st: re: one-sided p-value using test x1=x2

[Kit Baum <baum@bc.edu>]

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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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