## _wp14107

## Source details

**Canonical URL:** [_wp14107](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14107.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14107.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14107.pdf.json)

---

### I. Introduction: purpose and core findings
- Context: Growing interest in structural fiscal policy in Europe; EU Fiscal Compact requires structural targets as part of fiscal rules.
- Core problem: Real-time estimates of actual and potential growth are subject to large revisions that often continue beyond the budget year.
- Paper objectives:
  - How large were errors in measuring the output gap?
  - What were the implications of revisions in potential GDP for the measurement of fiscal effort?
  - Can an indicative rule of thumb be observed between revisions in actual and potential growth?
- Summary of key answers:
  - Output gap errors averaged about 1½ percent of potential GDP in absolute terms between budget assumptions and first post-budget evaluation; during non-crisis years averaged almost 1 percent of potential GDP.
  - Mean absolute revision in CAPB over the budget horizon: almost 1¾ percent of GDP.
  - Peak crisis years 2008–2009: mean absolute CAPB revision about 3 percent of GDP.
  - On average about 30 percent of the revision in actual growth reflected revisions in potential growth (β≈0.3).

### II. Data, horizon definitions, and decomposition methodology
- Data:
  - Source: European Commission’s semi-annual (fall and spring) economic forecasts covering 2003–12.
  - Potential output estimates: Production Function method (EC estimates underpinning cyclically adjusted balances in general government forecast tables).
  - Additional data: general government revenues, expenditures, GDP deflator from EC Economic Forecasts.
- Budget evaluation horizon:
  - Defined as difference between estimate at budget preparation (t-1, fall vintage for budget year t) and first budget evaluation (t+1, spring vintage).
- CAPB decomposition:
  - Cross-vintage change in CAPB ratio to GDP decomposed into contributions from: nominal government spending (dGN), GDP deflator (dP), output (dY), potential output (dY*), interest payments (dInt), and residual cross-term (dRes).
  - Output contribution accounts for denominator effect and endogenous impact on revenues.
- CAPB defined as a share of GDP of year t as of vintage v via components: real revenue (function of output), nominal government spending, nominal interest spending, GDP deflator, levels of real output and potential output, and revenue/expenditure elasticities (EC methodology in Girouard and Andre (2005)).

### III. Magnitude and distribution of revisions (EU-27, 2003–2012 / 2004–2012)
- CAPB and output gap revisions:
  - Mean absolute revision in CAPB over the budget horizon: almost 1¾ percent of GDP.
  - Peak crisis years 2008–2009: mean absolute CAPB revision about 3 percent of GDP.
  - Non-crisis years 2005–07 and 2010–11: mean absolute CAPB revision 1½ percent of GDP.
  - Median across countries: crisis period mean absolute revision 2.3 percent of GDP; non-crisis period median 1 percent of GDP; overall median absolute revision 1¼ percent of GDP.
- Output gap revisions:
  - Mean absolute value of output gap revisions over 2003–12 for the budget horizon: 1.3 percent of GDP.
  - Crisis years (2008–2009) output gap revisions up to some 3 percent of GDP; non-crisis years average 0.8 percent of GDP.
  - Median absolute revision in output gap across countries: 0.9 percent of GDP (2.5 percent during crisis; 0.6 percent during non-crisis).
  - Sign changes in output gap occurred in about one fifth of cases; excluding initial gaps less than 1 percent in absolute terms, sign changes drop to less than 7 percent of observations.
- Longer horizon:
  - Mean absolute error from budget preparation vintage to final vintage three years later was 2.6 percent of GDP (compared with 1.3 percent over the budget horizon).
- Long-term (3.5 year) horizon:
  - Output gap revisions nearly 2 ½ –3 ½ percent of potential GDP.
  - Output and potential output growth revisions at the 3.5 year horizon range between 1–3 ½ percent.

### IV. Illustrative country example (Spain) — role of potential output revisions
- Revisions (percent change or percentage points):
  - 2007: Output 2.2; Potential Output 1.2; Output Gap 1.1
  - 2008: Output -1.8; Potential Output -4.5; Output Gap 2.9
  - 2009: Output -7.3; Potential Output -4.4; Output Gap -3.0
  - 2010: Output 1.8; Potential Output 1.5; Output Gap 0.3
- Interpretation: Potential output revisions played a large role in output gap revisions for Spain during the crisis.

### V. Decomposition results: contribution of potential output to CAPB revisions
- Finding: Revisions in potential GDP were a large contributing factor to CAPB changes.
- Years highlighted:
  - 2009: Potential GDP accounted for the largest share of CAPB revisions in the EU, on average, more than changes in primary spending (dGN).
  - 2010: Potential GDP continued to account on average for a large share of CAPB revisions, though it was no longer the dominant factor in most countries.
- Heterogeneity: Cross-country comparisons show large variation; in 2009 potential GDP contribution larger than other factors for the majority of countries; in 2010, still significant but not dominant in most cases.
- Decomposition variables: dGN, dP, dY, dY*, dInt, dRes.

### VI. Rule of thumb linking short-term growth surprises to long-run potential revisions
- Main empirical result:
  - A 1 percentage point short-term output growth revision results on average in some 0.2–0.3 percentage point revision in potential growth in the long term in the same direction.
  - On average about 30 percent of short-term growth revisions should be considered as reflecting a change in potential growth (β=0.3).
  - A 95 percentile range around the 0.3 average relationship suggests values for β between 0.1 and 0.4.
  - During crisis periods, β may be larger; during normal periods, β may be smaller.
- Numerical illustration:
  - If growth is lower by 1 percent and budgetary semi-elasticity is 0.5, headline deficit would be higher by 0.5 percent of GDP.
  - If that higher deficit were purely cyclical, structural balance would not change.
  - Given that only 70 percent of the short-term growth revision is cyclical (30 percent is structural), the structural balance should be expected to have worsened by 30 percent of 0.5 percent = 0.15 percent of GDP.
  - Offsetting measures of 0.15 percent of GDP would be needed to keep structural balance constant; the headline deficit should be allowed to increase by only 0.5 percent − 0.15 percent = 0.35 percent of GDP to maintain structural balance.
- Policy interpretation:
  - Short-run growth revisions include a permanent (structural) component that affects the structural fiscal position.
  - If fiscal policy objectives are based on structural balance targets, measures are needed to compensate for the structural balance change implied by growth surprises.
- Practical recommendation:
  - Use the 30 percent rule of thumb (β=0.3) as a second-best, transparent adjustment when potential output is difficult to estimate in ways less prone to forecast error.

### VII. Regression evidence and robustness (selected results)
- Baseline spring revision (∆gY* = vintage(t+3, s) - vintage(t,s); ∆gY = vintage(t,f) - vintage(t,s)):
  - Pooled OLS b1 = 0.24***; Country effects b1 = 0.2**; Time effects b1 = 0.3***; Country and time effects b1 = 0.26***
  - Nobs = 188 each; Adjusted R2 = 0.09, 0.22, 0.37, 0.52
- Baseline fall revision (∆gY* = vintage(t+3, s) - vintage(t-1,f); ∆gY = vintage(t,s) - vintage(t-1,f)):
  - Pooled OLS b1 = 0.32***; Country effects b1 = 0.28***; Time effects b1 = 0.54***; Country and time effects b1 = 0.39***
  - Nobs = 186 each; Adjusted R2 = 0.31, 0.42, 0.52, 0.61
- Subsample checks:
  - EU New Member States and EU Old Member States show broadly similar b1 estimates with variation in significance and adjusted R2; examples include pooled OLS b1 ranging from 0.23** to 0.36*** in subsamples.
- Alternative final vintage and longer sample:
  - Using vintage(2013, s) as final vintage yields pooled OLS b1 = 0.26*** (spring) and 0.35*** (fall) with Nobs = 242 and 240 respectively.
- Alternative decision-horizons:
  - Budget preparation horizon: b1 ≈ 0.26*** (pooled).
  - Budget evaluation horizon: b1 ≈ 0.31*** (pooled).
  - Budget implementation horizon: b1 ≈ 0.28*** (pooled).
- Semi-annual rolling and non-crisis subsamples:
  - Semi-annual estimates and exclusion of 2008–09 yield stable positive b1 estimates typically around 0.27–0.31***.
- Controlling for multi-year growth revisions:
  - When ∆gY(t), ∆gY(t+1), ∆gY(t+2) included, coefficients remain positive and significant (examples: ∆gY(t) ≈ 0.28***, ∆gY(t+1) ≈ 0.41***, ∆gY(t+2) ≈ 0.25*** in spring baseline).
- Alternative specification using log differences:
  - Baseline spring revision in levels: pooled OLS b1 = 0.77***; fall pooled OLS b1 = 0.74*** (Nobs = 146 and 144 respectively).

### VIII. Quantitative measures of revision magnitudes and errors (selected RMSEs and means by horizon)
- RMSE of differences in output gap by horizon (from -4.5y to -0.5y): 4.4 4.2 3.5 3.0 2.5 2.1 1.6 1.2 0.7
- Mean of the absolute error of differences in output gap by horizon: 3.4 3.3 2.6 2.2 1.8 1.5 1.1 0.9 0.5
- RMSE of percent change in output level by horizon: 9.2 8.3 7.1 4.9 3.7 2.8 1.8 1.5 0.4
- Mean of the absolute error of percent change in output level by horizon: 6.9 6.1 5.2 3.3 2.5 1.8 1.1 0.8 0.2
- RMSE of percent change in potential output level by horizon: 5.7 5.4 5.1 3.9 3.5 3.0 2.3 1.8 0.8
- Mean of the absolute error of percent change in potential output level by horizon: 3.7 3.7 3.6 2.7 2.5 2.1 1.6 1.2 0.5
- RMSE of differences in output growth by horizon: 4.7 4.4 3.4 1.9 1.4 1.2 0.7 0.6 0.3
- Mean of the absolute error of differences in output growth by horizon: 2.8 2.8 2.2 1.3 1.0 0.7 0.4 0.4 0.1
- RMSE of differences in potential output growth by horizon: 2.2 1.8 1.4 1.2 1.0 0.9 0.7 0.5 0.3
- Mean of the absolute error of differences in potential output growth by horizon: 1.4 1.2 0.9 0.8 0.7 0.6 0.5 0.4 0.2

### IX. Policy implications and recommended practices
- First-best: estimate potential GDP using methods or data less prone to forecast errors or revisions (e.g., alternative data sources such as surveys) where feasible.
- Second-best: apply a simple, transparent rule of thumb allocating about 30 percent (β=0.3) of short-term growth surprises to permanent changes in potential output when real-time potential output estimates are unreliable.
- Use cases for the rule of thumb:
  - Calibrate correction mechanisms in structural balance rules that activate once deviations exceed thresholds.
  - Improve communication and transparency of real-time CAPB estimates by acknowledging the structural component of growth surprises.
  - Compare CAPB with a “CAPB at Risk” measure capturing country-specific structural balance estimate variance from forecast error variance in output and potential output.
- Caveat: β is country- and period-specific; during crisis periods β may be larger and during normal periods smaller — judgment required.

### X. Conclusion
- Potential GDP and output gap are subject to significant revisions, especially during crisis periods; these revisions substantially affect CAPB measurement.
- Accounting for the empirical correlation between short-term growth surprises and long-run potential growth revisions (empirical β≈0.2–0.3 pooled; commonly summarized as β=0.3) can strengthen structural balance rules while preserving simplicity and transparency.
- Structural fiscal rules should be designed to be robust to revisions and include transparent correction mechanisms.

*Source: European Commission economic forecasts (2003–12) and IMF staff estimates as presented in _wp14107 (PDF).*

### References .............................................................................................................

### _wp14107 - References

### Appendices
- 1. Methodology for Decomposing the Revision to the CAPB .................................................17
- 2. The Size and Distribution of Revisions to Output and Potential Output Over Alternative Horizons ...............................................................................................................................18
- 3. Estimating the Cross-Vintage Correlation of Output and Potential Output Growth ...........21

### Figures
- 1. Time Horizon for Evaluating Fiscal Stance for Budget Year t ..............................................6
- 2. During Crisis Years CAPBs Were Revised Downwards for Most Countries .......................8
- 3. The Size of the Output Gap Grew During Crisis Years Irrespective of Sign ........................9
- 4. Revisions in the Spanish Output Gap Illustrate the Large Role Played by Potential Output Revisions ................................................................................................................10
- 5. Revisions in Estimates of Potential GDP Are a Large Factor Contributing to Revisions in the CAPBs......................................................................................................................11
- 6. Depending on the Share of a Growth Surprise that Is Permanent (β), the Impact on CAPB Revisions Can Vary ................................................................................................13

### Table
- 1. EU: Revisions in Output and Potential Output over the Budget Horizon, Average ............10

*Source: _wp14107 - References (PDF).*

### References .............................................................................................................

### References

### I. Introduction
- Context: Increasing interest in adopting a more structural approach to fiscal policy in Europe; the EU Fiscal Compact requires inclusion of structural targets as part of fiscal rules.
- Core assumption and problem: Successful implementation of structural targets relies on accurate estimates of both actual and potential growth; real-time estimates of both are often subject to significant revisions that can continue beyond the budget year.
- Paper objectives:
  - How large were the errors in measuring the output gap?
  - What were the implications of revisions in potential GDP for the measurement of fiscal effort?
  - Can an indicative rule of thumb be observed between revisions in actual and potential growth?
- Summary of key answers:
  - Output gap errors averaged about 1½ percent of potential GDP in absolute terms between budget assumptions and first post-budget evaluation; during non-crisis years averaged almost 1 percent of potential GDP.
  - CAPB revisions were substantial; potential GDP revisions contributed significantly, especially during crisis years (more than key fiscal variables such as primary expenditure deviations from target).
  - On average about 30 percent of the revision in actual growth reflected revisions in potential growth; short-run growth revisions include a permanent structural component. Policy implication: “letting automatic stabilizers operate fully” in response to growth shocks likely implies a strengthening/weakening of the structural position.

### II. Literature review (selected findings)
- Orphanides and van Norden (2002, 2005): Real-time output gap revisions in the US (1969–2003) are as large as historical estimates; sign differences across methods are common.
- Cayen and van Norden (2005): Canadian output gap revisions significant; data revision was main cause.
- Massimiliano and Musso (2011): For euro area countries since 1999, ex-post revisions of estimated output gaps are of same order as estimated gaps; uncertainty driven by parameter instability, model uncertainty, unreliable end-of-sample trend estimates.
- Koske and Pain (2008): For 1995–2003, output and unemployment gap revisions accounted for revisions around 0.4 percentage points of GDP in CAPB across G7 and 21 OECD economies.
- Bouis and others (2012): Revisions of 1 to 1.5 percentage points to output gaps are relatively common in OECD sample.
- Hallett and others (2009): CAPB revisions over 1 percent of GDP in most euro area countries due to output gap revisions; real-time CAPBs have low power to detect fiscal slippages.
- Jonung and Larch (2006): Systematic upward bias in government forecasts of potential output made real-time fiscal assessments overly optimistic.
- Ley and Misch (2013): Revisions in output have substantial effects on structural balance estimates (WEO data for 175 countries).

### III. Evaluating fiscal effort: data, methodology, and magnitude of revisions
- Data:
  - Source: European Commission’s semi-annual (fall and spring) economic forecasts covering 2003–12.
  - Potential output estimates: Production Function method (EC estimates underpinning cyclically adjusted balances in general government forecast tables).
  - Additional data: general government revenues, expenditures, GDP deflator from EC Economic Forecasts.
- Budget evaluation horizon:
  - Defined as difference between estimate at budget preparation (t-1, fall vintage for budget year t) and first budget evaluation (t+1, spring vintage).
- Decomposition methodology:
  - Cross-vintage change in CAPB ratio to GDP decomposed into contributions from: nominal government spending (dGN), GDP deflator (dP), output (dY), potential output (dY*), interest payments (dInt), and residual cross-term (dRes).
  - Output contribution accounts for denominator effect and endogenous impact on revenues.
- Key magnitude findings:
  - Mean absolute revision in CAPB over the budget horizon: almost 1¾ percent of GDP.
  - Peak crisis years 2008–2009: mean absolute CAPB revision about 3 percent of GDP.
  - Non-crisis years 2005–07 and 2010–11: mean absolute CAPB revision 1½ percent of GDP.
  - Median across countries: crisis period mean absolute revision 2.3 percent of GDP; non-crisis period median 1 percent of GDP; overall median absolute revision 1¼ percent of GDP.
  - Mean absolute value of output gap revisions over 2003–12 for the budget horizon: 1.3 percent of GDP.
  - Crisis years (2008–2009) output gap revisions up to some 3 percent of GDP; non-crisis years average 0.8 percent of GDP.
  - Median absolute revision in output gap across countries: 0.9 percent of GDP (2.5 percent during crisis; 0.6 percent during non-crisis).
  - Sign changes in output gap occurred in about one fifth of cases; excluding initial gaps less than 1 percent in absolute terms, sign changes drop to less than 7 percent of observations.
  - Longer horizon: mean absolute error from budget preparation vintage to final vintage three years later was 2.6 percent of GDP (compared with 1.3 percent over the budget horizon).
- Illustrative country example (Spain):
  - Revisions (percent change or percentage points):
    - 2007: Output 2.2; Potential Output 1.2; Output Gap 1.1
    - 2008: Output -1.8; Potential Output -4.5; Output Gap 2.9
    - 2009: Output -7.3; Potential Output -4.4; Output Gap -3.0
    - 2010: Output 1.8; Potential Output 1.5; Output Gap 0.3
  - Shows large role of potential output revisions in output gap revisions.

### IV. Decomposition results: contribution of potential output to CAPB revisions
- Finding: Revisions in potential GDP were a large contributing factor to CAPB changes.
- Years highlighted:
  - 2009: Potential GDP accounted for the largest share of CAPB revisions in the EU, on average, more than changes in primary spending.
  - 2010: Potential GDP continued to account on average for a large share of CAPB revisions, though it was no longer the dominant factor in most countries.
- Heterogeneity: Cross-country comparisons show large variation; in 2009 potential GDP contribution larger than other factors for the majority of countries; in 2010, still significant but not dominant in most cases.
- Decomposition variables noted: dGN (government primary expenditure), dP (GDP deflator), dY (output), dY* (potential output), dInt (interest payments), dRes (residual cross term).

### V. Fiscal policy implications and rule of thumb
- Practical problem: Estimating unobserved potential output in real time is inherently difficult; alternate approaches (less forecast-error-prone or less revision-prone data sources) are first-best but often infeasible.
- Proposed second-best: A simple quantitative rule of thumb based on historical correlation between short-term revisions in output growth and long-term revisions in potential growth to reduce CAPB measurement errors.
- Empirical result:
  - A 1 percentage point short-term output growth revision results on average in some 0.2–0.3 percentage point revision in potential growth in the long term in the same direction.
  - Robust across estimation methods, country samples, time horizons, and spring/fall revision vintages.
  - On average about 30 percent of short-term growth revisions should be considered as reflecting a change in potential growth.
- Policy interpretation:
  - Short-run growth revisions include a permanent (structural) component that affects the structural fiscal position.
  - A positive/negative growth shock implies a strengthening/weakening of the structural position.
  - If fiscal policy objectives are based on structural balance targets, measures are needed to compensate for the structural balance change implied by growth surprises.
- Illustrative numerical example:
  - If growth is lower by 1 percent and budgetary semi-elasticity is 0.5, headline deficit would be higher by 0.5 percent of GDP.
  - If that higher deficit were purely cyclical, structural balance would not change.
  - Given that only 70 percent of the short-term growth revision is cyclical (30 percent is structural), the structural balance should be expected to have worsened by 30 percent of 0.5 percent = 0.15 percent of GDP.
  - Offsetting measures of 0.15 percent of GDP would be needed to keep structural balance constant; the headline deficit should be allowed to increase by only 0.5 percent − 0.15 percent = 0.35 percent of GDP to maintain structural balance.

*Source: European Commission economic forecasts (2003–12) and IMF staff estimates as presented in this content unit.*

### 0.35 percent of GDP in response to the short-term growth revision to keep the structural

### _wp14107 - 0.35 percent of GDP in response to the short-term growth revision to keep the structural

### Key empirical findings on growth surprises and CAPB revisions
- A 0.35 percent of GDP adjustment is discussed in response to the short-term growth revision to keep the structural deficit unchanged.
- Symmetrically, if growth surprises on the upside, the headline deficit would fall by 0.5 percent of GDP.
- A structural improvement in the deficit of 0.15 percent of GDP would thus be implied and permanent deficit increasing measures of this magnitude could be implemented without worsening the structural balance.
- About a third of a growth surprise reflects on average a permanent change in potential growth (β=0.3).
- A 95 percentile range around the 0.3 average relationship suggests values for β between 0.1 and 0.4.
- During crisis periods, β may be larger; during normal periods, β may be smaller. Judgment is required country-by-country.

### Implications for cyclically-adjusted primary balance (CAPB) estimation and rules
- The correlation between real-time growth surprises and potential GDP growth revisions affects CAPB revisions and should be accounted for when interpreting CAPBs as indicators of fiscal effort.
- The 30 percent rule of thumb (β=0.3) can improve CAPB estimation by allocating part of a real-time growth surprise to permanent changes in potential output.
- Incorporating this correlation can:
  - Help calibrate correction mechanisms in structural balance rules that activate once deviations exceed thresholds.
  - Improve accuracy of real-time estimates of potential GDP growth, especially when growth surprises are large.
- The CAPB estimate could be compared with a “CAPB at Risk” measure capturing country-specific structural balance estimate variance from forecast error variance in output and potential output.

### Conclusion and policy implications
- Successful implementation of structural fiscal targets requires measuring potential output and output gaps accurately in real time; these are inherently uncertain.
- First-best: estimate potential GDP in ways less prone to forecast errors or relying on data less affected by revisions (e.g., surveys).
- Complementary approach: an approximate rule of thumb that accounts for the correlation between actual growth surprises and long-term potential growth revisions can strengthen structural balance rules while preserving simplicity and transparency.
- Potential GDP and output gap are subject to significant revisions, especially during crisis periods; structural balance rules should be robust to these revisions and include correction mechanisms.

### Magnitude and distribution of revisions (EU-27, 2003–2012 / 2004–2012 results)
- Output gap revisions over a 3.5 year horizon (typical long-term horizon) are nearly 2 ½ –3 ½ percent of potential GDP.
- Output and potential output growth revisions at the 3.5 year horizon range between 1–3 ½ percent.
- Revisions reflect both GDP forecast error and revisions to potential GDP estimates; ex-ante GDP revisions dominate, ex-post potential revisions become more important.
- Distributional patterns:
  - Output gap revisions were generally skewed positive (output gap larger following revision) with sizable dispersion around the median.
  - Median revision for output was positive (output revised upwards); median revision for potential output was negative (initial potential over-optimistic and subsequently revised down).
  - Ex-post downward revision of potential output likely reflects long-term forecast uncertainty (end-point bias) rather than ex-post output data revisions.

### Quantitative measures of revision magnitudes and errors (Table A2.1 / Table A2.2)
- Root mean squared error (RMSE) of differences in output gap by horizon (from -4.5y to -0.5y): 4.4 4.2 3.5 3.0 2.5 2.1 1.6 1.2 0.7
- Mean of the absolute error of differences in output gap by horizon: 3.4 3.3 2.6 2.2 1.8 1.5 1.1 0.9 0.5
- RMSE of percent change in output level by horizon: 9.2 8.3 7.1 4.9 3.7 2.8 1.8 1.5 0.4
- Mean of the absolute error of percent change in output level by horizon: 6.9 6.1 5.2 3.3 2.5 1.8 1.1 0.8 0.2
- RMSE of percent change in potential output level by horizon: 5.7 5.4 5.1 3.9 3.5 3.0 2.3 1.8 0.8
- Mean of the absolute error of percent change in potential output level by horizon: 3.7 3.7 3.6 2.7 2.5 2.1 1.6 1.2 0.5
- RMSE of differences in output growth by horizon: 4.7 4.4 3.4 1.9 1.4 1.2 0.7 0.6 0.3
- Mean of the absolute error of differences in output growth by horizon: 2.8 2.8 2.2 1.3 1.0 0.7 0.4 0.4 0.1
- RMSE of differences in potential output growth by horizon: 2.2 1.8 1.4 1.2 1.0 0.9 0.7 0.5 0.3
- Mean of the absolute error of differences in potential output growth by horizon: 1.4 1.2 0.9 0.8 0.7 0.6 0.5 0.4 0.2

### Appendix: methodology highlights for CAPB decomposition
- CAPB defined as a share of GDP of year t as of vintage v via components: real revenue (function of output), nominal government spending, nominal interest spending, GDP deflator, levels of real output and potential output, and revenue/expenditure elasticities with respect to the output gap.
- Elasticity values for revenue and expenditures follow the EC methodology in Girouard and Andre (2005).
- Cross-vintage change in CAPB ratio to GDP decomposed into contributions of sub-components (real spending, interest spending, GDP deflator, output, potential output) plus a residual cross-term by allowing one component to change while keeping others constant.
- Contribution of output accounts for both denominator effect and endogenous impact on revenues.

### Estimation approach for cross-vintage correlation
- Short-term revision: difference between a new real-time estimate of growth for year t and the estimate produced one semester before (spring t,s vs fall t-1,f; and fall t,f vs spring t,s).
- Long-term revision: difference between final estimate (proxy: EC spring of third year following given year, t+3,s) and the real-time estimate produced during the spring of the given year (t,s) or fall of preceding year (t-1,f).
- Regression framework: long-term revisions in potential growth regressed on a constant and short-term real-time growth revisions (with country and time effects). Interpretation: coefficient = fraction of short-term revision interpreted as permanent (1 = all permanent, 0 = all cyclical).
- Estimation sample covers data from 2003–2010 (extending to t+3,s loses last two years).

### Estimation result (headline)
- A 1 percentage point short-term output growth revision results on average in some 0.2–

*Source: IMF staff analysis based on European Commission vintages and IMF staff calculations as presented in the source PDF.*

### 0.3 percentage point revision in long run potential growth in the same direction (Table

### _wp14107 - 0.3 percentage point revision in long run potential growth in the same direction (Table

### Main finding: correlation between real-time revisions in actual growth and long-run revisions in potential growth
- Baseline spring revision (∆gY* = vintage(t+3, s) - vintage(t,s); ∆gY = vintage(t,f) - vintage(t,s)):
  - Pooled OLS b1 = 0.24***; Country effects b1 = 0.2**; Time effects b1 = 0.3***; Country and time effects b1 = 0.26***
  - Nobs = 188, 188, 188, 188
  - Adjusted R2 = 0.09, 0.22, 0.37, 0.52
- Baseline fall revision (∆gY* = vintage(t+3, s) - vintage(t-1,f); ∆gY = vintage(t,s) - vintage(t-1,f)):
  - Pooled OLS b1 = 0.32***; Country effects b1 = 0.28***; Time effects b1 = 0.54***; Country and time effects b1 = 0.39***
  - Nobs = 186, 186, 186, 186
  - Adjusted R2 = 0.31, 0.42, 0.52, 0.61

### Subsample checks: EU New Member States vs EU Old Member States
- EU New Member States (Table A3.3):
  - Baseline spring revision:
    - Pooled OLS b1 = 0.24**; Country effects b1 = 0.23*; Time effects b1 = 0.36***; Country and time effects b1 = 0.36***
    - Nobs = 120, 120, 120, 120
    - Adjusted R2 = 0.10, 0.14, 0.41, 0.49
  - Baseline fall revision:
    - Pooled OLS b1 = 0.25***; Country effects b1 = 0.23***; Time effects b1 = 0.5***; Country and time effects b1 = 0.42***
    - Nobs = 120, 120, 120, 120
    - Adjusted R2 = 0.26, 0.30, 0.48, 0.53
- EU Old Member States (Table A3.4):
  - Baseline spring revision:
    - Pooled OLS b1 = 0.23**; Country effects b1 = 0.19*; Time effects b1 = 0.34***; Country and time effects b1 = 0.3***
    - Nobs = 68, 68, 68, 68
    - Adjusted R2 = 0.07, 0.18, 0.42, 0.58
  - Baseline fall revision:
    - Pooled OLS b1 = 0.34***; Country effects b1 = 0.3***; Time effects b1 = 0.54***; Country and time effects b1 = 0.35***
    - Nobs = 66, 66, 66, 66
    - Adjusted R2 = 0.32, 0.40, 0.53, 0.63

### Robustness: alternative final vintage and longer sample
- Alternative spring revision (∆gY* = vintage(2013, s) - vintage(t,s); ∆gY = vintage(t,f) - vintage(t,s)) (Table A3.5):
  - Pooled OLS b1 = 0.26***; Country effects b1 = 0.25***; Time effects b1 = 0.3***; Country and time effects b1 = 0.29***
  - Nobs = 242, 242, 242, 242
  - Adjusted R2 = 0.13, 0.23, 0.31, 0.43
- Alternative fall revision (∆gY* = vintage(2013, s) - vintage(t-1,f); ∆gY = vintage(t,s) - vintage(t-1,f)):
  - Pooled OLS b1 = 0.35***; Country effects b1 = 0.32***; Time effects b1 = 0.52***; Country and time effects b1 = 0.44***
  - Nobs = 240, 240, 240, 240
  - Adjusted R2 = 0.35, 0.41, 0.49, 0.54

### Alternative decision-horizons for correlation estimates (Table A3.6)
- Budget preparation horizon (∆gY*, ∆gY = vintage(t+3,s) - vintage(t-1,f)):
  - b1 = 0.26*** (Pooled); 0.23*** (Country); 0.34*** (Time); 0.29*** (Country and time)
  - Nobs = 186 each; Adjusted R2 = 0.49, 0.61, 0.65, 0.75
- Budget evaluation horizon (∆gY*, ∆gY = vintage(t+1,s) - vintage(t-1,f)):
  - b1 = 0.31*** (Pooled); 0.3*** (Country); 0.35*** (Time); 0.35*** (Country and time)
  - Nobs = 240 each; Adjusted R2 = 0.73, 0.73, 0.81, 0.82
- Budget implementation horizon (∆gY*, ∆gY = vintage(t+3,s) - vintage(t,s)):
  - b1 = 0.28*** (Pooled); 0.24*** (Country); 0.33*** (Time); 0.29*** (Country and time)
  - Nobs = 188 each; Adjusted R2 = 0.22, 0.34, 0.46, 0.59

### Semi-annual rolling horizons and persistence over shorter horizons (Table A3.7)
- Selected semi-annual rolling estimates (examples):
  - vintage(t,s) - vintage(t-1,f): b1 = 0.29***, 0.29***, 0.29***, 0.3***; Nobs = 240; Adjusted R2 = 0.79, 0.79, 0.79, 0.79
  - vintage(t,f) - vintage(t,s): b1 = 0.29***, 0.3***, 0.31***, 0.32***; Nobs = 242; Adjusted R2 = 0.54, 0.54, 0.60, 0.60
  - vintage(t+1,s) - vintage(t,f): b1 = 0.39***, 0.43***, 0.26***, 0.3***; Nobs = 252; Adjusted R2 = 0.36, 0.40, 0.47, 0.49
  - vintage(t+3,s) - vintage(t+2,f): b1 = 0.11**, 0.08, 0.07**, 0.03; Nobs = 212; Adjusted R2 = 0.01, -0.07, 0.45, 0.43

### Non-crisis subsample (excluding 2008-09) at semi-annual horizons (Table A3.8)
- Examples for t=2003-07,2010:
  - vintage(t,s) - vintage(t-1,f): b1 = 0.3***, 0.27***, 0.3***, 0.27***; Nobs = 186; Adjusted R2 = 0.42, 0.43, 0.41, 0.42
  - vintage(t,f) - vintage(t,s): b1 = 0.27***, 0.28***, 0.3***, 0.34***; Nobs = 188; Adjusted R2 = 0.39, 0.34, 0.45, 0.42
  - vintage(t+3,s) - vintage(t+2,f): b1 = 0.13**, 0.16**, 0.04*, 0.05; Nobs = 158; Adjusted R2 = 0.00, -0.12, 0.47, 0.44

### Controlling for multi-year growth revisions (Table A3.9)
- Baseline spring revision with ∆gY(t), ∆gY(t+1), ∆gY(t+2) included:
  - ∆gY(t) coefficients: 0.28***, 0.29***, 0.32***, 0.32***
  - ∆gY(t+1) coefficients: 0.41***, 0.41***, 0.29***, 0.3***
  - ∆gY(t+2) coefficients: 0.25***, 0.26***, 0.23***, 0.24***
  - Nobs = 188 each; Adjusted R2 = 0.49, 0.62, 0.57, 0.72
- Baseline fall revision with ∆gY(t), ∆gY(t+1), ∆gY(t+2) included:
  - ∆gY(t) coefficients: 0.4***, 0.36***, 0.53***, 0.49***
  - ∆gY(t+1) coefficients: 0.3***, 0.27***, 0.49***, 0.45***
  - ∆gY(t+2) coefficients: 0.23***, 0.2***, 0.28***, 0.23***
  - Nobs = 186 each; Adjusted R2 = 0.68, 0.72, 0.76, 0.78

### Alternative specification using log differences in output and potential output levels (Table A3.10)
- Baseline spring revision (∆Y* = vintage(t+3, s) - vintage(t,s); ∆Y = vintage(t,f) - vintage(t,s)):
  - Pooled OLS b1 = 0.77***; Country effects b1 = 0.66***; Time effects b1 = 0.74***; Country and time effects b1 = 0.63***
  - Nobs = 146 each; Adjusted R2 = 0.16, 0.19, 0.52, 0.63
- Baseline fall revision (∆Y* = vintage(t+3, s) - vintage(t-1,f); ∆Y = vintage(t,s) - vintage(t-1,f)):
  - Pooled OLS b1 = 0.74***; Country effects b1 = 0.63***; Time effects b1 = 0.95***; Country and time effects b1 = 0.67***
  - Nobs = 144 each; Adjusted R2 = 0.24, 0.27, 0.56, 0.63

*Source: _wp14107 - 0.3 percentage point revision in long run potential growth in the same direction (Table*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14107.pdf_