Modifying the “Generalized Exactly Additive Decomposition” Decomposition”of GDP and Aggregate Labor Productivity Growth in Practice for Consistency with Theory

• Main Author: Dumagan, Jesus C.
• Format: text
• Published: Animo Repository 2018
• Subjects: Growth decomposition; productivity analysis; relative prices; index number theory; Growth and Development; Labor Economics
• Online Access: https://animorepository.dlsu.edu.ph/res_aki/28; https://animorepository.dlsu.edu.ph/cgi/viewcontent.cgi?article=1034&context=res_aki
• Institution: De La Salle University

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.