3.2 Different index formula

The three most famous names in the world of indices are Etienne Laspeyres, Hermann Paasche and Irving Fisher. In Finland the name that has gained most international recognition in this field is Leo Törnqvist.

The Laspeyres index formula

The price P of commodity i at time _t is multiplied by the quantity Q of commodity i at base period _o (Pi_tQi_o). The sum of the products of all commodities at the time of calculation (Pi_tQi_o) is divided by the sum of the products of all commodity prices and quantities (Pi_oQi_o). In other words, the value of the commodity basket at the time of calculation, based on the quantities at base period, is divided by the value of the commodity basket at base period.

Pi_t = Price of commodity i at calculation time
Pi_o = Price of commodity i at base period
Qi_o = Quantity of commodity i at base period

The Paasche index formula

The price P of commodity i at the time of calculation _t is multiplied by the quantity Q of commodity i at the time of calculation _t (Pi_tQi_t ). The sum of the products of all commodities at the time of calculation (Pi_tQi_t) is divided by the sum of the products of prices at base period and quantities at calculation time (Pi_oQi_t).

The Fisher index formula

The Fisher index formula calculates the geometric mean of the Laspeyres and Paasche indices.

The Laspeyres formula tends to give too fast a rate and the Paasche formula too slow a rate for the growth of the consumer price index. The Fisher formula is the most accurate of all three, giving an index change rate that falls in-between the former two.

Examples