<p><a href="https://i.sstatic.net/chGpg.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/chGpg.png" alt="enter image description here"></a></p>

<p><a href="http://www.uio.no/studier/emner/sv/oekonomi/ECON4325/v14/pensumliste/cgg2000.pdf" rel="nofollow noreferrer">Clarida, Gali, Gertler(1999)</a> show the optimal monetary policy problem of central bank for minimizing loss function under "Commitment"</p>

<p><img src="https://latex.codecogs.com/gif.latex?x_t" title="x_t" /> is a output gap, <img src="https://latex.codecogs.com/gif.latex?%5Cpi_t" title="\pi_t" /> is a inflation rate, <img src="https://latex.codecogs.com/gif.latex?%5Cinline&space;u_t" title="u_t" />~AR(1) is a supply shock.</p>

<p>I want to know why rational expectations term, <img src="https://latex.codecogs.com/gif.latex?%5Cinline&space;E_t" title="E_t" /> , is omitted in the FOCs of the lagrangian above the Appendix.</p>

<p>For some variable <img src="https://latex.codecogs.com/gif.latex?%5Cinline&space;y_%7Bt&plus;1%7D" title="y_{t+1}" />, <img src="https://latex.codecogs.com/gif.latex?%5Cinline&space;E_ty_%7Bt&plus;1%7D=0" title="E_ty_{t+1}=0" /> does not imply <img src="https://latex.codecogs.com/gif.latex?%5Cinline&space;y_%7Bt&plus;1%7D=0" title="y_{t+1}=0" />.</p>

<p>Thank you for your answer.</p>

CC BY-SA 3.0
2016-12-18T08:52:38.017Z
If you read Gali's book http://press.princeton.edu/titles/10495.html, he says they use the law of iterated expectations to remove $E_t$ from the FOCS
PostDocing
CC BY-SA 3.0
2017-03-12T18:06:23.840Z
My question is about omitted expectation operator "in the FOCs" not "in the lagrangian"
Esprit
<macroeconomics><monetary-policy>
Optimal monetary policy under commitment & FOCs
Esprit
# Optimal monetary policy under commitment & FOCs

(Asked by: username_0 on 2016-06-20)

[![enter image description here](https://i.sstatic.net/chGpg.png)](https://i.sstatic.net/chGpg.png)

[Clarida, Gali, Gertler(1999)](http://www.uio.no/studier/emner/sv/oekonomi/ECON4325/v14/pensumliste/cgg2000.pdf) show the optimal monetary policy problem of central bank for minimizing loss function under "Commitment"

![](https://latex.codecogs.com/gif.latex?x_t "x_t")

I want to know why rational expectations term, ![](https://latex.codecogs.com/gif.latex?%5Cinline&space;E_t "E_t") , is omitted in the FOCs of the lagrangian above the Appendix.

For some variable ![](https://latex.codecogs.com/gif.latex?%5Cinline&space;y_%7Bt+1%7D "y_{t+1}"), ![](https://latex.codecogs.com/gif.latex?%5Cinline&space;E_ty_%7Bt+1%7D=0 "E_ty_{t+1}=0") does not imply ![](https://latex.codecogs.com/gif.latex?%5Cinline&space;y_%7Bt+1%7D=0 "y_{t+1}=0").

Thank you for your answer.

**Tags:** macroeconomics, monetary-policy
> **Comments:**
> **username_1**: If you read Gali's book http://press.princeton.edu/titles/10495.html, he says they use the law of iterated expectations to remove $E_t$ from the FOCS  
> **username_0**: My question is about omitted expectation operator "in the FOCs" not "in the lagrangian"  

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## 0 answers

