Patrick Dongelmans 10216049
University of Amsterdam Master Economics
Monetary Policy, Banking and Regulation Thesis supervision: Dr. Kostas Mavromatis
Can a European safe asset raise welfare in the
European Economic and Monetary Union?
Master Thesis 2015/2016
Abstract
Using a stylized two-country model I analyse the effect a safe union-wide security has on union welfare. My findings show that forcing banks to invest in the risk-free security increases union welfare and eliminates uncertainty in output and the solvency of banks as it insulates banks from developments in sovereign debt markets by breaking the link between sovereign default risk and the banks’ balance sheet. Evaluating the fundamentals in the EMU gives the insight that such a safe union-wide security might be necessary for economic stability in the Eurozone.
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Statement of Originality
This document is written by Patrick Dongelmans who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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Table of content
1. Introduction ... 4
2. Literature review ... 5
2.1 The link between sovereign debt and banks ... 5
2.2 The pooling of European debt ... 9
3. The model ... 11
3.1 Periphery ... 12
3.1.1 Periphery government ... 12
3.1.2 Periphery banking sector ... 14
3.2 Core ... 16
3.2.1 Core government ... 16
3.2.2 Core banking sector... 17
4. The economies without a European safe asset ... 18
4.1 Periphery government debt decision ... 18
4.2 Periphery banks ... 22
4.2.1 No default of the Periphery government ... 22
4.2.2 Default of the Periphery government ... 23
4.3 Core banks ... 24
4.3.1 No default of the Periphery government ... 24
4.3.2 Default of the Periphery government ... 25
4.4 Discussion ... 26
5. The economies with a safe European security ... 27
5.1 Periphery government ... 28 5.2 Bank lending ... 30 5.2.1 Periphery... 30 5.2.2 Core ... 31 5.3 Discussion ... 31 6. Union welfare ... 32
6.1 Union welfare without a European safe asset ... 33
6.2 Union welfare with a European safe asset ... 36
6.3 Analysis of optimal arrangement ... 38
7. Application to the European Economic Monetary Union ... 41
8. Conclusion ... 42
Bibliography ... 44
Graphs ... 46
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1. Introduction
Until this day there is no single European bond market. As a result, interest rates on sovereign bonds differ between member states. These differences occur as member states have different levels of public indebtedness and risk premia. Those disparities are at the root of the asymmetries and political tensions in the European Economic and Monetary Union (EMU) (Pagano, 2014). In the years before the financial crisis that started in 2008, sovereign spreads between EMU member states were low even though debt-to-GDP levels were different.1 This could have implied that investors did not expect EMU members to default. In addition to this, the current European crisis has exposed several flaws in the design of the Eurozone’s financial system. One of these flaws is that Basel bank regulations treats sovereign debt essentially as risk-free, thereby implicitly assuming that there will always be a bailout in case of sovereign distress. This induced European banks to take on excessive exposure to their own sovereign credit risk (Brunnermeier et al., 2011). In 2009, sovereign spreads started to widen for vulnerable countries like Greece, Spain, Portugal and Ireland. Interest rates rose considerably, pushing the governments of these countries into trouble as they were hardly able to face interest or debt payments. As banks were heavily exposed to domestic debt, the plummeting bond prices led to a deterioration of banks’ balance sheets. With these developments, the chance of a public bailout increased, further increasing the riskiness of sovereign debt and creating a negative feedback loop (or diabolic loop) between banks and sovereign debt. Another flaw in the design of Eurozone’s financial system is the possibility for self-fulfilling flights to safe assets. Countries seeing their bond price collapse have to tighten their budgets, but as this leads to a contraction of their economies it validates the market's pessimistic expectations (Brunnermeier et al., 2011).
In such a context, from 2010 on, a debate has risen about the implementation and creation of a common European bond. The creation of a common European bond takes the spread between different sovereign bonds away and creates a single European bond market. This bond could be considered risk-free due to the diversification, which follows from the pooling of European debt, or the guarantee provided by a European authority or member states. But, even though creating a single European bond might diffuse the diabolic loop between the financial system and sovereigns, it could also stimulate excessive risk taking in the countries with a weak record of budgetary discipline. Breaking the link between sovereign debt and the
1 See Graph 1 and Graph 2.
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financial system means such sovereigns might become less reluctant towards issuing debt as a default has less implications for their economy. Thereby, the moral hazard problem fiscally undisciplined countries face increases. This could be welfare reducing for the Eurozone as a whole as the higher level of sovereign debt becomes more vulnerable to shocks and it might lead to less effort towards economic reform.
To my knowledge, there is currently no work that combines these two conflicting aspects (the moral hazard problem and the negative feedback loop) in a theoretical framework. With my thesis I intend to research this uncharted field. In this research paper I want to answer the question: can a European safe asset raise welfare in the EMU?
To do so, I construct a two-period model with two countries, Core and Periphery, that represent the Eurozone. This paper is structured as follows. In Chapter 2 I elaborate on the feedback loop between banks and sovereign debt, the different proposals that urge for a safe European asset, discuss other advantages of a safe security and review the relevant literature so far. The model will be explained in Chapter 3 and in Chapter 4 I analyse the situation without a European safe asset. After this, Chapter 5 describes the situation where there is a European safe asset, whereas in Chapter 6 union welfare under both situations is explored. In Chapter 7 I apply my analysis to the Eurozone. Chapter 8 concludes.
2. Literature review
2.1 The link between sovereign debt and banks
Two recent examples of the negative feedback loop between sovereign debt and financial markets are the cases of Ireland and Greece. After the Irish government bailed out its banks in 2010, it ran a public deficit of 32%. This development forced the Irish government to seek financial support with the IMF and the EU in November 2010. After the Greek sovereign debt write-down at the end of 2011, the four largest Greek banks suffered severe losses of more than 28 billion euros, a total of 13% of GDP. This amount affected their balance sheet significantly and was large enough to erase almost all of the banks’ combined capital and led to serious problems in the banking sector (Cooper and Nikolov, 2015, Pagano, 2014).
These examples perfectly illustrate that the feedback loop between banks and their respective sovereign works both ways. In Ireland’s case, the continued concern in the markets about the contingent liabilities for the government to bailout its large and insolvent banking system caused the government itself to suffer from a withdrawal of funding; the problems of the distressed banking sector spread to government financing. In Greece, the channel worked
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the other way around: the banking sector was solvent, until the government defaulted on part of its debt.
At the root of this problem are both the fragility in sovereign debt and the fragility in the banking sector (Cooper and Nikolov, 2015). Banking sector fragility arises due to the liquidity and solvency risks banks internalize. Banks provide liquidity insurance to their depositors, whereas they hold long-term risky assets on their balance sheets. As it is costly to liquidate these long-term assets, a certain drop in the value of their short term investment can push banks into solvency problems (Diamond and Dybvig, 1983). Because banks’ intermediation process is very important in contemporary societies, the collapse of the banking system leads to large welfare losses (Hoggarth, Reis, and Saporta, 2002). Sovereign debt is fragile due to a strategic complementarity between the buyers of government bonds and the government default decision (Calvo, 1988). Since the government's ability to repay debt depends inversely on the real interest rate it has to pay, this opens up the possibility of self-fulling pessimistic equilibria in which the high interest rate needed to compensate bond holders for high expected default risk weakens the government's solvency and validates the pessimistic default expectations (Gärtner and Griesbach, 2012). I do not intend to model these self-fulling equilibria but its implications are easily interpreted in the result of my analysis.
There has been a growing literature regarding the link between banks and sovereign debt. Cooper and Nikolov (2015) show in a theoretical model that the diabolic loop is a Nash equilibrium of the interaction between banks and the government arising from instability in debt markets and financial arrangements. Because banks have such an important role in society, it is optimal for governments to bail-out banks ex-post. This induces a moral hazard problem for banks, as they expect the government to protect the financial system and thus to bail-out distressed banks. Ex-ante, banks take advantage of the ‘heads-I-win, tails-you-lose’ nature of the financial safety net the government provides and rationally prefer to remain overexposed to their own sovereign debt. Cooper and Nikolov (2015) identify two main channels that trigger the diabolic loop between government debt and financial markets. The first channel is this strong tendency by banks to hold their domestic sovereign debt both as a long-term investment and as a source of liquidity, known as the home bias. The second channel arises due to the explicit (via deposit insurance) or implicit guarantees that governments provide to their banking systems. This means that investors expect banks to be bailed-out by national governments. Brunnermeier (2016) identifies a third channel that stimulates the feedback loop, which is free capital mobility. This ensures that the international investors’ perception of future sovereign solvency are incorporated in the domestic sovereign debt market value. As the market value of
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sovereign debt depends on the investors’ perception of government solvency, the earlier mentioned self-fulfilling equilibria can push sovereigns in trouble. This is a development that was present in recent sovereign debt crisis as the ‘flight to safety’. These three ingredients of the diabolic loop are also recognized by the European Systemic Risk Board (2015). To break the diabolic loop, policy should be designed to eliminate these channels and address the earlier mentioned fragilities of both the banking sector and sovereign debt.
Cooper and Nikolov (2015) provide two solutions. One suggestion is simply letting the banking system fail, the other one is imposing capital requirements on banks sovereign debt holdings. However, current macro-prudential regulation gives preferential treatment to sovereign debt exposures compared to loans to households and firms (Brunnermeier et al. (2011). This preferential treatment is questionable as it stimulates the moral hazard problem previously described and it amplifies the transmission of sovereign stress onto the banking sector (Altavilla, Pagano and Simonelli, 2016). Another solution put forward by Brunnermeier et al. (2011), Shambaugh (2012) and Delpla and Von Weizsäcker (2011) is the creation of a single, safe European bond market. This will be the solution I will analyse in this paper.
Empirical evidence for the interaction between sovereign and banks’ balance sheets is found by Reinhart and Rogoff (2010). They find a strong link between banking crises and sovereign default across the economic history of many countries. Using a multi-century span of data for 70 countries they establish support for three hypotheses. Namely that public sector borrowing surges as a sovereign debt crises nears and that banking crises are preceded by a sharp rise in both private and public debt. The third result is that banking crises often precede or accompany sovereign debt crises. Reinhart and Rogoff (2010) identify the same causal chain that makes the two crises coincide as I described earlier. They state that possible financial repression and international capital controls may give the government scope to coerce otherwise healthy banks to buy government debt in significant quantities.2 A government default, in those circumstances, would directly impact the banks’ balance sheet. The two crises may be more or less simultaneous. But even if banks are not overly exposed to government paper, the “sovereign ceiling” in which corporate borrowers are rated no higher than their national governments may make banks’ offshore borrowing very costly or altogether impossible. This is further evidence that supports the home bias of banks in distressed countries, which feeds the diabolic loop.
Uhlig (2014) focusses on the interplay between sovereign debt, banks and central bank’s
2 This also known as the moral suasion argument that is discussed later on. See alsoAltavilla, Pagano and
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guarantees in a monetary union. He analyses in a theoretical model that the home bias is stimulated by a monetary union guarantee scheme. His research shows that regulators in risky countries have an incentive to let their banks hold home sovereign bonds and bear part of sovereign default risk, while regulators in safer countries will impose tighter restrictions on its banking sector and in the end regulate their banking sector in such a way that most losses are borne privately. Risky governments know that if the banking sector and sovereign debt are highly interconnected, they would always be financed by the guarantee scheme of the monetary union.3 So part of the loss is not for the government itself but for the central bank.4 Also, governments might realize that purchases of their bonds by domestic banks are necessary to receive any form of finance at all.
Altavilla, Pagano and Simonelli (2016) provide empirical evidence that in vulnerable EMU countries, publicly owned and less strongly capitalized banks react to sovereign stress by increasing their domestic government debt holdings more than strongly capitalized and/or private banks.5 This suggests that their choices are affected by both moral suasion and by yield-seeking.6 Acharya and Steffen (2015) find more evidence for this. The moral suasion is in line with the model and arguments that Uhlig (2014) presents. Hence, banks take advantage of the ‘heads-I-win, tail-you-lose’ safety net that either a European authority or the national government provides to pursue a more yield seeking strategy.7 Furthermore, larger sovereign exposure is associated with an amplifying transmission of sovereign stress to bank risk and lending policy. Consequently, the link between banks and sovereigns becomes stronger, fuelling the negative feedback loop.
Further, Acharya, Drechsler and Schnabl (2011) find empirical evidence for the connection between the financial sector and sovereign credit risk. They show that the announcement of a financial sector bailout was associated with an immediate, unprecedented widening of sovereign Credit Default Swaps (CDS) spreads and a narrowing of bank CDS spreads. The effect is statistically insignificant for both the pre-bailout period as well as the post-bailout period. The results suggest that the rise in sovereign CDS is triggered by the bailout
3 Battistini, Pagano and Simonelli (2014) find support for this effect by analyzing the effects of an increase in
country-specific risk on the holdings of government debt by southern European banks. Periphery banks increase their domestic exposure in response to increases in country risk, while in core countries they do not.
4 This is in line with the empirical findings by Acharya, Drechsler and Schnabl (2011). 5 The vulnerable countries are: Greece, Ireland, Italy, Portugal and Spain (GIIPS).
6 For more evidence see Ongena, S., A. Popov, and N. van Horen (2015), “The Invisible Hand of the
Government: Moral Suasion during the European Sovereign Debt Crisis.”
7 The increase in government default risk causes a rise of the bonds interest rates. As banks are expected to be
bailed out if they become insolvent they increase their domestic bond holding as they yield a higher return if the government is able to repay its debt. If the government default, banks take the gamble of resurrection.
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and that the sovereign takes some of the credit risk away from the banks and bears it itself. In addition to this, the Eurozone’s and ECB’s reaction to provide bailouts to countries and funding in support of distressed banks caused the CDS rates on some of the strongest Eurozone countries to respond by rising noticeably thereby causing a spillover effect in the Eurozone. This means that the feedback loop is also present when a European authority sacrifices its creditworthiness to save banks in difficulty.
Shambaugh (2012) points out that euro area has faced three interlocking crises that together challenge the viability of the currency union. Namely, a banking crisis, a sovereign debt crisis and an economic growth crisis. He points out that these crises connect with one another in several ways: the problems of weak banks and high sovereign debt are mutually reinforcing, and both in turn constrain growth. The policies pursued by the European and national authorities, like bailouts of national banking systems, austerity to balance budgets and massive infusion of liquidity to allow banks to buy more sovereign debt, have been effective at treating the symptoms of one of the three crises, but often only temporarily or at the cost of worsening one or both of the other two. Therefore he suggests that, next to an area-wide regulator for bank supervision, a common risk-free bond to break the link from sovereigns to banks.
2.2 The pooling of European debt
Proposals to pool sovereign debt in the Eurozone have been the subject of debate for several years. A measure that is already in place in the EMU is the possibility of joint lending to fiscally distressed governments, or extending guarantees to borrowers on a multilateral basis. This is done through the European Stability Mechanism (ESM), which makes up to 700 billion euros available through multilateral guarantees for conditional lending. However, the loans in this facility are backed by the member states and their taxing power over their citizens. If there are any losses, it will be a burden for the taxpayers.
In 2011 the European Commission issued a green paper in which it suggests Stability Bonds. In this report three different options for common issuance of Stability Bonds are put forward, based on the degree of substitution of national issuance and the nature of the underlying guarantee. Another proposal that is known as the ‘blue and red’ bonds proposal is introduced by Delpla and Von Weizsäcker (2011). The Eurozone members pool their public debt up to 60% of GDP under joint and several liabilities as senior (blue) debt, whereas any debt above this threshold of 60% is issued as junior (red) debt and is not guaranteed by another
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country.
Further, Brunnermeier et al. (2011) suggest creating a safe European asset, by having a European debt agency repackage members’ debts into a safe European asset. His proposal consists of pooling and tranching Eurozone’s debt into a senior (risk-free) and junior tranche. The senior tranche, named “European Safe Bonds” (ESBies) will be completely risk free. The junior tranche, named “European Junior Bonds” (EJBies), will carry the main exposure to sovereign risk. In his concept, banks are forced to hold the senior bonds, so the balance sheets of the banks do not respond to a possible sovereign default. This is largely in line with the proposal by Delpla and Von Weizsäcker, except for the fact that the Eurozone members’ public debt above this threshold of 60% of GDP is also pooled.
Pooling and tranching European sovereign could solve two of the main problems present in the Eurozone hitherto. Firstly, if banks are forced to hold the risk-free European asset, the pooling and tranching offers the opportunity to break the aforementioned diabolic loop as banks are not exposed to their domestic sovereign default risk. Investors that want to hedge (or even speculate) on the ability of European member states to repay their debt would be willing to hold and trade the junior tranche or simply the unguaranteed ‘red’ bonds. Because banks are not allowed to invest in these risky bonds, their balance sheet is not affected by investors’ speculative behavior.
The creation of such a safe asset also provides other advantages. Firstly, equity cushions make banks more resistant to sovereign debt shocks. However, the funds that banks hold on their balance sheet in order to coincide with capital regulations is not invested in profitable investment opportunities. A safe European security means less equity requirements as there is less risk on the banks’ balance sheet. Consequently, banks are able to increase lending, which has a positive effect on the real economy. Popov and Udell (2012) document that small firms become more credit constraint when capital requirements put banks under pressure. When banks are struggling to satisfy capital requirements, they seek risk-free assets.8 As a result, credit supply to the riskiest borrowers, like small firms or firms with few tangible assets, is reduced and contributes to a decline in real activity (Peek and Rosengreen, 2000).
Secondly, Europe, in spite of the size of its economy and its developed financial markets and home to one of the worlds' reserve currencies, does not supply a safe asset that rivals the U.S. Treasuries. Currently, there is a large demand for safe assets because banks want to satisfy the required Basel capital requirements. Due to the diversification and seniority, this safe
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European asset is able to fulfill this demand (Shambaugh, 2012).
Nonetheless, a European wide safe asset has its opponents. If part of a sovereign’s debt is guaranteed, these countries have an incentive to increase their public spending beyond their means as their interest rate (might) become less responsive to an individual debt increase, prolonging the countries reliance on debt (Issing, 2009). Gennaioli, Martin and Rossi (2014) present a model in which government defaults are costly as it destroys the balance sheets of domestic banks. Using a large panel of countries the authors find evidence that for countries with developed financial institutions and banks that hold more government bonds, default is less likely. So banks’ domestic government debt exposures have a potential to serve as a government commitment device against sovereign default. This conclusion provides evidence that sovereigns are aware of the feedback loop between the financial system and their sovereign debt. Breaking this feedback loop might give an incentive for the respective government to increase debt issuance.
The literature deals mainly with the features of Eurobonds, the pros and the cons, but from a theoretical perspective there is little work on the macroeconomic effects. Beetsma and Mavromatis (2014) build a political economy model (with strategic choices over two periods) that describes the behavior of a less budgetary disciplined country in a currency union. They show that the maximum guarantee of repayment by other countries should be sufficiently low to incite a government not to put into more debt than if it had no guarantee at all. Also, a limited guarantee conditional on structural reform may induce governments to reform. The effect the safe asset has on the banks’ balance sheet is excluded in their analysis.
All in all, the pooling and tranching of debt offers many advantages at first sight. A European bond that is very liquid and safe has the potential to lower volatility in sovereign bond markets. Further, the seniority means the default risk would be very small. If banks are only allowed to hold senior bonds, the banks’ balance sheets would be unresponsive to changes in sovereign default risk and the negative feedback loop is effectively interrupted. However, this might also stimulate moral hazard in countries with a weak record of budgetary records.
3. The model
I construct a two-period model with two countries representing a currency union: Core and Periphery. The countries are of equal size but of unequal economic strength. Periphery suffers a political distortion which makes them accumulate excessive debt in period 1. This follows the framework put forward by Beetsma and Mavromatis (2014). Both countries have a perfectly competitive banking sector. Periphery banks only hold domestic sovereign debt whereas the
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Core banks hold both domestic and Periphery sovereign debt. Banks funding consists of equity and deposits. I start with a description of the Periphery economy, the Core region follows thereafter.
3.1 Periphery
3.1.1 Periphery government
Periphery social welfare is given by: 𝑈𝑃𝑆(𝑓
1, 𝑔1, 𝑓2, 𝑔2) = 𝑢(𝑓1+ 𝑔1) + 𝐸[𝑓2+ 𝑔2+ 𝑦𝑃], (1)
where 𝑓𝑡 ≥ 0 and 𝑔𝑡≥ 0 are public goods in period 𝑡 and 𝐸[ . ] indicates the expectation operator taken at the beginning of period 1. The function 𝑢(𝑥) is twice continuously differentiable with 𝑢’(𝑥) > 0 and 𝑢′′(𝑥) < 0. In addition 𝑢’(𝑥), 𝑢′′(𝑥) → 0 when 𝑥 → ∞. Further, I assume that 𝑢(0) = 0 and 𝑢′(1) = 1. To simplify the algebra, I also assume risk-neutrality with respect to the period 2 outcomes.
In Periphery there are two political parties that have the potential to take seat in the government. This is party 𝑓 and party 𝑔. One of the parties is randomly selected to take seat in the government in period 1. If elected, the government issues an amount 𝑏𝑃 of debt in period 1 to finance the production of public good 𝑓 and 𝑔 respectively. Political party 𝑓 only cares about the public good 𝑓 and poltical party 𝑔 only attached utility to the public good 𝑔. For each political party the utility function looks as follows:
𝑈𝑓(𝑓1, 𝑔1, 𝑓2, 𝑔2) = 𝑢(𝑓1) + 𝐸⌊𝑓2⌋, 𝑈𝑔(𝑓1, 𝑔1, 𝑓2, 𝑔2) = 𝑢(𝑔1) + 𝐸⌊𝑔2⌋.
Each party has a exogenous probability of 𝑝 to be re-elected in period 2, where 0 < 𝑝 ≤ 1. For 𝑝 < 1, the party that is in office at period 1 realizes that it might not be in office the next period, so the second period resources could be spent on the public good it does not attach utility to. If some party loses power but leaves a lot of debt to its successor, the party that takes over can only afford rather meager expenses in the other public good it has a preference for while repaying the debt under the budget constraint stated below. This political distortion captures the short-sightedness of governments and causes the party that is in office in period 1 to issue
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excessive debt from a society optimum perspective.9 I further assume that the government has access to unrestricted borrowing on the world capital markets. For notation simplicity I assume that party 𝑓 is in office in period 1. Obviously, presuming party 𝑔 to be in office does not change the outcomes.
The period’s resource constraints for the Periphery government are as follows:
Period 1:
𝑓1 + 𝑔1 = 1 + 𝑏𝑃. (2)
Period 2:
𝑓2 + 𝑔2 = 1 − 𝜑 − 𝑏𝑃(1 + 𝑟) + 𝜖, (3)
where 𝑏𝑃 is the amount of debt that is issued, 𝑟 the interest rate on this debt and 𝜖 a mean zero shock that is uniformly distributed with density function 𝑔(𝜖) and support [𝜖𝐿, 𝜖𝐻]. Because shock 𝜖 is mean zero, 𝜖𝐿 = −𝜖𝐻. Hence, 𝑔(𝜖) =𝜖 1
𝐿−𝜖𝐻= 1
2𝜖𝐻 . The term 𝑏𝑃(1 + 𝑟) is the
second-period debt repayment to the investors. Further, 𝜑 is a fixed default cost the government incurs whenever it partially or entirely defaults on its debt. The value of 𝜑 is given by the indicator function:
𝜑 = {𝑋 𝑖𝑓 𝜖 < 𝜖0 𝑖𝑓 𝜖 ≥ 𝜖𝐿+ 𝑏𝑃(1 + 𝑟)
𝐿+ 𝑏𝑃(1 + 𝑟), (4)
with 0 < 𝑋 < 1. I assume a lower bound on Periphery’s period 2 resources of 0 < 𝜌𝐿< 1. As long as this minimum is not reached, debt and interest are paid off. However, if repayment 𝑏𝑃(1 + 𝑟) is so large that second-period resources fall below this minimum 𝜌𝐿, then repayment is limited to the amount that leaves second-period resources exactly at 𝜌𝐿. This is the equivalent of a partial default by the Periphery government and is in line with the empirical findings by Cruces and Trebesch (2013) and Panizza et al. (2009). As there are limits to how far the government can go in depressing its population just to repay its investors, the Periphery government’s ability or willingness to tax its population is limited and defaults tend to be partial.10 In the following I make:
9 This short-sightedness would be secured if we would assume that both party 𝑓 and 𝑔 cared about both public
good but with different relative magnitudes. This would be a less abstract approach that complicates the analysis but does not change the quantitative outcomes.
10 This is in consonance with the Laffer curve. One implication of the Laffer curve is that increasing tax rates
14 Assumption 1. 1 + 𝜖𝐿+ 𝜑 = 𝜌𝐿.
Due to this assumption, the possibility that 1 + 𝜖𝐿+ 𝜑 < 𝜌𝐿 is excluded. This is necessary to rule out the occurrence that there are shock realizations for which second period resources would fall below 𝜌𝐿, even with zero debt. The option of 1 + 𝜖𝐿 + 𝜑 > 𝜌𝐿, where debt is never fully repaid when 𝑏𝑃 > 0, is also excluded to simplify the algebra.
The government realizes that if it defaults, there are going to be significant costs to the economy. Therefore, 𝜑 are extra costs the government incurs associated with a default. A default can trigger loss of confidence in the economy, which can lower tax-income. However, this term can also be seen as the political cost for the respective political party that has seat in the government when it defaults. This is in line with the findings by Gennaioli, Martin and Rossi (2013) who find that banks’ domestic sovereign debt exposures have a potential to serve as a commitment device against sovereign default.
3.1.2 Periphery banking sector
The banking sector in Periphery is perfectly competitive with a continuum of risk-neutral banks with mass 1 that behave mechanical in both periods. Periphery banks (indicated with subscript 𝑃) start in period 1 with an initial exogenous capital endowment either being derived from previous period retained earnings or capital injections. In period 1, Periphery banks also attract deposits. With these funds, Periphery banks buy a significant amount of domestic government bonds. Sovereign bonds are highly liquid financial instruments that can be easily sold.Because loans are usually a long-term illiquid investment, banks are assumed to hold liquid securities like government bonds as it is costly to liquidate loans early. 11 After buying the domestic government bonds, period 1 ends for the Periphery banks.
Balance sheet at the end of period 1:
(1 − 𝛿𝑃)(𝑞1,𝑃+ 𝐷𝑃) = 𝛼𝑏𝑃, (5)
where 𝑞1,𝑃 is the initial exogenous capital endowment and 𝐷𝑃 are the attracted deposits. The right-hand side of (5) consists of the investment in Periphery government bonds: 𝛼𝑏𝑃. The
revenues it would be optimal for the government to set tax rates above this point. It is also a question until what level it is moral to let the tax-payer pay for the consequences of the government default.
11 Banks need liquid assets to be able to supply funds for early depositors. See Diamond, D. W., & Dybvig, P. H.
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amount of funds the banks can use to invest in Periphery government debt is not fixed but can actually be influenced by an independent national supervisory authority via the macro prudential parameter 𝛿𝑃. Changing this parameter alters the amount of equity banks are compelled to transfer to period 2. The supervisory authority can change this parameter if banks get involved in risky activities and the authority demands a larger equity cushion. An high 𝛿𝑃 means that the respective supervisory authority is able to guarantee that banks provide loans even in the case of a strong adverse shock. However, it lowers the amount of funds that are available to investment in government bonds.12 As Periphery banks invest in domestic sovereign debt, the supervisor sets 𝛿𝑃 > 0, because they know a possible default of the government could trigger the diabolic loop and start turmoil in the economy. To simplify the algebra I make the following assumption:
Assumption 2: Irrespective of how much debt the Periphery government issues, Periphery
banks always buy a share 𝛼 of Periphery government bonds, with 0 < 𝛼 < 1, until their bond holdings reach a certain amount 𝑏̃. Hence 𝑏𝑃 ̃ = 𝛼𝑏𝑃 𝑃.
The consequence of this assumption is that that banks do not increase their government debt holdings the more debt the Periphery government issues. It would be interesting to solve the model while relaxing this assumption as Battistini, Pagano and Simonelli (2014) and Altavilla, Pagano and Simonelli (2016) provide evidence that banks react to sovereign stress by increasing their domestic government debt holdings.13
The level of equity at the end of period 2 depends on the ability of the Periphery government to repay its debt. This is to model the negative link between sovereign debt and the balance sheet of banks. A possible default of the government can push Periphery banks into solvency problems. As the government bonds are not risk-free, holders of these bonds demand a return. The Periphery banks are paid back in period 2 with 𝛼𝑏𝑃(1 + 𝑟) when the government does not default. At the beginning of period 2 the Periphery banks receive the return from their government bond holdings and use these proceeds together with the amount of equity transferred from period 1 through the liquidity parameter 𝛿𝑃, to provide loans to firms.
𝐿𝑃 = 𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃) + 𝑎𝑏𝑃(1 + 𝑟). (6)
12 Because we assume Periphery banks only invest in domestic government bonds they do not have the
opportunity to invest in some other asset. In reality, banks have the option to invest in a large amount of liquid assets next to government bonds.
13 For this effect to be present, the banks would need to have the opportunity to invest in a second financial
asset, which holdings should decrease as Periphery banks use a larger share of their funds to invest in Periphery bonds.
16
Production takes place in period 2. Firms only need capital in the form of bank loans to produce private goods. I assume that firms only borrow from their domestic banks, cross-border lending is absent in this model. Periphery firms borrow the amount 𝐿𝑃 that the Periphery banks are able to provide at the beginning of period 2. This amount of loans 𝐿𝑃 is processed one-on-one for capital in the production process 𝐾𝑃, so 𝐿𝑃 = 𝐾𝑃. Final good production 𝑦𝑃 is given by 𝐴𝐾𝑃, such that 𝐴 > 1. Capital fully depreciates in production so capital is equal to investment. Because 𝐴 > 1 Periphery firms will borrow up to the maximum possible. The Periphery banks demand a return on their loans of 𝑟𝑃𝐿. When production is realized, banks are paid back. At the end of period 2 the proceeds from the loans provided is equal to (1 + 𝑟𝑃𝐿)𝐿
𝑃. With these returns the banks pay back their depositors 𝐷𝑃. Any money that is left over is distributed to firms through dividends. The Periphery banking sectors’ balance sheets expressed as the level of equity at the end of period 2 will be:
𝑞2,𝑃 = (1 + 𝑟𝑃𝐿)𝐿
𝑃− 𝐷𝑃. (7)
Plugging in 𝐿𝑃 gives:
Balance sheet at the end of period 2:
𝑞2,𝑃 = (1 + 𝑟𝑃𝐿)[𝛿𝑃(𝑞1,𝑃 + 𝐷𝑃) + 𝑎𝑏𝑃(1 + 𝑟)] − 𝐷𝑃. (8)
If 𝑞2,𝑃 < 0, there is a banking crisis and Periphery banks would have to be recapitalized. To close the model I assume that when 𝑞2,𝑃 < 0, a union-wide authority intervenes and recapitalizes the banks such that 𝑞2,𝑃 = 0. As banks are forced to take part of their initial endowment as a liquidity requirement to period 2, banks cannot use these funds to buy government bonds that produce a return at the beginning of period 2. This leads to a lower supply of loans if the government does not default and has a negative effect on economic activity.
3.2 Core
3.2.1 Core government
The Core government does not face a political distortion and they do not suffer from any potential fiscal problem. They borrow at the risk-free rate, which is 0. However, Core does have a banking sector that is consistent with the banking sector in Periphery, with one difference:
17
Core banks hold both Periphery and Core government bonds. This generates interdependence between the Core and Periphery region and captures the interaction between Periphery sovereign debt and the Core banks. A potential debt default in Periphery provokes a spillover effect to Core via this channel. I use this setup to investigate which policies eliminate the possible contagion effects between the two regions.
3.2.2 Core banking sector
In the Core region (indicated by subscript 𝐶) there is a perfectly competitive banking sector with a continuum of risk-neutral banks with mass 1 that work in a mechanical way in both periods. Just as the Periphery banks, the banks in the Core region start in period 1 with an initial exogenous capital endowment and attract depositors. With these funds Core banks buy a significant amount of Periphery sovereign debt 𝛽𝑏𝑃 up until the amount 𝑏̅̅̅, with 0 < 𝛽 < 1 𝑃 and 𝛽 < 𝛼. Consequently, 𝑏̅̅̅ < 𝑏𝑃 ̃. This implies that Core banks are less exposed to Periphery 𝑃 bonds than Periphery banks.14 In addition, the Core banks buy domestic government bonds: 𝑏𝐶. Opposed to Periphery bonds, Core government bonds are risk-free and carry an interest rate of 0. After purchasing the Core and Periphery bonds the period 1 ends for the Core banks.
Balance sheet at the end of period 1:
(1 − 𝛿𝐶)(𝑞1,𝐶+ 𝐷𝐶) = 𝛽𝑏𝑃+ 𝑏𝐶, (9)
where 𝑞1,𝐶 is the initial exogenous capital endowment and 𝐷𝐶 are the attracted deposits. The investment in Periphery debt is given by 𝛽𝑏𝑃 whereas the investment in Core government debt is given by 𝑏𝐶. The macro prudential liquidity parameter for the Core banks set by the independent supervisory authority is given by 𝛿𝐶. As I assume that Core banks are less exposed to Periphery bonds than the Periphery banks, the supervisor sets 𝛿𝐶 lower than 𝛿𝑃. This implies that Core banks can invest a larger share of its funds in government bonds. At the beginning of period 2 the Core banks receive the returns from their government bond holding and use these funds and the funds transferred from period 1, to provide loans to firms in their own region:
𝐿𝐶 = 𝛿𝐶(𝑞1,𝐶+ 𝐷𝐶) + 𝛽𝑏𝑃(1 + 𝑟) + 𝑏𝐶. (10)
14 This seems to be well in line with realityas banks have a home bias regarding government bonds. Acharya
18
Again, production takes place in period 2. Firms in Core only need capital in the form of bank loans to produce private goods. They borrow the amount 𝐿𝐶 that the Core banks are willing to provide at the beginning of period 2. Loans are processed one-on-one for capital in the production process 𝐾𝐶, so 𝐿𝐶 = 𝐾𝐶. Final good production 𝑦𝑐 is given by 𝐴𝐾𝐶, such that 𝐴 > 1. Capital fully depreciates in production so capital is equal to investment. Because 𝐴 > 1 firms will borrow up to the maximum possible. The Periphery banks demand a return on their loans of 𝑟𝐶𝐿.When production is realized, banks are paid back. At the end of period 2 the proceeds from the loans provided is equal to (1 + 𝑟𝐶𝐿)𝐿
𝐶. With these returns the Core banks pay back their depositors 𝐷𝐶. Any money that is left over is distributed to firms through dividends. The Core banking sectors’ balance sheets expressed as the level of equity at the end of period 2 is given by:
𝑞2,𝐶 = (1 + 𝑟𝐶𝐿)𝐿𝐶− 𝐷𝐶. (11)
Plugging in 𝐿𝐶 gives:
Balance sheet at the end of period 2:
𝑞2,𝐶 = (1 + 𝑟𝐶𝐿)[𝛿𝐶(𝑞1,𝐶+ 𝐷𝐶) + 𝛽𝑏𝑃(1 + 𝑟) + 𝑏𝐶] − 𝐷𝐶. (12) If 𝑞2,𝐶 < 0, there is a banking crisis and Core banks would have to be recapitalized.
To close the model I assume that when 𝑞2,𝐶 < 0, a union-wide authority intervenes and recapitalizes the banks such that 𝑞2,𝐶 = 0.
4. The economies without a European safe asset
4.1 Periphery government debt decisionFirst I will analyse the exclusion of a European safe asset. Ultimately, there is no safe union-wide security that Core and Periphery banks hold on their balance sheet and the Periphery government is fully responsible for repaying its own debt. As mentioned in the previous section, the Periphery government chooses an amount debt to issue to finance a certain public good. In period 1 the government solves
max 𝑏𝑃 𝑈𝐹= 𝑢(1 + 𝑏𝑃 ) + 𝑝 [ ∫ (𝜌𝐿− 𝜑)𝑔(𝜖)𝑑𝜖 𝜖𝐿+𝑏𝑃(1+𝑟) 𝜖𝐿 + ∫ (1 + 𝜖 − 𝑏𝑃(1 + 𝑟)) 𝑔(𝜖)𝑑𝜖 𝜖𝐻 𝜖𝐿+𝑏𝑃(1+𝑟) ], (13)
19
with the restriction that 𝑟 is determined by the requirement that the risk-neutral investors are repaid in expected terms. This means that the interest rate of Peripheries sovereign debt is determined by the smallest non-negative solution to
𝑏𝑃 = ∫ (1 + 𝜖 − 𝜌𝐿)𝑔(𝜖)𝑑𝜖 𝜖𝐿+𝑏𝑃(1+𝑟) 𝜖𝐿+𝜑 + ∫ 𝑏𝑃(1 + 𝑟)𝑔(𝜖)𝑑𝜖 𝜖𝐻 𝜖𝐿+𝑏𝑃(1+𝑟) . (14)
In the case of a favorable shock 𝜖 ≥ 𝜖𝐿+ 𝑏𝑃(1 + 𝑟), debt-servicing costs are fully honoured, while for an unfavorable shock 𝜖𝐿+ 𝜑 ≤ 𝜖 < 𝜖𝐿+ 𝑏𝑃(1 + 𝑟), they are at most partly honoured, up to the amount 𝜖 − 𝜖𝐿, so that Periphery’s second-period resources are at the minimum 𝜌𝐿. For 𝜖𝐿 ≤ 𝜖 < 𝜖𝐿+ 𝜑 the investors do not receive a payment at all as the shock is not large enough to offset the default costs the Periphery government incurs. The costs of default are thus transmitted onto the investors. A negative interest rate is excluded, because risk-neutral investors would never be prepared to buy Periphery bonds as they would under all states of the world receive a repayment less than their initial investment. Differentiating the government’s objective function, and applying Leibniz’ integral rule, the first-order condition for an internal optimum is (see Appendix A):
𝑢′(1 + 𝑏 𝑃) = 𝑝 [1 + 𝑟 + 𝑏𝑃( 𝑑𝑟 𝑑𝑏𝑃)] [1 − 𝑏𝑃(1 + 𝑟) 2𝜖𝐻 ], (15)
where I have used that 𝜖 is uniformly distributed with 𝜖𝐿 = −𝜖𝐻 and that the interest rate responds to the debt level via (14). Working out (14), it is found that a proper solution for the interest rate requires that 𝑏𝑃(1 + 𝑟) < 2𝜖𝐻, while upon differentiating (14) (see Appendix B), I obtain the dependency of the interest rate on debt explicitly as:
𝑑𝑟 𝑑𝑏𝑃 = 1 𝑏𝑃 2𝜖𝐻− (1 + 𝑟)[2𝜖𝐻− 𝑏𝑃(1 + 𝑟) − 𝜑] 2𝜖𝐻− 𝑏𝑃(1 + 𝑟) − 𝜑 , (16)
Substituting this into previous equation, the first-order condition of the government becomes:
𝑢′(1 + 𝑏
𝑃) = 𝑝 [
2𝜖𝐻− 𝑏𝑃(1 + 𝑟)
20
The second-order condition for an internal maximum is fulfilled as the second derivative of the objective function with respect to 𝑏𝑃, 𝑢′′(1 + 𝑏
𝑃) −[2𝜖 2𝜖𝐻𝜑
𝐻−𝑏(1+𝑟)−𝜑]3, is negative. The first-order condition (17) equates the marginal utility of an additional euro of debt issued in period 1 to the expected marginal disutility of the repayment, which, taking into account the response of the interest rate, is equal to the re-election probability times the marginal utility of public consumption in period 2.15 Equation (17) yields a unique solution for 𝑏𝑃, which, by the properties of function 𝑢(. ), is positive if 𝑝 < 1 such that the whole right-hand side of (17) is smaller than 1.16 Define this solution as 𝑏𝑃𝑁𝑃 > 0 and the associated interest rate as 𝑟𝑁𝑃, where the superscript 𝑁𝑃 indicates the case of ”no pooling”, i.e. of no debt mutualisation and no union-wide asset. A decrease in the re-election probability implies a lower value of 𝑏𝑃𝑁𝑃, ceteris
paribus. The reason is that re-election uncertainty (a fall in 𝑝) increases the likelihood that
second-period resources are spend on the good that the current officeholder does not attach utility to. The lower 𝑝, the more heavily the party in office discounts the future and, for that reason, issues more debt in period 1. Setting 𝜑 = 0 gives us a marginal utility in period 2 of 1 times the re-election probability 𝑝. Hence, 𝑢′(1 + 𝑏) = 𝑝, which implies a higher level of debt as the decrease in the marginal utility means an increase in Periphery debt due to the specification of the utility function 𝑢′(𝑥) > 0 and 𝑢′′(𝑥) < 0. Conclusively, the default cost the Periphery government faces induces the government to restrain debt accumulation. This brings us to the following result:
Result 1: The presence of default cost 𝜑 causes the Periphery government to issues less debt
than if this cost would absent.
The intuition behind this result is that the default cost lowers the amount of resources the party in office can spend on its preferred public good in period 2 if it defaults. As the government maximizes over the two periods it is thus optimal to make default less likely, which reduces the chance the respective government incurs the extra cost of default. Hence, it issues less debt.
Appendix B shows that the explicit expression for 𝑟𝑁𝑃 is given by 17
15 The marginal utility of public consumption in period 2 is given by 2𝜖𝐻−𝑏𝑃(1+𝑟)
2𝜖𝐻−𝑏𝑃(1+𝑟)−𝜑.
16 We stated that 𝑢′(1) = 1, which is true for 𝑏
𝑃= 0. In order for the Periphery government to issue debt, the
re-election probability most be sufficiently small such that the right-hand side of (17) is smaller than 1.
17 We see that the default cost increases the interest rate on government debt as investors want to be
compensated for this extra cost in case of a default. This changes the debt accumulation of the government as the rise in 𝑟 makes issuing debt more costly. So even though the government transmits the default costs to the
21
𝑟𝑁𝑃 = 2𝜖𝐻− √𝜖𝐻[𝜖𝐻− 𝑏𝑃𝑁𝑃− 𝜑]
𝑏𝑃𝑁𝑃 −
𝜑
𝑏𝑃𝑁𝑃− 1. (18)
The effect of a ‘flight-to-safety’ is now easily seen. Consider that a large share of investors (wrongly) think the underlying risk of the sovereign bonds is not correctly reflected by the interest rate they receive on those bonds. As a response they dumb their bonds on the world market, exogenously increasing the interest rate given by (18). Due to this, debt-servicing costs increase for the Periphery government, increasing the interval over which it defaults and making the interval of full repayment smaller. The ‘flight-to-safety’ thus increases the probability of default as the interval for which the Periphery defaults becomes larger, creating a self-fulling pessimistic effect.
Further, because first-order condition (17) does not exclude that 𝑏𝑃𝑁𝑃 exceeds 𝜖 𝐻, I make:
Assumption 3: Re-election chance 𝑝 is sufficiently high that 𝑏𝑃𝑁𝑃+ 𝜑 ≤ 𝜖𝐻 but sufficiently low such that (17) is larger than 1, and 𝑏𝑃𝑁𝑃 > 0.
This assumption is necessary to have a solution for the interest rate given by (18). Now it is seen that if the debt burden ranges from 0 to 𝜖𝐻, total debt-servicing costs 𝑏𝑃(1 + 𝑟) range from 0 to 2𝜖𝐻 as 𝑟 cannot exceed 1. In fact, if 𝑏𝑃 goes to 𝜖𝐻, the restriction that second-period resources cannot fall below 𝜌𝐿 is always binding, except for the most favourable shock 𝜖 = 𝜖𝐻. Also notice that, if 𝑏𝑃 → 1, 𝑟 → 1. So the reaction of the interest rate on government debt issuance is the counteracting power that prevents the government from issuing more debt than 𝑏𝑃𝑁𝑃 when there is a possibility of (partial) default. You can easily see this by setting 𝑟 = 0 and
𝑑𝑟
𝑑𝑏𝑃= 0 in (15), in which case this condition reduces to:
𝑢′(1 + 𝑏
𝑃) = 𝑝 [1 − 𝑏𝑃
2𝜖𝐻]. (19)
In the following I make:
Assumption 4: Equation (19) has at least one solution 0 ≤ 𝑏𝑃 ≤ 2𝜖𝐻. The smallest of these solution is given by 𝑏𝑃𝐺.
purchasers of government debt, the fact that this increases the interest rate investors demand causes the government to issue less debt.
22
As the reaction of the interest rate on government debt issuance is the counteracting power that prevents the government from issuing more debt than 𝑏𝑃𝑁𝑃, (19) cannot have a solution 0 ≤ 𝑏𝑃𝐺 ≤ 𝑏
𝑃𝑁𝑃. Hence, if the interest rate fails to react to the debt level, any internal solution for debt implied by (19) must exceed 𝑏𝑁𝑃: 𝑏
𝑃𝐺 > 𝑏𝑃𝑁𝑃. Intuitively, if debt would not carry an interest rate at all, issuing debt becomes more attractive as debt-servicing costs in period 2 would be lower for given 𝑏𝑃, causing the government to accumulate more debt.
4.2 Periphery banks
In period 1 the government chooses its debt level 𝑏𝑃𝑁𝑃. As discussed earlier, banks in the union use their funds available to invest in government debt. At the beginning of the second period, the shock to government resources has materialized and the Periphery banks receive the returns on their investment. If the Peripheries government defaults entirely or partially on its debt, the Periphery banks do not get the full return on their government debt holdings. I first consider the case where there is a benign shock 𝜖 ≥ 𝜖𝐿+ 𝑏𝑃(1 + 𝑟) and the Periphery government does not default. I analyse the effects on the banks’ balance sheet and output in the Periphery.
4.2.1 No default of the Periphery government
Without default, the government is able to pay the amount 𝑏𝑃(1 + 𝑟) of debt-servicing costs in period 2. With these returns, and the amount of equity transferred from period 1 by the liquidity parameter 𝛿𝑃, the Periphery banks provide loans to domestic firms:
𝐿𝑃 = 𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃) + 𝑎𝑏𝑃(1 + 𝑟). (20) Production takes place in period 2 and the loans provided yield their return 𝑟𝑃𝐿 at the end of the period. The banking sectors’ balance sheets expressed as the level of equity at the end of period 2 will be:
𝑞2,𝑃 = (1 + 𝑟𝑃𝐿)𝐿𝑃− 𝐷𝑃. (21)
Plugging in 𝐿𝑃 given by (20) gives
𝑞2,𝑃 = (1 + 𝑟𝑃𝐿)[𝛿𝑃(𝑞1,𝑃 + 𝐷𝑃) + 𝑎𝑏𝑃(1 + 𝑟)] − 𝐷𝑃, (22)
which is always positive. As loans are processed one-on-one for capital and output is given by 𝑦𝑃 = 𝐴𝐾𝑝, realized output expands to
23
𝑦𝑃 = 𝐴𝐾𝑝 = 𝐴𝐿𝑃 = 𝐴[𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃) + 𝑎𝑏𝑃(1 + 𝑟)]. (23)
In the case where the materialization of a benign shock makes the government repay its debt it is shown that the maximum amount of loans are provided and output in the Periphery is maximized. In addition to this, 𝑞2,𝑃 > 0 so no recapitalization is necessary as Periphery banks are completely solvent at the end of period 2. Hence, a banking crisis in the Periphery is absent.
4.2.2 Default of the Periphery government
Now consider the case where the government partially or entirely defaults. With an adverse shock 𝜖𝐿 ≤ 𝜖 < 𝜖𝐿 + 𝑏𝑃(1 + 𝑟) the government will not be able to pay back the full amount 𝑏𝑃(1 + 𝑟) due in period 2. Loan supply with an adverse shock at the beginning of period 2 is given by
𝐿𝑃 = 𝛿𝑃(𝑞1,𝑃 + 𝐷𝑃) + ∫ 𝛼(1 + 𝜖 − 𝜌𝐿)𝑔(𝜖) 𝑑𝜖, 𝜖𝐿+𝑏𝑃(1+𝑟)
𝜖𝐿+𝜑
(24)
where 𝛿𝑃(𝑞1,𝑃 + 𝐷𝑃) are the funds transferred from period 1 and the last term in (24) is the debt repayment when the Periphery government defaults. Repayment depends on the asperity of the shock on the Periphery government period 2 resources. The closer 𝜖 is to its lower bound 𝜖𝐿, the lower the amount of loans provided. We see that if 𝜖 = 𝜖𝐿, (24) reduces to 𝐿𝑃 = 𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃) . Because the supervising authority sets 𝛿𝑃 > 0 , the banks are capable of providing some credit to the firms in the Periphery when 𝜖 = 𝜖𝐿. The policy parameter thus sets a lower bound on the provided loans. However, the amount of loans provided with an adverse shock is always lower compared to the case with a favourable shock, simply because with a government default the return on the government bonds is lower. Again, production takes place in period 2 and the loans are paid back to the banks with their return 𝑟𝑃𝐿 at the end of period 2. The balance sheet expressed as the level of equity at the end of period 2 is again given by (21). Plugging in (24) gives 𝑞2,𝑃 = (1 + 𝑟𝑃𝐿) [𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃) + ∫ 𝛼(1 + 𝜖 − 𝜌𝐿)𝑔(𝜖) 𝑑𝜖 𝜖𝐿+𝑏𝑃(1+𝑟) 𝜖𝐿+𝜑 ] − 𝐷𝑃. (25)
24
If the partial default is large enough that 𝑞2,𝑃 < 0 the bank becomes insolvent and banks would have to be recapitalized; a banking crisis occurs in the Periphery. Output is given by:
𝑦𝑃 = 𝐴𝐾𝑃 = 𝐴𝐿𝑃 = 𝐴 [𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃) + ∫ 𝛼(1 + 𝜖 − 𝜌𝐿)𝑔(𝜖) 𝑑𝜖 𝜖𝐿+𝑏𝑃(1+𝑟)
𝜖𝐿+𝜑
]. (26)
The parameter 𝛿𝑃 > 0 sets a lower bound on the negative effect the government default has on output. Hence, a minimum amount of loans of 𝐿𝑃 = 𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃) is supplied, causing output to not drop below 𝐴[𝛿𝑃(𝑞1,𝑃+ 𝐷𝑃)]. If the supervisory authority would set 𝛿𝑃 = 1 so banks are obliged to transfer all their funds to period 2, output would be equal to 𝑦𝑃 = 𝐴[𝑞1,𝑃+ 𝐷𝑃]. There is thus a range of shocks 𝜖𝐿 ≤ 𝜖 < 𝜖𝐿+ 𝑏𝑃+ 𝜑 for which output would be lower than this maximum lower bound the supervisory authority can set (see Appendix C). 18,19
4.3 Core banks
The same result applies to the Core banks. If the Periphery government defaults entirely or partially on its debt, the Core banks do not get the full return on their Periphery government bond holdings.
4.3.1 No default of the Periphery government
With a benign shock 𝜖 ≥ 𝜖𝐿+ 𝑏𝑃(1 + 𝑟), the government is able to pay the full amount 𝑏𝑃(1 + 𝑟) in period 2. With these returns, and the amount of equity transferred from period 1 by the liquidity parameter 𝛿𝐶, the Core banks provide loans to domestic firms:
𝐿𝐶 = 𝛿𝐶(𝑞1,𝐶+ 𝐷𝐶) + 𝛽𝑏𝑃(1 + 𝑟) + 𝑏𝐶. (27)
After production has taken place the Core banks receive their return on the provided loans. The banking sector balance sheet expressed as the level of equity at the end of period 2 is given by
18 We will see in section 5.2 that this is the range of shocks for which output without a European safe asset is
lower than if banks were compelled to invest in the safe security. This result for 𝜖𝐿≤ 𝜖 < 𝜖𝐿+ 𝑏𝑃+ 𝜑 holds for
the Core banks as well.
19 For the range of shocks 𝜖
𝐿+ 𝑏𝑃+ 𝜑 ≤ 𝜖 < 𝜖𝐻, output without a European safe asset is higher than if banks
25
𝑞2,𝐶 = (1 + 𝑟𝐶𝐿)[𝐿𝐶] − 𝐷𝐶. (28) Plugging in 𝐿𝐶 gives
𝑞2,𝐶 = (1 + 𝑟𝐶𝐿)[𝛿
𝐶(𝑞1,𝐶+ 𝐷𝐶) + 𝛽𝑏𝑃(1 + 𝑟) + 𝑏𝐶] − 𝐷𝐶, (29)
which is always positive. Hence, there is no need to recapitalize Core banks as they are completely solvent at the end of period 2; a banking crisis is absent. In the case where the materialization of a benign shock makes the government to repay its debt we see that output in Core is maximized as the maximum amount of loans possible are provided:
𝑦𝐶 = 𝐴𝐾𝐶 = 𝐴𝐿𝐶 = 𝐴[𝛿𝐶(𝑞1,𝐶+ 𝐷𝐶) + 𝛽𝑏𝑃(1 + 𝑟) + 𝑏𝐶]. (30)
Consequently, when the Periphery government does not default there is no contagion effect from the Periphery government to the Core banking sector.
4.3.2 Default of the Periphery government
Now consider the case where the Periphery government partially or entirely defaults. With an adverse shock 𝜖𝐿 ≤ 𝜖 < 𝜖𝐿+ 𝑏𝑃(1 + 𝑟), the Periphery government will not be able to pay back the full debt-servicing costs in period 2. Repayment depends on the asperity of the shock on the Periphery government period 2 resources. Loan supply to the Core firms at the beginning of period 2 is given by:
𝐿𝐶 = 𝛿𝐶(𝑞1,𝐶+ 𝐷𝐶) + ∫ 𝛽(1 + 𝜖 − 𝜌𝐿)𝑔(𝜖) 𝑑𝜖 𝜖𝐿+𝑏𝑃(1+𝑟)
𝜖𝐿 +𝜑
+ 𝑏𝐶. (31)
where 𝛿𝐶(𝑞1,𝐶+ 𝐷𝐶) are the funds transferred from period 1, 𝑏𝐶 is the proceed of the Core government bonds and the second term on the right-hand side of (31) is the debt repayment of the defaulting Periphery government. The amount of loans provided with an adverse shock is always lower compared to the case with a favourable shock, simply because with a government default 𝜖 < 𝜖𝐿+ 𝑏𝑃(1 + 𝑟). Again, production takes place in period 2 and the loans are paid to the Core back with their return 𝑟𝐶𝐿.The banking sector balance sheet expressed as the level of equity at the end of period 2 is given by (28). Plugging (31) in (28) gives
26 𝑞2,𝐶 = (1 + 𝑟𝐶𝐿) [𝛿 𝐶(𝑞1,𝐶+ 𝐷𝐶) + ∫ 𝛽(1 + 𝜖 − 𝜌𝐿)𝑔(𝜖) 𝑑𝜖 𝜖𝐿+𝑏𝑃(1+𝑟) 𝜖𝐿+𝜑 + 𝑏𝐶] − 𝐷𝐶. (32)
If the shock and the exposure of the Core banks to Periphery government bonds is large enough such that 𝑞2,𝐶 < 0, a default in the Periphery triggers a banking crisis and Core banks would have to be recapitalized. There is thus a contagion effect of the Periphery sovereign default to the Core banks. The lower return Core banks get from their Periphery debt holdings leads to a lower loan supply and ultimately to lower resources in the economy. Output is given by
𝑦𝐶 = 𝐴𝐾𝐶 = 𝐴𝐿𝐶 = 𝐴 [𝛿𝐶(𝑞1,𝐶+ 𝐷𝐶) + ∫ 𝛽(1 + 𝜖 − 𝜌𝐿)𝑔(𝜖) 𝑑𝜖 𝜖𝐿+𝑏𝑃(1+𝑟)
𝜖𝐿+𝜑
+ 𝑏𝐶]. (33) If the supervisory authority would set 𝛿𝐶 = 1 , output would be equal to 𝑦𝐶 = 𝐴[𝑞1,C+ 𝐷𝐶+ 𝑏𝐶]. Just as discussed in Section 5.3.1, there is a range of shock 𝜖𝐿 ≤ 𝜖 < 𝜖𝐿+ 𝑏𝑃 + 𝜑 for which output would the lower than this maximum lower bound the supervisory authority can set (see Appendix C).
4.4 Discussion
I have showed that it is optimal for the government to issue a certain level of debt 𝑏𝑃𝑁𝑃 and that this debt is vulnerable to default risk. Due to this risk, the model shows multiple states of the world. In the case of an adverse shock there is both a Periphery sovereign debt crisis as well lower output in both Core and Periphery when compared with the situation without default. A strong adverse shock could also push banks in both regions into insolvency if the return on the amount of loans provided is not enough to pay back depositors in the respective region. Further, as Periphery banks are more exposed to Periphery government debt than Core banks, a banking crisis is more likely to occur in the Periphery region than in the Core region. The higher exposure also means the contraction in the real economy might be more persistent in Periphery than in Core. This depends on the macro-prudential parameters 𝛿𝐶 and 𝛿𝑃 that decides how exposed banks in each region are to Periphery sovereign distress.
In the case of a favorable shock, the Periphery government is able to service its debt payments. In this case there is no sovereign debt crisis and no possibility of a banking crises. Further, because the banks risky investment yields a return, Periphery and Core banks are able to supply loans such that output is higher than with a default.
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Result 2. Consider the case where there is no safe European security.
i. When 𝜖 > 𝜖𝐿+ 𝑏𝑃(1 + 𝑟) there is no contraction in output in both the Core and
Periphery region. Further a banking crisis and a sovereign debt crisis are absent. ii. When 𝜖 < 𝜖𝐿+ 𝑏𝑃(1 + 𝑟) such that 𝑞2,𝑃 > 0, output decreases in Core and Periphery
and there is a sovereign debt crisis in Periphery. A banking crisis is absent in both regions.
iii. When 𝜖 < 𝜖𝐿+ 𝑏𝑃(1 + 𝑟) such that 𝑞2,𝑃 < 0 but 𝑞2,𝐶 > 0, output decreases in Core
and Periphery and there is a sovereign debt crisis and banking crisis in Periphery. iv. When 𝜖 < 𝜖𝐿+ 𝑏𝑃(1 + 𝑟) such that 𝑞2,𝑃 < 0 and 𝑞2,𝐶 < 0, output decreases and there
is a banking crisis in both Periphery and Core, together with a sovereign debt crisis in Periphery.
Point iv. seems well in line with the situation of the European sovereign debt crisis. As Shambaugh (2012) points out that euro area has faced three interlocking crises: a banking crisis, a sovereign debt crisis and a growth crisis.
5. The economies with a safe European security
In this section I assume that the Periphery government can issue two types of debt, in line with the proposal made by Delpla and von Weizsäcker (2011), but also applicable to the proposal of Brunnermeier et al. (2011). The first type of debt, also referred to as “senior” (indexed by superscript 𝑠), is fully guaranteed and, therefore, carries an interest rate of zero. The amount of senior debt cannot exceed a certain threshold 𝑏̂ . This is often a certain 𝑃 percentage of GDP that is seen as optimal for countries. In the EMU there is the 60% benchmark from the Maastricht treaty. The second type of debt, referred to as “junior” (indexed by superscript 𝑗), is not guaranteed. Because it will carry a positive interest rate, it will only be issued when the amount of senior debt is set at its allowed maximum 𝑏̂. In addition to this, 𝑃 banks in both regions are, by law, only allowed to invest in the senior, risk-free bond. This is to break the link between sovereign default and the banking sector. Knowing that a default does not trigger a negative feedback loop between excessive debt issuance and credit in the economy, default costs are considered to be lower in this case. For simplicity I assume that when banks only invest in the senior sovereign bonds, default costs are absent:
Assumption 5: When banks only hold the senior sovereign bonds, the diabolic loop is absent
