How Do Sectoral Shocks Shape Future GDP?

A production sector's size, as measured by its Domar weight, captures the contemporaneous aggregate effect of its productivity shocks. However, the presence of investment means that these aggregate effects can persist over time. We derive a dynamic generalization of Hulten's theorem in an environment that features sectoral linkages in both intermediate-inputs and investment. This generalization follows from production efficiency alone, and 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 alternatively be described as weighted sums of all sectors' Domar weights, with weights primarily dictated by the network positions and capital shares of downstream sectors. 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.