ARCHIVED: In Stata, how do I conduct the Chow Test?

The Chow Test examines whether parameters (slopes and the intercept) of one group are different from those of other groups. If you are interested only in differences among intercepts, try a dummy variable regression model (fixed-effect model).

Suppose you suspect that the impact of salary on employees' motivation varies across companies; the slope of salary of one company is different from the slopes of other companies. For the sake of convenience, consider only two companies (d=1 or 0) here; size and culture are covariates.

The pooled model, which assumes both companies have the same slopes and intercept, is as follows:

  . regress motivation salary size culture

You may fit separate regressions as follows:

  . regress motivation salary size culture if d==1 // for company 1
  . regress motivation salary size culture if d==0 // for company 2

For the Chow Test, create an interaction term of the regressor salary and the dummy variable d, and then fit the model with the interaction and the dummy as follows:

  . gen salary_d = salary * d
  . regress motivation salary salary_d d size culture 

The coefficient of d is the deviation of the second company's intercept from the baseline intercept (d=0). Likewise, the coefficient of salary is the slope of the baseline company, and the coefficient of salary_d is the deviation of the comparison group's slope from the baseline slope.

Now, conduct the Chow Test using the .test command. The null hypothesis is that two companies have equal parameters for salary and intercept; deviations of the slope and intercept are not statistically discernible from zero.

  . test _b[salary_d]=0, notest
  . test _b[d]=0, accum

The notest option suppresses the output, and accum tests a hypothesis jointly with a previously tested one. Rejection of the null hypothesis means that two companies do not share the same intercept and slope of salary.

For more details about the Chow Test, see Stata's Chow tests FAQ.