## wpiea2026042-source-pdf ## Source details **Canonical URL:** [wpiea2026042-source-pdf](https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026042-source-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2026/english/wpiea2026042-source-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2026/english/wpiea2026042-source-pdf.pdf.json) --- ### Research question and motivation - Debt crises create a trade-off between debt sustainability and redistribution when output contracts and external debt accumulates until constrained by repayment capacity. - Austerity (higher taxes or lower government spending) can expand repayment capacity but imposes unequal burdens across residents. - Empirical observation motivating the paper: inequality and external debt jointly rose for the sample of countries with positive external debt over 1985–2015 (data sources: Lane and Milesi-Ferretti (2018); Solt (2019)). ### Core theoretical mechanism and main results - Redistributive motives generate an endogenous cost of default because default into financial autarky increases reliance on distortionary labor taxation for redistribution. - Private agents borrow abroad and do not internalize that their borrowing tightens the sovereign’s limited-commitment constraint → overborrowing externality. - Optimal borrowing tax corrects the externality and yields redistributive benefits because high-skilled agents hold more foreign debt and bear a larger share of the tax burden. - Proposition 2.1 (External Debt Sustainability): - Under Assumptions 1–3 (separable utility, impatience, deviation value = financial autarky) and positive aggregate labor distortion in financial autarky, the optimal external debt is positive in the long run. - Comparative-static implication: higher inequality raises sustainable external debt because it increases distortionary costs of redistribution under autarky, strengthening incentives to repay. ### Quantification and calibration (Italy) - Calibration highlights (selected parameters and targets preserved exactly): - r^* Risk-free rate: 0.017 — Target: Avg. real return on German bond - β Discount factor: 0.967 — Target: Avg. Italian real interest rate = 3.4% - σ Intertemporal elasticity: 1 - 1/ν Labor elasticity: 0.5 - ω Labor utility weight: 1 - θ_H/θ_L Wage ratio: 1.89 — Mean top50% wage / mean bottom50% wage - ρ_z Auto-corr. of prod.: 0.927 — Auto-corr. of log GDP - σ_z Std. dev. of prod. res.: 0.0205 — Std. dev. log GDP - ̄g Govt. spending: 0.202 — Avg. govt. consumption-to-GDP - Population: two types with θ_H, θ_L and π_H = π_L = 0.5; planner utilitarian (λ_H = λ_L). - Period = 1 year; output series: log-linear detrended real GDP 1985–2015. - Initial conditions: B_0 = 0; a^H_0 = a^L_0 = 0; economy starts at mean of productivity distribution. ### Quantitative moments and model fit (selected exact figures) - Targeted moments: - Std. output (%): Data 5.3 ; Baseline 5.3 ; No inequality 5.4 ; Skill-dependent lump sum tax 5.4 - Avg. govt. expenditure/output (%): 19 19 19 19 - Non-targeted external debt moments: - Avg. external debt/output (%): Data 24 ; Baseline 17 ; No inequality 2.9 ; Skill-dependent lump sum tax 2.9 - Std. external debt/output (%): Data 2.7 ; Baseline 2.1 ; No inequality 0.45 ; Skill-dependent lump sum tax 0.45 - Cyclical properties: - Std. consumption / Std. output: Data 1.0 ; Baseline 1.2 ; No inequality 1.2 ; Skill-dependent lump sum tax 1.1 - Std. net savings/output (%): Data 1.5 ; Baseline 1.8 ; No inequality 1.8 ; Skill-dependent lump sum tax 1.7 - Correlation with output (%): Consumption: Data 97 ; Baseline 95 ; No inequality 95 ; Skill-dependent lump sum tax 95 - Correlation with output (%): Net savings/output: Data 40 ; Baseline 31 ; No inequality 36 ; Skill-dependent lump sum tax 35 ### Decomposition: redistribution vs insurance - Baseline generates around 17% external debt-to-output vs 24% in Italian data. - Turning off inequality (θ_H = θ_L) reduces external debt from 17% to 2.9% of GDP. - Quantitative statement: roughly 60 percent of external debt is accounted for by the redistributive channel in the baseline calibration; the standard aggregate insurance channel explains only 12 percent. ### Comparative statics and historical decomposition (Italy subperiods) - Exercise comparing 1985–2001 vs 2002–2015: - ∆ Pre-tax Gini: Data 3.0% ; Model 3.0% - ∆ External debt/output: Data 14% ; Model 10% - Model interpretation: calibration reproducing observed wage-ratio-induced pre-tax Gini change accounts for approximately 71 percent of the increase in Italy’s external-debt-to-output ratio across the two periods (10% modeled vs 14% data). ### Impulse responses and optimal austerity design - Shock experiment: - 30,000 simulated paths over 2,050 periods; periods 1–2050 allow cross-sectional convergence; period 2051 productivity drops by one standard deviation; impulse responses reported for 2050–2055. - Qualitative IRF findings: - Negative productivity shock → output and consumption fall; external debt increases. - Utility inequality (u_H − u_L) initially declines then rises: short-run higher redistribution, long-run lower redistribution. - Government response in baseline: temporarily accumulates external debt, reduces average tax rates, expands redistribution, then consolidates later by raising taxes and reducing redistribution (gradual consolidation). - No-inequality model: external-debt-to-output increases more sharply initially and declines more rapidly; baseline borrows less initially but sustains higher debt later — redistribution motive produces more gradual fiscal adjustment. ### Sensitivity analysis (selected exact table entries) - Columns: Baseline | No govt. exp. (g = 0) | Deterministic (σ_z = 0) | Lower discount (β = 0.95) - Avg. external debt/output (%): 17 | 17 | 22 | 12 - Std. external debt/output (%): 2.1 | 0.9 | -1.8 | -1.8 - Std. consumption / Std. output: 1.2 | 0.96 | -1.2 | -1.2 - Std. net savings/output (%): 1.8 | 1.5 | -0.62 | -0.62 - Correlation with output (%): Consumption 95 | 97 | -99 ; Net savings/output 31 | 29 | -−1.1 - Takeaways: - Removing government expenditure: average external debt unchanged at 17% but second moments smaller. - Deterministic economy (σ_z = 0): sustains higher debt (22% vs baseline 17%) — aggregate uncertainty in baseline limits debt accumulation via precautionary motive. - Lower discount factor (β = 0.95): average external-debt-to-output ratio lower at 12%; lower-β model poorly matches second moments of net savings. ### Empirical cross-country evidence - Regression dependent variable: Net foreign liability-to-GDP (%) from External Wealth of Nations. - Key coefficient (pre-tax Gini, %): - Column (1): 0.773*** (0.222) - Column (2): 0.472** (0.236) - Column (3): 4.947*** (0.664) - Column (4): 5.456*** (0.749) - Sample: No. Countries = 30 across specifications. - Interpretation: pre-tax Gini is positively and statistically significantly associated with higher net foreign liability-to-GDP, consistent with model predictions. ### Policy implications - Macroprudential: decentralized private borrowing exceeds the social optimum; borrowing taxes improve debt sustainability and reallocate tax burdens toward higher-skilled/higher-debt agents. - Fiscal policy design: redistribution concerns justify more gradual fiscal adjustments in unequal economies — initial borrowing and redistribution followed by gradual consolidation (higher taxes, reduced transfers). - Redistribution raises the endogenous cost of default; hence policy tools that affect labor-tax distortion or the distribution of wealth alter sustainable external indebtedness. ### Supplementary model structure and data notes - Model features: heterogeneous agents, affine taxes (marginal labor tax τ^n_t captures labor distortion and progressivity), state-contingent domestic and foreign bonds, planner problem maximizing weighted utility subject to resource, implementability, and sustainability constraints. - Appendix highlights: - Proposition 3.1: under Assumption 4, aggregate labor distortion is positive in financial autarky. - Proposition 3.2: aggregate labor distortion is zero if either no heterogeneity or λ_i = φ_i. - Appendix E: data sources cover mainly 1985–2015; SHIW microdata used for Italian wage-inequality analysis with final sample size 67,176 (heads aged 25–60). - Country list in Appendix A includes: Argentina, Bolivia, Brazil, Cameroon, Colombia, Costa Rica, Ecuador, Egypt, El Salvador, Greece, Guatemala, Honduras, India, Indonesia, Italy, Ireland, Malaysia, Mexico, Morocco, Nigeria, Pakistan, Peru, Philippines, Portugal, Spain, Sri Lanka, Thailand, Tunisia, Turkey, Venezuela. *Source: wpiea2026042-source-pdf* ### References27 ### wpiea2026042-source-pdf - References27 ### Bibliography - Bibliography27 ### Appendices - AList of Countries30 - B Sovereign Game30 - C Characterizing Sustainable Allocation and Optimal Tax Policies31 - D Proofs33 - EData40 ### Figures - 1Income Inequality and External Debt . . . . . . . . . . . . . . . . . . . . .2 - 2Time Paths of Aggregates: Equilibrium vs. Autarky . . . . . . . . . . . . . . 12 - 3Impulse Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 ### Tables - 1Parameters and Targets . . . . . . . . . . . . . . . . . . . . . . . . 19 - 2Moments: Data, Baseline, and Alternative Models. . . . . . . . . . . . 20 - 3Comparative Statics . . . . . . . . . . . . . . . . . . . . . . 22 - 4Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . 24 - 5Regression Result: Income Inequality and External Debt . . . . . . . 25 *Source: wpiea2026042-source-pdf - References27* ### Introduction ### Introduction ### Research question and motivation - Debt crises create a trade-off between debt sustainability and redistribution when output contracts and external debt accumulates until constrained by repayment capacity. - Austerity (higher taxes or lower government spending) can expand repayment capacity but imposes unequal burdens across residents. - Inequality and external debt have jointly risen across many economies for the sample of countries with positive external debt (1985-2015), as documented by the paper (Figure 1 plots net foreign liability-to-GDP (%) and pre-tax Gini (%) over 1985-2015; Panel (a) GDP-weighted average; Panel (b) GDP-weighted interquartile range). Sources: Lane and Milesi-Ferretti (2018), and Solt (2019). ### Main contributions - Develops a theory of external debt sustainability driven by redistributive motives: costly redistribution generates an endogenous cost of default because default into financial autarky increases reliance on distortionary taxation. - Quantifies the redistributive cost of default via calibration to Italy: - Redistribution accounts for roughly 60 percent of Italy’s long-run external debt. - The standard aggregate insurance channel explains only 12 percent. - Characterizes optimal austerity design with inequality: - Optimal adjustment to a negative productivity shock is gradual: government initially expands borrowing and redistribution, then consolidates by raising taxes and reducing redistribution. ### Mechanism and key economic channels - Cost of redistribution arises because redistribution uses distortionary labor taxes to reallocate resources across agents; higher inequality or stronger redistributive motives increase these efficiency costs. - Sustaining external debt mitigates redistribution costs by allowing substitution away from distortionary taxation (access to international financial markets). - Private agents are impatient and borrow abroad without internalizing that their borrowing tightens the sovereign’s limited-commitment constraint, producing an overborrowing externality. - An optimal borrowing tax corrects the externality and yields redistributive benefits because high-skilled agents hold more foreign debt and thus bear a larger share of the tax burden. - Default into financial autarky removes the borrowing-tax instrument and forces exclusive reliance on distortionary labor taxes for redistribution, raising the cost of default. ### Comparative-static implications and predictions - Higher inequality implies a higher equilibrium level of sustainable debt: by raising distortionary costs of redistribution under default, inequality strengthens incentives to repay and sustain higher debt. - The model predicts a positive correlation between inequality and sustainable external indebtedness, consistent with observed comovement across countries. ### Policy implications - Macroprudential implications: decentralized private borrowing exceeds the social optimum; borrowing taxes improve debt sustainability and change distribution of tax burdens across agents. - Fiscal policy design: redistribution concerns provide a rationale for more gradual fiscal adjustments (austerity) in unequal economies — front-loading borrowing and redistribution followed by gradual consolidation. ### Theoretical framework (model overview) - Small open economy model with aggregate uncertainty, heterogeneous agents (productivity types θ_i with population shares π_i), a benevolent government, and competitive domestic and international financial markets. - Government uses a lump-sum tax T_t, marginal labor tax τ^n_t, and marginal tax on returns to private saving τ^a_t (uniform across agents). - Private agents face sequential budget constraint (equation (2)) and no-arbitrage implies q^d_t = q^f_t = 1/(1+r^*_t) (equation (3)). - Aggregate resource constraint (present-value): Σ_t Q^*_t[F(L_t,t) − C_t − G_t] ≥ B_0 (equation (7)). - Competitive equilibrium characterized via Negishi weights φ_i and an implementability constraint (equation (10)); Proposition 1.1: an allocation {C_t, L_t} is supporting iff resource constraint holds and there exist φ and lump-sum tax T such that implementability (10) holds for all agents. ### Definition of sustainable equilibrium and enforcement - Government objective: weighted utility Σ_i λ_i π_i Σ_t β^t U_i(c_{i,t}, l_{i,t}) (equation (11)). - Sustainable equilibrium: subgame perfect equilibrium of a repeated game (government, domestic agents, external creditors) satisfying Proposition 1.1 conditions and the sustainability constraint (12): - Σ_i λ_i π_i Σ_{k≥t} β^{k−t} U_i(c_{i,k}, l_{i,k}) ≥ U_t, ∀t, - where U_t is the one-shot deviation value when the government defaults and fully redistributes. - Sustainable allocation maximizes social welfare subject to resource constraint, implementability, and sustainability constraint (Problem (P) statement). ### Main theoretical result on optimal debt policy - Assumptions used: - Assumption 1 (Separable Utility Function): U(c,n)=u(c)−v(n), with u′, v′ > 0, u″, v″ < 0, bounded marginal utilities and elasticities (examples include separable isoelastic preferences U(c,n)=c^{1−σ}/(1−σ) − ω n^{1+ν}/(1+ν) with σ, ω, ν > 0). - Assumption 2 (Impatience): exists 0 < M < 1 and T such that for all t > T, β R^*_t < M < 1. - Assumption 3 (Deviation value = financial autarky): U_t equals the value of the economy under financial autarky where all private and public debts are erased, net supplies of domestic and external bonds are zero, and the government still levies labor and lump-sum taxes. - Proposition 2.1 (External Debt Sustainability): Suppose Assumptions 1–3 hold. If the aggregate labor distortion is positive in financial autarky and the steady state allocation exists, then the optimal external debt is positive in the long run. - Intuition: impatience induces front-loading consumption and leisure via borrowing abroad; because financial autarky entails higher labor distortions (higher distortionary labor taxes for redistribution), deviating to autarky is unattractive—sustaining positive external debt is optimal. ### Cost of redistribution as endogenous cost of default (illustration) - Financial autarky forces heavier reliance on labor taxation for redistribution, depressing labor supply and output. - Access to international financial markets allows borrowing taxes and external debt that reduce labor distortions, yielding a benefit to sustaining debt. - Simulation illustration (Figure 2; time paths of aggregates: equilibrium vs autarky): - Under autarky: optimal labor tax strictly positive and constant; borrowing tax zero; −A_t = B_t = 0. - Under optimal contract: impatient private agents borrow → higher private liability and external liability; borrowing tax corrects overborrowing and provides redistribution; labor tax initially higher than autarky but declines over time and falls below autarky level in the long run, increasing labor supply and expanding debt capacity. - The endogenous cost of default is driven by the difference between the labor tax under the optimal contract and under financial autarky. ### Robustness and model ingredients discussion - Default consequences: model assumes default wipes out all outstanding private and public debts (breakdown of enforcement infrastructure → financial autarky). Default is redistributive: - Cancellation of domestically held public debt is progressive (richer households hold more government debt). - Cancellation of private external debt is regressive (richer households are more indebted abroad). - Aggregate private sector is net debtor (a_i < 0), so default reduces redistribution overall, adding incentive to sustain debt. - Mechanism persists under partial default on external liabilities with domestic markets active after default; key channel is the overborrowing externality and borrowing tax on external liabilities. - Debt portfolio indeterminacy: model pins down total private liabilities, government liabilities, and country external liability B_t, but not the split between domestic and foreign holdings; alternative decentralizations (e.g., only government borrows abroad) are discussed. - Redistributive taxation: model uses affine taxes where marginal labor tax τ^n captures labor distortion and progressiveness. Stronger progressivity (e.g., nonlinear marginal rates) would increase distortionary costs and strengthen the debt-sustainability result; affine taxation is chosen for transparency and its near-optimality in related work. *Source: wpiea2026042-source-pdf - Introduction.* ### Section 2 establishes that debt sustainability arises as the optimal policy when financial au- ### Section 2 — Debt sustainability arises as the optimal policy when financial autarky exhibits aggregate labor distortions driven by redistributive motives ### Preferences and aggregate representation - Utility of an agent with productivity θ_i over consumption c_i ≥ 0 and efficiency-unit labor l_i ≥ 0: - ∞∑_{t=0} β^t [ c_i^{1−σ}/(1−σ) − ω ( l_i/θ_i )^{1+ν}/(1+ν) ] (equation (13)), with σ, ω, ν > 0. - Time-invariant, proportional individual allocation: - c_{i,t} = ψ_i c_{C,t}, l_{i,t} = ψ_i l_{L,t} (equation (14)). - Aggregate value functions inherit separable isoelastic properties: - V(C_t, L_t; φ) = Φ^V_C C_t^{1−σ}/(1−σ) − Φ^V_L L_t^{1+ν}/(1+ν), - U_P(C,L; φ, λ) = Φ^P_C C_t^{1−σ}/(1−σ) − Φ^P_L L_t^{1+ν}/(1+ν), - where Φ^V_C, Φ^V_L depend on φ, and Φ^P_C, Φ^P_L depend on φ, λ (see Appendix C.1 for the formulas). ### Implementability constraint - Individual implementability constraint: - ∑_{t≥0} β^t [ Φ^V_C ψ_i c_C^{1−σ}_t − Φ^V_L ψ_i l_L^{1+ν}_t ] = Φ^V_C C_0^{−σ} [ a_{i,0} − T ] (equation (15)). ### Assumption 4 (additional assumptions) - The welfare weights, skill distribution, and initial wealth distribution satisfy: 1. Redistributive motive towards the low skills: θ_i < θ_j ⇐⇒ λ_i > λ_j, ∀i,j∈I 2. Perfect correlation between skill and initial wealth: θ_i > θ_j ⇐⇒ a_{i,0} > a_{j,0}, ∀i,j∈I 3. Elasticity of substitution is such that σ ≥ 1 - Interpretation of assumptions: - (1) Government assigns relatively high weight to redistribution toward lower-skill, lower-income individuals (inequality aversion). - (2) Ordering of skill inequality coincides with that of initial wealth: higher-skill individuals have higher initial wealth. - (3) Intratemporal elasticity of substitution is at least above the log-preference benchmark; parameter values commonly used in quantitative macroeconomic analysis satisfy this assumption. ### Key propositions and results - Proposition 3.1: - Suppose Assumption 4 holds, then the aggregate labor distortion is positive in financial autarky. - Proof: See Appendix. - Mechanism: - The key component governing aggregate labor distortion is the ratio between Pareto and Negishi weights λ_i / φ_i, capturing divergence between government distributional preferences and market equilibrium allocation of individual utilities. - If λ_i = φ_i, ∀i∈I (distributional preference agrees with market distribution), then there is no aggregate labor distortion. - This no-distortion result occurs under two cases: the representative-agent case and the heterogeneous-agent case with λ_i = φ^*_i, ∀i∈I. - Proposition 3.2 (Zero aggregate labor distortion): - The aggregate labor distortion in financial autarky is zero if either of the following cases holds: 1. There is no heterogeneity: θ_i = θ_j, a_{i,0} = a_{j,0}, ∀i,j∈I. *Source: wpiea2026042-source-pdf — Section 2.* ### 2. There existsφ ### 2. There existsφ ### Proof statement and implication - Claim: ∗ such that λ_i = φ∗_i, ∀i ∈ I. - Proof: See Appendix. - Implication highlighted in text: In the above cases, redistribution comes with no efficiency costs. Consequently, access to international financial markets yields no additional benefits. By contrast, default enables the government to raise consumption without financing the external debt. Ex ante, this implies that the sustainable level of debt is zero. ### Quantitative analysis: overview - The quantitative analysis proceeds in three parts: - Introduce a stochastic version of the model with state-contingent domestic and foreign bonds, where the government values external debt both for redistribution and for insurance against aggregate shocks. - Quantify the relative importance of redistribution and insurance for debt sustainability using Italian data. - Characterize optimal austerity policies. ### Stochastic economy with state-contingent debt: setup and constraints - Aggregate shocks s_t ∈ S; histories s_t = (s_0, s_1, ..., s_t); probabilities Pr(s_t) and Pr(s_{t+1}|s_t). - Individual utility: E_0 Σ_{t=0}^∞ β^t U_i(c_{i t}, l_{i t}). - Production function: F(L, s_t, t) (later specified linear in labor with aggregate productivity z_t). - Individual budget constraint: - c_{i t} + Σ_{s_{t+1}} q^d_{t+1}(s_{t+1}) a^d_{i t+1}(s_{t+1}) + Σ_{s_{t+1}} q^f(s_{t+1}) a^f_{i t+1}(s_{t+1}) ≤ (1−τ^n_t) w_t l_{i t} + (1−τ^a_t) a^d_{i t} + (1−τ^a_t) a^f_{i t} − T_t. - Government budget constraint: - G_t + B^d_t + B^f_t ≤ τ^n_t w_t L_t + τ^a_t [A^d_t + A^f_t] + T_t + Σ_{s_{t+1}} q^d_{t+1}(s_{t+1}) B^d_{t+1}(s_{t+1}) + Σ_{s_{t+1}} q^f_{t+1}(s_{t+1}) B^f_{t+1}(s_{t+1}). - International price: Q^*_t = Pr(s_t)/(Π_{τ=0}^t R^*_τ), price of one unit of consumption at history s_t in period-0 units. - Planner problem (P) maximizes E_0 Σ_{t≥0,s_t} β^t U_P(C_t, L_t; φ, λ) subject to aggregate present-value feasibility, individual participation constraints, and sustainability constraints specified in the text. ### Parametrization - Population: two types with productivities {θ_H, θ_L}, θ_H ≥ θ_L > 0, π_H = π_L = 0.5. - Planner is utilitarian: λ_H = λ_L. - Preferences: U(c,n) = c^{1−σ}/(1−σ) − ω n^{1+ν}/(1+ν) with σ, ω, ν > 0. - Production: linear in labor, F(L,z) = z L, where z is aggregate productivity. - Productivity process: log z_t = ρ_z log z_{t−1} + ε^z_t, ε^z_t ∼ N(0, σ_z). Discretized via Tauchen with 31 evenly-spaced nodes. - Government expenditure constant: G_t = ̄g. - Initial debt and assets: B_0 = 0 and a^H_0 = a^L_0 = 0. Economy starts at mean of productivity distribution. - Deviation utility U(z_t, t) computed from closed-economy version with z_t, zero external debt, and equal initial wealth. - Parameters to assign: (i) ρ_z, σ_z; (ii) θ_H/θ_L; (iii) β, σ, ω, ν; (iv) ̄g; (v) r^*. - Period = 1 year. Output series: log-linear detrended real GDP 1985–2015. Table 1: Parameters and Targets (selected entries preserved exactly) - r^* Risk-free rate: 0.017 — Target: Avg. real return on German bond - β Discount factor: 0.967 — Target: Avg. Italian real interest rate = 3.4% - σ Intertemporal elasticity: 1 — Standard literature value - 1/ν Labor elasticity: 0.5 — Standard literature value - ω Labor utility weight: 1 — Standard literature value - θ_H/θ_L Wage ratio: 1.89 — Mean top50% wage / mean bottom50% wage - ρ_z Auto-corr. of prod.: 0.927 — Auto-corr. of log GDP - σ_z Std. dev. of prod. res.: 0.0205 — Std. dev. log GDP - ̄g Govt. spending: 0.202 — Avg. govt. consumption-to-GDP Calibration notes: - Wage ratio from Survey on Household Income and Wealth (SHIW). - β set to match average real domestic interest rate 3.4% for Italy 2002–2015. - Risk-free rate = real return on German government bonds 2002–2015. - σ_z and ̄g chosen by simulated method of moments to match (i) standard deviation of logged output and (ii) government final consumption-to-GDP for 1985–2015. - Initial external debt-to-output ratio is not targeted. ### Quantitative results — key moments and model fit Table 2: Moments: Data, Baseline, and Alternative Models (selected rows, numbers preserved) - Targeted moments: - Std. output (%): Data 5.3 ; Baseline 5.3 ; No inequality 5.4 ; Skill-dependent lump sum tax 5.4 - Avg. govt. expenditure/output (%): 19 19 19 19 - Non-targeted moments — External debt property: - Avg. external debt/output (%): Data 24 ; Baseline 17 ; No inequality 2.9 ; Skill-dependent lump sum tax 2.9 - Std. external debt/output (%): Data 2.7 ; Baseline 2.1 ; No inequality 0.45 ; Skill-dependent lump sum tax 0.45 - Cyclical property: - Std. consumption / Std. output: Data 1.0 ; Baseline 1.2 ; No inequality 1.2 ; Skill-dependent lump sum tax 1.1 - Std. net savings/output (%): Data 1.5 ; Baseline 1.8 ; No inequality 1.8 ; Skill-dependent lump sum tax 1.7 - Correlation with output (%): - Consumption: Data 97 ; Baseline 95 ; No inequality 95 ; Skill-dependent lump sum tax 95 - Net savings/output: Data 40 ; Baseline 31 ; No inequality 36 ; Skill-dependent lump sum tax 35 Findings: - External debt: - Model generates around 17% external debt-to-output vs 24% in the Italian data. - Volatility of external debt-to-output ratio is matched reasonably: model std. 2.1% vs data 2.7%. - These outcomes arise with a relatively high discount factor and without exogenous output/productivity costs of default. - Cyclical properties: - Consumption as volatile as output and strongly procyclical; net saving much less volatile and positively correlated with output. - Baseline model closely matches these empirical patterns because occasionally binding borrowing constraints prevent full insurance even with state-contingent assets. - Channels of debt sustainability: - Redistributive channel is quantitatively important. - Comparing baseline to no-inequality (θ_H = θ_L) reduces external debt from 17% to 2.9% of GDP — implying the insurance channel explains only a small fraction. - Roughly 60% of external debt is accounted for by the redistributive channel in the baseline calibration. - Skill-dependent lump-sum taxation that eliminates labor distortions substantially lowers both level and volatility of external debt; in the baseline, distortionary labor taxation strengthens incentive to sustain external debt. ### Effect of inequality on external debt over time: comparative statics - Exercise comparing subperiods 1985–2001 and 2002–2015 (earlier period: lower inequality, lower external debt on average). Table 3: Comparative Statics (numbers preserved) - ∆ Pre-tax Gini: Data 3.0% ; Model 3.0% - ∆ External debt/output: Data 14% ; Model 10% - Model interpretation: Under calibration where wage ratio set to reproduce observed pre-tax Gini change, the model accounts for approximately 71 percent of the increase in Italy’s external-debt-to-output ratio across the two periods (10% of the modeled change vs 14% in data). ### Optimal austerity policies: impulse response results - Experiment: negative productivity shock; impulse responses averaged across simulated paths. - Simulation details: 30,000 paths over 2,050 periods; periods 1–2050 allow cross-sectional distribution convergence; period 2051 productivity drops by one standard deviation of the innovation; impulse responses reported for periods 2050–2055. - Impulse response patterns (qualitative summary preserved in text): - Negative productivity shock reduces output and consumption, larger contraction in output. - External debt increases in response. - Utility inequality (u_H − u_L) initially declines then rises, reflecting short-run higher redistribution and long-run lower redistribution. - Mechanism: negative shock lowers deviation utility; sustainability constraint temporarily slackens; government accumulates external debt, reduces average tax rates, and expands redistribution; later taxes rise to service debt, reducing redistribution. - No-inequality model shows similar output and consumption dynamics but external-debt-to-output increases more sharply initially and declines more rapidly than baseline. - In baseline, government borrows less initially but pursues more gradual fiscal consolidation (sustaining higher debt in later periods) through reduced redistribution — redistribution motive yields more gradual consolidation. ### Sensitivity analysis Table 4: Sensitivity Analysis (selected numbers preserved) Columns: Baseline | No govt. exp. (g = 0) | Deterministic (σ_z = 0) | Lower discount (β = 0.95) - Avg. external debt/output (%): 17 | 17 | 22 | 12 - Std. external debt/output (%): 2.1 | 0.9 | -1.8 | (value shown in table as -1.8) - Std. consumption / Std. output: 1.2 | 0.96 | -1.2 | (value shown in table as -1.2) - Std. net savings/output (%): 1.8 | 1.5 | -0.62 | (value shown in table as -0.62) - Correlation with output (%): Consumption 95 | 97 | -99 ; Net savings/output 31 | 29 | -−1.1 Takeaways: - Removing government expenditure: average external debt unchanged (17%), but second moments smaller. - Deterministic economy (no aggregate uncertainty): model sustains higher debt (22% vs baseline 17%); baseline uncertainty creates a precautionary motive that limits debt accumulation. - Lower discount factor (β = 0.95): average external-debt-to-output ratio is lower (12%); higher β in baseline makes autarky less valuable, allowing more debt accumulation. Lower-β model poorly matches second moments of net savings. ### Empirical evidence: cross-country regression - Dependent variable: Net foreign liability-to-GDP (%) (negative of net foreign assets) from External Wealth of Nations database. - Key independent variable: Gini index, pre tax (%) from SWIID (Solt, 2019). Table 5: Regression Result: Income Inequality and External Debt (selected coefficients preserved) - Gini index, pre tax (%): column (1) 0.773*** (0.222); (2) 0.472** (0.236); (3) 4.947*** (0.664); (4) 5.456*** (0.749). - Controls: GDP per capita (log); Real GDP per capita growth (%): coefficient -1.311** (0.638) in one specification; Current account-to-GDP (%) coefficient -2.061*** (0.297) in one specification; Inflation (%) positive small coefficients. - No. Countries: 30 across specifications. - Interpretation: Across specifications, pre-tax Gini coefficient is positively and statistically significantly associated with higher net foreign liability-to-GDP, consistent with model prediction that higher inequality associates with higher sustainable external debt. ### Conclusion: mechanisms and policy implications - Core theoretical contribution: redistribution that requires distortionary taxation creates an endogenous cost of default; higher inequality raises distortionary cost of taxation, increases the cost of financial autarky, and thereby increases incentives to sustain higher external debt. - Quantitative findings (case of Italy): - Redistribution channel is central: model attributes only 12 percent of long-run debt to the standard insurance channel, while the redistribution channel accounts for 60 percent. - Policy implication for austerity: optimal austerity policies are shaped by distributional concerns — following negative shocks, governments expand borrowing and redistribution initially and consolidate later via higher taxes and reduced transfers; more unequal economies should expect more gradual fiscal adjustment. - Paper’s scope: abstracts from equilibrium default risk to highlight redistribution as a central determinant of debt sustainability; suggests future work to incorporate equilibrium default risk and alternative forms of debt crises. *Italic: Source — wpiea2026042-source-pdf - 2. There existsφ* ### Bibliography ### wpiea2026042-source-pdf - Bibliography ### Key literature cited - Foundational and recent works on sovereign debt, default, and fiscal policy, including (exact citations as listed): - Aguiar, Mark and Gita Gopinath, “Defaultable debt, interest rates and the current account,” Journal of International Economics, 2006,69(1), 64–83. - Aguiar and Manuel Amador, “Growth in the Shadow of Expropriation,” Quarterly Journal of Economics, 2011,126(2), 651–697. - Aguiar, et al., “Sovereign debt,” Handbook of International Economics, 2014,4, 647–87; and “Fiscal policy in debt constrained economies,” Journal of Economic Theory, 2016,161, 37–75. - Arellano, Cristina, “Default risk and income fluctuations in emerging economies,” American Economic Review, 2008,98(3), 690–712; and with Yan Bai, “Fiscal austerity during debt crises,” Economic Theory, 2016, pp. 1–17. - Barro, Robert J., “On the determination of the public debt,” Journal of Political Economy, 1979, 87(5), 940–71. - Bhandari, Anmol, David Evans, Mikhail Golosov, and Thomas J. Sargent, “Fiscal policy and debt management with incomplete markets,” Quarterly Journal of Economics, 2016,132(2), 617–663; and with Thomas J Sargent, “Public debt in economies with heterogeneous agents,” Journal of Monetary Economics, 2017,91, 39–51. - Bianchi, Javier, “Overborrowing and Systemic Externalities in the Business Cycle,” American Economic Review, December 2011,101(7), 3400–3426; and with Pablo Ottonello and Ignacio Presno, “Fiscal stimulus under sovereign risk,” Journal of Political Economy, 2023,131(9), 2328–2369. - Broner, Fernando, Alberto Martin, and Jaume Ventura, “Sovereign Risk and Secondary Markets,” American Economic Review, September 2010,100(4), 1523–55; and with Jaume Ventura, “Globalization and risk sharing,” The Review of Economic Studies, 2011, 78(1), 49–82. - Bulow, Jeremy and Kenneth Rogoff, “Sovereign debt: Is to forgive to forget?,” The American Economic Review, 1989,79(1), 43–50. - Chari, Varadarajan V. and Patrick J. Kehoe, “Sustainable plans,” Journal of Political Economy, 1990, pp. 783–802; and “Sustainable plans and debt,” Journal of Economic Theory, 1993,61(2), 230–261; and with Lawrence J. Christiano, “Optimal fiscal policy in a business cycle model,” Journal of Political Economy, 1994,102(4), 617–652. - Chatterjee, Satyajit and Burcu Eyigungor, “Maturity, indebtedness, and default risk,” American Economic Review, 2012,102(6), 2674–99. - Cuadra, Gabriel, Juan M. Sanchez, and Horacio Sapriza, “Fiscal policy and default risk in emerging markets,” Review of Economic Dynamics, 2010,13(2), 452–469. - D’Erasmo, Pablo and Enrique G. Mendoza, “Distributional incentives in an equilibrium model of domestic sovereign default,” Journal of the European Economic Association, 2016,14(1), 7–44; and “History remembered: Optimal sovereign default on domestic and external debt,” Journal of Monetary Economics, 2020. - Eaton, Jonathan and Mark Gersovitz, “Debt with potential repudiation: Theoretical and empirical analysis,” Review of Economic Studies, 1981,48(2), 289–309. - Heathcote, Jonathan, Kjetil Storesletten, and Giovanni L. Violante, “Optimal Tax Progressivity: An Analytical Framework*,” The Quarterly Journal of Economics, 06 2017,132(4), 1693–1754. - Jappelli, Tullio and Luigi Pistaferri, “Does consumption inequality track income inequality in Italy?,” Review of Economic Dynamics, 2010,13(1), 133–153. - Jeon, Kiyoung and Zeynep Kabukcuoglu, “Income Inequality and Sovereign Default,” Journal of Economic Dynamics and Control, 2018,95(C), 211–232. - Mendoza, Enrique G. and Vivian Z. Yue, “A general equilibrium model of sovereign default and business cycles,” Quarterly Journal of Economics, 2012,127(2), 889–946. - Neumeyer, Pablo and Fabrizio Perri, “Business cycles in emerging economies: the role of interest rates,” Journal of Monetary Economics, 2005,52(2), 345–380. - Roldán, Francisco, “The Aggregate-Demand Doom Loop: Precautionary Motives and the Welfare Costs of Sovereign Risk,” American Economic Journal: Macroeconomics, July 2025,17(3), 160–204. - Solt, Frederick, “Measuring income inequality across countries and over time: The standardized world income inequality database,” 2019. - The World Bank, “World development indicators database,” 2019. - Tran-Xuan, Monica, “Optimal redistributive policy in debt constrained economies,” Journal of International Economics, 2023,144, 103785. - Werning, Iván, “Optimal fiscal policy with redistribution,” Quarterly Journal of Economics, 08 2007,122(3), 925–977. - Additional manuscripts and working papers addressing taxation, redistribution, political economy, and sovereign games are cited (examples in the source list include works by Balke, Karantounias, Jiang et al., Pouzo and Presno, Ferriere, Dovis et al., and others). ### Appendix A — List of Countries - Countries included in the analysis: Argentina, Bolivia, Brazil, Cameroon, Colombia, Costa Rica, Ecuador, Egypt, El Salvador, Greece, Guatemala, Honduras, India, Indonesia, Italy, Ireland, Malaysia, Mexico, Morocco, Nigeria, Pakistan, Peru, Philippines, Portugal, Spain, Sri Lanka, Thailand, Tunisia, Turkey, Venezuela. ### Appendix B — Sovereign game (model setup and sustainable equilibrium) - Government default decision variable: - δ ∈ {0,1} with δ = 0 implies default. - Government budget constraint (as presented): - G_t + δ_t B^d_t + δ_t B^f_t ≤ τ^n_t w_t L_t + τ^a_t [A^d_t + A^f_t] + T_t + q^d_{t+1} B^d_{t+1} + q^f_{t+1} B^f_{t+1}. - Timing and actions each period: - Government chooses z^G_t = [τ^n_t, τ^a_t, T_t, δ_t, B^d_{t+1}, B^f_{t+1}] ∈ Π consistent with the budget constraint. - Agents choose allocations z^{H,i}_t = [c^i_t, l^i_t, a^{i,d}_{t+1}, a^{i,f}_{t+1}]. - Firm chooses z^F_t = (L_t). - International lenders choose z^*_t = [B^f_{t+1}, A^f_{t+1}] given r^*_t. - Definitions: - History h_t = {h_{t−1}, z^G_t, [z^{H,i}_t]_{i∈I}, z^F_t, z^*_t, p} ∈ H_t. - h^p_t = {h_{t−1}, z^G_t} ∈ H^p_t after government announces policies. - Strategies: σ^G_t : H_{t−1} → Π; σ^{H,i}_t : H^p_t → R^3_+ × R; σ^F_t : H^p_t → R^2_+; σ^*_t : H^p_t → R^2_+. - Pricing rule: p : H^p_t → R_+. - Definition B.1 (Sustainable equilibrium): - A tuple (σ^G, σ^H, σ^F, σ^*) such that (i) for all h_{t−1}, z^G_t induced maximizes weighted utility by λ subject to government budget constraint (6); (ii) for all h^p_t, induced policy path, allocations, and prices {r^*_t} constitute a competitive equilibrium with taxes. - Proposition B.1 (Sustainable equilibrium characterization): - An allocation and policy [z^{H,i}]_{i∈I}, z^F, z^G is part of a sustainable equilibrium iff: - (i) given z^G there exist prices p such that [z^{H,i}]_{i∈I}, z^F, z^G, p is a competitive equilibrium with taxes for an open economy; and - (ii) for any t there exists U_t such that [z^{H,i}]_{i∈I}, z^F, z^G satisfies the constraint: - Σ_{k=t}^∞ β^{k−t} Σ_{i∈I} λ_i π_i U_i(c^i_k, l^i_k) ≥ U_t. (Equation (12)) - Note: paper focuses on characterizing the no-default equilibrium; the main text takes into account government will pay back its debt (δ_t = 1). ### Appendix C — Characterizing sustainable allocation and optimal tax policies - Lagrangian setup: multipliers - μ : multiplier on resource constraint. - π_i η_i : multipliers on implementability constraints for agent i. - β^t γ_t : multiplier on aggregate debt constraint for period t. - Pseudo-utility definition: - U_W[t; φ, λ, η] ≡ Σ_{i∈I} λ_i π_i U_i(t; φ) + Σ_{i∈I} π_i η_i [V_C(t; φ) h_{i,c}(t; φ) + V_L(t; φ) h_{i,l}(t; φ)]. - First-order conditions (as stated): - U_W_C(t; φ) + U_P_C(t; φ) Σ_{k=0}^t γ_k = μ Q^*_t β^t (C.1) - U_W_L(t; φ) + U_P_L(t; φ) Σ_{k=0}^t γ_k = μ Q^*_t β^t F_L(L_t) (C.2) - Σ_i π_i η_i = 0 (C.3) - Optimal tax policy formulas: - τ^n_t = 1 − [U_W_C(t; φ) + U_P_C(t; φ) Σ_{k=0}^t γ_k] / [ (U_W_L(t; φ) + U_P_L(t; φ) Σ_{k=0}^t γ_k) V_L(t; φ) / V_C(t; φ) ] (C.4) [presentation preserved exactly as in source] - τ^a_{t+1} = 1 − [U_W_C(t+1; φ) + U_P_C(t+1; φ) Σ_{k=0}^{t+1} γ_k] / [ (U_W_C(t; φ) + U_P_C(t; φ) Σ_{k=0}^t γ_k) V_C(t; φ) / V_C(t+1; φ) ] (C.5) [presentation preserved exactly as in source] - Section C.1 — Formulas for separable isoelastic preferences: - Consumption and labor shares: - ψ^i_c = [φ_i]^{1/σ} / Σ_{i∈I} π_i (φ_i)^{1/σ} - ψ^i_l = (θ_i)^{(1+ν)/ν} [φ_i]^{−1/ν} / Σ_{i∈I} π_i (θ_i)^{(1+ν)/ν} (φ_i)^{−1/ν} (C.6) - Derived aggregates (as listed): - Φ_V_C = [Σ_i π_i (φ_i)^{1/σ}]^σ - Φ_V_L = ω [Σ_i π_i (φ_i)^{−1/ν} (θ_i)^{(1+ν)/ν}]^{−ν} - Φ_P_C = Φ_V_C Σ_{i∈I} π_i λ_i φ_i ψ^i_c - Φ_P_L = Φ_V_L Σ_{i∈I} π_i λ_i φ_i ψ^i_l - Φ_W_C = Φ_V_C Σ_{i∈I} π_i ψ^i_c [λ_i φ_i + (1−σ) η_i] - Φ_W_L = Φ_V_L Σ_{i∈I} π_i ψ^i_l [λ_i φ_i + (1+ν) η_i] ### Appendix D — Proofs (selected highlights and results) - D.1 Proof of Proposition 1.1: - Shows equivalence between an aggregate allocation {C_t, L_t} that satisfies aggregate resource and implementability constraints and existence of taxes τ^n_t, τ^a_t, transfers T_t, and prices Q^*_t yielding a competitive equilibrium with government policies. - Rewrites government budget constraint and agent aggregation to demonstrate feasibility and construction of wages {w_t} and taxes {τ^n_t, τ^a_t}. - Important displayed inequality (D.1): - Σ_{t=0}^∞ Q^*_t {C_t − (1 − τ^n_t) w_t L_t + T_t} + Σ_{t=0}^∞ Q^*_t [G_t − τ^n_t w_t L_t − T_t] ≤ −B_0. - D.2 Proof of Proposition 2.1 (three-step result on sustainability and long-run debt): - Step 1: The sustainability constraint binds infinitely often in the long run; γ_t > 0 and Σ_{k=0}^t γ_k → ∞ as t → ∞. - Step 2: Long-run sustainable allocation converges to the maximal steady-state debt allocation that maximizes repayment capacity: - max_{C,L} [ (1 + r^*) / r^* (F(L) − C − G) ] s.t. U_P(C, L; φ^*) ≥ U_P(C^*_∞, L^*_∞; φ^*). - First-order conditions given with multiplier ψ_u: ψ_u U_{P,C}(C^*_ss, L^*_ss; φ) = 1 and −ψ_u U_{P,L}(C^*_ss, L^*_ss; φ) = F_L(C^*_ss, L^*_ss). - Step 3: Financial autarky allocation is never optimal at any point; constructs a feasible alternative allocation that improves welfare for small ε > 0, contradicting autarkic optimality. - D.3 Proof of Proposition 3.1 (aggregate labor distortion in autarky is strictly positive): - Establishes Lemmas D.1–D.3 on monotonicity and boundedness of marginal utilities. - Shows cov(ψ^i_c, λ_i φ_i) < 0 and cov(ψ^i_l, λ_i φ_i) < 0 (Lemma D.4). - Aggregate labor distortion in autarky: - Ω_a = 1 − (Φ_W_C / Φ_P_L) (Φ_W_L / Φ_P_C) and proves Ω_a > 0. - D.4 Proof of Proposition 3.2: - In the special case λ_i = φ_i and η_i = 0, Φ_W_C = Φ_P_C and Φ_W_L = Φ_P_L, leading to: - Ω_a = 1 − (Φ_W_C / Φ_P_L) (Φ_W_L / Φ_P_C) = 0. ### Appendix E — Data (calibration and microdata) - E.1 Macroeconomic data descriptions and sources (most annual, covering 1985-2015; some 2002-2015): - Net foreign liability: negative of net foreign asset (NFA) from External Wealth of Nations Database, Lane and Milesi-Ferretti (2018). - Net international investment position: official IIP from External Wealth of Nations Database, Lane and Milesi-Ferretti (2018). - Pre-tax Gini Index: market Gini from Standardized World Income Inequality Database, Solt (2019). - GDP per capita: constant 2010 US Dollar GDP per capita from World Development Indicator Database, The World Bank (2019). - GDP growth: log difference of constant 2010 US Dollar GDP from World Development Indicator Database, The World Bank (2019). - Inflation: annual inflation measured by GDP deflator from World Development Indicator Database, The World Bank (2019). - Real GDP: GDP in constant local currency units from World Development Indicator Database, The World Bank (2019). - Real return on German bond: interest rate on German bond adjusted for inflation measured by GDP deflator; long-term interest rate for convergence purposes from Eurostat Database (2019); 10-year maturity, denominated in Euro. - Real interest rate: lending interest rate adjusted for inflation measured by GDP deflator from World Development Indicator Database, The World Bank (2019). - Italy’s cross-sectional wage inequality: calculated from micro-data by Jappelli and Pistaferri (2010) using Surveys of Household Income and Wealth (Bank of Italy) for 1980-2006. - Government consumption: general government final consumption expenditure from World Development Indicator Database, The World Bank (2019). - Private consumption: households and NPISHs final consumption expenditure from World Development Indicator Database, The World Bank (2019). - E.2 Italian Household Survey (SHIW) microdata used for wage-inequality analysis: - Data period: 1987 to 2014 (survey biennial except 1995–1998 with a 3-year interval). - Original individual sample size: 329,446 units (1987–2014). - Selection: heads of households aged between 25 and 60 → reduces sample to 71,621 units. - Outlier exclusions: observations with no hours worked, negative income, or hourly wage in the bottom 0.5% of distribution removed. - Final sample size used: 67,176. *Content derived from the PDF chapter/section labeled "Bibliography" and appended appendices in the provided source.* --- _Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026042-source-pdf.pdf_