Many environments in economics feature a cross-section of units or agents linked by a network of bilateral ties. This dissertation consists of four chapters that study time series dynamics of cross-sectional variables exploiting this network structure. In Chapter 1, I develop the proposed econometric framework and discuss inference. The Network-VAR (NVAR) is a vector autoregression in which innovations transmit cross-sectionally only via bilateral links and which can accommodate rich patterns of how network effects of higher order accumulate as time progresses. It can be used to estimate dynamic network effects, whereby the network can be taken as given or inferred from dynamic cross-correlations in the data. It also offers a dimensionality-reduction technique for modeling (cross-sectional) processes, owing to networks’ ability to summarize complex relations among units by relatively few non-zero bilateral links. Analytical expressions for (conditional) estimators – with both frequentist and Bayesian interpretation – are readily available. In Chapter 2, I show that a Real Business Cycle (RBC) input-output economy with time lags between the production of goods and their subsequent use as intermediaries in producing other goods leads to sectoral prices and output evolving as an NVAR. In turn, I estimate how sectoral productivity shocks transmit along supply chain linkages and affect dynamics of sectoral prices in the US economy. The analysis suggests that network positions can rationalize not only the strength of a sector’s impact on aggregates, but also its timing. In Chapter 3, I discuss the merits of the NVAR for parsimoniously approximating time series dynamics. The theoretical comparison to factor models suggests that the NVAR is preferred whenever dynamics are driven by many micro links rather than a few dominant units. Consistent with that, in my application to monthly industrial production growth across 44 countries, I obtain reductions in out-of-sample mean squared errors of up to 23% relative to a principal components factor model. In Chapter 4, co-authored with Arnaud Mehl and Ine Van Robays, we assess why a dominant currency in international trade invoicing can be replaced with another by contrasting two hypotheses stressed in recent theory: increased trade and reduced exchange rate volatility vis-à-vis the emergent dominant currency area. We show how theory maps itself into a network which links together invoicing currency decisions across countries, and we use a generalized version of the NVAR to jointly model invoicing, trade and exchange rate volatility dynamics across 13 European countries that saw marked increases in the euro at the expense of the US dollar in trade invoicing. For each country, we identify a “trade shock" and an “exchange rate volatility shock", finding significant evidence in support of the increased trade hypothesis.