2
$\begingroup$

I am wondering how Gali derived equation (25) in chapter 5 of his book Monetary Policy, Inflation, and the Business Cycle (2015).

We have equation (21): $$ \vartheta \hat{x}_{t} = -\kappa \hat{p}_{t} + \Lambda $$ and equation (23): $$ \hat{p}_{t} = \delta\hat{p}_{t-1} + \frac{\delta}{1-\delta\beta\rho_u}u_{t} + \frac{\delta}{1-\delta\beta}\frac{\kappa\Lambda}{\vartheta}. $$ Gali then combines (21) and (23) to get (25): $$ \hat{x}_t = \delta\hat{x}_{t-1} - \frac{\kappa\delta}{\vartheta(1-\delta\beta\rho_u)}u_t. $$

Now, unless I've made some kind of silly algebraic mistake, I'm not quite sure how he no longer has a constant term in (25). Or maybe I'm missing a simplifying assumption regarding some of the variables?

If someone can briefly explain this, it would be much appreciated.

Improve this question
$\endgroup$
2
  • $\begingroup$ Could you specify what page and edition the equations are? In edition of Gali I have in chapter 5 equations are only numbered up 20, there are more equations in chapter 5 without numbering and some of them are almost same to yours, and if they were numbered they would have that numbering, but are not 100% same - now I am not sure if the above equations have typo or you are using different edition where the equations are set up differently $\endgroup$
    – 1muflon1 ♦
    Commented Jan 3, 2021 at 18:29
  • $\begingroup$ Hi, the version I have the 2015 version (the second edition, I think). The pages for these equations are p.142-143. $\endgroup$
    – dhs20393541
    Commented Jan 4, 2021 at 2:02

1 Answer 1

Reset to default
1
$\begingroup$

pls check the 1st edition of this textbook, which contains the constant term.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.