Loglinearization of balance of payment

Hi everyone,

I’m trying to log-linearize the balance of payment equation in my model. I have read some papers which linearize the BoP equation, but the results of them are different in the coefficient of interest rate. I attach the file that shows my procedure and result, but it is different from others. I don’t know whether it is wrong or not. The confusing point is the deviation form of interest rate. Could you please give me some hints?

Log-linearization .pdf (99.5 KB)

In my case I use a Taylor approximation of order 1 around the steady state and the coefficient of \widehat{r}_{t} is r_{ss}, the steps are as follows:





Hi Manuel,

Thanks for your reply. The deviation form of net interest rate should be r_hat= r_t-rss instead of r_hat= (r_t-r_ss)/r_ss because net interest rate is a very small value. So the coefficient of r_hat should be 1 in your case. Is that right?

Btw, how do you put maths equations in the text?


Yes, you are right, I forget that detail; this will make the coefficient of the net interest rate equal to 1. However, on the other hand, operating in the same way but using the gross interest rate, I get the following:


which is similar to the result you got. In fact,

R_{ss}\widehat{R}_{t} = (1 + r_{ss})(\frac{1 + r_{t} - 1 - r_{ss}}{1 + r_{ss}}) = \widehat{r}_{t}.

Note: To use mathematical expressions, just include the $ sign before and at the end of each expression and use the LaTeX language.

Thanks, Manuel. It seems that most of papers I’ve read ignore the detail.