# Re: st: AW: Question about "testparm"

 From Kit Baum <[email protected]> To [email protected] Subject Re: st: AW: Question about "testparm" Date Sat, 31 Jan 2009 17:10:43 -0500

```<>
Ted wrote

Why is one constraint redundant?
My three dummy variables are three categories of a nominal variable,
but my nominal variable has four categories. So, knowing the value of
two variables does not necessarily indicate the value of the third.

If the single tests are accumulated into "one big
test", that does not seem to answer my question,
which was to find out if the three coefficients
vary among themselves. With three coefficients,
isn't that three questions (does a=b, does b=c,
does a=c)? How can "one big test" answer all
three questions?

```
If you have three dummy variables in the equation (based on four possible values), think about what it means to constrain them to have the same coefficients. Say these are D1, D2, D3 and you want to test whether their coefficients differ. To estimate a model in which they do not,
```
generate DD = D1 + D2 + D3

```
and put DD into the regression. You are now estimating one coefficient rather than three. The coefficient vector has been shortened by two. Thus you have placed two constraints on the vector, not three, and the F-statistic that answers your question has two numerator degrees of freedom corresponding to the two constraints on the original model implied by your test statement.
```
```
If you want to assert that the coefficients on D1, D2, D3 are equal to each other and furthermore each equal zero, that is three constraints, and given that you have an omitted level of the variable is equivalent to asserting that the variable does not belong in the regression.
```
```
You could conduct three separate t-tests, of D1 v D2, D1 v D3, D2 v D3, but that would not answer your question, as each t-test would only consider the equality of two coefficients.
```
Kit

PS> What's a "dialog box"?

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html

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