Wald Test for logit models

[Jon Ko]

Hi,

I have a quick question to make sure I understand the use of Wald tests correctly.

1) I have a panel regression with various independent variables on a continuous dependent variable. Using xtreg, I estimate the model. Amongst others, I have two variables A and B, which are both highly significant. For those variables I perform an ex post Wald test using test A == B to find out whether they are the same or not. I hope, I'm correct so far.

2) A second panel regression looks almost identical except the dependent variable, which happens to be binary. I therefore use xtlogit instead. Again, A and B are both highly significant. I would also like to perform an ex post Wald test using test A == B, which is technically no problem at all. However, I'm not sure whether it is correct to perform a Wald test with coefficients of a logit model considering the log nature of the coefficient.

Can I simply use the same approach for logit models? If not, what would be another way to check whether A == B?

Thanks for your help!!

[Clyde Schechter]

First, let's get our language straight. You don't test whether A == B. You are more or less testing whether the coefficient of A is equal to the coefficient of B in your model. Actually, what you are really testing is whether the difference between those coefficients is or is not greater than the precision with which you can estimate the difference. Another way of saying it is that you are testing whether your data are consistent with a model in which A and B are assigned the same coefficient, to the degree of precision that your data can estimate that. Whether you are in a logistic regression or a linear regression, the -test- command is equally valid for this purpose.

That said, it is important to remember that conclusions drawn about the equality (or not) of the coefficients of A and B should not be confused with conclusions about the two variables A and B being equally important, or equally strong predictors of the outcome, or anything of that sort. The latter inferences would only be sustained if it is also true that A and B are measured in the same units and exhibit the same variance in your data sample.

And as an aside, testing for equality of the coefficients of A and B in no way requires that both coefficients (or either of them, for that matter) be "statistically significant."

[Jon Ko]

Fantastic - that was extremely helpful!!