<h2>To test market efficiency, you always need to specify the market's model of price formation</h2>

<p>Tests of the efficient markets hypothesis must always include a model of how the market forms prices. One of Fama's big contributions was that you cannot separate these two things in a test. Tests of efficient markets and models of price formations are inherently linked. So, in this case, the assumption of constant real interest rates is merely an assumption of how the market forms prices. Only after assuming this, can we test market efficiency. You might disagree with the model---more sophisticated models will repeat this experiment in that way---but the point is that you <em>have</em> to assume some model for price formation.</p>

<h2>Further reading</h2>

<p>For more information about this, check out Fama's <a href="http://faculty.chicagobooth.edu/eugene.fama/research/" rel="nofollow">website</a>. You'll find some links to some books of his. It would be helpful to read at least the first two sections of <a href="http://faculty.chicagobooth.edu/eugene.fama/research/Foundations%20of%20Finance/Chapter%205%20Efficient%20Capital%20Markets.pdf" rel="nofollow">chapter 5 of his book, "Foundations of Finance."</a></p>

<p>The argument that he makes in that chapter is approximately the following (borrowing his notation, but changing $\phi$ to $I$).
The point that he makes is that we want to test if the information sets are equal
$I_{t-1}^m = I_{t-1}$, where $I_{t-1}^m$ is the information that the market possesses. But because we can't test this directly, we would like to test
whether the distributions of prices are the same
$$
f_m(p_1,...,p_n \mid I_{t-1}^m) = f(p_1,..., p_n \mid I_{t-1}).
$$
However, this is impossible too. The equality possesses no testable content because we only observe $f(p_1,..., p_n \mid I_{t-1})$ and not $f_m(p_1,...,p_n \mid I_{t-1}^m)$ (see the top of page 137 of the linked chapter). I do not observe the latter because I do not know what $I_{t-1}^m$, except that $I_{t-1}^m \subseteq I_{t-1}$, and I do not know how the market uses this information. For this reason, we specify a model for how the market takes information and turns it into prices. Thus, we specify $f_m$ ourselves (in turn, also specifying what information $I_{t-1}^m$ the market uses). That is, we specify what data the market uses and the way in which it uses that data.</p>

<p>On page 134, Fama says</p>

<blockquote>
  <p>the statement that prices in an efficient market "fully reflect" available information conveys
  the general idea of what is meant by market efficiency, but the statement is too general to be
  testable. Since the goal is to test the extent to which the market is efficient, the proposition
  must be restated in a testable form. ... this requires a more detailed specification of the process of price formation, one that gives testable content to the term "fully reflect."</p>
</blockquote>

<h2>Why assume constant rates in the example in Hayashi?</h2>

<p>I think it's just an assumption made in that particular example. If you read a little further into the linked chapter, you'll see that Fama discusses 4 different models of market equilibrium. The first two are ridiculous, but he's doing it just to demonstrate the concept. (Part of the reason is that some of the previous ideas about market efficiency had some bizarre consequences, which he demonstrates through those examples.) The point is that any test of market efficiency is always tied to the model that is assumed. If the test fails, you know one of two things: either the market is inefficient or your model of the market is wrong. The unfortunate truth, however, is that you will never know which one it is. </p>

CC BY-SA 3.0
2018-02-23T21:00:24.007Z
The question and answer deals with what is called the "joint hypothesis problem" in finance. This is related to issues that come up in tests of rational expectations. (I'm adding this comment to help make this more searchable)
jmbejara
CC BY-SA 3.0
2015-01-06T23:21:54.997Z
According to the book notation we have access to the market information set, but not to the 'true' info set $I_{t-1}$. This seems different from what you wrote. Also, I understand the 'rational/efficient aspect' of assuming rational expectations. But what is the efficient aspect for assuming constant ex-antes real interest rates? what is the rationale for it?
An old man in the sea.
CC BY-SA 3.0
2015-01-06T23:57:36.067Z
Thanks for checking. I've added a little in the body of the second section. Let me know what you think. As for the rationale behind assuming constant rates, I've added another section to discuss that. Again, lemme know what you think.
jmbejara
CC BY-SA 3.0
2015-01-05T18:37:51.833Z
2015-01-07T00:01:24.460Z
2015-01-07T00:01:24.460Z
jmbejara
<p>According to Hayashi's Econometrics (page 151), efficient market hypothesis is a joint hypothesis combining:</p>

<p><strong>Rational expectations</strong> $\rightarrow$ expected inflation$= \mathbb{E}(\pi_{t+1}|I_t)$, where $I_t$ is the information available at the beginning of the period.</p>

<p><strong>Constant Real Rates</strong> $\rightarrow$ The ex-ante real interest rate is constant.</p>

<p>Why is the second one also included? I've searched the wikipedia, but I didn't find anything helpful. </p>

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

<macroeconomics><econometrics>
Efficient Market Hypothesis and constant ex-ante real interest rates?
An old man in the sea.
# Efficient Market Hypothesis and constant ex-ante real interest rates?

(Asked by: username_0 on 2015-01-05)

According to Hayashi's Econometrics (page 151), efficient market hypothesis is a joint hypothesis combining:

**Rational expectations** $\rightarrow$ expected inflation$= \mathbb{E}(\pi\_{t+1}|I\_t)$, where $I\_t$ is the information available at the beginning of the period.

**Constant Real Rates** $\rightarrow$ The ex-ante real interest rate is constant.

Why is the second one also included? I've searched the wikipedia, but I didn't find anything helpful.

Any help would be appreciated.

**Tags:** macroeconomics, econometrics

---

## 1 answers

### Answer by username_1 on 2015-01-05. Score: 6 | Accepted answer

## To test market efficiency, you always need to specify the market's model of price formation

Tests of the efficient markets hypothesis must always include a model of how the market forms prices. One of Fama's big contributions was that you cannot separate these two things in a test. Tests of efficient markets and models of price formations are inherently linked. So, in this case, the assumption of constant real interest rates is merely an assumption of how the market forms prices. Only after assuming this, can we test market efficiency. You might disagree with the model---more sophisticated models will repeat this experiment in that way---but the point is that you *have* to assume some model for price formation.

## Further reading

For more information about this, check out Fama's [website](http://faculty.chicagobooth.edu/eugene.fama/research/). You'll find some links to some books of his. It would be helpful to read at least the first two sections of [chapter 5 of his book, "Foundations of Finance."](http://faculty.chicagobooth.edu/eugene.fama/research/Foundations%20of%20Finance/Chapter%205%20Efficient%20Capital%20Markets.pdf)

The argument that he makes in that chapter is approximately the following (borrowing his notation, but changing $\phi$ to $I$).
The point that he makes is that we want to test if the information sets are equal
$I\_{t-1}^m = I\_{t-1}$, where $I\_{t-1}^m$ is the information that the market possesses. But because we can't test this directly, we would like to test
whether the distributions of prices are the same
$$
f\_m(p\_1,...,p\_n \mid I\_{t-1}^m) = f(p\_1,..., p\_n \mid I\_{t-1}).
$$
However, this is impossible too. The equality possesses no testable content because we only observe $f(p\_1,..., p\_n \mid I\_{t-1})$ and not $f\_m(p\_1,...,p\_n \mid I\_{t-1}^m)$ (see the top of page 137 of the linked chapter). I do not observe the latter because I do not know what $I\_{t-1}^m$, except that $I\_{t-1}^m \subseteq I\_{t-1}$, and I do not know how the market uses this information. For this reason, we specify a model for how the market takes information and turns it into prices. Thus, we specify $f\_m$ ourselves (in turn, also specifying what information $I\_{t-1}^m$ the market uses). That is, we specify what data the market uses and the way in which it uses that data.

On page 134, Fama says

> the statement that prices in an efficient market "fully reflect" available information conveys
> the general idea of what is meant by market efficiency, but the statement is too general to be
> testable. Since the goal is to test the extent to which the market is efficient, the proposition
> must be restated in a testable form. ... this requires a more detailed specification of the process of price formation, one that gives testable content to the term "fully reflect."

## Why assume constant rates in the example in Hayashi?

I think it's just an assumption made in that particular example. If you read a little further into the linked chapter, you'll see that Fama discusses 4 different models of market equilibrium. The first two are ridiculous, but he's doing it just to demonstrate the concept. (Part of the reason is that some of the previous ideas about market efficiency had some bizarre consequences, which he demonstrates through those examples.) The point is that any test of market efficiency is always tied to the model that is assumed. If the test fails, you know one of two things: either the market is inefficient or your model of the market is wrong. The unfortunate truth, however, is that you will never know which one it is.

> **Comments:**
> **username_0**: According to the book notation we have access to the market information set, but not to the 'true' info set $I_{t-1}$. This seems different from what you wrote. Also, I understand the 'rational/efficient aspect' of assuming rational expectations. But what is the efficient aspect for assuming constant ex-antes real interest rates? what is the rationale for it?  
> **username_1**: Thanks for checking. I've added a little in the body of the second section. Let me know what you think. As for the rationale behind assuming constant rates, I've added another section to discuss that. Again, lemme know what you think.  
> **username_1**: The question and answer deals with what is called the "joint hypothesis problem" in finance. This is related to issues that come up in tests of rational expectations. (I'm adding this comment to help make this more searchable)  

---

