1 forgive or buy back: an experimental study of debt relief vivian lei, steven tucker, and filip...

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Forgive or Buy Back: An Experimental Study of Debt Relief

Vivian Lei, Steven Tucker, and Filip Vesely

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Motivation

Bono, Brad Pitt, the Dalai Lama, the late Pope John Paul II, …, and the Jubilee Debt Campaign Call for 100% cancellation of the massive external debt

owed by the world’s poorest countries. Demand an end to “the scandal of poor countries paying

money to the rich world”. “I encourage you in your advocacy for total debt cancellation for

poor countries because, frankly, it is a scandal that we are forced to choose between basic health and education for our people and repaying historical debt.” (President Mkapa of Tanzania, 2005)

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Motivation

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Motivation

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Motivation HIPCs has received significantly more capital inflow in the

form of new lending and foreign aid than their debt service. Capital outflow in the form of debt service: 3% of the GDP Capital inflow in the forms of new lending and aid: 15% of the GDP

Reducing poor countries’ heavy debt burden has always been on developed countries’ agenda since 1970s.

The Paris Club Rescheduled payment deadlines for 81 countries between 1976 and

1988 The Brady Plan

Reduced US$60 billion of debt for 16 middle-income countries during the early 1990s.

The HIPC (Highly Indebted Poor Countries) Initiative Reduced US$37 billion of debt for 30 HIPC countries by the end of 2005.

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Motivation Question 1: Will debt relief really help poor

countries and also benefit their creditors? Krugman (1988): Yes, as long as a debt

overhang is present. Debt overhang:

The expected present value of a country’s future resource transfers is less than its debt.

Impede investment and growth and thus increase the probability of a default in the future.

Decrease the expected value of repayments.

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Motivation

Question 2: Which debt relief scheme is best to relieve debt burden? Krugman (1989):

Compare debt forgiveness vs. more market-based schemes such as debt buybacks

Forgiveness: a once-and-for-all reduction in the future obligations of a debtor country

Buyback: allows a debtor country to buy back its own debt at a discount

As long as the debtor country is initially on the downward-sloping side of the debt Laffer curve, both creditors (acting collectively) and debtors should be indifferent, in expected terms, between the two schemes.

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Motivation Question 3: What does the empirical literature say

about the efficiency or effectiveness of different relief schemes to solve for the problem of debt overhang? Not much.

Most empirical studies aim to investigate if debt overhang really exists.

Regress growth rate of GDP/investment on debt stock/flow, using linear/nonlinear specifications and various techniques to control for endogeneity.

Results are far from conclusive. No study has compared the relative effectiveness of different

relief schemes because developed countries use the case-by-case approach to deal with poor countries’ debt problems.

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Objective

To investigate the effectiveness of debt forgiveness and debt buybacks in the presence of debt overhang in the lab. Study the impact of different relief schemes on

creditors’ behavior How much debt are creditors willing to reduce?

debtors’ behavior How much effort are debtors willing to exert to improve their

economic conditions? expected payoffs of both sides

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Design

2x2 design: treatment variables are Relief scheme

Debt forgiveness Debt buybacks

Number of creditors One creditor Two creditors

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Design

4 Treatments: Forgiveness/1 creditor Buyback/1 creditor Forgiveness/2 creditors Buyback/2 creditors

Due to project overhang!

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Numerical Example

Consider a risk-neutral debtor country Inherits a nominal debt of $120, which is greater

than its current resources, $40. Has a chance to invest and, with some

uncertainty, generate more income in the future. With probability p, the investment succeeds and the

debtor receives extra $80. With probability 1-p, the investment fails and the

debtor receives nothing. debt overhang

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Numerical Example

Consider a risk-neutral debtor country (cont’d) Incur cost to strive for the extra income.

The cost function, e(p), is a convex function of p. Decision needs to be made:

How much effort it is willing to exert (how much cost it is willing to incur) in order to generate extra $80?

Decision variable: p (or equivalently effort cost e)

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Suppose there is no debt relief. How much is the expected value of debt

repayment (EV)? EV ＝ p (40 ＋ 80) ＋ (1 － p) 40 ＝ 40 ＋ 80p

How much is the debtor’s expected payoff (EU)? EU ＝ 40 ＋ 80p － EV － e(p) ＝－ e(p) 0 ≦

There is no incentive for the debtor country to undertake any investment (political or economic reform) when they have to repay a full amount.

Numerical Example

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Consider a two-stage game in which creditor countries, acting collectively, are willing to reduce some debt. Stage 1: The representative creditor decides how much

debt, if any, will be relieved. Debt forgiveness: decide the amount to be forgiven (F ＜ 80) Debt buyback: decide the price (P ＜ 1) at which the creditor is

willing to sell for each dollar of the debt claims Stage 2: The debtor chooses the effort level, represented

by p, that would generate the extra income.

Numerical Example

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Numerical Example

Debt forgiveness How much is the expected value of debt repayment (EV)?

EV ＝ p [40 ＋ (80 － F)] ＋ (1 － p) 40 ＝ 40 ＋ p (80 － F) How much is the debtor’s expected payoff (EU)?

EU ＝ 40 ＋ 80p － EV － e(p) ＝ pF － e(p) ＞＝＜ 0

e(p):

p 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

e 0 1 3 7 13 20 29 30 51 65 80

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Debt forgiveness (cont’d) Expected payoffs

Creditor

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0 [ 40, 0] [ 48, -1] [ 56, -3] [ 64, -7] [ 72,-13] [ 80,-20] [ 88,-29] [ 96,-39] [104,-51] [112,-65] [120,-80] 10 [ 40, 0] [ 47, 0] [ 54, -1] [ 61, -4] [ 68, -9] [ 75,-15] [ 82,-23] [ 89,-32] [ 96,-43] [103,-56] [110,-70] 20 [ 40, 0] [ 46, 1] [ 52, 1] [ 58, -1] [ 64, -5] [ 70,-10] [ 76,-17] [ 82,-25] [ 88,-35] [ 94,-47] [100,-60] 30 [ 40, 0] [ 45, 2] [ 50, 3] [ 55, 2] [ 60, -1] [ 65, -5] [ 70,-11] [ 75,-18] [ 80,-27] [ 85,-38] [ 90,-50] 40 [ 40, 0] [ 44, 3] [ 48, 5] [52, 5] [ 56, 3] [ 60, 0] [ 64, -5] [ 68,-11] [ 72,-19] [ 76,-29] [ 80,-40] 50 [ 40, 0] [ 43, 4] [ 46, 7] [ 49, 8] [ 52, 7] [ 55, 5] [ 58, 1] [ 61, -4] [ 64,-11] [ 67,-20] [ 70,-30] 60 [ 40, 0] [ 42, 5] [ 44, 9] [ 46, 11] [ 48, 11] [ 50, 10] [ 52, 7] [ 54, 3] [ 56, -3] [ 58,-11] [ 60,-20] 70 [ 40, 0] [ 41, 6] [ 42, 11] [ 43, 14] [ 44, 15] [ 45, 15] [ 46, 13] [ 47, 10] [ 48, 5] [ 49, -2] [ 50,-10] 80 [ 40, 0] [ 40, 7] [ 40, 13] [ 40, 17] [ 40, 19] [ 40, 20] [ 40, 19] [ 40, 17] [ 40, 13] [ 40, 7] [ 40, 0] 90 [ 30, 10] [ 30, 17] [ 30, 23] [ 30, 27] [ 30, 29] [ 30, 30] [ 30, 29] [ 30, 27] [ 30, 23] [ 30, 17] [ 30, 10]100 [ 20, 20] [ 20, 27] [ 20, 33] [ 20, 37] [ 20, 39] [ 20, 40] [ 20, 39] [ 20, 37] [ 20, 33] [ 20, 27] [ 20, 20]110 [ 10, 30] [ 10, 37] [ 10, 43] [ 10, 47] [ 10, 49] [ 10, 50] [ 10, 49] [ 10, 47] [ 10, 43] [ 10, 37] [ 10, 30]120 [ 0, 40] [ 0, 47] [ 0, 53] [ 0, 57] [ 0, 59] [ 0, 60] [ 0, 59] [ 0, 57] [ 0, 53] [ 0, 47] [ 0, 40]

Debtor (Probability p )

(Forgiven Debt F)

unique Pareto-dominant subgame-perfect equilibrium

Numerical Example

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Prediction for debt forgiveness: F ＝ 40 (the amount of relief) p ＝ 30% EV ＝ 52 EU ＝ 5

Numerical Example

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Numerical Example Debt buybacks

The debtor country benefits by buying back as much debt as possible.

If P is relatively high, then the debtor would spend all $40 of its current resources to buy back 40/P amount of debt.

Example: If P ＝ 0.5, then the debtor would be able to buy back 40/0.5 ＝ $80 at a total price of $40.

Remaining debt ＝ $120 － $80 ＝ $40 Amount of relief ＝ $80 － $40 ＝ $40

If P is relatively low, then the debtor would spend 120P to buy back all $120 of the debt.

Example: If P ＝ 0.2, then the debtor would be able to buy back all $120 of debt at a total price of $24.

Remaining debt ＝ $0 Amount of relief ＝ $120 － $24 ＝ $96

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Numerical Example

Debt buybacks (cont’d) How much is the expected value of debt repayment (EV)?

EV ＝ 40 ＋ p(120 － 40/P) How much is the debtor’s expected payoff (EU)?

EU ＝ p[80 － (120 － 40/P)] － e(p) ＝ p(40/P － 40) － e(p) ＞＝＜ 0

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Debt buybacks (cont’d) Expected payoffs unique subgame-perfect

equilibrium

Numerical Example

Creditor

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

100% [ 40, 0] [ 48, -1] [ 56, -3] [ 64, -7] [ 72,-13] [ 80,-20] [ 88,-29] [ 96,-39] [104,-51] [112,-65] [120,-80] 90% [ 40, 0] [ 48, -1] [ 55, -2] [ 63, -6] [ 70,-11] [ 78,-18] [ 85,-26] [ 93,-36] [100,-47] [108,-61] [116,-76] 80% [ 40, 0] [ 47, 0] [ 54, -1] [ 61, -4] [ 68, -9] [ 75,-15] [ 82,-23] [ 89,-32] [ 96,-43] [103,-56] [110,-70] 70% [ 40, 0] [ 46, 1] [ 53, 0] [ 59, -2] [ 65, -6] [ 71,-11] [ 78,-19] [ 84,-27] [ 90,-37] [ 97,-50] [103,-63] 60% [ 40, 0] [ 45, 2] [ 51, 2] [ 56, 1] [ 61, -2] [ 67, -7] [ 72,-13] [ 77,-20] [ 83,-30] [ 88,-41] [ 93,-53] 50% [ 40, 0] [ 44, 3] [ 48, 5] [52, 5] [ 56, 3] [ 60, 0] [ 64, -5] [ 68,-11] [ 72,-19] [ 76,-29] [ 80,-40] 40% [ 40, 0] [ 42, 5] [ 44, 9] [ 46, 11] [ 48, 11] [ 50, 10] [ 52, 7] [ 54, 3] [ 56, -3] [ 58,-11] [ 60,-20] 30% [ 36, 4] [ 36, 11] [ 36, 17] [ 36, 21] [ 36, 23] [ 36, 24] [ 36, 23] [ 36, 21] [ 36, 17] [ 36, 11] [ 36, 4] 20% [ 24, 16] [ 24, 23] [ 24, 29] [ 24, 33] [ 24, 35] [ 24, 36] [ 24, 35] [ 24, 33] [ 24, 29] [ 24, 23] [ 24, 16] 10% [ 12, 28] [ 12, 35] [ 12, 41] [ 12, 45] [ 12, 47] [ 12, 48] [ 12, 47] [ 12, 45] [ 12, 41] [ 12, 35] [ 12, 28] 0% [ 0, 40] [ 0, 47] [ 0, 53] [ 0, 57] [ 0, 59] [ 0, 60] [ 0, 59] [ 0, 57] [ 0, 53] [ 0, 47] [ 0, 40]

Debtor (Probability p )(Buyback Price P)

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Prediction for debt buybacks: P ＝ 0.5 Amount of relief ＝ 40 (the same as F under the

forgiveness scheme) p ＝ 30% EV ＝ 52 EU ＝ 5

Numerical Example

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Some Experimental Features

Each session consisted of 16 subjects. Randomly assigned 8 subjects to be debtors and 8 to be

creditors. Subjects interacted with each other via the

computer for 20 periods. Random matching protocol:

Subjects were re-matched every period. Zero probability of being matched with the same

counterpart for two consecutive periods.

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6 sessions (3 for each treatment) which lasted about two hours

96 subjects 960 observations Average earnings: NZ$25.41 (roughly

US$17.64) Creditors: NZ$40.90 Debtors: NZ$ 9.93

Available Data

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Result 1: Amount of Debt Relief

Debt Relief

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Forgive Buyback Prediction

Forgive: 45.54

Buyback: 37.11

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There is significantly more debt being relieved under the Forgive treatment.

Result 1: Amount of Debt Relief

Constant PeriodForgive Dummy

Relief Amount

35.08***

(3.01)

0.19

(0.16)

8.43*

(4.53)

Panel Data Approach: GLS with Random Effects

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Result 2: Project Success Rate (p)

Probability of Project Success

0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


Forgive: 36.92% Buyback: 35.73%

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Debtor’s effort in terms of the project success rate is significantly smaller under the Forgive treatment once the amount of debt relief is controlled for.

The more the creditor relieves the debt, the more the debtor reciprocates.



Relief Amount

(Relief Amount)2

Project Success

Rate

10.54**

(4.89)

–0.33

(0.22)

–4.88**

(2.54)

0.87***

(0.11)

–0.002**

(0.001)


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Debtor’s effort exhibits greater volatility from one period to the next under the Forgive treatment.



Volatility in Relief

Dummy * Volatility in Relief

Volatility in p

51.93

(51.59)

5.56

(3.61)

34.62

(43.50)

1.92***

(0.11)

1.03**

(0.54)


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Result 3: Expected Payoffs

Expected Payoff - Creditor

42

46

50

54

58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


Buyback: 52.64

Forgive: 50.53

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Expected Payoff - Debtor

-4

0

4

8

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


Forgive: 3.89

Buyback: 2.68

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Given the amount of debt relief, debt forgiveness has a significantly negative impact on creditor’s expected payoff but not on debtor’s.



Relief Amount

(Relief Amount)2

EV (creditor)

48.40***

(1.88)

–0.15*

(0.09)

–1.71**

(0.74)

0.50***

(0.06)

–0.01***

(0.0006)

EU (debtor)

–2.60*

(1.35)

0.07**

(0.03)

–0.73

(0.73)

–0.07

(0.05)

0.004***

(0.0004)


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Conclusion

Creditors tend to relieve more debt under the Forgive treatment.

Debtors do reciprocate, but they don’t reciprocate significantly more under the Forgive than under the Buyback treatment. That is, creditors pay more for the same outcome under

the Forgive treatment. Debt forgiveness is a less efficient scheme for

creditors to relieve the debt.

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Debt Relief

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

F2 B2 F2_prediction B2_prediction


0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20



0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


Debt Relief

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


One Creditor Two Creditors

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-4

0

4

8

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


Expected Payoff - Creditor

42

46

50

54

58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20



-4

0

4

8

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


Expected Payoff - Creditors

42

46

50

54

58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

F2 B2 F2_B2_prediction

One Creditor Two Creditors

1 forgive or buy back: an experimental study of debt relief vivian lei, steven tucker, and filip...

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