Compare two coefficients in one regression

[Bene Eil]

Hey everybody,

I have a regression:

xi: reg riskadj sranklow srankhigh franklow frankhigh diffmed_sd a_sd1 DummyGRI DummyGRO DummySMA i.year i.mgmt_cd

I want to show that the coefficient of "sranklow" is higher than the coefficent of "srankhigh".
This is the case but both are statistically not significant.

So, is there a possibility just to test whether "sranklow" is statistically higher than "srankhigh" with the result of my regression?

Thank you in advance!

Cheers
Bene

[Dave Airey]

Do the confidence intervals for the estimates help? You can also form linear combinations of beta coefficients with the -lincom- command, but you have to ask yourself whether the meaning of the difference in the coefficients and its test answer your intended question.

[Bene Eil]

The problem is that my regression suffers multicollinearity.
So my standard errors are very so that my coefficients are not significant.
But the estimates are still blue.

The coeffients are:
sranklow: 0.0007452
srankhigh: 0.0000879

Obviously, they are different but not significant.

My aim is to prove that sranklow>srankhigh and that both have a influence on my y-variable.


It is not possible to change my regression in order to handle the multicollinearity.

[Clyde Schechter]

Even though neither coefficient is statistically significantly different from zero, it is possible that they differ from each other by a statistically significant amount.

test sranklow = srankhigh

will tell you.

[Bene Eil]

Thank you.
Is it also possible to test: sranklow>srankhigh?

[Clyde Schechter]

I am not aware of any Stata commands that test composite hypotheses such as this > that. Or are you thinking of a one-tailed test of sranklow = srankhigh? You can get that just by dividing the p-value from the two-tailed test by two. But you would need some a priori justification from the science of what you are studying for using a one-tailed test.

[Bene Eil]

I just want to prove that sranklow has an higher influence on the y-variable but as I mentioned both variables are not significant.

So as a second step, I just want to show that the coefficient of sranklow is bigger at least.

[Clyde Schechter]

Well, you have the results of testing whether they are equal. If you concluded that they are not equal, then it is obvious from inspection that sranklow is the bigger of the two. But that is not the same thing as testing sranklow > srankhigh.

As I said in #6, there is the option of applying a one-tailed test of sranklow = srankhigh. And that is often "significant" when the two-tailed test is not. But applying a one-tailed test just to obtain a "significant" result is not science or statistics, it's p-hacking. Only if there is a scientific justification, some reason why, in theory, sranklow < srankhigh is simply not possible, or perhaps possible but irrelevant, is it appropriate to use a one-tailed test.

[Bene Eil]

Thank you again.

It just my hypothesis I want to prove. In general, sranklow < srankhigh is possible.

Then it is not appropriate to test a one-tailed test?

[Clyde Schechter]

One tailed tests are appropriate when the underlying science says that only one direction of difference is possible or meaningful. As I don't know what these variables are, or even what discipline you are working in, I can't say whether that is the case here or not. You have to make that decision yourself, or perhaps in conjunction with one of your colleagues who knows your particular field well.

[Bene Eil]

I will talk to my colleagues.

Thank you very much!