The Chow Test with Time Series-Cross Section Data

Abstract

Abstract The Chow test is the standard method to test for differences in regression response across groups. In some cases, the groups being tested are composed of a time series of cross sections. For example, when testing for differences across industries, each industry may be composed of several observations on several individual firms. If the individuals themselves have systematic differences, the Chow test will be compromised: the individual and group effects become confounded. This can cause rejections in the absence of the group effect of interest. We illustrate the problem with a Monte Carlo analysis, and show that the effects cannot be separated. We propose a bootstrap-like testing procedure that can eliminate excessive Type I errors, and when used with the standard Chow test can help to arrive at an appropriate conclusion when both effects are present. JEL classification numbers: C01, C10, C12, C15, C18. Keywords: Chow test, Bootstrap, Empirical distribution, Statistical testing, Econometrics.