Quantifying risks to sovereign market access : methods and challenges.
Date: 2020-03-16
Institutions: European Stability Mechanism
Subjects: econometrics, economic forecasting, economic indicator, economic model, euro area, financial market, financial risk, market access, monetary crisis

Working Paper Series  | 42 |  2020

Quantifying risks to sovereign market 
access: Methods and challenges

This paper uses a rich dataset of financial and macroeconomic 
variables for euro area economies, and a range of econometric 
techniques, to discuss challenges in predicting episodes of market 
access tensions by sovereign borrowers.

Diana Zigraiova  
 European Stability Mechanism, Charles University
Aitor Erce
 European Investment Bank, European University Institute 
Xu Jiang
European Stability Mechanism

Disclaimer
This working paper should not be reported as representing the views of the 
ESM. The views expressed in this Working Paper are those of the authors and 
do not necessarily represent those of the ESM or ESM policy.

Working Paper Series  |  42  |  2020

Quantifying risks to sovereign market
access: Methods and challenges

Diana Zigraiova 1 European Stability Mechanism 
Aitor Erce 2 European Investment Bank, European University Institute 
Xu Jiang 3 European Stability Mechanism 

Abstract
In this paper we use data from the euro area to study episodes when sovereigns lose market access. 
We  construct  a  detailed  dataset  with  potential  indicators  of  market  access  tensions,  and  evaluate 
their  ability  to  forecast  episodes  when  market  access  is  lost,  using  various  econometric  approaches. 
We find that factors associated with high market access tensions are not limited to financial markets, 
but also encompass developments in global demand, macroeconomic conditions and the fiscal stance. 
Using the top-performing indicators, we construct a number of market tension indices and use them 
as  single  predictors  of  market  access  tensions.  While  such  indices  are  helpful  in  capturing  worsening 
conditions, they do not yield satisfactory out-of-sample results. On the other hand, using the same top-
performing indicators in various multivariate models generates good forecasts of upcoming difficulties 
in  accessing  sovereign  bond  markets.  Our  results  thus  point  to  a  trade-off  between  communicability 
and  accuracy  that  policymakers  face  in  the  search  for  tools  to  evaluate  risks  to  market  access.

Keywords:  Euro area sovereign bond market; forecasting; sovereign debt crises, 
sovereign market access; variable selection

JEL codes: C53, G01, G15

1 d.zigraiova@esm.europa.eu
2 erceaitor@gmail.com
3 k.jiang@esm.europa.eu

Disclaimer
This  Working  Paper  should  not  be  reported  as  representing  the  views  of  the  ESM.  The  views 
expressed in this Working Paper are those of the authors and do not necessarily represent those of 
the ESM or ESM policy. No responsibility or liability is accepted by the ESM in relation to the accuracy 
or completeness of the information, including any data sets, presented in this Working Paper.

© European Stability Mechanism, 2020 All rights reserved. Any reproduction, publication and reprint in the form of a 
different publication, whether printed or produced electronically, in whole or in part, is permitted only with the explicit 
written authorisation of the European Stability Mechanism.

ISSN 2443-5503 
ISBN 978-92-95085-83-1

doi:10.2852/207770
EU catalog number DW-AB-20-001-EN-N

Quantifying risks to sovereign market access: 
Methods and challenges 

Diana Zigraiova 

Aitor Erce 

Xu Jiang 

January 2020 

Abstract: In this paper we use data from the euro area to study episodes when sovereigns 
lose market access. We construct a detailed dataset with potential indicators of market 
access tensions, and evaluate their ability to forecast episodes when market access is lost, 
using various econometric approaches. We find that factors associated with high market 
access tensions are not limited to financial markets, but also encompass developments in 
global demand, macroeconomic conditions and the fiscal stance. Using the top-performing 
indicators,  we  construct  a  number  of  market  tension  indices  and  use  them  as  single 
predictors of market access tensions. While such indices are helpful in capturing worsening 
conditions, they do not yield satisfactory out-of-sample results. On the other hand, using 
the  same  top-performing  indicators  in  various  multivariate  models  generates  good 
forecasts of upcoming difficulties  in accessing sovereign bond markets. Our results thus 
point to a trade-off between communicability and accuracy that policymakers face in the 
search for tools to evaluate risks to market access.  

Introduction 

The lack of a central bank explicitly playing the role of lender-of-last-resort for governments, combined 
with the magnitude of public debt stocks, had two negative consequences that exacerbated the euro 
area crisis. First, markets for government bonds lacked a stabilizing tool against the ongoing liquidity 
runs, and this triggered a recessionary tightening of financing conditions. Second, domestic banks were 
induced to become lenders of last resort, setting the stage for destabilising doom-loops that reinforced 
the effect of the worsening financing conditions. Such extreme tensions in deep and highly liquid public 
bond markets caught most by surprise (Casalinho et al. 2016).1 

While  the  theoretical  literature  is  large,  there  is  just  a  handful  of  papers  that  have  focused  on 
understanding empirically what drives tensions in euro area public bond markets.  A consequence of 
this  is  that,  as  recently  acknowledged  by  the  International  Monetary  Fund  in  its  2018  Review  of 
Conditionality (ROC, 2018), existing policy tools for detecting sovereign debt crises and risks to market 

  We  thank  Jaroslav  Baran,  Anastasia  Guscina,  Carlos  Martins,  Jacques  Netzer,  Stephanie  Pamies,  Markus  Rodlauer,  Rolf 
Strauch, Sheetal Tewari and seminar participants at the IMF workshop on "Fiscal Policies in a Challenging World" and  the 
European Stability Mechanism for their suggestions. We are grateful to the European Stability Mechanism’s Investment and 
Funding teams, who provided us with two separate detailed lists of market indicators to be tracked. Diana is with the European 
Stability Mechanism and Institute of Economic Studies at Charles University. Xu is with the European Stability Mechanism. 
Aitor is with the European Investment Bank and the European University Institute. Disclaimer: This paper does not develop an 
operational methodology for determining market access for evaluating eligibility for precautionary financing by the European 
Stability Mechanism. All the views presented in this paper are the authors’ and not those of the institutions the authors are 
affiliated with. 
 Corresponding author: Diana Zigraiova, d.zigraiova@esm.europa.eu 
1 The ample literature studying public debt auctions in advanced economies does not consider LMA episodes (Sigaux 2018 or 
Belton et al. 2018). Sovereign loss of market access has traditionally been focused on emerging countries (Gelos et al. 2004). 

1 

 
 
 
                                                           
access  were  designed for countries  with  critically  different  public  debt  markets  than  those  in  more 
advanced economies – where markets are deeper, more liquid, and debt is mostly denominated in the 
local currency. In fact, while Greece has become the poster child for the potentially devastating effects 
of losing the confidence of market creditors, there is still a lack of analytical understanding on how to 
predict an episode of a sovereign losing access to its domestic bond market.2 This paper contributes to 
filling this analytical gap. 

De Broeck & Guscina (2011) study the effect of  the global crisis on  issuance strategies of advanced 
economy sovereigns. They document a deviation away from plain-vanilla bond issuance, especially in 
countries with high deficits and high debt levels. Bassanetti, Cottarelli & Presbitero (2016) study the 
role  of  debt  flows  for  understanding  market  access.  Fisher  (2012)  discusses  the  importance  of 
understanding the drivers of demand for public debt. Casalinho et al. (2016) review the experience of 
Ireland,  Portugal,  Cyprus  and  Spain  in  re-accessing  the  market  after  their  official  programs  ended. 
Schalck (2017) estimates reaction functions to identify shifts in the behaviour of public debt managers, 
and  shows  that,  following  the  crisis,  France’s  funding  strategy  shifted  towards  cost  minimisation. 
Guscina, Malik & Papaioannou (2017) provide an operational definition of loss of market access (LMA) 
and  examine  the  predictive  capacity  of  potential  leading  indicators  of  LMA.3  One  lesson  from  the 
literature and from our discussions with bond traders is that market access depends on a host of factors 
and, depending on the information available, can be assessed in a variety of ways. 

In this paper we contribute to this literature in at least two fronts. First, using a selected set of indicators 
chosen by two teams of financial market participants (experts on primary and secondary markets) and 
a  thorough  reading  of  the  academic  literature,  we  construct  an  extensive  and  detailed  dataset  of 
potential leading indicators of market access tensions. Second, we evaluate these selected indicators 
systematically,  using  a  variety  of  univariate  and  multivariate  econometric  frameworks.  We  use 
univariate analysis to select the best indicators from our rich dataset. While forward rate difference 
from the best performer emerged as the most important predictor of market access tensions, we find 
that factors associated with high market access tensions are not limited to financial markets, but also 
encompass developments in global demand, macroeconomic factors and the fiscal stance.  

We  propose  an  easy-to-construct  and  transparent  index  summarising  the  set  of  best  indicators  of 
market access tensions, and use it to understand the driving forces of past episodes of market access 
tensions. We also use a variety of econometric methods to predict future tensions to market access. 
We  show  that  multivariate  methods  perform  better  than  the  univariate  index.  We  also  show  that 
models allowing for endogenous selection of explanatory variables perform better in terms of detecting 
increased market access tensions, although that may come at the cost of more false alarms. 

The  rest  of  this  paper  is  organized  as  follows:  Section  2  provides  our  definition  of  episodes  when 
sovereigns lose market access. Section 3 lists those primary market, secondary market and demand and 
supply side indicators that can be useful in capturing high market access tensions. Section 4 summarizes 
our  data  collection  and  variable  transformations,  yielding  an  extensive  set  of  potentially  useful 
indicators  of  market  access  tensions.  Section  5  applies  a  univariate  evaluation  and  identifies  those 
indicators  that  are  the  most  useful  for  signalling  upcoming  loss  of  market  access  (LMA)  episodes. 
Section 6 builds our market access tensions indices. Section 7 presents the methodology, evaluates the 
performance  of  different  econometric  approaches  and  compares  their  performance  out  of  sample. 

2 The IMF is revising its debt sustainability analysis for countries with market access after its failure to predict the euro area 
crisis. 
3 For analyses of euro area public bond markets not considering market access risks see Eidam (2017) or Beetsma et al. (2018). 

2 

 
                                                           
Section  8  analyses  usefulness  of  our  framework  for  policymakers  with  asymmetric  preferences  and 
Section 9 checks robustness of our baseline results. 

2. Defining episodes of high sovereign bond market tensions 

When countries effectively lose market access, they either default or ask for official support. Thus, one 
straightforward way to determine whether a country suffered a loss of market access (LMA) is to check 
whether the country announced a debt restructuring or requested concessional support from official 
lenders (Gelos et al. 2004). Things get more complicated when one wants to determine episodes in 
which market access conditions became more difficult. In this case, countries may have continued to 
access bond markets for financing, but the conditions on which they did so were hard to sustain in the 
long run. According to Guscina, Malik and Papaioannou (2017) an assessment of whether a sovereign 
continues to have market access would be based on whether the sovereign can tap bond markets on a 
sustained  basis,  across  a  range  of  maturities  (in  both  local  and  foreign  currencies)  at  interest  rates 
compatible with reasonable medium-term growth rates and an achievable primary fiscal position. More 
precisely,  Guscina,  Malik  and  Papaioannou  (2017)  employ  a  decision  rule  according  to  which  they 
identify periods associated with default or restructuring as LMA. They further identify as suspect LMA 
episodes periods in which issuance deviates from its established pattern.4 Aloong these lines, we define 
periods of high sovereign bond market tensions using the union of the following three definitions of 
loss of market access: 

I. 

II. 

III. 

ESM/IMF program dates 

Periods identified by Guscina, Malik & Papaioannou (2017) 

Periods when 10-year spread to Germany is above the 90th  percentile of the spread distribution 
for the full sample, which corresponds approximately to 350 basis points 5 

We  mark  the  start  of  a  LMA  event  in  our  dataset  by  whichever  event  from  the  three  definitions 
materialized  first.  For  Greece  and  Ireland,  all  three  definitions  materialized  simultaneously  in  2010. 
According  to  the  above  definitions,  since  2000  Q1  there  have  been  LMA  episodes  in  9  euro  area 
countries. Starting dates by definition are shown in Table 1.6 

Given our interest in forecasting sovereign bond market tensions up to one year ahead, we transform 
our LMA variable into a pre-LMA dummy the following way. We create a dummy to which we assign a 
“1” in the four quarters preceding LMA episodes and we assign a value 0 in the remaining periods. In 
addition, we exclude high market access tension periods and four quarters following these periods from 
our analysis to avoid post-crisis bias (Bussiere & Fratzscher, 2006). In a robustness exercise, we also 
perform the analysis excluding episodes identified using the spread level. 

4  To  confirm  whether  the  identified  suspect  LMA  cases  are  indeed  LMA,  they  further  investigate  explanations  for  lack  of 
issuance such as lack of funding needs and prefunding. 
5 The chosen level threshold corresponds to 92.7 percentile of the spread distribution, which indicates spread levels beyond 
350 basis points fall into extreme values of the distribution and could be understood as market tensions. We also tried with a 
country specific approach, as in Baldacci et al. (2011). We used two standard deviations above a country’s historical rolling 
average of the spread as our definition. In Figure A5 in the appendix, we show that this approach delivers distress episodes 
even for countries which clearly did not experience any, such as Austria or Netherlands. 

6 Figure A3 in the Appendix provides an overview of LMA episodes by country and definition. 

3 

 
 
 
                                                           
Table 1: Start of LMA episodes 

COUNTRY 

ESM/IMF PROGRAM  GUSCINA ET AL. (2017) 

SPREAD LEVEL 

AUSTRIA 

BELGIUM 

CYPRUS 

GERMANY 

ESTONIA 

SPAIN 

FINLAND 

FRANCE 

GREECE 

IRELAND 

ITALY 

LITHUANIA 

LUXEMBOURG 

LATVIA 

MALTA 

NETHERLANDS 

PORTUGAL 

SLOVENIA 

SLOVAKIA 

2012 Q2 

2013 Q2 

2016 Q1 

2012 Q3 

2011 Q4 

2010 Q2 

2010 Q4 

2010 Q2; 2014 Q4 

2010 Q4 

2010 Q2 

2010 Q4 

2011 Q4; 2012 Q37 

2008 Q4 

2008 Q4 

2008 Q4 

2011 Q2 

2011 Q2 

2010 Q4; 2017 Q1 

2013 Q1 

3. Universe of sovereign bond market tension indicators  

For a sovereign to lose market access, it must be the case that it finds no adequate demand for its debt 
supply. For that reason, the framework places a lot of weight into understanding future demand and 
future supply. We categorize information into buckets reflecting both the different potential sources of 
information and the need to identify supply and demand drivers. 

Given the relevance of bond markets for sovereign financing, the use of market data is critical.  One 
block of information focuses on primary markets data, and another block on secondary markets data. 
Market  data  provides  information  about  countries’  fundamental  and  liquidity  risks  in  the  timeliest 
manner, and is available with high frequency. To further enhance the framework´s ability to understand 
future  demand  and  supply  dynamics,  the  third  block  collects  potential  demand  and  supply  drivers 
through the use of other macroeconomic, global and geopolitical variables. 

3.1 Preferred primary market indicators 

Maturity at issuance: generally, a decline in the average maturity at issuance in a short period of time 
may signal the increasing difficulty to fund in the sovereign markets. The maturity at issuance is a result 
of an intertemporal trade-off between the lower costs of holding short-term debt against the likelihood 
of a debt roll-over crisis, owing to an unexpected surge in repayment risks (Broner et al, 2013).  The 
cost-risk trade-off usually translates into issuance across the maturity spectrum (Abbas, et al, 2014). 

7 An additional metric could be the presence of extensive support from the Central Bank. Using such logic, for Italy we can 
define start of an LMA episode the quarter of Draghi’s “Whatever it takes” speech. In robustness checks we remove this event. 

4 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                                                           
Therefore, excessive reliance on short-term debt may expose the government to volatile and potentially 
increasing debt costs if financial market conditions tighten quickly. 

Share of bill financing: a sudden shift to bill issuance may signal that the treasury finds it increasingly 
difficult  to  finance  through  medium-  and  long-term  bonds  given  the  size  of  gross  financing  needs. 
During the European debt crisis, the share of bill issuance temporarily increased in larger issuers, such 
as Germany, France and Italy, and was the only instrument issued by most countries that entered an 
EFSF/ESM financial assistance programme. 

Issuance patterns: shifting away from the standard funding practices – competitive auctions of debt 
instruments with a fixed coupon, long maturities, and local currency denomination may reflect changes 
in  macroeconomic  conditions  and  investor  sentiment  (De  Broeck  &  Guscina  2011),  such  as  a 
manifestation of structural shifts in fiscal policy imperatives and sovereign borrowing needs, currency 
regimes,  financial  market  architecture,  and  financial  market  conditions  (Abbas,  et  al,  2014). 
Nevertheless,  bonds  with  various  currencies  and  coupon  features  can  be  helpful  to  expand  and 
maintain the investor base and diversify funding sources.8 

Distribution methods (syndications and private placements): the aim of syndications is to issue new 
benchmarks and/or raise relatively larger amounts.  Their use may reflect the quality of market access 
of the issuers. De Broeck & Guscina (2011) documented that the 2007-2008 financial crisis led to an 
increasing use of syndications as a distribution method in a number of euro area countries, such as 
Greece, Cyprus, Belgium, Finland, and so on.  In an ideal situation, an analysis of the investor base in 
these transactions and of the new issue premium the treasuries pay would help to evaluate the quality 
of market access. Private placements can be tailor-made to meet the needs of specific types of investors 
and to maintain  the investor base.  This distribution method  is only occasionally used  in some small 
issuers (such as Cyprus and Ireland) and not utilized in countries with solid market access (Germany). 

Pace  of  issuance  relative  to  targets:  a  slower-than-usual  issuance  pace  may  reflect  the  increased 
difficulty of placing bonds in the prevailing market conditions.  

Auction  frequency:  treasuries  usually  have  a  pre-determined  funding  schedule.  Changes  in  auction 
frequency may be used to meet structural/temporary variations in funding needs. A marked deviation 
from the usual pattern, either an increase or decrease of the number of auctions, may hint at weakened 
market access. De Broeck & Guscina (2011) documented an increased number of auctions in almost all 
euro  area  countries  during  the  European  debt  crisis  compared  to  pre-crisis  periods  as  a  result  of 
elevated gross financing needs.   

Auction volume:  treasuries usually come to markets with a pre-determined schedule  for their  bond 
auctions. A deviation from the usual pattern, either an increase or decrease of the accepted volume of 
auctions, can be a warning sign.  

Auction tail: it is the difference between the accepted average and minimum prices, or the difference 
between average and maximum accepted yields. A large auction tail in general is not a good sign, as 

8  Portugal  is  an  example  of  increased  use  of  floating  coupon  bonds  in  the  run-up to  LMA  in  2010  Q4.  In  November  2010 
Portugal issued 10-year floating coupon bonds at more than 6% despite the total size was small - below €500 million. Shortly 
after, in February 2011, the issuance of a fixed coupon bond at 6.4% was deemed an unsustainable funding cost, triggering 
the formal request for an official program. 

5 

 
                                                           
the marginal buyer is only willing to pay a lower price than the average for additional allotment.9 But 
this measure can be noisy (auction tails can be large because of a few aggressive bidders). 

Auction overbidding: it is the difference between the average price at which a bond is sold at an auction 
and the market price of that bond at the auction bidding deadline. If the auctioned price is higher than 
the  prevailing  market  price  at  bidding  deadline,  there  is  overbidding;  in  the  opposite  case,  there  is 
underbidding.  In  general,  the  higher  the  overbidding  vs  prior  auctions,  the  stronger  an  auction  is 
deemed to be. 

New issue premium: this measures the difference between primary accepted prices and secondary fair 
prices.  Generally,  higher  new  issue  premium  means  the  treasuries  will  need  to  pay  more  given  a 
desirable  amount  of  new  issues.  But  the  estimation  of  fair  value  is  model  specific  and  it  is  hard  to 
compile historical data on it across countries based on public information.  

Auction cycle/Concession: Secondary market yields rise preceding auctions and decline afterwards. This 
affects  the  cost  of  the  auctions  in  the  primary  market  and  they  may  provide  an  indication  of  the 
potential  roll-over  risk  associated  with  the  public  debt  (Beetsma  et  al.,  2018).  Typically,  a  rise  in 
secondary yields before an auction signals good demand for that auction. 

Auction  cancellation/delay:  auction  cancellation  can  be  a  result  of  a  pre-funding  (e.g.  end  of  year 
cancellations) and an auction can be delayed in order to avoid heightened market volatilities. 

Bid-to-cover  ratio:  this  measures  over-subscription  from  investors  (demand)  relative  to  supply. 
Generally,  the  higher  it  is,  the  better  the  auction.  Beetsma  et  al.  (2018)  find  that  more  successful 
auctions of euro area public debt, as captured by higher bid-to-cover ratios, lead to lower secondary-
market yields following the auctions. .However, the reliability of this indicator is debatable: (1) bid-to-
cover ratios can be inflated due to market design (the way auctions are organized); (2) when a treasury 
issue several bonds in a day, it can play with the allotment, making individual bid-to-cover less reliable. 

Auction  allotment  relative  to  indicative  targets:  this  compares  actual  allotment  to  targeted  size  or 
range. Treasuries face a trade-off between announcing a high target, which increases the chance that 
a given auction fails and yields are driven up, and announcing a low target, which forces them to more 
frequently  organize  auctions,  and  incur  the  associated  costs  and risks  (Beetsma  et  al.,  2018).  If  the 
issuer does not receive enough bids to cover the desirable allotment, it is a sign of weak demand. If the 
increase in size results in weaker pricing, it is likely the issuer is attempting to ‘stuff’ the market. 

Ratio  of  non-competitive  allotment  to  total  accepted  amount:  generally,  a  certain  percentage  of 
competitive allotment is made available for (selected) primary dealers to submit non-competitive bids 
within a short time window, such as one day or two. Presumably, the higher the ratio is, the stronger 
the investor demand, as primary dealers could not buy sufficiently either in the auctions and/or from 
the prevailing secondary markets.  

3.2 Preferred secondary market indicators 

Yield curve: Using yields of short- and long-term maturities, we can construct the yield curve of interest 
rates.  A  rapid  increase  in  the  short-term  rates  relative  to  long-term  ones,  resulting  in  a  flat  or  an 
inverted curve, generally signals elevated near-term risks. Estrella & Mishkin (1998), Bordo & Haubrich 
(2008) and Gerlach & Stuart (2018), among others, show that slope of the yield curve has predictive 

9 Some auctions are run as “Dutch auctions” in which uniform price is applied, and therefore no auction tails are observed. 

6 

 
                                                           
power for US growth10. The yield curve also affects the maturity of debt a government will choose to 
supply. In times of rising short-term rates, a country will likely issue debt over longer maturities and 
vice versa (Broner & Lorenzoni). 

Spreads  of  sovereign  bond  yields:  sovereign  spreads  are  the  most  widely  used  measures  in  the 
academia and markets, and are typically monitored to evaluate the overall risk premium emerging from 
credit,  liquidity  and  political  uncertainties  (Guscina,  Malik  &  Papaioannou,  2017).  Typically,  a  sharp 
increase  in  sovereign  yield  levels  and  spreads  indicates  an  increased  sovereign  stress  as  investors 
demand extra premium to hold such securities. This will lead to the shortening of debt maturity issued 
by the sovereign (Arellano & Ramanarayanan, 2012).  

Bid-ask spreads: the bid-ask spread measures the costs of hypothetically carrying out small round trip 
trades. Basically, it informs the market participant how much one needs to pay to buy one security and 
immediately sell it back (in the secondary market). Generally, a higher level of bid-ask spreads indicates 
a relatively high degree of illiquidity. Bid-ask spreads capture a price dimension, rather than a quantity 
dimension, of market liquidity.11  

CDS  prices:  a  sovereign  CDS  contract  provides  protection  against  the  default  of  the  underlying 
sovereign.  A  sharp  increase  in  CDS  prices  generally  signals  the  increased  risk  of  sovereign  default 
(Guscina, Malik & Papaioannou, 2017). 5-year Senior USD CDS is arguably the most liquid and mostly 
traded CDS instrument in the markets.12 

Trading  volume:  the  level  of  trading  volume  in  a  security  or  its  turnover  (volume  divided  by  the 
outstanding amount of that security) is used as an indicator of market liquidity of a sovereign bond. 
Trading volume tends to increase when new information reaches the market, typically a time of higher 
market volatility and concomitantly wide bid-ask spreads. Therefore, turnover can be high when trading 
costs increase (i.e. if there is turmoil around political elections).  

Bond forwards: periods of high expected yield represent increased costs for future government debt 
issuance. In order to optimize costs, a country will likely increase its debt supply in immediate future 
and as such prefund for the upcoming periods of increased costs. To capture this effect, one can collect 
forward rates of the 10-year bonds in three months’ time and calculate forward premium/discount as 
the difference between the forward rate and current ten-year yield, as well as difference between this 
forward rate and the benchmark rate, which during our sample period is the best performer’s ten-year 
forward rate. 

Investor base: monitoring investor holdings by residence and sector helps to assess sovereign market 
access from a complementary angle. Evidence shows that the changing dynamics in sectoral investor 
base is associated with sovereign yield dynamics (Arslanalp & Poghosyan 2014, Hauner & Kumar 2006, 
Jaramillo & Zhang 2013). A rapid sell-off by foreign investors is often an underlying driver of sharp pick-
up in yields and spreads, which can quickly jeopardize a sovereign’s market access. 

3.3 Other demand and supply factors 

10 Estrella & Hardouvelis (1991) argue that the slope of the yield curve has extra predictive power over the index of leading 
indicators, real short‐term interest rates, lagged growth in economic activity, and lagged rates of inflation.  
11 The size of bid-ask spreads is structurally different among countries, reflecting variations in the depth and market design. 
12 The spread between USD and euro-denominated CDS prices and different vintages of CDS contracts, if data are available, 
can potentially be used as a measure of redenomination risk. 

7 

 
                                                           
Growth outlook: We aim to capture this using GDP growth and growth expectations. Alesina et al. 1992) 
and  Bernoth  et  al.,  (2004)  argued  that  sovereign  debt  becomes  riskier  during  periods  of  economic 
slowdown.  Therefore,  an  increase  (reduction)  in  growth  performance  is  assumed  to  improve 
(deteriorate) creditworthiness. 

Risk  aversion:  We  approximate  investor  risk  aversion  by  means  of  the  VIX  index  and  its  European 
equivalent, the V2X index. Since these indices capture expected future market volatility, they can be 
used as a proxy for appetite of investors for safe assets, i.e. sovereign bonds, given the flight to quality 
phenomenon (Baur and Lucey, 2009). We additionally include the MOVE index, the US Treasury option 
implied  volatility  index  produced  by  Merrill  Lynch.  The  MOVE  index  can  thus  serve  as  a  proxy  for 
investor appetite for other safe assets, such as non-US government bonds. 

Sentiment and uncertainty: To account for investor sentiment and uncertainty perceptions vis-à-vis a 
country’s economic policy,  we use the  European Commission’ sentiment index13  (Gelper  and Croux, 
2009) as well as the Economic Policy Uncertainty index (Baker et al, 2016).  

Expected financing needs: In principle, countries with larger financing needs will be more dependent 
on bond markets. Beyond a certain level, the larger this future supply, the more jittery markets become.  
In order to operationalize this concept, we put together information regarding expected deficits and 
refinancing  needs.14  This  flow  measure  should  provide  more  information,  compared  to  the  stock 
measure, on a sovereign’s likelihood of distress (Gabriele et al, 2017).  

Future redemptions profile: Countries with large amounts of maturing debt have greater funding needs 
and potentially are at risk of not meeting them via debt issuance. This will probably lead to heightened 
roll-over risks, which are higher when the maturity profile is concentrated on or around a particular 
maturity  and  when  the  maturity  profile  is  short  with  large  individual  redemptions  (Jonasson  and 
Papaioannou, 2018). We capture amounts of maturing debt over the following three years as share of 
total maturing debt over the next ten years, as well as debt maturing in the medium term (four to six 
years) and in the long term (eight to ten years). 

Bank  CDS  and  public  bailouts  (contingent  liabilities):  this  captures  implicit  liabilities  materializing  in 
adverse  scenarios.  Following  bank  crises,  contingent  liabilities  from  the  banking  sector  could  be  a 
significant determinant of sovereign risk (Arslanalp and Liao, 2014). We collect data on bank bailouts 
by governments and CDS prices of banks active within a country. These indicators capture government 
costs related to domestic banks’ distress and represent an additional funding need for a country. 

Banking  sector  index:  a  country-level  index  measuring  the  performance  of  average  banking  equity 
prices weighted by market capitalization on the same day. Generally, increases in the index indicate 
positive investor sentiment towards that country’s banking sector. Sovereign and banking distress feed 
into  each  other,  with  balance  sheet  interconnections,  credit  dynamics,  financial  openness  and 
economic growth being important ((Erce and Balteanu 2017, Del’Ariccia et al. 2018). 

Stock market index: the performance of the stock market informs about investor sentiment on the state 
of the economy. Generally, increases in stock market indices signal positive investor sentiment. Also, 

13Available  at:  https://ec.europa.eu/info/business-economy-euro/indicators-statistics/economic-databases/business-and-
consumer-surveys_en 
14 We approximate a country’s expected financing needs over the next year as the sum of the expected deficit for that year 
(we assume it is the same as the current year’s deficit) and future debt redemptions over the same year. 

8 

 
                                                           
volatilities in stock markets can be related to variations in the underlying macroeconomic factors, such 
as GDP growth, inflation and short-term interest rates (Engel and Rangel, 2007). 

Cash  position:  indicative  of  a  sovereign’s  need  for  financing  through  debt  markets.  Large  cash  or 
liquidity  reserves  lower  the  need  for  a  government  to  issue  debt.  Sovereign  debt  managers  view  a 
liquidity  buffer  as  an  effective  tool  to  address  re-financing  risk  and  liquidity  risk  that  may  arise  for 
reasons such as unexpected increases in borrowing needs, short-term mismatches in fiscal cash flows 
or the temporary loss of market access (OECD, 2018). 

Fiscal outlook: Indicators capturing fiscal position, debt/GDP and deficit/GDP, provide a picture of how 
much a country will need to raise to finance its position. Projections of key fiscal variables should help 
to inform the fiscal sustainability risks associated with a government’s possible inability to roll over its 
outstanding stock of debts (Baldacci et al. 2011). 

Shocks  to  foreign  investors:  Negative  shocks  to  a  government’s  bondholders  adversely  affect  their 
demand for government bonds. We proxy these shocks using GDP growth in large countries. Therefore 
we assume that if there is a negative output shock, their shares of debt holdings will increase.  

4.  Collecting and transforming the data 

We  collected  48  raw  underlying  indicators,  listed  in  Table  2,  from  primary  and  secondary  markets, 
capturing  global  demand  and  government  supply,  for  19  euro  area  countries.  We  generated 
transformations  of  these  indicators  to  capture  proportions  on  debt  issuance, share  of  GDP, moving 
averages  over  one  and  two  years,  differences  to  these  moving  averages,  standard  deviation  and 
skewness of selected indicators over moving one-year horizon, as well as per current period, year-on-
year  differences,  and  differences  compared  to  Germany  and  the  best  performing  country.  The 
transformations yielded 242 variables altogether.  

Several indicators such as bid-to-cover ratios, PMI, Italian futures rate, the forecast of fiscal balance as 
share of GDP, and forecast of  general government structural balance as  a  percent of potential GDP 
suffer from serious data limitations in the form of either short time series or restricted availability across 
countries. Thus, we exclude them from further analysis. We also exclude yield spreads to Germany on 
6-month T-bills, 2-year, 5-year and 10-year sovereign bonds since these overlap with our definition of 
LMA episodes. We also eliminate Cyprus, Estonia, Malta, Lithuania and Luxembourg due to significant 
data limitations across indicators from primary and secondary markets, global demand and government 
supply side. All the indicators and their transformations were lagged by one quarter to account for data 
publication lags. 

Table 2. Underlying data and sources 

1.      Bid-to-cover on 6-month government bills  
2.      Bid-to-cover on 10-year government bonds  
3.      Syndicated issuance  
4.      Foreign currency issuance  
5.      Floating coupon issuance  
6.      Inflation-linked issuance  
7.      Volume issued  
8.      Number of issuances  
9.      Yield to maturity  

Bloomberg 
Bloomberg 
Dealogic 
Dealogic 
Dealogic 
Dealogic 
Dealogic 
Dealogic 
Dealogic 

9 

 
 
10.   Years to maturity  

11.   Bills issued  

12.   Domestic long-term fixed-coupon issuance  
13.   Slope of the yield curve  
14.   10-year forward rate in 3 months’ time  

15.   Bid-ask spread on 2-, 5- and 10-year bonds and 6-month T-bills  

16.   Spread to Germany on 6-month bills, 2-, 5- and 10-year bonds  

17.   CDS rate  
18.   Foreign debt holdings  
19.   Economic sentiment index  
20.   GDP  
21.   GDP of US and China  
22.   VIX  
23.   V2X  
24.   MOVE  
25.   PMI – Purchasing managers’ index  
26.   German, Italian futures rate  
27.   European economic policy uncertainty index  
28.   GDP year-on-year change, forecast  

29.   Interest expense as percent of GDP, forecast  

30.   Gross debt as percent of GDP, forecast  

31.   Primary balance as percent of GDP, forecast  

32.   Deficit as percent of GDP, forecast  

33.   General government structural balance as percent of potential GDP, 
forecast  
34.   Fiscal balance as share of GDP, forecast 1-year ahead  
35.   Systemic crisis dummy  
36.   Deficit  
37.   Debt  
38.   Government expenditure  
39.   Cash balances  
40.   Primary balance  
41.   Interest payable  
42.   Government liability structure  

43.   Bank equity index weighted by market capitalization 

44.   Stock market index 
45.   Bank bailouts  
46.   Contingent liabilities  
47.   Future redemptions, debt securities  

48.   Gross financing needs 

Dealogic 
ECB SDW, Bloomberg, Own 
calculations 
Dealogic 
Bloomberg and Haver 
Bloomberg 
Bloomberg, Own 
calculations 
Bloomberg, Own 
calculations 
Bloomberg and Datastream 
IMF, Bruegel, and Haver 
Haver 
Haver 
Bloomberg 
Bloomberg 
Bloomberg 
Bloomberg 
Bloomberg 
Bloomberg 
Haver 
WEO, Own calculations 
AMECO EC, Own 
calculations 
AMECO EC. Own 
calculations 
AMECO EC. Own 
calculations  
AMECO EC, Own 
calculations 

WEO 
Haver, Own calculations 
Lo Duca et al. (2017) 
ECB SDW 
Haver 
Haver 
Eurostat 
Haver 
ECB SDW 
ECB SDW 
Bloomberg, Own 
calculations 
Bloomberg 
Eurostat 
Eurostat 
Dealogic 
ECB SDW, Dealogic, Own 
calculations 

10 

 
 
Adding normalized transformations. To increase the ability of our indicators to predict market distress, 
we  also  built  transformations  comparing  indicator  dynamics  to  either  country-specific  history  or 
against-peers  at  a  point  in  time.  We  also  add  normalized  forms  of  the  indicators  and  their 
transformations both within and across countries. We based the normalization of individual indicators 
on  comments  from  ESM  Funding  and  Investment  teams,  reading  of  the  relevant  literature  and  the 
indicators’ dynamics.15 

After extending the set of indicators and their transformations with their normalized transformations 
both by country and across countries, the final dataset comprises 657 indicators altogether. 

5. Univariate (signalling) analysis of indicators 

To  identify  indicators  most  suitable  for  signalling  increased  sovereign  bond  market  tensions,  we 
evaluate the usefulness of all the collected indicators individually. For this purpose we employ signalling 
analysis as well as calculate area under receiver operating characteristic curve (AUROC) on data until 
2011 Q2. The data after this point we reserve for out-of-sample testing. 

In the signalling approach, a warning signal is issued when an indicator exceeds a threshold, which we 
define  by  a  particular  percentile  of  an  indicator’s  own  cross-country  distribution.  This  approach 
assumes an extreme non-linear relationship between the indicator and the event to be predicted. Each 
quarter for each indicator falls into one of the four quadrants of the matrix below. 

Table 3: Classification matrix 

Loss of market access 

No loss of market access 

Signal issued 

True positive 

 False positive (False alarm) 

No signal issued 

 False negative (Missed event) 

True negative 

Missed  events  rate  (Type  I)  error  can  be  obtained  by  dividing  the  number  of  missed  events  by  the 
number of periods in which sovereign bond market tensions were high: 

𝑇𝑦𝑝𝑒 𝐼 =

∑ 𝐹𝑎𝑙𝑠𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒
∑ 𝐹𝑎𝑙𝑠𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + ∑ 𝑇𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒

(1) 

False alarm rate (Type II error) can be calculated by dividing the number of false alarms by the number 
of periods in which there were no high sovereign bond market tensions: 

𝑇𝑦𝑝𝑒 𝐼𝐼 =

∑ 𝐹𝑎𝑙𝑠𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒
∑ 𝐹𝑎𝑙𝑠𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + ∑ 𝑇𝑟𝑢𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒

(2) 

Following Alessi and Detken (2011) we calculate the overall utility of each indicator using the function: 

U = min(𝜃;  1 − 𝜃) −  𝜃

𝐹𝑁
(𝐹𝑁+𝑇𝑃)

+ (1 − 𝜃)

𝐹𝑃
(𝐹𝑃+𝑇𝑁)

, where 

𝐿 = 𝜃

𝐹𝑁
(𝐹𝑁+𝑇𝑃)

+ (1 − 𝜃)

𝐹𝑃

(𝐹𝑃+𝑇𝑁), 

(3) 

(4) 

15  Normalization results in  loss of observations for some indicators where we choose to stress country-specific dynamics. 
Floating coupon issuance share and foreign currency issuance share are examples of such indicators. These indicators manifest 
zero variance until 2011 Q2. To preserve as many observations as possible, we do not normalize indicators with zero variance. 

11 

 
 
 
 
 
                                                           
where  FN,  FP,TP  and  TN  stand  for  false  negative,  false  positive,  true  positive  and  true  negative, 
respectively. L stands for loss function of the policymaker, which combines both error types as well as 
her  relative  risk  aversion  between  Type  I  and  Type  II  errors.  A  𝜃  lower  than  0.5  shows  that  the 
policymaker is less averse towards missing a signal for high sovereign market tensions than towards 
receiving a false alarm. A policymaker can always realize a loss of min (𝜃;  1 − 𝜃) by not accounting for 
an indicator. If 𝜃 is smaller than 0.5, the benchmark is obtained by ignoring the indicator, which means 
there will be no signal issued so that TP = FP = 0. The resulting loss according to the utility function is 𝜃. 
If  𝜃  exceeds  0.5,  the  benchmark  is  assuming  there  are  costly  sovereign  bond  market  tensions 
developing, i.e. assuming a signal is always issued so that FN =  TN = 0. The resulting loss is 1-𝜃. An 
indicator is then useful to the extent that it produces a loss lower than min(𝜃;  1 − 𝜃) for a given 𝜃.  

We search for the value threshold of each indicator which maximizes the utility function (3), given that 
we assume neutral policymaker preferences between both error types (i.e. 𝜃 = 0.5). 

In addition to the signalling analysis of individual indicators, we calculate for each indicator the area 
under the ROC curve (AUROC) whose use is advocated in the context of evaluating the performance of 
early warning models by e.g. Candelon et al. (2012).  The ROC curve plots a false positive rate (number 
of false positives over the number of all negative sample periods) against a true positive rate (number 
of true positives over the number of all positive sample periods) for individual threshold values of an 
indicator. The best possible prediction would yield a point in the upper left corner (point (0, 1)) of the 
ROC space, which indicates a 100% true positive rate and a 0% false positive rate. This point is called 
the perfect classification point. A random guess would give a point along a diagonal line (line of no-
discrimination) from the left bottom to the top right corner. The diagonal divides the ROC space as 
follows: points above the diagonal represent good classification results (better than random); points 
below the line represent bad results (worse than random). The area under the diagonal equals 0.5, thus 
AUROC greater than 0.5 shows an indicator is useful, i.e. it gives better than random results. 

The  AUROC  is  greater  than  0.5  for  468  indicators  (out  of  657),  indicating  better  than  random 
performance for predicting high bond market tensions over the 4-quarter forecasting horizon:  

  Among primary market indicators, the difference in country-specific normalization of changes 
in an 8-quarter moving average of the number of issuances is the most useful indicator over the 
4-quarter forecast horizon, with the highest AUROC of 0.82 and maximum utility of 0.29. 

  From  among  secondary  market  variables,  the  most  useful  predictor  is  the  cross-country 
normalization of  difference of 10-year forward rate from the best performing country  in  the 
given year-quarter, with AUROC of 0.916 and maximum utility of 0.386. The second most useful 
indicator is the cross-country normalization of the forward premium (difference between long-
term forward rate and the spot yield on bonds of the same maturity), which yields AUROC of 
0.85 and maximum utility of 0.30. 

  From our demand indicators, year-on-year difference in forecast of interest expense two years 
ahead (as a share on GDP) is most useful. Its AUROC is 0.78 and maximum utility is 0.30.  

  Finally, among supply side indicators, the country-specific normalization of ratio of government 
expenditure over GDP is the best-performing indicator with AUROC of 0.85 and utility of 0.35. 

To check for consistency of the useful indicators over time, we also conduct a signalling analysis on all 
the  original  and  normalized  indicators  over  the  whole  sample,  i.e.  until  2018  Q4.  Overall,  the  best 
performing  indicators  remain  broadly  unchanged.  Using  primary  markets  data,  cross-country 

12 

 
normalization  of  changes  in  an  8-quarter  moving  average  of  the  number  of  issuances  is  the  best 
predictor with AUROC of 0.732 but a quite high Type II error rate of 0.4. Using secondary markets data, 
cross-country normalization of difference of the 10-year forward rate from the best performing country 
remains the most useful indicator, with AUROC of 0.936 and utility of 0.397. Within demand and supply 
side indicators, year-on-year growth in the inverse of a 4-quarter moving average of the banking sector 
index is the most useful indicator with utility of 0.301 and AUROC of 0.846. The second most useful 
indicator is cross-country normalization of the year-on-year difference in debt-to-GDP ratio with AUROC 
of 0.83 and utility of 0.25.  

5.1 Selection of the indicators to be monitored 

Following the results of the signalling analysis, we proceed to identify and pre-select the most useful 
indicators on a univariate basis for further use within a multivariate framework. For this purpose, we 
use the area under the ROC curve and Type I and Type II error rates calculated for each indicator in a 
univariate analysis on the sample ending in 2011 Q2.  

First, we discard indicators whose AUROC, a global measure of usefulness to predict periods leading to 
high sovereign bond market tensions, does not exceed 0.5; the number corresponding to an indicator 
yielding random results. Next, we discard those indicators for which either Type I or Type II error equals 
or exceeds 0.4. That is we exclude indicators that either fail to issue a signal or emit false alarms in 40 
percent and more quarters of high tension episodes or tranquil periods, respectively. Subsequently, we 
select the best performing transformation of the underlying indicator that meets both of the above 
criteria:  AUROC  above  0.5  and  Type  I  and  Type  II  error  below  0.4.  These  conditions  leave  us  with 
substantially reduced sets of useful univariate indicators, especially from the primary markets. For this 
reason,  we  also  consider  such  transformations of  the  primary market  indicators  that do  not strictly 
meet the error type condition, but have AUROC and usefulness sufficiently high and which outperform 
other primary market indicators. Similarly, we retain the best performing transformations of the V2X 
index  and  US  GDP  growth  in  order  to  control  for  global  demand  factors.  On  the  supply  side,  best 
performing transformations of GDP growth forecast and gross financing needs were retained to ensure 
comprehensiveness. Table 4 presents the set of the best-performing indicators. 

The set of the most useful indicators contains the following transformations of the raw indicators: 

  Primary market: country-specific normalization of difference in moving average of number of 
issuances over 8 quarters, country-specific normalization of ratio of bills issuance to GDP, cross-
country normalization  of difference  in  moving  average  of  share of floating  coupon  issuance 
over  8  quarters,  cross-country  normalization  of  difference  in  moving  average  of  share  of 
syndicated issuance over 8 quarters. 

  Secondary  market:  cross-country  normalization  of  bid-ask  spread  on  2-year  bonds,  cross-
country normalization of standard deviation of bid-ask spread on 5-year bonds, cross-country 
normalization of bid-ask spread on 10-year bonds, cross-country normalization of difference in 
foreign-held  debt  share  on  total  debt,  cross-country  normalization  of  difference  of  10-year 
forward  rate  from  the  best-performing  country,  cross-country  normalization  of  forward 
premium, cross-country normalization of year-on-year difference in CDS rate. 

  Supply and global demand indicators: year-on-year difference in forecast of interest expense 
share  on  GDP  in  two  years,  cross-country  normalization  of  European  economic  uncertainty 

13 

 
 
index,  cross-country  normalization  of  US  GDP  growth,  cross-country  normalization  of  V2X 
index,  cross-country  normalization  of  year-on-year  difference  in  stock  market  index,  cross-
country  normalization  of  difference  in  GDP  growth  forecast  in  three  years,  cross-country 
normalization  of  difference  in  gross  debt  over  GDP  forecast  in  a  year,  country-specific 
normalization of government expenditure over GDP, cross-country normalization of year-on-
year  difference  in  debt-to-GDP  ratio,  cross-country  normalization  of  difference  in  interest 
payable  to  GDP,  cross-country  normalization  of  rate  of  change  in  banking  sector  index 
(weighted average of bank equity prices by market capitalization), cross-country normalization 
of difference in 4-quarter moving average of gross financing needs over  GDP, cross-country 
normalization of difference in bailouts to GDP. 

Table 4: Identified top indicators for the forecast horizons of 4 quarters 

Variable 

Usefulness 

Threshold 

Threshold 
(percentile) 

AUC 

Type I 

Type II 

Primary market 

No. of issuances 

Bills issued 

Floating coupon issuance 

Syndicated issuance 

Secondary market 

Bid-ask 2Y 

Bid-ask 5Y 

Bid-ask 10Y 

Foreign debt 

Forward rate 

Forward premium 

Global demand and supply 

CDS 

Interest forecast 

Economic policy uncertainty 

US GDP 

V2X 

Stock market 

GDP forecast 

Debt forecast 

Government expenditure 

Debt 

Interest payable 

Bank index 

Gross financing needs 

0.291 

0.205 

0.218 

0.110 

0.273 

0.254 

0.220 

0.199 

0.386 

0.302 

0.262 

0.297 

0.215 

0.180 

0.187 

0.143 

0.237 

0.254 

0.347 

0.280 

0.213 

0.198 

0.204 

-0.064 

1.338 

0.136 

0.592 

-0.045 

-0.151 

-0.015 

0.288 

0.015 

0.187 

0.311 

0.400 

0.175 

-0.488 

-0.334 

-0.076 

0.969 

0.049 

0.172 

0.790 

0.233 

0.100 

0.784 

0.555 

0.897 

0.843 

0.793 

0.663 

0.596 

0.782 

0.661 

0.751 

0.734 

0.842 

0.873 

0.645 

0.334 

0.423 

0.643 

0.874 

0.709 

0.650 

0.843 

0.758 

0.593 

0.827 

0.819 

0.708 

0.609 

0.562 

0.781 

0.729 

0.719 

0.673 

0.916 

0.848 

0.797 

0.781 

0.727 

0.679 

0.613 

0.591 

0.697 

0.775 

0.852 

0.832 

0.709 

0.695 

0.691 

Bailouts 

0.610 
Notes: AUC stands for area under receiver’s operating characteristics curve (ROC).  

-0.204 

0.834 

0.252 

0.000 

0.500 

0.417 

0.583 

0.143 

0.111 

0.368 

0.292 

0.042 

0.158 

0.391 

0.333 

0.250 

0.000 

0.083 

0.375 

0.417 

0.250 

0.000 

0.333 

0.375 

0.222 

0.458 

0.375 

0.418 

0.089 

0.147 

0.197 

0.310 

0.380 

0.191 

0.310 

0.186 

0.237 

0.084 

0.073 

0.319 

0.640 

0.543 

0.339 

0.109 

0.241 

0.306 

0.107 

0.200 

0.382 

0.134 

0.121 

14 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5.2 Dynamics of the identified top indicators 

This  subsection  investigates  the  dynamics  of  the  top  indicators  identified  using  univariate  analysis. 
Figure A1 in the appendix shows the median dynamics of each indicator in the four quarters prior to 
the start of the  loss of market access episodes,  as well as in  the four  quarters following the loss of 
market access incidence. The dashed red line represents the median behaviour around LMA episodes 
and  the  shaded  area  highlights  interquartile  range  or  the  difference  between  the  75th  and  the  25th 
percentile of the indicator distribution around LMA episodes. The green line shows the median of the 
indicator before the Global Financial Crisis, i.e. in the period from 2003 Q4 until 2005 Q4. The black line 
indicates  an  indicator-specific  threshold  for  issuing  signals.  Overall,  given  their  observed  dynamics, 
most selected indicators would issue a signal either during full four quarters leading to the LMA episode 
or at least at some point in this four-quarter window. However, four indicators do not show good ability 
to  correctly  signal  high  stress  periods  leading  to  an  LMA  event:  the  ratio  of  bills  issuance-to-GDP, 
changes in the 8-quarter moving average of syndicated issuance share, year-on-year difference in 3-
years  ahead  GDP  growth  forecast,  and  year-on-year  change  in  4-quarter  moving  average  of  gross 
financing needs to GDP. The median dynamics of these indicators during high-tensions pre-LMA periods 
are quite close in direction and magnitude to those during tranquil times, and as such, fail to exceed 
their  indicator-specific thresholds. Consequently,  we infer  that  median dynamics of  these indicators 
cannot be relied upon to provide a good early warning signal of sovereign market access tensions. This 
unsatisfactory  performance  can  be  attributed  to  a  relatively  large  Type  I  error  rate  of  these  four 
indicators, i.e. exceeding 0.4, and in the case of the ratio of bills issuance-to-GDP and the changes in 
the  8-quarter  moving  average  of  syndicated  issuance  share  even  exceeding  0.5.  Table  5  presents  a 
detailed list of those quarters in the year preceding the start of LMA episodes per country that were 
successfully identified by our selected indicators of market tensions. 

Table 5: Identified periods of up to 4 quarters prior to LMA by top indicators 

Spain 

Greece 

Ireland 

Italy 

Latvia 

Portugal 

Slovenia 

Quarters before LMA episodes 

LMA 
episode 1 

LMA 
episode 2 

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

    

       

 

  

    

    

    

    

   

    

  

   

    

   

     

     

  

  

      

  

Interest 
forecast 
No. of 
issuance
s 
Governm
ent 
expendit
ure 
Bid-ask 
2Y 
Bid-ask 
10Y 
Bid-ask 
5Y 
volatility 
V2X 
Economi
c policy 
uncertai
nty 

15 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    

    

   

Debt 
forecast 
Debt 
Bailouts       
Interest 
payable 
Foreign 
debt 
(inverse) 
US GDP     

        

     

     

    

    

  

    

    

  

Bills 
issuance 
Forward 
rate 
(differen
ce to 
best) 
Forward 
premium 
Bank 
index 
(inverse) 
Stock 
index 
(inverse) 
Syndicat
ed 
issuance 
Floating 
coupon 
issuance 
CDS 

GFN 
GDP 
forecast 
MTI -
large 
MTI -
smaller 
MTI-
smallest 

      

   

  

     

     

  

      

    

     

   

    

  

   

    

    

     

    

       

       
  

   
   

    

    
    

    

    

   

 

   

   

   

  

        

   

  

Notes: GFN stands for Gross Financing Needs. MTI stands for Market Tensions Index, as described in the text. 

5.3 Presenting results of the univariate analysis 

We build on the identified individual thresholds to depict developments in our selected indicators over 
the four-quarter forecast horizon for the period from 2008 Q1 to 2018 Q4.  

Figure A2 in the Appendix depicts indicator dynamics by comparing their current level to their identified 
thresholds from 2008 Q1 to 2018 Q4 for each EA 14 country in our sample. The red colour shows year-
quarters in which the threshold was exceeded for an indicator, while blue colour marks year-quarters 
in which an indicator remained below the threshold, thus not emitting signals for the potential high 
bond market tensions. The darker the colour, the further away from its threshold an indicator is; dark 
blue therefore shows that an indicator is far below its threshold, while dark red points to an indicator 
that has far exceeded its threshold, thus marking very high likelihood of bond market tensions. The 
vertical lines mark the first quarters of identified LMA episodes based on our definition. 

16 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
In  line  with  what  one  would  expect,  for  Ireland,  Portugal  and  Greece,  various  indicators  started  to 
deteriorate as the countries were in the run-up to their corresponding official assistance programs. In 
contrast, for Germany and Netherlands, the figure shows a (blue) sea of smooth market access. 

6. Market access tensions index 

This  section  builds  on  the  univariate  identification  of  the  most  useful  predictors  of  sovereign  bond 
market tensions conducted in the previous section. We construct a composite index that aggregates 
the  most  useful  predictors.  For  this  purpose,  we  apply  to  bond  market  tensions  the  methodology 
outlined  in  Lang  et  al.  (2019),  who  construct  a  composite  index  of  financial  stress.  We  follow  this 
approach to ensure the transparency, interpretability and tractability of the results for policy use.  

First, we calculate each indicator’s difference from the optimal threshold we identified in the univariate 
analysis.16 Second, we normalize this difference from threshold on a cross-country basis, by subtracting 
the sample mean of the difference from threshold and dividing it by its standard error. Third, to ensure 
the resulting index is parsimonious, i.e. does not incorporate highly correlated indicators, we evaluate 
pairwise correlations between the normalized top indicators’ differences from threshold and eliminate 
highly  correlated  ones.  Consequently,  we  eliminate  cross-country  normalization  of  year-on-year 
difference in debt-to-GDP ratio and cross-country normalization of US GDP growth due to their high 
correlations with the debt-to-GDP forecast and interest forecast, which we consider important from 
the forward-looking perspective. We also exclude cross-country normalization of banking sector index 
rate of change due to very low correlation with our dependent, cross-country normalization of year-
on-year difference in CDS rate due to data limitations for  the countries in the sample, cross-country 
normalization of bid-ask spread on 10-year bonds due to its high correlation with bid-ask indicators for 
2-year and 5-year bonds, cross-country normalization of V2X index and cross-country normalization of 
year-on-year difference in stock index due to their high correlations with banking sector index.  

Fourth, we aim  to aggregate individual component indicators into the index based  on  their  optimal 
indicator weights. We obtain the optimal weights by running a univariate linear regression of our LMA 
dummy dependent on the normalized difference of an indicator from its threshold and by using the 
estimated coefficient as weight. The weights are constrained to sum to 1 by dividing each indicator’s 
estimated  coefficient  by  the  sum  of  all  the  estimated  coefficients  from  univariate  regressions.  We 
proceed to construct the market access tensions index as follows: 

𝑀𝑎𝑟𝑘𝑒𝑡 𝑎𝑐𝑐𝑒𝑠𝑠 𝑡𝑒𝑛𝑠𝑖𝑜𝑛𝑠 𝑖𝑛𝑑𝑒𝑥 =   ∑ 𝜔𝑗 ∙ ∆𝑥̃

𝑗
𝑖,𝑡

(5) 

𝑗=1

𝐽

𝑗

𝑖,𝑡

)/∆𝑥𝑆𝐷

𝑗 = (∆𝑥𝑖,𝑡

𝑗 − ∆𝑥𝑀𝑒𝑎𝑛

𝑗  denotes the normalized difference of sub-indicator from its threshold, i 
∆𝑥̃
indicates a country,  t  a year-quarter  and  j  an  individual sub-component. As observed  by Lang et al. 
(2019), optimal country-specific weights are difficult to estimate due to the scarcity of loss of market 
access episodes. By using cross-country normalisation and applying constant weights across countries 
and time we assume a common patterns across market access tension episodes in individual countries 
and  at different  points in  time. Applying the cross-country aggregation  also mitigates  overfitting for 

16 To construct our composite market tensions measure, we need to ensure all the identified top indicators presented in Table 
4 are related to our loss of market access dummy in a positive way. Since foreign-held debt ratio, US GDP growth, rate of 
change of a country’s banking sector index and difference in a country’s stock index are typically negatively related to loss of 
market access episodes, we invert their sign by multiplying them by minus one.  

17 

 
 
 
                                                           
individual LMA events. Furthermore, constraining the sum of weights of individual subcomponents to 
1 allows us to decompose the market access tensions index (MTI) into its drivers at any quarter in our 
sample. Figure A4 in the Appendix shows the MTI decomposition for EA 14 countries. 

Out of the best performing indicators in Table 4, based on their subpar median dynamics over the start 
of loss of market access episodes (see Figure A1 in the Appendix), we exclude from the composite index 
the  following  indicators:  ratio  of  bills  issuance-to-GDP,  difference  in  moving  average  of  syndicated 
issuance share over the last 2 years, year-on-year difference in GDP growth forecast in 3 years, and 
year-on-year difference in moving average of gross financing needs to GDP over previous 4 quarters.17  

Due to data constraints, we construct an alternative (smaller) market access tensions index comprising 
fewer indicators. Due to data limitations for Ireland, Latvia and Slovenia, we eliminate the two bid-ask 
indicators (spread on 2-year bond and volatility of spread on 5-year bond). We then exclude the forward 
premium, which is missing for Latvia and Slovenia, and calculate the “smallest” market tensions index, 
comprising  10  indicators  from  Table  4.  The  calculated  optimal  weights  for  individual  indicators  are 
shown in Table 6. Figure 1 compares the dynamics of the “largest” market tensions index (comprising 
13 sub-components) with the “smallest” index. While the indices co-move strongly, in most countries 
the  largest  index  appears  shifted  downwards  compared  to  the  more  parsimonious  version.  For 
illustrative purposes in Figure 1 the resulting indices are rescaled between 0 and 1.  

Figure 1. Sovereign bond market tensions index 

Notes:  The  vertical  axis  measures  the  probability  of  losing  market  access  within  up  to  4  quarters.  LMA  shows  periods  of 
identified  high  market  access  tensions  while  pre-LMA  identifies  periods  of  up  to  4  quarters  prior  to  LMA.  Country  name 
abbreviations are as follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, 
IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

17 These indicators behave similarly around LMA events and tranquil times, failing to issue signals of elevated market tensions. 

18 

 
 
                                                           
Table 6: Optimal weights for sub-components of market access tension indices 

Sub-component 

Largest 
Index 

Smaller 
index 
Weight 

Smallest 
index 

Primary market 

No. of issuances 

Bills issued 

Floating coupon issuance 

Syndicated issuance 

Secondary market 

Bid-ask 2Y 

Bid-ask 5Y 

Bid-ask 10Y 

Foreign debt 

Forward rate 

Forward premium 

Global demand and supply 

CDS 

Interest forecast 

Economic policy uncertainty 

US GDP 

V2X 

Stock market 

GDP forecast 

Debt forecast 

Government expenditure 

Debt 

Interest payable 

Bank index 

Gross financing needs 

0.05 

- 

0.04 

- 

0.13 

0.15 

- 

0.03 

0.27 

0.02 

- 

0.13 

0.02 

- 

- 

- 

- 

0.04 

0.04 

- 

0.04 

- 

- 

0.07 

- 

0.06 

- 

- 

- 

- 

0.04 

0.37 

0.03 

- 

0.18 

0.03 

- 

- 

- 

- 

0.06 

0.06 

- 

0.05 

- 

- 

0.07 

- 

0.06 

- 

- 

- 

- 

0.04 

0.40 

- 

- 

0.18 

0.03 

- 

- 

- 

- 

0.06 

0.06 

- 

0.05 

- 

- 

Bailouts 

0.04 

0.05 

0.05 

To  evaluate  how  successful  these  indices  are  in  capturing  tensions  in  sovereign  bond  markets,  we 
compare year-on-year changes in the indices during the four quarters leading to LMA episodes with 
those in tranquil periods. We conduct difference-in-means testing to assess if on average the composite 
indices succeed in capturing increases in market tensions for individual countries. Figure 3 shows the 
results. In all countries that experienced an LMA episode, all three constructed indices of market access 
tensions capture increases in market tensions in pre-LMA times. Average increases in market tensions 
in pre-LMA times are more positive and statistically significantly different from those in tranquil times 
at least at 5% significance level18 

18 Statistical significance is depicted by a hollow shape above bars; a circle for significance at 10% level, a square at 5% and a 
triangle for significance at 1% level. 

19 

 
 
 
 
 
 
 
 
 
 
 
 
 
                                                           
Figure 3: Average difference in market tensions: pre-LMA vs. tranquil times (All countries) 

Notes: Average difference between pre-LMA and tranquil periods as captured by market tensions indices. A circle denotes 
statistically significant difference at 10% level, a square at 5% level and a triangle at 1% level.  

6.1 Dynamics of market tensions index around identified loss of market access episodes  

Figure 4 compares the median dynamics (red line) of individual market tensions indices around LMA-
episodes  with  median  values  in  tranquil  times  (green  line).  The  horizontal  black  line  shows  the 
calculated optimal threshold for the index using data until 2011 Q2 and the full data ending in 2018 Q4, 
respectively. The median index is above its threshold four quarters before as well as after the start of 
LMA episodes, thus providing a good early warning signal of rising market tensions. 

                                Figure 4. Market tensions index dynamics around LMA episodes 

20 

 
 
 
Furthermore,  we perform  univariate  testing  of  the composite  market  tensions indices  on  data until 
2011 Q2 (upper panel of Table 7) to ensure comparability with individual indicators. The top performing 
indicator in our dataset is cross-country normalization of difference of 10-year forward rate from the 
best performing country, with usefulness of 0.386, AUROC of 0.916 and Type I and Type II error rate of 
0.042 and 0.186, respectively. The composite market tensions indices outperform the 10-year forward 
rate, while the smallest index has only marginally better performance with AUROC of 0.931 on data 
until  2011  Q2.  However,  using  the  full  data  until  2018  Q4  (bottom  panel  of  Table  7)  marginal 
performance of the smallest market tensions index improves over the best performing single indicator; 
AUROC increases to 0.943 and utility rises to 0.4. 

Table 7: Univariate assessment of composite market tensions indices 

Market tensions index 
(largest) 
Market tensions index 
(smaller) 
Market tensions index 
(smallest) 
Market tensions index 
(largest) 
Market tensions index 
(smaller) 
Market tensions index 
(smallest) 

Usefulness 

Threshold 

Threshold 
(percentile) 

AUC 

Type I 

Type II 

0.462 

0.234 

0.860 

0.969 

0.000 

0.075 

0.440 

0.357 

0.804 

0.957 

0.000 

0.121 

0.385 

0.198 

0.730 

0.931 

0.042 

0.188 

0.420 

0.234 

0.859 

0.960 

0.100 

0.059 

0.427 

0.357 

0.826 

0.959 

0.074 

0.072 

0.400 

0.181 

0.731 

0.943 

0.063 

0.138 

Notes: AUC stands for the area under receiver’s operating characteristics curve (ROC) 

7. Multivariate analysis and out-of-sample forecasting 

After  evaluating  the  indicators using data until 2011 Q2  on a  univariate basis, and identifying  those 
most useful for forecasting episodes of market tensions over a four-quarter horizon, we are left with 
24 best performing indicators. However, these are still too numerous to be meaningfully used within a 
multivariate  model  that  generalizes  well  out  of  sample.  Furthermore,  in  our  analysis  we  face  the 
problem of perfect separation of 1 and 0 outcomes when all 24 indicators are included in the logistic 
regression, which is demonstrated by failure of logistic regression maximum likelihood estimation to 
converge. As a result, traditional maximum likelihood coefficient estimates do not exist. We tackle this 
issue by relying on statistical techniques to resolve model uncertainty, i.e. which variables should be 
included in the final model.  

Classic techniques for model building and variable selection, for instance generalized linear models with 
stepwise selection, are known to be unreliable and often biased (Koop, 2003). The main problem with 
these  techniques  is  that  in  applying  (one-at-a-time  or)  sequential  variable  elimination  (backward 
selection),  useful  variables  may  be  excluded  each  time  the  test  is  performed  (i.e.  the  model  is  re-
estimated on the new subset of variables). Moreover, while the removal of less significant predictors 
can  increase  the  significance  of  the  remaining  variables,  it  may  also  lead  to  overstating  their 
importance. Finally, stepwise variable selection tends to pick models that are smaller than desirable for 
prediction purposes (Roecker, 1991). 

21 

 
 
 
Recent advancements in statistics have focused on the development of algorithms for model building 
and variable selection (Hastie et al. 2009). In particular, a variety of statistical techniques to select the 
most informative variables out of a large set of predictor variables have been developed during the past 
years  (e.g.  Hastie  et  al.  2009).  To  properly  address  the  above  concerns,  we  consider  the  following 
approaches for dealing with model uncertainty. 

7.1 Modelling approaches 

7.1.1  Logistic regression with backward sequential variable selection 

To ascertain the relationship between our dependent variable capturing periods of up to four quarters 
prior  to  identified  loss  of  market  access  episodes  and  the  identified  most  useful  indicators  of  high 
market access tensions, a logistic regression is first applied. Logit model is specified as follows:  

𝑃(𝑌 = 1) =

𝑒 𝑥𝛽
1 + 𝑒𝑥𝛽 

(6) 

Where 𝑃(𝑌 = 1) is probability of an episode of high market access tensions arising within four quarters, 
X is the set of useful predictors for high market access tensions. The model is estimated using maximum 
likelihood estimation, which yields coefficients that are consistent and asymptotically efficient.  

Estimating the model with all 24 indicators is, however, not desirable nor is it in our case feasible. For 
the  model  containing  all  the  identified  useful  indicators,  maximum  likelihood  estimation  does  not 
converge, i.e. the model suffers from separation which indicates that the outcome can be perfectly 
predicted using a linear combination of explanatory variables.19. This issue can be typically remedied by 
excluding  the  problematic  indicators  from  the  model  until  estimation  is  achieved.  However,  this 
elimination of indicators can inadvertently exclude the strongest predictors. 

Despite the downsides of sequential variable selection, we apply sequential elimination of indicators 
based on their relative usefulness. For this exercise, we apply Recursive Feature Elimination function 
with logistic regression in Python.  

7.1.2  Generalized regression models via penalized maximum likelihood 

These models aim is to solve the following function: 

1
𝑁

𝑁
∑ 𝑤𝑖𝑙(𝑦𝑖, 𝛽0 + 𝛽𝑇𝑥𝑖) + 𝜆 [
𝑖=1

(1 − 𝛼)
2

min
𝛽0,𝛽

∥ 𝛽 ∥2

2+ 𝛼 ∥ 𝛽 ∥1]

(7) 

over a grid of values of  𝜆, where 𝑙(𝑦, 𝜂)  is the negative log-likelihood contribution of observation i. The 
elastic  net  penalty  is  controlled  by  𝛼  and  bridges  the  gap  between  lasso  (𝛼 = 1)  and  ridge  (𝛼 = 0). 
Parameter  𝜆  controls  the  overall  strength  of  the  penalty.  The  ridge  penalty  shrinks  coefficients  of 
correlated predictors towards each other while lasso tends to pick one of them and discard the others. 
The elastic net penalty mixes the two – if predictors are correlated in groups, values of  𝛼 close to 𝛼 =
0.5  tend to select the groups in or out together. Parameters are selected by optimizing a loss function 
(mean  squared  error  for  Gaussian  models,  misclassification  error  or  AUROC  for  two-class  logistic 
regressions as in our case) using k-fold cross-validation. In our analysis, we have applied 10-fold cross-

19 In this case, estimated coefficients are infinite and the optimization process tries to solve this iteratively. As a consequence, 
in each step of the estimation process the estimated coefficient is marginally increased ad infinity. 

22 

 
 
 
                                                           
validation  over  our  training  dataset,  i.e.  data  until  2011  Q2,  to  select  optimal  (objective  function-
minimizing) value of 𝜆 in the logistic model with lasso penalty.20  

However, despite its variable selection capacity, penalized estimation is characterized by reducing the 
variance of estimators by introducing substantial bias. For this reason, the bias of each estimator is a 
major component of its mean squared error (variance constitutes only a small part). As a result, in most 
applications  it  is  not  feasible  to  obtain  a  sufficiently  precise  estimate  of  the  bias  for  penalized 
regressions. Reporting a standard error of penalized regression estimates can thus lead to erroneous 
conclusions, since these would ignore inaccuracy caused by the bias. Friedman et al. (2008) provide 
more details on this technique. 

7.1.3  Model-based boosting 

Model-based  boosting  is  a  machine  learning  method  for  optimizing  prediction  accuracy  and  for 
obtaining  statistical  model  estimates  via  gradient  descent  techniques.  An  important  feature  of  the 
method  is  that  it  carries  out  variable  selection  during  the  fitting  process  (Buhlmann  &Yu,  2003, 
Buhlmann, 2006) without relying on heuristic techniques such as stepwise variable selection.  

The approach models the relationship between the dependent y and a set of predictors x by minimizing 
a loss function 𝜌(𝑦, 𝑓) ∈ ℝ over a prediction function f depending on x. For generalized linear models 
the loss function is typically the negative log-likelihood function of the outcome distribution. For the 
binary dependent in our analysis f is a logistic function of x and 𝜌 corresponds to misclassification error 
or  (inverse)  AUROC.  In  the  gradient-boosting  approach  the  aim  is  to  estimate  optimal  prediction 
function 𝑓∗ defined by  

𝑓∗ = 𝑎𝑟𝑔𝑚𝑖𝑛𝑓Ε𝑌,𝑋[𝜌(𝑦, 𝑓(𝑥𝑇))] 

                            (8) 

𝑛
𝑖=1

where the loss function 𝜌 is assumed to be differentiable with respect to f. In practice, the expectation 
in (8) is not known and only the realization of (𝑦, 𝑥𝑇) is observed. Therefore, instead of minimizing the 
expected  value  in  (8),  boosting  algorithms  minimize  the  observed  mean,  called  the  empirical 
risk ∑ 𝜌(𝑦𝑖, 𝑓(𝑥𝑇))
. The algorithm adds an estimate of the true negative gradient of empirical risk to 
the current estimate of 𝑓∗ in each iteration. The component-wise boosting algorithm descends along 
the gradient of the empirical risk. The empirical risk is thus minimized in a stage-wise fashion, and a 
structural  (regression)  relationship  between  y  and  x  is  established.  The  algorithm  also  carries  out 
variable selection and model choice.21  

7.1.4  Bayesian model averaging 

Another method to deal with model uncertainty in the parametric model space is by averaging over 
different  models  sampled  from  variables  in  covariate  space,  which  also  enables  Bayesian  variable 
selection.  Bayesian  model  averaging  (BMA)  estimates  a  number  of  models  that  use  subsets  of  all 
explanatory variables on the right-hand side. For a large number of variables, all the possible models 
are  not  enumerated  but  they  are  sampled  from  the  model  space  using  an  algorithm.  In  most 
applications, Markov Chain Monte Carlo (MCMC) sampler is used. This sampler only goes through the 
most important part of the model space (there are 2𝑘 possible models in total, where k is the number 
of covariates). Each estimated coefficient (posterior mean) is the average coefficient of all the models 

20 R implementation of this technique in the glmnet package uses cyclical coordinate descent which optimizes the objective 
function over each parameter with other parameters fixed and cycles until convergence is reached.  
21 The detailed steps of the algorithm that minimizes the observed mean over f are provided in Hofner et al. (2014). 

23 

 
 
 
                                                           
weighted  by  the  posterior  model  probability,  which  is  akin  to  adjusted  R-squared  in  frequentist 
econometrics. Another important concept, posterior inclusion probability, is the sum of all posterior 
model probabilities of the model in which a particular variable is included and reports how likely it is 
the variable is included in the true model. The posterior standard deviation is analogous to the standard 
error and follows the distribution of a coefficient from all estimated models.22  

7.2 Results of Multivariate Approaches 

7.2.1 Logistic regression with the market tensions index 

After  verifying that the composite indices built in  section  6  capture  well  the  build-up of tensions in 
sovereign bond markets, we now investigate their predictive performance both in sample and out of 
sample.  We run panel logistic regression with random effects using only the composite market tensions 
index as an explanatory variable and the binary indicator capturing periods of up to four quarters prior 
to identified loss of market access as the dependent. Table 8 presents the results for univariate logistic 
regressions using each of the three constructed market tensions indices.  

Table 8: Estimated coefficients from univariate logit with market tensions index 

Market tensions index (large) 

7.660*** 
(2.071) 

Market tensions index (smaller) 

Market tensions index (smallest) 

Univariate Logit 

4.823*** 
(0.986) 

Intercept 

Obs. 
Number of countries 

-6.044*** 
(1.845) 
293 
11 

-4.712*** 
(0.837) 
326 
13 

4.651*** 
(0.837) 
-4.553*** 
(0.785) 
397 
14 

Notes: Standard errors are in parentheses. *** indicate 1%, ** 5% and * 10% significance level. 

As expected due to the construction of the index, the estimated coefficients for the market tensions 
index are positive and highly significant. Moreover, with a decreasing number of sub-indicators included 
in the composite index, the estimated slope coefficient decreases while the number of observations 
and countries included in the regression increases. Figure 5 presents the predicted probabilities from 
univariate panel logistic regressions with random effects using only the market tensions index as  an 
explanatory variable both in sample and out of sample. The logit model using the market tensions index 
adequately captures the build-up of vulnerabilities in periods leading to high market access tensions 
episodes. 

Out of sample, the MTI predicts well elevated probabilities of high market tensions after the outbreak 
of  a  market  loss  episode. However,  the  predicted  probabilities  tend  to  be relatively  low  in  the four 
quarters  preceding  loss  of  market  access  episodes  and  decrease  relatively  rapidly  to  tranquil  levels 
following a few quarters after  the identified start of market loss episodes. For Portugal, the second 
identified episode of high market tensions was not identified by the univariate logit model even though 
there was a small increase in probability in the four quarters preceding the episode. 

22 For more information on the technique and on its R implementation see Clyde et al. (2018). 

24 

 
  
 
 
  
 
 
 
 
  
 
 
 
 
  
 
 
  
 
                                                           
Figure 5: Predicted probability using the market access tensions index 

Notes: Probability of market access tensions from logistic regression using the smallest market tensions index. The vertical axis 
measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access 
tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample 
forecast  and  the  dashed  line  shows  out-of-sample  forecast  probabilities  of  market  access  tensions.  Country  name 
abbreviations are as follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, 
IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

7.2.2 Logistic regression with backward sequential variable selection 

Despite the shortcomings of stepwise variable selection approaches mentioned above, we nevertheless 
apply  a  sequential  backward  variable selection  within  logistic  regression  in  Python  as  a first step  to 
evaluating market access conditions using a multivariate framework. Following the pre-selection of the 
most useful market tensions indicators on data until 2011 Q2, we estimate out of sample probabilities 
using logistic regression containing only these selected indicators. The selected indicators from logistic 
regression  with backward sequential variable selection  are presented in  Table 9  together  with  their 
coefficients and the corresponding 95% confidence interval. 

25 

 
 
 
 
 
 
 
 
 
 
Figure 6: Predicted probability from logistic regression with backward sequential variable selection 

Notes: Probability of market access tensions from logistic regression using backward sequential variable selection. The vertical 
axis measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market 
access tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-
of-sample forecast and the dashed line shows out-of-sample forecast probabilities of market access tensions. Country name 
abbreviations are as follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, 
IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

7.2.3 Penalized and boosted logistic regression 

Table 9 shows the results of running the logistic regression with backward sequential variable selection, 
with  lasso  penalty  and  with  the  component-wise  boosting  on  the  24  pre-selected  indicators.  Most 
indicators selected by the algorithms use secondary and primary markets data, and indicators reflecting 
global demand and government supply side. Coefficient estimates are overall positive since the selected 
indicators were adjusted to be positively related to high sovereign bond market tensions.  

Overall, both methods result in similar out-of-sample predicted probabilities of high sovereign bond 
market  tensions.  The  predicted  elevated  probabilities  coincide  with  actual  LMA  episodes,  with 
estimated probabilities at least increasing in the four quarters leading to the LMA episode. Only one 
false  alarm  would  be  issued  by  the  models  for  Slovakia,  at  the  end  of  2011,  when  the  estimated 
probability exceeds 0.5 but no LMA was identified using our definition. 

26 

 
 
 
 
 
 
 
Figure 7: Predicted probability from penalized logistic regression 

Notes: Probability of market access tensions from penalized logistic regression with loss-minimizing lambda (black line) and 
lambda,  for  which  model  error  is  within  one  standard  error  of  the  minimum  (brown  line).  The  vertical  axis  measures  the 
probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access tensions while 
pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample forecast and 
the  dashed  line  shows  out-of-sample  forecast  probabilities  of  market  access  tensions.  Country  name  abbreviations  are  as 
follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, IT=Italy, LV=Latvia, 
NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

27 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 8: Predicted probability from boosted logistic regression 

Notes: Probability of market access tensions from boosted logistic regression. The vertical axis measures the probability of 
losing market access within up to 4 quarters. LMA shows periods of identified high market access tensions while pre-LMA 
identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample forecast and the dashed 
line  shows  out-of-sample  forecast  probabilities  of  market  access  tensions.  Country  name  abbreviations  are  as  follows: 
AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy,  LV=Latvia, 
NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

28 

 
 
Indicator 
Primary market 
No. of  issuances 
Bills issued 
Floating coupon 
issuance 
Syndicated issuance 
Secondary market 
Bid-ask 2Y 
Bid-ask 5Y 
Bid-ask 10Y 
Foreign debt 
Forward rate 
Forward premium 
Global demand and 
supply 
CDS 
Interest forecast 
Economic policy 
uncertainty 
US GDP 
V2X 
Stock market 
GDP forecast 
Debt forecast 
Government 
expenditure 
Debt 
Interest payable 
Bank index 
Gross financing needs 
Bailouts 
Intercept 

Table 9: Selected Indicators and their coefficient estimates 

Logit with Sequential Selection 

Penalized Logit 

Boosted Logit 

Coefficient 

95% confidence interval 

Coefficient (lambda min) 

Coefficient (lambda 1SE) 

Coefficient 

95% confidence interval 

- 
3.126 

3.288 

- 

- 

10.927 
6.058 
14.33 
- 

-3.812 
2.103 

- 

- 
-5.047 
- 
- 
- 

- 

- 
- 
- 
- 
- 
-7.142 

- 
-1.066 

-0.288 

- 

- 

-3.548 
-2.253 
-2.529 
- 

-11.214 
-1.346 

- 

- 
-11.234 
- 
- 
- 

- 

- 
- 
- 
- 
- 
-16.174 

- 
7.319 

6.864 

- 

- 

25.403 
14.368 
31.19 
- 

3.59 
5.55 

- 

- 
1.14 
- 
- 
- 

- 

- 
- 
- 
- 
- 
1.889 

- 
0.24 

0.652 

- 

- 
- 
0.937 
0.521 
2.942 
- 

- 
0.453 

- 

- 
-0.272 
- 
- 
- 

0.132 

- 
- 
- 
- 
- 
-3.12 

- 
0.063 

0.542 

- 

- 
0.019 
0.579 
0.235 
2.61 
- 

- 
0.297 

- 

- 
- 
- 
- 
- 

- 

- 
- 
- 
- 
- 
-3.134 

- 
0.02 

0.436 

- 

- 
0.086 
0.317 
0.217 
2.053 
- 

- 
0.306 

- 

- 
- 
- 
- 
- 

- 

- 
- 
- 
- 
- 
-2.509 

- 
0 

0 

- 

- 
0 
0 
0 
0.757 
- 

- 
0 

- 

- 
- 
- 
- 
- 

- 

- 
0.319 

0.811 

- 

- 
0.649 
1.038 
0.438 
2.574 
- 

- 
1.103 

- 

- 
- 
- 
- 
- 

- 

- 
- 
- 
- 
- 
-3.219 

- 
- 
- 
- 
- 
-1.921 

29 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
7.2.4 Bayesian Model Averaging 

Figure  10  shows  out-of-sample  predicted  probabilities  of  high  market  tensions  based  on  top  5000 
sampled models from Bayesian model averaging (BMA). Due to the nature of our binary dependent, we 
are fitting logistic regressions using uninformative beta-binomial priors for distribution across models 
and robust distribution for coefficient estimates. Due to a large number of potential models (there are 
224 since there are 24 potentially useful predictors) we use Monte Carlo Markov Chain (MCMC) sampler 
with Bayesian Adaptive Sampling (BAS) that samples models without replacement, i.e. models that have 
been already sampled by the algorithm are excluded from further sampling. Clyde et al. (2018) provide 
more details on the sampling technique.  

Figure 9 summarizes the top 20 models, by model fit, from the model space, visited by the sampling 
MCMC  algorithm  with  BAS  sampling  method.  Rows  correspond  to  top  indicators  while  columns 
represent individual models. The models are ranked by their posterior model probability from the best 
on the left to worst on the right. Top x-axis shows the models’ rank. In each model, missing are in black, 
while included variables are coloured. The colour corresponds to the log of the posterior probability of 
that model. These posterior probabilities are scaled so that the worst model in the top 20 models is 
assigned  0.  The  values  on  the  lower  x-axis  correspond  to  log  Bayes  factors  to  allow  for  model 
comparison to the lowest probability model in the top 20 models. Models with the same colours have 
similar log Bayes factors, i.e. the difference in their Bayes factors is not worth a mention. 

Figure 9: Top 20 models from Bayesian Model Averaging 

30 

 
 
Figure 10: Predicted probability of market tensions from Bayesian Model Averaging 

Notes:  Probability  of  market  access  tensions  from  Bayesian  Model  Averaging  with  logistic  regressions.  The  vertical  axis 
measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access 
tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample 
forecast  and  the  dashed  line  shows  out-of-sample  forecast  probabilities  of  market  access  tensions.  Country  name 
abbreviations are as follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, 
IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

Overall, Bayesian model averaging increases the rate of detection of loss of market access episodes in 
the periods leading to the event substantially. Nevertheless, the method generates more false alarms 
than  the  penalized  and  boosted  logistic  models.  Using  BMA,  the  predicted  probability  of  market 
tensions  was  especially  high  for  Ireland  in  2017-2018.  Similarly,  as  with  the  penalized  and  boosted 
logistic models, the BMA model signals spikes of high market tensions for Slovakia in 2012/2013 and in 
2015 despite the fact we have not identified LMA episodes at these points in time for these countries.  

7.3 Comparison of performance 

The previous subsection presented forecast probabilities of high sovereign bond market tensions from 
different  econometric  models.  Overall,  based  on  Figures  6-8  and  10,  it  appears  all  the  presented 
techniques  perform  quite  well  in  and  out  of  sample.  To  compare  the  models’  performance  more 
rigorously,  we  focus  on  the  predicted  probabilities  of  market  tensions  in  the  periods  of  up  to  four 
quarters prior to the identified loss of market access. Table 11 summarizes the predicted probabilities 
from each technique for these periods by country. Probabilities highlighted dark grey are the highest 
for that country-period from among the applied econometric approaches.  

Probabilities  from  the  Bayesian  Model  Averaging  (BMA)  approach  are  the  highest  from  among  the 
tested  techniques  in  all  periods  for  which  they  are  available,  apart  from  the  period  preceding  the 
second  Portuguese  LMA  episode  by  three  quarters.    However,  despite  the  correctly  predicted  high 
market tensions probabilities, BMA does not generate forecasts for Ireland, Latvia and Slovenia due to 

31 

 
 
increased  data  limitations  for  some  indicators  for  these  countries.  An  additional  concern  with  such 
methods is that BMA generates more false alarms than the other techniques. 

Table 11: Predicted probabilities in periods of up to 4 quarters 

Logit w/ Market tensions 
index 

Penalized logit 

Large 
index 

Smaller 
index 

Smallest 
index 

Logit w/ 
sequential 
selection 

Optimal 
lambda 

1 SE 
lambda 

Boosted 
logit 

BMA 

Spain 

Greece 

Ireland 

Italy 

Latvia 

Portugal 

Slovenia 

Quarters 
before 
LMA 
episodes 

LMA 
episode 1 

LMA 
episode 2 

0.025 

0.044 

0.263 

0.031 

0.924 

0.140 

0.924 

0.985 

0.014 

0.033 

0.268 

0.094 

0.020 

0.028 

0.042 

0.175 

0.002 

0.005 

0.014 

0.026 

-4 

-3 

-2 

-1 

-4 

-3 

-2 

-1 

-4 

-3 

-2 

-1 

-4 

-3 

-2 

-1 

-4 

-3 

-2 

-1 

-4 

-3 

-2 

-1 

-4 

-3 

-2 

-1 

-4 

-3 

-2 

-1 

0.097 

0.147 

0.064 

0.072 

0.933 

0.265 

0.899 

0.972 

0.918 

0.897 

0.255 

0.375 

0.063 

0.133 

0.235 

0.226 

0.054 

0.067 

0.069 

0.297 

0.009 

0.020 

0.052 

0.094 

0.048 

0.066 

0.167 

0.110 

0.167 

0.075 

0.083 

0.937 

0.286 

0.891 

0.970 

0.914 

0.892 

0.265 

0.390 

0.072 

0.149 

0.250 

0.241 

0.032 

0.005 

0.117 

0.302 

0.056 

0.067 

0.075 

0.324 

0.010 

0.024 

0.061 

0.105 

0.026 

0.054 

0.070 

0.174 

0.606 

0.638 

0.837 

0.668 

0.983 

0.907 

0.562 

0.885 

0.591 

0.734 

0.924 

0.844 

0.126 

0.084 

0.351 

0.857 

0.059 

0.089 

0.441 

0.823 

0.433 

0.516 

0.666 

0.515 

0.922 

0.720 

0.326 

0.659 

1 

1 

1 

1 

1 

1 

1 

1 

0.439 

0.512 

0.681 

0.594 

0.999 

1 

1 

1 

0.110 

0.105 

0.241 

0.676 

0.089 

0.180 

0.360 

0.528 

0.999 

0.999 

0.999 

1 

0.149 

0.030 

0.819 

1 

0.528 

0.645 

0.832 

0.706 

0.980 

0.896 

0.381 

0.808 

0.425 

0.326 

0.416 

0.821 

0.481 

0.568 

0.797 

0.669 

0.082 

0.083 

0.315 

0.852 

0.045 

0.096 

0.351 

0.662 

0.270 

0.200 

0.673 

0.424 

0.539 

0.702 

0.545 

0.951 

0.758 

0.269 

0.654 

0.389 

0.301 

0.223 

0.437 

0.516 

0.688 

0.589 

0.066 

0.062 

0.209 

0.752 

0.052 

0.126 

0.322 

0.534 

0.224 

0.192 

0.680 

Notes: Optimal lambda denotes loss-minimizing lambda and 1 SE lambda indicates lambda, for which model error is within 
one standard error of the minimum. 

Without including interaction terms among explanatory variables into the set of potential predictors of 
LMA  episodes,  the  multivariate  approaches  presented  in  this  paper  do  not  account  for  conditional 
relations  between  right-hand  side  indicators.  Such  relationships  can  be  intuitively  expressed  using 

32 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
decision tree structures. Classification and regression trees (CART) and their aggregation using bagging, 
i.e. the random forest (Breiman, 2001), boosting, i.e. extreme gradient boosting or XGBoost (Chen and 
Guestrin,  2016),  or  CRAGGING  (Vezzoli  and  Stone,  2007)  are  all  methods  that  apply  the  tree-like 
partitioning  of  data  using  conditional  thresholds.  For  instance,  in  an  economic  context  Alessi  and 
Detken  (2018)  apply  the  random  forest  to  identify  excessive  credit  and  the  associated  build-up  of 
systemic risk in the banking system while Gabriele (2019) combines the regression tree approach with 
the CRAGGING algorithm to build an early warning model of systemic banking crises.  Consequently, 
CART-based models might be useful  to study episodes of loss of market access further as well as to 
allow for interplay of various indicators within the same framework. 

8. Preferences between missed crises and false alarms 

In practice, policymakers will likely not be indifferent between failing to issue a signal of market access 
tensions  and  emitting  a  false  alarm.  For  this  reason,  in  this  section  we  consider  alternative  sets  of 
preferences  for  Type  I (missed  crisis)  and  Type  II (false  alarm)  errors.  A  policymaker  who  cares  less 
about  emitting  false  alarms  than  about  missing  an  LMA  would  put  𝜃 > 0.5  in  the  loss  function  L  in 
equation (4) to penalize failure to issue a signal relatively more than emitting false alarms. Alternatively, 
a policymaker who wishes to avoid false alarms more than missing crises would choose 𝜃 < 0.5 in the 
loss function L in equation (4). To take into account such potential differences in preferences, we repeat 
the univariate evaluation of our full set of potentially useful LMA indicators on a sample until 2011 Q2 
under two alternative preferences. For a policymaker who cares more about failure to provide a signal, 
we assume weights of 80% and 20% for Type I and Type II error, respectively. Symmetrically, we adopt 
weights of 20% and 80% for Type I and Type II error, respectively, for a policymaker who cares more 
about false alarms. 

Tables  A1  and  A2,  in  Appendix  A,  present  the  results  of  univariate  evaluation  of  the  top  primary, 
secondary market and global demand and supply indicators  which  reflect  policymaker’s  asymmetric 
preferences. Under both preference schemes, indicators from the primary and secondary market, as 
well  as  demand  and  supply  side  are  represented.  Indicators  capturing  primary  market  issuance 
(number/quantity)  are  retained  under  alternative  preferences.  Among  secondary  market  indicators, 
forward rates, forward premia, the share of foreign investors, and bid-ask spreads remain among the 
top predictors. Among demand and supply indicators, US GDP growth, debt to GDP ratio, CDS, GDP 
forecasts and interest rate forecasts are the top indicators regardless of the policymaker’s preferences.  

Univariate evaluation yields critical thresholds for individual indicators, which allow to visually represent 
indicator  dynamics  using  country-specific  heatmaps.  Figure  A6  in  Appendix  A  shows  the  signals 
provided by the top LMA indicators under preference weights of 80/20 for Type I and Type II errors (on 
the  left)  and  20/80  (on  the  right).  For  the  policymaker  with  a  preference  for  not  missing  potential 
distress, it is particularly noteworthy that most of the indicators flash red throughout our sample, even 
in  countries  that  did  not  experience  high  market  access  tensions  in  the  past.  Instead,  when  a 
policymaker cares more about false alarms, the heatmaps stay predominantly blue (below their critical 
thresholds) but they still flash red in periods in which countries experienced LMA episodes according 
to our definition. Therefore, heatmaps fail to accurately depict market access tensions when used by a 
policymaker  that  cares  more  about  missed  crises,  but  remain  useful  for  a  policymaker  that  is  more 
concerned about issuing too many false alarms. 

33 

 
 
As a last step, we use the two alternative sets of top indicators  chosen by the 80/20 and the 20/80 
policymakers  as  explanatory  variables  in  one  of  the  multivariate  models  used  in  our  benchmark 
calculations, a penalized logistic regression. Tables 12 and 13 evaluate, respectively, the in-sample and 
out-of-sample  performance  of  the  penalized  logit  model  for  the  specifications  under  alternative 
preferences,  and  compare  it  to  the  performance  under  the  baseline  specification.  We  present 
estimated coefficients for indicators selected endogenously by the model in Tables A3 and A4 under 
preferences of 80/20 and 20/80 for Type I and Type II errors, respectively. Figure A7 shows in-sample 
and  out-of-sample  predicted  probabilities  of  high  market  access  tensions  for  the  two  preference 
specifications as well as for the benchmark specification. 

Table 12: In-sample model performance under various preferences 

Model 

U 

Threshold 

Threshold 
(percentile) 

AUC 

Type I 

Type II 

True 
positive 

True 
negative 

Model A 
(benchmark) 
Model B 
(benchmark) 
Model A 
(missing/false: 
80/20) 
Model B 
(missing/false: 
80/20) 
Model A 
(missing/false: 
20/80) 
Model B 
(missing/false: 
20/80) 

0.122 

0.270 

0.863 

0.951 

10.5% 

7.1% 

89.5% 

92.9% 

0.114 

0.209 

0.862 

0.939 

11.1% 

8.0% 

88.9% 

92.0% 

0.174 

0.222 

0.890 

0.993 

5.9% 

1.8% 

94.1% 

98.2% 

0.144 

0.159 

0.866 

0.970 

0.0% 

7.1% 

100.0% 

92.9% 

0.193 

0.391 

0.894 

0.999 

0.0% 

0.9% 

100.0% 

99.1% 

0.189 

0.299 

0.890 

0.998 

0.0% 

1.4% 

100.0% 

98.6% 

Notes: Model A stands for penalized logistic regression with loss-minimizing lambda while model B stands for penalized logistic 
regression with lambda, for which model error is within one standard error of the minimum. U stands for usefulness of a model 
calculated from equation (3) given a policymaker’s preference for Type I and Type II error. AUC stands for the area under 
receiver’s operating characteristics curve (ROC). 

Compared  to  50/50  preferences,  an  80/20  policymaker  would  lower  Type  I  but  also  Type  II  errors. 
Instead, a 20/80 policymaker would lower Type II error relatively even more in sample. Things change 
out of sample. Across all weight specifications, there is a relatively large increase in Type I error while 
the  false alarms  rate  tends  to slightly decrease compared to  in-sample performance.  Models under 
20/80 tend to deteriorate comparatively more with respect to Type I error. One reason for this could 
be  the  presence  of  collinearity  among  explanatory  variables.23  A  more  likely  explanation  is  that,  as 
observed in Figure 7 and Table 11, the penalized logit tends to generate more Type I than Type II errors 
out of sample. Under the 20/80 preference specification, a policymaker penalizes missing events much 
less than false alarms, inflating the Type I error rate compared to the 50/50 benchmark. 

23 Two of the candidate indicators in this specification, deficit forecast and primary balance forecast, are indeed very highly 
correlated.  The  resulting  model,  however,  contains  only  one  of  these  indicators,  deficit  forecast.  Nevertheless,  we  re-
estimated the penalized logit using the input set of candidate indicators that excludes primary balance forecast. We find that 
the final model contains the same 9 indicators for which even the estimated coefficients are identical to those in the original 
calculation under these unequal preferences. Consequently, we do not believe collinearity is the issue here. 

34 

 
 
 
                                                           
Table 13: Out-of-sample model performance under various preferences 

Model 

Model A  (benchmark) 

Model B (benchmark) 

Model A (missing/false: 80/20) 

Model B  (missing/false: 80/20) 

Model A  (missing/false: 20/80) 

Model B  (missing/false: 20/80) 

Type I 

37.5% 

37.5% 

33.3% 

33.3% 

66.7% 

66.7% 

Type II 

True positive 

True negative 

1.8% 

1.9% 

1.9% 

2.2% 

0.0% 

0.0% 

62.5% 

62.5% 

66.7% 

66.7% 

33.3% 

33.3% 

98.2% 

98.1% 

98.1% 

97.8% 

100.0% 

100.0% 

Notes: Model A stands for penalized logistic regression with loss-minimizing lambda while model B stands for penalized logistic 
regression with lambda, for which model error is within one standard error of the minimum. 

The performance of the penalized logit model under different preferences can be visually summarized 
using heatmaps as in Figure A8 in the Appendix. The predicted probabilities of market access tensions 
generally  exceed  identified  probability  thresholds  in  quarters  around  identified  LMA  episodes.  The 
models which penalize false alarms relatively more fail to issue signals during the second Portuguese 
LMA episode, while models penalizing failure to signal emit a false alarm for Slovakia. 

Overall,  our  results  show  that  following  signals  from  multivariate  models  with  indicator  selection 
provides a more reliable early warning signal of market access tensions under alternative policymaker’s 
preferences than output from a univariate analysis of the top indicators of LMA. 

9. Robustness checks 

To test the stability of our benchmark results, as well as their sensitivity to different specifications, such 
as definition of the loss of market access episodes and  indicator availability,  we perform a series of 
robustness  exercises  within  the  setting  of  policymaker’s  equal  preferences.  The  first  robustness 
exercise applies a different definition of market access episodes. More specifically, we apply only the 
first  two  conditions  for  identification  of  LMAs  from  Table  1:  ESM/IMF  program  dates  and  episodes 
identified by Guscina et al. (2017).  Second, we exclude forward rate, forward premium and CDS rate 
indicators  from  our set  of  LMA predictors.  The  reasoning behind  this decision  arises  from  concerns 
about self-fulfilling forward market movements that might impact sovereign bond spot markets in the 
future. Furthermore, CDS rates can move the underlying bond spot rates.24 

The results of both sets of robustness exercises are presented in sections B1 and B2 in the Appendix, 
respectively.  When  forward  rate  difference  to  top  performer,  forward  premium  and  CDS  rate  are 
excluded due to potential endogeneity, the  importance of the same primary and  secondary market 
indicators as in our baseline framework is confirmed. However, the set of global demand and supply 
indicators  identified  by  multivariate  approaches  expanded  to  include  economic  policy  uncertainty 
index, banking sector index, government debt and gross financing needs. 

Notably, when we adopt the alternative definition of LMA episodes to exclude those identified by the 
spread level condition (third column of Table 1), the importance of the forward rate difference from 
the best performer, our best single predictor decreases. Under this narrower LMA definition, all models 

24 Fontana and Scheicher (2016), who analyse euro area sovereign bond and CDS markets, observe that while in some countries 
price discovery takes place in the CDS market, in others price discovery is observed in the bond market. 

35 

 
 
                                                           
still report small to moderate increases in market access distress probabilities in late 2011/2012 for 
Italy.25  

Conclusions 

In this paper we study episodes of sovereign loss of market access. We construct a detailed dataset 
with potential indicators of market access tensions, as identified by market experts and the academic 
literature, and evaluate their ability to forecast market access tensions.  

Univariate analysis shows that factors associated with high market access tensions are not limited to 
financial markets, but encompass also developments in global demand, macroeconomic factors and 
the  fiscal  stance.  Forward  rate  difference from  the  best  performer  emerged  as the  most  important 
predictor of market access tensions. The identified informative indicators of market access tensions 
are, however, too numerous to be meaningfully included within a multivariate model that generalizes 
well out of sample. To select which variables should be included in the final model, we apply several 
approaches to resolving model uncertainty; we construct  a market tensions  index (MTI) to use as  a 
single predictor; we sequentially eliminate variables one by one from conventional logit model; and we 
estimate lasso and boosted logit models. Lastly, we run logit models using many combinations of the 
top identified LMA indicators and report the weighted results from the model space. We find that the 
more  complex  methods  outperform  predicted  probabilities  from  simple  logit  with  MTI,  which  are 
generally quite low in the quarters preceding LMA outbreaks. The most complex method, BMA, yields 
the highest probabilities of LMA in the quarters leading to the LMA incidence across countries included 
in our panel. In contrast, BMA also generates more false alarms than the other methods.  

We consider two scenarios when a policymaker is not indifferent between missing an LMA episode and 
issuing a false alarm. In one scenario, a policymaker cares more about missing an LMA event. In the 
other, she is more concerned about issuing false alarms. Regardless of the policymaker’s preference, 
the number and quantity of primary market issuance, forward rates, forward premia, bid-ask spreads, 
the share of foreign investors, US GDP growth, debt to GDP ratio, CDS, GDP forecasts and interest rate 
forecasts are among the top indicators of market access tensions. We further show that a policymaker 
who  cares more about missing an LMA episode would  not be able to provide an  appropriate policy 
response based on univariate signals from individual indicators which flash red over most periods in our 
sample, even in countries that did not experience high market access tensions. Instead, signals from a 
univariate analysis would still be useful and flash red in periods in which countries experienced an LMA 
episode  if  the  policymaker  is  more  concerned  about  issuing  false  alarms.  In  a  multivariate  setting, 
models with indicator selection provide a more reliable early warning signal of market access tensions 
than individual indicators separately under both types of policymaker’s asymmetric preferences. 

Our results point to a trade-off between transparency/communicability and accuracy that policymakers 
face  in  the  search  for  tools  to  evaluate  risks  to  market  access.  While  transparent  and  easy  to 
communicate,  single  indices  of  market  tensions  can  capture  worsening  conditions  in  accessing 
financing from bond markets but do not typically yield satisfactory out-of-sample results. Conversely, 
multivariate models perform better, but are harder to explain in a simple and transparent way.  

25 The spike in the projected probability of tensions in the Italian bond market represents, in a strict sense, a false alarm.  One 
could, however, link this increase in predicted market tensions to another policy reaction, which reportedly aimed at reducing 
tensions in sovereign bond markets, because they were hampering the transmission of monetary policy - Draghi’s “Whatever 
it takes” speech.  

36 

 
                                                           
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Appendix 

Section A 

Figure A1: Median indicator dynamics around start of LMA episodes 

40 

 
 
 
 
 
   
 
Notes: IQR stands for interquartile range; the difference between 75th and 25th percentile of indicator distribution 

41 

 
   
    
 
 
 
 
Figure A2. Indicator dynamics vis-à-vis their respective thresholds: Heatmaps 

42 

 
 
 
43 

 
 
 
44 

 
 
 
Notes: The black vertical line shows year-quarter of the start of identified LMA episodes. 

45 

 
 
 
 
 
 
 
 
 
 
 
Figure A3. Overview of LMA episodes per country and definition 

Notes:  Country  name  abbreviations  are  as  follows:  AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy,  LV=Latvia,  NL=Netherlands, 
PT=Portugal, SI=Slovenia, SK=Slovakia. 

46 

 
 
Figure A4. Decomposition of the smallest MTI 

47 

 
 
 
48 

 
 
 
49 

 
 
 
       Notes: The red vertical line shows year-quarter of the start of identified LMA episodes. 

50 

 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A5. LMA identification from alternative spread level definition (two standard deviations above country-specific historical rolling average) 

Notes:  Country  name  abbreviations  are  as  follows:  AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy,  LV=Latvia,  NL=Netherlands, 
PT=Portugal, SI=Slovenia, SK=Slovakia. 

51 

 
 
Table A1: Identified top indicators under preference weights of 80%/20% for Type I vs. Type II error 

Variable 

Usefulness 

Threshold 

Threshold (percentile) 

AUC 

Type I 

Type II 

Primary market 
No. of issuances 
Syndicated issuance 
Secondary market 
Slope of yield curve 
Forward rate (difference from the best) 
Forward premium 
Bid-ask 5Y 
Bid-ask 10Y volatility 
Bid-ask 5Y volatility 
Foreign debt (inverse) 
Global demand and supply 
CDS 
Government expenditure 
GDP forecast (inverse) 
Debt 
Interest forecast 
Economic policy uncertainty 
US GDP (inverse) 
VIX 
Ratio of loans to bonds 
Bank index (inverse) 

0.116 
0.022 

0.169 
0.139 
0.096 
0.098 
0.028 
0.035 
0.051 

0.025 
0.139 
0.094 
0.061 
0.076 
0.072 
0.072 
0.073 
0.067 
0.019 

-0.064 
-0.506 

0.803 
-0.242 
0.026 
-0.276 
-0.153 
-0.151 
-0.816 

-0.208 
0.172 
0.394 
-0.603 
-0.200 
-0.496 
-0.488 
-0.418 
-0.540 
-0.044 

0.555 
0.432 

0.789 
0.640 
0.462 
0.464 
0.536 
0.596 
0.241 

0.589 
0.650 
0.754 
0.277 
0.352 
0.334 
0.334 
0.334 
0.305 
0.515 

0.819 
0.674 

0.949 
0.916 
0.848 
0.748 
0.738 
0.729 
0.670 

0.797 
0.852 
0.843 
0.788 
0.797 
0.727 
0.679 
0.618 
0.611 
0.680 

0.000 
0.083 

0.000 
0.000 
0.000 
0.000 
0.105 
0.111 
0.000 

0.130 
0.000 
0.083 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.111 

0.418 
0.558 

0.158 
0.305 
0.519 
0.511 
0.440 
0.380 
0.746 

0.354 
0.306 
0.197 
0.695 
0.621 
0.640 
0.640 
0.634 
0.664 
0.460 

             Notes: AUC stands for the area under receiver’s operating characteristics curve (ROC). 

52 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table A2: Identified top indicators under preference weights of 20%/80% for Type I vs. Type II error 

Variable 

Usefulness 

Threshold 

Threshold (percentile) 

AUC 

Type I 

Type II 

Primary market 
Quantity issued 
Bills issuance 
Floating coupon issuance 
Domestic long-term fixed coupon issuance 
(inverse) 
Secondary market 
Slope of yield curve 
Forward rate (difference from the best) 
Forward premium 
Foreign debt 
Bid-ask 5Y (skewness) 
Global demand and supply 
CDS 
GDP forecast (inverse) 
Debt 
Interest forecast 
Gross financing needs 
Debt forecast 
Bailouts 
US GDP 
Deficit forecast 
Primary balance forecast 
German GDP 

0.030 
0.046 
0.013 

0.018 

0.096 
0.084 
0.061 
0.048 
0.001 

0.069 
0.062 
0.029 
0.075 
0.030 
0.034 
0.052 
0.026 
0.052 
0.043 
0.039 

1.903 
1.609 
0.356 

1.387 

1.504 
0.427 
0.487 
1.979 
1.412 

0.618 
0.679 
1.111 
0.400 
1.089 
1.098 
0.106 
1.604 
3.000 
0.952 
1.516 

                Notes: AUC stands for the area under receiver’s operating characteristics curve (ROC). 

0.944 
0.927 
0.871 

0.909 

0.937 
0.832 
0.908 
0.953 
0.912 

0.886 
0.835 
0.850 
0.873 
0.872 
0.940 
0.881 
0.913 
0.904 
0.894 
0.913 

0.725 
0.708 
0.609 

0.552 

0.949 
0.916 
0.838 
0.728 
0.635 

0.797 
0.843 
0.788 
0.781 
0.776 
0.738 
0.610 
0.576 
0.573 
0.559 
0.520 

0.667 
0.542 
0.458 

0.045 
0.058 
0.119 

0.667 

0.061 

0.389 
0.167 
0.421 
0.667 
0.667 

0.478 
0.208 
0.417 
0.333 
0.500 
0.667 
0.417 
0.625 
0.542 
0.542 
0.583 

0.033 
0.103 
0.068 
0.023 
0.082 

0.044 
0.120 
0.109 
0.073 
0.088 
0.041 
0.081 
0.061 
0.050 
0.060 
0.056 

53 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A6. Indicator dynamics vis-à-vis their respective thresholds under unequal preferences: Heatmaps 

54 

 
 
 
55 

 
 
 
56 

 
 
 
57 

 
 
 
58 

 
 
 
59 

 
 
 
Notes: Left: preferences of 80%/20% for Type I vs. Type II errors, Right: preferences of 20%/80% for Type I vs. Type II errors. 

60 

 
 
 
Table A3: Selected Indicators and estimated coefficients – preferences: 80%/20% for Type I/Type II 

Penalized logit (Type I/Type II error weights: 80%/20%) 

Indicator 

Primary market 

No. of issuances 

Syndicated issuance 

Secondary market 

Slope of yield curve 

Forward rate (difference from the best) 

Forward premium 

Bid-ask 5Y 

Bid-ask 10Y volatility 

Bid-ask 5Y volatility 

Foreign debt (inverse) 

Global demand and supply 

CDS 

Government expenditure 

GDP forecast (inverse) 

Debt 

Interest forecast 

Economic policy uncertainty 

US GDP (inverse) 

VIX 

Ratio of loans to bonds 

Bank index (inverse) 

(Intercept) 

Coefficient (lambda min) 

Coefficient (lambda 1SE) 

1.680 

3.971 

0.720 

1.031 

-0.087 

-0.019 

-0.425 

-0.832 

-4.027 

1.420 

3.491 

0.598 

0.807 

-0.181 

-0.707 

-3.829 

61 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table A4: Selected Indicators and estimated coefficients – preferences: 20%/80% for Type I/Type II 

Penalized logit (Type I/Type II error weights: 20%/80%) 

Indicator 

Primary market 

Quantity issued 

Bills issuance 

Floating coupon issuance 

Domestic long-term fixed coupon issuance 
(inverse) 

Secondary market 

Slope of yield curve 

Forward rate (difference from the best) 

Forward premium 

Foreign debt 

Bid-ask 5Y (skewness) 

Global demand and supply 

CDS 

GDP forecast (inverse) 

Debt 

Interest forecast 

Gross financing needs 

Debt forecast 

Bailouts 

US GDP 

Deficit forecast 

Primary balance forecast 

German GDP 

(Intercept) 

Coefficient (lambda min) 

Coefficient (lambda 1SE) 

-0.110 

0.975 

1.798 

4.317 

0.248 

-0.406 

0.001 

0.131 

0.037 

0.251 

0.801 

1.467 

3.607 

0.174 

-0.154 

0.109 

0.029 

0.125 

62 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A7. Predicted probability from penalized logistic regression under different policymaker’s preferences 

Notes: Probability of market access tensions from penalized logistic regression with loss-minimizing lambda under different preferences for Type I and Type II error. The vertical axis measures the 
probability of losing market access within up to 4 quarters. The dash line indicates out-of-sample predicted probabilities of market access tensions. LMA shows periods of identified high market 
access  tensions  while  pre-LMA  identifies  periods  of  up  to  4  quarters  prior  to  LMA.  Country  name  abbreviations  are  as  follows:  AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland, 
FR=France, GR=Greece, IE=Ireland, IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

63 

 
 
Figure A8. Penalized logit probability vis-à-vis model thresholds under different preferences: Heatmaps 

64 

 
 
 
 
65 

 
 
 
66 

 
 
 
 
67 

 
 
 
 
Notes: Lasso logit stands for penalized logistic regression. 

68 

 
 
 
 
 
 
 
 
 
 
 
 
 
Section B1 – Alternative loss of market access episodes definition 

Figure B1.1: Predicted probability from logistic regression using the smallest market tensions index 

Notes: Probability of market access tensions from logistic regression using the smallest market tensions index. The vertical axis 
measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access 
tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample 
forecast  and  the  dashed  line  shows  out-of-sample  forecast  probabilities  of  market  access  tensions.  Country  name 
abbreviations are as follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, 
IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

69 

 
 
Table B1.1: Estimated coefficients from univariate logit with MTI 

Large MTI 

Smaller MTI 

Smallest MTI 

12.91* 
(6.844) 

Univariate logit 

5.323*** 
(1.234) 

Constant 

-13.75** 
(5.677) 
295 
11 
Notes: Standard errors are in parentheses. *** indicate 1%, ** 5% and * 10% significance level. 

-6.405*** 
(1.337) 
328 
13 

Observations 
Number of countries 

5.406*** 
(1.203) 
-7.027*** 
(1.604) 
399 
14 

Figure B1.2: Predicted probability from logistic regression with backward sequential variable 
selection 

Notes: Probability of market access tensions from logistic regression with backward sequential variable selection. The vertical 
axis measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market 
access tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-
of-sample forecast and the dashed line shows out-of-sample forecast probabilities of market access tensions. Country name 
abbreviations are as follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, 
IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

70 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure B1.3: Predicted probability from penalized logistic regression 

Notes: Probability of market access tensions from penalized logistic regression with loss-minimizing lambda (black line) and 
with lambda, for which model error is within one standard error of the minimum (brown line). The vertical axis measures the 
probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access tensions while 
pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample forecast and 
the dash line shows out-of-sample forecast probabilities of market access tensions. Country name abbreviations are as follows: 
AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy,  LV=Latvia, 
NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia.

71 

 
 
Figure B1.4: Predicted probability from boosted logistic regression 

Notes: Probability of market access tensions from boosted logistic regression. The vertical axis measures the probability of 
losing market access within up to 4 quarters. LMA shows periods of identified high market access tensions while pre-LMA 
identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample forecast and the dash 
line  shows  out-of-sample  forecast  probabilities  of  market  access  tensions.  Country  name  abbreviations  are  as  follows: 
AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy,  LV=Latvia, 
NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

72 

 
 
Table B1.1: Selected indicators and their coefficient estimates 

Logit with Sequential Selection 

Penalized Logit 

Indicator 

Coefficient 

95% confidence interval 

Coefficient (lambda min) 

Coefficient (lambda 1SE) 

Coefficient 

Boosted Logit 

95% confidence 
interval 

Primary market 
No. of issuances 
Bills issued 
Floating coupon issuance 
Syndicated issuance 
Secondary market 
Bid-ask 2Y 
Bid-ask 5Y 
Bid-ask 10Y 
Foreign debt 
Forward rate 
Forward premium 
Global demand and 
supply 
CDS 
Interest forecast 
Economic policy 
uncertainty 
US GDP 
V2X 
Stock market 
GDP forecast 
Debt forecast 
Government expenditure 
Debt 
Interest payable 
Bank index 
Gross financing needs 
Bailouts 
Intercept  

- 
- 
- 
-7.03 

- 
-8.03 
17.91 
- 
10.16 
- 

- 
19.36 

- 

- 
- 
- 
-208.63 

- 
-420.01 
-253.66 
- 
-456.25 
- 

- 
- 
- 
194.56 

- 
403.96 
289.48 
- 
476.57 
- 

- 
-1227.14 

- 
1265.85 

- 

- 

- 
0.92 
0.27 
-0.25 

- 
-1.59 
4.30 
- 
2.99 
- 

- 
3.39 

- 

- 
0.30 
- 
-0.51 

- 
-0.17 
1.60 
- 
2.15 
- 

- 
2.77 

- 

- 
- 
- 
-0.18 

- 
- 
0.45 
- 
1.24 
- 

- 
1.36 

- 

- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
-3.03 
Notes: lambda min denotes loss-minimizing lambda and lambda 1 SE indicates lambda, for which model error is within one standard error of the minimum. 

-596.08 
-926.90 
- 
- 
- 
- 
-1029.40 
- 
- 
- 
- 
-563.07 

581.08 
906.66 
- 
- 
- 
- 
1049.92 
- 
- 
- 
- 
539.25 

-7.50 
-10.12 
- 
- 
- 
- 
10.26 
- 
- 
- 
- 
-11.91 

- 
-1.04 
-0.17 
- 
- 
- 
- 
0.06 
-3.25 
- 
- 
-4.71 

- 
- 
-0.13 
- 
- 
- 
- 
0.00 
-2.94 
- 
- 
-4.81 

- 
- 
- 
-0.39 

- 
- 
0.00 
- 
0.10 
- 

- 
0.00 

- 

- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
-3.70 

- 
- 
- 
0.00 

- 
- 
2.16 
- 
1.63 
- 

- 
1.86 

- 

- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
-2.53 

73 

 
  
  
  
  
  
  
  
  
  
 
 
 
  
  
 
 
 
  
  
  
  
  
  
  
  
Figure B1.5: Predicted probability from Bayesian Model Averaging 

Notes:  Probability  of  market  access  tensions  from  Bayesian  Model  Averaging  with  logistic  regressions.  The  vertical  axis 
measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access 
tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample 
forecast and the dash line shows out-of-sample forecast probabilities of market access tensions. Country name abbreviations 
are  as  follows:  AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy, 
LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia.

74 

 
 
Figure B1.6: Top 20 models from Bayesian Model Averaging 

Notes: Top 20 models from Bayesian Model Averaging ranked (top x-axis) by their posterior model probability from the best 
(left) to worst (right). Rows correspond to top indicators while columns represent individual models.  In each model, missing 
variables are in black, while included variables are coloured. The colour corresponds to the log of the posterior probability of 
that model. Posterior probabilities are scaled so that the worst model in the top 20 models is assigned 0. Models with the 
same colours have similar log Bayes factors, i.e. the difference in their Bayes factors is not worth a mention.

75 

 
 
 
Table B1.2. Predicted probabilities in periods of up to 4 quarters 

Logit w/ Market tensions index 

Penalized logit 

Spain 

Greece 

Ireland 

Latvia 

Portugal 

Quarters 
before LMA 
episodes 

-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 

Smaller 
index 

Smallest 
index 

Large 
index 

0.000 
0.000 
0.000 
0.009 
0.653 
0.001 
0.654 
0.970 

0.018 
0.028 
0.048 
0.249 
0.845 
0.089 
0.769 
0.938 
0.811 
0.765 
0.084 
0.146 

0.000 
0.002 
0.013 
0.312 

0.017 
0.104 
0.249 
0.732 

0.011 
0.018 
0.030 
0.171 
0.803 
0.058 
0.671 
0.909 
0.734 
0.673 
0.051 
0.095 
0.003 
0.000 
0.017 
0.063 
0.009 
0.070 
0.197 
0.692 

Logit w/ 
sequential 
selection 
0.664 
0.000 
0.000 
1.000 
1.000 
1.000 
1.000 
1.000 

Optimal 
lambda 

1 SE 
lambda 

Boosted 
logit 

0.119 
0.196 
0.156 
0.499 
0.798 
0.630 
0.462 
0.523 

0.109 
0.111 
0.086 
0.918 
0.970 
0.970 
0.915 
0.887 
0.255 
0.643 
0.095 

0.049 
0.218 
0.183 
0.862 
0.955 
0.883 
0.689 
0.716 
0.194 
0.510 
0.038 

BMA 

0.081 
0.098 
0.110 
0.878 
1.000 
1.000 
1.000 
1.000 

1.000 
1.000 
1.000 
1.000 

0.543 
0.926 
0.999 
1.000 

0.212 
0.706 
0.957 
0.985 

0.145 
0.391 
0.666 
0.817 

1.000 
1.000 
1.000 
1.000 

76 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Section B2 – Excluding forward rate, forward premium and CDS 

Figure B2.1: Predicted probability from logistic regression using the smallest market tensions index 

Notes: Probability of market access tensions from logistic regression using the small alternative market tensions index. The 
vertical axis measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high 
market access tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start 
of  out-of-sample  forecast  and  the  dash  line  shows  out-of-sample  forecast  probabilities  of  market  access  tension.  Country 
name  abbreviations  are  as  follows:  AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece, 
IE=Ireland, IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

77 

 
 
Table B2.1: Estimated coefficients from univariate logit with alternative MTI 

VARIABLES 

Large alternative MTI 

Smallest alternative MTI 

Constant 

Univariate logit 

4.689*** 
(1.036) 

-5.278*** 
(1.183) 

2.519*** 
(0.450) 
-4.277*** 
(0.675) 

Observations 
Number of countries 

339 
12 

419 
14 

Notes: Standard errors are in parentheses. *** indicate 1%, ** 5% and * 10% significance level. 

Figure B2.2: Predicted probability from logistic regression with backward sequential variable 
selection 

Notes: Probability of market access tensions from logistic regression with backward sequential variable selection. The vertical 
axis measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market 
access tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-
of-sample forecast  and the dash  line shows out-of-sample forecast probabilities of market access tensions. Country name 
abbreviations are as follows: AT=Austria, BE=Belgium, DE=Germany, ES=Spain, FI=Finland, FR=France, GR=Greece, IE=Ireland, 
IT=Italy, LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

78 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure B2.3: Predicted probability from penalized logistic regression 

Notes: Probability of market access tensions from penalized logistic regression with loss-minimizing lambda. The vertical axis 
measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access 
tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample 
forecast and the dash line shows out-of-sample forecast probabilities of market access tensions. Country name abbreviations 
are  as  follows:  AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy, 
LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia. 

79 

 
 
Figure B2.4: Predicted probability from boosted logistic regression 

Notes: Probability of market access tensions from boosted logistic regression. The vertical axis measures the probability of 
losing market access within up to 4 quarters. LMA shows periods of identified high market access tensions while pre-LMA 
identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample forecast and the dash 
line  shows  out-of-sample  forecast  probabilities  of  market  access  tensions.  Country  name  abbreviations  are  as  follows: 
AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy,  LV=Latvia, 
NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia

80 

 
 
Table B2.1: Selected indicators and their coefficient estimates 

Logit with Sequential Selection 

Penalized Logit 

Boosted Logit 

Coefficient 

95% confidence interval 

Coefficient (lambda min) 

Coefficient (lambda 1SE) 

Coefficient 

95% confidence interval 

- 
- 
- 
- 

- 
- 
- 
- 
- 
- 

- 
2.08 

- 

- 
- 
- 
- 
- 
- 
- 
- 
0.67 
- 
- 
-2.74 

- 
- 
- 
- 

- 
- 
- 
- 
- 
- 

- 
1.14 

- 

- 
- 
- 
- 
- 
- 
- 
- 
-5.23 
- 
- 
-3.35 

- 
- 
- 
- 

- 
- 
- 
- 
- 
- 

- 
3.02 

- 

- 
- 
- 
- 
- 
- 
- 
- 
6.57 
- 
- 
-2.13 

- 
0.35 
0.70 
- 

- 
0.47 
0.79 
0.59 
- 
- 

- 
1.55 

0.96 

- 
-0.63 
- 
- 
- 
- 
0.22 
0.01 
0.40 
0.03 
- 
-2.58 

- 
- 
- 
- 

- 
- 
- 
- 
- 
- 

- 
- 

- 

- 
- 
- 
- 
- 
- 
- 
- 

- 
- 
-3.09 

- 
0.07 
0.56 
- 

- 
0.37 
0.43 
0.21 
- 
- 

- 
0.91 

0.10 

- 
- 
- 
- 
- 
- 
0.14 
- 
- 
0.05 
- 
-2.35 

- 
0.00 
0.00 
- 

- 
0.00 
0.00 
0.00 
- 
- 

- 
0.00 

0.00 

- 
- 
- 
- 
- 
- 
0.00 
- 
- 
0.00 
- 
-3.77 

- 
0.20 
1.41 
- 

- 
1.13 
2.33 
0.46 
- 
- 

- 
1.70 

0.35 

- 
- 
- 
- 
- 
- 
0.39 
- 
- 
0.27 
- 
-1.88 

Indicator 
Primary market 
No. of issuances 
Bills issued 
Floating coupon issuance 
Syndicated issuance 
Secondary market 
Bid-ask 2Y 
Bid-ask 5Y 
Bid-ask 10Y 
Foreign debt 
Forward rate 
Forward premium 
Global demand and 
supply 
CDS 
Interest forecast 
Economic policy 
uncertainty 
US GDP 
V2X 
Stock market 
GDP forecast 
Debt forecast 
Government expenditure 
Debt 
Interest payable 
Bank index 
Gross financing needs 
Bailouts 
Intercept  

Notes: lambda min denotes loss-minimizing lambda and lambda 1 SE indicates lambda, for which model error is within one standard error of the minimum. 

81 

 
  
 
  
  
  
  
  
  
  
  
 
 
 
  
  
 
 
 
  
  
  
  
  
  
  
  
  
 
Figure B2.5: Predicted probability from Bayesian Model Averaging 

Notes:  Probability  of  market  access  tensions  from  Bayesian  Model  Averaging  with  logistic  regressions.  The  vertical  axis 
measures the probability of losing market access within up to 4 quarters. LMA shows periods of identified high market access 
tensions while pre-LMA identifies periods of up to 4 quarters prior to LMA. The red vertical line indicates start of out-of-sample 
forecast and the dash line shows out-of-sample forecast probabilities of market access tensions. Country name abbreviations 
are  as  follows:  AT=Austria,  BE=Belgium,  DE=Germany,  ES=Spain,  FI=Finland,  FR=France,  GR=Greece,  IE=Ireland,  IT=Italy, 
LV=Latvia, NL=Netherlands, PT=Portugal, SI=Slovenia, SK=Slovakia.

82 

 
 
 
Figure B2.6: Top 20 models from Bayesian Model Averaging 

Notes: Top 20 models from Bayesian Model Averaging ranked (top x-axis) by their posterior model probability from the best 
(left) to worst (right). Rows correspond to top indicators while columns represent individual models.  In each model, missing 
variables are in black, while included variables are coloured. The colour corresponds to the log of the posterior probability of 
that model. Posterior probabilities are scaled so that the worst model in the top 20 models is assigned 0. Models with the 
same colours have similar log Bayes factors, i.e. the difference in their Bayes factors is not worth a mention.

83 

 
 
 
Table B2.2. Predicted probabilities in periods of up to 4 quarters 

Spain 

Greece 

Ireland 

Quarters before 
LMA episodes 

Italy 

Latvia 

Portugal 

Slovenia 

LMA episode 1 

LMA episode 2 

Logit w/ MTI 

Large index 
0.012 
0.013 
0.064 
0.010 
0.503 
0.068 
0.769 
0.896 

0.012 
0.024 
0.135 
0.057 

0.037 
0.053 
0.044 
0.049 
0.004 
0.006 
0.012 
0.020 

Smallest index 
0.040 
0.040 
0.018 
0.022 
0.576 
0.105 
0.751 
0.859 
0.727 
0.718 
0.137 
0.104 
0.038 
0.066 
0.106 
0.114 
0.013 
0.012 
0.140 
0.142 
0.070 
0.087 
0.060 
0.087 
0.012 
0.017 
0.034 
0.050 
0.019 
0.037 
0.041 
0.044 

-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 
-4 
-3 
-2 
-1 

Penalized logit 
Logit w/ sequential selection  Optimal lambda 

0.022 
0.023 
0.019 
0.018 
0.674 
0.668 
0.659 
0.629 

0.019 
0.019 
0.112 
0.110 

0.077 
0.072 
0.071 
0.074 
0.008 
0.030 
0.031 
0.031 

0.181 
0.118 
0.360 
0.111 
0.883 
0.798 
0.511 
0.703 
0.282 
0.345 
0.301 

0.196 
0.185 
0.728 
0.521 

0.081 
0.148 
0.378 
0.376 
0.010 
0.060 
0.425 
0.730 

Boosted logit 
0.096 
0.069 
0.229 
0.072 
0.688 
0.614 
0.408 
0.536 

BMA 
0.619 
0.709 
0.679 
0.674 
0.888 
0.965 
0.931 
0.931 

0.136 
0.134 
0.520 
0.340 

0.604 
0.746 
0.877 
0.955 

0.138 
0.176 
0.217 
0.197 
0.025 
0.049 
0.125 
0.225 

0.422 
0.431 
0.799 
0.701 
0.002 
0.205 
0.981 
0.997 

84 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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