Technical note:
Measures of underlying inflation
The Riksbank’s inflation target is defined in terms of the Consumer Price Index (CPI),
as this index represents common purchases and is well known to the public. In
addition, CPI statistics are of good quality, are not normally revised and are published
soon after the end of the month. However, although inflation is formulated in terms
of the CPI, other measures of inflation may be useful to analyse and forecast the
development of inflation. The CPI is often affected by factors that are expected to
have only temporary effects on inflation and that the Riksbank should therefore not
react to. To describe the development of inflation and to better explain the monetary
policy stance, the Riksbank may then choose to highlight measures of so-called
underlying inflation. There are many different ways to calculate underlying inflation.
Here we present two such measures: Und24 and Trim85.
Background and Purpose
Inflation entails a general increase in prices and is generally measured as the annual
percentage change in the Consumer Price Index (CPI). The Riksbank’s inflation target
of 2 per cent is expressed in terms of the annual percentage change in the CPI.1
The CPI is a so-called cost-of-living index that aims to measure the development of
the cost of living for households over time. It records price changes for a wide range
of goods and services whose significance for the measure as a whole depends on the
consumption patterns of the households. The higher the proportion of their
consumption, in terms of value, that households devote to a particular good or
service, the higher the significance (weight) attributed to this good or service in the
CPI.
The rate of change in the CPI can periodically be driven substantially up or down by
price changes for one group, or a few groups, of, goods or services. On such
occasions it may be particularly important to attempt to determine the level of
underlying inflation, or trend inflation (see for example Clark, 2001).2
1
For more information on the Riksbank’s inflation target and the choice of the CPI see “Monetary Policy in
Sweden”, Sveriges Riksbank, 2010.
2
Another reason for studying measures of underlying inflation relates to the fact that, for various reasons, the
change in the CPI is not considered to be a good measure of inflation, see Bryan and Cecchetti (1994). A third
reason for studying such measures relates to sampling theory. The aim here is to measure the same thing that
the CPI attempts to measure, but more effectively, see Bryan, Cecchetti and Wiggins II (1997), A fourth reason
relates to the idea that a central bank that wants to pursue a policy designed to maximise welfare should only
try to stabilise prices that are sticky, see Woodford (2003).
1 [12]
There is no clear-cut definition of the term underlying inflation and it can therefore
be measured in different ways. A common feature of all of the approaches to
measuring underlying inflation is, however, that they attempt to distinguish between
a general price increase and a temporary relative price change. The aim is to reduce
temporary fluctuations and thus get a better picture of the more persistent inflation
trend. The most common approach is to use so-called exclusion measures in which
various sub-groups in the CPI are excluded. It is then customary to exclude groups
for which prices have, historically, fluctuated considerably as a result of temporary
changes in supply from the overall measure. It is, for example, common to exclude
energy and food prices. Figure 1 below shows such exclusion measures of the CPI. It
can be seen that in a period such as 2008 it may be important to examine different
measures of underlying inflation to get a better idea of the actual rate of inflation. In
this period, inflation measured in terms of the CPI increased, but when measured in
terms of the CPI excluding interest rates, energy and food inflation fell. In the
Monetary Policy Reports, for example, the Riksbank presents outcomes and forecasts
for the CPIF excluding energy. In the United States and the euro area, inflation
measures that exclude both energy and food prices are often analysed to get a
picture of underlying inflation. Exclusion measures are calculated by subtracting the
weight of one or several groups from the overall measure, thus reducing the total
weight. This retains the relative weights of the remaining groups in the exclusion
measure.
Another way of measuring underlying inflation is, in connection with each new
outcome, to the sub-groups that have increased most and those that have increased
least in price to create a so-called trimmed inflation measure. Trimming can be
carried out on the basis of monthly, quarterly or annual changes in the overall
measure. Yet another method of measuring underlying inflation is to revise the
weights of the sub-groups in the CPI so that the groups that have fluctuated more in
the most recent period are given a lower weight while the groups that have
fluctuated less are given a higher weight.
Common to all these different ways of measuring underlying inflation is that they
reduce the significance of price changes in specific sectors in the overall measure and
create a more stable measure of inflation; that is a measure that does not fluctuate as
much. Two different measures of underlying inflation are now available on our
website: Trim 85 and Und 24 (see Figure 2).
Data and updating
In the calculations of the two measures of underlying inflation now published on the
Riksbank’s website, that is Und24 and Trim 85, monthly figures (outcomes) from
January 1995 to the present day have been used. Revised shadow index figures that
correspond to the indexes used to measure CPI inflation have been used for periods
for which these have been calculated by Statistics Sweden3. The CPI, divided into
approximately 70 sub-groups (see Table 1), has been used as a basis for calculating
the two measures of underlying inflation.
3
See for example the latest shadow index for the period May 2009 to April 2010 in connection with the revisions
of the effects of the ROT scheme (tax deductions for repairs, maintenance, conversions and extensions) on the
CPI.
2 [12]
Both Und24 and Trim 85 are updated in connection with each new outcome for the
CPI and are published on the Riksbank’s website on the same day that new outcomes
are received.
Method and Calculation
The trimmed measure, Trim85, is calculated on the basis of annual percentage
changes in the CPI. We have excluded 7.5 per cent of the highest and lowest price
change rates for the sub-groups included in the CPI each month. The remaining
groups are then weighed together, while retaining their relative weights, to arrive at a
total inflation figure. The CPI divided in to 70 sub-groups is used (see Table 1). In this
measure, 85 per cent of the total weight of the CPI thus remains after 7.5 per cent of
the groups with the highest, and 7.5 per cent those with the lowest rate of price
changes have been excluded.
Statistics Sweden does not calculate the CPI on the basis of annual percentage
changes but uses a more complicated method. In this method, sub-indexes based on
the average index levels for the whole year two years ago are weighed together to
form a total index level. This index series is then used when the SCB calculates the
annual percentage change in the CPI. Figure 3 below presents a comparison of the
annual rate of increase in the CPI with an aggregate of the annual rates of increase in
the 70 different sub-groups. CPI trim zero (i.e. where nothing has been trimmed
away) does not therefore completely correspond to the CPI as calculated by Statistics
Sweden. Since 1995, the CPI has increased by an average of 1.24 per cent, while the
aggregate 12-month changes have increased by an average of 1.38 per cent (see
Figure 3).
The calculation of Und24 is also based on the CPI divided into 70 sub-groups. All of
the sub-groups are retained in Und24 but are given different weights than in the CPI.
The new weights are calculated on the basis of the standard deviation in the
difference between the rate of change in the respective sub-groups and the rate of
change in the CPI over the last 24 months; the higher the standard deviation the
lower the weight. Formally, the weights are calculated as the inverse of this standard
deviation. These new weights are then normalised so that they add up to 1, which
becomes the total weight for the Und24 measure. In the CPI the weights add up to
1,000. Calculations of Und24 are also based on annual percentage changes in the
sub-groups of the CPI. Consequently, this measure also differs from the CPI, even
without a readjustment of the weights, as the weighing method is different to that in
the CPI.
Figure 4 shows the annual percentage change in the various inflation measures from
January 1995 to January 2011. The average annual rate of increase in Und24 is higher
than in the CPI. For the trimmed measures, the average rate of increase, for a
trimming level of zero, is somewhat higher than for the CPI. The average rate of
change falls initially, but for trimming levels of above 5 per cent the difference
increases. The average rate of increase in the underlying measures of inflation is also
higher than in the CPI.
Figure 4 also shows the difference between the CPI and the CPI trim zero that stems
from the fact that the annual percentage changes for the respective groups are
weighed together differently. If the same method were used to weigh together the
groups, the CPI and the CPI trim zero would have the same average rate of change.
3 [12]
One way of measuring the variation in the different measures of inflation is to
compare the standard deviation in the rate of change from one month to another.
This is done in Figure 5 for the annual percentage change in the respective measures
during the period January 1995 to January 2011. In terms of the annual percentage
rate of change it is, not surprisingly, Und 24 that has the lowest variation. When one
uses a trimmed measure of the CPI, the variation is lowest at a trimming level of
approximately 30 per cent; that is when approximately 30 per cent of the CPI’s total
weight has been removed at each end of the scale. However, all of the measures vary
much less than the total CPI, irrespective of the size of the trim.
Analysis and Evaluation
The evaluation period comprises January 1995 to January 2011. Monthly figures for
the 12-month change in the CPI have been used.
As measures of underlying inflation should reflect the more persistent inflationary
pressures in the economy, the measures should also be good indicators of future
inflation. In order to study this, we compare the deviation (i.e. the Root Mean Square
Error (RMSE)) between the inflation measured in the period according to the CPI,
Und24 and Trim-CPI and the level of inflation 3, 6 and 12 months ahead as follows:
RMSEi 

N
t 1
( KPI ,t  j   i ,t )
N
Where  i,t is inflation according to measure i in period t and where j is 3, 6 or 12.
With regard to the annual percentage changes, Figure 6a shows that trimming the
total weight of the CPI by 0 to 2 per cent at each end of the scale provides the most
accurate forecasts of the CPI three months ahead, with a level of accuracy equal to
that of the CPI as a whole. Accuracy declines for trims higher than this. The Und24
measure provides significantly poorer forecasts than the CPI over a three-month
horizon. Over a forecast horizon of six months, trims of up to approximately 10 per
cent provide better forecasts than the CPI, while the accuracy of the Und24 is still
poorer than that of the CPI even over an horizon of six months (see Figure 6b).
However, over a horizon of 12 months both Und24 and trimmed measures of the CPI
are more accurate than the CPI. This applies to all trim sizes. The best trim size, that is
the one that gives the lowest RMSE and is therefore the most accurate, appears to be
trimming levels of 15-20 per cent. As the CPI is measured in terms of 12-month
changes, an outcome today is largely dependent on the state of the CPI 12 months
ago. This means that it is primarily at horizons of 12 months and more that we can
expect the underlying measures of the CPI to be more accurate than the CPI itself.
There is no self-evident target value to relate these RMSE figures to. If a forecaster
had constantly forecast an inflation rate of 2 per cent, the RMSE would have been
approximately 1.43 percentage points. This actually provides a lower RMSE 12
months ahead than that achieved by using the outcome of Und24 or trimmed 12month changes in the CPI as a forecast (see Figures 8a-c). It also provides a lower
RMSE than that achieved by using the CPI as a forecast of the CPI at a 12-month
horizon. It can also be noted that all the RMSE values are higher than the standard
4 [12]
deviation in the annual rate of increase in the CPI in the period from 1995 to 2011,
which is approximately 1.2 per cent.
It may also be relevant to compare with the Riksbank’s published CPI forecasts in the
Monetary Policy Reports. The RMSE for the Riksbank’s forecasts of the annual rate of
increase in the CPI 12 months ahead has been approximately 0.4 percentage points
at a 3-month horizon, 0.7 at 6 months and 1.2 at a 12-month horizon since 1998.
That is, lower than the RMSE for the measures of underlying inflation at all horizons.
This comparison is slightly misleading, however, as it does not compare forecasts for
exactly the same periods given that the Riksbank’s published forecasts are only
available from 19984.
The forecasting performance of underlying measures of inflation such as Und24 and
Trim85 is thus relatively poor in the short term, but they can help to provide a better
picture of trend inflation right now. Their forecasting capacity is also better at
horizons longer than 12 months and they can be used as a complement to other
models for forecasting inflation in the longer term.
Figures and tables
Figure 1. Exclusion measures of the CPI: CPI, CPI excluding interest rates, CPI
excluding interest rates, energy, CPI excluding interest rates, energy and food
Annual percentage change
5
5
CPI
CPIxi
4
4
CPIxie
CPIxief
3
3
2
2
1
1
0
0
-1
-1
-2
-2
00
01
02
03
04
05
06
07
08
09
10
11
Sources: Statistics Sweden and the Riksbank
4
For a comparison of RMSEs over the same period see Figure 3 in Sveriges Riksbank Economic Review 2008:2
“Why do we need measures of underlying inflation?"
5 [12]
Figure 2. Measures of underlying inflation; Und24 and Trim85, annual
percentage change
5
5
CPI
4
4
Und24
Trim85
3
3
2
2
1
1
0
0
-1
-1
-2
-2
00
01
02
03
04
05
06
07
08
09
10
11
Sources: Statistics Sweden and the Riksbank
Figure 3. CPI (according to Statistics Sweden) and aggregated 12-month
changes in CPI sub-groups to total CPI
5
5
CPI
4
4
CPI, aggregated 12-month changes
3
3
2
2
1
1
0
0
-1
-1
-2
-2
95
96
97
98
99
00
01
02
03
04
05
06
07
08
09
10
11
Sources: Statistics Sweden and the Riksbank
6 [12]
Figure 4. Average annual percentage change since 1995
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.4
CPI (trim)
CPI (yoy)
Und24
0.6
0.4
0.2
0.2
0.0
0.0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Note. The X axis shows the trim size from 0 to 50, where 0 is the total CPI and 50 is the weighted
mean. The unbroken, black, vertical line shows Trim 85.
Sources: Statistics Sweden and the Riksbank
Figure 5. Standard deviation as annual percentage changes from 1995
2.0
2.0
1.8
CPI (trim)
1.8
1.6
CPI (yoy)
1.6
1.4
Und24
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Note. The X axis shows the trim size from 0 to 50, where 0 is the total CPI and 50 is the weighted
mean. The unbroken, black, vertical line shows Trim 85.
Sources: Statistics Sweden and the Riksbank
7 [12]
Figure 6a. Forecasting capacity of the annual percentage change in the CPI 3
months ahead of 12-month changes in various measures of underlying inflation
(RMSE)
2.0
2.0
CPI (trim)
1.8
1.6
CPI (yoy)
Und24
1.8
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Note. Monthly observations from 1995 to January 2011 have been used. The unbroken, black,
vertical line shows Trim 85.
Sources: Statistics Sweden and the Riksbank
Figure 6b. Forecasting capacity of the annual percentage change in the CPI 6
months ahead of 12-month changes in various measures of underlying inflation
(RMSE)
2.0
1.8
2.0
CPI (trim)
1.8
CPI (yoy)
1.6
Und24
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Note. Monthly observations from 1995 to January 2011 have been used. The unbroken, black,
vertical line shows Trim 85.
Sources: Statistics Sweden and the Riksbank
8 [12]
Figure 6c. Forecasting capacity of the annual percentage change in the CPI 12
months ahead of 12-month changes in various measures of underlying inflation
(RMSE)
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
CPI (trim)
CPI (yoy)
0.8
0.8
Und24
0.6
0.6
0.4
0.4
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Note. Monthly observations from 1995 to January 2011 have been used. The unbroken, black,
vertical line shows Trim 85.
Sources: Statistics Sweden and the Riksbank
Table 1. Sub-groups in the CPI
Code
110
120
130
140
150
161
162
163
169
170
180
190
199
210
221
222
223
229
Designation
FLOUR, GRAIN AND BREAD
MEAT
FISH AND TINNED FISH
MILK, CHEESE AND EGGS
COOKING FAT
VEGETABLES, SWEDISH
VEGETABLES AND FRUIT, IMPORTED
VEGETABLES AND FRUIT, MIXED
VEGATABLES, FRUIT AND BERRIES
COFFEE, TEA AND COCOA
OTHER FOODSTUFFS
SOFT DRINKS AND NON-ALCOHOLIC BEER
FOODSTUFFS
BEER,CLASS II
SPIRITS, SYSTEMBOLAGET
WINE, SYSTEMBOLAGET
BEER, SYSTEMBOLAGET
SPIRITS, WINE AND BEER, SYSTEMBOLAGET
Weight
20.5
24.68
7.8
22.74
3.5
4.27
6.61
17.49
28.37
4.13
20.73
6.67
139.12
1.99
5.45
10.95
5.74
22.14
9 [12]
230
299
310
320
330
340
370
399
405
406
410
450
461
462
463
464
465
467
469
471
472
479
499
510
520
530
540
550
599
610
621
622
623
624
629
631
632
639
641
642
649
TOBACCO
ALCOHOLIC DRINKS AND TOBACCO
WOMEN’S WEAR
MENSWEAR
CHILDREN’S WEAR, SPORTSWEAR
TEXTILE FABRICS, YARNS AND HABERDASHERY
SHOES, EXCLUDING HEELING
CLOTHING AND SHOES, EXCLUDING SERVICES
RENTED FLATS, TENANT-OWNED APARTMENTS,
BASIC RENT
GARAGE COSTS
RENTED FLAT, TENANT-OWNED APARTMENT,
GARAGE
GAS AND ELECTRICITY, RENTED FLAT AND
TENANT–OWNED APARTMENT
OWNER-OCCUPIED HOUSING: INTEREST COSTS
OWNER-OCCUPIED HOUSING: WRITE-OFFS
OWNER-OCCUPIED HOUSING: SITE LEASEHOLD,
PROPERTY TAX
OWNER-OCCUPIED HOUSING: INSURANCE FEES
OWNER-OCCUPIED HOUSING: WATER, SEWAGE,
REFUSE COLLECTION, CHIMNEY SWEEPING
OWNER-OCCUPIED HOUSING: REPAIRS, GOODS
OWNER-OCCUPIED HOUSING, HOUSING
OWNER-OCCUPIED HOUSING: HEAT EXCLUDING
ELECTRICITY
OWNER-OCCUPIED HOUSING: ELECTRICITY
OWNER-OCCUPIED HOUSING, HEAT AND
HOUSEHOLD ELECTRICITY
HOUSING, HEAT AND HOUSEHOLD ELECTRICITY
FURNITURE, CARPETING AND LIGHTING
HOUSEHOLD TEXTILES, OTHER FURNISHING
HOUSEHOLD APPLIANCES EXCLUDING REPAIRS
HOUSEHOLD UTENSILS
HOUSEHOLD ITEMS
MOVABLES AND UTENSILS
VEHICLE PURCHASES
AUTO REPAIRS AND MAINTENANCE
AUTO SPARE PARTS ETC.
FUELS
VEHICLE TESTING, DRIVING LESSONS, AUTO
INSURANCE
VEHICLE RUNNING COSTS, TOTAL
DOMESTIC TRAVEL EXCLUDING BOAT TRIPS AND
REMOVALS
FOREIGN TRAVEL
TRAVEL AND TRANSPORT
POSTAL SERVICES
TELECOMMUNICATIONS
POSTAL SERVICES AND TELECOMMUNICATIONS
15.75
39.88
20.04
18.97
6.08
0.74
8.55
54.38
130.1
1.47
131.57
16.67
42.73
17.81
6.63
3.06
7.39
4.88
82.5
4.94
28.32
33.26
264
18.41
10.05
5.49
11.43
6.8
52.18
31.38
13.34
9
38.87
14.09
75.3
22.79
20.56
43.35
1.96
34.04
36
10 [12]
699
710
720
730
740
750
760
770
781
782
783
789
791
792
795
799
911
912
913
914
919
921
922
929
931
932
939
940
950
960
965
966
970
980
981
985
986
987
991
992
993
994
995
996
997
TRANSPORT AND COMMUNICATIONS
RADIO, TELEVISION, VIDEO ETC.
CAMERAS INCLUDING COLOUR FILM
MUSICAL INSTRUMENTS, CD, DVD
FLOWERS ETC.
SPORTING ARTICLES AND LEISURE GOODS
TOYS, GAMES AND HOBBY ITEMS
DIVERSE LEISURE GOODS EXCLUDING REPAIRS
ENTRERTAINMENT AND RECREATION EXCLUDING
TELEVISION LICENCE AND GAMBLING
TELEVISION LICENCE
LOTTERIES, POOLS AND TOTE BETTING
ENTERTAINMENT AND RECREATION
BOOKS
NEWSPAPERS AND MAGAZINES
BOOKS, NEWSPAPERS AND MAGAZINES
LEISURE ACTIVITIES, ENTERTAINMENT AND
CULTURE
PHARMACEUTICALS
HEALTH AND MEDICAL CARE ITEMS
MEDICAL CARE
DENTAL CHARGES
HEALTH AND MEDICAL CARE, TOTAL
PERSONAL HYGIENE, GOODS
PERSONAL HYGIENE, SERVICES
PERSONAL HYGIENE, GOODS AND SERVICES
DIVERSE GOOD EXCLUDING REPAIRS AND GOLD
GOLD ITEMS
DIVERSE ITEMS FOR PERSONAL USE
WINES, SPIRITS, BEER: RESTAURANTS
EATING OUTSIDE THE HOME
ACCOMODATION
FUNERAL COSTS
HOME INSURANCE, BANKING SERVICES,
EDUCATION
FUNERALS, HOME INSURANCE, BANKING,
EDUCATION
DIVERSE SERVICES
REPAIRS, HOUSEHOLD SERVICES
H GOODS
H SERVICES EXCLUDING HOUSING
H HOUSING
H FOODSTUFFS, SWEDISH
H OTHER GOODS, DOMESTIC PRODUCTION
H SERVICES
H FLATS, RENT
H OTHER, OWNER-OCCUPIED HOUSING
H DOMESTICALLY-PRODUCED GOODS AND
SERVICES
H IMPORTED GOODS AND SERVICES
186.03
15.18
1.34
4.37
6.59
5.19
7.58
11.13
26.4
5.24
12.9
44.54
3.42
7.21
10.63
106.55
10.78
4.68
9.98
10.56
36
11.88
14.29
26.17
6.18
2.09
8.27
7.87
42.71
7.42
1.93
20.96
22.89
151.33
6.53
462.43
275.04
262.53
130.37
60.76
260.4
148.24
55.82
655.59
301.68
11 [12]
998
999
H MORTGAGES
CONSUMER PRICE INDEX TOTAL
42.73
1000
Note. The CPI in accordance with the division above is published monthly by Statistics Sweden.
References
Bryan, M. F. & S. G. Cecchetti (1994), “Measuring Core Inflation,” in N. G. Mankiw
(ed.), Monetary Policy. Chicago: University of Chicago Press, pp. 195–215.
Bryan, M. F., S. G. Cecchetti & R. L. Wiggins II (1997), ”Efficient Inflation
Estimation”, NBER Working Paper, No. 6183.
Clark, T. (2001), “Comparing Measures of Core Inflation”, Economic Review,
Second Quarter 2001, Federal Reserve Bank of Kansas City.
Hansson. J., Johansson. J. and Palmqvist. S. (2008) ”Why do we need measures of
underlying inflation?” Sveriges Riksbank Economic Review, 2008:2.
Woodford, M. (2003), “Interest and Prices: Foundations of a Theory of Monetary
Policy”, Princeton University Press.
Sveriges Riksbank ( 2010) ”Monetary Policy in Sweden”
12 [12]