<p>pls check the 1st edition of this textbook, which contains the constant term.</p>

CC BY-SA 4.0
2024-07-05T12:04:25.530Z
2024-07-05T12:04:25.530Z
Li Wang
<p>I am wondering how Gali derived equation (25) in chapter 5 of his book <em>Monetary Policy, Inflation, and the Business Cycle</em> (2015).</p>
<p>We have equation (21):
<span class="math-container">$$
\vartheta \hat{x}_{t} = -\kappa \hat{p}_{t} + \Lambda
$$</span>
and equation (23):
<span class="math-container">$$
\hat{p}_{t} = \delta\hat{p}_{t-1} + \frac{\delta}{1-\delta\beta\rho_u}u_{t} + \frac{\delta}{1-\delta\beta}\frac{\kappa\Lambda}{\vartheta}.
$$</span>
Gali then combines (21) and (23) to get (25):
<span class="math-container">$$
\hat{x}_t = \delta\hat{x}_{t-1} - \frac{\kappa\delta}{\vartheta(1-\delta\beta\rho_u)}u_t.
$$</span></p>
<p>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?</p>
<p>If someone can briefly explain this, it would be much appreciated.</p>

CC BY-SA 4.0
2021-01-03T18:29:25.607Z
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
CC BY-SA 4.0
2021-01-04T02:02:46.493Z
Hi, the version I have the 2015 version (the second edition, I think). 

The pages for these equations are p.142-143.
dhs20393541
<macroeconomics><monetary-policy><new-keynesian-economics><dsge>
Derivation question: Gali (2015), chapter 5, equation 25
dhs20393541
# Derivation question: Gali (2015), chapter 5, equation 25

(Asked by: username_0 on 2021-01-03)

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.

**Tags:** macroeconomics, monetary-policy, new-keynesian-economics, dsge

> **Comments:**
> **username_1**: 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  
> **username_0**: Hi, the version I have the 2015 version (the second edition, I think).   The pages for these equations are p.142-143.  

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## 1 answers

### Answer by username_2 on 2024-07-05. Score: 1

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


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