## Appendix I. Data

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---

### Introduction and scope
- Period analyzed: 1990-2014.
- Data vintages:
  - Data availability since 1991 in the WEO; final estimate defined as the estimate measured seven years after the period in question.
  - The WEO is released twice a year (spring and fall); analysis is performed with fall vintages.
- Sample size:
  - Baseline dataset has an average sample size of 176 countries per year, for a total of 3,018 observations.
- Focus:
  - Quantify uncertainty surrounding initial real-time output gap estimates by examining statistical properties and revisions.
  - Restrict analysis to ex-post revisions (data revisions and changes in trend/cycle decomposition).
  - Compare HP-filtered output gap estimates with desk-provided WEO estimates where available.

### Output gap definition and vintages
- Definition:
  - Output gap (ỹ) = (y − y*) / y* (percent of potential).
- Vintage definitions:
  - Forecast: estimate made before or during year t.
  - Initial estimate: first estimate in which data for year t is known.
  - Revised estimates: subsequent estimates until the final estimate.
  - Final estimate: estimated output gap seven years after the period in question.
- Sources of deviations (summary):
  - Forecast: Policy reactions, forecast error, data revisions, uncertainty over potential output.
  - Initial estimate: Data revisions, uncertainty over potential output.
  - Revised estimates: Data revisions, uncertainty over potential output.
  - Final estimate: None, by definition.
- Scope exclusion:
  - Paper restricts attention to ex-post revisions and does not model policy reactions or forecast errors.

### Data and methodology (HP filter and comparators)
- Desk-provided WEO real-time output gap estimates used where available; for broad coverage, potential GDP estimated by applying the Hodrick-Prescott (HP) filter on real GDP data from the WEO.
- HP smoothing parameter testing:
  - Common annual choices assessed: λ = 100 and λ = 6.25.
  - Regression fit suggests λ = 100 is a better analog of WEO and OECD desk data.
  - Baseline: HP-filtered data with λ set to 100 for all countries; robustness checks with λ = 6.25 and desk-provided estimates.
- Implementation detail:
  - HP filter run over all available historical data plus the forecast available in the WEO database to mitigate endpoint problems.
  - For HP-filtered WEO data: lambda set to 100; run on each country-vintage if data from 1980 onward and at least 15 consecutive observations; WEO forecasts five years ahead included.
  - For national-authority based output gaps in LA-5: HP smoothing parameter of 400 with observed real GDP spliced with real GDP growth expectations to extend series.

### Initial estimates and revisions — key findings and statistics
- Magnitude and persistence:
  - Revisions to the output gap are of the same order of magnitude as the initial estimates themselves.
  - About one-third of economies have an output gap that changes signs between the initial and final estimates.
  - Revisions are larger for emerging and low-income economies than for advanced economies; sign switches more likely in those groups.
- Quantitative revision dynamics:
  - One year after the initial estimate, the output gap of the typical country is revised by 0.9 percentage points (absolute value).
  - Two years after the initial estimate, the absolute value of the median revision remains nearly half a percentage point.
  - Seven years after the year under analysis:
    - A quarter of all countries experience revisions of half a percentage point.
    - Ten percent of all countries experience an output gap revision of a full percentage point.
- Directional bias:
  - Initial assessments overstate slack:
    - Initial estimates indicate actual output is 1.0 percent below potential output.
    - Final estimates indicate actual output is 0.2 percent below potential output.

### Excess capacity bias and revision patterns
- Term: “excess capacity bias.”
- Summary table (selected figures verbatim):
  - All countries: Number countries 176; Percent of Median Standard deviation Median Standard deviation Median Standard deviation switching signs row shows: -0.97 5.12 -0.22 5.57 0.75 3.89 32.3
  - Advanced: 24; -0.24 1.61 0.27 2.49 0.51 1.67 22.9
  - Emerging: 122; -0.98 5.47 -0.34 5.90 0.64 4.11 32.7
  - Low-income: 30; -1.77 5.28 -0.22 5.93 1.55 4.16 38.8
- Two interacting factors produce excess capacity bias:
  - Initial estimates of activity tended to be revised upward in later vintages.
  - Economic activity tended to underperform IMF forecasts.
- Net effect on potential growth:
  - Cumulative revisions to estimated potential growth were roughly neutral, at less than 0.1 percent of potential output, on average.

### Magnitude and timing of revisions (distributional patterns)
- Initial assessments are least reliable during recessions.
- Absolute revisions to the output gap, actual growth, and potential growth are 30 to 50 percent larger during downturns than in normal times.
- Distribution of revisions during downturns is wider—30 percent higher than in the full sample.
- Vintage dynamics reported as marginal output gap revisions in absolute value (percent of potential GDP) across vintages t+2 to t+7 (median, 75th percentile, 90th percentile).

### Robustness checks and alternative measures
- HP parameter sensitivity:
  - Median revisions are much lower with lambda = 6.25.
  - Ratios of standard deviations to medians are dramatically larger with lambda = 6.25.
- Cross-source comparisons (advanced economies):
  - OECD and WEO country-desk estimates display at least as much persistent uncertainty and excess capacity bias as HP-filtered estimates.
  - Typical revisions from OECD and WEO are larger and more variable than HP-filtered data.
- United States (CBO production-function estimates):
  - CBO and HP-filtered estimates show similar persistent uncertainty; distribution of revisions slightly less wide for CBO.
  - Sign changes: 7 out of 18 initial estimates change sign by the final estimate for the CBO, OECD, and WEO datasets; 5 out of 18 for HP-filtered estimates.
- Other robustness:
  - Results robust to subsample splits (1990s vs 2000s).
  - Filtered data excluding the forecast are even more volatile and subject to revision.
  - Results insensitive to changing the vintage for the final estimate to six or eight years rather than seven.

### Determinants of output gap revisions — empirical approach
- Objective: explain size of cumulative absolute output gap revisions (final t+7 minus initial t+1).
- Estimation:
  - OLS on pooled panel (robust to heteroskedasticity and autocorrelation); robustness with cross-sectional dependence correction (PCSE).
  - Probit (population-averaged panel probit) for probability that sign of output gap at final vintage is opposite to initial sign (considering episodes where revision > 0.5 percentage point).
- Regressor categories:
  1. Domestic/world GDP dynamics: Abs. output gap at t+1; domestic and world real GDP growth surprises at t+1.
  2. Macroeconomic uncertainty proxies: Real GDP growth SD over last 10 years (t+1); Rents/GDP; Inflation.
  3. Policy frameworks: Inflation targeting dummy; cyclical fiscal rules dummy.
  4. Statistical capacity and country characteristics: OECD dummy; LIC dummy; Small economy dummy (population below 10th percentile).

### Determinants — main statistical findings (selected verbatim coefficients)
- Baseline sample: 2,943 observations for 171 countries over 1990-2007 using HP-filtered real GDP data.
- Selected coefficients and significance (preserve reported values and standard errors where given):
  - Abs. output gap: 0.109***; (0.035) in column 1 (one percentage point increase in abs. output gap → 0.11 percentage point increase in revision).
  - Abs. real GDP growth surprise: 0.074*** (one percentage point increase → 0.07 percentage points).
  - Abs. world real GDP growth surprise: 0.189** (0.077) in column 1; other columns show 0.200** (1) etc.
  - Rents/GDP:
    - Column 1: 0.020*** (0.007).
    - Column 2: 0.021*** (0.006).
    - In some OECD/WEO specifications coefficient is negative and significant (e.g., -0.054***, -0.056**).
  - Inflation: mixed (e.g., column 1: 0.009 (0.007); column 5: 0.114** (0.055)).
  - Inflation targeting dummy:
    - Column 1: -0.362*** (0.135).
    - Column 2: -0.330** (0.154).
  - Cyclical fiscal rules: not robust (e.g., column 1: 0.056 (0.167)).
  - OECD dummy: -0.542*** (0.151) in some specs.
  - LIC dummy: 0.503** (0.230) in some specs.
  - Small economy dummy: 0.790*** (0.216) in some specs.
- Model fit and sample notes:
  - Column 1 (HP filtered): Observations 2,943; R-squared 0.164; Number of economies 171.
  - Column 3 (WEO data): Observations 437; R-squared 0.407; Number of economies 29.
  - Column 5 (OECD data): Observations 299; R-squared 0.157; Number of economies 26.
  - ***, **, * indicate significance at 1, 5 and 10 percent, respectively.

### Interpretation and residual uncertainty
- Several variables are significant predictors, but a large share of revisions remains unexplained.
- Many revisions may not be predictable at the time policy decisions are made; residual unpredictability complicates reliance on real-time output gap estimates for policy stance.

### Additional numerical summaries (selected from extensions and tables)
- Main empirical findings summary:
  - Goodness of fit of specifications falls in the 10 to 41 percent range.
  - A large component of revisions behaves as a white noise process.
  - Output gap revisions are positively associated with the absolute value of the initial estimate; real GDP growth surprises make subsequent revisions larger.
  - Inflation targeting regimes have lower output gap revisions.
  - OECD countries have revisions over half a point smaller; LICs about half a point larger; small countries about 0.79 percentage points larger.
- Determinants (selected estimates from Table 5):
  - Abs. output gap: 0.109*** (Columns 1–2); 0.108** (3); 0.107** (4); 0.051 (5).
  - Abs. real GDP growth surprise: 0.074*** (1–2); 0.081*** (3–4); 0.065*** (5).
  - Abs. world real GDP growth surprise: 0.200** (1); 0.189** (2); 0.164* (3); 0.166* (4); 0.214*** (5).
  - Rents/GDP: 0.021*** (1); 0.020*** (2); 0.017** (3–4); 0.015** (5).
  - Inflation targeting: -0.394*** (1); -0.361*** (2); -0.274* (3); -0.304** (4); -0.344*** (5).
  - OECD: -0.578*** (1); -0.544*** (2); -0.328* (3); -0.316* (4); -0.549*** (5).
  - LIC: 0.542** (1); 0.506** (2); 0.482* (3); 0.538** (4); 0.582** (5).
  - Small economy: 0.828*** (columns where included).
  - Observations examples: 2,943 (Columns 1–2); 2,241 (Columns 3–4); 2,942 (Column 5).
  - R-squared examples: 0.165 (1); 0.164 (2); 0.183 (3–4); 0.185 (5).

### Determinants of probability of sign change (selected marginal effects)
- Abs. output gap: -0.071*** (Columns 1–3); -0.087*** (4); -0.086*** (5); -0.065*** (6).
- Abs. real GDP growth surprise: 0.005* (1–3); 0.003 (4–5); 0.008*** (6).
- Inflation: 0.002** (Columns where significant).
- Inflation targeting: -0.085*** (1); -0.055** (2); -0.085*** (3); -0.077*** (4); -0.081*** (5); -0.085*** (6).
- Cyclical fiscal rules: 0.116* (1); 0.143** (2); 0.116* (3); 0.112* (4); 0.102 (5); 0.114* (6).
- OECD: -0.135*** (1); -0.131*** (2); -0.135*** (3); -0.102*** (4); -0.141*** (5); -0.133*** (6).
- LIC: 0.106*** (1); 0.100*** (2); 0.106*** (3); 0.100** (4); 0.130*** (5); 0.096*** (6).
- SDDS: -0.071*** (when included).
- Abs. average future real GDP growth differential: -0.019*** (column with that regressor).
- Observations examples: 2,943; 2,412; 2,942. Number of economies examples: 171; 129.

### Monetary policy implications and LA-5 country evidence (Brazil, Chile, Colombia, Mexico, Peru)
- Confidence intervals around initial/revised output gap estimates can be constructed using historical distributions of cumulative revisions; initial estimates have the widest intervals.
- LA-5 real-time output gaps (quarterly, HP filter smoothing parameter 1600, series extended using GDP growth expectations) show substantial revisions across vintages for Brazil, Chile, Colombia, Mexico, Peru.
- Estimated real-time monetary policy reaction function (instrument responds to expected inflation and lagged output gap, with lagged policy rate persistence). Table 7 coefficients (by country: Brazil, Chile, Colombia, Mexico, Peru):
  - α0 (intercept): 4.72; 4.59**; 2.52**; 1.94**; 2.91**.
  - απ (response to expected inflation): 1.16; 3.04**; 3.18*; 2.51**; 1.56**.
  - αy (response to output gap): 1.89**; 0.96**; 0.74**; 0.43**; 0.88*.
  - ρ (persistence on lagged policy rate): 0.82**; 0.77**; 0.73**; 0.66**; 0.85**.
  - Adjusted r-squared: 0.94; 0.97; 0.95; 0.98; 0.90.
  - Standard error of the regression: 0.77; 0.34; 0.52; 0.30; 0.40.
- Key LA-5 implications:
  - Central banks react strongly to increases in inflation expectations (statistically significant except for Brazil where estimate is less precise).
  - Central banks counter increases in the output gap by raising interest rates (αy positive and statistically significant in all cases).
  - Lagged interest rate persistence strongly significant.
  - Using revised data to compute counterfactual policy prescriptions shows deviations over 100 basis points in multiple episodes; some episodes last over a year.
  - Regressions linking inflation to initial output gap estimates and revisions indicate:
    - Initial estimates are often not informative about future inflation (except Colombia).
    - Output gap revisions are highly informative about future inflation in all LA-5 countries, explaining 40 to 50 percent of variation in inflation on average.

### Policy implications (summary)
- Confidence intervals based on historical output gap revisions are typically so wide at initial estimate time that they often span positive and negative values.
- Reliance on real-time assessments of cyclical position is a key weakness for monetary policy rules.
- Central banks should:
  - Recognize large real-time uncertainty around output gap estimates when designing policy rules.
  - Use a broad set of indicators and judgment to supplement noisy output gap measures.
  - Consider robustness of policy prescriptions to plausible revisions in the output gap.
- Revisions contain information about future inflation not available in real time; this suggests value in accounting for likely future revisions in policy design.

### Countries included and variable definitions (selected)
- Advanced economies: OECD members as of 1990.
- Low-income economies: GNI per capita of $1,045 or less in 2012.
- Emerging economies: all remaining economies in the sample.
- Country list and full variable definitions (sources and measurement timing) preserved in the dataset: examples include Abs. output gap revision (IMF WEO; t+7, t+1), Rents/GDP (World Bank WDI), Inflation (IMF WEO), Inflation targeting (IMF Finance & Development dummy), Cyclical fiscal rules (IMF Fiscal Rules Dataset dummy), OECD dummy, LIC dummy, Small economy dummy, GDDS/SDDS dummies, Conflict dummy, Bureaucratic quality, Control of corruption, Abs. average future real GDP growth differential (IMF WEO; t+7), Output gap (initial/final) constructed with HP filters (lambda 400 for national-authority series; lambda 100 for WEO HP series), real GDP expectations, headline/core inflation, policy rate.
- HP filter implementation details reiterated:
  - HP-filtered WEO data: lambda = 100; require data from 1980 onward and at least 15 consecutive observations; include WEO forecasts five years ahead.
  - Output gap (initial) from national authorities: HP smoothing parameter = 400 and observed real GDP spliced with growth expectations to avoid endpoint bias.

*Appendix I. Data — IMF working paper content as presented in the supplied PDF excerpt.*

### Appendix I. Data .......................................................................................................

### Appendix I. Data

### Introduction and scope
- Study period and data vintages:
  - Period analyzed: 1990-2014.
  - Data availability since 1991 in the WEO; final estimate defined as the estimate measured seven years after the period in question.
  - The WEO is released twice a year (spring and fall); analysis is performed with fall vintages.
- Sample size:
  - Baseline dataset has an average sample size of 176 countries per year, for a total of 3,018 observations.
- Focus of the appendix:
  - Quantify uncertainty surrounding initial real-time output gap estimates by examining statistical properties and revisions.
  - Isolate revisions arising from data revisions and changes in trend/cycle decomposition by restricting analysis to ex-post estimates (those made after data for the period under study has been released).
  - Compare HP-filtered output gap estimates with desk-provided WEO estimates where available.

### Output gap definition and concept
- Definition:
  - Output gap (ỹ) is the deviation of actual output (y, measured by real GDP) from potential output (y*), expressed as a percent of potential: ỹ = (y − y*) / y*.
  - A negative (positive) output gap indicates output is below (above) potential.
- Vintage definitions:
  - Forecast: estimate made before or during year t.
  - Initial estimate: first estimate in which data for year t is known.
  - Revised estimates: subsequent estimates until the final estimate.
  - Final estimate: the estimated output gap seven years after the period in question (chosen because revisions typically level off within seven years).
- Sources of deviations between forecast/initial/revised estimates and the final estimate (Table 1):
  - Forecast: Policy reactions, forecast error, data revisions, uncertainty over potential output.
  - Initial estimate: Data revisions, uncertainty over potential output.
  - Revised estimates: Data revisions, uncertainty over potential output.
  - Final estimate: None, by definition.
- Scope exclusion:
  - The paper restricts attention to ex-post revisions (data revisions and potential output decomposition uncertainty) and does not model policy reactions or forecast errors.

### Data and methodology (HP filter and comparators)
- Estimation approaches:
  - Desk-provided WEO real-time output gap estimates are used where available.
  - For broad country coverage, potential GDP is estimated by applying the Hodrick-Prescott (HP) filter on real GDP data from the WEO.
- HP filter smoothing parameter (λ) testing:
  - Common annual choices assessed: λ = 100 and λ = 6.25.
  - The HP-filtered series with different λ values were regressed on WEO and OECD estimates to test which λ better fits desk data.
  - Table 2 reported the following figures as computed by the authors (as presented):
    - (λ=100)(λ=6.25)(λ=100)(λ=6.25)
    - Observed WEO data2.112.250.470.40
    - Observed OECD data1.101.470.720.51
    - Source: Authors' calculations.
    - Labels shown: RMSER-squared HP filtered WEO dataHP filtered WEO data
  - Conclusion from the comparison:
    - The results suggest that λ set to 100 is a better analog of both WEO and OECD data (country desks tend to interpret changes in real GDP as changes in cycle rather than in trend).
  - Baseline choice for the analysis:
    - Use HP-filtered data with λ set to 100 for all countries.
    - Robustness checks performed using desk-provided estimates and HP-filtered data with λ set to 6.25.
  - Implementation detail:
    - HP filter run over all available historical data plus the forecast available in the WEO database to mitigate endpoint problems.

### Initial estimates and revisions — key findings and statistics
- Magnitude and persistence of revisions:
  - Revisions to the output gap are of the same order of magnitude as the initial estimates themselves.
  - About one-third of economies have an output gap that changes signs between the initial and final estimates.
  - Revisions are larger for emerging and low-income economies than for advanced economies, and sign switches are more likely in those groups.
- Quantitative revision dynamics:
  - One year after the initial estimate, the output gap of the typical country is revised by 0.9 percentage points (absolute value).
  - Two years after the initial estimate, the absolute value of the median revision remains nearly half a percentage point.
  - Seven years after the year under analysis:
    - A quarter of all countries experience revisions of half a percentage point.
    - Ten percent of all countries experience an output gap revision of a full percentage point.
- Directional bias in initial estimates:
  - Initial assessments overstate slack:
    - Initial estimates indicate actual output is 1.0 percent below potential output.
    - Final estimates indicate actual output is 0.2 percent below potential output.
  - Median revisions to the output gap exceed (sentence in source truncated at this point).

### Country group definitions (used in comparisons)
- Advanced economies:
  - Include all OECD members as of 1990 (the beginning of the sample).
- Low-income economies:
  - Any country with a GNI per capita of $1,045 or less in 2012.
- Emerging economies:
  - All countries not included in the other two groups.

*Appendix I. Data — IMF working paper content as presented in the supplied PDF excerpt.*

### 0.5 percent of potential for all types of countries (Table 1; Figure 2, left panel). We call this

### _wp1514 - 0.5 percent of potential for all types of countries (Table 1; Figure 2, left panel). We call this

### Excess capacity bias and revision patterns
- Term defined: “excess capacity bias.”
- Summary table (as presented):
  - NumberPercent of MedianStandardMedianStandardMedianStandardswitching
  - countriesdeviationdeviationdeviationsigns
  - All countries176-0.975.12-0.225.570.753.8932.3
  - Advanced24-0.241.610.272.490.511.6722.9
  - Emerging122-0.985.47-0.345.900.644.1132.7
  - Low-income30-1.775.28-0.225.931.554.1638.8
- Two interacting factors produce excess capacity bias:
  - Initial estimates of economic activity tended to be revised upward in later vintages (Figure 2, middle panel).
  - Economic activity tended to underperform IMF forecasts (consistent with Ho and Mauro (2014) and Timmermann (2007)).
- Net effect on potential growth:
  - Cumulative revisions to estimated potential growth were roughly neutral, at less than 0.1 percent of potential output, on average (Figure 2, right panel).
  - Combination of upward revisions to past activity and downward revisions to current activity (relative to forecasts) yields lower measured excess capacity in final estimates compared to initial estimates.

### Magnitude and timing of revisions
- Median and distributional patterns (Figure 2 and Figure 3):
  - Initial assessments are least reliable during recessions.
  - Absolute revisions to the output gap, actual growth, and potential growth are 30 to 50 percent larger during downturns than in normal times.
  - The distribution of revisions during downturns is wider—30 percent higher than in the full sample—indicating additional uncertainty when growth is negative.
- Vintage dynamics (Figure 1; Figure 2 vintage panels):
  - Marginal output gap revisions are presented in absolute value (percent of potential GDP) across vintages t+2 to t+7 (median, 75th percentile, 90th percentile).

### Robustness checks and alternative measures
- HP filter sensitivity:
  - Using HP-filter parameter lambda = 6.25 vs lambda = 100 changes results:
    - Median revisions are much lower with lambda = 6.25.
    - Ratios of standard deviations to medians are dramatically larger with lambda = 6.25, implying higher normalized volatility and more evenly dispersed revisions across zero.
- Cross-source comparison (advanced economies):
  - Sources compared: HP-filtered estimates, OECD Economic Outlook database estimates, WEO country-desk estimates.
  - Country-desk estimates (OECD and WEO) display at least as much persistent uncertainty and excess capacity bias as HP-filtered estimates.
  - Typical revisions from OECD and WEO are larger and more variable than HP-filtered data (Figure 4).
- United States: production-function (CBO) estimates
  - CBO and HP-filtered estimates show similar persistent uncertainty; distribution of revisions slightly less wide for CBO estimates.
  - Sign changes in initial vs final estimates:
    - 7 out of 18 initial estimates change sign by the final estimate for the CBO, OECD, and WEO datasets.
    - 5 out of 18 initial estimates change sign by the final estimate for the HP-filtered estimates.
- Other robustness observations:
  - Results robust to subsample splits (1990s vs 2000s).
  - Filtered data excluding the forecast are even more volatile and subject to revision than those with the forecast included.
  - Results insensitive to changing the vintage for the final estimate to six or eight years rather than seven.

### Key implications for policymakers
- Main challenges:
  - High degree of uncertainty in initial estimates of output gap that persists several years beyond the analyzed period.
  - Initial estimates have an excess capacity bias (tend to overestimate spare capacity).
  - Increased uncertainty around cyclical turning points, especially during recessions.
- Practical consequences:
  - Assessments made at the time of policy decisions are likely to be revised substantially later and likely overstate excess capacity.
  - Revisions larger during turning points imply greater policy risk when using real-time output gap estimates.

### Determinants of output gap revisions — empirical approach
- Objective: explain size of cumulative absolute output gap revisions (final estimate at t+7 minus initial estimate at t+1).
- Model for absolute revision (notation in text):
  - Equation (2): regress absolute cumulative revision on covariates available at time t+1 and other time-invariant covariates; estimate by OLS on pooled panel, robust to heteroskedasticity and autocorrelation; robustness with cross-sectional dependence correction.
- Probit model for sign changes:
  - Equation (3): population-averaged panel probit estimating probability that sign of output gap at final vintage is opposite to initial sign, considering only episodes where revision > 0.5 percentage point of potential GDP; marginal effects reported.
- Categories of regressors:
  1. Domestic or world GDP dynamics:
     - Absolute value of output gap at t+1.
     - Domestic and world real GDP growth surprises at t+1 (deviation from 10-year mean).
  2. Macroeconomic uncertainty proxies:
     - Real GDP growth standard deviation over last 10 years (measured at t+1).
     - Rents/GDP (sum of oil, natural gas, coal, mineral, and forest rents) as proxy for resource-driven structural changes.
     - Inflation.
  3. Policy frameworks:
     - Dummies for inflation targeting and cyclical fiscal rules (fiscal rules specified in terms of cyclically adjusted aggregates).
  4. Statistical capacity and country characteristics:
     - Dummies for OECD country, low-income country (LIC), and small economy (population below 10th percentile).

### Determinants — main statistical findings (Table 4 highlights)
- Sample and estimation:
  - Baseline sample: 2,943 observations for 171 countries over 1990-2007 using HP-filtered real GDP data.
  - When using WEO and OECD country-desk estimates, sample sizes fall to about a sixth and a tenth, respectively.
- Selected marginal effects / coefficients (preserve reported values and significance):
  - A one percentage point increase in the (absolute value of the) output gap is associated with a 0.11 percentage point increase in its revision (column 1: 0.109***; (0.035)).
  - A one percentage point increase in the deviation of domestic real GDP growth from its past 10 years’ mean raises the revision by 0.07 percentage points (reported text: 0.07 percentage points).
  - Absolute world real GDP growth surprise shows a positive association in several specifications (e.g., column 1: 0.189** (0.077)).
  - Rents/GDP:
    - Column 1: 0.020*** (0.007).
    - Column 2: 0.021*** (0.006).
    - In some specifications (OECD/WEO columns) coefficient is negative and significant (e.g., -0.054***, -0.056**).
  - Inflation: mixed results across specifications (e.g., column 1: 0.009 (0.007); column 5: 0.114** (0.055)).
  - Inflation targeting dummy: negative and significant in main specs (column 1: -0.362*** (0.135); column 2: -0.330** (0.154)), indicating smaller revisions where inflation targeting is present.
  - Cyclical fiscal rules: coefficients not robust/significant across specifications (e.g., column 1: 0.056 (0.167)).
  - OECD dummy: negative and significant where applicable (e.g., -0.542*** (0.151)).
  - LIC dummy: positive and significant where applicable (e.g., 0.503** (0.230)).
  - Small economy dummy: positive and significant where applicable (e.g., 0.790*** (0.216)).
- Model fit and sample notes:
  - Observations and R-squared across columns:
    - Column 1 (HP filtered): Observations 2,943; R-squared 0.164; Number of economies 171.
    - Column 3 (WEO data): Observations 437; R-squared 0.407; Number of economies 29.
    - Column 5 (OECD data): Observations 299; R-squared 0.157; Number of economies 26.
  - Notes: Heteroskedasticity and autocorrelation robust standard errors in parentheses for OLS and FGLS; PCSE columns also correct for cross-sectional dependence; ***, **, * indicate significance at 1, 5 and 10 percent, respectively; # denotes variables measured at time t+1.

### Interpretation and residual uncertainty
- While several variables are significant predictors of the magnitude of absolute revisions, a large share of revisions remains unexplained by the models.
- Unpredictability implication:
  - Many revisions may not be predictable at the time policy decisions are made.
  - This residual unpredictability complicates reliance on real-time output gap estimates for policy stance decisions.

*Source: Authors' calculations.*

### 0.19 percentage points.

### 0.19 percentage points.

### Main findings on determinants of output gap revisions
- Evidence on the effects of macroeconomic uncertainty on output gap revisions is mixed.
- The coefficient on historical growth volatility is insignificant, suggesting that historically volatile countries are not subject to greater uncertainty around output gap estimates.
- Resource-rich countries: an increase of one percentage point in rents as a share of GDP brings about an increase in the revision by 0.02 percentage points.
- Inflation targeting regimes: these countries have output gap revisions that are 0.36 percentage points lower than other countries, holding other factors constant.
- Fiscal rules are not reflected in any significant change in the size of the revisions.
- Quality (including timeliness) of data is a statistically significant determinant of the revisions:
  - OECD countries have revisions over half a point smaller than those of other countries.
  - LICs have revisions that are about half a point larger than other countries.
  - Small countries have even larger revisions—0.79 percentage points greater than the rest of the sample.

### Robustness checks and alternative data sources
- Correcting for cross-sectional dependence of standard errors yields results very similar to the preferred specification, suggesting such dependence is not pervasive in the data (Column 2).
- Using WEO output gap estimates (Columns 3 and 4) and OECD estimates (Columns 5 and 6) produces generally consistent results, though some statistically significant coefficients are larger in magnitude in these alternatives:
  - The magnitude of the coefficients for the size of the output gap and surprises in world real GDP growth are about six and four times larger, respectively, when WEO data are used.
  - These same coefficients are 1¼ and 4 times larger when OECD data are used.
  - Coefficients for real GDP growth volatility and inflation targeting regime are significant when OECD data are used and maintain a similar magnitude.

### OECD-specific and country-sample findings
- Two variables become statistically significant when using OECD output gap estimates:
  - Rents (as a share of GDP) take a negative sign, suggesting that the size of the revisions is smaller when the country is resource rich. This counterintuitive result is mainly driven by large rents in Norway, Canada, and Australia—countries with a high degree of macroeconomic stability.
  - Estimating a regression including an interaction term between rents and a dummy variable taking a value of one for Norway, Canada, and Australia yields a non-significant coefficient on rents.
- Caution: these robustness checks should be taken with caution because:
  - The sample is only a fraction of the one in Column 1.
  - The subset of countries used in Columns 3 to 6 may suffer from selection bias because the countries included are mainly advanced economies.

### HP-filter smoothing parameter check
- The same specifications in Columns 1 and 2 are run using HP-filtered WEO data that are generated by   equal to 6.25.
- The results are very similar to the ones reported in Columns 1 and 2 and suggest that the choice of the smoothing parameter does not affect the main findings.

*Source: _wp1514 - 0.19 percentage points.*

### conclusions.

### conclusions.

### Main empirical findings
- The goodness of fit of the different specifications falls in the 10 to 41 percent range.
- A large component of the revisions behaves as a white noise process and thus cannot be explained by factors known to policymakers.
- Initial assessments of an economy’s cyclical position overestimate the amount of slack in the economy; revisions are persistent, especially during recessions.
- Output gap revisions are positively associated with the absolute value of the initial estimate of the output gap, and real GDP growth surprises tend to make subsequent output gap revisions larger.
- Evidence on the effects of macroeconomic uncertainty on output gap revisions is mixed, while quality of data is a statistically significant determinant of the revisions.
- Countries with inflation targeting regimes have lower output gap revisions.
- Overall, regressions predict a low share of the variation in output gap revisions; ex ante predictability (when useful for policy) is likely even lower.

### Determinants of the absolute output gap revisions (selected estimates from Table 5, extensions)
- Abs. output gap: 0.109*** (Columns 1–2); 0.108** (3); 0.107** (4); 0.051 (5).
- Abs. real GDP growth surprise: 0.074*** (Columns 1–2); 0.081*** (3–4); 0.065*** (5).
- Abs. world real GDP growth surprise: 0.200** (1); 0.189** (2); 0.164* (3); 0.166* (4); 0.214*** (5).
- Rents/GDP: 0.021*** (1); 0.020*** (2); 0.017** (3–4); 0.015** (5).
- Inflation targeting: -0.394*** (1); -0.361*** (2); -0.274* (3); -0.304** (4); -0.344*** (5).
- OECD: -0.578*** (1); -0.544*** (2); -0.328* (3); -0.316* (4); -0.549*** (5).
- LIC: 0.542** (1); 0.506** (2); 0.482* (3); 0.538** (4); 0.582** (5).
- Small economy: 0.828*** (columns where included).
- Abs. average future real GDP growth differential (Column 5): 0.123***.
- Constant terms (examples): 1.458*** (1); 1.441*** (2); 1.484*** (3); 1.494*** (4); 1.327*** (5).
- Observations: 2,943 (Columns 1–2); 2,241 (Columns 3–4); 2,942 (Column 5).
- R-squared examples: 0.165 (1); 0.164 (2); 0.183 (3–4); 0.185 (5).
- Number of economies: 171 (Columns 1–2); 129 (Columns 3–4); 171 (Column 5).

Notes from extensions:
- GDDS and SDDS dummies: GDDS insignificant (Column 1); SDDS insignificant in Table 5 but later SDDS is significant and negative in probit extensions.
- Conflict dummy (loss of life due to conflict) statistically insignificant (Column 2).
- Institutional quality measures (bureaucratic quality, control of corruption) insignificant in Table 5 but become significant with expected negative sign when country-group dummies are excluded (results not shown).

### Determinants of the probability of the output gap changing sign (selected marginal effects from Table 6)
- Abs. output gap: #-0.071*** (Columns 1–3); #-0.087*** (4); #-0.086*** (5); #-0.065*** (6).
- Abs. real GDP growth surprise: #0.005* (1–3); 0.003 (4–5); 0.008*** (6).
- Inflation: 0.002** (Columns where significant).
- Inflation targeting: -0.085*** (1); -0.055** (2); -0.085*** (3); -0.077*** (4); -0.081*** (5); -0.085*** (6).
- Cyclical fiscal rules: 0.116* (1); 0.143** (2); 0.116* (3); 0.112* (4); 0.102 (5); 0.114* (6).
- OECD: -0.135*** (1); -0.131*** (2); -0.135*** (3); -0.102*** (4); -0.141*** (5); -0.133*** (6).
- LIC: 0.106*** (1); 0.100*** (2); 0.106*** (3); 0.100** (4); 0.130*** (5); 0.096*** (6).
- SDDS: -0.071*** (when included).
- Abs. average future real GDP growth differential: -0.019*** (Column with that regressor).
- Observations: 2,943 (many specifications); 2,412 or 2,942 in others.
- Number of economies examples: 171; 129 in some columns.

Interpretation:
- A one percentage point increase in the size of the output gap reduces the probability of a sign change by 0.07 percent.
- An increase in inflation by one percentage point increases the probability of a sign change by 0.002 percent.
- Cyclical fiscal rules are associated with a 0.12 percent increase in probability of sign change in some specifications.
- Being an OECD country reduces the sign-change probability; being a LIC increases it.

### Monetary policy implications and LA-5 (Brazil, Chile, Colombia, Mexico, Peru)
- Confidence intervals around initial or revised output gap estimates can be constructed using historical distributions of cumulative revisions; widths vary by country and vintage, with initial estimates having the widest intervals.
- For LA-5, initial real-time output gap estimates (quarterly, HP filter with smoothing parameter of 1600, series extended 5–8 quarters using GDP growth expectations to mitigate endpoint problems) show substantial revisions when compared with later vintages; examples:
  - Brazil: latest estimate suggests higher capacity utilization from 2010 to 2012 than initial estimates.
  - Chile and Mexico: initial estimates revised up substantially from 2006 to 2008.
  - Colombia: initial estimates revised up in 2008.
  - Peru: initial estimates showing output above potential in 2005–2007 were later reversed as potential output was revised upward.
- Real-time monetary policy reaction function modeled as: instrument responds to expected inflation and (lagged) output gap, with lagged policy rate included (persistence).

Estimated monetary policy reaction functions (Table 7) — coefficients by country (Brazil, Chile, Colombia, Mexico, Peru)
- α0 (intercept): 4.72; 4.59**; 2.52**; 1.94**; 2.91**.
- απ (response to expected inflation): 1.16; 3.04**; 3.18*; 2.51**; 1.56**.
- αy (response to output gap): 1.89**; 0.96**; 0.74**; 0.43**; 0.88*.
- ρ (persistence on lagged policy rate): 0.82**; 0.77**; 0.73**; 0.66**; 0.85**.
- Adjusted r-squared: 0.94; 0.97; 0.95; 0.98; 0.90.
- Standard error of the regression: 0.77; 0.34; 0.52; 0.30; 0.40.

Key implications from reaction functions:
- In all LA-5 cases the central bank reacts strongly to increases in inflation expectations; response is statistically significant except for Brazil (where the inflation response is less precisely estimated).
- LA-5 central banks also counter increases in the output gap by raising interest rates; αy is positive and statistically significant in all cases.
- Lagged interest rate persistence is strongly significant in all cases.
- These estimated rules provide a close fit to actual policy interest rates over 2005–2014.

### Policy deviations and informational content of revisions
- Combining reaction functions with revised real GDP data shows substantial deviations between actual policy and the policy that would have been prescribed using revised data; deviations of over 100 basis points occur in multiple episodes across all LA-5 countries and some episodes last over a year.
- Using a three-quarter moving average of the output gap produces deviations similar in magnitude but with more persistence.
- Regressions linking inflation to initial output gap estimates and to revisions (with four lags and Wald F-tests for joint significance) yield two key findings:
  - Initial estimates of the output gap are measured with such error that other than in Colombia they are not informative about the future direction of inflation.
  - Output gap revisions are highly informative about future inflation in all countries, explaining 40 to 50 percent of the variation in inflation on average.
- These results hold when excluding contemporaneous output gap terms and when using core rather than headline inflation.
- Interpretation: noisy initial output gap estimates surround formulation of countercyclical policy with substantial uncertainty; revisions contain information relevant for inflation that is not incorporated in real time.

### Policy implications (summary messages)
- Confidence intervals based on historical output gap revisions are typically so wide at the time of the initial estimate that they often span positive and negative values, making it rare to be confident whether policy should be contractionary, neutral, or expansionary.
- Reliance on real-time assessments of the cyclical position of the economy is a key weakness for monetary policy rules: the level of economic activity relative to potential is often unknown with much certainty until long after policy decisions are made.
- Central banks using inflation-targeting frameworks should be aware that output gap revisions contain information about future inflation not available in real time; this implies value in:
  - Recognizing the large real-time uncertainty around output gap estimates when designing policy rules.
  - Using a broad set of indicators and judgment to supplement noisy output gap measures.
  - Considering robustness of policy prescriptions to plausible revisions in the output gap.

*Source: Authors' calculations; conclusions section of the provided IMF working paper content.*

### Appendix I. Data

### Appendix I. Data

### Countries Included in the Analysis
- Advanced economies (OECD member economies since 1990) marked with an asterisk (*):  
  - Australia * +, Austria *, Belgium *, Canada * +, Denmark * +, Finland *, France *, Germany * +, Iceland *, Ireland *, Italy *, Japan *, Luxembourg *, Netherlands * +, New Zealand *, Norway * +, Portugal *, Spain *, Sweden *, Switzerland * +, United Kingdom * +, United States * +
- Countries included in WEO data regressions are marked with an asterisk (*).
- Countries included in OECD data regressions are marked with a plus sign (+).
- Full list of countries in sample (verbatim ordering from source):
  - Australia * +, Denmark * +, Greece * +, Japan * +, Norway * +, Switzerland * +
  - Austria * +, Finland * +, Iceland * +, Luxembourg * Portugal * + Turkey +
  - Belgium * +, France * +, Ireland * +, Netherlands * +, Spain * +, United Kingdom * +
  - Canada * +, Germany * +, Italy * +, New Zealand * +, Sweden * +, United States * +
  - Albania, Cape Verde, Gabon, Latvia, Papua New Guinea, St. Vincent & Grens.
  - Algeria, Chile, Georgia, Lebanon, Paraguay, Sudan
  - Angola, China, P.R.: Mainland, Ghana, Lesotho, Peru, Suriname
  - Antigua and Barbuda, China, P.R.: Hong Kong *, Grenada, Libya, Philippines, Swaziland
  - Argentina, Colombia, Guatemala, Lithuania, Poland +, São Tomé & Príncipe
  - Armenia, Congo, Republic of, Guinea, Macedonia, FYR, Qatar, Thailand
  - Azerbaijan, Rep. of, Costa Rica, Guyana, Malaysia, Romania, Tonga
  - Bahamas, The, Croatia, Honduras, Maldives, Russian Federation, Trinidad and Tobago
  - Bahrain, Kingdom of, Cyprus *, Hungary +, Mauritania, Samoa, Tunisia
  - Barbados, Czech Republic +, India, Mauritius, Saudi Arabia, Turkmenistan
  - Belarus, Côte d'Ivoire, Indonesia, Mexico, Senegal, Ukraine
  - Belize, Djibouti, Iran, I.R. of, Moldova, Seychelles, United Arab Emirates
  - Bhutan, Dominica, Israel *, Mongolia, Singapore *, Uruguay
  - Bolivia, Dominican Republic, Jamaica, Morocco, Slovak Republic, Uzbekistan
  - Bosnia & Herzegovina, Ecuador, Jordan, Namibia, Slovenia *, Vanuatu
  - Botswana, Egypt, Kazakhstan, Nicaragua, Solomon Islands, Venezuela, Rep. Bol.
  - Brazil, El Salvador, Kiribati, Nigeria, South Africa, Vietnam
  - Brunei Darussalam, Equatorial Guinea, Korea, Republic of *, Oman, Sri Lanka, Yemen, Republic of
  - Bulgaria, Estonia, Kuwait, Pakistan, St. Kitts and Nevis, Zambia
  - Cameroon, Fiji, Lao People's Dem. Rep, Panama, St. Lucia
  - Bangladesh, Central African Rep., Ethiopia, Kyrgyz Republic, Nepal, Tanzania
  - Benin, Chad, Gambia, The, Madagascar, Niger, Togo
  - Burkina Faso, Comoros, Guinea-Bissau, Malawi, Rwanda, Uganda
  - Burundi, Congo, Dem. Rep. of, Haiti, Mali, Sierra Leone
  - Cambodia, Eritrea, Kenya, Mozambique, Tajikistan
- Classification rules noted:
  - Low income countries correspond to all countries with a GNI per capita of $1,045 or less in 2012.
  - Emerging economies are all remaining economies in the sample not classified as advanced or low income.

### Description and Sources of Variables
- Time notation used in variable definitions: t+1 and t+7 and explicit "Annual data" / "Quarterly data" where indicated.
- Variables, sources, time of measurement, and definitions (verbatim where specified):

  - Abs. output gap revision  
    - Source: IMF WEO; Authors' calculations  
    - Time of measurement: t+7; t+1  
    - Definition: Absolute value of the cumulative output gap revision of time t, measured between time t+1 and t+7 in percent of potential GDP. Output gap deviations are calculated using HP filtered WEO data, observed WEO data, or observed OECD data.

  - Abs. output gap (HP filtered WEO data)  
    - Source: IMF WEO; Authors' calculations  
    - Time of measurement: t+1  
    - Definition: Absolute value of the initial output gap in time t, in percent of potential GDP. Potential GDP is calculated using a Hodrick-Prescott filter on real GDP data from each fall WEO vintage between 1990 and 2014 . The smoothing parameter lambda is set to 100 to replicate WEO output gap estimates as close as possible. To ensure accurate smoothing, we run the HP filter on each country-vintage if there is available data from 1980 onwards and at least 15 consecutive observations. WEO data for forecasts five years ahead is included in the HP filter to avoid endpoint bias.

  - Abs. output gap (observed WEO/OECD estimate)  
    - Source: IMF WEO; OECD  
    - Time of measurement: t+1  
    - Definition: Absolute value of the initial output gap in time t, in percent of potential GDP. Estimates are obtained from the IMF WEO or the OECD economic outlook.

  - Abs. real GDP growth surprise  
    - Source: IMF WEO; OECD; Authors' calculations  
    - Time of measurement: t+1  
    - Definition: Difference between real GDP growth and the mean growth of the last 10 years, in absolute terms. Data are calculated using observed WEO data or observed OECD data.

  - Abs. world real GDP growth surprise  
    - Source: IMF WEO; OECD; Authors' calculations  
    - Time of measurement: t+1  
    - Definition: Difference between real world GDP growth and the mean world growth of the last 10 years, in absolute terms. Data are calculated using observed WEO data or observed OECD data.

  - Real GDP growth SD  
    - Source: IMF WEO; OECD; Authors' calculations  
    - Time of measurement: t+1  
    - Definition: Standard deviation of domestic real GDP growth over the last 10 years. Data are calculated using observed WEO data or observed OECD data.

  - Rents/GDP  
    - Source: World Bank Worldwide Development Indicators  
    - Definition: Total natural resources rents, in percent of GDP. Defined as the sum of oil, natural gas, coal, mineral, and forest rents.

  - Inflation  
    - Source: IMF WEO; Authors' calculations  
    - Definition: Bounded CPI-based inflation indicator, derived from the inter-temporal consumption optimization of consumer in a discrete time framework. The indicator is calculated as the inflation rate divided by one plus the rate of inflation - expressed in decimals rather than percent - such that the indicator is always bounded between zero and one.

  - Inflation targeting  
    - Source: IMF Finance & Development  
    - Definition: Dummy variable for an inflation targeting framework; 1 = yes, 0 = no.

  - Cyclical fiscal rules  
    - Source: IMF Fiscal Rules Dataset  
    - Definition: Dummy variable for a national or supranational stabilization fiscal rule; 1 = yes, 0 = no.

  - OECD  
    - Source: Authors' calculations  
    - Definition: Dummy variable for OECD member economy as of 1990; 1 = yes, 0 = no.

  - LIC  
    - Source: IMF; Authors' calculations  
    - Definition: Dummy variable for low income country as classified by the IMF; 1 = yes, 0 = no.

  - Small economy  
    - Source: Authors' calculations  
    - Definition: Dummy variable for small economy; 1 = yes, 0 = no. Defined as economies with average populations below the 10th percentile of the population distribution.

  - Time index  
    - Source: Authors' calculations  
    - Definition: Linear trend accounting for the learning process of estimating the output gap across the sample period.

  - GDDS  
    - Source: IMF; Authors' calculations  
    - Definition: Dummy variable for IMF member using the General Data Dissemination System; 1 = yes, 0 = no.

  - SDDS  
    - Source: IMF; Authors' calculations  
    - Definition: Dummy variable for IMF member using the Special Data Dissemination System; 1 = yes, 0 = no.

  - Conflict  
    - Source: World Bank Worldwide Development Indicators  
    - Definition: Dummy variable based on battle-related deaths; 1 = more than 1,000 deaths, 0 = all other cases.

  - Bureaucratic quality  
    - Source: International Country Risk Guide  
    - Definition: Ranking of quality of bureaucracy and institutional strength. Higher ranking corresponds to stronger bureaucratic institutions.

  - Control of corruption  
    - Source: International Country Risk Guide  
    - Definition: Ranking of corruption within the political system. Higher ranking corresponds to less corruption.

  - Abs. average future real GDP growth differential  
    - Source: IMF WEO; Authors' calculations  
    - Time of measurement: t+7  
    - Definition: Absolute value of the difference between the mean real GDP growth of the last five years and the mean real GDP growth of the following five years.

  - Output gap (initial)  
    - Source: National authorities; Authors' calculations  
    - Time of measurement: t+1  
    - Definition: Value of the initial output gap in time t, in percent of potential GDP. Potential GDP is calculated using a Hodrick-Prescott filter on real GDP data with a smoothing parameter of 400. To avoid endpoint bias in the HP filter, observed real GDP data is spliced with real GDP growth expectations data to extend the series past the endpoint of actual data.

  - Output gap (final)  
    - Source: National authorities; Authors' calculations  
    - Definition: Constructed using the same method as the initial output gap, with data available through 2014Q2.

  - Real GDP  
    - Source: National authorities  
    - Time of measurement: t+1  
    - Definition: Real GDP in local currency.

  - Real GDP expectations  
    - Source: National authorities  
    - Time of measurement: t+1  
    - Definition: Real GDP growth expectations of market participants surveyed by country central banks, in percent.

  - Headline inflation  
    - Source: National authorities  
    - Time of measurement: t+1  
    - Definition: Consumer price index, 12 month percent change.

  - Core inflation  
    - Source: National authorities  
    - Time of measurement: t+1  
    - Definition: Core consumer price index, 12 month percent change.

  - Inflation expectations  
    - Source: National authorities  
    - Time of measurement: t+1  
    - Definition: Twelve-month ahead inflaton expectations of market participants surveyed by country central banks, in percent.

  - Policy rate  
    - Source: National authorities  
    - Time of measurement: t+1  
    - Definition: Nominal interest rate, in percent.

- Note on data frequency labels present in table: "Annual data" and "Quarterly data."

### Notes and Classification Criteria
- Advanced economies correspond to OECD member economies since 1990.
- Low income countries correspond to all countries with a GNI per capita of $1,045 or less in 2012.
- Emerging economies are all remaining economies in the sample.
- HP filter implementation details preserved:
  - For HP-filtered WEO data, the smoothing parameter lambda is set to 100 for WEO vintages between 1990 and 2014; the HP filter is run on each country-vintage if there is available data from 1980 onwards and at least 15 consecutive observations. WEO data for forecasts five years ahead is included to avoid endpoint bias.
  - For Output gap (initial) constructed using national authorities and authors' calculations, the HP filter uses a smoothing parameter of 400 and observed real GDP is spliced with real GDP growth expectations to extend past the endpoint.

*Appendix I. Data (table A1 and table A2) from the source PDF.*

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