Quality & Quantity 38: 81–93, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
Another Look at Chow’s Test for the Equality of
Two Heteroscedastic Regression Models
Stockholm University, Department of Statistics, SE-106 91, Stockholm, Sweden
Abstract. This paper reviews tests of equality between the sets of coefﬁcients in the two linear
regression models, and examines the effect of heteroscedasticity in each model on the behaviour of
one such test. A Monte Carlo evaluation, of the size in particular, shows that the usual Chow’s F-
ratio is well behaved as long as the sample sizes in the two models are equal and the two models
exhibit the same form of heteroscedasticity which is moderate in the context of the values used. In
such situations it is recommended that the test be used directly to avoid the extra efforts involved in
transforming the original data in order to attain homoscedasticity.
Key words: Chow test, inter-model heteroscedasticity, intra-model heteroscedasticity.
When a linear regression is used to represent an economic relationship, the ques-
tion often arises as to whether the relationship remains stable in two periods of
time, or whether the same relationship holds for two groups of economic units.
Do tax policies today affect the economic structure in the same way as they did
several years ago? Does a change in price of a given commodity alter its demand
in two income groups similarly? These questions can statistically be answered by
testing whether two sets of observations can be regarded as belonging to the same
S TEST FOR THE EQUALITY OF TWO REGRESSION MODELS
The importance of tests for equality of two regression models is well recognized
and a large number of tests have been proposed. The Chow test (Chow, 1960) which
is now widely used in econometric and other research consists of equality of error
variances in the two models as part of the maintained hypothesis.
The author is grateful to Anders Ågren for valuable insights and programming assistance at the
very initial stage of preparing this paper.