Shock Diffusion: Does Inter-Sectoral Network Structure Matter?

This paper introduces the concept of diffusion of shocks in a macroeconomic network consisting of inter-sectoral production linkages. I show that if sectors have different reaction horizons it would lead to diffusion of shocks through the network over time which prevents the inter-sectoral linkages to form the feedback loop structure essential to generate aggregate volatility. This result is different from other recent papers which have single period model with contemporaneous production linkages between different sectors thus generating sectoral shock amplification as one sector reacts to another contemporaneously resulting in bigger aggregate fluctuations. In contrast if sectors have different production horizons due to varying complexity of their production process or supply chain, it would break down the feedback architecture present in single period models. I further show that if the diffusion rate is varied for different sectors, the contribution of network structure to aggregate volatility can be insignificant. Also, it is no longer sufficient to characterize this contribution of inter-sectoral production network to aggregate volatility by just looking at input-output matrix or its summary statistics like degree distribution. The paper thus highlights the stark difference between the study of financial and inter-sectoral production networks because of the possibility of contemporaneous amplification and hence cascades in the case of financial networks. In the end, I propose lead time indicator as a possible proxy for measuring differential sectoral diffusion rates.