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 b_t, 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.