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  • 1, International Monetary Fund
  • | 2, International Monetary Fund
  • | 3, International Monetary Fund
  • | 4, International Monetary Fund


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Appendix 1: Sovereign debt as collateral

In this appendix, we show that nothing substantial changes if sovereign debt can also be pledged as collateral. Assume, for instance, that the credit constraint of Equation (4) is given by:


In this case, we have that the law of motion takes the following form:


where k¯t+1 is now defined as follows:


There are two key differences with Equations (9)-(10) in the main body of the paper. The first is that ϕ no longer shows up in the first flat of the law of motion, (αρ/pt+1+δ1)11α. The reason is that, once capital and debt can be equally pledged as collateral, ϕ does not affect the relative return of both assets. The second difference is that dt is no longer pre-multiplied by ρρϕ. This relects the assumption that investors can borrow against the debt they hold, which provides additional resources for investment. These are the only changes to our baseline model and they do not affect any of our main results.

Appendix 2: Taxing investment

We assume throughout the paper that the government taxes only consumption. This assumption is convenient but it does not affect our main results. Its main implication is that all taxes are paid by the old and the impatient young. If the patient young also paid some taxes, their wealth would be reduced and, as a result, so would their investment. To see how this innovation would affect our model, we use ι to denote the share of taxes that are paid by the patient young. Then, we just need to modify the law of motion as follows:


where k¯t+1 is now deined as:


The main difference with Equations (9)-(10) is the appearance of the new term −ιxt. Taxing the young means that sovereign debt has two effects on investment and growth when compared to the economy without government in Equation (5): the crowding-out effect that we emphasize in the main text and a wealth effect. Both lower investment and growth, for different reasons. The crowding-out effect arises because sovereign debt displaces investment from the portfolio of investors, and its size depends on the importance of discrimination, pt. The wealth effect arises because taxation reduces the portfolio of investors, and its size depends on the distribution of taxes, ι. Thus, adding taxes on investment reinforces the notion that sovereign debt reduces investment and growth.

Appendix 3: Long-term bonds

In this appendix, we examine the implications of having different types of debt. We start by assuming that there are two types of debt: (i) a short-term bond issued in period t at price one that promises a payment Rt+1S in period t + 1; and (ii) a long-term bond issued in period t also at price one that promises a payment of Rt+2L in period t + 2. We define qt+1 as the price of this long-term bond one period before maturity (or one period after issuance). As usual, defaulting on short-term bonds automatically implies default on long-term bonds.

Assume first that the government defaults on both domestic and foreign creditors, i.e. ptF=ptD=0. This means that all bonds held by domestic and foreign creditors become worthless. This implies that:


In period t, creditors can choose among short-term bonds and long-term bonds that mature in periods t+1 and t+2. Equation (27) says that all these bonds must offer the same expected return and, since the international financial market is risk-neutral, this expected return must equal the interest rate ρ. Under these circumstances, all bonds are perfect substitutes from the perspective of both domestic and foreign creditors. The presence of different maturities does not change the analysis, and the law of motion of the economy is still given by Equation (5). Thus, in the absence of discrimination, introducing long-term bonds does not affect the dynamics of the economy.

Assume now that the government defaults on foreign creditors only, i.e. ptF=0 and ptD=1pt. This means that all bonds held by foreign creditors become worthless. What happens to the different bonds held by domestic creditors in a default? In the main text, there are only short-term bonds and we make the assumption that domestic creditors receive the contractual rate Rt+1S. A natural assumption would be that long-term bonds that mature in the same period are also paid the contractual rate Rt+1L. This means that all maturing bonds held by domestic creditors are perfect substitutes and, as a result, we have that:


Equation (28) says that, if the return to investment net of financing costs exceeds the expected return on maturing bonds, the domestic private sector does not buy the maturing debt and the marginal buyer is a foreign creditor. If instead the return to investment net of financing costs falls short of the expected return on maturing bonds, the domestic private sector buys the maturing debt and the marginal buyer is a domestic creditor.

What happens to non-maturing bonds held by domestic creditors in a default? Let vt+1 be the price that these creditors receive as a share of the price that these bonds would have had in the absence of default. Then, we have that:


Equation (29) is analogous to Equation (28). It says that if the return to investment net of financing costs exceeds the expected return on non-maturing bonds, the domestic private sector does not buy the non-maturing bonds and the marginal buyer is a foreign creditor. If instead the return to investment net of financing costs falls short of the expected return on non-maturing bonds, the domestic private sector buys the maturing bonds and the marginal buyer is a domestic creditor.

If vt+1 = 1, domestic creditors recefive the same from these bonds regardless of whether or not there is a default. Maturing and non-maturing bonds are thus treated equally and, as a result, they become perfect substitutes and their expected returns are equalized always. In this case, introducing long-term bonds does not affect the analysis in the main text. In particular, the law of motion is still given by Equations (9)-(10). This confirms that our model is unaffected by the maturity structure of debt under two conditions: (i) when the government defaults, it does so simultaneously on all maturities, and; (ii) in the event of a default, bonds of all maturities are treated equally.

The introduction of different maturities only affects the analysis if they are treated asymmetrically in the event of a default. Assume, for instance, that non-maturing bonds are paid at face value, i.e. Rt+2L if the default occurs in period t+1. It follows that vt+1=Rt+2Lqt+11>1, because the bond pays at face value but one period before the original maturity. This means that non-maturing bonds are treated better than maturing bonds in the event of a default and, as a result, they are more attractive to domestic creditors. Under this assumption, the law of motion becomes:


where dtN is the non-maturing debt and k¯t and k¯t are defined as:


The main difference with Equations (9)-(10) is the appearance of an additional step in the crowding-out region. The intuition is simple. If ktk¯t domestic creditors purchase only non-maturing debt, if any, because the return to investment is high. If k¯t<kt<k¯t the return to investment is lower and domestic creditors purchase the entire stock of non-maturing debt along with some maturing debt. If ktk¯t, the return to investment is so low that domestic creditors purchase the entire stock of debt, both maturing and non-maturing. In this particular example, then, long-term debt enlarges the crowding-out region and thus the crisis zone.

Appendix 4: Data description

To support the analysis on the paper, whenever possible, we collected a database comprising seven Euro Area countries (Germany, France, Italy, Spain, Portugal, Ireland and Greece) for the period 2000-2012. Almost all data series cover the full sample period, but a few cover only until 2010. The data contains information on GDP and GDP growth, spreads, public debt and deficits and their components, banks’ allocation of credit by sector, sovereign debt holdings by residence and sector, and public debt maturity structure. The data on nominal GDP used throughout the empirical part was obtained from Eurostat. A detailed description of the rest of the data sources is presented in what follows.

Spreads: We collected data on public and private spreads. For sovereign spreads, we used quarterly data from Datastream. The spreads equal the difference in yield between the corresponding reference 10-year bond and the German 10-year Bund. Information on private-sector spreads was derived separately for corporates and households. Data on yields on corporate loans and consumption loans for households come from Haver Analytics. Corporate yields refer to loans above 1 million euro and maturities between 1 and 5 years for all countries but Greece, where long time series were only available for loans of maturities up to one year, and Ireland and Portugal, where loans of all maturities are pooled. Household yields refer to loans with maturities between 1 and 5 years for all sample countries. Private spreads are also calculated against the benchmark 10-year German Bund. All spreads presented in Figure 1, 4, 6 and 8, are measured in basis points (Bps).

Public debt, public deficit and subcomponents: Figure 2 represents a decomposition of both public debt and deficits. Data, on an annual basis, was obtained from the OECD’s Economic Outlook Database. More specially, from this source we gathered the following general-government series: financial balance; cyclically-adjusted balance; underlying balance adjusted for the cycle and one-offs; underlying primary balance adjusted for the cycle and one-offs and excluding net interest payments (i.e. the structural primary balance), net debt interest payments, and gross financial liabilities (i.e. public debt). Using these variables, we calculated the general government primary balance by subtracting net debt interest payments from the financial balance. Additionally, we disaggregated the primary balance into the structural primary balance component (underlying primary balance) and the cyclical primary balance component. The cyclical primary balance was derived by subtracting from the primary balance the underlying primary balance and one-offs. One-offs, in turn, are the difference between underlying balance and cyclically-adjusted balance. The other adjustments category was obtained by subtracting the interest component, growth component, cyclical component and structural component from the change in public debt.

Government debt maturity structure: In order to gauge the relevance of public debt maturity we collected data on government debt average term to maturity (Figure 3a) and short-term debt as a percent of total debt (Figure 3b). The data on average term to maturity comes from the OECD for Ireland and Germany, from the Ministry of Finance for Spain, and from the ECB for the France, Portugal, Italy, and Greece. The OECD’s dataset unfortunately ends in 2010, so for Ireland and Germany it does not cover our intended time span. Short-term debt refers to gross government debt with residual maturities up to one year. The term government debt refers to general government debt for all countries apart from Ireland, which refers to central government debt. End-of-the-year data for Germany, France, Spain, Greece, Italy and Portugal comes from the European Central Bank. Quarterly data for Ireland comes from the Central Bank of Ireland.37

Sovereign debt holdings: In order to understand the nationality of the agents holding the outstanding sovereign debt we resorted to a variety of sources feeding from our sample-countries Central Banks. We combined various sources as our interest was in obtaining, whenever possible, information regarding nominal holdings, avoiding mark to market measures which can be significantly affected by price dynamics.38 More speciically, data on sovereign debt holdings of France, Germany, Greece, Ireland and Italy comes from Merler and Pisani-Ferry (2012). In turn, data on sovereign debt holdings of Spain and Portugal comes from Andritzky (2012). Data for Spain was complemented using information from the Bank of Spain. Unfortunately the definition of sovereign debt is not homogeneous among countries. Sovereign debt holdings refer to central government OATs (medium-long term securities) for France, to general government debt for Germany, to central government long term bonds for Ireland, and to central government securities for Spain, Greece, Italy and Portugal. As shown in Figure 5, the data on holdings by residents comes disaggregated by different economic agents. In order to present the data using a foreign-domestic divide, as in Figure 4, we added together the corresponding categories of resident debtholders.39

Allocation of bank credit by sector: In order to understand the allocation of credit among the different economic sectors we resorted to each country’s National Central Banks’ Monetary Surveys. From these surveys we obtained data on bond holdings and loan provisioning by banks vis-a-vis the following sectors: non-financial corporations, households and the public sector. In order to get the total credit exposure by sector we added the information on bond holdings and loans provided to each sector. The data was collected on a monthly format for Germany, France, Italy and Greece, and on a quarterly fashion for Spain, Ireland and Portugal. We used quarterly data on nominal GDP from Eurostat to calculate bank credit as percentage of GDP. This set of data was used to construct Figures 7 and 8. While Figure 7 simply depicts our credit series by sector, Figure 8 presents a ratio of public-sector credit to private-sector credit. We derfived such ratio by dividing credit to the general government (loans plus bonds) by the sum of credit to non-financial corporations (bonds plus loans) and credit to households (loans). In France, the existing data for monetary financial institutions prevented us from separating data on loans for households and non-financial corporations. For that reason we used instead information for credit institutions.


We thank Tom Schmitz and Beatriz Urquizu for excellent research assistance. We received valuable comments from Mark Wright and participants at presentations held at the Bank of Spain, Carnegie-Rochester-NYU conference, Harvard, MIT, Princeton, and World Bank. We acknowledge financial support from the Spanish Ministry of Science and Innovation, the Spanish Ministry of Economy and Competitiveness Severo Ochoa Program, the Generalitat de Catalunya, and the European Research Council (Starting Grant FP7-263846 and Advanced Grant FP7-249588). The paper was partly written while Broner was visiting MIT and while Martin was a Research Fellow at the IMF.


Of course, there was more heterogeneity among GIIPS’ economies than this description suggests. In particular, Portugal and Italy were growing more slowly, Portugal and Greece had larger deficits, and Italy and Greece had larger public debts.


Brutti and Sauré (2013) have emphasized this aspect of the crisis and carefully documented it. Arslanalp and Tsuda (2012) and Merler and Pisani-Ferry (2012) have also noticed this pattern. More generally, Broner et al. (2013) show that periods of financial turbulence are often accompanied by a reduction in gross capital flows, in which foreigners reduce their purchases of domestic assets and domestic residents reduce their purchases of foreign assets.


Additionally, the ECB has modified its collateral rules to accept lower rated sovereign debt, provided liquidity through the Long-Term Repurchase Operations (LTRO), and even announced (on August 2012) the possibility of purchasing unlimited amounts of sovereign securities through Outright Monetary Transactions (OMT).


Our narrative has been, per force, short and focused on the elements that we emphasize later in the theory. See Ardagna and Caselli (2012), Lane (2012) and Shambaugh (2012) for detailed and very useful descriptions of the European sovereign debt crisis. See also the many references therein for further details. Bolton and Jeanne (2011), Catão et al. (2012), Roch and Uhlig (2012), and Conesa and Kehoe (2013) also use formal models to study this episode.


Sturzenegger and Zettelmeyer (2007), Cruces and Trebesch (forthcoming), and Erce (2012 and forthcoming) document the existence of breaches in inter-creditor equity during sovereign defaults, and that domestic residents are more likely to be treated preferentially. Erce (2012) points to three additional determinants of discrimination: the composition of debt, the health and size of the financial sector, and the private sector’s reliance on external sources of finance.


The assumption that the loss imposed by creditors is increasing in the size of the economy is standard in the literature. This would be the case if, for example, defaults lead to lower productivity or, in a richer model, an increase in the cost of trading goods with foreigners.


Consistent with the evidence presented by Cruces and Trebesch (forthcoming), we assume that penalties are increasing in the size of the default.


Examples of such operations include governments borrowing to finance bank recapitalization programs or privatizations. In these cases there is a change in gross assets and liabilities but not in net assets so that it does not appear in official deicit statistics. In the case of bank recapitalizations, if and when losses are realized they will affect the deicit.


The data on government finances comes from the OECD’s Economic Outlook Database and the data on nominal GDP from Eurostat.


Our measure of deficit includes a variety of factors that partially obscures its interpretation. First, a decomposition of deficit into structural and cyclical (using OECD data) shows that GIIPS’high deficits are almost solely explained by their cyclical component, reinforcing our observation that debt dynamics are driven by the deep recessions they face. In fact, fiscal austerity in these countries has eliminated their structural deficits by now. Second, the very low deicit in Greece relects the reduction in debt due to its restructuring. Third, our measure of deficits have been especially large due stock-low adjustments in those countries that spent substantial resources recapitalizing their banks.


The data on average maturity is from the ECB, the OECD, and the Spanish Ministry of finance. The data on short-term debt is from the ECB, the Irish Central Bank, and the Spanish Ministry of Finance.


National sources include Treasuries and Central Banks. For Greece the only data available mixes nominal and market prices. For France, the non-financial and public domestic sectors cannot be disentangled.


Several recent papers have also analyzed the behavior of sovereign debt holdings for GIIPS, including IMF’s Global Financial Stability Report (2011), Arslanalp and Tsuda (2013), and Brutti and Sauré (2013). These papers combine data from the IMF’s International Financial Statistics on domestic sovereign debt holdings with data from the BIS on public debt holdings by non-resident banks. An advantage of these data sources is that the BIS data is bilateral. This allows Brutti and Sauré (2013) to analyze the differential behavior of banks within and outside the Euro area. A disadvantage of these data sources is that debt is valued at market prices, making it difficult to disentangle changes in portfolios due to trading and price changes. Arslanalp and Tsuda (2013) adressed this problem by converting the data back to face value using each countries’s reported valuation method.


These data are from each country’s Financial Accounts and from their National Central Banks’ Monetary Surveys. We also use 10-year sovereign bond spreads from Datastream.


Since spreads are computed relative to German bonds, the spread is zero by definition for Germany.


In Greece the ratio of public to private credit fell with the sovereign debt restructuring in 2012, but it has started to increase again since then. In Germany there was also an increase credit to the public in 2008 due to the need to recapitalize banks after the subprime crisis, but this was reversed soon afterwards.


For instance, the private sector cannot pledge future output, but it can pledge some undepreciated capital. Under this interpretation, we have that ϕ∈ [0,1-δ].


When the constraint is binding, we have that ft=ϕkt+1ρ and kt+1=sktα+ft. Combining these observations, we find the maximum attainable investment.


We only consider paths of xt that ensure that the debt never explodes.


For instance, if xt = x and pt= p, the maximum debt that the government can issue is pρpx. And the welfare of taxpayers declines by x. The path of kt is unaffected, though. This is due to our assumption that taxation does not affect investment. Appendix 1 relaxes this assumption and shows that this does not affect our main results, though.


While the presence of a credit constraint is crucial for our results, its specific form is not. Appendix 2 shows the case in which sovereign debt can also be pledged as collateral.


We shall choose one specific way to do this in Section 4 below.


For a more thorough discussion see Broner et al. (2010).


Appendix 3 extends our model to the case of different maturities. It also identifies sufficient conditions for the valuation wedge to be the same for all maturities: (i) when the government defaults, it does so simultaneously on all maturities, and; (ii) in the event of a default, bonds of all maturities are treated equally.


These dynamics are all conditional on default not taking place, of course. Technically, once default occurs the debt goes to zero and the economy behaves as the baseline model of section 2.1. This only shows that our model has been designed to study the macroeconomic effects of a positive probability of default. It has not been designed to study the aftermath of default.


When governments cannot discriminate between domestic and foreign creditors they might repay foreigners to avoid the cost of domestic default. This effect is absent here because we are ignoring costs of domestic defaults.


Unlike other models in the sovereign-debt literature (and reviewed in the introduction), the maturity structure of debt is basically irrelevant here. To understand why this is the case, consider a government that has issued debts of different maturities. If expectations are pessimistic, foreign creditors can sell both maturing and non-maturing debts to domestic creditors. Thus, the potential for crowding-out depends on the full amount of debt, not only on maturing debts. We show this in Appendix 3 where we extend the model to the case of different maturities.


Once again, we remind the reader that these dynamics are all conditional on default not taking place.


Another manageable approach would be to re-interpret the model developed so far as a model for the union and define member countries as subsets of the population. This alternative approach assumes that goods and factors markets are so integrated that wages and rental rates are equalized across the union.


To simplify the discussion, we ignore the possibility of multiple equilibrium. That is, we assume that default penalties are negligible.


This is actually the way both the EFSF and the ESM work. These institutions use the combined guarantee of the various Euro Area countries to borrow at low rates and provide loans to stressed countries at a cost below their respective market rates.


Even in this case, of course, it must be that RS,t+1ρU,t+1pU because otherwise the union’s private sector would demand debt.


In its European edition of December 2nd, 2010 The Economist dedicated a full-length article to this possibility.


For a detailed description of these debt-purchase programs see


Although less explicitly, bond purchases under the earlier ECB’s SMP program and the current ESM play a similar role.


In this paper, we have emphasized the crowding-out effects of domestic purchases of government debt before maturity because they provide a natural explanation for many aspects of the European crisis. But, in some cases, these purchases can have countervailing effects. For example, if it is difficult to discriminate between domestic and foreign creditors a higher share of debt held domestically can reduce the incentives to default.


Specifically, we used the Statistical Appendix - Section E - Table E.1 Government Debt, from the Irish Central Bank Quarterly Bulletin.


Actually, the data is nominal value for all countries but Greece where, according to the Bank of Greece, it mixes market and nominal values.


For Ireland and Spain the data on holdings by financial institutions includes the Central Bank.

Sovereign Debt Markets in Turbulent Times: Creditor Discrimination and Crowding-Out
Author: Fernando Broner, Aitor Erce, Alberto Martin, and Jaume Ventura