The generalized exactly additive decomposition (GEAD) of GDP and aggregate labor
productivity (ALP) growth, originated by Tang and Wang (2004), is gaining attention in the
literature and acceptance in practice. This paper shows, however, that the original GEAD is not
always consistent with the “theory” that aggregate GDP growth is pure quantity growth and ALP
growth depends only on productivity and labor share changes. This paper modifies the original
GEAD for consistency, subject to certain requirement, depending on the GDP quantity index that
in current practice is either (1) chained Laspeyres, (2) direct Laspeyres, or (3) chained Fisher.
GEAD employs relative price to obtain contributions that exactly add up to GDP or ALP growth.
Sector contributions equal pure growth effect plus price change effect (PCE) to GDP growth and
with-in sector productivity growth effect plus inter-sectoral reallocation effect to ALP growth.
When relative prices change, a sector’s PCE could be positive, zero, or negative but this paper
shows that consistency with the above theory requires the Sum of PCE = 0 for all sectors. That
is, there are no residual price effects. However, the original GEAD yields Sum of PCE = 0 only
if the GDP quantity index is chained Laspeyres and, therefore, this paper modifies GEAD for
theoretical consistency if the index is direct Laspeyres or chained Fisher. The findings are
globally relevant because these three indexes underpin GDP in all countries in current practice.
