Dear Johannes,

In my DSGE model:

Utility: U=log(C)+log(1-V*L)
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-V*L should be smaller than 1.

Labor utilization shock follows an autoregressive process:

V=Vbar+Rho* (V(-1)-Vbar)+Epsilon

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 V

*L still be smaller than 1 or is there a possibility that V*L may be greater than 1?

Thank you very much and look forward to hearing from you.

Best regards,

Jesse