CHOW TEST

Question 1

What does the Chow Test do?

Answer 1

It tests whether two subgroups can be described by the same regression model, or if they required two separate regressions.

Question 2

Purpose, H0, H1?

Answer 2

Purpose: Tests whether the regression coefficients (including the intercept) are the same across two groups.

Null hypothesis (H₀): No structural break; all coefficients (including intercept) are the same across the groups.

Alternative hypothesis (H₁): At least one coefficient differs.

Question 3

Chow F-Statistic

Answer 3

​(RSSp - (RSS1 + RSS2))/k
/
(RSS1 + RSS2)/ (n1+n2-
2k)

k = number of parameters including intercept

Question 4

Relation to the F-Test

Answer 4

The Chow test is an F-test but specifically designed to test for structural breaks across groups.

It differs from a regular F-test using dummies because:

a) It directly compares an unrestricted model (separate regressions on subsamples) to a restricted model (where all data is used in one regression).

b) A dummy variable F-test keeps the data pooled and includes interaction terms.

Question 5

Limitations…

Answer 5

a) It assumes homoskedasticity (equal error variance across groups)

b) All parameters including the intercept must be the same under H0.

c) Sensitive to small sample sizes.