Divisia index

A Divisia index is a theoretical construct to create index number series for continuous-time data on prices and quantities of goods exchanged. The name comes from François Divisia who first proposed and formally analyzed the indexes in 1926, and discussed in related 1925 and 1928 works.

The Divisia index is designed to incorporate quantity and price changes over time from subcomponents that are measured in different units, such as labor hours and equipment investment and materials purchases, and to summarize them in a time series that summarizes the changes in quantities and/or prices. The resulting index number series is unitless, like other index numbers.

In practice, economic data are not measured in continuous time. Thus, when a series is said to be a Divisia index, it usually means the series follows a procedure that makes a close analogue in discrete time periods, usually the Törnqvist index procedure or the Fisher Ideal Index procedures.

Divisia-type indices are used in these contexts for example:

The theory of the Divisia indexes of goods (say, inputs to a production process, or prices for consumer goods) uses these components as data input:

Then a price index P(t) and quantity index Q(t) are the solution to a differential equation and if P(0) and Q(0) were chosen suitably the series summarize all transactions in the sense that for all t:

In practices, discrete time analogues to Divisia indexes are the ones computed and used. To define and compute changes in a discrete time index closely analogous to a Divisia index from time 0 to time 1:

Divisia indexes were proposed and analyzed formally by François Divisia in 1926, and discussed in related 1925 and 1928 works.

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