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Question
Define Time Reversal Test
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Solution
It is an important test for testing the consistency of a good index number.
This test maintains time consistency by working both forward and backward with respect to time (here time refers to base year and current year).
Symbolically the following relationship should be satisfied.
P01 × p10 = 1
Fisher’s index number formula satisfies the above relationship
`"P"_01^"F" = sqrt((sum"p"_1"p"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1))`
When the base year and current year are interchanged, we get
`"P"_10^"F" = sqrt((sum"p"_0"q"_1 xx sum"p"_0"q"_0)/(sum"p"_1"q"_1 xx sum"p"_1"q"_0))`
`"P"_01^"F" xx "P"_10^"F"` = 1
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Index Number is a technique of measuring changes in a variable or group of related variables with reference to time, geographical location and other characteristics. Index Number is very useful for economists, farmers, traders, government, educationalists and trade union leaders for planning and implementing the plans according to their sector. The scope of index number is not limited to only one subject but it extends to many subjects such as Economics, Educational science, Psychology, History, Sociology, Geography etc. While framing index number its objective must be determined. To attain the objective the information is collected in various ways and this information is used for comparing two different time periods. For this purpose, the base year’s index is assumed as 100 and accordingly the value of the current year is calculated. Laspeyre, Paasche and Fisher have suggested different methods for constructing index numbers. |
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