"Irrational exuberance" in the Pigou cycle under collateral constraints

The boom-bust cycles such as the episode of the "Internet bubble" in the late 1990s may be described as the business cycle driven by changes in expectations, which is called the Pigou cycle by Beaudry and Portier (An exploration into Pigou's theory of cycles, Journal of Monetary Economics, 2004). The key feature of the notion of the Pigou cycle is the comovements in the consumption, the labor, and the investment, in response to changes in expectations. We show that with the assumption that firms are subject to the collateral constraint in financing labor input (and investment), a fairly standard neoclassical model can generate the Pigou cycle. We also show that the collateral-constraint model with the private information can generate the "irrational exuberance," i.e., a boom in which each firm correctly anticipates that its own productivity will not rise, while it also believes wrongly that the productivity of the other firms will rise dramatically.