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.
|structural break||program evaluation|
Comparison of 2 different programs (red, green) existing in a common data set, separate regressions for both programs deliver a better modelling than a combined regression (black).
Suppose that we model our data as
If we split our data into two groups, then we have
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 (in this case, 3). Then the Chow test statistic is
- Doran, Howard E.(1989) Applied Regression Analysis in Econometrics. CRC Press, ISBN 0-8247-8049-3, p. 146 (restricted online version (Google Books))
- Dougherty, Christopher (2007) Introduction to Econometrics. Oxford University Press ISBN 0-19-928096-7, p. 194 (restricted online version (Google Books))
- Computing the Chow statistic, Chow and Wald tests, Chow tests: Series of FAQ explanations from the Stata Corporation at http://www.stata.com/support/faqs/