## _wp1431

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### Major findings on information rigidities and forecast formation
- Two main classes of theories on expectation formation:
  - Sticky information (Mankiw and Reis (2002)): infrequent updating because of fixed (“menu”) costs of acquiring information.
  - Noisy/imperfect information (Woodford (2002) and Sims (2003)): continual updating but with noisy signals of the true state.
- Canonical prediction: average forecast errors should be correlated with the past forecast revision (Coibion and Gorodnichenko (2010, 2012)).
- Equivalent diagnostic proposed: correlation between the current forecast revision and the past forecast revision (revision–revision correlation).
  - Advantage: does not require construction of forecast errors or data-vintage collection (e.g., initial vs. final GDP releases).
  - Empirical result: for most countries, degree of information rigidity using the revision–revision correlation is similar to Coibion and Gorodnichenko.
- Individual-level vs. consensus evidence:
  - Individual-level forecasts are updated quite frequently — more consistent with noisy/imperfect information than with sticky information.
  - Averaging forecasts induces additional stickiness relative to individual forecasts.

### Methodology and estimation framework
- Revision definition and data structure:
  - Average forecasts X̄_{i,t,h} for country i, target year t, horizons h = 24, 23, ..., 1.
  - Revision over k* months: Δ̄_{i,t,h} ≡ X̄_{i,t,h} − X̄_{i,t,h−k*} with k* = 3.
- Primary test (Nordhaus framework):
  - Δ̄_{i,t,h} = α_i + λ Δ̄_{i,t,h−k*} + ε_{i,t,h}  (equation (1)).
  - Under full-information rational expectations, λ = 0; λ ≠ 0 implies correlated revisions and rejects forecast efficiency.
- Mapping λ to theories:
  - Sticky information: λ maps directly to degree of information rigidity.
  - Noisy/imperfect information: similar mapping (λ equals informational rigidity, 1 − G in the theoretical model).
- Horizon heterogeneity:
  - Interaction terms added: Δ̄_{i,t,h} = α_i + λ Δ̄_{i,t,h−k*} + Σ_m λ_m 1_{h=h_m} Δ̄_{i,t,h−k*} + ...
  - Coefficients λ_m expected positive and rising with horizon if rigidity increases with horizon.
- Estimation:
  - Fixed-effect panel OLS with Driscoll and Kraay (1998) standard errors.
  - Nickell (1981) bias of order 1/T considered modest.
  - Individual-forecast regression analogous: Δ_{j,i,t,h} = α_{j,i} + λ Δ_{j,i,t,h−k*} + Σ_m λ_m 1_{h=h_m} Δ_{j,i,t,h−k*} + ...  (equation (6)).
  - GMM (Arellano-Bond / Arellano-Bover) used as robustness; focus remains on OLS due to weak/invalid instruments in many cases.
  - Non-parametric update probability: fraction of individuals who updated at least once in the 3 months prior to a given point (consistent with k* = 3).

### Data and descriptive statistics
- Data source: Consensus Economics Inc. monthly survey of annual GDP growth forecasts; submissions during first two weeks of each month; data published mid-month.
- Panel structure: for each target year, sequence of 24 forecasts per panelist between January of year before target and December of target year.
- Sample construction:
  - Included all countries reporting individual forecasts; forecasters reporting at least 10 times.
  - Harmonized forecaster identifiers; handled mergers/acquisitions by keeping the continuing forecaster when evident.
- Sample size and coverage:
  - 188,639 individual forecasts from 36 countries.
  - 104,894 forecasts from 14 advanced economies.
  - Forecasts span target years between 1989 and 2011.
  - On average, nearly 16 individual forecasts per period for each country (Average number of forecasts per country per target year: 15.5 Full Sample; 17.2 Advanced; 13.7 Emerging).
- Forecast errors, revisions, and dispersion:
  - RMSFE declines with forecast horizon.
  - RMSFEs for emerging economies are, on average, more than twice as high as for advanced economies for large horizons and still almost 75 percent higher at the end of the target year.
  - Revisions:
    - Advanced economies: revisions larger around the turn of the year; average size does not vary much with horizon.
    - Emerging economies: revisions much smaller at very long horizons and much higher during the target year (h <= 12); at h = 1 average revision in emerging economies is about twice as large as for advanced economies.
  - Distributional features:
    - High density of small or zero revisions (spikes at zero); otherwise unimodal bell-shaped distributions.
    - Revisions more flattened for emerging economies (large revisions more frequent).
    - Revisions significantly negatively skewed for all horizons.
  - Forecast dispersion:
    - Forecasts become more clustered as horizon shrinks.
    - Advanced economies: very few deviations larger than 0.5 percentage point.
    - Emerging economies: larger dispersion and considerable disagreement even at h = 1.

### Empirical results — Average (consensus) forecasts
- Estimation details:
  - Revisions over k = 3 months; horizons used: h = 1, 4, 7, 10, 13, 16.
  - One observation per target year lost due to lagged revision inclusion (h = 19 lost).
- Main findings:
  - Strong and consistent evidence of information rigidities in consensus forecasts: positive and highly statistically significant correlation between current forecast revision and its first lag for all country groups and estimation methods.
  - Degree of informational rigidity similar between advanced and emerging economies:
    - At very short horizons, coefficient on lagged revisions: 0.41 for emerging economies vs. 0.37 for advanced economies.
  - Horizon pattern:
    - Informational rigidities larger around the turn of the year (h between 13 and 10).
    - Coefficients on interaction terms positive and statistically significant only for horizons 10 (emerging economies) and 13 (advanced economies); other horizons’ additional effects small and not significant.
  - Aggregate estimate ignoring horizon: λ = 0.5 for both advanced and emerging economies.
    - Interpretation under sticky information (quarterly measurement): forecasters update about every six months on average.
    - Interpretation under imperfect information: weight of about 0.5 assigned to past forecasts in current forecasts (cf. equation (4)).
    - Comparison: these estimates are higher than some previous studies (e.g., Coibion and Gorodnichenko estimate 0.14 for the United States).

- Selected quantitative entries (Table 3):
  - Past revision (Average Forecasts): 0.404*** (Full Sample), 0.370*** (Advanced Economies), 0.409*** (Emerging Economies).
    - t-statistics: 6.7, 6.1, 5.6 respectively.
  - Number of observations: 3408 (Average Forecast regressions, Full Sample), 1698 (Advanced), 1710 (Emerging).
  - Note: Omitting forecast data made in December 2008 for the growth rate of 2009; including them increases "Past revision*Horizon 13" to about 0.84 and could imply a total rigidity parameter above 1.

### Empirical results — Individual forecasts
- Update frequency and implied stickiness:
  - Share of forecasters who updated at least once in the three months prior ranges between 0.8 and 0.9 over horizons (Figure 6).
    - Average fractions higher for advanced economies (0.85) than for emerging economies (0.79).
    - Slight increase in update share as horizon shrinks; hump around h ≈ 13.
  - Comparison to implied update probabilities from average-forecast regressions:
    - Average-forecast coefficients imply update-quarter probabilities between 1 − .94 = 0.06 and 1 − .25 = 0.75.
    - Individual-data fractions (0.8–0.9) indicate higher updating frequency than average-forecast regressions suggest.
    - Conclusion: sticky information plays a smaller role than consensus-based estimates imply.
- Forecast smoothing at individual level:
  - Past revision (Individual Forecasts): 0.203*** (Full Sample), 0.127** (Advanced Economies), 0.223*** (Emerging Economies).
    - t-statistics: 6.3, 2.7, 6.1 respectively.
  - Degree of smoothing smaller at individual level than consensus:
    - Ratio of Coefficients on Past Revisions (individual / average): 0.50 (Full Sample), 0.32 (Advanced Economies), 0.55 (Emerging Economies).
    - Interpretation: persistence in forecast revisions about halved at individual level; averaging induces additional stickiness.
  - Country-group differences:
    - Coefficients higher for emerging economies (0.23) than for advanced economies (0.13) at individual level.
    - Possible causes: greater lags in data releases, weaker quality of statistics, fewer resources for forecasting in emerging economies.
  - Horizon effects at individual level:
    - Non-monotonic; evidence of variation is weak and often not statistically significant.
- Cross-country heterogeneity:
  - Substantial variation across countries in λ from average and individual regressions (Table 4).
  - For 29 out of 31 countries, smoothing parameter from average forecasts is higher than from individual forecasts (often substantially).
  - Examples (Table 4 selected entries):
    - Germany: λ (average) = 0.613, sd = 0.044, N = 364, R2 = 0.35; Avg. λ (individual) = 0.337, Avg. sd = 0.103, Avg. N = 200.3, Avg. R2 = 0.35, Avg. Frac. = 0.78.
    - USA: λ (average) = 0.330, sd = 0.051, N = 364, R2 = 0.10; Avg. λ (individual) = 0.037, Avg. sd = 0.339, Avg. N = 121.4, Avg. R2 = 0.02, Avg. Frac. = 0.84.
    - China: λ (average) = 0.577, sd = 0.052, N = 277, R2 = 0.31; Avg. λ (individual) = 0.032, Avg. sd = 0.276, Avg. N = 106.4, Avg. R2 = 0.00, Avg. Frac. = 0.66.
    - India: λ (average) = −0.079, sd = 0.058, N = 277, R2 = 0.01; Avg. λ (individual) = −0.243, Avg. sd = 0.154, Avg. N = 63.3, Avg. R2 = 0.02, Avg. Frac. = 0.83.
  - Note: λ denotes estimated coefficient for the first lag of the 3-month revision. Avg. Frac. = fraction of forecasters that, on average, adjust their forecasts at least once during a three months period.

### Summary quantitative tables and figures (select figures and table summaries)
- Table 1 (Basic features):
  - Number of target years: 23 (Full Sample, Advanced Economies, Emerging Economies).
  - Number of countries: 36 (Full Sample), 14 (Advanced), 22 (Emerging).
  - Number of individual forecast observations: 188 639 (Full Sample), 104 894 (Advanced), 83 745 (Emerging).
  - Average forecast Mean: 3.2 (Full Sample), 2.1 (Advanced), 4.6 (Emerging).
  - Average forecast Median: 3.0 (Full Sample), 2.4 (Advanced), 4.8 (Emerging).
  - Average forecast errors Mean: 0.0 (Full Sample), −0.1 (Advanced), 0.1 (Emerging).
  - Average forecast errors Median: 0.2 (Full Sample), 0.1 (Advanced), 0.4 (Emerging).
- Table 2 (Mean Absolute Deviation from Consensus at horizons h=18, h=12, h=6, h=1):
  - Full sample: 0.29, 0.26, 0.19, 0.10.
  - Advanced economies: 0.24, 0.22, 0.15, 0.07.
  - Emerging economies: 0.36, 0.32, 0.28, 0.15.
  - Variance of Deviation from Consensus (Full sample): 0.42, 0.39, 0.31, 0.17.
  - Variance of Deviation from Consensus (Advanced): 0.33, 0.29, 0.21, 0.11.
  - Variance of Deviation from Consensus (Emerging): 0.56, 0.52, 0.45, 0.25.
- Table 3 and figures:
  - Past revision (Average Forecasts): 0.404*** (Full Sample).
  - Past revision (Individual Forecasts): 0.203*** (Full Sample).
  - Figures illustrate RMSFE over horizons, mean absolute revisions, distributions of revisions and deviations, informational rigidities across horizons, fractions of revised individual forecasts, and distribution of information rigidity coefficients across countries.

### Conclusions, interpretation, and policy implications
- Main conclusions:
  - Degree of rigidity is less pronounced in individual data than in consensus data; average smoothing parameter based on average revisions is about 3 times as large as that based on individual revisions.
  - No substantial difference in average rigidity between advanced and emerging economies; estimates somewhat more dispersed within emerging economies.
  - Country-specific average fractions of forecasters updating at least once in three months: Advanced economies 0.85; Emerging economies 0.79; standard deviation across countries ≈ 0.06 in both groups.
- Implications for theory:
  - Evidence against the pure sticky information model as a primary description of growth-forecast dynamics.
  - Consensus-based measures overstate forecasters’ inattentiveness; individual-level update shares support imperfect/noisy information explanations.
  - Predictability of individual forecast revisions and high update shares indicate limited role for sticky information.
- Policy and research implications:
  - Models of forecast formation and policy analysis should account for higher individual updating frequency than consensus-based estimates suggest.
  - Further research directions: investigate herding and interaction with forecast smoothing; explore nonlinearities in forecast smoothing; study implications of uncertainty for macro forecasting dynamics; examine evolution of forecast rigidities over the business cycle.

*Source: _wp1431 - References and Section IV empirical results.*

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

### _wp1431 - References

### Major findings on information rigidities and forecast formation
- Two main classes of theories on the formation of expectations are highlighted:
  - Sticky information (Mankiw and Reis (2002)): forecasters update information sets infrequently because of fixed (“menu”) costs of acquiring information.
  - Noisy/imperfect information (Woodford (2002) and Sims (2003)): forecasters continually update information sets but receive noisy signals of the true state of the economy.
- Canonical versions of both classes predict that average forecast errors should be correlated with the past forecast revision (Coibion and Gorodnichenko (2010, 2012)).
- An equivalent test for information rigidities is proposed: examine the correlation between the current forecast revision and the past forecast revision.
  - Advantage: does not require construction of forecast errors or collection of various versions of ex post data (e.g. initial releases of GDP vs. final estimates), which is especially useful when analyzing a large number of countries.
  - Empirical result: for most countries, the degree of information rigidity in average forecasts using this revision–revision correlation approach is similar to that reported by Coibion and Gorodnichenko.
- Distinction between sticky information and noisy information is attempted by using individual-level forecasts in addition to average/consensus forecasts.
  - Finding: at the individual level, forecasts are updated quite frequently, which is more consistent with the noisy information class of theories than with the sticky information model where agents do not change forecasts for extended periods due to menu costs.
- Cross-country heterogeneity:
  - The degree of information rigidity varies across countries for both average and individual-level forecasts.
  - There is heterogeneity within advanced countries and within emerging market economies.
  - No systematic differences in the extent of information rigidity are found between advanced and emerging market country groups.

### Methodology and data approach
- Methodological innovation:
  - Use correlation between current and past forecast revisions as a diagnostic of information rigidity; avoids reliance on ex post data vintages.
- Data scope and advantages:
  - Broad country coverage enables comparison of forecast smoothing across advanced and emerging economies.
  - Use of individual-level forecast data helps avoid aggregation bias noted in the literature (Crowe (2010)); individual data approach aligns with recommendations from Andrade and Le Bihan (2013).
- Paper organization relevant to methodology and data:
  - Section II discusses the methodology for testing the degree of forecast smoothing using average and individual forecast data.
  - Section III describes the data on international growth forecasts and highlights stylized facts.

### Empirical illustrations and summary materials (listed in source)
- Tables:
  - 1. Basic Features of Forecast Data
  - 2. Revisions and Deviations from the Average Forecast
  - 3. Information Rigidity and Forecast Smoothing
  - 4. Country-Specific Estimates
- Figures:
  - 1. Root Mean Squared Forecast Errors over Forecast Horizons
  - 2. Mean Absolute Revisions over Forecast Horizons
  - 3. Distribution of Forecast Revisions
  - 4. Distribution of Deviation of Individual Forecasts from Average
  - 5. Informational Rigidities at Different Forecast Horizons
  - 6. Fractions of Revised Individual Forecasts
  - 7. Distribution of Information Rigidity Coefficients across Countries

*Source: _wp1431 - References.*

### Section IV presents the empirical results. The last section concludes.

### _wp1431 - Section IV presents the empirical results. The last section concludes.

### Methodology for testing for forecast smoothing
- Data structure and basic definitions:
  - Sequence of (average) forecasts X̄_{i,t,h} for country i and target year t made at horizons h = 24, 23, ..., 1.
  - Revision of the average forecast computed over k* months: Δ̄_{i,t,h} ≡ X̄_{i,t,h} − X̄_{i,t,h−k*}. The authors set k* = 3.
- Nordhaus (1987) testing framework:
  - Primary regression for average forecasts: Δ̄_{i,t,h} = α_i + λ Δ̄_{i,t,h−k*} + ε_{i,t,h}  (equation (1)).
  - Under full information rational expectations, λ = 0 (forecasts are weakly efficient); λ ≠ 0 indicates correlated revisions and rejects forecast efficiency.
- Mapping to theoretical frameworks:
  - Sticky information (Reis, Mankiw and Reis): average forecast follows X̄_{i,t,h} = (1 − λ) X̄_{i,t,h−k*} + (1 − λ) x_{i,t}^{RE} + noise (equations (2)–(3)); regression coefficient λ maps directly to degree of information rigidity.
  - Noisy/imperfect information (Coibion and Gorodnichenko; Woodford; Sims): agents update using Kalman filter; formulation similar to sticky information (equation (4)); λ again equals the degree of informational rigidity (1 − G in the theoretical model).
- Horizon heterogeneity:
  - Expectation that informational rigidities may vary with forecast horizon h; interaction terms between horizons and lagged revisions added to (1) to obtain equation (5): Δ̄_{i,t,h} = α_i + λ Δ̄_{i,t,h−k*} + Σ_m λ_m 1_{h=h_m} Δ̄_{i,t,h−k*} + ...
  - m indexes interaction terms; 1_{(h=h_m)} is an indicator function. Coefficients on interaction terms expected to be positive and rising with horizon if rigidity increases with horizon.
- Estimation:
  - Fixed-effect panel OLS estimator with Driscoll and Kraay (1998) standard errors to correct for complex cross-sectional and temporal correlation.
  - Nickell (1981) bias of order 1/T considered modest given large T.
- Individual-forecast testing:
  - Analogous individual-forecast regression: Δ_{j,i,t,h} = α_{j,i} + λ Δ_{j,i,t,h−k*} + Σ_m λ_m 1_{h=h_m} Δ_{j,i,t,h−k*} + ...  (equation (6)).
  - Interpretation: λ at individual level measures general forecast smoothing (behavioral deviations) but cannot be directly mapped to sticky/imperfect information parameters.
  - GMM (Arellano-Bond / Arellano-Bover) used as robustness check; results similar to OLS and instruments often invalid/weak, so focus on OLS.
  - Non-parametric estimator of update probability: fraction of individuals who updated their forecasts at least once in the 3 months prior to a given point (consistent with k* = 3).

### Data and descriptive statistics
- Data source and scope:
  - Consensus Economics Inc. survey of monthly forecasts for annual GDP growth; forecasters submit during first two weeks of each month; data published mid-month.
  - Panel structure: for each target year, sequence of 24 forecasts per panelist made between January of the year before the target year and December of the target year (three-dimensional panel).
- Sample construction and cleaning rules:
  - Included all countries reporting individual forecasts; included forecasters reporting at least 10 times.
  - Harmonized forecaster identifiers (concatenated variant names); handled mergers/acquisitions by keeping forecasts from the continuing forecaster when evident.
- Sample size and coverage:
  - 188,639 individual forecasts from 36 different countries.
  - 104,894 forecasts are from 14 advanced economies.
  - Forecasts span target years between 1989 and 2011.
  - On average, the data set includes nearly 16 individual forecasts per period for each country.
- Forecast error and revision patterns:
  - RMSFE declines with forecast horizon (errors smaller as h approaches 1).
  - RMSFEs for emerging economies are, on average, more than twice as high as for advanced economies for large forecast horizons and still almost 75 percent higher at the end of the target year.
  - Size of forecast revisions over horizons:
    - Advanced economies: revisions larger around the turn of the year; average size does not vary much with forecast horizon.
    - Emerging economies: revisions much smaller at very long horizons and much higher during the target year (h <= 12); at h = 1 the average revision in emerging economies is about twice as large as for advanced economies.
  - Distributional features:
    - High density of small or zero revisions (spikes at zero); otherwise unimodal bell-shaped distributions.
    - Distribution of revisions more flattened for emerging economies (large revisions more frequent).
    - Revisions are significantly negatively skewed for all horizons (negative revisions less frequent but larger).
  - Forecast dispersion:
    - Forecasts become more clustered as horizon shrinks.
    - Advanced economies: very few deviations larger than 0.5 percentage point.
    - Emerging economies: larger dispersion and considerable disagreement even at h = 1.

### Empirical findings — Average forecasts
- Estimation details:
  - Revisions calculated over k = 3 months; chosen horizons for estimation: h = 1, 4, 7, 10, 13, 16.
  - One observation per target year lost due to lagged revision inclusion (h=19 lost).
- Main results:
  - Strong and consistent evidence of information rigidities in consensus forecasts: positive and highly statistically significant correlation between current forecast revision and its first lag for all country groups and estimation methods.
  - Degree of informational rigidity similar between advanced and emerging economies:
    - At very short forecast horizons, coefficient on lagged revisions: 0.41 for emerging economies vs. 0.37 for advanced economies.
  - Horizon pattern:
    - Information rigidities larger around the turn of the year (h between 13 and 10).
    - Coefficients on interaction terms positive and statistically significant only for horizons 10 (emerging economies) and 13 (advanced economies); for other horizons additional effects small and not significant.
  - Aggregate estimate ignoring horizon: degree of informational rigidity λ = 0.5 for both advanced and emerging economies.
    - Interpretation under sticky information (quarterly measurement): forecasters update about every six months on average.
    - Interpretation under imperfect information: weight of about 0.5 assigned to past forecasts in current forecasts (cf. equation (4)).
    - Comparison: these estimates are higher than estimates in some previous studies (e.g., Coibion and Gorodnichenko estimate 0.14 for the United States).

### Empirical findings — Individual forecasts
- Information stickiness (from individual data):
  - Share of forecasters who updated at least once in the three months prior to a given forecast horizon ranges between 0.8 and 0.9 over horizons (Figure 6).
    - Indicates most forecasters update quite frequently.
    - Average fractions higher for advanced economies than for emerging economies.
    - Slight increase in update share as horizon shrinks; hump around the turn of the year (h ≈ 13).
  - Comparison to implied update probabilities from average-forecast regressions:
    - Coefficients on lagged revisions from average forecasts imply update-quarter probabilities between 1 − .94 = 0.06 and 1 − .25 = 0.75, contrasted with 0.8–0.9 from individual data.
    - Conclusion: individual-data fractions imply higher updating frequency than suggested by average-forecast regressions; thus sticky information plays a smaller role in explaining overall information rigidity.
  - Implication for theory:
    - High update shares (0.8–0.9) are consistent with imperfect information theory (pure form predicts continuous updating); rounding conventions can produce realistic shares (Andrade and Le Bihan, 2013).
    - Findings broadly consistent with imperfect information and provide evidence against pure sticky information.
- Forecast smoothing (individual-level regression results):
  - Regression of individual revisions on lagged revisions (equation (6)) yields positive and statistically significant coefficient on lagged revision in all specifications — strong evidence of forecast smoothing in individual forecasts.
  - Degree of smoothing is smaller at the individual level than for consensus (average) forecasts:
    - Ratio of Coefficients on Past Revisions (individual / average) ≈ 0.5 — persistence in forecast revisions is about halved at individual level.
    - Implication: averaging forecasts induces additional stickiness.
  - Differences across country groups:
    - Coefficients on lagged revisions higher for emerging economies (0.23) than for advanced economies (0.13).
    - Possible causes: greater lags in data releases, weaker quality of statistics, fewer resources devoted to forecasting for emerging economies.
  - Horizon effects at individual level:
    - Non-monotonicity: for advanced economies, interaction terms positive for horizons 7, 10, 13 (largest at h = 13), but Driscoll-Kraay standard errors show effects not significantly different from zero in most cases.
    - For emerging economies, interaction-term results weaker and not significant.
    - Overall: weak evidence that individual-level smoothing varies systematically with horizon.
- Cross-country heterogeneity:
  - Country-specific estimations of equation (1) on average forecast revisions and summary statistics from forecaster-specific estimations show substantial variation across countries (Table 4).
  - For 29 out of 31 countries, smoothing parameter from average forecasts is higher than that from individual forecasts (usually by a substantial margin).
  - Some countries exhibit substantial explanatory power of lagged revisions at individual level (e.g., average R^2: Germany .35, Italy .44), but generally individual revisions are largely unpredictable from past revisions.

*Source: _wp1431 - Section IV presents the empirical results. The last section concludes.*

### conclusions can be drawn from this graph, both of which confirm the previous panel-based

### _wp1431 - conclusions can be drawn from this graph, both of which confirm the previous panel-based

### Main findings on forecast smoothing and informational rigidity
- The degree of rigidity is less pronounced in the individual data than in the consensus data; the average smoothing parameter based on average revisions is about 3 times as large as the average smoothing parameter based on individual revisions.
- There is no substantial difference in the average rigidity between advanced economies and emerging economies; estimates are somewhat more dispersed within the group of emerging economies compared to advanced economies.
- Country-specific estimates for the fraction of forecasters that, on average, update their growth forecasts at least once during a three months period:
  - Advanced economies: 0.85
  - Emerging economies: 0.79
  - Standard deviation across countries: approximately 0.06 in both cases (difference statistically insignificant).

### Data set and scope
- Panel of individual forecasters in 36 advanced and emerging market economies for the period 1989 to 2011.
- The data set is larger than previous panels used in the literature and covers a wide range of countries.

### Evidence on theoretical explanations (sticky information vs alternatives)
- Persistence in average forecast revisions is confirmed using an equivalent test of forecast revisions on past forecast revisions.
- Evidence against the usefulness of the sticky information model to describe the dynamics of growth forecasts:
  - Estimates of informational rigidity based on consensus (average) forecasts overstate the true degree of forecasters’ inattentiveness.
  - When consensus forecasts are used, estimates suggest forecasts are updated on average every 6 months.
  - Analysis of fractions of forecasters who update forecasts points to a higher frequency of updating; evidence based on fractions suggests a small role of sticky information.
  - The predictability of individual forecast revisions casts doubt on the validity of the sticky information theory.

### Heterogeneity and nonlinearities
- Degree of forecast smoothing differs widely across individuals and countries.
- Some country-specific estimates reveal negative values for the smoothing parameter λ for a few countries (e.g. India). Negative λ values are interpreted as behavior in which forecasters react too strongly to new information so that some revisions are reversed in the next period.
- There is evidence of nonlinearities: smoothing is less pronounced in the tails of the distribution of individual forecast revisions than in the main body of the distribution (preliminary evidence noted in the working paper version).

### Key quantitative summaries from tables and figures
- Table 1: Basic features
  - Number of target years: 23 (Full Sample, Advanced Economies, Emerging Economies)
  - Number of countries: 36 (Full Sample), 14 (Advanced), 22 (Emerging)
  - Number of individual forecast observations: 188 639 (Full Sample), 104 894 (Advanced), 83 745 (Emerging)
  - Average number of forecasts per country per target year: 15.5 (Full Sample), 17.2 (Advanced), 13.7 (Emerging)
  - Average forecast Mean: 3.2 (Full Sample), 2.1 (Advanced), 4.6 (Emerging)
  - Average forecast Median: 3.0 (Full Sample), 2.4 (Advanced), 4.8 (Emerging)
  - Average forecast errors Mean: 0.0 (Full Sample), -0.1 (Advanced), 0.1 (Emerging)
  - Average forecast errors Median: 0.2 (Full Sample), 0.1 (Advanced), 0.4 (Emerging)

- Table 2: Mean Absolute Deviation from Consensus (horizons h=18, h=12, h=6, h=1)
  - Full sample: 0.29, 0.26, 0.19, 0.10
  - Advanced economies: 0.24, 0.22, 0.15, 0.07
  - Emerging economies: 0.36, 0.32, 0.28, 0.15
  - Variance of Deviation from Consensus (Full sample): 0.42, 0.39, 0.31, 0.17
  - Variance of Deviation from Consensus (Advanced): 0.33, 0.29, 0.21, 0.11
  - Variance of Deviation from Consensus (Emerging): 0.56, 0.52, 0.45, 0.25

- Table 3: Information Rigidity and Forecast Smoothing (selected coefficients)
  - Ordinary Least Squares with Driscoll-Kraay Robust Errors
  - Past revision (Average Forecasts): 0.404*** (Full Sample), 0.370*** (Advanced Economies), 0.409*** (Emerging Economies)
    - t-statistics: 6.7, 6.1, 5.6 respectively
  - Past revision (Individual Forecasts): 0.203*** (Full Sample), 0.127** (Advanced Economies), 0.223*** (Emerging Economies)
    - t-statistics: 6.3, 2.7, 6.1 respectively
  - Past revision*Horizon 4 and other interactions reported with coefficients and t-statistics in table (see source for full matrix).
  - Ratio of coefficients on past revisions (Individual/Consensus): 0.50 (Full Sample), 0.32 (Advanced Economies), 0.55 (Emerging Economies)
  - Number of observations: 3408 (Average Forecast regressions, Full Sample), 1698 (Advanced), 1710 (Emerging); 35578 (Individual Forecast regressions, Full Sample), 21054 (Advanced), 14524 (Emerging)
  - Note: Results omit forecast data made in December 2008 for the growth rate of 2009; including them increases "Past revision*Horizon 13" to about 0.84 and would imply a total rigidity parameter above 1, which is not consistent with the theories considered.

- Table 4: Country-specific λ estimates (selected entries)
  - Advanced economies (examples):
    - Australia: λ = 0.337, sd = 0.052, N = 365, R2 = 0.10; Avg. λ (individual) = 0.065, Avg. sd = 0.057, Avg. N = 131.1, Avg. R2 = 0.02, K = 36, Avg. Frac. = 0.86
    - Germany: λ = 0.613, sd = 0.044, N = 364, R2 = 0.35; Avg. λ = 0.337, Avg. sd = 0.103, Avg. N = 200.3, Avg. R2 = 0.35, K = 42, Avg. Frac. = 0.78
    - USA: λ = 0.330, sd = 0.051, N = 364, R2 = 0.10; Avg. λ = 0.037, Avg. sd = 0.339, Avg. N = 121.4, Avg. R2 = 0.02, K = 60, Avg. Frac. = 0.84
  - Emerging economies (examples):
    - China: λ = 0.577, sd = 0.052, N = 277, R2 = 0.31; Avg. λ = 0.032, Avg. sd = 0.276, Avg. N = 106.4, Avg. R2 = 0.00, K = 39, Avg. Frac. = 0.66
    - India: λ = -0.079, sd = 0.058, N = 277, R2 = 0.01; Avg. λ = -0.243, Avg. sd = 0.154, Avg. N = 63.3, Avg. R2 = 0.02, K = 30, Avg. Frac. = 0.83
    - Mexico: λ = 0.638, sd = 0.060, N = 151, R2 = 0.43; Avg. λ = 0.141, Avg. sd = 0.146, Avg. N = 67.4, Avg. R2 = 0.20, K = 44, Avg. Frac. = 0.83
  - Note: λ denotes the estimated coefficient for the first lag of the 3-months revision. Avg. Frac. displays the fraction of forecasters that, on average, adjust their forecasts at least once during a three months period.

- Figures (select qualitative summaries)
  - Root Mean Squared Forecast Errors plotted over horizons h=18, h=12, h=6, h=1 for Full sample, Advanced, Emerging (figure shows increasing error with horizon).
  - Mean Absolute Revisions over horizons h=18, h=12, h=6, h=1 for Full sample, Advanced, Emerging (figure shows larger mean absolute revisions for emerging economies).
  - Distributional figures show revisions and deviations from consensus vary by horizon; tails are thinner for individual forecast revisions than for consensus-based revisions.

### Policy implications and avenues for future research
- The limited role of sticky information suggested by the analysis implies models of forecast formation and policy analysis should account for higher updating frequency at the individual level than consensus-based estimates imply.
- Further research suggested:
  - Investigate herding and its interaction with forecast smoothing.
  - Explore the nonlinearities in forecast smoothing and link them to theories of forecast generation.
  - Study implications of uncertainty for the dynamics of macroeconomic forecasting.
  - Examine evolution of forecast rigidities over the business cycle.

*Source: Authors' estimates contained in the provided IMF working paper chapter content.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1431.pdf_