Quantity Measurement And Balanced Growth In Multi Sector Growth Models

Multi-sector models typically rely on a numeraire to aggregate quantities whereas NIPA uses the chain index. For three popular versions of the multi-sector growth model, we provide analytical expressions for the growth of aggregate quantities under both measurement methods and establish that the compound differences are sizeable over long horizons. We show that using the chain index captures more accurately the aggregate effects of secular changes in relative prices. For example, in a standard model of structural transformation, measuring GDP growth with the chain index captures that Baumol's disease reduces welfare growth, which using a numeraire misses.