Unhedgeable shocks and statistical economic equilibrium

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.