Sovereign Credit Ratings in the

European Union: A

Model-Based Fiscal Analysis

Vito Polito (University of Bath)

Mike Wickens (University of York)

Bratislava, June 1, 2015

Introduction

� Motivation - EU downgrades in 2011; EC 2011 pro-posal; EC 2013 new regulations; EU-based CRA

� Contribution - Black and Scholes model, GBC, modelfor debt forecasts and debt limits

� Findings - earlier downward shift in the credit ratingdistribution, �scal consolidation in the EU

� Outline - historic credit rating, methodology, debtlimit, model-based credit rating

� Previuos work on U.S. and the U.K.

Historic credit rating

Table 1: Rating scales adopted by the three main CRAs.

Moody�s Fitch S&P Credit quality

Investment Aaa AAA AAA Prime

grade (I.G.) Aa1 AA+ AA+ High

Aa2 AA AA grade... ... ...

Baa3 BBB- BBB-

Speculative Ba1 BB+ BB+

grade (S.G.) Ba2 BB BB Speculative

Ba3 BB- BB-... ... ...

Ca CC CCC for recovery

C C

DDD, DD, D D In default

Source: Authors�classi�cation based on Gaillard (2012)

Facts about historic credit ratings of EU countries

1. The sovereign credit ratings of the EU14 countriestaken as a group has been higher than those of othercountries.

2. The cross-section distribution of the EU14 countriessovereign credit ratings has been stable within theinvestment grade at least until 2010.

3. Sharp changes in this distribution have occurred, par-ticularly since 2010.

4. Fluctuations in EU14 sovereign credit ratings haveincreased as the ratings have fallen.

5. Changes in the sovereign credit ratings of several EU14 countries appear to be unrelated to the market�sperception of the probability of sovereign default.

Table 2: Distribution of historic sovereign credit ratingsof EU14 countries at selected dates.

90 95 00 05 06-08 09 10 11 12

Aaa 50% 36% 57% 71% 71% 64% 57% 57% 50%

Aa 36% 43% 36% 21% 21% 29% 21% 7% 14%

A 7% 14% 7% 7% 7% 7% 7% 14% 7%

Baa 7% 7% 0% 0% 0% 0% 7% 0 7%

Ba 0% 0% 0% 0% 0% 0% 7% 14% 14%

B 0% 0% 0% 0% 0% 0% 0% 0 0%

C 0% 0% 0% 0% 0% 0% 0% 7% 7%

Share of investment grade (in percentage)

EU14 100 100 100 100 100 100 93 79 79

ARC 86 78 59 63 n.a. n.a. 61 n.a. 60

Notes: ARC=All Rated Countries in a speci�c year; n.a.=not available.

Source: Moody�s (2012)

1990 95 00 05 10 12:4C

CaaB2

Ba3Ba1

Baa2A3A1

Aa2Aaa

Rat

ing

AUS, GER, NET , UK

1990 95 00 05 10 12:4C

CaaB2

Ba3Ba1

Baa2A3A1

Aa2Aaa

Rat

ing

DEN FIN FRA

1990 95 00 05 10 12:4C

CaaB2

Ba3Ba1

Baa2A3A1

Aa2Aaa

Rat

ing

BEL IT A SWE

1990 95 00 05 10 12:4C

CaaB2

Ba3Ba1

Baa2A3A1

Aa2Aaa

Rat

ing

GRE IRE POR SPA

Historic sovereign credit rating of EU14 countries,1990-2012.

08 09 10 11 12 130

160AU S

08 09 10 11 12 130

350BEL

08 09 10 11 12 130

150D EN

08 09 10 11 12 130

100F IN

08 09 10 11 12 130

180F R A

08 09 10 11 12 130

100GER

08 09 10 11 12 130

15000GR E

08 09 10 11 12 130

1200IR E

08 09 10 11 12 130

500ITA

08 09 10 11 12 130

140N ET

08 09 10 11 12 130

1600POR

08 09 10 11 12 130

500SPA

08 09 10 11 12 130

160SW E

08 09 10 11 12 130

180U K

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

08 09 10 11 12 13C

Baa3

Aaa

C D SR ating

Sovereign credit ratings and 5-year credit default swapprices for EU14 countries, 14/12/2007 - 22/03/2013.

Methodology

� Adapt to GBC Black�Scholes (1973) formula for prob-ability of exercising a European-style call option.

� This gives sovereign default probabilities at di¤erenttime horizons.

� Use CRAs tables to convert into credit rating.

� Debt limit: State-dependent measures from a DSGEmodel of the economy. Time series of the maximumborrowing capacity of an economy.

� (1) Default probability, (2) mapping credit rating,(3) debt-GDP forecasts and volatility; (4) debt limit.

Methodology (Default probability)

bt+hyt+h

= �hXj=1

"�js=1

�1 + �t+s

� dt+jyt+j

#+�hs=1

�1 + �t+s

� btyt

default threshold (debt limit):bt+hyt+h

pt;t+h = pt+h�1� pt+h�1

� �1� pt+h�2

�::: (1� pt+1)

pt+h = Pr

bt+hyt+h

� bt+hyt+h

j�t!

distance-to-default: DDt+h =Etbt+hyt+h

� bt+hyt+h

��;t+h

Methodology (Credit rating)

Rating Cumulative default probabilityLong-term 1-year 5-year 10-year averageAaa 0.000 0.000 0.000 0.000Aa1 0.008 0.215 0.715 0.265Aa2 0.015 0.430 1.429 0.529Aa3 0.023 0.646 2.144 0.794A1 0.030 0.861 2.858 1.058A2 0.038 1.076 3.573 1.323... ... ... ... ...B3 2.724 11.158 18.541 10.887Caa 11.142 21.083 26.005 19.711Ca 19.561 31.008 33.469 28.534C 27.979 40.933 40.933 37.358

Source: www.moodys.com; and authors�calcs

Table 3: Mapping from cumulative default probabilitiesto sovereign credit rating.

Debt limit

� Ad hoc?

� agnostic (ability/willingness)

� Reinhart, Rogo¤ and Savastano (2003): likely tovary from country to country, as well as over time

� From a structural model of the economy

� Open economy RBC with distortionary taxationon income from capital, labor and consumption

� Similar to Trabandt and Uhlig (2011)

� Financial ability only

� Anticipated or unanticipated �scal policy

Debt limit (model)

� Preferences

U0 = E0

1Xt=0

�tu (ct; 1� nt)

� Households budget constraint

(1� �nt )wtnt +�rkt � �

� �1� �kt

�kt�1

+kt�1 + [1 + (1� �t) rt � �t] bDt�1+zt + (1 + r

�t ) stft�1

= (1 + �ct)ct + kt + bDt + stft

� Consumption

ct =

"��cHt�1�1� + (1� �) �cFt �1�1�

# 1

1�1�

� Production

yt = k�t (Atnt)

1��

� Government budget constraint

gt + (1� �t) rtbt�1 + (1� �t) bt�1 + zt= �ctct + �

nt wtnt + �

kt

�rkt � �

�kt�1 + bt

� BoP

stft�bFt = xt+(1 + r�t ) stft�1�[1+(1� �t) rt��t]bFt�1

� Economy constraint

yt = ct + gt + kt � (1� �) kt�1 + xt

Debt limit (model)

Stationary equilibrium solution

b

y

IGBCL

=1

r

8>><>>:�c�

�1'k � 1

�+ �n (1� �)+

�k�

"1� �

���1�11��k + �

��1#� gy �

zy

9>>=>>;b

y

NDL

=1

r

8>><>>:�c�

�1'k � 1

�+ �n (1� �)+

�k�

"1� �

���1�11��k + �

��1#9>>=>>;

b

y

FL

=1

r

8>><>>:�c�

�1'k � 1

�+ �n;max (1� �)+

�k;max�

"1� �

���1�11��k;max + �

��1#� (g+z)

y

9>>=>>;b

y

MDL

=1

r

8>><>>:�c�

�1'k � 1

�+ �n;max (1� �)+

�k;max�

"1� �

���1�11��k;max + �

��1#9>>=>>;

r =r� + �1� �

� Related literature: Davig, Leeper and Walker (2010);Trabandt and Uhlig (2011)

Debt limit (model)

� Perturbation/projection method?

� Monte Carlo Markov Chain algorithm

� Based on the simulation method for solving ra-tional expectations models

� Judd (1998), Coleman�s (1991)

� Bi (2011) for FL in industrialized countries

� Feed in time-varying mean and volatility of (i) the ra-tio of government expenditures to GDP, (ii) the ratioof transfers to GDP, (iii) the shocks to technologicalprogress and (iv) the actual tax rates

� Country-speci�c �

9 5 0 0 0 5 0 8 1 2

2 0

4 0

A US

9 5 0 0 0 5 0 8 1 2

2 0

4 0

B E L

9 5 0 0 0 5 0 8 1 2

2 0

4 0

DE N

9 5 0 0 0 5 0 8 1 2

2 0

4 0

FIN

9 5 0 0 0 5 0 8 1 2

2 0

4 0

FRA

9 5 0 0 0 5 0 8 1 2

2 0

4 0

G E R

9 5 0 0 0 5 0 8 1 2

2 0

4 0

G RE

9 5 0 0 0 5 0 8 1 2

2 0

4 0

IRE

9 5 0 0 0 5 0 8 1 2

2 0

4 0

IT A

9 5 0 0 0 5 0 8 1 2

2 0

4 0

NE T

9 5 0 0 0 5 0 8 1 2

2 0

4 0

P O R

9 5 0 0 0 5 0 8 1 2

2 0

4 0

S P A

9 5 0 0 0 5 0 8 1 2

2 0

4 0

S W E

9 5 0 0 0 5 0 8 1 2

2 0

4 0

UK .

E X P

T RA

M A X RE V

A CT RE V

Components of the theory-based debt limits for EU14countries, 1995:4-2012:4. All variables are as a

proportion to GDP.

95 00 05 08 120

5AU S

95 00 05 08 120

5BEL

95 00 05 08 120

5D EN

95 00 05 08 120

5F IN

95 00 05 08 120

5F R A

95 00 05 08 120

5GER

95 00 05 08 120

5GR E

95 00 05 08 120

5IR E

95 00 05 08 120

5ITA

95 00 05 08 120

5N ET

95 00 05 08 120

5PO R

95 00 05 08 120

5SPA

95 00 05 08 120

5SW E

95 00 05 08 120

5U K.

IGBC LF LD ebt ­GD P

IGBCL, FL and debt-GDP ratio in EU14 countries,1995:4 - 2012:4.

­1 0 1 2 3 4 50

5

1 0

A U S

­1 0 1 2 3 4 50

5

1 0

B E L

­1 0 1 2 3 4 50

5

1 0

D E N

­1 0 1 2 3 4 50

5

1 0

F I N

­1 0 1 2 3 4 50

5

1 0

F R A

­1 0 1 2 3 4 50

5

1 0

G E R

­1 0 1 2 3 4 50

5

1 0

G R E

­1 0 1 2 3 4 50

5

1 0

I R E

­1 0 1 2 3 4 50

5

1 0

I T A

­1 0 1 2 3 4 50

5

1 0

N E T

­1 0 1 2 3 4 50

5

1 0

P O R

­1 0 1 2 3 4 50

5

1 0

S P A

­1 0 1 2 3 4 50

5

1 0

S W E

­1 0 1 2 3 4 50

5

1 0

U K .

a v e ra g e   2 0 0 1 ­2 0 0 72 0 1 0 2 0 1 2

State-dependent probability density function of the FLof EU14 countries at selected dates.

Methodology (debt-GDP forecasts and volatility)

� Reduced-form VAR model

� Time-varying parameters

� Rolling-window estimation

Methodology (debt-GDP forecasts and volatility)

Symbol Description AcronymsCountry-speci�c variables

btyt

Debt-GDP ratio DEBTdtyt

Primary de�cit-GDP ratio DEF t Growth rate real GDP GDP�t In�ation rate INFrst Short-term interest rate IRSrlt Long-term interest rate IRLet Real exchange rate depreciation EXCxtyt

Current account-GDP CAC�ot Oil in�ation rate OIL

Table 4: Variables included in the ROVAR model

� Data: 1975:2 to 2012:4; from 1977:2 for Portugal

� Countries: AUS, BEL, DEN, FIN, FRA, GER, GRE,IRE, ITA, NET, POR, SPA, SWE, UK

9 5 0 0 0 5 1 0 1 20

0 . 1

0 . 2

0 . 3

0 . 4A U S

9 5 0 0 0 5 1 0 1 26 0

7 0

8 0

9 0

1 0 0

9 5 0 0 0 5 1 0 1 20

0 . 5

1B E L

9 5 0 0 0 5 1 0 1 25 0

1 0 0

1 5 0

9 5 0 0 0 5 1 0 1 20

0 . 20 . 40 . 60 . 8

1D E N

9 5 0 0 0 5 1 0 1 202 04 06 08 01 0 0

9 5 0 0 0 5 1 0 1 20

0 . 5

1F I N

9 5 0 0 0 5 1 0 1 24 0

6 0

8 0

9 5 0 0 0 5 1 0 1 20

0 . 2

0 . 4F R A

9 5 0 0 0 5 1 0 1 25 0

1 0 0

1 5 0

9 5 0 0 0 5 1 0 1 20

0 . 10 . 2

0 . 30 . 40 . 5

G E R

9 5 0 0 0 5 1 0 1 25 06 07 0

8 09 01 0 0

9 5 0 0 0 5 1 0 1 20

0 . 5

1G R E

9 5 0 0 0 5 1 0 1 20

1 0 0

2 0 0

9 5 0 0 0 5 1 0 1 20

0 . 5

1

1 . 5

2I R E

9 5 0 0 0 5 1 0 1 20

5 0

1 0 0

1 5 0

2 0 0

9 5 0 0 0 5 1 0 1 20

0 . 5

1I TA

9 5 0 0 0 5 1 0 1 21 0 0

1 2 0

1 4 0

9 5 0 0 0 5 1 0 1 20

0 . 20 . 40 . 60 . 8

1N E T

9 5 0 0 0 5 1 0 1 25 06 07 08 09 01 0 0

9 5 0 0 0 5 1 0 1 20

0 . 5

1P O R

9 5 0 0 0 5 1 0 1 25 0

1 0 0

1 5 0

9 5 0 0 0 5 1 0 1 20

0 . 20 . 40 . 60 . 8

1S P A

9 5 0 0 0 5 1 0 1 202 04 06 08 01 0 0

9 5 0 0 0 5 1 0 1 20

0 . 20 . 40 . 60 . 8

1S W E

9 5 0 0 0 5 1 0 1 202 04 06 08 01 0 0

9 5 0 0 0 5 1 0 1 20

0 . 5

1U K .

9 5 0 0 0 5 1 0 1 20

1 0 0

2 0 0

S t .   d e v .   1 ­q u a rt e r   a h e a d   f o re c a s t   e rro r

A c t u a l  d a t a

Debt-GDP ratio in EU14 countries, 1995:1-2012:4:actual observation (solid line) and standard deviation of1-period ahead forecast error (dotted line) from ROVAR

model.

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

A U S

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

B E L

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

D E N

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

F IN

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

F R A

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

G E R

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

G R E

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

IR E

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

IT A

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

N E T

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

P O R

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

S P A

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

S W E

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

U K .

IG B C L

F L

M D L

h i s to r i c

Model-based (5-year horizon) and historic credit ratingsin EU14 countries, 1995:4-2012:4.

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

A U S

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

B E L

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

D E N

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

F I N

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

F R A

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

G E R

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

G R E

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

I R E

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

I T A

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

N E T

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

P O R

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

S P A

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

S W E

9 5 0 0 0 5 0 8 1 2C

B a a 3

A a a

U K .

m o d e l

h i s t o r i c

Model-based (5-year ahead) and historic credit ratingsfor EU14 countries, 1995:4 - 2012:4. Debt limit rangesfrom IGBCL to FL. Dotted lines denote con�dence

bands.

0 8 0 9 1 0 1 1 1 2 1 30

1 6 0

A U S

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

3 5 0

B E L

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 5 0

D E N

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 0 0

F I N

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 8 0

F R A

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 0 0

G E R

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 5 0 0 0

G R E

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 2 0 0

I R E

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

5 0 0

I T A

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 4 0

N E T

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 6 0 0

P O R

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

5 0 0

S P A

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 6 0

S W E

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

0 8 0 9 1 0 1 1 1 2 1 30

1 8 0

U K

0 8 0 9 1 0 1 1 1 2 1 3C

B a a 3

A a a

C D S

C r e d i t   r a t i n g   ( H i s t o r i c )

C r e d i t   r a t i n g   ( M o d e l )

Sovereign credit ratings (historic and model-based) and5-year credit default swap prices of EU14 countries,

14/12/2007 - 22/03/2013.

Table 5: Model-based and historic sovereign credit ratingof EU14 countries, summary statistics.

Average credit rating

Model Historic

1995-2012 2008-2012 1995-2012 2008-2012

AUS Aaa Aaa Aaa Aaa

BEL Aaa Aaa Aa1 Aa1

DEN Aaa Aaa Aaa Aaa

FIN Aaa Aaa Aaa Aaa

FRA Aaa Aaa Aaa Aaa

GER Aaa Aaa Aaa Aaa

GRE C C Baa1 Ba1

IRE Aa1 Aa2 Aa1 A1

ITA Ba2 Ba3 Aa3 Aa3

NET Aaa Aaa Aaa Aaa

POR Aa3 Baa2 Aa3 A3

SPA A1 Aa2 Aa1 Aa2

SWE Aaa Aaa Aa1 Aaa

UK Aa1 Aa3 Aaa Aaa

Credit rating changes

Model Historic

1995-2012 2008-2012 1995-2012 2008-2012

Total 168 98 40 24

Downgrades 82 61 24 24

Notes: Authors�calculations based on data in Figure 12.

Table 6: Distribution of the model-based sovereign creditrating of EU14 countries at selected dates based on themedian value rating when the debt limit ranges betweenFL and IGBCL.

00 05 06 07 08 09 10 11 2012

Aaa 79% 86% 86% 79% 50% 64% 50% 50% 50%

Aa 7% 0% 0% 14% 36% 7% 21% 21% 14%

A 0% 0% 0% 0% 0% 7% 7% 7% 14%

Baa 7% 7% 7% 0% 0% 0% 0% 0% 0%

Ba 0% 0% 0% 0% 7% 14% 7% 7% 7%

B 0% 0% 0% 0% 0% 0% 7% 0% 7%

C 7% 7% 7% 7% 7% 7% 7% 14% 7%

IG 93% 93% 93% 93% 86% 79% 79% 79% 79%

Notes: IG=Investment grade. Source: Authors�calculations.