## _wp06197

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---

### I. Introduction and primary findings
- Headline inflation in the euro area has remained above the European Central Bank’s (ECB) “close to but below” 2 percent target since 2000 and is forecast to continue to do so through 2007.
- Core inflation measures (excluding energy and unprocessed food) declined since 2004—to around 1½ percent in the spring of 2006—suggesting subdued inflationary pressures.
- Other near-term indicators (mild wage and unit labor cost growth) indicate little immediate inflationary pressure and no second-round effects from rising oil prices.
- Key analytic questions addressed:
  - How useful are indicators of underlying inflation in forecasting future inflation?
  - Are there gains from using information from a large set of indicators and different modeling approaches?
  - Where is inflation headed over the medium-term (the ECB’s monetary policy horizon)?
- Main findings:
  - Inflation forecast errors over a 24-month horizon resulting from model misspecification are larger than errors resulting from forecasting of exogenous variables.
  - Measures derived using the generalized dynamic factor model (GDFM) overperform other measures over the monetary policy horizon and are leading indicators of headline inflation.
  - Trimmed means, although weaker than GDFM indicators, have good forecasting performance over a 24-month horizon.
  - Indicators by permanent exclusion (notably core inflation) underperform but provide useful information about short-term dynamics.
  - The forecasting performance of theoretically-founded models that relate monetary aggregates, the output gap, and inflation improves with the time horizon but generally falls short of that of the GDFM.
  - A composite measure of underlying inflation, derived by averaging the statistical indicators and the model-based estimates, improves forecast accuracy by eliminating bias, and offers valuable insight about the distribution of risks.

### II. Taxonomy of underlying inflation indicators
- Purpose: disentangle idiosyncratic/temporary and policy-related/persistent forces driving inflation; separate persistent “common” component and transient “noise.”
- Two main groups:
  - Statistical indicators:
    - Time series methods (univariate filters).
    - Cross-section distribution of prices (permanent exclusion, e.g., core inflation; variable exclusion, e.g., trimmed means).
    - Panel data methods (generalized dynamic factor model, GDFM).
  - Theoretical/structural measures:
    - Long-run Phillips curve frameworks (e.g., SVAR, reduced-form Phillips curve).
    - Quantity-theory-based approaches (money demand equations, P* models).

### III. Comparative properties, volatility, and bias
- Volatility (standard deviation relative to HICP standard deviation):
  - GDFM measures: standard deviation ranging from 32 to 77 percent of HICP standard deviation for indicators with 1 and 2 dynamic factors, respectively.
  - Theoretically-based (Quah and Vahey and Phillips curve) measures: standard deviations of 38 percent and 54 percent, respectively.
  - Trimmed mean indicators: variability declines as the share of excluded goods increases.
  - Core inflation indicators: rank last in noise reduction.
- Bias:
  - GDFM and model-based indicators: unbiased.
  - Trimmed means: small (0.1 percentage points) but statistically significant downward bias.
  - Core measures: highest downward bias (0.2 percentage points in the sample).
- Qualitative assessment:
  - GDFM measures have good leading indicator properties; signaled the inflation pickup starting in 1999 and suggest underlying inflation has remained stable since 2002.
  - Indicators suggest underlying inflation has been moving broadly sideways over the past year and is currently in a range of 1½ to 2¼ percent, with most indicators pointing to a figure under 2 percent.

### IV. Forecasting methodology and implementation
- Forecast horizons and timing:
  - Simulated out-of-sample forecasts evaluated at 6, 12, 18, and 24 months.
  - Simulated out-of-sample 24-month ahead forecasts start in November 2000 and sample ends November 2005, giving 61 forecast rounds.
  - Number of observations for RMSE and bias equals forecast rounds minus horizon length: 24-month horizon: 37 observations; 18-month horizon: 43 observations; 12-month horizon: 49 observations; 6-month horizon: 55 observations.
- Two forecasting approaches for 24-month ahead forecasts:
  - with 1-month lag equations, and
  - with 24-month lag equations.
- Trade-offs:
  - Advantage of 1-month lag: estimated equations have better goodness of fit statistics and smaller standard errors than 24-month lag equations.
  - Disadvantage of 1-month lag: indicators must be forecast 24 months ahead, adding exogenous variable forecast error.
  - The relative performance depends on which forecast error is smaller—the one from model misspecification or the one from exogenous variable forecast.
- Projection of right-hand side variables: all RHS variables at forecast time are treated as unknown and projected using a nonparametric spectral density filter.
- Estimation windows used:
  - (i) expanding window (initial point fixed, end point extended by one month), and
  - (ii) 4-year rolling window (both initial and end points moved forward by one month each time).
  - The results from both methods are similar.
- Equations and model types (brief):
  - Static equation: πt = x t–h + εt.
  - Spectral density filter: nonparametric frequency-domain forecasting device.
  - Semi-structural equation controlling for oil and exchange rate: πt = α + β x t–1 + γ oil t–1 + δ z t–1 + εt (and variant with x at 24-month lag).
  - Distributed lag equation: πt = A(L) πt–1 + B(L) x t–1 + εt.
  - Gap equation: πt − πt–1 = α + β (x t–1 − πt–1) + εt (and variants).
  - Reduced-form Phillips curve: πt = α + β gap t–1 + γ oil t–1 + δ z t–1 + η πt–1 + εt.
  - P* model: p* t = y* t − m t + ν* t; inflation dynamics presented in source.
  - Bivariate SVAR: variables Δyt and πt; underlying inflation as component driven by short-run shock.

### V. Forecast evaluation metrics and empirical findings
- Forecast evaluation metrics:
  - RMSE and bias defined as in the source: RMSE = sqrt[(1/T) ∑ (πt+h − π̂t+h)^2]; Bias = (1/T) ∑ (πt+h − π̂t+h).
- Relative performance (key exact comparisons and rankings preserved):
  - Forecasts with a 1-month lag overperform those with a 24-month lag, suggesting model misspecification errors exceed exogenous variable forecast errors (Tables 4, 5, and 6).
    - Exceptions: trimmed means and M2 perform better with the 24-month lag distributed lag equation.
    - 5 and 10 percent trimmed means and M3 perform better with the 24-month lag gap equation.
    - However, RMSE of best indicators with 24-month lag equations are larger than best indicators with 1-month lag equations.
  - Benchmarks and model set:
    - Random walk forecast; two spectral density forecasts (levels and first differences); indicators (GDFM, core, trimmed mean) with static and model-based forecast types; structural forecasts (SVAR, Phillips curve, P* models).
  - Indicator ranking by performance:
    - GDFM measures outperform other statistical measures, including the random walk, across time and models (superior by both RMSE and bias).
    - Trimmed means come second; by RMSE trimmed means perform slightly worse than random walk, but they are best for short run (6 to 12 months).
    - Core indicators have the worst performance.
    - Labor market variables (wages, unit labor cost, unemployment) perform on average better than monetary aggregates (M1–M3) by RMSE; by bias they are somewhat worse than monetary aggregates.
  - Model specification performance:
    - Static equation overperforms all other specifications at the 24-month horizon.
    - Gap equation comes second; strong performance with labor market variables (and monetary aggregates less M3) over the long run; RMSE of gap equation with these variables improves significantly with forecast horizon.
    - Semi-structural equation controlling for oil and exchange rate has good performance with GDFM and trimmed means.
    - Distributed lag model: acceptable over short run (6 to 12 months); performance deteriorates significantly towards medium term across all indicators.
  - Theoretical model measures:
    - Phillips curve models outperform the P* model at the 24-month horizon by RMSE.
    - Phillips curve comparable to trimmed means and labor market variables by RMSE.
    - P* model performs significantly worse (possible explanation: instability of money velocity over sample period).
    - SVAR model performance is similar to Phillips curve, but measurement error concerns: probability of measurement error exceeding 0.5 percentage points is in the range of 40 to 60 percent (source note).
- Combining forecasts:
  - A simple average of all forecasts results in zero bias and RMSE similar to best performing indicators.
  - Combined forecasts reduce bias, provide a measure of uncertainty around central tendency, and improve efficiency; pooled forecasts perform better in presence of structural breaks.
- Central tendency and projected paths (model-based comparisons):
  - Combined forecasts suggest declining inflationary pressures over next two years; all forecasts show inflation declines towards end of forecast horizon.
  - Static equation-based measures and semi-structural equation controlling for oil and exchange rates predict inflation declines to around 1¾ percent by end of 2007.
  - Distributed lag specifications (including inflation inertia) show inflation slightly above 2 percent by end-2007.
  - Phillips curve and bivariate SVAR forecast inflation slightly below 2 percent by end-2007.
  - P* model projects declining inflation but remains above 2 percent by 2007.
  - Combination of all forecasts projects inflation declining to slightly above 2 percent by end-2007.

### VI. Persistence, distributional assessment, and risks
- Persistence and lagged inflation:
  - The coefficient for lagged inflation is high in the estimated equations.
  - Uncertainty whether high coefficient reflects repeated hikes in oil and administrative prices since 2001 or true persistence (second-round wage effects).
  - Literature mixed: O’Reilly and Whelan (2004) find stability in persistence post-1970; Altissimo and others (2005) find high aggregate persistence that declines after allowing time variation in inflation mean.
  - Estimates from a 4-year rolling AR1 process (Figure 13) suggest a declining coefficient on lagged inflation, possibly indicating falling inflation persistence in the euro area over past several years.
- Distribution and risk assessment:
  - Assessment of inflation risks by analyzing distribution of forecasts (parameters estimated from data).
  - If distribution skewed to the right (outliers left of mean) risks considered negative; skewed to the left implies positive risks.
  - Static equation forecasts lower average inflation but suggest upside risks; other models forecast higher average inflation but imply downside risks.
  - Overall, distribution for all forecasts implies roughly balanced inflation risks, with inflation falling to close to 2 percent in the course of 2007.

### VII. Policy-relevant conclusions and recommendations
- Forecasts with 1-month lag outperform 24-month lag forecasts; model misspecification errors exceed exogenous variable forecast errors—implication: prioritize better-specified short-lag models and account for exogenous-variable forecast uncertainty when using long-lag specifications.
- Among statistical and 1-month lag specifications, GDFM indicators overperform all other measures over the two-year policy horizon and are leading indicators of inflation—implication: incorporate GDFM-based signals into monetary-policy monitoring.
- Trimmed means rank second with good predictive power; standard core indicators underperform—implication: prefer trimmed means to permanent-exclusion core measures for medium-term forecasting.
- Simple averaging (combining) of forecasts:
  - Eliminates bias,
  - Produces RMSE similar to best indicators,
  - Provides a fuller picture of uncertainty and risks, and
  - Improves efficiency and robustness to structural breaks—implication: use forecast combinations for policy communication and scenario assessment.
- Theoretically-founded models (e.g., reduced-form Phillips curve) are valuable for policy analysis because they:
  - Offer comparable forecasting ability to trimmed means by RMSE,
  - Allow decomposition of inflation drivers into domestic demand factors, exogenous supply shocks, and exchange rate effects, aiding monetary policy decision making.
- Outlook implied by models and combinations: inflation generally projected to decline toward or slightly above 2 percent by end-2007, with the exact pace dependent on specification choices (notably inclusion of lagged inflation) and on oil price and exchange rate stabilization.

*Content derived from the PDF chapter "References" of _wp06197 as provided.*

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

### _wp06197 - References..............................................................................................................

### I. Introduction and primary findings
- Headline inflation in the euro area has remained above the European Central Bank’s (ECB) “close to but below” 2 percent target since 2000 and is forecast to continue to do so through 2007.
- Core inflation measures (excluding energy and unprocessed food) declined since 2004—to around 1½ percent in the spring of 2006—suggesting subdued inflationary pressures.
- Other indicators (mild wage and unit labor cost growth) indicate little near-term inflationary pressure and no second-round effects from rising oil prices.
- Key questions addressed:
  - How useful are indicators of underlying inflation in forecasting future inflation?
  - Are there gains from using information from a large set of indicators and different modeling approaches?
  - Where is inflation headed over the medium-term (the ECB’s monetary policy horizon)?

Main findings:
- Inflation forecast errors over a 24-month horizon resulting from model misspecification are larger than errors resulting from forecasting of exogenous variables.
- Measures derived using the generalized dynamic factor model (GDFM) overperform other measures over the monetary policy horizon and are leading indicators of headline inflation.
- Trimmed means, although weaker than GDFM indicators, have good forecasting performance over a 24-month horizon.
- Indicators by permanent exclusion (notably core inflation) underperform but provide useful information about short-term dynamics.
- The forecasting performance of theoretically-founded models that relate monetary aggregates, the output gap, and inflation improves with the time horizon but generally falls short of that of the GDFM.
- A composite measure of underlying inflation, derived by averaging the statistical indicators and the model-based estimates, improves forecast accuracy by eliminating bias, and offers valuable insight about the distribution of risks.

### II. Taxonomy of underlying inflation indicators
- Purpose: disentangle idiosyncratic/temporary and policy-related/persistent forces driving inflation; separate persistent “common” component and transient “noise.”
- Two main groups:
  - Statistical indicators:
    - Time series methods (univariate filters).
    - Cross-section distribution of prices (permanent exclusion, e.g., core inflation; variable exclusion, e.g., trimmed means).
    - Panel data methods (generalized dynamic factor model, GDFM).
  - Theoretical/structural measures:
    - Long-run Phillips curve frameworks (e.g., SVAR, reduced-form Phillips curve).
    - Quantity-theory-based approaches (money demand equations, P* models).

### III. Features and comparative properties of indicators
- General tradeoffs:
  - Statistical indicators: less volatile than headline inflation; not backed by economic theory.
  - Theoretical measures: macroeconomic foundations and interpretability; harder to identify structural shocks and estimate parameters; vulnerable to behavioral invariance (Lucas critique).
- Rationale for broad set of indicators: gauge uncertainty, provide comparative perspective, deal with single-forecast uncertainty, and enable risk assessment.
- Volatility and bias (comparative statistics):
  - Volatility (standard deviation relative to HICP):
    - GDFM measures: standard deviation ranging from 32 to 77 percent of HICP standard deviation for indicators with 1 and 2 dynamic factors, respectively.
    - Theoretically-based (Quah and Vahey and Phillips curve) measures: standard deviations of 38 percent and 54 percent, respectively.
    - Trimmed mean indicators: variability declines as the share of excluded goods increases.
    - Core inflation indicators: rank last in noise reduction.
  - Bias:
    - GDFM and model-based indicators: unbiased.
    - Trimmed means: small (0.1 percentage points) but statistically significant downward bias.
    - Core measures: highest downward bias (0.2 percentage points in the sample).
- Qualitative performance observations:
  - GDFM measures appear to have good leading indicator properties and signaled the inflation pickup that started in 1999; they suggest underlying inflation has remained stable since 2002.
  - Core and trimmed mean indicators performed well over 1997–99, lagged headline inflation during 1999–2001, and implied declining (core) or stable (trimmed means) underlying inflation since 2004.
  - Model-based estimates (Quah and Vahey and Phillips curve) anticipated the 1999 pickup and indicate roughly stable underlying inflation over recent years; the Phillips curve indicator points to a slight increase of inflation since mid-2004 driven by high energy prices.
  - Quantitative range: indicators suggest underlying inflation has been moving broadly sideways over the past year and is currently in a range of 1½ to 2¼ percent, with most indicators pointing to a figure under 2 percent.

### IV. Forecasting methodology and assessment of forecasting performance
- Forecast evaluation approach:
  - Simulated out-of-sample forecasts are used to assess forecasting performance of statistical indicators.
  - For statistical indicators (core, trimmed means, and GDFM) univariate, bivariate, and multivariate specifications are used to forecast headline inflation.
  - Inflation forecasts are also produced with non-price variables: industrial production, monetary aggregates, wages, unit labor cost, unemployment, and interest rates.
  - Simulated out-of-sample 24-month ahead forecasts start in November (sample and exact start point given in full paper).
- Comparative performance summary:
  - GDFM indicators generally outperform other measures over the monetary policy horizon and are leading indicators.
  - Trimmed means perform well over a 24-month horizon but are weaker than GDFM.
  - Indicators by permanent exclusion (core inflation) perform less well for medium-term forecasting but remain useful for short-term dynamics.
  - Theoretical models (SVAR, Phillips curve, P* variants) improve with forecast horizon but generally do not match GDFM performance.
  - A composite indicator, averaging statistical and model-based estimates, reduces bias and improves forecast accuracy while providing insight into risk distribution.

*Italic source attribution: Content derived from the PDF chapter "References" of _wp06197 as provided.*

### 2000. The equations are re-estimated each time a new month is added.

### _wp06197 - 2000. The equations are re-estimated each time a new month is added.

### Forecasting approaches and implementation
- 24-month ahead forecasts are produced using two approaches:
  - with 1-month lag equations, and
  - with 24-month lag equations.
- Trade-offs:
  - Advantage of 1-month lag: estimated equations have better goodness of fit statistics and smaller standard errors than 24-month lag equations.
  - Disadvantage of 1-month lag: indicators must be forecast 24 months ahead, adding exogenous variable forecast error to model forecast error.
  - The relative performance depends on which forecast error is smaller—the one from model misspecification or the one from exogenous variable forecast.
- At the time of the forecast, all right-hand side variables (including the indicator for models where the indicator is lagged one month) are assumed unknown and are projected using a nonparametric spectral density filter.
- Two estimation window methods were used:
  - (i) expanding window (initial point fixed, end point extended by one month), and
  - (ii) 4-year rolling window (both initial and end points moved forward by one month each time).
  - The results from both methods are similar.
- Sample period for estimates with year-on-year data: January 1997–November 2005. Forecasting performance assessed over a common sample constrained by data availability since January 1996.

### Equations and models (brief descriptions)
- Static equation:
  - Defined as πt = x t–h + εt (headline inflation equals indicator of underlying inflation at lag h plus error).
- Spectral density filter:
  - A nonparametric frequency-domain technique similar in nature to ARMA but not dependent on lag selection.
- Semi-structural equation controlling for oil and exchange rate:
  - Unrestricted version of the static equation extended with oil prices and the exchange rate:
    - πt = α + β x t–1 + γ oil t–1 + δ z t–1 + εt
    - (Also estimated with x at 24-month lag: πt = α + β x t–24 + γ oil t–24 + δ z t–24 + εt)
  - 1−t oil is oil prices in euros; 1−t z is the exchange rate.
  - 24-month ahead simulated out-of-sample forecast: first RHS variables forecast with spectral density filter, then solve for πt.
- Distributed lag equation:
  - Form: πt = A(L) πt–1 + B(L) x t–1 + εt (also estimated with 24-month lag: x t–24)
  - A(L) and B(L) are lag polynomials (lag selection by Akaike and Schwartz information criteria).
- Gap equation:
  - For statistical indicators:
    - πt − πt–1 = α + β (x t–1 − πt–1) + εt  (also with 24-month lag)
  - For non-price variables c t (wages, monetary aggregates, etc.), estimated in deviation from means:
    - πt − π̄ = α + β (c t–1 − c̄) + εt  (also with 24-month lag).
- Reduced form Phillips curve model:
  - πt = α + β gap t–1 + γ oil t–1 + δ z t–1 + η πt–1 + εt
  - gap t–1 is output gap; z t is change in exchange rate; oil t–1 is change in oil prices.
- P* model:
  - P* indicator: p* t = y* t − m t + ν* t (all logs; y* potential output; m current money stock; ν* equilibrium velocity).
  - Inflation dynamics: πt − λ1 πt–1 − λ2 π* t–1 + εt (stylistically presented in source).
- Bivariate SVAR:
  - Variables: Δyt (change in industrial production) and πt (headline inflation).
  - Underlying inflation defined as the unobserved component driven by the short-run shock; inflation decomposed into cumulative effects of the two disturbances.

### Forecast evaluation methodology
- Forecast performance evaluated by:
  - root mean square error (RMSE), and
  - bias.
- Forecast horizons: 6, 12, 18, and 24 months.
- Simulated out-of-sample forecasts start in November 2000 and sample ends November 2005, giving 61 forecast rounds.
- Number of observations for RMSE and bias equals forecast rounds minus horizon length:
  - 24-month horizon: 37 observations,
  - 18-month horizon: 43 observations,
  - 12-month horizon: 49 observations,
  - 6-month horizon: 55 observations.
- RMSE and bias definitions:
  - RMSE: sqrt[(1/T) ∑ (πt+h − π̂t+h)^2]
  - Bias: (1/T) ∑ (πt+h − π̂t+h)
  - (Formulas shown in source text.)

### Forecast performance findings (exact reported comparisons)
- Forecasts with a 1-month lag overperform those with a 24-month lag, suggesting model misspecification errors exceed exogenous variable forecast errors (Tables 4, 5, and 6).
  - Exceptions: trimmed means and M2 perform better with the 24-month lag distributed lag equation.
  - 5 and 10 percent trimmed means and M3 perform better with the 24-month lag gap equation.
  - However, RMSE of best indicators with 24-month lag equations are larger than best indicators with 1-month lag equations.
- Benchmark forecasts and models compared:
  - Random walk forecast (future inflation = current inflation).
  - Two spectral density forecasts (levels and first differences).
  - Indicators: GDFM, core, trimmed mean.
    - Forecast types: static (headline = current indicator) and model-based (distributed lag, gap, semi-structural).
  - Structural forecasts: SVAR, Phillips curve, P* models.
- Relative performance by indicator and model:
  - GDFM measures outperform other statistical measures, including the random walk, across time and models (Table 4).
    - GDFM superior according to both RMSE and bias.
  - Trimmed means come second; by RMSE trimmed means perform slightly worse than random walk, but they are best for short run (6 to 12 months).
  - Core indicators have the worst performance.
  - Labor market variables (wages, unit labor cost, unemployment) perform on average better than monetary aggregates (M1–M3) by RMSE; by bias they are somewhat worse than monetary aggregates.
- Model specification performance:
  - Static equation overperforms all other specifications at the 24-month horizon.
  - Gap equation comes second; strong performance with labor market variables (and monetary aggregates less M3) over the long run; RMSE of gap equation with these variables improves significantly with forecast horizon.
  - Semi-structural equation controlling for oil and exchange rate has good performance with GDFM and trimmed means.
  - Distributed lag model: acceptable over short run (6 to 12 months); performance deteriorates significantly towards medium term across all indicators.
- Theoretical model measures:
  - Phillips curve models outperform the P* model at the 24-month horizon by RMSE.
  - Phillips curve comparable to trimmed means and labor market variables by RMSE.
  - P* model performs significantly worse (possible explanation: instability of money velocity over sample period).
  - SVAR model performance is similar to Phillips curve, but usefulness for monetary policy is questioned due to measurement error probabilities (see source note: probability of measurement error exceeding 0.5 percentage points is in the range of 40 to 60 percent).
- Combining forecasts:
  - A simple average of all forecasts results in zero bias and RMSE similar to best performing indicators; reasonable in-sample forecasting error for 24-month ahead forecast (Figure 9).
  - Combined forecasts reduce bias, provide a measure of uncertainty around central tendency, and improve efficiency; pooled forecasts perform better in presence of structural breaks.
- Central tendency of forecasts and projections:
  - Combined forecasts suggest declining inflationary pressures over next two years; all forecasts show inflation declines towards end of forecast horizon.
  - Static equation-based measures and semi-structural equation controlling for oil and exchange rates predict inflation declines to around 1¾ percent by end of 2007.
  - Distributed lag specifications (including inflation inertia) show inflation slightly above 2 percent by end-2007.
  - Phillips curve and bivariate SVAR forecast inflation slightly below 2 percent by end-2007.
  - P* model projects declining inflation but remains above 2 percent by 2007.
  - Combination of all forecasts projects inflation declining to slightly above 2 percent by end-2007.
- Persistence and lagged inflation:
  - The coefficient for lagged inflation is high in the estimated equations.
  - Uncertainty whether high coefficient reflects repeated hikes in oil and administrative prices since 2001 or true persistence (second-round effects on wages).
  - Literature mixed on persistence: O’Reilly and Whelan (2004) find stability in persistence post-1970; Altissimo and others (2005) find high aggregate persistence that declines after allowing time variation in inflation mean.
  - Estimates from a 4-year rolling AR1 process (Figure 13) suggest a declining coefficient on lagged inflation, possibly indicating falling inflation persistence in the euro area over past several years.
- Distribution and risk assessment:
  - Assessment of inflation risks by analyzing distribution of forecasts (parameters estimated from data, not judgment).
  - If distribution skewed to the right (outliers left of mean) risks considered negative; skewed to the left implies positive risks.
  - Static equation forecasts lower average inflation but suggest upside risks; other models forecast higher average inflation but imply downside risks.
  - Overall, distribution for all forecasts implies roughly balanced inflation risks, with inflation falling to close to 2 percent in the course of 2007.

### Key conclusions and policy-relevant findings
- Forecasts with 1-month lag outperform 24-month lag forecasts; model misspecification errors exceed exogenous variable forecast errors.
- Among statistical and 1-month lag specifications, GDFM indicators overperform all other measures over the two-year policy horizon and are leading indicators of inflation.
- Trimmed means rank second with good predictive power; standard core indicators underperform.
- Simple averaging (combining) of forecasts:
  - Eliminates bias,
  - Produces RMSE similar to best indicators,
  - Provides a fuller picture of uncertainty and risks, and
  - Improves efficiency and robustness to structural breaks.
- Theoretically-founded models (e.g., reduced form Phillips curve) are valuable for policy analysis because they:
  - Offer comparable forecasting ability to trimmed means by RMSE,
  - Allow decomposition of inflation drivers into domestic demand factors, exogenous supply shocks, and exchange rate effects, aiding monetary policy decision making.
- Outlook implied by models and combinations: inflation generally projected to decline toward or slightly above 2 percent by end-2007, with the exact pace dependent on specification choices (notably inclusion of lagged inflation) and on oil price and exchange rate stabilization.

*Source: _wp06197 - 2000. The equations are re-estimated each time a new month is added.*

### References

### References

### Bibliographic references
- Aiolfi, M. and A. Timmermann, 2004, “Structural Breaks and the Performance of Forecast Combinations” (unpublished; Bocconi University).
- Altissimo, F., L. Bilke, A. Levin, T. Mathä, and B. Mojon, (2005) “Sectoral and Aggregate Inflation Dynamics in the Euro Area,” paper presented at the 20th Annual Congress of the European Economic Association, Amsterdam.
- Blix, Mårten, 1995, “Underlying Inflation—A Common Trends Approach,” Bank of Sweden Working Paper No. 23.
- Blix, Mårten, and P. Sellin, 1999, “Inflation Forecasts with Uncertainty Intervals,” Sveriges Riksbank Quarterly Review 2: pp. 12–28.
- Bryan, M. F., and S. G. Cecchetti, 1994, “Measuring Core Inflation,” in Monetary Policy, ed. by N. Gregory Mankiw, (Chicago: The University of Chicago Press).
- Bryan, M. F., and S. G. Cecchetti, 1996, “Inflation and the Distribution of Price Changes,” NBER Working Paper No. 5793, (Cambridge, Massachusetts: National Bureau of Economic Research).
- Bryan, M. F., and R. L. Wiggins II, 1997, “Efficient Inflation Estimation,” NBER Working Paper No. 6183, (Cambridge, Massachusetts: National Bureau of Economic Research).
- Coats, Warren, 2000, Inflation Targeting in Transition Economies: The Case of the Czech Republic, ed. by Warren Coats, (Prague: Czech National Bank).
- Coletti, D., B. Nunt, D. Rose and R. Tetlow, 1996, “Bank of Canada’s New Quarterly Projection Model. Part 3, The Dynamic Model: QPM,” Bank of Canada Technical Report No. 75 (Ottawa: Bank of Canada).
- Cristadoro, R., M. Forni, L. Reichlin, and G. Veronese, 2001, “A Core Inflation Index for the Euro Area,” CEPR Discussion Paper No. 3097, (London: Centre for Economic Policy Research).
- Faruqee, H., 2005, Declining Money Velocity in the Euro Area: Implications for the ECB’s Monetary Analysis, IMF Country Report No. 05/259 (Washington: International Monetary Fund).
- Folkertsma, C.K., and K. Hubrich, 2001, “Performance of Core Inflation Measures,” The Economist, Vol. 149, No. 4, pp. 455-508.
- Forni, M., M. Hallin, M. Lippi, and L. Reichlin, 2000, “The Generalized Factor Model: Identification and Estimation,” Review of Economics and Statistics, Vol. 82, No. 4, pp. 540−54.
- Forni, M., M. Hallin, M. Lippi, and L. Reichlin, 2003, “The Generalized Factor Model: One-Sided Estimation and Forecasting” (unpublished).
- Hahn, E. (2002), “Core Inflation in the Euro Area: An Application of the Generalized Dynamic Factor Model,” Center for Financial Studies Working Paper No. 2002/11 (Frankfurt: Center for Financial Studies).
- Hall, S. G. and J. Mitchell, 2004, “Density Forecast Combination,” NIESR Discussion Papers (London: National Institute of Economic and Social Research).
- Hamilton, J. D., 1994, Time Series Analysis, (Princeton University: Princeton University Press).
- Hendry, D. F. and K. Hubrich, 2006, “Forecasting Economic Aggregates by Disaggregates,” ECB Working Paper No. 589 (Frankfurt: European Central Bank).
- Nicoletti Altimari, S., 2001, “Does Money Lead Inflation in the Euro Area?” ECB Working Paper No. 63 (Frankfurt: European Central Bank).
- O’Reilly, G., and K. Whelan, 2004, “Has Euro Area Inflation Persistence Changed Over Time?” ECB Working Paper No. 335 (Frankfurt: European Central Bank).
- Quah, D. and S. Vahey, 1995, “Measuring Core Inflation,” The Economic Journal, Vol. 105, 86 (1), pp. 1130−44.
- Timmermann, Allan, 2005, “Forecast Combinations,” CEPR Discussion Paper No. 5361 (London: Centre for Economic Policy Research).
- Vega, J. L. and M. A. Wynne, 2002, “A First Assessment of Some Measures of Core Inflation for the Euro Area,” Federal Reserve Bank of Dallas Working Paper No. 0205.

### Figures (topics and captions)
- Figure 1: Euro Area: Headline and Core Inflation (In percent). Series noted: Forecast; Core inflation excluding energy and unprocessed food (year-on-year); Headline inflation excluding administrative prices (December, year average); ECB target; Headline inflation (year-on-year); Headline inflation (December, year average).
- Figure 2: Euro Area: Headline and GDFM Estimates of Underlying Inflation (In percent). Source: IMF staff estimates. Panels compare 1 dynamic factor and 2 dynamic factors; comparisons of year-on-year and month-on-month data.
- Figure 3: Euro Area: Headline and Permanent Exclusion Core Inflation (Year-on-year, in percent). Source: Eurostat. Series include HICP excluding energy, food, alcohol and tobacco; HICP excluding energy; HICP excluding energy and seasonal food; HICP excluding energy and unprocessed food.
- Figure 4: Euro Area: Headline and Variable Exclusion Core Inflation (Year-on-year, in percent). Source: IMF staff estimates. Series include trimmed means at 5, 10, 15, 50 percent.
- Figure 5: Euro Area: Headline and Model-based Underlying Inflation (Year-on-year, in percent). Series include Quah-Vahey underlying inflation and Reduced form Phillips curve underlying inflation (Dynamic simulation).
- Figure 6: Euro Area: Underlying Inflation and Macroeconomic Factors (Year-on-year, in percent). Source: IMF staff estimates. Note: Dynamic real time forecast with reduced form Phillips curve. Panels show Oil Price Effect, Output Gap Effect, Exchange Rate Effect with underlying inflation, oil prices, industrial production gap, and exchange rate.
- Figure 7: Euro Area: Underlying Inflation and Macroeconomic Factors (Year-on-year, in percent). Source: IMF staff estimates. Note: Out-of-sample forecast with reduced form Phillips curve; oil prices, industrial production gap, and exchange rate are forecast with an ARMA process. Panels show Oil Price Effect, Output Gap Effect, Exchange Rate Effect with forecasts.
- Figure 8: Euro Area: Projection Comparisons (Year-on-year, in percent). Source: IMF staff estimates. Panels compare ARMA forecasts and WEO interpolated forecasts for Oil, GDP and Industrial Production Gaps, and Exchange Rate.
- Figure 9: Euro Area: 24-month In-sample Forecast with the Composite Indicator (Year-on-year, in percent, all indicators excluding ARDL). Series: Inflation Average, Median, +1 Standard deviation, -1 Standard deviation.
- Figure 10: Euro Area: Static Equation Forecasts (Year-on-year, in percent). Source: IMF staff estimates. Panels: Headline Inflation — Average, Median, +1 Standard deviation, -1 Standard deviation; also static equation forecasts controlling for exchange rate and oil prices (13 Forecasts).
- Figure 11: Euro Area: Time Series Models Forecasts (Year-on-year, in percent). Source: IMF staff estimates. Panels include Distributed Lag Equation and All Forecasts (103 forecasts).
- Figure 12: Euro Area: Forecasts with Theoretical Models (Year-on-year, in percent). Series: Headline HICP inflation; Forecast; P*; Phillips curve; SVAR.
- Figure 13: Euro Area: Persistence of Headline Inflation (Estimates from a 4-year rolling regression). Panels show autoregressive coefficient with +1 and -1 standard error bands.
- Figures 14–16: Probability Distribution Function and Kernel Density Estimates for Static, Bivariate/Multivariate, and All Forecasts; reported skew statistics: Figure 14 skew = 0.2449; Figure 15 skew = -0.2678; Figure 16 skew = -0.25338.

### Tables (titles and key statistics)
- Table 1: Taxonomy of Underlying Inflation Indicators. Categories listed: Theoretical/Structural measures, Time series, Cross-section, Panel; approaches include Bottom up, Exclusion measures, Dynamic factor models, P* models, Structural VARs, Single Phillips curve equations, Aggregate supply/demand models, Money demand models, etc.
- Table 2: Euro Area: Descriptive Statistics of HICP Components (2005). Sources: EUROSTAT; and IMF staff estimates. Note: 1/ Annualized. (Table lists component codes, Description, Weight, Mean m-o-m, 1/y-o-y, etc. across many HICP components.)
- Table 3: Euro Area: Headline and Underlying Inflation Indicators: Descriptive Statistics (Year-on-year, in percent). Sources: Eurostat; and IMF staff calculations. 1/ Sample: January, 1997-December, 2005. 2/ Relative to headline inflation.
  - Headline inflation — Mean 1.92; Median 2.03; Maximum 3.10; Minimum 0.8; Standard Deviation 1.00.
  - Example GDFM indicators: Prices only: 1 dynamic factor — Mean 1.91; Median 1.82; Maximum 2.3; Minimum 1.6; Standard Deviation 0.32.
  - Example Core indicators: Headline excluding energy — Mean 1.71; Median 1.63; Maximum 3.00; Minimum 0.7; Standard Deviation 1.08.
  - Trimmed means/median and model measures (Vahey&Quah, Phillips curve) are tabulated with precise numeric summaries.
- Table 4: Euro Area: Forecast Performance of Indicators of Underlying Inflation 1/ (Root mean square error/RMSE/ and bias in percentage points). Source: IMF staff estimates. 1/ Forecast evaluation for estimates with year-on-year inflation. Table provides RMSE and Bias for multiple forecast horizons and many indicator types including HICP inflation (First difference and Level), HICP inflation (Random walk--benchmark), GDFM estimates (1 and 2 factors, with and without non-price data), Core inflation measures by exclusion, Trimmed means/median, Non-price indicators (M1, M2, M3, Wages, ULC, Unemployment, Industrial production, Interest rates), Structural measures (Quah&Vahey SVAR, Reduced form Phillips curve, P* model), Composite indicators, Bivariate and Multivariate models. Forecast horizons shown include 6, 12, 18, 24 months; various RMSE and Bias entries reported throughout the table.
- Table 5: Euro Area: Forecast Performance of Indicators of Underlying Inflation 1/ (Root mean square error/RMSE/ and bias in percentage points). Source: IMF staff estimates. 1/ Forecast evaluation for estimates with year-on-year inflation. (Continuation/variation of Table 4 with extensive RMSE and Bias entries across horizons and models.)
- Table 6: Euro Area: 1-month Lag versus 24-month Lag Model Forecast Performance 1/ (Root mean square error/RMSE/ and bias in percentage points). Source: IMF staff estimates. 1/ Forecast evaluation for estimates with year-on-year inflation; 1-month lag minus 24-month lag.
  - Selected entries (1-month minus 24-month lag differences, RMSE and Bias):
    - GDFM estimates of underlying inflation — HICP components only: 1 factor — -2.14 (RMSE difference), 0.18 (Bias difference), -0.26, -0.44, -1.95, -0.14 (various forecast-horizon cells).
    - Core inflation measures by exclusion — Excluding energy — 0.41 (RMSE difference), 0.12 (Bias difference), -0.21, 0.14, -1.22, -1.39.
    - Trimmed means/median — 5 percent — 3.37, 1.54, 0.93, 0.35, -1.03, -1.42; 10 percent — 8.94, 3.27, 0.34, 0.16, -1.16, -1.47; and other trimmed percentages reported.
    - Non-price indicators — M1 — -1.59, -1.64, -0.62, -0.79; M2 — 1.26, 0.32, -0.06, 0.03; M3 — -0.87, -0.96, 0.21, -0.08; and others (Wages, ULC, Unemployment, Industrial production, Interest rates).

*Italicized source attribution: Content derived from _wp06197 - References (IMF staff estimates, EUROSTAT, and cited working papers).*

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