# Derivation question: Gali (2015), chapter 5, equation 25

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.

• 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 – 1muflon1 Jan 3 at 18:29
• Hi, the version I have the 2015 version (the second edition, I think). The pages for these equations are p.142-143. – dhs20393541 Jan 4 at 2:02