## 1. Effect of a One-time Permanent Fiscal Tightening

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### Introduction and policy context
- Key policy challenge: design multi-year fiscal adjustment plans that balance short-term output losses and medium-term debt dynamics.
- Trade-offs:
  - Large or front-loaded fiscal adjustment → larger short-term output loss and possibly temporary increase in headline debt ratio, but quicker improvement in underlying debt dynamics.
  - Smaller or gradual adjustment → smaller immediate output hit but potential for a longer (if shallower) recession and persistently higher debt levels.
- Markets focus on both output and fiscal/debt dynamics, complicating pace decisions.
- Framework purpose:
  - Assess dynamic output and debt outcomes under various fiscal adjustment scenarios.
  - Integrate cumulative fiscal multipliers over time, allow for varying multipliers (as a function of output gap), hysteresis effects, and endogenous financing costs of public debt.
  - Flexible for country-specific calibration and sensitivity analysis.
- High-level implications (stylized and country examples):
  - For economies with high initial deficits and high public debt, front-loaded adjustment tends to allow an earlier turnaround in the debt-to-GDP path and persistently lower debt in the medium term, at the cost of larger short-term output loss and possibly a temporary rise in the debt-to-GDP ratio.
  - Front-loaded adjustment may be required where urgent restoration of fiscal sustainability and tight financing constraints exist.
  - Gradual consolidation is preferable if hysteresis effects are important, or where debt levels are lower and/or large-scale official financing at low cost is available.
  - If extreme front-loading would cause major output collapse while unsustainable debt remains, debt restructuring could restore sustainability relatively quickly with less output loss than extreme consolidation.

### Literature synthesis relevant to the framework
- Three strands: size of short-term fiscal multiplier, persistence/long-term impact of fiscal adjustment, effect on public debt and financing costs.
- Short-term multipliers can exceed unity when:
  - The economy is in recession.
  - Monetary policy is constrained by the zero lower bound.
  - External demand is weak and trading partners consolidate simultaneously.
- Multiplier estimates vary with model specification, monetary response assumptions, development stage, exchange rate regime, and openness.
- Long-run effects debated: arguments for long-run neutrality vs. hysteresis and productive public capital channels.
- Market reaction: consolidation measures that depress growth and fail to convince markets can raise borrowing costs.
- Slow, protracted adjustment can fail to restore confidence and may defer private investment via debt overhang.

### Framework structure: methodology and key assumptions
- Incorporated, calibratable elements:
  - Short- and long-term fiscal multiplier effects.
  - Multiplier variation with output gap (state dependence).
  - Hysteresis effects under large negative output gaps.
  - Endogenous interest rates responding to debt and growth.
- Fiscal stance measurement:
  - Change measured by identified structural fiscal adjustment measures or change in structural primary balance.
  - Example divergence: over 2009-11, Ireland took fiscal measures totaling almost 10 percent of GDP, while the structural primary balance improved by only 6 percent of GDP.
  - A multiplier estimated against the structural balance can be more than 1½ times the size of one estimated against measures in such periods.
- Multiplier persistence and peak:
  - Peak multiplier = maximum output effect from a permanent fiscal adjustment in a given year.
  - Baseline assumption of long-run fiscal neutrality: effect of a permanent fiscal stance change on the level of output eventually fades to zero.
  - Hysteresis effects are introduced in extended model versions.
- Assumed baseline time profile of multiplier effects:
  - Multiplier effects last for seven years.
  - 80 percent of the peak fiscal multiplier effect realized in the first year of adjustment.
  - 100 percent (peak effect) realized in the second year.
  - Gradual decline to zero over the remaining years.
  - Sensitivity tested with five-year and ten-year persistence; results are very similar.
  - Linear convergence paths assumed for simplicity; template allows flexible evolution paths.

### Multiplier effects under long-run fiscal neutrality
- Year-by-year GDP effects sequence (assumed): 0.8 percent in the current year, reaching 1.0 percent in the second year, and then 0.8 percent, 0.6 percent, 0.4 percent, 0.2 percent, and finally reverting to zero level effect in subsequent years.
- Fiscally adjusted potential GDP, Ỹ, constructed by aggregating past and present changes in structural primary balance (going back to t-6 under seven year persistence) multiplied by year-specific fiscal multipliers (fm s’s).
- If fiscal policy dominates deviations of output from potential, the multiplier-adjusted path estimates “fiscally adjusted potential GDP”; actual GDP may deviate due to other factors (credit or asset booms/busts, commodity price cycles).

### Data inputs and practical implementation
- Required inputs:
  - Real GDP and potential GDP (potential GDP should be estimated without the effect of fiscal adjustment).
  - Change in fiscal stance (percent of potential GDP) — use planned structural measures or change in structural primary balance (percent of potential GDP), computed via standard elasticity approach and adjusted for one-offs.
- Potential GDP estimation approaches: filtering approach or production-side approach.
- Note on growth impact of debt overhang:
  - Using Cecchetti, Mohanty, and Zampolli (2011): once public debt reaches 85 percent of GDP, an additional 10 percentage point increase in the ratio of public debt to GDP is associated with a 17–18 basis point reduction in subsequent average annual growth.
  - Authors attempted to include this effect; it had only a marginal impact and is not reported in main results.

### Taking debt dynamics into account
- Debt dynamics and financing costs integrated alongside output effects.
- Baseline assumption: constant interest rate; extension allows endogenous interest rate.
- Structural debt condition emphasis:
  - Headline debt-to-GDP can be misleading because GDP includes a cyclical component.
  - Preferred metric: ratio of debt to potential GDP (structural debt position), with caveats.
  - Risk: measuring debt relative to potential GDP can understate problems if potential GDP is overestimated; same bias affects structural fiscal balances.
  - Recommendation: present structural debt and deficit ratios under a wide range of potential output estimates.
- Debt calculation assumption: revenues change in proportion to real output so revenue-to-output ratio remains constant, implying all consolidation comes from spending cuts (adjustable for country specifics).

### Stylized example of an advanced economy with high multipliers
- Basic setup and key numeric assumptions (Box 1):
  - Initial (2009) debt-to-GDP ratio: 100 percent.
  - The 2009 structural primary deficit: 5 percent of potential GDP.
  - Cumulative fiscal adjustment: 10 percent of potential GDP.
    - Front-loaded adjustment improves structural primary balance by 6 percent, 3 percent and 1 percent in 2010, 2011 and 2012, respectively.
    - Even adjustment spreads 2 percent a year from 2010 to 2014.
  - Potential GDP: flat at 100 over 2009-12, then grows 2 percent a year from 2013.
  - Non-fiscal output gap: -4 percent in 2009, closing autonomously over three years.
  - Fiscal multiplier (basic setup): 1.5 with persistence of 7 years; GDP impact of fiscal tightening in year t takes full effect in year t+1 and gradually reverses thereafter.
  - Nominal interest rate assumed constant at 5 percent; revenue-to-GDP, GDP deflator and nominal exchange rate constant.
- Findings with fiscal multiplier effects only:
  - With a large multiplier, front-loaded adjustment yields a deeper initial recession but a quicker restoration of growth; total output loss is the same under front-loaded and even-phased adjustment scenarios (technical note: output loss slightly larger under gradual adjustment because potential GDP assumed to start growing from 2013, making a cumulative adjustment of 10 percent over 2010-14 slightly larger in level terms than one over 2010-12, but difference negligible).
  - Welfare and political tradeoffs: U-shaped output path could yield higher social welfare under a quadratic welfare function; political credibility and reform fatigue may favor a V-shaped (front-loaded) approach.
  - Debt-path outcomes:
    - Medium-term debt path markedly better under front-loaded adjustment, especially when measured against potential GDP.
    - Short-run counterproductive effect: front-loaded consolidation can cause debt-to-GDP to rise initially if GDP decline outweighs debt reduction; this is temporary because consolidation’s effect on debt is permanent while effect on GDP is mostly temporary.
    - When debt is measured against potential GDP, the initial counterproductive effect under frontloading disappears and debt dynamics are uniformly better under frontloading.
    - Under even adjustment, debt ratio rises more slowly initially but peaks much later and remains persistently higher than under frontloading.

### Fiscal multiplier varying with output gap (advanced economy)
- Alternative assumption:
  - Multiplier is 0.5 with positive and small negative output gaps.
  - Multiplier increases linearly up to a maximum of 2 for an output gap of -5 percent of potential GDP or wider.
  - Example: multiplier of 1.25 when output gap is -2.5 percent of potential GDP.
- Sensitivity and results:
  - Varying multiplier does not materially change policy implications: front-loaded adjustment results in larger short-term output loss but quicker turnaround in output and debt paths.
  - With parameters used, total output loss is somewhat larger under even-adjustment because prolonged consolidation keeps the output gap (and multiplier) relatively large for longer.
  - Debt dynamics better under front-loaded adjustment aside from headline debt-GDP effect in first two years.
  - Result on total output loss is sensitive to multiplier sizes used.

### Incorporating hysteresis effects
- Rationale: in deep recessions hysteresis effects (permanent losses to potential output) are relevant.
- Stylized example assumptions:
  - Permanent hysteresis takes effect if output gap larger than a threshold.
  - Hysteresis coefficient: 0.15 (based on DeLong and Summers (2012) range 0 to 0.2; value of 0.1 suggested for the US).
  - Interpretation: if output is well below potential in any year, then 15 percent of the output gap is lost permanently (reducing potential output going forward).
- Additional assumptions for phase-of-adjustment experiments:
  - Permanent hysteresis effect takes effect if previous year’s negative output gap is wider than 4 percent.
  - Intuition: expect large hysteresis under front-loaded adjustment and little or none under gradual adjustment.
- Findings:
  - With large total fiscal adjustment needs, hysteresis effects could be sizeable even under gradual adjustment, though smaller than under front-loading.
  - Under front-loaded adjustment, the economy is quickly pushed into the “hysteresis zone”.
  - Under gradual adjustment, the economy may eventually enter the hysteresis zone if adjustment continues, causing permanent losses.
  - Eliminating hysteresis would require a very long and gradual adjustment path (adjustment must start only when private gap closes and would take more than a decade to complete the 10 percentage points total adjustment).
    - Practical concern: maintaining credibility of such a long, gradual adjustment may be difficult (not modeled).
  - Trade-offs:
    - Lower short-term output losses under gradual adjustment must be balanced against worse debt dynamics.
    - With hysteresis, both short-term and longer-term output losses are larger under front-loaded scenario.
    - Larger hysteresis coefficients worsen output losses under front-loaded relative to gradual adjustment.
    - Policy implication: countries without financing constraints and debt sustainability problems should prefer gradual adjustment; those with financing and debt sustainability concerns may need front-loaded adjustment.
    - If front-loading is too onerous and back-loading leaves debt too high, debt restructuring may be required.

### Incorporating endogenous interest rates
- Interest-rate schedule assumptions (illustrative):
  - Interest rate is 3 percent up to a debt-to-GDP ratio of 90 percent.
  - Interest rate increases linearly with debt up to a maximum of 12 percent for a debt-to-GDP ratio of 200 percent and above.
  - Additional risk premium when real GDP growth turns negative: rising linearly from zero at zero growth to 200 basis points for growth of -2 percent or worse.
  - Government debt turns over with average maturity of 5 years.
- Implications and findings:
  - Large debt overhang feeds higher financing costs; front-loaded adjustment is needed to restore sustainability in highly-indebted economies.
  - Larger debt overhang from gradual adjustment leads to higher financing cost, increasing the debt stock—a vicious cycle that can outweigh fiscal adjustment efforts.
  - Under even-adjustment scenario, debt-to-GDP is not on a declining trend in the longer term.
  - Delayed adjustment (for three years until private-sector output gap closes) suggests debt would be explosive in this scenario.
  - Caveat: very large-scale low-cost official financing or reserve-currency privileges can short-circuit the feedback loop, though large debt overhang may still inhibit growth later.
  - Note: framework does not model explicit loss of market access; in practice some countries may lose access before interest rate reaches 12 percent.

### Stylized example of an emerging market (Box 2)
- Key numeric assumptions:
  - Initial (2009) debt-to-GDP ratio: 60 percent.
  - 2009 structural primary deficit: 4 percent of potential GDP.
  - Potential GDP: flat at 100 over 2009-12; grows 4percent a year from 2013.
  - Non-fiscal output gap: -4 percent in 2009, closes autonomously over three years.
  - Fiscal multiplier: varying 0.5 to 1 for an output gap of 0 to -5 percent with persistence of 7 years; baseline illustrative multiplier: 0.5.
  - Hysteresis coefficient: 0.1.
  - Nominal interest rate schedule:
    - 5 percent for debt up to 60 percent of GDP.
    - For debt between 60 and 120 percent of GDP, nominal interest rates increase linearly to 20 percent.
    - Remains at 20 percent for debt levels higher than 120 percent of GDP.
    - Additional risk premium rising to 4 percent for growth between 0 to -2 percent.
  - Average debt maturity: five years.
  - Revenue-to-GDP, GDP deflator and nominal exchange rate assumed constant.
- Fiscal adjustment scenarios:
  - Total cumulative fiscal adjustment: 8 percent of potential GDP.
    - Front-loaded: structural primary balance improves by 5 percent in 2010, 2 percent in 2011, and 1 percent in 2012.
    - Even: 1.6 percent a year from 2010 to 2014.
- Findings and robustness:
  - Output and debt dynamics and policy implications similar to advanced-economy example when calibrated for emerging market features.
  - Using HP100 and smaller multipliers produces smoother potential output trends and results not very different from baseline.
  - Assuming multipliers significantly exceeding unity (e.g., fixed 1.25 or varying up to 2) can imply implausible private-sector responses in some post-crisis consolidations.
  - Assessment of multiplier size depends critically on assumed potential output path.

### Overall findings and policy implications
- With high fiscal multipliers:
  - Front-loaded adjustment tends to allow an earlier turnaround in the debt-to-GDP path and persistently lower debt levels in the medium term, at the cost of larger short-term output loss and a temporary rise in the debt-to-GDP ratio in the near term.
  - For countries facing urgent need to restore fiscal sustainability and tight financing constraints, front-loaded adjustment may be appropriate or unavoidable.
- With hysteresis effects and for countries without urgent financing constraints:
  - Gradual fiscal consolidation is likely more desirable because it reduces permanent output losses.
  - Gradual consolidation is more feasible for countries with lower debt levels and/or availability of large-scale official financing at lower costs.
- Caveat on multipliers:
  - The analysis assumes the same size and functional form of multipliers under different adjustment scenarios; in practice, multipliers may differ by scenario.

*Source: IMF working paper content (content unit _wp13182).*

### 1. Effect of a One-time Permanent Fiscal Tightening ...............................................................9

### 1. Effect of a One-time Permanent Fiscal Tightening

### Introduction and policy context
- Key policy challenge: design multi-year fiscal adjustment plans that balance short-term output losses and medium-term debt dynamics.
- Trade-off highlighted:
  - Large or front-loaded fiscal adjustment → larger short-term output loss and possibly temporary increase in headline debt ratio, but quicker improvement in underlying debt dynamics.
  - Smaller or gradual adjustment → smaller immediate output hit but potential for a longer (if shallower) recession and persistently higher debt levels.
- Markets focus on both output and fiscal/debt dynamics, making the appropriate pace of adjustment difficult to gauge.
- Framework purpose:
  - Assess dynamic output and debt outcomes under various fiscal adjustment scenarios.
  - Integrate cumulative fiscal multipliers over time, allow for varying multipliers (as a function of output gap), hysteresis effects, and endogenous financing costs of public debt.
  - Be flexible for country-specific calibration and sensitivity analysis.
- High-level policy implications (from stylized and country examples):
  - For economies with high initial deficits and high public debt, front-loaded adjustment tends to allow an earlier turnaround in the debt-to-GDP path and persistently lower debt in the medium term, at the cost of a larger short-term output loss and possibly a temporary rise in debt-to-GDP in the near term.
  - Front-loaded adjustment may be appropriate or unavoidable where there is an urgent need to restore fiscal sustainability and tight financing constraints.
  - Gradual fiscal consolidation is more desirable if hysteresis effects are important, or where debt levels are lower and/or large-scale official financing at low cost is available.
  - When extreme front-loading would cause a major output collapse and unsustainable debt remains, debt restructuring could restore sustainability relatively quickly with less output loss than extreme consolidation.

### Literature synthesis relevant to the framework
- Three strands emphasized: size of short-term fiscal multiplier, persistence/long-term impact of fiscal adjustment, and effect of fiscal adjustment on public debt and financing costs.
- Short-term multipliers can be significantly higher than unity when:
  - The economy is in recession.
  - There is lack of offsetting monetary policy support due to the zero lower bound.
  - External demand is weak and trading partners consolidate simultaneously.
- Multiplier estimates vary with model specification, monetary response assumptions, development stage, exchange rate regime, and openness.
- Long-run effects are debated:
  - Some argue for neutrality of government spending in the long run.
  - Others highlight hysteresis (permanent reduction in potential output) and channels through productive public capital.
- Market reaction to consolidation can raise borrowing costs if measures depress growth and fail to convince markets of sustainability.
- A slow, protracted adjustment can fail to restore confidence and may defer private investment via debt overhang.

### Framework structure: methodology and key assumptions
- Elements incorporated and calibratable to country conditions:
  - Short- and long-term fiscal multiplier effects.
  - Potential variation in multiplier with output gap (state dependence).
  - Potential hysteresis effects under large negative output gaps.
  - Endogenous interest rates responding to debt and growth.
- Definition and measurement of fiscal stance:
  - Change in fiscal stance can be measured by identified structural fiscal adjustment measures or by change in structural primary balance.
  - These two measures can differ substantially in recessions: example given—over 2009-11, Ireland took fiscal measures totaling almost 10 percent of GDP, while the structural primary balance improved by only 6 percent of GDP.
  - A multiplier estimated against the structural balance can be more than 1½ times the size of one estimated against measures for such a period.
- Multiplier persistence and peak definition:
  - Peak multiplier = maximum output effect from a permanent fiscal adjustment undertaken in a particular year.
  - Baseline assumption of long-run fiscal neutrality: effect of a permanent fiscal stance change on the level of output eventually fades to zero (no long-run effect on potential GDP), implying a permanent tightening is initially contractionary but contributes positively to growth in outer years under neutrality.
  - Hysteresis effects (permanent loss of potential output) are introduced in extended versions of the model.
- Assumed time profile of multiplier effects (baseline):
  - Multiplier effects last for seven years.
  - 80 percent of the peak fiscal multiplier effect realized in the first year of adjustment.
  - 100 percent (peak effect) realized in the second year.
  - Gradual decline to zero over the remaining years.
  - Sensitivity tested with five-year and ten-year persistence; results are very similar.
  - Linear convergence paths assumed for simplicity; template allows flexible evolution paths.

### Data inputs and practical implementation
- Required inputs:
  - Real GDP and potential GDP (potential GDP should be estimated without the effect of fiscal adjustment to avoid double counting).
  - Change in fiscal stance (in percent of potential GDP) — template allows use of planned structural measures or change in structural primary balance (percent of potential GDP), computed via standard elasticity approach and adjusted for one-offs.
- Potential GDP estimation approaches: filtering approach or production-side approach.
- Note on growth impact of debt overhang:
  - Using Cecchetti, Mohanty, and Zampolli (2011) finding: once public debt reaches 85 percent of GDP, an additional 10 percentage point increase in the ratio of public debt to GDP is associated with a 17–18 basis point reduction in subsequent average annual growth.
  - The authors tried to include this effect; it has only a marginal impact on their results and hence is not reported in main results.

### Limitations and cautions
- Fiscal multipliers are simplified "rule of thumb" representations of complex processes; policy conclusions should be drawn with caution.
- The framework is mechanical and does not explicitly model monetary policy response (unlike DSGE models); the monetary policy effect is reflected implicitly via fiscal multiplier assumptions (which can vary with output gap).
- Some parameters require judgment; sensitivity analysis is essential.

*IMF working paper section: 1. Effect of a One-time Permanent Fiscal Tightening*

### 0.8 percent in the current year, reaching 1.0 percent in the second year, and then 0.8 percent, 0.6 percent,

### _wp13182 - 0.8 percent in the current year, reaching 1.0 percent in the second year, and then 0.8 percent, 0.6 percent,

### Multiplier effects under long-run fiscal neutrality
- Sequence of assumed year-by-year GDP effects: 0.8 percent in the current year, reaching 1.0 percent in the second year, and then 0.8 percent, 0.6 percent, 0.4 percent, 0.2 percent, and finally reverting to zero level effect in subsequent years.
- Fiscally adjusted potential GDP, Ỹ, is constructed by aggregating past and present changes in structural primary balance that are still influencing output (going back to t-6 under the assumption of seven year persistence) multiplied by year-specific fiscal multipliers (fm s’s).
- Under the assumption that fiscal policy is the dominant factor driving deviations of output from potential, the multiplier-adjusted path provides an estimate of “fiscally adjusted potential GDP”; actual GDP may deviate because of other factors (credit or asset booms or busts, commodity price cycles).
- Illustration details:
  - Figure 1: Effect of a One-time Permanent Fiscal Tightening (illustrates fiscal multiplier effect under long-run fiscal neutrality).
  - Figure 2 (left chart): Aggregation of single-year multiplier effects under a five-year fiscal adjustment to determine implied real output path.
  - Figure 2 (right chart): Stylized example of a country starting at potential, implementing a year of fiscal expansion followed by two years of consolidation.

### Taking debt dynamics into account
- Debt dynamics and financing costs are integrated into the framework alongside output effects.
- Baseline assumption: constant interest rate; extension allows endogenous interest rate (see ¶29).
- Structural debt condition emphasis:
  - Headline debt-to-GDP ratio can be misleading because GDP includes a cyclical component.
  - Proposed preferred metric: ratio of debt to potential GDP (structural debt position), with caveats.
  - Risk: measuring debt as a ratio to potential GDP can understate debt problems if potential GDP is overestimated; the same overestimation bias affects structural fiscal balances even more (affecting both numerator and denominator).
  - Recommendation: present structural debt and deficit ratios under a wide range of potential output estimates.
- Assumption for debt calculations: revenues change in proportion to real output so the revenue-to-output ratio remains constant, implying all fiscal consolidation comes from spending cuts (this can be adjusted for country-specific composition).

### Stylized example of an advanced economy with high multipliers
- Purpose: illustrate output and debt dynamics under different multi-year fiscal adjustments for a highly-indebted advanced economy; highlight tradeoffs between short-term output pain and long-term debt gains.
- Methodology: start with a simple setup with a fixed fiscal multiplier; sequentially extend framework to include potential hysteresis effects and endogenous interest rates to show each factor’s role.
- Basic setup findings (with fiscal multiplier effects only):
  - With a large fiscal multiplier, front-loaded fiscal adjustment yields a deeper initial recession but a quicker restoration of growth; total output loss is the same under front-loaded and even-phased adjustment scenarios (technical note: output loss is slightly larger under the gradual adjustment scenario because potential GDP is assumed to start growing from 2013, making a cumulative adjustment of 10 percent (of potential GDP) over 2010-14 slightly larger in level terms than a 10 percent adjustment over 2010-12, but the difference is negligible).
  - Welfare and political tradeoffs:
    - U-shaped output path could yield higher social welfare under a quadratic welfare function.
    - Political concerns about credibility and reform fatigue could favor a V-shaped (front-loaded) approach.
  - Other considerations: resilience of the financial sector and availability of financing to run temporarily higher deficits under back-loading.
- Debt-path outcomes:
  - Medium-term debt path is markedly better under front-loaded adjustment, especially when measured against potential GDP.
  - Short-run “counterproductive” effect: front-loaded consolidation can cause debt-to-GDP to rise initially if the GDP decline outweighs debt reduction; this effect is temporary because consolidation’s effect on debt is permanent while its effect on GDP is mostly temporary.
  - When debt is measured against potential GDP (to remove cyclical denominator effects), the initial counterproductive effect under frontloading disappears and debt dynamics are uniformly better under frontloading.
  - Comparative dynamics: under even adjustment, the debt ratio rises more slowly initially but peaks much later and remains persistently higher than under frontloading.

*Source: IMF working paper content provided in the supplied PDF excerpt.*

### Box 1. A Stylized Example: Basic Assumptions for an Advanced Economy

### Box 1. A Stylized Example: Basic Assumptions for an Advanced Economy

### (i) Fiscal adjustment scenarios
- Initial (2009) debt-to-GDP ratio is assumed to be 100 percent.
- The 2009 structural primary deficit is 5 percent of potential GDP.
- A cumulative fiscal adjustment of 10 percent of potential GDP is implemented under two alternative scenarios (with a “no adjustment” scenario also shown for comparison):
  - Front-loaded adjustment improves the structural primary balance by 6 percent, 3 percent and 1 percent in 2010, 2011 and 2012, respectively.
  - Even adjustment has the same adjustment spread over five years, 2 percent a year from 2010 to 2014.

### (ii) Potential GDP and non-fiscal output gap
- Potential GDP is assumed to be flat at 100 over 2009-12 and then to grow 2 percent a year from 2013.
- A non-fiscal driven output gap is assumed to be -4 percent in 2009, and to close autonomously over the next three years.
  - Purpose: illustrate private-sector driven contractions (e.g., asset and credit busts) and allow experiments on timing of fiscal consolidation.

### (iv) Fiscal multiplier baseline assumption (basic setup)
- A fiscal multiplier of 1.5 is assumed with persistence of 7 years, with the GDP impact of fiscal tightening in year t taking the full effect in year t+1 and gradually reversing in subsequent years.
- The paper uses a very large multiplier to illustrate difficult circumstances; it does not argue for a specific size of the multiplier.
- For illustration and simplicity, nominal interest rate is assumed to be a constant at 5 percent, and revenue-to-GDP, GDP deflator and nominal exchange rate are assumed to remain constant.

### (ii, alternative) Fiscal multiplier varying with output gap
- Literature suggests fiscal multipliers can be larger when the economy is in recession.
- Assumed varying multiplier:
  - Multiplier is 0.5 with positive output gaps and small negative output gaps.
  - Multiplier increases linearly up to a maximum of 2 for an output gap of -5 percent of potential GDP or wider.
  - Example: multiplier of 1.25 when the output gap is -2.5 percent of potential GDP.
- Sensitivity and results:
  - Application of a varying multiplier does not appear to have major effects on policy implications.
  - Front-loaded adjustment results in larger short-term output loss but a quicker turn around in both the output and the debt paths.
  - With the parameters used, total output loss is somewhat larger under the even-adjustment scenario, as an extended period of fiscal consolidation keeps the output gap and hence the fiscal multiplier relatively large for a longer period.
  - Front-loaded adjustment results in a very large output gap (and fiscal multiplier) initially, but which narrows more quickly.
  - The debt dynamics are better under the front-loaded adjustment, aside from the headline debt-GDP effect in first two years.
  - Note: The result on total output loss is sensitive to the effective size of the multipliers used.

### (iii) Incorporating hysteresis effects
- Rationale: many countries undertaking fiscal consolidation are in deep recessions; hysteresis effects (permanent losses to potential output) are relevant.
- Assumptions in the stylized example:
  - Permanent hysteresis would be in effect if the output gap is larger than a threshold.
  - Hysteresis coefficient is 0.15.
    - Parameterization based on DeLong and Summers (2012), which suggest the hysteresis coefficient could range between 0 to 0.2, with a value of 0.1 suggested for the US.
  - Interpretation: if output is well below potential in any year, then 15 percent of the output gap is lost permanently (potential output going forward is reduced by this amount).
- Implementation detail:
  - The real output with both the fiscal multiplier and the hysteresis effect in year t is calculated as described in the Box (equation notation retained in source).
- Additional assumptions added to the basic setup for phase-of-adjustment experiments:
  - A permanent hysteresis effect takes effect if previous year’s negative output gap is wider than 4 percent.
  - Intuition: expect large hysteresis effect under front-loaded adjustment and no (or little) hysteresis effect under gradual adjustment.
- Findings:
  - With large total fiscal adjustment needs, hysteresis effects could be sizeable even under gradual fiscal adjustment, though smaller than under the front-loaded scenario.
  - Under front-loaded adjustment, the economy is quickly pushed into the “hysteresis zone”.
  - Under gradual adjustment, the economy does not get into the “hysteresis zone” immediately, but continued adjustment can eventually push the economy into it and cause permanent losses.
  - To completely eliminate the hysteresis effect, a very long and gradual adjustment path is needed: adjustment must start only when the private gap closes and it would take more than a decade to complete the 10 percentage points of total adjustment.
    - Practical concern: maintaining credibility of such a long and gradual fiscal adjustment may be difficult (not modeled).
  - Trade-offs:
    - Lower output losses under gradual adjustment need to be balanced against worse debt dynamics.
    - With hysteresis effects, both short-term and longer-term output losses are larger under the front-loaded scenario.
    - The larger the hysteresis coefficient assumed, the worse the output losses are under the front-loaded scenario relative to the gradual adjustment one.
    - Policy implication: countries without financing constraints and debt sustainability problems should find gradual adjustment more desirable (unless political economy considerations argue otherwise).
    - For countries with financing and debt sustainability concerns, priority may need to be debt reduction, tilting the balance towards the front-loaded scenario.
    - If front-loaded adjustment leads to too onerous an output path, and back-loaded path leads to too-high debt, the remaining option would be debt restructuring.

### (iv) Incorporating endogenous interest rates
- Interest-rate schedule assumptions (illustrative, reflecting some European experiences):
  - Interest rate is 3 percent up to a debt-to-GDP ratio of 90 percent.
  - Interest rate then increases linearly with debt up to a maximum of 12 percent for a debt-to-GDP ratio of 200 percent and above.
  - Additional risk premium when real GDP growth turns negative: rising linearly from zero at zero growth to 200 basis points for growth of -2 percent or worse.
  - Government debt turns over with an average maturity of 5 years.
- Implications and findings:
  - As a large debt overhang feeds into higher financing cost, front-loaded adjustment is needed to restore debt sustainability in highly-indebted economies.
  - A larger debt overhang from gradual adjustment leads to higher financing cost, which results in an even larger debt stock—a vicious cycle that outweighs fiscal adjustment efforts.
  - Consequently, despite fiscal adjustment efforts, the debt-to-GDP ratio is not on a declining trend in the longer term under the even-adjustment scenario.
  - Delayed adjustment (for three years until the private sector output gap closes) suggests debt would be explosive in this scenario.
  - Caveat: if very large-scale low-cost official financing is available, or if the country enjoys a reserve currency status that allows it to retain access to favorable financing rates at high debt levels, this would short-circuit the debt-financing cost feedback loop. However, the large debt overhang may still inhibit growth down the road.
  - Note: In practice, some countries may have already lost market access before interest rate reaches 12 percent; the framework does not explicitly model loss of market access.

### A stylized example of an emerging market
- Parameterization changes for emerging market characteristics:
  - Emerging markets tend to have smaller fiscal multipliers, more flexible labor markets (especially in the informal sector), lower debt tolerance, and steeper interest rate schedules.
- Outcome summary:
  - Output and debt dynamics, as well as policy implications, are very similar to the advanced-economy stylized example when calibrated for emerging market features.
  - Short-term/long-term tradeoffs and policy implications are largely the same.

### Overall findings and policy implications
- With high fiscal multipliers:
  - Front-loaded adjustment tends to allow an earlier turnaround in the debt-to-GDP path and persistently lower debt levels in the medium term, at the cost of a larger short-term output loss and a temporary rise in the debt-to-GDP ratio in the near term.
  - Therefore, for countries facing an urgent need to restore fiscal sustainability and tight financing constraints, front-loaded adjustment may be appropriate or unavoidable.
- With hysteresis effects and for countries without urgent financing constraints:
  - Gradual fiscal consolidation is likely more desirable because it reduces permanent output losses.
  - Gradual consolidation is more feasible for countries with lower debt levels and/or availability of large-scale official financing at lower costs.
- Caveat on multipliers:
  - The analysis so far assumes the same size and functional form of multipliers under different adjustment scenarios; in practice, multipliers may differ by scenario.

*Source: Box 1, “A Stylized Example: Basic Assumptions for an Advanced Economy,” (content unit _wp13182).*

### Box 2. A Stylized Example of an Emerging Market

### Box 2. A Stylized Example of an Emerging Market

### Key assumptions
- Initial (2009) debt-to-GDP ratio: 60 percent.
- 2009 structural primary deficit: 4 percent of potential GDP.
- Potential GDP path:
  - Flat at 100 over 2009-12.
  - Grows 4percent a year from 2013.
- Non-fiscal driven output gap: -4 percent in 2009, closes autonomously over the next three years.
- Fiscal multiplier:
  - Varying multiplier of 0.5 to 1 for an output gap of 0 to -5 percent with persistence of 7 years.
- Hysteresis coefficient: 0.1.
- Nominal interest rate schedule:
  - 5 percent for debt up to 60 percent of GDP.
  - For debt between 60 and 120 percent of GDP, nominal interest rates increase linearly to 20 percent.
  - Remains at 20 percent for debt levels higher than 120 percent of GDP.
  - Additional risk premium rising to 4 percent for growth between 0 to -2 percent.
- Average debt maturity: five years.
- Revenue-to-GDP, GDP deflator and nominal exchange rate: assumed to remain constant.
- Composition (revenue vs. expenditure) of the adjustment: assumed the same under all scenarios in this stylized example.

### Fiscal adjustment scenarios
- Total cumulative fiscal adjustment: 8 percent of potential GDP (implemented under alternative phasing scenarios and a "no adjustment" scenario for comparison).
- Front-loaded adjustment:
  - Structural primary balance improves by 5 percent in 2010, 2 percent in 2011, and 1 percent in 2012.
- Even adjustment:
  - Same total 8 percent spread evenly at 1.6 percent a year from 2010 to 2014.

### Output, multipliers, and persistence
- Baseline illustrative multipliers for emerging market examples: 0.5.
- Persistence of multiplier effects: 7 years.
- HP100 used in sensitivity analysis to estimate smoother potential output trends where appropriate.
- Alternative multipliers and scenarios explored:
  - Smaller multipliers case: GRC=0.75, PRT=0.5, others=0.25 (used with HP100).
  - Higher fixed multiplier test for Greece: 1.25 (and robustness checks with varying multipliers in the range 0.5–2).
  - Illustration suggesting a multiplier around 1.75 would be needed if potential output is 10 percentage points higher for Greece (illustrative exercise).

### Interest-rate and debt dynamics assumptions (stylized)
- Debt cost feedback captured via the nominal interest rate schedule above.
- Average debt maturity of five years implies turnover and interest-rate sensitivity consistent with the schedule.

### Findings from the stylized emerging market example and broader analysis
- Fiscal multipliers are an important influence on growth declines in some cases, but private sector-driven contractionary effects can be more significant in many advanced and emerging market examples.
- In the stylized emerging market setup:
  - The baseline multiplier of 0.5 is used to illustrate effects on actual and potential GDP (2009 real GDP = 100 normalization).
- Robustness and sensitivity results:
  - Using HP100 and smaller multipliers produces smoother potential output trends and results not very different from baseline, supporting use of HP100 in some cases.
  - Assuming multipliers significantly exceeding unity (e.g., fixed 1.25 or varying up to 2) can imply implausible private-sector positive boosts to match observed output, casting doubt on very large multipliers in post-crisis consolidations.
  - The assessment of multiplier size depends critically on the assumed potential output path; higher assumed potential output can require larger multipliers to “fit” observed low output, but may overstate peak-to-trough declines.

### Policy implications and recommendations
- The framework helps compare output and debt outcomes under different fiscal adjustment phasings and calibrations, allowing choice of an appropriate consolidation path adjusted to country-specific parameters (multipliers, hysteresis, endogenous interest rates).
- For highly-indebted economies undertaking large multi-year fiscal consolidation:
  - Large multipliers do not automatically argue against front-loaded adjustment; tradeoffs between output and debt dynamics must be balanced.
  - Hysteresis effects tend to favor more gradual adjustment.
  - Endogenous interest-rate responses tend to favor more front-loaded consolidation in high debt situations.
  - Beyond the short term, more gradual adjustment does not necessarily lead to a lower debt ratio measured in structural terms (e.g., debt-to-potential GDP) compared with a front-loaded path.
- If tradeoffs are unbearable (very large short-term output losses versus unsustainable debt):
  - Consider debt restructuring.
  - Consider large-scale access to less costly official financing or the privileges of a reserve-currency issuer to break the debt–financing-cost feedback loop and provide space for adjustment.
- Tailor conclusions to individual countries via careful calibration of the framework to country-specific circumstances.

*Source: Box 2. A Stylized Example of an Emerging Market (extracted content).*

### References

### References

### Fiscal multipliers and fiscal policy
- Alesina, A. and S. Ardagna. 2010. “Large Changes in Fiscal Policy: Taxes vs Spending.” Tax Policy and the Economy.
- Auerbach, Alan, and Yuriy Gorodnichenko, 2012a, “Measuring the Output Responses to Fiscal Policy,” American Economic Journal – Economic Policy 4(2012): pp. 1–27.
- Auerbach, Alan, and Yuriy Gorodnichenko, 2012b, “Fiscal Multipliers in Recession and Expansion,” in Fiscal Policy after the Financial Crisis, Alberto Alesina and Francesco Giavazzi, eds., University of Chicago Press, 2012.
- Baum, Anja, Marcos Poplawski-Ribeiro, and Anke Weber, 2012, “Fiscal Multipliers and the State of the Economy,” IMF Working Paper, No. 12/286.
- Blanchard, Olivier, and Daniel Leigh, 2013, “Growth Forecast Errors and Fiscal Multipliers”, IMF Working Paper, No. 13/1.
- Delong, Bradford, and Lawrence Summers, 2012 , “Fiscal Policy in a Depressed Economy”, Brookings, 20 March.
- Eichengreen, Barry, Kevin H O’Rourke, 2012, “Gauging the Multiplier: Lessons from History,” Vox EU (23 October 2012).
- Hall, Robert E., 2009, “By How Much Does GDP Rise If the Government Buys More Output?” Brookings Papers on Economic Activity, Fall 2009, pp. 183-249.
- Ilzetzki, Ethan, Enrique G. Mendoza and Carlos A. Végh, 2011, “How Big (Small?) are Fiscal Multipliers?”, IMF Working Paper, No. WP/11/52.
- Michael Woodford, 2011. "Simple Analytics of the Government Expenditure Multiplier," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(1), pages 1-35, January.
- Corsetti, Giancarlo, 2012, “Has austerity gone too far?”, VoxEU.org, April 2012.
- Cotteralli, Carlo, and Laura Jaramillo, 2012, “Walking Hand in hand: Fiscal Policy and Growth in Advanced Economies”, IMF Working Paper No. WP/12/137.
- International Monetary Fund, 2010, “Will It Hurt? Macroeconomic Effects of Fiscal Consolidation”, World Economic Outlook 2010 (Washington, DC: IMF).
- International Monetary Fund, 2012, “Balancing Fiscal Policy Risks”, Finscal Monitor 2012 April (Washington DC: IMF).

### Public debt, fiscal consolidation, and debt sustainability
- Agénor, Pierre-Richard, and Devrim Yilmaz. 2011. “The Simple Dynamics of Public Debt with Productive Public Goods.” Working Paper.
- Batini, Nicoletta, Giovanni Callegari, and Giovanni Melina, 2012, “Successful Asuterity in the United States, Europe and Japan,” IMF Working Paper, No. 12/190.
- Padoan, Pier Carlo, Urban Sila, and Paul van den Noord, 2012, “Avoiding Debt Traps: Fiscal consolidation, financial backstops and structural reforms”, OECD Journal: Economic Studies.
- Reinhart, Carmen, Vincent Reinhart, and Kenneth Rogoff, 2012, “Debt Overhangs: Past and Present”, Working Paper.

### Long-run growth theory, public capital, and endogenous growth
- Barro, R. (1990), "Government Spending in a Simple Model of Economic Growth", Journal of Political Economy, 98, S103-S125.
- Cass, D. (1965), "Optimum Growth in an Aggregative Model of Capital Accumulation", Review of Economic Studies, 32: 233-240.
- Koopmans, T. (1965), "On the Concept of Optimal Economic Growth", Potificiae Academiae Scientiarum Scripta Varia, 28: 225-300.
- Romer, P. (1986), "Increasing Returns and Long-Run Growth", Journal of Political Economy, 94: 1002-1037.
- Solow, R. (1956), "A Contribution to the Theory of Economic Growth", Quarterly Journal of Economics, 70: 65-94.
- Yakita, Akira. 2008. “Sustainability of Public Debt, Public Capital Formation, and Endogenous Growth in an Overlapping Generations Setting.” Journal of Public Economics 92:897914.

### Historical comparisons, lessons, and methods
- Almunia, Miguel, Agustin Benetrix, Barry Eichengreen, Kevin O’Rourke and Gisela Rua (2010), “From Great Depression to Great Credit Crisis: Similarities, Differences and Lessons,” Economic Policy 25.
- Alesina, Alberto, and Roberto Perotti, 1996, “Fiscal Adjustments in OECD Countries: Composition and Macroeconomic Effects”, NBER working paper series.
- Congressional Budget Office, 2004, “A Summary of Alternative Methods for Estimating Potential GDP”, Background Paper.

*Source: _wp13182 - References*

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