Gambling for Redemption and Self-Fulfilling Debt Crises

Gambling for Redemption and Self-Fulfilling Debt Crises Juan Carlos Conesa Universitat Autònoma de Barcelona and Barcelona GSE Timothy J. Kehoe University of Minnesota and Federal Reserve Bank of Minneapolis UAB May 2013

Jumps in spreads on yields on bonds of PIIGS governments (over yields on German bonds) 18 16 Greece Portugal 14 12 percent per year 10 8 6 Italy Ireland 4 Spain 2 Germany 0 2005 2006 2007 2008 2009 2010 2011 2012 Yields on 5-year government bonds 2

Definition Crisis: government forced to default because of inability to rollover debt. Note 1: Paying high yields to place bonds is not a crisis. Note 2: As of today, only Greece has suffered a crisis. 3

Theory of self-fulfilling debt crises (Cole-Kehoe) Spreads reflect probabilities of crises For low enough levels of debt, no crisis is possible For high enough levels of debt, default For intermediate levels of debt (crisis zone) optimal policy is to run down debt 4

but PIIGS ran up debt. 180 160 Greece 140 percent 2007 GDP 120 100 80 60 Germany Portugal Italy 40 Spain 20 Ireland 0 2005 2006 2007 2008 2009 2010 2011 Government debt 5

What is missing in Cole-Kehoe? 6

Severe recession in PIIGS, still ongoing 110 Real GDP per working-age person (2007 = 100) 105 100 95 90 85 Italy Germany Portugal Spain Greece Ireland 80 2005 2006 2007 2008 2009 2010 2011 Real GDP 7

government revenues also depressed. 110 real revenue per working age person (2007 = 100) 105 Germany 100 Portugal 95 Italy 90 Greece 85 Ireland Spain 80 2005 2006 2007 2008 2009 2010 2011 Government revenues 8

This paper Extends Cole-Kehoe to stochastic output. Standard consumption smoothing argument (as in Aiyagari, Chaterjee et al, Arellano) can imply running up debt. When running up debt is optimal, we call it gambling for redemption. Use model to evaluate impact of EU-IMF policy. 9

Two policy experiments Lend at onset of crisis at interest rate above pre-crises level (Clinton s bailout of Mexico in 1995). Lend before onset of crisis at below-market interest rate (EU- IMF rescue packages and ECB lending policies in 2010 2012). 10

Main mechanism of our theory Model characterizes two forces in opposite directions: 1. Run down debt (as in Cole-Kehoe) 2. Run up debt (consumption smoothing) Which one dominates depends on parameter values and EU- IMF policies. 11

Run down debt In crisis zone run down debt if: Interest rates are high. Costs of default are high. 12

Run up debt In recession run up debt if: Interest rates are low. Costs of default are low. Recession is severe. Probability of recovery is high. 13

General model Agents: Government International bankers, continuum [0,1] Consumers, passive (no private capital) Third party in policy experiments 14

General model State of the economy: s ( Baz,, 1, ) B: government debt a: private sector, a 1 normal, a 0 recession z 1: previous default z 1 1 no, z 1 0 yes : realization of sunspot GDP: 1a 1 z yaz (, ) A Z y 1 A 0, 1Z 0 parameters. 15

Model with no recovery (Cole-Kehoe) State of the economy: s ( B,1, z 1, ) B: government debt z 1: previous default z 1 1 no, z 1 0 yes : realization of sunspot GDP: 1 z y(1, z) Z y 1Z 0 parameter. 16

Model without crises State of the economy: s ( Ba,,1, ) B: government debt a: private sector, a 1 normal, a 0 recession GDP: 1a ya (,1) A y 1 A 0 parameter. 17

General model Before period 0, a 1, z 1. In t 0, a0 0 unexpectedly, GDP drops from y to Ay y. In t 1,2,..., a t becomes 1 with probability p. 1 A is severity of recession. Once a 1, it is 1 forever. t 1 Z is default penalty. Once z 0, it is 0 forever. t 18

A possible time path for GDP y y Ay AZy Zy recession default recovery t 19

Sunspot Coordination device for international bankers expectations. t U[0,1] B t outside crisis zone: if t is irrelevant B inside crisis zone: if 1 bankers expect a crisis ( t arbitrary) t 20

Government s problem Depends on timing, equilibrium conditions, to be described. Government tax revenue is y( az, ), tax rate is fixed. Choose cgb,, ', z to solve: V() s max u(, c g) EV(') s s.t. c (1 ) y( a, z) g zb y( az, ) qb ( ', sb ) ' z 0 if z 1 0. 21

International bankers Continuum [0,1] of risk-neutral agents with deep pockets First order condition and perfect foresight condition: qb ( ', s) EzB ( '( s'), s', qb ( '( s'), s')). bond price = risk-free price probability of repayment 22

Timing a t, t realized, st ( Bt, at, zt 1, t) government offers Bt 1 bankers choose to buy Bt 1 or not, q t determined government chooses z t, which determines y t, c t, and g t 23

Notes Time-consistency problem: when offering Bt 1 for sale, government cannot commit to repay B t Perfect foresight: bankers do not lend if they know the government will default. Bond price depends on Bt 1; crisis depends on B t. 24

Recursive equilibrium Value function for government V( s ) and policy functions B'( s ) and z( B', s, q ) and g( B', s, q ), and a bond price function qb ( ', s ) such that: 25

1. Beginning of period: Given z( B', s, q ), g( B', s, q ), qb ( ', s ) government chooses B ' to solve: V() s max u(, c g) EV (') s s.t. c (1 ) yazb (, ( ', sqb, ( ', s)) g( B', sqb, ( ', s)) zb ( ', sqb, ( ', s)) B y( az, ) qb ( ', sb ) ' 2. Bond market equilibrium: q( B'( s), s) Ez( B'( s), s', q( B'( s), s')). 26

3. End of period: Given V( B', a', z, ') and B' B'( s) and q q( B'( s), s), government chooses z and g to solve: max ucg (, ) EV( B', a', z, ') s.t. c (1 ) y( a, z) g zb y( a, z) qb' z 0 or z 1 z 0 if z 1 0. 27

Characterization of government s optimal debt policy Four cutoff levels of debt: b( a ), Ba, ( ) a 0,1: If B b( a), repay If b( a) B B( a), default if 1 If B B( a), default 28

We can show: b(0) b(1), b(0) B(0), b(1) B(1), and B(0) B(1). b (1), B (0)? Most interesting case: b(0) b(1) B(0) B(1). Other cases (catastrophic recessions): b(0) B(0) b(1) B(1) b(0) b(1) B(0) B(1). 29

Characterization of equilibrium prices After default bankers do not lend: qb ( ',( Ba,,0, )) 0. During a crisis bankers do not lend: If B b( a) and 1, qb ( ',( Ba,,1, )) 0 Otherwise, q depends only on B '. 30

In normal times (as in Cole-Kehoe): if B' b(1) qb ( ',( B,1,1, )) (1 ) if b(1) B' B(1) 0 if B(1) B' In a recession (for the most interesting case): if B' b(0) p(1 p)(1 ) if b(0) B' b(1) qb ( ',( B,0,1, )) (1 ) if b(1) B' B(0) p(1 ) if B(0) B' B(1) 0 if B(1) B' 31

Bond prices as function of debt and a qb ( ', a ) qb ( ',1) qb ( ',0) b (0) b (1) B (0) B (1) B ' 32

Characterization of optimal debt policy Two special cases with analytical results: p 0 (no gambling for redemption) 0 (no crises) General model with numerical experiments: V() s has kinks and B'( s ) is discontinuous because of discontinuity of qb ( ', s. ) V() s is discontinuous because government cannot commit not to default.. 33

Self-fulfilling liquidity crises, no gambling p 0, also limiting case where a 0 and p 0: Replace y with Ay. Cole-Kehoe without private capital. 34

Start by assuming that 0. When s ( Baz,, 1, ) ( B,1,1, ), V( B,1,1, ) u((1 ) y, y (1 ) B). 1 When default has occurred, s ( Baz,, 1, ) ( B,1,0, ), V( B,1,0, ) u((1 ) Zy, Zy). 1 35

b (1): Utility of repaying even if bankers do not lend: u((1 ) y, y B) u((1 ) y, y) 1 Utility of defaulting if bankers do not lend: b (1) is determined by u((1 ) Zy, Zy). 1 u((1 ) y, y) u((1 ) Zy, Zy) u((1 ) y, y b(1)) 1 1 36

Determination of B (1) requires optimal policy. If B0 b(1) and the government decides to reduce B to b (1) in T periods, T 1,2,...,. First-order conditions imply T g g ( B ). t T 1 (1 ) g B y B b 1 ( (1 )) T1 ( 0) 0 ( (1 )) (1) T g ( B ) lim g ( B ) y (1 (1 )) B. T 0 T 0 0 0. 37

T Compute V ( B 0) : T T 1 ( (1 )) T V ( B0) u((1 ) y, g ( B0)) 1 (1 ) u Zy Zy 1 (1 ) 1 T 1 1 ( (1 )) ((1 ), ) ( (1 )) T 2 u((1 ) y, y) 1 38

To find B (1), we solve V B V B V B 1 2 max ( (1)), ( (1)),..., ( (1)) u((1 ) Zy, Zy (1 ) B(1)) u((1 ) Zy, Zy). 1 V( B,1,1, ) u((1 ) y, Zy) if B b(1) 1 1 2 max V ( B), V ( B),..., V ( B) if b(1) B B(1), 1 u((1 ) Zy, Zy) if b(1) B B(1), 1 1 u((1 ) Zy, Zy) if B(1) B 1 39

Equilibrium with self-fulfilling crises, no crises B t B (1) always default q 0 crisis zone q (1 ) b (1) q 0 1 2 3 4 t 40

Consumption smoothing without self-fulfilling crises a 0 and 0. Private sector is in a recession and faces the possibility p of recovering in every period. 41

Uncertainty tree with recession path highlighted a 1 a 1 a 1 a 0 a 1 a 0 a 1 a 1 a 0 42

Two cases: Government chooses to never violate the constraint B B(0) and debt converges to B (0) if a 0 sufficiently long. Government chooses to default at T if a 0 sufficiently long. 43

Equilibrium with no default B t always default q 0 B (1) B (0) default unless a 1 q p q 0 1 2 3 4 t 44

Equilibrium with eventual default B t always default q 0 B (1) B (0) default unless a 1 q p q 0 1 2 3 4 t 45

Some possible phase diagrams in general model case 1 case 2 case 3 case 4 case 5 b (0) b (1) B (0) B(1) B 46

Crucial parameters: p,, A and Z. p small means that we are in case 1. p large and 1 A small means that we are in case 2. small and 1 Z large mean that we are in case 3. small and 1 Z small mean that we are in case 4. Case 5 is an intermediate possibility. 47

Quantitative analysis in a numerical model c ( g g) ucg (, ) where 1 Parameter Value A 0.90 Z 0.95 p 0.20 0.96 0.03 0.50 0.4041 y 100 g 28 48

Parameters are such that, if B 10, in the initial steady state g 40. We work with one-year bonds. Maturity structure makes a difference, not just average maturity! 49

Maturity of debt in 2010 Weighted average years until maturity Percent debt with one year or less maturity at issuance Germany 6.8 7.2 Greece 7.1 11.9 Ireland 6.4 0.0 Italy 7.1 19.2 Portugal 6.0 12.6 Spain 6.8 16.1 50

Model with multi period bonds Chatterjee and Eyigungor (2011) A fraction of bonds become due every period. Average maturity of bonds is 1/. Government s (reduced form) problem: V() s max u(, c g) EV (') s s.t. c (1 ) y( a, z) gz Byaz (, ) qb ( ', s)( B' (1 ) B) z 0 if z 1 0. Bond prices: q( B', s) Ez( B'( s'), s', q( B'( s'), s')) (1 ) q( B'( s'), s') 51

Results: The benchmark economy in normal times 40 35 30 25 20 15 b (1) B(1) B'( B) 10 5 0 0 5 10 15 20 25 30 35 40 52

Then, a recession hits 40 35 30 25 20 B'( B) 15 10 5 0 b (0) b (1) B(0) B(1) 0 5 10 15 20 25 30 35 40 53

Policy implications Policy 1: Lend at onset of crisis at interest rate above precrises level Providing credit at interest rate higher than 1 1 (1 ) prevents crisis, but leaves incentives to run down debt. Bill Clinton s 1995 loan package for Mexico 54

Policy 2: Lend before onset of crisis at interest rate below precrises level Providing credit at interest rate lower than 1 1 (1 ) 1 1 or ( p(1 p)(1 )) provides incentive to gamble for redemption. EU-IMF 2010 rescue package for Greece 55

Policy 2: third party lends at r 0.04 in normal times 50 45 40 35 30 25 20 15 B'( B) 10 5 0 b (1) B(1) 0 5 10 15 20 25 30 35 40 45 50 56

The upper threshold goes up. Debt can go up even in normal times. 57

and in a recession 50 45 40 35 30 25 B'( B) 20 15 10 5 0 b (0) B (0) 0 5 10 15 20 25 30 35 40 45 50 More gambling for redemption. 58

Sensitivity analysis: the impact of in normal times 59

Sensitivity analysis: the impact of in recession 60

Extensions: Keynesian features Panglossian borrowers á la Krugman (1998) 61

Keynesian features Government expenditures are close substitutes for private consumption expenditures: ucg (, ) ( c g c g) 1. Probability of recovery p( g ) varies positively with government expenditures: p '( g) 0. 62

Panglossian borrowers Krugman (1998), Cohen and Villemot (2010) The government is overly optimistic about the probability of a recovery: g p p where p is the probability that international lenders assign to a recovery. 64

Proposition: Suppose that qb ( ', s) p(1 p)(1 ) or qb ( ', s) p(1 ). Then holding B'( B, s ). g p fixed and lowering p results in lower Similarly, holding p fixed and increasing B'( B, s ). g p results in lower 65

We could also analyze the case where the government is overly optimistic about the probability of a self-fulfilling crisis: g and obtain similar results. Bottomline: Optimistic governments feel the market charges too much of a premium and hence want to reduce debt. Pessimistic governments (or governments with private information about the low probability of recovery) want to increase debt. 66

Time varying risk premia Two different probabilities of a self-fulfilling crisis, 2 1, transitions follow a Markov process: 11 12 21 22. A country can be repaying its debts when faced with 1, then make the transition to 2 and be forced to default. 67

Concluding remarks Quantitative model provides: Plausible explanation for the observed behavior of PIIGS. Plausible explanation for impact of rescue packages and subsidized loans. Why Greece and not Belgium? 68