## _wp1619

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---

### I. Introduction — research questions and aims
- Core policy question: "Was [SBV's] response warranted, or warranted to the extent that it was undertaken?" in response to high inflation episodes in 2008 and 2011.
- Motivations:
  - "A substantive part of the headline inflation in both episodes was associated with global rice and oil price movements."
  - Headline inflation rose and fell quickly over 6-8 months, suggesting "these changes may have been more in the nature of temporary, external supply shocks than persistent, domestic demand shocks."
  - Policy-rate increases "lagged headline inflation and generated large swings in the real interest rate," raising funding costs and impacting balance sheets.
- Primary objective: "construct and evaluate alternative measures of core inflation."
- Organization:
  - Section II: overview of inflation process in Vietnam.
  - Section III: literature survey, definitions and construction of core inflation measures (CIM).
  - Section IV: construct and evaluate CIMs for Vietnam.
  - Section V: concluding remarks and recommendations, including identification of CIMs for SBV internal use and for external communications and the role of CIMs in a potential shift to an inflation targeting regime.

### II. Inflation process in Vietnam — historical episodes and statistical properties
- Historical magnitudes and episodes:
  - Hyperinflation peaked at "775 percent at end-1986."
  - With doi moi in 1986, inflation fell to single digits for the first time in 1993.
  - Inflation stayed in the single digits for over a decade during "1996-2007."
  - Headline inflation "peaking at 28½ percent y/y in August 2008," then fell to single-digit levels six months later as global rice and oil prices fell.
  - Headline inflation "edged up to 23 percent y/y in August 2011" and then "declined to single digits in a space of about eight months."
  - Inflation "has since then stayed in the single digits and has been stable around 5 percent for most of 2013 and 2014."
- Sample summaries and implications (2000-14):
  - "12-month inflation was over 7½ percent"
  - "with a range of over 30 percent"
  - "standard deviation of 6¾ percent"
  - Headline inflation in Vietnam was higher and more variable than comparator groups (Asian NIEs, ASEAN-4, wider emerging/developing countries).
- Subsample behavior:
  - Subsamples used for analysis: "1999-2007 and 2008-14" in addition to full sample.
- Seasonal pattern linked to Tet:
  - January/February inflation high (averaging "1-2 percent")
  - About "½ percent" until November
  - December inflationary rise in run-up to Tet
- Food inflation: "very highly correlated with global rice prices."
- Distributional properties of component inflation: "positively skewed and leptokurtic"; "absence of normality in the component series" affects CIM construction and evaluation.

### III. Core inflation — concepts, construction methods, and prior Vietnam evidence
- Conceptual definitions cited (examples):
  - Okun (1970): core inflation as "... a condition of generally rising prices"
  - Flemming (1976): "... the rate at which the general level of prices in [the] economy is changing"
  - Eckstein (1981): "... the trend increase of the cost of the factors of production"
  - Quah and Vahey (1995): core inflation as "... component of measured inflation that has no medium- to long-term impact on real output"
  - Roger (1998): divides definitions into "persistent" and "generalized" views
- Measurement approaches: "exclusion-based methods, imputation methods, limited influence estimators, reweighting, and economic modeling."
- Exclusion-based measures (EBMs):
  - Common exclusions: food and energy, administered prices, indirect taxes, interest (mortgage) payments.
  - Operationalization: "weights of excluded items are reduced to zero, and the weights of the remaining included items are increased proportionately (to sum up to 1)."
  - Caution: exclusion may remove signal as well as noise, especially where "food often account[s] for a large portion of CPI basket."
- Limited influence measures (LIMs) / Trimmed means and weighted median:
  - Trimmed (symmetric) means omit predetermined upper and lower tails (e.g., "CPI1010 would exclude 10 percent of the weight at the top and bottom").
  - Weighted median is the middle price change value by expenditure share.
  - Advantages: "robustness to price shocks" and capture inflationary trends relative to noise.
  - Challenges: non-normality suggests "asymmetrically trimmed means"; LIMs are "harder to communicate," sensitive to aggregation and sample length; transitory vs. persistent shocks may still be mixed.
- Prior Vietnam evidence:
  - IMF technical-assistance reports suggested EBMs (especially CPIxF and CPIxFEA) could "potentially serve as CIMs" but did not conduct formal tests; recommended TMMs theoretically.
  - Lai (2013) found "the output-neutral inflation satisfies almost all of the evaluation criteria," and recommended trimmed-mean or weighted median "for communication purposes."
  - This paper uses a longer sample and adopts different evaluation criteria, notably the "‘attractor’ conditions proposed by Marques et. al."

### IV. Data, construction of CIMs, and analysis design
- CPI data and splicing:
  - Monthly CPI data from General Statistics Office (GSO).
  - Splice four segments into a single series for January 1998-December 2014:
    1. Period 1: "January 1998-June 2001, base year 1995, with 300 components;"
    2. Period 2: "July 2001-April 2006, base year 2000, including 390 items;"
    3. Period 3: "May 2006- October 2009, base year 2005, including 496 components;"
    4. Period 4: "November 2009-December 2014, with 572 items."
  - "The 87th component (sewing machine) appears only in Period 1 with negligible weight and was dropped."
- Construction steps for 12-month CIMs:
  - Rebasing and splicing of component indices.
  - EBMs: "Setting zero weight for excluded items", "Reweighting", "Normalizing the weight", "Calculating CPIx", "Calculating inflation".
  - TMMs/LIMs: "Calculating sub-inflations", "Sorting category inflation" with "time-varying weights", "Ranking", "Set zero weight for trimmed percentile", "Trimming", "Calculating core inflation".
  - Full sample period for constructed CIMs given as "January 1999-December".
- Evaluation samples:
  - Full sample: "1999-2014"
  - Subsamples: "1999-2007" and "2008-14"
- Tables and figures used for analysis include comparative and evaluation tables for EBMs and TMMs, Cogley test statistics, and charts of headline vs. CIMs.

### Definitions and excluded weights (EBMs — Table 3)
- CPIxA: excludes 4 items of administered prices: water, electricity, public transport services. Excluded weights — 2.1 3.2 5.0 3.7
- CPIxAHE: excludes 4 items of administered prices, health care services and education services. Excluded weights — 3.9 6.2 11.6 12.4
- CPIxE: excludes electricity, gas, and fuel. Excluded weights — 6.7 5.4 8.5 8.3
- CPIxF: excludes 8 items of raw food: rice, wheat cereal, fresh meat, eggs, fresh seafood, vegetables, and fruits. Excluded weights — 43.5 29.6 26.5 24.1
- CPIxFA: excludes 8 items of raw food and 4 items of administered prices. Excluded weights — 45.5 32.8 31.5 27.7
- CPIxFE: excludes 8 items of raw food, electricity, gas, and fuel. Excluded weights — 50.1 35.0 35.0 32.3
- CPIxFEA: excludes 8 items of raw food, 3 items of energy, and 4 items of administered prices. Excluded weights — 50.7 36.1 36.6 33.5
- CPIxFEAHE: excludes 8 items of raw food, 3 items of energy, 4 items of administered prices, health care services, and education services. Excluded weights — 52.5 39.1 43.1 42.2
- Source for table values: GSO; and authors’ calculations.

### Evaluation framework for CIMs
- Three-step evaluation process:
  - Step 1: CIM must satisfy Marques et. al. (2003) “attractor” necessary conditions (Conditions 1–3).
  - Step 2: Compare CIMs satisfying attractor conditions on deviations from a reference series using RMSD or MAD; compare variability using standard deviation (SD) and coefficient of variation (CV) relative to headline inflation; reference series typically MA12(CPI).
  - Step 3: Examine CIMs’ ability to forecast headline inflation at different horizons using Cogley (2002) tests (regression (5): core deviation at time t predicting subsequent inflation changes).
- Marques et. al. conditions (summary):
  - Condition 1a: Headline inflation and CIM cointegrated with unit coefficient.
  - Condition 1b: Test beta=1 (with alpha=0) in cointegration relation.
  - Condition 2: CIM is an attractor of headline inflation — error correction representation; null gamma=0 not accepted.
  - Condition 3: Headline inflation should not be an attractor of CIM; Condition 3a weak exogeneity requires lambda=0; Condition 3b strong exogeneity requires thetas=0 given lambda=0.
- Cogley (2002) test:
  - Regression (5): (π_t* − π_t) related to future inflation change (π_{t+H} − π_t); null hypothesis α_H = 0 and β_H = −1 (mean-zero transients and one-for-one correction over horizon H). R^2 used for goodness-of-fit.

### V. Empirical tests and results — EBMs (full sample 1999-2014)
- Main findings:
  - "None of the EBMs satisfies all Marques et. al. “attractor” conditions."
  - Strong exogeneity problematic for many EBMs (dynamics of EBMs affected by headline inflation).
  - Two EBMs biased: CPIxA and CPIxAHE.
  - Two EBMs not attractors despite satisfying strong exogeneity: CPIxE and CPIxAHE.
  - Not all EBMs are less variable or smoother than headline inflation.
  - CPIxF and CPIxFE are less variable but also less smooth (relative to MA12(CPI)) than headline inflation.
- Selected statistics (1999-2014, Table 4):
  - Headline CPI: mean: 7.4; median: 6.8; standard deviation: 6.5; skewness: 1.2; kurtosis: 4.5.
  - CPIxF: mean: 6.7; standard deviation: 4.7; RMSD: 2.3; MAD: 1.9.
  - CPIxFE: mean: 6.4; standard deviation: 4.5; RMSD: 2.6; MAD: 2.1.
  - Significance notation: *** 1 percent; ** 5 percent; * 10 percent.

### V. Empirical tests and results — Trimmed Mean Measures (TMMs)
- Data and construction:
  - Monthly CPI disaggregated into 86 components at the 2-digit level.
  - Symmetric and asymmetric trims constructed with left and right trims between 15 percent and 30 percent at 1 percent intervals — around 225 TMMs constructed and evaluated.
  - Procedure repeated for subsamples: "1999-2007" and "2008-14".
- Full-sample (1999-2014) results:
  - Strong exogeneity difficult to satisfy for many TMMs.
  - Attractor condition (Condition 2) requires trims on both tails and larger trims on the right tail (reflecting skewness).
  - Wide range of trim combinations satisfy Conditions 1 and 2; almost all lie in the northeastern quadrant in Figure 3.
  - Only two TMMs satisfy all Marques conditions for full sample: TMM2226 and TMM2227.
  - Smoothness/variability: Several TMMs are smoother and less variable than headline inflation, but the two fully admissible TMMs (TMM2226 and TMM2227) are both less smooth and more variable than headline inflation.

### Subsample analysis (1999-2007 and 2008-2014)
- Subsample statistics:
  - 1999-2007: mean inflation "4½ percent" and SD "3.9 percent".
  - 2008-2014: mean inflation "11 percent" and SD "7.3 percent".
  - Component inflation skewness: full sample "1.13"; first subsample "0.92"; latter subsample "1.39".
- EBMs over subsamples:
  - EBMs fare poorly on Marques conditions in both subsamples.
  - First subsample: several EBMs biased or not strongly exogenous; none satisfies attractor property.
  - Latter subsample: two EBMs — CPIxFE and CPIxFEA — satisfy all conditions except unbiasedness (both with a downward bias); given low power of ADF test, these EBMs could be considered useful during high inflation periods.
- TMMs over subsamples:
  - 1999-2007 (low inflation): smaller trims required and larger trims on left tail; two trims satisfy Marques conditions: TMM1407 and TMM1408.
  - 2008-2014 (high inflation): several trims satisfy Marques conditions; larger trims needed due to higher skewness and larger outliers.
  - Conclusion: “one trim does not fit all times”.

### Cogley tests and reversion horizons
- Tests assess predictive power of current core deviation for changes in headline inflation at horizons H = 1–12 months.
- Table 7: Wald F-statistics for null α=0 and β=−1 (Horizons 1–12 months)
  - For 1999-2014, TMM2226: H1:0.00; H2:0.00; H3:0.07; H4:0.31; H5:0.54; H6:0.54; H7:0.37; H8:0.20; H9:0.11; H10:0.06; H11:0.04; H12:0.03
  - For 1999-2007, TMM147: H1:0.00; H2:0.39; H3:0.17; H4:0.10; H5:0.04; H6:0.00; H7:0.00; H8:0.00; H9:0.00; H10:0.00; H11:0.00; H12:0.01
  - For 2008-14, TMM2119: H1:0.00; H2:0.05; H3:0.28; H4:0.52; H5:0.72; H6:0.80; H7:0.74; H8:0.58; H9:0.41; H10:0.27; H11:0.19; H12:0.16
- Interpretation: Cogley tests provide information on horizons over which headline inflation reverts to CIMs but are valid only if null α=0 and β=−1 is not rejected.

### Policy rate and implications of CIM choice
- Main conclusions relevant for policy:
  - EBMs generally do not satisfy desired statistical conditions for admissible CIMs; TMMs perform better.
  - Admissible TMMs depend on the sample period (inflation regime and component properties). High, variable inflation requires larger trims.
  - Headline inflation traces admissible TMMs more closely than commonly used EBM (CPIxFE) across samples.
  - Under/overprediction of underlying inflation pressures by EBMs (relative to TMMs) during 2008-14 ranged between "−8 and 6 percent."
  - Speed of rise and fall in underlying inflation differs between EBMs and TMMs:
    - EBMs suggest slower increases and declines in core inflation than TMMs.
    - Using TMM2226, policy rates would have needed to be raised earlier and cut faster than suggested by EBM guidance — notably in 2012 and 2013 where EBM continued to suggest double-digit core inflation while TMM2226 indicated single-digit core inflation.
  - Implication: Relying on EBMs for policy action may lead to delayed responses in tightening or loosening; TMMs can offer timelier guidance but require ongoing recalibration to the inflation regime.

### Concluding remarks and policy recommendations
- Empirical findings:
  - "Commonly used exclusion-based measures (EBMs) do not perform well against statistical criteria for admissible CIMs; trimmed mean measures (TMMs) perform better."
  - "One trim does not fit all periods."
- Policy recommendations:
  - Policymakers should test and update CIMs on an ongoing basis to form a firmer basis for policy actions.
  - TMMs, with sample-specific trims, provide closer tracking of headline inflation and more timely signals for policy rate adjustments than EBMs.
  - EBMs may still be useful for communication purposes given simplicity, but should not be sole guides for monetary policy decisions.
  - Use of replicable EVIEWS and MATLAB programs (accompanying the paper) allows quick replication of CIMs as new data become available.
- Broader implication:
  - Although results are specific to Vietnam’s experience (heavy weighting of food and fuel in CPI and exposure to external shocks), findings may carry over to other countries with similar structures.

*Source: _wp1619 - References*

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

### _wp1619 - References

### I. Introduction — Research questions and aims
- Core policy question: "Was [SBV's] response warranted, or warranted to the extent that it was undertaken?" in response to high inflation episodes in 2008 and 2011.
- Key motivations for the question:
  - "A substantive part of the headline inflation in both episodes was associated with global rice and oil price movements."
  - Headline inflation rose and fell quickly over 6-8 months, suggesting "these changes may have been more in the nature of temporary, external supply shocks than persistent, domestic demand shocks."
  - Policy-rate increases "lagged headline inflation and generated large swings in the real interest rate," raising funding costs and impacting balance sheets.
- Primary objective of the paper: "construct and evaluate alternative measures of core inflation."
- Organization highlights:
  - Section II: overview of inflation process in Vietnam.
  - Section III: literature survey, definitions and construction of core inflation measures (CIM).
  - Section IV: construct and evaluate CIMs for Vietnam.
  - Section V: concluding remarks and recommendations, including identification of CIMs for SBV internal use and for external communications and the role of CIMs in a potential shift to an inflation targeting regime.

### II. Inflation process in Vietnam — historical episodes and statistical properties
Findings and historical magnitudes:
- After the failure of the 1985 reform package, hyperinflation peaked at "775 percent at end-1986."
- With doi moi in 1986 and subsequent measures, inflation fell to single digits for the first time in 1993.
- Inflation stayed in the single digits for over a decade during "1996-2007."
- Under pressures, inflation rose rapidly in 2007, "peaking at 28½ percent y/y in August 2008," then fell to single-digit levels six months later as global rice and oil prices fell.
- A similar episode in 2011: headline inflation "edged up to 23 percent y/y in August 2011" and then "declined to single digits in a space of about eight months."
- Inflation "has since then stayed in the single digits and has been stable around 5 percent for most of 2013 and 2014."

Statistical properties (sample summaries and implications):
- Over 2000-14:
  - "12-month inflation was over 7½ percent"
  - "with a range of over 30 percent"
  - "standard deviation of 6¾ percent"
- Implication: headline inflation in Vietnam was higher and more variable than several comparator countries (Asian NIEs, ASEAN-4, and a wider set of emerging and developing countries).
- Subsample behavior matters: inflation was "high and more variable in the pre-1996 and post-2008 subsample," motivating analysis for the full sample and two subsamples: "1999-2007 and 2008-14."
- Seasonal pattern linked to Tet:
  - January/February inflation high (averaging "1-2 percent")
  - About "½ percent" until November
  - December inflationary rise in run-up to Tet
- Food inflation in Vietnam "is very highly correlated with global rice prices."
- Distributional properties of component inflation: "positively skewed and leptokurtic" and "absence of normality in the component series" affects CIM construction and evaluation.

### III. Core inflation — concepts, construction methods, and prior Vietnam evidence
Definitions and conceptual views:
- Literature provides multiple definitions; examples cited:
  - Okun (1970): core inflation as "... a condition of generally rising prices"
  - Flemming (1976): "... the rate at which the general level of prices in [the] economy is changing"
  - Eckstein (1981): "... the trend increase of the cost of the factors of production"
  - Quah and Vahey (1995): core inflation as "... component of measured inflation that has no medium- to long-term impact on real output"
  - Roger (1998): divides definitions into "persistent" and "generalized" views
- Measurement approaches: "exclusion-based methods, imputation methods, limited influence estimators, reweighting, and economic modeling."

Exclusion-based measures (EBMs):
- Common practice: exclude components like food and energy, administered prices, indirect taxes, interest (mortgage) payments.
- Operationalization: "weights of excluded items are reduced to zero, and the weights of the remaining included items are increased proportionately (to sum up to 1)."
- Caution: exclusion may remove signal as well as noise, particularly where "food often account[s] for a large portion of CPI basket."

Limited influence measures (LIMs) / Trimmed means and weighted median:
- Trimmed (symmetric) means omit predetermined upper and lower tails (e.g., "CPI1010 would exclude 10 percent of the weight at the top and bottom").
- Weighted median is the middle price change value by expenditure share.
- Advantages: "robustness to price shocks" and capture inflationary trends relative to noise.
- Challenges: distributional non-normality (right-skew, leptokurtosis) suggests need for "asymmetrically trimmed means"; LIMs are "harder to communicate," sensitive to aggregation and sample length; transitory vs. persistent shocks may still be mixed.

Empirical literature for Vietnam:
- IMF technical-assistance reports suggested EBMs (especially CPIxF and CPIxFEA) could "potentially serve as CIMs" but did not conduct formal tests; recommended TMMs theoretically.
- Lai (2013) evaluated five CIMs: excluding food price, trimmed-mean, weighted median, exponentially smoothed, and output-neutral inflation; found "the output-neutral inflation satisfies almost all of the evaluation criteria," and recommended trimmed-mean or weighted median "for communication purposes."
- This paper uses a longer sample than Lai and adopts different evaluation criteria, notably the "‘attractor’ conditions proposed by Marques et. al."

### IV. Data, construction of CIMs, and analysis design
Data splicing and CPI component coverage:
- Monthly CPI data from General Statistics Office (GSO).
- Splice four segments into a single series for January 1998-December 2014:
  1. Period 1: "January 1998-June 2001, base year 1995, with 300 components;"
  2. Period 2: "July 2001-April 2006, base year 2000, including 390 items;"
  3. Period 3: "May 2006- October 2009, base year 2005, including 496 components;"
  4. Period 4: "November 2009-December 2014, with 572 items."
- Note: "The 87th component (sewing machine) appears only in Period 1 with negligible weight and was dropped."

Construction steps for 12-month CIMs (procedure summarized):
- Rebasing and splicing of component indices.
- For EBMs:
  - "Setting zero weight for excluded items"
  - "Reweighting" and "Normalizing the weight"
  - "Calculating CPIx" and "Calculating inflation"
- For TMMs/LIMs:
  - "Calculating sub-inflations"
  - "Sorting category inflation" with "time-varying weights"
  - "Ranking" and "Set zero weight for trimmed percentile"
  - "Trimming" then "Calculating core inflation"
- Full sample period for constructed CIMs: "January 1999-December" (text truncated in source; analysis uses "full sample period is January 1999-December" as given).

Evaluation samples and figures/tables used:
- CIMs constructed and evaluated for:
  - Full sample "1999-2014"
  - Subsamples "1999-2007" and "2008-14"
- Figures and tables in the source that structure analysis include:
  - Table 1. Headline Inflation: Cross-Country Comparison
  - Table 2. Cross-Country Practices: Exclusion-based CIMs
  - Table 3. Exclusion-based CIMs: Definitions and Excluded Weights
  - Tables 4–6. Evaluation of Exclusion-based CIMs (12-month)—samples 1999-2014, 1999-2007, 2008-2014
  - Table 7. Cogley Test Wald F-statistics
  - Figures on construction, evaluation, trimmed-mean metrics, smoothness and volatility, Cogley tests, and headline vs. CIMs.

### V. Findings, implications, and policy recommendations (as stated)
Findings and implications emphasized in the source:
- High-frequency external shocks (global rice and oil prices) were important contributors to headline inflation spikes in 2008 and 2011.
- Rapid reversals in headline inflation suggest a large temporary component to those spikes.
- Policy responses that increase policy rates with lags can generate "large swings in the real interest rate" with potentially adverse effects on enterprise funding costs and financial-sector balance sheets.
- The non-normal distribution of CPI component price changes (skewness and leptokurtosis) affects choice and construction of CIMs, pushing toward LIMs with asymmetry or careful exclusion choices.

Policy recommendations and suggested uses of CIMs:
- Identify CIMs that SBV could use:
  - For internal analytical and policy-making purposes: CIMs that best track underlying/persistent inflation (paper constructs and evaluates alternatives to identify these).
  - For external communications: CIMs that are more transparent and easier to communicate (e.g., trimmed-mean or weighted median as suggested in prior literature).
- Longer-term recommendation: "Over the longer term, reliable CIMs could form the basic foundation of a shift to an inflation targeting regime in Vietnam."

Analytical approach to policy guidance:
- Evaluate alternative CIMs against Marrques et. al. "attractor" conditions, smoothness/volatility criteria, predictive and tracking properties, and cointegration with headline inflation (evaluation details and test statistics presented in Tables and Figures listed in the source).

*Source: _wp1619 - References (IMF working paper content as supplied).*

### 2014. Table 3 provides definitions and excluded weights for eight EBMs analyzed in this

### _wp1619 - 2014. Table 3 provides definitions and excluded weights for eight EBMs analyzed in this

### Definitions and excluded weights (Table 3)
- CPIxA: excludes 4 items of administered prices: water, electricity, public transport services. Excluded weights (1998M1:2001M6:2001M7:2006M4:2006M5:2009M10:2009M11:2014M12) — 2.1 3.2 5.0 3.7
- CPIxAHE: excludes 4 items of administered prices, health care services and education services. Excluded weights — 3.9 6.2 11.6 12.4
- CPIxE: excludes electricity, gas, and fuel. Excluded weights — 6.7 5.4 8.5 8.3
- CPIxF: excludes 8 items of raw food: rice, wheat cereal, fresh meat, eggs, fresh seafood, vegetables, and fruits. Excluded weights — 43.5 29.6 26.5 24.1
- CPIxFA: excludes 8 items of raw food and 4 items of administered prices. Excluded weights — 45.5 32.8 31.5 27.7
- CPIxFE: excludes 8 items of raw food, electricity, gas, and fuel. Excluded weights — 50.1 35.0 35.0 32.3
- CPIxFEA: excludes 8 items of raw food, 3 items of energy, and 4 items of administered prices. Excluded weights — 50.7 36.1 36.6 33.5
- CPIxFEAHE: excludes 8 items of raw food, 3 items of energy, 4 items of administered prices, health care services, and education services. Excluded weights — 52.5 39.1 43.1 42.2
- Source for table values: GSO; and authors’ calculations.

### Evaluation framework for Core Inflation Measures (CIMs)
- Three-step evaluation process:
  - Step 1: CIM must satisfy Marques et. al. (2003) “attractor” necessary conditions (Conditions 1–3).
  - Step 2: Compare CIMs that satisfy attractor conditions on deviations from a reference series using RMSD or MAD; compare variability using standard deviation (SD) and coefficient of variation (CV) relative to headline inflation; reference series typically 12-month centered moving average of CPI inflation (MA12(CPI)).
  - Step 3: Examine CIMs’ ability to forecast headline inflation at different horizons using Cogley (2002) tests (regression (5): core deviation at time t predicting subsequent inflation changes).
- Marques et. al. conditions (summary):
  - Condition 1a: Headline inflation and CIM cointegrated with unit coefficient (treatment of t_u stationary with zero mean).
  - Condition 1b: Test beta=1 (with alpha=0) in cointegration relation.
  - Condition 2: CIM is an attractor of headline inflation — error correction representation; null gamma=0 not accepted.
  - Condition 3: Headline inflation should not be an attractor of CIM; Condition 3a weak exogeneity requires lambda=0; Condition 3b strong exogeneity requires thetas=0 given lambda=0 (and additional theta restrictions for strong exogeneity).
- Cogley (2002) test:
  - Regression (5): (π_t* − π_t) related to future inflation change (π_{t+H} − π_t); hypothesis α_H = 0 and β_H = −1 (null of mean-zero transients and one-for-one correction over horizon H). R^2 used to assess goodness-of-fit.

### Empirical tests — full sample (1999-2014)
- EBMs (Table 4) — main findings:
  - None of the EBMs satisfies all Marques et. al. “attractor” conditions.
  - Strong exogeneity is especially problematic for many EBMs (implying dynamics of EBMs are affected by headline inflation, possibly via adaptive expectations).
  - Two EBMs are biased: CPIxA and CPIxAHE.
  - Two EBMs are not attractors for CPI despite satisfying strong exogeneity: CPIxE and CPIxAHE.
  - Variability and smoothness:
    - Not all EBMs are less variable or smoother than headline inflation.
    - CPIxF and CPIxFE are less variable but also less smooth (relative to MA12(CPI)) than headline inflation.
- Selected statistics from Table 4 (1999-2014):
  - Headline CPI mean: 7.4; median: 6.8; standard deviation: 6.5; skewness: 1.2; kurtosis: 4.5.
  - CPIxF mean: 6.7; standard deviation: 4.7; RMSD: 2.3; MAD: 1.9.
  - CPIxFE mean: 6.4; standard deviation: 4.5; RMSD: 2.6; MAD: 2.1.
  - Significance notation: *** 1 percent; ** 5 percent; * 10 percent.

### Empirical tests — Trimmed Mean Measures (TMMs)
- Data and construction:
  - Monthly CPI disaggregated into 86 components at the 2-digit level (higher disaggregation than in previous studies).
  - Symmetric and asymmetric trims constructed with left and right trims ranging between 15 percent and 30 percent at 1 percent intervals — around 225 TMMs constructed and evaluated.
  - Procedure repeated for subsamples: 1999-2007 and 2008-14.
- Full-sample (1999-2014) results:
  - Strong exogeneity condition is difficult to satisfy for many TMMs.
  - Attractor condition (Condition 2) requires trims on both tails and larger trims on the right tail (reflecting skewness of component inflations).
  - Wide range of trim combinations satisfy Conditions 1 and 2; almost all lie in the northeastern quadrant in Figure 3.
  - Only two TMMs satisfy all Marques conditions for full sample: TMM2226 and TMM2227.
  - Smoothness/variability: Several TMMs are smoother and less variable than headline inflation, but the two fully admissible TMMs (TMM2226 and TMM2227) are both less smooth and more variable than headline inflation.

### Subsample analysis (1999-2007 and 2008-2014)
- Differences between subsamples:
  - 1999-2007: mean inflation and SD were 4½ percent and 3.9 percent, respectively.
  - 2008-2014: mean inflation and SD were 11 percent and 7.3 percent, respectively.
  - Component inflation skewness: full sample 1.13; first subsample 0.92; latter subsample 1.39.
- EBMs over subsamples:
  - EBMs fare poorly on Marques conditions in both subsamples.
  - Several EBMs are biased or not strongly exogenous in the first subsample; none satisfies the attractor property in first subsample.
  - In the latter subsample, two EBMs — CPIxFE and CPIxFEA — satisfy all conditions except unbiasedness (both have a downward bias). With low power of ADF test, these EBMs could be considered useful during periods of high inflation.
- TMMs over subsamples:
  - 1999-2007 (low inflation): trims required are smaller and larger on the left tail; two trims satisfy Marques conditions: TMM1407 and TMM1408.
  - 2008-2014 (high inflation): several trims satisfy Marques conditions; larger trims needed due to higher skewness and larger outliers in component inflations.
  - Conclusion: “one trim does not fit all times”.

### Cogley tests and reversion horizons
- Cogley tests assess predictive power of current core deviation for subsequent changes in headline inflation at horizons H = 1–12 months.
- Figure 9 displays estimated βs with 95 percent confidence intervals for:
  - D12_TM_2226 (full sample)
  - D12_TM_147 (earlier sample)
  - D12_TM_2119 (latter sample)
- Table 7: Wald F-statistics for null hypothesis α=0 and β=−1 (Horizons 1–12 months)
  - For 1999-2014, TMM2226: F-statistics by horizon: 1:0.00; 2:0.00; 3:0.07; 4:0.31; 5:0.54; 6:0.54; 7:0.37; 8:0.20; 9:0.11; 10:0.06; 11:0.04; 12:0.03
  - For 1999-2007, TMM147: F-statistics by horizon: 1:0.00; 2:0.39; 3:0.17; 4:0.10; 5:0.04; 6:0.00; 7:0.00; 8:0.00; 9:0.00; 10:0.00; 11:0.00; 12:0.01
  - For 2008-14, TMM2119: F-statistics by horizon: 1:0.00; 2:0.05; 3:0.28; 4:0.52; 5:0.72; 6:0.80; 7:0.74; 8:0.58; 9:0.41; 10:0.27; 11:0.19; 12:0.16
- Interpretation:
  - Cogley tests provide information on horizons over which headline inflation reverts to CIMs but are valid only if the null α=0 and β=−1 is not rejected.

### Policy rate and implications of CIM choice
- Main conclusions relevant for policy:
  - EBMs generally do not satisfy desired statistical conditions for admissible CIMs; TMMs perform better.
  - Admissible TMMs depend on the sample period (i.e., inflation regime and component properties). Periods with high, variable inflation require larger trims.
  - Headline inflation traces admissible TMMs more closely than commonly used EBM (CPIxFE) across samples (Figure 10).
  - Under/overprediction of underlying inflation pressures by EBMs (relative to TMMs) during 2008-14 ranged between −8 and 6 percent.
  - Speed of rise and fall in underlying inflation differs between EBMs and TMMs:
    - EBMs suggest slower increases and declines in core inflation than TMMs.
    - Using TMM2226, policy rates would have needed to be raised earlier and cut faster than suggested by EBM guidance — notably in 2012 and 2013 where EBM continued to suggest double-digit core inflation while TMM2226 indicated single-digit core inflation.
  - Implication: Relying on EBMs for policy action may lead to delayed responses in tightening or loosening; TMMs can offer timelier guidance but require ongoing recalibration to the inflation regime.

### Concluding remarks and policy recommendations
- Empirical findings:
  - Commonly used exclusion-based measures (EBMs) do not perform well against statistical criteria for admissible CIMs; trimmed mean measures (TMMs) perform better.
  - Even among TMMs, no single trim is appropriate across all periods: “one trim does not fit all periods”.
- Policy recommendations:
  - Policymakers should test and update CIMs on an ongoing basis to form a firmer basis for policy actions.
  - TMMs, with sample-specific trims, provide closer tracking of headline inflation and more timely signals for policy rate adjustments than EBMs.
  - EBMs may still be useful for communication purposes given simplicity, but should not be sole guides for monetary policy decisions.
  - Use of replicable EVIEWS and MATLAB programs (accompanying the paper) allows quick replication of CIMs as new data become available, making them valuable monetary policy tools for the State Bank of Vietnam.
- Broader implication:
  - Although results are specific to Vietnam’s experience (heavy weighting of food and fuel in CPI and exposure to external shocks), findings may carry over to other countries with similar economic structures.

*Source: Authors’ calculations and analysis in the provided content.*

### References

### _wp1619 - References

### Conceptual and Measurement Literature
- Bryan, Michael F. and Cecchetti, Stephen G. "Inflation and the distribution of price changes." The Review of Economics and Statistics 81, no. 2 (May 1999): 188-196.
- Bryan, Michael; Cecchetti, Stephen G. and Wiggins II, Rodney L. "Efficient Inflation Estimation." NBER Working Paper 6183 (1997).
- Cogley, Timothy. "A simple adaptive measure of core inflation." Journal of Money, Credit and Banking 34, no. 1 (Febuary 2002): 94-113.
- Eckstein, O. Core inflation. Englewood Cliffs, N.J.: Prentice-Hall, 1981.
- Flemming, J. Inflation. London: Oxford University Press, 1976.
- Marques, Carlos Robalo and Joao Machado Mota. "Using the assymmetric trimmed mean as a core inflation indicator." Economic Bullentin, Banco de Protugal, September 2000: 85-95.
- Marques, Carlos Robalo, Pedro Duarte Neves, Luis Morais Sarmento. "Evaluating core inflation indicators." Economic Modelling 20 (2003): 765-75.
- Quah, Danny and Shaun P. Vahey. "Measuring Core Inflation." The Economic Journal 105, no. 432 (September 1995): 1130 - 1144.
- Roger, Scott. "Core Inflation: concepts, uses and measurement." Reserve Bank of New Zealand Discussion paper G98/9 (1998).
- Wynne, Mark A. "Core Inflation: A review of some conceptual issues." Federal Reserve Bank of St. Louis Review 90, no. 3, Part 2 (May/June 2008): 205-28.

### Country-Specific and Empirical Studies
- Ginting, Edimon. "Is inflation in India an attractor of inflation in Nepal." IMF Working Paper, no. WP/07/269 (2007).
- Lai, Ngoc-Anh. "Which core inflation measures for Vietnam?" A part of Ph.D thesis at Universite Paris I Patheon-Sorbonne, August 2013.
- Nguyen, Huu Minh; Cavoli, Tony and Wilson, John K. "The Determinants of Inflation in Vietnam, 2001-09." ASEAN Economic Bulletin 29, no. 1 (2012): 1-14.
- Roger, Scott. "Vietnam core inflation measuremnet and forecasting issues." International Monetary Fund, January 2008.

### IMF and Policy-Oriented Working Papers
- Silver, Mick. "Core inflation measures and statistical issues in choosing among them." IMF Working paper WP/06/97 (2006).

### Historical and Policy Perspectives
- Okun, A. "Inflation: the problems and prospects before us." In Inflation: the problems it creates and the policies it requries, by A Okun, M Gilbert, H Fowler, 3-53. New York: New York University press, 1970.

*Source: _wp1619 - References*

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