Page 226 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes LP
+
P =
01 2
where L = Laspeyre’s Index
P = Paasche’s Index
or

Σ 10 + Σpq p q
1 1
Σ Σpq pq
P = 00 0 1 ×100
01 2
4. Fisher’s Ideal Index: Prof. Irving Fisher has given a number of formulae for constructing index
numbers and of these he calls one as the ‘ideal’ index. The Fisher’s Ideal Index is given by the
formula:

Σ 10 Σpq pq
1 1
P = × × 100
01 Σ 00 Σpq pq
01
or
×
P = LP
01
It shall be clear from the above formula that Fisher’s Ideal Index is the geometric mean of the
Laspeyre and Paasche indices. Thus in the Fisher method we average geometrically formulae
that are in opposite directions.

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 above formula is known as ‘Ideal’ because of the following reasons:
(i) It is based on the geometric mean which is theoretically considered to be the best average
for constructing index numbers.
(ii) It takes into account both current year as well as base year prices and quantities.
(iii) It satisfies both the time reversal test as well as the factor reversal test as suggested by
Fisher.
(iv) It is free from bias. The two formulae (Laspeyre’s and Paasche’s) that embody the opposing
type and weight biases are, in the ideal formula, crossed geometrically, i.e., by the averaging
process that of itself has no bias. The result is the complete cancellation of biases of the
kinds revealed by time reversal and factor reversal tests.
It is not, however, a practical index to compute because it is excessively laborious. The data,
particularly for the Paasche segment of index, are not really available. In practice, statisticians
will continue to rely upon simple, although perhaps less exact, index number formulae.
5. Marshall-Edgeworth Method: In this method also both the current year as well as base year
prices and quantities are considered. The formula for constructing the Index is:
Σ ( + q q 1 ) 0 p 1
P = × 100
01 Σ ( + q q 1 ) 0 p 0

220 LOVELY PROFESSIONAL UNIVERSITY