Definition:
Index Numbers
This is a statistical method of measuring a variable or a group of related variables with respect to its value at a particular period or time. An index number is a time series which shows how figures compare by using ratios. Index number reflects price or quantity compared with a standard/reference/base value. The base usually equals 100 and the index number is usually expressed as 100 times the ratio to the base value.
Spiegel defined an index number as “a statistical measure designed to show changes in variable or a group of related variables with respect to time, geographic location or other characteristic”
Suppose that a tin of peak milk on OAU campus cost 75k in 1995. In 2002, an identical tin of peak milk cost 99k. How has the price changed between 1995 and 2002? The particular time period of 1995 which we've chosen to compare against, is called the base period.
The variable for that period, in this case the 75k, is then given a value of 100, corresponding to 100%. The index can then be calculated for the later period of 2002 as a proportionate change as follows:
The index number/100 = 99/75
So, the index number = 99/75 * 100 = 132
The index number shows us that there has been a price increase of 32% since the base period. An index number for a single price change like this is called a price relative.
Characteristics of index numbers are apparent.
1. Index numbers are specified averages.
2. Index numbers are expressed in percentage.
3. Index numbers measure changes not capable of direct measurement.
4. Index numbers are for comparison.
Types of Index numbers:
There are various types of index numbers, but in this class, we shall consider three kinds and they are: (a) Price Index, (b) Quantity Index and (c) Value Index
(a) Price Index:
For measuring the value of money, in general, price index is used. It is an index number which compares the prices for a group of commodities at a certain time as at a place with prices of a base period. There are two price index numbers such as whole sale price index numbers and retail price index numbers. The wholesale price index reveals the changes into general price level of a country, but the retail price index reveals the changes in the retail price of commodities such as consumption of goods, bank deposits, etc.
This is a measure of change in a set of prices, consisting of a series of numbers arranged so that a comparison of the values for any two periods or places will show the change in prices between periods or the difference in prices between places. Price indexes were first developed to measure changes in the cost of living in order to determine the wage increases necessary to maintain a constant standard of living.
(b) Quantity Index:
Quantity index number is the changes in the volume of goods produced or consumed. They are useful and helpful to study the output in an economy.
A measure reflecting the average of the proportionate changes in the quantities of a specified set of goods and services between two periods of time. Usually a quantity index is assigned a value of 100 in some selected base period and the values of the index for other periods are intended to indicate the average percentage change in quantities compared with the base period.
A quantity index is built up from information on quantities such as the number or total weight of goods or the number of services; the quantity index has no meaning from an economic point of view if it involves adding quantities that are not commensurate.
(c) Value Index
Value index numbers compare the total value of a certain period with total value in the base period. Here total value is equal to the price of commodity multiplied by the quantity consumed.
Notation: For any index number, two time periods are needed for comparison. These are called the Base period and the Current period. The period of the year which is used as a basis for comparison is called the base year and the other is the current year. The various notations used are as given below:
P1 = Price of current year
P0 = Price of base year
q1 = Quantity of current year
q0 = Quantity of base year
Weighted aggregate indexes
Weighted aggregate indexes weight each price according to the quantity bought in a particular time period which could be the base period or the current period. In order to attribute appropriate importance to each of the items used in an aggregate index number some reasonable weights must be used.
There are various methods of assigning weights and consequently a large number of formulae for constructing index numbers have been devised of which some of the most important ones are:
1. Laspeyre’s method
2. Paasche’s method
3. Fisher’s ideal Method
4. Bowley’s price index
5. Marshall-Edgeworth method
