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Sovereign debt and structural reforms

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A dynamic theory of sovereign debt and structural reforms with three interacting frictions: limited enforcement, limited commitment, and incomplete markets.

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Sovereign debt and structural reforms

  1. 1. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Sovereign Debt and Structural Reforms A. Müller K. Storesletten F. Zilibotti ADEMU Seminar Series CERGE-EI Prague, March 20, 2017 Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  2. 2. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion The Debt Dilemma The Great Recession hit some Euro countries hard (Portugal, Ireland, Italy, Greece, Spain). Natural policy response to a negative income shock: 1 Borrow against future (higher) income to achieve consumption smoothing. 2 Structural reforms to spur growth and speed up recovery Problem: sovereign lacks commitment to honor debt Additional debt increases default risk premia Incentives to reform might be a¤ected by debt burden Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  3. 3. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Building Blocks A sovereign country has fallen in a recession. Recovery can be accelerated by costly structural reforms. Debt repayment is subject to limited enforcement (the Troika cannot bomb Athens). Renegotiation can avert (mitigate) the cost of default. Stochastic default costs determine the terms of renegotiation - e.g., internal politics, international sympathy, value of trade see evidence in Sturzenegger&Zettelmeyer (JIMF2011), Reinhart&Trebesch (JEEA2016). Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  4. 4. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Questions Study interaction of three frictions in a dynamic model: 1 Limited enforcement (debt can be reneged on) 2 Limited commitment (market cannot commit to punish a sovereign based on past actions) 3 Incomplete markets (no state-contingent debt) Under what conditions does the market attain/fail to attain e¢ ciency? Quantitative questions: 1 How large are the potential welfare gains? 2 Would ruling out renegotiation improve welfare? 3 How large are gains from introducing GDP-linked bonds? Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  5. 5. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Related Literature Model is related to Bulow&Rogo¤ (1989) Renegotiation entails no cost; (Potential) default cost de…nes threat point for renegotiation; Repeated renegotiation is equilibrium outcome. Add to B&R: risk aversion, a borrowing motive (consumption smoothing in recess.), reform e¤ort, and quantitative analysis Quantitative models with costly default and renegotiation Arellano (2008), Aguiar and Gopinath (2006), etc. Models of sovereign debt restructuring Ex-post ine¢ cient restructuring improves incentives to honor debt, e.g., Yue (2011), Benjamin&Wright (2008), Bolton&Jeanne (2007), Dovis (2016), Amador&al. (2015). Debt a¤ects incentives to undertake productive investments: Krugman (1988), Atkeson (1991). Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  6. 6. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Environment: Technology Stochastic aggregate endowments, w 2 [w, ¯w] (“recession” and “normal times”). A two-state Markov switching regime pt 2 [0, 1] is the (endogenous) probability of leaving the low state (w); "normal" is an absorbing state (relaxed later). Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  7. 7. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Environment: Preferences Representative in…nitely-lived agent with preferences: E0 ∑ βt u (ct ) φt Ifdefault in tg X (pt ) . X is the cost of reform, assumed to be an increasing convex function of the probability of recovery: X0 (p) > 0 and X00 (p) > 0. In normal times, X = 0. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  8. 8. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion (First-Best) Pareto Optimum Consider a planner who has access to a savings technology with return R = 1/β. Maximize agent’s utility subject to lifetime budget constraint expected PV of income equals expected PV of consumption. Assume that the planner can dictate both consumption and e¤ort choice, The optimal allocation: 1 Constant consumption sequence 2 Constant reform e¤ort during recession. Note that if R < 1/β, the planner frontloads consumption and backloads e¤ort. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  9. 9. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Markets A benevolent government issues one-period discount bonds b0, i.e., claims to one unit of next-period consumption. The bond price is denoted by Q. Small open economy: Bonds are purchased by risk neutral foreign investors; Risk-free world interest rate: R. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  10. 10. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Default and Renegotiation I Every period, the government decides whether to honor the outstanding debt, repudiate it (“inexcusable default”), or renegotiate it. Default is subject to a stochastic (i.i.d.) cost, φ, drawn from a p.d.f. f (φ) (c.d.f. F (φ)). The realization of the default cost is common knowledge. The government decides whether to honor after observing the realization of w and φ. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  11. 11. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Default and Renegotiation II Whenever the default threat is credible, creditors make a take-it-or-leave-it renegotiation o¤er. The o¤er keeps the government indi¤erent between defaulting and honoring the renegotiated debt level. No cost is due under renegotiation (for simplicity). When the risk of renegotiation is positive, Q < 1/R. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  12. 12. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Equilibrium Concept: Markov Equilibrium Focus on Markov equilibria Equilibrium functions only depend on payo¤-relevant state variables, i.e., b, φ, and w. Rules out reputational equilibria (e.g. equilibria conditional on e¤ort previous period) Direct default cost vs. reputation (B&R 2015). Captures assumption that the market cannot commit to punish sovereign for past behavior. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  13. 13. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Value Functions V (b, φ, w) = max fW (b, w) , W (0, w) φg , where: W (b, w) = max b0 u Q b0 , w b0 + w b + Z b0 , w , Z b0 , ¯w = β EV b0 , φ0 , ¯w , Z b0 , w = max p 8 < : X (p) + β 2 4 (1 p) EV (b0, φ0, w) + pEV (b0, φ0, ¯w) 3 5 9 = ; . Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  14. 14. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Renegotiation Threshold De…ne ˆb (φ, w) as the renegotiated debt that keeps the sovereign indi¤erent between repaying ˆb (φ, w) and outright default: W ˆb (φ, w) , w = W (0, w) φ. Given the realization of φ and w, the sovereign will threaten to default if b > ˆb (φ, w) . Or, identically, 9 ¯Φ (b) (resp. Φ (b)) such that the sovereign will threaten to default if φ < ¯Φ (b) (resp. φ < Φ (b)). ¯Φ (b) < Φ (b) (default is more likely in recession). Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  15. 15. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Normal Times and Recession Characterize equilibrium in two steps Normal times (after recession ends) Recession (with endogenous reform e¤ort) Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  16. 16. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Normal Time: Debt Price Since investors are risk neutral, the expected rate of return on the sovereign debt must equal R Q b0 , ¯w = 1 R 1 F Φ b0 , ¯w | {z } probability full repayment + 1 R 1 b0 Z ¯Φ(b0) 0 ˆb φ0 , ¯w f φ0 dφ0 | {z } expected debt recovery under reneg. (φ0<F (Φ(b0, ¯w ))) Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  17. 17. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.8 0.85 0.9 0.95 Bondprice,Q(b',w) Debt issued, b' Risk-free price, 1/R Normal time bar(b) Figure: Bond price function Q (b, ¯w) during normal times Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  18. 18. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Normal Times: Conditional Euler Equation Conditional on no renegotiation (H="honor debt"), a version of the Euler equation (CEE) holds: u0 (C) u0 (C0) H = u0 (Q (b0, ¯w) b0 + ¯w b) u0 (Q (B (b0, ¯w) , ¯w) B (b0, ¯w) + ¯w b0) = βR In case of renegotiation, consumption increases (relative to case when debt is honored) u0 (C) u0 (C0) R > βR Henceforth, set βR = 1. When debt is honored, the CEE yields constant consumption and debt. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  19. 19. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion 0 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 Time Debt Consumption Figure: Debt and consumption during normal times. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  20. 20. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Normal Times and Recession Characterize equilibrium in two steps Normal times (after recession ends) Recession (with endogenous reform e¤ort) Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  21. 21. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Timing 1 Aggregate state w is observed; 2 Outside option φ is observed; 3 Sovereign decides whether to honor outstanding debt (in case not, renegotiation game is played); 4 Sovereign issues new debt and consumes; 5 Sovereign exerts reform e¤ort. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  22. 22. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Bondprice,Q(b',w) Debt issued, b' Risk-free price, 1/R Normal Recession b_bar b: F(Φ(b,w l ))=1 Figure: Bond price function in normal time and recession Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  23. 23. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Reform E¤ort I Recall timing: the government chooses b0 …rst, and then p. Investors have rational expectations over p. The reform e¤ort solves: Ψ b0 = arg max p 8 < : X (p) + +β [pEV (b0, φ0, ¯w) + (1 p) EV (b0, φ0, w)] 9 = ; . The …rst order condition yields: X0 Ψ b0 | {z } marg. cost reform. = β Z ∞ 0 V b0 , φ0 , ¯w V b0 , φ0 , w dF φ0 | {z } expected bene…t of leaving the recession . Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  24. 24. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Reform E¤ort II Note: If recession ends, then the price of debt increases because the set of defaults states shrinks. Problem: reform e¤ort is chosen by the debtor after debt is issued. part of the gains from reform accrue to creditors. RESULT: Reform e¤ort is underprovided: it would be larger if this period’s e¤ort were contractible. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  25. 25. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Reform E¤ort III Two opposite forces regulate incentives to reform over time: 1 E¢ ciency: When debt is high, consumption is low, so the marginal utility of consumption is high ! ! a higher debt strengthens the incentive to reform in order to leave the recession. 2 Debt overhang: However, higher debt also makes the moral hazard problem more severe ! ! debt overhang (Krugman 1988). The e¢ ciency e¤ect dominates for a range of low b. The debt-overhang e¤ect dominates for a range of high b. RESULT: Equilibrium reform e¤ort is hump-shaped in b. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  26. 26. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Debt, b 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 ReformEffort,(b) 0.1 0.12 0.14 0.16 0.18 0.2 Figure: Reform e¤ort function Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  27. 27. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Time 1 5 T=10 15 Debt 0.6 0.8 1 1.2 1.4 1.6 Consumption 0.5 0.6 0.7 0.8 0.9 1 1.1 Debt Consumption Time 1 5 T=10 ReformEffort 0.15 0.16 0.17 0.18 0.19 0.2 Figure: Simulation of debt, consumption and e¤ort. Note: debt increases into the debt-overhang area in equilibrium Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  28. 28. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion GDP-linked debt We have exogenously assumed that the interest rate on debt is the same irrepective of the realization of the income shock (in the literature, “non-state-contingent debt”) The analysis can be extended to allow for GDP-linked debt. Market for GDP-linked debt cannot restore e¢ ciency. Culprit: moral hazard problem and limited commitment. Key insight: state-contingent debt is of limited use State-contingent debt would allow the country to insure against the continuation of the recession However, insurance mitigates incentives to reform Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  29. 29. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion GDP-linked debt (details) Let bw and b ¯w denote recession-contingent debt and recovery-contingent debt. Denote their prices by Qw b0 w , b0 ¯w and Q ¯w b0 w , b0 ¯w . The budget constraint in recession is: Qw b0 w , b0 ¯w b0 w +Q ¯w b0 w , b0 ¯w b0 w = B (b, φ, w) +c w. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  30. 30. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion GDP-linked debt (details) The value function is: V (b, φ, w) = max fb0 w ,b0 ¯w g u Qw b0 w , b0 ¯w b0 w + Q ¯w b0 w , b0 ¯w b0 ¯w + w B (b, φ, w) X Ψ b0 w , b0 ¯w + β 1 Ψ b0 w , b0 ¯w EV b0 w , w + Ψ b0 w , b0 ¯w EV (b0 ¯w , ¯w) . If the probability that the recession ends was exogenous, Ψ0 = 0, consumption would be independent of the realization of the aggregate state: c0jH,w = c0jH, ¯w = c. However, due to moral hazard, consumption falls and recession-contingent debt increases whenever the economy remains in recession and debt is honored. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  31. 31. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion A Planning Problem A dynamic principle-agent problem with one-sided commitment. Planner faces the same limited enforcement constraint as the market, but ... can commit to future policies ... can make state-contingent promises. There is a limit to the punishment that the planner can in‡ict to the agent ! send her to the market equilibrium. Promised utility approach, following Thomas and Worrall (1988). Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  32. 32. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Two cases 1 Planner can observe reform e¤ort (as can markets). 2 Planner cannot observe reform e¤ort. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  33. 33. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Constrained Optimum: E¤ort Deviation Contract speci…es e¤ort & maximizes punishment for dev. Max punishment: terminate contract and impose default cost. More formally, continuation utility from a deviation is given by ζdev X (pdev ) + β 0 @ (1 pdev ) W (0, w) +pdev W (0, ¯w) E [φ0] 1 A , where E [φ0] denotes the expected value of φ0 and pdev = arg max p f X (p) + β ((1 p) W (0, w) + pW (0, ¯w))g ) X0 (pdev ) = β [W (0, ¯w) W (0, w)] . Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  34. 34. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Constrained Optimum (in recession) P (v) = max f ¯ωφ,ωφ,cφ,pφg Z @ 2 4w cφ + β 0 @ 1 pφ P(ωφ) +pφ ¯P( ¯ωφ) 1 A 3 5 dF (φ) subject to Z @ u(cφ) X(pφ) + β (1 pφ)ωφ + pφ ¯ωφ dF (φ) = v (PKC) u(cφ) X(pφ) + β 1 pφ ωφ + pφ ¯ωφ W (0, w) φ (PC) X pφ + β 1 pφ ωφ + pφ ¯ωφ ζdev (IC) 1 P, ¯P can be interpreted as PV of creditors’exp. pro…ts 2 ωφ is the promised utility conditional on the state (i.e., the realization of φ) Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  35. 35. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Optimal Contract with Slack IC Time 1 5 T=10 15 Consumption 0.75 0.775 0.8 0.825 0.85 Time 1 5 T=10 ReformEffort 0.12 0.13 0.14 0.15 0.16 Figure: Cons. and e¤ort in the planning problem with slack IC Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  36. 36. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Optimal Contract with Initially Binding IC Time 1 5 T=10 15 Consumption 0.55 0.6 0.65 0.7 0.75 0.8 0.85 ReformEffort 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 Consumption Reform Effort Time 1 5 T=10 15 PromisedUtility,Recession -11.2 -11.1 -11 -10.9 -10.8 PromisedUtility,Recovery -1.55 -1.5 -1.45 -1.4 Recession Recovery Figure: Cons., e¤ort, and promised util. when the IC is initially binding Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  37. 37. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Normal Times and Value of Commitment Proposition: if the economy starts in normal times, then the constrained optimal allocation is equivalent to the laissez-faire equilibrium (assuming planner breaks even) Allowing for renegotiation of the bond is equivalent to introducing a full set of state-contingent securities. This equivalence does not extend to recessions with moral hazard in reform e¤ort, the lack of commitment imposes an e¢ ciency loss. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  38. 38. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Assistance Plan An agency (e.g., the IMF)... 1 Buys the outstanding initial debt b0 2 sets a constant transfer (loan) per period 3 requests a repayment (bn) as soon as the recession ends 4 sweetens the deal each time the borrower gets a low φ 5 out-of-equilibrium threat: drop borrower if e¤ort deviation Initial promise ν0 depends on the expected pro…t of the intervention: Here zero pro…t implies: P(ν0) = R ˆQ(b0, w)b0. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  39. 39. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Time 1 5 T=10 15 Debt 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Consumption 0.7 0.75 0.8 0.85 0.9 Debt Consumption Time 1 5 T=10 ReformEffort 0.12 0.13 0.14 0.15 0.16 Figure: Implementation of constrained e¢ ciency by means of an assistance program: simulation of consumption, e¤ort and "implicit debt" over time. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  40. 40. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion If the Planner Cannot Observe E¤ort... Proposition: if the planner does not observe e¤ort, then the planning (constrained optimal) allocation is equivalent to the laissez-faire equilibrium with state-contingent debt. Note: the result requires that the punishment for deviation is to go to the mkt with state-contingent debt. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  41. 41. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Recurrent recessions Exogenous (low) probability of falling into recession βR < 1 (to have a stationary debt distribution) during normal times debt (wealth) tends to a target level during recessions debt increases IC constraint binds recurrently Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  42. 42. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Parameters calibrated externally A period corresponds to one year Recession causes a 40% income fall (Greece 2007-13) Probability of falling back into a recession: 1% Annual real gross interest rate: R = 1.02 CRRA-utility with risk aversion of 2 E¤ort cost is iso-elastic: X (p) = ξ p1+ϕ Assume that ¯φ φ is distributed exponential, with truncation point ¯φ and rate parameter η. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  43. 43. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Targeted Moments Target Data Model Par. Value Average debt: 54.9% 54.0% β 0.972 (% GDP, GIIPS, 1950-2015) Bond spread: 4.04% 3.99% η 1.804 (GIIPS, at 100% debt-output ratio, 2008-2012) Maximum debt level: 178% 176% ¯φ 2.134 (% of normal output, Collard et al. 2015) Expected recession duration: 5 4.95 ϕ 14.24 (at max. reform e¤ort, years) Expected recession duration: 10 9.99 ξ 14.55 (at the debt limit ¯b, years) Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  44. 44. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Time 1 5 10 15 20 25 30 35 40 45 50 Consumption 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Market equilibrium, (a) ReformEffort 0.1 0.2 0.3 0.4 0.5 Consumption Reform Effort Time 1 5 10 15 20 25 30 35 40 45 50 Debtaccumulation 0 0.2 0.4 0.6 0.8 1 1.2 Market equilibrium, (b) Recession Debt accumulation Time 1 5 10 15 20 25 30 35 40 45 50 Consumption 0.75 0.8 0.85 0.9 Second-best, (c) ReformEffort 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Time 1 5 10 15 20 25 30 35 40 45 50 Consumption 0.7 0.8 0.9 1 1.1 First-best, (d) ReformEffort 0 0.025 0.05 0.075 0.1 0.125 0.15 Figure: Simulation of market equilibrium, second-best, and …rst-best. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  45. 45. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Non-Targeted Moments Calibration yields an average bond spread of 3%, in line with data for GIIPS-vs-Germany 1992-2015 (2.5%). Renegotiation probability is 6.5%, in line with Tomz and Wright (2013). Average haircut conditional on renegotiation is 41%, in line with Tomz and Wright (2013). Variation in haircuts is in line with Cruces and Trebesch (2013). Average debt relief (market value) 21%, in line with Reinhart and Trebesch (2016). Debt-GDP ratio’s are higher in renegotiation periods (89.7%) compared to the average debt-GDP ratio (53.7%), in line with Asonuma and Trebesch (2016). Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  46. 46. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Quantitative Welfare E¤ects Compute welfare gain of going from benchmark economy (competitive equilibrium) to an alternative economy, measured as equivalent variation (in % of consumption). Evaluated at 100% debt-GDP ratio during recession Experiment Total Debt Equivalent (% of Rec. GDP) First Best 13.17 577 State-Cont. Debt 0.94 34 State-Cont. Debt & Contr. E¤ort 2.96 113 Commitment to Honor Debt 10.97 475 Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  47. 47. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Quantitative Welfare E¤ects: Decomposition Decompose total welfare gain of going from competitive equilibrium to …rst best into a volatility e¤ect, a level e¤ect, and a discounting e¤ect. Discounting Volatility Level 75% 21% 4% Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  48. 48. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Choking Renegotiation Experiments: 1 disallow renegotiation (New York versus Argentina) either honor debt or outright default (Arellano, 2008) 2 assistance program, but commit to punish any deviation (debt renegotiation or reforms) with termination of contract E¤ects: default occurs in equilibrium larger default premium less borrowing (and less risk sharing) in equilibrium Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  49. 49. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion 0 10 20 30 40 50 Initial debt (% of GDP) -3.5 -3 -2.5 -2 -1.5 -1 -0.5 Consumptionequivalentwelfareloss(%) (a) No Renegotiation =1 =2 =3 0 20 40 60 80 100 120 Initial debt (% of GDP) -2.5 -2 -1.5 -1 -0.5 0 (b) Grexit =1 =2 =3 Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  50. 50. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Summary I A simple model of sovereign debt and reform e¤ort to evaluate the welfare e¤ect of di¤erent policies. The model is tractable: analytical characterization of the stochastic equilibrium, including CEE, the equilibrium price of debt and the probability of renegotiation. We compare the competitive equilibrium with economies with less frictions. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  51. 51. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Summary II For an economy in recession, the market (laissez-faire equilibrium) yields excessive consumption (and reform) volatility; suboptimal reform e¤ort; for large debt levels, incentive to reform falls with debt (“debt overhang”); equilibrium outcome: an “unlucky” borrower (recession drags on) will eventually enter the debt overhang region. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  52. 52. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Summary III An e¢ cient assistance program requires: ! budget support (i.e., loans) during recession followed by settling the sovereign country with a (large) debt on market terms upon recovery; & monitoring of reform e¤ort; & …scal austerity. When faced by a credible default threat, the “agency” gives in and sweetens the deal: higher consumption, lower reform e¤ort. ! no Grexit. Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti
  53. 53. Introduction Setup Competitive Equilibrium Planning Problem (one-sided commitment) Quantitative Analysis Conclusion Summary IV Time consistent? Yes, our model incorporates that a large debt increases the probability that Greece does not repay after recovering. The model is quantitatively consistent with realistic (high) debt, plausible default premium, and with the empirical haircuts after renegotiation Sovereign Debt and Structural Reforms A. Müller, K. Storesletten, F. Zilibotti

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