Chow test

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The Chow test is a statistical and econometric test of whether the coefficients in two linear regressions on different data sets are equal. The Chow test was invented by economist Gregory Chow. In econometrics, the Chow test is most commonly used in time series analysis to test for the presence of a structural break. In program evaluation, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population.

Suppose that we model our data as

If we split our data into two groups, then we have

and

The Chow test asserts that a₁ = a₂, b₁ = b₂, and c₁ = c₂. In another word, the null hypothesis is no break.

Let S_C be the sum of squared residuals from the combined data, S₁ be the sum of squares from the first group, and S₂ be the sum of squares from the second group. N₁ and N₂ are the number of observations in each group and k is the total number of parameters (in this case, 3). Then the Chow test statistic is

The test statistic follows the F distribution with k and N₁ + N₂ − 2k degrees of freedom.

[edit] References

• Howard E. Doran: Applied Regression Analysis in Econometrics. CRC Press 1989, ISBN 0824780493, p. 146 (restricted online version (Google Books))
• Christopher Dougherty: Introduction to Econometrics. Oxford University Press 2007, ISBN 0199280967, p. 194 (restricted online version (Google Books))
• Gregory C. Chow (1960). "Tests of Equality Between Sets of Coefficients in Two Linear Regressions". Econometrica 28(3): 591–605. 
• [1] [2] [3] Series of explanations from the Stata Corporation