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 labour productivity in a neoclassical growth model. The depreciation rate is modeled as a Markov 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 non-linear decision rules in the dynamic stochastic general equilibrium model (DSGE). Our contribution to DSGE solution methodologies in the presence of Markov switching is to apply Judd's (1998) projection method to non-linear decision rules. This approach allows for non-linear 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.