The effect of changes in the terms of trade on GDP and welfare: a Divisia approach to the SNA

What effect, if any, do changes in the terms of trade have on the level of output (GDP) or welfare? I examine this issue through two versions of a textbook, Hecksher-Ohlin-Samuelson (HOS), two-good model of a small, open economy. In the first version both goods are for final consumption. In the second, one good is an imported intermediate input into the other. In both versions, economic theory suggests that an improvement in the terms of trade raises welfare (consumption) but leaves aggregate output (GDP) unchanged. I then show that a national income accountant applying the principles of the 2008 System of National Accounts (SNA) would reach the same conclusions. This follows from a continuous-time analysis using Divisia index numbers. However in the case where imports are intermediate inputs and competition is imperfect, an improvement in the terms of trade does raise GDP: the size of the effect depends on the size of the markup of price over marginal revenue. I argue that the continuous time Divisia approach is the right framework for national income accounting, even though it can only be implemented approximately in practice. For the time being the chained Fisher index (as in the US and Canada) or the chained Tornqvist are the best approximations rather than the chained Laspeyres (as used in Europe). But eventually it may be possible to develop indices which are good approximations to Divisia indices while also (unlike the Fisher and the Tornqvist) possessing their other desirable properties.