Calcoulate significant difference between betas

[Eliborg Borgeli]

I have a null hypothesis that Beta1 = Beta2 = Beta 3 = Beta 4 = Beta 5 = 0.

I want to calculate whether there are significant risk-differences in the portofolio for big 5 audit firms. Using regression I have Risk as an dependent categorical variable (1 to 3), big 5 audit firms as 5 independent dummy-variables, and some controll-variable like total assets, leverage, age, loss, etc.

To answer the null hypothesis I think I have to use the f-test. But if I want to look at the significant difference between Beta 1 and Beta 2 for example, how can I do this?

Here is my regression result from STATA.In our dataset we have both companies that are audited by big 5 auditors and Non-big 5 auditors.

[Clyde Schechter]

-help test- or -help lincom-

[Eliborg Borgeli]

Thank you for the reply Clyde.

I have used lincom-command to calculate the difference between each coefficient.

The next thing I want to control the nullhypotesis beta1 = beta2 = beta3 = beta4 = beta5 = 0. Using the command "testparm BDO DELOITTE EY KPMG PWC, equal" only gives BDO - Deloitte, BDO - EY, BDO - KPMG and BDO - PWC. I also want to include DELOITTE - EY, DELOITTE - KPMG, DELOITTE - PWC, EY - KPMG, EY - PWC and KPMG - PWC in the same table. Do you know if this is possible?

[Clyde Schechter]

No, it's not possible, and there is no need to do it. BDO-Deloitte = 0 implies BDO = DELOITTE. BDO-EY = 0 implies BDO = EY, BDO-KPMG - 0 implies BDO = KPMG, and BDO-PWC = 0 implies BDO = PWC. Since equality is a transitive relationship, the other differences are all automatically 0 if the ones that Stata tested are. So you have a complete test of your omnibus null hypothesis that all five of these effects are equal. The other differences that Stata did not look at are not independent differences, so you cannot add them to the test calculations, but they would add no information even if you could.