Dynamic Innovation Transmission Through Networks: Theory, Large T-Inference, and Business Cycles by Lagged Input-Output Conversion

Abstract

I develop an econometric framework that rationalizes the dynamics of a cross-sectional variable by lagged transmissions of innovations along bilateral links between units. While nesting the Spatial Autoregression and Spatial Error Model as limits and producing equivalent impulse-responses in the long run, the Network-Vector-Autoregression (NVAR) I propose can accommodate general transmission patterns over time and yields "networked" transition dynamics distinct from those implied by autocorrelated innovations. I discuss large $T$-inference conditional on a network. I then estimate an NVAR for US sectoral output, as derived under a Real Business Cycle economy with lagged input-output conversion. Under the preferred specification, lagged transmissions of productivity shocks along supply chains account for 85% of the persistence in aggregate output growth and reduce shock-variances relative to an economy with contemporaneous input-output conversion by 73% on average across sectors.