Dear All:
For a general production function, we always have Y_t=A_t K_t^{\alpha} L_t^{1-\alpha}. I know that i can not directly get the K_t data from Fred or any other source. So, I constructed a K_t by using law of motion and initial starting quarter. But i have an issue regarding to the L_t, which is usually standardized and between 0 and 1. In my case, it is 0.3 (steady-state).
If I need to know the exact time value of the 0.3, for example, 30 hours a week or something like that, can I just take the average of weekly working hours data from the Fred and make it equal to 0.3, so that i can get the exact weekly hourly value of standardized L=1. am i doing correct?.
Thanks your help.
What are you trying to do? The model features constant returns to scale, so L_t can be arbitrarily scaled.
Dear JPFEIER:
I want to extract total productivity shock A_t from the production function. This is constant returns to scale production function.
The scale of A_t will also not be well-defined, only its percentage fluctuation around the arbitrary normalization. So if you normalize hours or use average weekly hours does not matter.
A similar question: I understand that working hours are generally set as 8 hours out of 24 hours, i.e., h=1/3. However, can we normalize this time to 1? What are the implications for interpretation? Are there any references or papers that take this approach? Thank you.
The scaling of utility functions is generally arbitrary as utility is typically only ordinal. Rescaling time would typically show up in an additional constant term in the utility function that would not affect the ordering of goods bundles. Morever, in many contexts, you have an additional parameter scaling the disutility from work relative to consumption, which subsumes this normalizing factor.
This seems to be a folk theorem type situation where something is so well-known that nobody bothers to formally show it.