## Index Numbers:

Index numbers are used to measure the changes in one or more variable over a period of time. These numbers are stated as a percentage of a base figure. Index numbers are the specialized averages that measure the change in level of a phenomenon. They measure the effect of changes over a period of time. A collection of index numbers for years is referred to as index series. Consider an example now.

Monica purchased an apartment in 2010 that she wishes to sell now. She wants to know the value of the apartment as on the present day so she can get the right price. She wants to know the present value of the money she spent to buy the apartment in 2010. How can she find that? There is no direct measure to study the change in the effect of such factors. This is when Index numbers come into play. An index number is calculated by finding the ratio of the current value to a base value.

### Formal Definitions:

Few Definitions of Index numbers:

According to Bowley, “Index numbers are used to measure the changes in some quantity which we cannot observe directly”.

According to Ronold, “Index numbers are quantitative measures of growth of prices, production, inventory and other quantities if economic interest.”

### Applications:

- In scenarios where inflation plays a major part, index numbers are useful in deflating.
- As these numbers aid in measuring the effect of change over a period of time they reveal various trends and tendencies.
- Using index numbers various suitable policies can be framed.
- They are used in the field of commerce, meteorology, industry etc.
- They measure the purchasing power of money.
- They are helpful in studying the difference between comparable categories of people and items.
- Index numbers of import and export prices of a country help measure the changes in trade of a country.
- They measure the seasonal and cyclical variations for a time period.

### What are the types of index numbers and how are they useful?

- Simple index number:

In the simple index number all the items of variables in the series are given equal weightage. They are all given equal importance. These index numbers are constructed form a single variable. This measures a relative change in single variable to its respective base.

- Composite index number:

Two or more indices when combined together form a composite index number. Consider an example for better understanding. Indices of consumer spending on gold and on all other accessories could be combined into one index.

- Price index number:

Price index number is a scale that is used to measure changes in the level of prices. It can be based on price of a single item or a selected group of items referred to as a market basket. Mostly, price indices are uses to measure inflation. The consumer price index is focussed on the goods and services consumed by households while the produce price index directs its focus towards the goods purchase by businesses that is used for further production.

To better understand the usage of price index, one must clearly understand what price means. Price is the value of money paid for the purchase of goods or services. When the price of a product falls, it means that the value of money has risen and when the price rises, it means that the value has fallen. A price index is a statistical measure that expresses a price change as a percentage of price in the base year. Some examples of price indices in India are index of retail prices, index of wholesale prices, cost of living index of industrial workers etc.

- Quantity index number:

These are the index numbers that measure the changes in the level of quantities consumed, produced and distributed for an item or group of items during a year under reference in relation to the base year. These are highly significant as they indicate the level of output in an economy.

### Methods of constructing index numbers:

- Simple Aggregate method:

It is the method of expressing the aggregate price of all the commodities in the year under reference as a percentage of the aggregate price in in the base year. By computing the price relatives and averaging them all, a simple price index is constructed. The price relatives are then added and divided by the number of items.

- Simple average of relatives method:

In this method the current year price is expressed as a price relative of the price in the base year. To arrive at the index number, these price relatives are averaged. The average used could be median, arithmetic mean or even geometric mean.

- Weighted aggregative Index numbers:

The fundamental difference between the simple aggregative type and the weighted aggregative type is that in case of latter, weights are assigned to the various items included in the index. The different methods used to calculate weighted aggregative index numbers are:

- Dorbish and bowley’s method
- Fisher’s ideal method
- Marshall-Edgeworth method
- Laspeyres method
- Paasche method
- Kelly’s method

- Weighted average of price relative method:

Here, the price relatives for the current year are calculated based on the prices of the base year. The respective weights of the items are multiplied with the price relatives. The resultant products are all summed up and that value is divided by the sum of weights.

Index numbers have uses that are widely applied in various scenarios. However, these are not free from problems. Look at a few problems related to index numbers:

- Choice of base period.
- Choice of an average
- Choice of commodities
- Choice of index
- Data collection.

Finally, to put it in a nutshell, index numbers are statistical devices that measure relative changes in large number of items. There are several formulae for computing index numbers based on the base year taken into consideration and also the question of interest. However, every formula that is used requires careful interpretation. The adequacy of the index number calculated could also be checked using four tests namely time reversal test, factor reversal test, unit test and circular test.

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