## _wp08152

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---

### Introduction and Research Purpose
- Purpose: Study how countries decide whether to respect sovereign debt repayment schedules or to default, assuming defaults occur because debtors do not want to repay rather than because they cannot.
- Enforcement channels reviewed:
  - No direct enforcement for sovereign external debt (no collateral; military enforcement obsolete).
  - Reputational enforcement: cutting or limiting access to international capital markets; trade sanctions.
- Political-economy insight:
  - Democratic heterogeneities matter: individuals differ in how much they value a country’s reputation in capital markets (example: young voters value continued access more than non-altruistic older voters).
  - If old voters who care less about future access form a majority, they can force default; if young voters are more numerous, they can force repayment.
- Empirical approach:
  - Data: macroeconomic variables (GDP growth rate and external debt); structural variables (population, age distribution, income distribution); political-economy variables (democratic structure).
  - Sample: countries that have had at least one episode of external debt default in their history through 2003.

### Theoretical model — Framework and key mechanisms
- Framework: Discrete-time overlapping-generations (OLG) model.
  - Economy: at each period there are N young and N old individuals; each individual lives exactly two periods.
  - No altruism between or within generations.
- Preferences and endowments:
  - Single perishable consumption good; Bernoulli utility u(c) with standard concavity properties (text: "with the following standard concavity properties:  and .").
  - Young discount future utility by β > 0.
  - Endowment w ∈ {w_h, w_l} with probabilities πh and πl such that πl + πh = 1 and πl << πh (text phrasing preserved).
  - Everybody receives same endowment realization each period (aggregate uncertainty persists).
- Insurance contracts and contracting environment:
  - Country-level, one-period insurance contracts offered by a risk-neutral foreign insurer; uninsured subsets cannot sign contracts.
  - Contracts specify net transfer τ for each realization; unpaid insurance payments remain outstanding until paid off.
  - Contracts are reputational (no premium, not enforceable by third party).
- Voting and default decision:
  - Voting rule: simple majority; default occurs only if more than 50 percent vote for default.
  - Turnout: the turn-out rate of the young is bigger or equal to the turn-out rate of the old with probability γ.
  - Young vote for default only if lifetime benefits of default outweigh costs; Lemma 1: the young vote for repayment only if 1 ≥ Z (Z defined as measure of desire for insurance).
  - Old often prefer default when realization is w_h (avoid payment); when insurance in place old vote against default.
- Contract concepts defined:
  - Default-free contract: bundle (τh, τl) accepted every period and insurer breaks even: 0 = + ll hh τ π τ π. Proposition 1: ),( lh τ τ is a default-free contract only if 1 = γ, 1] )()()()( [)= l π β ,,,( ≥− +− −+ h h h l l l w u w u w u w u w w Z π τ τ τ and 0 = + ll h τ π τ h π.
  - Default-repayment contract: offered and accepted at t = k, defaulted upon at t + 1, repaid at t + j + k; insurer breaks even in each offered period. Proposition 2: For 10 << γ, ),( lh τ τ is a default-repayment contract if 1] )()()()( [)= l β τ ,,, hlh w w τ (≥− +− −+ h h h l l l w u w u w u w u Z γ π τ τ π and 0 = + ll hh τ π τ π.
  - Default-renegotiation contract: allows partial default and repayment over two periods; Lemma 2 and Proposition 3 specify conditions (verbatim inequalities preserved in source).
- Population and heterogeneity:
  - Baseline: equal generation sizes N; later extensions consider α_t in (0.15 ≤ α_t ≤ 1) with income heterogeneity across young i ∈ [0,1], endowments w_i uniform on [0,1] plus shock ε_t ∈ {l_t, h_t}.
  - Modified Z for heterogeneous incomes is given explicitly in source; sign of ∂Z/∂w can be positive or negative depending on parameters and preference form (Example 3 for quadratic preferences).

### Empirical specification and variables
- Dependent variable:
  - Default: S&P. Binary: 1 if the country defaulted on its external debt; 0 otherwise.
- Explanatory variables (as in Table 1):
  - Debt/GDP: WEO. Total External Debt as a Percentage of GDP.
  - Unemployment: WEO. Rate of unemployment.
  - GDP/Capita: WEO. Real GDP per Capita in year-2000 USD.
  - Democracy: WB, Database of Political Institutions. Binary: 1 if the president/prime minister has finite term in office; 0 otherwise.
  - Population 15–59 (%): UN Population Database. Population of the "young", as a percentage of total population of adults.
- Estimation method:
  - Pooled panel probit regression:
    - Default_it = α_it.Macro_it + β_it.Political_it + error_it
    - Macro_it contains GDP growth per capita, debt/GDP and unemployment.
    - Political_it reported only for variable Democracy (binary).
  - Rationale: scarcity of structural and political variable data motivates pooled approach.

### Empirical results — key regression findings (annual data 1975-2003)
- Notes: * Represents significance at 95% confidence level. Sources: Database of Political Institutions, Population Database, Standard and Poor’s, World Economic Outlook, and World Bank.
- Selected coefficient estimates and exact statistics (Model number and reported coefficient (standard error); z-value):
  - Model 1:
    - Debt/GDP: 1.156* (0.141); z=8.21
    - Unemployment: 0.014* (0.006); z=2.31
    - GDP/Capita: 0.259* (0.135); z=1.92
    - Democracy: -0.052* (0.011); z=-4.74
    - Population 15-59 (%): 1.598* (0.644); z=2.48
    - Constant: 0.150
  - Model 2:
    - Debt/GDP: 1.326* (0.127); z=10.45
    - Unemployment: 0.013* (0.005); z=2.30
    - Democracy: -1.164* (0.106); z=-11.02
    - Constant: 0.128
  - Model 3:
    - Debt/GDP: 1.272* (0.149); z=8.54
    - Unemployment: 0.014* (0.006); z=2.24
    - GDP/Capita: 0.000067* (0.000024); z=2.77
    - Democracy: 0.216 (0.136); z=1.58
    - Population 15-59 (%): -0.063* (0.012); z=-5.37
    - Constant: 2.020* (0.665); z=3.04
  - Model 4:
    - Debt/GDP: 0.4138* (0.0449); z=9.21
    - GDP/Capita: 0.000025 (0.000019); z=1.31
    - Unemployment: 0.061 (0.070); z=0.88
    - Democracy: -0.0235* (0.008); z=-2.89
    - Constant: 0.554 (0.419); z=1.32
    - Population 15-59 (%): 0.049
  - Model 5:
    - Debt/GDP: 1.2348* (0.1461); z=8.45
    - Unemployment: 0.0123 (0.0057); z=2.16
    - GDP/Capita: 0.000076 (0.000024); z=3.18
    - Democracy: -0.065* (0.012); z=-5.67
    - Constant: 2.335* (0.650); z=3.59
    - Population 15-59 (%): 0.156
  - Model 6:
    - Debt/GDP: 1.4159* (0.1443); z=9.81
    - Unemployment: 0.0157* (0.0059); z=2.67
    - GDP/Capita: 0.000021 (0.000022); z=0.95
    - Democracy: 0.158 (0.134); z=1.18
    - Population 15-59 (%): -1.432* (0.182); z=-7.88
    - Constant: 0.132
  - Model 7:
    - Debt/GDP: 0.0194* (0.0056); z=3.43
    - GDP/Capita: 0.0000039 (0.000023); z=0.17
    - Unemployment: 0.036 (0.128); z=0.28
    - Democracy: -0.089* (0.011); z=-7.93
    - Constant: 4.497* (0.601); z=7.48
    - Population 15-59 (%): 0.083
  - Model 8:
    - Debt/GDP: 1.4001* (0.1408); z=9.94
    - Unemployment: 0.0126 (0.0055); z=2.3
    - GDP/Capita: 0.000028 (0.000022); z=1.26
    - Democracy: -1.278* (0.140); z=-9.15
    - Constant: 0.129
  - Model 9:
    - Debt/GDP: 0.3995* (0.0434); z=9.2
    - Unemployment: 0.074 (0.069); z=1.07
    - Democracy: -0.018* (0.007); z=-2.59
    - Population 15-59 (%): 0.330 (0.382); z=0.86
    - Constant: 0.049
- Empirical interpretations highlighted in text:
  - Models 2 and 8: higher indebtedness (debt/GDP) or unemployment lead to higher probability of default.
  - GDP per capita generally not significant in explaining default when all significant regressors are included — interpreted as evidence that countries default often because they do not want to, not because they cannot.
  - Model 1 (preferred): indicates democracies are more likely to default on sovereign debt (but democracy not significant in some other models); younger economies (higher percentage of people aged 15–59) are less likely to default — consistent with theory that younger people value reputational access more.

### Main theoretical and policy-relevant conclusions
- Core findings:
  - Incentive for sovereign governments to honor external liabilities is sensitive to national economy and within-country heterogeneities, in addition to international environment.
  - Interactions within borrowing countries (heterogeneities across individuals, finite lives) materially affect sovereign debt decisions.
- Theoretical contributions:
  - Replaces infinitely lived representative agent with an economy of heterogeneous selfish individuals with finite lives.
  - Characterizes conditions for default-free, default-repayment, and default-renegotiation contracts; shows how finitely lived selfish voters can shorten effective reputational horizon.
  - Even if good international reputation is socially beneficial, selfish voters might vote for default.
- Comparative insight:
  - Democratic countries might be less creditworthy than non-democratic ones depending on parameter values: distribution of income shocks, population structure, risk-aversion, voter income heterogeneity, and alternative asset market richness.
- Policy interpretation:
  - Democracy per se is not a categorical bar to international loans; creditworthiness depends on parameter values that affect voters’ incentives.
- Model limitations:
  - Default arises solely from voters’ willingness to default; model does not capture defaults due to lack of foreign reserves.

### Extensions and suggested further research
- Political structures: study effects of parties and interest groups; equilibria with default may persist when finitely lived selfish voters can form decisive coalitions.
- Income-shock processes: allow richer persistence structures (e.g., expansions longer than recessions, persistent disasters).
- Domestic insurance markets: adding domestic insurance markets could alter results; baseline rules them out except under some heterogeneity.
- Information asymmetry: relax symmetric information assumptions between borrowers and foreign lenders.

### Appendix — Selected formal results and illustrative examples (preserved expressions)
- Lemma 1: The young vote for repayment only if 1 ≥ Z.
- Corollary 1: Given 1 = γ, existence and uniqueness of a default-free contract depends only on the shape of the utility function (w_h, w_l, π_h, π_l, β).
- Corollary 2: There is a default-free contract for sufficiently risk-averse preferences.
- Corollary 3: As the country ages, a default-free contract becomes less likely.
- Proposition 1 (condensed verbatim): ),( lh τ τ is a default-free contract only if 1 = γ, 1] )()()()( [)= l π β ,,,( ≥− +− −+ h h h l l l w u w u w u w u w w Z π τ τ τ and 0 = + ll h τ π τ h π.
- Proposition 2 and Proposition 3: Existence conditions for default-repayment and default-renegotiation contracts given in source (preserved inequalities and parameter ranges, including statements "For 10 << γ" and definitions of penalties f and Ẑ).
- Example 1 (quadratic preferences): For u(x)=a x − b x^2, a default-free contract exists for sufficiently high risk aversion (small ( ) 2 b ) and small enough l π (full expressions in source).
- Example 2 (quadratic preferences): constructive expressions for τh and τl showing existence of default-repayment contracts for any γ and sufficiently small l π (exact algebraic choices preserved in source).
- Example 3 (quadratic preferences): condition for monotonicity of Z in w:
  - 0 > ∂Z/∂w occurs if 2 1 h l π l hh π τ ε ε + > −
  - 0 < ∂Z/∂w occurs if 2 1 h l π l hh π τ ε ε + < −

*Source: IMF Working Paper WP/08/152 — "A Model of Sovereign Debt in Democracies", Sections 1–4 (PDF _wp08152)*

### Section 1

### A Model of Sovereign Debt in Democracies — Section 1

### Introduction
- Purpose: Study how countries decide whether to respect sovereign debt repayment schedules or to default, assuming defaults occur because debtors do not want to repay rather than because they cannot.
- Key enforcement channels reviewed:
  - No direct enforcement for sovereign external debt (no collateral; military enforcement obsolete).
  - Reputational enforcement: cutting or limiting access to international capital markets; trade sanctions.
- Main political-economy insight:
  - Democratic heterogeneities matter. Individuals differ in how much they value a country’s reputation in capital markets (e.g., young voters value continued access more than non-altruistic older voters).
  - If old voters who care less about future access form a majority, they can force default; if young voters are more numerous, they can force repayment.
- Empirical approach overview:
  - Data set: macroeconomic variables (GDP growth rate and external debt); structural variables (population, age distribution, income distribution); political-economy variables (democratic structure).
  - Sample: countries that have had at least one episode of external debt default in their history through 2003.

### Relevant Literature and Contribution
- Key prior models:
  - Eaton and Gersovitz (1981): reputational model for sovereign debt repayment.
  - Bulow and Rogoff (1989): critique of reputational enforcement via alternative lenders/asset markets (example with $1 million loan).
  - Amador (2003): political uncertainty can restore reputational incentives via politicians’ saving behavior.
- Empirical literature: Van Rijckeghem and Weder (2005) finds many macroeconomic and political variables correlate with default (debt/GDP, GDP growth, currency crises, openness, democracy).
- Two stated contributions of this paper:
  - Develop a comprehensive model that explains both episodes of default and episodes of repayment within a single framework.
  - Show that domestic democratic forces (voting) can significantly affect default/repayment decisions.
- Theoretical model predictions (novel):
  - Citizens shape a country’s decisions about debt repayment by voting.
  - Macroeconomic conditions affect individual voting decisions.
  - Individual heterogeneities (age, income) affect voting decisions.
  - Individuals vote for repayment only insofar as they care about the country’s reputation in international capital markets, which provides insurance against future shocks.

### Empirical Specification and Variables
- Variables and sources (as presented in Table 1):
  - Default: S&P. Binary: 1 if the country defaulted on its external debt; 0 otherwise.
  - Debt/GDP: WEO. Total External Debt as a Percentage of GDP.
  - Unemployment: WEO. Rate of unemployment.
  - GDP/Capita: WEO. Real GDP per Capita in year-2000 USD.
  - Democracy: WB, Database of Political Institutions. Binary: 1 if the president/prime minister has finite term in office; 0 otherwise.
  - Population 15–59 (%): UN Population Database. Population of the "young", as a percentage of total population of adults.
- Estimation method:
  - Pooled panel probit regression:
    - Default_it = α_it.Macro_it + β_it.Political_it + error_it
    - Default_it is binary (1 if country i defaulted at period t).
    - Macro_it contains GDP growth per capita, debt/GDP and unemployment.
    - Political_it reported only for variable Democracy (binary = 1 if executive has finite term).
  - Rationale: Scarcity of structural and political variable data makes pooled approach the feasible estimation method.
- Note on Democracy variable:
  - Captures degree of democracy and transitions between autocracy and democracy, useful for studying regime effects on debt behavior.

### Theoretical Model — Overview
- Framework: Discrete-time overlapping-generations (OLG) model.
  - Economy: at each period there are N young and N old individuals.
  - Each individual lives exactly two periods (young at t, old at t+1).
  - No altruism between or within generations.
- Consumption and preferences:
  - Single perishable consumption good; individuals get utility from consumption c with Bernoulli utility u(c) such that 0' > 0 and 0'' < 0 (text: "with the following standard concavity properties:  and .").
  - Young individuals discount future utility by β > 0.
- Endowments and uncertainty:
  - At beginning of each period t, each individual receives w units; endowment is stochastic: {wh, wl}.
  - Probabilities: wh occurs with probability πh and wl occurs with probability πl such that πl + πh = 1 and πl << πh (text gives "1 l π 1=+ lh ππ<<π" — interpreted as πl + πh = 1 and πl << πh).
  - Assumption: everybody receives same endowment realization each period (aggregate uncertainty persists even for large N).
  - Assumption of non-zero endowments consistent with the observation that defaulting countries often can partially afford repayment.
- Population assumption and extensions:
  - For most of the model the population of each generation is fixed at N; later the paper discusses different generation sizes and income heterogeneity (stated that main results do not hinge on identical endowments).

### Theoretical Model — Insurance Contracts (summary of setup)
- Country-level insurance only:
  - The country (as a whole) can buy insurance from a risk-neutral foreign insurer; no proper subset of the population can sign contracts.
- Available contract:
  - Only one-period insurance contracts available at time t (called the “time t + 1” insurance contract).
  - Contract specifies a net transfer of τ for each realization of w from the foreign insurer to the country at time t+1, where τ depends on the realization.
  - Unpaid (defaulted) insurance payments remain outstanding until paid off.

### Empirical and Theoretical Linkages (as described)
- The empirical model is derived from the theoretical OLG framework with voting determining default/repayment decisions.
- Political variables (e.g., Democracy, age distribution Population 15–59 (%)) capture how internal democratic forces influence the voting outcomes that determine whether a country honors insurance/debt contracts to preserve market reputation and future access.

*Source: IMF Working Paper WP/08/152 — "A Model of Sovereign Debt in Democracies", Section 1*

### Section 2

### _wp08152 - Section 2

### Model setup and payments
- Insurance contract offered at each period only if the country does not have any outstanding debt from previous insurance contracts.
- As soon as the country pays off all its previous debt (if any) at time t, the “time t + 1” insurance contract becomes available.
- For simplicity: zero interest rates and no late fees for repayment of debt.
- Payments are in units of the consumption good per person. Population each period is fixed at 2N, so total payments would be )(2 h w N τ and )(2 l w N τ.
- Any positive inflow is distributed equally among all living individuals as a poll subsidy; any positive outflow is financed by taxing all living individuals equally through poll taxes. Tax/subsidy system assumed to have no transaction costs.
- No domestic insurance markets (to concentrate on sovereign debt); domestic markets ruled out when young are identical. When income heterogeneity is introduced, domestic insurance markets would be permitted but are assumed away here.
- Insurance rule chosen to avoid complications from strategic interaction of different foreign insurers.

### Definition of default and sequence of events
- At each period t, after realization of the endowment w_t, the country chooses:
  - Default: not make the transfer payment of )(. t t w τ on outstanding debt due to previous insurance contracts. This makes the country unable to sign an insurance contract for period t + 1.
  - Repay: make the transfer payment of ,)( t t w τ the outstanding debt from previous defaults; this entitles the country to sign an insurance contract for t + 1.
- Default is unlikely when the realization is h_t w = w_h because the country is entitled to receive funds from the foreign insurer; more interesting cases follow low realizations l_t w = w_l.
- Sequence of events each period:
  1. Previous period’s young become old (N individuals); new generation of young (N) eligible to vote.
  2. Endowment is realized and observed by everybody.
  3. Individuals vote for default or repayment by simple majority rule; outcome executed via poll taxes/subsidies.
  4. Individuals consume remaining resources.
  5. If the country chose repayment, it signs an insurance contract for next period; otherwise no contract is offered.

### Foreign insurer
- Insurer has limited strategic role; offers time-independent but (first order) history-dependent insurance contracts: for period t it offers contract ),( lh τ τ if the country has no outstanding debt due to prior defaults; otherwise the contract is offered only after the country has repaid all of its debt.
- The insurance contract is a purely reputational contract: requires no premium payment and is not enforceable by a third party.
- Contracts are indexed ),( lh τ τ for t ∈ {0,1,2,...}.

### Voting, turnout, and individual incentives
- Voting rule: simple majority. Default occurs only if more than 50 percent vote for default; in baseline model a default occurs only if both the young and the old vote for it.
- Turn-out rate: the turn-out rate of the young is bigger or equal to the turn-out rate of the old with probability γ.
- Young voters:
  - Vote for default only if lifetime benefits of default outweigh costs.
  - Young discount old-time consumption at rate β.
  - When country has no outstanding debt and has period t insurance, young do not vote for default because insurance entitles them to a positive transfer.
  - When country has outstanding debt from previous defaults and low endowment realization w_l, young may vote for default if l π is large enough (example condition hl π π > given in text).
  - Lemma 1 and definition of Z: Z is defined (text) as a measure of desire for insurance; higher Z implies higher desire for insurance. If young are indifferent about insurance, then 1 = Z. For 1 ≥ Z, the young have enough desire for insurance to vote for repayment.
  - Notice that 0 < ∂Z/∂γ. Interpretation: higher expected turn-out of the young decreases their desire for insurance because a young individual expects her next-period vote for default is more likely to fall into the minority.
- Old voters:
  - If the endowment realization is h_t w = w_h, the old avoid payment to the foreign insurer and prefer default on the outstanding debt (in many cases).
  - If country has no outstanding debt and has period t insurance, old are entitled to a positive transfer and vote against default.

### Contract concepts: default-free, default-repayment, default-renegotiation
- Default-Free Contract:
  - Bundle ),( lh τ τ is a default-free contract if offered and accepted every period such that insurer breaks even in expected value at each period: 0 = + ll hh τ π τ π (as presented).
  - Because hl w w < and 0,0< (notation as in text), it should be the case that 0 < h τ and 0 > l τ (text statements kept).
  - Old and young voters maximize expected lifetime utility under the contract.
  - Proposition 1 (verbatim conditions): ),( lh τ τ is a default-free contract only if 1 = γ, 1] )()()()( [)= l π β ,,,( ≥− +− −+ h h h l l l w u w u w u w u w w Z π τ τ τ and 0 = + ll h τ π τ h π. In other words, ),( lh τ τ is a default-free contract only if the young are in the majority (1 = γ) and have sufficient desire for insurance (1),,,( ≥ l h l h w w Z τ τ), and the foreign insurer breaks even (0 = + ll h τ π τ h π).
  - Corollary 1: Given ),( lh τ τ, when the young are pivotal voters, the existence and uniqueness of a default-free contract depends only on the shape of the utility function l h l h w w , , , , π π β.
  - Corollary 2: There is a default-free contract for sufficiently risk-averse preferences.
  - Example 1 (quadratic preferences): For a country in which the young are pivotal and have quadratic preferences x u = a x − b x^2 (text notation), a default-free contract exists for sufficiently high risk aversion (small ( ) 2 b ) and small enough l π.
- Default-Repayment Contract:
  - Bundle ),( lh τ τ is a default-repayment contract if offered and accepted at some period t = k, defaulted upon at t + 1, but repaid at some period t + j + k (indices as in text), such that insurer breaks even in expected value at each period that a contract is offered: 0 = + ll hh τ π τ π, and old and young maximize expected utility.
  - Proposition 2 (verbatim): For 10 << γ, ),( lh τ τ is a default-repayment contract if 1] )()()()( [)= l β τ ,,, hlh w w τ (≥− +− −+ h h h l l l w u w u w u w u Z γ π τ τ π and 0 = + ll hh τ π τ π.
  - Remark 1: Case 0 = γ is trivial: the old are always in the majority and default on any payment; as a result no contract is offered.
  - Comparison: sustaining a default-free contract requires the young always be in the majority (1 = γ). For a default-repayment contract, sometimes young and sometimes old are majority.
  - Example 2: For quadratic preferences, there is a default-repayment contract for sufficiently small l π (text).
- Default-Renegotiation Contract:
  - Allows partial default: country may pay an installment f with h f τ − < at one period and the remainder later; a payment of amount f entitles the country to an insurance contract of ),( f h l h ++ τ τ τ (text).
  - Bundle ),( lh τ τ is a default-renegotiation contract if offered at period t = k, defaulted upon at t + 1, and repaid over two periods t + j_k and t + k_j with indices as in text; insurer breaks even at each offered period and voters maximize utility.
  - Lemma 2: If h t w = w_h and country does not have a time t contract due to prior defaults, then the young vote for payment of h f τ − < if payment entitles the country to an insurance contract ),( f τ ++ hl h and if ),( f Z τ )()()()( ),( hh hl f w u w u fw Z τ τ − − ≥ + + , , hl h w τ h h h w u w u τ + − (verbatim textual condition).
  - Proposition 3 (verbatim): For 10 << γ, ),( lh τ τ P is a default-renegotiation contract if )()()( h h u w w − − )( ,,,( h h l h l h f w u u w w Z τ τ τ − + for h f τ − <, and h h ) u f ≥ + h h w τ +.
  - Interpretation: f is a penalty for current citizens because the country defaulted in the past.
  - Define Ẑ (text): ),()()()( ),,,(),,,,,( h h h hh hl hl w u w u f w u w u f w w Z f τ τ τ τ + − − − ++ = . Ẑ interpreted like Z; measure of desire for insurance for a country that defaulted in previous period. Text notes 0 < ∂ Ẑ / ∂ f (actually shows 0 ˆ < ∂/∂ f Z), indicating desire for insurance decreases as f increases.
  - Existence: given existence of default-repayment equilibrium and continuity, for f smaller but very close to h τ a default-renegotiation equilibrium is same as default-repayment equilibrium.

### Income heterogeneity and population mixture
- Introduce heterogeneity: continuum of individuals on [0,1]; fraction α_t (0.15 < = α_t ≤ 1) of population is young and rest are old (text uses fraction )15.0(, < ≤ t t α α but preserves original phrasing).
- At beginning of each period t, each young individual i has endowment w_i uniformly distributed on [0,1]; endowment experiences exogenous shock ε_t ∈ {l_t, h_t} with h_t ε < l_t ε (text notation). Net endowment (w_i + ε_t) positive for all i.
- Shock probabilities l_t π and h_t π with 1 = l_t π + h_t π and 0 < l_t π, h_t π < 1.
- Modified Z (text): Z = ] )()()()( [ ),,,, ( ll hl hi w Z π β τ τε ε = h h h i h i i l l i w u w u w u w u w u w u π τε ε τε − + + − + − ++ (text preserves original formula notation).
- Consider cases sign(∂Z/∂w):
  - If 0 > ∂Z/∂w or 0 < ∂Z/∂w: as an individual becomes richer, desire for insurance may increase or decrease depending on parameters and preference form.
  - Example 3 (quadratic preferences): ∂Z/∂w > 0 (or < 0) occurs if difference in shock sizes relative to insurance payments is such that 2 1 h l h h π π ε ε + > − (or < − ) and l τ conditions as in text.
- Proposition 4 (verbatim parts):
  - (i) Suppose 0 > ∂ w ∂ Z. If there is an individual i with endowment w_i = w such that 1 ,,,( lh w Z τ τε ε, then there exists a default-free contract on ), = lh τ l y if 1 2 1 1 − < α + t w.
  - (ii) Likewise, for ∂ ∂ w Z w w i = = 0 < , if there is an individual i with endowment such that 1),,,, ( l h l h w Z τ τ ε ε there then exists a default-free contract only if, =, th 1 2 1 α .
  - (iii) If 1), < l τ for all i, there then is no default-free contract.
  - (iv) If for all i, then is a default-free contract. (Text preserves original phrasing; corollary 3: as the country ages a default-free contract becomes less likely — foreign countries less likely to insure older economies.)
- Intuition: old have less taste for insurance than young; aging population lowers likelihood of default-free contract.

### Empirical results (section IV)
- Regression results for nine different models reported in Table 2 (dependent variable: default on sovereign debt).
- Models 2 and 8: link default to macroeconomic variables alone; higher indebtedness (debt/GDP ratio) or unemployment lead to higher probability of default.
- No significant relationship between GDP/capita and probability of default in Models 2 and 8.
- Model 1 (preferred model): adds political-economy explanatory variables to Model 2.
  - Estimation indicates democracies are more likely to default on sovereign debt (note: “democracy” not significant in some other models in Table 2; robustness requires alternative democracy measures).
  - Model 1 suggests younger economies (higher percentage of people aged 15–59 in total population) are less likely to default — consistent with intuition that younger people care more about reputation in international capital markets.
- Notable observation: GDP per capita does not significantly explain default in any models with all-significant regressors — evidence that countries default not because they cannot service debt but because they do not want to.

*Source: _wp08152 - Section 2*

### Section 3

### _wp08152 - Section 3

### Regression Results
- Dependent Variable: Default
- Table (coefficients, standard errors in parentheses, z-values):
  - Model 1:
    - Debt/GDP: 1.156* (0.141); z=8.21
    - Unemployment: 0.014* (0.006); z=2.31
    - GDP/Capita: 0.259* (0.135); z=1.92
    - Democracy: -0.052* (0.011); z=-4.74
    - Population 15-59 (%): 1.598* (0.644); z=2.48
    - Constant: 0.150
  - Model 2:
    - Debt/GDP: 1.326* (0.127); z=10.45
    - Unemployment: 0.013* (0.005); z=2.30
    - Democracy: -1.164* (0.106); z=-11.02
    - Constant: 0.128
  - Model 3:
    - Debt/GDP: 1.272* (0.149); z=8.54
    - Unemployment: 0.014* (0.006); z=2.24
    - GDP/Capita: 0.000067* (0.000024); z=2.77
    - Democracy: 0.216 (0.136); z=1.58
    - Population 15-59 (%): -0.063* (0.012); z=-5.37
    - Constant: 2.020* (0.665); z=3.04
  - Model 4:
    - Debt/GDP: 0.4138* (0.0449); z=9.21
    - GDP/Capita: 0.000025 (0.000019); z=1.31
    - Unemployment: 0.061 (0.070); z=0.88
    - Democracy: -0.0235* (0.008); z=-2.89
    - Constant: 0.554 (0.419); z=1.32
    - Population 15-59 (%): 0.049
  - Model 5:
    - Debt/GDP: 1.2348* (0.1461); z=8.45
    - Unemployment: 0.0123 (0.0057); z=2.16
    - GDP/Capita: 0.000076 (0.000024); z=3.18
    - Democracy: -0.065* (0.012); z=-5.67
    - Constant: 2.335* (0.650); z=3.59
    - Population 15-59 (%): 0.156
  - Model 6:
    - Debt/GDP: 1.4159* (0.1443); z=9.81
    - Unemployment: 0.0157* (0.0059); z=2.67
    - GDP/Capita: 0.000021 (0.000022); z=0.95
    - Democracy: 0.158 (0.134); z=1.18
    - Population 15-59 (%): -1.432* (0.182); z=-7.88
    - Constant: 0.132
  - Model 7:
    - Debt/GDP: 0.0194* (0.0056); z=3.43
    - GDP/Capita: 0.0000039 (0.000023); z=0.17
    - Unemployment: 0.036 (0.128); z=0.28
    - Democracy: -0.089* (0.011); z=-7.93
    - Constant: 4.497* (0.601); z=7.48
    - Population 15-59 (%): 0.083
  - Model 8:
    - Debt/GDP: 1.4001* (0.1408); z=9.94
    - Unemployment: 0.0126 (0.0055); z=2.3
    - GDP/Capita: 0.000028 (0.000022); z=1.26
    - Democracy: -1.278* (0.140); z=-9.15
    - Constant: 0.129
  - Model 9:
    - Debt/GDP: 0.3995* (0.0434); z=9.2
    - Unemployment: 0.074 (0.069); z=1.07
    - Democracy: -0.018* (0.007); z=-2.59
    - Population 15-59 (%): 0.330 (0.382); z=0.86
    - Constant: 0.049
- Notes:
  - Annual data for 1975-2003.
  - * Represents significance at 95% confidence level.
  - Sources : Database of Political Institutions, Population Database, Standard and Poor’s, World Economic Outlook, and World Bank.

### V. Conclusion — Main Findings and Interpretation
- Core findings:
  - The incentive for a sovereign government to honor external liabilities is sensitive to the national economy and heterogeneities within it, in addition to the international financial environment.
  - Interactions within borrowing countries (heterogeneities across individuals) are important in sovereign debt decisions; the literature has mostly ignored this.
- Methodological contributions:
  - Explained sovereign debt repayment decisions by solving the basic utility maximization problems of individuals.
  - Replaced the infinitely lived representative agent with an economy of heterogeneous selfish individuals with finite lives.
- Key theoretical results:
  - Characterized conditions where a debtor country sometimes defaults and other times repays outstanding debt.
  - Characterized situations where international reputational risk-sharing is impossible because losses to current finitely lived voters from payment dominate benefits of insurance.
  - Even if good international reputation is socially beneficial, selfish voters might vote for default.
  - Effective reputational horizon is shortened by finitely lived selfish voters; risk-neutral international insurers may not find it profitable to insure governments domestically constrained from repayments.
- Comparative insight:
  - Results imply democratic countries might be less creditworthy than non-democratic ones depending on parameters: distribution of income shocks, population structure, risk-aversion of voters, voter income heterogeneity, richness of alternative asset markets.
  - This is in line with, but stronger than, Bulow and Rogoff (1989), because political uncertainty is included.
- Model limitations:
  - Default in the model occurs solely from voters’ willingness to default; model does not capture defaults due to lack of foreign reserves.
- Policy-relevant interpretation:
  - Democracy per se is not a categorical bar to international loans; creditworthiness depends on parameter values that affect voters’ incentives.

### Extensions and Directions for Further Research
- Alternative political structures:
  - Study effects of parties and interest groups.
  - Conjecture: equilibria with default cannot be ruled out as long as voters are finitely lived and selfish; each person votes for default at least once (e.g., the last period of life), and if such voters form a strong group they can force default.
- Alternative income-shock distributions:
  - Current model uses simple i.i.d. binary output shocks; richer processes (e.g., expansions longer than recessions, persistent natural disasters) would enrich analysis.
- Domestic insurance markets:
  - Adding domestic insurance markets could alter results; most of the paper rules them out by assuming the young (no markets), though some heterogeneity among the young permits domestic insurance markets.
- Information asymmetry:
  - Relax symmetric information and beliefs among players; borrowing countries may know their economies better than foreign lenders, though information technology and credit rating firms reduce asymmetries.

### Appendix — Selected Formal Results (Summarized)
- Lemma 1:
  - The young vote for repayment only if 1≥Z (given notation in text).
- Lemma 2:
  - If the country lacks a time t contract due to prior defaults, the young vote for payment of f if it entitles the country to an insurance contract and a specified inequality in the text holds (see source).
- Corollaries:
  - Corollary 1: Given 1=γ, existence and uniqueness of a default-free contract depends only on utility function shape (w_h, w_l, π_h, π_l, β).
  - Corollary 2: A default-free contract exists if preferences are sufficiently risk-averse.
  - Corollary 3: As the country ages, a default-free contract becomes less likely.
- Propositions (selected statements):
  - Proposition 1: A contract is default-free only if (i) 1=γ (young are majority), (ii) 1≥Z (young sufficiently desire insurance), and (iii) insurer breaks even (0=+ ll hh τ π τ π).
  - Proposition 2: For 10<<γ, there exists a default-repayment contract under specified inequalities (see source).
  - Proposition 3: For 10<<γ, there exists a default-renegotiation contract under specified inequalities and conditions (see source); total debt never exceeds h τ−.
  - Proposition 4: Conditions relating ∂Z/∂w sign, existence of individuals with particular endowments, and threshold inequalities for existence of default-free contracts (see source for full formal statements).
- Example 1:
  - For quadratic preferences u(x)=ax−bx^2 (in text notation), a default-free contract exists if risk aversion is sufficiently high (b/a) and l π is small (full derivation in source).

*Source: _wp08152 - Section 3 (PDF).*

### Section 4

### _wp08152 - Section 4

### Existence of a default-free contract (general model)
- Requirement to find a bundle (τh, τl) such that, for 1=γ:
  - 1] )()([),,,(≥−+−= hhhh llhlh wuwu wwZ π τ πβττ and 0=+ llhh τπτπ.
- Z is positive for plausible values of the model parameters. (Since , the denominator of the above inequality is positive.)
- The size of the insurance contract is less than double the size of the endowment plausibly assuming 0)('> h wu and hl −ττ )(2 lh ww−<) and solving for l τ from the above inequality gives:
  - 1≥ Z S
- Parameter restrictions derived (preserve exact algebraic expressions from source):
  - 0*)1(2≥−++ b a ww lhhh βπβπ
  - Combined with 0)('> h wu implies: )( *222 lhhhh www b a w++≤≤βπ .
- Conclusion: If )( *222 lhhhh www b a w++≤≤βπ, then a default-free contract exists.

### Example 2 — Quadratic preferences: default-repayment contract exists
- Claim: For quadratic preferences, there exists a default-repayment contract for any γ and sufficiently small l π.
- Need to show existence of a bundle (τh, τl) for 1=γ such that:
  - 1] )()()()([≥−+−−+ hhhh llh l wuwu wuwu γπ τ τ πβ and 0=+ llhh τπτπ.
- Constructive choices (exact expressions from source):
  - Choose ) )2(22 ,0max( h l lh hlhh l www π π βγπβπ βπ τ ++ − − > and l l h h τ π π τ − = .
- As in the default-free contract case (Proposition 2), for sufficiently small l π (big h π), τh and τl satisfy:
  - 1 2 )(2 ≥ + −+− hh hlhl h w ww τ γττγ βπ
  - and hence is a default-repayment contract.

### Example 3 — Quadratic preferences: comparative statics of Z with respect to w
- Setup: Case 0=+ llhh τπτπ and bundle (τh, τl).
- Result on monotonicity of Z in w:
  - 0> ∂ ∂ w Z (aE) occurs if the difference of shock sizes, relative to insurance payments, is big (sm ll) enough that:
    - 2 1 h l π l hh π τ ε ε + > −
  - Conversely, 0< ∂ ∂ w Z occurs if:
    - ( 2 1 h l π l hh π τ ε ε + < − ).
- Proof sketch preserves the algebraic derivation:
  - Z expression and algebraic manipulations (as in source) lead to the derivative of Z with respect to w and the condition for sign change.
  - Use zero profit condition ) to solve: 022<−−+ llhh τετε which simplifies under 0=+ llhh τπτπ to:
    - 2 1 h l π l hh π τ ε ε + < −

*Source: _wp08152 - Section 4*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08152.pdf_