  Many environments in economics feature a cross-section of units linked by
bilateral ties. I develop a framework for studying dynamics of cross-sectional
variables exploiting this network structure. It 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
over time. The model can be used to estimate dynamic network effects, with the
network given or inferred from dynamic cross-correlations in the data. 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 non-zero bilateral links.
In a first application, 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 a
second application, I model industrial production growth across 44 countries by
assuming global business cycles are driven by bilateral links which I estimate.
This reduces out-of-sample mean squared errors by up to 23% relative to a
principal components factor model.
