Sovereign Debt and Structural Reforms

Transcription

1 Sovereign Debt and Structural Reforms Andreas Müller Kjetil Storesletten Fabrizio Zilibotti Working paper Presented by Ruben Veiga April 2017 Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

2 Introduction This paper: dynamic theory of sovereign debt and structural reforms. Model 1: Reforms help getting out of recessions. Default and debt renegotiation. Moral hazard. Model 2: One sided commitment program. Principal (IMF) sets an austerity program. Results/Contributions: In equilibrium there are large fluctuations of effort and consumption. Even with complete markets, fiscal policies are not optimal. Comparison with a bail-out program. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

3 Setting Small endowment economy populated by an infinite-lived representative agent. Endowment: Two state Markov: w {w, w}. Recession and normal times. Start in recession w. Good times are absorbing Switches to normal times with prob. p. Stays in recession with 1 p. p is both the probability of recovery and the reform effort. Preferences: E 0 β t [u(c t ) φ t I {default in t} X t (p t )] φ t : iid default cost. F (.) X t (p t ): reform cost. Increasing and convex. = 0 in normal times. One period bonds. 1 unit tomorrow sells at Q(b, w). Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

4 First Best Perfect insurance: c FB (b, w) = (1 β)w + βpfb (b)w 1 β(1 p FB (b)) (1 β)b Constant reform effort: β 1 β(1 p FB ) c FB (b, w) decreasing in b. p FB (b) increasing in b. (w w)u (c FB (b, w)) }{{} increase in output if recovery + X(p FB ) }{{} saved effort = X (p FB ) Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

5 Competitive Equilibrium Timing 1 Country start with b and observes w, φ. 2 Decides to default or not. 3 If threat credible (φ suff. low) creditors offer a haircut B(b, φ, w) b. 4 Country accepts or reject the offer. 5 Country issues new debt b s.t. Qb = B(b, φ, w) + c w. 6 Consumption is realized and decides reform effort. Bound on debt: b [b, b] where b = w/(r 1). If country could commit to repay Q = 1/R. Due to default risk: Q < 1/R Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

6 Competitive Equilibrium A MPE is value functions {V, W }, renegotiation threshold Φ, price Q, optimal policies {B, B, C, Ψ} such that: Value function: where: V (b, φ, w) = Max{W (b, w), W (0, w) φ} W (b, w) = Max u ( Q(b, w)b + w b ) + Z (b, w) b Z (b, w) = Max X(p) + β ( pe[v (b, φ, w)] + (1 p)e[v (b, φ, w)] ) p Z (b, w) = βe[v (b, φ, w)] Threshold renegotiation function Φ: Φ(b, w) = W (0, w) W (b, w) Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

7 Competitive Equilibrium Renegotiation offer (creditors extract full surplus): {ˆb(φ, w) if φ Φ(b, w) B(b, φ, w) = b if φ > Φ(b, w) W (ˆb(φ, w), w) = W (0, w) φ B(B(b, φ, w), w), C(B(b, φ, w), w), Ψ(b ) are the optimal sovereign decisions rules. Some arbitrage conditions on Q. Full (expected return=risk free return R) Consistency: b = B(B(b, φ, w), w) ; p = Ψ(b ) Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

8 Remarks Lemma Suppose W (b, w) exists and is strictly decreasing in b. Then, ˆb(Φ(b, w), w) = b and Φ(b, w) is strictly increasing in b. Proposition A Markov equilibrium exist with V, W continuous and non-increasing in b, Φ, Q, Ψ continuous in b, Q(b, w)b and B(b, w) non-decreasing in b. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

9 CE in Normal times Conditional Euler Equation (when φ induces honoring debt next period) { βr u (c }{{} H,w ) = u c = C(B(b, φ, w).w) (c) ; c H,w = C(B(B(b, φ, w)), w) =1 When debt is renegotiated, consumption increases: u (c t )/u (c t+1 ) > βr = 1 Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

10 CE in a recession Under some conditions C(b, w) < C(b, w). Then: Default more credible when recession Φ(b, w) > Φ(b, w) Renegotiation level lower in recession Price of debt higher in good times Better off in good times ˆb(φ, w) < ˆb(φ, w) Q(b, w) < Q(b, w) W (b, w) < W (b, w) Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

11 CE in a recession Under some conditions C(b, w) < C(b, w). Then: Default more credible when recession Φ(b, w) > Φ(b, w) Renegotiation level lower in recession Price of debt higher in good times Better off in good times ˆb(φ, w) < ˆb(φ, w) Q(b, w) < Q(b, w) W (b, w) < W (b, w) Φ(b, w) > Φ(b, w) implies three regions: b < b : country honors debt with positive prob. in normal and bad times. b [b, b]: renegotiates if recession continues for sure. b > b: always renegotiates. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

12 CE in a recession Reform effort Marginal cost of effort=gain in expected utility from escaping recession: X (Ψ(b )) = β [ EV (b, φ, w) EV (b, φ, w) ] Not efficient: Creditors reap part of the gains from recovery. Non-monotonic. For b [b, b] effort decreases in b. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

13 CE in a recession Dynamics Newly issued debt affects ex-post incentives to make reforms. [ ] MUt+1 E H = 1 + Ψ (b t+1 ) MU t Pr(H) R[Q(b t+1, w) ˆQ(b t+1, w)]b t+1 When debt is low, Ψ > 0, higher debt accumulation with moral hazard. When debt is high, Ψ < 0, lower debt accumulation with moral hazard. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

14 CE with GDP-linked debt Budget constraint in a recession: Q w (b w, b w )b w + Q w (b w, b w )b w = B(b, φ, w) + c w If recovery probability were independent of effort, we would have perfect insurance. However, with moral hazard, there is a trade-off between incentives and insurance. More recession-contingent debt strengthens the incentives to make reforms. The country issue less recession-contingent debt than in the absence of moral hazard. No full insurance even with complete markets. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

15 One-sided commitment Thomas and Worrall (1990) IMF problem (in normal times): Similarly in recession with an additional IC constraint. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

16 One-sided commitment Comparison with CE Constant consumption while PC not binding. When PC binds, renegotiation occurs and higher utility is promised. Reform effort decrease over time! It would be suboptimal for the IMF to commit never to accept any renegotiation. (inefficient default, country would not accept low consumption initially.) Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

17 Quantitative analysis Calibration: UE debt crisis (GIIPS). Calibration Welfare analysis. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

18 Conclusions With default, reforms and recessions, the CE is not efficient. Completing markets helps but does not address moral hazard problem. An intervention by an international institution with commitment (and observable effort) can improve welfare by: Smoothing consumption by transfers during recession. A well-designed program that embraces future renegotiations! Limitations: Exogenous default cost φ. Observability of effort. Costless renegotiation. One period debt. Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

19 Arbitrage conditions Back Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

20 Calibration Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18

21 Back Müller-Storesletten-Zilibotti Sovereign ( Working Debt and paper Structural Presented Reforms by Ruben Veiga ) April / 18