Long-Run Comparative Statics

What are the long-run effects of permanent changes to productivities, taxes, and other economic parameters, accounting for changes in the capital stock? We show that balanced growth paths of dynamic open economies can be represented as equilibria of equivalent static economies, in which capital services are intermediate inputs subject to wedges that capture deviations from the Golden Rule of savings. Hence, tools developed for distorted static economies can be used to characterize long-run comparative statics. The long-run impact of any shock on consumption has two components. First, a mechanical technological impact captured by a cost-based Domar weight, which we show far exceeds the sales share for investment industries and their suppliers. Second, there is a resource reallocation effect, which increases consumption if it raises capital intensity, with the magnitude determined by how much the reallocation lowers the aggregate labor share. These reallocations can be quantitatively significant: tariffs, for example, generate long-run consumption losses that far exceed their static GDP impact, by reallocating resources away from capital formation. The magnitude of losses from tariffs depends primarily on the economy’s internal elasticities – such as the elasticity of substitution between capital and labor and the elasticity of household asset demand to interest rates – rather than on the trade elasticities that are central in static models.