Predator-Prey: An Efficient-Markets Model of Stock Market Bubbles and the Business Cycle

Abstract

This paper develops a microeconomic model of the business cycle, based on the classical Lotka-Volterra predator-prey dynamic system, in which agency costs play the role of the predatory activity. The result is a system where producers (i.e., managers, workers and all those in direct, hands-on contact with production) gradually gain control of the productive process when the times are good, and use this control to enhance their own well-being at the expense of the investors (thus increasing agency costs) until this depredation drives the system into a crisis that leads the investors to tighten their bureaucratic controls on the producers, which eventually brings the system back to the growth path. The model is compatible with the Efficient Markets Hypothesis, and therefore the resulting cycle is fully discounted by the investors out of the future expected path but, as the market rate of return is assumed to be distributed according to a Wiener diffusion process, the key variables are subject to a geometric Brownian perturbation and thus the growth rate we should expect to observe in the direct analysis of a sufficiently long time series is the median path, not the mean - whereas the market discounts the future impact of the cycle from the mean (i.e., the expected) path, not the median. The resulting model also predicts that stock market valuations would present instances of bubbles and crashes more or less synchronised with the Business Cycle, without this implying any irrational behaviour on the part of the investors. Based on a preliminary analysis of the features of this model against well-known stylised facts, this paper suggests that it may be able to perform better against empirical validation than the Real Business Cycle model. This paper represents a revised version of the one previously published in SSRN under the title Predator-Prey: An Efficient-Markets Model of the Business Cycle.