An Alternative Core Inflation Measure for the Philippines ... · Amstad et al. (2014) argued that the trimmed mean and weighted median are essentially exclusion-based methods as these

Bangko Sentral Review 2017

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The authors are Zeno Ronald R. Abenoja (Senior Director), Joselito R. Basilio (Acting Deputy Director), Cherrie F. Ramos (Bank Officer V) and Joan Christine S. Allon (Senior Research Specialist) of the Department of Economic Research. The views and opinions expressed in this article are those of the authors and do not necessarily reflect those of the Bangko Sentral ng Pilipinas.

An Alternative Core Inflation Measure for the Philippines using Principal Components Analysis

Zeno Ronald R. Abenoja Cherrie F. RamosJoselito R. Basilio Joan Christine S. Allon

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I. Introduction

Monetary authorities take a keen interest on core inflation measures. Both inflation targeting (IT) and non-inflation targeting central banks routinely monitor core inflation as a key indicator in its real and financial sector assessments. However, core inflation becomes an even more important consideration from an IT central bank’s perspective, even as in many cases the target index is the headline inflation. Headline inflation measures the change in the price of a standard basket of goods and services typically purchased by consumers. It is a good measure of changes in the cost of living based on adjustments in prices and, as such, has direct implication on the welfare of consumers. Moreover, the general public is more familiar with this indicator. Given these considerations, the BSP specifies its inflation target in terms of the average headline inflation for a particular year. However, headline inflation tends to be volatile. Transitory shocks in certain economic sectors could lead to deviations of inflation from its underlying trend. For instance, weather-related disturbances could trigger temporary large price increases in agricultural products and translate into a spike in headline inflation even if the prices of the other commodities are broadly stable. Historical data also show that volatile energy prices lead to sharp swings in inflation. Core inflation measures are designed to strip away the impact of these temporary disturbances. Accurate estimates of core inflation serve as indicator for monetary authorities in assessing whether current movements in consumer prices represent short-lived shocks or have permanent effects on the long-run path of inflation. This is integral information for policymaking since monetary action is intended to respond to the underlying trend component of inflation or to price trends that are tied primarily to macroeconomic fundamentals, including sustained domestic demand over which monetary policy has some influence. Generally speaking, monetary authorities look through transient noise in the price data except when these are judged to be sufficiently large and persistent that could generate secondary effects. Thus while the target inflation is the headline inflation, one could consider core inflation as a key gauge of underlying price dynamics, which helps guide policymakers in the stabilization of headline inflation over the medium term.

There are a number of ways to estimate core inflation. The most common technique is the exclusion method which removes a fixed, pre-defined set of items from the consumer price index (CPI) basket. Core inflation could also be measured using limited influence estimators such as the trimmed mean and weighted median where the items excluded from the CPI could vary every estimation run subject to a criterion that defines extreme price movements. Amstad et al. (2014) argued that the trimmed mean and weighted median are essentially exclusion-based methods as these still involve the removal of certain CPI components. Meanwhile, factor models are gaining prominence as another approach to estimate the underlying inflation. Core inflation derived using principal components analysis (PCA) and dynamic factor models (DFMs) fall under this category. Unlike the exclusion method, factor models do not discard any of the CPI components. For some DFMs, price data are even augmented by non-price data that could be useful predictor of price trends. Some examples of research on the use of PCA to derive core inflation include Marques et al. (2001) for Portugal, Leung et al. (2010) for Hong Kong


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and Khan et al. (2013) for Canada. Meanwhile, Amstad et al. (2014) and Kim et al. (2010) utilized DFMs to model underlying trend inflation for the US and Korea, respectively.

The objective of this study is to produce an additional core inflation measure for the Philippines using PCA. The remainder of this paper is divided into four sections. Section II provides an overview of the existing core inflation measures for the Philippines. Section III discusses the methodology and data. Section IV presents the empirical results and their assessment. These include a description of the statistical properties of the new estimates and a comparison with headline inflation and other core inflation measures. The results are also assessed based on the criteria for evaluation of core inflation indicators put forward by Marques et al. (2001). Finally, Section V offers a summary of findings and conclusions.

II. Existing Core Inflation Measures for the PhilippinesThe official core inflation measure for the Philippines is defined as headline CPI excluding selected food and energy items. The excluded items and their corresponding share in the CPI basket (2006=100) are: rice (8.9 percent); corn (0.7 percent); meat, fresh, chilled or frozen (4.9 percent); fruits, fresh (1.5 percent); vegetables, cultivated for their roots, fresh or dried (0.6 percent); vegetables, cultivated for their fruits, fresh or dried (1.2 percent); natural gas, liquefied or in a gaseous state (1.5 percent) and gas oils for motor vehicles (0.7 percent). Taken together, the excluded items account for 20.0 percent of the 2006-based CPI basket and are subject to review whenever the CPI is rebased.

The decision to adopt an exclusion-based official core inflation definition was agreed upon during inter-agency technical discussions in 2003 among representatives of the former National Statistics Office (NSO), the former National Statistical Coordination Board (NSCB), the former Statistical Research and Training Center (SRTC), the National Wage and Productivity Commission (NWPC), the Department of Trade and Industry (DTI) and the Bangko Sentral ng Pilipinas (BSP).1 The official conceptual and operational definitions and methodology for core inflation were formalized under NSCB Resolution No. 6, Series of 2003, dated 23 June 2003. Guinigundo (2004) documented the key considerations that shaped the discussions during the inter-agency technical meetings.

The official core inflation measure is estimated and published by the Philippine Statistics Authority (PSA). At the same time, the BSP also generates internal estimates of alternative core inflation measures as follows:2

a. Trimmed mean. This is estimated as the average inflation rate of the (weighted) middle 70 percent of the CPI basket based on a lowest to highest ranking of the year-on-year inflation rates for all CPI components.

b. Weighted median. This represents the middle inflation rate (corresponding to a cumulative CPI weight of 50.0 percent) in a lowest to highest ranking of year-on-year inflation rates for all CPI components.

c. Net of Volatile Items. This is measured by excluding bread and cereals, meat, fish, fruits, vegetables, gas, solid fuels, fuels and lubricants for personal transport equipment and passenger transport by road. These items represent 39.0 percent of the basket.

1 Pursuant to Republic Act No. 10625, otherwise known as the Philippine Statistical Act of 2013, the NSO and NSCB, along with the Bureau of Labor and Employment Statistics (BLES) and the Bureau of Agricultural Statistics (BAS) were reconstituted into the Philippine Statistics Authority (PSA) beginning 29 December 2013. This Act also created the Philippine Statistical Research and Training Institute to replace the SRTC.

2 The BSP-generated alternative core inflation measures are published in the BSP website.

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In general, the official core inflation and the alternative core inflation measures move in the same direction but there are also occasions when the estimates diverge.3 These measures are regularly monitored, assessed, and used mainly to determine if the trend in headline inflation could be something that is persistent and not driven only by the volatile food and energy items in the CPI basket. Furthermore as core inflation attempts to weed out sector-specific disturbances, these measures could also be used as a gauge for domestic demand.

III. Methodology and DataPCA is a statistical procedure that is used to extract a linear combination of the original set of variables that captures the maximum possible proportion of total variance in the dataset. Rummel (2015) posited that the PCA is a dimension-reduction tool that can be used to reduce a large set of variables to a small set that still contains most of the information in the large set. There is no explicit economic theory behind PCA but, as a statistical technique, it is able to compress large datasets into a measure that accounts for the greatest possible variability in the data.

A principal component (or a factor) is a composite variable that summarizes the information from the original set of variables that went into its construction. It is a weighted average (a linear combination) of the original set of variables where the weights (factor loadings) are such that it could capture the largest variation in the dataset. For any given matrix of n explanatory variables, one may be able to extract up to n principal components. Each principal component would be a linear combination of the n explanatory variables and are orthogonal to each other. The first principal component represents the highest proportion of variation for the given dataset. The succeeding principal components would account for a lower marginal proportion of the variation in the data than the previous principal component.4

Khan et al. (2013) outlined how the principal components analysis could be employed to extract core inflation from the inflation rates of the subcomponents of headline inflation. According to Khan et al. (2013), the inflation rate of each subcomponent of headline inflation can be decomposed into the common component that affects all subcomponents and sector-specific idiosyncratic shock. Thus,

(1)

where is the inflation rate for inflation subcomponent i at time t, is the common trend that influences the inflation rates of all i subcomponents and is an idiosyncratic shock to inflation subcomponent i. On one hand, is the more permanent component of the inflation process that influences all prices and as such is representative of the underlying inflation. On the other hand, are transitory and affect only a particular sector of the economy. Essentially, these are the commodity-specific noise terms that cause the volatility in the headline inflation.

It is therefore easy to see that if the first principal component accounts for the largest proportion of the movements in the prices of all the CPI subcomponents, then the first principal component is the common factor that defines the underlying inflation process. Extracting the first principal component would, technically, isolate the most common trend across all CPI subcomponents from the commodity-specific shocks. Khan et al. (2013) also chose to focus on the first principal component, motivated by the intuition 3 See Guinigundo (2004) for an evaluation of the various core inflation measures for the Philippines.4 Please refer to Rummel (2015) for a detailed discussion of PCA.


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that there should, in principle, be only one common component to all items in the CPI.

Following Khan et al. (2013), the factor model of (1) is

(2)

where Λi are the factor loadings and is the common factor. is assumed to be uncorrelated with . Hence, the underlying inflation could be estimated as:

(3)

where Λ is the matrix of factor loadings.

Compared to other techniques in measuring core inflation, the PCA has the advantage of using all the components of headline inflation in the computation. Amstad et al. (2014) argued that the exclusion of volatile items or those that show large price changes in the core inflation measure could also remove early signals of changes in the inflation process that tend to show up in tails of the price change distribution. This could make exclusion-based core inflation measures a lagging indicator for changes in the underlying inflation process.5

For this paper, the PCA is applied to the 11 subcomponents of the Philippine CPI series (2006 = 100). Table 1 lists down these subcomponents and their share in the CPI basket. The data used covers the period from January 2005 to June 2017. The series are expressed as changes on a year-on-year basis, which removes the need to seasonally adjust the CPI data. However, some components were found to still be non-stationary in this form. For this reason, this paper adopted the standardization equation proposed by Marques et al. (2001) as follows:

(4)

where is the standardized series of each subcomponent i, the mean of the year-on-year series and the standard deviation of the first difference of the year-on-year inflation rates.6

5 This also makes a strong case for the use of DFMs in measuring underlying inflation. Apart from inflation data, DFMs incorporate real and financial variables that could be useful predictors of future price pressures.

6 It could be noted that this standardization technique was used by Marques et al. (2001) and Leung et al. (2010) for their PCA-based core inflation estimates for Portugal and Hong Kong, respectively.

PSA Code Components Share in CPI basket (in percent)

0 All Items 100.00

01 Food and Non-Alcoholic Beverage 38.98

02 Alcoholic Beverages and Tobacco 2.00

03 Clothing and Footwear 2.95

04 Housing, Water, Electricity, Gas, and Other Fuels 22.47

05 Furnishings & Household Equipment 3.22

06 Health 2.99

07 Transport 7.81

08 Communication 2.26

09 Recreation 1.93

10 Education 3.36

11 Restaurant and Miscellaneous Goods 12.03

Table 1CPI subcomponents (2006 =100)

Source: Philippine Statistics Authority (PSA)

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Consistent with existing literature, the first principal component is used as there should only be one common underlying trend or component across the CPI subcomponents. The first principal component is then rescaled to be comparable with headline inflation as well as the other measures of core inflation. This is done by multiplying the first principal component with the standard deviation of first difference of the headline inflation and then adding back the mean (Khan et al. (2013)).

IV. Results and AssessmentsComparison with Other Inflation Measures 7

Figures 1 and 2 show the extracted first principal component of the CPI, along with headline inflation and the various measures of core inflation, respectively. The first principal component of CPI is noticeably smoother than the headline inflation, as is expected of an underlying inflation measure. During the 2008 global financial crisis, broad commodity price increases were captured by the first principal component which climbed but did not peak as much as headline inflation. The oil price slump from 2014-2016 also showed the first principal component easing but still remaining within the government’s target range of 2-4 percent, while headline inflation undershot the government target in 2015-2016.

Compared to the other measures of core inflation in the Philippines, the first principal component is seen to follow a similar path. However, visual inspection of Figure 2 indicates that the first principal component is relatively more stable than the other core inflation measures. It could be noted that in 2015-2016, most measures of core inflation fell below the inflation target band while, as discussed above, the first principal component remained within target. This suggests that the first principal component is more resistant to supply shocks and could instead be capturing relatively strong demand dynamics during the said period.

7 Only data for 2007 – June 2017 are reported for consistent sample size across all measures.

Figure 1:Headline Inflation and the First Principal Component

Monthly data, year-on-year growth (%)

Source: PSA and authors’ estimate


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Table 2 presents the descriptive statistics for headline and core inflation indicators. Measured in standard deviation of year-over-year changes, the first principal component of CPI registered the least volatility when compared to headline inflation and the various measures of core inflation, except for net of volatile items (which strips out 39 percent of the basket). Table 2 also shows that the measure is strongly positively correlated with the other inflation series.

Relationship between the first principal component and individual CPI componentsFigure 3 depicts the relationship between the weights of each CPI sub-index in the first principal component and the corresponding volatility evaluated by σ∆πi, the volatility of the change in inflation. As shown in the figure, there is a negative relationship between the volatility of each item in the CPI index and the corresponding weight in the first principal component. This suggests that the most volatile series obtain reduced weights in the first principal component and vice versa for the smoothest series.

Figure 2:Measures of Core Inflation


Source: BSP, PSA and authors’ estimate

Y-o-Y Inflation(January 2007 to June 2017)

Mean(in percent)

Standard Deviation

Correlation with the First Principal Component

Headline Inflation 3.71 1.99 0.93

Core Inflation 3.41 1.24 0.95

Trimmed Mean 3.29 1.57 0.96

Weighted Mean 2.99 1.34 0.95

Net of Volatile Items 3.05 1.00 0.89

First Principal Component 3.71 1.19 -

Table 2Descriptive Statistics

Source: Authors’ estimates

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In fact, Figure 4 shows that volatile CPI items with larger weights in the CPI end up with smaller weights in the first principal component. For example, the principal component weights of “Food and Non-Alcoholic Beverages” and “Housing, Water, Electricity, Gas and Other Fuels” are smaller than their weights in the CPI basket. In contrast, less volatile sub-indices with smaller weights in the CPI exhibit a larger weight in the first principal component. Combined, the two figures explain why the first principal component is smoother than the headline inflation.8

Likewise, the inflation rates of a majority of the CPI sub-indices (10 of 11, comprising 97.7 percent of the basket) are positively correlated with the first principal component (Table 3). This suggests the same directional response of most consumer prices to common sources of variation. Notably, the first principal component of CPI also explains only about 51 percent of the total variance of the 11 CPI components.9 This suggests that around half of the movements in total inflation are component-specific and the other half are reflective of movements common across CPI components.

8 This is broadly similar to the findings in Marques et al. (2001) and Leung et al. (2010).9 This refers to the adjusted R-squared obtained from a regression of each individual component’s inflation rate on the first principal component

of CPI over the full estimation sample.

Figure 3:Volatility and Weights in the First Principal Component

Source: Authors’ estimate

Figure 4:Weights in the First Principal Component and the CPI

Source: PSA and authors’ estimate


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Properties of the First Principal Component as a Measure of Underlying InflationThe viability of the first principal component as well as other measures of underlying inflation, as a measure of underlying inflation can be assessed through the following dimensions as identified by Rummel (2015): (i) volatility— a good measure should be less volatile than CPI inflation, as it is supposed to capture the underlying trend in inflation; (ii) unbiasedness— a good measure of core inflation should be unbiased relative to CPI inflation in terms of mean inflation; (iii) predictive ability— because core inflation should capture underlying inflationary pressures, headline inflation is expected to converge to core inflation; and (iv) real-time stability— from a policy perspective, the core inflation measure should be available in a timely manner and should not be subject to substantive revisions.

As shown earlier, the first principal component meets the first criterion as it is relatively smoother than headline inflation. The estimated first principal component is also observed to be smoother than all but one of the alternative measures of core inflation.

In evaluating the second and third criteria, Marques et al. (1999, 2000) proposed the following conditions: (i) the difference between headline inflation and the core inflation must be a zero-mean stationary variable; (ii) the core inflation must behave as an attractor for the headline inflation, such that it functions as a leading indicator of headline inflation and that headline inflation converges to core inflation; and (iii) the headline inflation should not be an attractor for the core inflation indicator and that the core inflation measure is strongly exogenous. To test for these conditions, this paper conducted a regression analysis on headline inflation and the first principal component of CPI using fully modified ordinary least squares (FMOLS) to determine the long-run relationship as well as error correction models for the short-run dynamics. 10

Table 4 summarizes the results of various tests for unbiasedness and predictive ability of the first principal component. Unbiasedness is determined via three tests, namely:

(1) cointegration between headline inflation and the first principal component;

(2) stationarity of residuals; and (3) zero mean of residuals.

The test for cointegration (Engle-Granger, 1987) is performed via FMOLS using the following equation:10 The FMOLS was used given the relatively short sample.

Components of CPI (y-o-y)January 2007 to June 2017 Correlation % of explained variance

HealthFurniture and Household EquipmentFood and Non-Alcoholic Beverages

Restaurants and Other Miscellaneous Activities

Clothing and FootwearTransportEducation

Housing, Water, Electricity, Gas and Other FuelsRecreation

Alcoholic Beverages and TobaccoCommunication

0.940.850.850.84

0.790.760.640.62

0.440.03-0.71

0.880.730.720.70

0.620.580.400.37

0.18-0.010.50

Average 0.55 0.51

Table 3Relationship between first principal component and individual components of CPI

Source: Author’s estimates

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(5)

where stands for the year-on-year headline inflation and stands for the first principal component of the CPI. The results of the Engle-Granger Test for Cointegration suggest that there exists a cointegrating relationship between headline inflation and the first principal component.

This paper also checked for stationarity of the equation’s residuals. The difference between headline and PCA-based core inflation was assessed via the Augmented Dickey Fuller (ADF) test and was found to be stationary.11 Meanwhile, the Wald’s test confirms that has a zero mean. Overall, the results of the three tests indicate that the first principal component is unbiased in its capacity as a measure of underlying inflation.

In evaluating predictive ability, an error correction model is estimated to test both the short-run and long-run relationship between the first principal component and the headline inflation. The coefficient of the error correction term (γ) for the equation:

(6)

was found to be negative and significant (see Table 4, bottom portion). This suggests that headline inflation is expected to converge to the first principal component. This relationship via the error correction term reinforces the importance of underlying inflation as a predictor of and an anchor to which headline inflation is expected to return over time.

In the case of the third criterion, the equation is inverted with the core inflation measure being the dependent variable and the headline inflation predictor:

(7)

The error correction term for the equation was found to be insignificant (see Table 4, bottom portion), suggesting that the headline inflation is not a leading indicator for first principal component. This suggests that the first principal component is exogenous with respect to the headline inflation because the estimated first principal component does not appear to be sensitive to headline inflation. Thus, the first principal component remains a valid reference for the future path of headline inflation.

These tests were also done for the existing core inflation measures and the results are

11 Unit root tests using Philipps-Peron (PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests yielded a similar conclusion. These results are no longer reported in this paper.


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similarly reported in Table 4.12 On the whole, it appears that the estimated measure of underlying inflation via PCA meets the conditions proposed by Rummel (2015) in terms of volatility, unbiasedness, and predictive ability. This is in contrast with other measures of core inflation, which do not meet the conditions on zero-mean stationarity for residuals (i.e., Wald test rejects the null of zero mean) and predictive ability (i.e., error term in test for convergence is insignificant while error term in test for strong exogeneity is significant).

In terms of the fourth criterion, the real time stability of core inflation estimates derived from the PCA methodology was assessed by simulating historical revisions. This was done by extracting the first principal component multiple times starting with 10 years of data, expanded one month at time. The results of this exercise (Figure 5) indicate that revisions for the full sample could be small, averaging 0.17 percentage point in absolute terms. Furthermore, this exercise shows that revisions are only relatively large at the start of the sample period when the sample size is small, since smaller sample sizes are more sensitive to additional observations. As such, revisions are markedly smaller in the latter part of the sample as the sample size increases. For example, revisions in the last three years averaged only 0.08 percentage point in absolute terms. It could be noted that as Khan et al. (2013) pointed out, changes in the statistical properties of headline inflation would result in revisions in the PCA-based estimates as these are scaled by the mean and volatility of headline inflation so such changes should be expected. However, for the sample used in this study, these revisions appear to be relatively small.

12 Unit root tests for the dt with other core inflation measures yielded similar conclusions using PP and KPSS tests except that for the dt between headline inflation and weighted median which passed these stationarity tests and failed the ADF test. These results are no longer reported in this paper.

Y-o-Y Inflation FirstPrincipal

Component

Official Core

Inflation

TrimmedMean

Net of Volatile Items

Weighted Median

Unbiasedness

Engle-Granger test statistic (H0: Series are not cointegrated)

ADF test statistic (H0: has a unit root where

Wald test statistic (H0: mean of dt = 0)

-3.36(0.05)*

-3.29(0.02)**

0.00(1.00)

-3.81(0.02)**

-3.80(0.00)***

11.16(0.00)***

-3.46(0.04)**

-3.38(0.01)**

50.96(0.00)***

-3.61

(0.03)**

-3.55

(0.01)***

31.82

(0.00)***

-3.28

(0.06)*

-2.48

(0.12)

69.38

(0.00)***

Predictive ability: Error Correction Terms

π converges to π*

π* is strongly exogenous to π

-0.14

(0.01)**

-0.03

(0.50)

-0.01

(0.84)

-0.20

(0.00)***

-0.12

(0.12)

-0.07

(0.29)

-0.05

(0.20)

-0.13

(0.01)**

-0.02

(0.73)

-0.26

(0.00)***

Table 4Summary of Results for Unbiasedness and Predictive Ability^

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V. ConclusionsThis paper estimated an underlying inflation measure using PCA. The resulting new measure has the desirable properties of a good core inflation indicator. The series is less volatile relative to headline inflation and available core inflation measures (with the exception of the net of volatile items core inflation indicator). The PCA-based core inflation has lower standard deviation than most core inflation measures even if the historically volatile CPI items are not excluded from its estimation. Moreover, the PCA-based core inflation is an unbiased estimator and thus could be capturing the systematic, underlying trend in price dynamics. This paper also showed that this core inflation measure could function as a leading indicator for headline inflation as the error correction model showed that headline inflation eventually converges to this particular measure. At the same time, the PCA-based core inflation does not converge to headline inflation. Finally, the measure can be estimated in real time and simulations using expanding window indicate relatively small revisions in estimates. Given the above findings, there is room to accommodate the PCA-based core inflation measure as an addition to the existing core inflation measures. Future line of research in this field could include building a DFM for headline inflation as a supplemental monitoring tool to gauge underlying inflation trend.

Source: Authors’ estimate

Figure 5:Revisions to PCA-based Core Inflation Estimates



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References:Amstad, M., S. Potter and R. Rich, 2014, “The FRBNY Staff Underlying Inflation Gauge: UIG”, BIS Working Papers No. 453, July.

Bangko Sentral ng Pilipinas, 2016, Primer on Core Inflation, September.

Coimbra, C. and P.D. Neves, 1997, “Trend Inflation Indicators”, Banco de Portugal Economic Bulletin, March.

Engle, R. F., & Granger, C. W. (1987). Co-integration and error correction: representation, estimation, and testing. Econometrica: Journal of the Econometric Society, 251-276.

Guinigundo, D., 2004, “An Official Core Inflation Measure for the Philippines” Bangko Sentral Review, July.

Khan, M., L. Morel and P. Sabourin, 2013, “The Common Component of CPI: An Alternative Measure of Underlying Inflation for Canada” Bank of Canada Working Paper 2013-35, October.

Kim, J.C., Y.W. Kim and S.Y. Lee, 2010, “Measure of Core inflation in Korea”, BIS Papers No.49, pp. 233-247.

Leung, F., K. Chow and S. Chan, 2010, “Measures of Trend Inflation in Hong Kong”, BIS Papers No.49, pp. 177-200.

Marques C.R., P.D. Nueves and A. G da Silva, 2001, “Using the First Principal Component as a Core Inflation Indicator”, Banco de Portugal Economic Bulletin, March.

Marques, C.R., P.D. Nueves and L.M. Sarmento, 2000, “Evaluating Core Inflation Indicators”, Banco de Portugal Working Papers 3-00, April.

Rummel, Ole, 2015, Dynamic factor models, the state-space approach and EViews, Centre for Central Banking Studies, Bank of England (unpublished manuscript)

Rummel, Ole, 2015, The common components of CPI: an alternative measure of underlying inflation, as presented in 2nd SEACEN Intermediate Course on Econometric Modelling and Forecasting, 27 September – 2 October 2015.

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Null Hypothesis: dt = πt – πt* has a unit root

t-Statistic Prob.*

Augmented Dickey-Fullertest statistic

-3.288976 0.0175

Test critical values:

1% level5% level

10% level

-3.483751-2.884856-2.579282

*MacKinnon (1996) one-sided p-values.

Wald Test:

Test Statistic Value df Probability

t-statisticF-statisticChi-square

-2.69E-15 7.26E-30 7.26E-30

125(1, 125)

1

1.0000 1.0000 1.0000

Null Hypothesis: C(1)=0Null Hypothesis Summary:

Normalized Restriction(= 0)

Value Std. Err.

C(1) -2.38E-16 0.088283

Restrictions are linear in coefficients.

Table 3Augmented Dickey-Fuller Test for Stationarity

Table 4Wald Test on the Mean of the Difference (dt)

Dependent Variable: D(π)Method: Least Squares

Sample: 2007M04 2017M06Included observations: 123 after adjustments

Variable Coefficient (p-value)

D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt-πt*)t-1

-0.404898(0.1682)*0.434503(0.1142)*0.733725

(0.0000)***-0.059286(0.6691)

-0.138732(0.0137)**

Adjusted R-squared: 0.345101Durbin-Watson Statistic: 2.067987*/**/*** denote significance at 10%, 5% and 1%, respectively

Dependent Variable: D(π*)Method: Least Squares



D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt*-πt)t-1

0.151365(0.2463)

0.135779(0.2655)

0.225196(0.0001)***-0.045173(0.4652)

-0.027435(0.4986)


Table 5 Error Correction Model: Headline Inflation and First Principal Component 1

1 Several specifications and lags were tested. Lags higher than two were found to have worse fit and insignificant variables.

Table 6Error Correction Model: First Principal Component

and Headline Inflation

Notes:• π pertains to headline inflation as obtained from the Philippine Statistics Authority.• π* pertains to the measure of core inflation which, in this set of tables, is the first principal component derived from Equation

3 of the main text.• α is the constant in Equation 3 of the main text.

EViews Output for the First Principal Component

Dependent Variable: πMethod: Fully Modified Least Squares (FMOLS)


Variable Coefficient(p-value)

α

π*

-1.837070(0.0000)***

1.502727(0.0000)***

Table 1Cointegrating Equation: Headline Inflation (π) and First

Principal Component Core Measure (π*)

Adjusted R-squared = 0.860756*/**/*** denote significance at 10%, 5% and 1%, respectively

Cointegration Test - Engle-GrangerNull hypothesis:

Series are not cointegrated maxlag=12

Value

Engle-Granger tau-statistic

Engle-Granger z-statistic

-3.357762 (0.0535)*

-22.532 (0.0258)**

*MacKinnon (1996) p-values.

Table 2Engle-Granger Test for Cointegration

*/**/*** denote significance at 10%, 5% and 1%, respectively

ANNEX


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EViews Output for the Official Core Inflation




α

π*

-1.223460(0.0007)***

1.455034(0.0000)***

Table 1Cointegrating Equation: Headline Inflation (π) and

Official Core Measure (π*)


Cointegration Test - Engle-GrangerNull hypothesis:

Series are not cointegrated maxlag=12

Value



-3.810221 (0.0166)**

-29.48030 (0.0048)***





t-Statistic Prob.*

Augmented Dickey-Fullertest statistic

-3.799123 0.0038


1% level5% level

10% level

-3.483751-2.884856-2.579282


Wald Test:



3.340588 11.15953 11.15953

125(1, 125)

1

0.0011 0.0011 0.0008



Value Std. Err.

C(1) 0.293635 0.087899







D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt-πt*)t-1

-0.285349(0.1207)

-0.175476(0.3542)

0.708915(0.0000)***

0.084562(0.5695)

-0.011180(0.8394)





D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt*-πt)t-1

0.229860(0.0732)*-0.145947(0.2748)

0.101782(0.2829)

0.025506(0.8054)

-0.200342(0.0013)***


Table 5Error Correction Model: Headline Inflation and Official

Core Measure

Table 6Error Correction Model: Official Core Measure

and Headline Inflation

Bang

ko S

entr

al R

evie

w 2

017

16


t-Statistic Prob.*

Augmented Dickey-Fullertest statistic -3.378557

0.0136


1% level5% level

10% level

--3.483751 -2.884856-2.579282



Wald Test:



7.138920 50.96418 50.96418

125(1, 125)

1

0.0000 0.0000 0.0000



Value Std. Err.

C(1) 0.415351 0.058181






D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt-πt*)t-1

0.128102(0.5369)

-0.056588(0.7813)

0.526427(0.0004)***

0.062721(0.6818)

-0.0122801(0.1215)





D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt*-πt)t-1

0.207806(0.1484)

-0.102712(0.4664)

0.190996(0.0601)*0.134880(0.2034)

-0.072436(0.2878)


Table 5Error Correction Model: Headline Inflation

and Trimmed Mean Core Measure

Table 6Error Correction Model: Trimmed Mean Core Measure and Headline Inflation

EViews Output for the Trimmed Mean




α

π*

-0.207848(0.3088)

1.193810(0.0000)***


Trimmed Mean Core Measure (π*)Cointegration Test - Engle-Granger

Null hypothesis: Series are not cointegrated maxlag=12

Value



-3.458264 (0.0419)**

-23.85501 ( 0.0189)**






17

EViews Output for the Net of Volatile Items




α

π*

-1.330728(0.0378)**

1.662180(0.0000)***

Table 1Cointegrating Equation: Headline Inflation (π) and Net

of Volatile Items Core Measure (π*)


Cointegration Test - Engle-GrangerNull hypothesis: Series are not cointegrated maxlag=12

Value



-3.613093 ( 0.0283)**

-26.28868 (0.0106)***


Table 2Table 2: Engle-Granger Test for Cointegration



t-Statistic Prob.*

Augmented Dickey-Fullertest statistic -3.545530 0.0083


1% level5% level

10% level

--3.483751-2.884856-2.579282



Wald Test:



5.640518 31.81544 31.81544

125(1, 125)

1

0.0000 0.0000 0.0000



Value Std. Err.

C(1) 0.654240 0.115989






D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt-πt*)t-1

-0.338750(0.0343)**-0.098887(0.5380)

0.709956(0.0000)***

0.028311(0.8252)

-0.046603(0.1978)





D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt*-πt)t-1

0.169143(0.1452)

-0.103428(0.3831)

0.029541(0.7321)

0.020573(0.8228)

-0.132014(0.0124)**


Table 5Error Correction Model: Headline Inflation and Net of Volatile Items Core Measure

Table 6Error Correction Model: Net of Volatile Items

Core Measure and Headline Inflation

Bang

ko S

entr

al R

evie

w 2

017

18

EViews Output for the Weighted Median




α

π*

-0.281627(0.3397)

1.344198(0.0000)***


Weighted Median Core Measure (π*)


Cointegration Test - Engle-GrangerNull hypothesis: Series are not cointegrated maxlag=12

Value



-3.276599 (0.0646)*

-19.90834 (0.0471)**


Table 2Table 2: Engle-Granger Test for Cointegration



t-Statistic Prob.*

Augmented Dickey-Fullertest statistic -2.475547 0.1239


1% level5% level

10% level

-3.483312-2.884665-2.579180



Wald Test:



8.329546 69.38134 69.38134

125(1, 125)

1

0.0000 0.0000 0.0000



Value Std. Err.

C(1) 0.716145 0.085976






D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt-πt*)t-1

0.098410(0.3967)

-0.217091(0.0596)*0.552345

(0.0000)***0.085254(0.4490)

-0.018565(0.7328)





D(π*)t-1

D(π*)t-2

D(π)t-1

D(π)t-2

(πt*-πt)t-1

0.015571(0.8793)

-0.141788(0.1589)

0.189773(0.0511)*0.050811(0.6014)

-0.262224(0.0003)***


Table 5Error Correction Model: Headline Inflation

and Weighted Median Core Measure

Table 6Error Correction Model: Weighted Median

Core Measure and Headline Inflation

Documents

An Alternative Core Inflation Measure for the Philippines ... · Amstad et al. (2014) argued that the trimmed mean and weighted median are essentially exclusion-based methods as these