To chain or not to chain? measuring real GDP in the US and the choice of index number

National Statistical Institutes (NSIs) in advanced countries have generally adopted chain-linking in their national accounts. The United States uses a chained Fisher, an example of a superlative index number, in its national accounts. However the Fisher is only one of an infinite number of superlative index numbers. So an important issue is how sensitive are the estimates of output growth to the choice of index number. This issue is analysed 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 the desirable characteristics of value consistency and aggregation consistency are satisfied for different superlative index numbers is also analysed. The desirability of chain-linking does not follow automatically just 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.