Page 225 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 16: Methods—Simple (Unweighted) Aggregate Method and Weighted Aggregate Method

Laspeyres Index attempts to answer the question: What is the change in aggregate value of Notes
the base period list of goods when valued at given period prices ? This index is very widely
used in practical work.
2. Paasche Method: In this method the current year quantities are taken as weights. The formula
for constructing the index is:
Σpq
11
P = ×100
01 Σpq
01
Steps:
(i) Multiply the current year prices of various commodities with base year weights and obtain
Σpq .
11
(ii) Multiply the base year prices of various commodities with the base year weights and
obtain Σpq .
01
(iii) Divide Σpq by Σpq and multiply the quotient by 100.
01
11
In general this formula answers the question: What would be the value of the given period list
of goods when valued at base-period prices ?
Comparison of Laspeyres and Paasche Methods. From a practical point of view, Laspeyres index is
often preferred to Paasche’s for the simple reason that in Laspeyres index weights (q ) are the
0
base-year quantities and do not change from one year to the next. On the other hand, the use of
Paasche index requires the continuous use of new quantity weights for each period considered
and in most cases these weights are difficult and expensive to obtain.
An interesting property of Laspeyres and Paasche indices is that the former is generally expected
to overestimate or to leave an upward bias, whereas the latter tends to underestimate, i.e., shows
a downward bias. When the prices increase there is usually a reduction in the consumption of
those items for which the increase has been the most pronounced, and hence, by using base
year quantities we will be giving too much weight to the prices that have increased the most
and the numerator of the Laspeyres index will be too large. When the prices go down, consumers
often shift their preference to those items which have declined the most and, hence, by using
base-period weights in the numerator of the Laspeyres index we shall not be giving sufficient
weights to the prices that have gone down the most and the numerator will again be too large.
Similarly because people tend to spend less on goods when their prices are rising the use of the
Paasche or current weighting produces an index which tends to underestimate the rise in prices,
i.e., it has a downward bias. But the above arguments do not imply that Laspeyres index must
necessarily be larger than the Paasche’s.
Unless drastic changes have taken place between the base year and the given year, the difference
between the Laspeyre’s and Paasche’s will generally be small and either could serve as a
satisfactory measure. In practice, however, the base year weighted Laspeyre’s type index remains
the most popular for reasons of its practicability. The Paasche type index can only be constructed
when up-to-date data for the weights are available. Furthermore, the price index of a given
year can be compared only with the base year. For example, let P =102, P = 130, and P = 145.
84
83
82
Then P and P are using different weights and cannot be compared with each other.
83 84
If these indices had been obtained by the Laspeyre’s formula they could be compared because
in that case the weights are the same base-year weights (q ). For these reasons, in practice the
0
Paasche formula is usually not used and the Laspeyre type index remains most popular for
reasons of its practicability.
3. Dorbish and Bowley’s Method: Dorbish and Bowley have suggested simple arithmetic mean
of the two indices (Laspeyres and Paasche) mentioned above so as to take into account the
influence of both the periods, i.e., current as well as base periods. The formula for constructing
the index is:

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