We study the growth properties of an economy where different sectors are linked by way of intermediates and potentially grow at different rates. We characterize the economy's equilibrium balanced growth path, and derive an analytical expression that summarizes how TFP growth in a given sector affects value added growth in every other sector and, therefore, aggregate GDP growth. We show in a special case that a version of Hulten's (1978) theorem, whereby the effects of changes in sector-specific productivity on GDP are entirely captured by that sector's share in GDP, also holds in growth rates along a balanced growth path. In that case, changes in TFP growth specific to that sector do not directly affect value added in other sectors regardless of its linkages in the economy. In the more general case, changes in sectors that are more capital intensive, and central as intermediate goods suppliers, have larger effects on value added growth in other sectors and aggregate GDP. In a calibrated version of our benchmark case, we find substantive quantitative differences in the effects of sectoral TFP growth changes on GDP relative to the case where these effects are given by sectoral value added shares only.