## _wp1360 - References

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---

### I. Purpose and scope
- Objective: assess the extent to which the reliability of early estimates of quarterly gross domestic product (GDP) of the Group of Twenty countries (G-20) was influenced by the 2008 financial crisis.
- Focus: descriptive analysis of revisions of quarterly GDP growth rates in 16 G-20 countries since 2000.
- Time coverage of main dataset: June 2000 to April 2012.
- Key takeaways:
  - During 2008 and 2009 (i) revisions to early estimates of quarterly GDP growth rates were of greater magnitude than in previous years, and (ii) downward revisions were more frequent and intense than in previous years; though for some G-20 countries the size of revisions was similar or smaller than in the past.

### II. Data sources and definitions
- Primary realtime data source: OECD Main Economic Indicators (MEI) Original Release Data and Revisions Database.
- Variable used: “GDP, Total Constant prices.”
- Countries analyzed (16): Australia, Brazil, Canada, France, Germany, India, Indonesia, Italy, Japan, Korea, Mexico, Russian Federation, South Africa, Turkey, United Kingdom (U.K.), United States of America (U.S.A.).
- Excluded G-20: Argentina, China, Saudi Arabia (quarterly GDP data not available in the OECD realtime database for the period considered).
- Seasonal adjustment and volume evaluation:
  - GDP data are expressed in seasonally adjusted (SA) form in the MEI, with some early estimates unadjusted for some countries (mostly before 2008).
  - Volume evaluation either in chain-linked form or at constant prices of a base year; methodological changes (base-year changes, chain-linking) are not controlled for in this analysis.
- Quarter spans:
  - For 11 countries (Australia, Canada, France, Germany, Italy, Japan, Korea, Mexico, Turkey, U.K., U.S.A.): 32 quarters before 2008 (2000:Q1 to 2007:Q4) and 15 quarters after 2008 (2008:Q1 to 2011:Q3).
  - Brazil, India, Indonesia, Russian Federation, South Africa: shorter spans; India and Indonesia have 22 and 23 quarters respectively.
- Quarterly growth definition used: year-on-year (q/q-4) growth rates for comparability across vintages and countries.

### III. Revision vintages and revision types
- Four vintages for each quarter t:
  - 1st_y = first estimate (published within the next quarter, usually between 25 and 80 days).
  - 3m_y = estimate released three months after the first estimate.
  - 1y_y = estimate released one year after the first estimate.
  - 2y_y = estimate released two years after the first estimate (treated as the final estimate in this study).
- Four revision measures:
  - r1 = 3m_y − 1st_y (first quarterly revision).
  - r2 = 1y_y − 3m_y (first annual revision).
  - r3 = 2y_y − 1y_y (second annual revision).
  - r4 = 2y_y − 1st_y (overall revision from first estimate to two-year estimate).
- Rationale for vintages:
  - 1st_y: limited indicators, relies more on forecasting/nowcasting assumptions.
  - 3m_y: incorporates a more comprehensive set of monthly/quarterly indicators.
  - 1y_y and 2y_y: incorporate provisional and more consolidated annual sources and benchmarking.

### IV. Analytical approach
- Sub-sample split to detect crisis effect:
  - Pre-2008 period: beginning quarter available for each country to 2007:Q4.
  - Post-2008 period: 2008:Q1 to 2011:Q3.
- Revisions statistics computed for each quarter and aggregated over pre-2008 and post-2008 subsamples.
- Main summary statistic: Mean Absolute Revision (MAR) to the first estimate (1st_y) measured against the two-year estimate (2y_y) — captures size of revisions irrespective of sign.
- Other statistics computed: Mean Revision (MR), Relative MAR, Standard Deviation of revisions, Minimum revision, Maximum revision, Range.

### V. Key empirical findings
- General growth deceleration after 2008:
  - Figure I.1 result: Indonesia apart, all countries experienced marked deceleration in GDP growth after 2008; growth was below 1 percent in four countries (France, U.S.A., Germany, Canada) and negative in three countries (Italy, Japan, U.K.).
- Revisions magnitude and direction:
  - Overall pattern: during 2008–2009 revisions to early quarterly GDP grew larger and downward revisions were more frequent and intense for many countries.
  - Heterogeneity across countries: some countries displayed smaller or unchanged revision magnitudes in the post-2008 period.
- Examples of MAR changes (pre-2008 vs. post-2008) for selected countries (MAR measured as absolute difference between 1st_y and 2y_y):
  - Japan: 0.68 percent vs. 1 percent.
  - South Africa: 0.38 percent vs. 0.84 percent.
  - Turkey: 0.44 percent vs. 0.81 percent.
  - U.S.A.: 1.13 percent vs. 0.53 percent.
- Around half of the G-20 countries show larger revisions to first estimates of quarterly GDP by the second annual revision for quarters in 2008–2009 compared with earlier quarters.
- The largest revisions (by MAR) after 2008 are for the U.K. and the U.S.A.
- Post-2008 overestimation in first releases is more frequent:
  - Eight countries have negative MR in the post-2008 period: U.S.A., India, Japan, France, Italy, Canada, Brazil, and Germany.
  - In the pre-2008 period only four countries had negative MR: U.S.A. (-0.51 percent), Japan (-0.13 percent), Mexico (-0.02 percent), and Italy (-0.01 percent).
  - Largest negative MR values in the post-2008 period: U.S.A. (-1.13 percent), India (-0.71 percent), Japan (-0.63 percent), France (-0.57 percent), and Italy (-0.43 percent).
- U.K. specifics:
  - Two-year MR near zero (0.02 percent post-2008 vs. 0.04 percent pre-2008) but large MAR after 2008 (0.95 percent) implying offsetting large positive and negative revisions.
  - MR by stage for U.K.: three-month MR = -0.09 percent; one-year MR = 0.15 percent; two-year average ~0.02 percent.
- U.S.A. timing:
  - MR at the four intervals after 2008 are all negative: -0.12 percent, -0.13 percent, -0.66 percent, and -1.13 percent, indicating systematic overestimation in first estimates.
  - Most revisions are introduced at the two-year estimate, reflecting access to more comprehensive annual survey data.
- Canada and Germany:
  - First estimates tend to be higher than the two-year estimates with MR values of -0.17 percent (Canada) and -0.06 percent (Germany) as reported.

### VI. Detection of direction and acceleration/deceleration (q/q-1 analysis)
- Analysis limited to eight countries with official seasonally adjusted GDP series since 2000: Australia, Canada, France, Germany, Italy, Japan, U.K., and U.S.A.
- Direction of change: two vintages a and b have the same direction when ΔGDPa_t and ΔGDPb_t share sign.
- Acceleration/deceleration: detected when second differences ΔΔGDPa_t and ΔΔGDPb_t share sign.
- Comparison with the two-year estimate for post-2008 quarters:
  - First estimate correctly identifies direction for all post-2008 quarters in three countries: Australia, Germany, and Italy.
  - One change of direction occurred in four countries: Canada, France, Japan, and U.S.A. (change from positive to negative).
  - Two changes of direction in the U.K.: positive to negative in 2008:Q2 and negative to positive in 2009:Q3.
  - Acceleration/deceleration after 2008 correctly estimated in four countries: France, Germany, Japan, and the U.K.
  - Examples of small-magnitude revisions producing direction changes: Australia 2008:Q3 first estimate -0.3% revised to +0.03%; 2009:Q4 first estimate +0.6% revised to -0.04%.

### VII. Mechanisms and interpretation
- Data-source representativeness:
  - Short-term indicators often sample large and medium enterprises; small and unincorporated enterprises may be out of scope or exhibit higher nonresponse in periods of rapid change, increasing survey errors and conservative bias.
- Statistical and compilation techniques:
  - Quarterly compilation procedures frequently assume linear short-term behavior (fixed-ratio assumptions, benchmarking to annual data, seasonal adjustment, imputation), which can extrapolate recent trends; abrupt departures from assumed paths generate larger revisions.
- Timeliness–accuracy trade-off:
  - Early vintages prioritize timeliness and therefore rely on partial information and forecasting (nowcasting) methods; later vintages incorporate more complete annual and administrative sources.
- Practical constraints for compilers:
  - Real-time information on nonresponse rates is typically not disseminated, complicating adjustments for differential nonresponse during expansions/recessions.
  - It is challenging in real time to determine whether quarterly assumptions (derived from annual accounts) are violated by sudden economic shifts.

### VIII. Limitations and caveats
- The study does not evaluate or compare the quality of national accounts systems across countries; many factors (including benchmark revisions and methodological changes) may influence revision behavior.
- Methodological changes in volume measures and seasonal adjustment are not controlled for in the analysis.
- Two-year vintage is treated as a practical final estimate for the purposes of this study, though the national accounts revision process can extend beyond two years.

### IX. Conclusions, policy recommendations, and further research
- Empirical outcome:
  - For many G-20 countries, 2008–2009 saw larger and more frequently downward revisions to early quarterly GDP estimates relative to the pre-2008 period, consistent with the hypothesis that business-cycle downturns increase revision size and downward bias.
  - Heterogeneity indicates that country-specific compilation practices and data-source structures mediate the effect.
- Policy recommendations and implications for statistical agencies:
  - Investigate country-specific quarterly revision patterns to improve reliability of future GDP estimates.
  - Consider broadening the spectrum of short-term indicators used in early estimates.
  - Improve statistical techniques in quarterly compilation systems, including benchmarking and seasonal adjustment procedures.
  - Use revisions analysis as an opportunity to investigate and address shortcomings in compilation systems; many countries have longstanding practices of conducting and disseminating revisions analysis.
- Suggested further research:
  - Decompose quarterly GDP revisions by underlying components (production, expenditure, income) to identify which components drive revisions; real-time component data available in OECD MEI could support this.
  - Investigate whether characteristics of GDP compilation systems (seasonal adjustment procedures, forecasting models for missing indicators, short-term data source selection) influence revisions, requiring detailed methodological information and appropriate statistical modeling.

### X. Appendix highlights (selected quantitative examples from country tables)
- Sample windows (selected):
  - Australia pre-2008: 2000:Q1–2007:Q4 (32 quarters); post-2008: 2008:Q1–2011:Q3 (15 quarters).
  - Brazil pre-2008: 2004:Q2–2007:Q4 (15 quarters); post-2008: 2008:Q1–2011:Q3 (15 quarters).
  - India pre-2008: 2004:Q4–2007:Q4 (13 quarters); post-2008: 2008:Q1–2010:Q1 (9 quarters).
- Selected country MAR, MR (first estimate vs. two-year estimate, pre-2008 and post-2008 where reported in tables):
  - Australia MAR (pre/post examples shown across stages): 0.14 0.32 0.19 0.38 0.16 0.24 0.24 0.50; MR: 0.03 0.07 0.00 0.10 0.06 0.04 0.03 0.30.
  - Brazil MAR (stages): 0.15 0.24 0.55 0.77 0.11 0.33 0.43 0.71; MR: 0.10 0.04 0.32 0.46 0.00 0.08 -0.04 -0.13.
  - Japan MAR (stages): 0.41 0.51 0.68 1.00 0.35 0.47 0.64 0.68; MR: -0.09 -0.17 0.14 -0.13 0.08 -0.09 -0.29 -0.63.
  - U.K. MAR (stages): 0.14 0.17 0.22 0.24 0.19 0.24 0.77 0.95; MR: 0.05 0.01 -0.02 0.04 -0.09 -0.03 0.15 0.02.
  - U.S.A. MAR (stages): 0.15 0.24 0.37 0.53 0.19 0.30 0.66 1.13; MR: 0.05 -0.21 -0.35 -0.51 -0.12 -0.13 -0.66 -1.13.
- Direction and acceleration success rates (selected percentages for post-2008 vs. pre-2008 in Tables I.3–I.4):
  - Australia direction: 100% 100% 100% (pre-2008) ; 100% (post-2008).
  - Canada direction: 97% 100% 97% (pre-2008) ; 100% 88% 88% (post-2008).
  - Table I.4 acceleration/deceleration (selected): France post-2008: 100% 100% 100%; U.K. post-2008: 93% 100% 100%; U.S.A. post-2008: 93% 88% 88%.

*Source: _wp1360 - References (excerpts of the working paper text provided).*

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

### _wp1360 - References

### I. Purpose and scope
- Objective: assess the extent to which the reliability of early estimates of quarterly gross domestic product (GDP) of the Group of Twenty countries (G-20) was influenced by the 2008 financial crisis.
- Focus: descriptive analysis of revisions of quarterly GDP growth rates in 16 G-20 countries since 2000.
- Time coverage of main dataset: June 2000 to April 2012.
- Key takeaways stated up front:
  - During 2008 and 2009 (i) revisions to early estimates of quarterly GDP growth rates were of greater magnitude than in previous years, and (ii) downward revisions were more frequent and intense than in previous years; though for some G-20 countries the size of revisions was similar or smaller than in the past.

### II. Data sources and definitions
- Primary realtime data source: OECD Main Economic Indicators (MEI) Original Release Data and Revisions Database.
- Variable used: “GDP, Total Constant prices.”
- Countries analyzed (16): Australia, Brazil, Canada, France, Germany, India, Indonesia, Italy, Japan, Korea, Mexico, Russian Federation, South Africa, Turkey, United Kingdom (U.K.), United States of America (U.S.A.).
- Excluded G-20: Argentina, China, Saudi Arabia (quarterly GDP data not available in the OECD realtime database for the period considered).
- Seasonal adjustment and volume evaluation notes:
  - GDP data are expressed in seasonally adjusted (SA) form in the MEI, with some early estimates unadjusted for some countries (mostly before 2008).
  - Volume evaluation either in chain-linked form or at constant prices of a base year; methodological changes (base-year changes, chain-linking) are not controlled for in this analysis.
- Quarter spans:
  - For 11 countries (Australia, Canada, France, Germany, Italy, Japan, Korea, Mexico, Turkey, U.K., U.S.A.): 32 quarters before 2008 (2000:Q1 to 2007:Q4) and 15 quarters after 2008 (2008:Q1 to 2011:Q3).
  - Brazil, India, Indonesia, Russian Federation, South Africa: shorter spans; India and Indonesia have 22 and 23 quarters respectively.
- Quarterly growth definition used primarily: year-on-year (q/q-4) growth rates; q/q-4 chosen over q/q-1 for comparability across vintages and countries.

### III. Revision vintages and revision types
- Four vintages considered for each quarter t:
  - 1st_y = first estimate (published within the next quarter, usually between 25 and 80 days).
  - 3m_y = estimate released three months after the first estimate.
  - 1y_y = estimate released one year after the first estimate.
  - 2y_y = estimate released two years after the first estimate (treated as the final estimate in this study).
- Four revision measures (differences between vintages):
  - r1 = 3m_y − 1st_y (first quarterly revision).
  - r2 = 1y_y − 3m_y (first annual revision).
  - r3 = 2y_y − 1y_y (second annual revision).
  - r4 = 2y_y − 1st_y (overall revision from first estimate to two-year estimate).
- Rationale for vintages:
  - 1st_y: limited indicators, relies more on forecasting/nowcasting assumptions.
  - 3m_y: incorporates a more comprehensive set of monthly/quarterly indicators.
  - 1y_y and 2y_y: incorporate provisional and more consolidated annual sources and benchmarking.

### IV. Analytical approach
- Sub-sample split to detect crisis effect:
  - Pre-2008 period: beginning quarter available for each country to 2007:Q4.
  - Post-2008 period: 2008:Q1 to 2011:Q3.
- Revisions statistics computed for each quarter and aggregated over pre-2008 and post-2008 subsamples.
- Main summary statistic highlighted: Mean Absolute Revision (MAR) to the first estimate (1st_y) measured against the two-year estimate (2y_y) — captures size of revisions irrespective of sign.

### V. Key empirical findings
- General growth deceleration after 2008:
  - Figure I.1 result: Indonesia apart, all countries experienced marked deceleration in GDP growth after 2008; growth was below 1 percent in four countries (France, U.S.A., Germany, Canada) and negative in three countries (Italy, Japan, U.K.).
- Revisions magnitude and direction:
  - Overall pattern: during 2008–2009 revisions to early quarterly GDP grew larger and downward revisions were more frequent and intense for many countries.
  - Heterogeneity across countries: some countries displayed smaller or unchanged revision magnitudes in the post-2008 period.
- Examples of MAR changes (pre-2008 vs post-2008) for selected countries (MAR measured as absolute difference between 1st_y and 2y_y):
  - Japan: 0.68 percent vs. 1 percent.
  - South Africa: 0.38 percent vs. 0.84 percent.
  - Turkey: 0.44 percent vs. 0.81 percent.
  - U.S.A.: 1.13 percent vs. 0.53 percent.
- Note on interpretation: MAR quantifies size of revisions regardless of sign; directional asymmetries (more frequent/intense downward revisions during recessions) are reported in the paper’s narrative and linked to business-cycle effects.

### VI. Mechanisms and interpretation
- Reasons why revisions may be influenced by the business cycle:
  - Data-source representativeness:
    - Short-term indicators often sample large and medium enterprises; small and unincorporated enterprises may be out of scope or exhibit higher nonresponse in periods of rapid change, increasing survey errors and conservative bias.
  - Statistical and compilation techniques:
    - Many quarterly compilation procedures assume linear short-term behavior (fixed-ratio assumptions, benchmarking to annual data, seasonal adjustment, imputation), which can extrapolate recent trends; abrupt departures from assumed paths generate larger revisions.
  - Timeliness–accuracy trade-off:
    - Early vintages prioritize timeliness and therefore rely on partial information and forecasting (nowcasting) methods; later vintages incorporate more complete annual and administrative sources.
- Practical constraints for compilers:
  - Real-time information on nonresponse rates is typically not disseminated, complicating adjustments for differential nonresponse during expansions/recessions.
  - It is challenging in real time to determine whether quarterly assumptions (derived from annual accounts) are violated by sudden economic shifts.

### VII. Limitations and caveats
- The study does not evaluate or compare the quality of national accounts systems across countries; many factors (including benchmark revisions and methodological changes) may influence revision behavior.
- Methodological changes in volume measures and seasonal adjustment are not controlled for in the analysis.
- Two-year vintage is treated as a practical final estimate for the purposes of this study, though the national accounts revision process can extend beyond two years.

### VIII. Conclusions and areas for further research
- Empirical outcome: for many G-20 countries, 2008–2009 saw larger and more frequently downward revisions to early quarterly GDP estimates relative to the pre-2008 period, consistent with the hypothesis that business-cycle downturns increase revision size and downward bias.
- Heterogeneity indicates that country-specific compilation practices and data-source structures mediate the effect.
- Suggested further research (implied by text):
  - Identification of factors responsible for revisions through analysis at more detailed levels (industry, component, survey nonresponse behavior).
  - Investigation of country-specific compilation procedures and the role of methodological changes (benchmarking, chain-linking, seasonal adjustment) in revision dynamics.

*Source: _wp1360 - References (excerpts of the working paper text provided).*

### 0.24 percent), and Italy (0.45 percent vs. 0.16 percent) presenting the largest differences.

### _wp1360 - 0.24 percent), and Italy (0.45 percent vs. 0.16 percent) presenting the largest differences.

### Revision measurement and visualization
- Later estimate L denotes the two-year estimate 2y and earlier estimate E denotes the first estimate 1st.
- Charts use dark blue for the pre-2008 period and light blue for the post-2008 period.
- MAR (mean absolute revision) values are plotted with pre-2008 values on the X-axis and post-2008 values on the Y-axis; proximity to the main diagonal indicates similar revision intensity across periods.
- MR (mean revision) indicates direction: positive MR → first estimate lower than the two-year estimate; negative MR → first estimate higher than the two-year estimate.
- Revision statistics reported for q/q-4 rates of change include: MAR, MR, relative MAR, standard deviation of revisions, minimum revision, maximum revision, and range (max revision – min revision).
- Revision staging: analysis distinguishes four stages of revision, with tables and bar charts showing MAR and MR across stages and periods; series of quarterly GDP growth rates are shown by time of publication (first estimate through two-year estimate).

### Major empirical findings
- Around half of the G-20 countries show larger revisions to first estimates of quarterly GDP by the second annual revision for quarters in 2008–2009 compared with earlier quarters.
- The largest revisions (by MAR) after 2008 are for the U.K. and the U.S.A.
- Some G-20 countries experienced lower revisions after 2008 despite marked deceleration (example: South Africa and Turkey).
- Post-2008 overestimation in first releases is more frequent:
  - Eight countries have negative MR in the post-2008 period: U.S.A., India, Japan, France, Italy, Canada, Brazil, and Germany.
  - In the pre-2008 period only four countries had negative MR: U.S.A. (-0.51 percent), Japan (-0.13 percent), Mexico (-0.02 percent), and Italy (-0.01 percent).
  - Largest negative MR values in the post-2008 period: U.S.A. (-1.13 percent), India (-0.71 percent), Japan (-0.63 percent), France (-0.57 percent), and Italy (-0.43 percent).
- The U.K. has a near-zero mean revision after two years (0.02 percent post-2008 vs. 0.04 percent pre-2008) but a large MAR after 2008 (0.95 percent), implying offsetting large positive and negative revisions.
- Revision timing in U.K. and U.S.A.:
  - Most revisions are introduced at the two-year estimate, reflecting access to more comprehensive annual survey data.
  - For the U.K., MR by stage: two-year average ~0.02 percent; three-month MR = -0.09 percent; one-year MR = 0.15 percent.
  - For the U.S.A., MR at the four intervals after 2008 are all negative: -0.12 percent, -0.13 percent, -0.66 percent, and -1.13 percent, indicating systematic overestimation in first estimates.
- For Canada and Germany, first estimates tend to be higher than the two-year estimates with MR values of -0.17 percent and -0.06 percent, respectively.

### Detection of direction and acceleration/deceleration (q/q-1 analysis)
- Analysis limited to eight countries with official seasonally adjusted GDP series since 2000: Australia, Canada, France, Germany, Italy, Japan, U.K., and U.S.A.
- Direction of change: two vintages a and b have the same direction when ΔGDPa_t and ΔGDPb_t share sign (both positive or both negative).
- Acceleration/deceleration: detected when second differences ΔΔGDPa_t and ΔΔGDPb_t share sign (both acceleration or both deceleration).
- Comparison with the two-year estimate for post-2008 quarters:
  - First estimate correctly identifies direction for all post-2008 quarters in three countries: Australia, Germany, and Italy.
  - One change of direction occurred in four countries: Canada, France, Japan, and U.S.A. (change from positive to negative).
  - Two changes of direction in the U.K.: positive to negative in 2008:Q2 and negative to positive in 2009:Q3.
  - Acceleration/deceleration after 2008 correctly estimated in four countries: France, Germany, Japan, and the U.K.
  - One change in Italy and the U.S.A. (both from acceleration to deceleration in 2009:Q3).
  - Two changes in Canada (deceleration to acceleration in 2009:Q2 and 2009:Q3).
  - Five changes in Australia (both directions); note small magnitudes can produce direction/acceleration changes (example: Australia 2008:Q3 first estimate -0.3% revised to +0.03%; 2009:Q4 first estimate +0.6% revised to -0.04%).

### Case study: 2008–2009 quarters in four countries
- U.S.A. and U.K.: earlier estimates of 2008:Q4 were revised downward; U.S.A. continued downward revisions through 2009 quarters; U.K. revised 2009:Q3 and 2009:Q4 upward offsetting 2008 downward revisions (leading to MR ≈ 0).
- Canada and Germany: sequence of estimates more stable across periods, but first estimates still tend to be higher than two-year estimates.

### Conclusions
- The paper examines quarterly GDP revisions in 16 G-20 countries over 2000–2011 to evaluate reliability of early quarterly GDP estimates during 2008–2009.
- Key conclusions:
  - Revisions by the second annual revision are larger for about half of the countries for 2008–2009 quarters relative to earlier periods.
  - Overestimation in first releases increased in frequency for 2008–2009 quarters compared with prior years (more negative MR values post-2008).
  - The U.S.A. and Japan show pronounced negative MR after 2008, while the U.K. shows near-zero two-year MR but larger absolute revisions (MAR).
- Caveats: findings are descriptive for this sample; several unaccounted factors may influence revision sizes; revision analysis alone is insufficient for judging GDP compilation quality.

### Policy recommendations and implications for statistical agencies
- Statistical agencies and compilers should:
  - Investigate country-specific quarterly revision patterns to improve reliability of future GDP estimates.
  - Consider broadening the spectrum of short-term indicators used in early estimates.
  - Improve statistical techniques in quarterly compilation systems, including benchmarking and seasonal adjustment procedures.
  - Use revisions analysis as an opportunity to investigate and address shortcomings in compilation systems; many countries have longstanding practices of conducting and disseminating revisions analysis.

### Suggestions for future research
- Decompose quarterly GDP revisions by underlying components (production, expenditure, income) to identify which components drive revisions; real-time component data available in OECD MEI could support this.
- Investigate whether characteristics of GDP compilation systems (seasonal adjustment procedures, forecasting models for missing indicators, short-term data source selection) influence revisions, requiring detailed methodological information and appropriate statistical modeling.

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

### Appendix I. Revisions Analysis of GDP: Summary Tables and Charts

### Appendix I. Revisions Analysis of GDP: Summary Tables and Charts

### Data and sample (Table I.1. GDP Quarters Considered in the Revision Analysis)
- Source: OECD Main Economic Indicators
- pre-2008 and post-2008 sample windows by country (First quarter / Last quarter / # quarters*):
  - Australia: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - Brazil: 2004:Q2 / 2007:Q4 / 15 ; 2008:Q1 / 2011:Q3 / 15
  - Canada: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - France: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - Germany: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - India: 2004:Q4 / 2007:Q4 / 13 ; 2008:Q1 / 2010:Q1 / 9
  - Indonesia: 2006:Q1 / 2007:Q4 / 8 ; 2008:Q1 / 2011:Q3 / 15
  - Italy: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - Japan: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - Korea: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - Mexico: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - Russian Federation: 2003:Q1 / 2007:Q4 / 20 ; 2008:Q1 / 2011:Q3 / 15
  - South Africa: 2002:Q1 / 2007:Q4 / 24 ; 2008:Q1 / 2011:Q3 / 15
  - Turkey: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - U.K.: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
  - U.S.A.: 2000:Q1 / 2007:Q4 / 32 ; 2008:Q1 / 2011:Q3 / 15
- Note: * maximum number of quarters compared in the sample

### Revision vintages and timing (Table I.2. GDP Revisions Vintages Considered for Each Quarter: The Case of 2009:Q1)
- Vintages considered for 2009:Q1 (months of publication and label of vintage):
  - Apr-09, May-09 (1st), Jun-09, Jul-09, Aug-09 (3m), Sep-09, ... , Apr-10, May-10 (1y), Jun-10, ... , Apr-11, May-11 (2y)
- Comparisons reported:
  - 3m-1st
  - 1y-3m
  - 2y-1st
  - 2y-1y

### Average GDP growth (Figure I.1. Average GDP Growth (percent))
- Pre-2008 and post-2008 average GDP growth (percent) by country (values presented visually in figure; listed here in apparent order shown):
  - Japan: -2
  - Italy: 0
  - Germany: 2
  - France: 4
  - USA: 6
  - Mexico: 8
  - Canada: 10
  - U.K.: 1.5
  - Australia: 1.6
  - S.Africa: 1.7
  - Brazil: 2.1
  - Turkey: 2.6
  - Korea: 2.7
  - Indonesia: 2.9
  - Russian F.: 3.1
  - India: 3.4
  - (Additional plotted numeric ticks visible: -2 0 2 4 6 8 10; and separate numeric list showing pre-2008 and post-2008 values: 1.5, 1.6, 1.7, 2.1, 2.6, 2.7, 2.9, 3.1, 3.4, 4.6, 4.7, 5.1, 5.2, 5.9, 7.7, 9.1 and -0.8, -1.1, 0.5, 0.1, 0.2, 1, 0.9, -0.7, 2.1, 2, 3.8, 3.1, 3.1, 5.8, 1.4, 7.4)
- The figure distinguishes pre-2008 and post-2008 averages.

### Mean absolute revisions to GDP q/q-4 growth rates (Figures I.2 and I.3)
- Figures compare Mean Absolute Revision to GDP q/q-4 Growth Rates (in percent): First Estimate vs. Two-Year Estimate.
- Scatter plots and country markers shown for pre-2008 and post-2008.
- Axis ticks illustrated: 0 0.2 0.4 0.6 0.8 1 1.2.
- Countries shown across plots include:
  - Brazil, Canada, Germany, Indonesia, Japan, South Africa, Turkey, Australia, France, India, Italy, Korea, Mexico, Russian F., U.K., USA
- Visual layout shows clustering differences between pre-2008 and post-2008 observations.

### Mean revisions to GDP q/q-4 growth rates (Figure I.4)
- Figure I.4 presents Mean Revision to GDP q/q-4 Growth Rates (in percent): First Estimate vs. Two-Year Estimate.
- Numeric axis ticks include -1 -0.5 0 0.5 1.
- Countries plotted with pre-2008 and post-2008 markers include:
  - USA, India, Japan, France, Italy, Canada, Brazil, Germany, UK, Korea, Indonesia, Turkey, Russian F., Australia, Mexico, South Africa
- Visual indicates direction and magnitude of mean revisions by country and period.

### Country time-series examples: 2008 and 2009 quarters over time (Figures I.5–I.8)
- Time-series plots of GDP q/q-4 growth rates for 2008 and 2009 quarters for selected countries show vintages:
  - Vintages labeled: 1st, 3m, 1y, 2y
- Countries with illustrated series:
  - U.S.A. (Figure I.5)
  - U.K. (Figure I.6)
  - Canada (Figure I.7)
  - Germany (Figure I.8)
- X-axis labels and plotted points include quarters:
  - 2008: 2008:Q1, 2008:Q2, 2008:Q3, 2008:Q4
  - 2009: 2009:Q1, 2009:Q2, 2009:Q3, 2009:Q4
- Y-axis ranges vary by country example:
  - Examples include ranges shown: -3 to 3, -6 to 1, -3 to 3, -6 to 0, -1 to 2, -4 to 2, -2 to 3, -7 to 0
- Each plot displays the evolution of first estimate, 3-month estimate, 1-year estimate, and 2-year estimate for the specified quarters.

### Direction and acceleration success rates (Tables I.3 and I.4)
- Table I.3: Percentage of Times Indicating Same Direction of Growth (pre-2008 and post-2008)
  - Columns: 3m-1st, 1y-1st, 2y-1st (pre-2008) and 3m-1st, 1y-1st, 2y-1st (post-2008)
  - Values (selected entries shown as in source):
    - Australia: 100% 100% 100% (pre-2008) ; 100% (post-2008)
    - Canada: 97% 100% 97% (pre-2008) ; 100% 88% 88% (post-2008)
    - France: 90% 94% 90% (pre-2008) ; 100% 100% 88% (post-2008)
    - Germany: 100% 94% 90% (pre-2008) ; 100% 100% (post-2008)
    - Italy: 90% 90% 94% (pre-2008) ; 100% 100% (post-2008)
    - Japan: 81% 84% 81% (pre-2008) ; 100% 100% 88% (post-2008)
    - U.K.: 97% 100% 100% (pre-2008) ; 100% 88% 75% (post-2008)
    - U.S.A.: 100% 90% 94% (pre-2008) ; 100% 88% 88% (post-2008)
- Table I.4: Percentage of Times Indicating Acceleration or Deceleration (pre-2008 and post-2008)
  - Columns: 3m-1st, 1y-1st, 2y-1st (pre-2008) and 3m-1st, 1y-1st, 2y-1st (post-2008)
  - Values (selected entries shown as in source):
    - Australia: 87% 84% 61% (pre-2008) ; 100% 75% 38% (post-2008)
    - Canada: 100% 100% 97% (pre-2008) ; 87% 88% 75% (post-2008)
    - France: 97% 97% 94% (pre-2008) ; 100% 100% 100% (post-2008)
    - Germany: 97% 97% 97% (pre-2008) ; 87% 100% 100% (post-2008)
    - Italy: 100% 100% 97% (pre-2008) ; 100% 88% 88% (post-2008)
    - Japan: 90% 77% 74% (pre-2008) ; 100% 88% 100% (post-2008)
    - U.K.: 100% 100% 100% (pre-2008) ; 93% 100% 100% (post-2008)
    - U.S.A.: 97% 94% 97% (pre-2008) ; 93% 88% 88% (post-2008)

*Source: Appendix I. Revisions Analysis of GDP: Summary Tables and Charts (figures and tables as presented in the source PDF).*

### Appendix II. Revisions Analysis of GDP:

### Appendix II. Revisions Analysis of GDP: Country Tables and Charts

### AUSTRALIA
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.14 0.32 0.19 0.38 0.16 0.24 0.24 0.50
- MR: 0.03 0.07 0.00 0.10 0.06 0.04 0.03 0.30
- Relative MAR: 0.04 0.10 0.06 0.12 0.08 0.11 0.12 0.26
- St. Dev. Revision: 0.03 0.10 0.05 0.13 0.05 0.12 0.10 0.19
- Minimum Revision: -0.62 -0.94 -0.49 -1.50 -0.35 -0.46 -0.63 -0.41
- Maximum Revision: 0.42 0.59 0.48 0.99 0.48 0.56 0.47 0.96
- Range (Maximum – Minimum): 1.04 1.53 0.97 2.49 0.84 1.02 1.09 1.36

### BRAZIL
- Sample: 2004:Q2–2007:Q4; 2004:Q2–2007:Q4; 2004:Q2–2007:Q4; 2004:Q2–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 15151515151288
- MAR: 0.15 0.24 0.55 0.77 0.11 0.33 0.43 0.71
- MR: 0.10 0.04 0.32 0.46 0.00 0.08 -0.04 -0.13
- Relative MAR: 0.04 0.06 0.13 0.17 0.02 0.06 0.10 0.17
- St. Dev. Revision: 0.08 0.13 0.20 0.26 0.04 0.15 0.22 0.38
- Minimum Revision: -0.19 -0.64 -1.11 -1.20 -0.51 -0.43 -0.93 -1.53
- Maximum Revision: 0.93 1.21 2.15 2.24 0.25 0.56 0.52 1.06
- Range (Maximum – Minimum): 1.11 1.84 3.26 3.43 0.76 0.98 1.45 2.59

### CANADA
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.10 0.20 0.23 0.31 0.12 0.10 0.21 0.24
- MR: -0.01 0.03 0.17 0.19 -0.02 0.03 -0.10 -0.17
- Relative MAR: 0.04 0.07 0.08 0.10 0.05 0.05 0.11 0.13
- St. Dev. Revision: 0.02 0.06 0.05 0.07 0.04 0.04 0.12 0.11
- Minimum Revision: -0.43 -0.62 -0.39 -0.51 -0.24 -0.19 -0.48 -0.47
- Maximum Revision: 0.34 0.60 0.55 0.80 0.19 0.28 0.17 0.20
- Range (Maximum – Minimum): 0.77 1.22 0.95 1.30 0.43 0.48 0.65 0.67

### FRANCE
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.13 0.23 0.30 0.40 0.14 0.21 0.14 0.57
- MR: 0.00 0.07 0.25 0.33 -0.11 -0.21 -0.14 -0.57
- Relative MAR: 0.07 0.13 0.14 0.19 0.08 0.12 0.07 0.30
- St. Dev. Revision: 0.03 0.06 0.07 0.10 0.05 0.05 0.05 0.10
- Minimum Revision: -0.60 -0.38 -0.35 -0.38 -0.69 -0.52 -0.31 -0.99
- Maximum Revision: 0.53 0.69 0.94 1.29 0.07 0.00 0.01 -0.31
- Range (Maximum – Minimum): 1.13 1.07 1.30 1.67 0.76 0.52 0.32 0.68

### GERMANY
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.10 0.11 0.16 0.32 0.14 0.15 0.30 0.23
- MR: 0.01 0.05 -0.02 0.04 0.07 0.14 -0.27 -0.06
- Relative MAR: 0.07 0.08 0.10 0.21 0.04 0.04 0.09 0.07
- St. Dev. Revision: 0.03 0.03 0.05 0.09 0.05 0.05 0.07 0.06
- Minimum Revision: -0.32 -0.22 -0.56 -0.73 -0.18 -0.04 -0.63 -0.32
- Maximum Revision: 0.30 0.63 0.46 0.90 0.45 0.36 0.06 0.28
- Range (Maximum – Minimum): 0.62 0.86 1.01 1.63 0.63 0.40 0.69 0.60

### INDIA
- Sample: 2004:Q4–2007:Q4; 2004:Q4–2007:Q4; 2004:Q4–2007:Q4; 2004:Q4–2007:Q4; 2008:Q1–2010:Q1; 2008:Q1–2010:Q1; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 131313139988
- MAR: 0.06 0.70 0.44 0.86 0.22 0.51 0.42 1.04
- MR: 0.03 0.68 0.02 0.73 0.18 -0.48 -0.37 -0.71
- Relative MAR: 0.01 0.08 0.05 0.09 0.03 0.07 0.07 0.17
- St. Dev. Revision: 0.05 0.15 0.15 0.16 0.11 0.26 0.24 0.43
- Minimum Revision: -0.19 -0.08 -1.29 -0.51 -0.21 -1.79 -1.56 -2.13
- Maximum Revision: 0.49 2.00 1.83 2.42 1.32 0.13 0.19 1.26
- Range (Maximum – Minimum): 0.68 2.07 3.11 2.93 1.52 1.92 1.75 3.39

### INDONESIA
- Sample: 2006:Q1–2007:Q4; 2006:Q1–2007:Q4; 2006:Q1–2007:Q4; 2006:Q1–2007:Q4; 2006:Q1–2011:Q3; 2006:Q1–2010:Q4; 2006:Q1–2009:Q4; 2006:Q1–2009:Q4
- Number of quarters: 8888151288
- MAR: 0.08 0.14 0.08 0.28 0.04 0.08 0.04 0.13
- MR: 0.05 0.00 0.02 0.07 0.01 -0.01 0.04 0.07
- Relative MAR: 0.01 0.02 0.01 0.05 0.01 0.01 0.01 0.02
- St. Dev. Revision: 0.03 0.07 0.03 0.10 0.01 0.04 0.01 0.06
- Minimum Revision: -0.13 -0.40 -0.15 -0.40 -0.17 -0.17 0.00 -0.16
- Maximum Revision: 0.34 0.32 0.21 0.60 0.08 0.21 0.10 0.29
- Range (Maximum – Minimum): 0.47 0.72 0.36 1.00 0.25 0.38 0.10 0.45

### ITALY
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.08 0.11 0.10 0.16 0.13 0.17 0.24 0.45
- MR: 0.01 -0.01 0.00 -0.01 0.00 -0.01 -0.24 -0.43
- Relative MAR: 0.06 0.09 0.08 0.13 0.06 0.07 0.07 0.14
- St. Dev. Revision: 0.02 0.03 0.02 0.05 0.06 0.07 0.05 0.14
- Minimum Revision: -0.25 -0.34 -0.31 -0.55 -0.43 -0.48 -0.47 -0.88
- Maximum Revision: 0.26 0.30 0.45 0.42 0.27 0.20 -0.14 0.10
- Range (Maximum – Minimum): 0.51 0.64 0.75 0.96 0.69 0.68 0.33 0.98

### JAPAN
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.41 0.51 0.68 1.00 0.35 0.47 0.64 0.68
- MR: -0.09 -0.17 0.14 -0.13 0.08 -0.09 -0.29 -0.63
- Relative MAR: 0.19 0.25 0.33 0.48 0.12 0.12 0.17 0.18
- St. Dev. Revision: 0.07 0.14 0.24 0.32 0.12 0.17 0.26 0.13
- Minimum Revision: -1.45 -1.33 -1.30 -1.87 -0.52 -1.27 -1.35 -1.55
- Maximum Revision: 0.96 1.65 2.75 3.61 1.58 1.15 1.12 0.22
- Range (Maximum – Minimum): 2.41 2.98 4.05 5.49 2.10 2.41 2.47 1.77

### KOREA
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.04 0.19 0.26 0.35 0.13 0.27 0.10 0.46
- MR: 0.02 0.01 0.22 0.25 0.06 -0.05 0.10 0.06
- Relative MAR: 0.01 0.04 0.05 0.07 0.03 0.06 0.03 0.12
- St. Dev. Revision: 0.01 0.06 0.06 0.07 0.04 0.15 0.03 0.25
- Minimum Revision: -0.08 -1.41 -0.29 -1.04 -0.21 -0.73 0.00 -0.74
- Maximum Revision: 0.19 0.73 0.84 1.12 0.31 0.42 0.25 0.81
- Range (Maximum – Minimum): 0.27 2.14 1.13 2.16 0.51 1.15 0.25 1.54

### MEXICO
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.08 0.17 0.23 0.33 0.16 0.31 0.41 0.50
- MR: 0.07 -0.09 0.00 -0.02 0.00 0.13 0.15 0.35
- Relative MAR: 0.02 0.05 0.07 0.10 0.04 0.07 0.10 0.12
- St. Dev. Revision: 0.04 0.05 0.05 0.07 0.08 0.08 0.14 0.21
- Minimum Revision: -0.10 -1.26 -0.35 -1.16 -0.49 -0.71 -0.79 -0.42
- Maximum Revision: 1.31 0.27 1.25 1.23 0.77 0.75 0.87 1.49
- Range (Maximum – Minimum): 1.41 1.53 1.60 2.39 1.26 1.46 1.66 1.91

### RUSSIAN FEDERATION
- Sample: 2003:Q1–2007:Q4; 2003:Q1–2007:Q4; 2003:Q1–2007:Q4; 2003:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q3; 2008:Q1–2009:Q3
- Number of quarters: 20202020151277
- MAR: 0.06 0.34 0.42 0.59 0.08 0.25 0.72 0.83
- MR: 0.05 -0.05 0.18 0.17 0.02 0.09 0.17 0.20
- Relative MAR: 0.01 0.05 0.06 0.08 0.01 0.04 0.10 0.11
- St. Dev. Revision: 0.03 0.10 0.11 0.15 0.04 0.08 0.23 0.33
- Minimum Revision: -0.08 -0.66 -1.44 -1.16 -0.19 -0.46 -1.93 -2.07
- Maximum Revision: 0.67 0.73 2.05 2.15 0.35 0.53 1.50 1.53
- Range (Maximum – Minimum): 0.76 1.39 3.49 3.32 0.54 0.99 3.43 3.61

### SOUTH AFRICA
- Sample: 2002:Q1–2007:Q4; 2002:Q1–2007:Q4; 2002:Q1–2007:Q4; 2002:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 24242424151288
- MAR: 0.10 0.53 0.33 0.84 0.04 0.27 0.25 0.38
- MR: 0.08 0.48 0.26 0.82 0.00 0.21 0.07 0.38
- Relative MAR: 0.03 0.13 0.07 0.19 0.02 0.10 0.10 0.15
- St. Dev. Revision: 0.05 0.12 0.09 0.14 0.02 0.12 0.14 0.06
- Minimum Revision: -0.10 -0.17 -0.31 -0.26 -0.22 -0.12 -0.53 0.05
- Maximum Revision: 1.34 1.25 1.10 1.81 0.09 0.86 0.55 0.71
- Range (Maximum – Minimum): 1.44 1.42 1.41 2.08 0.31 0.98 1.08 0.66

### TURKEY
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.30 0.47 0.32 0.81 0.24 0.47 0.44 0.44
- MR: 0.23 0.33 0.11 0.67 0.05 0.32 -0.14 0.08
- Relative MAR: 0.04 0.07 0.05 0.11 0.03 0.07 0.08 0.08
- St. Dev. Revision: 0.07 0.11 0.11 0.18 0.10 0.12 0.19 0.10
- Minimum Revision: -0.42 -0.91 -0.80 -0.65 -0.73 -0.60 -1.49 -0.81
- Maximum Revision: 1.82 1.77 1.74 3.76 0.45 1.07 0.76 0.70
- Range (Maximum – Minimum): 2.24 2.68 2.54 4.41 1.18 1.68 2.25 1.51

### UNITED KINGDOM
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.14 0.17 0.22 0.24 0.19 0.24 0.77 0.95
- MR: 0.05 0.01 -0.02 0.04 -0.09 -0.03 0.15 0.02
- Relative MAR: 0.06 0.07 0.09 0.10 0.08 0.09 0.27 0.34
- St. Dev. Revision: 0.03 0.04 0.07 0.07 0.06 0.10 0.52 0.57
- Minimum Revision: -0.60 -0.47 -0.64 -0.53 -0.78 -0.41 -0.84 -1.22
- Maximum Revision: 0.41 0.31 0.43 0.51 0.14 0.36 2.04 2.43
- Range (Maximum – Minimum): 1.01 0.77 1.07 1.04 0.91 0.76 2.88 3.65

### UNITED STATES OF AMERICA
- Sample: 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2000:Q1–2007:Q4; 2008:Q1–2011:Q3; 2008:Q1–2010:Q4; 2008:Q1–2009:Q4; 2008:Q1–2009:Q4
- Number of quarters: 32323232151288
- MAR: 0.15 0.24 0.37 0.53 0.19 0.30 0.66 1.13
- MR: 0.05 -0.21 -0.35 -0.51 -0.12 -0.13 -0.66 -1.13
- Relative MAR: 0.05 0.08 0.14 0.20 0.09 0.13 0.27 0.47
- St. Dev. Revision: 0.03 0.06 0.08 0.12 0.07 0.17 0.11 0.24
- Minimum Revision: -0.51 -0.89 -1.35 -1.62 -0.68 -1.01 -0.99 -2.58
- Maximum Revision: 0.35 0.22 0.20 0.15 0.23 0.36 -0.35 -0.42
- Range (Maximum – Minimum): 0.86 1.12 1.56 1.76 0.92 1.38 0.64 2.16

*Appendix II. Revisions Analysis of GDP: Country Tables and Charts (tables and figures reproduced as in source).*

### Appendix III. Statistical Analysis of Revisions

### Appendix III. Statistical Analysis of Revisions

### Definition of a revision
- A revision is defined as the difference between a later (more recent) estimate and an earlier estimate.
- Let L_t y and E_t y denote respectively the later and earlier estimates of a same variable y in period t.
- Revision ,LE_t r is calculated as:
  - (1.1) ,LE_t r = L_t y − E_t y

- Note: The variable can be expressed in level or in a transformation of it, for instance rates of change. (footnote 19)

### Summary indicators for a sequence of revisions
- Suppose revisions are observed for N consecutive quarters, denoted with t = 1,..,N. The following summary indicators are used to characterize the revision process.

- Mean Absolute Revision (MAR)
  - Definition (equation as in source):
    - (1.2) , , 1 1 N LE LE t t MAR r N = = ∑
  - Interpretation:
    - The MAR measures the average absolute size of revisions.
    - By using absolute values, MAR compensates revisions with different signs and provides information on magnitude.
    - The minimum value of MAR is zero, attained when there are no revisions (,LE_t r = 0 for any t); revisions different from zero lead to positive MAR values.

- Mean Revision (MR)
  - Definition (equation as in source):
    - (1.3) , , 1 1 N LE LE t t MR r N = = ∑
  - Interpretation:
    - MR indicates the direction of revisions and systematic patterns.
    - When MR is positive (negative), the earlier estimate underestimates (overestimates) the later estimate.
    - MR can be zero even when revisions are nonzero if positive and negative revisions perfectly compensate.
    - Values of MR significantly far from zero indicate a systematic difference between the earlier and later estimates.

- Relative MAR (RMAR)
  - Definition (equation as in source):
    - (1.4) , , , 1 11 1 11 N LE LE t LE t NN LL tt tt r MAR N RMAR yy NN = == == ∑ ∑ ∑
  - Interpretation:
    - RMAR adjusts MAR for the mean absolute size of the variable in the period and is useful to compare relative size of revisions across variables with different magnitudes.

- Standard Deviation of Revisions (SDR)
  - Definition (equation as in source):
    - (1.5) () 2 , , , , , 12 12 3 142 (1)33 NN N LE LE LE LELE LE ttttt tt t SDR r r r r r NN −− == = ⎡⎤ = + + ⎢⎥ − ⎣⎦ ∑∑ ∑
  - Interpretation:
    - SDR measures variability of revisions around their average (MR).
    - SDR is small when revisions are concentrated around the mean revision.

- Minimum Revision (MinR)
  - Definition:
    - (1.6) , , min LE LR t t MinR r =
  - Interpretation:
    - The minimum revision observed in the period t = 1,..,N.

- Maximum Revision (MaxR)
  - Definition:
    - (1.7) , , max LE LR t t MaxR r =
  - Interpretation:
    - The maximum revision observed in the period t = 1,..,N.

- Range
  - Definition:
    - (1.8) , , LE LE LE Range MaxR MinR = −
  - Interpretation:
    - The range is the maximum interval that contains all observed revisions.
    - It is a measure of variability but is less robust than SDR because it is affected by abnormal revisions.

### Estimation note on SDR
- As suggested in Di Fonzo (2005), the variance estimator proposed by Newey and West (1987) is used to adjust for the presence of both heteroskedasticity and autocorrelation of unknown form in the revisions.
- The Newey-West estimator is the one calculated in the spreadsheets available from the OECD MEI website. (footnote 21)

*Source: Appendix III. Statistical Analysis of Revisions*

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