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Sovereign Debt Maturity and Debt-to-GDP Dynamics in Six Euro Area Countries

Juan Equiza ECARES, SBS-EM, Université Libre de Bruxelles

ECARES working paper 2014-44

Sovereign debt maturity and debt-to-GDP dynamicsin six Euro area countries∗

Juan Equiza†

October 22, 2014

Abstract

At a time when debt-to-GDP ratios are closely monitored in the Euro area, thispaper generates a set of stylized facts about sovereign debt and yields. First, Ipresent a new dataset on outstanding debt securities and yields for six EA countries(Belgium, Finland, France, Germany, Italy and Spain) from 1991 to 2013 that Ibuilt combining different sources. Thus, I can document, for example, that EAdebt duration increased by 2 years, mainly driven by demand. Second, based onthe government budget constraint, I calculate past contributions of returns on debtwith different maturities, inflation and other factors to EA debt-to-GDP changes andcompare them with the US experience. While primary deficits played an importantrole in the latter, returns on debt is the key factor in EA countries, especially whenlarge capital gains were paid to long-term bondholders before the introduction of theEuro. Also, although GDP growth contributions were similar, the EA relied moreon inflation and the US on real output growth. Finally, I estimate that 1% futurepermanently higher inflation would reduce EA debt ratios by 4%, an effect 2.4 timeshigher than the expected change in the US.JEL codes: E23, E31, E43, G12, H63

∗I am grateful to my adviser Robert Kollmann and to participants at the Belgian MacroeconomicsWorkshop 2014†ECARES, Université Libre de Bruxelles (ULB), B-1050 Brussels, Belgium. E-mail: jequizag at

ulb.ac.be

1

1 Introduction

The financial crisis increased substantially debt-to-GDP ratios in the Euro area, raisingdoubts about the sustainability of some countries’ debt and the survival of the currencyunion as a whole. Consequently, there is a renewed interest in understanding debt-to-GDP dynamics and in finding stabilizing policies. Theory has pointed at debt maturitymanagement as a key tool: first, because it determines the extent to which the real value ofdebt can be inflated away –e.g. Lustig et al. (2008) or Faraglia et al. (2013)– and, second,because bond prices can absorb adverse fiscal shocks and facilitate tax smoothing; e.g.Lucas and Stokey (1983) or Buera and Nicolini (2004).

This paper studies the role of debt maturity in debt/GDP dynamics empirically, generat-ing a set of stylized facts on sovereign debt and yield dynamics for the EA. In particular,its contribution is threefold: (i) it documents a new dataset that I constructed on out-standing debt securities and yields for six Euro area countries (Belgium, Finland, France,Germany, Italy and Spain) from 1991-2013; (ii) based on the government budget con-straint, it studies past contributions of returns on debt with different maturities, inflationand other factors to debt/GDP changes; and (iii) this paper provides estimates of theimpact of higher future inflation on EA debt ratios. Finally, these facts are comparedwith those resulting from the US experience during the same timespan.

Two findings are worth stressing when comparing US and EA debt-to-GDP dynamics.First, primary deficits played a significant role in the US but not in the EA. Instead,debt returns in the EA were the main factor pushing up debt ratios. In particular,the interest rate convergence process caused by the monetary union project brought thehighest returns on EA debt of the sample period, with substantial capital gains for long-term bondholders. In the US, however, more costly short-term debt represented 18% ofdebt returns, six times more than in the EA. Second, although the EA had lower GDPgrowth than the US, it also had higher debt-to-GDP ratios to erode during most of thesample period. As a result, the contribution of the denominator to debt-to-GDP changeswas similar in both economies. Average inflation was close to 2% in both regions, so thedifference in GDP growth responded to relatively higher US output growth.

Other stylized facts distilled in the comparison are: (i) the economically relevant valueof debt is its face value which has been around 95% of its market value in both regions;(ii) US average debt maturity has fluctuated between 4.5 and 6 years, while in the EA itincreased from 4.5 to 6.5 years; (iii) since the Euro started, debt maturity has been mainlydriven by demand, but before supply played an important role in Italy and Belgium; (iv)real returns on debt averaged 3% in the US, while 3.3% in the EA; and (v) 1% permanentlyhigher future inflation would reduce EA debt ratios by 4%, 2.4 times more than in the US.

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This quantitative exercise is particularly relevant given the ongoing debate on increasingthe inflation target for monetary policy and the currently low inflation forecasts.

Since my dataset contains information about outstanding debt for each of the countriesstudied, cross-country differences of debt dynamics are also discussed in the paper. In-creasing primary deficits in France is revealed as the main factor differentiating Frenchfrom German debt dynamics, while there are minor differences regarding other determi-nants. Yields for Italy and Spain decreased remarkably in 1995-1999 as steps towardsthe establishment of the monetary union were taken. I document that this fall in yieldswas deeper than the one observed in the US after Volcker’s intervention in the early 80’s.While Italy paid high returns to bondholders as a result of previous efforts to increasedebt maturity, Spain lengthened its debt maturity after yields in the EA had alreadyconverged, avoiding in this way the payment of substantial capital gains. Simulations ofSpanish debt having longer maturity in 1994 show that –all other things equal– Spanishdebt/GDP in 1999 would have been almost 5% higher. Finally, it is worth stressing thatBelgium is the country that would benefit most from higher inflation, with a 6% reductionof its debt ratio. The reason behind this large estimate is that Belgium’s debt has thehighest duration (6.1 years) among all countries studied and one of the larger ratios thatcan possibly be inflated away (104%) as it has not issued inflation-indexed bonds.

Currently, Finland is known in the EA for its low debt ratio and recent increase indebt maturity. With the financial conditions currently faced by EA countries, wheneven long-term yields for Italy and Spain are close to their historical minimum, my worksuggests that all EA countries would benefit from increasing their debt maturity. Veryprobable higher yields for EA countries in the coming years will imply more negativereturns the longer their sovereign debt maturity (similarly to the way in which longermaturity brought higher positive debt returns when yields fell strongly in the 90’s).

This paper contributes to recent studies of the debt-to-GDP dynamics and is especiallyrelevant for ongoing research on debt maturity management. There are many theoreticalcontributions in this literature but little empirical work: e.g. Faraglia et al. (2008), Halland Sargent (2011) and Berndt et al. (2012). This paper documents valuable new data onEuro area sovereign debt securities that allows to empirically test the policy recommen-dations from theoretical models on optimal debt management. Moreover, my estimates ofdebt returns are motivated by the government budget constraint, thus capturing capitalgains and losses. Therefore, they are conceptually and quantitatively different from theinterest expenditures officially reported that include payment obligations on an accrualbasis. By quantifying the cost of funds –cfr. Hall et al. (1997)– and market value ofdebt with different maturities, this paper contributes to bringing closer theory to practiceby building a more theory-based accounting framework, as stressed by Hall and Sargent(2011) or Missale (2012).

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2 Review of related literature

Sharp debt surges in advanced economies following the financial crisis have motivatedseveral empirical studies of debt dynamics. Abbas et al. (2011) use a new databasecovering nearly all IMF members and an exceptionally long timespan to document thatdebt and growth are negatively correlated. Abbas et al. (2013) look at 30 advancedeconomies in 1980-2011 and finds debt-to-GDP reductions to be associated with primarysurpluses and strong growth. This confirms the previous finding of Giannitsarou andScott (2008) that since 1960 more than 80% of the efforts enhancing fiscal sustainabilitywere done through primary surpluses in industrialized countries.

Reinhart and Sbrancia (2011) study a sample of 12 countries (including Belgium, France,Italy and the US) and finds that inflation and financial repression1 implied annual sav-ings on average interest expenses ranging between 1 and 5% of GDP during 1945-1980.Aizenman and Marion (2011) document a large erosion of the US Federal debt-to-GDPratio caused by inflation in the aftermath of WWII and facilitated by a long maturitystructure. Hall and Sargent (2011) confirm the role played by inflation during these yearsbut clarify that, nonetheless, in 1945-2009 debtholders were paid on average positive re-turns. They also point at real output growth as the main factor holding down the USdebt-to-GDP ratio. Hilscher et al. (2014) assess the effect of changes in the probabilitydistribution of US inflation on this country’s debt ratio using detailed information aboutmaturity structure and claimholders. Their estimate for the impact of 1% permanentlyhigher future inflation is a 1.75% reduction in the debt ratio, much lower than previousestimates.

My work compares debt-to-GDP dynamics in the EA with the US and uses debt values andestimates of returns conceptually equivalent to those of the government budget constraint,as in Hall and Sargent (2011). These authors describe the discrepancies between thecost of funds derived from the government budget constraint and the interests paymentsreported by the US government. They point at capital gains and losses on debt withmaturity longer than one year as responsible of the higher volatility characterizing theirestimates of returns. Similarly, interest on EA sovereign debt recorded according to theESA95 accounting rules –recently replaced by the ESA2010 guidelines– also leaves outcapital gains and losses2. However, the latter are key to assess the role played by debtmaturity in debt-to-GDP dynamics: the main focus of this paper.

There is a vast literature on optimal management of debt maturity. The seminal work ofLucas and Stokey (1983) showed that, under complete markets, government debt man-

1They define financial repression as interest rate ceilings, large scale official intervention and otherpolicies dampening nominal interest rates.

2The interest series defined in the ESA95 accounting rules are accessible in Eurostat and AMECO.

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agement could increase welfare by minimising the costs of distortionary taxation. Later,Angeletos (2002) and Buera and Nicolini (2004) –among others– extended this analysisto incomplete markets. Their results hinge on the ability of debt management to reducefinancing needs when facing adverse fiscal shocks (known as fiscal insurance). More re-cently, Lustig et al. (2008) and Faraglia et al. (2013) present models with sticky pricesand incomplete markets in which longer maturity contributes optimally to the liquidationof a significant amount of debt through higher inflation.

In contrast, there are few papers describing empirically the maturity of sovereign debtand its effect in the evolution of debt-to-GDP ratios. In early work by Missale andBlanchard (1994), the search of credibility explains the inverse relation of debt ratiosand debt maturity for Italy, Belgium and Ireland in 1960-1990. Importantly, in theirpaper shorter maturities signal the commitment of not using inflation to reduce debt.Recently, Faraglia et al. (2008) study 11 OECD countries in 1970-2000 and find almostno connection between the degree of fiscal insurance and cross-country variations in debtissuance patters. Berndt et al. (2012) use estimates of holding returns rates of US Treasurybonds like the ones calculated in my paper. Regressing news on defence spending growthinto innovations in returns and surplus growth, they find that 9 % of the spending shockis absorbed through the debt valuation channel. They also document that long-term debtis more effective in absorbing fiscal shocks than short-term debt.

The analysis in this paper follows closely the approach of Hall and Sargent (2011)3 andHilscher et al. (2014). Both studies are based on detailed information on all outstandingbond liabilities (principal and stripped coupons) for the US Federal government from theCenter for Research in Security Prices (CRSP) Monthly US Treasury Database. Usingestimates of zero-coupon yield curves, they calculate the market value of all payment obli-gations and –in the case of the former– also returns on debt with different maturities. Mywork updates their analysis for the US to 2013, describes a new dataset that I constructedfor six Euro area countries in 1991-2013 with similar characteristics to the CRSP data onUS Treasury securities, and generates stylized facts on sovereign debt and yield dynamicsin the EA. Thus, my paper complements previous work on the composition of sovereigndebt in the EA as in Lojsch et al. (2011). More recently, Abbas et al. (2014) examines13 advanced economies from 1900 to 2011 and document that short-term debt was usedintensively in debt build-ups, except in the 80’s and 90’s were demand facilitated usingdebt with longer maturity.

3Das (2011) compares debt/GDP dynamics of the US and the United Kingdom in 1984-2011.

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3 Basic framework

As in Hall and Sargent (2011), my work exploits the law of motion of debt described inthe budget constraint of the government for any period t. If a government issues debtthat matures in j = 1, 2, ..., J periods (years), the period t budget constraint takes theform:

J∑j=1

pj−1t Qjt−1 = St +

J∑j=1

pjtQjt (1)

where St is the primary surplus of year t, Qjt is the nominal value of outstanding net

debt obligations at the end of that year maturing after j periods, and pjt is the price intime t euros of an asset that delivers 1 euro in year t + j (typically, called IOUs) wherepjt =

(1 + yt(j)

)−j and yt(j) is the yield at time t for zero-coupon bonds with maturity j .

Debt securities that pay coupons can be easily included in the model by unbundlingprincipal and coupons into separate payment obligations. Also, the rate of return paid tobondholders each period can be calculated as rjt−1,t = (pj−1t −pjt−1)/p

jt−1, so that, Equation

1 can be rewritten as

J∑j=1

pjt−1Qjt−1 +

J∑j=1

rjt−1,tpjt−1Q

jt−1 = St +

J∑j=1

pjtQjt (2)

Applying the usual no-Ponzi game condition, the present-value budget constraint is

J∑j=1

pj−1t Qjt−1 = St +

∞∑j=1

Et[mt(j)St+j] = St +∞∑j=1

pjtEtSt+j +∞∑j=1

covt(mt(j), St+j

)(3)

wheremt(j) = βju′(Ct+j)/u′(Ct) and Et[mt(j)] = pjt , and I use the fact that Et[mt(n)]pjt+n

is equal to Et[mt(n+ 1)]pj−1t+n+1. Because a longer maturity amplifies the effect of interestrate changes, an increase (decrease) in the yield curve implies –approximately– a biggerdecrease (increase) in the present value of future primary surpluses (right-hand side)than for the stock of liabilities (left-hand side). However the longer the maturity of thegovernment’s debt, the lower is the necessary increase (decrease) in current and futuresurplus. This effect has the benefit of stabilizing the excess burden of taxation and thelevel of debt.

Missale (2012) stresses the role played by a long debt maturity in the presence of riskof default. Think of p̃jt =

(1 + yt(j) + ρ

)−j< pjt as the price of a security that pays

one euro after j periods but might be cancelled with probability ρ in each period untilmaturity. The presence of this default risk implies that Et[mt(n)]p̃jt+n is then smaller thanEt[mt(n+ 1)]p̃j−1t+n+1 and, thus, it appears the last term in Equation 4. Intuitively, current

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and expected future surpluses have to compensate the payment of higher future returnson rolled-over debt. However, this is partially accommodated by a decrease of the currentvalue of debt. Because the unconditional probability of a default occurring at any futuredate increases with the horizon considered, the risk premium is higher (and the price ofa bond lower) the longer its maturity. Thus, the longer the maturity of debt, the smallerthe necessary adjustment on surpluses.

J∑j=1

p̃j−1t Qjt−1 = St+

∞∑j=1

Et[mt(j)St+j]−∞∑s=1

Etmt(s)

[ ∞∑j=1

(mt+s(1)p̃j−1t+s+1− p̃

jt+s

)Qj

t+s

](4)

Finally, simple arithmetic allows a comparison of the contribution of nominal returns ondebt with different maturities with other important factors: inflation, real GDP growthand primary deficits. Since my database contains outstanding quantities of gross debt,a residual term is included, reflecting mainly returns received from assets and changes intheir stock. Therefore, dividing Equation 2 by nominal output Yt and redefining Qj

t asthe nominal value of outstanding gross debt obligations at the end of year t that maturein j periods, I obtain changes in the (gross) debt/GDP ratio to be

J∑j=1

pjtQjt

Yt−

J∑j=1

pjt−1Qjt−1

Yt−1=

J∑j=1

(rjt−1,t − πt−1,t − gt−1,t)pjt−1Q

jt−1

Yt−1− St

Yt+SFAt

Yt(5)

where πt−1,t, gt−1,t are the inflation4 and real output growth rates. I label SFAt theresiduals that I obtain. These are similar to the stock-flow adjustment terms used insimilar decompositions –cfr. Campos et al. (2006) or Eurostat (2013)– which reflectmainly the acquisition of assets.

4 Data and methodology

Estimates of contributions to debt-to-GDP changes based on the accounting identity pre-sented in Section 3 require a complete description of the outstanding stocks of sovereigndebt as well as its characteristics, namely maturity dates and promised coupons. In thecase of the US, this information is available at the Center for Research in Security Prices(CRSP) Monthly US Treasury Database on a security-by-security basis. Following Halland Sargent (2011), I also use data from the Treasury Bulletin on non-marketable debtand inflation protected securities, called TIPs. Although CRSP provides the evolution ofsecurities’ prices, I use estimates of the zero-coupon yield curve provided by Gürkaynak

4Following Hall and Sargent (2011), TIPs for the US where included as separate bonds whose returncontribution is not affected by inflation.

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et al. (2007) –and Gürkaynak et al. (2010) for TIPs– to price all promised payments: prin-cipals and stripped coupons5. Data for GDP, inflation and primary deficits are calculatedusing calendar yearly data from the NIPA tables, as defined in Hall and Sargent (2011).

Data for the central government of Euro area countries on deficits and net interest pay-ments can be found in Eurostat: Government revenue, expenditure and main aggregates.Net interest payments are calculated as Property income: Payable minus Receivable. Val-ues for GDP and its deflator are taken from the Annual National Accounts available inEurostat. Unfortunately, data on debt on a security-by-security basis is not easily acces-sible in any database for these countries. Thus, I built my own dataset with informationabout each outstanding security published in the reports of the Treasuries, debt man-agement agencies and central banks. The Appendix A explains in detail all sources aswell as the criteria used to complete the timespan 1991-2013 in cases where security-by-security data was not available. Figure B.1 plots annual promised payments (includingboth principals and stripped coupons) on marketable debt with different maturities foreach country6.

The market value of debt is calculated as the sum of all promised payments discountedusing zero-coupon yield estimates available in the BIS databank7. These estimates areavailable for all countries but do not cover the complete timespan for Italy, Belgium andFrance; thus yield estimates offered by Bloomberg are used in some cases. Figure B.2shows 1-, 4-, 7- and 10-years yields for each European country separately. Figure B.3compares the average residual maturity of central government debt officially reported andits counterpart in my dataset. It confirms that the database contains the main changesin these countries’ debt maturity structure. Importantly, this figure also shows that themarket values of debt in securities resulting from my model replicate the values officiallyreported in the financial accounts8.

In addition, Figure B.4 plots the contribution of each factor in the budget constraintof the government to debt changes (and not yet to debt-to-GDP dynamics, that willbe discussed throughly in the next sections). The main purpose of Figure B.4 is todocument the accuracy of primary deficits and my estimates of debt returns to replicate

5Hall and Sargent (2011) show that using these yield estimates instead of actual prices result in verysimilar debt values.

6Italy and France have issued indexed securities, thus reference indexes have been taken into accountfor determining realized coupon payments. Assuming perfect foresight, actual realization of these indexeshave also been used to quantify future promised payments. These two countries, together with Germany,have also issued inflation-protected securities. Italian and French securities received the same treatmentas their indexed securities. However, since the amount of inflation-protected German debt is very small,a constant inflation rate slightly below 2% have been applied instead.

7The estimation procedure followed is the methodology of Nelson and Siegel or Svensson’s extension.More details can be found at BIS (2005).

8ESA95 and ESA2010 rules determine that securities should be included as assets or liabilities in thebalance sheet of any economic sector at their market value. ESA rules consider the central governmenta subsector of the general government (S13).

8

debt changes and the resulting residuals. As mentioned in Section 3, my dataset containsdata on outstanding gross debt and both asset holdings and their returns are determinantsof gross debt changes. Given the lack of data on asset holdings and their maturitystructure, my analysis captures these factors in the residual. Figure B.4 plots the seriesfor asset acquisitions provided in Eurostat9 and shows that they are highly correlatedwith my residuals. As stressed in Eurostat (2013), stock-flow adjustments (that includeasset acquisitions and are conceptually similar to my residual) have been an importantfactor increasing debt since the beginning of the financial crisis. Nonetheless, they arestill residuals and should be interpreted cautiously10 .

5 A first look to the data

This section gives a first description of the data included in my dataset: sovereign debtpayments obligations, their maturity structure, and estimated zero-coupon yields for gov-ernment bonds with different maturities. In order to make the exposition easier, I com-pared US observations with an average for the six EA countries in my sample. Thus,EA values are calculated weighting each country’s value by its share on total GDP in thecorresponding year. These shares are close to 36% in the case of Germany and 26% forFrance (representing more than 60% of the EA series), 21% and 12% for Italy and Spain(representing one third of the EA sample), and 4% and 2% for Belgium and Finland (andtherefore playing a minor role in aggregate EA debt dynamics).

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 1330

40

50

60

70

80

90

100

110

de

bt−

to−

GD

P (

%)

Debt ratios and market to face debt value

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

ma

rke

t−to

−fa

ce

va

lue

US debt/GDPEA debt/GDPUS market/faceEA market/face

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

20

40

60

80

100

120

140Debt−to−GDP ratio (in %)

BE FI FR DE IT ES

Figure 1: Debt-to-GDP ratios for US and EA9Available in the table describing the Transition from the deficit/surplus to the change in debt or as

annual sums of transactions in assets from the Quarterly financial accounts.10This is especially true at the beginning of the sample period because there is less data available.

9

Figure 1 shows, on the left-hand side, the debt ratio for the US and the Euro area11. Botheconomies increased their debt-to-GDP ratios substantially between 1991 and 2013 (by26% and 40% respectively). The main reason for this difference is that the EA increasedits debt ratio by 2.35% annually in 1991-1999 while the US decreased it by 1.2% annually.The sharper increase in US debt during the turbulent years 2007-2013 (an annual increase1.6% larger than in Euro zone countries) cannot compensate this earlier difference. Also,both regions decreased their debt ratios slightly in the 2000’s. In addition, Figure 1shows the ratio of the market value to the face value of debt that fluctuates in botheconomies around 105%. Policy discussions typically focus on nominal debt, while theeconomically relevant value should be computed at market prices. My calculations showthat, nonetheless, there are not big differences between both measures.

On the right-hand side of Figure 1 we can see the debt-to-GDP ratio of each of the six EAcountries selected. We could distinguish three pairs of countries. France and Germany hadlow initial ratios (below 30% of GDP) that increased almost without interruption duringthe sample period. Belgium and Italy, on the contrary, had high initial ratios (around100% of GDP) but consolidated between 1998 and 2007 (approximately, 30% the formerand 18% the latter). Finland in the early 90’s and Spain in recent years had build-ups of60% in their debt ratios. Both countries took measures to rescue their banking sector inthe midst of a strong recession during these episodes.

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100

sha

re o

f o

uts

tan

din

g b

on

ds

(%)

Maturity structure of debt (US)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

<=1y <=4y <=7y <=10y

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100Maturity structure of debt (EA)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

time

to

ma

turity

(ye

ars

)

av.residual duration

Figure 2: Average residual maturity, duration and maturity structure in US & EA11There are three US debt-to-GDP ratios that could be shown: debt held by the public (i.e. private

investors), debt held by the public and the Federal Reserve, and total outstanding debt. The debtvalues calculated for European countries include all debt issued by the central government held by othereconomic sectors. In other words, debt held by the private sector, the ECB or even other generalgovernment subsectors. Since EA central government debt held by the Social Security sector and stateor local governments is much smaller than in the case of the US, I consider comparing EA values withUS debt held by the Federal Reserve and private investors to be the best option.

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Figure 2 shows the evolution of the maturity structure of sovereign debt in both economies.Four solid lines show the share of the total bond outstanding maturing in less than one,four, seven and ten years, as specified on the left axes. In addition, two measures ofthe time to maturity are shown in the right axes: average residual term to maturity andMacaulay duration. Duration is equal to the sum of the residual time to maturity ofboth principal and coupon repayment obligations weighted by the relative present valueof these cash flows.

Average debt maturity in the US has fluctuated between 6 years in 2000 and 4 years in2008, when bailouts of financial institutions increased financing needs almost overnight.Recently, US debt maturity was raised substantially, mainly due larger holdings of long-term bonds by the Federal Reserve. Close to one fourth of US had typically maturitylonger than 10 years while 35% has typically been short-term debt12. On the contrary,the Euro area had 20% of debt with maturity lower than one year and increased its shareof very long-term debt from 5% to 18%. As a result, the EA average residual maturityincreased from 4.5 to 6.5 years in 2007, when generalized sudden increases of financingneeds first, and sharp increases in interest rates for some countries afterwards, stabilizedEA’s aggregate debt maturity13. Nonetheless, most of the sample shows higher averagematurity for the EA as a whole than for the US. Figure 3 shows the evolution of averageresidual maturity of each of the six EA countries studied. The biggest increases tookplace in the 90’s, being these very large in the case of Italy and Spain. Lately, Belgiumand, especially, Finland show also large increases, while Spain and Italy shortened debtmaturity during the Euro crisis.

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

2

3

4

5

6

7

8Average debt maturity (in years)

BE FI FR DE IT ES

Figure 3: Average residual maturity in each EA country12Higher shares of US debt in the maturity spectrum explain the larger difference between its average

residual maturity and duration than in the EA.13De Broeck and Guscina (2011) also document a shortening in the maturity as one of the changes

brought in debt issuance practices in 16 EA countries and Denmark after the financial crises.

11

91 92 93 94 95 96 97 98 992

4

6

8

10

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14

16

91 92 93 94 95 96 97 98 992

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99 00 01 02 03 04 05 06 070

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BEFIFRDEITESUS

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BEFIFRDEITESUS

07 08 09 10 11 12 13 140

1

2

3

4

5

6

7

07 08 09 10 11 12 13 140

1

2

3

4

5

6

7

Figure 4: Evolution of short (left) and long-term (right) interest rates

12

Figure 4 shows the evolution of 1-year (left column) and 10-year (right column) yields forEA countries and the US, the latter with a dashed line. We can easily distinguish threedifferent subperiods marked by the introduction of the Euro and the financial crisis: inthe top row, 1991-1999; in the middle row, 1999-2007; and in the bottom row, 2007-2014.

The early 90’s are characterized by financial turbulences and a recession that depressedbond yields (both short-term and long-term) in 1993. During 1995, the agreement for theestablishment of a currency union in 1999 reduced yields by at least 3% in all countriesand initiated a convergence process observed at all maturities, although slightly faster for10-year yields. For countries like Italy and Spain, this episode brought down yields by 8and 6% respectively, a larger fall than the 5% change observed in the US after Volcker’sintervention contributed to bringing inflation under control.

Between 1999 and 2007, yields in the EA behaved like a single yield curve highly correlatedwith the one of the US. There were not large changes, but the reduction of 2.5% in yieldsuntil mid 2005 provided capital gains to long-term bondholders that were not compensatedby the 1.5% increase in yields that followed.

The financial crisis brought back fragmentation in the sovereign bond market of EAcountries. Although yields fell for all countries until 2009, especially short-term yields,risk premia appeared at all maturities afterwards. In particular, on average Italy andSpain were asked an interest rate 1.5% higher than Germany for 1-year bonds, while2.5% for 10-year bonds. Other countries also paid at times sizeable risk premia, likeBelgium that was asked on average a 0.3 and 0.9% interest rate differential with respectto Germany.

Table 1: Has debt maturity been driven by demand or supply?

91-99 99-07 07-13 91-13US -0.3 -0.9 -0.3 -0.1BE 1.6 -0.5 -0.1 0.2FR -0.3 -0.3 0.2 -0.3DE -1.3 -0.1 -0.5 -1.0IT 1.7 1.9 -0.4 0.9ES -0.8 -0.8 -0.6 -0.8

Finally, Table 1 shows the correlation of each country’s term spread (10-year minus 1-year yields) with its average residual maturity, after controlling for the US term spreadand the average maturity of other EA countries. These correlations have mainly negativesigns, meaning that relative prices and quantities of bonds moved in same direction (i.e.responded to demand shifts). Thus, I conclude that, since the Euro started, bond demandis the main driver of debt maturity in EA. Before, supply seem to have played an importantrole in Italy and Belgium.

13

6 Comparing debt-to-GDP dynamics in US and EA

Before doing a cross-country comparison of debt-to-GDP dynamics in the Euro area, thissection discusses similarities and differences between the US and the EA as a whole. Thetop row in Figure 5 summarizes these results showing the cumulative contribution to debt-to-GDP changes of primary deficits, nominal debt returns, inflation and output growth,relative to each country’s debt ratio in 1991. The bottom row displays the cumulativecontribution of returns on debt with different maturities. More information can be foundin Tables B.1 to B.5 of Appendix B.

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5

3Cumulative contribution to debt−to−GDP ratio (US)

DeficitReturnInflationOutput growthResid

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5

3Cumulative contribution to debt−to−GDP ratio (EA)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.05

1.1

1.15

1.2

1.25

1.3

1.35Cumulative contributions of returns by mat. (US)

>7year4−7year1−4year<1year

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8Cumulative contributions of returns by mat. (EA)


Figure 5: Cumulative contributions to changes in debt to GDP ratio

The first stylized fact shown in Figure 5 is that primary fiscal deficits do not play animportant role in the Euro area, but they are key for the US. Concretely, primary deficitsare responsible of an annual increase of 1.6% in the US debt ratio, implying that the USdebt-to-GDP in 1991 would be multiplied by 1.8 if the contributions of primary deficits

14

–and only those– were added to the initial ratio. It fact, it is remarkable how theircumulative contribution resembles the evolution of the debt ratio itself in Figure 1. Inthe EA, however, the initial debt ratio would be multiplied only by 1.45 if only primarydeficits are taken into consideration and mainly due to contributions in recent years.

The biggest contributor pushing up debt-to-GDP ratios in both economies was debt re-turns. Note also that holding returns were more relevant in the EA (a contribution of3.3% annually) than for the US (a 2.1% contribution). This explains that, due to debtreturns, the initial US debt ratio would have doubled, while on average the initial EAratios would have been multiplied by 2.7. The bottom row shows that returns on short-term debt were six times more important in the US than in the EA. This is case not onlybecause the US had more short-term debt (36% vs. 22% in EA) but also because it hasbeen more costly (3.4% return rate vs. 2% in EA). Similarly, the share of US returnscoming from debt maturing after 7 years was larger than in the EA (44% vs. 33%). Thereason was that long-term debt had been more costly in the EA (on average) than in theUS, given that both economies had similar fractions of total debt with this maturity.

The negative contributors to debt-to-GDP changes in Equation 5 come from inflation andreal output growth. These growth rates are shown in Figure B.6 and Table B.1. Both, theUS and Europe, had on average 2% inflation during the last 22 years but, since the EAaccumulated higher debt ratios it this period, the contributions of inflation were relativelyhigher than in the US. Inflation was specially high in the US during the housing boompreceding the financial crises, while in the early 90’s in the case of the EA. The US had2.6% real output growth, doubling that in the EA and doing in a bigger contribution todebt ratio erosion (-1.2% in the US versus -0.8% in the EA).

The top part of Figure 6 shows my estimates of the average real return rate for the USdebt and the rate resulting from dividing officially reported interest payments by thenominal stock of debt and, afterwards, subtracting inflation. It is clear that my estimatesare more volatile than those based on officially reported interest payments. The reason is–as explained in Hall and Sargent (2011)– that the official figures on interest payments donot include capital gains and losses paid to holders of bonds with maturity longer thanone year. Thus, I can document that US medium- and long-term bondholders sufferedconsiderable losses during four years: from 2002 to 2006.

The middle part in Figure 6 shows the same series for the EA average. The ESA guidelinesfor reporting interest payments in the Euro area government accounts determine thatit should be recorded as the sum of coupon payments (and/or the difference betweenthe principal repayment obligation and the initial price received) following the accrualprinciple. Thus, as in the case of the US, official figures in the EA also exclude capitalgains and losses. Figure 6 shows clearly a significant reduction on real returns paid since

15

the introduction of the Euro (3.1% before 1999 vs. 2.2% afterwards) including capitallosses for bondholders. Before the crisis, real returns were even lower (1.25% on average),but since 2007 long-term bondholders have been paid considerable capital gains.

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−4

−2

0

2

4

6

8

10

12

14

%

Average real rate of return (in %)

US av. real returnUS real interest paid

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−4

−2

0

2

4

6

8

10

12

14

%


EA av. real returnEA real interest paid

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−4

−2

0

2

4

6

8

10

12

14

%


US av. real returnEA av. real return

Figure 6: Average real returns on debt including capital gains/losses

16

Finally, the graph at the bottom of Figure 6 compares my estimates of average real returnrates for both economies. As shown also in Table 6, debt returns were less costly for theUS than for the EA. It is also clear that all countries in the Euro area paid lower returnssince the introduction of the Euro but benefited less after 2007. An exception is Germanythough: mainly, because the low inflation registered in this country between 1999 and2007 German inflation was increased by half of a percentage point in 2007-2013. Anotherconclusion distilled from Table 6 is that most EA countries paid an average 3.6% realreturn on the debt with the exception of Spain that paid 1.3%. One reason for thisdifference is that Spain had 3% inflation on average, much higher than the 1.9% EAaverage. Another complementary explanation is that Spain borrowed short-term untilthe convergence process in the 90’s was completed. Thus, by borrowing cheaper, Spainsaved considerably on returns paid to long-term bondholders.

Table 2: Av. real return rate (%)

91-99 99-07 07-13 91-13US 4.2 3.0 1.5 3.0EA 5.2 2.0 2.8 3.3BE 6.0 2.1 2.4 3.6FI NaN 1.8 1.9 1.9FR 5.9 2.1 3.0 3.7DE 5.0 3.1 2.6 3.6IT 6.4 1.9 2.8 3.6ES 1.3 -0.3 3.2 1.3

7 Debt-to-GDP dynamics in EA countries

This section discusses cross-country differences in debt-to-GDP dynamics in EA countries.More information can be found in Appendix B: Tables B.6 to B.17 and Figures B.7 toB.11. I first compare the two biggest economies of the Euro zone: Germany and France.Afterwards, I study Italy and Spain, two large economies with similar experiences duringthe convergence (and recent fragmentation) processes in debt markets. Finally, I presentthe results of Belgium and Finland.

7.1 France and Germany: the need of growth

Annual nominal output growth was on average 1.4% lower in the EA than in the US.In recent years, close to zero economic growth in Italy and Spain has been the main

17

contributor bringing down EA output growth. However, the countries that performedworse than the average EA country were France and Germany, the two biggest economiesin the region. This reduced significantly their output growth contribution to the erosionof the aggregate EA debt-to-GDP ratio. France had an increasingly higher debt-to-GDPratio relative to Germany in the years studied. As a result, between 1991 and 2013 therewas an annual reduction in the French debt-to-GDP ratio of 1.6% while of only 1% in theGerman case. On the contrary, US output growth implied an annual reduction of 2.1%.This shows the importance of GDP growth in stabilizing debt-to-GDP ratios: the USenjoyed an annual extra erosion of respectively 0.5 and 1% as a result of output growth.Nonetheless, growth contributions alone would have halved their low initial debt ratios.

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5

3Germany (DE)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5

3France (FR)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2Germany (DE)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2France (FR)


Figure 7: Cumulative contributions to changes in debt-to-GDP ratio in DE and FR

As mentioned, inflation played a bigger role than real growth in eroding the debt-to-GDPratio of the average EA country studied. In the case of France and Germany, however, thecontribution of GDP growth is equally split between both factors, as can be clearly seen

18

in Figure 7. The former relied especially on inflation in the years preceding the financialcrisis, while the latter mainly at the beginning of the sample period (i.e. in 1991-1995). Inthe last period 2007-2013, inflation was similar in both countries but nominal GDP grewless in France. As a result, the contribution of inflation relative to that of real outputgrowth in France is higher than in Germany.

Regarding the other factors (i.e. primary deficits and debt returns), their combinedcontribution in Germany was lower than the EA average (2.2% versus 3.5%) while inFrance it was above average (in particular, 4.1%). The relative contribution of nominalreturns is equal in both countries, multiplying by 2.8 their initial debt ratios. However,Figure 7 shows clearly that France did not keep the contributions of primary deficits undercontrol. This figure also reports higher contributions of the residual in Germany than inFrance in recent years, pointing at more costly asset purchases, although this conclusionshould be taking cautiously because, as explained before, these residuals might also beinfluenced by other factors.

Finally, the two graphs in the bottom row of Figure 7 show the contributions of debt withdifferent maturities. Returns on long-term debt (meaning, bonds maturing after 7 years)was the biggest contributor, however it played a more important role in France than inGermany. The opposite can be said for short-term debt (i.e. bonds maturing no laterthan in 1 year). This is mainly due to the fact that Germany held 58% of its debt in bondswith medium- and short-term residual maturity, while France 44%. Also France had 34%of debt maturing after 7 years and Germany only 21%. Thus, larger contributions of somematurities mainly reflect higher stocks of debt with these maturities.

7.2 Italy and Spain: the benefits/costs of longer maturity

The two second biggest economies in the Euro area are Italy and Spain. Both countriesincreased their debt ratios in 1991-1999: Italy by 2.5% and Spain by 2% annually. Bothconsolidated in 1999-2007: Italy reduced debt-to-GDP by 1.5% annually and Spain dou-bled that change. And both increased it again in 2007-2013: Italy by 5.4% and Spaindoubled. However, in the whole sample Spain increased its debt ratio by 60% and Italyby 40%.

The factors contributing to debt-to-GDP changes in these countries behaved quite differ-ently. Inflation was 2.6% in Italy and 3% in Spain, the highest among the six EA countriesstudied. Real growth was strong also in Spain (2.1%), the maximum in the EA region,whereas Italy had the lowest (0.7%). Thus, the big difference in its cumulative impact ineach country’s debt ratio. The recent crises were particularly severe in their economies,with negative contributions on real output growth pushing up their debt-to-GDP ratios.

19

Residuals in Spain accumulate a 25% contribution since 2007, pointing at the big impactof bank bailouts and a related EU rescue package granted in 2012. Italian primary sur-pluses alone would have halved its initial 90% debt ratio, however this only covered 30%of all contributions done by nominal debt return payments. Spain kept primary deficitsunder control until 2008, date when contributions of this factor rised to a new average of4.3% a year.

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5

3Italy (IT)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5

3Spain (ES)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45Italy (IT)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45Spain (ES)


Figure 8: Cumulative contributions to changes in debt-to-GDP ratio in IT and ES

The evolution of these countries’ debt maturity is very similar, though. Both increasedtheir average debt maturity substantially (3.5 years in Italy, 4.3 in the case of Spain)up to near 6.5 years. The highest increases took place between 1991 and 1999, while inrecent years these countries issued more short-term debt. The bottom part of Figure 8shows that Italy paid particularly high returns on medium-term debt in the 90’s and,together with Spain, on long-term debt in recent years. Instead, returns on 1-year debtwere particularly low (almost null) in both countries after 1999 and on long-term debt

20

in 2005-2011. The main difference between these countries’ debt returns happened in1991-1999 when this factor alone would have doubled the Italian debt-to-GDP while inSpain would have been multiplied by 1.5. Afterwards, the relative contributions of debtreturns were similar.

The reason behind the difference in debt returns in 1991-1999 is the increase in Italiandebt maturity that took place earlier than in Spain. Concretely, Spain increased 2 yearsits average maturity during 1997 and 1998, and Italy 1.7 years in 199414. These areboth bigger changes than the 1.5-years lengthening that the US did in 1981-1989, wheninflation and yields fell in response to the monetary tightening did by the Fed with PaulVolcker as Chairman. Notably, Italy and Spain also experienced a drastic drop in theiryields in 1991-1999 in anticipation of the monetary union. In fact, the downward shift inthese countries’ yields –from around 11%, for Spain, and 13%, for Italy, down to around5%– was deeper than for the US –from 13 to 8%– after Volcker’s decision.

I perform model simulations to evaluate the impact in returns and debt ratios of alterna-tive strategies of debt maturity management for Italy and Spain. In these exercises, thevalues of primary deficits, output growth, inflation and yields are actual historical values.Given the downward shift in these countries’ yield curves is generally understood to bethe result of expectations of economic convergence raised by the monetary union, this is areasonable assumption. My simulations consist in changing the maturity structure of debt–in particular, the share of promised payments for each maturity– and iterate Equation5 to obtain counterfactual values of debt and returns.

The first row in Figure 9 shows the impact of a bringing forward Spain’s maturity length-ening from 1997-1998 to 1994-1995, i.e. before the Spanish yield curve started to falland converge with that of the rest of EA countries15. Thus, I impose the distributionof promised payments across maturities in 1994 and 1995 to be equal to the distributionobserved in 1997 and 1998. Simultaneously, I put the distribution of years 1996-1998equal to the distribution in 1998. This counterfactual maturity structure would implythat Spain had entered the years of convergence with longer debt maturity. As a result,this small policy change would have brought higher return payments to long-term bond-holders and a debt-to-GDP ratio close to 5% larger. Given the small policy change andthe difficulties of reducing debt ratios using alternative tools, the reduction resulting fromdebt maturity management is, by no means, trivial.

14The solid line in the bottom row of Figure B.11 is the average maturity of nominal principal payments,which also the statistic that is typically reported officially. The dashed line is the average maturity of allpromised payments, including principal and coupons. The top row shows yields and inflation rates forSpain, the U.S. and Italy.

15This is done quarterly, that is, using the yields shown at quarterly frequency in Figure B.2 andinterpolating the annual ratio of payments at each maturity to total promised payments.

21

91 92 93 94 95 96 97 98 991.5

2

2.5

3

3.5

4

4.5

5

5.5Average maturity of payments in years (ES)

HistoricalCounterfactual

91 92 93 94 95 96 97 98 99−4

−2

0

2

4

6

8

10

12Returns share of GDP in % (ES)


91 92 93 94 95 96 97 98 9935

40

45

50

55

60

65

70Debt−to−GDP ratio in % (ES)


91 92 93 94 95 96 97 98 992.5

3

3.5

4

4.5

5

5.5

6Average maturity of payments in years (IT)


91 92 93 94 95 96 97 98 99−5

0

5

10

15

20

25

30Returns share of GDP in % (IT)


91 92 93 94 95 96 97 98 9980

85

90

95

100

105

110

115Debt−to−GDP ratio in % (IT)


Figure 9: Simulated effect of change in debt maturity management for ES and IT

22

The second row in Figure 9 studies the impact of delaying Italy’s maturity lengtheningfrom 1994 to 1997, i.e. until the convergence process is quite advanced. In the coun-terfactual exercise, Italy would have had a shorter debt maturity when yields fell, thereturns paid would have been lower, and the debt ratio 2% smaller. Although the effectis quite limited, it is worth noting that the policy change is minor and the effect wouldbe higher in case of delaying Italy’s maturity lengthening one or two years more. Inany case, my simulation illustrates that the timing of the increase of debt maturity wascostly. Nonetheless, both countries entered the recent crises with similar average debtmaturity and, therefore, benefited equally from its implied fiscal insurance, illustrated bythe negative returns paid around 2011.

7.3 Belgium and Finland: recent increases in maturity

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5Belgium (BE)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130.8

0.9

1

1.1

1.2

1.3

1.4

1.5Finland (FI)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45Belgium (BE)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

1.05

1.1

1.15Finland (FI)


Figure 10: Cumulative contributions to changes in debt-to-GDP ratio in BE and FI

23

The two smallest economies in the sample are Belgium and Finland, whose debt-to-GDPdynamics are shown in Figure 10. As explained in Appendix A, there is not data availableon the latter to study the complete timespan, so I focus in 2003-2013. Nonetheless, Finlandis the country that achieved the largest reduction of debt ratios from 80% in 1996 to below40% in 2007. The annual negative contribution of GDP growth is 2.3%, slightly abovethe EA average, while primary deficits did a substantial contribution of 2%.

Belgium stands out as the country with highest debt ratios from the sample. Debt returnsconstituted the biggest factor pushing up the debt-to-GDP ratio, as it is typically the casein highly indebted countries; however they were half-compensated by primary deficits.Strong growth of 3.7% also did a substantial annual contribution of -4.1% that lookslower than in other countries relative to its extremely high initial ratio.

The bottom raw in Figure 10 shows the contribution of returns of debt with differentmaturities. In both cases, long-term debt was the largest contributor, especially in recentyears. This is the case because both increased their average debt maturity substantiallysince 2009: Belgium almost 2 years while Finland even more. The recession and thesubsequent expansionary response of monetary policy had already pushed down the yieldcurve to the extremely low levels recently observed. Importantly, it is foreseeable thatyields will stay low or increase in the next years, thus higher debt maturity will materializein negative returns on debt and lower debt ratios. In view of the evidence in this paperon the role of maturity management on debt-to-GDP dynamics, this seems the correctpolicy. As yields in 2014 fell also for Italy or Spain –whose yields spiked around 2012 as aresult of risk premia– this policy recommendation can be extended to these countries. Infact, recent figures reported by these countries confirm that their Treasuries have alreadystarted lengthening again average sovereign debt maturity.

8 Estimates on the impact of higher inflation

The previous section studied past contributions of inflation and other factors to debt-to-GDP dynamics. One of the conclusions drawn is that inflation contributed more tobring down the debt ratio in the EA than in the US. This section estimates the impactof permanent higher future inflation on the debt-to-GDP ratio. As explained in Hilscheret al. (2014), the present value of debt is based on expectations about the distribution offuture inflation. The effect of shifting the probability distribution of future inflation by 1%can be easily calculated in the framework of this paper. Assuming that this change doesnot affect the real discounting rate for future payments, an extra 1% inflation implies anincrease of 1% in the nominal rate at which future debt payments are discounted. Thus,

24

∆J∑

j=1

pjtQjt

Yt=

J∑j=1

exp(−j · yjt )Qj

t

Yt−

J∑j=1

exp(−j · [yjt + ∆πt])Qj

t

Yt

≈ −∆πt

J∑j=1

[j · exp(−j · yjt )

Qjt

Yt

]

(6)

In other words, the impact of 1% higher inflation is approximately equal to 1% times theshare of debt that can be actually inflated away times its Macaulay duration. Hilscheret al. (2014) show that it is important to use duration and not average residual term tomaturity because this measure acknowledges that coupon payments would be rolled-overat nominal yields that will reflect the 1% extra inflation. They also stress that actual debtfigures that can be inflated away should not include inflation-indexed bonds or stocks heldby the central bank.

Table 3: Estimated reduction in debt-to-GDP ratio (data from 2013)

My estimates Basic approximationDuration Adj.Ratio Impact Av.Mat Ratio Impact

US 3.3 56% 1.68% 5.6 74% 4.14%EA 5.75 77.3% 4.04% 6.60 83.3% 5.51%BE 6.10 103.8% 5.98% 7.44 105.7% 7.86%FI 6.00 54.1% 3.09% 6.47 54.1% 3.50%FR 6.09 82.0% 4.71% 7.01 84.4% 5.92%DE 6.02 51.1% 2.78% 6.35 51.1% 3.24%IT 5.25 105.1% 4.74% 6.42 125.7% 8.07%ES 4.90 95.8% 4.48% 6.44 99.6% 6.38%

Ad.Ratio removes inflation-indexed bonds and CB holdings

Table 3 shows my estimates debt-to-GDP reductions resulting from 1% permanentlyhigher future inflation and compares them with approximations used in the literature, e.g.Missale and Blanchard (1994) and Aizenman and Marion (2011). I also show measuresof debt’s life (either duration or average residual maturity) and debt ratios correspondingto both estimates offered. As stressed by Hilscher et al. (2014), the estimated effect forthe US becomes much smaller if Federal Reserve holdings and TIPs are subtracted, re-ducing substantially duration. Estimates for the EA do not change much if you account

25

for central bank holdings and inflation-indexed bonds 16. However, it is clear that the EAwould obtain 2.4 times the reduction estimated for the US as a result of higher inflation.These estimates contribute to the current discussion about the convenience of increasingthe inflation target in the Euro area. They are also relevant for policymakers to under-stand the impact that decreasing inflation forecasts will have in the balance sheets of thesovereigns.

Belgium stands out as the country that would benefit most from higher inflation, as it hasa large debt ratio with the highest duration. However, only a 2.8% loss will be imposed tonon-resident holders, the same estimate as France17. Also Spanish residents debt-holderswould face losses due to higher inflation since they hold close to 65% of this country’sdebt. The average reduction of EA countries’ debt imposed to non-residents will be 2.4%,4.2 times that of the US. Although many of these non-residents are actually residentsof other EA countries, these estimates quantify the incentives of individual countries toinflate away their debt.

9 Conclusion

The US financial crises and subsequent Euro debt crises have increased debt-to-GDPratios in the EA (and the US) drastically. As a result, EU leaders and national politiciansagree in the need of monitoring debt ratio developments so that the necessary measures toguarantee their stability can be taken timely. In particular, the so called Fiscal Compactbrings new relevance to instruments like the Excessive Deficit Procedure. However, therules included are based in an accounting framework very different from the concepts usedin theoretical models on debt management. My paper helps reconciling both approachesby documenting a new dataset on European sovereign debt securities and computingreturns on debt with different maturities complementary to the officially reported valuesof interest payments.

Based on my unique dataset, this paper has generated a set of stylized facts aboutsovereign debt and yields of interest for both academics and policy-makers working indebt maturity management. After considering some general features of debt maturity inthe EA and the evolution of yields, I calculated past contributions of inflation, growth,

16Central bank holdings are taken from Bruegel database of sovereign debt holdings, Merler and Pisani-Ferry (2012). Table B.18 summarizes debt-holder shares in the latest date available. Since my dataset isbased on information security by security, I can easily leave out inflation-indexed bonds. However, someflexible coupon rate bonds would automatically increase future payments in response to higher inflationexpectations. This is especially relevant for Italy, whose estimate should be consider simply as a lowerbound.

17Losses imposed to non-resident bondholders are shown in Table B.18.

26

deficits and returns on debt of different maturity to debt-to-GDP dynamics in 1991-2013. Icompared the experience in the Euro area with that of the US and discussed cross-countrydifferences within the six currency union members of my sample. Finally, I provided es-timates of the impact of future inflation in EA debt ratios and documented an effect 2.4times higher (on average) than for the US.

One possible extension of my work will be to compare debt-to-GDP dynamics for thebiggest EA economies and the United Kingdom. An even more interesting application ofmy estimates of returns on debt with different maturities would be to test the implicationsof recent developments in the theory of optimal debt management to the Euro area, e.g.Faraglia et al. (2013), as previously mentioned. In other words, my rich dataset canbe used to quantify the contribution of inflation in reducing the real cost of funds inresponse to aggregate demand shocks, unexpected increases in government spending, etc.A similar study was recently performed in Berndt et al. (2012) for the US case findingthat long-term debt played a significant role in financing fiscal shocks through lower debtreturns.

27

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Gürkaynak, R. S., Sack, B., and Wright, J. H. (2007). The us treasury yield curve: 1961to the present. Journal of Monetary Economics, 54(8):2291–2304.

Gürkaynak, R. S., Sack, B., and Wright, J. H. (2010). The tips yield curve and inflationcompensation. American Economic Journal: Macroeconomics, pages 70–92.

Hall, G. J. and Sargent, T. J. (2011). Interest rate risk and other determinants of post-wwiius government debt/gdp dynamics. American Economic Journal: Macroeconomics,3(3):192–214.

Hall, G. J., Sargent, T. J., et al. (1997). Accounting for the federal government’s cost offunds. Economic Perspectives-Federal Reserve Bank of Chicago, 21:18–28.

Hilscher, J., Raviv, A., and Reis, R. (2014). Inflating away the public debt? an empiricalassessment.

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Lustig, H., Sleet, C., and Yeltekin, Ş. (2008). Fiscal hedging with nominal assets. Journalof Monetary Economics, 55(4):710–727.

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Reinhart, C. M. and Sbrancia, M. B. (2011). The liquidation of government debt. Tech-nical report, National Bureau of Economic Research.

29

A Data sources

A.1 United States

The analysis for the United States relies heavily on Hall and Sargent (2011). I obtainquantities and characteristics of outstanding marketable nominal bonds (i.e. TreasuryBills, Notes and Bonds) from the Center for Research in Security Prices (CRSP) AnnualUS Treasury Database (2013). Similar data for TIPs (inflation-protected securities) isretrieved from December issues of the US Treasury’s Monthly Statement of Public Debt for1997-2013. Moreover, series of nominal non-marketable debt are December observationstaken from the Treasury Bulletin18. Finally I price all payments using the nominal andreal zero-coupon yield curves computed by Gürkaynak et al. (2007) and Gürkaynak et al.(2010).

A.2 Belgium

Belgostat, the online database of the National Bank of Belgium (NBB), shows the out-standing amounts of Treasury debt by currency and type of instrument: Linear Bonds(also called OLOs), State Notes and classic loans, that yield coupons and have maturitylonger than one year; and Treasury Certificates and Bills, for zero-coupon short-termdebt. However, the annual reports from the Belgian Debt Agency also include significantamounts of Treasury Bonds issued by the Silver Fund as well as small amounts from arecent program designed to attract German investors called Schuldscheine and EMTNs.This paper’s database collects the details for each outstanding OLO, clasic loan and Sil-ver Fund bond available in these reports and uses information about issuances to build asimilar description for State Notes19.

The Belgian Debt Agency does not publish reports before 1999, however the report corre-sponding to that year gives a detailed description of the maturity structure of public debtsince 198620. The outstanding amount of debt with each residual maturity is, nonetheless,the sum of debt issued in different dates and therefore it is unclear which coupon ratewould correspond to the outstanding principals. The criterium followed is that debt attime t maturing in j periods is the sum of debt issued at time t-1 with maturity j+1 plus(plausibly) new debt maturing after j periods (i.e. issued at time t). In this way, I assignthe year of issuance for different tranches of debt with the same residual maturity and

18Table OFS-1: Distribution of Federal Securities by Class of Investors and Types of Issue.19The small amounts of Schuldscheine and EMTNs are not included because their information is

incomplete. For simplicity, the total amounts of debt with maturity lower than one year have beenincluded as one security that matures after one year.

20Table 13 in the report.

30

assume as coupon rate the estimated yield-to-maturity corresponding to the last day ofthat year.

In order to price these outstanding payments at different maturities, I use the yield curvesestimated by the NBB which are available at the BIS data bank since 1997. For 1991-1996,I interpolated and smoothed the average yield-to-maturity rates of OLOs that the NBBmakes available at different maturities in Belgostat. Finally, the small difference betweenthe face value of all above-mentioned debt and the gross (nominal) debt officially reportedby the Treasury is added directly to market value of debt resulting from the model.

Figure B.3 compares the resulting market value of debt with the Total Liabilities reportedby the OECD’s Belgian balance sheet for the central government21. It also compares theaverage debt maturity of the data with the average residual maturity from the OECD’scentral government database. Although the resulting market values for this country aremore different to the official numbers than for other countries, yearly changes in debtmaturity are definitely correctly captured.

A.3 Finland

The database of the Finnish State Treasury shows the stocks of debt by currency andtype of industry since 2002. Most of this debt is denominated in euros and issued in seriallong-term bonds and Treasury Bills, representing around 90% of all debt in securities.Upon request, the Treasury facilitated the stocks and main characteristics (i.e. maturitydate and coupon rate) for each end-of-year outstanding serial bond, as well as the averageFinnish debt maturity since 199122.

In order to price the implied promised payments at different maturities, I use the yieldcurves published by Bloomberg since 1998. The nominal value of the 10% of debt in se-curities with unspecified maturity is added to the market value of all promised payments.Figure B.3 compares the resulting market value of securities with the Liabilities in secu-rities reported by the OECD’s Finnish balance sheet for the central government. It alsocompares the reported average debt maturity with that coming from the data collected.Both series are well matched and therefore can be reliably used to study the impact ofdebt maturity changes on debt values dynamics since 2002.

Finally, changes in debt in instruments other than securities should be taken into consid-eration in the exercise of decomposing debt-to-GDP changes. The values of liabilities in

21As I cannot separate debt in securities from other instruments for the complete timespan, I comparewith the value of all liabilities in the balance sheet.

22As a result, the information necessary and available for our model starts in 2002. Differently thanfor France and Germany, few information available about previous years is not enough to get a goodassessment of the debt maturity structure in that period.

31

loans and currency have been retrieved from the OECD’s Finnish balance sheet for thecentral government. It is clear from this balance sheet that the Finnish central governmentholds assets whose value represents around 50% of the value of all liabilities. Althoughthe returns on these assets imply a significant source or revenue, the model does not in-clude assets holdings. Instead, it is assumed that asset holdings have a maturity structuresimilar to that of securities. As a result debt returns net of asset returns would be a shareof the returns for all securities derived in the model. Values for these shares –capturingthe changing ratio of assets to liabilities– are taken also from the OECD’s Finnish balancesheet.

A.4 France

The website of the Agence France Tresor, the French Treasury, makes available sinceJanuary 1998 the Monthly Bulletins published by this institution. These bulletins containall the characteristics and quantities of the securities outstanding at the end of the previousmonth. These securities are zero-coupon one-year bonds (or BTFs), five-year bonds (orBTANs), and long-term bonds (also called OATs). The Treasury also issues floating-ratebonds (TEC 10 OATs pegged to the constant 10-year maturity rate) and inflation-indexedbonds (OATi, for French inflation; and OATiEUR, for Euro area inflation). Historicalseries for these indexes are also available in the Treasury’s website. Differently than forthe US, there are not estimates available of the yield curve for these special bonds. Myapproach consists on assuming perfect knowledge of future realizations of these indexesand apply then in the calculation of future promised payouts. As a result, I can pricethem as any other standard security.

Moreover, the OECD’s central government database provides the stocks of debt for 1991-1996 for each type or class of bond. It is therefore possible to make some assumptionsto describe their maturity structure in these years. I choose to assume recursively andbackwards that the difference in each year between the total stock outstanding for eachclass of bonds (i.e. BTFs, OATs, etc) and the sum of outstanding bonds in that classwhose details (maturity, coupon rate, etc) are included in my database has its origin onbonds issued one year before. Whenever a coupon rate needs to be fixed, the estimatedyield-to-maturity corresponding to that issuance period will be assigned. Following thismethodology, the share of unknown (and assumed) information about the maturity struc-ture increases when moving further back in time, but the stocks of debt assigned to eachclass of bond are exactly those reported by the OECD.

In order to price these outstanding payments at different maturities, I use the yield curvesestimated by the Banque de France (BdF) since the beginning of 1992 until June 2004available at the BIS data bank. For 2004-2013, I interpolated and smoothed the yield

32

curve estimates offered by Bloomberg. Figure B.3 shows that the resulting market valueof debt and average debt maturity follow closely the Liabilities in securities and averageresidual maturity reported by the OECD in its Belgian balance sheet for the centralgovernment and central government database23.

Finally, changes coming from variations in debt in instruments other than securities shouldbe taken into consideration in the exercise of decomposing debt-to-GDP changes. Valuesfor debt in loans, currency and deposits are taken from the Quarterly series of governmentdebt in Eurostat for 2000-2013 complemented with data for 1991-1999 from the OECD’scentral government database.

A.5 Germany

The website of Bundesbank makes publicly available the estimates of zero-coupon yieldsfor German government bonds performed by this institution since 1973. Therefore, pricingGerman debt following the methodology of this paper is straightforward. However thequantities and characteristics of each outstanding bond have not been reported to thepublic. Upon request, the Bundesbank provides the data that allows to construct acomplete description of end-of-year outstanding amounts of Bubills, Schatze, Bobls andBunds auctioned since the end of 2000 and their characteristics24.

The German Central Bank also makes available on its website the total nominal stocksof debt (i.e. principal payments promised) for Federal savings notes (with maturitiesof 1 and 2 years) and Federal Treasury financing papers (maturities of 6 and 7 years).Lacking more detailed information, their nominal value is added directly to the marketvalue of the other securities in the model. Finally, the Federal Debt Agency provides uponrequest some data on bonds issued by especial funds like Bundesbahn or Treuhandanstalt.Similarly, their nominal value is added directly whenever the stocks, promised coupons,and maturity are not known. Notice also that with each auction the Federal Governmentretains a certain nominal amount for secondary market operations. In this paper, onlythe amounts net of own funds have been taken into consideration.

Although the detailed information available for Bunds actually goes back to 1997, for1991-1999 only data on the total nominal stocks for each class of bond was provided bythe Federal Debt Agency. Therefore, it is necessary to make some assumptions to describe

23This database does not cover the years after 2010, therefore the average residual maturity values for2011-2013 have been completed with data from the Monthly Bulletin of the Treasury, the original source.

24Bubills –also called Treasury discount paper– have a maturity lower than one year, and Schatze –orFederal Treasury notes– have 2-years maturity. A few Bobls –or Five-year Federal Notes– and Bunds–long-term bonds– are linked to inflation but, since they represent a very small fraction of all issuedbonds, I add them with fixed coupons equal to the corresponding spread over an assumed 2% inflationrate.

33

the maturity structure of German sovereign bonds since 1991. I choose to assume recur-sively and backwards that the difference between the total stock for each class of bonds(i.e. Bubills, Schatze, etc) and the sum of outstanding bonds in that class whose details(maturity, coupon rate, etc) are included in my database has its origin on bonds issued oneyear before. Whenever a coupon rate needs to be fixed, the estimated yield-to-maturitycorresponding to that issuance period will be assigned. Following this methodology, theshare of information on the maturity structure unknown (and assumed) increases whenmoving further back in time, but the stocks of debt assigned to each class of bond areexactly those reported by the Federal Debt Agency25.

All promised payments at different maturities have been priced using the zero-couponyields estimated by the Bundesbank and available both on its website and the BIS data-bank. Figure B.3 compares the market value of debt resulting from the model with theLiabilities in securities reported by the OECD’s German balance sheet for the centralgovernment26. It also compares the average maturity of securities of the data with theaverage residual maturity (before swaps) reported by the Federal Debt Agency in reports.Both series are reasonably matched except for the maturity average at the beginning ofthe 90’s, the years for which more assumptions were necessary. Finally, in the exercisedecomposing debt-to-GDP changes, debt in instruments other than securities should alsobe taken into consideration. This series is calculated as the difference between TotalLiabilities and Liabilities in securities from the OECD’s German balance sheet.

A.6 Italy

Since June 2000, the Italian Treasury (Tesoro d’Italia) publishes monthly reports withthe stocks and main characteristics of each outstanding bond. Moreover, this institutionprovides annual reports with a government debt breakdown by instrument since 1982 andtime series starting around 1980 with data (stocks and characteristics) on the issuance ofBOT, BTP and CCT securities, the most frequently used. Combining these sources andassuming that all securities issued were paid not earlier than maturity, I construct a de-tailed description of the stocks, promised coupons and maturity of end-of-year outstandingbonds since 199127.

25Also, the debt of special funds was taken over by the Federal government in 1999, but I include it ascentral government debt since 1991 because the ESA95 concept of central government is larger than thecentral state.

26The values reported start in 1995; for 1991-1994 I assigned 90% of quantities in the general governmentbalance sheet because that is the share of outstanding general government securities issued by the centralgovernment subsector in the rest of the 90’s.

27In 1991-1995, the annual amounts of outstanding CCTs are larger than the sums of CCTs not re-deemed and issued after 1990. I used backwards (and recursively) the assumption that annual differencescome from securities issued before 1990.

34

The securities included are: zero-coupon bonds (called BOTs for short-term debt andCTZs for long-term securities) as well as securities yielding fixed coupons (BTPs), flexiblecoupons (CCTs, whose coupon rate applies a spread to the yield of the 6-month BOTissuance celebrated immediately before the beginning of the accrual period) and couponsindexed to the Euribor (called CCTeu) or inflation rates (or BTPi and BTPitalia) issuedby the Italian central government in Italian markets. Their market value is calculatedby discounting principal and coupon payment promises with estimated yields28. Theyrepresent around 95% of all Italian government debt issued in securities; the rest is mainlyissued in foreign currency whose nominal value is added to the market value of thosedenominated in euros.

Yield curves estimates for Italy following the Nelson-Siegel methodology can be found inthe BIS databank starting in 1995. Note that in the estimation before 1998q1 Liborand swap data was used instead of data on government bonds. As a result, I usedyield curve estimates available in Bloomberg for 1994q4-1997q4. For 1991q4-1994q3, Iinterpolated and smoothed data on yields to maturity of BOTs and BTPs. The marketvalue of securities calculated with these yield estimates is compared in Figure B.3 withvalue of Liabilities in securities reported by the OECD’s Italian balance sheet for thecentral government since 199529. Also, residual maturity averages from the OECD’scentral government database (until 2010) and Tesoro d’Italia (for recent values) are shown.However, in the exercise decomposing debt-to-GDP changes, debt in instruments otherthan securities should be taken into consideration. I calculated its value as the differencebetween the nominal values provided by Banca d’Italia30. with the total nominal valueof securities reported by Tesoro d’Italia. This debt represents around one fourth of totaldebt but, since its maturity structure is not specified in the data collected for the paper,its nominal value is simply added to the market value of securities.

A.7 Spain

Data for Spanish outstanding central government bonds is easily accessible at the Bank ofSpain (BdE) website, where Public Debt Market timeseries at daily frequency are availablestarting in 1988. The files used in this paper are labelled sald (outstanding amountsfor each security) and carv (charateristics of each security: coupon rate, maturity date,coupon frequency, etc). Central State debt in securities is issued in Letras (maturingafter 3-18 months), medium-term securities called Bonos (with 2-5 years maturity), and

28Future coupon payments for flexible rate and indexed bonds is calculated assuming perfect knowledgeabout future realizations of their rates or indexes of reference.

29The financial accounts of Italy are also accessible in the database of Banca d’Italia since 1997.30Detailed data since 1997 can be found the database The Public Finances, Borrowing Requirement

and Debt (TCCE0375 - Gross Central Government Debt Position: by instrument, maturity, currencyand residence). For previous values, see the Historical tables Debito delle Amministrazioni pubbliche.

35

long-terms bonds named Obligaciones (with maturity up to 30 years). To the extent ofmy knowledge, Spain issued exclusively fixed-rate debt until June 2014 when it startedissuing inflation-indexed bonds. Each of these securities is unbundled into coupon andprincipal payment promises and priced using the zero-coupon yields estimated by the BdEand available at the BIS databank.

In addition, the Bank of Spain provides data on securities issued by other units alsoclassified as central government: FFPP, FROB, etc. They are stripped and priced also,but their total face value is lower than the quantities reported in Table 12.09 (line 4) of theBdE Statistical Bulletin, therefore the difference is added without specifying its maturitystructure31. The Statistics Bulletin of Tesoro Público, the Spanish Treasury, also reportsdebt in foreign currency whose face value is also added directly to the market value ofsecurities denominated in euros because its maturity structure is unknown.

Figure B.3 compares the model’s value of all securities with the market value of Liabilitiesin securities reported by the OECD’s Spanish balance sheet for the central government32.Also, officially reported residual maturity averages from the OECD’s central governmentdatabase (until 2010) and the Statistics Bulletin from the Spanish Treasury (for recentvalues) are shown. Both series are reasonably well matched.

Finally, the exercise of decomposing debt-to-GDP changes requires values for primarysurpluses in 1991-1994 which have been calculated with information from the NationalStatistical Institute (INE): National Accounts Base 86 (Capacidad o necesidad de finan-ciación + Intereses efectivos). Quarterly data on asset acquisitions is taken from Table12.05 (line 1) of BdE Statistical Bulletin and the value of debt in instruments other thansecurities is calculated as Total liabilities minus Liabilities in securities from the OCDE’sbalance sheet for Spain.

31The series in Table 12.09 of the BdE Statistical Bulletin starts in 1994, so values for 1991-1993 havebeen obtained as the difference of Total securities in Table 21.12 (line 1) and the face value of Bonos,Obligaciones and Valores en monedas distintos del euro (line 12).

32The financial accounts of Spain are also accessible in the website of BdE.

36

B Tables and figures

Table B.1: Annual nominal and real output growth rates

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

US nom 5.5 5.9 4.4 5.8 2.5 -0.2 3.8 4.0 4.6real 3.3 4.4 2.4 2.9 1.0 -1.5 2.2 2.3 2.6

EA nom 4.6 3.5 3.7 4.3 1.2 -0.6 3.1 1.0 3.2real 1.3 2.1 1.7 2.4 -0.1 -2.1 2.1 -0.4 1.3

BE nom 5.0 3.5 3.7 5.0 2.2 0.7 4.1 1.6 3.7real 2.2 2.7 1.7 2.6 0.4 -0.9 2.1 0.0 1.8

FI nom 3.1 6.3 4.5 5.4 1.3 -2.0 4.7 1.2 3.9real 0.8 4.7 2.9 4.2 -0.7 -4.1 3.1 -1.2 2.1

FR nom 2.8 3.4 3.8 4.4 1.5 0.0 3.0 1.4 3.0real 1.3 2.5 1.8 2.3 0.1 -1.6 1.9 0.1 1.5

DE nom 4.8 2.0 1.8 3.1 2.1 -1.1 4.8 2.4 2.7real 1.3 1.6 1.1 2.2 0.7 -2.0 3.7 0.5 1.3

IT nom 5.5 4.5 4.3 3.7 0.1 -1.1 2.0 -0.6 3.3real 1.2 1.5 1.5 1.6 -1.5 -3.3 1.1 -2.1 0.7

ES nom 6.9 6.7 7.8 7.7 -0.5 -0.2 0.0 -1.1 5.2real 1.8 3.9 3.6 3.6 -1.0 -1.5 -0.1 -1.4 2.1

Table B.2: Annual contributions to debt-to-GDP ratio changes (US)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 50.3 38.6 37.2 36.6 74.4 55.2 71.8 74.4 74.4start 48.3 50.3 38.6 37.2 36.6 36.6 55.2 71.8 48.3

ann. ∆debt 0.5 -2.9 -0.4 -0.1 6.3 9.3 8.3 1.3 1.2

prim. deficit 0.9 -2.4 -0.7 1.1 6.4 6.3 8.1 4.8 1.6nom. return 3.4 2.5 2.5 1.5 1.4 1.3 3.5 -0.5 2.1

inflation -1.1 -0.7 -0.7 -1.0 -0.9 -0.5 -0.9 -1.2 -0.9real return 2.3 1.7 1.7 0.5 0.5 0.7 2.5 -1.7 1.2

real growth -1.6 -2.1 -0.9 -1.0 -0.7 0.7 -1.3 -1.7 -1.2resid -1.1 -0.2 -0.6 -0.6 0.1 1.5 -1.1 -0.1 -0.4

37

Table B.3: Maturity of securities and annual debt returns (US)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

(A) Change in mean maturity (in years) and % shares of debt by maturity

TIPs 0.0 1.0 2.2 8.5 7.9 8.5 7.2 7.9 4.3<=1year 37.3 37.6 41.3 36.9 30.8 38.4 28.4 25.6 36.22-4years 30.2 29.8 25.1 26.1 27.6 23.8 28.8 30.1 27.74-7years 11.7 9.8 8.8 9.5 17.0 13.5 18.3 19.1 11.9>7years 20.8 21.8 22.6 18.9 16.7 15.8 17.2 17.2 19.9

∆maturity -0.7 0.8 -1.0 -0.2 0.9 0.0 0.6 0.3 -0.2

(B) Annual return & inflation % rate and excess real return on long-term debt

nominal 7.2 5.0 6.8 4.2 3.0 3.8 5.6 -0.4 5.0inflation 2.2 1.5 2.0 2.9 1.5 1.4 1.6 1.6 2.0

TIPs 0.0 4.0 6.8 4.7 1.8 1.9 7.2 -3.6 3.0real 5.0 3.5 4.8 1.2 1.5 2.4 4.0 -2.0 3.0

of which with residual maturity<=1year 2.6 3.8 1.8 0.5 -0.7 0.5 -1.2 -1.5 1.42-4years 4.2 3.7 4.6 0.5 0.9 2.6 1.4 -1.2 2.64-7years 6.8 3.3 8.1 1.6 3.8 5.0 7.9 -1.6 4.6>7years 12.9 3.1 11.1 4.3 6.0 4.9 18.4 -5.4 7.3excess 10.3 -0.8 9.3 3.8 6.7 4.4 19.6 -3.9 5.9

(C) Annual contribution of real debt returns to debt-to-GDP changes

total 2.03 1.49 1.51 0.44 0.48 0.62 2.38 -1.56 1.12of which with residual maturity<=1year 0.44 0.64 0.23 0.05 -0.15 0.04 -0.21 -0.27 0.22-4years 0.61 0.54 0.42 0.04 0.07 0.23 0.23 -0.26 0.314-7years 0.36 0.16 0.27 0.05 0.23 0.17 0.76 -0.23 0.22>7years 0.67 0.17 0.54 0.21 0.29 0.13 1.35 -0.6 0.37

TIPs 0 0.01 0.09 0.09 0.04 0.05 0.3 -0.22 0.05

38

Table B.4: Annual contributions to debt-to-GDP ratio changes (EA)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 56.6 61.3 61.1 56.0 84.7 68.4 73.1 84.2 83.9start 41.8 57.6 62.3 60.8 55.6 55.7 68.4 72.8 42.9

ann. ∆debt 3.7 0.9 -0.3 -1.2 4.8 6.4 2.3 5.7 1.9

prim. deficit 1.1 -0.9 -0.8 -0.3 1.3 1.5 1.8 0.7 0.2nom. return 4.8 4.0 3.1 1.9 2.8 3.0 1.6 3.6 3.3

inflation -1.6 -1.0 -1.3 -1.2 -0.9 -1.0 -0.7 -1.1 -1.2real return 3.2 3.0 1.8 0.7 1.8 2.1 0.9 2.5 2.1

real growth -0.7 -1.3 -1.0 -1.4 0.2 1.4 -1.3 0.5 -0.8resid 0.2 0.2 -0.2 -0.2 1.5 1.4 1.0 2.0 0.4

Table B.5: Maturity of securities and annual debt returns (EA)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13


<=1year 25.0 20.8 20.4 20.2 22.0 22.2 23.5 20.2 22.01-4years 33.0 34.2 35.0 31.2 29.7 30.4 29.5 29.3 32.24-7years 22.0 23.6 20.1 20.1 17.8 18.2 17.4 17.7 20.3>7years 20.0 21.3 24.6 28.6 30.5 29.2 29.7 32.8 25.4

∆maturity 0.44 0.72 0.16 0.74 -0.17 -0.26 0.21 -0.12 1.99


nominal 9.0 6.0 5.0 2.8 4.1 5.3 2.8 4.2 5.2inflation 3.2 1.3 1.9 1.9 1.3 1.5 1.0 1.4 1.9

real 5.7 4.7 3.1 0.9 2.8 3.8 1.8 2.7 3.3of which with residual maturity<=1year 1.2 1.0 -0.4 -0.8 -0.6 -0.3 -0.5 -1.1 0.01-4years 5.3 3.4 2.2 0.4 1.7 3.2 0.8 0.9 2.54-7years 7.9 6.4 4.2 1.1 4.0 5.6 2.5 3.8 4.6>7years 11.5 10.1 6.5 2.7 6.2 6.9 5.4 6.3 7.3excess 10.3 9.1 6.9 3.4 6.9 7.1 6.0 7.4 7.3


total 2.43 2.49 1.57 0.47 1.68 1.92 0.75 2.30 1.72of which with residual maturity<=1year 0.38 0.18 -0.06 -0.09 -0.09 -0.04 -0.08 -0.14 0.052-4years 0.73 0.62 0.42 0.09 0.31 0.50 0.15 0.26 0.424-7years 0.67 0.81 0.44 0.13 0.42 0.52 0.21 0.51 0.49>7years 0.64 0.88 0.76 0.34 1.04 0.94 0.46 1.67 0.76

39

Table B.6: Annual contributions to debt-to-GDP ratio changes (BE)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 120.4 110.9 103.3 87.4 105.9 100.5 103.5 105.9 105.9debt 112.2 120.4 110.9 103.3 87.4 87.4 100.5 103.5 112.2

ann. ∆debt 2.0 -2.4 -1.9 -4.0 3.1 6.5 1.5 1.2 -0.3

prim. deficit -3.6 -4.4 -4.9 -2.7 0.4 -0.2 0.8 0.6 -2.7nom. return 11.6 6.8 6.1 2.9 4.0 4.7 2.7 4.7 6.1


real growth -2.6 -3.2 -1.8 -2.6 -0.4 0.9 -2.1 -0.1 -2.0resid 0.2 -0.5 1.0 0.6 0.8 2.6 2.2 -2.4 0.5

Table B.7: Maturity of securities and annual debt returns (BE)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13



∆maturity 1.29 0.26 0.09 0.62 1.22 -0.58 0.68 1.12 3.49



real 7.2 4.7 3.6 0.6 2.4 3.5 0.6 3.1 3.6of which with residual maturity<=1year 4.5 2.6 0.9 -0.6 -0.8 0.2 -1.3 -1.3 1.11-4years 7.0 3.9 2.6 0.4 1.7 3.7 0.4 1.0 3.04-7years 9.0 5.5 4.5 0.8 3.9 5.6 1.0 5.1 4.7>7years 9.8 7.0 5.8 1.6 5.2 5.0 2.6 7.9 5.8excess 5.4 4.4 5.0 2.1 5.9 4.8 3.8 9.2 4.7


total 8.33 5.62 3.76 0.66 2.25 3.13 0.62 3.01 3.96of which with residual maturity<=1year 1.71 0.67 0.18 -0.12 -0.20 0.06 -0.34 -0.33 0.392-4years 2.02 1.26 0.73 0.10 0.36 0.76 0.10 0.23 0.854-7years 2.53 1.55 1.09 0.20 0.73 1.03 0.21 0.96 1.18>7years 2.07 2.15 1.76 0.48 1.36 1.28 0.65 2.15 1.54

40

Table B.8: Annual contributions to debt-to-GDP ratio changes (FI)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 75.8 65.6 49.2 34.5 54.1 42.6 49.6 54.1 54.1start 18.7 75.8 65.6 49.2 34.5 34.5 42.6 49.6 18.7

ann. ∆debt 14.3 -2.6 -4.1 -3.7 3.3 4.1 3.5 2.3 1.6

prim. deficit 8.9 0.3 -2.6 -0.5 3.4 2.3 4.2 3.6 2.0nom. return NaN NaN NaN 0.5 0.5 0.4 0.8 0.5 0.5

inflation -1.1 -1.2 -0.9 -0.5 -0.9 -0.8 -0.7 -1.3 -0.9real return NaN NaN NaN 0.0 -0.4 -0.4 0.0 -0.8 -0.2

real growth -0.9 -3.6 -1.7 -1.9 0.2 1.4 -1.4 0.6 -1.4resid NaN NaN NaN -1.4 0.0 0.6 0.6 -1.2 -0.5

Table B.9: Maturity of securities and annual debt returns (FI)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13


<=1year NaN NaN NaN 20.8 24.4 26.7 28.1 18.3 23.01-4years NaN NaN NaN 39.6 32.9 37.3 33.0 28.5 35.64-7years NaN NaN NaN 22.8 21.4 20.6 20.3 23.3 22.0>7years NaN NaN NaN 16.7 21.3 15.4 18.6 29.8 19.4

∆maturity -0.80 0.40 -0.80 0.03 2.55 0.37 0.87 1.31 1.37


nominal NaN NaN NaN 3.0 4.0 5.5 4.4 2.1 3.6inflation 2.2 1.5 1.6 1.2 2.1 2.2 1.5 2.5 1.7

real NaN NaN NaN 1.8 1.9 3.3 2.9 -0.4 0.8of which with residual maturity<=1year NaN NaN NaN 0.6 -1.2 -0.3 -1.0 -2.4 -0.21-4years NaN NaN NaN 1.3 0.6 2.6 0.9 -1.8 0.24-7years NaN NaN NaN 2.1 3.5 5.6 4.5 0.4 1.8>7years NaN NaN NaN 4.0 6.9 8.1 10.4 2.3 6.6excess NaN NaN NaN 3.4 8.2 8.4 11.4 4.7 6.7


total NaN NaN NaN 0.66 0.62 0.95 1.10 -0.20 0.35of which with residual maturity<=1year NaN NaN NaN 0.04 -0.11 -0.03 -0.10 -0.19 -0.012-4years NaN NaN NaN 0.19 0.06 0.28 0.12 -0.22 0.064-7years NaN NaN NaN 0.19 0.24 0.34 0.34 0.04 0.12>7years NaN NaN NaN 0.25 0.43 0.36 0.75 0.17 0.18

41

Table B.10: Annual contributions to debt-to-GDP ratio changes (FR)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 44.0 50.8 58.0 53.8 84.4 68.8 75.5 84.4 84.4start 27.7 44.0 50.8 58.0 53.8 53.8 68.8 75.5 27.7

ann. ∆debt 4.1 1.7 1.8 -1.0 5.1 7.5 3.3 4.5 2.6

prim. deficit 2.8 0.9 1.1 0.8 2.9 3.3 3.4 1.9 1.8nom. return 2.2 2.4 2.5 1.5 2.7 2.9 2.5 2.6 2.3


real growth -0.5 -1.2 -1.0 -1.3 -0.2 1.0 -1.3 -0.1 -0.8resid 0.1 0.1 0.2 -0.8 0.6 1.2 -0.4 1.1 0.1

Table B.11: Maturity of securities and annual debt returns (FR)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13



∆maturity 0.07 -0.07 -0.45 1.33 -0.13 -0.47 0.48 -0.14 0.74



real 6.9 4.8 3.4 0.7 3.0 4.1 2.6 2.5 3.7of which with residual maturity<=1year 1.3 0.5 -0.7 -1.2 -0.9 -0.6 -0.9 -1.3 -0.31-4years 7.0 3.6 2.5 0.6 1.5 3.5 1.0 0.1 2.94-7years 8.7 5.2 4.2 0.9 4.1 5.8 3.6 3.0 4.6>7years 9.7 7.2 5.5 1.9 5.9 6.4 5.7 5.8 6.0excess 8.4 6.7 6.1 3.1 6.9 7.0 6.6 7.0 6.3


total 1.80 2.00 1.58 0.39 1.83 2.07 1.73 1.69 1.55of which with residual maturity<=1year 0.06 0.04 -0.06 -0.11 -0.13 -0.06 -0.14 -0.17 -0.052-4years 0.47 0.39 0.33 0.09 0.23 0.50 0.18 0.01 0.304-7years 0.49 0.52 0.48 0.12 0.43 0.53 0.41 0.36 0.41>7years 0.78 1.06 0.83 0.29 1.30 1.10 1.29 1.50 0.89

42

Table B.12: Annual contributions to debt-to-GDP ratio changes (DE)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 36.1 40.1 40.8 40.7 53.0 47.6 55.1 53.0 53.0start 22.7 36.1 40.1 40.8 40.7 40.7 47.6 55.1 22.7

ann. ∆debt 3.4 1.0 0.2 0.0 2.0 3.4 3.8 -1.1 1.4

prim. deficit 1.8 0.0 -0.6 0.2 0.1 -0.1 1.1 -0.6 0.3nom. return 2.5 1.8 2.0 1.3 1.9 2.3 2.9 0.5 1.9

inflation -0.9 -0.2 -0.3 -0.4 -0.7 -0.4 -0.6 -1.0 -0.5real return 1.6 1.6 1.7 0.9 1.2 1.9 2.3 -0.5 1.4

real growth -0.4 -0.6 -0.4 -1.0 -0.4 0.9 -1.9 -0.3 -0.5resid 0.4 -0.1 -0.5 -0.2 1.1 0.8 2.3 0.3 0.2

Table B.13: Maturity of securities and annual debt returns (DE)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13



∆maturity -0.24 0.87 0.26 0.29 -0.05 -0.37 0.15 0.17 1.12



real 5.5 4.4 4.2 1.9 2.6 4.5 4.4 -1.1 3.6of which with residual maturity<=1year -0.7 1.1 0.6 0.2 -0.9 0.1 -0.8 -1.9 0.01-4years 3.1 2.8 3.0 1.3 0.7 3.0 0.8 -1.7 2.04-7years 6.9 5.7 5.1 1.9 3.3 6.0 4.7 -0.8 4.5>7years 14.3 10.0 9.2 4.4 8.3 9.9 15.0 0.1 9.2excess 15.0 8.8 8.5 4.2 9.2 9.7 15.9 2.0 9.1


total 1.27 1.35 1.51 0.75 1.10 1.78 2.06 -0.55 1.19of which with residual maturity<=1year -0.01 0.06 0.04 0.02 -0.09 0.01 -0.10 -0.18 -0.012-4years 0.31 0.37 0.45 0.18 0.10 0.43 0.13 -0.27 0.274-7years 0.37 0.47 0.36 0.16 0.28 0.48 0.43 -0.06 0.32>7years 0.60 0.46 0.66 0.39 0.81 0.86 1.60 -0.03 0.60

43

Table B.14: Annual contributions to debt-to-GDP ratio changes (IT)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 101.0 104.9 97.6 92.5 124.7 107.9 101.7 124.7 124.7start 84.4 101.0 104.9 97.6 92.5 92.5 107.9 101.7 84.4

ann. ∆debt 4.1 1.0 -1.8 -1.3 5.4 7.7 -3.1 11.5 1.8

prim. deficit -1.8 -4.6 -2.6 -1.2 -0.8 -0.6 -0.1 -1.6 -2.1nom. return 12.7 10.1 5.7 3.6 4.7 5.3 -0.7 9.5 7.1

inflation -4.0 -3.1 -2.8 -2.0 -1.6 -2.2 -0.9 -1.7 -2.6real return 8.8 6.9 2.8 1.6 3.1 3.1 -1.6 7.9 4.5

real growth -1.3 -1.6 -1.5 -1.6 1.5 3.2 -1.2 2.3 -0.7resid -1.2 0.6 -0.5 0.0 1.5 1.8 -0.3 2.8 0.2

Table B.15: Maturity of securities and annual debt returns (IT)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13



∆maturity 1.81 0.75 0.50 0.80 -0.36 0.33 -0.06 -0.63 3.49


nominal 11.4 8.6 4.9 2.9 4.3 5.3 -1.6 9.3 6.2inflation 4.2 2.9 2.8 2.1 1.6 2.3 0.9 1.5 2.6

real 7.2 5.6 2.1 0.8 2.8 2.9 -2.4 7.8 3.6of which with residual maturity<=1year 4.9 1.7 -0.9 -1.0 -0.6 -0.8 -0.3 -0.7 0.71-4years 8.4 4.8 2.0 0.6 2.8 3.0 0.5 4.8 3.64-7years 9.5 9.2 3.8 1.2 4.3 4.9 -2.3 10.3 5.5>7years 10.9 15.1 4.8 2.6 4.5 4.6 -5.8 14.6 7.3excess 5.9 13.4 5.6 3.5 5.1 5.4 -5.6 15.3 6.6


total 5.26 5.06 1.87 0.66 2.44 2.40 -2.31 7.23 3.00of which with residual maturity<=1year 1.53 0.54 -0.20 -0.18 -0.12 -0.15 -0.05 -0.15 0.272-4years 1.91 1.43 0.70 0.15 0.69 0.71 0.13 1.24 0.954-7years 1.42 1.81 0.58 0.20 0.57 0.61 -0.35 1.45 0.89>7years 0.40 1.29 0.79 0.49 1.29 1.23 -2.04 4.69 0.89

44

Table B.16: Annual contributions to debt-to-GDP ratio changes (ES)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13

end 56.7 56.2 44.8 32.9 99.6 51.7 62.4 99.6 99.6start 40.5 56.7 56.2 44.8 32.9 32.9 51.7 62.4 40.5

ann. ∆debt 4.1 -0.1 -2.9 -3.0 11.1 9.4 5.3 18.6 2.7

prim. deficit 1.5 0.2 -0.8 -1.4 4.3 5.4 3.0 4.6 1.1nom. return 2.7 3.2 2.3 1.1 2.1 1.5 0.5 4.1 2.2

inflation -2.4 -1.6 -2.1 -1.7 -0.2 -0.4 0.0 -0.3 -1.5real return 0.3 1.6 0.2 -0.6 1.8 1.1 0.5 3.8 0.8

real growth -1.0 -2.4 -1.9 -1.5 0.6 0.6 0.0 1.0 -1.1resid 3.2 0.5 -0.4 0.4 4.4 2.3 1.8 9.1 1.9

Table B.17: Maturity of securities and annual debt returns (ES)

year 91-95 95-99 99-03 03-07 07-13 07-09 09-11 11-13 91-13



∆maturity 1.47 2.38 0.83 0.85 -1.23 -0.48 0.01 -0.76 4.31



real -0.6 3.1 0.7 -1.4 3.2 3.4 0.6 5.7 1.3of which with residual maturity<=1year -0.8 0.0 -2.6 -2.6 0.6 0.1 0.8 0.9 -0.91-4years 2.2 2.2 -0.8 -2.6 2.7 3.2 1.2 3.6 0.94-7years 5.7 6.6 2.1 -1.1 5.1 5.4 2.3 7.6 3.8>7years 6.6 9.2 3.6 -0.1 4.7 4.5 -0.8 10.4 4.8excess 7.4 9.2 6.2 2.5 4.1 4.4 -1.6 9.5 5.7


total 0.32 1.42 0.32 -0.49 1.63 1.05 0.35 3.48 0.73of which with residual maturity<=1year -0.13 0.02 -0.22 -0.17 0.08 0.01 0.10 0.12 -0.072-4years 0.20 0.25 -0.12 -0.26 0.40 0.29 0.19 0.73 0.124-7years 0.01 0.46 0.14 -0.08 0.41 0.32 0.18 0.75 0.21>7years 0.24 0.69 0.52 0.03 0.74 0.43 -0.11 1.89 0.47

45

Table B.18: Debt-holders shares (Bruegel)

Impact onResidents CB Non-residents non-residents

US 66.1 % (10.70 %) 33.9 % 0.57 %EA 40.1 % NaN 59.9 % 2.42 %BE 53.5 % (1.80 %) 46.5 % 2.78 %FI 9.0 % (0.10 %) 91.0 % 2.81 %FR 41.0 % NaN 59.0 % 2.78 %DE 39.6 % (0.20 %) 60.4 % 1.68 %IT 61.1 % (5.70 %) 39.0 % 1.85 %ES 66.9 % (3.80 %) 33.1 % 1.48 %

Bruegel database of sovereign bond holdings,Merler and Pisani-Ferry (2012)

46

10

20

3091 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

0

2

4

6

8

10

12

x 104

years

Belgium (BE)m

illio

ns

10

20

3091 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x 104

years

Finland (FI)

mill

ion

s

10

20

3091 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

0

0.5

1

1.5

2

2.5

3

3.5

x 105

years

France (FR)

mill

ion

s

10

20

3091 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

0

0.5

1

1.5

2

2.5

3

x 105

years

Germany (DE)

mill

ion

s

10

20

3091 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

0

0.5

1

1.5

2

2.5

3

3.5

4

x 105

years

Italy (IT)

mill

ion

s

10

20

3091 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x 105

years

Spain (ES)

mill

ion

s

Figure B.1: Stripped payment obligations by residual maturity

47

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10Belgium (BE)

1year4year7year10year

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6Finland (FI)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10France (FR)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

2

4

6

8

10Germany (DE)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

2

4

6

8

10

12

14

16

18Italy (IT)


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

2

4

6

8

10

12

14Spain (ES)


Figure B.2: Estimate of yield to maturity by country

48

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5x 10

5 Belgium (BE)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10Market value of liabilities (official)Market value of liabilities (model)Face value of liabilitiesAverage maturity (official)Average maturity (model)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 135

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10x 10

4 Finland (FI)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10Market value of bonds (official)Market value of bonds (model)Face value of bondsAverage maturity (official)Average maturity (model)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

6 France (FR)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 132.5

3.75

5

6.25

7.5

8.75

10

11.25

12.5

13.75

x 105 Germany (DE)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4x 10

6 Italy (IT)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9


91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130.8

1.6

2.4

3.2

4

4.8

5.6

6.4

7.2

8

8.8x 10

5 Spain (ES)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9


Figure B.3: Comparison of official market value of bonds and average maturity with model values

49

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−2

−1

0

1

2

3

4x 10

4 Belgium (BE)

∆ DebtDeficitReturnResid∆ Asset

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−1

−0.5

0

0.5

1

1.5

2x 10

4 Finland (FI)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−0.5

0

0.5

1

1.5

2

2.5x 10

5 France (FR)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3x 10

5 Germany (DE)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−1

−0.5

0

0.5

1

1.5

2

2.5x 10

5 Italy (IT)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−0.25

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25x 10

5

mill

ion

s

Spain (ES)


Figure B.4: Sources of debt changes derived from budget constraint

50

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−4

−2

0

2

4

6

8

10Primary deficit to GDP (in %)

US prim. Deficit to GDPEA prim. Deficit to GDP

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−2

−1

0

1

2

3

4

5

6

7Nominal debt returns to GDP (in %)

US nom. returns to GDPEA nom. returns to GDP

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−20

−10

0

10

20

30

40

%

One−period real rate of return (US)

<=1y>7yTIPsall

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−6

−4

−2

0

2

4

6

8

10

12Primary deficit to GDP (in %)

BEFIFRDEITES

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−5

0

5

10

15

20Nominal debt returns to GDP (in %)

BEFIFRDEITES

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−15

−10

−5

0

5

10

15

20

25

30

%

One−period real rate of return (EA)

<=1y>7yall

Figure B.5: Evolution of debt, (primary) deficits and return payments to GDP ratios

51

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−4

−2

0

2

4

6

8Nominal output growth (in %)

US GDP growthEA GDP growth

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

0.5

1

1.5

2

2.5

3

3.5

4

4.5Inflation rate (in %)

US inflationEA inflation

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−5

−4

−3

−2

−1

0

1

2

3

4

5Real output growth (in %)

US real GDP growthEA real GDP growth

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−8

−6

−4

−2

0

2

4

6

8

10

12Nominal output growth (in %)

BEFIFRDEITES

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−1

0

1

2

3

4

5

6

7

8Inflation rate (in %)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−13

−11

−9

−7

−5

−3

−1

1

3

5

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−10

−8

−6

−4

−2

0

2

4

6

8Real output growth (in %)

BEFIFRDEITES

Figure B.6: Nominal GDP growth, inflation and real GDP growth rates

52

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−4

−2

0

2

4

6

8

10

12

14

16Belgium (BE)

Av. nom.ReturnAv. real ReturnInflationreal GDP growth

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−10

−8

−6

−4

−2

0

2

4

6

8Finland (FI)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−5

0

5

10

15

20France (FR)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−6

−4

−2

0

2

4

6

8

10

12

14Germany (DE)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−10

−5

0

5

10

15

20

25Italy (IT)


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−6

−4

−2

0

2

4

6

8

10

12Spain (ES)


Figure B.7: Average return, inflation and real output growth rates

53

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100Belgium (BE)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

<=1y <=4y <=7y <=10y

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100Finland (FI)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

<=1y <=4y <=7y <=10y

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100France (FR)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

<=1y <=4y <=7y <=10y

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100Germany (DE)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

<=1y <=4y <=7y <=10y

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100Italy (IT)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

<=1y <=4y <=7y <=10y

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

10

20

30

40

50

60

70

80

90

100Spain (ES)

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130

1

2

3

4

5

6

7

8

9

10

<=1y <=4y <=7y <=10y

Figure B.8: Nominal debt by residual maturity and average maturity

54

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−10

−5

0

5

10

15

20

25Belgium (BE)

<=1y1−4y4−7y>7y

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−6

−4

−2

0

2

4

6

8

10

12Finland (FI)

<=1y1−4y4−7y>7y

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−15

−10

−5

0

5

10

15

20

25

30France (FR)

<=1y1−4y4−7y>7y

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−15

−10

−5

0

5

10

15

20

25

30Germany (DE)

<=1y1−4y4−7y>7y

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−20

−10

0

10

20

30

40Italy (IT)

<=1y1−4y4−7y>7y

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−15

−10

−5

0

5

10

15

20

25

30Spain (ES)

<=1y1−4y4−7y>7y

Figure B.9: One-period real rate of return by residual maturity

55

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−30

−20

−10

0

10

20

30

40

50Belgium (BE)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

2

3

4

5

6

7

8

9Excess return >7y to <=1Excess return 4−7y to <=1Excess return 1−4y to <=1Average maturity

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−30

−20

−10

0

10

20

30

40

50Finland (FI)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

2

3

4

5

6

7

8


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−30

−20

−10

0

10

20

30

40

50France (FR)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

2

3

4

5

6

7

8


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−20

−10

0

10

20

30

40Germany (DE)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 132

3

4

5

6

7


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−30

−20

−10

0

10

20

30

40

50Italy (IT)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 131

2

3

4

5

6

7

8


92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13−20

−10

0

10

20

30

40Spain (ES)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 132

3

4

5

6

7


Figure B.10: Excess rate of real return of long-term debt with short-term

56

91 92 93 94 95 96 97 98 990

2

4

6

8

10

12

14

16Spain (ES)

1year4year7year10yearInflation

81 82 83 84 85 86 87 88 890

2

4

6

8

10

12

14

16United States (US)


91 92 93 94 95 96 97 98 990

2

4

6

8

10

12

14

16Italy (IT)


91 92 93 94 95 96 97 98 991.5

2

2.5

3

3.5

4

4.5

5

5.5Average debt maturity in years (ES)

only principalsprincipal & coupons

81 82 83 84 85 86 87 88 893.5

4

4.5

5

5.5

6

6.5

7Average debt maturity in years (US)


91 92 93 94 95 96 97 98 992.5

3

3.5

4

4.5

5

5.5

6Average debt maturity in years (IT)


Figure B.11: Comparison yield and inflation rates (and average debt maturity) for US, ES and IT

57

sovereign debt maturity and debt-to-gdp dynamics …...ecares ulb - cp 114/04 50, f.d. roosevelt...

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