Dynamic Innovation Transmission Through Networks: Theory, Large $T$-Inference, and the Role of Input-Output Conversion in Business Cycles

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. The NVAR I propose is parameterized by $\alpha \in \mathbb{R}^p$, $p \in \mathbb{N}$ -- showing the time profile of transmission along a direct link -- and $q \in \mathbb{N}$ -- showing the relative frequency of network interactions to observation. While nesting the Spatial Autoregression and Spatial Error Model in the limit as $q \to \infty$ and producing equivalent impulse-responses in the long run for any finite $q$, it can accommodate general transmission patterns over time and yields ``networked'' transition dynamics distinct from those implied by autocorrelated innovations. For a given network, $\alpha$ is identified at least up to alternating sign and its Gaussian Maximum Likelihood estimator is consistent and asymptotically Normal under mild assumptions. I then estimate an NVAR for monthly industrial production among 23 US manufacturing sectors, as derived under a Real Business Cycle economy with lagged input-output conversion (IOC), and I quantify the extent to which business cycles can be endogenized by the lagged transmission of productivity shocks along supply chains. Compared to an economy with contemporaneous IOC, the preferred lagged-IOC specification reduces the estimated shock-variances on average by 73\% and accounts for around 85\% of the persistence in aggregate output growth. In this environment, a single common productivity shock explains 90\% of aggregate fluctuations, leaving a negligible role for sector-specific shocks once sectoral heterogeneity in the temporal exposure to common shocks is accounted for.