<p>Suppose,</p>
<p>the <strong>Aggregate supply</strong> is given by the Lucas Supply Curve -</p>
<p><span class="math-container">$y_t = ȳ + b(P_t - E_{t-1}P_t) + μ_t$</span></p>
<p>where <span class="math-container">$μ_t$</span> is stochastic supply shock (following standard normal error properties).</p>
<p><strong>Aggregate demand</strong> equation is given by -</p>
<p><span class="math-container">$y_t = m_t - P_t + v_t$</span></p>
<p>where <span class="math-container">$v_t$</span> is stochastic demand shock (following standard normal error properties).</p>
<p>Monetary authorities follows the <strong>policy rule</strong> -</p>
<p><span class="math-container">$m_t = \bar{m} + m_{t-1} - cy_{t-1} + dμ_t +fv_{t-1}$</span></p>
<p>For the system, after solving for <span class="math-container">$y_t$</span> under the assumption of rational expectations (ie. Agents incorporate monetary policy changes into their decisions), I get it as a function of demand and supply shock.</p>
<p><span class="math-container">$y_t$</span> = <span class="math-container">$b/(1+b) v_t$</span> + <span class="math-container">$(1+bd)/(1+b) μ_t$</span></p>
<p>Here, though <span class="math-container">$y_t$</span> is a function of policy parameter 'd' but <span class="math-container">$μ_t$</span>, being supply shock of the current period equally random to both public and monetary authorities, is unanticipated part of money supply.</p>
<p>PIP argues that any anticipated changes in money supply cannot affect real variables. Since, <span class="math-container">$μ_t$</span> is unanticipated so by this regard PIP must hold. But since the policy parameter 'd' enters the output decision so monetary policy do have some influence over real variable. Then does it mean PIP doesn't hold.</p>
<p>I am confused between the two arguments. It will be helpful if someone can explain which one of the two is right? (Whether PIP holds or not and why?)</p>

CC BY-SA 4.0
2020-07-21T21:02:14.737Z
Please don’t post pictures of a question typeset them. See the rules for homework questions here: https://economics.meta.stackexchange.com/questions/1888/update-to-homework-policy-2018
1muflon1
CC BY-SA 4.0
2020-07-21T22:00:56.420Z
Done! Thanks for the correction
Elina Gilbert
CC BY-SA 4.0
2020-07-22T02:07:51.480Z
Hi: I'm not clear on what the problem is. ( but there might be one. I'm still trying to learn RE myself ). PIP says that, in RE environment, agents know as much as the econometrician so they anticipate anticipated changes so anticipated policy changes have no effect.  Since the money supply has an UN-anticipated shock in the form of $\mu_t$, PIP doesn't hold because it's an unanticipated component of the policy.
mark leeds
CC BY-SA 4.0
2020-07-22T02:12:56.740Z
Hi: Just one more thing to be clear:  The line that you wrote here: "Since $\mu_t$ is unanticipated so by this regard PIP must hold" is either a typo or not correct because it should be "doesn't" rather than "must".
mark leeds
CC BY-SA 4.0
2020-07-22T03:10:07.673Z
Thanks for replying @markleeds. There is no typo. Since $μ_t$ is a random shock then by that regard it is unknown to both public and monetary authorities in period t. Thereby, any money supply changes brought down by change in the supply shock will be random and unanticipated. Thus, output is changing because of random shock. So, PIP holds.
Elina Gilbert
CC BY-SA 4.0
2020-07-22T03:18:07.807Z
But when we look it closely there is coefficient attached to $μ_t$ in policy rule so policy authorities are deliberately choosing to change money ss due to current supply shock. But since public cannot fathom exact supply shock, they cannot guess exact money ss & thus it end up affecting output. So, PIP doesn't hold.
Elina Gilbert
CC BY-SA 4.0
2020-07-22T03:27:18.740Z
So, my question is which one of the two is correct? Does PIP hold, because afterall monetary authorities are as unaware about supply shock as public and thus, monetary authorities cannot change the money supply deliberately. But then what does the policy parameter, d, in output decision will indicate. Doesn't it mean that monetary policy is affecting output in ways that public cannot fathom (as policy parameters are the choice of the monetary authorities through econometrics exercises).
Elina Gilbert
CC BY-SA 4.0
2020-07-22T17:33:27.493Z
I have zero economics background so don't feel too comfortable trying to answer. I think is that this is an example of PIP not holding because shocks are not "intended". They can be negative or positive. PIP holds when the government purposely tries to change something but the "actors" anticipate the change so nothing actually happens. There's an example at the beginning of Shaw's "Introduction to RE" book. There may also be an example in the paper "a child's guide to RE". I'm gonna see if I can find that paper when get a chance. If someone can  chime in here to help us out, it's appreciated.
mark leeds
CC BY-SA 4.0
2020-07-22T17:36:38.690Z
Elina: One more thing. Note that the fact that $d$ multiplies the supply shock still doesn't make it intended or anticipatory. It's still a "surprise" if you will so PIP doesn't hold and doesn't need to hold. PIP applies only when there are expected changes.
mark leeds
CC BY-SA 4.0
2020-07-22T20:13:24.963Z
Thank you @markleeds. Your answer make sense. But I guess you mean PIP holds. Because *intended* money change, captured by coefficients of $m_{t-1}$, $y_{t-1}$ and $v_{t-1}$ is not part of output choice. So, any intentional policy changes will be ineffective in bringing change in real variables
Elina Gilbert
CC BY-SA 4.0
2020-07-23T04:33:19.487Z
Hi Elina: I think we're on the same page but I'm not sure if "PIP holds" is the right way to say it because, since $y_t$ will respond to a shock, that means that supply-demand does have un-antipicated behavior. It's the anticipated policy that it doesn't respond to. So, I guess you're right that PIP still holds in the sense that policy isn't changing supply-demand.  Like I said, hopefully someone else can confirm or respond or correct because RE is still a little fuzzy to me. I'm self taught and the road hasn't been an easy one. Still, I think we are in agreement.
mark leeds
CC BY-SA 4.0
2020-07-23T04:45:29.347Z
Hi Elina: I'm too tired to read it carefully right now but there's a very nice example at the end of this in appendix B ( that I read a while back )  that tells me that what you said in your last comment is correct. thanks for the refresher on RE. It tells me that I did an okay job teaching myself. https://pdfs.semanticscholar.org/e99e/ae142ac95128a58648a809d3ccdf935d4ab9.pdf?_ga=2.139348211.1944023391.1595479312-1280865350.1551495286
mark leeds
CC BY-SA 4.0
2020-07-23T04:53:13.853Z
@markleeds Thanks a ton. You did great job in explaining and steering me into right direction.
Elina Gilbert
CC BY-SA 4.0
2020-07-23T14:14:04.353Z
@Elina: I'm glad to hear that and don't sell yourself short either. I learned something also.
mark leeds
<macroeconomics><finance><monetary-policy><self-study>
Policy ineffectiveness proposition
Elina Gilbert
# Policy ineffectiveness proposition

(Asked by: username_0 on 2020-07-21)

Suppose,

the **Aggregate supply** is given by the Lucas Supply Curve -

$y\_t = ȳ + b(P\_t - E\_{t-1}P\_t) + μ\_t$

where $μ\_t$ is stochastic supply shock (following standard normal error properties).

**Aggregate demand** equation is given by -

$y\_t = m\_t - P\_t + v\_t$

where $v\_t$ is stochastic demand shock (following standard normal error properties).

Monetary authorities follows the **policy rule** -

$m\_t = \bar{m} + m\_{t-1} - cy\_{t-1} + dμ\_t +fv\_{t-1}$

For the system, after solving for $y\_t$ under the assumption of rational expectations (ie. Agents incorporate monetary policy changes into their decisions), I get it as a function of demand and supply shock.

$y\_t$ = $b/(1+b) v\_t$ + $(1+bd)/(1+b) μ\_t$

Here, though $y\_t$ is a function of policy parameter 'd' but $μ\_t$, being supply shock of the current period equally random to both public and monetary authorities, is unanticipated part of money supply.

PIP argues that any anticipated changes in money supply cannot affect real variables. Since, $μ\_t$ is unanticipated so by this regard PIP must hold. But since the policy parameter 'd' enters the output decision so monetary policy do have some influence over real variable. Then does it mean PIP doesn't hold.

I am confused between the two arguments. It will be helpful if someone can explain which one of the two is right? (Whether PIP holds or not and why?)

**Tags:** macroeconomics, finance, monetary-policy, self-study
> **Comments:**
> **username_1**: Please don’t post pictures of a question typeset them. See the rules for homework questions here: https://economics.meta.stackexchange.com/questions/1888/update-to-homework-policy-2018  
> **username_0**: Done! Thanks for the correction  
> **username_2**: Hi: I'm not clear on what the problem is. ( but there might be one. I'm still trying to learn RE myself ). PIP says that, in RE environment, agents know as much as the econometrician so they anticipate anticipated changes so anticipated policy changes have no effect.  Since the money supply has an UN-anticipated shock in the form of $\mu_t$, PIP doesn't hold because it's an unanticipated component of the policy.  
> **username_2**: Hi: Just one more thing to be clear:  The line that you wrote here: "Since $\mu_t$ is unanticipated so by this regard PIP must hold" is either a typo or not correct because it should be "doesn't" rather than "must".  
> **username_0**: Thanks for replying @markleeds. There is no typo. Since $μ_t$ is a random shock then by that regard it is unknown to both public and monetary authorities in period t. Thereby, any money supply changes brought down by change in the supply shock will be random and unanticipated. Thus, output is changing because of random shock. So, PIP holds.  
> **username_0**: But when we look it closely there is coefficient attached to $μ_t$ in policy rule so policy authorities are deliberately choosing to change money ss due to current supply shock. But since public cannot fathom exact supply shock, they cannot guess exact money ss & thus it end up affecting output. So, PIP doesn't hold.  
> **username_0**: So, my question is which one of the two is correct? Does PIP hold, because afterall monetary authorities are as unaware about supply shock as public and thus, monetary authorities cannot change the money supply deliberately. But then what does the policy parameter, d, in output decision will indicate. Doesn't it mean that monetary policy is affecting output in ways that public cannot fathom (as policy parameters are the choice of the monetary authorities through econometrics exercises).  
> **username_2**: I have zero economics background so don't feel too comfortable trying to answer. I think is that this is an example of PIP not holding because shocks are not "intended". They can be negative or positive. PIP holds when the government purposely tries to change something but the "actors" anticipate the change so nothing actually happens. There's an example at the beginning of Shaw's "Introduction to RE" book. There may also be an example in the paper "a child's guide to RE". I'm gonna see if I can find that paper when get a chance. If someone can  chime in here to help us out, it's appreciated.  
> **username_2**: Elina: One more thing. Note that the fact that $d$ multiplies the supply shock still doesn't make it intended or anticipatory. It's still a "surprise" if you will so PIP doesn't hold and doesn't need to hold. PIP applies only when there are expected changes.  
> **username_0**: Thank you @markleeds. Your answer make sense. But I guess you mean PIP holds. Because *intended* money change, captured by coefficients of $m_{t-1}$, $y_{t-1}$ and $v_{t-1}$ is not part of output choice. So, any intentional policy changes will be ineffective in bringing change in real variables  
> **username_2**: Hi Elina: I think we're on the same page but I'm not sure if "PIP holds" is the right way to say it because, since $y_t$ will respond to a shock, that means that supply-demand does have un-antipicated behavior. It's the anticipated policy that it doesn't respond to. So, I guess you're right that PIP still holds in the sense that policy isn't changing supply-demand.  Like I said, hopefully someone else can confirm or respond or correct because RE is still a little fuzzy to me. I'm self taught and the road hasn't been an easy one. Still, I think we are in agreement.  
> **username_2**: Hi Elina: I'm too tired to read it carefully right now but there's a very nice example at the end of this in appendix B ( that I read a while back )  that tells me that what you said in your last comment is correct. thanks for the refresher on RE. It tells me that I did an okay job teaching myself. https://pdfs.semanticscholar.org/e99e/ae142ac95128a58648a809d3ccdf935d4ab9.pdf?_ga=2.139348211.1944023391.1595479312-1280865350.1551495286  
> **username_0**: @markleeds Thanks a ton. You did great job in explaining and steering me into right direction.  
> **username_2**: @Elina: I'm glad to hear that and don't sell yourself short either. I learned something also.  

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## 0 answers

