# Critical Value for Chow Test

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

• Chow tests are covered in most econometrics textbooks. I think it's okay. Jun 14, 2023 at 7:24
• @RichardHardy econometrics questions are on topic according to our help center
– 1muflon1
Jun 14, 2023 at 12:17
• @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. Jun 14, 2023 at 12:56

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, $$q=2k+1$$.