Page 233 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

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

Fisher’s Ideal Index Number for 2010 Notes

∑ pq × ∑ p q
or P = 10 11 × 100
01 ∑ pq × 00 ∑ pq
0 1
102 112
= × × 100
122 134

= .84 .84 100× × = .84 ×100 = 84
Self-Assessment

1. Which of the following statements is True or False:
(i) The base period should be a normal period.
(ii) Unweighted indices are actually implicitly weighted.
(iii) Bowley’s index is the geometric mean of Laspeyre and Paasche Index.
(iv) Marshall-Edgeworth’s method satisfies the time reversal test.
(v) In the Paasche’s Price index, the weights are determined by quantities in the base period.
16.3 Summary

• Simple Index Number is that Index number in which all the items are assigned equal importance. In
other words, weights are not assigned to the different commodities and as such it is also called
unweighted Index Number.
• In constructing simple index numbers, all commodities are given equal importance but in
practice, all commodities don’t have equal importance. For example, for a consumer, wheat is
more important than vegetable or pulse. Similarly, clothes are more important than a video. To
express the relative importance of different commodities, weights on some definite basis are
used. When index numbers are constructed taking into consideration the importance of different
commodities, then they are called weighted index numbers.
• This is the simplest method of constructing Index Number. In this method the total of current
year prices for the various commodities is divided by the total of base year prices, the resultant so
obtained is multiplied by 100 to get the Index Numbers for the current year in terms of percentage.
• Simple aggregative method of index number construction is very easy but it can be applied
only when the prices of all commodities have been expressed in the same unit.
• These indices are of the simple aggregative type with the fundamental difference that weights
are assigned to the various items included in the index. There are various methods of assigning
weights and consequently a large number of formulae for constructing index numbers have
been devised of
• 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 base-year quantities and do not change from
0
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.
• 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.
• 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

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