Chow-Test

The Chow test is a statistical test which allows for testing the coefficients of two linear regressions for equality. The test is named after its inventor, the economist Gregory Chow, named.

The Chow test is used in econometrics to test time series structural breaks. Another field of application is the program evaluation, in this case, two different sub-groups (programs), such as two types of school, compared with one another. In contrast to the time series analysis here will allow the two sub-groups assigned to any successive intervals, instead, the classification is done by a qualitative aspect, such as the type of school.

In a structural break is present regressions on the sub-intervals and provide better modeling than the regression over the Gesamtinterval (dashed)

Comparison of two programs ( red, green) in the same record, separate regressions on the belonging to a program data provide a better modeling than the regression on the entire data set ( black)

Procedure

Given a data set for, the relationship is described by a linear function having a normal distribution error () with an expected value of 0 ( ) ( multiple regression analysis ), ie one has

It is believed, however, that the record can be divided into two groups of sizes and split, which are better described by two different linear functions.

It should be and it is the hypothesis tested against. Denoting with the sum of squared residuals of the regression on the entire data set with and the two sub- groups, and then follows the defined below test size of an F distribution with degrees of freedom and.

Example

Is given, the following data set, the relationship should be modeled by the linear function:

A data plot suggests that when a structural break is present, so one divides the data set into two intervals and takes over this, in addition to the regression over the entire data set, separate regressions. Then tests whether the two partial regressions produce the same linear function, that is to

Regression on the entire data set:

Regression to

Regression to

Calculation of the test statistic:

Because of ( significance level ) is considered. Thus, the null hypothesis can be rejected. That is, the two regression lines in the sub-intervals are not identical. There is therefore a structural break and the partial regressions provide a better modeling than the regression on the entire data set.