## 6. Comparison of Predicted and Announced Fiscal Consolidation Assuming Fiscal Multiplier is 0.75, 2011–15

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### Introduction and purpose
- Develops a tractable inter-temporal model to elicit country preferences over balancing fiscal consolidation and reducing slack (output gap) for six European countries: Germany, France, Italy, Ireland, the Netherlands, and the U.K.
- Uses sustainability gaps (stock and flow measures) as the preferred indicator of fiscal health and compares model-predicted consolidation paths with near-term announced adjustment paths.
- Performs a sensitivity test raising the fiscal multiplier from 0.5 to 0.75 to assess implications for optimal consolidation.

### Estimating the fiscal sustainability gap (definitions and key numeric findings)
- Fiscal sustainability defined via the government inter-temporal budget constraint; sustainability gap in flow terms is the constant change to the primary balance (percent of GDP) that makes the present-value stock gap zero.
- Structural primary balance formulation incorporates output gap with elasticity parameter  as: p_t* = p_t -  O_t.
- Aging impact estimates sourced from EC 2009a and EC 2009b; initial structural primary balance and public debt from IMF staff projections as of March 2011.
- Selected country sustainability gap estimates for Year t = 2011:
  - Italy: 2½ percent of GDP
  - Ireland: 12¼ percent of GDP
- Cross-indicator comparisons:
  - Italy: high public debt but small sustainability gap due to structural primary surplus and pension reforms.
  - Netherlands: low debt but large sustainability gap because of weak structural balance and large aging impact (notably old age care).
  - France and Germany: comparable debt and similar sustainability gaps; France weaker structural balance but lower aging impact.
- Demographic projection caveat:
  - For Netherlands, Statistics Netherlands' projections imply aging pressures peak around 2040 and then decline, shaving off about one percent of GDP from the sustainability gap compared with EC projections.

### Model structure and intuition (objective, dynamics, policy rule)
- Authorities minimize a quadratic loss over output gaps and sustainability gaps:
  - Objective: sum over t of ( O_t^2 +  S_t^2) discounted by  with 1/(1+r) = .
  - Weights:  (output-gap weight) and  (sustainability-gap weight), with renormalization 1 =  +  and 0 ≤  ≤ 1.
- Output gap dynamics: O_t =  O_{t-1} -  f_{t-1} (autoregressive closure parameter  and fiscal multiplier ).
- Sustainability gap evolution approximated by S_{t} = (1 + g)/(1 + r) S_{t-1} + f_t (approximation consistent when r > g).
- Policy (fiscal consolidation) rule conjectured linear: f_t = A S_{t-1} + B O_{t-1}, with closed-form solutions for A and B derived in the text.
- Model captures the trade-off: tightening (f > 0) reduces S but worsens O; loosening does the opposite.

### Calibration and revealed preferences (exact parameter values and ordering)
- Calibrated parameters:
  - Discount rate r = 5 percent
  - Fiscal multiplier  = 0.5 (October 2010 WEO estimate for advanced European countries)
  - Output-gap autoregression parameter  = 0.5 (implying an output gap of 2 percent closes after six years absent fiscal action)
  - Growth rate g: geometric average using IMF staff projections to 2015 and EC 2009 beyond
  - Time preference  such that  = 1/(1 + r)
- Authorities’ preference weights (revealed by matching announced 2011 structural primary balance change):
  - Renormalized with 1 =  +  and 0 ≤  ≤ 1; higher  indicates greater sensitivity to output gaps (less hawkish).
  - Estimated ordering (values of  from highest to lowest): Germany highest , Netherlands, U.K., Ireland, France, Italy lowest .
  - Interpretation: authorities across countries place significantly greater weight on closing the output gap than on closing the sustainability gap; only Italy’s  approaches 0.5.

### Application: predicted vs announced consolidation paths (2011–15)
- Data basis: announced tightening = change in the structural primary balance in IMF staff projections as of March 2011.
- Broad result: predicted and announced paths broadly consistent for most countries in 2011–15 under baseline calibration ( = 0.5).
- Notable deviations and plausible explanations:
  - Netherlands: announced consolidation tends to decline faster than predicted; possible explanations include higher  or larger fiscal multiplier than calibrated.
  - U.K.: announced consolidation somewhat more ambitious than predicted; possible interpretation is lower persistence of output gaps (higher ) or country-specific multiplier assumptions.
  - Italy: only 2011–12 measures announced, so comparisons beyond two years limited.
- Predicted path properties:
  - Some front-loading of adjustment in all countries.
  - Full elimination of sustainability gaps occurs over a long horizon with smooth closure of output gaps driven by authorities’ preference for limiting output losses.

### Projected timing to sustainability and cost of delay (quantified ranges)
- Projected time to achieve sustainability (qualitative ordering from model):
  - Ireland: projected to achieve sustainability after about 20 years.
  - Netherlands: reaches sustainability more than a decade later than Ireland.
  - U.K.: achieves sustainability slightly later than Ireland.
  - Germany: prolonged period to achieve sustainability, about the same timing as Netherlands.
  - Italy and France: shortest projected periods to achieve sustainability.
- Additional fiscal effort (above the initial sustainability gap) required because of delay:
  - Ranges from 0.1 percent of GDP for Italy to one percent of GDP for Netherlands.
  - Less than ½ percent of GDP for all countries except Germany (¾ percent of GDP) and Netherlands (1 percent of GDP).
- Interpretation: modest costs of delay reflect that calibrated pace of consolidation keeps S on a strongly declining path; costs would be much higher under prolonged inaction followed by catch-up.

### Fiscal balances, debt projections, and aging effects (2011–60)
- Primary and overall balance evolution:
  - Strong initial improvement in primary balances in all countries due to consolidation, later partially offset as aging pressures increase.
  - Italy: primary balance improves again after 2040 as pension reforms' effects amplify; consequence is Italian public debt remains high over 2011–60 and still well above 100 percent of GDP by 2060 (but declines thereafter as pension reform effects continue).
  - Ireland: projected debt turns significantly negative by 2060 under baseline assumptions (allowing for a small primary deficit by 2060), but results sensitive to assumed discount rate and borrowing costs.
- General government debt:
  - Sustained fall in public debt projected over 2011–60 for most countries except Italy (where debt remains high through 2060 under back-loaded pension reform benefits).

### Sensitivity to fiscal multiplier (increase from 0.5 to 0.75) — key quantitative effects
- When fiscal multiplier is increased from 0.5 to 0.75 (all else equal), predicted optimal consolidation paths change markedly:
  - Predicted adjustment in 2011 is much smaller in all countries compared with announced plans.
  - For Germany, predicted policy with a 0.75 multiplier indicates an actual fiscal loosening for 2011.
- Mechanism:
  - Larger  increases the output-gap impact of a given fiscal tightening, and authorities’ revealed preference for smaller output gaps (higher ) reduces their willingness to tighten when  is larger.
  - Differentiation of policy functions with respect to  confirms raising the multiplier reduces predicted tightening for the observed  values.
- Policy implication: modest upward revisions to the fiscal multiplier could render announced 2011 consolidation plans substantially more ambitious than what national authorities’ revealed preferences would suggest; concerns about simultaneous tightenings and multiplier spillovers are therefore warranted.

### Main policy-relevant findings and implications (concise bullets)
- Model reproduces broadly the announced 2011 consolidation measures across six European countries under baseline calibration ( = 0.5).
- Authorities systematically place higher weight on closing output gaps than on closing sustainability gaps; this tilts optimal policy toward smoothing consolidation and delaying full elimination of sustainability gaps.
- Front-loading of consolidation is optimal but full sustainability is a long-horizon objective under quadratic preferences and calibrated parameters.
- Small increases in the fiscal multiplier materially reduce predicted optimal tightening in the near term and may imply that announced 2011 plans are excessively ambitious relative to authorities’ implied preferences.
- Costs of delay in implementing consolidation (measured as additional percent of GDP effort) are modest under the calibrated, continuous adjustment paths (0.1 percent to 1 percent of GDP across countries), but costs would be much larger if delay consisted of multi-year inaction followed by aggressive catch-up.

### Concluding remarks
- The tractable inter-temporal model provides a reasonable approximation to announced fiscal tightening plans and illuminates the trade-offs authorities face between sustaining fiscal positions and limiting output losses.
- Given wide error margins in long-run projections (notably demographics and aging pressures), a policy strategy emphasizing sustained, credible reduction of the sustainability gap over a long horizon is supported by the analysis.
- The model cautions that higher-than-expected fiscal multipliers would justify materially slower near-term consolidation given revealed preferences that favor limiting output gaps.

*Source: _wp11164 - 6. Comparison of Predicted and Announced Fiscal Consolidation Assuming Fiscal Multiplier is 0.75, 2011–15 (IMF staff calculations and text).*

### Bibliography ...........................................................................................................

### Bibliography

### Figures listing
- 1. Fiscal Indicators for Selected European Countries ................................................................8
- 2. Comparison of Predicted and Announced Fiscal Consolidation, 2011–15 .........................15
- 3. Predicted Fiscal Adjustment Paths and Associated Output Gaps, 2011–60 ........................17
- 4. Projected Paths for Closing Sustainability Gaps, and Costs of Delay .................................18
- 5. Projected Evolution of Fiscal Balances and Debt, 2011–60 ................................................20

*Source: _wp11164 - Bibliography.*

### 6. Comparison of Predicted and Announced Fiscal Consolidation Assuming Fiscal Multiplier

### _wp11164 - 6. Comparison of Predicted and Announced Fiscal Consolidation Assuming Fiscal Multiplier is 0.75, 2011–15

### Introduction and purpose
- Develops a tractable inter-temporal model to elicit country preferences over balancing fiscal consolidation and reducing slack (output gap) for six European countries: Germany, France, Italy, Ireland, the Netherlands, and the U.K.
- Uses sustainability gaps (stock and flow measures) as the preferred indicator of fiscal health and compares model-predicted consolidation paths with near-term announced adjustment paths.
- Performs a sensitivity test raising the fiscal multiplier from 0.5 to 0.75 to assess implications for optimal consolidation.

### Estimating the fiscal sustainability gap (key definitions and findings)
- Fiscal sustainability defined via the government inter-temporal budget constraint; sustainability gap in flow terms is the constant change to the primary balance (percent of GDP) that makes the present-value stock gap zero.
- Structural primary balance formulation incorporates output gap with elasticity parameter  as: p_t* = p_t -  O_t.
- Aging impact estimates sourced from EC 2009a and EC 2009b; initial structural primary balance and public debt from IMF staff projections as of March 2011.
- Selected country sustainability gap estimates for Year t = 2011:
  - Italy: 2½ percent of GDP (smallest sustainability gap)
  - Ireland: 12¼ percent of GDP (largest sustainability gap)
- Cross-indicator comparisons:
  - Italy: high public debt but small sustainability gap due to structural primary surplus and pension reforms.
  - Netherlands: low debt but large sustainability gap because of weak structural balance and large aging impact (notably old age care).
  - France and Germany: comparable debt and similar sustainability gaps; France weaker structural balance but lower aging impact.
- Demographic projection caveat:
  - For Netherlands, Statistics Netherlands' projections imply aging pressures peak around 2040 and then decline, shaving off about one percent of GDP from the sustainability gap compared with EC projections.

### Model structure and intuition
- Authorities minimize a quadratic loss over output gaps and sustainability gaps:
  - Objective: sum over t of ( O_t^2 +  S_t^2) discounted by  with 1/(1+r) = .
  - Weights:  (output-gap weight) and  (sustainability-gap weight), with renormalization 1 =  +  and 0 ≤  ≤ 1.
- Output gap dynamics: O_t =  O_{t-1} -  f_{t-1} (autoregressive closure parameter  and fiscal multiplier ).
- Sustainability gap evolution approximated by S_{t} = (1 + g)/(1 + r) S_{t-1} + f_t (approximation consistent when r > g).
- Policy (fiscal consolidation) rule conjectured linear: f_t = A S_{t-1} + B O_{t-1}, with closed-form solutions:
  - A = ( +  ^2) / (   +   ) (expressions as derived in text)
  - B = [ (1 + g)/(1 + r) + 1 ] * ( +  ^2) /   (see text for full algebraic forms)
- Model captures trade-off: tightening (f > 0) reduces S but worsens O; loosening does the opposite.

### Calibration and revealed preferences
- Calibrated parameters:
  - Discount rate r = 5 percent (from EC Sustainability Report 2009)
  - Fiscal multiplier  = 0.5 (October 2010 WEO estimate for advanced European countries)
  - Output-gap autoregression parameter  = 0.5 (implying an output gap of 2 percent closes after six years absent fiscal action)
  - Growth rate g: geometric average using IMF staff projections to 2015 and EC 2009 beyond
  - Time preference  such that  = 1/(1 + r)
- Authorities’ preference weights (revealed by matching announced 2011 structural primary balance change):
  - Renormalized with 1 =  +  and 0 ≤  ≤ 1; higher  indicates greater sensitivity to output gaps (less hawkish).
  - Estimated ordering (values of  from highest to lowest): Germany highest , Netherlands, U.K., Ireland, France, Italy lowest .
  - Interpretation: authorities across countries place significantly greater weight on closing the output gap than on closing the sustainability gap; only Italy’s  approaches 0.5.

### Application: predicted vs announced consolidation paths (2011–15) — key comparisons
- Data basis: announced tightening = change in the structural primary balance in IMF staff projections as of March 2011.
- General result: predicted and announced paths broadly consistent for most countries in 2011–15.
- Notable deviations:
  - Netherlands: announced consolidation tends to decline faster than predicted; possible explanations include higher  or larger fiscal multiplier than calibrated.
  - U.K.: announced consolidation somewhat more ambitious than predicted; possible interpretation is lower persistence of output gaps (higher ) or country-specific multiplier assumptions.
  - Italy: only 2011–12 measures announced, so comparisons beyond two years limited.
- Predicted path properties:
  - Some front-loading of adjustment in all countries.
  - Full elimination of sustainability gaps occurs over a long horizon with smooth closure of output gaps driven by authorities’ preference for limiting output losses.

### Projected timing to sustainability and cost of delay
- Projected time to achieve sustainability (qualitative results from model):
  - Ireland: projected to achieve sustainability after about 20 years (despite largest initial gap).
  - Netherlands: reaches sustainability more than a decade later than Ireland.
  - U.K.: achieves sustainability slightly later than Ireland.
  - Germany: prolonged period to achieve sustainability, about the same timing as Netherlands.
  - Italy and France: shortest projected periods to achieve sustainability.
- Additional fiscal effort (above the initial sustainability gap) required because of delay:
  - Ranges from 0.1 percent of GDP for Italy to one percent of GDP for Netherlands.
  - Less than ½ percent of GDP for all countries except Germany (¾ percent of GDP) and Netherlands (1 percent of GDP).
- Interpretation: moderate costs of delay reflect that calibrated pace of consolidation keeps S on a strongly declining path; costs would be much higher under prolonged inaction followed by catch-up.

### Fiscal balances, debt projections, and aging effects (2011–60)
- Primary and overall balance evolution:
  - Strong initial improvement in primary balances in all countries due to consolidation, later partially offset as aging pressures increase.
  - Italy: primary balance improves again after 2040 as pension reforms' effects amplify; consequence is Italian public debt remains high over 2011–60 and still well above 100 percent of GDP by 2060 (but declines thereafter as pension reform effects continue).
  - Ireland: projected debt turns significantly negative by 2060 under baseline assumptions (allowing for a small primary deficit by 2060), but results sensitive to assumed discount rate and borrowing costs.
- General government debt:
  - Sustained fall in public debt projected over 2011–60 for most countries except Italy (where debt remains high through 2060 under back-loaded pension reform benefits).

### Sensitivity to fiscal multiplier (increase from 0.5 to 0.75)
- When fiscal multiplier is increased from 0.5 to 0.75 (all else equal), predicted optimal consolidation paths change markedly:
  - Predicted adjustment in 2011 is much smaller in all countries compared with announced plans.
  - For Germany, predicted policy with a 0.75 multiplier indicates an actual fiscal loosening for 2011.
- Mechanism:
  - Larger  increases the output-gap impact of a given fiscal tightening, and authorities’ revealed preference for smaller output gaps (higher ) reduces their willingness to tighten when  is larger.
  - Differentiation of policy functions with respect to  confirms raising the multiplier reduces predicted tightening for the observed  values.
- Policy implication: modest upward revisions to the fiscal multiplier could render announced 2011 consolidation plans substantially more ambitious than what national authorities’ revealed preferences would suggest; concerns about simultaneous tightenings and multiplier spillovers are therefore warranted.

### Main policy-relevant findings and implications
- Model reproduces broadly the announced 2011 consolidation measures across six European countries under baseline calibration ( = 0.5).
- Authorities systematically place higher weight on closing output gaps than on closing sustainability gaps; this tilts optimal policy toward smoothing consolidation and delaying full elimination of sustainability gaps.
- Front-loading of consolidation is optimal but full sustainability is a long-horizon objective under quadratic preferences and calibrated parameters.
- Small increases in the fiscal multiplier materially reduce predicted optimal tightening in the near term and may imply that announced 2011 plans are excessively ambitious relative to authorities’ implied preferences.
- Costs of delay in implementing consolidation (measured as additional percent of GDP effort) are modest under the calibrated, continuous adjustment paths (0.1 percent to 1 percent of GDP across countries), but costs would be much larger if delay consisted of multi-year inaction followed by aggressive catch-up.

### Concluding remarks
- The tractable inter-temporal model provides a reasonable approximation to announced fiscal tightening plans and illuminates the trade-offs authorities face between sustaining fiscal positions and limiting output losses.
- Given wide error margins in long-run projections (notably demographics and aging pressures), a policy strategy emphasizing sustained, credible reduction of the sustainability gap over a long horizon is supported by the analysis.
- The model cautions that higher-than-expected fiscal multipliers would justify materially slower near-term consolidation given revealed preferences that favor limiting output gaps.

*Source: _wp11164 - 6. Comparison of Predicted and Announced Fiscal Consolidation Assuming Fiscal Multiplier is 0.75, 2011–15 (IMF staff calculations and text).*

### BIBLIOGRAPHY

### BIBLIOGRAPHY

### References
- Alesina, A., R. Perotti, J. Tavares, M. Obstfeld, and B. Eichengreen, 1998, “The Political Economy of Fiscal Adjustments,” Brookings Papers on Economic Activity, vol 1998, No 1 (1998), pp197-266.
- Chalk, N.A., 2002, “Structural Balances and All That: Which Indicators to Use in Assessing Fiscal Policy,” International Monetary Fund, Working Paper No. WP/02/101.
- Christiano, L., M. Eichenbaum, and S. Rebelo, 2010, “When is the Government Spending Multiplier Large?” unpublished paper, Northwestern University.
- Coenen, C., M. Mohr, and R. Straub, 2008, “Fiscal Consolidation in the Euro Area: Long-Run Benefits and Short-Run Costs,” European Central Bank, Working Paper Series, No 902, May 2008.
- Cournede, B., 2007, “The Political Economy of Delaying Fiscal Consolidation,” OECD Economics Department Working Papers, No 548, OECD Publishing.
- van Ewjik, C., N. Draper, H. ter Rele, and E. Westerhout, 2006, “Ageing and the Sustainability of Dutch Public Finances,” CPB Netherlands Bureau for Economic Analysis, The Hague.
- European Commission, 2009, “The 2009 Ageing Report: Economic and Budgetary Projections for the EU-27 member States (2008-2060),” European Commission, Directorate General for Economic and Financial Affairs, European Economy No. 2/2009.
- European Commission, 2009, “Sustainability Report 2009,” European Commission, Directorate General for Economic and Financial Affairs, European Economy No. 9/2009.
- International Monetary Fund, 2010, “Will it Hurt? The Macroeconomic Effects of Fiscal Consolidation,” Chapter 3 of World Economic Outlook: Recovery, Risk, and Rebalancing, October 2010, International Monetary Fund, Washington DC.
- Guichard, S., M. Kennedy, E. Wurzel, and C. Andre, 2007, “What Promotes Fiscal Consolidation: OECD Country Experiences,” OECD Economics Department Working Papers, No 533, OECD Publishing.

*BIBLIOGRAPHY.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11164.pdf_