<p>The numerator degrees of freedom is the number of restrictions. In a standard Chow test, I think there are <span class="math-container">$k$</span> variables of interest (<span class="math-container">$k+1$</span> if we're considering a constant as well), and the variables are allowed to have different coefficients for two sets of observations. The null hypothesis (which defines the restriction) is that the coefficients are the same for all observations, and thus there are <span class="math-container">$k$</span> restrictions (<span class="math-container">$k+1$</span> if you are considering the constant possibly differing as well).</p>
<p>The denominator degrees of freedom is <span class="math-container">$n-q$</span> where <span class="math-container">$q$</span> is the number of coefficients in the unrestricted model. With <span class="math-container">$k$</span> variables and considering that the constant may differ, <span class="math-container">$q=2k+2$</span>. With <span class="math-container">$k$</span> variables and not considering that the constant may differ, <span class="math-container">$q=2k+1$</span>.</p>

CC BY-SA 4.0
2023-06-14T07:29:29.470Z
2023-06-14T07:29:29.470Z
Michael Gmeiner
<p>What are the degrees of freedom for the F-distribution used to find critical values for the Chow Test?</p>

CC BY-SA 4.0
2023-06-14T07:24:36.403Z
Chow tests are covered in most econometrics textbooks. I think it's okay.
Michael Gmeiner
CC BY-SA 4.0
2023-06-14T12:17:26.937Z
@RichardHardy econometrics questions are on topic according to our help center
1muflon1
CC BY-SA 4.0
2023-06-14T12:56:14.110Z
@MichaelGmeiner and 1muflon1, OK, I give in; vote retracted. I guess my point was that it makes more sense to concentrate all questions on the same topic on a single site rather than scatter them across many sites. Since this is primarily a statistical question with no economic content, the most fitting site for it is Cross Validated. We could probably ask it on a number of different sites as Chow test may be used in many fields, but it makes more sense to me to ask it on the dedicated statistics site. But I see your point.
Richard Hardy
<econometrics><regression><time-series>
Critical Value for Chow Test
raynerk
# Critical Value for Chow Test

(Asked by: username_0 on 2023-06-13)

What are the degrees of freedom for the F-distribution used to find critical values for the Chow Test?

**Tags:** econometrics, regression, time-series

> **Comments:**
> **username_1**: Chow tests are covered in most econometrics textbooks. I think it's okay.  
> **username_2**: @username_3 econometrics questions are on topic according to our help center  
> **username_3**: @username_1 and username_2, OK, I give in; vote retracted. I guess my point was that it makes more sense to concentrate all questions on the same topic on a single site rather than scatter them across many sites. Since this is primarily a statistical question with no economic content, the most fitting site for it is Cross Validated. We could probably ask it on a number of different sites as Chow test may be used in many fields, but it makes more sense to me to ask it on the dedicated statistics site. But I see your point.  

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## 1 answers

### Answer by username_1 on 2023-06-14. Score: 1 | Accepted answer

The numerator degrees of freedom is the number of restrictions. In a standard Chow test, I think there are $k$ variables of interest ($k+1$ if we're considering a constant as well), and the variables are allowed to have different coefficients for two sets of observations. The null hypothesis (which defines the restriction) is that the coefficients are the same for all observations, and thus there are $k$ restrictions ($k+1$ if you are considering the constant possibly differing as well).

The denominator degrees of freedom is $n-q$ where $q$ is the number of coefficients in the unrestricted model. With $k$ variables and considering that the constant may differ, $q=2k+2$. With $k$ variables and not considering that the constant may differ, $q=2k+1$.


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