DP308 | Solving Stochastic Saddlepoint Systems: A Qualitative Treatment with Economic Applications

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We examine the effect 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. The first application analyzes how financial markets might react to the implementation of fiscal stabilization policy where public expenditures are only adjusted when GNP moves outside a threshold around a target level. The second application examines exchange rate behavior in the presence of a currency subject to a known realignment rule requiring an adjustment to monetary polic.