Stochastic Capital Depreciation and the Comovement of Hours and Productivity

In this article, we demonstrate that a small degree of stochastic variation in the depreciation rate of capital can greatly reduce the comovement between hours worked and labor productivity in a neoclassical growth model. The depreciation rate is modeled as a Markov process, as opposed to a linear autoregressive process, to place a strict upper bound and to ensure that variation and not the level of the rate is driving the result. Markov switching implies nonlinear decision rules in the dynamic stochastic general equilibrium model (DSGE). Our contribution to solving DSGE models with Markov switching is to apply Judd's (1998) projection method to capture the nonlinearity in the decision rules. This approach allows for nonlinear decision rules in a richer set of models with many more state variables than can be solved with grid-based approximations. The results presented here suggest that Markov switching parameters offer a powerful extension to DSGE models.