PaascheIndex

The Paasche index, named after the economist Hermann Paasche, is a price index used to measure changes in the general price level between two periods, weighting prices by the current period’s quantities. It reflects how much the current basket would cost in the current period compared with how much the same current-period basket would cost in the base period.

For a set of goods i, with prices p_i^t and p_i^0 in the current (t) and base (0) periods, and quantities q_i^t in the current period, the Paasche price index is defined as P_P = (sum_i p_i^t q_i^t) / (sum_i p_i^0 q_i^t). The numerator is the total expenditure required to buy the current-period quantities at current prices, and the denominator is the same expenditure evaluated at base-period prices. Thus, P_P > 1 indicates overall price increases, while P_P < 1 would indicate price declines.

The Paasche index uses current-period quantities as weights, in contrast to the Laspeyres index, which uses base-period quantities. As a result, the Paasche index incorporates substitution effects: if consumers shift toward cheaper goods, the Paasche index tends to show a smaller rate of price rise than the Laspeyres index under the same data. In practice, both indices are used in conjunction with each other, or combined (e.g., Fisher index) to mitigate bias.

Limitations include data requirements for current-period quantities and potential bias from product entry and quality changes. The Paasche index remains a fundamental concept in index number theory and national price statistics.