Exact and inexact decompositions of international price indices

Decompositions of international price indices are usually inexact in the sense that the underlying aggregator formula is not exactly reproduced. In this paper, we compare analytically the exact and inexact decompositions of international price indices, paying particular attention to the bias in aggregate inflation occurring from using the first order Taylor series approximation and not the quadratic approximation lemma to a geometric average of price levels. Our calculations, using the Norwegian clothing industry as an illustration, reveal that the bias in aggregate inflation over the sample period of 1997−2016 is quite substantial and as high as 0.5 percentage points in some years. We therefore conclude that the quadratic approximation lemma should be used in practise to exactly reproduce the underlying aggregator formula.