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Many environments in economics involve units linked by bilateral ties. I develop an econometric framework that rationalizes the dynamics of cross-sectional variables as the innovation transmission along fixed bilateral links and that can accommodate rich patterns of how network effects of higher order accumulate over time. The proposed Network-VAR (NVAR) can be used to estimate dynamic network effects, with the network given or inferred from dynamic cross-correlations in the data. In the latter case, it also offers a dimensionality-reduction technique for modeling high-dimensional (cross-sectional) processes, owing to networks' ability to summarize complex relations among variables (units) by relatively few bilateral links. In a first application, I show that sectoral output growth in an RBC economy with lagged input-output conversion follows an NVAR. I characterize impulse-responses to TFP shocks in this environment, and I estimate that the lagged transmission of productivity shocks along supply chains can account for a third of the persistence in aggregate output growth. The remainder is due to persistence in the aggregate TFP process, leaving a negligible role for persistence in sectoral TFP. In a second application, I forecast macroeconomic aggregates across OECD countries by assuming and estimating a network that underlies the dynamics. In line with an equivalence result I provide, this reduces out-of-sample mean squared errors relative to a dynamic factor model. The reductions range from -12% for quarterly real GDP growth to -68% for monthly CPI inflation.