Gambling for Redemption and Self-Fulfilling Debt Crises

Transcription

1 Gambling for Redemption and Self-Fulfilling Debt Crises Juan Carlos Conesa Stony Brook University Timothy J. Kehoe University of Minnesota and Federal Reserve Bank of Minneapolis The Monetary and Fiscal History of Latin America Becker Friedman Institute, University of Chicago April 2014

2 Jumps in spreads on yields on bonds of PIIGS governments (over yields on German bonds) Greece Portugal 12 percent per year Spain Ireland 4 Italy 2 Germany Yields on 10-year government bonds 2

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 3

4 but PIIGS ran up debt. 160 Greece Italy percent of 2007 GDP Portugal Spain Germany Ireland Government debt 4

5 What is missing in Cole-Kehoe? 5

6 Severe recession in PIIGS, still ongoing 110 GDP per working age person (2007 = 100) Ireland Germany Portugal Spain Italy Greece Real GDP 6

7 government revenues also depressed. 110 Portugal 105 Germany revenue (2007 = 100) Italy Greece Ireland 85 Spain Real government revenues 7

8 This paper Extends Cole-Kehoe to stochastic output. Standard consumption smoothing argument (as in Aiyagari, Huggett, Chaterjee et al, Arellano, Aguiar-Gopinath) can imply running up debt. When running up debt is optimal, we call it gambling for redemption. Use model to evaluate impact of Troika (EU-ECB-IMF) policy, compare with the Clinton (1995) bailout of Mexico. 8

9 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 Troika policies. 9

10 Run down debt In crisis zone run down debt if: Interest rates are high. Costs of default are high. 10

11 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. 11

12 General model Agents: Government International bankers, continuum [0,1] Consumers, passive (no private capital) Third party in policy experiments 12

13 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. 13

14 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. 14

15 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. 15

16 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 16

17 A possible time path for GDP y y Ay AZy Zy recession default recovery t 17

18 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 18

19 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

20 International bankers Continuum [0,1] of risk-neutral agents with deep pockets First order condition and perfect foresight condition: qb ( ', s) EzB ( ', s', qb ( ', s')). bond price = risk-free price probability of repayment 20

21 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 21

22 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. 22

23 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: 23

24 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')). 24

25 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

26 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 26

27 We are interested in parameter values for which 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). 27

28 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 '. 28

29 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' 29

30 Bond prices as function of debt and a qb ( ', a ) qb ( ',1) qb ( ',0) b (0) b (1) B (0) B (1) B ' 30

31 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.. 31

32 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. 32

33 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 33

34 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))

35 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

36 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 36

37 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) 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 37

38 Equilibrium with self-fulfilling crises, no crises B t B (1) always default q 0 crisis zone q (1 ) b (1) q t 38

39 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. 39

40 Uncertainty tree with recession path highlighted a 1 a 1 a 1 a 0 a 1 a 0 a 1 a 1 a 0 40

41 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. 41

42 Equilibrium with no default B t always default q 0 B (1) B (0) default unless a 1 q p q t 42

43 Equilibrium with eventual default B t always default q 0 B (1) B (0) default unless a 1 q p q t 43

44 Quantitative analysis in a numerical model ucg (, ) log( c) log( g g) Parameter Value A 0.90 Z 0.95 p y 100 g 25 44

45 We work first with one-year bonds. We then extend model to multi-year bonds. 45

46 Results: The benchmark economy in normal times b (1) B (1)

47 Then, a recession hits b (0) b (1) B (0) B (1)

48 Maturity of debt in 2011 Weighted average years until maturity Germany 6.4 Greece 15.4 Ireland 4.5 Italy 6.5 Portugal 5.1 Spain 5.9 Think of results in terms of debt needing refinancing every year say one-sixth, as in Spain. 48

49 The extended model The government s problem is to choose cgb,, ', z to solve V() s = max u(, c g) + bev(') s s.t. c= (1- q) y( a, z) ( ) g+ zdb= qy( a, z) + q( B', s) B' -(1- d) B z 0 if z 1 0. Here [ 0,1] d Î is the fraction of the stock of debt due every period. Debt is memoryless, as in Hatchondo-Martinez, Chaterjee- Eyigungor. 49

50 Prices are also adjusted In the benchmark case b(0) < b(1) < B(0) < B(1) : ìï bd [ + (1- d) Eq '] if B ' b (0) b( p+ (1-p)(1 - p) )[ d+ (1- d) Eq' ] if b(0) < B' b(1) qb ( ', s) = ï íb(1 - p) [ d+ (1- d) Eq' ] if b(1) < B' B(0) bp(1 - p) [ d+ (1-d) Eq' ] if B(0) < B' B(1) ï 0 if B(1) < B' ïî where Eq' Eq( B'( B', s), s'). 50

51 Benchmark is d = b (0) b (1) B (0) B (1)

52 With d = b (0) b (1) B (0) B (1)

53 With d = b (0) b (1) 60 B (0) B (1)

54 With d = b (0) b (1) B (0) B (1)

55 As d becomes smaller: The thresholds shift to the right and get closer together. Gambling for redemption also for low (but vulnerable) levels of debt. In the limit, 0 d = (consuls) the lower and upper thresholds coincide and huge levels of debt can be sustained (larger than 700 percent GDP). 55

56 Extensions: Keynesian features Panglossian borrowers á la Krugman (1998) Time varying risk premia 56

57 Keynesian features Government expenditures are close substitutes for private consumption expenditures: ucg (, ) log( c gc g). Probability of recovery pg ( ) varies positively with government expenditures: p'( g) 0. 57

58 Keynesian features Government expenditures are close substitutes for private consumption expenditures: ucg (, ) log( c gc g). Probability of recovery pg ( ) varies positively with government expenditures: p'( g) 0. Keynesian features make gambling for redemption more attractive! 58

59 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. 59

60 Suppose that qb ( ', s) p(1 p)(1 ) or qb ( ', s) p(1 ). Then holding B '( Bs., ) g p fixed and lowering p results in lower Similarly, holding p fixed and increasing B'( B, s ). g p results in lower 60

61 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. Bottom line: 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. 61

62 Time varying risk premia Two different probabilities of a self-fulfilling crisis, 2 1, transitions follow a Markov process: A country can be repaying its debts when faced with 1, then make the transition to 2 and be forced to default.. 62

63 Concluding remarks Model provides: Plausible explanation for the observed behavior of PIIGS. Reasonable quantitative predictions for longer maturities. Why Greece and not Belgium? 63

64 Concluding remarks Model provides: Plausible explanation for the observed behavior of PIIGS. Reasonable quantitative predictions for longer maturities. Why Greece and not Belgium? Why the Eurozone and not the United States? What about bailouts and costly reforms? 64

65 Role of bailouts: Conesa-Kehoe, Is it too late to bail out the troubled countries in the Eurozone? Suppose that when a panic occurs, a third party (Troika) offers access to credit at a penalty interest rates and imposes collateral requirements (Bagehot, Clinton) Results: If premium is small, continue gambling If premium is high enough to discourage gambling, then it is optimal to default instead of accepting the bailout for debt levels higher than around 80 percent GDP. 65