The Encyclopedia of Economic Principals

Chapter 76

Commitment, Credibility, Sovereign Risk, and Conflict

A promise counts only if keeping it pays when the time comes.

Four of the chapter's worked examples, made interactive: escrow that makes a contract penalty credible, a sovereign bond priced on beliefs about repayment, the inflation bias of a central bank without commitment, and a peace deal undone by shifting power. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Escrow makes a penalty credible

Why does a large contract penalty fail to deter, and how does escrow fix it?

A threat deters only if carrying it out is in the threatener's interest when the time comes. Escrow does not raise the penalty; it removes the costly step that made the lab back down.

Equation, written in LaTeX: 45-52=-7,

Equation, written in LaTeX: 80-18=62<80.

Equation, written in LaTeX: 80-45p.

Equation, written in LaTeX: p\geq\frac{18}{45}=0.40.

Scroll sideways for the whole equation

The supplier is paid 80; high quality costs 18. The contract penalty is 45. Collecting it by lawsuit costs the lab 52; under escrow the deposit moves automatically when inspection detects a defect, which happens with probability p.

Predict first. Under escrow with only 60 percent detection, will the supplier still cheat?

Your prediction

Choose an example

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Figure: Escrow makes a penalty credible. Left: the game tree under a lawsuit with the equilibrium path highlighted. Right: the supplier's payoff from high quality, 62, against 80.00 from low quality.
Enforcement: Lawsuit, Inspection detection probability: 1
Constructed example: the chapter's hypothetical laboratory and supplier (80, 18, 45, 52; detection 1 and 0.60, threshold 0.40); detection 0.20 is added for comparison.

Calculated values

Lab's net from suing
-7
Supplier, high quality
62.00
Supplier, low quality (expected)
80.00
Supplier's choice
Low quality
Deterrence threshold p
0.40

Suing would win 45 but cost 52, so the lab's net is 45 - 52 = -7 and it forgives. The supplier therefore compares 80 - 18 = 62 from high quality with 80 from low quality and cheats. Detection at 1.00 changes nothing, because a detected defect still goes unpunished.

Worked steps

  1. Lab's net from suing = 45 - 52 = -7, below 0 from forgiving, so it forgives
  2. High quality: 80 - 18 = 62
  3. Low quality: 80, because the penalty is never collected
  4. 62 < 80: low quality

Use the idea

When a contract relies on a penalty, check whether the party who must enforce it would actually gain from doing so after the breach.

Where the conclusion applies

Payoffs in units, no false positives, and escrow administration of 3 borne by the lab, which does not change the supplier's choice. Detection 0.20 is added for comparison.

Check your understanding: Under escrow, what is the minimum detection rate that deters low quality?
62 >= 80 - 45p gives p >= 18 / 45 = 0.40; at p = 0.60 low quality yields 80 - 27 = 53 < 62.

Chapter 76 source: section "Credible Commitment and Credible Threats".

Demonstration 2 of 4

Sovereign bond price and willingness to repay

How do default beliefs set what a government can borrow, and when are those beliefs justified?

The price depends on the expected repayment rate, not the face promise. Whether a low default belief is justified depends on the government's payoffs when payment falls due: repayment is credible only when the default penalty exceeds the debt service.

Equation, written in LaTeX: q=\frac{0.70(150)}{1.08}=97.22.

Equation, written in LaTeX: q=\frac{0.92(150)}{1.08}=127.78,

Equation, written in LaTeX: 180-150=30.

Equation, written in LaTeX: 180-165=15<30,

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The bond promises 150 next period; investors earn 8 percent elsewhere and recover nothing on default. q is the price they pay today. The project yields 180; defaulting keeps the 150 but costs the continuation penalty P.

Predict first. If institutions cut perceived default risk to 8 percent, is the project funded?

Your prediction

Choose an example

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Figure: Sovereign bond price and willingness to repay. Left: bond price 97.22 against a funding need of 120. Right: repayment payoff 30 against a default payoff of 15.
Perceived default probability: 0.3, Default penalty: 165
Constructed example: the chapter's hypothetical government (face 150, 8 percent, need 120, default beliefs 0.30 and 0.08, output 180, penalties 165 and 100); belief 0.20 and penalty 150 are added for comparison.

Calculated values

Bond price q
97.22
Funded (q at least 120)
no
Repay payoff
30
Default payoff
15
Repayment credible
yes

At default probability 0.30, the bond is worth (1 - 0.30) x 150 / 1.08 = 97.22, not enough to raise 120. Repaying leaves 30 against 15 from default, so the promise is credible.

Worked steps

  1. q = (1 - 0.30) x 150 / 1.08 = 105.00 / 1.08 = 97.22
  2. 97.22 < 120: not funded
  3. Repay: 180 - 150 = 30
  4. Default: 180 - 165 = 15
  5. 30 > 15

Use the idea

Before relying on a borrower's promise, compare what they keep by paying with what they keep by defaulting once the money is spent.

Where the conclusion applies

One period, zero recovery, risk-neutral investors and a project that always produces 180. Inability to pay after a disaster is a different case from unwillingness.

Check your understanding: With penalty 100, is repayment credible, and what belief should investors hold?
Default leaves 180 - 100 = 80, more than 30, so repayment is not credible; the 0.08 belief is unjustified and the bond reverts to a low value.

Chapter 76 source: section "Credible Commitment and Sovereign Default".

Demonstration 3 of 4

Discretion versus commitment in monetary policy

Why does a central bank that wants zero inflation end up with positive inflation and no extra output?

After wages are set, surprise inflation raises output toward the bank's target, so a zero promise is tempting to break. Wage setters anticipate this, and the only consistent outcome is where the reaction line meets the 45 degree line.

Equation, written in LaTeX: L=\pi^2+0.5(\pi-\pi^e-2)^2.

Equation, written in LaTeX: \pi=\frac{\pi^e+2}{3}.

Equation, written in LaTeX: L_D=1^2+0.5(0-2)^2=3.

Equation, written in LaTeX: L_C=0^2+0.5(0-2)^2=2.

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pi is inflation, pi^e expected inflation fixed in wage contracts and y - y^n = pi - pi^e the output gap. The bank's loss is pi^2 + b[(y - y^n) - k]^2, where k is its output ambition above natural (2 in the book) and b the weight on the gap (0.5 in the book). The general reaction pi = b(pi^e + k)/(1 + b) reduces to the book's (pi^e + 2)/3.

Predict first. If the bank wanted output only at its natural level (k = 0), is there an inflation bias?

Your prediction

Choose an example

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Figure: Discretion versus commitment in monetary policy. The bank's reaction line pi = b(pi^e + k)/(1 + b) with b = 0.50 and k = 2 crosses the 45 degree line at 1.00; commitment sits at the origin.
Output ambition above natural: 2, Weight on output gap: 0.5
Constructed example: the chapter's hypothetical central bank (ambition 2, weight 0.5); ambitions 0, 1 and 3 and weights 0.25 and 1 are added for comparison.

Calculated values

Reaction to pi^e = 0
0.6667
Discretionary inflation
1.00
Loss under discretion
3.0000
Loss under commitment
2.0000
Extra loss from discretion
1.0000

Once wages expect zero inflation, the bank's best response is 0.50 x 2 / 1.50 = 0.6667, so the zero promise is not time-consistent. In equilibrium pi = pi^e = 0.50 x 2 = 1.00 with output at its natural level. Loss is 3.0000 under discretion and 2.0000 under commitment: discretion adds 1.0000 with no lasting output gain.

Worked steps

  1. Reaction: pi = 0.50 x (pi^e + 2) / 1.50; at pi^e = 0, pi = 1.00 / 1.50 = 0.6667
  2. Equilibrium pi = pi^e: pi = 0.50 x 2 = 1.00
  3. L_D = 1.00^2 + 0.50 x (0 - 2)^2 = 1.0000 + 2.0000 = 3.0000
  4. L_C = 0^2 + 0.50 x (0 - 2)^2 = 2.0000

Use the idea

When a policymaker announces a rule, ask what it would want to do after others have acted on the announcement.

Where the conclusion applies

A linear surprise supply curve, quadratic loss and rational expectations. Ambitions 0, 1 and 3 and weights 0.25 and 1 are added; the book's numbers are k = 2 and weight 0.5.

Check your understanding: Using the book's reaction function with pi^e = pi, what is equilibrium inflation, and what are the two losses?
pi = (pi + 2) / 3 gives 3pi = pi + 2, so pi = 1; L_D = 1 + 0.5 x 4 = 3 against L_C = 2 under commitment.

Chapter 76 source: section "Time Inconsistency and Commitment Devices".

Demonstration 4 of 4

Shifting power and the commitment problem in war

Why can two states fail to keep a peace deal that both prefer to war today?

The deal fails not because there is no division both prefer to war, but because B cannot promise today not to use its future strength. A third-party penalty restores the promise by lowering B's payoff from revision below what the deal gives it.

Equation, written in LaTeX: w_A(1)=0.65(100)-15=50

Equation, written in LaTeX: w_B(1)=0.35(100)-20=15.

Equation, written in LaTeX: w_A(2)=0.20(100)-15=5

Equation, written in LaTeX: w_B(2)=0.80(100)-20=60.

Equation, written in LaTeX: 60-20=40

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The prize is worth 100. w_A and w_B are each state's expected war payoff: win probability times 100 minus the cost of fighting (15 for A, 20 for B), today (1) and after B's military program (2). A guarantor can impose a penalty on B for forcing a revision of a signed deal.

Predict first. Can any guarantor penalty smaller than 15 save the 55 to 45 deal when A's future chance is 0.20?

Your prediction

Choose an example

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Figure: Shifting power and the commitment problem in war. Ranges of A's share that both sides prefer to war: today 50 to 85, after the shift 5 to 40, and with a guarantor penalty of 0 up to 40. The 55 to 45 offer is marked at 55.
A's future win probability: 0.2, Guarantor penalty: 0
Constructed example: the chapter's hypothetical states (prize 100, costs 15 and 20, win chances 0.65 today and 0.20 later, a 55 to 45 offer, a 20 guarantor penalty); a future chance of 0.40 and penalties of 10 and 30 are added for comparison.

Calculated values

w_A(1)
50
w_B(1)
15
w_A(2)
5
w_B(2)
60
B's revision payoff
60
Deal survives
no

Today war gives A 0.65 x 100 - 15 = 50 and B 15, so any share for A between 50 and 85 beats fighting. If A's future win chance is 0.20, B's future war payoff is 0.80 x 100 - 20 = 60. After the shift B can get 60 - 0 = 60 by forcing a revision, more than the 45 it is promised, so the 55 to 45 division cannot survive. A could keep at most 100 - 60 = 40 later, below its war payoff of 50 today, so A prefers to fight now.

Worked steps

  1. w_A(1) = 0.65 x 100 - 15 = 50; w_B(1) = 0.35 x 100 - 20 = 15
  2. w_A(2) = 0.20 x 100 - 15 = 5; w_B(2) = 0.80 x 100 - 20 = 60
  3. B's revision payoff = 60 - 0 = 60
  4. 60 > 45: B revises

Use the idea

When a settlement depends on a party that is growing stronger, ask what enforces the terms after the balance of power shifts.

Where the conclusion applies

A divisible prize, known war probabilities and costs, and a guarantor whose penalty is credible. A future win chance of 0.40 and penalties of 10 and 30 are added for comparison.

Check your understanding: With a 20 penalty and A's future chance 0.20, does B honor the agreement?
Revision gives 60 - 20 = 40 < 45, so B honors; A gets 55 > 50 and B 45 > 15.

Chapter 76 source: section "Commitment-problem theory of war".