# Index Numbers

## Definition

### Health Economics

The most common forms of index met in health economics are price and quantity indices. A price (cost of living) index measures the change in the weighted prices of a (constant) bundle of goods or services over time. It is the standard measure of inflation. A quantity index (standard of living) measures the change in the weighted quantities of goods or services when prices are constant. The procedure in each case is basically the same: the current data are compared with those in a 'base' (usually earlier) period and presented either as a ratio or (if multiplied by 100) as a percentage. The weights used may be either those of the current period or those of the base period. Thus:

*P*_{L}= SP_{n}Q_{0}/SP_{0}Q_{0}is the Laspeyres price index,

*P*is the price per unit in period_{n}*n*and*Q*is the quantity produced in base period 0 using base period quantities as weights in both period_{0}*n*and period 0. The Laspeyres price index thus measures the change in cost of purchasing the same basket of goods and services in the current period as was purchased in a specified base period. It is named after German economist, Etienne Laspeyres (he preferred it pronounced Las-pey-res) (1834-1913).*P*_{P}= SP_{n}Q_{n}/SP_{0}Q_{n}is the Paasche price index, which compares the cost of purchasing the current basket of goods and services with the cost of purchasing the same basket in an earlier period. Prices are weighted by current quantities.

*P*is the price per unit in period_{n}*n*and*Q*is the quantity produced in period_{n}*n*. It is named after another German economist Hermann Paasche (the 'e' is not silent) (1851-1925).Quantity indices weight different bundles by the prices obtaining either in period

*n*or period 0.Other indices include Fisher's ideal index (the geometric mean of the Laspeyres and Paasche indices of price or quantity). This is named after the US economist Irving Fisher (1867-1947); the Malmquist index, a method of measuring productivity change that does not depend upon knowledge of the prices of inputs or outputs provided that a production frontier is known. It is used in data envelope analysis ; and the Trnqvist index, the weighted average change in the log of price or quantity in the measurement of changes in (e.g.) productivity over time.