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This paper analyses the impact of fiscal spending shocks in a dynamic, multi-country model with international production networks. The response of real gross domestic product to a fiscal spending shock can be decomposed into a direct effect, income effect and price effect. The direct effect depends only on input-output linkages, while the price effect is zero in the aggregate. We apply this decomposition to the Eurozone, and find that fiscal spillovers from Germany and the core Eurozone countries can be large, and within the range of empirical estimates. Without international production networks, spillovers would be significantly smaller. In an empirical application, using the decomposition, we find results strongly consistent with the model.