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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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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.
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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.
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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.
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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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20
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80
100
120
CPI components
vari
ance
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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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
Overall CPI Inflation
30% Trimmed Mean Inflation
Median Inflation
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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.
MAS Occasional Paper No. 10, Dec 98
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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
MAS Occasional Paper No. 10, Dec 98
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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
Volatility-AdjustedInflation
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.
MAS Occasional Paper No. 10, Dec 98
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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).
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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).
MAS Occasional Paper No. 10, Dec 98
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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
Volatility-AdjustedInflation
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.
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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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
MAS Occasional Paper No. 10, Dec 98
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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
Overall CPI Inflation
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.
MAS Occasional Paper No. 10, Dec 98
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• 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
MAS Occasional Paper No. 10, Dec 98
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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.
MAS Occasional Paper No. 10, Dec 98
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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.
MAS Occasional Paper No. 10, Dec 98
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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.
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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.
MAS Occasional Paper No. 10, Dec 98
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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]
MAS Occasional Paper No. 10, Dec 98
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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,
MAS Occasional Paper No. 10, Dec 98
Economics Department, Monetary Authority of Singapore
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.
MAS Occasional Paper No. 10, Dec 98
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Hamilton, J.D. 1994. Time Series Analysis, Princeton University Press, New
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* 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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