<p>At least in the 3d edition, Blanchard writes:</p>

<blockquote>
  <p>"In the medium run, the unemployment rate <em>must</em> be constant (my emphasis).
  The unemployment rate cannot be decreasing or increasing forever."</p>
</blockquote>

<p>This is an inherent characteristic of <em>the definition</em> of the "medium run": that in it, some <em>core</em> magnitudes are constant. In some models, <em>levels</em> are constant (eg. aggregate consumption, aggregate capital stock, etc). In other models, <em>growth rates</em> are constant, and the model "has a steady-sate in growth rates". This means that <em>levels</em> grow indefinitely of course, but it is not wise (or useful, or meaningful) to project economic concepts to "infinite future". </p>

<p>Now for unemployment, it makes no sense to <em>not</em> be constant in equilibrium (at this simple level of exposition). In more sophisticated models, one could have the unemployment rate approaching asymptotically a constant (zero or not) without ever actually reaching it, but this is usually mathematical gadgetry with not much of economic intuition. (And in futuristic models, one could have unemployment approaching asymptotically unity, as machines and Artificial Intelligence take over all jobs). </p>

<p>Can this constant-by-conception-in-the-medium-run unemployment rate $u^* =const.$ be something else than the "natural rate of unemployment" $u_n$?</p>

<p>The natural rate of unemployment is  <em>defined</em> through the Phillips Curve, as that rate of unemployment at which realized inflation equals expected inflation (see previous chapters). Note that it is not assumed a priori that the natural rate of unemployment will be strictly positive -it could very well be zero. It is actual data that tells us that inflation stabilizes at strictly positive rates of unemployment. Then it is constant when inflation is a constant, and Blanchard discusses why inflation will also be a constant in the medium run. So it obtains that in the medium run $u_t = u_n =const.$.  </p>

<p>Since the current unemployment rate stabilizes when inflation becomes constant, which happens in the medium run, the constants <em>must</em> coincide. If $u^* \neq u_n$ inflation will not be constant and we would violate another condition for the characterization of the medium run.</p>

<p>And Blanchard writes correctly</p>

<blockquote>
  <p>"In the medium run the unemployment rate <strong><em>must</em></strong> be equal to the
  natural rate of unemployment". </p>
</blockquote>

<p>So it does <em>not</em> assume what he wants to prove. The natural rate of unemployment is defined separately and with its own logic to be a constant, from the medium-run unemployment rate which is constant based on other arguments than those related to the natural rate of unemployment. </p>

<p>I hope this helps.</p>

CC BY-SA 3.0
2015-09-08T08:29:06.940Z
Alecos, thanks for the help. I still got a doubt, though. I thought that the definition of medium run was when the expected price level was equal to actual price level. Or is it when all expectations of certain variables are equal to their actual levels? 
In this exposition, Blanchard considers productivity expectations and labour growth, which means AS relation is now: $P=A^eP^e \frac{(1+\nu)}{A}F(1-Y_t/(A_tL_t),z)$. Only with all expectations equal to their respective variable levels, we get $\frac{1}{1+\nu}=F(u_t,z)$, which would imply that $u_t$ is constant.
An old man in the sea.
CC BY-SA 3.0
2015-09-08T11:49:10.380Z
@Anoldmaninthesea. That is an equivalent approach, isn't it?
Alecos Papadopoulos
CC BY-SA 3.0
2015-09-08T12:00:37.693Z
Alecos, you're right,  if the medium run is when all expectations are equal to their levels... My doubt in the comment is precisely if medium run can be thought as expectations equal to their levels.
An old man in the sea.
CC BY-SA 3.0
2015-09-08T18:47:44.020Z
@Anoldmaninthesea. In my opinion, the main value-added of Blanchard's book over other textbooks, is that it separates the future in _three_ segments, short-run, medium run, long-run, while the traditional approach is "short-run/long-run". It is crucial to think hard on the distinction between short-run and medium run, and between medium run and long-run. It will pay handsomely.
Alecos Papadopoulos
CC BY-SA 3.0
2015-09-08T19:30:57.763Z
Alecos, just checked. You're right. In the medium run, all expectations are equal to actual values. Thanks ;)
An old man in the sea.
CC BY-SA 3.0
2015-09-07T23:15:53.677Z
2015-09-07T23:15:53.677Z
Alecos Papadopoulos
<p>In Blanchard's Macroeconomics, page 211, 5th edition, the author using the following three mathematical equalities</p>

<ul>
<li><p>Okun's law : $u_t-u_{t-1}=-\beta(g_{yt}-\bar{g_y})$, where
$\bar{g_y}$ is defined as the output growth rate when the
unemployment rate is constant, $g_{yt}$ output growth rate from year
t-1 to t.</p></li>
<li><p>expectations-augmented Philips curve, </p></li>
<li><p>and assuming a functional form  for the aggregate demand relation
that allows to deduce  $g_{yt}=g_{mt}-\pi_t$, where $g_{mt}$ is nominal
money growth rate</p></li>
</ul>

<p>makes a reasoning on what happens in the medium-run when the central bank maintains a constant growth rate of nominal money, concluding that although changes in the growth rate of nominal money doesn't change unemployment rate, it does change the inflation rate one-for-one. One of the first assumptions of the reasoning is that in the medium run the unemployment rate is constant. But why can we assume this?</p>

<p>In previous chapters, we had assumed that output would change one-for-one with employment, and that the labour force was constant. Then, when the expected price level were equal to the actual price level, the economy would be in natural output level, and that would imply from previous two assumptions that unemployment rate would also be the natural one. However, in this chapter, when the author was deriving the Okun's law, we explicitly assumed that labour force was no longer constant, and that employment would respond less than one-for-one to output, and that changes in employment are not negatively reflected one-for-one in the unemployment. 
Also, in same page 211, it's the author's conclusion that the unemployment rate in the medium-run is the natural unemployment rate. So, we cannot assume what we're trying to conclude... </p>

<p>Therefore, why can we assume that the unemployment rate must be constant in the medium run?</p>

<p>Any help would be appreciated. </p>

CC BY-SA 3.0
2015-09-07T00:08:42.050Z
I only have the book's 3d edition. Please state _name_ of chapter, sub-chapter etc, to see whether I can match it.
Alecos Papadopoulos
CC BY-SA 3.0
2015-09-07T22:08:44.553Z
@AlecosPapadopoulos the name of the chapter is "Inflation, Activity, and Nominal Money Growth", in subchapter "The effects of money growth", in "The Medium Run" section.
An old man in the sea.
<macroeconomics>
Medium run conclusions from Okun's Law and Expectations-Augmented Philips Curve
An old man in the sea.
# Medium run conclusions from Okun's Law and Expectations-Augmented Philips Curve

(Asked by: username_0 on 2015-08-30)

In Blanchard's Macroeconomics, page 211, 5th edition, the author using the following three mathematical equalities

* Okun's law : $u\_t-u\_{t-1}=-\beta(g\_{yt}-\bar{g\_y})$, where
  $\bar{g\_y}$ is defined as the output growth rate when the
  unemployment rate is constant, $g\_{yt}$ output growth rate from year
  t-1 to t.
* expectations-augmented Philips curve,
* and assuming a functional form for the aggregate demand relation
  that allows to deduce $g\_{yt}=g\_{mt}-\pi\_t$, where $g\_{mt}$ is nominal
  money growth rate

makes a reasoning on what happens in the medium-run when the central bank maintains a constant growth rate of nominal money, concluding that although changes in the growth rate of nominal money doesn't change unemployment rate, it does change the inflation rate one-for-one. One of the first assumptions of the reasoning is that in the medium run the unemployment rate is constant. But why can we assume this?

In previous chapters, we had assumed that output would change one-for-one with employment, and that the labour force was constant. Then, when the expected price level were equal to the actual price level, the economy would be in natural output level, and that would imply from previous two assumptions that unemployment rate would also be the natural one. However, in this chapter, when the author was deriving the Okun's law, we explicitly assumed that labour force was no longer constant, and that employment would respond less than one-for-one to output, and that changes in employment are not negatively reflected one-for-one in the unemployment.
Also, in same page 211, it's the author's conclusion that the unemployment rate in the medium-run is the natural unemployment rate. So, we cannot assume what we're trying to conclude...

Therefore, why can we assume that the unemployment rate must be constant in the medium run?

Any help would be appreciated.

**Tags:** macroeconomics

> **Comments:**
> **username_1**: I only have the book's 3d edition. Please state _name_ of chapter, sub-chapter etc, to see whether I can match it.  
> **username_0**: @username_1 the name of the chapter is "Inflation, Activity, and Nominal Money Growth", in subchapter "The effects of money growth", in "The Medium Run" section.  

---

## 1 answers

### Answer by username_1 on 2015-09-07. Score: 2 | Accepted answer

At least in the 3d edition, Blanchard writes:

> "In the medium run, the unemployment rate *must* be constant (my emphasis).
> The unemployment rate cannot be decreasing or increasing forever."

This is an inherent characteristic of *the definition* of the "medium run": that in it, some *core* magnitudes are constant. In some models, *levels* are constant (eg. aggregate consumption, aggregate capital stock, etc). In other models, *growth rates* are constant, and the model "has a steady-sate in growth rates". This means that *levels* grow indefinitely of course, but it is not wise (or useful, or meaningful) to project economic concepts to "infinite future".

Now for unemployment, it makes no sense to *not* be constant in equilibrium (at this simple level of exposition). In more sophisticated models, one could have the unemployment rate approaching asymptotically a constant (zero or not) without ever actually reaching it, but this is usually mathematical gadgetry with not much of economic intuition. (And in futuristic models, one could have unemployment approaching asymptotically unity, as machines and Artificial Intelligence take over all jobs).

Can this constant-by-conception-in-the-medium-run unemployment rate $u^\* =const.$ be something else than the "natural rate of unemployment" $u\_n$?

The natural rate of unemployment is *defined* through the Phillips Curve, as that rate of unemployment at which realized inflation equals expected inflation (see previous chapters). Note that it is not assumed a priori that the natural rate of unemployment will be strictly positive -it could very well be zero. It is actual data that tells us that inflation stabilizes at strictly positive rates of unemployment. Then it is constant when inflation is a constant, and Blanchard discusses why inflation will also be a constant in the medium run. So it obtains that in the medium run $u\_t = u\_n =const.$.

Since the current unemployment rate stabilizes when inflation becomes constant, which happens in the medium run, the constants *must* coincide. If $u^\* \neq u\_n$ inflation will not be constant and we would violate another condition for the characterization of the medium run.

And Blanchard writes correctly

> "In the medium run the unemployment rate ***must*** be equal to the
> natural rate of unemployment".

So it does *not* assume what he wants to prove. The natural rate of unemployment is defined separately and with its own logic to be a constant, from the medium-run unemployment rate which is constant based on other arguments than those related to the natural rate of unemployment.

I hope this helps.

> **Comments:**
> **username_0**: username_1, thanks for the help. I still got a doubt, though. I thought that the definition of medium run was when the expected price level was equal to actual price level. Or is it when all expectations of certain variables are equal to their actual levels?  In this exposition, Blanchard considers productivity expectations and labour growth, which means AS relation is now: $P=A^eP^e \frac{(1+\nu)}{A}F(1-Y_t/(A_tL_t),z)$. Only with all expectations equal to their respective variable levels, we get $\frac{1}{1+\nu}=F(u_t,z)$, which would imply that $u_t$ is constant.  
> **username_1**: @Anoldmaninthesea. That is an equivalent approach, isn't it?  
> **username_0**: username_1, you're right,  if the medium run is when all expectations are equal to their levels... My doubt in the comment is precisely if medium run can be thought as expectations equal to their levels.  
> **username_1**: @Anoldmaninthesea. In my opinion, the main value-added of Blanchard's book over other textbooks, is that it separates the future in _three_ segments, short-run, medium run, long-run, while the traditional approach is "short-run/long-run". It is crucial to think hard on the distinction between short-run and medium run, and between medium run and long-run. It will pay handsomely.  
> **username_0**: username_1, just checked. You're right. In the medium run, all expectations are equal to actual values. Thanks ;)  

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