Recovering from Crash States: A ''New'' Algorithm for Solving Dynamic Stochastic Macroeconomic Models

We introduce a ''new'' algorithm that can be used to solve stochastic dynamic general equilibrium models. This approach exploits the fact that the equations defining equilibrium can be viewed as set of algebraic equations in the neighborhood of the steady-state. Then a recursive scheme, which employes Upwind Gauss Seidel method at each step of iteration, can be used to determine the global solution. This method, within the context of a standard real business cycle model, is compared to projection, perturbation, and linearization approaches and is shown to be fast and globally accurate. Furthermore, we show that the gain in efficiency becomes more significant if the number of discrete states of the problem grows, and hence the method allows us to avoid the state space limitation. This comparison is done within a discrete state setting in which there is a low probability, crash state for the technology shock. Critically, this environment introduces heteroscedasticity in the technology shock and we show that linearization methods perform poorly in this environment even though the unconditional variance of shocks is relatively small and similar to that typically used in RBC analysis. We then use this solution method to analyze the equilibrium behavior of the crash state economy. We demonstrate that the welfare costs of a crash state are high and lead to a larger average capital stock due to precautionary savings. Also, we analyze the behavior of the term premia (both conditional and unconditional) and demonstrate how these affect the business cycle characteristics of the yield curve