In my DSGE model:
where U is utility, C is consumption, L is working hours (maximum of working hours is 1), V is labor utilization shock, in this setting 1-VL should be smaller than 1.
Labor utilization shock follows an autoregressive process:
where V is labor utilization shock, Vbar is steady state of labor utilization shock, Rho is autoregressive parameter, Epsilon is labor utilization innovation and follows N(0, SigmaV^2)
SigmaV is the standard deviation of labor utilization innovation.
In this setting, because L represents working hours supply, L is defined to be smaller than 1 (only a proportion of hours will be devoted to work),
However, after I attach labor utilization shock V to working hours supply L,
will VL still be smaller than 1 or is there a possibility that VL may be greater than 1?
Thank you very much and look forward to hearing from you.