Exact and inexact decompositions of trade price indices

Abstract

AbstractA reasonable concept for the true trade price index in situations where low-price countries capture market shares from high-price countries is the average price paid by importers for the same quality of good or service from all exporting countries. However, decompositions of trade price indices are usually inexact in the sense that the average price used as the underlying aggregator formula is not exactly reproduced. In this paper, we compare analytically exact and inexact decompositions of trade price indices, paying particular attention to the bias in aggregate inflation occurring from applying the first-order Taylor series approximation and not the quadratic approximation lemma to a geometric average price. 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 much as 0.6 percentage point in some years. We therefore conclude that the quadratic approximation lemma should be used in practice to exactly reproduce the underlying aggregator formula.