Solving DSGE Models Without a Law of Motion: An Ergodicity-Based Method and an Application

This paper develops a novel method to solve dynamic stochastic general equilibrium models globally and accurately without specifying the law of motion. The method is based on the ergodic theorem: if a simulated path of the aggregate shock is long enough, all the possible equilibrium allocations are realized somewhere on the path. Then, the rationally expected future value function at each period on the path can be completely characterized by identifying the periods with each possible future state realization and by combining the corresponding time-specific value functions. The method provides an accurate solution even for models with highly nonlinear aggregate fluctuations. I apply this method to a heterogeneous-firm business cycle model with the corporate saving glut where the aggregate corporate cash stocks nonlinearly fluctuate. This nonlinearity passes through the dividend, leading to a state-dependent TFP shock sensitivity of consumption.