Hey everyone. I am trying to solve Gali’s Chapter 3 in the first Edition of his book. Now I am getting confused when he is calculating the output when the economy is hit by a technology shock on page 54. Output is the sum of natural output (p. 48) and output gap (also p. 54). But it looks like he did not insert the second term of the natural output when insterting natural output and output gap into the equation. Is this a mistake or is there a meaning behind this?
Which second term are you referring to? You mean the constant term \vartheta_y^n? You can leave all the constants out as the steady states are the same. See https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Gali_2008/Gali_2008_chapter_3.mod
Yes that is the term I mean. I would just have thought that I simply get different values for y_t when leaving this constant term out as it is greater than zero?
That term affects the steady state, but not the dynamics. If you are only interested in the IRFs, which show deviations from the steady state, you can safely ignore it.
Okay I understand. Thank you for your help!
Hello again. Now a new Question regarding this term arrised: I cannot figure out why this term is greater than 0, because the fraction itself should be positive regarding all Parameters but the minus turns it negative.
As far as I can see that term is indeed negative. But keep in mind that we are talking about log output, not the level of output. If the level of output is between 0 and 1, log output will be negative.