I’m working with a DSGE model and I doubt how to do the log-linearize the following equation:
R^{*}_{t} = R^{W}_{t} + \phi_{B} (exp(\bar{b} - b^{*}_{t}) -1)
My result:
\hat{R}^{*}_t = \hat{R}^{W}_t -\phi_{B} b^{*} \hat{b}^{*}_{t}
Please could anyone help me?
Can you use in-built LaTeX functionality to make your equations more readable?
Yes, that result looks correct.
I see the equation in Latex form. My doubt is related to the country risk premium that should add to the World interest rate (INT rate = World rate + country risk premium)
I put it int \LaTeX. The question is your definition of b_t. In it’s current form, if positive b_t is indebtedness of the domestic economy, then the original equation should have
+\phi e^{b^*_t-\bar b}
to have debt increase the risk premium. Obviously, the problem is not the linearization.
You are right. Thanks!