sovereign debt and structural reforms

Sovereign Debt and Structural Reforms

Andreas Muller Kjetil Storesletten Fabrizio Zilibotti

Working paper

Presented by Ruben Veiga

April 2017

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

Introduction

This paper: dynamic theory of sovereign debt and structuralreforms.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.

Setting

Small endowment economy populated by an infinite-livedrepresentative agent.Endowment:

Two state Markov: w ∈ {w ,w}. Recession and normal times.Start in recession w . Good times are absorbingSwitches to normal times with prob. p. Stays in recession with1− p.p is both the probability of recovery and the reform effort.

Preferences:

βt [u(ct )− φt I{default in t} − Xt (pt )]

φt : iid default cost. ∼ F (.)Xt (pt ): reform cost. Increasing and convex. = 0 in normal times.

One period bonds. 1 unit tomorrow sells at Q(b,w).

First Best

Perfect insurance:

cFB(b,w) =(1− β)w + βpFB(b)w

1− β(1− pFB(b))− (1− β)b

Constant reform effort:

1− β(1− pFB)

(w − w)u′(cFB(b,w))︸︷︷︸increase in output if recovery

+ X (pFB)︸︷︷︸saved effort

= X ′(pFB)

cFB(b,w) decreasing in b.pFB(b) increasing in b.

Competitive EquilibriumTiming

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

Competitive Equilibrium

A MPE is value functions {V ,W}, renegotiation threshold Φ, price Q,optimal policies {B,B,C,Ψ} such that:

Value function:

V (b, φ,w) = Max{W (b,w),W (0,w)− φ}

where:

W (b,w) = Maxb′

u(Q(b′,w)b′ + w − b

)+ Z (b′,w)

Z (b′,w) = Maxp−X (p) + β

(pE [V (b′, φ′,w)] + (1− p)E [V (b′, φ′,w)]

)Z (b′,w) = βE [V (b′, φ′,w)]

Threshold renegotiation function Φ:

Φ(b,w) = W (0,w)−W (b,w)

Competitive Equilibrium

Renegotiation offer (creditors extract full surplus):

B(b, φ,w) =

{b(φ,w) if φ ≤ Φ(b,w)

b if φ > Φ(b,w)

W (b(φ,w),w) = W (0,w)− φ

B(B(b, φ,w),w),C(B(b, φ,w),w),Ψ(b′) are the optimal sovereigndecisions rules.Some arbitrage conditions on Q. Full

(expected return=risk free return R)Consistency:

b′ = B(B(b, φ,w),w) ; p = Ψ(b′)

Remarks

LemmaSuppose W (b,w) exists and is strictly decreasing in b. Then,b(Φ(b,w),w) = b and Φ(b,w) is strictly increasing in b.

PropositionA Markov equilibrium exist with V ,W continuous and non-increasing inb, Φ,Q,Ψ continuous in b, Q(b,w)b and B(b,w) non-decreasing in b.

CE in Normal times

Conditional Euler Equation (when φ′ induces honoring debt nextperiod)

βR︸︷︷︸=1

u′(c′|H,w ) = u′(c) ;

{c = C(B(b, φ,w).w)

c′|H,w = C(B(B(b, φ,w)),w)

When debt is renegotiated, consumption increases:

u′(ct )/u′(ct+1) > βR = 1

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

b(φ,w) < b(φ,w)

Price of debt higher in good times

Q(b,w) < Q(b,w)

Better off in good times

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 badtimes.b ∈ [b−,b]: renegotiates if recession continues for sure.b > b: always renegotiates.

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

b(φ,w) < b(φ,w)

Price of debt higher in good times

Q(b,w) < Q(b,w)

Better off in good times

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 badtimes.b ∈ [b−,b]: renegotiates if recession continues for sure.b > b: always renegotiates.

CE in a recessionReform effort

Marginal cost of effort=gain in expected utility from escapingrecession:

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.

CE in a recessionDynamics

Newly issued debt affects ex-post incentives to make reforms.

MUt|H]

= 1 +Ψ′(bt+1)

Pr(H)R[Q(bt+1,w)− Q(bt+1,w)]bt+1

When debt is low, Ψ′ > 0, higher debt accumulation with moralhazard.When debt is high, Ψ′ < 0, lower debt accumulation with moralhazard.

CE with GDP-linked debt

Budget constraint in a recession:

Qw (b′w ,b′w )b′w + Qw (b′w ,b

′w )b′w = B(b, φ,w) + c − w

If recovery probability were independent of effort, we would haveperfect insurance.However, with moral hazard, there is a trade-off betweenincentives and insurance.More recession-contingent debt strengthens the incentives tomake reforms.The country issue less recession-contingent debt than in theabsence of moral hazard.No full insurance even with complete markets.

One-sided commitmentThomas and Worrall (1990)

IMF problem (in normal times):

Similarly in recession with an additional IC constraint.

One-sided commitmentComparison with CE

Constant consumption while PC not binding.When PC binds, renegotiation occurs and higher utility ispromised.Reform effort decrease over time!It would be suboptimal for the IMF to commit never to accept anyrenegotiation. (inefficient default, country would not accept lowconsumption initially.)

Quantitative analysis

Calibration: UE debt crisis (GIIPS). Calibration

Welfare analysis.

Conclusions

With default, reforms and recessions, the CE is not efficient.Completing markets helps but does not address moral hazardproblem.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.

Arbitrage conditions

Calibration

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