This paper provides a general framework to study the role of production networks in international GDP comovement. We first derive an additive decomposition of bilateral GDP comovement into components capturing shock transmission and shock correlation. We quantify this decomposition in a parsimonious multi-country, multi-sector dynamic network propagation model, using data for the G7 countries over the period 1978-2007. Our main finding is that while the network transmission of shocks is quantitatively important, it accounts for a minority of observed comovement under the estimated range of structural elasticities. Contemporaneous responses to correlated shocks in the production network are more successful at generating comovement than intertemporal propagation through capital accumulation. Extensions with multiple shocks, nominal rigidities, and international financial integration leave our main result unchanged. A combination of TFP and labor supply shocks is quantitatively successful at reproducing the observed international business cycle.