Paasche Price Index

The Paasche price index is defined reciprocally to the Laspeyres index by using the values of the later period t as weights, and a harmonic average of the relatives:



The Paasche index is estimated using a formula with price ratios multiplied by current expenditure shares. To derive a formula so that current prices cancel in the numerator of the expenditure share proportion of the formula with the denominator in the price ratio portion of the formula a reciprocal price ratio – p₀/p_t – is used. This results in the formula becoming a harmonic mean (reciprocal).

The Paasche index represents the lower boundary of ‘true’ inflation.

The Paasche index, as the Laspeyres index, fails the time reversal, the circularity as well as the factor reversal tests, but the remaining tests, the proportionality, the commensurability, and the monotonicity, hold.

Note! An arithmetic averageof the price relatives using current period weights results in a Palgrave index. The Palgrave index is not a recommended index. In most cases, the Palgrave is constructed because there is confusion about how to construct a Paashe.



The Palgrave index will generally overstate the price changes because the implicit weighting structure is constantly changing – the denominator of the price ratio has a different period of reference, 0, than the weights, t – and tends to give more weight to price increases and less to price decreases. Thus,


The Palgrave index is not recommended for any purpose.