I have two coefficients estimates from a regression, each of which has an estimated standard error.
I would like to know the quotient of these two estimates -- that is, divide one of the estimates by the other. What would be the corresponding standard error?

Would this be a candidate for the Delta Method?

If so, how should the formula be applied? If this is not something that can be computed in a straight forward manner, is there a way to do this in Stata?

In particular, I am interested in the Wald Estimator. In the Delta Method, there is a covariance term typically. Is it zero or non-zero in this case; that is, when can we assume that the two estimates are independent?