0.29

0.64

0.21

0.03

1

-0.28

-0.14

-0.06

0.20

0.64

0.33

0.46

1

0.31

0.32

-0.70

-0.37

0.24

-0.03

1

0.98

-0.43

-0.74

0.36

0.23

1

-0.54

-0.73

0.42

0.33

1

0.57

-0.34

-0.38

1

-0.12

-0.06

1

0.54

1

ECB Working Paper 2037, March 2017 34Table A3: Logit estimates, credit cards, 2003q1-2010q2

Explanatory variable logit LDG

(1)

(2)

(3)

Coefficient

SE

Coefficient

SE

Coefficient

SE

Client specific

All variables, no lags

All variables, lags included

0.163
0.008
0.369
0.191
0.222

0.163
0.009
0.368
0.220
0.234

0.125
-0.014*
0.749**
0.296
0.345

0.074
-0.003
0.838**
-0.261
-0.039

Client- specific factors
Exposure at default
Relationship with bank
Age    
Children
Phone  
Macroeconomic variables, current values
Real Investment Growth (y-o-y)   
Total employment (in thds)
Property prices (y-o-y)
Default rate   
Retail loan growth (y-o-y)
Macroeconomic variables, lagged and lead values
Real Pribor3m (t-1)
Real Pribor3m (t-2)
Total employment (in thds) (t-8)
Property prices (y-o-y) (t-6)
Constant
Alpha
Observations
Adjusted R-squared
AIC
Note: *, **, *** stand for 10 %, 5 %, and 1 % significance levels respectively. Robust standard errors reported.
The values of Alpha stand for the elastic net weighting parameter with lowest residual mean-squared error.

-1.894
0.8
2784
0.003
17484.893

-238.201
0.9
2784
0.023
17438.26

-0.014
2.33
6.393*
-0.866
-8.335

0.047
2.734
3.619
0.843
5.636

231.413

2.125

0.11
-0.01
0.623*

0.355

0.161
0.008
0.349

0.233

0.161
0.151
0.75
1.163
61.819

0.147
0.188
1.515**
6.249***
-134.564**
0.9
2784
0.025
17424.22

Figure A1: Beta coefficients from regressions of average LGD on individual lagged values of 

macroeconomic variables (2003q1–2010q2) 

3M default rate

Defaulted loans growth (y-o-y)

0.1

-0.1

1.00

0.00

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Δ3M default rate

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

0.5

0.0

-0.5

0.0

-0.1

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

NPL on retail loans

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

ECB Working Paper 2037, March 2017 350.5

0.0

-0.5

-1.0

0.5

0.0

-0.5

2.0

0.0

-2.0

0.1

0.0

-0.1

10.0

0.0

-10.0

0.1

0.0

-0.1

Retail loans growth (y-o-y)

Unemployment rate 

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

ΔUnemployment rate

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

0.2

0.0

-0.2

10.0

0.0

-10.0

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Total employment

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Property price index (y-o-y)

Real wage growth (y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Real GDP growth (y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Real ind. production growth (y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Real investment growth (y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

0.2

0.0

-0.2

0.2

0.0

-0.2

0.1

0.0

-0.1

0.2

0.0

-0.2

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

ΔReal GDP growth (y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Real consumption growth (y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Real Pribor3m 

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

ECB Working Paper 2037, March 2017 36Rate on retail loans

Retail rate spread

0.2

0.0

-0.2

0.1

0.0

-0.1

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

CPI(y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

0.2

0.0

-0.2

0.5

0.0

-0.5

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Stock market index (PX-50) (y-o-y)

t

t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8

Note: Solid lines represent correlations significant at the 5 % level. For selected variables a shorter sample 
starting up to 2005q1was used, see also Note in Table 5). 

ECB Working Paper 2037, March 2017 37Acknowledgements 

The authors would like to thank Marek Rusnák and referees for helpful comments and useful recommendations. However, all errors and 
omissions are those of the authors. The findings, interpretations, and conclusions expressed in this paper are entirely those of the 
authors and do not represent the views of any of the above-mentioned institutions. The authors acknowledge the support of the Czech 
National Bank (CNB Research Project No. C4/10) and the support of the Czech Science Foundation (grant no. P402/12/G097). 

Tomáš Konečný  
European Systemic Risk Board and Czech National Bank; email: tomas.konecny@ecb.europa.eu 

Jakub Seidler 
Chief Economist at the ING Bank NV, Prague, Czech Republic and was at the Financial Stability Department, Czech National Bank, 
Prague, Czech Republic at the time this paper was written 

Aelita Belyaeva 
Československá obchodní banka, a. s., Prague; email: aelita.belyaeva@gmail.com 

Konstantin Belyaev 
Československá obchodní banka, a. s., Prague; email: konstbell@gmail.com 

© European Central Bank, 2017 

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This paper can be downloaded without charge from www.ecb.europa.eu, from the Social Science Research Network electronic library or 
from RePEc: Research Papers in Economics. Information on all of the papers published in the ECB Working Paper Series can be found 
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ISSN  
ISBN  

1725-2806 (pdf) 
978-92-899-2759-8 (pdf) 

DOI 
EU catalogue No 

10.2866/52109 (pdf) 
QB-AR-17-049-EN-N (pdf)