## _pdp10 - 0.5 percent of GDP, and facing an 3.2 percent interest rate on international markets. The

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---

### Setup and baseline assumptions
- Primary deficit is 0.5 percent of GDP throughout.
- Market interest rate on standard (plain vanilla) debt contracts: 3.2 percent.
- Alternative indexed bond structure:
  - Yearly coupon payments of 3.2 percent plus 0.7 times the difference between actual growth and “trend growth” of 3 percent.
  - A yearly insurance premium of 0.4 percentage point, payable regardless of the growth rate.
- All variables are in real terms; the (real) exchange rate is perpetually fixed.
- Focus is on sovereign debt exclusively.
- Debt dynamics identity used: Dt/Yt = (1+ r - gt) (Dt-1/Yt-1) - st, where Dt is government debt, Yt is output, st is the primary surplus as a share of GDP, gt is growth rate, and r is the interest rate.

### Scenario outcomes (simplest scenarios; Figure 1)
- Common setup for these scenarios:
  - The primary deficit is 0.5 percent of GDP throughout.
  - Output growth is 3 percent until period 5; thereafter scenarios diverge.
  - The interest rate on standard debt contracts is assumed to be 3.2 percent.
  - With indexing, the interest rate is reduced by 0.7 times the difference between the actual growth and trend growth of 3 percent.
  - The insurance premium is 0.4 percentage points, added to the market interest rate.
- Scenario 1: Growth drops
  - Growth drops to 0.5 percent from year 6 onwards.
  - By year 20:
    - Debt/GDP ratio rises to 71 percent without indexation.
    - Debt/GDP ratio rises to 52 percent with indexation.
- Scenario 2: Growth rises
  - Growth rises to 7 percent from year 6 onwards.
  - By year 20:
    - Debt/GDP ratio falls to 24 percent without indexation.
    - Debt/GDP ratio rises to 38 percent with indexation.
- Interpretation:
  - Indexation can substantially reduce debt/GDP accumulation in downside growth scenarios but can raise debt/GDP in strong growth scenarios when the primary surplus is held constant.

### Fiscal behavior, welfare implications, and cyclical smoothing
- GDP-indexation reduces the need for procyclical fiscal tightening in downturns:
  - When GDP growth is below trend, governments can run a lower primary surplus (higher primary spending and lower taxes) with indexation than without it.
  - When GDP growth is above trend, governments will need a higher primary surplus (lower primary spending and higher taxes) with indexation.
- GDP-indexation tends to smooth paths of the primary surplus, taxes, and primary spending over the cycle.
- With diminishing marginal benefits to primary spending and increasing marginal costs of taxation, GDP indexation will tend to improve welfare.
- Adjusting the primary balance during economic and financial distress (e.g., raising new taxes or laying off government employees) may be especially costly.

### Model with fiscal–growth feedback (Box 1 and Figure 2)
- Government reaction function (Box 1):
  - st = (Dt/Yt)·[(1+φ)r - (φg + (1-φ)gt)] (as expressed in the source formula).
  - In words: the government responds to growth slowdowns by increasing the primary surplus (procyclical fiscal policy).
- Growth response to primary surplus:
  - gt = g + γ (s - s̄) + ut, for all st ≥ s̄, where s̄ is the critical level of the primary surplus, g is a constant, ut is an exogenous shock to growth, and γ = 5.
  - Critical level s̄ = 0.1 percent of GDP.
- Indexed interest rate under Box 1:
  - Under standard debt contracts the interest rate is constant: r = 3.2 percent.
  - Under GDP indexation, the interest rate is r = 3.2 + Ω + α (g - gt), with Ω = 0.4 and α = 0.7.
- Simulation shocks (Figure 2):
  - Exogenous shock ut takes the value –4 percentage points (“growth drops” scenario) or +4 percentage points (“growth rises” scenario), beginning in year 4.
  - Figure 2 caption: market interest rate assumed 3.2 percent; output growth 3 percent until period 3; thereafter negative or positive shock of 4 percentage points. Government sets the primary surplus such that the debt/gdp ratio would be constant if growth were a weighted average of long-run growth and actual growth (with weights of 0.8 and 0.2, respectively). A primary surplus above a minimum threshold adversely affects current growth rate.
- Result:
  - Allowing for fiscal feedback increases the benefits of indexation when governments otherwise respond to slowdowns by tightening fiscal policy.

### Diversifiability of growth across countries and the insurance premium
- Large unrealized gains from international risksharing arise because income growth rates are not highly correlated across countries at various horizons.
- Athanasoulis and van Wincoop (2000) and Athanasoulis, Shiller, and van Wincoop (1999) estimated probabilities that per capita GDP will unexpectedly rise by 50 percent in the best performing country relative to the worst:
  - 20 percent at the 15-year horizon,
  - 40 percent at the 20-year horizon,
  - 80 percent at the 25-year horizon,
  - 100 percent at the 35-year horizon.
- CAPM-based pricing implications:
  - Only the systematic portion of risk is reflected in expected returns; unsystematic risk can be diversified away.
  - The systematic portion of an individual country’s GDP growth rate is typically rather small.
  - Simple regressions of individual countries’ GDP growth on worldwide growth show unsystematic variation is far larger than systematic variation for emerging markets:
    - R2 coefficient ranges from 0.00 (Argentina, Bulgaria, etc.) to 0.39 (Botswana) with an average of 0.10 for 1970–2001.
    - Beta coefficients range from –1.4 (Jordan) to 3.00 (Botswana), with an unweighted average of 0.81.
    - The average of the absolute value of the difference between 1 and the beta coefficient is 0.78.
  - Regressions using U.S. GDP growth, world real stock returns, or U.S. real stock returns yield even lower R2 coefficients and typically lower beta coefficients.
- Implication:
  - The insurance premium on GDP-indexed bonds issued by emerging markets would likely be small because much of country-specific growth risk is diversifiable.

### Box 2. The Size of the Insurance Premium in CAPM-like Reasoning
- CAPM derivation of the insurance premium:
  - Return on GDP-indexed bonds: ) ~( iii ggR−+= αρ where R is the interest rate on plain vanilla bonds, α determines the degree of indexation, and gi is the country’s output growth rate, with i g~ being equal to actual growth and ig being equal to trend growth.
  - CAPM pricing condition applied to GDP-indexed bonds yields an expression where the premium depends on the covariance of country growth with the market portfolio and the market risk premium.
- Numerical illustration assumptions and result:
  - Relevant portfolio: US stock market.
  - Risk-free rate of return: 3 percent.
  - Expected return on the market portfolio: 8 percent.
  - β of Argentina’s growth rate with respect to US stock market return (from Table 1b): 0.22.
  - α = 1.
  - Computation of indexation premium: 1*(8-3)*0.22, i.e., approximately 1 percentage point per year.
  - Clarification: This premium is in excess of the rate the country pays on plain vanilla bonds; it is in addition to the premium that compensates for default risk. The example assumes default risk is uncorrelated with GDP growth risk.
- Implications when default risk is correlated with growth:
  - If default risk rises when growth falls, the appeal of indexed bonds increases relative to the uncorrelated-default-risk case.
  - Converting a large portion of debt into indexed bonds could plausibly reduce default risk significantly.
- Investor willingness and instrument complexity:
  - International investors already invest heavily in emerging-market stocks, which are much more volatile than those countries’ GDP growth rates.
  - Under standard debt contracts investors are already implicitly exposed to GDP risk via default outcomes.
  - It is preferable for investors to receive lower debt repayments through pre-agreed indexation than to face uncertain recovery values through chaotic default processes.
  - GDP-indexed bonds are essentially floating-rate bonds where the coupon is tied to the borrower’s GDP growth rather than LIBOR or another interest rate; the indexation mechanism is analogous to established inflation-indexed bonds.
- Risks of GDP misreporting and safeguards:
  - Concern: If GDP-indexed debt becomes a large fraction of external debt, authorities might be tempted to understate growth rates.
  - Counterarguments / mitigating factors:
    - High growth is typically politically desirable and likely to be reported as success; sustained understatement would risk reputation.
    - Domestic investors might hold a portion of the new bonds and could lobby for accurate statistics.
    - International efforts to increase transparency and improve statistics could include GDP in monitoring drives.
    - Precedent: the EU’s Maastricht convergence process and the Stability and Growth Pact, with Eurostat’s role.
    - CPI-indexed bonds in many countries, including Chile, show statistical offices can provide sufficient guarantees, although real GDP measurement may be more difficult than CPI measurement.
- Moral hazard and incentives to grow:
  - Concern: GDP-indexed bonds increase repayments when growth is high, which could, in principle, reduce incentives for policies that promote growth.
  - Assessment:
    - Main determinants of growth are decisions by individual businesses, which are unlikely to alter behavior because public debt is GDP-indexed.
    - Any moral hazard operates primarily through government policy choices that affect growth (e.g., public investment).
    - The extent to which GDP-indexed bonds would induce governments to alter growth-orientation substantially for many years is an open question.
    - Indexed debt is particularly appealing for countries that can credibly commit to good policies (e.g., via an IMF-supported program or fiscal rules and peer monitoring).
  - Theoretical perspective: models of optimal incentive-compatible contracts in sovereign debt typically indicate the optimal contract is of a contingent type, even with moral hazard.

### Chapter 6) — Trade-offs, alternatives, market barriers, and roles for IFIs
- Trade-off: insurance benefits versus moral hazard and measurement problems
  - The paper contends that, in the trade-off between insurance and moral hazard/measurement problems, the optimal share of GDP-indexed bonds is likely to be non-zero.
  - Incentives to misreport GDP and to adopt policies aimed at objectives other than growth will be low if the amount of GDP-indexed debt is small; correspondingly, the related insurance benefits would be limited.
- Indexing to commodity prices versus GDP:
  - Krugman (1988) argument: indexing to commodity prices (over which an individual country usually has no control) may be preferable to indexing to GDP.
  - Commodity price indexing would be more appealing to Mexico (oil) or Chile (copper) than to Argentina or Brazil.
  - Empirical note: vector autoregressions tend to find that, for the typical emerging market country, a relatively small share of output fluctuations can be attributed to terms of trade shocks (e.g., no more than 10 percent according to Hoffmaister and Roldós, 1997).
  - Market consideration: existing markets for futures and options on commodity prices may provide sufficient opportunities for insurance against commodity price fluctuations, although liquidity of these markets is rather low beyond a few years.
  - GDP-indexed bonds would create a new opportunity for investors to take a view on a country’s economic growth prospects, particularly attractive where the stock market is not well diversified.
- Alternative variables to index to (exports, industrial production):
  - Basic objective: preserve debt sustainability by choosing a contingency that adjusts the value of debt to the repayment capacity.
  - For government external debt, the volume of exports is probably a relevant measure of repayment capacity; the debt-to-exports ratio is a closely watched indicator.
  - Indexing to exports may be a reasonable alternative; for many developing countries data on exports tend to be more reliable than data on GDP.
  - Industrial production could be an alternative, being highly correlated with GDP for some emerging market countries.
  - While GDP is the most comprehensive measure of a country’s income, other measures might be more accurate and harder to tamper with depending on the country.
  - Desirability of common indexation variable: it would be desirable for the bonds of different countries to be indexed to the same economic variable (GDP, exports, or industrial production) to make it easier for investors to diversify risk across countries.
- Enforceability in high-growth scenarios and the incentive-compatibility constraint:
  - Most models of sovereign debt assume the debtor will repay only if the amount to be repaid is lower than the cost of sanctions (the incentive compatibility constraint).
  - The cost of sanctions is typically assumed to be proportional to the country’s output.
  - Observation: it is extremely rare for countries to default on their external debt obligations in times when their output growth is relatively high.
  - Implication: if output growth is higher-than-expected the amount to be repaid would be higher than average, but the cost of sanctions would probably also be higher than average.
- Callability and recall concerns:
  - GDP-indexation is unlikely to be consistent with the callability of bonds.
  - If a GDP-indexed bond were callable and GDP growth turned out better than expected, the borrower would have an incentive to recall the indexed bonds and issue plain vanilla bonds at a lower interest rate.
  - Current market fact: less than 5 percent of all emerging market bonds are effectively callable.
  - Callability is an important form of insurance against fluctuations in interest rates; the appeal of GDP-indexed bonds depends on the relative importance of uncertainty over interest rates versus uncertainty over GDP growth.
- Reasons for limited adoption so far:
  - Investor-side barriers:
    - New and complex instruments tend to be illiquid, and pricing them involves computational costs.
    - In the absence of a concerted effort to ensure a certain “critical mass” for the new instruments, investors have reacted coolly to the idea of GDP-indexed bonds.
  - Borrower-side barriers:
    - Unsustainable debt positions typically take years to emerge; the proposed indexation system is likely to make a substantial difference only for relatively long-term bonds, with an original maturity of—say—5 years or more.
    - Politicians’ horizons are often shorter than that; current finance ministers may be unlikely to pay an insurance premium to issue indexed bonds that might make life significantly easier for their successors several years down the road.
- Differences from Shiller-type securities:
  - Three key differences:
    1. Shiller-type securities are perpetual claims on a country’s GDP, whereas the GDP-indexed portion of the bonds proposed here matures at the same time as the bonds do.
    2. Shiller envisages individuals buying and selling Shiller-type securities, whereas initially GDP-indexed bonds would probably be issued only by governments.
    3. Introducing GDP-indexation can be done by adding a related clause to standard sovereign debt contracts; a market for GDP-indexed bonds could piggy-back on existing markets for sovereign bonds.
  - Conclusion: a market for GDP-indexed bonds appears to be a less ambitious, practical step relative to Shiller-type securities.
- Role for official intervention and market failures affecting financial innovation:
  - Market failures identified: product uncertainty; externalities and coordination problems; highly competitive financial markets reducing private incentives to innovate.
  - Government intervention has historically fostered financial innovation (examples include mortgage-backed securities and CPI-indexed bonds).
  - For GDP-indexed bonds issued by sovereign governments, international institutions could play a leading role in fostering market creation.
- Concluding remarks — potential roles for International Financial Institutions (IFIs):
  - IFIs could gauge interest on the supply side through surveillance dialogue and promote the use of bonds indexed to GDP.
  - IFIs could gauge interest on the demand side among potential investors and provide information on the likelihood of achieving a critical mass of issuing countries.
  - IFIs could encourage countries to ensure the independence of their statistical agencies and provide technical assistance to improve national income statistics.
  - IFIs could contribute to gathering necessary information for pricing the instruments, including estimates of comovement of output among countries and the relationship between economic variables and default risk.

*Source: _pdp10 - 0.5 percent of GDP, and facing an 3.2 percent interest rate on international markets. The*

### 0.5 percent of GDP, and facing an 3.2 percent interest rate on international markets. The

### _pdp10 - 0.5 percent of GDP, and facing an 3.2 percent interest rate on international markets. The

### Setup and baseline assumptions
- Primary deficit is 0.5 percent of GDP throughout.
- Market interest rate on standard (plain vanilla) debt contracts: 3.2 percent.
- Alternative indexed bond structure:
  - Yearly coupon payments of 3.2 percent plus 0.7 times the difference between actual growth and “trend growth” of 3 percent.
  - A yearly insurance premium of 0.4 percentage point, payable regardless of the growth rate.
- All variables are in real terms; the (real) exchange rate is perpetually fixed.
- Focus is on sovereign debt exclusively.
- Debt dynamics identity used: Dt/Yt = (1+ r - gt) (Dt-1/Yt-1) - st, where Dt is government debt, Yt is output, st is the primary surplus as a share of GDP, gt is growth rate, and r is the interest rate.

### Scenario outcomes (simplest scenarios; Figure 1)
- Common setup for these scenarios:
  - The primary deficit is 0.5 percent of GDP throughout.
  - Output growth is 3 percent until period 5; thereafter scenarios diverge.
  - The interest rate on standard debt contracts is assumed to be 3.2 percent.
  - With indexing, the interest rate is reduced by 0.7 times the difference between the actual growth and trend growth of 3 percent.
  - The insurance premium is 0.4 percentage points, added to the market interest rate.
- Scenario 1: Growth drops
  - Growth drops to 0.5 percent from year 6 onwards.
  - By year 20:
    - Debt/GDP ratio rises to 71 percent without indexation.
    - Debt/GDP ratio rises to 52 percent with indexation.
- Scenario 2: Growth rises
  - Growth rises to 7 percent from year 6 onwards.
  - By year 20:
    - Debt/GDP ratio falls to 24 percent without indexation.
    - Debt/GDP ratio rises to 38 percent with indexation.
- Interpretation: Indexation can substantially reduce debt/GDP accumulation in downside growth scenarios but can raise debt/GDP in strong growth scenarios when the primary surplus is held constant.

### Fiscal behavior, welfare implications, and cyclical smoothing
- GDP-indexation reduces the need for procyclical fiscal tightening in downturns:
  - When GDP growth is below trend, governments can run a lower primary surplus (higher primary spending and lower taxes) with indexation than without it.
  - When GDP growth is above trend, governments will need a higher primary surplus (lower primary spending and higher taxes) with indexation.
- GDP-indexation tends to smooth paths of the primary surplus, taxes, and primary spending over the cycle.
- With diminishing marginal benefits to primary spending and increasing marginal costs of taxation, GDP indexation will tend to improve welfare.
- Adjusting the primary balance during economic and financial distress (e.g., raising new taxes or laying off government employees) may be especially costly.

### Model with fiscal–growth feedback (Box 1 and Figure 2)
- Government reaction function (Box 1): the government sets the ratio of the primary surplus to GDP, st, equal to the debt/GDP ratio times the difference between the interest rate, r, and a weighted average of “trend” growth, g, and current growth, gt: st = (Dt/Yt)·[(1+φ)r - (φg + (1-φ)gt)] (as expressed in the source formula).
  - In words: the government responds to growth slowdowns by increasing the primary surplus (procyclical fiscal policy).
- Growth response to primary surplus:
  - gt = g + γ (s - s̄) + ut, for all st ≥ s̄, where s̄ is the critical level of the primary surplus, g is a constant, ut is an exogenous shock to growth, and γ = 5.
  - Critical level s̄ = 0.1 percent of GDP.
- Indexed interest rate under Box 1:
  - Under standard debt contracts the interest rate is constant: r = 3.2 percent.
  - Under GDP indexation, the interest rate is r = 3.2 + Ω + α (g - gt), with Ω = 0.4 and α = 0.7 (i.e., coupon reduced by 70 basis points if growth falls short of trend by one percent).
- Simulation shocks (Figure 2):
  - Exogenous shock ut takes the value –4 percentage points (“growth drops” scenario) or +4 percentage points (“growth rises” scenario), beginning in year 4.
  - Figure 2 caption: market interest rate assumed 3.2 percent; output growth 3 percent until period 3; thereafter negative or positive shock of 4 percentage points. Government sets the primary surplus such that the debt/gdp ratio would be constant if growth were a weighted average of long-run growth and actual growth (with weights of 0.8 and 0.2, respectively). A primary surplus above a minimum threshold adversely affects current growth rate.
- Result: Allowing for fiscal feedback increases the benefits of indexation when governments otherwise respond to slowdowns by tightening fiscal policy.

### Diversifiability of growth across countries and the insurance premium
- Large unrealized gains from international risksharing arise because income growth rates are not highly correlated across countries at various horizons.
- Athanasoulis and van Wincoop (2000) and Athanasoulis, Shiller, and van Wincoop (1999) estimated probabilities that per capita GDP will unexpectedly rise by 50 percent in the best performing country relative to the worst:
  - 20 percent at the 15-year horizon,
  - 40 percent at the 20-year horizon,
  - 80 percent at the 25-year horizon,
  - 100 percent at the 35-year horizon.
- CAPM-based pricing implications:
  - Only the systematic portion of risk is reflected in expected returns; unsystematic risk can be diversified away.
  - The systematic portion of an individual country’s GDP growth rate is typically rather small.
  - Simple regressions of individual countries’ GDP growth on worldwide growth show unsystematic variation is far larger than systematic variation for emerging markets:
    - R2 coefficient ranges from 0.00 (Argentina, Bulgaria, etc.) to 0.39 (Botswana) with an average of 0.10 for 1970–2001.
    - Beta coefficients range from –1.4 (Jordan) to 3.00 (Botswana), with an unweighted average of 0.81.
    - The average of the absolute value of the difference between 1 and the beta coefficient is 0.78.
  - Regressions using U.S. GDP growth, world real stock returns, or U.S. real stock returns yield even lower R2 coefficients and typically lower beta coefficients.
- Implication: The insurance premium on GDP-indexed bonds issued by emerging markets would likely be small because much of country-specific growth risk is diversifiable.

*Source: _pdp10 - 0.5 percent of GDP, and facing an 3.2 percent interest rate on international markets. The*

### Box 2.  The Size of the Insurance Premium in CAPM-like Reasoning

### Box 2.  The Size of the Insurance Premium in CAPM-like Reasoning

### CAPM derivation of the insurance premium
- Return on GDP-indexed bonds:
  - ) ~( iii ggR−+=αρ
  - where R is the interest rate on plain vanilla bonds, α determines the degree of indexation, and gi is the country’s output growth rate, with i g~ being equal to actual growth and ig being equal to trend growth.
- CAPM pricing condition for any asset with return i r~:
  - )
~(
)
~,~
(
])
~([)
~(
M
Mi
FMFi
rVar
rrCov
rrErrE−+=
  - where Fr is the risk-free rate and Mr~ is the return on the market portfolio.
- Applying CAPM to GDP-indexed bonds:
  - )
~(
}
~)],
~({[
])
~([][
M
Mii
FMFi
rVar
rggRCov
rrErE
−+
−+=
α
ρ
  - which can be rewritten as:
  - )
~(
)
~,~
(
])
~([)(
M
Mi
FMFi
rVar
rgCov
rrErE
−+=αρ
- Note: the argument abstracts from the distinction between R and Fr.

### Numerical illustration
- Assumptions in the example:
  - Relevant portfolio: US stock market.
  - Risk-free rate of return: 3 percent.
  - Expected return on the market portfolio: 8 percent.
  - β of Argentina’s growth rate with respect to US stock market return (from Table 1b): 0.22.
  - α = 1.
- Computation of indexation premium:
  - 1*(8-3)*0.22, i.e., approximately 1 percentage point per year—fairly small compared with the spreads often observed in emerging markets.
- Clarification:
  - This premium is in excess of the rate the country pays on plain vanilla bonds; it is in addition to the premium that compensates for default risk.
  - The example assumes default risk is uncorrelated with GDP growth risk.

### Implications when default risk is correlated with growth
- If default risk rises when growth falls (i.e., default risk positively correlated with low growth), the appeal of indexed bonds increases relative to the uncorrelated-default-risk case.
- Converting a large portion of debt into indexed bonds could plausibly reduce default risk significantly.

### Investor willingness and instrument complexity
- Evidence and arguments:
  - International investors already invest heavily in emerging-market stocks, which are much more volatile than those countries’ GDP growth rates.
  - Under standard debt contracts investors are already implicitly exposed to GDP risk via default outcomes.
  - It is preferable for investors to receive lower debt repayments through pre-agreed indexation than to face uncertain recovery values through chaotic default processes.
- Complexity considerations:
  - GDP-indexed bonds are essentially floating-rate bonds where the coupon is tied to the borrower’s GDP growth rather than LIBOR or another interest rate.
  - The indexation mechanism is analogous to established inflation-indexed bonds.
  - Some emerging-market bonds already include payment conditions contingent on GDP or exports.

### Risks of GDP misreporting and safeguards
- Concern:
  - If GDP-indexed debt becomes a large fraction of external debt, authorities might be tempted to understate growth rates.
- Counterarguments / mitigating factors:
  - High growth is typically politically desirable and likely to be reported as success; sustained understatement would risk reputation.
  - Domestic investors might hold a portion of the new bonds and could lobby for accurate statistics.
  - International efforts to increase transparency and improve statistics could include GDP in monitoring drives.
  - Precedent: the EU’s Maastricht convergence process and the Stability and Growth Pact, with Eurostat’s role, shows countries can agree common statistical standards for GDP data.
  - CPI-indexed bonds in many countries, including Chile, show statistical offices can provide sufficient guarantees, although real GDP measurement may be more difficult than CPI measurement.

### Moral hazard and incentives to grow
- Concern:
  - GDP-indexed bonds increase repayments when growth is high, which could, in principle, reduce incentives for policies that promote growth.
- Assessment:
  - Main determinants of growth are decisions by individual businesses, which are unlikely to alter behavior because public debt is GDP-indexed.
  - Any moral hazard operates primarily through government policy choices that affect growth (e.g., public investment).
  - The extent to which GDP-indexed bonds would induce governments to alter growth-orientation substantially for many years is an open question.
  - Indexed debt is particularly appealing for countries that can credibly commit to good policies (e.g., via an IMF-supported program or fiscal rules and peer monitoring).
- Theoretical perspective:
  - Models of optimal incentive-compatible contracts in sovereign debt typically indicate the optimal contract is of a contingent type, even with moral hazard.

*Source: Box 2, “The Size of the Insurance Premium in CAPM-like Reasoning,” from the provided IMF content unit.*

### Chapter 6).

### Chapter 6)

### Trade-off: insurance benefits versus moral hazard and measurement problems
- The paper contends that, in the trade-off between insurance and moral hazard/measurement problems, the optimal share of GDP-indexed bonds is likely to be non-zero.
- The incentives for countries to misreport their GDP and to adopt policies aimed at pursuing other objectives than growth will be low if the amount of GDP-indexed debt is small; correspondingly, the related insurance benefits would be limited.

### Indexing to commodity prices versus GDP
- Krugman (1988) argument: indexing to commodity prices (over which an individual country usually has no control) may be preferable to indexing to GDP (over which a country’s authorities have some degree of control).
- Commodity price indexing reduces uncertainty regarding the debt/GDP ratio to the extent that commodity prices determine a country’s revenues and GDP developments.
- Commodity price indexing would be more appealing to Mexico (oil) or Chile (copper) than to Argentina or Brazil.
- Empirical note: vector autoregressions tend to find that, for the typical emerging market country, a relatively small share of output fluctuations can be attributed to terms of trade shocks (e.g., no more than 10 percent according to Hoffmaister and Roldós, 1997).
- Market consideration: existing markets for futures and options on commodity prices may provide sufficient opportunities for insurance against commodity price fluctuations, although liquidity of these markets is rather low beyond a few years.
- By contrast, GDP-indexed bonds would create a new opportunity for investors to take a view on a country’s economic growth prospects, particularly attractive for emerging market countries where the stock market is not well diversified and where stock market fluctuations may have little to do with fundamental growth prospects.

### Alternative variables to index to (exports, industrial production)
- Basic objective: preserve debt sustainability by choosing a contingency that adjusts the value of debt to the repayment capacity.
- For government external debt, the volume of exports is probably a relevant measure of repayment capacity; the debt-to-exports ratio is a closely watched indicator.
- Indexing to exports may be a reasonable alternative; for many developing countries data on exports tend to be more reliable than data on GDP.
- Government policies may affect trade openness more directly than they affect GDP.
- Industrial production could be an alternative, being highly correlated with GDP for some emerging market countries.
- While GDP is the most comprehensive measure of a country’s income, other measures might be more accurate and harder to tamper with depending on the country.
- Desirability of common indexation variable: it would be desirable for the bonds of different countries to be indexed to the same economic variable (GDP, exports, or industrial production) to make it easier for investors to diversify risk across countries.

### Enforceability in high-growth scenarios and the incentive-compatibility constraint
- Most models of sovereign debt assume the debtor will repay only if the amount to be repaid is lower than the cost of sanctions (the incentive compatibility constraint).
- The cost of sanctions is typically assumed to be proportional to the country’s output.
- Observation: it is extremely rare for countries to default on their external debt obligations in times when their output growth is relatively high.
- Implication for GDP-indexed bonds: if output growth is higher-than-expected the amount to be repaid would be higher than average, but the cost of sanctions would probably also be higher than average.

### Callability and recall concerns
- GDP-indexation is unlikely to be consistent with the callability of bonds.
- If a GDP-indexed bond were callable and GDP growth turned out better than expected, the interest rate on plain vanilla bonds would presumably fall; the borrower would then have an incentive to recall the indexed bonds and issue plain vanilla bonds at a lower interest rate.
- Current market fact: less than 5 percent of all emerging market bonds are effectively callable.
- Callability is an important form of insurance against fluctuations in interest rates; the appeal of GDP-indexed bonds depends on the relative importance of uncertainty over interest rates versus uncertainty over GDP growth.
- Countries facing substantial uncertainty over GDP growth are expected to draw clear advantages from GDP indexation.

### Reasons for limited adoption so far
- Investor-side barriers:
  - New and complex instruments tend to be illiquid, and pricing them involves computational costs.
  - In the absence of a concerted effort to ensure a certain “critical mass” for the new instruments (helping guarantee market liquidity and spread computational costs), investors have reacted coolly to the idea of GDP-indexed bonds.
- Borrower-side barriers:
  - Unsustainable debt positions typically take years to emerge; the proposed indexation system is likely to make a substantial difference only for relatively long-term bonds, with an original maturity of—say—5 years or more.
  - Politicians’ horizons are often shorter than that; current finance ministers may be unlikely to pay an insurance premium to issue indexed bonds that might make life significantly easier for their successors several years down the road.

### Differences from Shiller-type securities
- GDP-indexed bonds consist of a plain vanilla bond plus a security indexed to a country’s GDP; three key differences from Shiller-type securities:
  1. Shiller-type securities are perpetual claims on a country’s GDP, whereas the GDP-indexed portion of the bonds proposed here matures at the same time as the bonds do; a limited horizon might increase marketability and reduce scope for speculative bubbles.
  2. Shiller envisages individuals buying and selling Shiller-type securities (directly or through intermediaries), whereas initially GDP-indexed bonds would probably be issued only by governments.
  3. Introducing GDP-indexation can be done by adding a related clause to standard sovereign debt contracts; a market for GDP-indexed bonds could piggy-back on existing markets for sovereign bonds, whereas Shiller-type securities would involve greater institutional set-up costs.
- Conclusion: while Shiller-like securities may one day provide broad risk-sharing benefits, a market for GDP-indexed bonds appears to be a less ambitious, practical step in the right direction.

### Role for official intervention and market failures affecting financial innovation
- Allen and Gale (1994) identify market failures that can hinder the emergence of new financial instruments:
  - Product uncertainty: investors uncertain about what they are buying demand a premium, deterring borrowers from issuing new instruments.
  - Externalities and coordination problems: individual issuers do not internalize the benefits of teaching investors to price new instruments or the social benefits of new risk-sharing opportunities; hence collective adoption is hard to achieve.
  - Highly competitive financial markets: private institutions face development costs but cannot maintain monopoly provision because imitation is easy; private incentives to innovate may be low even if social benefits are high.
- Government intervention has historically fostered financial innovation (examples given include mortgage-backed securities in the US and bonds indexed to consumer prices in various countries).
- For GDP-indexed bonds issued by sovereign governments, international institutions could play a leading role in fostering market creation.

### Concluding remarks — potential roles for International Financial Institutions (IFIs)
- The paper argues GDP-indexed bonds could help prevent future debt crises and IFIs are ideally placed to foster market creation.
- Potentially fruitful IFI areas of involvement:
  - Gauging interest on the supply side through IFIs’ privileged position vis-à-vis member governments; promoting the use of bonds indexed to GDP through the surveillance dialogue; encouraging country authorities to take a longer-horizon perspective than electoral cycles often allow.
  - Gauging interest on the demand side among potential investors using IFI contacts on international capital markets; providing information on the likelihood that a critical mass of issuing countries would be willing to use GDP-indexed bonds.
  - Encouraging countries to ensure the independence of their statistical agencies; providing technical assistance to improve the quality and transparency of national income statistics and helping guarantee their reliability.
  - Contributing to gathering necessary information for pricing the instruments, including estimates of comovement of output among countries and the relationship between economic variables and default risk.

*Source: Chapter 6) from the provided PDF content.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/pdp/2002/_pdp10.pdf_