# Problems In The Construction Of Index Numbers
Before constructing index numbers a careful thought must be given the following problems:
## 1. The purpose of the index.
At the very outset the purpose of constructing the index must be very clearly, decided – what the index is to measures and why? There is no all-purpose index. Every index is of limited and particular use. Thus, a price index that is intended to measure consumers’ prices must not include wholesale prices. And if such an index in intended to measure the cost of living of poor families, great care should be taken not to include goods ordinarily used by middle class and upper-income groups.
## 2. Selection of a base period.
Whenever index numbers are constructed a reference is made to some base period. The base period of an index number (also called the reference period) is the period against which comparisons are made.
### (i) The base period should be normal one.
The period that is selected as base should be normal, i.e., it should be free from abnormalities like wars, earthquakes, famines, booms, depressions, etc. However, at times it is really difficult to select year which is normal in al respects – a year which is normal in one respect may be abnormal in another.
### (ii) The base period should not be too distant in the past.
It is desirable to have an index based on a fairly recent period, since comparison with a familiar set of circumstances is more helpful than comparison with vaguely remembered conditions.
### (iii) Fixed base or chain base.
While selecting the base a decision has to be made as to whether the base shall remain fixed or not, i.e., whether we have a fixed base or chain base index.
## 3. Selection of number of items.
The items included in an index should be determined by the purpose for which the index is constructed. Every item cannot be included while constructing an index number and hence once has to select a sample. It is also necessary to decide the grade or quality of the items to be included in the index. Index numbers shall give wrong result if at one time one set of qualities is included and at another time another set.
## 4. Price quotations.
After the commodities have been selected, the next problem is to obtain price quotations for these commodities. It is a will known fact that prices of many commodities vary from place to place and even from shop to shop in the same market. It is impracticable to obtain price quotations from all the places where a commodity is dealt in. A selection must be made of representative places and persons. These places should be those which are well known for trading for that particular commodity.
## 5. Choice of an Average.
Theoretically speaking, geometric mean is the best average in the construction of index numbers because of following reasons: (i) in the constructions of index number we are concerned with ratios of relative changes and the geometric mean gives equal weights to equal ratio of change; (ii) geometric mean is less susceptible to major variations as a result of violent fluctuations in the values of the individual items; and (iii) index numbers calculated by using the average are reversible and, therefore, base shifting is easily possible. The geometric mean index always satisfies the time reversal test.
## 6. Selection of appropriate weights.
The problem of selecting suitable weights in quite important and at the same quite difficult to decide. The term ‘weight’ refers to the relative importance and hence it is necessary to devise some suitable method whereby the varying importance of the different items by taken into account. This is done by allocating weights. Thus, in the former case, no specific weights are assigned whereas in the latter case specific weights are assigned to various items. It may be pointed out here that no index is unweighted in strict sense of the term as weights implicitly enter the unweighted indices because we are giving equal importance to all the items and hence weights are unity. It is, therefore, necessary to adopt some importance to all the items and hence weights are unity. It is, therefore, necessary to adopt some suitable method of weighting so that arbitrary and haphazard weights may not affect the results. There are two methods of assigning weights: (i) implicit, and (ii) explicit.
## 7. Selection of an appropriate formula.
A large number of formulae have been devised for constructing the index. The problem very often is that of selecting the most appropriate formula. The choice of the formula would depend not only on the purpose of the index but also on the data available.
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