## Reducing risk while sharing it: a fiscal recipe for the EU at the time of COVID-19 (wpiea2020181-print-pdf)

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---

### Major context and motivation
- Global Coronavirus Crisis (GCC) described as joint health and economic crisis; by end-November 2020 contagion affected over 54 million people causing over 1.3 million deaths.
- GCC prompted broad “lock-downs” and large fiscal responses; crisis is likely to put undue fiscal stress on the EU because the common shock hits member countries asymmetrically due to differences in policy space, economic structure, and growth outlooks.

### EU policy response: measures and magnitudes
- European Commission mid-May 2020 package: 540 billion euros (4 percent of EU27 GDP), comprising:
  - Pandemic Crisis Support (ESM): financing health-related spending up to 2 percent of 2019 GDP for each euro area country (up to 240 billion euros in total).
  - 25 billion euros in government guarantees to the European Investment Bank (EIB) to extend loans to companies (up to 200 billion euros in loans).
  - SURE (temporary loan-based instrument): up to 100 billion euros to mitigate unemployment, supported by guarantees from EU Member States.
- EU Budget-related measures: about 37 billion euros and 0.3 percent of 2019 EU27 GDP, including CRII and CRII+, modified Solidarity Fund scope, credit holidays, and a 3 billion euros macro-financial assistance (MFA) package for enlargement and neighborhood partners.
- General escape clause: European Commission activated the general escape clause in the EU fiscal rules.
- Next Generation EU (NGEU) proposal: 750 billion euros total:
  - 390 billion euros in grants and 360 billion euros in loans.
  - Of the 390 billion euros in grants, 312 billion euros allocated to the EU Recovery and Resilience Facility.
  - 77.5 billion euros of the grant fund added to existing EU budgetary programs.
  - Member states can access their share of the 312 billion euros from 2021 to 2023; grant aid access conditioned on national recovery and resilience plans for 2021-2023.
  - Resources to be raised on capital markets and paid back over a 30-year period between 2027 and 2058, in part with new taxes (including green and digital taxes).
- Total EU-level financial firepower reaches 1.85 trillion, equivalent to around 13% of EU GDP at 2019 levels.

### ECB monetary policy support (March–early 2020 measures)
- additional asset purchases of 120 billion euros until end-2020 under the existing program (APP);
- temporary additional auctions at more favorable conditions under TLTRO-III between June 2020 and June 2021;
- new liquidity facility (PELTRO): series of non-targeted Pandemic Emergency Longer-Term Refinancing Operations at an interest rate 25bp below the average MRO rate prevailing over the life of the operation;
- additional 750 billion euros asset purchase program (Pandemic Emergency Purchase Program, PEPP) until end-2020 for private and public sector securities;
- expanded range of eligible assets under the corporate sector purchase program (CSPP);
- relaxation of collateral standards for Eurosystem refinancing operations (MROs, LTROs, TLTROs);
- broad package of collateral easing measures for Eurosystem credit operations announced in early April 2020.

### Symmetry of the shock and fiscal space implications
- Initial shock and health measures are fundamentally symmetric, but duration and strength vary across countries due to contagion evolution, lock-down regulations, pre-existing public finance conditions, and structural economic environments.
- IMF illustrative numbers: decline in output alone could raise debt/GDP by close to 20 percentage points for Greece and by 15 percentage points for Italy, restricting fiscal space.
- Symmetric shocks can become asymmetric; common insurance across the EU is needed to increase resilience.

### Modeling contribution and structure
- Extends Berger et al. (2019) to include:
  - country decision on COVID-related spending financed through national debt;
  - impact of additional debt on sovereign risk, default costs, and moral hazard;
  - joint roles of fiscal centralization (delegation to Brussels) and fiscal risk sharing.
- Model set-up: interaction between the EU and one member country (or group), where the latter may be relatively vulnerable and benefit from risk sharing.
- Highlights trade-off between ex-ante support (risk sharing) and ex-post bailouts, and emphasizes fiscal centralization as a hedge versus moral hazard.

### Key analytical results (three main findings)
- Credibility of exclusion: any EU response strategy that excludes mutual financial support for a member country rendered insolvent by COVID-related spending substantially lacks credibility (assuming EU cost of insolvency > cost implied by risk sharing).
- Risk sharing plus centralization: some form of fiscal risk sharing is better than none even with large discrepancies in crisis-related spending; optimal policy pairs risk sharing with fiscal centralization to hedge moral hazard.
- Sensitivity to delegation costs:
  - Desirable centralization increases monotonically with the stock of a country’s debt issued to finance COVID-related spending.
  - Degree of optimal risk sharing responds non-linearly to rising debt.
  - When costs of delegating fiscal authority are relatively low: optimal policy entails increasingly higher delegation and lower fiscal risk sharing as sovereign risk rises.
  - When delegation costs are relatively high: optimal mix favors more risk sharing alongside more delegation as COVID-related debt rises.
  - Beyond a certain level of sovereign risk, full centralization of fiscal authority at Brussels becomes optimal.

### Principal-agent model: key relationships and equations
- Amount of risk sharing: f ∈ [0,1]. Increment in national COVID-related debt: X ∈ [0,1].
- Probability of sovereign debt crisis:
  - p_B = 1 − f(1 − X).  (Equation (2))
- Bailout cost for a country with debt level B = b + X, with b > 0.
- Expected welfare loss from a bailout:
  - ȂB = (b + X) p_B = (b + X)[1 − f(1 − X)].  (Equation (3))
- Expected level of fiscal risk sharing:
  - ˆf = p_B + (1 − p_B) f = 1 − (1 − X) f + (1 − X) f^2.  (Equation (4))
- Moral hazard (MH) depends positively on expected formal risk sharing and negatively on degree of power centralization d ∈ [0,1]:
  - MH = ˆf (1 − d) = [1 − (1 − X) f + (1 − X) f^2] (1 − d).  (Equation (5))
  - In the case d = 1 (complete fiscal union), MH = 0.
- Cost of delegation:
  - C = c d^2 / 2, with c > 0.  (Equation (6))
- Social planner welfare:
  - W = (1 − MH) ˆf − ȂB − C = {1 − [1 − (1 − X) f + (1 − X) f^2] (1 − d)} [1 − (1 − X) f + (1 − X) f^2] − (b + X)[1 − f(1 − X)] − c d^2 / 2.  (Equation (7))
- First-order condition for d:
  - ∂W/∂d = 0 ⇐⇒ [1 − (1 − X) f + (1 − X) f^2]^2 − d c = 0.  (Equation (8))
  - Optimal d:
    - d^* = [1 − (1 − X) f + (1 − X) f^2]^2 / c.  (Equation (9))
- First-order condition for f:
  - ∂W/∂f = 0 ⇐⇒ (1 − X){(1 − 2 f)[2 ˆf (1 − d) − 1] + b + X} = 0.  (Equation (10))

### Main analytical insights and quantitative scenarios
- Positive fiscal risk sharing improves welfare even when COVID-related debt (X) and bailout cost (b) are very low; example: for small b and X the planner sets f^* close to 1/2.
- Interaction of X, f, and d:
  - As X increases, responsiveness of expected risk sharing (ˆf) to formal risk sharing (f) falls because high X raises likelihood of ad-hoc full support.
  - Larger X requires monotonically higher d (more centralization), but optimal d is constrained by centralization cost c.
  - When centralization is low, optimal risk sharing must be rather large (f^* > 1/2) and a surge in X requires increasing f.
  - When centralization is high, optimal risk sharing is low (f^* < 1/2) and further increases in X make f^* shrink further.
- Three broad results restated:
  1. Positive fiscal risk sharing is welfare improving even for small X and small bailout cost b.
  2. Relationship between optimal risk sharing and optimal centralization depends on X: higher X weakens insurance effect of f on crisis probability and makes centralization relatively more important.
  3. Costs of centralization (c) shape the optimal mix:
     - When centralization is expensive, optimal policy uses higher f (f^* > 1/2) and f^* increases with X.
     - When centralization is cheap, optimal policy relies more on delegation (d increases) and f^* < 1/2; additional X induces further centralization and lower f^*.

### Numerical parameter configurations and scenario markers (preserved exactly)
- Parameter configuration for Figure 3: c = 1 and b = 0.01.
- Two scenario comparisons for Figure 4:
  - Low delegation costs: c_low = 1, b = 0.1.
  - High delegation costs: c_high = 100, b = 0.1.
- Sensitivity of optimal risk sharing and delegation to b:
  - Panels shown for b = 0.01 and b = 0.2 across X in the range 0 to 0.91 for c_low and c_high.
- Sensitivity to c (b = 0.1):
  - c values: c = 0.8, c = 1, c = 15, c = 50, c = 100.
  - Panels show f* and d* across X in the range 0 to 0.91 for these c values.
- Notable numeric statement: the maximal delegation at the optimum corresponds to d* = 1/c = 0.01 (reported for a high-delegation-cost example).

### Policy implications and recommendations
- Introduce some form of EU-level fiscal risk sharing: welfare improving across a range of X and bailout costs.
- Pair risk sharing with mechanisms that mitigate moral hazard:
  - Increase fiscal centralization (delegation of spending/tax authority to EU) where feasible, since MH = 0 at d = 1.
  - Balance trade-offs: centralization is costly (C = c d^2 / 2), so choice between greater f or greater d depends on c and X.
- Practical guidance:
  - If centralization costs are high (large c): rely more on ex ante fiscal risk sharing (set higher f), and increase f as X rises.
  - If centralization costs are low (small c): prefer greater delegation to the EU (raise d) and reduce formal risk sharing (lower f), using centralization to offset moral hazard.
- Design considerations:
  - Ex post ad-hoc interventions (modeled as f = 1 when they occur) are more costly in welfare terms than formally agreed ex ante sharing; credible ex ante arrangements preferable when possible.
  - When member countries’ COVID-related borrowing needs are near extreme (X close to 1), ex ante commitments matter less because ad-hoc support becomes likely; in that limit maximal centralization may be optimal (d^* = 1 / c when X = 1 in the model’s limit).

### Risk sharing, fiscal delegation, and conditionality in practice
- SURE, the Recovery Fund and the ECB’s quasi-fiscal stimulus involve substantial risk sharing.
- Conditionality under SURE and the Recovery Fund mimics fiscal delegation: Brussels decides how monies should be spent at the country level and monitors deployment.
- Choice of delegation stringency should reflect administrative and political costs of fiscal conditionality.
- Benefits from delegation depend on economic and social returns of fiscal conditionality; spending on projects that make recovery more durable and sustainable increases net benefits.
- Monitoring and enforcement are inherent to the conditionality mechanisms described for SURE and the Recovery Fund.
- Formal risk sharing instruments discussed: common fiscal backstops for bank resolutions, EU-wide unemployment insurance, rainy day funds, EMS mobilization, quasi-fiscal helicopter money, joint EU bonds (e.g., NGEU), Pandemic Solidarity Instrument (PSI), and one-shot European wealth tax proposals.

*Source: “Reducing risk while sharing it: a fiscal recipe for the EU at the time of COVID-19”, Nicoletta Batini, Francesco Lamperti, and Andrea Roventini, December 11, 2020 (excerpt from wpiea2020181-print-pdf).*

### 1. INTRODUCTION   ______________________________________________________________________________ 2

### Reducing risk while sharing it: a fiscal recipe for the EU at the time of COVID-19

### Major context and motivation
- The Global Coronavirus Crisis (GCC) is described as a joint health and economic crisis of unprecedented proportions; by end-November 2020 the contagion had affected over 54 million people causing over 1.3 million deaths.
- The GCC prompted broad “lock-downs” and large fiscal responses; debates center on the size and timing of fiscal stimulus versus health-focused, paced responses.
- The crisis is likely to put undue fiscal stress on the European Union because the common shock hits member countries asymmetrically due to differences in policy space, economic structure, and growth outlooks.

### The EU policy response (measures and magnitudes)
- European Commission mid-May 2020 package: 540 billion euros (4 percent of EU27 GDP), comprising:
  - Pandemic Crisis Support (ESM): financing health-related spending up to 2 percent of 2019 GDP for each euro area country (up to 240 billion euros in total).
  - 25 billion euros in government guarantees to the European Investment Bank (EIB) to extend loans to companies (up to 200 billion euros in loans).
  - SURE (temporary loan-based instrument): up to 100 billion euros to mitigate unemployment, supported by guarantees from EU Member States.
- EU Budget-related measures: about 37 billion euros and 0.3 percent of 2019 EU27 GDP, including CRII and CRII+, modified Solidarity Fund scope, credit holidays, and a 3 billion euros macro-financial assistance (MFA) package for enlargement and neighborhood partners.
- General escape clause: the European Commission activated the general escape clause in the EU fiscal rules (suspending fiscal adjustment requirements for countries not at their medium-term objective).
- Next Generation EU (NGEU) proposal: 750 billion euros total, comprised of:
  - 390 billion euros in grants and 360 billion euros in loans.
  - Of the 390 billion euros in grants, 312 billion euros allocated to the EU Recovery and Resilience Facility (about 4/5ths).
  - 77.5 billion euros of the grant fund added to existing EU budgetary programs.
  - Member states can access their share of the 312 billion euros from 2021 to 2023; grant aid access conditioned on national recovery and resilience plans for 2021-2023.
  - Resources to be raised on capital markets and paid back over a 30-year period between 2027 and 2058, in part with new taxes (including green and digital taxes).

### Modeling contribution and structure
- Builds on Berger et al. (2019); model extended to include:
  - A country’s decision on COVID-related spending financed through national debt.
  - The impact of additional debt on sovereign risk, default costs, and moral hazard (incentives to overspend when risk is shared).
  - Emphasis on joint roles of fiscal centralization (delegation of fiscal authority to Brussels) and fiscal risk sharing.
- Model set-up: interaction between the European Union and one member country (or group), where the latter may be relatively vulnerable and benefit from risk sharing.
- Relation to other literature: shares features with Gourinchas et al. (2020) in the trade-off between ex-ante support and ex-post bailouts, but differs in instruments considered and stresses fiscal centralization as hedge versus moral hazard.

### Key analytical results (three main findings)
- Credibility of exclusion: Any EU response strategy that excludes mutual financial support to a member country at risk of insolvency as a direct result of COVID-related spending substantially lacks credibility (under the assumption that the cost to the EU of a member going insolvent are larger than those implied by risk sharing).
- Risk sharing plus centralization: Some form of fiscal risk sharing is better than none even with large discrepancies in crisis-related spending across countries; optimal policy pairs risk sharing with fiscal centralization to hedge moral hazard.
- Sensitivity to costs of delegation:
  - The desirable level of centralization increases monotonically with the stock of a country’s debt issued to finance COVID-related spending.
  - The degree of optimal risk sharing responds non-linearly to rising debt.
  - When costs of delegating fiscal authority are relatively low: optimal policy entails increasingly higher delegation and lower fiscal risk sharing as sovereign risk rises.
  - When costs of transferring fiscal powers are relatively high (e.g., political constraints): the optimal mix favors more risk sharing alongside more delegation as COVID-related debt rises.
  - Beyond a certain level of sovereign risk in a member country (or countries), full centralization of fiscal authority at Brussels becomes the optimal policy.

### Policy implications and interpretation for EU arrangements
- The combination of fiscal risk sharing instruments and delegation (fiscal conditionality) reflected in EU proposals for the COVID-19 shock aligns with the model’s core insights:
  - Mutual financial support instruments (loans, guarantees, grants) increase credibility and reduce the probability of sovereign insolvency spillovers.
  - Delegation of fiscal authority to a central capacity can mitigate moral hazard induced by risk sharing; optimal balance depends on the political and economic costs of centralization.
- Practical trade-offs: where political or administrative costs of centralization are high, the EU may need to rely more on explicit risk-sharing instruments (grants, loans, guarantees) and conditionality; where delegation is feasible and costs are low, shifting powers to the center can reduce the need for ex-ante risk sharing.

*Source: “Reducing risk while sharing it: a fiscal recipe for the EU at the time of COVID-19”, Nicoletta Batini, Francesco Lamperti, and Andrea Roventini, December 11, 2020.*

### 1.1 trillion, the total financial firepower of the EU budget reaches 1.85 trillion, equivalent to around

### wpiea2020181-print-pdf - 1.1 trillion, the total financial firepower of the EU budget reaches 1.85 trillion, equivalent to around

### EU fiscal package and ECB measures
- Total EU-level financial firepower reaches 1.85 trillion, equivalent to around 13% of EU GDP at 2019 levels.
- The NGEU involves loans and grants allocated based on needs, implying considerable risk sharing and conditionality agreed at the EU level; requests to tap the fund must be signed off by the European Commission and the EU Council of Ministers to ensure investments and reforms are "green, digital and more resilient."
- ECB monetary policy support (March 2020 and early 2020 measures):
  - additional asset purchases of 120 billion euros until end-2020 under the existing program (APP);
  - temporary additional auctions at more favorable conditions under TLTRO-III between June 2020 and June 2021;
  - new liquidity facility (PELTRO): series of non-targeted Pandemic Emergency Longer-Term Refinancing Operations at an interest rate 25bp below the average MRO rate prevailing over the life of the operation;
  - additional 750 billion euros asset purchase program (Pandemic Emergency Purchase Program, PEPP) until end-2020 for private and public sector securities;
  - expanded range of eligible assets under the corporate sector purchase program (CSPP);
  - relaxation of collateral standards for Eurosystem refinancing operations (MROs, LTROs, TLTROs);
  - broad package of collateral easing measures for Eurosystem credit operations announced in early April 2020.

### Risk sharing, fiscal centralization, and conditionality
- NGEU entails a degree of fiscal centralization: surrender of fiscal sovereignty to Brussels in deciding how to use jointly raised resources.
- Formal risk sharing arrangements discussed include common fiscal backstops for bank resolutions, EU-wide unemployment insurance programs, rainy day funds, EMS mobilization, quasi-fiscal helicopter money, and issuance of joint EU bonds (e.g., NGEU).
- Fiscal centralization proposals and instruments mentioned:
  - Pandemic Solidarity Instrument (PSI) proposal to issue a one-off EU asset guaranteed by the EU budget for disaster-relief and medical equipment;
  - one-shot European wealth tax proposed to fund European expenditures.
- Conditionality: plans required to boost growth and jobs and reinforce economic and social resilience; green criteria expected to apply to instruments like the solvency instrument.

### Symmetry of the COVID-19 shock and implications
- Initial shock and health-measure impacts are fundamentally symmetric, but duration and strength vary across countries due to:
  - different severity, evolution, and duration of contagion and lock-down regulations;
  - different pre-existing public finance conditions (different fiscal spaces and costs of debt-financed spending);
  - different structural economic environments (sectoral composition and supply-chain links).
- IMF illustrative numbers: decline in output alone could raise debt/GDP by close to 20 percentage points for Greece and by 15 percentage points for Italy, restricting fiscal space.
- Symmetric shocks can become asymmetric; hence common insurance across the EU is needed to increase resilience.

### Analytical framework and model assumptions
- Objective: identify a joint fiscal strategy that maximizes both EU collective welfare and individual member-country welfare, comparing alternative combinations of fiscal responses, risk sharing, and fiscal centralization in a COVID-19–like shock.
- Key assumptions:
  - the EU can opt for different levels and forms of risk sharing and decide on bailouts for sovereign debt crises;
  - fiscal risk sharing improves individual welfare ex ante by lowering borrowing costs for a given resource deployment;
  - bailout probability depends positively on the country’s debt size and negatively on the level of formal EU risk sharing;
  - bailouts and formal fiscal risk sharing are costly for the EU but less costly than allowing a member default;
  - expectation of fiscal risk sharing generates moral hazard reducing fiscal prudence;
  - fiscal authority can be enforced at EU, national, or intermediate levels, giving different degrees of fiscal centralization;
  - fiscal centralization reduces moral hazard and default likelihood but generates administrative, legislative and political costs that rise with centralization;
  - legislative and political costs of providing risk sharing mechanisms are negligible relative to costs of delegating fiscal authority.

### Model 1: Strategic behaviors and EU risk sharing
- Sequential game between the EU and a representative member country ("Gov"):
  - Gov chooses "Intervention" (spend to confront pandemic) or "No Intervention";
  - After observing Gov's choice, the EU decides whether to introduce "Fiscal Risk Sharing";
  - A public-debt shock ("Shock") then determines the probability of default: q if no risk sharing, p if risk sharing is present, with p < q.
  - If a sovereign debt crisis occurs, the EU can "Bailout" or choose "No Bailout" (leading to default).
- Payoff ordering for the country: πhG > πmG > πlG > π0G.
- EU welfare: better when both default and bailout are avoided (πhEU); welfare loss from bailout (πlEU) is smaller than from default (π0EU).
- Risk sharing imposes cost k on the EU and provides benefit b to the rescued member country.
- Solving by backward induction yields:
  - Gov intervenes to tackle the emergency irrespective of EU choice.
  - EU introduces fiscal risk sharing when its expected payoff with risk sharing is no less than without it. Condition (as stated in the source):
    q − p ≥ k / (πhEU − πlEU).  (Equation (1) in the text)
- Comparative statics and qualitative insights:
  - The larger the impact of emergency spending on national debt (higher q), the greater the benefit for the EU to set up fiscal risk sharing.
  - The more effective the risk sharing (lower p), the greater the incentive for the EU to introduce it.
  - The lower the implementation cost k of risk sharing, the more appealing it is.
  - The larger the relative welfare cost of a debt crisis for the EU (πhEU − πlEU), the more desirable risk sharing becomes.
- Conclusion from Model 1: In the absence of moral hazard, an EU risk sharing mechanism is win-win for both the EU and member countries; further analysis of moral hazard is explored subsequently.

*Source: Excerpt from wpiea2020181-print-pdf (IMF working paper content as provided).*

### 3.2    COVID-related debt, moral hazard and EU fiscal centralization

### 3.2    COVID-related debt, moral hazard and EU fiscal centralization

### Model setup and key relationships
- Principal-agent problem between the EU (welfare from sharing risk) and member countries (incentive to overspend when financed by joint EU resources).  
- Amount of risk sharing: f ∈ [0,1].  
- Increment in national COVID-related debt: X ∈ [0,1].  
- Probability of sovereign debt crisis (p_B):
  - p_B = 1 − f(1 − X). (2)
- Bailout cost for a country with debt level B = b + X, with b > 0.  
- Expected welfare loss from a bailout (ȂB):
  - ȂB = (b + X) p_B = (b + X)[1 − f(1 − X)]. (3)
- Expected level of fiscal risk sharing (ˆf):
  - ˆf = p_B + (1 − p_B) f = 1 − (1 − X) f + (1 − X) f^2. (4)
  - Interpretation: support can come through formal ex ante risk sharing (f) or ad-hoc ex post intervention (modeled as f = 1 when it occurs).
- Moral hazard (MH) depends positively on expected formal risk sharing (ˆf) and negatively on degree of power centralization d ∈ [0,1]:
  - MH = ˆf (1 − d) = [1 − (1 − X) f + (1 − X) f^2] (1 − d). (5)
  - In the case d = 1 (complete fiscal union), MH = 0.
- Cost of delegation/centralization:
  - C = c d^2 / 2, with c > 0. (6)
  - Centralization costs reflect administrative, legislative and political processes necessary to centralize fiscal authority.

### Social planner welfare objective
- Social planner welfare (W) combining net benefits of risk sharing (net of moral hazard), expected bailout cost, and centralization costs:
  - W = (1 − MH) ˆf − ȂB − C = {1 − [1 − (1 − X) f + (1 − X) f^2] (1 − d)} [1 − (1 − X) f + (1 − X) f^2] − (b + X)[1 − f(1 − X)] − c d^2 / 2. (7)
- First-order condition for fiscal centralization (d):
  - ∂W/∂d = 0 ⇐⇒ [1 − (1 − X) f + (1 − X) f^2]^2 − d c = 0. (8)
  - Optimal d (d^*):
    - d^* = [1 − (1 − X) f + (1 − X) f^2]^2 / c. (9)
- First-order condition for fiscal risk sharing (f):
  - ∂W/∂f = 0 ⇐⇒ (1 − X){(1 − 2 f)[2 ˆf (1 − d) − 1] + b + X} = 0. (10)
  - Optimal f (f^*) depends on X, b, and d; optimal d depends on f, X, and c.

### Main analytical insights and quantitative scenarios
- General confirmation of prior result (Berger et al. 2019):
  - A positive amount of fiscal risk sharing improves welfare even when COVID-related debt (X) and bailout cost (B) are very low.
  - Example: assuming b and X positive but close to zero, the first-order condition for d implies the planner sets f^* close to 1/2.
- Interaction between X, f, and d:
  - As X increases, the responsiveness of expected risk sharing (ˆf) to formal risk sharing (f) falls, because high X raises the likelihood of ad-hoc full support independently of ex ante commitments.
  - Larger X requires monotonically higher d (more centralization), but optimal d is constrained by centralization cost c.
  - When centralization is low (d small), optimal risk sharing must be rather large (f^* > 1/2) and a surge in X requires increasing f.
  - When centralization is high, optimal risk sharing is low (f^* < 1/2) and further increases in X make f^* shrink further.
- Three broad results:
  1. Positive fiscal risk sharing is welfare improving even for small X and small bailout cost B.
  2. The relationship between optimal risk sharing and optimal centralization depends on the level of COVID-related debt X:
     - Higher X weakens the insurance effect of f on crisis probability and makes centralization relatively more important.
  3. Costs of centralization (c) shape the optimal risk-sharing/centralization mix:
     - When centralization is expensive, optimal policy uses higher f (f^* > 1/2) and f^* increases with X.
     - When centralization is cheap, optimal policy relies more on delegation (d increases) and f^* < 1/2; additional X induces further centralization and lower f^*.

- Numerical scenario illustrations in the text / figures:
  - Parameter configuration for Figure 3: relatively low costs of centralization (c = 1) and of sovereign bailout (b = 0.01).
  - Two scenario comparisons for Figure 4:
    - Low delegation costs: c_low = 1, b = 0.1.
    - High delegation costs: c_high = 100, b = 0.1.
  - Interpretations:
    - c ≤ 1: marginal costs of transferring fiscal authority rise less than benefits → stronger fiscal integration is supported when COVID-related borrowing is large.
    - c > 1: delegation is more expensive → optimal centralization is lower and must be compensated by larger fiscal risk sharing.

### Policy implications and recommendations
- Introduce some form of EU-level fiscal risk sharing: it is welfare improving across a range of X and bailout costs.
- Pair risk sharing with mechanisms that mitigate moral hazard:
  - Increase fiscal centralization (delegation of spending/tax authority to EU) where feasible, since higher d reduces MH (MH = 0 at d = 1).
  - Recognize trade-offs: centralization is costly (C = c d^2 / 2), so the choice between greater f or greater d depends on c and the level of COVID-related debt X.
- Practical guidance based on costs and debt levels:
  - If centralization costs are high (large c): rely more on ex ante fiscal risk sharing (set higher f), and increase f as X rises.
  - If centralization costs are low (small c): prefer greater delegation to the EU (raise d) and reduce formal risk sharing (lower f), using centralization to offset moral hazard.
- Design of EU interventions:
  - Recognize that ex post ad-hoc interventions (modeled as f = 1 when they occur) are more costly in welfare terms than formally agreed ex ante sharing; thus, credible ex ante arrangements are preferable when possible.
  - When member countries’ COVID-related borrowing needs are near extreme (X close to 1), ex ante commitments matter less because ad-hoc support becomes likely; in that limit, maximal centralization may be optimal (d^* = 1 / c when X = 1 in the model’s limit).

*Source: IMF Working Paper — section 3.2, "COVID-related debt, moral hazard and EU fiscal centralization".*

### Section 2, both the SURE, the Recovery Fund and the ECB’s quasi-fiscal stimulus involve substantial

### wpiea2020181-print-pdf - Section 2, both the SURE, the Recovery Fund and the ECB’s quasi-fiscal stimulus involve substantial

### Risk sharing and fiscal delegation: summary findings
- Both the SURE, the Recovery Fund and the ECB’s quasi-fiscal stimulus involve substantial risk sharing.
- Conditionality under SURE and the Recovery Fund mimic a mechanism of fiscal delegation, whereby Brussels decides the way monies should be spent at the country level and monitors deployment.
- 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.
- The benefits from delegation will depend on the economic and social returns of fiscal conditionality. Ensuring that monies are spent on projects capable of making the recovery more durable and more sustainable should reinforce the benefits of delegation.
- The paper does not examine empirically the economic and social returns of fiscal conditionality; this is noted as beyond the scope of the paper.

### Policy-relevant implications and considerations
- Choice of delegation stringency:
  - Weigh administrative and political costs of fiscal conditionality when deciding on the rigidity of spending conditions.
  - Stronger delegation increases central control over spending but implies higher delegation costs that can offset benefits.
- Targeting of funds:
  - Prioritize projects likely to make the recovery more durable and more sustainable to increase the net benefits of delegation.
- Monitoring and enforcement:
  - Central monitoring of deployment is inherent to the conditionality mechanisms described for SURE and the Recovery Fund.

### Analytical results — welfare function and first-order conditions
- Welfare function of the social planner (as reported):
  - W = (1−MH) ˆf − ˆB − C = {1−[1−(1−X)f+ (1−X)f^2](1−d)}[1−(1−X)f+ (1−X)f^2] − (b+X)[1−f(1−X)] − c d^2/2.
- First-order condition with respect to d:
  - ∂W/∂d = [1−(1−X)f+ (1−X)f^2]^2 − dc = 0, from which Equation (9) is immediate.
- First-order condition with respect to f (sequential algebra presented):
  - ∂W/∂f reduces to (1−X){(2f−1)[1−2(1−d)ˆf] + b + X} = 0, where ˆf = 1−(1−X)f+ (1−X)f^2.

### Optimal delegation and sensitivity results (key numeric values and configurations)
- Optimal delegation with high delegation costs:
  - The maximal delegation at the optimum corresponds to d* = 1/c = 0.01.
- Sensitivity analyses reported (parameter configurations preserved exactly as presented):
  - Sensitivity of optimal fiscal risk sharing and delegation to the center to b (welfare costs of bailout). Parameter configuration: c_low = 1, c_high = 100.
    - Panels shown for b = 0.01 and b = 0.2:
      - For b = 0.01: figures display Optimal risk sharing - f* and Optimal delegation - d* across COVID-related var. gov. debt - X in the range 0 to 0.91 for both Low delegation costs and High delegation costs.
      - For b = 0.2: analogous panels for Optimal risk sharing - f* and Optimal delegation - d* across COVID-related var. gov. debt - X in the range 0 to 0.91 for Low delegation costs and High delegation costs.
  - Sensitivity of optimal fiscal risk sharing and delegation to the center to c (cost of delegation). Parameter configuration: b = 0.1.
    - c values reported: c = 0.8, c = 1, c = 15, c = 50, c = 100.
    - Panels show:
      - (a) Optimal fiscal risk sharing: Optimal risk sharing - f* across COVID-related var. gov. debt - X in the range 0 to 0.91 for the c values above.
      - (b) Optimal delegation to the center: Optimal degree of delegation to the center across COVID-related var. gov. debt - X in the range 0 to 0.91 for the c values above.

### Acknowledgments (from source)
- The authors thank Martina Occelli, Elisa Palagi and Gianluca Pallante for useful discussions and comments.
- All usual disclaimers apply. The views expressed are of the authors alone and do not necessarily reflect the views of the International Monetary Fund, its Board of Directors, or of the Independent Evaluation Office of the IMF.
- Andrea Roventini and Francesco Lamperti acknowledge support by the European Union Horizon 2020 research and innovation program under grant agreement No. 822781 - GROWINPRO.

*Source: wpiea2020181-print-pdf - Section 2, both the SURE, the Recovery Fund and the ECB’s quasi-fiscal stimulus involve substantial*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020181-print-pdf.pdf_