A consumer price index
(CPI) is a measure
estimating the average price of consumer
by households. A consumer price index measures a price change for a
constant market basket
of goods and
services from one period to the next within the same area (city,
region, or nation). It is a price index
determined by measuring the price of a standard group of goods
meant to represent the typical market basket of a typical urban
consumer. Related, but different, terms are the
Kingdom's CPI, RPI, and RPIX.
It is one of several price indices
calculated by most national
statistical agencies. The percent change in the CPI is a measure
. The CPI can be used
to index (i.e., adjust for the effect of inflation on the real
value of money: the medium of exchange) wages, salaries, pensions
, and regulated or contracted prices. The
CPI is, along with the population census
the National Income
and Product Accounts
, one of the most closely watched national
Two basic types of data are needed to construct the CPI: price data
and weighting data. The price data are collected for a sample of
goods and services from a sample of sales outlets in a sample of
locations for a sample of times. The weighting data are estimates
of the shares of the different types of expenditure as fractions of
the total expenditure covered by the index. These weights are
usually based upon expenditure data obtained for sampled decades
from a sample of households. Although some of the sampling is done
using a sampling frame and probabilistic sampling
is done in a commonsense way (purposive sampling) that does not
permit estimation of confidence intervals. Therefore, the sampling
variance is normally ignored, since a single estimate is required
in most of the purposes for which the index is used. Stocks greatly
affect this cause.
The index is usually computed yearly, or quarterly in some
countries, as a weighted average of sub-indices for different
components of consumer expenditure, such as food, housing,
clothing, each of which is in turn a weighted average of
sub-sub-indices. At the most detailed level, the elementary
aggregate level, (for example, men's shirts sold in department
stores in San Francisco), detailed weighting information is
unavailable, so elementary aggregate indices are computed using an
or geometric mean
of the prices of the sampled
product offers. (However, the growing use of scanner
data is gradually making weighting
information available even at the most detailed level.) These
indices compare prices each month with prices in the
price-reference month. The weights used to combine them into the
higher-level aggregates, and then into the overall index, relate to
the estimated expenditures during a preceding whole year of the
consumers covered by the index on the products within its scope in
the area covered. Thus the index is a fixed-weight index, but
rarely a true Laspeyres index
the weight-reference period of a year and the price-reference
period, usually a more recent single month, do not coincide. It
takes time to assemble and process the information used for
weighting which, in addition to household expenditure surveys, may
include trade and tax data.
Ideally, the weights would relate to the composition of expenditure
during the time between the price-reference month and the current
month. There is a large technical economics literature on index formulae
approximate this and which can be shown to approximate what
economic theorists call a true cost
of living index
. Such an index would show how consumer
expenditure would have to move to compensate for price changes so
as to allow consumers to maintain a constant standard of living.
Approximations can only be computed retrospectively, whereas the
index has to appear monthly and, preferably, quite soon.
Nevertheless, in some countries, notably in the United States and
Sweden, the philosophy of the index is that it is inspired by and
approximates the notion of a true cost of living (constant utility)
index, whereas in most of Europe it is regarded more
The coverage of the index may be limited. Consumers' expenditure
abroad is usually excluded; visitors' expenditure within the
country may be excluded in principle if not in practice; the rural
population may or may not be included; certain groups such as the
very rich or the very poor may be excluded. Saving and investment
are always excluded, though the prices paid for financial services
provided by financial intermediaries may be included along with
The index reference period, usually called the base year, often
differs both from the weight-reference period and the price
reference period. This is just a matter of rescaling the whole
time-series to make the value for the index reference-period equal
to 100. Annually revised weights are a desirable but expensive
feature of an index, for the older the weights the greater is the
divergence between the current expenditure pattern and that of the
Example: The prices of 95,000 items from 22,000 stores, and 35,000
rental units are added together and averaged. They are weighted
this way: Housing: 41.4%, Food and Beverage: 17.4%, Transport:
17.0%, Medical Care: 6.9%, Other: 6.9%, Apparel: 6.0%,
Entertainment: 4.4%. Taxes (43%) are not included in CPI
CPI= (Productrep X
Weights and sub-indices
Weights can be expressed as fractions or ratios summing to one, as
percentages summing to 100 or as per mille numbers summing to
In the European Union's Harmonised Index of Consumer Prices, for
example, each country computes some 80 prescribed sub-indices,
their weighted average constituting the national Harmonised Index.
The weights for these sub-indices will consist of the sum of the
weights of a number of component lower level indexes. The
classification is according to use, developed in a national
accounting context. This is not necessarily the kind of
classification that is most appropriate for a Consumer Price Index.
Grouping together of substitutes or of products whose prices tend
to move in parallel might be more suitable.
For some of these lower level indexes detailed reweighing to make
them be available, allowing computations where the individual price
observations can all be weighted. This may be the case, for
example, where all selling is in the hands of a single national
organisation which makes its data available to the index compilers.
For most lower level indexes, however, the weight will consist of
the sum of the weights of a number of elementary aggregate indexes,
each weight corresponding to its fraction of the total annual
expenditure covered by the index. An 'elementary aggregate' is a
lowest-level component of expenditure, one which has a weight but
within which, weights of its sub-components are usually lacking.
Thus, for example:Weighted averages of elementary aggregate indexes
(e.g. for men’s shirts, raincoats, women’s dresses etc.) make up
low level indexes (e.g. Outer garments),
Weighted averages of these in turn provide sub-indices at a higher,
more aggregated level,(e.g. clothing) and weighted averages of the
latter provide yet more aggregated sub-indices (e.g. Clothing and
Some of the elementary aggregate indexes, and some of the
sub-indexes can be defined simply in terms of the types of goods
and/or services they cover, as in the case of such products as
newspapers in some countries and postal services, which have
nationally uniform prices. But where price movements do differ or
might differ between regions or between outlet types, separate
regional and/or outlet-type elementary aggregates are ideally
required for each detailed category of goods and services, each
with its own weight. An example might be an elementary aggregate
for sliced bread sold in supermarkets in the Northern region.
Most elementary aggregate indexes are necessarily 'unweighted'
averages for the sample of products within the sampled outlets.
However in cases where it is possible to select the sample of
outlets from which prices are collected so as to reflect the shares
of sales to consumers of the different outlet types covered,
self-weighted elementary aggregate indexes may be computed.
Similarly, if the market shares of the different types of product
represented by product types are known, even only approximately,
the number of observed products to be priced for each of them can
be made proportional to those shares.
The outlet and regional dimensions noted above mean that the
estimation of weights involves a lot more than just the breakdown
of expenditure by types of goods and services, and the number of
separately weighted indexes composing the overall index depends
upon two factors:
- The degree of detail to which available data permit breakdown
of total consumption expenditure in the weight reference-period by
type of expenditure, region and outlet type.
- Whether there is reason to believe that price movements vary
between these most detailed categories.
How the weights are calculated, and in how much detail, depends
upon the availability of information and upon the scope of the
index. In the UK the RPI does not relate to the whole of
consumption, for the reference population is all private households
with the exception of a) pensioner households that derive at least
three-quarters of their total income from state pensions and
benefits and b) “high income households” whose total household
income lies within the top four per cent of all households. The
result is that it is difficult to use data sources relating to
total consumption by all population groups.
For products whose price movements can differ between regions and
between different types of outlet:
- The ideal, rarely realisable in practice, would consist of
estimates of expenditure for each detailed consumption category,
for each type of outlet, for each region.
- At the opposite extreme, with no regional data on expenditure
totals but only on population (e.g. 24% in the Northern region) and
only national estimates for the shares of different outlet types
for broad categories of consumption (e.g. 70% of food sold in
supermarkets) the weight for sliced bread sold in supermarkets in
the Northern region has to be estimated as the share of sliced
bread in total consumption × 0.24 × 0.7.
The situation in most countries comes somewhere between these two
extremes. The point is to make the best use of whatever data are
The nature of the data used for weighting
No firm rules can be suggested on this issue for the simple reason
that the available statistical sources differ between countries.
However, all countries conduct periodical Household Expenditure
surveys and all produce breakdowns of Consumption Expenditure in
their National Accounts. The expenditure classifications used there
may however be different. In particular:
- Household Expenditure surveys do not cover the expenditures of
foreign visitors, though these may be within the scope of a
Consumer Price Index.
- National Accounts include imputed rents for owner-occupied
dwellings which may not be within the scope of a Consumer Price
Even with the necessary adjustments, the National Account estimates
and Household Expenditure Surveys usually diverge.
The statistical sources
required for regional and
outlet-type breakdowns are usually weaker. Only a large-sample
Household Expenditure survey can provide a regional breakdown.
Regional population data are sometimes used for this purpose, but
need adjustment to allow for regional differences in living
standards and consumption patterns. Statistics of retail sales and
market research reports can provide information for estimating
outlet-type breakdowns, but the classifications they use rarely
correspond to COICOP categories.
The increasingly widespread use of bar codes, scanners in shops has
meant that detailed cash register printed receipts are provided by
shops for an increasing share of retail purchases. This development
makes possible improved Household Expenditure surveys, as
Statistics Iceland has demonstrated. Survey respondents keeping a
diary of their purchases need to record only the total of purchases
when itemised receipts were given to them and keep these receipts
in a special pocket in the diary. These receipts provide not only a
detailed breakdown of purchases but also the name of the outlet.
Thus response burden is markedly reduced, accuracy is increased,
product description is more specific and point of purchase data are
obtained, facilitating the estimation of outlet-type weights.
There are only two general principles for the estimation of
weights: use all the available information and accept that rough
estimates are better than no estimates.
Ideally, in computing an index, the weights would represent current
annual expenditure patterns. In practice they necessarily reflect
past expenditure patterns, using the most recent data available or,
if they are not of high quality, some average of the data for more
than one previous year. Some countries have used a three-year
average in recognition of the fact that household survey estimates
are of poor quality. In some cases some of the data sources used
may not be available annually, in which case some of the weights
for lower level aggregates within higher level aggregates are based
on older data than the higher level weights.
Infrequent reweighing saves costs for the national statistical
office but delays the introduction into the index of new types of
expenditure. For example, subscriptions for Internet Service
entered index compilation with a considerable time lag in some
countries, and account could be taken of digital camera prices
between re-weightings only by including some digital cameras in the
same elementary aggregate as film cameras.
Between 1971 and 1977, the United States CPI increased 47%.
In 2009 the Consumer Price Index fell for the first time since
- Bloomberg Business News, Social Security Administration
- Harper's Magazine
- Specific countries