<p>I am currently reading <a href="http://www.columbia.edu/~mw2230/G_ASSA.pdf" rel="nofollow noreferrer">Woodford (2010)</a> and I have understood it for the most part. However, as I am new to solving these kind of models I have a question regarding a specific type of monetary policy rule. Namely one where the domestic central bank pegs domestic rates to foreign interest rates (due to e.g a currency peg).</p>

<p>The examples I have working with involved a Taylor rule of the form:</p>

<p>$i_{t} = \bar{r} + \phi \pi_{t}$ 
I then use the method of undetermined coefficients and assume a solution on the form:</p>

<p>$i_{t} = \bar{r} + \gamma_{i} \hat{g}_{t}$, $\pi_{t} = \gamma_{\pi}$ $\hat{g}_{t}$ , $y_t = \gamma_y \hat{g}_t$</p>

<p>and do the appropriate substitution in to the IS function:</p>

<p>$\hat{y_{t}} = E_t \hat{y}_{t+1} + \sigma^{-1}(i_{t} - E_t \pi_{t+1} - \bar{r})$  </p>

<p>So the term inside the brackets become:</p>

<p>($\phi$ $\gamma_{\pi}$ $\hat{g}_{t}$ - $\gamma_{\pi}$ $\hat{g}_{t+1}$) and after assuming a functional form of $g_{t}$ I am able to solve the model.</p>

<p>However, now when the monetary policy rule is to peg the interest rate I am unsure how to guess the form of the solution. </p>

<p>My monetary policy rule is:</p>

<p>$i_{t} = i_{t}^{*}$ where $i_t^*$ is the interest rate of the foreign country. My initial thought was to do something like:</p>

<p>$i_{t}^* = \gamma_{i^*} \hat{g}_{t} $ but then when I try to solve it I end up with two equations (PC and IS ) and three unknowns ($\gamma_\pi,\gamma_i^*,\gamma_y$). TO clarify what I mean, consider again the term in brackets from the IS function:</p>

<p>$(\gamma_i^*\hat{g}_t - \gamma_\pi \hat{g}_{t+1})$, it's the $\gamma_i$ that is causing me problems. With the Taylor rule I was able to deal with it because the policy rule implies:</p>

<p>$\gamma_i = \phi \gamma_\pi$</p>

<p>Any ideas where I am going wrong?</p>

CC BY-SA 3.0
2017-11-24T18:18:46.483Z
I am not very familiar with undetermined coefficients but to me, $i_{t}^* = \gamma_{i^*}\hat{g}_{t}$ doesn't make much sense. Surely shocks to domestic government spending does not affect foreign interest rates?
user11767
CC BY-SA 3.0
2017-11-24T19:35:14.513Z
Thank you Ben for the reply. What you say seems logical but I can't really elaborate further because I have no idea how else I could proceed. Do you know of any other methods for finding the multiplier?
Kronecker
CC BY-SA 3.0
2017-11-24T20:16:36.153Z
It is very likely I am wrong here (someone please correct me) but if you peg interest rates, shouldn't that fix the path of expected inflation due to the Fisher reaction? I.e $\bar{r} = i_{t} - E_t \pi_{t+1}$, if $i_t = i_t^*$, then $E_t \pi_{t+1}$ should be a constant. Again, don't take this as an answer, I am most likely wrong.
user11767
CC BY-SA 3.0
2017-11-25T16:53:01.953Z
I see. I'll try using the Fisher equation and see if I get an answer. Thanks once again for trying.
Kronecker
<new-keynesian-economics><government-spending>
Government spending dynamics
Kronecker
# Government spending dynamics

(Asked by: username_0 on 2017-11-23)

I am currently reading [Woodford (2010)](http://www.columbia.edu/~mw2230/G_ASSA.pdf) and I have understood it for the most part. However, as I am new to solving these kind of models I have a question regarding a specific type of monetary policy rule. Namely one where the domestic central bank pegs domestic rates to foreign interest rates (due to e.g a currency peg).

The examples I have working with involved a Taylor rule of the form:

$i\_{t} = \bar{r} + \phi \pi\_{t}$
I then use the method of undetermined coefficients and assume a solution on the form:

$i\_{t} = \bar{r} + \gamma\_{i} \hat{g}\_{t}$, $\pi\_{t} = \gamma\_{\pi}$ $\hat{g}\_{t}$ , $y\_t = \gamma\_y \hat{g}\_t$

and do the appropriate substitution in to the IS function:

$\hat{y\_{t}} = E\_t \hat{y}\_{t+1} + \sigma^{-1}(i\_{t} - E\_t \pi\_{t+1} - \bar{r})$

So the term inside the brackets become:

($\phi$ $\gamma\_{\pi}$ $\hat{g}\_{t}$ - $\gamma\_{\pi}$ $\hat{g}\_{t+1}$) and after assuming a functional form of $g\_{t}$ I am able to solve the model.

However, now when the monetary policy rule is to peg the interest rate I am unsure how to guess the form of the solution.

My monetary policy rule is:

$i\_{t} = i\_{t}^{\*}$ where $i\_t^\*$ is the interest rate of the foreign country. My initial thought was to do something like:

$i\_{t}^\* = \gamma\_{i^\*} \hat{g}\_{t} $ but then when I try to solve it I end up with two equations (PC and IS ) and three unknowns ($\gamma\_\pi,\gamma\_i^\*,\gamma\_y$). TO clarify what I mean, consider again the term in brackets from the IS function:

$(\gamma\_i^\*\hat{g}\_t - \gamma\_\pi \hat{g}\_{t+1})$, it's the $\gamma\_i$ that is causing me problems. With the Taylor rule I was able to deal with it because the policy rule implies:

$\gamma\_i = \phi \gamma\_\pi$

Any ideas where I am going wrong?

**Tags:** new-keynesian-economics, government-spending
> **Comments:**
> **username_1**: I am not very familiar with undetermined coefficients but to me, $i_{t}^* = \gamma_{i^*}\hat{g}_{t}$ doesn't make much sense. Surely shocks to domestic government spending does not affect foreign interest rates?  
> **username_0**: Thank you Ben for the reply. What you say seems logical but I can't really elaborate further because I have no idea how else I could proceed. Do you know of any other methods for finding the multiplier?  
> **username_1**: It is very likely I am wrong here (someone please correct me) but if you peg interest rates, shouldn't that fix the path of expected inflation due to the Fisher reaction? I.e $\bar{r} = i_{t} - E_t \pi_{t+1}$, if $i_t = i_t^*$, then $E_t \pi_{t+1}$ should be a constant. Again, don't take this as an answer, I am most likely wrong.  
> **username_0**: I see. I'll try using the Fisher equation and see if I get an answer. Thanks once again for trying.  

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## 0 answers

