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Mays Instability in Large Economies

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Document pages: 35 pages

Abstract: Will a large economy be stable? Building on Robert May s original argumentfor large ecosystems, we conjecture that evolutionary and behavioural forcesconspire to drive the economy towards marginal stability. We study networks offirms in which inputs for production are not easily substitutable, as inseveral real-world supply chains. Relying on results from Random Matrix Theory,we argue that such networks generically become dysfunctional when their sizeincreases, when the heterogeneity between firms becomes too strong or whensubstitutability of their production inputs is reduced. At marginal stabilityand for large heterogeneities, we find that the distribution of firm sizesdevelops a power-law tail, as observed empirically. Crises can be triggered bysmall idiosyncratic shocks, which lead to "avalanches " of defaultscharacterized by a power-law distribution of total output losses. This scenariowould naturally explain the well-known "small shocks, large business cycles "puzzle, as anticipated long ago by Bak, Chen, Scheinkman and Woodford.

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