Title: Will a Large Economy Be Stable?,
Abstract: We study networks of firms with Leontief production functions. Relying on
results from Random Matrix Theory, we argue that such networks generically
become unstable when their size increases, or when the heterogeneity in
productivities/connectivities becomes too strong. 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.