Hypothesis Testing on coefficients

[Dhruv Jain DSE]

Hi

I am interested in testing the hypothesis highlighted in the picture. Ho: gamma>=beta and Ha: gamma<beta

Is there a way in stata to do this? The test command-- test beta=gamma (after running the regression) only checks for the equality and not the inequality! I am interested in the latter!


Thanks
Dhruv

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data. Pictures are not encouraged.

I know there are various papers about testing such inequalities, but I don't know of a Stata routine that does them. You should look at section 12.3.3 (page 408) in Cameron & Trivedi's Microeconometrics Using Stata.

[Clyde Schechter]

You can do this kind of one-tailed hypothesis testing by using -lincom- to get a confidence interval around the difference and then looking at the location of the upper and lower limits with respect to zero. Here's an example of the code:

sysuse auto, clear

regress mpg headroom weight

lincom headroom - weight, level(90)
if r(lb) > 0 {
    display "Reject headroom < weight"
}
else if r(ub) < 0 {
    display "Reject headroom > weight"
}
else {
    display "No one-dimensional hypotheses rejected"
}

Note that for a 0.05 level test of a one-tailed hypothesis you must use a 90% confidence interval, not a 95% CI. The point is that from a 90% two-sided CI (which is what -lincom, level(90)- gives you), you can derive that from the lower bound to negative infinity is a 5% probability rejection area for the null hypothesis that the difference is > 0 (or >= 0). Similar considerations apply in the other direction.