Chow test

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The Chow test is a statistical and econometric test of whether the coefficients in two linear regressions on different data sets are equal. The Chow test was invented by economist Gregory Chow. In econometrics, the Chow test is most commonly used in time series analysis to test for the presence of a structural break. 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

y=a+bx_1 + cx_2 + \varepsilon.\,

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

y=a_1+b_1x_1 + c_1x_2 + \varepsilon. \,

and

y=a_2+b_2x_1 + c_2x_2 + \varepsilon. \,

The Chow test asserts that a1 = a2, b1 = b2, and c1 = c2.

Let SC be the sum of squared residuals from the combined data, S1 be the sum of squares from the first group, and S2 be the sum of squares from the second group. N1 and N2 are the number of observations in each group and k is the total number of parameters (in this case, 3). Then the Chow test statistic is

\frac{(S_C -(S_1+S_2))/(k+1)}{(S_1+S_2)/(N_1+N_2-2k-2)}.

The test statistic follows the F distribution with k and N1 + N2 − 2k degrees of freedom.

[edit] References

  • [1] [2] [3] Series of explanations from the Stata Corporation
  • Gregory C. Chow (1960). "Tests of Equality Between Sets of Coefficients in Two Linear Regressions". Econometrica 28(3): 591–605. 
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