Different ways of measuring
the Consumer Price Index (CPI)
Economics,
Economic / Financial Data
The consumer
price index
(CPI) is used as an estimate of the
general price level of an economy.
The
percentage change in the CPI is used as an estimate of the
rate of
inflation.
CPI data is gathered by sampling
prices and using a ‘basket’
of goods as weights.
This basket would be renewed every few years. In some countries CPI figures are released monthly,
while
in other countries they are released quarterly.
The following sections describe some of the different
methods for calculating CPI. These indices are
typically multiplied by
1000 so that the base period index would equal 1000.
Laspeyres Index
Published CPI
figures for
most countries are usually described as having been calculated using a
Laspeyres index, but the actual calculation could differ due to the
base period
price and quantity / expenditure data being recorded at slightly
different
times. The
conventional methods are more
accurately described as a Lowe index (explained
later) that either conforms or closely conforms to a
Laspeyres index.
CPI (Laspeyres) formula:

Where:
is
the price of item
i at
time 0 (the base period)
is the price of item
i at
time t
is the quantity
consumed of item i
at time 0
An
alternative formula for the Laspeyres index is as follows:

Where
is the level of expenditure
of item i at
time 0.
An advantage of the Laspeyres index is that it is relatively
easy to get timely figures. If
you
already have the prices and weights for the base period, you would only
need
prices for the period you want to investigate.
For most other indices, you would need both prices
and weights to be
up-to-date for that period.
A disadvantage of the Laspeyres index, is that it can suffer
from item substitution bias (explained
later).
Paasche Index
The CPI
calculated via a
Paasche index, helps give an idea of what today’s ‘basket’ would have cost at
yesterday’s prices.
CPI (Paasche) formula:

Where:
is
the price of item
i at
time 0 (the base period)
is the price of item
i at
time t
is the quantity
consumed of item i
at time t
An
alternative formula for the Paasche index is as follows:

Where
is the level of
expenditure of item i at
time t.
Fisher Index
The Fisher
index is calculated by taking the geometric mean of the Laspeyres and
Paasche indices:

The Fisher index helps overcome the problem of item
substitution bias.
Item Substitution
Bias
The
law of
demand states that if the price of a good increases, the quantity
demanded of
that good decreases, and vice versa (with
all other variables remaining the same).
Let’s
say
the price increases for a good with a high weighting and the price
remains the
same for a good with a low weighting.
If
consumers respond to the price increase of the first good, by
substituting it
with the second, the overall inflation estimate would be overstated if
a
Laspeyres index is used. This
is an
example of item substitution bias.
The
Laspeyres method tends to over-estimate the general price level, while
the
Paasche method tends to under-estimate it.


The above table and
graph are from:
OECD
Seminar 2005, Inflation Measures: too high – too low
– internationally comparable?
Measurement Issues in the New Zealand Consumers Price Index.
https://www.oecd.org/dataoecd/4/32/35081389.pdf
Lowe Index
The Lowe index has a relatively
generalised formula, where
the quantities / expenditure weights could potentially have a different
reference period to the base or latest periods.
Laspeyres and Paasche indices are special cases of
the Lowe index. The
reference period for the weights, could
be before the base period.
CPI (Lowe) formula:

Where:
is
the price of item
i at
time 0 (the base period)
is the price of item
i at
time t
is the quantity
consumed of item i
at time r
An
alternative formula for the Lowe index is as follows:

Where is the level of
expenditure of item i at
time r.
Törnqvist Index
Like the Fisher index, the
Törnqvist index can help overcome
item substitution bias.

OR

Walsh Index
Like the Fisher
index, the Walsh index can help overcome
item substitution bias.

See
also:
Index
Numbers
Elementary
Indices
Axiomatic
Analysis of
Elementary Indices
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