Sovereign Debt, Bail-Outs and Contagion in a Monetary Union

Transcription

1 Sovereign Debt, Bail-Outs and Contagion in a Monetary Union Sylvester C.W. Eijffinger Tilburg University, CentER, European Banking Center, CEPR Michal L. Kobielarz Tilburg University, CentER, European Banking Center Burak R. Uras Tilburg University, CentER, European Banking Center January 2016 Abstract The European sovereign debt crisis is characterized by the simultaneous surge in borrowing costs in the peripheral euro area countries after We present a theory, which can account for the behavior of sovereign bond spreads in Southern Europe between 1998 and Our key theoretical argument is related to implicit bail-out guarantees provided by a monetary union, which endogenously vary with the number of member countries in sovereign debt trouble. We incorporate this theoretical foundation in an otherwise standard small open economy DSGE model and explain (i) the convergence of interest rates on sovereign bonds following the European monetary integration in late 1990s, and (ii) - following the heightened default risk of Greece - the sudden surge in interest rates in countries with relatively sound economic and financial fundamentals. We calibrate the model to match the behavior of the Portuguese economy over the period of 1998 to We also explain why the famed statement by Mario Draghi in 2012 was able to stop the recessionary trend in Europe and we quantify the macroeconomic implications of the Draghi effect for the Portuguese economy. Keywords: bail-out, contagion, interest rate spreads, sovereign debt crisis. JEL Classification Numbers: F33, F34, F36, F41. We thank Andrea Ferrero, Tommaso Monacelli, Ctirad Slavik, Harrie Verbon, Wolf Wagner, Jean-Pierre Zigrand and the seminar participants at the ECB, Goethe University Frankfurt, Tilburg University, the EBC Junior Fellow Workshop and the Warsaw International Economic Meeting for useful comments and discussions. Corresponding author: m.l.kobielarz@tilburguniversity.edu

2 1 Introduction The sovereign debt crisis in the euro area is characterized by the simultaneous surge in borrowing costs in Southern Europe after As we document in figure 1, at the dawn of the crisis in late 2008 the spread on Greek government bonds (relative to German bonds) rose from 50 basis points (bps) to 200 bps within a couple of months, and further increased to 1000bps by Shortly after the outbreak of the Greek debt trouble, the bond spreads started to rise in Portugal, Italy and Spain as well (Fig.1). As we also present in figure 1, by the time the European Monetary Union was first established back in late 1990s, these Southern European countries experienced a simultaneous convergence in their government bond spreads vis-à-vis Germany an empirical pattern, which is almost the mirror image of the diverging spreads between 2008 and In this paper, we present a theory, which can account for the behavior of sovereign bond spreads in Southern European countries between 1998 and Our key theoretical argument is related to an implicit bail-out guarantee - and its limitations - provided by a monetary union. We incorporate this theoretical foundation in an otherwise standard small open economy DSGE model and explain (i) the convergence of interest rates on sovereign bonds following the European monetary integration in late 1990s, and (ii) - following the heightened default risk of Greece - the sudden surge in interest rates in countries with relatively sound economic and financial fundamentals, Portugal in particular. In our theoretical setting, we explicitly model the endogenous bail-out decision of the European Monetary Union (EMU). We assume that for EMU the cost of bailing out a country is taking over a fraction of the debt burden of that particular country. To the end of benefits of bailing out, we first assume that a country who defaults on its sovereign debt can no longer remain in the monetary union. 1 Building upon this assumption, we introduce an explicit value function for the union, which measures by how much the monetary union values each country s membership. This value function exhibits a local increasing returns to scale property such that the marginal loss associated with letting a country leave the union is the highest if that particular country is the first one to leave. This mechanism reflects the credibility loss associated with the first-exit. Specifically, the union desires to stay as a whole with all of its union members. Once the first country is gone, letting a second country default and leave the union is not that costly anymore. Our theoretical mechanism implies endogenous bail-out guarantees for members of the 1 This assumption is based on the observation of the Eurozone Crisis, where the countries were bailed out to prevent them from exiting the union. Although this motivation is of political nature, one could think of economic reasons why a defaulting government that is being cut off from financial markets needs the power to print its own currency to finance its spending. 2

3 currency union. A bail-out guarantee for a risky country reduces the interest rates on its sovereign debt, since investors expect their losses to be partially covered by the bail-out funds of the monetary union. The situation changes for an untroubled - yet risky - country, such as Portugal, after a troubled union member (Greece) ends up at the door of the currency union for an actual bail-out. From this moment on, any additional bail-out decision will need to be considered simultaneously with the first one. Because of the particular shape of the currency union value function the maximum debt level that can be supported for untroubled countries suddenly contracts - leading to the contagion of sovereign debt default risk to those countries with sufficiently high sovereign debt levels. Government bond spread (% points) 28 Greece Italy Portugal Spain Euro introduction Greek crisis Figure 1: Spreads on government bonds of GIPS (relative to German bonds). Monthly data on long-term yields, obtained from Eurostat. We introduce this theoretical mechanism into a small open economy DSGE model together with two additional features. The first one is the explicit modeling of sovereign default as a random event, as proposed by Bi (2012), and Bi and Traum (2012), where a government is assumed to default whenever its debt level exceeds its fiscal limit - a random variable drawn from a known distribution. This simplification allows us to highlight the macroeconomic implications of the contagion mechanism for an untroubled but risky country in the monetary union. 2 Second, we incorporate a sovereign risk channel that transmits the movement in sovereign 2 This approach deviates from the traditional line of literature started by Eaton and Gersovitz (1981) where default is a strategic decision. 3

4 interest rates into domestic private interest rates. This assumption has been utilized for the context of the euro area crisis by Corsetti et al. (2014), and also more broadly when studying sovereign defaults in emerging markets by Mendoza and Yue (2012). The sovereign risk channel allows us to analyze the implications of the monetary union membership on the real economy. In particular we capture an initial prolonged period of low interest rates, which leads to high output levels and debt accumulation. Once a union member is troubled, the sudden surge in borrowing costs, caused by contagion, triggers a recession and may lead to a sovereign debt crisis. We calibrate the small open economy model to match the key moments that we observe for Portugal over the period of 1998 to Portugal is particularly interesting for our analysis because it illustrates well the idea of a relatively sound country pushed to the edge of a sovereign debt crisis by contagion. Although it went through a period of slow growth prior to the crisis, its sovereign debt as a share of GDP was at the average euro area level, and the GDP contraction it experienced was milder than in most of the EMU. Therefore, it appears that the Portuguese debt problems started with the surge of borrowing costs and the repeated downgrading by the main rating agencies that followed in We investigate the macroeconomic implications of two exogenous shocks on the behavior of sovereign debt spreads: the introduction of the euro and the Greek crisis. Despite the relative simplicity of the framework, the model performs quite well in replicating the behavior of key macroeconomic variables, such as GDP and employment, as well as sovereign interest rates. Additionally, we also study a political experiment, where the first-exit premium is increased in the middle of the sovereign debt crisis, reflecting the intervention of the ECB president Mario Draghi on July 26, 2012, when he stated that the ECB is ready to do whatever it takes to preserve the euro. The speech is believed to have raised the credibility of the euro area and decreased sharply the interest rate spreads. The model is able to replicate the discussed reduction in spreads and, hence, quantifies the Draghi effect. Our paper is related to two strands of literature. Recent empirical studies discuss the puzzling behavior of spreads in the euro-area sovereign bond markets. Bernoth et al. (2012), Aizenman et al. (2013), Beirne and Fratzscher (2013) and Ghosh et al. (2013) using either yield spreads or CDS spreads document that sovereign interest rates were mostly insensitive to fiscal variables prior to the crisis, and that this changed drastically during the crisis. Moreover, Mink and de Haan (2013), Ludwig (2014), and Brutti and Saur (2015) find empirical evidence for contagion in sovereign debt markets within the EMU. Our paper complements 3 An interesting example of an opposite situation is Belgium, which had much higher debt levels, similar output performance and a series of political crises, which resulted in 535 days without a government in , but experienced no sovereign debt crisis in this period. We come back to the case of Belgium in our discussion in section 5. 4

5 the empirical literature on the spreads in the EMU by providing a theoretical framework. Our model is able to explain the observed differences in sensitivity of interest rates to fiscal variables over time. Our work is also related to theories which aim to investigate the euro area crisis. Broner et al. (2014) build a small open economy model with creditor discrimination to explain the rapid increase in the share of sovereign bonds held by domestic investors in the southern euro area countries. Aguiar et al. (2013) and Corsetti and Dedola (2013) show how a credible central bank may prevent a self-fulfilling sovereign debt crisis in a stand-alone country and argue that this ability is lost within a monetary union. Corsetti et al. (2014) investigate in a two-region monetary union how high debt levels in one of the regions may lead to a self-fulfilling sovereign debt crisis in the whole union. Forni and Pisani (2013) evaluate the effects of sovereign debt restructuring within a monetary union using a two-region DSGE model. Beetsma and Mavromatis (2014) consider different forms of debt mutualisation in a monetary union. Finally, the decision of a potential euro area break-up is considered by Alvarez and Dixit (2014). The rest of the paper is organized as follows. Section 2 presents the basic mechanism of our theory. Section 3 outlines the small open economy model, which we use to consider the dynamic implications of the monetary union and regimes. Section 4 is devoted to the quantitative analysis of our model calibrated to the Portuguese economy. Section 5 considers potential extensions of the theory and its policy implications. Finally, section 6 concludes. 2 The key mechanism Let us consider a government of a small open economy within a monetary union. Every period the country issues some amount of one-period bonds, B t. These bonds pay a net return r t and are traded on international capital markets. We assume that the international investors are risk neutral, which implies that the required expected return on government bonds has to equal the risk-free interest rate, which we denote with r. The no-arbitrage condition of a risk-neutral investor in the international market is expressed as follows 1 + r = (1 p(b t )) (1 + r t ) + p(b t )(1 d r θ)(1 + r t ), (1) where p(b t ) is the probability of default, θ is the expected loss of an investor in case the country defaults on its debt obligation, and d r is a variable in the range [0, 1] indicating the share of losses taken by the investor in the case of default. The effective loss burden placed on the investors, d r θ, will be key for our analysis. 5

6 Following Bi (2012) and Bi and Traum (2012), a country s default is defined as an event, at which the debt level exceeds the fiscal limit, B t > Bt+1. The fiscal limit is a stochastic variable with a known distribution; and therefore, we can reduce the probability of default to p(b t ) = P (B t > Bt+1). 2.1 Monetary union and regimes The effective loss of an investor from a defaulting country depends on the prevailing bailout regime provided by institutional arrangements of the monetary union. For a country, for whom there is no one to step in to provide financial support, d r = 1 - inducing the international investor to suffer losses from a default. The scenario with no external support during troubled times will be referred to as the stand-alone regime. If a county is bailed out by other member countries in the case of default, d r = 0 - and hence, the international investor suffers no losses. 4 Such a bail-out arrangement by the monetary union may be explicit in the form of an international treaty, or implicit. An implicit guarantee results from the fact that investors anticipate that other countries in the union will support the troubled country to keep it within the monetary union. 5 In this paper, we concentrate on implicit bail-out guarantees provided by a monetary union and call the scenario which incorporates the ex-ante bail-out expectations of an international investor as the cooperative regime. The decision of the monetary union to bail out a troubled member country is modeled as a comparison of the costs of the bail-out and the benefits of keeping the country within the union.we assume that a defaulting country has to leave the monetary union, unless it is bailed out. Although this assumption is mainly of political nature, one could think of economic reasons why a defaulting government that is being cut off from accessing financial markets needs the power to print its own currency to finance its spending and hence would desire to leave the monetary union. The other countries in the union attach some value M to the monetary union, which depends on the number of countries that continue to exist within the union (k) { m 0 + m 1 k if k = N M(k) =, (2) m 1 k if k < N. where m 0, m 1 > 0 are parameters, and N is the initial number of countries within the union before any bail-out (and exit) decision is made. This simple specification assumes that the 4 One could imagine a bail-out with partial losses to investors, 0 < d r < 1. Nevertheless, to keep the model simple we will assume that d r = 0 whenever there is a bail-out. 5 For a discussion of implicit bail-out guarantees in the context of the East Asian crisis see e.g. Corsetti et al. (1999). 6

7 countries attach some constant value to keeping each member within the union, m 1, but they also attach some value to keeping all countries within the union at the same time. This local increasing returns to scale feature reflects the idea that the first country leaving a monetary union would imply a union-wide loss to the valuation of the union. 6 We refer to this as the first-exit cost. Such costs can be associated with increases in the volatility of the common currency (such as the euro) and an increase in the instability of the union-wide financial system (such as the European banking network). In this paper, we concentrate on investigating the potential general equilibrium implications of first exit costs - without specifying particular sources that can explain such costs. The cost of a bail-out equals to the expected losses that need to be financed because of the default, i.e. θ(1 + r t )B t. In normal times the probability of multiple countries running into debt trouble at the same time is very low, implying, the bail-out decision to be considered separately for each member of the union. This means that the bail-out condition boils down to θ(1 + r t )B t < M(N) M(N 1) = m 0 + m 1. (3) It is important, however, to keep in mind that the interest rate depends on the regime. Therefore, the conditions for the prevailing regime can be stated as Cooperative, if B t < B, Regime = Multiple equilibria, if B B t < B, Stand-alone, if B Bt, where B is the level of debt, which solves (3) with equality under the stand-alone regime, and B is the solution to the same under the cooperative regime. Due to the effect the regimes have on interest rates, it always holds that B B. The above condition states that if the expected bail-out costs are lower than the maximum bail-out benefit m 0 +m 1 that a country can generate, then the union countries are expected to intervene and the cooperative regime prevails. If the cost of bailing out under the cooperative regime exceeds the maximum benefit from bailing out a country, then investors expect no intervention; hence, the stand-alone regime prevails. Finally, if the result of a comparison of the expected costs and benefits of a bail-out depends on the prevailing regime then both regimes are self-fulfilling equilibria. Stated differently, if the investors expect either of the two regimes to prevail, then they will charge the appropriate interest rates. If the government (4) 6 The linear functional form is used only for simplicity. In fact, all the result in this section hold for any M(k) that exhibits local increasing returns to scale, such that the marginal loss associated with the first-exit is the highest, or stated differently, the results hold for any M(k) that satisfies N>k>1 M(N) M(N 1) > M(k) M(k 1). 7

8 bail out costs BO SA BO CO m 0 + m 1 CO regime multiple equilibria B B SA regime B Figure 2: Determination of the prevailing regime. Bail-out costs (BO) are weighed against the cost of the country exiting the union (m 0 + m 1 ). happens to default then the cost of a bail-out depends on the chosen interest rate. This implies that there will be no bail-out if investors expected the stand-alone regime to prevail and charged a high interest rate. The country will be supported - and hence bailed out - if investors expect the cooperative regime to prevail and charge a low interest rates. This analysis is also presented in a graphical form in figure 2. The two curves named BO SA and BO CO represent the expected bail-out costs under the stand-alone and the cooperative regime, respectively. The points where the two curves cross the horizontal line - representing the maximum bail-out value that can be associated with an individual country m 0 + m 1 - determine the threshold debt levels, B and B, which endogenously characterize the prevailing regime. 2.2 Contagion The bail-out decision looks different when one of the countries within the union is already undergoing a debt trouble and is receiving financial aid for a bail-out. Then, any other contemporaneous bail-out decision will have to be considered jointly with this initial bailout, which is already underway. This modifies the optimal bail-out condition to J θ(1 + r t,j )B t,j < M(N) M(N J) = m 0 + Jm 1, (5) j=1 8

9 where J is the total number of countries in need of a bail-out, and the subscript j denotes j-th country. In general, whenever some of the J countries may need a bail-out simultaneous to the country already going through a bail-out, the maximal bail-out available to any of the J countries will be lower than m 0 + m 1. This shift in the maximum available bail-out funds may lead to a situation in which some countries exceed the debt threshold B and hence switch from the cooperative regime to the stand-alone regime. 7 bail out costs BO SA BO CO m 0 + m 1 m 1 B t B B B Figure 3: Contagion mechanism within a monetary union. A shift in the maximum available bail-out (from m + m 0 to a new, lower level) leads to a switch from the cooperative to the stand-alone regime. The possibility of contagion associated with multiple countries ending up in distress simultaneously is presented in figure 3. In this scenario, the country has a debt level B t, which is lower than B if the maximum bail-out is m 0 + m 1. This means that the country operates under the cooperative regime. The situation changes, however, once the maximum bail-out falls from m 0 + m 1 to a new lower level (somewhere between m 0 + m 1 and m 1 ), because another country is already going through a bail-out phase. The country debt level does not change, but the debt thresholds do, and it leads to B t > B. Hence, the country switches to the stand-alone regime and its borrowing costs surge, potentially leading to a higher accumulation of debt. This may turn an initially fiscally sound country into a troubled 7 This analysis looks only at the expected costs of a bail-out, hence, a regime switch does not mean that the country necessarily defaults. 9

10 economy. The risk of a regime switch depends on the initial sovereign debt level of a given country. In general, whenever the debt level satisfies m 1 θ(1 + r t ) < B t < m 0 + m 1 θ(1 + r t ) this country may experience a regime switch caused by the sovereign-debt contagion. That risk depends on the fiscal position of the remaining countries in the union and their probability of a debt crisis. Applying the above described theoretical mechanism to the situation in the European Monetary Union, one could expect two regime switches. The first one took place around 1999 when the European Monetary Union came into life and the creditors started to expect that the repayments on sovereign debt of each Euro-zone country will be guaranteed by the whole monetary union. This is a switch from the stand-alone to the cooperative regime - causing a contraction in borrowing rates for Southern European countries. The next regime switch took place during the global financial crisis. The first country hit by the crisis was Greece, and the countries of the euro area were quick to react. But the amount of financial support committed to Greece might have been higher than the marginal value of keeping Greece within the monetary union, which is m 1 in our model. If that was the case, then the maximum support that could be available for the next troubled country is strictly less than m 0 + m 1. This would imply a downward shift in the maximum debt level supporting the cooperative regime, B. For the case of countries with moderately high debt levels, this will translate into an endogenous switch from the cooperative regime into the stand-alone regime, causing the sudden rise in borrowing costs as observed in several Southern European countries - simultaneous to the Greek bail-out discussions. 8 3 The DSGE model In order to investigate the dynamic properties of the described contagion mechanism and the potential consequences of regime switches, we need to incorporate our theoretical framework into a full-fledged macroeconomic model. For this purpose we develop a small open economy DSGE model - similar to the framework analyzed by Schmitt-Grohe and Uribe (2003), and Neumeyer and Perri (2005) - with three key features. The first characteristic of our framework is related to the incorporation of government s (2014). 8 The political economy aspects involved in the Greek bail-outs are discussed in Ardagna and Caselli 10

11 default risk. We explicitly model default risk of a country s government as the probability that its debt level exceeds the fiscal limit. This modelling approach that was first introduced by Bi (2012) and Bi and Traum (2012). The second key feature of the model is the introduction of the bail-out decision by the group of the monetary union members - excluding the member country whose macroeconomic behavior we analyze. The union decides about its bail-out support for a country by comparing the costs of bailing out that particular country s government with the foregone benefits of letting that country exit the monetary union following a default. This decision affects the losses that the international investors have to bear on sovereign bonds. Additionally, we assume that a bail-out is not a one-time transfer, but a commitment to financially support the defaulting country over a number of periods - as we delineate below. Finally, the last key characteristic of our model is the assumption concerning the country specific interest rate. We assume that the interest rate on a country s sovereign bonds is also the interest rate offered to households and firms. This assumption allows the private interest rates to react to regime switches and is conceptually related to two (similar) alternative assumptions made in the literature on sovereign default. According to the first one, used by Mendoza and Yue (2012), private credit repayments might be partially diverted in the event of a sovereign default. The second one, made by Corsetti et al. (2013, 2014), introduces a sovereign risk channel, which makes private risk premia dependent on domestic sovereign risk. Both assumptions imply that private interest rates follow the dynamics of the interest rates faced by the government. Corsetti et al. (2013) provide evidence that this effect was economically significant in the euro area countries during the recent crisis. 3.1 Households Consider a small open economy populated by an infinite number of identical households, which derive utility from consumption, c t, and disutility from hours worked, l t, as follows E 0 t=0 β t U(c t, l t ), (6) where β (0, 1) is the discount factor, and U is the period utility. For the utility we assume a functional form of U(c, l) = 1 1 σ [c χlυ ] 1 σ with σ, χ > 0 and υ > 1. Households own all the physical capital in the economy, k t, which evolves according to k t+1 = (1 δ)k t + i t, (7) 11

12 where δ (0, 1) is the depreciation rate of capital, and i t denotes investment in future capital. The agents in this model face a sequence of period budget constraints given by b t = (1 + r t 1 )b t 1 + c t + i t + Φ(k t+1 k t ) + Ψ(b t ) w t l t u t k t + T t G t, (8) where b t is the household s net debt position at the end of period t, r t is the interest rate on household debt, 9 Φ( ) is the capital adjustment cost, Ψ( ) is the portfolio adjustment cost. The variable w t l t is the labor income, u t k t is the income from the rental of physical capital that accrue to the household. Finally, the variables T t and G t denote the lump-sum taxes and the government expenditures, respectively. 10 Capital adjustment costs take the functional form Φ(x) = (φ/2)x 2, where φ > 0, while portfolio adjustment costs are assumed to be equal Ψ(x) = (ψ/2)(x b) 2, where ψ > 0 and b are constants. 11 The problem of the household can be represented as maximizing (6) subject to (7) and (8). The first order conditions associated with household s problem yield [ ] Uc (c t+1, l t+1 ) β(1 + r t )E t = 1 ψ(b t U c (c t, l t ) b), (9) U l (c t, l t ) = w t U c (c t, l t ), (10) (1 + r t ) [1 + E t Φ (k t+1 k t )] = E t F k(k t+1, l t+1 ) + 1 δ + E t Φ (k t+2 k t+1 ), (11) where (9) is the standard intertemporal Euler equation associated with the debt/savings decision, (10) determines labor supply, and (11) is the Euler equation associated with capital investment. 3.2 Firms Firms are perfectly competitive. They rent capital and hire labor from households to produce the homogeneous good using a Cobb-Douglas production function F (k, l) = Ak α l 1 α. (12) 9 We introduce the sovereign risk channel in the simplest possible way by assuming that the interest rate faced by households equals the interest rate on sovereign bonds as highlighted above. 10 All variables in this model are real and expressed in terms of consumption units and prices are assumed to be constant and equal to the overall price level in the monetary union. This simple approach follows from the assumption of purchasing power parity and a common currency in the whole monetary union. Price and inflation level differences within the EMU are a well known fact and have been reported by i.a. Turunen et al. (2011) and Estrada et al. (2013). The analysis of this issue is intentionally left for future research. 11 Portfolio adjustment costs, also known as debt holding costs, are needed to guarantee the stability of the model. For alternative ways of closing a SOE model see Schmitt-Grohe and Uribe (2003). 12

13 Due to a friction in the labor market firms need to borrow the funds necessary to pay the wage bill at the beginning of the period, which resembles a working capital constraint. Hence, profits earned by firms can be expressed as Π(k, l) = F (k, l) uk (1 + r)wl. (13) Each period firms choose production factors to maximize profits, which give rise to the following first order conditions w = F l(k, l) 1 + r, (14) u = F k (k, l). (15) Since the production function is homogeneous of degree one the profits always equal to zero. 3.3 Government The government finances its spending, G t through taxes on households, T t and debt, B t. The budget constraint of the government takes the form G t + (1 + r t 1 )B t 1 = B t + T t. (16) As in Corsetti et al. (2014), we let the tax revenues to behave according to a reaction function T t = τ Y [ ρ τ Y t + (1 ρ τ )Ȳ ] + τ B ( B t 1 B ), (17) where both parameters τ Y and τ B are positive, and Ȳ, B are steady state values of output and debt, respectively. This form of a reaction function indicates that tax revenues increase with the improvement in economic activity, as well as with rising debt. Additionally, τ B is assumed to be large enough to prevent debt from exploding. At the same time we assume government spending to be constant over time, with G t = Ḡ.12 As in section 2, we assume that default takes place when the sovereign debt level exceeds the fiscal limit, B. Following Bi (2012) and Bi and Traum (2012), we specify the cumulative density function of the fiscal limit distribution as a logistical function. Then the default 12 Since neither taxes, nor government spending are distortive in this model, the role of taxes and government spending is limited to the role played by the primary surplus. Therefore, the assumption of constant government spending and reactive tax revenues is not too restrictive as it is equivalent to any other combination of the two that yields the same behavior of the primary surplus. 13

14 probability takes the form of p(b t ) = exp(η 1 + η 2 B t ) 1 + exp(η 1 + η 2 B t ), (18) where η 1 and η 2 are time-invariant parameters dictating the shape of the distribution. In the event of default, the investors suffer a loss - θ - unless the country is bailed out by the other members of the monetary union. The losses are drawn from a known distribution, once the country faces a default, where θ and θ are the minimum and maximum haircut levels, respectively. The no-arbitrage condition of a risk-neutral investor in the international market is expressed as 1 + r = [1 p(b t )] (1 + r t ) + p(b t )P (θ(1 + r t )B t BO max )(1 + r t ) +p(b t ) [1 P (θ(1 + r t )B t BO max )] E t [1 θ no bail-out] (1 + r t ), (19) where BO max is the maximum bail-out level supported by the union. 13 The right hand side of the above equation is the sum of the returns in the three possible default realizations: Specifically, no default, default with a bail-out and a default without bail-out, weighted by the probabilities of those cases realizing next period. In the first two cases the investors bear no losses, hence the returns are simply 1 + r t. In the third case they suffer a loss, therefore the return is multiplied by E t [1 θ no bail-out], which is the expected value of the fraction of the return left after the haircut, given that there was no bail-out. In general, the equation simplifies to 1 + r = 1 + r t, for debt levels below a threshold value B for which bail-outs always occur, and to 1 + r = (1 + r t )(1 θp(b t )) for debt levels above B, at which bail-outs are never granted. The lower debt threshold represents the highest debt level at which it is optimal to bail out a defaulting country even in the case of the highest possible losses θ. Therefore, B has to satisfy θ(1 + r)b = BO max. (20) The upper-bound is the lowest debt level at which it is too costly to bail out a defaulting country even in the case of the lowest possible haircut draw. Hence, the upper-bound is defined by the following condition θ(1 + r) B = BO max. (21) 13 In the basic model described in section 2, BO max = m 0 + m 1 in the case of a one-country bail-out decision. 14

15 The debt levels below B and above B correspond to the cooperative and stand-alone regimes, respectively. For debt levels between those threshold values the bail-out decision depends on the actual draw of θ. We refer to this as the hybrid regime in which bail-outs occur with some probability Dynamic bail-outs In contrast to the one-time character of bail-outs in the basic model of section 2, in the small open economy model we consider bail-outs to be spread over several periods. If the member countries decide to bail out a country, they make a commitment to cover the losses of the investors, θ(1 + r t )B t, by covering a fraction ρ m of the outstanding bail-out every period. As a consequence of this dynamic bail-out setup, the decision whether to continue with the bail-out is to be made in each period, with a monotonically contracting cost of bail-out, because the member countries cannot recover the previous tranches and treat them as sunk cost. The idea of dynamic bail-outs is inspired by the shape of the financial aid programs in the EMU, which always came in tranches spread over several years. In our small economy model, whose macroeconomic behavior we analyze before and after another member country applies for a bail-out, the dynamic character of the aid package allows us to capture the slow phasing out of contagion. The gradual disappearance of contagion is caused by the fact that the cost of the first bail-out has the largest impact on the maximum bail-out available to the other countries in the first period of the bail-out. After that, the remaining size of the bail-out decreases steadily and as a result causes the maximum bail-out benefits available to the other countries to rise until the troubled country reaches its pre-crises conditions. 4 Quantitative analysis In this section we turn to describe the quantitative properties of our DSGE model. We first calibrate the model to match the Portuguese economy and then consider a scenario with two events, i.e. a switch from a stand-alone to the cooperative regime by the time of the introduction of the euro, and then a sharp reduction in the maximum bail-out benefits by the time the global crisis hit Europe and Greece got into debt trouble, which triggers a switch from the cooperative to the hybrid regime. We compare those results with the actual dynamics of macroeconomic variables within this period in order to assess whether 14 The hybrid regime replaces the multiple regimes range of the basic model presented in section 2. Depending on the possible values of θ the range corresponding to the hybrid regime might be much larger than the multiple regimes range. Uniqueness is obtained thanks to a stochastic θ. 15

16 our model can capture some of the developments observed in Portugal over the time horizon of interest. We also present an alternative quantitative experiment, where we study a sudden increase of the credibility term, m 0, in the midst of the crisis. We refer to the rise in credibility as the Draghi effect as it is meant to capture the effect of the statement made by the ECB president Mario Draghi on July 26, 2012, that the ECB is ready to do whatever it takes to preserve the euro. This single statement by the ECB president reversed market sentiments and, as the results of our simulation suggest, saved Europe from a prolonged depression. For the simulations of the model we use the perfect foresight approach with the exception that the regime switches are unexpected. 15 In practice, this translates into calculating two transition paths between two different steady states. First, the economy is assumed to be in the stand-alone steady state right before the introduction of the euro, and that is also the starting point for the transition path into the cooperative regime. The second regime switch takes place ten years after the first switch, and there is no anticipation of the switch. This means that the second transition path is simply calculated as a separate perfect foresight path starting at the eleventh year of the previous transition path and converging to the hybrid regime steady state. The Greek bail-out, which triggers the second regime switch, reduces the maximum bail-out benefits and this effect phases out gradually due to the dynamic character of the bail-out - as described in the previous section. Assuming that the regime switches are unexpected is a simplification. The first switch might have been anticipated, so one could assume that all the results around this period would have been smoother if we were to incorporate the initial switch in expectations. However, the unexpected switch assumption is definitely more plausible in the case of the second regime switch as the Greek sovereign debt crisis was indeed unexpected. Investors and policymakers failed to realize how the financial crisis was going to spread in Europe. Furthermore, the picture of the Greek fiscal situation was additionally blurred by manipulations in official statistical reports. 4.1 Calibration We calibrate the model to match the macroeconomic behavior of the Portuguese economy. We set one model-period as one year. 16 The parameterization of the model is presented in 15 An exception from the perfect foresight approach is also made for the fiscal limit, hence, also for the default decision. In the considered scenarios a sovereign default is always considered ex ante as possible, but it never occurs. 16 The most popular alternative would be to set one period to a quarter. We have chosen one year because data on the government sector are usually reported on an annual basis. Another argument for this choice is the medium term focus of this paper, as compared to traditional business cycle DSGE models. 16

17 table 1. The long-run tax rate, τ Y, is set equal to the average ratio between tax revenues and GDP in Portugal for the years between 1997 and The parameter ρ τ is set equal to 0.25 to reflect the low variability of tax revenues in the pre-crisis period. The level of government expenditures, G, is chosen so that in the steady state the primary surplus of the government allows to cover the interest payments on debt, with a steady state level of debt equaling 65% of GDP. This debt/gdp ratio reflects the average for the pre-crisis ( ) period. Table 1: Parametrization of the model Households Government Discount factor β = 0.95 Steady state tax rate τ Y = 0.40 Utility curvature σ = 2.00 Sensitivity of taxes to output ρ τ = 0.25 Labor curvature υ = 1.60 Sensitivity of taxes to debt τ B = 0.35 Relative weight of labor χ = 3.50 Long-run government spending G = 0.36 Depreciation rate of capital δ = 0.10 Minimum losses on bonds θ = Capital adjustment costs φ = 1.50 Maximum losses on bonds θ = Portfolio adjustment costs ψ = 0.12 Fiscal limit distribution η 1 = 11 η 2 = 11 Firms Monetary Union Technology parameter A = 1.93 First-exit premium m 0 = 0.07 Effective capital share α = 0.33 Intrinsic value m 1 = 0.08 Bail-out tranche ρ m = 0.20 Since there are no realizations of sovereign default in developed countries in the modern history, the parameters of the fiscal limit distribution (η 1 and η 2 ), and the losses in case of default (θ) have to be based on data for emerging countries and the current risk evaluations in the euro area. Therefore, we assume that θ is drawn from a uniform distribution with a domain of [0.025; 0.225]. This specification for the distribution of θ results in expected default losses that match investors effective default losses on emerging market bonds - as computed by Bi (2012). We then calibrate the parameters of the fiscal limit distribution to follow the actual relationship between Portuguese debt levels and the spread between Portuguese and German sovereign bond interest rates during the debt crisis. The calibrated parameters are η 1 = 11 and η 2 = 11, which are close to the coefficient estimates for Italy and Greece by Bi and Traum (2012). Finally, the portfolio adjustment costs parameter, ψ, is calibrated to match a current account reversal of approximately 10%, as observed in Portugal in the first few years after the Greek crisis. The parameters governing the household s problem are chosen based on values traditionally used in macroeconomic studies. The discount factor, β = 0.95, and the depreciation rate 17

18 of capital, δ = 0.1, are annual equivalents of the commonly used quarterly values of and 0.025, respectively. The utility curvature parameters, as well as the capital adjustment costs, are standard values commonly used in developed small open economy models. 17 We choose the relative weight of labor in the utility function to target the actual average share of time spent at work in Portuguese households. The two parameters defining the production function are the effective share of capital, α, and the technology parameter, A. As standard in the literature, we set α = 0.33, which is also consistent with Portuguese macroeconomic data. We set A equal to 1.93 in order to normalize the steady-state output level to 1. The parameters of the monetary union s value function (m 0 and m 1 ) cannot be observed directly. Therefore, we deduct the implicit values implied by these two parameters. First of all, we assume that the criteria of the Maastricht Treaty are informative for the political preferences of the union members and the 60% debt-to-gdp threshold was chosen in such a way that the expected losses in the case of a defaulting country that complied with this threshold are not higher than the intrinsic value associated with a particular country, i.e. m 1. This way a complying country may expect a bail-out, no matter what is the situation of the other countries in the union. Moreover, we observe that the interest rates of Portugal prior to the financial crisis were insensitive to changes in fiscal variables, as discussed in the literature review, which implies that Portugal was effectively in the cooperative regime. Based on this observation, we assume that m 0 + m 1 - which is the maximum benefit from a bail-out for the union - is at least equal to the worst possible losses in the case of a default, when the debt level is at its steady state value. Utilizing these two conditions jointly allows us to identify m 0 and m 1. The size of the bail-out tranches, ρ m, corresponds to the assumption that approximately half of the bail-out is paid out in the first three years of a bail-out process. 4.2 EMU and the two regime switches In this section, we investigate the dynamic macroeconomic effects of the two regime switches, specifically, the transition from the stand-alone to the cooperative regime by the time of the euro introduction, and from the cooperative to the hybrid regime following the Greek crisis. The channel that generates contagion is the reduction of the maximum bail-out benefits available for Portugal, which pushes the country from the cooperative regime to the hybrid regime. The behavior of the government expenditures generated by our model right after the emergence of the Greek debt crisis is chosen to capture the actual government debt dynamics observed in Portuguese data: This means that in our quantitative exercise we 17 See, e.g. Gorodnichenko et al. (2012). 18

19 capture a sharp increase in government spending in the early stage of the crisis, and then a gradual introduction of austerity measures Basic simulation Data 4 Interest rate spread (% points) Euro introduction Greek crisis Output Gap (%) Euro introduction Greek crisis Government Debt (% GDP) Employment Euro introduction Greek crisis 0.86 Euro introduction Greek crisis Figure 4: Effects of the introduction of the euro and contagion from the Greek crisis modeled as a regime switch from the stand-alone to the cooperative and from the cooperative to the hybrid regime, respectively. Data were obtained from the Eurostat and OECD databases. Figure 4 presents the behavior of the macroeconomic variables when the economy transits into a steady state equilibrium with zero sovereign-debt spreads, and the movement of the 18 Here, austerity is meant only in terms of spending cuts and/or tax increases, without any impact on the national economy, except for the indirect effect going through interest rates. This allows us to refrain from the fiscal policy oriented austerity versus stimulus discussion. For recent contributions to this discussion the reader may refer to i.a. Mendoza et al. (2014), Corsetti et al. (2013), and the discussion in Corsetti (2012). 19

20 macro variables following the reemergence of spreads. The first drop in interest rates is relatively low. This results from the fact that the spread in the model reflects only default risk, whereas the pre-emu spreads were largely driven by exchange rate risk in high inflation countries. 19 Nevertheless, the model is capable of reproducing an important empirical feature of Portuguese interest rates, which is the insensitivity of the interest rate to fiscal variables in between 1999 and This is a qualitative feature, which would not be possible to obtain in a model that solely concentrates on inflation risk or exchange rate risk. The model also captures the positive effect of the euro introduction on output and employment, but the effect is underestimated. This might be due to the lack of a channel that links the impact of exchange rate risk on trade and employment. The model replicates the recession triggered by the Greek contagion quite well. The model can account for both the depth as well as the duration of the economic downturn and predicts a prolonged recovery. The model also matches the surge in borrowing costs in between 2009 and 2012, i.e. up to the time of the statement made by the ECB president Mario Draghi on July 26, The sharp rise of interest rates transmitted to the borrowing rates in the private sector triggers the prolonged recession with both output and employment falling to levels well below their steady state values. Even though the model performs relatively well in the initial period of the crisis, it fails to capture the dynamics of the variables after the Draghi s speech in Therefore, next we study an additional quantitative experiment, where we incorporate the Draghi effect into our framework. 4.3 Draghi effect The statement made by Mario Draghi on July 26, 2012, that the ECB is ready to do whatever it takes to preserve the euro pushed the sovereign interest rates of the GIPS countries down. This speech might have prevented the complete breakdown of the EMU and a transformation of an already severe recession into a depression. In terms of our model, we could think of this particular statement by Draghi as an exogenous rise in the credibility parameter, m 0, which would push Portugal into a more favorable version of the hybrid regime. Since we lack the possibility of directly calibrating a rise in m 0 that Mario Draghi might have caused with his speech, we simply assume that he doubled it. Therefore, the augmented simulation experiment considers one additional event, on top of the earlier mentioned two regime switches: An unexpected increase in the maximum available benefits of a bail-out for 19 This has been also argued by i.a. Kan (1998) and Bassetto (2006). 20

21 Interest rate spread (% points) Basic simulation With the Draghi effect Data Euro introduction Greek crisis Output Gap (%) Euro introduction Greek crisis Government Debt (% GDP) Employment Euro introduction Greek crisis 0.86 Euro introduction Greek crisis Figure 5: Effects of the introduction of the euro and contagion from the Greek crisis modeled as a regime switch from the stand-alone to the cooperative and a decrease in the maximum available bail-out, respectively. The Draghi effect is modeled as an increase in m 0. Data were obtained from the Eurostat and OECD databases. the EMU following Mario Draghi s July 2012 speech. The simulation results are presented in figure 5. The Draghi effect is clearly visible as a sharp reduction of sovereign interest rate spreads after The transmission of the lower interest rates to the private sector stops the recession and generates a slow recovery. Lower interest rates and higher economic activity allow for a quick reduction in the debt-to-gdp ratio, which reinforces the Draghi effect by further lowering the sovereign interest rates. 21