Double deflation: theory and practice

Real GDP measured from the output side, GDP(O), should equal real GDP measured from the expenditure side, GDP(E), just as corresponding two approaches to measuring GDP in current prices are necessarily equal. But this is only the case even in theory if real value added in each industry is measured by double deflation. We set out the theory of double deflation using a matrix algebra treatment based on the framework of the Supply and Use Tables. The context is the UK’s national accounts which measures volume growth by chained Laspeyres indices and which currently use single not double deflation. Initially we use simplified assumptions about prices. Later we introduce more realistic assumptions. We analyse the conditions on prices under which real GDP(O) equals real GDP(E). We consider three alternative methods of implementing double deflation. The preferred method makes use of all the price indices which the Office for National Statistics currently collects: Producer Price Indices, Services Producer Price Indices, Consumer Price Indices, Export Price Indices and Import Price Indices. We implement a simplified version of double deflation, using the same data as in the latest vintage of the national accounts, and compare our estimates with the official ones. In this version the same price index is used for each product regardless of whether the product is an output or an input. We find that double-deflated industry growth rates are consistently lower than the official single-deflated ones and also considerably more variable year-to-year. We interpret this finding as reinforcing the case for careful selection of the set of deflators to use for double deflation.