Stochastic Capital Depreciation and the Co-movement of Hours and Productivity

An unresolved question concerning stochastic depreciation shocks is whether they have to be unrealistically large to have any useful role in a dynamic general equilibrium model economy, as Ambler and Paquet (1994) first suggested. We first consider implied depreciation rates from sectoral data from the Bureau of Economic Analysis. These depreciation rates vary across time solely due to compositional changes within each sector. Hence, they tend to understate the range of fluctuation that would hold if the economic shelf life of capital varied endogenously as in Cooley et al. (1997). We find, however, that if depreciation rates follow a Markov switching process, a low variance of the depreciation rate is sufficient to allow a model economy to match the low correlation between hours worked and productivity observed in the data. White noise and autoregressive depreciation shocks, in contrast, require a counterfactually large variance in the depreciation rate to reduce the hours-productivity correlation. We also illustrate the level effects implied by nonlinear decision rules in simulations of dynamic general equilibrium models that include Markov switching parameters. Linear decision rules, in contrast, imply certainty equivalence and ignore the aversion that agents have to the skewed shock distributions that characterize Markov switching.