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

Abstract

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, Greenwood and Yorukoglu (1997). We find, however, that if depreciation rates follow a Markov switching process, a low variance of the depreciation rate can generate the low correlation between hours worked and productivity in a simple model economy. 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.

Detecting and Analyzing the Effects of Time‐varying Parameters in Dsge Models

“…The law of motion of (β t , δ t ) is described next. Dueker et al (2007), Liu et al (2011), Gourio (2012, and Meier and Sprenger (2015) provide evidence that these parameters are indeed varying over time. None of the arguments here depend on which parameter is allowed to be time varying.…”

“…Such a requirement is crucial, for example, to distinguish structural from reduced-form models and to conduct correctly designed policy counterfactuals. Dueker et al (2007), Fernandez-Villaverde and Rubio-Ramirez (2007), Canova (2009), Liu et al (2011), Vavra (2008), Dew-Backer (2014), Meier and Sprengler (2015), Seoane (2016), Castelnuovo and Pellegrino (2018), among others, have shown that the parameters of dynamic stochastic general equilibrium (DSGE) models are not time invariant and that variations are small but persistent. Parameter variations do not necessarily imply that DSGE models are not structural (see, e.g., Cogley and Yagihashi, 2010, Chang et al, 2013, Schmitt-Grohe and Uribe, 2003, Hansen and Sargent, 2010, and Cogley et al, 2015, but they create concerns about the economic interpretation of the results.…”

Indeterminacy, change points and the price puzzle in an estimated DSGE model

“…4 It is only the econometrician who is assumed to have to infer the timing of the breaks. Recent work on DSGE models with Markov switching parameters has derived valid forward-looking solutions (Dueker et al, 2006;Leeper, 2006, 2007;Farmer et al, 2006) but the model solution methods to date have not been fast enough to be used in the estimation of DSGE models, so we leave this topic for future work.…”

Fisheries Management Under Irreversible Investment: Does Stochasticity Matter?

“…The intuition of having a stochastic depreciation rate is that the actual depreciation rates of assets are hard to observe as they are inextricably intertwined with many other environmental factors (Yiu, 2007) rather than the most common approach of treating the depreciation rate as an exogenous variable (Dueker et al, 2007). Furthermore, an increase in the capital utilization may induce an overuse of the capital and therefore an unexpected increase in its depreciation rate (Bourguignon, 1974).…”

“…Furthermore, an increase in the capital utilization may induce an overuse of the capital and therefore an unexpected increase in its depreciation rate (Bourguignon, 1974). Moreover consideration of stochastic depreciation allows depreciation shocks to serve as an additional driving force behind macroeconomic fluctuations along with technology shocks (Dueker, et al, 2007). Furthermore, the uncertainty may potentially have a great impact on the investment decisions of the fishing firms and the capacity development of their capital resources (Nøstbakken, et al, 2011).…”