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Recognize that any F statistic with one numerator d.f. and K
denominator d.f.s is the square of a t-statistic with K d.f., and has
exactly the same p-values. So you can always turn an F test that
involves one numerator d.f. (which may involve more than two
coefficients, by the way) into a t-test.
When doing one-sided tests, the important thing is to recognize that if
the point estimate is on the 'wrong' side, you can never reject. So if
Ho: \beta_1 >= \beta_2 vs Ha: \beta_1 < \beta2, and your point
estimate for \beta_1 is greater than your estimate for \beta_2, you can
never reject the null. You need a \beta_1 that is sufficiently less
than \beta_2 to do so. That said, if you're on the 'right' side, you
can halve the reported p-value, as it is calculated for a two-tailed
test.
sysuse auto,clear
reg price i.foreign#c.mpg
test 0b.foreign#c.mpg = 1.foreign#c.mpg
In this example the domestic coefficient (\beta_1) is less than the
foreign coefficient (\beta_2), and on a one-tailed test we can reject
at better than 99%.
Kit Baum | Boston College Economics & DIW Berlin |
http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming |
http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata |
http://www.stata-press.com/books/imeus.html
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