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Debt limits and sovereign default in the euro area

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Presentation from ADEMU Fiscal Risk and Public Sector Balance Sheets Conference at the University of Bonn, July 6-7

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Debt limits and sovereign default in the euro area

  1. 1. Debt limits and sovereign default in the euro area Niccolò Battistini European Central Bank ADEMU Workshop Fiscal Risk and Public Sector Balance Sheets 6 July 2017 The views expressed in this paper are those of the author only and do not represent those of the European Central Bank.
  2. 2. Outline Outline Introduction The model Quantitative assessment Conclusions Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 1 / 20
  3. 3. Introduction Outline Introduction The model Quantitative assessment Conclusions Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 1 / 20
  4. 4. Introduction Exceptional fiscal challenges... 2000 2005 2010 2015 0 50 100 150 Debt-to-GDP 2000 2005 2010 2015 -10 -5 0 5 Deficit-to-GDP 2000 2005 2010 2015 0 2 4 6 10-year spread 2000 2005 2010 2015 -10 0 10 Real GDP 2000 2005 2010 2015 -10 0 10 Real consumption 2000 2005 2010 2015 0 5 10 15 Unemployment Notes: The charts show the cross-country median variables (together with the 25th and the 75th percentiles) for the distribution of euro area countries. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 2 / 20
  5. 5. Introduction Sustainability and welfare ' & $ % Fiscal policy dual objective Stabilisation Sustainability
  6. 6. Introduction Sustainability and welfare ' $ % Fiscal policy dual objective Stabilisation Sustainability ? ' $ % Fiscal space Leeway in pursuing stabilisation while ensuring sustainability
  7. 7. Introduction Sustainability and welfare ' $ % Fiscal policy dual objective Stabilisation Sustainability ? ' $ % Fiscal space Leeway in pursuing stabilisation while ensuring sustainability ' $ % 5PR IMF Commission Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 3 / 20
  8. 8. Introduction Questions on sustainability and welfare What is the effect of domestically held debt on default incentives and investor pricing decisions? Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 4 / 20
  9. 9. Introduction Questions on sustainability and welfare What is the effect of domestically held debt on default incentives and investor pricing decisions? What is the effect of supranational fiscal rules on default incentives and investor pricing decisions? Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 4 / 20
  10. 10. Introduction Questions on sustainability and welfare What is the effect of domestically held debt on default incentives and investor pricing decisions? What is the effect of supranational fiscal rules on default incentives and investor pricing decisions? What is the assessment of debt sustainability for euro area sovereigns? Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 4 / 20
  11. 11. Introduction Questions on sustainability and welfare What is the effect of domestically held debt on default incentives and investor pricing decisions? What is the effect of supranational fiscal rules on default incentives and investor pricing decisions? What is the assessment of debt sustainability for euro area sovereigns? Do euro area sovereigns face a trade-off between welfare and debt sustainability? Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 4 / 20
  12. 12. Introduction Some answers Higher domestic share of debt increases incentives to repay and expands debt limit. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 5 / 20
  13. 13. Introduction Some answers Higher domestic share of debt increases incentives to repay and expands debt limit. Credible supranational fiscal rules reduce the optimal debt level and foster market-based fiscal discipline. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 5 / 20
  14. 14. Introduction Some answers Higher domestic share of debt increases incentives to repay and expands debt limit. Credible supranational fiscal rules reduce the optimal debt level and foster market-based fiscal discipline. Average euro area country faces a low risk of default. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 5 / 20
  15. 15. Introduction Some answers Higher domestic share of debt increases incentives to repay and expands debt limit. Credible supranational fiscal rules reduce the optimal debt level and foster market-based fiscal discipline. Average euro area country faces a low risk of default. Average euro area country can reap both welfare and sustainability gains through fiscal consolidation. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 5 / 20
  16. 16. Introduction Main contributions Application of model-based framework with strategic sovereign default for debt sustainability analysis. Definition of probabilistic measure of debt limit at medium-term horizon. Analysis of debt sustainability in light of welfare considerations. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 6 / 20
  17. 17. Introduction Main contributions Application of model-based framework with strategic sovereign default for debt sustainability analysis. Definition of probabilistic measure of debt limit at medium-term horizon. Analysis of debt sustainability in light of welfare considerations. Novel features to reflect salient characteristics of euro area economies: Domestic debt without additional state variable. Supranational fiscal rules without perfect commitment technology. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 6 / 20
  18. 18. The model Outline Introduction The model Quantitative assessment Conclusions Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 7 / 20
  19. 19. The model Main features of the model Small open real economy with discrete time and infinite horizon Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  20. 20. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  21. 21. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  22. 22. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  23. 23. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  24. 24. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Sovereign debt markets: Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  25. 25. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  26. 26. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  27. 27. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Exclusion from markets upon default Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  28. 28. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Exclusion from markets upon default Fixed probability to re-access upon agreement over a recovery rate Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  29. 29. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Exclusion from markets upon default Fixed probability to re-access upon agreement over a recovery rate Debt matures next period with fixed probability Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  30. 30. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Supranational fiscal authorities → fiscal rules Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Exclusion from markets upon default Fixed probability to re-access upon agreement over a recovery rate Debt matures next period with fixed probability Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  31. 31. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Supranational fiscal authorities → fiscal rules Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Exclusion from markets upon default Fixed probability to re-access upon agreement over a recovery rate Debt matures next period with fixed probability No enforceability of fiscal rules and no commitment technology Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  32. 32. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Supranational fiscal authorities → fiscal rules Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Exclusion from markets upon default Fixed probability to re-access upon agreement over a recovery rate Debt matures next period with fixed probability No enforceability of fiscal rules and no commitment technology Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  33. 33. The model Main features of the model Small open real economy with discrete time and infinite horizon Agents and optimal decisions: Households → private consumption + labour supply Firms → labour demand Government → default + borrowing + fiscal policy (public consumption + taxes on private consumption and labour income) Pool of (foreign and domestic) lenders → relative shares of total debt + prices Supranational fiscal authorities → fiscal rules Sovereign debt markets: Incomplete markets (non-state-contingent debt only asset) No enforceability of debt contracts and no commitment technology Exclusion from markets upon default Fixed probability to re-access upon agreement over a recovery rate Debt matures next period with fixed probability No enforceability of fiscal rules and no commitment technology Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 8 / 20
  34. 34. The model Timing of events ‚ productivity sovereign debt markets at t − 1 t x A             d d d d d d repayment default x E A c tax policy e e e… stage 1 auction c stage 2 trades ¡ ¡ ¡ debt policy sovereign debt markets c public and private consumption x B T T x         θ A d d d dd‚1 − θ B t + 1 Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 9 / 20
  35. 35. The model Domestic debt and aggregate welfare (1/2) Two-stage interaction between government and pool of lenders: First stage (primary markets): Domestic and foreign lenders post their bids in auction for government bonds. Domestic and foreign lenders bargain over the share of total debt. Perfect competition ensures participation in auction and bargaining game. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 10 / 20
  36. 36. The model Domestic debt and aggregate welfare (1/2) Two-stage interaction between government and pool of lenders: First stage (primary markets): Domestic and foreign lenders post their bids in auction for government bonds. Domestic and foreign lenders bargain over the share of total debt. Perfect competition ensures participation in auction and bargaining game. Second stage (secondary markets): By the law of one price, bond prices must converge to a single price. Single price is the weighted average of domestic and foreign prices. Single price becomes the only relevant price for all agents. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 10 / 20
  37. 37. The model Domestic debt and aggregate welfare (1/2) Two-stage interaction between government and pool of lenders: First stage (primary markets): Domestic and foreign lenders post their bids in auction for government bonds. Domestic and foreign lenders bargain over the share of total debt. Perfect competition ensures participation in auction and bargaining game. Second stage (secondary markets): By the law of one price, bond prices must converge to a single price. Single price is the weighted average of domestic and foreign prices. Single price becomes the only relevant price for all agents. Given the price, the sovereign determines the total amount of debt. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 10 / 20
  38. 38. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  39. 39. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and default on higher debt ⇒ higher losses (returns) for private (public) sector. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  40. 40. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and default on higher debt ⇒ higher losses (returns) for private (public) sector. Main results: If marginal utility of private sector marginal utility of public sector ⇒ private cost of default public benefit of default Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  41. 41. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and default on higher debt ⇒ higher losses (returns) for private (public) sector. Main results: If marginal utility of private sector marginal utility of public sector ⇒ private cost of default public benefit of default ⇒ aggregate net benefit of default increases with total debt Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  42. 42. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and default on higher debt ⇒ higher losses (returns) for private (public) sector. Main results: If marginal utility of private sector marginal utility of public sector ⇒ private cost of default public benefit of default ⇒ aggregate net benefit of default increases with total debt ⇒ default incentives increase with total debt. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  43. 43. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and default on higher debt ⇒ higher losses (returns) for private (public) sector. Main results: If marginal utility of private sector marginal utility of public sector ⇒ private cost of default public benefit of default ⇒ aggregate net benefit of default increases with total debt ⇒ default incentives increase with total debt. If ↑ domestic share of total debt Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  44. 44. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and default on higher debt ⇒ higher losses (returns) for private (public) sector. Main results: If marginal utility of private sector marginal utility of public sector ⇒ private cost of default public benefit of default ⇒ aggregate net benefit of default increases with total debt ⇒ default incentives increase with total debt. If ↑ domestic share of total debt ⇒ ↓ default incentives Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  45. 45. The model Domestic debt and aggregate welfare (2/2) Notice that default induces private losses and public returns in terms of consumption; and default on higher debt ⇒ higher losses (returns) for private (public) sector. Main results: If marginal utility of private sector marginal utility of public sector ⇒ private cost of default public benefit of default ⇒ aggregate net benefit of default increases with total debt ⇒ default incentives increase with total debt. If ↑ domestic share of total debt ⇒ ↓ default incentives ⇒ ↑ borrowing opportunities (debt limit). Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 11 / 20
  46. 46. The model Fiscal rules and credibility (1/2) Possibility of self-fulfilling debt crisis via credibility channel: Supranational fiscal authorities impose fiscal rules: Fiscal rules resemble SGP deficit and debt criteria. No enforcement power by supranational fiscal authorities. No commitment technology by government. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 12 / 20
  47. 47. The model Fiscal rules and credibility (1/2) Possibility of self-fulfilling debt crisis via credibility channel: Supranational fiscal authorities impose fiscal rules: Fiscal rules resemble SGP deficit and debt criteria. No enforcement power by supranational fiscal authorities. No commitment technology by government. If two conditions hold, i.e. 1. sovereign is credit constrained (i.e. debt reduction is suboptimal to default) 2. sovereign deviates from applicable fiscal rule(s) ⇒ lenders perceive negative signal about sovereign credibility and trigger a self-fulfilling debt crisis. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 12 / 20
  48. 48. The model Fiscal rules and credibility (2/2) Main results: If credible fiscal rules are imposed 1. ⇒ ↑ borrowing opportunities ⇒ debt limit. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 13 / 20
  49. 49. The model Fiscal rules and credibility (2/2) Main results: If credible fiscal rules are imposed 1. ⇒ ↑ borrowing opportunities ⇒ debt limit. 2. ⇒ ↓ optimal debt level ⇒ ↑ market-based fiscal discipline. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 13 / 20
  50. 50. Quantitative assessment Outline Introduction The model Quantitative assessment Conclusions Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 14 / 20
  51. 51. Quantitative assessment Results Average euro area country Debt limit distribution Panel A. Debt limit – bw t+n(φn t ) (% of GDP) 1 year 2 years 5 years 2016 Optimal L M H L M H L M H Baseline 81.44 65.59 122.21 135.94 161.55 120.54 133.35 161.55 119.83 130.04 161.49 Deficit rule 81.44 65.25 122.21 135.94 161.55 120.54 133.35 161.55 119.83 130.04 161.49 Debt rule 81.44 64.78 122.21 135.94 161.55 120.54 133.35 161.55 119.83 130.04 161.49 Both rules 81.44 64.78 122.21 135.94 161.55 120.54 133.35 161.55 119.83 130.04 161.49 Panel B. Debt margin – fw t+n(φn t ) (% of GDP) 1 year 2 years 5 years Excess L M H L M H L M H Baseline 15.85 40.77 54.5 80.11 39.1 51.91 80.11 38.39 48.6 80.05 Deficit rule 16.19 40.77 54.5 80.11 39.1 51.91 80.11 38.39 48.6 80.05 Debt rule 16.66 40.77 54.5 80.11 39.1 51.91 80.11 38.39 48.6 80.05 Both rules 16.66 40.77 54.5 80.11 39.1 51.91 80.11 38.39 48.6 80.05 Panel C. Effects of adjustment from current debt level under both rules (%) 1 year 2 years 5 years Optimal L M H L M H L M H Sustainability gain 0.01 -0.40 -30.00 -100.00 -0.40 -30.00 -100.00 -0.40 -30.00 -100.00 Welfare gain 0.34 -1.54 -0.31 -0.06 -1.82 -0.44 -0.06 -2.00 -0.66 -0.06 Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 15 / 20
  52. 52. Quantitative assessment Results Greece Panel A. Debt limit – bw t+n(φn t ) (% of GDP) 1 year 2 years 5 years 2016 Optimal L M H L M H L M H Baseline 179.03 161.26 154.40 178.41 236.80 149.90 173.26 236.80 147.96 167.65 229.68 Deficit rule 179.03 161.26 159.93 183.43 240.81 155.42 178.28 240.81 153.90 172.66 232.76 Debt rule 179.03 161.26 158.42 181.42 240.81 153.41 176.97 240.81 150.98 170.66 233.69 Both rules 179.03 161.26 158.42 181.42 240.81 153.41 176.97 240.81 150.98 170.66 233.69 Panel B. Debt margin – fw t+n(φn t ) (% of GDP) 1 year 2 years 5 years Excess L M H L M H L M H Baseline 15.68 -22.54 1.47 59.86 -27.04 -3.68 59.86 -28.98 -9.29 52.74 Deficit rule 15.68 -17.01 6.49 63.87 -21.52 1.34 63.87 -23.04 -4.28 55.82 Debt rule 15.68 -18.52 4.48 63.87 -23.53 0.03 63.87 -25.96 -6.28 56.75 Both rules 15.68 -18.52 4.48 63.87 -23.53 0.03 63.87 -25.96 -6.28 56.75 Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 16 / 20
  53. 53. Quantitative assessment Debt limits and default risk in the euro area Calibration Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 17 / 20
  54. 54. Conclusions Outline Introduction The model Quantitative assessment Conclusions Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 18 / 20
  55. 55. Conclusions Conclusions Structural model-based framework with utility-based default to assess fiscal sustainability. Suitability for policy evaluation under a wide range of economic conditions. Inclusion of novel features (domestic debt and fiscal rules) ⇒ model economy appropriate for studying advanced economies such as euro area countries. At the current juncture, the average euro area country does not face a trade-off between welfare and sustainability gains ⇒ fiscal consolidation improves both welfare and sustainability. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 19 / 20
  56. 56. Conclusions THANK YOU! Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 20 / 20
  57. 57. Back-up slides Back-up slides Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 21 / 20
  58. 58. Back-up slides Households Main features Households’ utility maximization: max ct ,ht E0 ∞ t=0 βt    κ ct − h 1+ 1 ν t 1+ 1 ν 1−σ 1 − σ + (1 − κ) g1−σ t 1 − σ    s.t. budget constraint: (1 + τc t )ct = (1 − τh t )wtht + pE t + pH t ⇒ labor supply function: ht = (1 − τh t )wt 1 + τc t ν Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 22 / 20
  59. 59. Back-up slides Firms Main features Firms’ profit maximization: max ht pE t = yt − wtht s.t. production function: yt = atht. ⇒ labor demand function: wt = at at ∼ F(at|at−1), at ∈ A = {a1 , ..., aN } ⊂ R++, approximating a first-order autoregressive (AR) process: log at = (1 − ρa) log ¯a + ρa log at−1 + εa t , εa t ∼ N(0, σ2 a) Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 23 / 20
  60. 60. Back-up slides Government (1/2) Main features Government’s default policy: V(at, bt) = max dt ∈{0,1} {(1 − dt)VR (at, bt) + dtVD (at, bt)} Policy under repayment (if dt = 0): VR (at, bt) = max bt+1∈B {u(ct, ht, gt) + βEt[V(at+1, bt+1)]} s.t. budget constraint and targeting rules: gt = τc t ct + τh t wtht + qt[bt+1 − (1 − λ)bt] − [λ + (1 − λ)z]bt τc t = ¯τc + ψc a(at − ¯a) + ψc b(bt − ¯b) τh t = ¯τh + ψh a(at − ¯a) + ψh b(bt − ¯b) besides private sector’s conditions. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 24 / 20
  61. 61. Back-up slides Estimates of elasticities ψc a -2 -1 0 1 2 ψc b -0.2 0 0.2 0.4 0.6 0.8 1 BE DE EE IE GRES FR IT CY LU LVLT MT NLAT PT SI SK FI EA Consumption tax rate ψh a -2 -1 0 1 2 ψh b -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 BE DE EE IE GR ES FR IT CY LU LV LT MT NL AT PT SI SK FI EA Labor tax rate only ψa ψa and ψb Notes: Markers for each point in the scatter plot refer to the statistical significance of the parameters as identified in the legend, on the basis of two-tail tests at the 10% significance level. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 25 / 20
  62. 62. Back-up slides Government (2/2) Main features Policy under default (if dt = 1): VD (at, bt) = u(ct, ht, gt) + βEt[(θV(at+1, (1 − δ)(1 + r)bt) + (1 − θ)VD (at+1, (1 + r)bt)] s.t. budget constraint and targeting rules: gt = τc t ct + τh t wtht τc t = ¯τc + ψc a(at − ¯a) τh t = ¯τh + ψh a(at − ¯a) besides private sector’s conditions. aD t = at − ω(at), where ω(at) = min{at, max{0, ω1at + ω2a2 t }}. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 26 / 20
  63. 63. Back-up slides Lenders (1/2) Main features Lenders Two-stage interaction between government and pool of lenders: First stage (primary markets – binding auction): max bH t+1∈(0,1) {(Et pH t+1)1−ζ (Et pF t+1)ζ } s.t. Et pH t+1 ≥ 0 Et pF t+1 ≥ 0 Et pH t+1 = Et M(at+1|at ) dt+1qD t+1+ (1 − dt+1)[λ + (1 − λ)(z + qt+1)]}} bH t+1bt+1 − qH t bH t+1bt+1 Et pF t+1 = Et (1 + r)−1 dt+1qD t+1+ (1 − dt+1)[λ + (1 − λ)(z + qt+1)]}} (1 − bH t+1)bt+1 − qF t (1 − bH t+1)bt+1 ⇒ bH t+1 = 1 − ζ. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 27 / 20
  64. 64. Back-up slides Lenders (2/2) Main features Lenders Second stage (secondary markets – law of one price): qt = bH t+1qH t + (1 − bH t+1)qF t where qH t = Et M(at+1|at) dt+1qD t+1+ (1 − dt+1)[λ + (1 − λ)(z + qt+1)]}} qF t = Et (1 + r)−1 dt+1qD t+1 +(1 − dt+1)[λ + (1 − λ)(z + qt+1)]}} Lenders’ perfect competition ensures bidding and participation in bargaining game. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 28 / 20
  65. 65. Back-up slides Fiscal rules and credibility (1/3) Main features Fiscal rules Deficit rule st ≥ ˆsyt, where bt − bt+1 = τc t ct + τh t wtht − gt primary surplus − (1 − λ)zbt interest payments headline surplus (st ) + (1 − qt)[(1 − λ)bt − bt+1] deficit-debt adjustments Debt rule: bt+1 ≤ bt − bt −ˆbyt ˆT . Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 29 / 20
  66. 66. Back-up slides Fiscal rules and credibility (2/3) Main features Fiscal rules Simultaneous game b/w borrower and lenders at every t: R D B 0, V+(at, bt) −r ˆMt+1∆t, ¯VD(at, bt) N 0, V−(at, bt) 0, ¯VD(at, bt) Value of debt contract: U(at, bt) = V+ (at , bt ) if ¯VD (at ) ≤ V− (at , bt ) (a) ¯VD (at ) if V+ (at , bt ) ¯VD (at ) (b) V+ (at , bt ) if V− (at , bt ) ¯VD (at ) ≤ V+ (at , bt ) and kt = 1 (c) ¯VD (at ) if V− (at , bt ) ¯VD (at ) ≤ V+ (at , bt ) and kt = 0, (d) (1) where V−(at, bt) is s.t. bt+1 ≤ (1 − λ)bt. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 30 / 20
  67. 67. Back-up slides Fiscal rules and credibility (3/3) Main features Fiscal rules Notes: These charts are produced with the benchmark calibration except for four parameters, namely β = 0.85, z = 0.1, λ = 1 Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 31 / 20
  68. 68. Back-up slides Calibration in the average euro area country parameter value target σ 2 standard macroeconomic literature ¯a 1 normalization ¯h 0.33 standard macroeconomic literature ˆs -0.03 EU fiscal governance framework ˆb 0.60 EU fiscal governance framework ˆT 20 EU fiscal governance framework ρa 0.38 TFP AR coefficient σa 0.0163 TFP shock standard deviation β 0.96 private sector’s average credit rate r 0.03 1-year Euribor θ 0.33 expected duration of economic adjustment programme ω1 -0.80 1% TFP loss at lower bound ω2 0.88 maximum TFP loss at upper bound ¯τc 0.27 tax rate on total consumption ¯τh 0.33 tax rate on total labor income ¯g/¯c 0.36 public-to-private consumption ratio λ 0.17 average maturity of government liabilities z 0.06 government implicit tax rate δ 0.65 haircut on net present value of sovereign liabilities ζ 0.55 share of total debt held by domestic residents ¯r 1.00 highest observed interest rate ψc b 0.13 elasticity of consumption tax rate to debt ψc a 0.19 elasticity of consumption tax rate to TFP ψh b 0.09 elasticity of labor tax rate to debt ψh a -0.13 elasticity of labor tax rate to TFP Debt limits all Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 32 / 20
  69. 69. Back-up slides Bond prices and default probability bt+1/¯y 0 1 2 3 0.2 0.4 0.6 0.8 1 1.2 qt low at mean at high at bt+1/¯y 0 1 2 3 % 0 10 20 30 40 50 rt bt+1/¯y 0 1 2 3 0 0.2 0.4 0.6 0.8 1 Et(dt+1) bt+1/¯y 0 1 2 3 % 0 0.2 0.4 0.6 0.8 1 rH∗ t − rF∗ t Notes: The variables are shown at the steady-state level for at and two standard deviations on each side of ¯a. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 33 / 20
  70. 70. Back-up slides Sensitivity analysis (1/3) Determinants of rightward shift in debt limit distribution: Riskiness and uncertainty: ↑ σ or ↓ σa ⇒ ↑ risk aversion or ↓ magnitude of shocks. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 34 / 20
  71. 71. Back-up slides Sensitivity analysis (1/3) Determinants of rightward shift in debt limit distribution: Riskiness and uncertainty: ↑ σ or ↓ σa ⇒ ↑ risk aversion or ↓ magnitude of shocks. Cost of default: ↓ θ or ↑ ω1 ⇒ ↑ cost of default. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 34 / 20
  72. 72. Back-up slides Sensitivity analysis (1/3) Determinants of rightward shift in debt limit distribution: Riskiness and uncertainty: ↑ σ or ↓ σa ⇒ ↑ risk aversion or ↓ magnitude of shocks. Cost of default: ↓ θ or ↑ ω1 ⇒ ↑ cost of default. Aggregate welfare: Steady-state tax rates: ↑ ¯τc or ¯τh ⇒ ↑ transfer of resources from the private to the public sector Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 34 / 20
  73. 73. Back-up slides Sensitivity analysis (1/3) Determinants of rightward shift in debt limit distribution: Riskiness and uncertainty: ↑ σ or ↓ σa ⇒ ↑ risk aversion or ↓ magnitude of shocks. Cost of default: ↓ θ or ↑ ω1 ⇒ ↑ cost of default. Aggregate welfare: Steady-state tax rates: ↑ ¯τc or ¯τh ⇒ ↑ transfer of resources from the private to the public sector Public-to-private consumption ratio: ↓ ¯g/¯c ⇒ ↑ relative weight κ of private consumption Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 34 / 20
  74. 74. Back-up slides Sensitivity analysis (1/3) Determinants of rightward shift in debt limit distribution: Riskiness and uncertainty: ↑ σ or ↓ σa ⇒ ↑ risk aversion or ↓ magnitude of shocks. Cost of default: ↓ θ or ↑ ω1 ⇒ ↑ cost of default. Aggregate welfare: Steady-state tax rates: ↑ ¯τc or ¯τh ⇒ ↑ transfer of resources from the private to the public sector Public-to-private consumption ratio: ↓ ¯g/¯c ⇒ ↑ relative weight κ of private consumption Foreign lenders’ bargaining power: ↓ ζ ⇒ ↑ exposure of domestic private sector to sovereign default Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 34 / 20
  75. 75. Back-up slides Sensitivity analysis (1/3) Determinants of rightward shift in debt limit distribution: Riskiness and uncertainty: ↑ σ or ↓ σa ⇒ ↑ risk aversion or ↓ magnitude of shocks. Cost of default: ↓ θ or ↑ ω1 ⇒ ↑ cost of default. Aggregate welfare: Steady-state tax rates: ↑ ¯τc or ¯τh ⇒ ↑ transfer of resources from the private to the public sector Public-to-private consumption ratio: ↓ ¯g/¯c ⇒ ↑ relative weight κ of private consumption Foreign lenders’ bargaining power: ↓ ζ ⇒ ↑ exposure of domestic private sector to sovereign default Debt elasticities of tax rates: ↓ ψl b for l ∈ {c, h} ⇒ ↑ τl t for bt ¯b ⇒ ↑ transfer of resources from the private to the public sector Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 34 / 20
  76. 76. Back-up slides Sensitivity analysis (1/3) Determinants of rightward shift in debt limit distribution: Riskiness and uncertainty: ↑ σ or ↓ σa ⇒ ↑ risk aversion or ↓ magnitude of shocks. Cost of default: ↓ θ or ↑ ω1 ⇒ ↑ cost of default. Aggregate welfare: Steady-state tax rates: ↑ ¯τc or ¯τh ⇒ ↑ transfer of resources from the private to the public sector Public-to-private consumption ratio: ↓ ¯g/¯c ⇒ ↑ relative weight κ of private consumption Foreign lenders’ bargaining power: ↓ ζ ⇒ ↑ exposure of domestic private sector to sovereign default Debt elasticities of tax rates: ↓ ψl b for l ∈ {c, h} ⇒ ↑ τl t for bt ¯b ⇒ ↑ transfer of resources from the private to the public sector TFP elasticities of tax rates: ↓ ψl a for l ∈ {c, h} ⇒ ↑ τl t for at ¯a ⇒ ↑ transfer of resources from the private to the public sector ⇒ ↓ marginal utility of public (vs) private consumption. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 34 / 20
  77. 77. Back-up slides Sensitivity analysis (2/3) Domestic debt bt+1/¯y 0 1 2 3 0 0.5 1 σ ∈ [1, 3] low mean high bt+1/¯y 0 1 2 3 0 0.5 1 ρa ∈ [0.18, 0.57] bt+1/¯y 0 1 2 3 0 0.5 1 σa ∈ [0.007034, 0.0255] bt+1/¯y 0 1 2 3 0 0.5 1 β ∈ [0.95, 0.97] bt+1/¯y 0 1 2 3 0 0.5 1 r ∈ [0.02, 0.04] bt+1/¯y 0 1 2 3 0 0.5 1 θ ∈ [0.22, 0.44] bt+1/¯y 0 1 2 3 0 0.5 1 ω1 ∈ [−0.89, −0.72] bt+1/¯y 0 1 2 3 0 0.5 1 ¯τc ∈ [0.21, 0.34] bt+1/¯y 0 1 2 3 0 0.5 1 ¯τh ∈ [0.23, 0.43] Notes: The default probabilities are shown at the steady-state level for at . The charts show debt limit distributions for the benchmark calibration (mean) and those implied by a calibration where only the analyzed parameter is changed over the grid of Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 35 / 20
  78. 78. Back-up slides Sensitivity analysis (3/3) Domestic debt bt+1/¯y 0 1 2 3 0 0.5 1 ¯g/¯c ∈ [0.29, 0.42] low mean high bt+1/¯y 0 1 2 3 0 0.5 1 z ∈ [0.0514, 0.0711] bt+1/¯y 0 1 2 3 0 0.5 1 δ ∈ [0.43, 0.87] bt+1/¯y 0 1 2 3 0 0.5 1 ζ ∈ [0.4, 0.69] bt+1/¯y 0 1 2 3 0 0.5 1 ψc b ∈ [−0.16, 0.42] bt+1/¯y 0 1 2 3 0 0.5 1 ψc a ∈ [−0.51, 0.89] bt+1/¯y 0 1 2 3 0 0.5 1 ψh b ∈ [−0.0181, 0.21] bt+1/¯y 0 1 2 3 0 0.5 1 ψh a ∈ [−0.6, 0.33] bt+1/¯y 0 1 2 3 0 0.5 1 λ ∈ [0.14, 0.2] Notes: The default probabilities are shown at the steady-state level for at . The charts show debt limit distributions for the benchmark calibration (mean) and those implied by a calibration where only the analyzed parameter is changed over the grid of Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 36 / 20
  79. 79. Back-up slides Debt limit, debt margin and welfare Table bt+1/¯y 0 0.2 0.4 0.6 0.8 0 0.5 1 Et(dt+n|low at) bt+1/¯y 0 0.2 0.4 0.6 0.8 0 0.5 1 Et(dt+n|high at) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.5 1 Et(dt+n|¯a) bt+1/¯y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.5 1 φn t n=1 n=2 n=5 Notes: The variables are shown at the steady-state level for at and two standard deviations on each side of ¯a. Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 37 / 20
  80. 80. Back-up slides Debt limit, debt margin and welfare Table Probability-φ debt limit bt+1(φ): bt+1(φ) = sup{bt+1 : Pr[VR (at+1, bt+1) VD (at+1)] ≤ φ} Probability-φ debt margin ft(φ): ft(φ) = bt+1(φ) − bt+1 Probability φn t of default in any period from t + 1 to t + n without defaulting in any previous period: φn t ≡ n s=1 Et(dt+s|dt+s = 0) = n s=1 Et(dt+s) s−1 r=0 [1 − Et(dt+r )] Welfare gain (under fiscal rules): W(bt+1) = U(at, bt, bt+1) U(at, bt, bt) 1 1−σ − 1 Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 38 / 20
  81. 81. Back-up slides Debt limit, debt margin and welfare Table Panel A. Debt limit – bw t+n(φn t ) (% of GDP) 1 year 2 years 5 years 2015 Optimal L M H L M H L M H Both rules 176.94 161.26 158.42 181.42 240.81 153.41 176.97 240.81 150.98 170.66 233.69 Panel B. Debt margin – fw t+n(φn t ) (% of GDP) 1 year 2 years 5 years Excess L M H L M H L M H Both rules 15.68 -18.52 4.48 63.87 -23.53 0.03 63.87 -25.96 -6.28 56.75 Battistini (ECB) Debt limits and sovereign default in the euro area 6 July 2017 39 / 20

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