EVALUATING CORE MEASURES OF
INFLATION IN GHANA
1.0 Introduction
The traditional function of every central bank is to achieve and maintain price
stability, which is a pre requisite for sustainable economic development. As
confirmed by many empirical studies, stable inflation rate provides the best
environment to promote growth. Similarly, Bank of Ghana is committed to
maintain price stability with a view to provide a necessary condition to foster
economic growth.
This role of monetary policy makes it essential for policy makers to focus and
distinguish the basis of price movements to enable them know the price
movements due to a persistent trend and the part that constitutes temporary
fluctuations to the price trend. This is founded on a widely shared view that
the monetary authorities cannot control all sources of inflation. A monetary
policy response to a transient shock, usually a supply shock, may aggravate
the inflationary pressures in the short term. As a result, monetary authorities
in assessing inflationary pressures prefer to focus on the persistent
component of inflation often referred to as core inflation.
The core inflation concept is based on the premise that in the long run it is
monetary policy that determines the price level, whereas in the short run nonmonetary factors are the likely reason behind temporary deviations of the
price level from its long-run trend.
It is therefore not surprising that some countries which have instituted explicit
inflation targeting framework focus on the persistent component of inflation
since that is the measure of inflation which monetary policy changes can
affect and further on to the headline inflation in an extended period of time.
Likewise, some of the central banks with inflation targeting framework have
adopted core inflation as their operational target for policy1.
Since there is no agreed method for the measurement of the core inflation
and also an observation that different measures of core inflation are
associated with different trends, it becomes imperative that these measures
of core inflation are evaluated to identify the measure that may be more
useful for policy in Ghana. Clark (2001) has indicated that whether one
particular measure or an indicator is better or superior than another depends
much on the practical considerations such as empirical performance and
difficulty in estimating it.
Again, Ghana has already implemented some elements of inflation targeting
and in the process to institute explicit inflation targeting framework and
therefore makes it crucial to identify an operational target, which can be
controlled by the policy makers.
1
Canada, United Kingdom, Thailand and South Africa
Following this, the paper seeks to evaluate the available core measures used
in Ghana to identify a suitable indicator that may be useful in formulating
monetary policy in Ghana. The paper will also review the theoretical literature
on core inflation concept. Various core measures of inflation in Ghana is
highlighted in section three while section four and five review the properties
of a good indicator of a core inflation as well as descriptive analysis of the
core measures respectively. The study further uses econometric tools to
evaluate the core measures and conclude with the summary of the results
and some policy recommendations.
2.0 Brief Theoretical Literature On Core Inflation Concept
Core inflation is a widely used measure of inflation by many central banks in
conducting monetary policy but there is still not a generalised theoretical
definition or an agreed method for its measurement. It has been observed
that all the practical forms of measuring the core inflation have focused on
two broad concepts as the persistent and the generalised components of
measured inflation. These concepts are linked with expectations and demand
pressure components of the measured inflation but exclude supply shocks.
2.0.1 Core Inflation As a Persistent Inflation
Friedman (1963) emphasised the distinction between a steady inflation and
an intermittent inflation. According to Friedman, the persistent element of
inflation tends to be incorporated into expectations, which will consequently
be relatively controlled whiles the transient inflation will be less benign, as it
will be less readily anticipated.
Laidler and Parkin (1975) also recognised the core inflation as the element of
persistent inflation through their definition of inflation as “… process of
continuously rising prices, or a continuously falling value of money”. It is
therefore clear from this that the persistence or the continuity of price
changes form the defining characteristic of inflation.
Perhaps from the above, Quah and Vahey (1995) define the core inflation as
“…. the component of the inflation that has no medium to long-term impact
on real output”. Following from this it can easily be indicated that the
component of inflation (output neutral over medium-long term) must reflects
inflation expectations.
Roger (1998), in an effort to throw more light into Quah and Vahey (1995)’s
definition indicated that, much is dependent on how one chooses to define
the distinction between the short and the medium term, Quah and Vahey
definition of core inflation does include cyclical movements in inflation
associated with excess demand pressures. This is clearly demonstrated from
the short run aggregate supply curve stated as follows:
∏
= ∏ LR + g ( X t −1 ) + vt
t
Where:
∏
∏
(0.1)
Is the aggregate inflation rate in period t
t
LR
varying)
X t −1
vt
Is the long run or trend inflation rate (which may be time
Is a measure of cyclical excess demand pressures.
Is a measure of transient disturbances to inflation.
Given the above, the Quah and Vahey definition of core inflation can be
characterised as:
∏
= ⎡⎣∏ t −vt ⎤⎦ = ∏ tLR + g ( X t −1 )
c
t
(0.2)
While non-core inflation is:
∏
(0.3)
nc
t
= vt
Eckestein (1981) noted that the core inflation as the persistent component of
inflation, implicitly in the definition of core inflation as the “ the trend increase
of the cost of the factors of production”. He further distinguished the
persistent component of measured inflation from inflation resulting from the
supply shocks and cyclical changes in inflation from aggregate demand
changes. Parkin (1984) indicated that Eckestein’s definition of core inflation
amounts to the expected steady-state inflation rate, consistent with
Friedman’s description of steady inflation explained above.
This can be expressed as follows:
∏
t
= ∏ e t + g ( X t ) + vt
(1.4)
Where:
∏
∏
Is the aggregate inflation rate in period t
t
Is the expected inflation rate
e
t
Is a measure of excess demand pressure
Is a measure of supply disturbances to inflation
Xt
vt
then in steady state, where X t = 0 and vt = 0
∏
t
=
∏
e
t
(1.5)
Eckstein’s definition of core inflation,
∏
c
t
= ⎡⎣∏ t − g ( X t ) − vt ⎤⎦ = ∏ te
∏
e
t
, is:
(1.6)
This equals the expected inflation rate in steady state, while non-core
inflation,
∏
nc
t
, is:
∏
nc
t
= g ( X t ) + vt
(1.7)
Clearly, given the two definitions, that is, Quah and Vahey and Eckstein, two
clear differences can be drawn from these definitions. The definition by the
Quah and Vahey includes inflation changes that can have a short-term impact
on output; implicitly corresponding to inflation related to excess demand
pressures. The second difference could be drawn from inflation expectations.
Whereas Eckstein’s definition seems to be more consistent with a long-term
inflation expectation, the Quah and Vahey’s definition is more consistent with
short-term expectations including cyclical influences.
The differences between the two definitions should not be over-drawn. In
reality, there is likely a continuous spectrum of degrees of persistence in
disturbances to inflation, so that the distinctions made between transient,
cyclical and long-term influences on inflation is a somewhat artificial
simplification. In such circumstances, the choice of definition of core inflation
should primarily reflect the length of the policy-maker’s horizon: if the
policymaker focuses on a medium-term horizon in setting the stance of policy,
then Quah and Vahey’s definition is appropriate. Alternatively, if the relevant
policy horizon is longer, then Eckstein’s definition of core inflation may be
more relevant. In both definitions, however, disturbances having only a
transient impact on inflation, usually associated with supply disturbances, are
outside the definition of core inflation. In principle, therefore, the core
inflation rate – whether Eckstein’s version or Quah and Vahey’s should exhibit
more persistence or less variability than the aggregate measured inflation
rate.
2.0.2 Generalised Components of Inflation
An alternative conception of core inflation is based on Arthur Okun’s (1970)
definition of inflation as “…a condition of generally rising prices.” In this
conception, measured inflation is viewed as comprising a generalised or core
inflation component associated with expected inflation and monetary
expansion, as well as a relative price change component, mainly reflecting
supply disturbances (Roger 1995). Relative price disturbances are regarded as
‘noise’ obscuring the more general or underlying evolution of prices.
Absolutely, advocates of core inflation as generalised inflation take the view
that supply shocks are the most important source of relative price changes. In
this case, the conception of core inflation as generalized inflation corresponds
closely to the definition proposed by Quah and Vahey, since supply-driven
relative price changes affecting the aggregate rate should only have a
transient effect.
3.0 Desirable Properties of Core Inflation
Generally, the central banks, especially with explicit inflation
concerned with both the recurring tendency of inflation as well
state or long-run expected value. However, central banks
distinguish between permanent and transient, or generalized
price inflation.
targets, are
as its steady
do seek to
and relative
Usually the core measure of inflation has fairly two distinctive uses, thus
formulating monetary policies, through its ability to track current and future
trend in inflation as well as providing policy accountability. These uses largely
determine the desirable properties of a measure of core inflation. Inferring
from this, the core measure of inflation is expected to exhibit the following
qualities2 for it to function effectively: thus a good indicator should be robust
and unbiased, timely and credible.
With respect to the quality of robust and unbiasedness, Roger (1998)
indiacted that a measure of underlying inflation that does a poor job in
distinguishing between persistent (demand related and expectations) and
transient (supply related) movements in inflation cannot play its role
effectively. Importantly, in both the policy formulation and the provision of
policy accountability, the measure must not be significantly biased relative to
the headline inflation. In other words, changes in headline inflation resulting
from the temporary effects should not be reflected in the underlying measure
of inflation. If the measure shows a persistent bias, its credibility in providing
a public accounting for inflation performance could be jeopardized.
It is important also to have a core measure of inflation, which is timely. If the
measure of core inflation is not timely, appropriate policy adjustments based
on the information conveyed by the measure will be delayed, with adverse
consequences for the variability of activity and inflation. Alternatively, policy
adjustments will be made without regard to the measure, in which case the
measure will be of little or no value in policy formulation.
Again, the core measure of inflation will not perform its function effectively if
the core measure of inflation itself is not credible. It is expected that
credibility will be assured if either the measure of inflation is calculated
2
As suggested by Roger (1998)
externally or can easily be verified by the external agents. This reduces the
uncertainty amongst the public, even if the central banks may be fair in
reporting underlying inflation, therefore enhancing credibility.
Credibility will also be enhanced if the measure is reasonably easily
understood by outside agents. Although it is probably not essential that the
technical construction of the measure be widely understood (just as the
intricacies of the construction of the CPI are not widely understood), it
probably is quite important that the basic approach taken to construct the
measure be able to be conveyed in a non-technical way. Similarly, the
deviation of the core inflation from the headline inflation must be explained in
a quite non-technical terms to the understanding of the outside agents.
4.0 Measures of Core Inflation in Ghana
The following measures of inflation will be considered, classified under the
broad categories, as core inflation by objective exclusion, core inflation by
systematic exclusion (Trimmed means), and underlying inflation by
smoothing.
4.0.1 Underlying Inflation by Objective Exclusion
The most commonly approach of measuring core inflation is the method
where certain items, usually the volatile, seasonal as well as the
administrative or control prices (energy and transport fares) are excluded
from the consumer price index. These measures, as with other exclusion
methods, use historical volatility of components to derive underlying inflation.
Usually food prices are subjected to seasonal fluctuations, as they have
exhibited to be volatile and often temporary in nature.
Clearly, significant fluctuations in food prices have always resulted from
seasonal factors and often these prices return to normal if supply is restored.
Therefore excluding these fluctuations and focusing on the core will go a long
way to reduce uncertainty around inflation trend.
Similarly, energy is mostly excluded on account that the production related
shocks from the consumer price index are removed. It has been indicated
that supply-side movements usually cause changes in energy prices which
often result from OPEC–led cutbacks in production, so they may not be the
underlying inflationary pressures prevailing in the domestic economy.
The advantages of exclusion measures are that they are timely, easy to
compute and explain. However, the downside is that they require (subjective)
judgment about what the least informative price components are for
estimating core inflation. To some extent, valuable information may be
ignored by exclusion.
In Ghana, this method is mostly used through INFXEU, INFXEUF, INFXEUFT
and INFXAFE and shown on the graphs below:
CPI Inflation and INFXEUF Core Inflation
CPI Inflation and INFXEU Core Inflation
INFXEU
CPI
INFXEUF
35.0
35.0
30.0
30.0
25.0
per cent
25.0
per cent
CPI
20.0
15.0
20.0
15.0
10.0
10.0
5.0
5.0
0.0
Ja
n03
Ap
r-0
3
Ju
l-0
3
O
ct
-0
3
Ja
n04
Ap
r-0
4
Ju
l-0
4
O
ct
-0
4
Ja
n05
Ap
r-0
5
Ju
l-0
5
O
ct
-0
5
Ja
n06
Ap
r-0
6
Ja
n0
M 3
ar
M 03
ay
-0
Ju 3
l- 0
Se 3
p0
N 3
ov
-0
Ja 3
n0
M 4
ar
M 04
ay
-0
Ju 4
l- 0
Se 4
p0
N 4
ov
-0
Ja 4
n0
M 5
ar
M 05
ay
-0
Ju 5
l- 0
Se 5
p0
N 5
ov
-0
Ja 5
n0
M 6
ar
-0
6
0.0
period
period
CPI Inflation and INFXAFE Core Inflation
CPI Inflation and INFXEUFT Core Inflation
INFXAFE
CPI
CPI
35.0
30.0
25.0
25.0
per cent
30.0
20.0
15.0
20.0
15.0
10.0
10.0
5.0
5.0
n03
Ap
r-0
3
Ju
l-0
3
O
ct
-0
Ja 3
n04
Ap
r-0
4
Ju
l-0
4
O
ct
-0
Ja 4
n05
Ap
r-0
5
Ju
l-0
5
O
ct
-0
Ja 5
n06
Ap
r-0
6
Ja
period
n0
Ap 3
r-0
3
Ju
l-0
3
O
ct
-0
Ja 3
n0
Ap 4
r-0
4
Ju
l-0
4
O
ct
-0
Ja 4
n0
Ap 5
r-0
5
Ju
l-0
O 5
ct
-0
Ja 5
n0
Ap 6
r-0
6
0.0
0.0
Ja
per cent
INFXEUFT
35.0
period
4.0.2 Systematic Exclusion - Trimmed Mean
Trimmed mean core inflation was proposed by Bryan and Cecchetti (1994) to
track the underlying inflation. The trimmed mean removes from overall
inflation all large relative price changes in each month, with the set of
excluded components changing from month to month. In particular, the
trimmed mean excludes the percent changes in price that rank among the
smallest and the largest (in numerical terms) changes for the month.
Generally, a higher trimmed mean size is selected if the CPI is often subjected
to extreme price movements, while a smaller value of trim mean is selected if
the CPI is subjected to fewer extreme price movements. These extreme price
movements are usually the result of seasonal factors as well as one-off policy
changes.
One advantage of the trimmed mean is its ability to eliminate all relative price
changes and therefore able to isolate the component of aggregate price
change expected to persist. It is however important to note that this method
has the potential to remove important information especially if the trim is
excessively large or tends to retain transitory components if the trim is very
low. As warned by Mio and Higo (1999) that large relative price movements
located in the tails of distribution may sometimes contain information for
future core inflation.
Bryan and Cecchetti (1994) proposed another trimmed mean measure of core
inflation and called it Median CPI. The weighted median is the mean of the
price indices of the CPI components with an equal weighted number of items
on each side of it. In calculating it, the monthly price changes for the items
are ranked from smallest to largest with their respective weights. When the
collective weight reaches 50 % the corresponding change in price represents
the weighted median inflation rate.
Currently, Bank of Ghana uses the 10 per cent trimmed mean underlying
inflation but for the purposes of this paper the 5 percent, 15 percent and 20
percent as well as the weighted median CPI would be considered. The
graphical representation of these core measures of inflation are shown below:
CPI Inflation and TM5% Core Inflation
TM5
CPI Inflation and TM10% Core Inflation
CPI
TM10
35.0
CPI
35.0
30.0
30.0
25.0
per cent
20.0
15.0
20.0
15.0
10.0
5.0
5.0
0.0
0.0
Ja
n03
Ap
r-0
3
Ju
l-0
3
O
ct
-0
3
Ja
n04
Ap
r-0
4
Ju
l-0
4
O
ct
-0
4
Ja
n05
Ap
r-0
5
Ju
l-0
5
O
ct
-0
5
Ja
n06
Ap
r-0
6
10.0
Ja
n03
Ap
r-0
3
Ju
l-0
3
O
ct
-0
3
Ja
n04
Ap
r-0
4
Ju
l-0
4
O
ct
-0
4
Ja
n05
Ap
r-0
5
Ju
l-0
5
O
ct
-0
5
Ja
n06
Ap
r-0
6
per cent
25.0
period
period
CPI Inflation and TM20% Core Inflation
CPI Inflation and TM15% Core Inflation
TM20
CPI
35.0
30.0
30.0
25.0
25.0
20.0
20.0
per cent
35.0
15.0
10.0
5.0
5.0
0.0
CPI
15.0
10.0
period
Ja
n03
Ap
r-0
3
Ju
l-0
3
O
ct
-0
3
Ja
n04
Ap
r-0
4
Ju
l-0
4
O
ct
-0
4
Ja
n05
Ap
r-0
5
Ju
l-0
5
O
ct
-0
5
Ja
n06
Ap
r-0
6
03
Ap
r-0
3
Ju
l-0
3
O
ct
-0
3
Ja
n04
Ap
r-0
4
Ju
l-0
4
O
ct
-0
4
Ja
n05
Ap
r-0
5
Ju
l-0
5
O
ct
-0
5
Ja
n06
Ap
r-0
6
0.0
nJa
per cent
TM15
period
CPI Inflation and WM Core Inflation
CPI Inflation and HP Core Inflation
HP Filter
CPI
35.0
35.0
30.0
30.0
25.0
25.0
20.0
per cent
per cent
CPI
15.0
WMA
20.0
15.0
10.0
10.0
5.0
5.0
0.0
period
Jan-06
Mar-06
Nov-05
Jul-05
Sep-05
May-05
Jan-05
Mar-05
Nov-04
Jul-04
Sep-04
May-04
Jan-04
Mar-04
Nov-03
Jul-03
Sep-03
May-03
Jan-03
Mar-03
Ja
n
-0
3
Ap
r-0
3
Ju
l-0
3
O
ct
-0
3
Ja
n04
Ap
r-0
4
Ju
l-0
4
O
ct
-0
4
Ja
n05
Ap
r-0
5
Ju
l-0
5
O
ct
-0
5
Ja
n06
Ap
r-0
6
0.0
period
4.0.3 Underlying Inflation By Smoothening
This is a smoothing method, which uses econometric tool to obtain a level
estimate of the long-term trend component of a series. Hodrick and Prescott
(1980) in an attempt to analyze postwar U.S. business cycles first used the
method and published it in a working paper3. In this case, it was used to
determine the underlying trend movement in prices. It works as a
smoothening of the headline inflation rate.
Brief notes on how the core measures were estimated:
•
•
•
•
•
•
•
•
•
3
The CPI inflation is the measure of consumer price inflation, consisting
of all items published by Ghana Statistical Service.
Infxeu is the CPI excluding energy and utility price charges.
Infxeuf is the CPI excluding energy, utility and selected volatile food
items.
Infxeuft excludes transport in Infxeu,
Infxafe excludes all food items, utility and transport.
TM5 is the 5 % trimmed mean, calculated from CPI excluding the top
and bottom 5% by volatility in the CPI regimen of sub component price
changes within the month
TM10 is the 10 % trimmed mean, calculated from CPI excluding the
top and bottom 10 % by volatility in the CPI regimen of sub
component price changes within the month.
TM15 is the 15 % trimmed mean, calculated from CPI excluding the
top and bottom 15 % by volatility in the CPI regimen of sub
component price changes within the month.
TM20 is the 20 % trimmed mean, calculated from CPI excluding the
top and bottom 20 % by volatility in the CPI regimen of sub
component price changes within the month.
Circulated in the early 1980's and published in 1997
5.0 Descriptive Statistics - Measures of Underlying Inflation for
Ghana–2003 (1)–06(4)
Before a more rigorous evaluation of the estimated core measures of
inflation, preliminary analysis on the characteristics of the core and headline
inflation are done to provide information on the relationship between the
headline and each core measure through descriptive statistics. The sample
period for the entire analyses cover January 2003 to April 2006.
Table 1: Distribution of Core Measures of Inflation (yr-on-yr)
TM10
TM15
TM20
INFXEU
INFXEUF INFXEUFT INFXAFE HP Filter
CPI
TM5
SA
WM
Mean
17.5
11.5
13.3
14.2
14.1
15.5
13.2
12.9
6.9
Median
14.9
9.1
10.4
10.5
10.7
13.5
10.7
10.2
5.9
16.4
17.5
13.1
16.0
15.0
10.8
Max
30.0
24.6
25.5
27.5
26.9
23.7
22.9
22.9
Min
9.5
2.1
5.8
5.5
5.8
9.7
7.0
7.1
11.9
21.6
29.5
22.4
3.7
11.9
9.4
Std Dev.
6.8
7.4
6.3
7.1
6.6
4.4
5.3
5.8
5.4
2.2
3.0
6.8
4.7
Skewness
0.8
0.6
0.9
0.9
0.9
0.9
0.9
0.8
1.0
0.2
0.8
0.8
Kurtosis
-0.9
-1.1
-0.8
-0.9
-0.8
-0.7
-0.9
-1.0
0.1
-1.3
-0.9
-0.5
The distribution of the sub components price movement is described by the
mean, variance, skewness as well as the kurtosis in table 1 above for all the
measures of inflation. It is clear that headline inflation has the highest mean
inflation than all the core measures suggesting the presence of volatile
components in the headline inflation, which do not persist over the period
considered.
The standard deviation, which measures the variability, indicated that most of
the underlying measures of inflation were lower than the headline inflation.
Also, all the underlying measures recorded positive skewness suggesting that
the skewness of the distribution, which represents the drift on either side of
the mean, was positive. The implication is that there were higher positive
changes than the negative changes. A confirmation of downward rigidities of
prices, that is, the magnitude of the price increase is usually greater than the
magnitude of price decrease.
Table 2: Correlation Matrix
HP
CPI
0.74
HP
1.00
INFXAFE
INFXEU
INFXEUF
INFXEUFT
TM10
TM15
TM20
TM5
WM
INFXAFE INFXEU INFXEUF INFXEUFT TM10 TM15 TM20 TM5
0.95
0.75
1.00
0.97
0.75
0.97
1.00
0.93
0.82
0.96
0.96
1.00
0.95
0.89
0.91
0.93
0.97
1.00
0.99
0.74
0.95
0.98
0.96
0.93
1.00
0.97
0.81
0.93
0.97
0.96
0.96
0.99
1.00
0.98
0.80
0.94
0.98
0.96
0.95
0.99
1.00
1.00
0.93
0.76
0.84
0.89
0.84
0.86
0.89
0.91
0.91
1.00
WM
0.95
0.80
0.93
0.96
0.92
0.92
0.97
0.98
0.99
0.90
1.00
The study further looked at the extent of the relationship existing between
the headline inflation and the core measures of inflation using correlation
matrix. The outcome is presented in table 2 above.
Analysis on the correlation matrix as depicted on table 2 measures the
relationship between each core measure of inflation and headline inflation.
Too high correlation suggests that the core captures more than just the
persistent component in prices, therefore part of the transitory movements in
the headline inflation have also been captured by the core measure. Unless it
is proven that the transitory components of headline inflation is very
insignificant and for that matter headline inflation and core inflation are
almost the same. It is however worthy to note that it has already been
proven in table 1 above that the mean of the headline inflation is higher than
all the core measures of inflation, indicating therefore the presence of
transitory components in the headline inflation. The HP, TM5 and Infxeuf in
that order recorded the lowest correlation coefficient.
It must however be pointed out that evaluating various measures of core
inflation in this way requires a lot of judgment to be made since core inflation
must also reflect the development in general price level over a long period,
therefore some level of positive correlation must exist between the core and
the headline inflation.
Table 3: Volatilities Around Trend
Core Measures
TM5
TM10
TM15
TM20
INFXEU
INFXEUF
INFXEUFT
INFXAFE
HP Filter
WM
Standard Deviation
(Volatility around the trend)
0.50
0.16
0.20
0.17
0.14
0.14
0.18
0.13
0.25
0.15
The paper also used the standard deviation of the difference between the
core inflation and the trend inflation4 to measure the accuracy with which the
core inflation can track persistent component of inflation. Here, core inflation
is expected to move closely with the trend inflation. For a good core indicator
to move closely with trend, the difference between the two must be small and
therefore expected to record a very low standard deviation. Given this
criterion, we conclude that the smallest volatility around the CPI inflation
trend were Infxafe, Infxeu, Infxeuf, WM and TM10. On the basis of this
4
Henderson Moving Averages were used to estimate the trend
criterion, the above-mentioned core measures are likely to track the
persistent component of inflation better than the other measures (Table 3).
6.0 Econometric Evaluation of Different Measures of Core Inflation
Basically, the steps to be followed to select the appropriate measures of core
inflation will be based on information from the literature. Figueiredo and
Staub (2000) have indicated that appropriate measure of the core inflation
remains a challenge. Roger (1998) emphasized on the properties of
timeliness, robustness, unbiasdness and verifiability as crucial elements to be
possessed by a good indicator while Wynne (1999) stressed on forwardlooking property as the very important characteristic that a core indicator
must possess.
Marques et al (2000) introduced statistical conditions that an appropriate
inflation indicator must satisfy. He emphasized the need for the policymaker
to exploit information contained in the differential between the core and
headline inflation. The overall aim is to ensure that headline inflation in the
long run converge with the core inflation.
This study therefore adopts Marques et al (2000) approach to select the
appropriate measure of core inflation. According to this approach, the
following steps will have to be satisfied:
•
•
•
Existence of a stable long run relationship between the core and
headline inflation.
Ability of the core measure to predict the headline inflation, and
That the targeted inflation should not be an 'attractor' of core inflation
(ie core inflation should be strongly exogenous).
Step 1
The first condition is to establish the existence of a stable long run
relationship between the core measure and the headline inflation. Intuitively,
inflation in any given time is broken down into a permanent and temporary
components defined as follows:
π t = π *t + u t
(1.8)
Where π t is headline inflation at time (t), π * t is the core inflation and the
u t represents the disturbance term. We can assume that the u t comprises the
temporary disturbances expected to exhibit zero mean and finite variance,
given that positive shocks are offset by the negative shocks indicating that
the u t is a stationary series.
In an attempt to establish the existence of a stable long run relationship, the
cointegration test between the headline and core inflation is conducted to
establish the existence of a long run relationship. As required by the standard
test of cointegration, the unit root tests for the staionarity of the headline and
core inflation is first established through Augmented Dicky Fuller (ADF) test.
Table 4: Results of the Unit Root Test
ADF (t-statistics)
Measures of Core Inflation
TM5
TM10
TM15
TM20
CPI Inflation
INFXEU
INFXEUF
INFXEUFT
INFXAFE
HP Filter
WM
** Indicates stationarity at 1%
Level
First Difference
-2.065
-2.014
-1.767
-1.787
-2.241
-1.867
-2.406
-2.168
-1.967
-3.620*
-1.810
-4.915**
-4.574**
-4.609**
-4.282**
-4.493**
-5.334**
-5.378**
-4.371**
-5.015**
-5.442**
-4.192*
* Indicates stationarity at 5%
The results of the Augmented Dickey-Fuller (ADF) tests of the series in the
study are shown in table 4. The tests were carried out in levels and first
differences and were performed by including a constant and a trend. The ADF
test showed that the variables were all not stationary at levels with the
exception of HP filter. Following this, the unit root tests of the first difference
of the variables were estimated and the ADF test rejected the hypotheses of
unit root, meaning all the variables were stationary after first differencing.
It is now clear to test for the existence of any possible co-integrating
relationship between each core measure of inflation and the headline inflation
to determine whether there exists a long run relationship among them. We
therefore use Granger (1987) residual-based approach, which is the unit root
test of the residuals from the following regression:
π t = α t + β π *t + u t
(1.9)
The results of the cointegration tests are reported on table 5 below. The
results show that all the measures are cointegrated with the headline
inflation, which therefore establishes the existence of a long run relationship
with each core inflation measure, and the headline inflation.
It can also be inferred from the results that the estimated coefficients (B) of
some of the core measures of inflation are closer to one, which suggests non-
permanent divergence between the core and the headline inflation. It is
worthy to note that this however is contingent on whether the second
condition holds. If the second condition therefore holds then we can say that
the core measures with closest unitary coefficient captures the bulk of the
trend component in headline inflation. INFXEUF and WM were found to be
the core measures of inflation with the coefficient closest to the unitary
coefficient.
Table5: Results of the Engle Granger Cointegration Tests
Measure of Core Inflation
Coefficient (B)
ADF t-statistics
(Residuals)
0.41
0.82
0.75
0.80
1.35
0.92
0.82
1.15
1.37
0.98
-2.070*
-2.395*
-2.668*
-2.281*
-2.043*
-1.960*
-2.568*
-2.306*
-2.110*
-2.867**
TM5
TM10
TM15
TM20
INFXEU
INFXEUF
INFXEUFT
INFXAFE
HP Filter
WM
** Indicates stationarity at 1%
* Indicates stationarity at 5%
Step 2
It has already been pointed out in the first step (from equation 1.9) that
where β ≠ 1 indicates a permanent divergence between the core inflation
and the headline inflation. However, following the existence of cointegration
between each core measure of inflation and the headline inflation (table 3)
we can conclude that there exists an error correction mechanism. It is
therefore expected that the headline inflation will converge to the core in the
long run depending on whether we can reject the null hypothesis that δ = 0
in the following error correction model of headline inflation:
∆π
t
=
m
∑
j =1
α j∆ π
t− j
+
n
∑
j −1
β j∆ π
*
t −1
− δ (π
t −1
−π
*
t −1
) + εt
(1.10)
If this hypothesis is rejected then the positive or negative differences
between headline inflation and core inflation in the previous period will have a
downward or upward effect on the change of the headline inflation at the
current period. Hence, the headline inflation is attracted by the core measures
of inflation to converge in the long run. Table 6 presents the results of the
above equation which tests whether the null hypothesis of δ = 0 is rejected
or not. It revealed that with the exception of TM15, all the other measures of
core inflation rejected the null at 10% significance level, which suggests that
almost all the core measures of inflation can draw the headline inflation (table
6).
Table 6: Results of Equation (1.10)
Measure of Core Inflation
TM5
TM10
TM15
TM20
INFXEU
INFXEUF
INFXEUFT
INFXAFE
HP Filter
WM
t-statistics
P-Values
-1.88
-2.70
-1.66
-1.84
-2.63
-2.56
-1.90
-2.36
-2.21
-2.18
0.07
0.01
0.11
0.07
0.01
0.02
0.06
0.03
0.03
0.04
Marques et al (2000) also in an effort to find out whether the core inflation
acts as an “attractor” to the headline inflation employed Granger causality
method. Similar method was employed to Ghana’s data to find out if the core
inflation is a leading indicator of the headline inflation. The results from table
7 show that the null hypothesis of the weighted median (WM), Infxeu, HP and
Infxafe were the core measures of inflation which were rejected at 10%,
therefore acting as the leading indicators of the headline inflation.
Table 7: Results of the Granger Causality Test
Null Hypothesis:
F-Statistic
P- values
TM5 does not Granger Cause CPI
TM10 does not Granger Cause CPI
TM15 does not Granger Cause CPI
TM20 does not Granger Cause CPI
INFXAFE does not Granger Cause CPI
INFXEU does not Granger Cause CPI
INFXEUF does not Granger Cause CPI
INFXEUFT does not Granger Cause CPI
HP does not Granger Cause CPI
WM does not Granger Cause CPI
0.3563
1.5393
0.0620
1.0156
10.634
3.3864
1.2140
0.5241
6.7487
7.8762
0.55
0.22
0.80
0.32
0.00
0.07
0.28
0.47
0.01
0.01
Step 3
The third step indicates that for the core inflation to adequately predict the
future path of the headline inflation and qualify to be used as a policy
variable, the relationship must not run both ways. It has been noted that a
good policy variable should not be bi-directional with other non-policy
variables. Again, core inflation is expected to lead and not to lag since
monetary policy in principle is forward looking.
Table 8: Results of the Granger Causality Test
Null Hypothesis:
F-Statistic
P-Values
CPI does not Granger Cause TM5
CPI does not Granger Cause TM10
CPI does not Granger Cause TM15
CPI does not Granger Cause TM20
CPI does not Granger Cause INFXAFE
CPI does not Granger Cause INFXEU
CPI does not Granger Cause INFXEUF
CPI does not Granger Cause INFXEUFT
CPI does not Granger Cause HP
CPI does not Granger Cause WM
0.0057
0.0505
0.0864
0.0669
3.2591
1.1144
0.3394
1.0544
4.9539
1.7700
0.94
0.82
0.77
0.79
0.08
0.29
0.56
0.31
0.03
0.20
The results as presented on table 8 above indicate that with the exception of
HP and Infxafe, the headline inflation does not help in forecasting any of the
core measures of inflation. Given this result and the outcome from step two
we can conclude that the weighted median (WM) and Infxeu are the core
measures which help to predict headline inflation or act as leading indicators
of headline inflation but the headline inflation does not help in forecasting
these measures of core inflation.
Table 9: Summary of Conditions Satisfied
Descript Stats
Variability Correlation
Std.
WMA
√
√
√
√
√
√
Step 1
Long Run
Step 2 (Attracting headline inflation)
Error Correction Granger Causality
Step 3
Feed-back
Around trend
√
TM5
TM10
TM15
TM20
INFXEU
INFXEUF
INFXEUFT
INFXAFE
HP
Matrix
Volatility
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
7.0 Conclusion and Recommendation
The consumer price index, which is the accepted way to measure price
developments in Ghana, has been established from our descriptive analysis to
include extreme price changes that are often transitory. It has therefore
become necessary that policymakers use the core inflation in formulating
monetary policy to ensure effective policy communication.
To identify an appropriate measure, descriptive as well as econometric tools
were used to evaluate the available measures of core inflation in Ghana. It
came out that all the measures performed well in some important respects, as
indicated in table 9.
With respect to core inflation tracking headline inflation, Infxafe, Infxeu,
Infxeuf, WM and TM10 were found to be superior measures from table (3).
All the core measures were also found to have a long run relation with the
headline inflation.
In terms of ability of the core indicator to predict and draw headline inflation
or act as a leading indicator to ensure that they both converge in the long run
without indicating a bi-directional relationship, Infxeu and WM were revealed
to be superior methods. This finding is consistent with inflation targeting
countries such as Canada and Thailand, which target core measures similar to
Infxeu.
As indicated earlier all the core measures are very important in some respects
but given the objective of the paper, emphasis is placed on the core’s ability
to act as a leading indicator of the headline inflation and at the same time
exogenous. On this basis, Infxeu and WM are found as the most appropriate
measures of core inflation in Ghana. However, given the relative complexity
to measure the weighted median (WM) compared with Infxeu, WM can be
used as an indicator in guiding policymakers while Infxeu maybe
communicated to the public.
References
Bank of Ghana Publications, Various Issues.
Bryan, M, and S Cecchetti (1993), ‘The Consumer Price Index as a measure of
inflation’, Federal Reserve Bank of Cleveland Economic Review (4), pp. 15-24.
——— 1994. ‘Measuring core inflation’, Chapter 6 in N G Mankiw,
Ed., Monetary Policy, University of Chicago Press (Chicago), pp. 195-215.
Cecchetti, Stephen G. 1997. “Measuring Short-Run Inflation for Central
Bankers,” Federal Reserve Bank of St. Louis, Review, May/June.
Dewan E., Gokal V., and Hussein, S (2003) “ Measurement of Underlying
Inflation in Fiji”, working Paper, Reserve Bank of Fiji.
Eckstein, Otto. 1981. Core Inflation. Englewood Cliffs, N.J.: Prentice-Hall.
Figueiredo, F.M.R. & R. B. Staub (2002). Evaluation and Combination of Core
Inflation Measures for Brazil, Central Bank of Brazil, Research Department.
Friedman, M (1963), Inflation. Causes and consequences, Asia Publishing
House (New York).
Statistical Newsletters, Various Issues, Published by Ghana Statistical Service
Marques, Carlos Robalo, Pedro Duarte Neves, and Luis Morais Sarmento.
2000. “Evaluating Core Inflation Indicators,” Bank of Portugal, working paper
no. 3-00, April.
Mio, M. and M. Higo (1999). Underlying Inflation and the Distribution of the
Price Change: Evidence from the Japanese Trimmed-Mean CPI, Institute of
Research and Economic Studies, Bank of Japan
Okun, A (1970), ‘Inflation: the problems and prospects before us’, in A Okun,
H Fowler and M Gilbert, Eds. Inflation: the problems it creates and the
policies it requires, New York University Press, (New York), pp. 3-53.
Parkin, M. 1984. “On Core Inflation by Otto Eckstein.” Journal of Monetary
Economics 14: 251–64.
Quah, D. and S.P. Vahey. 1995. “Measuring Core Inflation.” The Economic
Journal Vol. 105, (September): 1130–44.
Roger, S. 1995. “Measures of Underlying Inflation in New Zealand, 1981–95.”
Reserve Bank of New Zealand, Discussion Paper No. G95/5.
———. 1997. “A Robust Measure of Core Inflation in New Zealand, 1949–96.”
Reserve Bank of New Zealand Discussion Paper No. G97/7.
———. 1998. “Core Inflation: Concepts, Uses and Measurement.” Reserve
Bank of New Zealand Discussion Paper No. 98/10.
———. 2000. “Relative Prices, Inflation and Core Inflation.” IMF Working
Paper No. 58.
Todd e. Clark (2001) “comparing measures of core inflation” Federal Reserve
Bank of Kansas City economic review, second quarter 2001.
Wynne, M (1997), ‘Commentary’, Federal Reserve Bank of St. Louis Review
(May/June),
pp. 161-67.