Re: st: Chow test to test only slope coefficient and importance of dummy variable?

[David Hoaglin <dchoaglin@gmail.com>]

Hi, Sarah.

As that FAQ explains, we would do well not to focus so firmly on the
"Chow Test."  Greg Chow's 1960 result was helpful years ago, but
software has given us the flexibility to do that test and much more.
For many statisticians, hiding a straightforward test behind the name
"Chow Test" will produce puzzled looks.

You can test whether only the slopes are different and allow each
group to have its own intercept.  In fact, that is the usual situation
(e.g., a one-way analysis of covariance fits a common slope and
separate intercepts).  As in the example in that FAQ, you can fit the
model that has separate intercepts and separate slopes and then test
whether the slopes are equal.

That example did not use "noconstant" to remove the intercept from the
model.  It used that option in order to use separate coefficients
(including the constant) for each group.  In the command
. regress price mpg weight mpg2 weight2 group2
_const is the intercept for Group 1, and _const + _b[group2] is the
intercept for Group 2.  Also, the coefficient of mpg for Group 2 is
_b[mpg] + _b[mpg2], so the test of whether the coefficients of mpg in
the two groups are equal is the test of whether _b[mpg2] = 0.  (I am
assuming that mpg2 equals the product of mpg and the Group 2
indicator.)

David Hoaglin

Chow GC (1960).  Tests of equality between sets of coefficients in two
linear regressions.  Econometrica 28:591-605.

On Wed, Nov 13, 2013 at 4:35 PM,  <savinett@ucalgary.ca> wrote:
> Hi,
>
> I am new to Stata and the Chow Test. I want to compare the slopes of two
> sets of time series data using the chow test, however I am not interested
> in any differences in the intercepts of these time series data.  I have
> read the FAQs section on this and found this one:
> http://www.stata.com/support/faqs/statistics/chow-tests/ to be very
> helpful.  I do, however, have two questions:
>
> 1.   Can I use the Chow Test to test that only the slopes are different
> (not both the slope and intercepts)? I still want to include the intercept
> in the model (i.e. not use the “noconstant”). However, for the Chow Test I
> would like it to reflect that if there is a significant difference between
> the groups that this is due to a difference in their slopes (as I expect
> that their intercepts will differ and am not interested this aspect).
>
> 2.  It is not clear to me why the in the example from the Chow Test FAQ
> (link in the first paragraph) “group2” (the dummy variable) is included in
> the regression:
> . regress price mpg weight mpg2 weight2 group2
>
> If someone could please provide me with some insight that would be amazing.
> Thank you very much in advance for your help with my questions!
>
> Sarah

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