What methods of Index Number calculation is used to calculate Cost of Living Index (CoLI).
Index Number: An Index number is a single figure that shows how the whole set of related variables has changed over time or from one place to another. Some commonly used indices are –Consumer Price index, producer price index, Stock market indices etc.
In particular, a price index reflects the overall change in a set of prices paid by a consumer or a producer, and is conventionally known as a Cost-of-Living index or Producer's Price Index as the case may be.
Price Index Numbers can be classified as simple price index number (mainly for one commodity) or composite index number (consisting of more than one commodity).
Calculation of Composite price index is carried out by two methods :- 1. Un-weighted aggregative method (Only prices of multiple commodities) 2. Weighted Aggregative method (Prices and Quantities of multiple commodities).
For calculation of CoLI which considers multiple commodities weighted aggregative method is used.
Three universally accepted price indices which depict the Cost of Living are :- 1. Laspeyres Price index : This is a fixed basket weighted price index calculated using quantity weights from a historical period.

This has an inherent upward bias since it does not consider the substitution commodities whose prices have increased in turn the quantity is substituted by a lesser priced commodity. Hence this acts as an upper bound on cost of Living. 2. Paasche Price index: Weighted index calculated using quantity weights from the current year.

This has an inherent downward bias. Hence it acts as the lower bound on cost of living.

3. Fisher Price index : This is the closest approximation of the Cost of Living and is calculated as the geometric mean of the Laspeyres and Paasche Price indices.

Since the Laspeyres and Paasche Price indices show the boundaries of the Cost of living, the Mean of the two indices is closest to the actual cost of living index.

Fisher Index which is the Geometric mean is taken to accommodate the fact that Laspeyres index acts as the arithmetic mean using weights from a previous period where as Paasche’s index acts a weighted harmonic average of the price relatives that uses the actual expenditure shares in the current period as weights.

Also the price and quantity changes over a period of time generally are negative for most commodities due the Bias arising from new products and substitution by the consumers.

The relation that holds true is

Laspeyres ≥ Fisher ≥ Paasche.

True value of the cost of living can never be absolutely determined but the closest portrayal of cost of living is given by the Fisher Price Index.

References:

Bibliography 1. Statistics for Business Economics. - Anderson, Sweeney, Williams 2. Basic Statistics for Business & Economics. - Lind, Marchel, Wathen, Waite.

Web Resources 1. Statistics SA website 2. AllBankingSolutions.com 3. Wikipedia