Abstract

A production sector's size, as measured by its Domar weight, captures the contemporaneous aggregate effect of its productivity shocks. Any future aggregate effects, however, depend on that sector's participation in the investment network. We derive a dynamic generalization of Hulten's theorem in an environment with intermediate-input and investment networks. This generalization, implied by production efficiency alone, decomposes each sector's Domar weight into an impact and a propagation component. The relative size of these components then determines how persistent the aggregate effects of sectoral shocks are, but cannot be known absent information on the economy's production structure. We show in a tractable structural model that future GDP responses to sectoral shocks can also be described as weighted sums of all sectors' Domar weights, with weights primarily dictated by these sectors' network positions and capital shares. Quantifying the model with U.S. production data, we find that i) Domar weights become progressively less informative about the aggregate effects of sectoral shocks as the horizon lengthens and ii) over a three-year horizon, goods-producing sectors have larger cumulative aggregate effects than service-producing sectors, despite goods only accounting for less than one-third of GDP. Model-free local projections of U.S. GDP growth on sectoral TFP growth confirm these findings.

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