Relative price effects on decompositions of change in aggregate labor productivity

It is economic doctrine that relative prices help in guiding resource allocation. Thus, it appears surprising that in determining intersectoral reallocation effects in decompositions of change in aggregate labor productivity (ALP), most decompositions do not explicitly account for
the effects of differences or changes in sectoral relative prices.

This paper shows that the decomposition of log-change in aggregate labor productivity (ALP) devised by Balk (2013) based on Sato-Vartia indexes is inexact when applied to GDP in chained or in constant prices so that sectoral contributions do not necessarily add up to “actual” log-change in ALP. However, this paper adjusts Balk’s decomposition by incorporating “relative prices”– from the “generalized exactly additive” (GEAD) decomposition of “arithmetic change” in ALP – and shows that the adjusted Balk decomposition is exact for GDP in chained or in constant prices like GEAD.

An important finding is that relative prices could reverse the signs of sectoral contributions from Balk’s inexact decomposition. Hence, results from related decompositions of logchange in ALP, e.g., those based on the Törnqvist framework, that do not explicitly recognize relative prices could be misleading and, therefore, may need reconsideration.

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Relative price effects on decompositions of change in aggregate labor productivity