## _wp06144 — Section 1 & Section 2

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---

### Introduction and key setup
- Emerging markets (EM) can be suddenly cut off from international capital markets; examples cited include Mexico (defaulted in 1982 and shut out for seven years), Mexico (1994–95 shutdown for seven months), Korea and Indonesia (late 1997), and Argentina (shut out months before formal default in December, 2001).
- Shutdowns are extreme sudden stops that occur when potential lenders cannot find a price at which lending is profitable: a higher lending price (spread) can increase default probability, which in turn can eliminate any profitable lending price.
- The paper presents a simple model showing that an EM borrower who might default can be shut out of international capital markets without warning and that a modest haircut on obligations can shut down lending.
- Country risk is distinguished from currency risk: in the model, lending is denominated in lenders’ currency, so lenders face no currency risk. Lenders are risk neutral and require a spread above the off-shore safe rate because defaults sometimes occur.
- Definition used: A default is any loan payment less than the contractually agreed payment, including rescheduling or partial payments.

### The model structure and lender pricing
- Model components:
  - Risk-neutral lender’s pricing/lending condition.
  - EM production/payoff process where borrowed capital k produces stochastic output y and borrower repays if output covers debt.
- Lender’s loan-pricing equation (risk-neutral indifference condition as presented in source):
  - L p R z p R + − = )1(
    - where R* = (1 + i*), i* is the safe interest rate, p is probability of no-default, (1−p) is probability of default, z is the return to the lender in default (z < 1 + i*), and RL = (1 + iL) is the no-default repayment.
- EM production:
  - y = k(1 + δ)
    - δ is the stochastic return on production.
  - p = prob(δ ≥ iL)

### Distributional assumptions and closed-form relationships
- δ is uniformly distributed with mean δ ≥ i*, upper boundary δ + a/2 and lower boundary δ − a/2.
- Frequency distribution f(δ) is a rectangle with base a and height 1/a; variance of δ is a^2/12.
- Constraint from nonnegative output: lowest δ = δ − a/2 ≥ −1, so 0 ≤ a ≤ 2(δ + 1).
- For the uniform case p is linear in iL:
  - p = 1/2 + (δ − iL)/a
- Explicit solutions for equilibrium p̂ and îL (hats denote solution values) as given:
  - p̂ = [a(1 − z) + 2δ − 2z + 2 ± sqrt(a^2(1 − z)^2 + 4a(z − δ)(1 − z) + 4(z − δ)^2)] / (4a)  [as in (5a)]
  - îL = δ − a(1 − p̂)/2  [as in (5b)]
- Equilibrium multiplicity and shut-down possibilities:
  - The system can have a unique solution (tangent), two solutions (a “good” equilibrium α and a “bad” equilibrium β), or no solution (lenders cannot find a profitable price and lending shuts down).

### Numerical illustration and haircut sensitivity (Figure 1 parameters)
- Parameter values used in example: i* = 0.03, δ = 0.03, a = 0.173.
- Comparative z (default-return) cases:
  - z = 1.02 → two solutions.
  - z = 1.015 → one solution.
  - z = 1 → no solutions.
- Interpretation:
  - A fairly modest haircut shuts down access to foreign private capital markets for these parameter values.
  - Critical numerical notes:
    - When z falls below 1.015, the market shuts down.
    - Example: z = 1.01 represents a haircut (loss) of 2 percent on the risk-free return and a haircut of 5 percent on the total return owed to creditors — less than half that suggested by Calomiris (2001).
- The model focuses on per-unit pricing decisions and is silent on the role of debt quantities in market shutdowns.

### Comparative statics (additional results)
- Starting point: default payment z = 1.02 and initial equilibrium at α (the good equilibrium).
- Increase in the risk-free rate i*:
  - The nonlinear lender curve (Equation (1)) shifts out.
  - New equilibrium has higher lending rate iL and reduced probability of repayment p.
  - Continued increases in i* can eliminate intersections; in the simulation, an increase of about 100 basis points over initial i* = 0.03 is enough to shut down lending.
  - If the economy were initially at β, small increases in i* could perversely lower the lending rate and increase repayment probability.
- Increase in δ (return to production):
  - The straight line (Equation (4)) shifts out/up.
  - From α, increased δ reduces lending rate and increases probability of repayment—productivity-raising reforms can mitigate haircut effects.
  - A market shutdown requires δ to decrease so the straight line shifts below the nonlinear lender curve.
  - If initially at β, an increase in δ perversely lowers p and increases iL.
- Increase in output variance a:
  - Rotates the straight line (Equation (4)) counter-clockwise.
  - For the specified parameter values, moving from α to a new equilibrium raises p and lowers iL.
  - Intuition: with mean δ = 0.03 equal to i* = 0.03 and less than the lending rate, on average the EM defaults; increased variance raises the probability of very good draws that allow repayment, increasing p and lowering iL.
  - For other equilibria (β), increased variance may have the opposite effect.
- Policy implication: Increased output volatility may increase the incentive to borrow under some parameter configurations; productivity-enhancing reforms that raise δ can help restore or sustain access.

### The value of financing and borrower payoff (Section 2)
- Domestic borrowers invest no capital of their own but sometimes obtain positive payout because international lenders provide access to productive capital.
- Let EV denote the expected value of the payout to domestic borrowers per unit of capital.
- Model expression for expected borrower payout (EV) as given (Equation (6) in source):
  - "])|([0*)1( LL iiEppEV−≥+−=δδ." (6)
- Interpretation of (6):
  - Expected payout per unit = (1 − p) × 0 + p × E[δ | δ ≥ L_i] − L_i.
  - The expected net payout to non-defaulters equals the expected value of the return on capital goods conditional on its being larger than L_i, namely ")|( L iE≥δδ," less L_i, the amount paid to lenders.
  - By lending to an emerging market country that might default, international lenders are granting a call option to domestic borrowers; the option goes “in the money” when L_i > δ.
- Closed-form EV under uniform δ distribution:
  - The expected net payout to non-defaulters is given as ")2(5.0)|(" "LL iaiE−+=≥δδδ."
  - Substituting into (6) and using earlier expressions for p and L_i yields the relationship printed in the source: "2 ˆ 2 pa EV=".

### Sensitivity of EV to output variance and multiple equilibria (Figure 2 setup)
- Parameters for plotting EV against a: i* = 0.03, δ = 0.03, and z = 1.02.
- Variance of the output shock is indicated as "(12 2 a)" and increases as a increases.
- Two possible EV branches when z = 1.02:
  - EV1: expected payout per unit capital when the lending rate is relatively low and the probability of repayment is relatively high.
  - EV2: expected payout when the lending rate is relatively high and the probability of repayment is relatively low.
- Comparative statics from example:
  - EV1 increases as output variance (a) increases: increased output variance raises the chance of a higher output return and reduces the lending rate, making it more likely that realized return on output will exceed the lending rate.
  - EV2 is near zero and essentially nonresponsive to output variance. Reason: greater output variance increases the chance of a higher output return but also increases the lending rate because the probability of repayment was already quite small; the net effect keeps expected payout close to zero.

### Borrower incentives, market shutdown threshold, and policy-relevant implications
- Incentive effects:
  - In an equilibrium with relatively high repayment probability (EV1 example: about 40 percent repayment probability), greater output variability induces borrowers who can default to undertake the riskiest projects possible to increase the option value of the loan.
  - In the low-repayment-probability equilibrium (EV2 example: about 10 percent), borrowers face near-zero expected payout and do not gain from increased variance.
- Market shutdown threshold:
  - Emerging market borrowers who might default can be shut out of international capital markets without lending rates becoming exorbitant; risk-neutral lenders stop lending when higher lending rates only increase default risk.
  - The calibrated model demonstrates that relatively small changes in foreign interest rates, returns to production (output growth), output variance, or the haircut offered creditors can completely shut down international lending to the emerging market borrower.
- Two overarching conclusions:
  - Emerging market borrowers who might default can be excluded from international capital markets without lenders charging exorbitant rates; small parameter changes can trigger a full market shutdown.
  - When countries default occasionally, the option value of not defaulting creates a systematic incentive for borrowers to choose high-variance projects for foreign financing. This helps explain why emerging markets have higher output variance than developed countries that seldom default.

*Source: WP/06/144 — "Getting Shut Out of the International Capital Markets: It Doesn’t Take Much" (Section 1 and Section 2).*

### Section 1

### _wp06144 - Section 1

### Introduction
- Emerging markets (EM) can be suddenly cut off from international capital markets; examples include Mexico (defaulted in 1982 and shut out for seven years), Mexico (1994–95 shutdown for seven months), Korea and Indonesia (late 1997), and Argentina (shut out months before formal default in December, 2001).
- Shutdowns are extreme sudden stops that occur when potential lenders cannot find a price at which lending is profitable. A higher lending price (spread) can increase default probability, which in turn can eliminate any profitable lending price.
- The paper presents a simple model showing that an EM borrower who might default can be shut out of international capital markets without warning and that a modest haircut on obligations can shut down lending.
- The result challenges views such as Charles Calomiris (2001), who argued that a modest 10–15 percent haircut for Argentina’s creditors might have preserved market access; the model suggests much smaller haircuts can be sufficient to shut down lending.
- “Country risk” is distinguished from “currency risk.” In the model, lending is denominated in lenders’ currency, so lenders face no currency risk. Lenders are risk neutral and require a spread above the off-shore safe rate because defaults sometimes occur.
- Definition: A default is any loan payment less than the contractually agreed payment, including rescheduling or partial payments.

### The Model
- Two parts:
  1. Risk-neutral lender’s pricing/lending condition.
  2. EM production/payoff process where borrowed capital k produces stochastic output y and borrower repays if output covers debt.
- Lender’s loan-pricing equation (risk-neutral indifference between safe lending and EM lending):
  - LpRzpR+−=)1(
    - where R* = (1 + i*), i* is the safe interest rate, p is probability of no-default, (1−p) is probability of default, z is the return to the lender in default (z < 1 + i*), and RL = (1 + iL) is the no-default repayment.
- EM production:
  - y = k(1 + δ)
    - δ is the stochastic return on production.
  - p = prob(δ ≥ iL)
- Distributional assumptions:
  - δ is uniformly distributed with mean δ ≥ i*, upper boundary δ + a/2 and lower boundary δ − a/2.
  - Frequency distribution f(δ) is a rectangle with base a and height 1/a; variance of δ is a^2/12.
  - Output must be positive: lowest δ = δ − a/2 ≥ −1, constraining 0 ≤ a ≤ 2(δ + 1).
- For the uniform case p is linear in iL:
  - p = 1/2 + (δ − iL)/a
- Explicit solutions for equilibrium p̂ and îL (hats denote solution values) are given by equations (5a) and (5b) in the source:
  - p̂ = [a(1 − z) + 2δ − 2z + 2 ± sqrt(a^2(1 − z)^2 + 4a(z − δ)(1 − z) + 4(z − δ)^2)] / (4a)  [as in (5a)]
  - îL = δ − a(1 − p̂)/2  [as in (5b)]
- Equilibrium multiplicity and shut-down possibilities:
  - The system can have: a unique solution (tangent), two solutions (a “good” equilibrium α and a “bad” equilibrium β), or no solution (lenders cannot find a profitable price and lending shuts down).
- Numerical illustration and haircut sensitivity (Figure 1 parameters):
  - Parameter values used: i* = 0.03, δ = 0.03, a = 0.173.
  - When z = 1.02 (creditors take a 1 percent haircut on the risk-free return), there are two solutions.
  - When z = 1.015, there is one solution.
  - When z = 1, there are no solutions.
  - For these parameter values, a fairly modest haircut shuts down access to foreign private capital markets.
- Haircut interpretation and examples:
  - In text, haircut specification: (1)(1 − h) i* + z ??? (source defines alternatives); effective haircut h with 1 > h > 0. (The source notes several equivalent ways to specify haircuts without changing substantive analysis.)
  - Critical numerical notes:
    - When z falls below 1.015, the market shuts down.
    - Example: z = 1.01 represents a haircut (loss) of 2 percent on the risk-free return and a haircut of 5 percent on the total return owed to creditors — less than half that suggested by Calomiris (2001).
  - The model is silent on the role of debt quantities in market shutdowns; focus is on per-unit pricing decisions.

### Additional Comparative Statics
- Starting point: default payment z = 1.02 and initial equilibrium at α (the good equilibrium).
- Increase in the risk-free rate i*:
  - The nonlinear lender curve (Equation (1)) shifts out.
  - New equilibrium has higher lending rate iL and reduced probability of repayment p.
  - Continued increases in i* can eliminate intersections; in the simulation, an increase of about 100 basis points over initial i* = 0.03 is enough to shut down lending.
  - Note: If the economy were initially at β, small increases in i* could perversely lower the lending rate and increase repayment probability (implausible comparative statics at β).
- Increase in δ (return to production):
  - The straight line (Equation (4)) shifts out/up.
  - From α, increased δ reduces lending rate and increases probability of repayment—successful productivity-raising reforms can mitigate haircut effects.
  - A market shutdown (no intersection) requires δ to decrease so the straight line shifts below the nonlinear lender curve.
  - If initially at β, an increase in δ perversely lowers p and increases iL (implausible comparative statics).
- Increase in output variance a:
  - Rotates the straight line (Equation (4)) counter-clockwise.
  - Moves economy from α to a new equilibrium with higher p and lower iL for the specified parameter values.
  - Intuition: with mean δ = 0.03 equal to i* = 0.03 and less than the lending rate, on average the EM defaults; increased variance raises the probability of very good draws that allow repayment, increasing p and lowering iL.
  - For other equilibria (β), increased variance may have the opposite, perverse effect.
- Policy implication: Increased output volatility may increase the incentive to borrow under some parameter configurations; productivity-enhancing reforms that raise δ can help restore or sustain access.

### The Value of Financing
- Domestic borrowers invest no capital of their own but sometimes obtain positive payout because international lenders provide access to productive capital.
- Let EV denote the expected value of the payout to domestic borrowers per unit of capital.
- (The source text continues beyond this point; Section IV begins analysis of borrower incentives and the value of access to financing, but supplied content ends mid-discussion.)

*Source: WP/06/144 — "Getting Shut Out of the International Capital Markets: It Doesn’t Take Much" (Section 1).*

### Section 2

### _wp06144 - Section 2

### Model expression for expected borrower payout (EV)
- Equation (6) as presented: 
  - "])|([0*)1( LL iiEppEV−≥+−=δδ." (6)
- Interpretation of (6):
  - The expected payout to domestic borrowers per unit of borrowed capital equals the probability of default, 1-p, times the payout to defaulting borrowers, 0, plus the probability of no default, p, times the expected net payout to borrowers who do not default.
  - The expected net payout to non-defaulters equals the expected value of the return on capital goods conditional on its being larger than L_i, namely ")|( L iE≥δδ," less L_i, the amount paid to lenders.
  - By lending to an emerging market country that might default, international lenders are granting a call option to domestic borrowers; the option goes “in the money” when L_i > δ.
- Closed-form EV under uniform δ distribution:
  - The expected net payout to non-defaulters is given as ")2(5.0)|(" "LL iaiE−+=≥δδδ."
  - Substituting into (6) and using earlier expressions for p and L_i yields the relationship printed in the source: "2 ˆ 2 pa EV=".

### Sensitivity to output variance and multiple equilibria
- General points:
  - Since EV is an option, its value should be sensitive to the variance of the underlying shock; other things equal, more variance should increase the call option’s value.
  - The results are not dependent on the assumed uniform distribution. Alternative distributions (thin-tailed exponential, trapezoid with one fat tail) can yield multiple equilibria, a unique equilibrium, or no equilibrium (a market shutdown) for a similar sensible range of parameter values. Comparative statics are similar under these alternatives.
- Numerical example and Figure 2 setup:
  - Parameters used for plotting EV against a (the width of the uniform output shock density): *i* = 0.03, δ = 0.03, and z = 1.02.
  - The variance of the output shock is indicated as "(12 2 a)" and increases as a increases.
- Two possible EV branches when z = 1.02:
  - EV1: expected payout per unit capital when the lending rate is relatively low and the probability of repayment is relatively high.
  - EV2: expected payout when the lending rate is relatively high and the probability of repayment is relatively low.
- Comparative statics from Figure 2:
  - EV1 increases as output variance (a) increases: increased output variance raises the chance of a higher output return and reduces the lending rate, making it more likely that realized return on output will exceed the lending rate.
  - EV2 is near zero and essentially nonresponsive to output variance. Reasoning provided:
    - Greater output variance increases the chance of a higher output return but also increases the lending rate because the probability of repayment was already quite small.
    - The chance that the return on output will exceed the lending rate does not improve materially; higher output variance also reduces the probability of repayment. The net effect keeps expected payout close to zero.

### Borrower incentives and equilibrium behavior
- Incentive effects:
  - In an equilibrium with a relatively high repayment probability (EV1 example: about 40 percent repayment probability), greater output variability induces borrowers who can default to undertake the riskiest projects possible to increase the option value of the loan.
  - In contrast, in the low-repayment-probability equilibrium (EV2 example: about 10 percent), borrowers face near-zero expected payout and do not gain from increased variance.
- Market shutdown threshold:
  - Emerging market borrowers who might default can be shut out of international capital markets without lending rates becoming exorbitant; risk-neutral lenders stop lending when higher lending rates only increase default risk.
  - The calibrated model demonstrates that relatively small changes in foreign interest rates, returns to production (output growth), output variance, or the haircut offered creditors can completely shut down international lending to the emerging market borrower.

### Conclusion: policy-relevant implications
- Two overarching conclusions emphasized:
  - First: Emerging market borrowers who might default can be excluded from international capital markets without lenders charging exorbitant rates; small parameter changes can trigger a full market shutdown.
  - Second: When countries default occasionally, the option value of not defaulting creates a systematic incentive for borrowers to choose high-variance projects for foreign financing. This helps explain why emerging markets have higher output variance than developed countries that seldom default.

*Source: _wp06144 - Section 2*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06144.pdf_