Cascading Failures in Production Networks

I show how the extensive margin of firm entry and exit can greatly amplify idiosyncratic shocks in an economy with a production network. I show that input-output models with entry and exit behave very differently to models without this margin. In particular, in such models, sales provide a very poor measure of the systemic importance of firms or industries. I derive a new notion of systemic influence called exit centrality that captures how exits in one industry will affect equilibrium output. I show that exit centrality need not be related to an industry’s sales, size, or prices. Unlike the relevant notions of centrality in standard input-output models, exit centrality depends on the industry’s role as both a supplier and as a consumer of inputs, as well as market structure. I show that, unlike competitive models, vanishingly small industries can have arbitrarily large effects on equilibrium outcomes. In this sense, the network can amplify shocks in a way that standard input-output models cannot.