I want to use Uhlig’s log-linearization method for a typical equation such as follows:
my main question is that how we should treat with a fixed parameter in the equation such as follows in Uhlig’s method for log-linearization? we should write only the fixed parameter such as follows?
\rm {MC_{ t }= \frac{\lambda-1}{ \lambda} +Y_{t} + X_{t} }
in a steady state situation we have:
\rm {\overline{MC}= \frac{\lambda-1}{ \lambda} +\overline{Y}+ \overline{X} }
if we log-linear the equation we have:
\rm {\overline{MC}(1+\hat {MC_{ t }})= \frac{\lambda-1}{ \lambda} +\overline{Y}(1+\hat {Y_{ t }}) + \overline{X}(1+\hat {X_{ t }}) }
and if we remove the steady state variables in both sides of the equation we have:
\rm {\overline{MC}\hat {MC_{ t }}= \overline{Y}\hat {Y_{ t }} + \overline{X}\hat {X_{ t }}}
is my method is correct or not?