Cross-Sectional Dynamics Under Network Structure: Theory and Macroeconomic Applications

Abstract

Many economic environments involve units linked by a network. I develop an econometric framework that derives the dynamics of cross-sectional variables from the lagged innovation transmission along bilateral links and that can accommodate general patterns of how higher-order network effects accumulate over time. The proposed NVAR rationalizes the Spatial Autoregression as the limit under an infinitely high frequency of lagged network interactions. The factor-representation of the NVAR suggests that at the cost of restricting factor dynamics, it naturally incorporates sparse factors as locally important nodes in the network. The NVAR can be used to estimate dynamic network effects. When the network is estimated as well, it also offers a dimensionality-reduction technique for modeling high-dimensional processes. In a first application, I show that sectoral output in a Real Business Cycle-economy with lagged input-output conversion follows an NVAR. In turn, I estimate that the dynamic transmission of productivity shocks along supply chains accounts for 61% of persistence in aggregate output growth, leaving minor roles for autocorrelation in exogenous productivity processes. In a second application, I forecast macroeconomic aggregates across OECD countries by estimating a network behind global business cycle dynamics. This reduces out-of-sample mean squared errors for one-step ahead forecasts relative to a dynamic factor model by -12% (quarterly real GDP growth) to -68% (monthly CPI inflation).