Stochastic Saddlepoint Systems, Stabilization Policy and the Stock Market

Abstract

We examine the effects of introducing stochastic shocks into a linear rational expectations model with saddlepoint dynamics generated by a forward-looking asset price. We derive the fundamental differential equation governing the path of the asset price as a function of the "sluggish" variable. The equation does not admit of closed form solutions in general, but we provide a complete qualitative characterization of the solution paths which are symmetric about equilibrium. These are the relevant solutions to consider in the presence of symmetric boundary conditions. We present an application of the analysis to fiscal stabilization policy where public expenditures are only adjusted when GNP moves outside a threshold around a target level. The impact of such a policy on the level of the stock market is considered, and it is shown how the market will anticipate such state-contingent policy changes. Whether the expectations are stabilizing or not is shown to depend on whether the stock market is positively or negatively correlated with GNP.

JEL Classification: E44