Statistical significance coefficients across 2 models

[Sarah Imlau]

Dear Stata List members,

I want to see whether the difference in coefficients from 2 models is statistically significant. I am doing a robustness test where I exchange a measure for financial development that is bank based against a measure that is stock market based. I have 5 explanatory variables (2 of them are interaction terms) and exchanging the financial development measure changes 2 explanatory variables, the financial development variable itself and 1 interaction term. The other interaction term, the one that remains unchanged, is actually of special interest for me. The coefficient increases and now I would like to test whether the difference to before is actually statistically significant. I read in Cross validated about a Z test (http://stats.stackexchange.com/quest...nt-regressions) but after checking the sources I am not sure whether I can apply this test in my case.

I appreciate any help!

Thanks, Sarah

[Alfonso Sánchez-Peñalver]

Is this what you're looking for? http://www.ats.ucla.edu/stat/stata/code/suest.htm

[Sarah Imlau]

No, I don't have different groups, I have 2 completely different proxies to measure financial development. I want to see whether my specification is robust with regard to those measures and it is. Bt the coefficient on the interaction term which has no financial development included increases in magnitude and I would like to know if the increase is statistically significant or, whether the difference in the 2 coefficients is. I can't use an LR test bcause I use robust errors and -test- and -testparm- did not work.
Also, I think SURE assumes the errors of the 2 models to be correlated, I don't want to make this assumption.

But thanks for your suggestion!

[Alfonso Sánchez-Peñalver]

So, basically you want to test the difference between two coefficients that you assume are independent? That's easy. Let the coefficients be b1 and b2. The null is H0: b1 = b2, which is equivalent to H0: b1 - b2 = 0. The issue is coming up with the standard error of the difference. This would have been difficult to get the covariance between both since they're coming from different regressions. But under the assumption of independence you have se(b1 - b2) = sqrt(se(b1)^2 + se(b2)^2). Your test statistic is z = (b1 - b2) / se(b1 - b2), and this should be asymptotically normal. You can get both the estimates and standard errors of both coefficients from your estimations.

The issue here is that if both estimators are not independent, then your test statistic may be off, and the result of your test is not valid. But if you're sure they're independent performing the test is easy.

[Sarah Imlau]

Thanks, that helps me!