Chow Test

A Chow Test is a statistical test for the null hypothesis of whether the linear regression coefficients of two different datasets are equal.

• AKA: Chow Criterion.
• Context:
  • It is a test for structure stability.
• See: Time Series, F distribution, Statistical Test, Regression Analysis.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Chow_test Retrieved 2016-08-21
  • The Chow test, proposed by econometrician Gregory Chow in 1960, is a test of whether the coefficients in two linear regressions on different data sets are equal. In econometrics, it is most commonly used in time series analysis to test for the presence of a structural break at a period which can be assumed to be known a priori (for instance, a major historical event such as a war). In program evaluation, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population.

Suppose that we model our data as

[math]\displaystyle{ y_t=a+bx_{1t} + cx_{2t} + \varepsilon.\, }[/math]

If we split our data into two groups, then we have

[math]\displaystyle{ y_t=a_1+b_1x_{1t} + c_1x_{2t} + \varepsilon. \, }[/math]

and

[math]\displaystyle{ y_t=a_2+b_2x_{1t} + c_2x_{2t} + \varepsilon. \, }[/math]

The null hypothesis of the Chow test asserts that [math]\displaystyle{ a_1=a_2 }[/math], [math]\displaystyle{ b_1=b_2 }[/math], and [math]\displaystyle{ c_1=c_2 }[/math], and there is the assumption that the model errors [math]\displaystyle{ \varepsilon }[/math] are independent and identically distributed from a normal distribution with unknown variance.

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