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In Chapter 3 of Gali's famous Monetary Policy book, he measures the effects of a monetary policy shock.

The interest rate rule is:

enter image description here

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:

enter image description here

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?

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    $\begingroup$ This question is not formulated in a such a way that any person without a copy of this specific text will be able to help you. You should define everything here etc. so that your question is self contained. $\endgroup$ – 123 Dec 9 '18 at 2:19
  • $\begingroup$ Okay, here you go:perhuaman.files.wordpress.com/2014/06/… $\endgroup$ – Mashim Dec 9 '18 at 2:29
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    $\begingroup$ this does not render your question self-contained. $\endgroup$ – E. Sommer Dec 9 '18 at 6:06
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As mentioned in the comments your question is not possible to answer as it is, but you should know that in macroeconomic models of growth exogenous shocks are measured by log-linearising equations around their steady state and then calculating impulse responses (that is, the magnitude and persistence of a shock to the variables of interest). This must be precisely what your book shows you, and unless you become familiar with macroeconomic modeling this question will hardly be answered any better than it is on your book.

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