Chow test


The Chow test, proposed by econometrician Gregory Chow in 1960, is a test of whether the true coefficients in two linear regressions on different data sets are equal. In econometrics, it is most commonly used in time series analysis to test for the presence of a structural break at a period which can be assumed to be known a priori. In program evaluation, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population.

Illustrations

Mathematical details

Suppose that we model our data as
If we split our data into two groups, then we have
and
The null hypothesis of the Chow test asserts that,, and, and there is the assumption that the model errors are independent and identically distributed from a normal distribution with unknown variance.
Let be the sum of squared residuals from the combined data, be the sum of squared residuals from the first group, and be the sum of squared residuals from the second group. and are the number of observations in each group and is the total number of parameters. Then the Chow test statistic is
The test statistic follows the F-distribution with and degrees of freedom.
Remarks