## _wp09167

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---

### I. Introduction: context and purpose
- Rapid rise in world commodity prices during 2008 coincided with a sharp increase in inflation in Sri Lanka in the first half of 2008.
- Headline inflation in Sri Lanka averaged nearly 20 percent during 2007-08.
- Central Bank of Sri Lanka (CBSL) introduced an official core inflation measure in April 2008 that excludes all food and fuel prices from the CPI.
- Purpose: evaluate the CBSL exclusion-based core inflation measure (excludes all food and energy prices) by comparing it with alternative measures using CPI component data for January 2003–October 2008 for 32 components of the Colombo CPI (2002=100).

### II. Motivation for measuring core inflation
- Desired properties for a useful core inflation measure:
  - (i) be a leading indicator of CPI inflation; and
  - (ii) strip out transitory shocks outside monetary authorities’ control.
- Rationale: CPI aggregates many shocks while monetary policy works with a considerable lag; seasonal influences, indirect taxes, and relative-price changes can affect CPI but may not warrant monetary policy response.

### III. Methods and alternative measures examined
- Methods evaluated:
  - Cross-sectional/exclusion-based methods
  - Limited influence estimators (trimmed means)
  - Reweighing methods (persistence-weighted)
  - Time series/econometric (Quah-Vahey and other model-based) decompositions

- Exclusion-based (official and alternatives):
  - CBSL official exclusion set: excludes food, electricity, gas, kerosene, firewood, petrol and other fuels (combined weight 54.6 percent).
  - Alternative exclusion-based measures: exclude most volatile 10, 20, 30, 40 percent items based on standard deviation of month-on-month changes; cumulative weight of excluded items varied from 4.8 percent (10 percent measure) to 22.32 percent (40 percent measure).

- Trimmed-mean estimators:
  - Trimmed means remove tails of cross-sectional distribution of component inflation rates; median trims 50 percent from each tail.
  - Asymmetric trimming recommended when distribution is skewed (Sri Lanka exhibits right skewness).
  - Trim proportions evaluated include 16.0 percent for symmetric trims and from 9 to 22.6 percent for asymmetric trims.
  - Asymmetric trim of 20 percent left tail and 5 percent right tail yielded the lowest RMSE in the study’s grid.
  - The inflation rate was at 20.6 percent according to the trimmed mean measure with the least RMSE.

- Persistence-weighted (reweighing) methodology:
  - Uses AR(1) for month-on-month inflation for each CPI component: π_{t,i} = α_i + ρ_i π_{t-1,i} + ε_{t,i}.
  - Estimated ρ_i indicates persistence; components with negative autocorrelation assigned weight zero.
  - Weights in core index proportional to ρ̂_i for positive ρ̂_i.

- Model-based (Quah-Vahey framework):
  - Decomposes measured inflation into components based on shocks with/without medium- to long-run impact on real output.
  - Implementation via VAR and Wold representation with restrictions imposing long-run neutrality.
  - Reported Quah-Vahey empirical results: core inflation reached 23.7 percent in September 2008; another model-based measure suggests core inflation was 33.6 percent in October 2008.

### IV. Key empirical findings and statistics
- Headline and official core dynamics:
  - Headline CPI inflation peaked at 28.2 percent y/y in June 2008 (new Colombo CPI) and dropped below double digits in February 2009.
  - Food and fuel price inflation on average accounted for 73 and 8 percent of overall CPI inflation in 2008 respectively.
  - Reserve money: CBSL revised target growth rate downward from 15 to 9.7 percent in three steps between April and November, 2008; reserve money in 2008 grew at an annual rate of 1.5 percent relative to 21.2 percent in 2006.
  - Headline inflation fell to below 1 percent y/y while official core inflation remained in double digits during second half of 2008; headline inflation was 1.7 percent below official core inflation in November 2008, gap widened to 10.2 percent four months later, then narrowed to 4.9 percent in July 2009.

- Range of underlying inflation estimates (end-October 2008 and 2008 episode):
  - Estimates of underlying inflation ranged from 9.0 to 33.6 percent compared to official core inflation of 18.6 percent and headline inflation of 20.2 percent.
  - At end-October 2008, alternative exclusion-based measures suggested core inflation between 17.3 percent and 18.9 percent compared to 18 percent in the authorities’ official measure (January 2004–October 2008 comparison).
  - Trimmed mean measures in October-2008 yielded estimates from 15.4 percent to (value truncated in source text); the trimmed mean with least RMSE reported 20.6 percent.
  - The majority of non-official measures during January-June 2008, and an average of more than 60 percent of measures during July-October 2008, suggested underlying inflation in 2008 was above the official measure of core inflation.
  - An average of 20 percent of the estimates (more during the first half of 2008) suggested underlying inflation was above headline inflation at the time.

- Trim and RMSE details:
  - Trim proportions evaluated: symmetric trims at 16.0 percent and asymmetric trims from 9 to 22.6 percent.
  - Figure 7 RMSE grid indicated the asymmetric trim 20 percent left tail and 5 percent right tail minimized RMSE on the evaluated grid (authors note grid fineness limited by low cross-sectional dimension).

### V. Statistical evaluation (Marques et al. tests and other diagnostics)
- Cointegration (headline − core) tests (ADF and KPSS):
  - KPSS indicates cointegration with headline inflation for: Quah-Vahey, Trimmed Mean 25L10R, Persistence Weighted, Exclusion 3, Exclusion 6.
  - KPSS indicates Official core, Trimmed Mean 15L5R, Trimmed Mean 20L5R, Trimmed Mean 25L5R are not cointegrated with headline inflation.
  - Trimmed Mean 25L10R strongly suggested cointegrated with headline inflation.

- Unbiasedness (mean zero test on u_t = π_t − π*_t):
  - KPSS t-test rejects null of non-zero mean in every case except Trimmed Mean 15L5R and Exclusion 3; thus only Trimmed Mean 15L5R and Exclusion 3 can be considered unbiased according to these tests.
  - ADF t-test noted to have low power and generally fails to reject no cointegration.

- Condition (ii): core as attractor of headline (error-correction γ test):
  - γ = 0 rejected (i.e., core attracts headline) for:
    - Official measure of core inflation
    - Trimmed Mean 25L10R
    - Exclusion 3
    - Exclusion 6

- Condition (iii): exogeneity tests (weak exogeneity λ = 0; strong exogeneity θ1 = ... = θs = 0 given λ = 0):
  - Weak exogeneity satisfied for all measures except Trimmed Mean 25L10R and Exclusion 6.
  - Among weakly exogenous measures, strong exogeneity null rejected only for Persistence Weighted measure (Persistence Weighted is not strongly exogenous).

- Selected test statistics (as reported; preserve exact figures):
  - Official Core: t = -1.79; LM = 0.67; P = 0.19; P = 0.00; P = 0.01; P = 0.65; P = 0.12
  - Quah Vahey: t = -0.97; LM = 0.33; P = 0.33; P = 0.00; P = 0.23; P = 0.65; P = 0.21
  - Trimmed Mean 15L5R: t = -1.94; LM = 0.78; P = 0.32; P = 0.18; P = 0.37; P = 0.92; P = 0.07
  - Trimmed Mean 20L5R: t = -2.11; LM = 0.66; P = 0.61; P = 0.00; P = 0.56; P = 0.67; P = 0.06
  - Trimmed Mean 25L5R: t = -2.21; LM = 0.47; P = 0.13; P = 0.00; P = 0.78; P = 0.47; P = 0.06
  - Trimmed Mean 25L10R: t = -2.91; LM = 0.17; P = 0.35; P = 0.01; P = 0.05; P = 0.00
  - Persistence Weighted: t = -0.66; LM = 0.39; P = 0.21; P = 0.00; P = 0.68; P = 0.42; P = 0.02
  - Exclusion 3: t = -0.90; LM = 0.15; P = 0.46; P = 0.10; P = 0.05; P = 0.13; P = 0.41
  - Exclusion 6: t = -1.29; LM = 0.15; P = 0.29; P = 0.00; P = 0.00; P = 0.02
  - ADF critical values (model with non-zero constant): -3.55 (1 percent), -2.91 (5 percent), -2.59 (10 percent).
  - KPSS critical values: 0.74 (1 percent), 0.46 (5 percent), 0.35 (10 percent).

- Interpretive summary of tests:
  - Official measure and Exclusion 3 behave as leading indicators of headline inflation (core → headline) and are exogenous (headline not an attractor for these core measures).
  - Quah-Vahey, Trimmed Mean 15L5R, Trimmed Mean 20L5R, Trimmed Mean 25L5R, and Persistence Weighted: not cointegrated with headline inflation (no error-correction representation).
  - Appropriate measure depends on intended purpose and may vary over time.

### VI. Practical considerations, limitations, and caveats
- No single measure satisfies all desirable criteria (timely, credible, transparent, unbiased, forward-looking, theoretical basis, not subject to revisions).
- Trade-offs:
  - Exclusion-based and limited-influence estimators: timely, transparent, easy to replicate, not subject to revisions.
  - Model-based and reweighting methods: more forward-looking and theoretically grounded but less transparent and subject to revision; potential credibility issues.
- Lucas critique and endogeneity: persistence-weighted and model-based weights may change if policymakers act on them.
- Tests (Marques et al.) may fail if authorities successfully target headline inflation; successful policy can make core measures appear not to satisfy attractor conditions even if informative.

### VII. Policy implications and recommendations
- The usefulness of the official exclusion-based measure as a leading indicator is questioned because official core inflation remained above headline inflation during late 2008–2009 episodes.
- Excluding food and fuel (54.6 percent weight) may omit informative price movements, especially when some food categories were among the least volatile.
- Asymmetric trimmed-mean and volatility-based exclusion measures can provide alternative perspectives; asymmetric trims may perform better where distributions are skewed.
- Ongoing work at the Central Bank to develop new measures of core inflation is appropriate and should be high on the agenda.
- Recommendation: construct a suite of core inflation measures that can be continuously updated and statistically evaluated; use multiple measures to gain confidence when they give similar results and insight when they differ.

*Source: _wp09167 - References (excerpt), IMF staff calculations and Central Bank of Sri Lanka data as provided in the source content.*

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

### _wp09167 - References

### I. Introduction: context and purpose
- Rapid rise in world commodity prices during 2008 coincided with a sharp increase in inflation in Sri Lanka in the first half of 2008.
- Headline inflation in Sri Lanka averaged nearly 20 percent during 2007-08, far exceeding regional peers (Figure 1).
- Central Bank of Sri Lanka (CBSL) introduced an official core inflation measure in April 2008 that excludes all food and fuel prices from the CPI.
- Although headline and official core inflation eased in recent months, official core inflation was higher than headline inflation since November 2008.
- Purpose: evaluate the CBSL official exclusion-based core inflation measure (excludes all food and energy prices) by comparing it with alternative measures proposed in the literature, using CPI component data for January 2003–October 2008 for 32 components of the Colombo CPI (2002=100).

### II. Motivation for measuring core inflation
- Rationale for core inflation measures:
  - CPI measures cost of attaining the same standard of living; monetary policy’s primary role differs.
  - Seasonal influences, indirect taxes, and relative-price changes can affect CPI but may not warrant monetary policy response.
  - CPI aggregates many shocks while monetary policy affects inflation with a considerable lag.
- Desired properties for a useful core inflation measure:
  - (i) be a leading indicator of CPI inflation; and
  - (ii) strip out transitory shocks outside monetary authorities’ control.

### III. Recent monetary developments and inflation dynamics in Sri Lanka
- Headline CPI inflation peaked at 28.2 percent y/y in June 2008 (new Colombo CPI) and dropped below double digits in February 2009.
- Food and fuel price inflation on average accounted for 73 and 8 percent of overall CPI inflation in 2008 respectively.
- Reserve money developments:
  - CBSL revised target growth rate of reserve money downward from 15 to 9.7 percent in three steps between April and November, 2008.
  - Reserve money in 2008 grew at an annual rate of 1.5 percent relative to 21.2 percent in 2006 (Figure 4).
- CBSL argued moderate core inflation plus deceleration in aggregate demand indicated success of demand management; implied headline inflation would decline toward core inflation.
- Headline inflation fell to below 1 percent y/y while official core inflation remained in double digits during the second half of 2008; headline inflation was 1.7 percent below official core inflation in November 2008, the gap widened to 10.2 percent four months later, then narrowed to 4.9 percent in July 2009.

### IV. Definitions and types of core inflation in the literature
- Different conceptions:
  - Bryan and Cecchetti (1993): core inflation reflects price changes attributable to growth rate of money supply.
  - Blinder (1997) and Marques et al. (2003): core inflation is the persistent or durable component.
  - Quah and Vahey (1995): component of measured inflation that has no medium to long-run impact on real output.
- Two uses identified by Mankikar and Paisley (2004) and Silver (2007):
  - Provide a measure stripped of noise for policy assessment.
  - Provide an estimate of future inflation (a leading indicator) to inform policy given monetary transmission lags.

### V. Alternative methods examined
- Cross-sectional/exclusion-based methods, limited influence estimators (trimmed means), reweighing methods, and time series/econometric decomposition methods.

A. Exclusion-based methods
- CBSL official core inflation excludes all food and energy prices with a cumulative weight of 54.6 percent in the CPI.
- Advantages: simplicity, stable component set over time.
- Disadvantages:
  - Assumes excluded components contain no information about underlying inflation.
  - Excluding all food may reduce credibility in developing countries where food dominates expenditure.
- Empirical comparison (January 2004–October 2008, 32 commodity groups):
  - Alternative exclusion-based measures (excluding most volatile 10, 20, 30, 40 percent items based on standard deviation of month-on-month changes) suggested core inflation between 17.3 percent and 18.9 percent at end-October 2008 compared to 18 percent in the authorities’ official measure.
  - Differences between official and alternative exclusion-based measures were significantly higher between late 2006 and September 2008, driven by the authorities’ exclusion of food (45.5 percent weight in CPI) while food inflation behaved as one of the less volatile components in this period.
  - The cumulative weight of excluded items in alternative measures varied from 4.8 percent (10 percent measure, excluding 3 most volatile items) to 22.32 percent (40 percent measure, excluding 12 most volatile items).
  - The authorities’ exclusion set: excludes food, electricity, gas, kerosene, firewood, petrol and other fuels (combined weight 54.6 percent).

B. Limited influence (trimmed-mean) estimators
- Trimmed means remove outlying portions of the cross-sectional distribution of component inflation rates; median trims 50 percent from each tail.
- Motivation: extremes likely contain less information about underlying price pressures.
- Advantages: timely, transparent, easy to replicate.
- Issues and empirical findings:
  - In cases where only a portion of firms raise prices in response to demand, trimmed mean can understate underlying inflation (tails may carry information).
  - Trimmed means often yield core inflation estimates systematically lower than CPI averages because distributions are typically right-skewed—Sri Lanka exhibits right skewness.
  - Asymmetric trimming is recommended when distribution is skewed: removing more of the left-hand tail can pull the mean upward.
  - Choosing trim percentages often follows Cecchetti (1997) by minimizing RMSE relative to a 37-month centered moving average of headline inflation, but this benchmark may not be universally appropriate.
- Sri Lanka results:
  - Asymmetric trim of 20 percent left tail and 5 percent right tail yielded the lowest RMSE (Figure 7).
  - Estimates for core inflation in October-2008 from trimmed measures ranged from 15.4 percent to [value truncated in source text].

### VI. Evaluation criteria and practical considerations
- No consensus exists on a single best measure of core inflation.
- Evaluation criteria discussed in literature include credibility (important if used as an inflation target), unbiasedness, and predictive ability.
- Many authors recommend using a suite of measures: if different measures give similar results, confidence in policy decisions increases.

### VII. Implications for monetary policy in Sri Lanka (summarized)
- Official exclusion-based measure’s usefulness as a leading indicator is questioned given official core inflation remained above headline inflation during late 2008–2009 episodes.
- Exclusion of food and fuel (54.6 percent weight) may omit informative price movements, especially when some food categories were among the least volatile.
- Trimmed-mean and volatility-based exclusion measures can provide alternative perspectives; asymmetric trims may perform better where the distribution of price changes is skewed.
- Policy makers should consider a suite of measures rather than relying on a single core inflation indicator.

*Italic: Source: _wp09167 - References (excerpt), IMF staff calculations and Central Bank of Sri Lanka data as provided in the source content.*

### 16.0 percent for symmetric trims and from 9 to 22.6 percent for asymmetric trims. The

### _wp09167 - 16.0 percent for symmetric trims and from 9 to 22.6 percent for asymmetric trims. The

### Trimmed mean inflation — empirical findings
- Trim proportions evaluated include 16.0 percent for symmetric trims and from 9 to 22.6 percent for asymmetric trims.
- The inflation rate was at 20.6 percent according to the trimmed mean measure with the least RMSE.
- Figure 6 (Trimmed Mean Inflation) presents:
  - Range of trimmed means
  - Headline inflation
  - Official core inflation
  - Time coverage shown in the figure: Jan-04 through Oct-08 (month labels include Jan-04, Apr-04, Jul-04, Oct-04, Jan-05, Apr-05, Jul-05, Oct-05, Jan-06, Apr-06, Jul-06, Oct-06, Jan-07, Apr-07, Jul-07, Oct-07, Jan-08, Apr-08, Jul-08, Oct-08)
- Sources cited for Figure 6: Central Bank of Sri Lanka.; and Fund staff estimates.

### RMSE analysis of alternative trimmed mean measures
- Figure 7 (Root Mean Squared Errors of Alternative Trimmed Mean Measures) reports RMSE as the evaluation metric.
- Axis labels indicated:
  - RMSE (vertical axis) with tick labels 0 through 8
  - Right tail trim (in percent) and Left tail trim (in percent) as horizontal axes with tick labels 0, 5, 10, 15, 20, 25
- Source for Figure 7: Authors' calculations.
- Note: A footnote states, "Our ability to use a finer grid to find the lowest RMSE was constrained by the low cross-sectional dimension of the Sri Lankan data."

### Reweighing the CPI — persistence-weighted core inflation methodology
- Core inflation reweighed by the signal each CPI component provides about underlying inflation.
- Methodological lineage:
  - Blinder (1997): identified core inflation with the durable or persistent component of inflation and suggested more weight be given to components with information about future inflation.
  - Cutler (2001): operationalized the approach by estimating an autoregressive model for each CPI component.
- The study uses an AR(1) model for month-on-month inflation:
  - Model equation (1): t i t i i i π = α + ρ π_{t-1} + ε_t  (presented in the source as an AR(1) specification)
  - t_i π denotes month-on-month inflation at time period t for commodity group i.
  - Estimate of ρ_i is the indicator of persistence for commodity group i.
  - Product groups with negative autocorrelation are assigned a weight of zero in the calculation of core inflation.
- Persistence-weighted index as given in equation (2):
  - The formula sums weights for components with positive estimated ρ (notation in source: ρ̂_i > 0 and summation shown as a ratio of weighted sums).

### Refinements and practical considerations
- Possible refinements:
  - Include further lags in equation (1).
  - Use different weights every year estimated recursively.
- Limitations and critiques:
  - Mankikar and Paisley (2004): methodology is subject to the Lucas critique—autoregressive coefficients will in part depend on past policy; if policymakers factor these weights into decisions, the weights would change and the core measure could become misleading.
  - Silver (2007): persistence-weighted core inflation could suffer from lack of transparency and thus credibility because it is relatively complex.

### Empirical implementation note
- Figure 8 plots a persistence-weighted measure of core inflation using weights estimated from the AR(1) model for month-on-month inflation for the period February 2003 to October (figure caption in source truncated at "October").

*Source: Excerpt from the supplied IMF PDF content unit.*

### 2008. This measure suggests that

### _wp09167 - 2008. This measure suggests that

### D. Model-based Methods
- Model-based measures of core inflation:
  - Are grounded in economic theory and provide economic interpretation of core inflation and deviations between headline and core inflation.
  - Are multivariate and use information from other variables to derive core inflation.
  - Suffer from lack of consensus on theoretical properties of core inflation:
    - Eckstein (1981): core inflation ≡ “...the trend increase of the cost of the factors of production.” Implication: core inflation should not be cyclical.
    - Quah and Vahey (1995): core inflation ≡ “...that component of measured inflation that has no medium to long-term impact on real output.” Implication: vertical long-run Phillips curve (output-neutral in the long run).
  - Are criticized because:
    - Historical data on core inflation must be revised each time new data arrives.
    - Estimates are typically hard to understand and hard to replicate, potentially lacking credibility with the public.

- Quah and Vahey framework used in the paper:
  - Variables: (log) economic activity (Y) and measured inflation (π), with Δ(π, X)' = η.
  - Disturbances η1 and η2 assumed pairwise orthogonal with Var(η) = I().
  - Long-run neutrality condition: upper left hand entries of sequence of matrices A sum to zero: Σk a1k = 0.
  - Measured inflation decomposition (equation (4)) and core inflation defined as process Σk a1k η1,t−k (movement associated with η1 which is output neutral in the long run).
  - Implementation: estimate a VAR, invert to Wold moving average, recover η1 under restrictions that make A(0) unique (three restrictions from (0)A(0)'A = Ω where Ω is variance-covariance of Wold innovations; fourth restriction is long-run output neutrality).

- Empirical result reported:
  - Quah and Vahey measure for Sri Lanka: core inflation reached 23.7 percent in September 2008 while headline inflation was 24.3 percent.
  - Another model-based note: a separate measure suggests core inflation was 33.6 percent in October 2008 (statement at top of source).

### IV. Conditions to Evaluate Measures of Core Inflation
- Practical criteria (Roger, 1998) for a core inflation measure:
  - (i) timely; (ii) credible (verifiable by independent observers); (iii) easily understood by the public; (iv) not significantly biased with respect to the targeted measure (headline inflation).
  - Additional proposed criteria: (i) computable in real time; (ii) forward looking; (iii) some theoretical basis; (iv) not subject to revisions.
- Trade-offs:
  - Exclusion-based and limited-influence estimators: good for public assessment (timeliness, credibility, simplicity, unbiasedness, not revised).
  - Model-based and CPI reweighting methods: better for guiding monetary policy (forward-looking, theoretical basis).
- No single measure satisfies all criteria; choice should be data-driven and purpose-specific (Silver, 2007; Ginting, 2007).

### A. Marques et al. (2004) Tests (as applied)
- Desired characteristic: headline inflation converges to core inflation in the long run but not vice versa.
  - Condition (i): headline and core inflation are cointegrated with unit coefficient → difference u_t = π_t − π*_t stationary with mean zero.
  - Testing approach:
    - Stage 1: test stationarity of u_t using ADF and KPSS (include constant). ADF null: unit root; KPSS null: stationarity.
    - Stage 2: test mean of zero by t-test on constant term.
  - Condition (ii): core inflation is an attractor of headline inflation (core Granger-causes headline via error-correction term). Test by estimating error-correction model for Δπ_t and testing γ = 0 in equation (5).
  - Condition (iii): headline inflation is not an attractor for core inflation (core is exogenous). Test weak exogeneity (λ = 0) and strong exogeneity (θ1 = ... = θs = 0 given λ = 0) in equation (6).

### V. Results (summary of empirical findings and test outcomes)
- Unit-root / cointegration tests (ADF and KPSS) on u_t = π_t − π*_t:
  - ADF has low power; except for Trimmed Mean 25L10R, ADF generally fails to reject no cointegration at 5 percent.
  - KPSS (null = stationarity) suggests cointegration with headline inflation for:
    - Quah-Vahey measure
    - Trimmed Mean 25L10R
    - Persistence Weighted measure
    - Both alternative exclusion-based measures (Exclusion 3 and Exclusion 6)
  - KPSS indicates that Official core, Trimmed Mean 15L5R, Trimmed Mean 20L5R, and Trimmed Mean 25L5R are not cointegrated with headline inflation.
  - Trimmed Mean 25L10R is strongly suggested cointegrated with headline inflation.

- Unbiasedness (mean zero test on u_t):
  - ADF t-test: low power; cannot reject null of constant ≠ 0 for any measure.
  - KPSS t-test: rejects null of non-zero mean in every case except:
    - Trimmed Mean 15L5R
    - Exclusion 3
  - Conclusion: only Trimmed Mean 15L5R and Exclusion 3 can be considered unbiased estimators according to these tests.

- Condition (ii): core inflation as attractor of headline inflation (test on γ in equation (5)):
  - Measures for which γ = 0 is rejected (i.e., core is attractor of headline):
    - Official measure of core inflation
    - Trimmed Mean 25L10R
    - Exclusion 3
    - Exclusion 6
  - Interpretation: these measures are attractors of headline inflation and satisfy condition (ii).

- Condition (iii): weak and strong exogeneity tests (equation (6)):
  - Weak exogeneity (λ = 0) satisfied for all measures except:
    - Trimmed Mean 25L10R
    - Exclusion 6
  - Strong exogeneity (θ1 = ... = θs = 0 given λ = 0) — among weakly exogenous measures, the null of strong exogeneity rejected only for:
    - Persistence Weighted measure (i.e., Persistence Weighted is not strongly exogenous)

- Overall interpretive summary:
  - Official measure and Exclusion 3: leading indicators of headline inflation (core → headline), but headline not an attractor for these core measures (i.e., core is exogenous for headline).
  - Quah-Vahey, Trimmed Mean 15L5R, Trimmed Mean 20L5R, Trimmed Mean 25L5R, Persistence Weighted: no error-correction representation for either headline or core inflation (not cointegrated with headline).
  - Trimmed Mean 15L5R, 20L5R, 25L5R findings are consistent across ADF and KPSS.
  - Appropriate measure of core inflation depends on intended purpose.

- Caveats highlighted:
  - If authorities successfully target headline inflation, Marques et al.’s tests may indicate failure of conditions (ii) and (iii) even though core measures can still be informative (Mankikar and Paisley, 2004).
  - Tests are subject to the Lucas critique: relationships may break down if policy responds to estimated relationships.

- Selected test statistics and reported values from Table 1 (preserve exact figures shown in source):
  - Official Core: t = -1.79; LM = 0.67; P = 0.19; P = 0.00; P = 0.01; P = 0.65; P = 0.12
  - Quah Vahey: t = -0.97; LM = 0.33; P = 0.33; P = 0.00; P = 0.23; P = 0.65; P = 0.21
  - Trimmed Mean 15L5R: t = -1.94; LM = 0.78; P = 0.32; P = 0.18; P = 0.37; P = 0.92; P = 0.07
  - Trimmed Mean 20L5R: t = -2.11; LM = 0.66; P = 0.61; P = 0.00; P = 0.56; P = 0.67; P = 0.06
  - Trimmed Mean 25L5R: t = -2.21; LM = 0.47; P = 0.13; P = 0.00; P = 0.78; P = 0.47; P = 0.06
  - Trimmed Mean 25L10R: t = -2.91; LM = 0.17; P = 0.35; P = 0.01; P = 0.05; P = 0.00
  - Persistence Weighted: t = -0.66; LM = 0.39; P = 0.21; P = 0.00; P = 0.68; P = 0.42; P = 0.02
  - Exclusion 3: t = -0.90; LM = 0.15; P = 0.46; P = 0.10; P = 0.05; P = 0.13; P = 0.41
  - Exclusion 6: t = -1.29; LM = 0.15; P = 0.29; P = 0.00; P = 0.00; P = 0.02

  - Note on critical values (as reported): ADF critical values (model with non-zero constant): -3.55 (1 percent), -2.91 (5 percent), -2.59 (10 percent). KPSS critical values: 0.74 (1 percent), 0.46 (5 percent), 0.35 (10 percent). ***, **, * denote significance at the one, five, and ten percent levels, respectively.

### VI. Concluding Remarks
- Context and motivation:
  - Debate in 2008 over usefulness of Sri Lanka’s official core inflation measure for predicting future headline inflation because:
    - (i) official core indicated underlying inflation was significantly lower than headline inflation;
    - (ii) central bank used it in communications to validate monetary policy stance;
    - (iii) it had been increasing rapidly as higher food and fuel prices were passed through to other CPI components.
- Purpose of paper: systematic analysis of official measure and comparison to other measures of underlying inflation.
- Empirical note reported in text:
  - At end October 2008, alternative measures analyzed in the paper reveal a wide range for the estimate of underlying inflation in Sri Lanka. (Source text ends: "the estimates ranged from" — no further numeric range provided in the supplied content.)

*Source: Fund staff estimates (excerpts from _wp09167 - 2008).*

### 9.0 to 33.6 percent compared to official core inflation of 18.6 percent and headline inflation

### _wp09167 - 9.0 to 33.6 percent compared to official core inflation of 18.6 percent and headline inflation of 20.2 percent

### Findings on measures of underlying (core) inflation
- Estimates of underlying inflation ranged from 9.0 to 33.6 percent compared to official core inflation of 18.6 percent and headline inflation of 20.2 percent.
- The majority of estimates—notably all the non-official measures of core inflation during January-June 2008 and an average of more than 60 percent of the measures during July-October 2008—suggest that underlying inflation in 2008 was above the official measure of core inflation.
- An average of 20 percent of the estimates (more during the first half of 2008) suggest that underlying inflation was above headline inflation at the time.
- The majority of the non-official measures of underlying inflation suggest that the official measure of core inflation might have understated inflationary pressures.

### Statistical evaluation and methodological insights
- The wide range of estimates is consistent with the consensus that the appropriate measure of core inflation depends on its ultimate purpose.
- A data driven approach to deciding among various measures of underlying inflation is appropriate because different methods perform differently across countries and over time.
- This paper evaluated a cross-section of alternative measures of underlying inflation against conditions proposed by Marques et al. (2003) to determine whether a core inflation measure is: (i) unbiased; (ii) a leading indicator of headline inflation; and (iii) whether headline inflation is not a leading indicator of core inflation.
- The Quah-Vahey estimate of core inflation is available up to September.

### Specific statistical results reported
- The official measure of core inflation and the exclusion measure are leading indicators of headline inflation (but not vice versa) and therefore provide a useful indication of the future path of headline inflation.
- Several measures, including the official measure of core inflation and some trimmed mean measures, were neither cointegrated with headline inflation nor unbiased.
- Overall, the official measure of core inflation in Sri Lanka does contain some useful information about the future path of headline inflation.
- The official measure of core inflation appears biased with respect to headline inflation, suggesting inadequacy as a communication tool in its current form.

### Policy implications and recommendations
- Ongoing work at the Central Bank to develop new measures of core inflation is appropriate and should be high on the agenda.
- A suite of core inflation measures that can be continuously updated and statistically evaluated would be helpful.
- Using multiple measures can provide confidence when they give similar results and insights into the inflationary process when they differ (consistent with Silver (2007): “If the resulting measures give similar results, then they should give some confidence to the monetary authorities in making decisions based on such measures. If they do not, differences in the nature of the measures used should, by construction, allow for insights into the inflationary process”).

### Additional insights on measurement uncertainty
- The range among different measures—including measures that statistical tests suggest are leading indicators of headline inflation—has at times been large, particularly during the run-up in fuel and food prices.
- The gap between the official core measure and alternative measures reflected differences in assumptions about the persistence of the run-up in commodity prices and the extent to which these would feed through into the rest of the CPI basket.
- The appropriate measurement of underlying inflation is unlikely to remain constant over time.

*Source: Excerpt from IMF Working Paper content unit _wp09167 - 9.0 to 33.6 percent compared to official core inflation of 18.6 percent and headline inflation of 20.2 percent*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09167.pdf_