APPENDIX
A Log-Linear Economy
In this appendix, we provide the dynamics of the economy using a log-linear approximation of the model following the techniques described in Uhlig (1995). This log-linear approximation is useful for simulation exercises in this research. From using the first order condition for and bt, we obtain the following relations:
and
Moreover, it can be seen that
and
Furthermore, the following variables, in equilibrium, satisfy
along with
It can be also shown that the nominal interest rate is given by
Where
Finally, and satisfies
and
This ends up the appendix.