## _wp10178

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---

### Introduction and key objective
- Consensus forecasts—mean or median forecasts from a panel of individual forecasters—are always inefficient if forecasters make individually rational forecasts based on different information sets.
- Paper tests this theoretical result using the Consensus Economics cross-country dataset of real GDP growth forecasts.
- Main headline empirical finding: out of sample efficiency gains (reduction in root mean square forecast error) from a simple adjustment technique are around 5 percent.

### Theoretical intuition and model
- Stylized Bayesian model:
  - Each agent forms a forecast from a private signal and a common prior via Bayesian updating (weighted average of prior and private signal; weights reflect relative variances).
  - Under symmetry Fi = F = α_X^2 / (α_X^2 + α_u^2 + α_Π^2). (Equation (4))
- Proposition 1 (consensus inefficiency):
  - Individual forecasts are efficient: E[fi (fi − y)] = 0. (Equation (5))
  - Consensus forecast f = E[fi] is correlated with its forecast errors: E[f (f − y)] = −F^2 α_Π^2 ≤ 0. (Equation (7))
  - Intuition: the consensus forecast over-weights the prior relative to new aggregate information because the mean private signal has lower variance than each individual private signal.
  - Optimal aggregate forecast f* differs from consensus by f* = f + (α_Π^2 / (α_X^2 + α_u^2)) (f − Ω). (Equation (10))
- Generalizations:
  - Result applies to the median if εi is symmetric.
  - Extends to heterogeneous σ^2_ε and finite-agent cases.

### Assumed information structure for empirical mapping
- Forecast target ycτ builds from 25 iid monthly shocks plus a final revision shock:
  - ycτ = Σ_{h=0}^H X_h, X_h iid (0, α_X^2). Horizon index H = 24. (Equation (11), text)
- Agents’ signals and forecasts:
  - Prior Ω_h = Σ_{j=h+1}^H X_j. (Equation (12))
  - Idiosyncratic signal x_ih = Ω_h + X_h + Π_ih. (Equation (13))
  - Agent optimal forecast f^i_h = Ω_h + F (X_h + Π_ih), F = α_X^2 / (α_X^2 + α_Π^2). (Equation (14))
  - Consensus forecast f_h = Ω_h + F X_h and underreacts to aggregate new information. (Equation (15))
  - Optimal aggregate-signal forecast f_h^* = Ω_h + X_h = f_h + ((1−F)/F) (f_h − Ω_h). (Equation (16))

### Empirical test strategy and regression implications
- Focus on relation between consensus forecast errors (f − y) and consensus forecast revisions (Δf = f_t − f_{t−1}).
- Two treatments of the prior Ω_chτ:
  - Naive priors: use previous consensus forecast as prior Ω_chτ = f_c(h+1)τ (bounded rationality).
  - Rational priors: forecasters use true prior Ω_h; implies forecast errors depend on all past forecast updates with alternating-signed coefficients B_jh = −(1−F)/F^{j+1−h}. (Equation (19), (26))
- Naive-priors baseline simplifies to:
  - f_chτ − y_chτ = −(1−F)/F (f_chτ − f_c(h+1)τ) + e_chτ = a_h − b_h Δf_chτ + e_chτ. (Equations (20), (25))
- If naive-priors is used but true priors are rational, naive estimate for slope b is biased toward zero: E[b] = ((1−F)/F) (F^2 / (F^2 + (1−F)^2)) < (1−F)/F. (Equation (23))
- Estimation proceeds separately by horizon h; an iterative residual-adjustment procedure is described to account for correlated residuals across horizons. (Equations (27)–(29))

### Data and sample
- Consensus Economics dataset of forecasts:
  - Forecasts for 38 countries over 1989-2008 at the individual-forecaster level.
  - Forecasts surveyed at start of each month; published around the 10th.
  - Forecasts are for annual economic growth over the current and next calendar year; forecast horizon varies from 1 to 24 months.
  - Number of forecasters per country/period/horizon varies between 5 and 39, interquartile range 14 to 21, mean around 18.
  - Dataset includes 167,802 individual forecasts.
- Baseline uses final data; robustness checks use WEO real-time vintages (May, year β+1) with similar results.
- Out-of-sample tests use a truncated sample up to 2006 for estimation; out-of-sample dataset includes forecasts for 2007 and 2008 made in 2007–2008 (horizons < 12 months included as specified).

### Main empirical results and coefficient estimates
- Evidence rejects the rational-priors (full-lag) pattern in favor of naive priors: only two additional lagged updates significant and one with the wrong sign (Table 2 summary).
- Baseline regressions (consensus forecast error on most recent update) — selected horizon update coefficients (clustered SEs shown in parentheses; significance *** 1%, ** 5%, * 10%):
  - Horizons 1–8 (raw errors, Table 3):
    - Horizon 1: Update -0.605*** (0.176); Constant -0.430** (0.203); Observations 475; R2 0.016
    - Horizon 2: Update -1.145*** (0.299); Constant -0.514*** (0.139); Observations 495; R2 0.035
    - Horizon 3: Update -1.150*** (0.177); Constant -0.512** (0.206); Observations 468; R2 0.046
    - Horizon 4: Update -1.057*** (0.205); Constant -0.476*** (0.141); Observations 489; R2 0.080
    - Horizon 5: Update -1.521*** (0.270); Constant -0.459** (0.194); Observations 466; R2 0.060
    - Horizon 6: Update -1.963*** (0.380); Constant -0.493*** (0.153); Observations 489; R2 0.129
    - Horizon 7: Update -1.218*** (0.438); Constant -0.422** (0.197); Observations 459; R2 0.076
    - Horizon 8: Update -3.442*** (0.566); Constant -0.478*** (0.161); Observations 470; R2 0.158
  - Iterative residual-adjusted regressions (Table 4) produce somewhat different magnitudes; representative Table 4 coefficients (clustered SEs):
    - Horizon 1: Update -0.816*** (0.213); Constant -0.330** (0.135); Observations 423; R2 0.038
    - Horizon 2: Update -1.208*** (0.174); Constant -0.423*** (0.032); Observations 422; R2 0.135
    - Horizon 3: Update -0.697*** (0.129); Constant -0.413*** (0.012); Observations 416; R2 0.248
    - Horizon 4: Update -0.634*** (0.093); Constant -0.370*** (0.024); Observations 416; R2 0.249
    - Horizon 5: Update -0.984*** (0.233); Constant -0.394*** (0.023); Observations 416; R2 0.222
    - Horizon 6: Update -1.072*** (0.207); Constant -0.376*** (0.021); Observations 416; R2 0.361
    - Horizon 7: Update -0.817*** (0.098); Constant -0.361*** (0.025); Observations 409; R2 0.360
    - Horizon 8: Update -2.195*** (0.537); Constant -0.299*** (0.033); Observations 409; R2 0.324
- Interpretation:
  - Table 4 estimates suggest the consensus forecast update coefficient generally lies in the range -0.5 to -1.5 at shorter horizons.
  - Implied value of F is around 0.5: consensus forecast typically absorbs only half of the aggregate new information available each period.

### Efficiency gains from adjusted consensus forecasts
- Adjustment method:
  - Under naive-priors, adjusted efficient forecast \^f_chτ* = f_chτ + b_h Δf_chτ. (Equation (30))
  - Efficiency Gain (%) = 100 · (RMSE_fchτ − RMSE_\^fchτ*) / RMSE_fchτ. (Equation (31))
- Headline efficiency gains:
  - Average efficiency gain from adjusted consensus versus raw consensus: 3.7 percent (All* column).
  - Efficiency gain for horizons of 12 months or less: 6.3 percent (≤12* column).
  - Out-of-sample headline: adjusted forecast gain ≤12* = 5.6 percent; All* = 3.5 percent (select out-of-sample summaries).
  - Adjustment typically yields larger error reductions than replacing current-month consensus with next-month consensus.
- Extremes and country highlights:
  - Maximum in-sample gain reported at 13 months: 9.9 percent.
  - In-sample country examples (selected):
    - Korea Republic of: Adjusted Forecast 11.0; Next Month's Consensus 4.9
    - Malaysia: Adjusted Forecast 13.1; Next Month's Consensus 4.3
    - Indonesia: Adjusted Forecast 7.8; Next Month's Consensus 5.5
    - United States: Adjusted Forecast 0.0; Next Month's Consensus 2.7
  - Out-of-sample country examples (selected):
    - Peru: Adjusted Forecast 13.6; Next Month's Consensus 5.0
    - Malaysia: Adjusted Forecast 9.0; Next Month's Consensus 2.5
    - Indonesia: Adjusted Forecast -59.6; Next Month's Consensus 8.5 (illustrates extreme out-of-sample deterioration in some cases)
    - United States: Adjusted Forecast 0.8; Next Month's Consensus 6.0

### Robustness checks and alternative datasets
- Median-consensus: replacing mean with median yields almost identical results (Table 9).
- Real-time WEO vintages (2002–08): results almost identical to baseline; negative and significant update coefficients across a wider set of horizons despite smaller sample (Table 10).
- SPF (Survey of Professional Forecasters) quarterly nominal U.S. GDP:
  - -b point estimates negative at all four SPF horizons; statistically significant at 2- and 3-quarter ahead horizons.
  - SPF efficiency gains broadly similar but slightly lower; largest SPF gain at 3-quarter ahead horizon is 5 percent.
  - Under-weighting of new information is somewhat less pronounced in SPF, consistent with greater public information availability for U.S. economy.

### Individual-forecaster diagnostics
- Martingale tests (individual forecaster regressions):
  - Sample: 1,342 individual forecasters; 125,545 observations.
  - Alpha mean = -0.010; Beta mean = 0.041; median Beta = 0.062.
  - Proportion of forecasters with statistically significant Beta coefficients (1 percent level): Positive 0.113; Negative 0.016.
  - Interpretation: modest under-weighting by individuals but substantially smaller than consensus-level under-weighting.
- SPF individual results:
  - Sample: 57 forecasters; 5,937 observations.
  - Alpha mean = 0.000; Beta mean = 0.148; median Beta = 0.085.
  - Proportion significant (1 percent): Positive 0.035; Negative 0.000.

### Theoretical and policy implications
- Aggregation problem:
  - Individual rationality does not guarantee efficient aggregate (consensus) forecasts; the economy does not behave as if populated by a single rational representative agent.
  - Consensus forecasts tend to overweight the prior and underreact to new aggregate information.
- Transparency and public information:
  - More accurate public information can, under certain parameter configurations, increase the mean squared error of the consensus forecast because forecasters collectively overweight the public signal (Morris and Shin (2002) related insight).
- Practical recommendations:
  - Consumers of consensus forecasts should be aware of underreaction; simple ex post adjustments can improve accuracy, especially for horizons of a year or less.
  - Forecast aggregation services should consider adjusting aggregation methodology (ex post adjustment or eliciting shading of priors; ask forecasters to submit forecasts based only on newest information).
  - Organizations producing internal forecasts: decentralize information-gathering but centralize production of final forecast; apply judgment at aggregate-forecast level to avoid compounding overweighting of priors.
- Relevance to finance and groupthink:
  - Findings relate to groupthink/collective delusion literature and may be relevant for understanding asset-price phenomena (momentum trading) though not explored in depth here.

### Conclusions
- Robust empirical evidence that consensus forecasts under-react to new information owing to aggregation of individually rational forecasts with dispersed private signals.
- Adjusting the consensus forecast using the change in the consensus from the previous month yields meaningful accuracy gains:
  - Average 3.7 percent overall; 6.3 percent for horizons ≤12 months.
  - Gains typically larger than those from waiting one additional month’s consensus.
- These inefficiencies are not corrected in practice by forecasters, implying consumers and producers of consensus forecasts could benefit from methodological changes.

*Source: _wp10178 — Appendix Tables section of the supplied IMF PDF excerpt.*

### Appendix Tables

### Appendix Tables

### Introduction and key objective
- Consensus forecasts—mean or median forecasts from a panel of individual forecasters—are always inefficient if forecasters make individually rational forecasts based on different information sets.
- This paper tests the empirical relevance of that theoretical result using the Consensus Economics cross-country dataset of real GDP growth forecasts.
- Main headline empirical finding: out of sample efficiency gains (reduction in root mean square forecast error) from a simple adjustment technique are around 5 percent.

### Theoretical intuition
- Stylized model: each agent forms a forecast from a private signal and a common prior via Bayesian updating (weighted average of prior and private signal; weights reflect relative variances).
- The consensus forecast effectively uses the same relative weights as individual forecasters but applies them to the prior and the average private signal.
- Because the mean private signal has lower variance than each individual private signal, the consensus forecast over-weights the prior and is therefore inefficient.
- Consequence: the consensus forecast is negatively correlated with its own forecast error.
- This result does not rely on strategic forecasting behavior or heterogeneous signal precision and is general.

### Empirical test strategy and initial evidence
- Test focuses on relationship between consensus forecast errors (consensus forecast minus actual realization) and consensus forecast revisions (current consensus minus previous consensus).
- Table 1 presents bivariate correlations between forecast updates and forecast errors for individual forecasts and consensus forecasts, across forecast horizons, using Consensus Economics real GDP growth forecasts.
- Initial evidence: strong negative correlation between consensus forecast updates and forecast errors, particularly at horizons of under 13 months; estimated negative correlation coefficients are as high as 40 percent in absolute value.
- Comparison with individual forecasts suggests the negative correlation for consensus forecasts is not driven by individual forecaster irrationality.
- Reported pooled correlation coefficients:
  - Individual: 0.13 *** 
  - Consensus: -0.15 ***
- Significance level denoted by *** (1 percent); ** (5 percent); * (10 percent).

### Econometric considerations and modeling
- Builds on literature on efficiency/rationality testing using forecast data (Zarnowitz, 1985; Keane and Runkle, 1990; Batchelor and Dua, 1991; Davies and Lahiri, 1995; Bonham and Cohen, 2001).
- Shows that the forecast structure in Davies and Lahiri (1995) is approximately correct in some contexts but inconsistent with rational forecaster behavior in a fully specified model of the information structure.
- Rational forecaster behavior in a fully specified model creates additional econometric challenges; the paper’s empirical strategy addresses these concerns.

### Main empirical results
- Strong evidence that consensus forecasts are inefficient, quantitatively important, particularly at forecast horizons of around 12 months or less.
- Results robust to:
  - Different definitions of the consensus forecast (mean vs median).
  - Different vintages of actual data (real time versus revised GDP estimates).
  - Different forecast datasets (including quarterly nominal U.S. GDP forecasts from the Survey of Professional Forecasters).
- Using the adjustment method (reducing overweighting on the prior via a linear combination of the consensus forecast and the prior) with the most recent previous consensus forecast as a proxy for the prior yields adjusted forecasts with mean squared errors on average more than 5 percent lower than raw consensus forecasts for horizons of a year or less, even out of sample.
- The reduction in forecast errors from the adjustment is typically greater than the reduction associated with using the next month’s consensus forecast (i.e., one month’s additional data).

### Policy and broader implications
- Caution urged in using consensus forecasts as best estimates conditional on aggregate information sets; consensus forecasts may not be the most efficient estimate and may flatter the performance of alternative forecasts when used as benchmarks.
- Implications for transparency debates: more transparent public information can increase the forecast error for the consensus forecast even as individual forecast errors fall (related to Morris and Shin (2002) insights and supplementary results by Amato and Shin (2006) and Roca (2009)).
- Connection to groupthink/collective delusion literature (Benabou, 2008): problem is failure to aggregate private signals; cure lies in more communication and ideally communication of idiosyncratic information rather than posterior beliefs.
- Aggregation problem between micro and macro: individual rationality (e.g., rational expectations) does not guarantee efficient aggregate forecasts; the economy does not behave as if populated by a single rational representative agent.
- Potential relevance to asset price phenomena (momentum trading strategies) noted but not explored in the paper.

### Adjustment method and practical findings
- An efficient forecast can be recovered by reducing the overweighting on the prior using a linear combination of the consensus forecast and the prior.
- The magnitude of the required adjustment increases with the relative variance of individual forecasters’ idiosyncratic private information.
- Empirical implementation:
  - Uses the most recent previous consensus forecast as a proxy for the prior.
  - Produces adjusted forecasts with mean squared errors on average more than 5 percent lower than raw consensus forecasts for horizons of a year or less, including out-of-sample tests.
- No evidence that forecasters themselves make the necessary adjustment to the previous month’s consensus forecast in updating their prior.

_Appendix Tables (content unit): summary of Introduction, theory, empirical strategy, main findings, and policy implications from the Appendix Tables section._

### Section IV provides a fuller discussion of how the results relate to some of the existing

### _wp10178 - Section IV provides a fuller discussion of how the results relate to some of the existing

### Model and key theoretical results
- Basic setup:
  - A variable y is distributed iid with mean μ and variance σ^2_ν: y = Ω + X. (Equation (1))
  - A continuum of agents i ∈ (0,1) each receive a private signal xi = y + u + Πi, where u is an aggregate error, iid mean-zero with variance σ^2_u, and εi are iid mean-zero idiosyncratic errors with variance σ^2_ε. (Equation (2))
  - Agents form Bayesian-updating forecasts: fi = F i xi + (1−F i) Ω, where Fi minimizes RMS forecast error. (Equation (3))
  - Under symmetry Fi = F = α_X^2 / (α_X^2 + α_u^2 + α_Π^2). (Equation (4))

- Proposition 1 (consensus inefficiency):
  - Individual forecasts are efficient (uncorrelated with their forecast errors): E[fi (fi − y)] = 0. (Equation (5))
  - The consensus forecast f = E[fi] = F (y + u) + (1−F) Ω is correlated with its forecast errors:
    - E[f (f − y)] = −F^2 α_Π^2 ≤ 0. (Equation (7))
  - Conclusion: The consensus forecast is inefficient, even though individual forecasts are all efficient. (Proposition 1, proof summarized)

- Interpretation and generalizations:
  - Result applies equally to the median if εi is symmetric (or median zero).
  - Generalizes to heterogeneous σ^2_ε or a finite number of agents (Kim, Lim and Shaw, 2001 proof for finite case).
  - Intuition: individually-rational weight F on the noisy individual signal exceeds the optimal weight F* for the aggregate signal, since the aggregate signal has lower variance:
    - F* = α_X^2 / (α_X^2 + α_u^2) = 1 + α_Π^2 / (α_X^2 + α_u^2) F > F. (Equation (8))
  - The optimal forecast f* (based on aggregate signal) is uncorrelated with its errors: E[f* (f* − y)] = 0. (Equation (9))
  - Relationship between consensus and optimal forecast:
    - f* = f + (F* − F)/F (f − Ω) = f + (α_Π^2 / (α_X^2 + α_u^2)) (f − Ω). (Equation (10))

### Assumed information structure of the data (matching forecasting environment)
- Forecast target and shocks:
  - Forecast target ycτ is a function of 25 iid monthly shocks (one per month during two-year max horizon) plus a final revision shock:
    - ycτ = Σ_{h=0}^H X_h, X_h iid (0, α_X^2). (Equation (11))
    - Horizon index: H = 24 (maximum forecasting horizon is two years). (Text)
    - Horizon-0 shock is due to data revision. (Text)

- Agents’ signals prior to each monthly forecast:
  - Common prior Ω_h = Σ_{j=h+1}^H X_j (based on shocks observed through previous month). (Equation (12))
  - Idiosyncratic signal: x_ih = Ω_h + X_h + Π_ih. (Equation (13))
  - Agents' optimal forecast given information:
    - f^i_h = Ω_h + F (X_h + Π_ih), with F = α_X^2 / (α_X^2 + α_Π^2). (Equation (14))
  - Consensus forecast:
    - f_h = Ω_h + F X_h. (Equation (15))
  - Optimal aggregate-signal forecast fully absorbs new shock:
    - f_h^* = Ω_h + X_h = f_h + ((1−F)/F) (f_h − Ω_h). (Equation (16))
  - Key characteristic: consensus forecasts underreact to aggregate new information (observable underreaction).

- Comparison with Davies and Lahiri (1995):
  - This paper derives dispersed signals endogenously; Davies and Lahiri assume idiosyncratic forecasting errors instead of deriving dispersion from idiosyncratic signals.
  - Davies and Lahiri implicitly set F = 1 and assume forecast dispersal as reporting errors; this paper shows that is inconsistent with optimal forecasting behavior.
  - Under derived optimal forecasts, the common component follows an MA(1) rather than white noise, implying richer autocorrelation structure and additional econometric challenges.

### Empirical methodology for testing consensus inefficiency
- Theoretical regression basis:
  - Under consensus underreaction, E[(f_chτ − Ω_chτ) (f_chτ − y_chτ)] = −F (1−F) α_X^2 ≤ 0. (Equation (17))
  - Using f_chτ − y_chτ = −(1−F)/F (f_chτ − Ω_chτ) + e_chτ where e_chτ = −Σ_{j=0}^{h−1} X_j (orthogonal to f_chτ − Ω_chτ). (Equation (18))

- Two empirical treatments of the prior Ω_chτ:
  - Naive priors case: forecasters use previous consensus forecast as prior Ω_chτ = f_c(h+1)τ (bounded rationality).
  - Rational priors case: forecasters use true prior μ_h (i.e., Ω_h), which requires including all past forecast updates in regressions.

- Implications for regression specifications:
  - If priors are rational, forecast errors depend on all past forecast updates:
    - f_chτ − y_chτ = Σ_{j=h}^{H−1} B_jh Δf_cjτ + e_chτ, where B_jh = −(1−F)/F^{j+1−h}. (Equation (19))
    - Rational-priors pattern predicts alternating signs in B_jh: B_hh ≤ 0, B_{h+1,h} ≥ 0, B_{h+2,h} ≤ 0, ... (Equation (26))
  - Naive-priors simplification (baseline): forecast errors rely only on the most recent update:
    - f_chτ − y_chτ = −(1−F)/F (f_chτ − f_c(h+1)τ) + e_chτ = a_h − b_h Δf_chτ + e_chτ. (Equations (20), (25))
  - If the rational case is falsely rejected in favor of naive priors, the naive-priors estimate for slope b is biased toward zero:
    - Expected biased coefficient E[b] = ((1−F)/F) (F^2 / (F^2 + (1−F)^2)) < (1−F)/F. (Equation (23))

- Estimation strategy and panel issues:
  - Errors e_chτ have complex serial structure across horizons and adjacent forecast periods; e_chτ = −Σ_{j=0}^{h−1} X_j is orthogonal to information through horizon h but correlates when pooling across horizons.
  - Estimation proceeds with separate regressions per horizon h for consistency.
  - Iterative efficiency-improving procedure under naive-priors assumption:
    - Estimate (25) for h = 1, where e_c1τ = −X_0. (Equation (27))
    - Use estimated residuals Σ e_c1τ to adjust left-hand side for h = 2 regression, where e_c2τ = −X_1, and so on. (Equations (28), (29))
    - Present results both from simple regressions of (25) and the iterative residual-adjusted procedure (acknowledging iterated residuals may add noise).

- Recovering efficient forecast and measuring efficiency gain:
  - Adjusted (efficient) forecast estimate: \^f_chτ* = f_chτ + b_h Δf_chτ. (Equation (30))
  - Efficiency Gain (%) = 100 · (RMSE_fchτ − RMSE_\^fchτ*) / RMSE_fchτ. (Equation (31))
  - This metric allows comparison of efficiency improvement across horizons and countries.

### Application to cross-country growth forecasts (data description)
- Dataset:
  - Forecasts of economic growth for 38 countries over 1989-2008 at the individual-forecaster level from Consensus Economics. (Text)
  - Forecasts surveyed at start of each month; published around the 10th. (Text)
  - Forecasts are for annual economic growth over the current and next calendar year; forecast horizon varies from 1 to 24 months (dated to end of forecast year). (Text)
  - Number of forecasters per country/period/horizon varies between 5 and 39, interquartile range 14 to 21, mean around 18. (Text)
  - Baseline sample drops outliers to prevent coding errors or extreme values. (Text)
  - Dataset includes 167,802 individual forecasts. (Text)
  - Efficiency gains calculated using a truncated sample up to 2006 to allow out-of-sample gains; out-of-sample dataset includes all forecasts for 2008 (made in 2007 and 2008) and forecasts for 2007 made in 2007 (forecast horizon < 12 months). (Text)
  - Consensus forecasts computed as simple arithmetic averages across forecasters for forecast year τ, horizon h and country c (robustness checks noted). (Text)

*Source: _wp10178 - Section IV provides a fuller discussion of how the results relate to some of the existing*

### Section III.D presents results using the median). The consensus dataset is therefore a three-

### _wp10178 - Section III.D presents results using the median). The consensus dataset is therefore a three-

### Data, sample, and measurement
- The consensus dataset is a three-dimensional panel covering up to 38 countries, 20 years and 24 forecast horizons.
- Forecast errors are calculated with respect to annual GDP growth in the calendar year in question, y_cτ taken from the IMF’s World Economic Outlook (WEO) database.
- The baseline results ignore questions of data revision by using final data.
- Robustness check: results also assessed using GDP estimates for each year τ taken from the May, year β+1, version of the IMF’s WEO dataset as a measure of real time data; results reported in section III.D support the conclusion that using final rather than real time data should not bias the estimates.
- Outliers are defined as the bottom and top 0.5 percent of the sample of individual forecast errors; results are very similar when these outliers are not dropped.

### Efficiency tests: specification and inference
- Tests estimate equation (24), including the full set of lagged forecast updates as in the rational priors case, to assess evidence of the aggregation problem.
- Weighted mean beta coefficient from the set of relevant per-forecast horizon regressions is reported (weighted by the inverse of the variance of the coefficient estimates).
- Significance levels are based on a z-test using the standard error of the weighted mean.
- The last two columns in the summary give the proportion of relevant per-forecast horizon regressions in which the beta coefficient is significant at the 1 percent level and the proportion with positive and negative sign, respectively.
- The predicted sign under the rational priors case is highlighted in bold in the original table.

### Key findings from the lagged-update regressions (Table 2 summary)
- Only two additional lagged forecast updates (in addition to the most recent update) are statistically significant; of these one has the wrong sign.
- The significant negative average coefficient on the first lagged update (as opposed to the positive coefficient predicted under rational priors) suggests that even the raw consensus forecast is not fully absorbed into the prior in the first month.
- Conclusion: the rational priors case can be rejected in favor of the simpler naive priors case; subsequent results assume naive priors and include only the most recent forecast update.

### Baseline efficiency tests (Table 3: raw forecast errors)
- Regressions: dependent variable = mean (consensus) forecast error; independent variable = most recent update to the consensus forecast.
- Selected detailed coefficients and statistics (per horizon columns retain values exactly as reported):
  - Horizons 1–8 (Update coefficients and constants with clustered standard errors):
    - Horizon 1: Update -0.605*** (0.176); Constant -0.430** (0.203); Observations 475; R2 0.016
    - Horizon 2: Update -1.145*** (0.299); Constant -0.514*** (0.139); Observations 495; R2 0.035
    - Horizon 3: Update -1.150*** (0.177); Constant -0.512** (0.206); Observations 468; R2 0.046
    - Horizon 4: Update -1.057*** (0.205); Constant -0.476*** (0.141); Observations 489; R2 0.080
    - Horizon 5: Update -1.521*** (0.270); Constant -0.459** (0.194); Observations 466; R2 0.060
    - Horizon 6: Update -1.963*** (0.380); Constant -0.493*** (0.153); Observations 489; R2 0.129
    - Horizon 7: Update -1.218*** (0.438); Constant -0.422** (0.197); Observations 459; R2 0.076
    - Horizon 8: Update -3.442*** (0.566); Constant -0.478*** (0.161); Observations 470; R2 0.158
  - Horizons 9–16:
    - Horizon 9: Update -1.065*** (0.292); Constant -0.397* (0.199); Observations 475; R2 0.044
    - Horizon 10: Update -2.115** (0.779); Constant -0.549*** (0.166); Observations 495; R2 0.102
    - Horizon 11: Update -1.572*** (0.432); Constant -0.420** (0.185); Observations 468; R2 0.063
    - Horizon 12: Update -0.253 (0.448); Constant -0.546*** (0.180); Observations 489; R2 0.005
    - Horizon 13: Update -3.078*** (0.654); Constant -0.364* (0.203); Observations 466; R2 0.125
    - Horizon 14: Update -2.228** (0.976); Constant -0.582*** (0.176); Observations 489; R2 0.032
    - Horizon 15: Update -0.632 (0.391); Constant -0.305 (0.216); Observations 459; R2 0.007
    - Horizon 16: Update 0.226 (0.583); Constant -0.360* (0.192); Observations 470; R2 0.001
  - Horizons 17–23:
    - Horizon 17: Update -0.764 (0.881); Constant -0.149 (0.190); Observations 417; R2 0.007
    - Horizon 18: Update -0.259 (0.871); Constant -0.317 (0.196); Observations 440; R2 0.000
    - Horizon 19: Update 0.267 (0.671); Constant -0.041 (0.199); Observations 410; R2 0.013
    - Horizon 20: Update -2.239* (1.323); Constant -0.32 (0.219); Observations 421; R2 0.001
    - Horizon 21: Update 0.38 (0.507); Constant -0.093 (0.202); Observations 398; R2 0.004
    - Horizon 22: Update -0.903 (1.391); Constant -0.386* (0.225); Observations 407; R2 0.003
    - Horizon 23: Update -0.821 (1.858); Constant -0.16 (0.204); Observations 353; R2 (blank)
- Standard Errors clustered by country.
- Significance Level denoted by *** (1 percent); ** (5 percent); * (10 percent).

### Efficiency tests with iterative error adjustment (Table 4: adjusted forecast errors)
- Dependent variable transformed by iterative subtraction of residuals as described in text.
- Selected detailed coefficients and statistics (per horizon columns retain values exactly as reported):
  - Horizons 1–8:
    - Horizon 1: Update -0.816*** (0.213); Constant -0.330** (0.135); Observations 423; R2 0.038
    - Horizon 2: Update -1.208*** (0.174); Constant -0.423*** (0.032); Observations 422; R2 0.135
    - Horizon 3: Update -0.697*** (0.129); Constant -0.413*** (0.012); Observations 416; R2 0.248
    - Horizon 4: Update -0.634*** (0.093); Constant -0.370*** (0.024); Observations 416; R2 0.249
    - Horizon 5: Update -0.984*** (0.233); Constant -0.394*** (0.023); Observations 416; R2 0.222
    - Horizon 6: Update -1.072*** (0.207); Constant -0.376*** (0.021); Observations 416; R2 0.361
    - Horizon 7: Update -0.817*** (0.098); Constant -0.361*** (0.025); Observations 409; R2 0.360
    - Horizon 8: Update -2.195*** (0.537); Constant -0.299*** (0.033); Observations 409; R2 0.324
  - Horizons 9–16:
    - Horizon 9: Update -1.179*** (0.348); Constant -0.303*** (0.022); Observations 401; R2 0.187
    - Horizon 10: Update -0.841*** (0.234); Constant -0.316*** (0.022); Observations 394; R2 0.154
    - Horizon 11: Update -0.527*** (0.170); Constant -0.327*** (0.017); Observations 394; R2 0.092
    - Horizon 12: Update -0.172*** (0.026); Constant -0.299*** (0.017); Observations 391; R2 0.103
    - Horizon 13: Update -0.946*** (0.296); Constant -0.242*** (0.052); Observations 381; R2 0.085
    - Horizon 14: Update -0.621*** (0.225); Constant -0.234*** (0.031); Observations 380; R2 0.052
    - Horizon 15: Update -0.468*** (0.064); Constant -0.204*** (0.012); Observations 373; R2 0.204
    - Horizon 16: Update -0.485 (0.295); Constant -0.060** (0.023); Observations 372; R2 0.093
  - Horizons 17–23:
    - Horizon 17: Update -0.249 (0.298); Constant -0.021 (0.016); Observations 371; R2 0.019
    - Horizon 18: Update -0.286** (0.133); Constant 0.024 (0.014); Observations 371; R2 0.024
    - Horizon 19: Update -0.181** (0.083); Constant 0.038*** (0.011); Observations 363; R2 0.064
    - Horizon 20: Update -0.617** (0.241); Constant 0.096*** (0.017); Observations 358; R2 0.059
    - Horizon 21: Update 0.169* (0.086); Constant 0.096*** (0.010); Observations 352; R2 0.025
    - Horizon 22: Update 0.222 (0.201); Constant 0.101*** (0.013); Observations 345; R2 0.059
    - Horizon 23: Update -0.083 (0.112); Constant 0.095*** (0.007); Observations 345; R2 0.01
- Standard Errors clustered by country.
- Significance Level denoted by *** (1 percent); ** (5 percent); * (10 percent).

### Interpretation: informational structure and coefficient magnitudes
- Using the results from Table 4 as representing the best estimates, the estimated coefficient on the consensus forecast update is generally in the range of -0.5 to -1.5 at the shorter horizons where the effect is significant.
- This suggests that the variance of forecasters’ idiosyncratic signals σ^2_ε, at the shorter forecast horizons where the effect is significant, is of a similar magnitude to the variance of the common signals, σ^2_ν.
- Implied value of F is around 0.5: the consensus forecast typically absorbs only half of the aggregate new information available each period.

### Efficiency gains from adjusted consensus forecasts (specification and results summary)
- Adjustment approach: assume naive priors; allow slope coefficient b_h to differ across each country c and within three broad time horizons H = 〈1−7, 8−14, 15−23〉 and run specification (32): f_chβ − y_cβ = a_c,H − b_c,H f_chβ − f_c(h+1)β + e_chβ. Corrected forecasts derived using (30).
- Tables 5 and 6 report in-sample efficiency gains by country and by forecast horizon; they also present efficiency gains from using the next month’s consensus forecast rather than the current month’s for comparison.
- The most significant efficiency gains occur at relatively short horizons, between 4 and 14 months.
- The maximum gain reported is at 13 months: 9.9 percent.
- Overall, efficiency gains average (text truncated in source at this point).

*Content summarized from the provided IMF PDF excerpt.*

### 3.7 percent, or 6.3 percent for horizons of 12 months or less. These efficiency gains are

### _wp10178 - 3.7 percent, or 6.3 percent for horizons of 12 months or less. These efficiency gains are

### Efficiency gains: headline results
- Average efficiency gain from adjusted consensus forecasts versus raw consensus: 3.7 percent (All* column).
- Efficiency gain for horizons of 12 months or less: 6.3 percent (≤12* column).
- The adjusted forecast improvement is marginally larger than the gain associated with replacing this month’s consensus forecast with next month’s consensus.
- Efficiency gains are generally largest for emerging markets and smallest for industrial countries; possible drivers include shorter available time series and greater growth volatility in emerging markets.

### In-sample country-level efficiency gains (select highlights from Table 5)
- Korea Republic of: Adjusted Forecast 11.0; Next Month's Consensus 4.9
- Malaysia: Adjusted Forecast 13.1; Next Month's Consensus 4.3
- Indonesia: Adjusted Forecast 7.8; Next Month's Consensus 5.5
- United States: Adjusted Forecast 0.0; Next Month's Consensus 2.7
- Notes: Forecasts made for years to 2006. Forecast horizon = 1 not included to facilitate comparison between columns 2 and 3. Efficiency Gain (Percent).

### Out-of-sample country-level efficiency gains (select highlights from Table 7)
- Peru: Adjusted Forecast 13.6; Next Month's Consensus 5.0
- Malaysia: Adjusted Forecast 9.0; Next Month's Consensus 2.5
- Indonesia: Adjusted Forecast -59.6; Next Month's Consensus 8.5 (illustrates extreme out-of-sample deterioration in some cases)
- United States: Adjusted Forecast 0.8; Next Month's Consensus 6.0
- Notes: Forecasts made from Jan 2007 onwards, for 2007/08. Forecast horizon = 1 not included. Efficiency Gain (Percent).

### Efficiency gains by forecast horizon (select highlights from Table 6 and Table 8)
- By horizon (in-sample summary, select rows):
  - ≤12*: Adjusted Forecast 6.3; Next Month's Consensus 5.5
  - All*: Adjusted Forecast 3.7; Next Month's Consensus 3.0
- By horizon (out-of-sample summary, select rows):
  - ≤12*: Adjusted Forecast 5.6; Next Month's Consensus 4.2
  - All*: Adjusted Forecast 3.5; Next Month's Consensus 2.7
- Notes: * indicates dropping forecast horizon = 1 to allow comparison between second and third columns. Efficiency Gain (Percent).

### Robustness checks and alternative datasets
- Median-consensus robustness: Replacing mean with median consensus yields results almost identical to baseline (Table 9).
- Real-time data robustness: Using 'real time' GDP estimates from the WEO archive (available 2002–08) yields results almost identical to baseline; coefficient on forecast update becomes negative and significant across a wider set of horizons despite smaller sample (Table 10).
- SPF (Survey of Professional Forecasters) robustness:
  - SPF nominal GDP quarterly results produce point estimates for -b with correct negative sign at all four horizons, statistically significant for 2- and 3-quarter ahead forecasts.
  - Efficiency gains for SPF are broadly similar but slightly lower than Consensus Economics dataset; largest gain at 3-quarter ahead horizon is 5 percent.
  - The under-weighting of new information is somewhat less pronounced in SPF than in CE data, consistent with greater public information availability for U.S. economy.

### Key empirical diagnostics and individual-forecaster tests (Appendix summary)
- Martingale tests (individual forecaster regressions):
  - Sample: 1,342 individual forecasters; 125,545 observations.
  - Alpha mean = -0.010; Beta mean = 0.041; median Beta = 0.062.
  - Proportion of forecasters with statistically significant Beta coefficients (1 percent level): Positive 0.113; Negative 0.016.
  - Interpretation: Some modest under-weighting of new information by individual forecasters, but substantially smaller than under-weighting identified for consensus forecasts.
- SPF individual results:
  - Sample: 57 forecasters; 5,937 observations.
  - Alpha mean = 0.000; Beta mean = 0.148; median Beta = 0.085.
  - Proportion significant (1 percent): Positive 0.035; Negative 0.000.
  - Interpretation: Modest evidence of under-weighting in SPF individual forecasts; still markedly less than consensus-level under-weighting.

### Theoretical interpretation and implications
- Over-weighting the prior in consensus forecasts:
  - Consensus forecasts tend to overweight the prior relative to new information, creating underreaction to new information even though individual forecasters respond more appropriately.
  - Pooling across forecast horizons and across forecasters exacerbates aggregation inefficiencies and can produce inconsistent coefficient estimates; OLS remains optimal for minimizing residual forecast error despite inconsistency in parameter estimation.
- Morris and Shin (2002) reassessment:
  - More accurate public information (lower σ2ν) can, under certain conditions, increase mean squared error of the consensus forecast because forecasters collectively over-weight the public signal; condition depends on relative variances of common and idiosyncratic components (see equations (33)–(39)).
  - Including the beauty contest element (weight r) modifies but does not eliminate the possibility that greater transparency harms consensus accuracy; the parameter space for harmful effects is larger for consensus forecasts than for individual forecasts.
- Groupthink and financial-sector relevance:
  - A lower-variance group prior (e.g., from sophisticated models) can directly improve perceived accuracy but indirectly induce managers to overweight the prior and underweight idiosyncratic signals, reducing collective forecast accuracy—an interpretation relevant to bank behavior in the subprime crisis.

### Policy and practical recommendations
- For consumers of consensus forecasts:
  - Be aware that consensus forecasts may inefficiently underweight new information; simple ex post adjustments (as in this paper) can improve accuracy, especially for horizons of a year or less.
  - Expect larger gains from adjustment for emerging markets than for industrial countries, on average.
- For forecast aggregation services:
  - Consider adjusting aggregation methodology to correct for over-weighting of priors (e.g., apply ex post adjustment or elicit additional information on forecasters' weighting of private signals).
  - Practical options: ask forecasters to submit both their best guess and a forecast based only on newest information, or design incentives for strategic forecasting to encourage differentiation.
- For organizations producing internal forecasts (central banks, large institutions):
  - Decentralize information-gathering but centralize production of final forecast; apply judgment/shading at aggregate-forecast level rather than at each model/individual level to avoid compounding overweighting of priors.

### Conclusions (summary)
- Robust empirical evidence that consensus forecasts under-react to new information due to aggregation processes, not because individual forecasters are irrational.
- Adjusting consensus forecasts using the change in the consensus forecast from the previous month yields meaningful accuracy gains (average 3.7 percent overall; 6.3 percent for horizons ≤12 months), and these gains are generally larger than those from having an additional month's worth of data.
- The inefficiency appears not to be corrected in practice by forecasters, implying consumers and producers of consensus forecasts may benefit from methodological changes.

*Author's calculations and analyses as presented in the supplied document.*

### REFERENCES

### _wp10178 - REFERENCES

### Information Value of Prices, Public Information, and Common Knowledge
- Amato, Jeffery D. and Hyun Song Shin. 2006, Imperfect common knowledge and information value of prices. Economic Theory Vol. 27 No. 1, pp. 213–41.
- Morris, Stephen and Hyun Song Shin, 2002, Social Value of Public Information. American Economic Review Vol. 92, pp. 1521–1534.
- Svensson, Lars, 2006, Social Value of Public Information: Comment: Morris and Shin, 2002 is Actually Pro-Transparency, not Con. American Economic Review Vol. 96, pp. 448–52.
- Roca, Mauro, 2009, Transparency and monetary policy with imperfect common knowledge. Washington, DC: International Monetary Fund (mimeo).
- Benabou, Roland, 2008, Groupthink: Collective Delusions in Organizations and Markets. Princetown University: Mimeo.

### Forecasting Methods, Forecast Combination, and Aggregation
- Granger, Clive W. J., 1989, Combining Forecasts—Twenty Years Later. Journal of Forecasting Vol. 8, pp. 167–73.
- Timmermann, Allan, 2006, Forecast Combinations. in Handbook of Economic Forecasting, Vol. 1 (Graham Elliot, Clive W. J. Granger and Allan Timmermann, eds.). Elsevier.
- Wallis, Kenneth F. (forthcoming) Combining Forecasts—Forty Years Later. Applied Economics.
- Bonham, Carl S. and Richard H. Cohen, 2001, To Aggregate, Pool, or Neither: Testing the Rational-Expectations Hypothesis Using Survey Data. Journal of Business and Economic Statistics, Vol. 19, pp. 278–91.
- Davies, Anthony and Kajal Lahiri, 1995, A new framework for analyzing survey forecasts using three-dimensional panel data. Journal of Econometrics Vol. 68, pp. 205-27.
- Isiklar, Gultekin, 2005, On aggregation bias in fixed-event forecast efficiency tests, Economics Letters Vol. 89, pp. 312–6.
- Figlewski, Stephen and Paul Wachtel, Rational Expectations, Informational Efficiency, and Tests Using Survey Data: A Reply. Review of Economics and Statistics, Vol. 65, pp.529–31.

### Survey Forecasts, Rationality Tests, and Panel Data Analyses
- Batchelor, Roy and Pami Dua, 1991, Blue Chip Rationality Tests, Journal of Money, Credit and Banking, Vol. 23, pp. 692–705.
- Keane, Michael P. and David E. Runkle, 1990, Testing the Rationality of Price Forecasts: New Evidence from Panel Data. American Economic Review, Vol. 80, pp.714–35.
- Harvey, David I., Stephen J. Leybourne, and Paul Newbold, 2001, Analysis of a panel of UK macroeconomic forecasts. Econometrics Journal 4, S37-S55.
- Bonham, Carl S. and Richard H. Cohen, 2001, To Aggregate, Pool, or Neither: Testing the Rational-Expectations Hypothesis Using Survey Data. Journal of Business and Economic Statistics, Vol. 19, pp. 278–91.
- Loungani, Prakash (2001). How accurate are private sector forecasts? Cross-country evidence from consensus forecasts of output growth. International Journal of Forecasting 17, 419-32.
- Zarnowitz, Victor, 1985, Rational Expectations and Macroeconomic Forecasts. Journal of Business and Economic Statistics vol. 3, pp. 293–311.

### Financial Markets, Momentum, and Forecast Use in Markets
- Hong, Harrison and Jeremy C. Stein, 1999, A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets, Journal of Finance, Vol. 54, pp. 2143–84.
- Jegadeesh, Narasimhan and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance, Vol. 48, pp. 65–91.
- Jegadeesh, Narasimhan and Sheridan Titman, 2001, Profitability of Momentum Strategies: An Evaluation of Alternative Explanations. Journal of Finance Vol. 56, 699–720.
- Ottaviani, Marco and Peter Norman Sørensen, 2006, The strategy of professional forecasting. Journal of Financial Economics Vol. 81, pp. 441–66.
- Ottaviani, Marco and Peter Norman Sørensen, 2009, Surprised by the Parimutuel Odds? American Economic Review 99 Vol. 5, pp. 2129–34.
- Gallo, Giampiero M., Clive W. J. Granger, and Yongil Jeon (2002). Copycats and Common Swings: The Impact of the Use of Forecasts in Information Sets. IMF Staff Papers, Vol. 49, pp. 4–21.
- Kim, Oliver, Steve C. Lim and Kenneth W. Shaw, 2001, The Inefficiency of the Mean Analyst Forecast as a Summary Forecast of Earnings. Journal of Accounting Research, Vol. 39, pp. 329–36.

### Monetary Policy, Interest Rates, and Shock Measures
- Romer, Christina D. and David H. Romer, 2000, Federal Reserve Information and the Behavior of Interest Rates. American Economic Review Vol. 90, pp. 429–57.
- Barakchian, S. Mahdi and Christopher Crowe, 2009, Monetary Policy Matters: New Evidence from a New Shock Measure. International Monetary Fund: Mimeo.

*References as provided in the source PDF.*

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