Is capacity utilization non-stationary?

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

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.

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?

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

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.

I got it. Thanks a lot.