Irreversible Investment in Stochastically Cyclical Markets

This paper studies entry and exit decisions in markets whose demand alternates between growth and decline phases at uncertain times. We introduce a stochastic process that captures these features of random market evolution, and we provide key mathematical results related to first passage times which make the characterization of entry and exit behavior quite simple and straightforward (even when the process is subject to an endogenously determined upper or lower barrier). We characterize entry and exit patterns in a dynamic competitive equilibrium, and we show why our results differ from those obtained if demand follows a diffusion process (e.g., a Geometric Brownian Motion). Despite the stochastic process of the underlying variable has a continuous sample path in both cases, we demonstrate in our setting that positive rates of entry and exit discontinuously fall to zero owing to informational overshooting. Another advantage of our framework is that it can explain discontinuities in firm values even if sample paths are continuous. Our framework is also amenable to empirical implementations (as we show using Corts’ 2008 offshore oil drilling application), and to an intuitive interpretation of optimal (dis) investment rules based on Bernanke’s (1983) “bad news principle of irreversible investment.”