Statistical Equilibrium in Economics: Method, Interpretation, and an Example

Statistical equilibrium is a short-run, temporary equilibrium model of market exchange which replaces the Walrasian picture of the market in equilibrium as a budget hyperplane defined by equilibrium relative prices with a scalar field of transactions probabilities. Statistical equilibrium synthesizes the classical notion of competition as a market with a large number of traders with the idea of liquidity limited by traders’ need to find actual counterpart transactors. From an economic point of view statistical equilibrium is the feasible Paretoimproving multilateral transaction that can be achieved in the largest number of distinct ways. On the assumption that all Pareto-improving transactions are equally likely, the statistical equilibrium can be characterized in terms of entropy maximization as a Gibbs distribution in which the transaction probability of any transaction is proportional to its value at equilibrium absolute entropy prices. The statistical equilibrium approximates, but does not in general achieve, Pareto-efficiency. A possible interpretation of the statistical equilibrium is as the statistical outcome of a sequence of identical repeated markets, in which the Gibbs probabilities are interpreted as flows of transactions per unit time. The phenomenon of market arbitrage is examined in the context of a simple model of an asset market, in which the statistical fluctuations of outcomes in each period represent shifts in the arbitrageur’s capital position.