## _wp11166 — Introduction, Model, Calibration, and Quantitative Results

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---

### Empirical regularities around sovereign default events
- Sample and scope:
  - Event window based on data for 23 default events over the 1977-2009 period.
- Typical macroeconomic patterns around defaults:
  - GDP and consumption fall about 5 percent below trend.
  - Imported inputs and total intermediate goods fall nearly 20 percent below trend.
  - Labor falls to a level about 15 percent lower than in the three years prior to the defaults.
  - Net exports jump about 10 percentage points of GDP in the span of the two quarters before and after default events.
  - Tomz and Wright (2007) found the maximum default frequency when output is at least 7 percent below trend.
- Sovereign spreads and debt levels:
  - Interest rates on sovereign debt peak at about the same time as output troughs and defaults occur, and are negatively correlated with GDP.
  - Reported cyclical correlations between GDP and country interest rates range from zero to -0.8, with averages of -0.55 and -0.42 in cited studies.
  - Mean debt ratio before default events in Figure 1 was about 50 percent, reaching about 72 percent at the time of defaults.
  - For emerging and developing countries (IMF (2006) definition), foreign debt was 1/3 of GDP on average over 1998-2005; highly indebted poor countries averaged about 100 percent of GDP; Eastern European and Western Hemisphere countries averaged about 50 and 40 percent of GDP respectively.
  - Reinhart et al. (2003) report an external debt ratio averaged 71 percent of GDP for developing country defaults in 1824-1999.

### Theoretical disconnect and paper objective
- Identified disconnect:
  - Business-cycle models explain countercyclical country interest rates by modeling sovereign interest as an exogenous cost on foreign working-capital loans to firms, but treat default as exogenous and cannot explain observed default-related output collapses or high debt ratios.
  - Sovereign-default models (Eaton and Gersovitz framework) generate countercyclical spreads by assuming exogenous output endowments with ad-hoc output costs of default, but cannot endogenously explain business-cycle output dynamics or observed debt dynamics.
- Paper objective:
  - Propose an equilibrium model that jointly determines sovereign default and business-cycle dynamics, linking endogenous default risk and private sector activity through the financing cost of working capital used to pay for a subset of imported inputs.

### Model mechanism and key assumptions
- Three critical model features:
  1. Final goods producers require working capital financing to pay for a subset of imported intermediate goods.
  2. Sovereign default induces an efficiency loss in final goods production because loss of access to credit for some imported inputs forces firms to substitute toward other imported inputs or domestic inputs, which are imperfect substitutes.
  3. The government can divert private firms' repayment when it defaults on its own debt.
- Production and finance:
  - Final goods producers use labor and an Armington aggregator of imported and domestic inputs; imported inputs are varieties in a Dixit-Stiglitz aggregator.
  - A subset of imported varieties j in [0; κ] requires payment in advance with foreign working-capital loans; 0<κ<1.
  - Working-capital loans ϕ_t satisfy ϕ_t (1 + r_t) = ∫_{0}^{κ} p̃_j m̃_{jt} dj.
  - Working-capital interest rate r_t = 1 / q_t(b_{t+1}; ε_t) − 1 links sovereign bond prices and private financing costs.
- Default dynamics:
  - Default leads to financial autarky (r_t → 1) for some time; varieties j in [0; κ] become unavailable and firms substitute imperfectly, reducing production efficiency.
  - Re-entry to world credit markets occurs with exogenous probability π each quarter.

### Endogenous output cost of default and quantitative implications
- Endogenous default cost:
  - Default generates an endogenous output cost that is an increasing, convex function of TFP.
  - This state-contingent endogenous cost contrasts with fixed-percentage or Arellano (2008) ad-hoc specifications.
- Quantitative advantages:
  - Baseline calibration supports a mean debt-output ratio of 23 percent (nearly four times Arellano (2008)’s 6 percent estimate in comparable setups).
  - Financial amplification: effect of TFP shocks on output is amplified by a factor of 2.7 when the economy defaults (amplification coefficient 13/4.75 = 2.73).
  - Default-triggered output collapses arise from the financial transmission mechanism rather than large exogenous endowment shocks.

### Role of substitution elasticities and labor supply
- Elasticities matter:
  - Lower elasticities of substitution between inputs (inputs less similar) increase and steepen the output cost of default in TFP.
  - Higher Frisch elasticity of labor supply amplifies the output cost because default triggers larger reductions in total labor usage.
  - Even with inelastic labor, required shifts among imported varieties and toward domestic inputs generate efficiency losses.

### Foreign lenders, arbitrage, and private financing
- Foreign lenders:
  - Risk-neutral, competitive, with opportunity cost r̄.
  - Bond pricing: q_t(b_{t+1}, ε_t) = 1/(1+r̄) if b_{t+1} ≥ 0; q_t(b_{t+1}, ε_t) = [1 − p_t(b_{t+1}, ε_t)]/(1+r̄) if b_{t+1} < 0. (equation (28))
- Arbitrage implication:
  - Because sovereigns divert repayment of working-capital loans when defaulting, foreign lenders assign the same default risk to private working-capital loans as to sovereign debt.
  - No-arbitrage condition: r_t(b_{t+1}, ε_t) = 1/q_t(b_{t+1}, ε_t) − 1. (equation (29))
- Empirical evidence:
  - Median correlation between country sovereign spreads and median firm effective interest rates is 0.7 in Table 1.
  - Country examples (Sovereign Interest Rates | Median Firm Interest Rates | Correlation): Argentina 13.32 | 10.66 | 0.87; Brazil 12.67 | 24.60 | 0.14; Malaysia 5.16 | 6.56 | 0.96; Russia 15.69 | 11.86 | −0.21; Turkey 9.80 | 29.26 | 0.88; Thailand 6.15 | 7.30 | 0.94.
  - Except for Argentina, China, and Russia, the median firm financing cost is higher on average than sovereign interest rates in the sample.

### Baseline calibration (Section 4.1): parameters and targets
- Calibrated parameters (Value — Target statistics):
  - Int. goods share in gross output of final goods m: 0.43 — Argentina’s national accounts
  - Capital share in gross output of final goods k: 0.17 — Standard capital share in GDP (0.3)
  - Labor share in gross output of final goods L: 0.40 — Standard labor share in GDP (0.7)
  - Labor share in GDP of int. goods: 0.7 — Standard labor share in GDP (0.7)
  - Coefficient of relative risk aversion γ: 2 — Standard RBC value
  - Risk-free interest rate r*: 1% — Standard RBC value
  - Curvature parameter of labor supply ϕ: 1.455 — Frisch wage elasticity (2.2)
  - Re-entry probability π: 0.083 — Dias and Richmond (2007)
  - Armington weight of domestic inputs ρ: 0.62 — Regression estimate
  - Armington curvature parameter ν: 0.65 — Regression estimate
  - Dixit-Stiglitz curvature parameter σ: 0.59 — Gopinath and Neiman (2010)
- Parameters set with SMM (Value — Targets from data):
  - Autocorrelation of TFP shocks ρ_ε: 0.95 — GDP autocorrelation 0.82
  - Standard deviation of TFP shocks σ_ε: 1.7% — GDP std. deviation 4.7%
  - Intermediate goods TFP coefficient A: 0.31 — Output drop in default 13%
  - Subjective discount factor β: 0.88 — Default frequency 0.69%
  - Upper bound of imported inputs with working capital κ: 0.7 — Working capital to GDP ratio estimate 6%
  - TFP semi-elasticity of exogenous capital flows χ: -0.67 — Net exports/GDP at default 10%
- Calibration notes:
  - M = 0.43 corresponds to average intermediate goods ratio for Argentina (1993–2005).
  - Given M, k = 0.17 implies capital income share in value added k/(1−M) = 0.17/(1−0.43) = 0.3.
  - Labor curvature ϕ = 1.455 implies Frisch wage elasticity 1/(ϕ − 1) = 2.2.
  - Re-entry probability π = 0.083 implies average exclusion of three years after default.
  - Armington estimates ν = 0.65 and ρ = 0.62 from Mexican data match imported-to-domestic input ratios of 18% (current prices) and 15.7% (constant prices).
- SMM results:
  - A = 0.31; β = 0.88; κ = 0.7; χ = −0.67.
- TFP process:
  - log ε_t = ρ_ε log ε_{t−1} + ε_t, with ε_t iid ∼ N(0, σ^2_ε); 25-state Markov approximation via Tauchen (1986).

### Baseline simulation: setup and selected quantitative findings
- Simulation setup:
  - 2000 simulations, each with 500 periods; truncate first 100 observations.
- Selected comparative moments (Data — Model — Model w/o x_t):
  - Average debt/GDP ratio: 35% — 22.89% — 21.52%
  - Average bond spreads: 1.86% — 0.71% — 1.02%
  - Std. dev. of bond spreads: 0.78% — 1.20% — 1.43%
  - Consumption std. dev./GDP std. dev.: 1.44 — 1.04 — 1.07
- Correlations with GDP (Data — Model — Model w/o x_t):
  - bond spreads: -0.62 — -0.21 — -0.25
  - trade balance: -0.87 — -0.53 — -0.32
  - labor: 0.39 — 0.52 — 0.53
  - intermediate goods: 0.90 — 0.99 — 0.99
- Correlations with bond spreads (Data — Model — Model w/o x_t):
  - trade balances: 0.82 — 0.19 — 0.11
  - labor: -0.42 — -0.24 — -0.34
  - intermediate goods: -0.39 — -0.23 — -0.24
- Historical default–output co-movements (Data — Model — Model w/o x_t):
  - correlation between default and GDP: -0.11 — -0.11 — -0.11
  - fraction of defaults with GDP below trend: 61.5% — 86% — 84%
  - fraction of defaults with large recessions: 32.0% — 37% — 47%
- Key model insights:
  - Model produces average debt-to-GDP ratio 22.89% at the 0.69% default frequency—higher than many sovereign-default models but below Argentina’s 35% observed ratio.
  - Mean bond spread in model (0.71%) is close to default frequency because of zero recovery and risk-neutral creditors linking spreads with default probabilities.
  - Model generates countercyclical spreads, countercyclical net exports, and consumption volatility exceeding output volatility, though magnitudes are understated relative to data.
  - Model matches correlation between defaults and GDP (-0.11) and produces a larger share of defaults occurring with GDP below trend (86% v. 61.5% cross-country).

### Role of exogenous capital flows x_t and working capital
- Motivation and specification:
  - Empirical fact: international capital flows and financed trade imbalances do not vanish completely when sovereigns default.
  - Exogenous capital flows specified as x_t = χ ln ε_t with semi-elasticity χ calibrated to Argentina (χ = -0.67) to capture continuing capital flows (e.g., repayments to international organizations).
- Effects:
  - Including x_t prevents zero net exports during financial autarky and replicates post-default trade surpluses.
  - Removing x_t raises mean spreads (default probability increases to about 1%) and makes trade balance less countercyclical (trade balance–GDP correlation moves from -0.53 to -0.32).
  - Working capital share calibrated to about 6% of GDP; even with average sovereign spread near 1.7%, fluctuations in interest rates and working capital materially affect dynamics.

### Macroeconomic dynamics around default events (Section 4.3)
- Event window and fit:
  - 12 quarters before and after defaults; model’s mean output dynamics closely match Argentina’s 2002 event when calibrated (A = 0.31).
  - Except for the quarter just before default, Argentina’s data remain inside model’s one-standard-error bands.
- Defaults and TFP shocks:
  - Average TFP decline in model default events: 7.95 percent (≈1.5 times σ_ε where σ_ε = 1.7%).
  - A 7.95 percent TFP shock produces mean output drop ~4.75 percent when no default, and 13 percent mean output drop when default occurs.
  - Amplification coefficient due to default: 13/4.75 = 2.73.
- Recovery dynamics:
  - Re-entry probability π = 0.083 per quarter (average exclusion ≈ three years).
  - Recovery driven by mean reversion of ε and efficiency gain upon re-entry (switch back to broader imported input mix).
  - Scenarios: continued exclusion for 12 quarters yields slower recovery; immediate re-entry after one period yields a large rebound.
- Cross-variable comparisons:
  - GDP, consumption, and net exports: model averages and one-standard-error bands closely track Argentina 2002 and cross-country medians, with larger calibrated drops for Argentina.
  - Imported inputs, total intermediate goods, and labor: model aligns qualitatively but predicts smaller declines in labor and intermediate goods than some data.
  - Debt/GDP: model underestimates actual debt ratios though supports higher ratios than many Eaton-Gersovitz–based models.
- Sudden Stops:
  - Credit-market exclusion endogenously generates Sudden Stop–like collapses in GDP, consumption, labor, and intermediate goods in the model.

### Sensitivity analysis (Section 4.4): robustness and parameter effects
- Overview:
  - Robustness evaluated against variations in κ, Armington parameters ρ and ν, within-variety σ, labor curvature ϕ, and re-entry probability π.
  - Main statistics in Table 4 include Output drop at default; Mean Debt/GDP; Mean spread; Std. dev. of spread; corr. GDP–spread; frequency of default; defaults with GDP below trend.
- (a) Working capital range κ:
  - κ = 0: Output drop 13% ; Mean Debt/GDP 8.99% ; Mean spread 0.05% ; Std. dev. spread 0.08% ; corr. with spread 0.24 ; default w. GDP below trend 75% — removing working-capital channel collapses model performance.
  - κ = 0.6: Output drop 13.6% ; Mean Debt/GDP 20.38% ; Mean spread 0.44% ; Std. dev. spread 0.88% ; default w. GDP below trend 83%
  - κ = 0.8: Output drop 14.44% ; Mean Debt/GDP 27.03% ; Mean spread 0.39% ; Std. dev. spread 0.89% ; default w. GDP below trend 96%
  - Interpretation: larger κ raises mean debt ratio and output cost of default; removing κ undermines default frequency and spread variability.
- (b) Armington aggregator parameters (ρ, ν):
  - Increasing substitutability (higher implied elasticity) reduces output cost at default and mean debt ratio but raises default frequency and spread variability.
  - Changing Armington weight ρ toward domestic inputs reduces relevance of imported-input working-capital channel and lowers mean debt ratio.
  - Extreme parameterizations can produce very high debt ratios at low default frequencies (documented as sensitivity).
- (c) Within-variety elasticity σ:
  - σ = 2.22: Output drop 14.46% ; Mean Debt/GDP 25.94% ; Mean spread 0.36% ; default w. GDP below trend 87%
  - σ = 2.89: Output drop 12.43% ; Mean Debt/GDP 19.77% ; Mean spread 0.73% ; default w. GDP below trend 83%
  - Interpretation: better substitutability across imported varieties weakens the working-capital channel and lowers output cost and mean debt ratio.
- (d) Frisch elasticity of labor (ϕ):
  - ϕ = 1.67 (Frisch = 1.6): Output drop 12.6% ; Mean Debt/GDP 22.34% ; Mean spread 0.81% ; default w. GDP below trend 84%
  - ϕ = 2.5 (Frisch = 1.4): Output drop 15.2% ; Mean Debt/GDP 24.35% ; Mean spread 0.46% ; default w. GDP below trend 70%
  - Interpretation: higher labor supply elasticity increases output cost at default and mean debt ratio; default probability and spread variability fall.
- (e) Re-entry probability π:
  - π = 0.05: Output drop 15.29% ; Mean Debt/GDP 37.23% ; Mean spread 0.26% ; default w. GDP below trend 77%
  - π = 0.1: Output drop 13.85% ; Mean Debt/GDP 19.73% ; Mean spread 0.61% ; default w. GDP below trend 89%
  - Interpretation: mean debt ratio declines monotonically as exclusion period shortens; effects on output drop and spread moments are non-monotonic.
- Robustness summary:
  - Main findings are robust: working-capital channel generates large endogenous output drops at default, supports higher mean debt ratios, and yields weakly countercyclical spreads.
  - Removing the working-capital channel (κ = 0) eliminates the endogenous output cost and causes the model to fail matching observed statistics.

### Theoretical properties and appendices
- Recursive equilibrium characterization:
  - Decision rules b_{t+1}(b_t, ε_t), V(b_t, ε_t), consumption c(b_t, ε_t), transfers T(b_t, ε_t), default set D(b_t), default probabilities p̄(b_{t+1}, ε_t), and bond pricing q̄(b_{t+1}, ε_t) satisfy government optimization, resource constraints, and foreign-lender arbitrage (equation (28)).
- Theorems:
  - Theorem 1: Monotonicity of default decision with debt (if default optimal at higher debt, also optimal at lower debt) and default probabilities increase with debt (proof in Appendix 3).
  - Theorem 2: Equilibrium bond prices decrease with higher default risk and debt (formal statement and proof in Appendix 3).
- Appendices:
  - Appendix 1: Firms’ dynamic optimization with working capital — working capital increases unit cost of imported inputs by κ(R_t − 1); firms with zero initial liabilities maintain zero liabilities in perpetuity; first-order conditions F_m = p[1 + κ(R_t − 1)] and F_L = w_t.
  - Appendix 2: Decentralized equilibrium — maps q_t and ε_t into competitive allocations; two treatments of diverted working capital repayments (cost of default vs. rebate) and implications for state variables.
  - Appendix 3: Theorem proofs.
  - Appendix 4: Data definitions and sources for event analysis, with exact BEC categories and data construction procedures.

*Source: _wp11166 - 1. Introduction; 2. Model (Sections 2.1–2.6); 4.1, 4.3, 4.4; Appendices (selected excerpts).*

### 1. Introduction ........................................................................................................

### _wp11166 - 1. Introduction ........................................................................................................

### Empirical regularities around sovereign default events
- Sample and scope:
  - Event window based on data for 23 default events over the 1977-2009 period.
- Typical macroeconomic patterns around defaults:
  - GDP and consumption fall about 5 percent below trend.
  - Imported inputs and total intermediate goods fall nearly 20 percent below trend.
  - Labor falls to a level about 15 percent lower than in the three years prior to the defaults.
  - Net exports jump about 10 percentage points of GDP in the span of the two quarters before and after default events.
  - Tomz and Wright (2007) found the maximum default frequency when output is at least 7 percent below trend.
- Sovereign spreads and debt levels:
  - Interest rates on sovereign debt peak at about the same time as output troughs and defaults occur, and are negatively correlated with GDP.
  - Reported cyclical correlations between GDP and country interest rates range from zero to -0.8, with averages of -0.55 (Neumeyer and Perri (2005)) and -0.42 (Uribe and Yue (2006)).
  - Mean debt ratio before default events in Figure 1 was about 50 percent, reaching about 72 percent at the time of defaults.
  - For emerging and developing countries (IMF (2006) definition), foreign debt was 1/3 of GDP on average over 1998-2005; highly indebted poor countries averaged about 100 percent of GDP; Eastern European and Western Hemisphere countries averaged about 50 and 40 percent of GDP respectively.
  - Reinhart et al. (2003) report an external debt ratio averaged 71 percent of GDP for developing country defaults in 1824-1999, similar to the 72 percent mean estimate reported for the default events in Figure 1.

### Theoretical disconnect and paper objective
- Identified disconnect:
  - Business-cycle models of emerging economies explain countercyclical country interest rates by modeling sovereign interest as an exogenous cost on foreign working-capital loans to firms, but treat default as exogenous and thus cannot explain observed default-related output collapses or high debt ratios.
  - Sovereign-default models (Eaton and Gersovitz framework) generate countercyclical spreads by assuming exogenous output endowments with ad-hoc output costs of default, but cannot endogenously explain business-cycle output dynamics or observed debt dynamics.
- Paper objective:
  - Propose an equilibrium model that jointly determines sovereign default and business-cycle dynamics, linking endogenous default risk and private sector activity through the financing cost of working capital used to pay for a subset of imported inputs.

### Model mechanism and key assumptions
- Three critical model features:
  1. Final goods producers require working capital financing to pay for a subset of imported intermediate goods.
  2. Sovereign default induces an efficiency loss in final goods production because loss of access to credit for some imported inputs forces firms to substitute toward other imported inputs or domestic inputs, which are imperfect substitutes.
  3. The government can divert private firms' repayment when it defaults on its own debt.
- Production structure and financing:
  - Final goods producers use labor and an Armington aggregator of imported and domestic inputs (imperfect substitutes).
  - Imported inputs are varieties in a Dixit-Stiglitz aggregator; a subset of these varieties requires payment in advance with foreign working-capital loans.
  - The optimal input mix depends on the country interest rate (inclusive of default risk) and on TFP.
- Default dynamics:
  - When the country has access to world financial markets, firms use a broad mix of imported and domestic inputs and fluctuations in default risk affect working-capital costs and induce regular fluctuations in factor demands and output.
  - When the country defaults, firms substitute away from imported inputs that require working-capital financing due to the surge in financing cost, reducing production efficiency because of imperfect substitutability and labor reallocation away from final goods production.
  - Government and firms are excluded from world credit markets upon default for some time, with an exogenous probability of re-entry, creating endogenous feedback between default probabilities, sovereign spreads, and firm financing costs.

### Endogenous output cost of default and its implications
- Endogenous default cost:
  - Default generates an endogenous output cost that is an increasing, convex function of TFP.
  - This endogenous, state-contingent cost contrasts with two common ad-hoc specifications:
    - Fixed-percentage cost of an exogenous endowment leads to low average debt ratios when calibrated to observed default frequencies.
    - Arellano (2008) asymmetric formulation (zero cost below a threshold, constant reduced income above) makes default cost increase linearly with endowment but still yields low calibrated debt ratios unless supplemented with other features.
- Advantages and quantitative implications:
  - The model's endogenous default cost allows support for higher mean debt ratios at observed default frequencies.
  - Baseline calibration supports a mean debt-output ratio of 23 percent (nearly four times larger than Arellano (2008)'s 6 percent).
  - The financial amplification mechanism amplifies the effect of TFP shocks on output by a factor of 2.7 when the economy defaults.
  - In contrast to models with exogenous endowments, output falls sharply at default in this model because of the financial transmission mechanism rather than large exogenous endowment shocks.

### Role of substitution elasticities and labor supply
- Elasticities matter:
  - The output cost of default is higher and steeper in TFP when elasticities of substitution between inputs are lower (inputs are less similar).
  - The elasticity of labor supply also influences the output cost: higher labor supply elasticity amplifies the cost because default triggers reductions in total labor usage.
  - Even with inelastic labor, output costs and efficiency losses persist due to required shifts among imported varieties and toward domestic inputs, and labor reallocation.

### Calibration references and comparisons to related literature
- Working capital and financing treatment:
  - Differs from Neumeyer and Perri (2005) and Uribe and Yue (2006) who treat working capital cost as exogenous; here both sovereign and firm interest rates are endogenously driven by sovereign risk.
  - Prior models used working capital to pay wages in full; this model assumes working capital finances only a subset of imported intermediate goods.
  - Empirical benchmarks: Schmitt-Grohe and Uribe (2007) estimate working capital at 9.3 percent annually for the United States; the paper estimates 6 percent for Argentina (Section 4).
- Empirical support for model assumptions:
  - Amiti and Konings (2007) and Halpern, Koren and Szeidl (2008) provide firm-level evidence of imperfect substitutability between foreign and domestic inputs and associated TFP effects.
  - Gopinath and Neiman (2010) document within-firm shifts from imported to domestic inputs in Argentina's 2001-2002 crisis.
  - Reinhart and Rogoff (2010) and Reinhart (2010) show close connections between banking crises, private-sector defaults, and sovereign defaults, including conversion of private debts to public debt after sovereign defaults.
- Trade credit and sanctions literature:
  - Kaletsky (1985) documents exclusion from trade credit during 1980s defaults.
  - Kohlscheen and O’Connell (2008) show declines in trade credit from commercial banks during default episodes.
  - Rose (2005) finds default has a large, persistent negative effect on bilateral trade between creditor and debtor countries.
  - Martinez and Sandleris (2008) provide further evidence linking sovereign defaults and declines in trade.

### Quantitative performance and model scope
- Model performance:
  - The model explains the three stylized facts of sovereign defaults: deep recessions at default, countercyclical sovereign spreads, and high external debt ratios around defaults.
  - Matches emerging markets business-cycle features such as high consumption variability, countercyclical net exports, and the correlation between output and default.
- Sensitivity and calibration notes (summary references):
  - Baseline calibration and sensitivity analysis are covered in Section 4 (Tables 2, 3, and 4; Figures 6–8).
  - The model yields higher average debt ratios and endogenous, state-dependent default costs relative to common Eaton-Gersovitz–based calibrations.

### Roadmap of the paper
- Section 2: Model presentation.
- Section 3: Partial equilibrium analysis of interest rate effects on production and factor allocations.
- Section 4: Quantitative analysis (baseline calibration, cyclical co-movements, macro dynamics around default events, sensitivity analysis).
- Appendices: Firms’ dynamic optimization with working capital, decentralized equilibrium, theorem proofs, and data definitions/sources.

*Source: _wp11166 - 1. Introduction.*

### Section 4 explores the full modelís quantitative implications. Section 5 concludes.

### _wp11166 - Section 4 explores the full modelís quantitative implications. Section 5 concludes.

### Model overview
- Four groups of agents: households, firms (two sectors: final goods f and intermediate goods m), sovereign government (domestic), and foreign lenders (abroad).
- Two production sectors in the domestic economy: final goods producers (f) and intermediate goods producers (m).
- Sovereign issues one-period, zero-coupon discount bonds with face value b_{t+1} and cannot commit to repay; default leads to exclusion from world credit markets in the same period and re-entry with exogenous probability .

### Households (Section 2.1)
- Households maximize time-separable utility:
  - Max_{c_t, L_t} E[ sum_{t=0}^1 ^t u(c_t - g(L_t)) ] where 0<<1, and c_t and L_t denote consumption and labor supplied in period t.
- Period utility and labor supply:
  - g(L) = L^{!} with !>1, giving Frisch elasticity = 1/(! - 1).
  - Period utility: u(c;L) = (c - L^{!}/!)^{1-} - 1 over 1- with >0 (constant-relative-risk-aversion form).
- Budget constraint (household takes wages, profits, transfers as given):
  - c_t = w_t L_t + ^f_t + ^m_t + T_t.
- Labor optimality condition:
  - g'(L_t) = w_t.  (Equation (3))

### Final goods producers (Section 2.2)
- Production uses labor L^f_t, intermediate goods M_t, and fixed capital k with Markov TFP shocks " _t with transition (" _t | " _t-1).
- Cobb-Douglas production function:
  - y_t = " _t [ M_t^{_M} (L^f_t)^{_L} k^{_k} ]  with 0<_L, _M, _k<1 and _L + _M + _k = 1.  (Equation (4))
- CES Armington aggregator for M_t combining domestic inputs m^d_t and imported inputs m^~_t:
  - M_t = [  (m^d_t)^{} + (1-) (m^~_t)^{} ]^{1/} with 0<<1 and 0≤<1.  (Equation (5))
  - Within-variety Dixit-Stiglitz aggregator for imported varieties m^~_{jt}, j in [0,1], with substitution parameter  (0<<1).
- A subset of imported varieties j in [0; ] requires working-capital pay-in-advance financing; 0<<1.
- Working capital loans _t are intraperiod loans repaid at end of period at interest rate r_t. Pay-in-advance condition:
  - _t (1 + r_t) =  ∫_{0}^{} p^~_j m^~_{jt} dj.  (Equation (6))
- Final-goods date-t profits:
  - ^f_t = " _t [ M_t^{_M} (L^f_t)^{_L} k^{_k} ] - ∫_{0}^{1} p^~_j m^~_{jt} dj - r_t ∫_{0}^{} p^~_j m^~_{jt} dj - p^m_t m^d_t - w_t L^f_t.  (Equation (7))
- CES price index for imported inputs depends on r_t:
  - P^~(r_t) = [ ∫_{1}^{} (p^~_j)^{/(-1)} dj + ∫_{0}^{} (p^~_j (1 + r_t))^{/(-1)} dj ]^{(-1)/}.
- In financial autarky (r_t → 1), imported varieties in [0; ] are not used and price index becomes:
  - P^~ = [ ∫_{1}^{} (p^~_j)^{/(-1)} dj ]^{(-1)/}.
- Two-stage firm problem yields first-stage FOCs (equations (9)-(11)):
  - (9) _M " _t k^{_k} [ M_t^{_M} (L^f_t)^{_L} k^{_k} ]^{_M - 1} (1-) (m^~_t)^{-1} = P^~(r_t)
  - (10) _M " _t k^{_k} [ M_t^{_M} (L^f_t)^{_L} k^{_k} ]^{_M - 1}  (m^d_t)^{-1} = p^m_t
  - (11) _L " _t k^{_k} [ M_t^{_M} (L^f_t)^{_L} k^{_k} ]^{_M} (L^f_t)^{-1} = w_t
- CES demand for imported varieties (r_t finite):
  - For j in [,1]: m^~_{jt} = [ p^~_j / P^~(r_t) ]^{-1/(1-)} M^~.
  - For j in [0,]: m^~_{jt} = [ p^~_j (1 + r_t) / P^~(r_t) ]^{-1/(1-)} M^~.
- In default (r_t → 1), varieties j in [0,] have m^~_{jt} = 0 and j in [,1] follow the limit demand.

### Intermediate goods producers (Section 2.3)
- Production A(L^m_t) with 0≤
≤1 and A>0; p^m_t is the price of domestic input m^d_t.
- Profit maximization:
  - Max_{L^m_t} ^m_t = p^m_t A(L^m_t) - w_t L^m_t.  (Equation (12))
- Labor demand condition:
  - 
 p^m_t A(L^m_t)^{
 - 1} = w_t.  (Equation (13))
- Relationship between A(L^m_t) and m^d_t:
  - A(L^m_t) = m^d_t.  (Equation (20))

### Equilibrium in factor markets and production (Section 2.4)
- For finite r_t and TFP " _t, factor allocations [m^~_t; m^d_t; L^f_t; L^m_t; L_t] and prices [p^m_t; w_t] solve the nonlinear system (14)-(20):
  - (14) _M " _t k^{_k} [ M_t^{_M} (L^f_t)^{_L} k^{_k} ]^{_M - 1} (1-) (m^~_t)^{-1} = P^~(r_t)
  - (15) _M " _t k^{_k} [ M_t^{_M} (L^f_t)^{_L} k^{_k} ]^{_M - 1}  (m^d_t)^{-1} = p^m_t
  - (16) _L " _t k^{_k} [ M_t^{_M} (L^f_t)^{_L} k^{_k} ]^{_M} (L^f_t)^{-1} = w_t
  - (17) 
 p^m_t A(L^m_t)^{
 - 1} = w_t
  - (18) g'(L_t) = w_t
  - (19) L^f_t + L^m_t = L_t
  - (20) A(L^m_t) = m^d_t
- Total value added at equilibrium relative prices:
  - Value added = (1 - _M) " _t (M_t)^{_M} (L^f_t)^{_L} k^{_k} + p^m_t A(L^m_t).
- Value of imported inputs at equilibrium:
  - P^~(r_t) m^~_t = _M " _t (M_t)^{_M} (L^f_t)^{_L} k^{_k} - p^m_t m^d_t.
- GDP definition (adjusting for time-invariant price index of imported inputs):
  - gdp_t ≡ y_t - P^~ m^~_t.
- During exclusion from world credit markets, equilibrium allocations are given by the limiting case r → 1 and sector f loses access to the subset of imported inputs requiring working capital.

### Sovereign government (Section 2.5)
- Bonds: set B = [b_{min}; b_{max}] ⊂ R, with b_{min} ≤ 0 ≤ b_{max}, and b_{min} > -y^r (largest debt repayable with full commitment).
- Government chooses debt policy and factor allocations solving a recursive social planner problem; state variables (b_t; " _t) and bond pricing function q_t(b_{t+1}; " _t).
- Link between default risk and private financing costs:
  - Working-capital interest rate r_t = 1 / q_t(b_{t+1}; " _t) - 1, so default risk premium on sovereign debt equals private financing costs.
  - Defaulting sovereign diverts repayments of firms' working capital loans to foreign lenders; firms and government default together.
- Planner payoff:
  - V(b_t; " _t) = max{ v_{nd}(b_t; " _t), v_d(" _t) }.  (Equation (21))
- Value of continuing (no default) v_{nd}(b_t; " _t):
  - Maximize over c_t, m^d_t, m^~_t, L^f_t, L^m_t, L_t, b_{t+1}:
    - v_{nd} = max [ u(c_t - g(L_t)) +  E[V(b_{t+1}; " _{t+1})] ]  subject to resource constraint (23), labor and input resource constraints, and equilibrium relations f(·)=M^{_M}(L^f_t)^{_L} k^{_k}.
  - Resource constraint (23):
    - c_t + q_t(b_{t+1}; " _t) b_{t+1} - b_t ≤ " _t f(M_t; L^f_t; k) - m^~_t P^~ [ 1 / q_t(b_{t+1}; " _t) - 1 ].
- Value of default v_d(" _t):
  - v_d = max [ u(c_t - g(L_t)) +  (1 - ) E[v_d(" _{t+1})] +   E[V(0; " _{t+1})] ] subject to default-period resource constraints where imported varieties in [0; ] are unavailable and P^~ corresponds to r → 1.  (Equations (24)-(25))
- Default set and probability:
  - Default set for given debt b_t: D(b_t) = { " _t : v_{nd}(b_t; " _t) ≤ v_d(" _t) }.  (Equation (26))
  - Perceived probability of default at t+1 as of t:
    - p_t(b_{t+1}; " _t) = ∫_{D(b_{t+1})} d(" _{t+1} | " _t).  (Equation (27))
- Model preserves Eaton-Gersovitz properties:
  - v_d(") independent of debt level given " _t; v_{nd} increases with b_{t+1}; default set and equilibrium default probability increase with debt.
- Theorem 1 (stated): Given a productivity shock " and bond positions b_0 < b_1 ≤ 0, if default is optimal for b_1 then default is also optimal for b_0 and equilibrium default probability satisfies p^*_{·}(b_0; ·) ≥ p^*_{·}(b_1; ·).  (Proof in Appendix 3)

*Source: _wp11166 - Section 4 explores the full modelís quantitative implications. Section 5 concludes.*

### 2.6  Foreign Lenders

### 2.6  Foreign Lenders

### Model assumptions and equilibrium pricing
- International creditors are risk-neutral and have complete information. They invest in sovereign bonds and in private working capital loans.
- Foreign lenders behave competitively and face an opportunity cost of funds equal to r̄.
- Competition implies zero expected profits at equilibrium and full arbitrage between sovereign debt and the world’s risk-free asset, summarized by equation (28):
  - q_t(b_{t+1},"_t) = (1/(1+r̄)) if b_{t+1} ≥ 0
  - q_t(b_{t+1},"_t) = [1 − p_t(b_{t+1},"_t)]/(1+r̄) if b_{t+1} < 0
- Implication: Equilibrium bond prices depend on default risk; higher debt increases default probability and thus lowers q_t. (Formalized in Theorem 2.)
- Theorem 2 (as stated): Given a productivity shock " and bond positions b_0 < b_1 ≤ 0, the equilibrium bond prices satisfy q̄(−b_0,") ≤ q̄(−b_1,"). (Proof in Appendix 3.)

### Arbitrage between sovereign bonds and private working-capital loans
- Because the sovereign diverts repayment of working-capital loans when it defaults, foreign lenders assign the same default risk to private working-capital loans as to sovereign debt.
- No-arbitrage condition between sovereign lending and working-capital loans (equation (29)):
  - r_t(b_{t+1},"_t) = 1/q_t(b_{t+1},"_t) − 1, if _t > 0
- Key empirical question raised: Are sovereign and private (corporate) interest rates closely related?

### Empirical evidence: sovereign versus corporate interest rates (Table 1)
- Firm-level effective interest rate constructed as (firm total debt service) / (firm total debt obligations) using the Worldscope database; aggregated by country as the median across 15 firms.
- Table 1 reports time-series averages over 1994 to 2005 and correlations between corporate median effective rates and the standard EMBI+ sovereign measure over the same period.
- Main quantitative findings from Table 1:
  - Median correlation across countries: 0.7.
  - Country-specific figures (Sovereign Interest Rates | Median Firm Interest Rates | Correlation):
    - Argentina: 13.32 | 10.66 | 0.87
    - Brazil: 12.67 | 24.60 | 0.14
    - Chile: 5.81 | 7.95 | 0.72
    - China: 6.11 | 5.89 | 0.52
    - Colombia: 9.48 | 19.27 | 0.86
    - Egypt: 5.94 | 8.62 | 0.58
    - Malaysia: 5.16 | 6.56 | 0.96
    - Mexico: 9.40 | 11.84 | 0.74
    - Morocco: 9.78 | 13.66 | 0.32
    - Pakistan: 9.71 | 12.13 | 0.84
    - Peru: 9.23 | 11.42 | 0.72
    - Philippines: 8.78 | 9.27 | 0.34
    - Poland: 7.10 | 24.27 | 0.62
    - Russia: 15.69 | 11.86 | −0.21
    - South Africa: 5.34 | 15.19 | 0.68
    - Thailand: 6.15 | 7.30 | 0.94
    - Turkey: 9.80 | 29.26 | 0.88
    - Venezuela: 14.05 | 19.64 | 0.16
- Additional empirical patterns:
  - The two interest rates are positively correlated in most countries; the relationship is particularly strong in some cases (illustrated in Figure 2).
  - Except for Argentina, China, and Russia, the median firm financing cost is higher on average than sovereign interest rates in the sample.

### Historical and empirical support for the model mechanism
- Historical studies (Reinhart and Rogoff (2010), Reinhart (2010), Boughton (2001)) document that governments commonly take over foreign obligations of the corporate sector during sovereign default episodes, especially when domestic banking crises accompany sovereign default.
- Empirical studies cited in the source:
  - Arteta and Hale (2007) and Kohlscheen and O’Connell (2008) document adverse effects of sovereign default on private access to foreign credit:
    - Arteta and Hale: strong negative effects on private corporate bond issuance during and after default.
    - Kohlscheen and O’Connell: volume of trade credit provided by commercial banks falls sharply when countries default; median drops in trade credit are about 35 and 51 percent two and four years after default events respectively.
  - Arellano and Kocherlakota (2007), Agca and Celasun (2009) find a positive relationship between private domestic lending rates and sovereign spreads.
  - Corsetti, Kuester, Meier and Muller (2010) document similar features in OECD data.

### Link to recursive equilibrium and implications
- The model’s recursive equilibrium (Definition 1) includes:
  - Decision rule b_{t+1}(b_t,"_t) and associated value function V(b_t,"_t), consumption rule c(b_t,"_t), transfers rule T(b_t,"_t), default set D(b_t) and default probabilities p̄(b_{t+1},"_t), and bond pricing function q̄(b_{t+1},"_t).
  - Conditions required:
    1. Government’s decision rule solves the social planner’s recursive maximization problem given q̄.
    2. Consumption plan satisfies the resource constraint.
    3. Transfers satisfy the government budget constraint.
    4. Bond pricing q̄ satisfies foreign-lender arbitrage condition (28) given D and p̄.
- Consequence: Returns on sovereign bonds and working-capital loans are fully arbitraged (equation (29)), so equilibrium interest rates on working capital follow from q̄(b_{t+1},"_t).
- Equilibrium solutions extend to sectoral factor allocations, wages, profits, and domestic input prices determined by firms’ optimality conditions.

*Source: _wp11166 - 2.6  Foreign Lenders (PDF chapter/section).*

### 4.1  Baseline Calibration

### _wp11166 - 4.1  Baseline Calibration

### Baseline calibration: parameter values and targets
- Calibrated Parameters (Value — Target statistics)
  - Int. goods share in gross output of final goods m: 0.43 — Argentina’s national accounts
  - Capital share in gross output of final goods k: 0.17 — Standard capital share in GDP (0.3)
  - Labor share in gross output of final goods L: 0.40 — Standard labor share in GDP (0.7)
  - Labor share in GDP of int. goods: 0.7 — Standard labor share in GDP (0.7)
  - Coefficient of relative risk aversion γ: 2 — Standard RBC value
  - Risk-free interest rate r*: 1% — Standard RBC value
  - Curvature parameter of labor supply !: 1.455 — Frisch wage elasticity (2.2)
  - Re-entry probability π: 0.083 — Dias and Richmond (2007)
  - Armington weight of domestic inputs ρ: 0.62 — Regression estimate
  - Armington curvature parameter ν: 0.65 — Regression estimate
  - Dixit-Stiglitz curvature parameter σ: 0.59 — Gopinath and Neiman (2010)

- Parameters set with SMM (Value — Targets from data)
  - Autocorrelation of TFP shocks ρ_ε: 0.95 — GDP autocorrelation 0.82
  - Standard deviation of TFP shocks σ_ε: 1.7% — GDP std. deviation 4.7%
  - Intermediate goods TFP coefficient A: 0.31 — Output drop in default 13%
  - Subjective discount factor β: 0.88 — Default frequency 0.69%
  - Upper bound of imported inputs with working capital κ: 0.7 — Working capital to GDP ratio estimate 6%
  - TFP semi-elasticity of exogenous capital flows χ: -0.67 — Net exports/GDP at default 10%

- Additional calibration notes and arithmetic:
  - M = 0.43 corresponds to the average ratio of intermediate goods to gross production for Argentina (1993–2005, UNData).
  - Given M, k = 0.17 implies capital income share in value added of the sector k/(1−M) = 0.17/(1−0.43) = 0.3 (standard 30 percent).
  - Labor share in gross output of final goods L = 1 − M − k = 0.40 implies labor share in value added L/(1−M) = 0.7 (standard 70 percent).
  - Labor share in intermediate goods production set to 0.7.
  - Risk aversion γ = 2; quarterly world risk-free interest rate r* = 1 percent.
  - Labor curvature ! = 1.455 implies Frisch wage elasticity 1/(! − 1) = 2.2.
  - Re-entry probability π = 0.083 implies average exclusion of three years after default.

- Armington and input-elasticity calibration:
  - Estimates from Mexican data (1988–2004) used to set ν = 0.65 and ρ = 0.62 via nonlinear regression of the optimality condition from (14) and (15); standard errors 0.11 and 0.12 respectively.
  - These estimates match average ratios of imported to domestic inputs at current and constant prices in the Mexican data: 18% and 15.7% respectively.
  - ν = 0.65 and ρ = 0.62 imply ϵ_m^d,m* = 2.9 and a small bias in favor of domestic inputs.
  - Firm-level estimate set ϵ_m^*j = 2.44 (v = 0.59) in line with Gopinath and Neiman (2010); their ϵ_m^d,m* = 2.08 (ρ = 0.519) is close to this calibration.

### SMM procedure and TFP process
- TFP process in final goods production:
  - log ε_t = ρ_ε log ε_{t−1} + ε_t, with ε_t iid ~ N(0, σ^2_ε).
  - Tauchen (1986) quadrature used to construct a Markov approximation with 25 realizations.
- Calibration targets and data:
  - Quarterly seasonally-adjusted real GDP from Argentina’s MECON for 1980Q1–2005Q4 used to obtain cyclical statistics.
  - Targeted cyclical statistics: standard deviation of cyclical GDP 4.7% and first-order autocorrelation 0.79.
  - SMM yields ρ_ε = 0.95 and σ_ε = 1.7 percent.
- Remaining SMM targets and rationale:
  - A set of moments targeted: decline in output at default, frequency of default, share of working capital financing in GDP, and rise in trade balance-GDP ratio at default.
  - Default frequency target: 0.69 percent quarterly (Argentina defaulted five times since 1824 → annual average 2.78% → 0.69% quarterly).
  - Output drop target: first quarter of 2002 output was 13 percent below trend.
  - Trade-balance output ratio rose by 10 percentage points in the quarter when Argentina defaulted.
  - Working capital proxy: firms’ share of M1 assumed two-thirds (U.S. estimate) applied to Argentina’s M1 → working capital ≈ 6% of GDP.
- SMM results:
  - A = 0.31
  - β = 0.88
  - κ = 0.7
  - χ = -0.67

### Baseline simulation: setup and key quantitative findings
- Simulation setup:
  - Feed the calibrated TFP process to the model.
  - Conduct 2000 simulations, each with 500 periods; truncate first 100 observations.
- Table 3: selected comparative moments (Data — Model — Model w/o x_t)
  - Average debt/GDP ratio: 35% — 22.89% — 21.52%
  - Average bond spreads: 1.86% — 0.71% — 1.02%
  - Std. dev. of bond spreads: 0.78% — 1.20% — 1.43%
  - Consumption std. dev./GDP std. dev.: 1.44 — 1.04 — 1.07
- Correlations with GDP (Data — Model — Model w/o x_t)
  - bond spreads: -0.62 — -0.21 — -0.25
  - trade balance: -0.87 — -0.53 — -0.32
  - labor: 0.39 — 0.52 — 0.53
  - intermediate goods: 0.90 — 0.99 — 0.99
- Correlations with bond spreads (Data — Model — Model w/o x_t)
  - trade balances: 0.82 — 0.19 — 0.11
  - labor: -0.42 — -0.24 — -0.34
  - intermediate goods: -0.39 — -0.23 — -0.24
- Historical default-output co-movements (Data — Model — Model w/o x_t)
  - correlation between default and GDP: -0.11 — -0.11 — -0.11
  - fraction of defaults with GDP below trend: 61.5% — 86% — 84%
  - fraction of defaults with large recessions: 32.0% — 37% — 47%
- Key quantitative insights and comparisons:
  - The model produces an average debt-to-GDP ratio of 22.89% at the 0.69% default frequency — higher than many quantitative sovereign-default models but below Argentina’s 35% observed ratio.
  - The mean bond spread in the model (0.71%) is close to the default frequency because of assumed zero recovery on defaulted debt and risk-neutral creditors linking spreads one-to-one with default probabilities.
  - The model generates countercyclical spreads (negative correlation with GDP), countercyclical net exports, and consumption volatility exceeding output volatility, though the model understates magnitudes relative to data.
  - Correlations of labor and intermediate goods with GDP and spreads are broadly consistent with data:
    - GDP vs intermediate goods: 0.90 (data) vs 0.99 (model).
    - GDP vs labor: 0.39 (data) vs 0.52 (model).
    - Spreads vs intermediate goods: -0.39 (data) vs -0.23 (model).
    - Spreads vs labor: -0.42 (data) vs -0.24 (model).
  - The model matches the historical correlation between defaults and GDP (-0.11) and produces a larger share of defaults occurring with GDP below trend (86% vs 61.5% in the cross-country data), while matching the fraction of defaults associated with very large recessions (37% vs 32%).

### Role of exogenous capital flows x_t and working capital
- Motivation for x_t:
  - Empirical fact: international capital flows and financed trade imbalances do not vanish completely when sovereigns default; trade balances often rise into surpluses after default.
  - Example: Argentina made repayments to international organizations of about 2.7% of GDP in 2002 and up to 5% of GDP by 2006.
  - To capture continuing capital flows (e.g., vis-à-vis international organizations), introduce exogenous capital flows x_t independent of borrowing and default decisions.
  - Specification: x_t = χ ln ε_t, with semi-elasticity χ calibrated to Argentina.
- Effects of x_t:
  - Including x_t prevents the model from predicting zero net exports during financial autarky and enables replication of post-default trade surpluses.
  - Removing x_t (Column (3) in Table 3) has small effects on most moments, but:
    - It makes the trade balance less countercyclical (trade balance–GDP correlation moves from -0.53 to -0.32).
    - It raises mean spreads because default probability increases to about 1% when x_t is removed, and mean spreads rise accordingly under risk-neutral lenders.
  - Conclusion: x_t plays a small role in the model’s bulk quantitative results, except for enabling the model to produce the surge in net exports during the exclusion period observed after default events.
- Working capital and interest-rate amplification:
  - Working capital share calibrated to about 6% of GDP (proxy from M1-based firm ownership).
  - Even with an average sovereign spread near the 1% risk-free rate, fluctuations in interest rates and working capital materially affect endogenous dynamics.
  - Compared with other studies that require high average interest rates (≈7%) and large working-capital shares to get significant effects, this model yields sizable working-capital effects with average interest rates around 1.7% and working capital ≈ 6% of GDP.

*Source: _wp11166 - 4.1  Baseline Calibration*

### 4.3  Macroeconomic Dynamics around Default Events

### 4.3  Macroeconomic Dynamics around Default Events

### Model fit to output dynamics around defaults
- Event window: 12 quarters before and after debt defaults, with default normalized to date 0 (Argentina HP detrended GDP: 1999Q1 to 2005Q3).
- The model's mean output dynamics closely match the data for Argentina:
  - The size of the output drop at the date of the default is matched by calibratingA.
  - Except for the quarter just before the default (model predicts higher output than data), output in the data remains inside the model's one-standard-error bands throughout the twenty-Öve quarter event window.
- Simulated GDP line represents the average behavior of output around defaults in the model’s stochastic stationary state; one-standard-error bands are shown around model simulation averages to compare with Argentina's single event.

### TFP shocks as default triggers and amplification
- Defaults in the model are triggered by adverse TFP shocks that are not unusually large:
  - On average, TFP declines by 7.95 percent in the model’s default events.
  - This is roughly 1.5 times of the 5.8 percent standard deviation of the calibrated TFP process ( " ).
  - Thus, defaults occur with a TFP shock of just about 1.5 standard deviation in size.
- Amplification quantification:
  - A 7.95 percent TFP shock produces a mean output drop of about 4.75 percent when there is no default.
  - The same 7.95 percent shock produces a 13 percent mean output drop when default occurs.
  - The amplification coe¢ cient due to default is 13=4:75 = 2:73:.

### Recovery dynamics and role of re-entry
- Two effects drive recovery of output after defaults:
  - Mean reversion of " (is mean-reverting and defaults occur with TFP below trend), so TFP improves on average after defaults; country typically remains in financial autarky on average for three years after a default.
  - Surge in output if the country re-enters credit markets (final goods producers switch back to a more e¢ cient mix of imported and domestic inputs).
- Probability of re-entry: 8.3 percent probability every quarter.
- Scenario comparisons (Figure 7, right panel):
  - Continued exclusion for 12 quarters after default: recovery reflects only mean reversion of "; GDP in this scenario is about the same as model average for ~7 quarters after default, then moves below model average as re-entry probability effects accumulate beyond 8 quarters.
  - Immediate re-entry one period after default: big rebound in GDP at t=1 because of the efficiency gain.
  - Model average lies uniformly below the immediate re-entry scenario because it assigns weight to continued exclusion and generally weighs more the effect of TFP recovery than credit market re-entry due to low re-entry probability.

### Comparison to cross-country and Argentina data across variables
- Figure 8 compares cross-country dataset medians, Argentina 2002 default, model mean, and one-standard-error bands for multiple variables: GDP, consumption, trade balance-GDP ratio, imported inputs, total intermediate goods, labor, country interest rate, debt-GDP ratio.
- Key matches and quantitative notes:
  - GDP, consumption and net exports: actual paths mostly within model's standard error bands and close to model averages for both Argentina 2002 and cross-country medians.
    - GDP and consumption drops at t=0 are larger in the model than in cross-country medians because the model is calibrated to match Argentina’s larger recession.
  - Net exports: model predicts relatively stable path before default, sudden increase around default date, and sustained surplus after default.
    - The adjustment to include exogenous component of capital flows is important for the sudden increase.
    - Rise in net exports at default is triggered by a low TFP realization "0 , which is associated with a surge in x0.
    - Without this, net exports would go to zero at t=0 and a small deficit on average during exclusion.
  - Imported inputs, total intermediate goods, and labor: qualitative features align with data, but quantitatively the model predicts smaller declines in labor and intermediate goods than observed in the data.
    - Drop in imported inputs in the model is similar to Argentina but larger than cross-country median.
  - Debt/GDP: model and data plotted with model on left axis and data on right axis; event plots account for inclusion of defaulted debt and interest in arrears as in World Bank dataset (mean debt ratio after default in model event plot is average of pre-default debt ratio and debt ratio chosen in case of re-entry).

### Interest rate and debt dynamics
- Interest rate:
  - Model produces a steady increase in the interest rate for the six quarters before default.
  - Interest rates in the model are relatively low because they are pinned down by the default frequency, given the arbitrage condition of risk neutral lenders, and the observed default frequency is low.
  - Interest rates for t≥0 are shown; interest rates for t<0 are not shown in default state because default risk is infinite.
- Debt ratio:
  - Relatively stable in the years before default, then surges with default, and drops in the years that follow.
  - The model underestimates actual debt ratios despite supporting significantly higher debt ratios than existing sovereign default models.

### Sudden Stops interpretation and model contribution
- The sharp declines in GDP, consumption, labor and intermediate goods when credit market access is lost indicate model predictions consistent with Sudden Stops observed in emerging economies.
- Distinction from literature:
  - In most Sudden Stops literature, loss of credit market access is modeled as exogenous.
  - In this model, exclusion from credit markets and the economic collapse are endogenous and influence each other.

*Source: _wp11166 - 4.3  Macroeconomic Dynamics around Default Events*

### 4.4  Sensitivity Analysis

### 4.4  Sensitivity Analysis

### Overview
- Purpose: Evaluate robustness of the model’s quantitative predictions to changes in:
  - range of imported inputs that require working capital (),
  - parameters of the Armington aggregator (_m_d, m__),
  - within-variety elasticity parameter (_m__j),
  - labor (Frisch) elasticity (!),
  - re-entry probability ().
- Main summary statistics used for evaluation are reported in Table 4 (rows (1)–(15)): Output drop at default; Mean Debt/GDP ratios; Mean spread; Std. dev. of spread; GDP correlation with spread; frequency of default; default with GDP below trend.
- Rows reproduced from Argentine data and the baseline model are:
  - (1) Data: Output drop at default 13% ; Mean Debt/GDP ratios 35% ; Mean spread 1.86% ; Std. dev. of spread 0.78% ; corr. with spread -0.62 ; frequency of default -0.11 ; default w. GDP below trend 62%
  - (2) Baseline: Output drop at default 13% ; Mean Debt/GDP ratios 22.89% ; Mean spread 0.71% ; Std. dev. of spread 1.20% ; corr. with spread -0.21 ; frequency of default -0.10 ; default w. GDP below trend 86%

### (a) Working capital ()
- Scenarios (rows (3)–(5)):
  - (3)  = 0: Output drop at default 13% ; Mean Debt/GDP ratios 8.99% ; Mean spread 0.05% ; Std. dev. of spread 0.08% ; corr. with spread 0.24 ; frequency of default -0.02 ; default w. GDP below trend 75%
    - When  = 0, working capital channel removed; an exogenous proportional cost of default is introduced so TFP falls as needed to reproduce a 13% output drop. Model performs much worse: frequency of defaults (proxied by mean spread) falls from 0.7 to 0.05 percent, variability of spreads nearly vanishes, spreads become procyclical, mean debt ratio drops to 9 percent.
  - (4)  = 0.6: Output drop at default 13.6% ; Mean Debt/GDP ratios 20.38% ; Mean spread 0.44% ; Std. dev. of spread 0.88% ; corr. with spread -0.12 ; frequency of default -0.07 ; default w. GDP below trend 83%
  - (5)  = 0.8: Output drop at default 14.44% ; Mean Debt/GDP ratios 27.03% ; Mean spread 0.39% ; Std. dev. of spread 0.89% ; corr. with spread -0.08 ; frequency of default -0.08 ; default w. GDP below trend 96%
- Interpretation:
  - Widening the range of imported input varieties requiring working capital ( ↑ to 0.8) increases mean debt ratio by about 4.5 percentage points of GDP and generates a larger output cost of default; probability and variability of spreads fall by about 30 basis points; correlation between GDP and spreads increases to -0.08.
  - Narrower range ( = 0.6) yields lower mean debt ratio than baseline but still higher output cost of default and correlation between GDP and spreads; frequency and variability of spreads fall.
  - Effects on mean debt ratio are monotonic with , but other moments show non-monotonic behavior due to opposing impacts on default incentives and production plans.
  - Distributional effect: higher  shifts defaults toward states with GDP below trend (annual frequency: 96% below trend for  = 0.8 v. 86% baseline v. 83% for  = 0.6). Correlation between GDP and default slightly changes to -0.07 for  = 0.8 or 0.6.

### (b) Parameters of the Armington Aggregator of Domestic and Imported Inputs
- Scenarios (rows (6)–(9)):
  - (6) _m_d,m_ = 2.63 ( = 0.62): Output drop at default 15.46% ; Mean Debt/GDP ratios 31.23% ; Mean spread 0.53% ; Std. dev. of spread 0.94% ; corr. with spread -0.16 ; frequency of default -0.09 ; default w. GDP below trend 88%
  - (7) _m_d,m_ = 3.10 ( = 0.68): Output drop at default 12.20% ; Mean Debt/GDP ratios 16.15% ; Mean spread 0.91% ; Std. dev. of spread 1.36% ; corr. with spread -0.15 ; frequency of default -0.10 ; default w. GDP below trend 80%
  - (8)  = 0.58: Output drop at default 16.30% ; Mean Debt/GDP ratios 39.07% ; Mean spread 0.28% ; Std. dev. of spread 0.80% ; corr. with spread -0.09 ; frequency of default -0.07 ; default w. GDP below trend 77%
  - (9)  = 0.66: Output drop at default 12.75% ; Mean Debt/GDP ratios 14.19% ; Mean spread 0.74% ; Std. dev. of spread 1.21% ; corr. with spread -0.18 ; frequency of default -0.08 ; default w. GDP below trend 88%
- Interpretation:
  - Increasing substitutability between domestic and imported inputs (higher _m_d,m_) reduces output cost at default and mean debt ratio, while increasing default frequency and spread variability (effects are monotonic).
  - Increasing Armington share of domestic inputs ( ↑) makes working-capital channel via imported inputs less relevant; thus output cost at default and mean debt ratio fall, while default frequency and spread variability increase.
  - Effects on business-cycle comovements are small; GDP-spread correlations remain weakly negative.
  - Plausibility: these alternative parameterizations change imported/domestic expenditure ratios away from baseline/Mexican calibration but remain within ranges documented by Goldberg and Campa (2006). Extreme parameter values can yield very high debt ratios at low default frequencies (examples from sensitivity narrative:  = 0.5 → mean debt ratio ≈ 93% at 0.2% default frequency; lowering _m_d,m_ to 1.96 → mean debt ratio ≈ 80% at negligible default frequency and output cost of default 22.6%).

### (c) Within-variety elasticity of imported input varieties (_m__j)
- Scenarios (rows (10)–(11)):
  - (10) _m__j = 2.22 ( = 0.55): Output drop at default 14.46% ; Mean Debt/GDP ratios 25.94% ; Mean spread 0.36% ; Std. dev. of spread 0.84% ; corr. with spread -0.07 ; frequency of default -0.07 ; default w. GDP below trend 87%
  - (11) _m__j = 2.89 ( = 0.65): Output drop at default 12.43% ; Mean Debt/GDP ratios 19.77% ; Mean spread 0.73% ; Std. dev. of spread 1.17% ; corr. with spread -0.12 ; frequency of default -0.18 ; default w. GDP below trend 83%
- Interpretation:
  - Making imported input varieties better substitutes (higher _m__j) weakens the working-capital channel: output drop at default and mean debt ratio fall; mean and std. dev. of spreads increase.
  - Fraction of defaults with output below trend falls from 87% to 83% as _m__j rises from 2.22 to 2.89.
  - Quantitatively, changes in _m_d,m_ have larger effects than comparable changes in _m__j on production and factor allocation responses to interest rate fluctuations.

### (d) Frisch elasticity of labor supply (!)
- Scenarios (rows (12)–(13)):
  - (12) ! = 1.67 (Frisch = 1.6): Output drop at default 12.6% ; Mean Debt/GDP ratios 22.34% ; Mean spread 0.81% ; Std. dev. of spread 1.22% ; corr. with spread -0.16 ; frequency of default -0.12 ; default w. GDP below trend 84%
  - (13) ! = 2.5 (Frisch = 1.4): Output drop at default 15.2% ; Mean Debt/GDP ratios 24.35% ; Mean spread 0.46% ; Std. dev. of spread 1.06% ; corr. with spread -0.03 ; frequency of default -0.07 ; default w. GDP below trend 70%
- Interpretation:
  - Higher Frisch elasticity of labor supply increases efficiency loss triggered by default (labor market adjusts with smaller wage decline and larger decline in total labor), so output drop at default and mean debt ratio are bigger.
  - Default probability (mean spread) and spread variability fall with higher labor elasticity.
  - Fraction of defaults with GDP below trend falls to 70% when Frisch elasticity is 2.5. GDP-spread correlation increases slightly but remains weakly negative.

### (e) Re-entry probability () — mean length of exclusion period
- Scenarios (rows (14)–(15)):
  - (14)  = 0.05: Output drop at default 15.29% ; Mean Debt/GDP ratios 37.23% ; Mean spread 0.26% ; Std. dev. of spread 0.71% ; corr. with spread -0.12 ; frequency of default -0.04 ; default w. GDP below trend 77%
  - (15)  = 0.1: Output drop at default 13.85% ; Mean Debt/GDP ratios 19.73% ; Mean spread 0.61% ; Std. dev. of spread 1.18% ; corr. with spread -0.11 ; frequency of default -0.08 ; default w. GDP below trend 89%
- Interpretation:
  - Non-monotonic effects: output drop at default higher, and frequency and variability of spreads lower, when mean exclusion period is either shorter or longer than baseline (baseline mean exclusion period = 3 years).
  - Mean debt ratio declines monotonically as exclusion period shortens (37% with 5 years exclusion to about 20% with 2.5 years).
  - Higher re-entry probability shifts defaults toward states with GDP below trend:  = 0.1 → 89% defaults below trend (v. 86% baseline);  = 0.05 → 77% below trend.
  - GDP correlations with defaults and spreads increase slightly but remain weakly negative.

### Summary of robustness and main findings
- Across parameter variations the main quantitative findings are robust:
  - The model produces large endogenous output drops at default due to the working-capital channel.
  - The model produces higher mean debt ratios at higher default frequencies than typical in the sovereign debt literature.
  - The model generates weakly counter-cyclical spreads; correlation between GDP and defaults remains slightly negative.
  - Frequency of defaults with GDP below trend remains mostly in the 73–88 percent range across scenarios (exception: working-capital removed,  = 0, where endogenous output cost of default is eliminated and the model fails to match observed statistics).
- Removing the working-capital channel ( = 0) and replacing it with an exogenous proportional cost calibrated to match the observed output drop causes the model to “fall apart”: produces small debt ratio at negligible default frequency and variability of spreads, and spreads become pro-cyclical.

*Source: _wp11166 - 4.4  Sensitivity Analysis*

### References

### References

### Key literature cited
- Works on sovereign debt, default, and emerging markets (examples listed):
  - Agca, Senay and Oya Celasun, 2009, “How Does Public External Debt A§ect Corporate Borrowing Costs in Emerging Markets?” IMF Working Paper WP/09/266.
  - Arellano, Cristina, 2008, “Default Risk and Income Fluctuations in Emerging Economies,” American Economic Review, Vol 98 (3), 690-712.
  - Bulow, Jeremy and Rogo§, Kenneth, 1989. “Sovereign Debt: Is to Forgive to Forget?,” American Economic Review, Vol. 79(1), 43-50.
  - Eaton, Jonathan and Mark Gersovitz, 1981, “Debt with Potential Repudiation: Theoretical and Empirical Analysis,” Review of Economic Studies, Vol 48(2), 289-309.
  - Uribe, Martin and Vivian Zhanwei Yue, 2006. “Country Spreads and Emerging Countries: Who Drives Whom?” Journal of International Economics, vol 69, 6-36.
  - Yue, Vivian Zhanwei, 2010. “Sovereign Default and Debt Renegotiation,” Journal of International Economics, 80 (2), 176-187.
- Methodological and modelling references:
  - Tauchen, George, 1986, “Finite State Markov-chain Approximations to Univariate and Vector Autoregressions,” Economic Letters, Vol 20, 177-181.
  - Christiano, Lawrence J and Eichenbaum, Martin, 1992. “Liquidity E§ects and the Monetary Transmission Mechanism,” American Economic Review, vol. 82(2), 346-53.
  - Schmitt-Grohe Stephanie and Martin Uribe, 2007, “Optimal, Simple, and Implementable Monetary and Fiscal Rules,” Journal of Monetary Economics 54, 1702-1725.
- Empirical and sectoral studies cited include works on trade liberalization, imported inputs, productivity, financial crises, and international risk sharing (examples: Amiti and Kronings 2007; Halpern, Koren, and Szeidl 2009; Gopinath and Neiman 2010).

*Appendices in the source develop formal model details that build on and reference this literature.*

*Source: _wp11166 - References*

### Appendix 1: The Firms’ Dynamic Optimization Problem with Working Capital

- Setup and assumptions
  - Representative firm in a small open economy produces output using imported intermediate goods and labor:
    - y_t = F(m_t; L_t); (31)
    - F is homogeneous of degree one, increasing, and concave.
  - All intermediate goods are imported; a single homogeneous foreign input with world relative price p.
  - Working capital constraint requires firms to pay in advance for a fraction κ of the cost of imported inputs:
    - θ_t R_t ≥ κ p m_t, κ ≥ 0; (timing notation indicates working capital holdings θ_t and one-period interest rate R_t)
  - Alternative “shopping time” formulation noted: increases input cost by κ(R_t − 1)/R_t instead of κ(R_t − 1), but the relevant interest rate is the same R_t.

- Firm debt evolution and net liabilities
  - Period-by-period budget constraint:
    - d_t = R_{t-1} d_{t-1} − F(m_t; L_t) + w_t L_t + p m_t + π_t − θ_{t-1} + θ_t.
  - Define total net liabilities at end of period t:
    - a_t ≡ R_t d_t − θ_t.
  - Rewritten constraint using a_t:
    - a_t / R_t = a_{t-1} − F(m_t; L_t) + w_t L_t + p m_t + π_t + [κ (R_t − 1)/R_t] θ_t.

- Key results (preserved exactly)
  - Result 1: The working capital constraint increases the unit cost of imported inputs by the amount κ(R_t − 1), and R_t is the same interest rate as the one charged on one-period debt. This is evident from:
    - a_t / R_t = a_{t-1} − F(m_t; L_t) + p m_t [1 + κ(R_t − 1)] + w_t L_t + π_t; (32)
  - Result 2: If firms maximize the present value of profits, they do not accumulate precautionary asset holdings. In particular, if firms start with zero liabilities, they maintain zero liabilities at the end of each period in perpetuity (a_t = 0 for all t ≥ 0), with distributed profits:
    - π_t = F(k_t; h_t) − p m_t [1 + κ(R_t − 1)] − w_t L_t.

- Firm’s optimization and first-order conditions
  - Firm maximizes present discounted value of profits with stochastic discount factor β_t (or equivalently discounting at world interest rates R_t). Objective:
    - max E_0 ∑_{t=0}^1 β_t π_t.
  - Using constraint (32), the problem becomes choosing a_t, m_t, L_t to maximize:
    - E_0 ∑_{t=0}^1 β_t [ a_t / R_t − a_{t-1} + F(m_t; L_t) − p m_t [1 + κ(R_t − 1)] − w_t L_t ],
      subject to no-Ponzi-game lim_{j→1} E_t a_{t+j} / ∏_{s=0}^j R_{t+s} ≤ 0.
  - First-order conditions:
    - Euler for net liabilities: β_t = β R_t E_t β_{t+1}.
    - Factor conditions:
      - F_m(m_t; L_t) = p[1 + κ(R_t − 1)]; (33)
      - F_L(m_t; L_t) = w_t. (34)
  - Interpretation: working capital requirement drives a wedge between marginal product of imported inputs and world price p; wedge increases with financing cost (R_t − 1) and κ.

- Implication on precautionary holdings
  - Because payoffs are linear in net liabilities and discount rates are independent of firm choices, any process a_t satisfying (32) and the no-Ponzi constraint is optimal.
  - If initial net liabilities are zero, optimal plan is a_t = 0 for all t ≥ 0 and no precautionary asset accumulation occurs.
  - Labor and imported input choices depend only on current factor prices, interest rate, and TFP through conditions (33)-(34).

*Source: _wp11166 - References*

### Appendix 2: Decentralized Equilibrium

- Purpose and approach
  - Decentralize the social planner’s problem (Section 2) by formulating the sovereign’s problem as a Ramsey-style optimal policy problem.
  - Government chooses debt policy (amounts and default/repayment) to maximize household welfare given bond pricing function q_t(b_{t+1}; ε_t) and subject to:
    - (a) private sector allocations must constitute a competitive equilibrium;
    - (b) government budget constraint must hold.

- Representation of competitive equilibrium
  - Use conditions (14)-(20) to write recursive functions that map bond prices and TFP into competitive allocations and factor prices:
    - τ(q_t(b_{t+1}; ε_t); ε_t), M(q_t(b_{t+1}; ε_t); ε_t), m^*(q_t(b_{t+1}; ε_t); ε_t),
      m^d(q_t(b_{t+1}; ε_t); ε_t), L^f(q_t(b_{t+1}; ε_t); ε_t), L^m(q_t(b_{t+1}; ε_t); ε_t), and L(q_t(b_{t+1}; ε_t); ε_t).
  - There is a one-to-one mapping between q_t(b_{t+1}; ε_t) and r_t.

- Treatment of diverted working capital repayments
  - Two cases:
    - (i) Diverted repayment treated as a cost of default → decentralized equilibrium allocations/prices coincide with the planner’s problem.
    - (ii) Government rebates diverted repayment as lump-sum transfer to households → stock of working capital becomes an extra state variable because of income effects.
  - State variables for government problem defined as (b_t; θ_{t-1}; ε_t), but θ_{t-1} matters only if repayments are rebated.
  - Note: θ_{t-1} is small in calibration; quantitative results change little whether rebates occur or not.

- Government recursive optimization problem (equations preserved)
  - V(b_t; θ_{t-1}; ε_t) = max { v_{nd}(b_t; ε_t), v_d(θ_{t-1}; ε_t) }. (35)
  - Continuation (repayment) value:
    - v_{nd}(b_t; ε_t) = max_{c_t, b_{t+1}} ( u(c_t − g(L(q_t(b_{t+1}; ε_t); ε_t))) + β E[V(b_{t+1}; θ(q_t(b_{t+1}; ε_t); ε_t); ε_{t+1})] ), (36)
      subject to resource constraint:
    - c_t + q_t(b_{t+1}; ε_t) b_{t+1} − b_t ≤ ε_t f( M(q_t(b_{t+1}; ε_t); ε_t), L^f(q_t(b_{t+1}; ε_t); ε_t), k ) − m^*(q_t(b_{t+1}; ε_t); ε_t) P^* m [ 1 / q_t(b_{t+1}; ε_t) − 1 ], (37)
      where f(·) = M(·)^{M} L_f^{L} k^{k} (notation preserved as in source).
  - Default value:
    - v_d(θ_{t-1}; ε_t) = max_{c_t} ( u(c_t − g( L̃(ε_t) )) + β(1 − ρ) E v_d(0; ε_{t+1}) + β ρ E V(0; 0; ε_{t+1}) ), (38)
      subject to:
    - c_t = ε_t f( M̃(ε_t), L̃^f(ε_t); k ) − m̃^*(ε_t) P̃^* + θ_{t-1}. (39)
  - In default, diverted repayment θ_{t-1} is appropriated by government and enters household income since T_t = θ_{t-1} on the date of default.

- Default set and probability
  - Default set:
    - D(b_t; θ_{t-1}) = { ε_t : v_{nd}(b_t; ε_t) ≤ v_d(θ_{t-1}; ε_t) }. (40)
  - The default set is two-dimensional (depends on b_t and θ_{t-1}) because working capital affects the gap between default and repayment values.
  - Despite two-dimensional default set, the probability of default perceived at date t for debt b_{t+1} and productivity ε_t depends only on b_{t+1} and ε_t, because θ_t is determined by ε_t and the interest rate (a function of b_{t+1} and ε_t):
    - p_t(b_{t+1}; ε_t) = ∫_{ε_{t+1} ∈ D(b_{t+1}; θ_t)} dπ(ε_{t+1} | ε_t), where θ_t = θ(q_t(b_{t+1}; ε_t); ε_t). (41)

- Equivalence to planner’s problem (no rebate case)
  - If diverted repayments are not rebated, θ_{t-1} is removed from state variables and default-branch resource constraint.
  - Recursive functions mapping q_t and ε_t into allocations ensure conditions (14)-(20) hold, matching planner first-order conditions for factor allocations.
  - For given q_t(b_{t+1}; ε_t), b_{t+1} and b_t, the resource constraints in continuation and default branches coincide with the planner’s, implying identical value functions and optimal bond decision rules (assuming well-defined).

*Source: _wp11166 - References*

### Appendix 3: Theorem Proofs

### Appendix 3: Theorem Proofs

### PROOF of THEOREM 1
- Given a productivity shock", the utility from defaulting v_d("0) is independent of b.
- The utility from not defaulting v_nd(b;"0) is increasing in b_{t+1}.
- Therefore, if Vb1;"0
 = v_d("0), then it must be the case that Vb0;"0
 = v_d("0).
- Hence, any "0 that belongs in Db1;"
 must also belong in Db0;"
.
- Let d(b;"0) be the equilibrium default decision rule. The equilibrium default probability is then given by
  - p(b;") = R db;"0
 d"0 j"
 :
- From Db1;"0
  Db0;"0
, if db1;"0
 = 1, then db0;"0
 = 1.
- Therefore,
  - pb0;"
  pb1;"
 :

### PROOF of THEOREM 2
- From Theorem 1, given a productivity shock " and b0 < b1  0, pb0;"
  pb1;"
.
- The equilibrium bond price is given by
  - qb0;"
 = 1p(b0;") 1 + r :
- Hence, using Theorem 1, we obtain that:
  - qb0;"
  qb1;"
 :

### Appendix 4: Data DeÖnition and Data Source (summary)
- Table A1 describes the variables and data sources of our data set for cross-country event studies.
- Table A2 summarizes the list of countries, default episodes, and the available variables in the analysis.
- Default episodes are based on Yeyati and Panizza (2011), Benjamin and Wright (2010), and Standard and Poors report.
- For event analysis we use the quarter after the default announcement date to measure economic variables reflecting the impact of default with some lag (same treatment as Yeyati and Panizza).
- GDP, consumption, and trade balance/GDP are from International Financial Statistics and Yeyati and Panizza(2011). Yeyati and Panizza(2011) compiled real GDP from national sources when IFS does not record GDP. GDP, consumption, and trade balance/GDP are H-P detrended.
- Imported intermediate inputs: sum of categories for intermediate goods based on Broad Economic Categories (BEC). Categories for intermediate goods listed exactly as in source:
  - (111*) Food and beverages, primary, mainly for industry
  - (121*) Food and beverages, processed, mainly for industry
  - (21*) Industrial supplies not elsewhere speciÖed, primary
  - (22*) Industrial supplies not elsewhere speciÖed, processed
  - (31*) Fuels and lubricants, primary
  - (322*) Fuels and lubricants, processed (other than motor spirit)
  - (42*) Parts and accessories of capital goods (except transport equipment)
  - (53*) Parts and accessories of transport equipment
- Intermediate goods are from United Nation, National Accounts O¢ cial Country Data. The data is taken from Table 4.1 Total Economy (S.1), I. Production account - Uses Intermediate consumption, at purchaserís prices.
- Labor data is total paid employment from LABORSTA dataset collected by International Labor Organization.
- Data treatment due to limitations:
  - Imported inputs and total intermediate goods are log-linearly detrended.
  - Labor data is indexed so that the employment 4 years before default is 1.
- Table A1: Variables and Sources (entries preserved)
  - Variable | DeÖnition Frequency | Sources
  - GDP | Real GDP quarterly | International Financial Statistics and Yeyati and Panizza(2011)
  - CON | Real consumption quarterly | International Financial Statistics
  - MS | Imported Intermediates (in dollars, deáated by US PPI) annual | United Nation comtrade (BEC code)
  - TB | Trade Balance/GDP quarterly | International Financial Statistics
  - IM | Intermediate goods (deáated by PPI) annual | United Nation
  - L | Labor (paid employment) annual | International Labor Organization
  - D | External debt/GNI annual | Global Development Finance
  - S | Sovereign bond spreads quarterly | EMBI+ and EMBI global (J.P. Morgan)
- Table A2: List of countries and variables included in the event analysis (entries preserved)
  - Argentina 1982Q2: GDP, L, D
  - Argentina 2002Q1: GDP, CON, MS, TB, IM, L, D, S
  - Chile 1983Q1: GDP, D
  - Croatia 1992Q2: GDP, L
  - Domin. Rep. 1993Q1: GDP, D
  - Ecuador 1999Q3: GDP, CON, MS, TB, IM, D, S
  - Indonesia 1998Q3: GDP, CON, TB, D
  - Mexico 1982Q4: GDP, L, D
  - Moldova 2002Q1: GDP, CON, MS, L, TB, D
  - Nigeria 1983Q1: GDP, D
  - Nigeria 1986Q4: GDP, D
  - Pakistan 1998Q3: GDP, D
  - Peru 1983Q2: GDP, D
  - Philippines 1983Q4: GDP, CON, TB, D
  - Russia 1998Q4: GDP, CON, TB, IM, L, D, S
  - South Africa 1985Q4: GDP, CON, TB, L, D
  - South Africa 1993Q1: GDP, CON, TB, IM, L, D
  - Thailand 1998Q1: GDP, CON, MS, TB, D, S
  - Ukraine 1998Q4: GDP, MS, IM, L, D, S
  - Uruguay 1990Q2: GDP, D
  - Uruguay 2003Q2: GDP, MS, IM, L, D, S
  - Venezuela 1995Q3: GDP, IM, D, S
  - Venezuela 1998Q3: GDP, IM, D, S

*Source: Appendix 3 and Appendix 4 (selected excerpts) from the provided PDF content.*

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