May's instability in large economies

Abstract

Will a large economy be stable? Building on Robert May's original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in which inputs for production are not easily substitutable, as in several real-world supply chains. Relying on results from Random Matrix Theory, we argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong or when substitutability of their production inputs is reduced. At marginal stability and for large heterogeneities, we find that the distribution of firm sizes develops a powerlaw 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. This scenario would naturally explain the well-known "small shocks, large business cycles" puzzle, as anticipated long ago by Bak, Chen, Scheinkman and Woodford. 1 arXiv:1901.09629v4 [physics.soc-ph] 21 Sep 2019 Why is the output of large economies so volatile? Why do small idiosyncratic fluctuations lead to large business cycles? These questions have been at the forefront of economic research for decades [1-4]. Naively, one would expect that the fluctuations of an economy made of N independent sectors should decay rather quickly, as N −1/2 [4, 5] because of the Central Limit Theorem. In order to explain why fluctuations survive at the aggregate level, three families of explanations have been proposed in the literature. The first one is that aggregate fluctuations are driven by global shocks, that affect all firms/sectors simultaneously. However, it is often not clear what these shocks might be 1 and, when identified, they appear too small to be responsible for the observed volatility of the aggregate industrial production. Bernanke et al. [3] have called this the small shocks, large cycles puzzle. One interesting possibility is that these shocks are self-fulfilling prophecies [6], perhaps due to collective opinion shifts or trust collapse, see e.g. [7-10] for various strands of literature on the subject.Another resolution has been proposed by Gabaix [11] and, in a slightly different context, by Wyart & Bouchaud [12], see also [13]. The argument is that the fat-tailed distribution of sizes of independent firms/sectors slows down the regression of fluctuations from the standard N −1/2 behaviour to N −α , with α ≤ 1/2 related to the tail exponent of the distribution. Although some empirical support for this scenario has been put forth [11, 14], other works suggest that network effects are in fact dominant [15][16][17], as idiosyncratic shocks can cascade along the input-output network and eventually become macroscopic 2 . One particular stigma of these network effects is the strong co-variation of fluctuations across different sectors [22] -but see also [23].While the cascade story is enticing, the baseline Cobb-Douglas network mod...

Linear stability analysis of large dynamical systems on random directed graphs

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Top eigenpair statistics for weighted sparse graphs

“…in terms of the quenched free energy of the model defined in (6). The average over J is computed using the replica trick as follows…”

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How directed is a directed network?

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