## 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.

If you have questions about using statistical and mathematical software at Indiana University, email UITS Research Analytics (formerly known as the Stat/Math Center). Research Analytics is located on the IU Bloomington campus at Woodburn Hall 200, and is open for consultation by appointment Monday-Friday 9am-5pm. For more, visit Research Analytics on the web, or call 812-855-4724 (IUB) or 317-278-4740 (IUPUI).

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