The size-centrality relationship in production networks

We study two key characteristics of producers in a production network – size and centrality – and their relationship, which are intimately related to the extent of shock transmission in production networks, both at a macro and micro level. Our contributions are fourfold. First, we show empirically that the UK’s production network has significant asymmetries in producer centrality, varies over time, and yields an empirical size-centrality relationship that tends to be positive in and outside of steady state. Second, we set up a static multisector model with a production network which allows us to link producer size and centrality to underlying shocks in the economy. We show that as long as input substitutability is less than unitary, technology shocks tend to induce negative (positive) co-movement between real output (Domar weights) and outdegrees, unlike preference shocks which tend to induce a positive size-centrality relationship. Third, we calibrate a dynamic model featuring a production network to UK data and use it to filter out technology and demand shocks. The implied size-centrality relationship from the filtered shocks confirms the intuition from the static model. Finally, we use this model to analyse the UK’s post-2010 productivity growth slowdown from a production network perspective, distinguishing industries’ accounting contributions from the contributions of industry-specific and common shocks. We find that idiosyncratic shocks to the manufacturing sector have played a key role in driving the aggregate productivity slowdown.