The Divisia approach to measuring output and productivity: with an application to the BEA-BLS integrated industry-level production account, 1987-2020

This paper analyses and illustrates the Divisia approach to measuring output and productivity. It argues that Divisia index numbers are the ideal to which real world index numbers should aspire. Divisia index numbers are consistent with production theory and have a number of desirable properties, principally value consistency and aggregation consistency. But they are defined in continuous time and so must be approximated in practice by discrete index numbers, such as the traditional Laspeyres or Paasche or one of the superlative index numbers introduced by Diewert (1976). The alternative approach is to ignore Divisia and start with discrete index numbers. The issues involved here are illustrated by examining data from the BEA/BLS industry-level integrated production account, 1987-2020. Estimates of superlative and other index numbers are presented for this dataset. The sensitivity of real GDP growth to the value of the crucial parameter in a superlative index number is tested. The extent to which value consistency and aggregation consistency are satisfied for different superlative index numbers are analysed. Chaining is a natural consequence of the Divisia approach but does not follow so automatically from the use of superlative indices. So I also compare chained and unchained versions of these same index numbers. Finally, Europe uses a different approach to output measurement to the US, chained Laspeyres versus chained Fisher. I look at how different US estimates would be if they employed European methodology.