Will a Large Economy Be Stable ?

We study networks of firms with Constant Elasticity of Substitution (CES) production functions. Relying on results from Random Matrix Theory, we argue that such networks generically become unstable when their size increases, when the heterogeneity in productivities/connectivities becomes too strong or when substitutability is reduced. At marginal stability and for large heterogeneities, we find that the distribution of firm sizes develops a power-law tail, as observed empirically. Crises can be triggered by small idiosyncratic shocks, which lead to "avalanches" of defaults characterized by a power-law distribution of total output losses. We conjecture that evolutionary and behavioural forces conspire to keep the economy close to marginal stability. This scenario would naturally explain the well-known "small shocks, large business cycles" puzzle, as anticipated long ago by Bak, Chen, Scheinkman and Woodford.