# Chain Base Method

In this method, there is no fixed base period. The year immediately preceding the one for which price index have to be calculated is assumed as the base year. Thus, for the year1994 the base year would be 1993, for 1993 it would be 1992 for 1992 it would be 1991 and so on. In his way there is no fixed base. It goes on changing. The chief advantage of this method is that the price relatives of a year can be compared with the price level of the immediately preceding year. Businessmen mostly interested in comparison of this type rather than in comparison relating to distant past. Yet another advantage of the chain base method is that it is possible to include new items in an index number or to delete old times which are no more important. In fixed base method it is not possible. But chain base method has drawback that comparison cannot be made over a long period.

In Chain Base,
Link relative of current years ${\text{ = }}\frac{{{\text{Price in the Current Year}}}}{{{\text{Price in the preceding Year}}}} \times 100$
or

Example:
Find index numbers for the following data taking 1980 as base year.

 Years $1974$ $1975$ $1976$ $1977$ $1978$ $1979$ Price $18$ $21$ $25$ $23$ $28$ $30$

Solution:

 Year Price Link Relatives $= \frac{{{P_n}}}{{{P_{n - 1}}}} \times 100$ Chain Indices $1974$ $18$ $\frac{{18}}{{18}} \times 100 = 100$ $100$ $1975$ $21$ $\frac{{21}}{{18}} \times 100 = 116.67$ $\frac{{100 \times 116.67}}{{100}} = 116.67$ $1976$ $25$ $\frac{{25}}{{21}} \times 100 = 119.05$ $\frac{{116.67 \times 119.05}}{{100}} = 138.9$ $1977$ $23$ $\frac{{23}}{{25}} \times 100 = 92$ $\frac{{138.9 \times 92}}{{100}} = 127.79$ $1978$ $28$ $\frac{{28}}{{23}} \times 100 = 121.74$ $\frac{{127.79 \times 121.74}}{{100}} = 155.57$ $1979$ $30$ $\frac{{30}}{{28}} \times 100 = 107.14$ $\frac{{155.57 \times 107.17}}{{100}} = 166.68$

Selection of the Suitable Average:

There are different averages which can be used in averaging the price relatives or link relatives of different commodities. Experts have suggested that the geometric mean should be calculated for averaging these relatives. But as the calculation of the geometric mean is difficult, it is mostly avoided and the arithmetic mean is commonly used. In some cases the median is used to remove the effect of the wile observations.

Selection of Suitable Weights:

In calculation of price index numbers all commodities are not of equal importance. In order to give them due importance, commodities are given due weights. Weights are of two kinds (a) Implicit weights, (b) Explicit weights. In the first kind of weights are not explicitly assigned to any commodity but the commodity to which greater importance is attached is repeated a number of times. A number of varieties of such commodities are included in the index number as separate items. Thus, if an index number wheat is to receive a weight of 3 and rice a weight of 2, three varieties of wheat and two varieties rice would be included in this method weights are not apparent, but items are implicitly weighted. Such weights are known as implicit weights. In the second kind weights are explicitly assigned to commodities. Only one variety of the commodity included in the construction of index number but its price relative is multiplied by the figure of weight assigned to it. Explicit weights are decided on some logical basis. For example, if wheat and rice are to be weighted in accordance with the value of their net output and if the ratio of their net output is 5:2, wheat would receive a weight of five and rice of two. Such weights are called explicit weights. Sometimes the quantities which are consumed are used as weights. These are called quantity weights. The amount spent on different commodities can also be use as their weights. These are called the value weights.