Implausible Equilibrium Solutions in Economics and Finance

When modelling the aggregate behavior of a population over long periods of time the standard approach is to consider the system as always being in equilibrium -- using averaging procedures based upon assumptions of rationality, utility-maximization and a high degree of independence amongst the agents. These analytically tractable models are fully determined by a small number of variables and the future evolution of the system is decoupled from its past. Previous studies [Akerlof and Yellen 1985, Scharfstein and Stein 1990] suggested that allowing a subset of the agents to be non-maximizing might shift the equilibrium solution but a logical flaw in those analyses prevented the possibility of non-equilibrium solutions. We show how equilibrium assumptions and solutions can be 'stress-tested' by embedding the models within frameworks capable of far-from-equilibrium dynamics. This procedure is applied to Brownian motion (Random walk) asset pricing which serves as our prototypical equilibrium model. The introduction of a simple, yet plausible, form of non-maximizing coupling between the agents results in endogenous fluctuations that destabilize the equilibrium solution. These fluctuations typically consist of long periods of increasingly severe mispricing followed by rapid, unannounced, corrections. Importantly, this occurs at realistic parameter values and is consistent with the observed price dynamics of real markets. Furthermore the mispricing phase may be mistaken for a trend in the fundamentals of the equilibrium model. We argue that the 'boom-bust' nature of the destabilizing endogenous dynamics is likely to be prevalent in economic systems at all scales