Chow test

Chow test is an F-test that checks whether a regression model's coefficients are stable across two groups or time periods. Three regressions are estimated: one on the full pooled sample and one on each sub-sample.

Also known aschow break test

ByHoang TruongUpdated June 30, 2026

FrameworkChow test

See it move

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A two-column comparison sets a pooled regression model against the split model used in the Chow test. The pooled model fits one line to all observations, yielding a larger residual sum of squares (RSS_pool), whilst the split model fits two separate lines to sub-samples A and B, producing a smaller combined RSS. The F-statistic — (RSS_pool − RSS_A − RSS_B) ÷ k divided by (RSS_A + RSS_B) ÷ (n − 2k) — tests whether the reduction in residuals is large enough to confirm a structural break.

Where it fits

SubjectData Analysis & StatisticsPeripheralTopicRegression Diagnostics & ProblemsPeripheral

The formula

LaTeX

F = \frac{(RSS_{\text{pool}} - RSS_A - RSS_B) / k}{(RSS_A + RSS_B) / (n_A + n_B - 2k)}

Variables

$R S S_{p} oo l$: residual sum of squares from the pooled regression
$R S S_{A}$: residual sum of squares from sub-sample A
$R S S_{B}$: residual sum of squares from sub-sample B
$k$: number of parameters in each sub-model (including intercept)
$n_{A}$: number of observations in sub-sample A
$n_{B}$: number of observations in sub-sample B

Follows an F(k, n_A + n_B − 2k) distribution under H₀ of coefficient stability. A large F rejects the null and signals a structural break.