Base shifting

Shifting of base period or reference period of the index is known as base shifting.

This can be done using the following relation as,

Example
The following are the index numbers of a commodity taking 1991 as the base.

 Years 1991 1992 1993 1994 1995 Index Numbers 100 120 150 180 225

Find the index numbers by changing the base to 1994.
Solution

Splicing

The process of combining two or more index numbers covering different bases into a single series is called splicing.

Suppose we have two series A and B, and if series A is spliced with B, then

If series B is spliced with A, then

Example
The following are two series A and B of the index numbers of a commodity taking 1991 and 1994 as the base years.

 Years Index Series A Index Series B 1991 100 - 1992 90 - 1993 125 - 1994 150 100 1995 - 120 1996 - 150 1997 - 200 1998 - 225

1. Splice the index series of A to B
2. Splice the index series of B to A
Solution
1. Index series A spliced with index series B

1. Index series B spliced with index series A

Deflating

It is a technique used to make allowances for the effect of changing price values. It is used to measure the purchasing power of money.

It can also be found using the relation

Example
The table below shows the income of a company and its price index taking the year 1991 as the base.

 Years 1991 1992 1993 1994 1995 1996 Income (in crores) 80 108 125 147 216 230 Price Index 100 120 125 140 180 200

Calculate the deflated value for every year taking 1991 as the base.
Solution