Synchronization of Endogenous Business Cycles

Comovement of economic activity across sectors and countries is a defining feature of business cycles. However, standard models that attribute comovement to propagation of exogenous shocks struggle to generate a level of comovement that is as high as in the data. In this paper, we consider models that produce business cycles endogenously, through some form of non-linear dynamics --- limit cycles or chaos. These models generate stronger comovement, because they combine shock propagation with synchronization of endogenous dynamics. In particular, we study a demand-driven model in which business cycles emerge from strategic complementarities across sectors in different countries, synchronizing their oscillations through input-output linkages. We first use a combination of analytical methods and extensive numerical simulations to establish a number of theoretical results. We show that the importance that sectors or countries have in setting the common frequency of oscillations depends on their eigenvector centrality in the input-output network, and we develop an eigendecomposition that explores the interplay between non-linear dynamics, shock propagation and network structure. We then calibrate our model to data on 27 sectors and 17 countries, showing that synchronization indeed produces stronger comovement, giving more flexibility to match the data