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# Fisher’s Index Number as an Ideal Method

A statistical measure that helps in finding out the percentage change in the values of different variables, such as the price of different goods, production of different goods, etc., over time is known as the Index Number. The percentage change is determined by taking a base year as a reference. This base year is the year of comparison. When an investigator studies different goods simultaneously, then the percentage change is considered the average for all the goods. Three methods of measuring Index Numbers are Laspeyre’s Method, Paasche’s Method, and Fisher’s Method.

### Fisher’s Method

The method of calculating Weighted Index Numbers under which the combined techniques of Paasche and Laspeyres are used is known as Fisher’s Method. In other words, both the base year and current year’s quantities are used as weights. The formula for Fisher’s Price Index is: Choosing the best method for constructing an index number depends upon the object with which a specific index number is constructed. An investigator can use various methods of constructing index numbers, but it is not necessary that every method is suitable for the purpose at hand. Therefore, it is essential to find an ideal method of calculating Index Number. Other methods of Index Number do not conform to consistency behaviour tests and provide biased results. However, Fisher’s Method is preferred by the investigators and is considered an ideal method.

### Fisher’s Method: An Ideal Method of Calculating Index Number

Fisher’s Method of calculating index number is considered an ideal method because of the following reasons:

1. Fisher’s Method is based on variable weights.

2. While calculating index number it takes price and quantities of both the base year and current year into consideration.

3. This method is based on Geometric Mean (GM), and GM is considered the best mean for determining index number.

4. Lastly, Fisher’s Method satisfies both tests; i.e., Time Reversal Test and Factor Reversal Test. According to the Time Reversal Test, a method of calculating Index Number should have a formula that will give the same ratio between the two points of comparison no matter which point is taken as the base. In simple words, Time Reversal means that if the base year changes to the current year and vice versa, then there should be unity in the product of those two indexes. Hence, it is essential for an index number to work backwards as well as forward. However, according to Factor Reversal Test, just like changing the base year to the current year and vice versa should not give inconsistent results, similarly, interchanging the prices and quantities should also not give inconsistent results. Simply put, the product of both indexes should provide an equal ratio.

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