{'fraction_non_alphanumeric': 0.02601339891451832, 'fraction_numerical': 0.011575644504748982, 'mean_word_length': 4.747410746923358, 'pattern_counts': {'":': 0, '<': 2, '<?xml version=': 0, '>': 4, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Reducing Risk While Sharing it: A Fiscal Recipe for the EU at the Time of COVID-19

The COVID-19 lockdowns have brought about the need of large fiscal responses in all European countries. However, countries across Europe are differently equipped to respond to the shock due to differences in economic conditions and fiscal space. We build on the model by Berger et al. (2019) to compare gains from alternative mechanisms of EU fiscal integration in the presence of moral hazard. We show that any EU response strategy to the COVID-19 crisis excluding mutual financial support to member countries lacks credibility. Some form of fiscal risk sharing is indeed better than none, especially in presence of increasing sovereign default risk of some EU member countries. The moral hazard created by risk sharing can be hedged by introducing some form of fiscal delegation to Brussels. The desirable level of delegation, however, depends on its costs. When these are low, risk sharing and delegation are substitutes and it is optimal to opt for high delegation and low risk sharing. On the contrary, when delegation costs are high, centralization and risk sharing are complements and both are needed. Proposed arrangements at the EU level in response to the COVID-19 shock seem to reflect these basic insights by rotating around a combination of fiscal risk sharing and delegation in the form of fiscal spending conditionality.


INTRODUCTION
The Global Coronavirus Crisis (GCC) is a joint health and economic crisis of unprecedented proportions in recent history. Reflecting the spread of the contagion, which had affected about 26 million people and caused over 850,000 deaths by end-August 2020, most governments have ordered "lockdowns", namely universal physical confinement to avoid contagion and closure of "non-essential" economic activities. As a result, global GDP has plummeted and a global recession of the magnitude of the Great Depression is in the making (IMF 2020). The crisis has been accompanied by historically unprecedented capital flight from emerging and developing countries and by a bout of financial market volatility unseen since the 1930s (Reinhart et al. 2020).
More so than in any previous crises, the GCC and the design of effective policies to respond to it are afflicted by extraordinary uncertainty, given the lack of clarity surrounding aspects about the disease, its path of contagion within and across countries, and the possibility of finding a cure or a vaccine in the very short term. It is thus no surprise that what constitutes the best economic policy response to the GCC is hotly debated. Many have been asking for a much larger fiscal stimulus than that for the Global Financial Crisis to defibrillate the global economy before it is too late (Draghi 2020, IMF 2020, Kapoor and Buiter 2020, Stiglitz 2020. Others believe that a more paced response, focused on health, food and essential services expenditure may be more appropriate during the initial phases of the pandemic to avoid front-loading fiscal insolvencies given the uncertain duration of the shock (Romer and Garber 2020, Krugman 2020, Griffith-Jones et al. 2020. In this case the bulk of the fiscal stimulus could be postponed to after the pandemic is over. Calls are also being made to make the post-coronavirus stimulus "green" as a way to ensure that climate change agendas do not get sidetracked (Green Stimulus Proposal 2020, Plant 2020, and efforts are being made both in the EU and in other countries to ensure that plans for the post-COVID recovery embed at least some clear green goals. The GCC is likely to put undue fiscal stress onto the European Union, given that the common COVID-19 shock will hit member countries asymmetrically, and not only from an epidemic perspective. Indeed, the ability to respond counter-cyclically is affected by stark differences in available policy space, the economic structure (prevalence of certain sectors) and growth outlooks (Bruegel 2020, IMF 2020, Chen et al. 2020). In the last few months EU countries have discussed fiercely over the desirable policy package to deploy against the crisis, knowing that the agreed solution will not only affect the pace of the recovery, but could jeopardize the same European project if not carefully planned to minimize differentials in its economic impact across the region. Reflecting these premises, a coordinated fiscal response has emerged so far, involving: (i) pandemic-crisis credit lines provided of the European Stability Mechanism; (ii) government guarantees to the European Investment Bank to extend loans to companies; (iii) SURE, a temporary loan-based instrument to mitigate the ©International Monetary Fund. Not for Redistribution surging unemployment supported by guarantees from EU countries. 4 In addition, there is a proposal of creating a 'recovery fund'-labelled "Next Generation EU" (NGEU)-of 750 billion euros to jumpstart European economies after the COVID-19 emergency is passed. Resources raised by the EU on capital markets and directed to the NGEU are going to be spent on health, green and digital policies.
In this paper, we contribute to this debate by modelling the interactions between the European Union and one or more of its member countries. In our set up, countries need to decide the size of fiscal intervention in response to the COVID-19 shock, considering that a weak response may be insufficient to deal effectively with the health and economic shock, while a strong one may put public debt on an unsustainable path.
Several proposals already exist on how to structure risk sharing in Europe. In particular, numerous scholarly contributions have helped shape the long-lasting debate on how to complete the architecture of the single currency area, a debate that gained momentum as weaknesses in the ability of the euro area to coordinate a response to the global financial crisis (GFC) became apparent in 2011-2012. Among these, many have called explicitly for the creation of a central fiscal capacity (CFC) aimed at dealing with major adverse shocks (Beblavý et al. 2015;Dolls et al., 2015;Carnot et al. 2017;Abraham et al. 2017;Beetsma et al., 2018;Berger et al. 2019;and Arnold et al. 2018). Alongside, Bénassy-Quéré et al. (2018) convincingly underscored that an effective solution requires progress on both frontsrisk sharing and risk reduction; and to that end have put forward an ingenuous proposal whereby euro area countries should finance new debt in excess of limits imposed by the EU expenditure fiscal rule with junior debt. The higher yield on junior than on senior debt would encourage fiscal discipline. Bénassy-Quéré et al. (2020b) further elaborated a modified plan to deal specifically with the COVID-19 crisis in which they call for a wide-ranging emergency package through which the EU would take responsibility for a substantial share of the overall emergency effort.
Our model builds on the work of Berger et al. (2019) to assess whether some forms of European fiscal risk sharing can lessen this trade-off affecting EU countries, allowing a rightly-sized response while minimizing the probability of a sovereign debt crisis that could damage the whole Union. 5 We add to that model a simple mechanism to capture moral hazard-the incentive for individual member countries to overspend or reduce fiscal discipline in presence of fiscal risk sharing. Our model also shares some features with the recent work by Gourinchas et al. (2020), in that it trades-off ex ante support measures versus 4 See Benassy-Quere and Weder di Mauro (2020) and Section 2 for further discussion. 5 In this paper we consider the strategic interaction between the EU and a member country (or group of countries), where the latter should be intended as the relatively "vulnerable" part of the union, which would benefit from risk sharing (via, for example, a lower cost of debt). As in Berger et al. (2019), the level of risk sharing is interpreted here as the degree by which countries are able to smooth consumption. ©International Monetary Fund. Not for Redistribution ex post bailout but differs in the spectrum of instruments considered and provides larger emphasis on the joint role of fiscal delegation and risk sharing.
We obtain three key results that make the findings in (Berger et al. 2019) useful to weigh EU fiscal policy choices at the time of COVID. First, any EU response strategy to the crisis that excludes mutual financial support of a member country at risk of insolvency as a direct result of the spending caused by the health crisis lacks credibility (under the assumption that the cost to the EU of a member going insolvent are larger than those implied by risk sharing). Second, at least some risk sharing is better than no risk sharing, even when there is a great discrepancy in crisis-related spending across the EU. In addition, it is optimal to accompany risk sharing with some level of delegation of fiscal authority to the European Union to hedge against the possible moral hazard of EU countries. The optimal level of fiscal delegation depends on its costs. When such costs are relatively low, risk sharing and delegation of fiscal authority are substitutes, and beyond a certain level of sovereign risk in one or more member countries, full centralization of fiscal authority at Brussels is the optimal policy. In contrast, if the transfer of fiscal authority to the center is costly and/or complicated (e.g. because of political constraints), the two mechanisms are complements and more risk sharing and more delegation are desirable the larger individual countries' debts following the COVID crisis.
The rest of the paper is organized as follows. In Section 2 we review the current EU proposal for a coordinated response to the COVID-19 crisis. The models are presented in Section 3. Finally, in Section 4 we discuss the key results from the analysis and ensuing policy implications.

THE EU RESPONSE TO THE COVID-19 CRISIS
European countries have been discussing fiercely over what constitutes the best policy response to tame the economic crisis triggered by the spread of the novel coronavirus. Finding an effective solution based on consensus is not only fundamental for coping with the current crisis but is likely to shape the future of the EU.
The EU's coordinated response that emerged so far seems both comprehensive and bold. On top of issuing recommendations for a coordinated health and economic policy response to the pandemics, 6 in mid-May 2020 the European Commission has launched a 540 billion euros (4 percent of EU27 GDP) economic package to support the bloc's economy during the pandemic and help it bounce back. The package includes: (i) a Pandemic Crisis Support to help finance health-related spending up to 2 percent of 2019 GDP for each euro area country (up to 240 billion euros in total) and based on existing credit lines of the European Stability Mechanism (ESM); (ii) 25 billion euros in government guarantees to the European Investment Bank (EIB) to extend loans to companies for up to 200 billion euros, with a focus on financing capital investment of small and medium enterprises (SMEs) especially after the initial phases of the pandemic; and (iii) a temporary loan-based instrument (SURE, for State Supported Short-time work or reduced work) of up to 100 billion euros to mitigate unemployment by protecting workers and jobs, supported by guarantees from EU Member States. The Pandemic Crisis Support from the ESM has become operational and the European Council has adopted the SURE.
Key, yet considerably more modest, measures for the EU Budget (about 37 billion euros and 0.3 percent of 2019 EU27 GDP) include creating two COVID-19 response investment initiatives (CRII and CRII+) to support investment in hospital infrastructure and smaller or hardest-hit economic players and regions; changes to the scope of the EU Solidarity Fund to accommodate public health crises; credit holidays to crisis-affected debtors; and a 3 billion euros macro-financial assistance (MFA) package to several enlargement and neighborhood partners to help them limit the economic fallout of the coronavirus pandemic. The European Commission also activated the general escape clause in the EU fiscal rules, which suspends the fiscal adjustment requirements for countries that are not at their medium-term objective and allows them to run deficits in excess of 3 percent of GDP; and has modified EU State Aid rules to make them more flexible especially for critical sectors such as aviation and tourism.
In addition to these measures, the European Council has proposed to create a 750 billion euros Next Generation EU fund meant to kick-start the European economy once the emergency is over. The NGEU, which, at the time of writing, still needs to be approved by the European Parliament, would be made up of 390 billion euros in grants and 360 billion euros in loans to be spent on green and digital policies as well as increased resilience to Covid-19-type crises. About 4/5ths (312 billion euros) of the 390 billion euros will be allocated to the so-called EU Recovery and Resilience Facility. Member states will access their share of these 312 billion euros from 2021 to 2023. In order to access the grant aid, which will not have to be paid back, member states must prepare national recovery plans making certain pledges based on explicit national recovery and resilience plans for 2021-2023. 7 The rest of the 390 billion grant fund-77.5 billion euros-will be added to existing EU budgetary programs which offer grant aid. The money would be raised on capital markets and paid back over a 30-year period between 2028 and 2058 in part with new taxes, including green and digital taxes. When adding the NGEU to the proposed size of the 2021-2027 multiannual financial framework of 1.1 trillion, the total financial firepower of the EU budget reaches 1.85 trillion, equivalent to around 13% of EU GDP at 2019 levels.
Since a large share of the EU stimulus is expected to be allocated on the base of needs, the package involves a considerable amount of risk sharing. Besides, both loans and grants distributed to EU member states under the NGEU are expected to meet certain criteria agreed jointly at the EU level, and any request to tap into the fund will have to be signed off by the European Commission and the EU Council of Ministers to ensure that investment and reforms financed through the NGEU help countries recover in a certain direction, which is green, digital and more resilient. 8 In this sense, the NGEU also entails a certain amount of fiscal delegation from member countries to the EU in the form of the surrender of fiscal sovereignty in the decision about how to use these resources.
Alongside these fiscal instruments, in March 2020, the European Central Bank provided monetary policy support through additional asset purchases of 120 billion euros until end-2020 under the existing program (APP), as well as temporary additional auctions at more favorable conditions under the existing targeted longer-term refinancing operations (TLTRO-III) between June 2020 and June 2021. The ECB also introduced a new liquidity facility (PELTRO), consisting of a series of non-targeted Pandemic Emergency Longer-Term Refinancing Operations carried out with an interest rate that is 25 basis points below the average MRO rate prevailing over the life of the operation. Further measures included an additional 750 billion euros asset purchase program of private and public sector securities (Pandemic Emergency Purchase Program, PEPP) until end-2020, an expanded range of eligible assets under the corporate sector purchase program (CSPP), and relaxation of collateral standards for Eurosystem refinancing operations (MROs, LTROs, TLTROs). The ECB also announced a broad package of collateral easing measures for Eurosystem credit operations in early April 2020.
As countries embark on negotiations to seal this proposal and the EU prepares to disburse the much needed funds to its member countries, it is useful to reflect on whether a joint stimulus package raised in large part by issuing EU bonds is an efficient policy solution for all individual member states and/or the Union as a whole, and what are, in that light, the optimal amounts of risk sharing and fiscal delegation to Brussels that should be pursued to ensure that the policy response is economically beneficial for all EU members and the Union itself as a whole.
The issue of what constitutes an efficient fiscal response for EU member countriesboth collectively and individually-can be explored systematically in a framework in which fiscal integration is defined along two dimensions involving the degree of risk sharing within EU countries and the degree of delegation of fiscal authority to the center. In order to design such framework, three issues need to be considered.
• What kind of risk sharing arrangement? Formal risk sharing entails a variety of possible arrangements that smooth the effects of (asymmetric) shocks. Such arrangements encompass, for example, common fiscal backstops for bank resolutions, EU-wide unemployment insurance programs, as well as rainy day funds. In the current emergency context, the use of the EMS, quasi-fiscal stimuli involving liquidity injections in the form of "helicopter money" (Galí 2020), and the issuance of joint EU bonds, like those postulated to finance the proposed NGEU, are all mechanisms of fiscal risk mitigation. Yet, while all these three arrangements offer ways to share risk, their effect and efficiency are different because of the way they affect member countries individual sovereign debt and risks, and thereby, individual countries' fiscal sustainability (Blanchard 2020). In turn, this can affect collective equilibria, if the arrangements are per se unsustainable or lack credibility. Mobilizing funds primarily via the EMS-even unconditionally-for instance, requires an increase in a member state's individual liabilities, with potential idiosyncratic sentiment implications for sovereign risk and debt sustainability. The Spring 2020 Economic Forecast of the EU Commission projects a sinister economic recession, close to the worst-case scenario assumed in the European Banking Authority (EBA) 2020 EU-wide stress test (ESRB 2020). If this recession was to materialize, it could lead by itself to an explosion of bad loans, deteriorating assets and plummeting share prices, a scenario that could be exacerbated if use of the ESM was to increase the sovereign risk of vulnerable countries or countries hit harder by the pandemic relative to other countries (Ewing 2020). Conversely, joint EU bonds like those proposed for the NGEU can redistribute risk across countries with different degrees of fiscal space. This way they can help lower the cost of financing for countries with less or no fiscal space, while buttressing all countries debt sustainability. In this sense, EU bonds are more likely to help shelter the EU from attacks to its common currency during this particularly severe health and economic crisis.
• What degree of fiscal centralization? European integration can come through centralization of fiscal authority. An EU-based fiscal capacity could provide area-wide public goods or long-term public investment financed by government contributions, taxes, or a combination of both (Arnold et al. 2018). While full centralization is politically impossible, some proposals towards centralization have started to emerge. For example, Grund et al. (2020) recently proposed to create a Pandemic Solidarity Instrument (PSI) that would lead to a partial sharing of the fiscal costs of the coronavirus crisis through the issuance of a one-off EU asset in the market, guaranteed by the EU budget and use it to provide disaster-relief and medical equipment. Eventually, European expenditures could be funded with a one-shot European wealth tax (Landais et al. 2020). In a sense this proposal goes in the same direction of the proposed NGEU, which essentially entails raising funds jointly at the EU level on capital markets by selling EU debt and paying this off through EU taxes.
• Is the COVID-19 shock symmetric or asymmetric? Beyond differences in lag and effect of different arrangements, the appropriateness of EU's fiscal policy response to the ©International Monetary Fund. Not for Redistribution COVID-19 outbreak also depends on the degree of symmetry of the pandemic shock. Here it is important to note that while it is commonly accepted that the initial shock (namely the emergence of a global epidemic of a highly contagious disease) and the economic impact of health measures (e.g. lockdowns and social distancing) have been fundamentally symmetric in nature, the duration and strength of the shock have been and remain variable across countries depending on, without loss of generality: (i) different severity, evolution, and duration of the contagion and, thus, necessary lock-down regulations; (ii) different pre-existing public finance conditions (which implies different fiscal spaces and costs for debt-financed fiscal spending); or (iii) different structural economic environments (e.g. prevalence of certain sectors as well as links to global supply chains). For example, IMF (2020) shows that reflecting the decline in output alone, the Greek debt/GDP ratio is estimated to rise by close to 20 percentage points, and by 15 percentage points in Italy, restricting fiscal space. Hence, as symmetric shocks could easily become asymmetric, a common insurance across the EU is needed to increase its resiliency.
The aim of this paper is to identify the joint fiscal strategy for the EU and its member countries that maximizes, at once, both the EU's collective and individual member countries welfare. To that end, in the next section we develop an analytical set up to compare the tradeoffs between the of alternative combinations of fiscal responses of individual EU member countries and the EU, considering different risk sharing and fiscal centralization arrangements in the face of a shock similar in nature to COVID-19.

THE MODELS
Building on the work of Berger et al. (2019), our models explicitly accounts for the strategic behavior on one side of the EU and, on the other side, of one of its member countries (or a group of them) that need to spend public funds to fight the pandemic.
As public spending swells and revenues drop because of the economic slowdown caused by the measures to contain contagion, public debt increases. Individual EU countries need then to decide how much to spend to contain the contagion, to provide adequate health services, and to sustain incomes during the lockdown, considering that the more they spend, the higher the likelihood of an increase in the cost of financing their debt and the risks, eventually, of an isolated or systemic sovereign debt crisis. As stressed by Bénassy-Quéré and Weder di Mauro (2020), it is in the self-interest of each member state-in principle-that the other member states have enough resources to fight the pandemic, and the pandemic does not trigger a sovereign debt crisis. 9 On the other hand, if effective at reducing contagion rates and at avoiding structural layoffs and market losses, their spending can dampen the economic slump, implying a more sustainable fiscal path characterized by lower debt service, lower future spending and higher future revenues.
The EU can smooth the trade-offs faced by countries between sovereign risks and economic and health risks by supporting their emergency spending during the crisis. However, this is costly, and the financial burden that may be generated as a result of the EUlevel support could be higher still in the case of a sovereign debt crisis as the welfare costs of the default for the EU (and the member countries not facing it) is increasing in the stock of sovereign debt. Crucially, offering support to individual member countries, raises the specter of moral hazard: knowing that financial help will be provided by the Union as a whole could push countries to overspend in the understanding that they would be bailed out by the EU in case of default-a problem long debated in the context of discussions for possible policy solutions to the EU's 2011 sovereign debt crisis.
As discussed in Section 2, the extent by which EU financial support is expensive and/or risky for the Union itself and for its member countries (with different economic and health risks characteristics) depends on the amount of risk shared as support is provided from the Union to individual countries. Mutualizing sovereign risks, for example by issuing EU bonds, implies lower individual countries' debt stocks in the face of the same amount of emergency spending, capping borrowing costs at the country level and thus minimizing risks of hikes in sovereign spreads and ensuing debt defaults. Likewise, the cost and riskiness of EU support depends on the amount of delegation to the center in the decisions involved on how to spend the funds received by the Union because this can reduce moral hazard by dissuading overspending, while still providing the public goods needed to overcome the health and economic crisis (Grund et al. 2020).
To capture these dynamics, we derive two models. The first model, presented in Section 3.a, explores alternative risk sharing arrangements, while the second model, presented in Section 3.b, adds in fiscal delegation and is employed to derive the optimal fiscal integration arrangement. Several assumptions are made in the analysis: • The EU can opt for different levels and forms of risk sharing and can decide to bailout a member country in case this is faced by a sovereign debt crisis; • The bailout is an ad-hoc intervention, the probability of which depends (positively) on the size of the debt of the member country being bailed out and (negatively) on the level of formal risk sharing eventually agreed by the EU; 10 • Both bailouts and formal fiscal risk sharing arrangements are costly for the EU, but less so than allowing a member country to default its fiscal obligations; • The expectation of fiscal risk sharing reduces incentives for fiscal prudence at the member country level, generating moral hazard; 11 • Fiscal authority can be enforced either at the EU or at the national level, or through some intermediate solutions, giving rise to different degrees of fiscal delegation; • Fiscal delegation to the EU reduces moral hazard and thus, the likelihood that a country faces default, but it generates administrative, legislative and political costs to the Union which are proportional to the amount of delegation attained.

a. Strategic behaviors and EU risk sharing
In the first model, we consider a sequential game (cf. Figure 1) between the EU and a representative member country ("Gov"). The country chooses to either spend to confront the health and economic emergency posed by the pandemic ("Intervention" strategy) or not ("No Intervention"). In the latter case, the health and economic fallout from the pandemic is higher. 12 After having observed the spending choice of the member country, the EU can decide either to introduce some forms of "Fiscal Risk Sharing" or not. The decision of the EU, in turn, affects the likelihood of a sovereign debt crisis hitting the member country. This event is modeled introducing a public-debt shock ("Shock"), which captures the uncertain reaction of markets to government's debt level and riskiness. More specifically, the probability of default is equal to q if no mechanism of risk sharing within the EU is in place, whereas it corresponds to p if risk sharing is present. 13 Naturally, p < q. Finally, if the country-EU decisions lead to a sovereign debt crisis, the EU can either bailout the country or not. In the latter case, the member country defaults on its debt obligations, causing losses also for the European Union. 14 Such sequence of events and decisions resembles well, in our view, the current European situation where, at the time of writing, the coordinated EU-level intervention has still to be ratified formally by the European Parliament but countries have already incurred in sizeable disaster relief spending. Figure 1: The role of fiscal risk sharing in the European Union. When the risk of insolvency critically increases in one member country, fiscal risk sharing becomes comparatively convenient to the whole Union. the probabilities p and q as well as the cost of bailout incurred by the EU and the benefit from the bailout b received by the country in need (to better understand the interaction of these variables). 14 In this model we implicitly model losses as lower ex-post payoffs; in section 3.2 we provide and endogenous formulation instead. Here we implicitly assume that the EU would be relatively unaffected if some of its member countries do not intervene to fight the pandemics. This is naturally unrealistic as the epidemic could spread crossing borders among EU countries. Relaxing this assumption would strengthen the results of the model. The payoffs of the game reflect the assumptions listed above. The worst scenario for the member country is not spending to fight the pandemic (πG 0 indicates the associated payoff). In case the country decides to intervene and spend, however, it gains more by overspending, going into default, and then being bailed out by the EU (πG h ) than by sticking to a more conservative fiscal spending plan and not facing default (πG l ). Conversely, the EU is better off when both a default and/or a bailout are avoided (πEU h ). According to our assumptions, the welfare loss induced by a bailout (πEU l ) are smaller than those produced by a default (πEU 0 ). 11 The introduction of some forms of risk sharing alters the likelihood of the country's default at the cost of imposing an additional burden c on the EU, while providing a benefit b for the member country being rescued. Finally, we assume that the country's welfare when risk is shared at the EU level and in absence of debt crisis (πG m ) is lower than the payoff it would get in case of a default with EU bailout, i.e.
. The game can be easily solved by backward induction. 15 Note that if there is no fiscal risk sharing and q = 1, the game boils down to the one in Berger et al. (2019). In this case, the "No Bailout" strategy of the EU is not time consistent. In our extended game, the equilibrium strategy of "Gov" implies intervening to tackle the health and economic emergency no matter what the EU decides to do. Differently, the optimal choices of the EU depend on the relative probabilities (p and q) of avoiding a sovereign debt crisis in presence of fiscal integration, the relative welfare loss of the bailout (πEU h − πEU l ) and the costs of the risk sharing mechanism (c). In particular, the EU is better off by introducing some fiscal risk sharing if its expected payoff under such a scenario is not inferior to the one generated in the absence of risk sharing. Such a condition holds whenever the difference in the probability of the occurrence of a debt crisis in presence or not of a risk sharing arrangement (q − p) is higher than the ratio between the cost of risk sharing and the relative welfare cost of a bailout: (1) A series of policy implications stem from this result. First, the greater the impact of emergency spending on the country's national debt, the higher the risk of a sovereign debt crisis (q grows), the greater the benefit to the EU from setting up a fiscal risk sharing mechanism to mitigate such risk. Moreover, the more effective the fiscal risk sharing arrangement at stabilizing the country's national debt (p decreases), the largest the incentive for the EU to introduce it. However, not all forms of fiscal risk sharing are the same: the lower the cost c to implement them, the more they are appealing for the EU. Finally, the introduction of a risk sharing mechanism becomes more desirable for the EU, as the relative welfare costs of a debt crisis for the EU (πEU h − πEU) increase.
These insights, which generalize the results of Berger et al. (2019) developed to examine EU-oriented solutions for the 2011 sovereign debt crisis, show that there is merit in advancing European fiscal integration to deal efficiently with the novel coronavirus health and economic crisis. The analysis indicates that an EU risk sharing mechanism is win-win for both the EU and its member countries at least in the absence of moral hazard. In the next section, we explore what happens to this result when moral hazard is present.

b. Moral hazard and EU fiscal delegation
If the EU introduces some forms of fiscal risk sharing, it must decide how much risk to share and whether, and if so to what extent, decisions on how to spend the EU-provided funds depend on conditions set by the EU's central fiscal authority. Both decisions should reflect moral hazard considerations. Here we modify the model to address such issues. Consider a principal-agent problem between (i) the EU, which is interested in the welfare benefits from sharing risk among multiple Union members (for example, through a "rainy-day" fund), and (ii) its member countries, which can in principle exploit the fact that some of their spending is financed with joint EU resources, and therefore be inclined to overspend. The amount of risk sharing is captured by f ∈ [0,1]. The EU fixes f taking into account that its member countries need to issue additional debt to cope with the crisis. The level of EU risk sharing and the increment in national debt X ∈ [0,1] that goes into COVIDrelated expenses affect the probability of a sovereign debt crisis. More precisely, the probability of the crisis (pB) is equal to: When X = 0, the model boils down to the one in Berger et al. (2019) and the likelihood of the debt crisis depends negatively only on the amount of risk sharing provided by the EU.
Indeed, a higher f reduces the domestic distress from an adverse shock by lowering the interest rate paid on the national debt rates and by isolating the economy from negative spillovers coming from shocks hitting other EU countries. On the contrary, if X reaches its upper bound (X=1), the surge in the public debt is assumed to trigger a crisis, i.e. pB = 1. As in the model in Section 3.a (and in line with Berger et al. 2019), once a sovereign debt crisis takes place, the EU has a clear incentive to bail out the country in order to minimize its losses whatever the degree of fiscal risk sharing implemented. Such an ad-hoc intervention would bring additional welfare costs for the EU which are proportional to the ©International Monetary Fund. Not for Redistribution debt level of the country, i.e. B = b + X, with b > 0. 16 Hence, the expected welfare loss from a bailout is: In this framework, the expected level fˆ of the fiscal risk sharing for the EU can be expressed as: 17 Equation (4) formalizes that support from the EU can come in two forms: through formal risk sharing, f, that reduces the probability of default or through the ad-hoc intervention that bails out the country when the default is certain. As in Berger and co-authors, we assume that the latter intervention requires the same level of support of the maximal risk sharing (f=1).
In the presence of an EU risk sharing mechanism, member countries can have an incentive to lessen or deviate from a path of fiscal discipline and/or create an extra amount of debt that is unrelated to the spending necessary to deal with the health and economic crisis from the pandemic. 18 However, delegation of fiscal authority to the EU can mitigate the risk that member countries engage in profligate fiscal policies. Indeed, when fiscal authority is more centralized, governments have a less tight control over taxes and expenditures. Thus, the moral hazard (MH) associated to countries' debt is an increasing function of the expected formal risk sharing (fˆ) and depends negatively on the degree of power delegation to the center, d ∈ [0,1]. Moral hazard is just equal to: 19 Of course, in the case of a complete fiscal union where all decisions are delegated to the center (d = 1), the MH disappears. We assume that the delegation of fiscal powers to a central authority is costly and increasing in the degree of delegation: , with c > 0. Delegation costs reflect expenses associated with the administrative, legislative and political processes and procedures necessary to attain and operate fiscal delegation from member countries to Brussels. In order to determine jointly the optimal level of European risk sharing (f) and fiscal delegation (d) to the EU for different level of countries' debt, we derive the social planner's welfare function: The first term captures the net benefit of risk sharing taking into account the possible moral hazard behavior of member countries while the second and third term represents the costs of bailout (Bˆ) and delegation (C). 20 Let us compute the first order condition for the fiscal delegation (d): .
The optimal level of fiscal delegation to the center (d * ) is equal to: 21 .
The function is U-shaped with respect to the degree of risk sharing, reaching its maximum when f = 0 or f = 1, reflecting the role played by moral hazard: when MH is stronger, that is when risk sharing is either minimal or extensive, delegation is more desirable. Figure 2a 20 As in Berger et al. (2019), we assume that moral hazard proportionally cuts the gross welfare benefits from risk sharing. Further, if moral hazard is maximal, the positive effect of risk sharing vanishes. 21 The algebraic passages to obtain d* and f* are spelled out in the Appendix. ©International Monetary Fund. Not for Redistribution shows the optimal level of delegation as a function of the surge in sovereign debt (X) related to the pandemics and the degree of risk sharing f. The rationale is clear: the EU needs a tighter control on the public finances of those member countries with higher level of national debts because fiscal profligacy in these countries would increase disproportionately the risks of their debt default. Indeed, in the limit case when a default is certain (X = 1), the optimal delegation to the EU is unique and envisages a maximal centralization, i.e. d * = 1/c. The optimal level of delegation depends also on the cost of transferring power to the center. When c ≤ 1, the marginal costs of transferring fiscal authority to the center rise less than the benefits of delegation obtained by the EU through it. In this case, the need of extraordinary and potentially un-repayable debt to fight the COVID-19 shock supports a process of fiscal integration through a central EU fiscal authority. On the contrary, when delegating to Brussels is more expensive (c > 1), the optimal level of delegation is lower, but needs to be compensated by larger fiscal risk sharing. To see this, one needs to compute the optimal level of risk sharing f * . The first order condition for the degree of fiscal risk sharing in the European Union is equal to: .
©International Monetary Fund. Not for Redistribution The optimal degree of formal risk sharing f * depends on the level of COVID-related debt (X), the welfare loss generated by a bailout and the degree of delegation to the center d. Figure 2b shows condition 10 by expressing f * as function of X and d. Two insights stem from such relationships.
First, in a more general setting we confirm the result of Berger et al. (2019): a positive amount of fiscal risk sharing improves the welfare of both the EU and its member countries even when the bailout costs b and COVID-related debt (X) are very low. 22 This result is in line with the intuition provided in Section 3.a: when there are tangible risks of a sovereign debt crisis, the presence of a risk sharing mechanism is desirable for the EU, independently from the size of the crisis itself. Second, we extend the results of Berger and co-authors. Indeed, the optimal degree of formal risk sharing might either increase or decrease with X, but such behavior depends on the degree of fiscal delegation to the center. When delegation is low, risk sharing must be rather large (f * > 1/2) and a surge in COVIDrelated debt requires increasing the degree of risk sharing; contrarily, when delegation is high, risk sharing is low (f * < 1/2) and a further increase in X makes f * shrinking further. To understand the intuition behind this finding imagine that X is at or close to 0 and f is low; hence, increasing f reduces the probability of ad-hoc support and the associated welfare loss from moral hazard by more than it lowers the expected level of risk sharing. However, when X raises, the effect of raising f on the likelihood of a sovereign crisis vanishes and it becomes optimal to reduce f * .
The level of delegation that can be sustained in the Union is adversely affected by delegation costs, as expressed in equation 8. Hence, to obtain the optimal scheme of fiscal integration one should study the system composed by equations 8 and 10. Figure 3 shows the results. 23 With high delegation costs, the optimal levels of both fiscal delegation and risk sharing increase with X until an upper bound, signaling that the two mechanisms are complements (see Figure 3, and Figure 4 in the Appendix for a zoom). Note that in this case full risk sharing (i.e. f * = 1) is an optimal solution even when a sovereign crisis is very likely but not certain (in our numerical example X = 0.9 implies pB = 0.9). On the contrary, when delegation costs are low, as the surge in sovereign debt becomes larger and larger, both the EU and its members are better off with an increasing transfer of fiscal authority to the center and a decreasing level of fiscal risk sharing. In this case, the two mechanisms become substitute. A special case is with X = 1, when a debt crisis will surely happen. In this extreme situation, the welfare of the EU always improves if the Union provides full fiscal support to 22 Assuming that b and X are positive but close zero, then the first-order condition for d implies that the planner sets f * close to 1/2. 23 We rely on two scenarios with low (c = 1) and high (c = 100) costs of delegation, fixing b = 0.01. Such settings are representative of two distinct behaviors of the optimal fiscal integration arrangements that are possible in our setting, and sensitivity analysis is performed in the Appendix (see Figure 5 and 6). The low-cost scenario is calibrated such that that the cost of full centralization would be slightly lower than the welfare cost of a sovereign bailout, while the high cost scenario implies that full delegation would cost 100 times the bailout. its defaulting member in the form of either full risk sharing when c is high, or complete delegation when c is low, to rule out moral hazard.

DISCUSSION AND CONCLUSIONS
In this paper we have employed the framework of Berger et al. (2019) to study whether there is merit in pursuing greater EU fiscal integration to respond to the health and economic crisis triggered by the COVID-19 pandemic. To that end, we have examined alternative strategic policy interactions between the EU and a representative member country that needs to decide the size of its fiscal response. The country faces a trade-off: a weak fiscal response may be insufficient to halt the pandemic and support the economy, while a stronger response may be out of reach if fiscal space is limited.
We show that fiscal integration is a desirable characteristic of the EU response to the COVID-19 crisis: the magnitude of the shock and its asymmetric nature imply a dispersion in the ability of countries to respond to the crisis and, thus, a heightened probability of sovereign debt crises in the EU absent mutualized support from the center. The analysis indicates that in this case the EU Treaty's "no-bailout" clause becomes not credible, while the introduction of some sort of fiscal risk sharing is welfare improving.
In this scenario, it is key to devise ways to ensure that mutualizing fiscal risks at the EU level does not give rise to moral hazard-the incentive for individual countries to overspend, freeriding on the risk sharing arrangements. Innovatively, we show that a strong delegation of fiscal authority to the EU is needed when moral hazard is high. With rising government debts, the optimal combination of risk sharing and fiscal delegation depends on the cost of delegation to the center-Brussels in the EU case. We demonstrate that when delegation costs are elevated, risk sharing and fiscal delegation are complementary: more risk sharing and more delegation are desirable the larger individual countries' debts. On the contrary, when delegation costs are low, fiscal delegation is a substitute for risk sharing: strong fiscal delegation is more efficient than a mix of delegation and risk sharing when public debts are elevated. Finally, we find that when the increase in public spending makes sovereign crises likely, it is preferable to pursue full European integration either via full risk sharing or via full fiscal delegation, irrespective of the level of delegation costs.
©International Monetary Fund. Not for Redistribution While stylized, our results provide basic insights on the relative costs and benefits of risk sharing versus delegation in the context of the current EU debate. The EU response so far has been broadly in the direction of providing a fiscally integrated response to the COVID crisis: as discussed in Section 2, both the SURE, the NGEU and the ECB's quasi-fiscal stimulus involve substantial risk sharing. At the same time, conditionality both under SURE and the NGEU mimic a mechanism of fiscal delegation, whereby Brussels decides the way monies should be spent at the country level and monitors deployment. Against that background, our findings tentatively indicate that aiming for more or less rigid spending conditions (i.e. a weaker or stronger delegation), should reflect the administrative and political costs of fiscal conditionality that comes with the funds. Finally, the benefits from delegation will depend on the economic and social returns of fiscal conditionality. While examining this is beyond the scope of this paper, it is plausible to expect that ensuring that monies are spent on projects capable of making the recovery more durable and more sustainable should reinforce the benefits of delegation.

First order conditions
Here we report the passages leading to the conditions from which we derive the optimal degree of delegation to the center d * and optimal level of formal fiscal risk sharing f * (see section 3.2). The welfare function of the social planner is given by .
We start by evaluating the first order con with respect to d: from which Equation (9) can be derived immediately. The first order condition with respect to f implies where fˆ= 1 − (1 − X) f + (1 − X)f 2 .  Figure 5: Sensitivity of the optimal fiscal risk sharing and delegation to the center to b (welfare costs of bailout). Parameter configuration: clow = 1, chigh = 100.