<p>I will answer the first question, I believe the second one can be found in the book's appendix.</p>

<p>"Price stickiness" is defined with respect to the optimal price level for the period (here denoted by a star) or equivalently in inflation terms. We do <em>not</em> have price stickiness if the current inflation equals the optimal inflation: </p>

<p>$$\pi_t = \pi^*_t$$</p>

<p>Looking at eq. $(9.26)$, written</p>

<p>$$\pi_t = \alpha\pi^*_t + \beta \pi^e_{t+1}$$</p>

<p>to allow for any expectations formation hypothesis (we will need this flexibility), here are the only two scenarios under which we do <em>not</em> have price stickiness, while also Wickens' "general formulation" holds:</p>

<p><strong>A.</strong> Assume $\beta = 1-\alpha$ and $\pi^e_{t+1} = \pi^*_t$. Then we get $\pi_t = \pi^*_t$. Now, $\pi^e_{t+1} = \pi^*_t$ can be observed, it may be the case under Rational Expectations to expect next period inflation to equal the current optimal inflation. But assuming $\beta = 1-\alpha$ is a very special and uninteresting case.</p>

<p><strong>B.</strong> <em>Impose</em> immediate and full adjustment, $\pi_t = \pi^*_t$, while respecting equation $(9.26)$: we get a very specific rule for expectations formation:</p>

<p>$$\pi^*_t = \alpha\pi^*_t + \beta \pi^e_{t+1} \implies \pi^e_{t+1} = \frac {1-\alpha}{\beta}\pi^*_t$$</p>

<p>This is clearly an ad hoc expectations formation assumption.</p>

<p>It follows that in any other case, eq. $(9.26)$ implies that $\pi_t \neq \pi^*_t$, i.e. we have partial adjustment. It is perhaps more illuminating to perform the above "what ifs" using eq. $(9.27)$ of the book that is written in terms of the price level (starting in long-run equilibrium, i.e. assuming $p_{t+1} = p^*_{t+1}$).</p>

CC BY-SA 3.0
2016-11-07T20:57:01.560Z
+1 right now, but I'll wait until the end of the bounty. We never know when someone might put forward a more complete answer, however unlikely it may be. ;)
An old man in the sea.
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2016-11-07T20:58:13.050Z
Certainly. I hope someone will present the more conventional approach to a partial adjustment model explanation.
Alecos Papadopoulos
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2016-11-07T21:01:11.407Z
www.youtube.com/watch?v=AhIXGqhunXQ I found this quite good, since I had never heard of it. Not sure this is what you mean/look for.
An old man in the sea.
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2016-11-06T22:07:11.383Z
2016-11-06T22:07:11.383Z
Alecos Papadopoulos
<p>In Wickens' macro book, page 227 (1st edition), the author states</p>

<p><a href="https://i.sstatic.net/qGsxW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qGsxW.png" alt="enter image description here"></a>
where $p^*_t$ is the optimal price at time $t$.
The three theories he is referring to are: Taylor Model of Overlapping contracts, Calvo pricing model, and Optimal Dynamic adjustment. He says that all can be encompassed in this reformulation. The author then proceeds to show why this general formulation of inflation exhibits price stickiness, and this is the part which I don't understand what he does, specifically what he calls the partial adjustment model:</p>

<p><a href="https://i.sstatic.net/Sgr3H.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Sgr3H.png" alt="enter image description here"></a></p>

<p>How can he deduce that equations (9.29) and (9.30) exhibit price stickiness?</p>

CC BY-SA 3.0
2016-11-06T23:46:29.003Z
https://www.youtube.com/watch?v=AhIXGqhunXQ

for an explanation of what is a partial adjustment model.
An old man in the sea.
<macroeconomics><academic-graduate><new-keynesian-economics>
A general formulation to capture price stickiness
An old man in the sea.
# A general formulation to capture price stickiness

(Asked by: username_0 on 2016-11-03)

In Wickens' macro book, page 227 (1st edition), the author states

[![enter image description here](https://i.sstatic.net/qGsxW.png)](https://i.sstatic.net/qGsxW.png)
where $p^\*\_t$ is the optimal price at time $t$.
The three theories he is referring to are: Taylor Model of Overlapping contracts, Calvo pricing model, and Optimal Dynamic adjustment. He says that all can be encompassed in this reformulation. The author then proceeds to show why this general formulation of inflation exhibits price stickiness, and this is the part which I don't understand what he does, specifically what he calls the partial adjustment model:

[![enter image description here](https://i.sstatic.net/Sgr3H.png)](https://i.sstatic.net/Sgr3H.png)

How can he deduce that equations (9.29) and (9.30) exhibit price stickiness?

**Tags:** macroeconomics, academic-graduate, new-keynesian-economics
> **Comments:**
> **username_0**: https://www.youtube.com/watch?v=AhIXGqhunXQ  for an explanation of what is a partial adjustment model.  

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## 1 answers

### Answer by username_1 on 2016-11-06. Score: 2 | Accepted answer

I will answer the first question, I believe the second one can be found in the book's appendix.

"Price stickiness" is defined with respect to the optimal price level for the period (here denoted by a star) or equivalently in inflation terms. We do *not* have price stickiness if the current inflation equals the optimal inflation:

$$\pi\_t = \pi^\*\_t$$

Looking at eq. $(9.26)$, written

$$\pi\_t = \alpha\pi^\*\_t + \beta \pi^e\_{t+1}$$

to allow for any expectations formation hypothesis (we will need this flexibility), here are the only two scenarios under which we do *not* have price stickiness, while also Wickens' "general formulation" holds:

**A.** Assume $\beta = 1-\alpha$ and $\pi^e\_{t+1} = \pi^\*\_t$. Then we get $\pi\_t = \pi^\*\_t$. Now, $\pi^e\_{t+1} = \pi^\*\_t$ can be observed, it may be the case under Rational Expectations to expect next period inflation to equal the current optimal inflation. But assuming $\beta = 1-\alpha$ is a very special and uninteresting case.

**B.** *Impose* immediate and full adjustment, $\pi\_t = \pi^\*\_t$, while respecting equation $(9.26)$: we get a very specific rule for expectations formation:

$$\pi^\*\_t = \alpha\pi^\*\_t + \beta \pi^e\_{t+1} \implies \pi^e\_{t+1} = \frac {1-\alpha}{\beta}\pi^\*\_t$$

This is clearly an ad hoc expectations formation assumption.

It follows that in any other case, eq. $(9.26)$ implies that $\pi\_t \neq \pi^\*\_t$, i.e. we have partial adjustment. It is perhaps more illuminating to perform the above "what ifs" using eq. $(9.27)$ of the book that is written in terms of the price level (starting in long-run equilibrium, i.e. assuming $p\_{t+1} = p^\*\_{t+1}$).

> **Comments:**
> **username_0**: +1 right now, but I'll wait until the end of the bounty. We never know when someone might put forward a more complete answer, however unlikely it may be. ;)  
> **username_1**: Certainly. I hope someone will present the more conventional approach to a partial adjustment model explanation.  
> **username_0**: www.youtube.com/watch?v=AhIXGqhunXQ I found this quite good, since I had never heard of it. Not sure this is what you mean/look for.  

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