Long-Run Comparative Statics

How do permanent changes in productivity, policies, and rates of return affect long-run consumption after capital has fully adjusted? We show that the balanced growth paths of a broad class of dynamic, multisector, open economies can be represented as equilibria of equivalent distorted static economies. In these equivalent economies, capital services are produced instantaneously from investment goods and sold at an as-if markup equal to the ratio of capital income to investment expenditure. This markup measures the economy’s deviation from the Golden Rule of savings. We use this representation to characterize long-run comparative statics in terms of expenditure shares, substitution elasticities, and initial wedges. We decompose the consumption effect of an industry-level productivity change into two components: a technological effect, measured by a cost-based Domar weight that incorporates both production and investment networks, and a reallocation effect, summarized by induced changes in aggregate labor-income shares. We show that the long-run consumption effects of distortions satisfy a dynamic analogue of Harberger’s formula: induced changes in capital stocks are weighted by the gap between capital income and investment expenditure. We also develop a small open economy analogue that can be used without requiring the solution of the full world equilibrium.