Core Measures Inflation for Singapore/media/MAS/Monetary Policy and... · OUTPUT-NEUTRAL CORE INFLATION 17 5. CONCLUSION 22 ... inflation via a bivariate vector ... and evaluates

Occasional Paper No. 10December 1998

Economics DepartmentMonetary Authority of Singapore

Measures of Core Inflationfor Singapore

MEASURES OF CORE INFLATION FOR SINGAPORE

BY

DOMESTIC ECONOMY DIVISION*ECONOMICS DEPARTMENT

MONETARY AUTHORITY OF SINGAPORE

December 1998

* THE VIEWS IN THIS PAPER ARE SOLELY THOSE OF THE STAFF OF THE DOMESTIC ECONOMY DIVISION, AND SHOULD NOT BE ATTRIBUTED TO THE MONETARY AUTHORITY OF SINGAPORE

THE MONETARY AUTHORITY OF SINGAPORE

JEL CLASSIFICATION NUMBER: E31

MEASURES OF CORE INFLATION FOR SINGAPORE

Page

EXECUTIVE SUMMARY i-ii

1. INTRODUCTION 1

2. MEASURES OF CORE INFLATION FOR SINGAPORE 3

3. EVALUATION OF CORE INFLATION MEASURES 11

4. OUTPUT-NEUTRAL CORE INFLATION 17

5. CONCLUSION 22

Appendix: Technical Note on Estimation of Output-Neutral Inflation 23

References 27

MAS Occasional Paper No. 10, Dec 98

Economics Department, Monetary Authority of Singapore

i

EXECUTIVE SUMMARY

1 The primary objective of monetary policy in Singapore is to promote

low inflation as a sound basis for sustained economic growth. Indeed, economic

policies in most industrial countries over the past two decades have given

prominence to reducing the rate of inflation. In fact, a number of central banks have

in recent years introduced what can be called "inflation target regimes", with explicit

quantitative inflation targets.

2 Although inflation targets have often been expressed in terms of the

"headline" or consumer price index (CPI) inflation, most central banks are also

guided by some measure of underlying or core inflation in their conduct of monetary

policy. The rationale for a core measure of inflation stems from the fact that

monetary policy affects inflation with long and variable lags and, hence, is not suited

to targeting short-term fluctuations in inflation. In addition, monetary policy should

not react to changes in the price level associated with supply shocks. The CPI

basket also contains items subject to price controls or special taxes, the price

movements of which do not reflect market forces. Core inflation measures are

designed to reflect the underlying trend in prices caused by demand pressures on

production capacity and changing expectations of inflation, and disregard temporary

fluctuations in inflation arising from supply shocks.

3 However, distinguishing between temporary and underlying changes in

the rate of inflation is easier in theory than in practice. Early attempts at constructing

core measures of inflation involved statistically smoothing out price shocks from the

CPI in an ad hoc fashion. Such attempts, however, have been criticised for being

devoid of economic rationale. More recent endeavours include the volatility-

adjusted, median and trimmed mean inflation measures, and the output-neutral

inflation of Quah & Vahey (1995).

4 This paper estimates several such measures of core inflation for

Singapore and compares them with the one underlying measure of inflation

monitored by the MAS, viz. CPI inflation excluding changes in cost of private road

transport and accommodation. The MAS underlying and volatility-adjusted inflation



ii

attempt to address the weakness of the overall CPI inflation by systematically

excluding those components that are volatile or subject to controls and hence likely

to cause distortion to the measurement of an economy's underlying inflation. The

median and trimmed mean measures of inflation approach the same task by

respectively taking the 50th percentile and trimming off extreme inflation rates, in

order to limit the influence of excessively large and small price movements. The

output-neutral inflation, on the other hand, is derived by decomposing overall CPI

inflation via a bivariate vector-autoregressive model of CPI and real output.

5 A series of tests performed on the statistical properties of the various

core inflation measures suggest that no single measure is superior to the others and

that all provide useful information on the underlying inflation process. Thus, while

the median and 30%-trimmed mean inflation measures relate more closely to the

long-term trend of inflation, the MAS underlying and volatility-adjusted inflation

measures provide better short-term forecasts of inflation. All four measures of core

inflation are also less volatile than and cointegrated with overall CPI inflation. The

output-neutral core inflation measure, on the other hand, displays a striking inverse

relationship with changes in the exchange rate, which is the principal monetary

policy tool in Singapore.

6 The five measures of core inflation estimated for Singapore in this

paper would provide useful and complementary information on the underlying

inflation process that will help to further illuminate on monetary and exchange rate

policy.



1

1 INTRODUCTION

1.1 The primary objective of monetary policy in Singapore is to

promote low inflation as a sound basis for sustained economic growth.

Indeed, economic policies in most industrial countries over the past two

decades have given prominence to reducing the rate of inflation, which in

most countries is now back at its 1960s' level of about 3% or less. Most

central banks now accept that low inflation is essential for sustainable

economic growth and not, as was once thought, an alternative to it. The

trade-off between a bit more inflation and a bit less unemployment can still

be made in the short term. But cross-country experience over the last three

decades has shown that attempts to apply it in the long term do not work.

They simply result in ever-rising inflation. Price stability is now generally

accepted as laying the best foundation for sustained economic growth.

1.2 In fact, a number of central banks have in recent years

introduced what can be called "inflation target regimes", with explicit

quantitative inflation targets: New Zealand (1989), Canada (1991), United

Kingdom (1992), Sweden (1993) and Finland (1993). Although the targets

have often been expressed in terms of the "headline" or consumer price

index (CPI) inflation, most of these central banks are also guided by some

measure of underlying or core inflation in their conduct of monetary policy.

For example, the Reserve Bank of New Zealand (RBNZ) monitors the CPI

inflation adjusted for specific significant price changes such as commodity

price shocks, government charges or taxes and interest rate effects, while

the Bank of England (BOE) targets an underlying inflation based on the

Retail Price Index excluding mortgage interest payment. In Singapore,

besides the overall CPI inflation, the Monetary Authority of Singapore (MAS)

also monitors an underlying measure of CPI inflation which excludes price

changes of accommodation and private road transport.

1.3 The rationale for an underlying or core measure of inflation

stems from the fact that monetary policy affects inflation with long and

variable lags and, hence, is not suited to targeting short-term fluctuations in



2

inflation. In addition, monetary policy should not react to changes in the

price level associated with supply shocks, of which two types could be

identified. The first type of shock, such as a price hike in food crops due to

poor harvest, has only a passing effect on both the price level and the rate of

inflation. The second type of shock, such as the introduction of Goods and

Services Tax, has a permanent effect on the price level but only a temporary

one on inflation. In either case, the effect of the shocks on the price level

should be allowed to pass through. Hence, the trend rate of inflation

amenable to monetary policy actions should reflect the underlying trend in

prices caused by demand pressures on production capacity and changing

expectations of inflation, and disregard temporary fluctuations in inflation

arising from supply shocks.

1.4 However, distinguishing between temporary and underlying

changes in the rate of inflation is easier in theory than in practice. Early

attempts at constructing core measures of inflation involved statistically

smoothing out price shocks from the CPI in an ad hoc fashion. Such

attempts, however, have been criticised for being devoid of economic

rationale. More recent endeavours include the volatility-adjusted, median,

trimmed mean and output-neutral inflation measures. This paper estimates

and evaluates several such measures of core inflation for Singapore.

Section 2 briefly reviews the shortcomings of the CPI inflation and discusses

three measures of core inflation, namely the volatility-adjusted, median and

trimmed mean inflation. It describes the assumptions, methodology,

advantages and disadvantages of each core inflation measure, and

estimates the corresponding series for Singapore. Section 3 then evaluates

the estimated core inflation measures for Singapore in terms of their

statistical efficiency, predictive power and cointegration with the "headline"

CPI inflation measure. Section 4 introduces another measure of core

inflation known as output-neutral inflation associated with Quah & Vahey

(1995), and discusses its potential policy relevance for Singapore. Finally,

Section 5 concludes.



3

2 MEASURES OF CORE INFLATION FOR SINGAPORE

Shortcomings of CPI Inflation

2.1 The conventional or "headline" measure of inflation in almost

all countries is the rate of change of the CPI. CPI inflation measures the

change in prices of a basket of goods and services consumed by a

representative household, with the quantity and quality of the items in the

basket fixed at a certain base period. There are in general two broad sets of

problems associated with measuring inflation, including the CPI. The first

relates to measurement biases resulting from the weighting schemes,

sampling techniques, and quality adjustments used in the compilation and

aggregation of the component price indices. The second concerns transient

phenomena such as changing seasonal patterns and supply shocks that

should not bear on monetary policy. While the second set of problems is by

definition temporary, the first is not. This paper is concerned with extracting

an underlying trend rate of inflation relevant to monetary policy and, hence,

deals with the second set of difficulties. For a survey of the biases in

inflation measurement and estimates of their magnitude and implications,

see, for example, Gordon (1992), Shapiro & Wilcox (1996), and Wynne &

Sigalla (1993).

2.2 For the purpose of this paper, one major shortcoming of CPI as

a measure of inflation is that high frequency (e.g. monthly) CPI data

encapsulate short-lived price shocks, which may be erroneously perceived

as increases in underlying inflation, thereby prompting unnecessary policy

reaction. These shocks are often associated with supply shocks such as

crop failures due to inclement weather. Although low frequency (e.g. annual)

data would mitigate this problem somewhat, the timeliness of information in

the CPI data on potential price pressures would be considerably reduced. In

addition, the CPI basket also contains regulated items (e.g. utilities) or items

subject to price controls or special taxes, the price movements of which do

not reflect the true price mechanism of the market. For example, in

Singapore, tobacco and liquor are heavily taxed to discourage consumption,

and their price hikes arising from imposition of higher taxes should therefore



4

be allowed to pass through to the consumers rather than be counteracted by

monetary policy. Also, in countries where mortgage interest payment forms

one component of the CPI basket, monetary policy could be complicated by

its obverse effects on CPI inflation. For example, a hike in interest rate

associated with a tightening in monetary policy would raise the interest

component of the CPI and, possibly, a paradoxical increase in overall CPI

inflation.

2.3 As such, an underlying or trend rate of inflation stripped of such

temporary price shocks and idiosyncrasies is desirable from the standpoint

of monetary policy. There is, however, no unique definition of underlying or

core inflation, although an ideal measure should have the following

characteristics: (1) it should be able to distinguish between underlying and

one-off price movements; (2) it should be readily available and timely; and

(3) it should be easily replicable and verifiable. Some measures of core

inflation rely on specific adjustment or adjustment by exclusion or

replacement of certain volatile components of the CPI basket. More recent

constructs are based on agnostic adjustment to the distribution of CPI

inflation components. Bryan and Pike (1991) were the first to use this latter

approach to derive a core inflation measure based on the median of

changes in the components of the US CPI. This was followed by Bryan and

Cecchetti (1993), who examined the weighted median and weighted

averages of truncated distributions of inflation, and by Roger (1995), who

compared several statistical measures of underlying inflation with the core

measure then used by RBNZ. This line of research was further extended by

Cecchetti (1996), Bryan, Cecchetti and Wiggins II (1997), and Roger (1997),

among others.

Volatility-Adjusted Inflation

2.4 The most common measure of core inflation is the volatility-

adjusted CPI inflation. Pioneered by the U.S. Department of Labour, this

measure removes those items that exhibit excessive price volatility from the

CPI basket. For example, the U.S. Department of Labour monitors a

volatility-adjusted CPI inflation purged of food and energy (Bryan and



5

Cecchetti [1993]). The Bank of Canada (BOC) uses a core CPI excluding

food, energy and the effect of indirect taxes (Mishkin and Posen [1997]).

The Reserve Bank of Australia (RBA) used to target an underlying measure

of inflation that retained only about 50% of the original CPI basket as interest

charges, public sector goods & services, tobacco & alcohol, and seasonal

items were discarded (Reserve Bank of Australia Bulletin, Aug 1994).

However, it has recently switched to targeting the new CPI compiled by the

Australian Bureau of Statistics that now excludes mortgage rates, interest

charges for loans on consumer products and prices of foods such as meat

and fish. Similarly, commodity price shocks, government charges or taxes

and interest components are omitted from the RBNZ's volatility-adjusted

core inflation measure (Roger [1994]). Also falling within this category is one

underlying measure of inflation monitored by the MAS, which is CPI inflation

excluding changes in cost of private road transport and accommodation,

henceforth termed the MAS underlying inflation.

2.5 The key advantage of the volatility-adjusted inflation is its

intuitive and straightforward computation. However, it is plagued by a

number of subjective issues such as which and how many components to

exclude from the CPI basket, and the level of aggregation of these

components. These issues become more pertinent when historical price

patterns no longer hold. In terms of the level of aggregation, this paper uses

the price changes in 35 components of Singapore's CPI basket to compute

the volatility-adjusted inflation and the next two measures of core inflation:

median and trimmed mean inflation. Although the CPI comprises 631 items

at the most detailed level, the 35 components used in this paper represent

the lowest possible level of aggregation with continuous data series for the

same number of components over a sufficiently long sample period. At more

detailed levels of aggregation, it would be difficult to obtain contiguous data

series due to periodic reviews of the CPI basket, which lead to changes to

the weights and definition of the existing components and the addition of

new ones. At higher levels of aggregation, on the other hand, extreme price

movements in some sub-components might be concealed.



6

2.6 Chart 2.1 plots, in ascending order, the variances in price

inflation of the 35 CPI components over the period Jan 84 to Dec 97.

Variance is a measure of inflation volatility: the larger the variance the

higher the inflation volatility. The components with the largest variances and

hence most volatile inflation are, in descending order: cooking oil & fats,

vegetables & vegetable products, alcoholic drinks & tobacco, private road

transport, haberdasheries, private rented accommodation and owner-

occupied accommodation. Together, these 7 components account for 27%

of the CPI basket and are excluded to compute the volatility-adjusted

inflation. As indicated earlier, the issue of how many items to exclude is a

subjective one but, as a general rule, this paper excludes not more than 30%

of the items so that the remaining CPI basket is still representative of the

underlying inflation process.

Chart 2.1Inflation Variance of CPI Components, Jan 84 – Dec 97

publ

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2.7 Chart 2.2 compares the volatility-adjusted inflation with the

overall CPI inflation and MAS underlying inflation. On average for the entire

sample period, the volatility-adjusted inflation was lower than overall CPI

inflation, although it was only marginally less volatile than the latter.

Nonetheless, it appears better able to capture price pressures associated

with normal business cycles such as the deflationary environment caused by



7

the 1985-86 recession and the high growth period of 1994-95 arising from

the global electronics boom. The volatility-adjusted inflation also tracks the

MAS underlying inflation very closely. The MAS underlying inflation

excludes the cost of private road transport and accommodation from the

overall CPI basket. The cost of private road transport is excluded as it is

largely policy driven, by, for example, import duties, parking charges, road

and fuel taxes, and a vehicle quota system with the aim of checking traffic

congestion and its associated externality costs. The exclusion of

accommodation cost, on the other hand, was due in large part to the way in

which the cost of owner-occupied accommodation is computed. The

imputed rent approach is used, based on some sample rents provided by the

Inland Revenue Authority of Singapore. However, given that the majority of

Singaporean households live in government-constructed, owner-occupied

housing where there is a limited rental market, the sample rents used may

not be representative. In addition, as the typical rental contract period is 2

years, the actual market trend in rentals may be reflected in the CPI only

with some lag and, even then, not completely. This problem on the

imputation of the cost of owner-occupied accommodation is particularly

acute for Singapore, given that it accounts for about 13% of the CPI basket,

due to the high home-ownership rate of about 90% in Singapore.

Chart 2.2Overall CPI, Volatility-Adjusted and MAS Underlying Inflation

84 85 86 87 88 89 90 91 92 93 94 95 96 97

-4

-2

0

2

4

6

Per

cent

Yea

r-on

-Yea

r

Overall CPI Inflation

MAS Underlying Inflation

Volatility-Adjusted Inflation



8

Median and Trimmed Mean Inflation

2.8 Two relatively new yardsticks of core inflation are the median

inflation, introduced by Bryan & Pike (1991), and trimmed mean inflation, first

developed by Bryan & Cecchetti (1993). Both are so-called limited-influence

estimators of underlying inflation as they place greater weight on the general

price trend or tendency of prices, and less or no weight on extreme or

"outlier" price movements than does overall CPI inflation, which is a mean

rate of inflation. They capture the notion that the types of shocks that cause

problems with price measurements are infrequent, and that these shocks

tend to be isolated in a few sectors of the economy, at least initially. This is

based on the observations that the distribution of prices are characterised by

skewness caused by asymmetric response of price-setting agents. Since

only those agents who have relatively low adjustment costs and relatively

large price shocks may choose to react immediately to price increases, using

the mean of the distribution of initial price changes may overstate the

response to shocks.

2.9 If the distribution of the component price movements in the CPI

basket is symmetric, then the difference among the mean, median and

trimmed mean measures of inflation is of little significance as all three would

capture the underlying price trend. One key advantage of this method of

deriving core inflation measure is its systematic and rule-based, rather than

arbitrary and judgmental, adjustment. The median is the 50th percentile

inflation rate at which half of the components in the CPI basket have higher

inflation, and the other half less. The trimmed mean, on the other hand, is

the weighted average inflation rate after removing a certain percentage (by

weight) of the CPI components with the smallest and largest rates of

inflation. This paper considers a 30% trimmed mean inflation measure,

which is obtained by eliminating 15% each from both ends of the distribution

of CPI component inflation.

2.10 To illustrate the computation of the median and trimmed mean

inflation measures, consider a stylised CPI basket comprising 4 components

labelled A, B, C and D with weights of 15%, 30%, 40% and 15% and inflation



9

rates, arranged in ascending order, of 1.9%, 2.0%, 2.1% and 10.0%

respectively. (See Table 2.1.)

Table 2.1A Stylised CPI Basket

CPI Components

A B C D

Inflation Rate (%): 1.9 2.0 2.1 10.0

Weight in Basket (%): 15 30 40 15

Cumulative Weight (%): 15 45 85 100

Weight Truncated 15% on Each Side: 0 30 40 0

2.11 In this example, the overall or "headline" CPI inflation is given

by:

Overall CPI Inflation = (1.9 x 0.15) + (2.0 x 0.3) + (2.1 x 0.4) + (10.0 x 0.15) = 3.23%

As the cumulative weighting reaches 50% in the CPI component C, its

inflation rate of 2.1% is thus the median inflation. Finally, the 30% trimmed

mean inflation is calculated after removing 15% each of the components with

the smallest and largest inflation rates (Chart 2.3), thus:

30% Trimmed Mean Inflation = 1.9 x (0.15 – 0.15) + 2.0 x 0.3 + 2.1 x 0.4 + 10.0 x (0.15 –

0.15) / 0.7

= 2.06%

Chart 2.3Trimmed Distribution of CPI Component Inflation

1.9 2 2.1 10 Inflation Rate (%)

15%trimmed off

15%trimmed off



10

2.12 Based on these definitions, the median and 30% trimmed

mean measures of core inflation are computed for Singapore and compared

with the overall CPI inflation in Chart 2.4. As shown in the chart, the two

inflation series broadly trace the movements of overall CPI inflation. They

are also on average lower and less volatile than overall CPI inflation.

Chart 2.4Median, 30% Trimmed Mean and Overall CPI Inflation

84 85 86 87 88 89 90 91 92 93 94 95 96 97

-4

-2

0

2

4

6

Per

cent

Yea

r-on

-Yea

r


30% Trimmed Mean Inflation

Median Inflation



11

3 EVALUATION OF CORE INFLATION MEASURES

3.1 All four measures of core inflation discussed so far – MAS

underlying, volatility-adjusted, median and 30% trimmed mean inflation – are

based on the monthly overall CPI inflation, and their construction

methodology is explicit. As such, they are readily available and timely; and

can be easily replicated and verified. These are some of the desirable

characteristics of core inflation measures referred to in the last section. This

section examines further the statistical properties of the MAS underlying,

volatility-adjusted, median and 30% trimmed mean inflation to determine

their usefulness as measures of the underlying inflation process in

Singapore. More specifically, it evaluates and compares their statistical

efficiency, predictive power and cointegration with overall CPI inflation.

Statistical Efficiency

3.2 Intuitively, an estimator that has a higher likelihood of being

equal to the value that it is trying to estimate, is better than one that has a

lower probability of being so. In statistics, this criterion of "higher likelihood"

is termed the efficiency of the estimator, which can be measured by its

variance: an estimator is more efficient the smaller is its variance.

3.3 To analyse the statistical efficiency of the various core inflation

measures, a Monte Carlo or bootstrapping simulation exercise based on

actual data was conducted. The approach follows that in Cecchetti (1996).

First, the difference between the monthly inflation of each of the 35 CPI

components and the 36-month centered moving average of overall CPI

inflation is computed. The 36-month moving average is chosen as the

benchmark because the results in Bryan & Cecchetti (1993) suggest that

CPI inflation may provide an accurate measure of inflation over longer

horizons.1 This exercise is carried out for every month in the sample. With

CPI inflation data from Jan 1984 to Dec 1997, this produces a matrix of

inflation deviations with dimensions of 35 components by 133 months.

1 This implicitly assumes that there is no bias in the long run trend of CPI inflation.



12

3.4 Next, from the inflation deviation matrix, one observation from

each of the 35 components is randomly drawn and then pooled together to

create one "sample" of inflation deviation from the long run. This exercise is

repeated to generate 5,000 "samples", through sampling with replacement.

Based on these "samples", the variance is computed for each of the 5

inflation measures: (1) CPI inflation itself, (2) MAS underlying inflation, (3)

volatility-adjusted inflation, (4) median inflation, and (5) 30% trimmed mean

inflation. The results, as tabulated in Table 3.1, show that all four measures

of core inflation are more efficient estimators than the CPI inflation itself.

These findings are consistent with Bryan & Cecchetti (1996) who noted that

inflation distributions are highly leptokurtic (or fatter-tailed than the Normal

distribution), leading to high probabilities of drawing skewed samples. With a

leptokurtic distribution, there is a higher chance of drawing an observation in

one tail of the distribution, which is not offset by an equally extreme

observation in the other tail.

Table 3.1Inflation Variance Based on 5,000 Bootstrapped "Samples"

CPIInflation

MASUnderlying

Inflation

Volatility-AdjustedInflation

MedianInflation

30%Trimmed

Mean

Mean 0.2337 -0.1443 -0.2552 -0.2683 -0.2031

Variance 0.7877 0.5279 0.4905 0.5568 0.4285

Predictive Power

3.5 Another useful test to evaluate the various measures of core

inflation is their ability to forecast future inflation. This is accomplished using

a univariate forecasting equation of the form:

ΠKt = θ0 + θ1πt

C + εt

where ΠKt = [ln(CPIt+K) – ln(CPIt)] / K, with K being 1, 2 or 3 years

πtC

= one of the core inflation measures εt = error term

θ0,θ 1 = coefficients



13

3.6 The forecast variable of interest, ΠKt, is the overall CPI inflation

taken over longer horizons to rid it of short-term noise contamination. The

forecast performance of the various core inflation measures and of CPI

inflation itself at 1-, 2- and 3-year horizons is expressed in root-mean-

squared errors (RMSE) in Table 3.2.

Table 3.2Inflation Forecast Performance: Root-Mean-Squared Errors (RMSE)

Overall CPIInflation

MASUnderlying

Inflation


MedianInflation

30% TrimmedMean

One-Year Ahead ForecastEstimation period: 1984:1 to 1995:8 Forecast period: 1995:9 to 1996:12

0.5213 0.3492 0.3758 0.5136 0.5528

Two-Year Ahead ForecastEstimation period: 1984:1 to 1994:8 Forecast period: 1994:9 to 1995:12

0.6085 0.8176 0.8670 0.5760 0.5532

Three-Year Ahead ForecastEstimation period: 1984:1 to 1993:8 Forecast period: 1993:9 to 1994:12

0.4809 0.6889 0.8286 0.3635 0.3501

3.7 Thus, the MAS underlying inflation and volatility-adjusted

inflation provide better forecasts of inflation than overall CPI inflation itself at

the 1-year horizon. However, they are less useful at forecasting inflation at

longer horizons. This is not unexpected as both measures of core inflation

are computed by removing those items in the CPI basket which are known to

give rise to short term inflation volatility. In contrast, the median and 30%

trimmed mean inflation yield better inflation forecasts 2 to 3 years ahead,

with the 30% trimmed mean inflation the best predictor of long-term inflation.

These results suggest that all four core inflation measures contain useful

information about the future path of inflation, albeit at different forecast

horizons.



14

Cointegration with CPI Inflation

3.8 The idea behind core inflation measures is that total or overall

CPI inflation can be decomposed into core and transitory components: πt =

πtC + πt

T. The transitory component πtT, which is due to temporary shocks

such as weather, can reasonably be expected to be random with zero mean

and finite variance, as positive shocks are offset by negative shocks. In

other words, πtT is a stationary series. Thus, if overall CPI inflation is non-

stationary and integrated of order d, or I(d), i.e. it needs to be differenced d

times to achieve stationarity, then the core component πtC should also be

I(d). In addition, for it to be a meaningful and useful measure of underlying

inflation, the core component πtC should be cointegrated with overall CPI

inflation πt.2

3.9 To evaluate if each of the four measures of core inflation is

cointegrated with overall CPI inflation, they are first tested, along with CPI

inflation, for stationarity. This is accomplished via the Augmented Dickey-

Fuller (ADF) unit root test:

∆Πt = λ + φΠt-1 + ζ1∆Πt-1 + ζ2∆Πt-2 + …..+ ζi-1∆Πt-i+1 + νt

where the number of lags i is chosen such that the error term νt is rendered

white noise. The test hypotheses are:

H0: φ = 0 (i.e. presence of unit root)

vs

H1: φ < 0 (i.e. stationary or no unit root)

3.10 The test results, summarised in Table 3.3, show that overall

CPI inflation and all four measures of core inflation contain a unit root each,

i.e. they are integrated of order one, or I(1).

2 The analysis here draws on Freeman (1998).



15

Table 3.3ADF Unit Root Test Results (1984-97)

ADF Test Stat(Level)

ADF Test Stat(1st Diff)

Overall CPI Inflation -2.0234 -7.4625

MAS Underlying Inflation -2.3480 -7.0329

Volatility-Adjusted Inflation -2.6171 -5.7608

Median Inflation -2.0786 -8.3047

30% Trimmed Mean Inflation -2.0495 -7.8029Test statistics are compared with 5% critical values of –2.8791 (level) and –1.9417 (1st diff).

3.11 The next step is to test for cointegration between each of the

core inflation measures with overall CPI inflation. For this purpose, the

Engle-Granger (1987) residual-based test procedure is used. It is essentially

a unit root test of the residuals from the regression where πt and πtC are

overall and core inflation respectively:

πt = α + β.πtC + vt

3.12 The test results, summarised in Table 3.4, show that all four

measures of core inflation are cointegrated with overall CPI inflation. These

results are both assuring, as these core inflation measures should by intent

reflect the underlying inflation trend, and not surprising, as these measures

are by construction based on the overall CPI inflation. In addition, all four

measures of core inflation also have coefficients relatively close to unity.

Table 3.4Engle-Granger Cointegration Test Results (1984–97)

Coefficient, ββ ADF Test Statistic for Residual

MAS Underlying Inflation 0.8524 -3.7136

Volatility-Adjusted Inflation 0.7547 -4.0276

Median Inflation 1.0353 -3.8462

30% Trimmed Mean Inflation 0.9799 -3.7614

A comparison with the 5% critical value of –3.37 shows cointegration exists for all measures. The critical value used takes intoaccount the estimation of the cointegrating regression, and is obtained from J.D. Hamilton (1994). The original sources are P.C.B.Phillips and S.Ouliaris (1990) and Wayne A. Fuller (1976).



16

Granger-Causality Test

3.13 Another test of the information content of the various core

inflation measures is the Granger-causality test. For cointegrated variables,

the Granger-causality test employs the following standard vector error-

correction model (VECM):

∆πt = µ1 + γ1(πt-1 - α - β πt-1C

) + Σδ11(i)∆πt-i + Σδ12(i)∆πt-iC + u1t

∆πtC = µ2 + γ2(πt-1 - α - β πt-1

C ) + Σδ21(i)∆πt-i + Σδ22(i)∆πt-i

C + u2t

Granger-causality is obtained when the coefficients δmn and γm in each

equation are jointly significantly different from zero. The number of lags i is

chosen based on the Akaike Information Criterion (AIC). The Granger-

causality test is essentially a test of "temporal precedence".

3.14 Table 3.5 presents the results of the Granger-causality tests

between overall CPI inflation and each of the four measures of core inflation.

The table shows that overall CPI inflation does not "Granger cause" any of

the core inflation measures, and only the MAS underlying inflation "Granger

causes" overall CPI inflation.

Table 3.5Granger-Causality Test Results

MASUnderlying

Inflation


MedianInflation

30% TrimmedMean Inflation

Hypothesis: CPI Inflation is not Granger-caused by …

F 2.6717 1.1870 1.0895 1.1593

p-value 0.0019** 0.2959 0.3738 0.3147

Hypothesis: CPI Inflation does not Granger-cause …

F 1.1225 1.0173 1.7649 1.7211

p-value 0.3448 0.4388 0.0554 0.0591

** Significant at the 95% confidence level.



17

4 Output-Neutral Core Inflation

4.1 This section examines one recent measure of core inflation

introduced by Quah & Vahey (1995). Known as the output-neutral inflation,

this measure of core inflation is perhaps one most grounded in economic

theory. It is based on the proposition that inflation is a process which results

from perturbations to the economy over time. These perturbations can be

meaningfully separated into those that do not affect real output in the long

run (nominal demand shocks) and those that do (supply shocks). Quah &

Vahey (1995) define core inflation as that component of inflation that is

attributed to nominal demand shocks and, thus, is uncorrelated with real

output in the long run. This concept of core inflation is consistent with the

widely held view in macroeconomics that, in the long run, the Phillips curve

is vertical, i.e. monetary shocks have no lasting impact on real output but will

affect inflation. As such, monetary policy could not and should not be used

to counteract price changes arising from supply-side shocks.

4.2 The output-neutral measure of core inflation is constructed

using a bivariate Structural Vector-Autoregressive (SVAR) model of CPI and

real GDP based on Blanchard & Quah (1989). Essentially, the model

decomposes CPI inflation into two components: the first is the non-core

component which is projected into the plane spanned by shocks affecting

long-run output; and the second is the output-neutral inflation component

which is orthogonal to the first. Thus, unlike the earlier four measures of

core inflation, the construction of output-neutral inflation does not require any

component of the CPI basket to be discarded a priori, which may lead to a

loss of important information about the inflationary process. It also does not

restrict the core inflation to be non-volatile. A more technical exposition of

the model for constructing output-neutral inflation is provided in the

Appendix.

4.3 The estimated output-neutral inflation for Singapore is

presented in Chart 4.1 and compared with the non-core component and



18

overall CPI inflation.3 By design, only a quarterly series of output-neutral

inflation could be constructed and the series of statistical tests of the last

section could not be entirely replicated. Nonetheless, there are a number of

noteworthy features. First, the output-neutral core inflation is on average

lower and less volatile than overall CPI inflation. For the period 1977-97, it

averaged around 0% p.a. with a standard deviation of about 1.95%,

compared with overall CPI inflation which averaged 2.8% p.a. with a

standard deviation of 2.54%.

Chart 4.1Output-Neutral (Core), Non-Core and Overall CPI Inflation

77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Per

cent

Yea

r-on

-Yea

r


Non-Core Inflation Output-NeutralCore Inflation

4.4 Second, the measured or "headline" CPI inflation in Singapore

has been largely driven by the non-core inflation component, with a high

correlation coefficient of 0.66. The non-core inflation component is, by

construction, a function of supply-side perturbations and its movements

during the study period captured the following major supply-side

phenomena:

3 The authors would like to thank Prof. Danny Quah for his advice and for making

available the programme source code for estimating the output-neutral inflation.Prof. Quah visited the MAS Economics Department in August 1997.



19

• Early 1980s: the second "oil price shock" and the implementation of

"high-wage" policy aimed at restructuring the economy towards more

capital-intensive industries.

• Mid-1980s: the collapse in world commodity prices and the

introduction of a package of cost-cutting measures to restore

Singapore's external competitiveness following the economic

recession in 1985-86.

• Early 1990s: the hike in oil prices as a result of the Gulf War.

4.5 Third, the output-neutral core inflation displays a striking

inverse relationship with changes in the nominal effective exchange rate

(NEER) of the Singapore dollar, particularly following the implementation of

an exchange rate-centred monetary policy in 1981. It also appears to

respond to exchange rate changes very quickly. (See Chart 4.2.) As the

output-neutral inflation component is, by construction, a function of nominal

demand shocks, these findings suggest that the exchange rate policy exert

an immediate salutary effect on demand-induced inflationary pressures.

This is not surprising given the small and open nature of the Singapore

economy, with its tight but fairly flexible labour market. As external demand

accounts for about two-thirds of total demand in Singapore, the exchange

rate has an important influence on demand for domestic resources,

especially the demand for labour. A weak exchange rate can lead to

overheating of the economy, a tighter labour market and a consequent

higher growth of domestic wages and other costs, which in turn result in

higher inflation. The converse is also true.

4.6 The trends in output-neutral inflation can be discussed in the

context of Singapore's monetary policy over the last 20 years or so. Thus,

the period 1976-79 was marked by sustained and healthy economic growth

against a background of low inflation. Given the contractionary impact of

government's fiscal surpluses, monetary policy during this period was aimed



20

largely at replenishing adequate liquidity into the banking system. During

1980-84, Singapore's GDP growth averaged 8.5% p.a. At the same time,

overall CPI inflation accelerated from 4.1% in 1979 to average 8.3% in 1982-

83, reflecting the effects of the second oil price shock, rise in world

commodity prices and the implementation of high wage policy to encourage

the restructuring of the economy towards capital-intensive industries.

Concomitantly, monetary policy, which began to focus on the exchange rate,

was tightened in response. Even so, as Chart 4.2 shows, the secondary

effects of these inflationary pressures could not be offset entirely and had

been passed through to the core inflation component. These inflationary

pressures only abated towards the end of the period.

Chart 4.2Output-Neutral Inflation and Change in NEER 4

77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Per

cent

Yea

r-on

-Yea

r

Output NeutralCore Inflation

Change in NEER

4.7 During 1985-87, Singapore experienced its first post-

independence economic recession in 1985, which was precipitated by a

confluence of factors including the collapse of construction boom and

cyclical downturns in electronics, ship-repairing, regional tourism and

entrepot trade. In response, the government implemented a package of cost

and tax reduction measures to restore Singapore's external competitiveness.

4 This is not the official NEER monitored by the MAS. The NEER series used in this

study is computed using the published trade weights of Singapore's top 10 tradingpartners.



21

This, together with an attenuation of external inflationary pressures, enabled

the exchange rate policy to be eased during this period to facilitate economic

recovery. As a result, GDP growth rebounded strongly to register 9.7% in

1987 and 11.6% in 1988. By mid-1988, the economy was at full

employment. As wage growth persistently outstripped productivity growth,

unit labour costs accelerated. With foreign inflationary pressures also

mounting, overall CPI inflation rose to 3.5% in 1990-91 from 1.5% in 1988.

The exchange rate policy during much of the period 1988-97 was thus aimed

at offsetting inflationary pressures from abroad and those generated

domestically. As a result, demand induced inflation, as evidenced by the

core measure, was on the whole absent during this period. (For a more

detailed discussion of monetary policy in Singapore over the last three

decades, see MAS [1996].)

4.8 In summary, overall CPI inflation in Singapore over the last 20

years or so has been mainly driven by supply-side shocks. Monetary policy

during this period has been quite effective in checking demand-induced

inflation, as shown by the trends in output-neutral inflation. Nonetheless, the

applicability of the output-neutral inflation as a potential target of exchange

rate policy in Singapore requires further analysis, particularly in respect of its

optimal level or band, before formal implementation can be considered.



22

5 Conclusion

5.1 This paper examines several measures of core inflation that

have received increasing attention by monetary policy makers in recent

years. These measures include the MAS underlying inflation, volatility-

adjusted inflation, median inflation, 30% trimmed mean inflation and the

output-neutral inflation of Quah & Vahey (1995). The MAS underlying and

volatility-adjusted inflation attempt to address the weakness of the overall

CPI inflation by systematically excluding those components that are volatile

and hence likely to cause distortion to the measurement of an economy's

underlying inflation. The median and 30% trimmed mean approach the same

task by respectively taking the 50th percentile and trimming off extreme

inflation rates, in order to limit the influence of excessively large and small

price movements. The output-neutral inflation, on the other hand, is derived

by decomposing overall CPI inflation via a bivariate VAR model of CPI and

real output.

5.2 The series of tests performed on the statistical properties of the

various core inflation measures suggest that no single measure is superior to

the others and that all provide useful information on the underlying inflation

process. Thus, while the median and 30% trimmed mean inflation measures

relate more closely to the long-term trend of inflation, the MAS underlying

and volatility-adjusted inflation measures provide better short-term forecasts

of inflation. All four measures of core inflation are also less volatile than and

cointegrated with overall CPI inflation. The output-neutral core inflation

measure, on the other hand, displays a striking inverse relationship with

changes in the exchange rate, which is the principal monetary policy tool in

Singapore.

5.3 As such, the five measures of core inflation estimated for

Singapore in this paper would provide useful and complementary information

on the underlying inflation process that will help to further illuminate on

monetary and exchange rate policy.



23

AppendixTechnical Note on Estimation of Output-Neutral Inflation

(Based on Quah and Vahey [1995])

Notation:

∆Y, ∆P : change over 4 quarters ago in logs of GDP and CPI

respectively5

η1,η2 : serially uncorrelated disturbance ("shock") terms

Define X = (∆Y, ∆P)' and η = (η1, η2)'

Let X be generated by the following "Moving Average-like" process:

X(t) = D(0)η(t) + D(1)η(t-1) +….

= ∑∞

=0j

D(j)η(t-j) Var(η) = Ι [1]

where D(j)s are (2x2) matrices of coefficients or in its decomposed form:

∆Y = d11(0)η1(t) + d12(0)η2(t) +

d11(1)η1(t-1) + d12(1)η2(t-1) +…

= ∑∞

=0j

d11(j)η1(t-j) + ∑∞

=0j

d12(j)η2(t-j) [1a]

∆P = d21(0)η1(t) + d22(0)η2(t) +

d21(1)η1(t-1) + d22(1)η2(t-1) +…

= ∑∞

=0j

d21(j)η1(t-j) + ∑∞

=0j

d22(j)η2(t-j) [1b]

where dmn(j) are elements of the D(j) matrices

5 Unit root tests show both series to be stationary over 1977-97, which is required for

the analysis.



24

Basically, equation [1] or its decomposed form says that output growth and

inflation can be attributed to current and past values of 2 types of

disturbances, η1 and η2.

Looking at [1a], the long run output-neutrality condition is given by:

∑∞

=0j

d11(j) = 0

i.e. the coefficients of η1(t),η1(t-1),η1(t-2),… sum to zero so that (collectively)

η1 will not cause any change in long run real output, Y, or output-neutral. As

such, ∆Y is now solely caused by η2.

On the other hand, ∆P (as shown in [1b]) is affected by both η1, which has

been rendered output-neutral in the above, and η2, which has an impact on

long run real output. A natural candidate for inflation that is output-neutral is

then the first summation term involving η1 in [1b] i.e.

∑∞

=0j

d21(j)η1(t-j)

Hence, to compute the output-neutral core inflation, values for d21(j) (the

bottom left-hand element of the D(j) matrices) and η1(t-j) (the first component

of η(t-j)) are needed.

To get estimates of d21(j) and η1(t-j), or more generally D(j) and η(t-j), from

the data, first estimate a Vector Autoregressive (VAR) for X. Invert it to

obtain its Moving Average (MA) representation:

X(t) = e(t) + C(1)e(t-1) + ….

= ∑∞

=0j

C(j)e(t-j) Var(e) = Ω [2]



25

Note the similarity between the estimated model [2] and the theoretical

model [1].

Assuming that η is a linear combination of e, the following conditions are

obtained from [1] and [2]:

e = D(0)η [3]

(To see this, compare the first terms of [2] and [1].)

D(j) = C(j)D(0) j=1,2,… [4]

(To see how [4] is obtained, substitute [3] into the second term in [2]. Now,

compare it to the second term in [1].)

Recall that the interest is in η(t-j), which appears in [3], and D(j), which

appears in [4].

From [2], the value of e(t-j) can be obtained. Thus, if D(0) is also known, η(t-

j) can be estimated using [3]. Similarly C(j) can be extracted from [2].

Knowing D(0) then allows the computation of D(j) via [4].

To compute D(0) (a 2x2 matrix), note that 3 restrictions are imposed on it by

D(0)D(0)'= Ω. To see this, note that [3] implies

Var(e) = D(0) Var(η) D(0)'

= D(0) D(0)' as Var(η)= I from [1]

From [2], Var(e)= Ω, therefore D(0)D(0)'= Ω.

The fourth restriction on D(0) is imposed by the long run output neutrality

condition. Specifically, let S be the unique lower triangular Cholesky factor of

Ω. Thus, D(0) is an orthonormal transformation of S. Given that S is known,



26

the identification of the orthonormal transformation then allows the

computation of D(0). To identify this orthonormal transformation, the

orthogonality condition implied by the output neutrality restriction is used.

With D(0) solved, η(t-j) can be calculated using [3] and e(t-j), which was

estimated in [2]. D(j), too, can be computed via [4], with C(j) also estimated

earlier on in [2].

To calculate core inflation, only the components d21(j) and η1(t-j) need to be

extracted from D(j) and η(t-j) respectively.



27

REFERENCES

Blanchard, O.J. and D.T. Quah. 1989. "The Dynamic Effects of Aggregate

Demand and Supply Disturbances", American Economic Review, 79, pp

655-673.

Bryan, M.F. and C.J. Pike. 1991. "Median Price Changes: An Alternative

Approach to Measuring Current Monetary Inflation", Federal Reserve Bank

of Cleveland Economic Commentary, December.

Bryan, M.F. and S.G. Cecchetti. 1993. "Measuring Core Inflation", NBER

Working Paper No. 4303. National Bureau of Economic Research,

Cambridge, MA.

Bryan, M.F., S.G. Cecchetti and R.L. Wiggins II. 1997. "Efficient Inflation

Estimation", NBER Working Paper No. 6183. National Bureau of Economic

Research, Cambridge, MA.

Cecchetti, S.G. 1996. "Measuring Short-Run Inflation for Central Bankers",

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Engle, R and C. Granger, 1987. "Cointegration and Error Correction:

Representation, Estimation and Testing," Econometrica, 35, pp 251-276

Freeman, D.G. 1998. "Do Core Inflation Measures Help Forecast

Inflation?", Economic Letters, 58, pp 143-147.

Fuller, W.A. 1976. Introduction to Statistical Time Series, Wiley, New York,

p.373.

Gordon, R.J. 1992. "Measuring the Aggregate Price Level: Implications for

Economic Performance and Policy", NBER Working Paper No. 3969.

National Bureau of Economic Research, Cambridge, MA.



28

Hamilton, J.D. 1994. Time Series Analysis, Princeton University Press, New

Jersey, Appendix B, p 766.

Johansen, S. 1991. "Estimation and Hypothesis Testing of Cointegration

Vectors in Gaussian Vector Autoregressive Models," Econometrica, 59, pp

1551-1580

Mishkin, F.S. and A.S. Posen. 1997. "Inflation Targeting: Lessons from

Four Countries", Federal Reserve Bank of New York Economic Policy

Review, Special Issue on Inflation Targeting, pp 9-110.

Monetary Authority of Singapore (MAS), 1996. Monetary Authority of

Singapore Annual Report 1995/96. Singapore.

Phillips, P.C.B. and S. Ouliaris. 1990. "Asymptotic Properties of Residual

Based Tests for Cointegration," Econometrica, 58, p 190

Quah, D.T. and S. P. Vahey. 1995. "Measuring Core Inflation", Centre for

Economic Policy Research Discussion Paper No. 1153.

Reserve Bank of Australia, 1994. Reserve Bank of Australia Bulletin, August

issue, pp 5-9.

Roger, S. 1994. "Alternative Measures of Underlying Inflation", Reserve

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Roger, S. 1995. "Measures of Underlying Inflation in New Zealand, 1981-

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1949-96", Discussion Paper No. G97/7. Reserve Bank of New Zealand,

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29

Shapiro, M.D. and D.W. Wilcox. 1996. "Bias in the Consumer Price Index",

in B. Bernanke and J. Rotemberg, eds. NBER Macroeconomics Annual,

Cambridge, MA.: MIT Press.

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Indexes", Federal Reserve Bank of Dallas Research Paper No. 9340.

* All MAS Occasional Papers in Adobe Acrobat (PDF) format can be downloaded at the MASWebsite at http://www.mas.gov.sg.

MAS OCCASIONAL PAPER SERIES*

Number Title Date

1 Current Account Deficits in the ASEAN-3: Is There Cause for Concern?

May 1997

2 Quality of Employment Growth in Singapore: 1983-96

Oct 1997

3 Whither the Renminbi? Dec 1997

4 Growth in Singapore's Export Markets, 1991-96: A Shift-Share Analysis

Feb 1998

5 Singapore’s Services Sector in Perspective: Trends and Outlook

May 1998

6 What lies behind Singapore’s Real Exchange Rate? An Empirical Analysis of the Purchasing Power Parity Hypothesis

May 1998

7 Singapore’s Trade Linkages, 1992-96: Trends and Implications

Aug 1998

8 Impact of the Asian Crisis on China: An Assessment

Oct 1998

9 Export Competition Among Asian NIEs, 1991-96: An Assessment

Oct 1998

10 Measures of Core Inflation for Singapore Dec 1998

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