## _wp13269

## Source details

**Canonical URL:** [_wp13269](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13269.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13269.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13269.pdf.json)

---

### Model setup and key assumptions
- Two-region monetary union: Home (small open economy) and the rest of the monetary union (Foreign).
- Each region produces nontradable final goods and tradable/nontradable intermediate goods; firms set prices under monopolistic competition.
- Monetary policy: union-level standard Taylor rule (inertial; previous-period weight = 0.85).
- Fiscal policy: country-level; fiscal rule stabilizes public debt using lump-sum transfers (instrument tr).
- Two bonds traded at union level, both denominated in union currency: one household-to-household bond B, and one government bond Bg.
- Sovereign restructuring modeled as an unexpected write-off (haircut) of public debt (Loss_Bgov) occurring in period t = 1.
- After restructuring both government and private sector face a spread φ above the risk-free rate r set by the central bank; φ is proportional to the size of the haircut and transmitted equally to private and public borrowing (φgov = φb = φ).
- Spread dynamics (equation 4): φt = φb1 (exp(Loss_Bgovt) − 1) + ρφ φt−1 + φb2 exp(−φb3 (b − b̄)−1 exp(−φb3 (b − b̄)−1) ) + 1 (parameters φb1, φb2, φb3, ρφ explained in text).
- Fiscal rule (equation 3): trt / trt−1 = (b_govt / b_gov,targ)^{φ1} (b_govt / b_gov,t−1)^{φ2} (GDPt / GDPt−1)^{φ3}, with φ1, φ2, φ3 < 0; in simulations φ1 = 0.5, φ2 = 25, φ3 = 25 and b_gov,targ reset to post-haircut level.
- Households are Ricardian in baseline; a rule-of-thumb (liquidity-constrained) household class (30 percent) is introduced in consolidation comparison.

### Calibration highlights (quarterly frequency)
- Home initial public debt: 150 percent of yearly GDP.
- Post-haircut baseline: nominal public debt reduced from 150 to 90 percent of yearly GDP (40 percent haircut).
- Home and Foreign households each hold 50 percent of Home government debt in baseline.
- Home private sector net foreign debt prior to restructuring: 100 percent of GDP.
- Cruces and Trebesch (2013) based spread calibration: effect on spread of a 40 percentage point haircut ≈ 300 basis points in year one, decreasing to ≈ 150 basis points in years four and five.
- Discount factor β = 0.992 (steady state real interest rate = 3.3 percent annualized).
- Tax rates: τℓ = 0.46, τk = 0.19, τc = 0.18.
- Population size of Home s = 0.05 (union normalized to 1).
- Adjustment costs on investment = 2.8.
- Elasticities and other parameters as reported in Tables (described in text).

### Baseline simulation results (40 percent haircut; 50 percent domestic holding; private foreign debt = 100 percent of GDP)
- Public debt: reduced permanently from 150 to 90 percent of annualized GDP; debt target reset and stabilized at new level via transfers.
- Spread: increases by about 3 (annualized) percentage points on impact; remains above 1 percent for about 5 years; then gradually declines (consistent with Cruces and Trebesch (2013)).
- GDP:
  - Decreases by 13 percent of the initial steady state level after one year.
  - Decreases by 10 percent after one and a half years.
  - Returns close to but still below its initial level after three years (recovery takes more than three years).
- Consumption and investment:
  - Consumption falls by 20 percent on impact.
  - Investment falls by 50 percent on impact.
  - Both recover gradually over time.
- Employment: decreases by about 20 percent.
- Inflation: Home CPI inflation falls by five (annualized) percentage points (driven by reduction in aggregate demand).
- External accounts:
  - Gross exports increase; imports decrease (Home tradables prices fall due to weaker aggregate demand).
  - Foreign asset position of Home improves; current account (as ratio to GDP) improves on impact thanks to lower interest payments on reduced foreign liabilities despite higher spread.
- Government finances:
  - Interest expenditure falls (reduction in nominal debt more than offsets higher spread).
  - Public transfers initially decrease, then permanently increase above initial level in long run as interest payments are lower and debt is stabilized.
  - Government primary balance always in surplus; overall government budget moves to surplus then returns to zero as debt stabilizes.

### Sensitivity analyses and scenario variants
- Haircut size: 20 percent vs 40 percent
  - 20 percent haircut results:
    - Spread increase ≈ 1.5 percentage points on impact (vs 3 percentage points in baseline).
    - GDP decreases by 6 percent after one year (vs ≈ 13 percent in baseline).
    - Inflation decreases by 1 percent (vs 2 percent in baseline).
    - Macroeconomic costs are quantitatively lower but qualitatively similar to baseline.
- No spread increase
  - If the spread does not increase after the haircut:
    - Economic activity responds positively: GDP, consumption and investment increase on impact as households receive positive wealth effect from haircut on foreign bondholders.
    - This isolates the spread channel as the key driver of the negative macroeconomic effects in the baseline.
- Ownership composition of public debt
  - Domestic households hold 100 percent of public debt:
    - GDP decreases by 17 percent (larger than baseline ≈ 13 percent).
    - No wealth transfer to domestic households from haircut; only the negative spread effect remains.
  - Foreign households hold 100 percent of public debt:
    - GDP decreases by 3 percent (much milder than baseline).
    - Larger reduction in country foreign debt position and larger positive wealth effect for domestic households.
  - Conclusion: macroeconomic costs of restructuring are larger when a greater share of public debt is domestically held; lower when foreign holdings are larger.
- Initial private foreign asset position
  - Baseline private foreign debt = 100 percent of GDP.
  - If private sector initial foreign asset position = 0:
    - GDP reduction ≈ 8 percent (vs 13 percent in baseline).
    - Rationale: with zero private foreign debt, households face smaller negative income effect from rolling over private debt at higher rates; the adverse private-sector financing channel is muted.

### Comparison: sovereign restructuring vs gradual fiscal consolidation (both reduce public debt by 40 percent)
- Fiscal consolidation scenario:
  - Debt reduced gradually over around 6-7 years by cutting lump-sum transfers; spread assumed not to increase (φ = 0).
  - Rule-of-thumb households (30 percent) introduced so transfers have real effects.
- Results:
  - Restructuring produces a much larger short- to medium-run GDP decline than gradual consolidation.
  - Under restructuring with liquidity-constrained households, GDP fall is larger than restructuring without rule-of-thumb households.
  - Under consolidation, consumption of liquidity-constrained households declines gradually; overall recessionary effects are smaller and more gradual.
- Conclusion: based on calibrations, negative effects on GDP are substantially smaller under fiscal consolidation in the short to medium run, though potentially slightly more persistent in some calibrations.

### Mechanisms emphasized and factors abstracted from
- Emphasized channels:
  - Reaction of international financial markets (increase in borrowing costs/spreads).
  - Net foreign asset position of the private sector.
  - Share of government debt held domestically vs abroad.
- Not considered / abstracted from:
  - Contagion and systemic crises.
  - Financial frictions, bank balance-sheet effects, and possible contagion within a financially integrated monetary union.
  - Cases where fiscal policy is not initially in equilibrium or where consolidation coincides with sovereign stress.
- Authors’ stated objective: highlight key channels shaping outcomes and assess their relative importance rather than produce point predictions for any specific country.

### Main conclusions and policy-relevant findings
- Sovereign restructurings that involve a significant haircut can generate sizable and persistent reductions in macroeconomic activity, primarily due to increased spreads that affect both public and private borrowing.
- The negative macroeconomic impact is:
  - Larger when the share of public debt held domestically is large.
  - Larger when the private sector has large foreign debt.
  - Sensitive to the magnitude of the haircut (larger haircuts → larger spreads → larger costs).
- If restructurings do not trigger higher spreads, the net wealth effect can be positive for domestic households and increase activity; thus the spread channel is decisive.
- Compared to a smooth fiscal consolidation that reduces debt by the same amount without raising spreads, a restructuring is likely to produce larger short- to medium-run declines in GDP.
- Quantifying declines in activity from restructurings is difficult and depends on many sovereign- and process-specific characteristics; results should not be mechanically applied to any specific country.

*Source: _wp13269 - conclusions.  Some papers point to relatively short periodsof exclusion from the international financial (conclusions section of the supplied PDF).*

### conclusions.  Some papers point to relatively short periodsof exclusion from the international financial

### _wp13269 - conclusions.  Some papers point to relatively short periodsof exclusion from the international financial

### Model setup and key assumptions
- Two-region monetary union: Home (small open economy) and the rest of the monetary union (Foreign).  
- Each region produces nontradable final goods and tradable/nontradable intermediate goods; firms set prices under monopolistic competition.  
- Monetary policy: union-level standard Taylor rule (inertial; previous-period weight = 0.85).  
- Fiscal policy: country-level; fiscal rule stabilizes public debt using lump-sum transfers (instrument tr).  
- Two bonds traded at union level, both denominated in union currency: one household-to-household bond B, and one government bond Bg.  
- Sovereign restructuring modeled as an unexpected write-off (haircut) of public debt (Loss_Bgov) occurring in period t = 1.  
- After restructuring both government and private sector face a spread φ above the risk-free rate r set by the central bank; φ is proportional to the size of the haircut and transmitted equally to private and public borrowing (φgov = φb = φ).  
- Spread dynamics (equation 4): φt = φb1 (exp(Loss_Bgovt) − 1) + ρφ φt−1 + φb2 exp(−φb3 (b − b̄)−1 exp(−φb3 (b − b̄)−1) ) + 1 (parameters φb1, φb2, φb3, ρφ explained in text).  
- Fiscal rule (equation 3): trt / trt−1 = (b_govt / b_gov,targ)^{φ1} (b_govt / b_gov,t−1)^{φ2} (GDPt / GDPt−1)^{φ3}, with φ1, φ2, φ3 < 0; in simulations φ1 = 0.5, φ2 = 25, φ3 = 25 and b_gov,targ reset to post-haircut level.  
- Households are Ricardian in baseline; a rule-of-thumb (liquidity-constrained) household class (30 percent) is introduced in consolidation comparison.  

### Calibration highlights (quarterly frequency)
- Home initial public debt: 150 percent of yearly GDP.  
- Post-haircut baseline: nominal public debt reduced from 150 to 90 percent of yearly GDP (40 percent haircut).  
- Home and Foreign households each hold 50 percent of Home government debt in baseline.  
- Home private sector net foreign debt prior to restructuring: 100 percent of GDP.  
- Cruces and Trebesch (2013) based spread calibration: effect on spread of a 40 percentage point haircut ≈ 300 basis points in year one, decreasing to ≈ 150 basis points in years four and five.  
- Discount factor β = 0.992 (steady state real interest rate = 3.3 percent annualized).  
- Tax rates: τℓ = 0.46, τk = 0.19, τc = 0.18.  
- Population size of Home s = 0.05 (union normalized to 1).  
- Adjustment costs on investment = 2.8.  
- Elasticities and other parameters as reported in Tables (described in text).

### Baseline simulation results (40 percent haircut; 50 percent domestic holding; private foreign debt = 100 percent of GDP)
- Public debt: reduced permanently from 150 to 90 percent of annualized GDP; debt target reset and stabilized at new level via transfers.  
- Spread: increases by about 3 (annualized) percentage points on impact; remains above 1 percent for about 5 years; then gradually declines (consistent with Cruces and Trebesch (2013)).  
- GDP:
  - Decreases by 13 percent of the initial steady state level after one year.  
  - Decreases by 10 percent after one and a half years.  
  - Returns close to but still below its initial level after three years (recovery takes more than three years).  
- Consumption and investment:
  - Consumption falls by 20 percent on impact.  
  - Investment falls by 50 percent on impact.  
  - Both recover gradually over time.  
- Employment: decreases by about 20 percent.  
- Inflation: Home CPI inflation falls by five (annualized) percentage points (driven by reduction in aggregate demand).  
- External accounts:
  - Gross exports increase; imports decrease (Home tradables prices fall due to weaker aggregate demand).  
  - Foreign asset position of Home improves; current account (as ratio to GDP) improves on impact thanks to lower interest payments on reduced foreign liabilities despite higher spread.  
- Government finances:
  - Interest expenditure falls (reduction in nominal debt more than offsets higher spread).  
  - Public transfers initially decrease, then permanently increase above initial level in long run as interest payments are lower and debt is stabilized.  
  - Government primary balance always in surplus; overall government budget moves to surplus then returns to zero as debt stabilizes.

### Sensitivity: haircut size (20 percent vs 40 percent)
- 20 percent haircut results:
  - Spread increase ≈ 1.5 percentage points on impact (vs 3 percentage points in baseline).  
  - GDP decreases by 6 percent after one year (vs ≈ 13 percent in baseline).  
  - Inflation decreases by 1 percent (vs 2 percent in baseline).  
  - Macroeconomic costs are quantitatively lower but qualitatively similar to baseline.  

### Sensitivity: no spread increase
- If the spread does not increase after the haircut:
  - Economic activity responds positively: GDP, consumption and investment increase on impact as households receive positive wealth effect from haircut on foreign bondholders.  
  - This isolates the spread channel as the key driver of the negative macroeconomic effects in the baseline.

### Sensitivity: ownership composition of public debt
- Domestic households hold 100 percent of public debt (all domestic):
  - GDP decreases by 17 percent (larger than baseline ≈ 13 percent).  
  - No wealth transfer to domestic households from haircut; only the negative spread effect remains.  
- Foreign households hold 100 percent of public debt (all foreign):
  - GDP decreases by 3 percent (much milder than baseline).  
  - Larger reduction in country foreign debt position and larger positive wealth effect for domestic households.  
- Conclusion: macroeconomic costs of restructuring are larger when a greater share of public debt is domestically held; lower when foreign holdings are larger.

### Sensitivity: initial private foreign asset position
- Baseline private foreign debt = 100 percent of GDP.  
- If private sector initial foreign asset position = 0:
  - GDP reduction ≈ 8 percent (vs 13 percent in baseline).  
  - Rationale: with zero private foreign debt, households face smaller negative income effect from rolling over private debt at higher rates; the adverse private-sector financing channel is muted.

### Comparison: sovereign restructuring vs gradual fiscal consolidation (both reduce public debt by 40 percent)
- Fiscal consolidation scenario:
  - Debt reduced gradually over around 6-7 years by cutting lump-sum transfers; spread assumed not to increase (φ = 0).  
  - Rule-of-thumb households (30 percent) introduced so transfers have real effects.  
- Results:
  - Restructuring produces a much larger short- to medium-run GDP decline than gradual consolidation.  
  - Under restructuring with liquidity-constrained households, GDP fall is larger than restructuring without rule-of-thumb households.  
  - Under consolidation, consumption of liquidity-constrained households declines gradually; overall recessionary effects are smaller and more gradual.  
- Conclusion: based on calibrations, negative effects on GDP are substantially smaller under fiscal consolidation in the short to medium run, though potentially slightly more persistent in some calibrations.

### Mechanisms emphasized and omitted factors
- Emphasized channels:
  - Reaction of international financial markets (increase in borrowing costs/spreads).  
  - Net foreign asset position of the private sector.  
  - Share of government debt held domestically vs abroad.  
- Not considered / abstracted from:
  - Contagion and systemic crises.  
  - Financial frictions, bank balance-sheet effects, and possible contagion within a financially integrated monetary union.  
  - Cases where fiscal policy is not initially in equilibrium or where consolidation coincides with sovereign stress.  
- Authors’ stated objective: highlight key channels shaping outcomes and assess their relative importance rather than produce point predictions for any specific country.

### Main conclusions and policy-relevant findings
- Sovereign restructurings that involve a significant haircut can generate sizable and persistent reductions in macroeconomic activity, primarily due to increased spreads that affect both public and private borrowing.  
- The negative macroeconomic impact is:
  - Larger when the share of public debt held domestically is large.  
  - Larger when the private sector has large foreign debt.  
  - Sensitive to the magnitude of the haircut (larger haircuts → larger spreads → larger costs).  
- If restructurings do not trigger higher spreads, the net wealth effect can be positive for domestic households and increase activity; thus the spread channel is decisive.  
- Compared to a smooth fiscal consolidation that reduces debt by the same amount without raising spreads, a restructuring is likely to produce larger short- to medium-run declines in GDP.  
- Quantifying declines in activity from restructurings is difficult and depends on many sovereign- and process-specific characteristics; results should not be mechanically applied to any specific country.

*Source: _wp13269 - conclusions.  Some papers point to relatively short periodsof exclusion from the international financial (conclusions section of the supplied PDF).*

### References

### _wp13269 - References

### References (selected)
- Benigno, P., 2009. Price Stability with Imperfect Financial Integration. Journal of Money, Credit and Banking, Volume 41, Issue s1, pp. 121–149.
- Broner F., A. Martin, and J. Ventura, 2010. Sovereign Risk and Secondary Markets. American Economic Review, Volume 100, No. 4.
- Campbell, J.Y., Mankiw, G., 1989. Consumption, income and interest rate: reinterpreting the time series evidence. In: Blanchard, O.J., Fisher, S. (Eds.), NBER Macroeconomics Annual 1989, MIT Press.
- Coenen, G., P. McAdam and Straub, R., 2008. Tax Reform and Labour-Market Performance in the Euro Area: A Simulation-Based Analysis Using the New Area-Wide Model. Journal of Economic Dynamics and Control, Volume 32, Issue 8, pp. 2543–2583.
- Corsetti, G., K. Kuester, A. Meier and G. Mueller, 2012. Sovereign Risk, Fiscal Policy and Macroeconomic Stability (2012). IMF Working Paper, 12/33, January.
- Cruces, J.J. and C. Trebesh, 2013. Sovereign Defaults: the Price of Haircuts. American Economic Journal: Macroeconomics, 5(3).
- Eaton, J. and M. Gersovitz, 1981. Debt with Potential Repudiation: Theoretical and Empirical Analysis. Review of Economic Studies, Volume 48, Issue 2, pp. 289–309.
- Eurostat (2008)
- Forni, L., Gerali A. and M. Pisani, 2010. The Macroeconomics of Fiscal Consolidations in Euro area Countries. Journal of Economic Dynamics and Control, Volume 34, Issue 9.
- Forni, L., Gerali A. and M. Pisani, 2010. Macroeconomic effects of greater competition in the service sector: the case of Italy. Macroeconomic Dynamics, Vol. 14.
- Forni, L., L. Monteforte, and L. Sessa, 2009, “The general equilibrium effects of fiscal policy: Estimates for the Euro area,” Journal of Public Economics, Vol. 93(3-4), pp.559-585.
- Galì, J., Lopez-Salido, D., Vallès, J. 2007. Understanding the Effects of Government Spending on Consumption. Journal of European Economic Association, Volume 5, pp. 227–270.
- Gomes, S., Jacquinot P., Pisani, M., 2010. The EAGLE. A model for policy analysis of macroeconomic interdependence in the euro area. ECB Working paper 1195, May.
- Mankiw, N.G., 2000. The Savers-Spenders Theory of Fiscal Policy. American Economic Review, Volume 90, Issue 2.
- Panizza, U., Sturzenegger, F. and J. Zettelmeyer, 2009. "The Economics and Law of Sovereign Debt and Default." Journal of Economic Literature, Volume 47, Issue 3, pp. 651–98.
- Pesenti, P. (2008) The Global Economy Model (GEM): Theoretical Framework, IMF Staff Papers, Volume 55, Issue 2, pp.243–284.

### Appendix — Model structure (excluding fiscal policy part)
- Model geography and agents
  - Two countries: Home and rest of the monetary union (size normalization: sum to 1; Home size parameter s with 0 < s < 1).
  - Shared currency and central bank; households, firms, capital owners, and differentiated labor suppliers in each region.
  - A fraction of households are non-optimizing and consume current wage income each period.

- Household behavior and financial markets
  - Households consume a final composite good of non-tradable, domestic tradable, and imported intermediate goods.
  - Access to financial markets: trade a risk-free one-period nominal bond.
  - Own domestic firms and capital stock rented to firms in a perfectly competitive market.
  - Households supply differentiated labor and set wages with a markup over marginal rate of substitution.

- Production structure
  - Final goods: private consumption, private investment, public consumption — produced via CES aggregation of intermediate goods.
  - Intermediate goods: tradable and non-tradable produced using capital and labor with CES production functions; tradables split into domestically-consumed and export goods.
  - Market segmentation assumed; law of one price for tradables does not hold → firms set separate domestic and export prices.

- Adjustment costs and nominal rigidities
  - Real-side quadratic adjustment costs on capital (investment adjustment): slow capital adjustment.
  - Nominal-side quadratic adjustment costs on prices and wages: price and wage stickiness.
  - Price adjustment costs enter sectoral pricing first-order conditions via terms like A_t(n) and A_t(h).

- Imperfect competition
  - Markups modeled via elasticities of substitution across differentiated goods and labor.
  - When elasticities (θ_N, θ_T, ψ) are large, competition drives prices closer to marginal costs; high markups imply larger price rigidity relevance.

### Key equations and blocks (expressed as in source)
- Final non-tradable consumption CES aggregator (firm indexed x ∈ (0, s]):
  - A_t(x) ≡ ( ... )^{φ_A/(φ_A−1)} with parameters ρ_A > 0, φ_A > 0, 0 < a_H < 1, 0 < a_T < 1 (full formula appears in source).
- Intermediate good demand (examples):
  - Q_HA(x), Q_FA(x*), Q_NA(x) defined as CES aggregates with elasticities θ_T, θ_N > 1 (equations 13–15).
  - Demand for a non-tradable intermediate input:
    - Q_A,t(n,x) = (1/s) (P_t(n)/P_N,t)^{−θ_N} Q_NA,t(x)  (equation 16).
  - Price index for local intermediates:
    - P_N,t = [∫_0^s P_t(n)^{1−θ_N} dn]^{1/(1−θ_N)}  (equation 17).

- Production supply of a Home non-tradable intermediate good n:
  - N_S,t(n) = [ (1−α_N)^{1/ξ_N} L_N,t(n)^{(ξ_N−1)/ξ_N} + α_N^{1/ξ_N} K_N,t(n)^{(ξ_N−1)/ξ_N} ]^{ξ_N/(ξ_N−1)}  (equation 18).
  - Input demands from cost minimization:
    - L_p,N,t(n) = (1−α_N) [ W_t / MC_N,t(n) ]^{−ξ_N} N_S,t(n)  (equation 19).
    - K_N,t(n) = α_N [ R_K,t / MC_N,t(n) ]^{−ξ_N} N_S,t(n).
  - Nominal marginal cost:
    - MC_N,t(n) = [ (1−α) W_t^{1−ξ_N} + α R_K,t^{1−ξ_N} ]^{1/(1−ξ_N)}  (equation 20).

- Price-setting with quadratic adjustment costs (non-tradables):
  - AC_p,N,t(n) ≡ κ_pN /2 [ P_t(n)/P_{t−1}(n) − 1 ]^2 Q_N,t , κ_pN ≥ 0.
  - First-order condition (in domestic consumption units):
    - p_t(n) = θ_N/(θ_N−1) mc_t(n) − A_t(n)/(θ_N−1)  (equation 21).
  - If prices were flexible:
    - p_t(n) = θ_N/(θ_N−1) mc_N,t(n)  (equation 22).

- Tradable intermediate sector pricing (domestic and export prices):
  - p_t(h) = θ_T/(θ_T−1) mc_t(h) − A_t(h)/(θ_T−1)  (equation 23).
  - p*_t(h) = θ*_T/(θ_T−1) mc_t(h) − A*_t(h)/(θ_T−1)  (equation 24).
  - If κ_pH = κ_pH* and θ_T = θ*_T then law of one price: p_t(h) = p*_t(h) (equation 25).

- Labor aggregation and wage setting
  - Labor input aggregator for non-tradable sector (j ∈ [0, s]):
    - L_N,t(n) ≡ (1/s)^{1/ψ} [ ∫_0^s L_t(n,j)^{ψ−1/ψ} dj ]^{ψ/(ψ−1)}  (equation 26).
  - Labor demand relation:
    - L_p,t(n,j) = (1/s) [ W_t(j) / W_t ]^{−ψ} L_p,N,t(j)  (equation 27).
  - Wage index:
    - W_t = [ (1/s) ∫_0^s W_t(h)^{1−ψ} dh ]^{1/(1−ψ)}  (equation 28).
  - Wage adjustment quadratic cost (in total wage bill terms):
    - AC_W,t = κ_W /2 [ W_t / W_{t−1} − 1 ]^2 W_t L_t  (equation 29).

- Monetary policy (Taylor rule in gross terms):
  - (1 + i_t)/(1 + i) = ((1 + i_{t−1})/(1 + i))^{ρ_i} (Π_MU,t)^{(1−ρ_i) ρ_π} ( GDP_MU,t / GDP_MU,t−1 )^{(1−ρ_i) ρ_GDP}  (equation 30).
  - CPI inflation for the union:
    - Π_MU,t ≡ (Π_t)^s (Π*_t)^{1−s}  (equation 31).
  - Union-wide GDP:
    - GDP_MU,t ≡ GDP_t + rer* GDP*_t  where rer is Home real exchange rate (equation 32).

### Calibration highlights (tables and exact numeric entries preserved)
- Table 1. Great Ratios and tax rates (Home / Rest of the monetary union)
  - MACRO VARIABLES:
    - Private consumption C: 52.6 / 56.6
    - Private Investment I: 18.2 / 20.2
    - Imports: 24.4 / -
    - Foreign debt (% annualized GDP): 100.0 / -
  - FISCAL VARIABLES:
    - Public purchases C_g: 10.0 / 10.0
    - Wage bill W L_g: 10.9 / 11.2
    - Interests: 4.9 / 1.9
  - Tax Rates:
    - on wage: 46 / 46
    - on rental rate of capital: 19 / 19
    - on price of consumption: 18 / 18
    - Debt (ratio to annual GDP): 150 / 60.0

- Table 2. Home country spread (Parameter values)
  - φ_b1 = 0.0162
  - φ_b2 = 0.002
  - φ_b3 = 0.002
  - ρ_φ = 0.927

- Table 3. Parametrization (selected entries; Home / Rest of monetary union)
  - Rate of time preference 1/β: 4 −1 *1003.3 / 3.3
  - Intertemporal elasticity of substitution 1/σ: 1.0 / 1.0
  - Frisch elasticity of labor 1/(τ−1): 0.5 / 0.5
  - Depreciation rate δ, δ*: 0.025 / 0.025
  - Substitution between private and public goods θ: 1.5 / 1.5
  - Bias towards private goods ω: 0.8 / 0.8
  - Tradable intermediate goods: ξ_T, ξ*_T = 0.9 / 0.9 ; α_T, α*_T = 0.6 / 0.65
  - Nontradable intermediate goods: ξ_N, ξ*_N = 0.9 / 0.9 ; α_N, α*_N = 0.57 / 0.6
  - Final consumption goods: φ_A, φ*_A = 1.5 / 1.5 ; a_H, a*_F = 0.5 / 0.9 ; ρ_A, ρ*_A = 0.5 / 0.5 ; a_T, a*_T = 0.5 / 0.5
  - Final investment goods: φ_E, φ*_E = 1.5 / 1.5 ; υ_H, υ*_F = 0.4 / 0.9 ; ρ_E, ρ*_E = 0.5 / 0.5 ; υ_T, υ*_T = 0.75 / 0.75
  - Sizes and (1−s): 0.05 / 0.95

- Table 4. Gross Markups (Markups and Elasticities of Substitution)
  - Tradables / Non-tradables / Wages
    - Home: 1.2 (θ_T = 6) / 1.3 (θ_N = 4.3) / 1.3 (ψ = 4.3)
    - Rest of the monetary union: 1.2 (θ*_T = 6) / 1.3 (θ*_N = 4.3) / 1.3 (ψ* = 4.3)

- Table 5. Real and Nominal Adjustment Costs (Home / Rest of the monetary union)
  - Real Adjustment Costs
    - Investment φ_I, φ*_I = 2.80 / 2.80
  - Nominal Adjustment Costs
    - Wages κ_W, κ*_W = 400 / 400
    - Price of domestically-produced tradables κ_H, κ*_F = 600 / 600
    - Price of non tradables κ_N, κ*_N = 600 / 600
    - Price of imported intermediate goods κ_F, κ*_H = 600 / 600
    - Indexation to past inflation α, α* = 0.5 / 0.5

- Table 6. Fiscal and Monetary Policy Rules (selected)
  - Fiscal policy rule (Home / RoMU / MU)
    - Public debt deviation from long run level φ_1, φ*_1: 0.5 / 0.5 / -
    - Public debt change φ_2, φ*_2: 25 / 25 / -
    - GDP growth φ_3, φ*_3: 25 / 25 / -
  - Common monetary policy rule (MU)
    - Lagged interest rate at t-1 ρ_i: -- / 0.85
    - Inflation ρ_Π: -- / 1.9
    - GDP growth ρ_GDP: -- / 0.4

### Figures and simulation scenarios (captions and focal experiments)
- Figures present dynamic responses (quarterly horizontal axis) to restructuring scenarios and sensitivity experiments:
  - 40 percent restructuring: fiscal variables and spread; real variables and inflation; asset positions (Figures 1–3).
  - 20 percent restructuring: fiscal variables and spread; real variables and inflation; asset positions (Figures 4–6).
  - Variants and sensitivity checks for 40 percent restructuring:
    - 40 percent restructuring and zero spread (Figure 7).
    - 40 percent restructuring with government bonds held by Home households (Figure 8).
    - 40 percent restructuring with government bonds held by Foreign households (Figure 9).
    - 40 percent restructuring and zero initial households’ foreign position (Figure 10).
    - 40 percent restructuring versus consolidation comparison (Figure 11).
  - Figure notes: horizontal axis denotes quarters; panels show outcomes such as public debt (% of annualized GDP), public expenditures (% of GDP), public deficit (% of GDP), spread (annualized p.p.), real GDP (% deviation from initial steady state), consumption and investment (% deviation), net exports, labor, consumer price inflation (annualized p.p. deviation), private debt (% of annualized GDP), bonds held by Home households and Foreign households, net foreign asset position, current account and interest payments (% of GDP).

*Content derived from the PDF chapter "_wp13269 - References" and its Appendix (model description, tables, and figure captions) as provided.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13269.pdf_
