Is capacity utilization non-stationary?

Dynare help (legacy posts)
1

Hi,

I am working with variable capacity utilization like in Jaimovich and Rebelo(2009). In my model, the technologies are random walk with drift.

Do I need to transform/normalize variable capacity utilization equation to make it stationary?

As far I know, capacity utilization is bounded between [0,1] like labor hour. In my model, I am not normalizing labor hour; should I do the same for capacity utilization?

My utilization equation is below:

δ_{t}^{i}=Φu_{t}^{i^{1/Φ}}

Thanks

2

No, with the typical function forms (see e.g. dx.doi.org/10.1016/j.jedc.2013.06.011, equation (9)), there is no reason to detrend capacity utilization, because it is stationary.

3

Thanks. I have another question:

Does shadow price or Lagrange multiplier also non-stationary in the random walk with drift model? What is the economic intuition?

4

Yes, the Lagrange multipliers also have trends. Take the Lagrange multiplier on the budget constraint. It is equal to marginal utility of wealth. With CRRA you have

lambda=c^(-sigma)

Consumption will grow with the rate of output along the BGP. The Lagrange multiplier therefore grows with the rate of output raised to the power of -sigma.

5

I got it. Thanks a lot.