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Unhedgeable shocks and statistical economic equilibrium

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Abstract

We develop a statistical concept of economic equilibrium as the stationary distribution of a random walk on the exchange equilibrium set (the contract set) of a pure exchange economy induced by unhedgeable shocks that perturb the economy from the exchange equilibrium set and subsequent disequilibrium trading that returns the economy to a new equilibrium. The Fokker–Planck equation for the resulting drift-diffusion process implies that the stationary distribution is independent of the size of the shock so that a small-disturbance limiting distribution is well defined. We present explicit solutions for the statistical equilibrium for the cases of quasilinear and Gorman-aggregatable Cobb–Douglas economies, and illustrate the results in the context of a generic dividend-discount model to emphasize the distinction between insurable risk and unhedgeable uncertainty in this context. The statistical equilibrium of income or wealth for quasilinear economies is described by an exponential Gibbs distribution. The statistical equilibrium income and wealth distributions for Gorman-aggregatable Cobb–Douglas economies can take a wider variety of forms, including power-law and gamma distributions. The statistical equilibria calculated for these examples suggest a close relation to widely observed statistical distributional regularities in real-world economies.

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Authors and Affiliations

  1. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA

    Eric Smith & Benjamin H. Good

  2. Department of Economics, New School for Social Research, 6 East 16th Street, New York, NY, 10003, USA

    Duncan K. Foley

  3. Department of Physics, Swarthmore College, Swarthmore, PA, 19081, USA

    Benjamin H. Good

Authors
  1. Eric Smith
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  2. Duncan K. Foley
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  3. Benjamin H. Good
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Correspondence to Eric Smith.

Additional information

The authors thank John Miller, Nathan Collins, and Steve Frank for their input and helpful suggestions, and anonymous referees of this journal for comments that helped us improve the exposition and argument of the paper. DES thanks Insight Venture Partners for support. BG thanks Aaron Clauset for computational resources and was supported by a grant from the James S. McDonnell Foundation at the Santa Fe Institute.

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Smith, E., Foley, D.K. & Good, B.H. Unhedgeable shocks and statistical economic equilibrium. Econ Theory 52, 187–235 (2013). https://doi.org/10.1007/s00199-011-0663-1

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