EFFECT OF GROUPING OF DATA ON THE DIVERGENCE BETWEEN LASPEYRES AND PAASCHE FORMS OF QUANTUM INDEXES*

Historical data for the manufacturing industry in the United States and United Kingdom are quoted, showing in most cases divergences between Laspeyres and Paasche forms of the quantum index that are by no means negligible. When the Paasche index for two of the series is recalculated with quantity indicators for industries instead of for products, the divergence is greatly reduced, and when quantity indicators for industry groups are substituted it almost disappears. This raises some questions about the practices of econometricians and statisticians, which are discussed. In a mathematical appendix by E. R. Coleman it is suggested that the grouping effect referred to does not depend on the particular way in which the data are grouped in most quantum indexes.