The Chow test

Summary

The Chow test

• Given: a regression model with two distinct subsamples, A and B.
• Example 1: Time series data divided into two subsamples based on a date.
• Example 2: Cross sectional data divided into two subsamples based on a dummy variable.
• Two choices:
• Run two regressions, one for each subsample.
• Run one regression using the entire (pooled) sample.
• \(H_0:\) There is no significant improvement in fit from running two regressions.
• \(RSS_A\) is defined as the \(RSS\) using only subsample \(A\)
• \(RSS_B\) is defined as the \(RSS\) using only subsample \(B\)
• \(RSS_P\) is defined as the \(RSS\) using the entire (pooled) sample
• The Chow test is an \(F\) -test with the following \(F\) -statistic:

\[F= \frac{\left( RSS_P-RSS_A-RSS_B \right)/k}{\left( RSS_A+RSS_B \right)/(n-2k) }\]

• Under \(H_0\) , the \(F\) -statistic follows an \(F\) -distribution with \(k\) and \(n-2k\) degrees of freedom.