Chow test

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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 1960. 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.

structural break program evaluation

Chow test structural break.png

Chow test substructures.png

At  x=1.7 there is a structural break, regression on the subintervals [0,1.7] and [1.7,4] delivers a better modelling than the combined regression(dashed) over the whole interval.

Comparison of 2 different programs (red, green) existing in a common data set, separate regressions for both programs deliver a better modelling than a combined regression (black).

Suppose that we model our data as


y_t=a+bx_{1t} + cx_{2t} + \varepsilon.\,

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


y_t=a_1+b_1x_{1t} + c_1x_{2t} + \varepsilon. \,

and


y_t=a_2+b_2x_{1t} + c_2x_{2t} + \varepsilon. \,

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

Let S_C be the sum of squared residuals from the combined data, S_1 be the sum of squared residuals from the first group, and S_2 be the sum of squared residuals from the second group. N_1 and N_2 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)}{(S_1+S_2)/(N_1+N_2-2k)}.

The test statistic follows the F distribution with k and N_1+N_2-2k degrees of freedom.

References[edit]

External links[edit]