In Chapter 3 of Gali's famous Monetary Policy book, he measures the effects of a monetary policy shock.
The interest rate rule is:
Then a shock $v_t > 0$ occurs.
He proceeds to measure how this affects $y$, $\pi$ and $r$ (output, inflation, and real interest).
As you would expect, $y, \pi$ go down, $r$ goes up. However, he then derives the following equation, which measures what happens to the nominal interest rate:
However, I simply cannot for the life of me figure out how he derives this equation. I mean, I totally get that he's just using the Fisher equation. But why doesn't he go back to the interest rate rule from the first picture and use that? Why is he suddenly ignoring his own rule and relying fully on a basic identity like the Fisher equation?