This paper describes the response of the economy to large shocks in a nonlinear production network. A sector's tail centrality measures how a large negative shock transmits to GDP, that is, the systemic risk of the sector. Tail centrality is theoretically and empirically very different from local centrality measures such as sales share—in a benchmark case, it is measured as a sector's average downstream closeness to final production. It also measures how large differences in sector productivity can generate cross‐country income differences. The paper also uses the results to analyze the determinants of total tail risk in the economy. Increases in interconnectedness can simultaneously reduce the sensitivity of the economy to small shocks while increasing the sensitivity to large shocks. Tail risk is related to conditional granularity, where some sectors become highly influential following negative shocks.