Using estimated coefficients from a regression as a dependent variable in another regression

[Mohsin Javed]

Suppose I run the following regression:

reg y i.class x z

and the variable class has 3 categories then i.class would make 2 dummies and the regression output would include these two dummies along with the coefficients for variables x, z and the constant.

Now suppose, I want to use the estimated dummies from the above regression as my dependent variable in another regression. How should I collect these coefficients?

[Clyde Schechter]

You shouldn't do this at all, so don't ask how.

First, the coefficients you get for i.class are artifacts of the choice of reference category for representing class as 2 indicators (dummies). If you choose a different reference category, you get different coefficients. Each coefficient represents not an attribute of its class, but rather the difference between the mean adjusted value of y in that class and the mean adjusted value of y in the reference category. If you choose a different reference category, the coefficients of the class indicators change, as does the constant term. So neither the constant term nor the coefficients of these variables have straightforward interpretations. The kinds of things that are independent of which category is chosen as reference and can be derived from this regression are things like the expected means, adjusted for x and z, in each level of class, which can be found by running -margins class-.

It is not clear what you mean when you say you want to use these results as dependent variables in another regression. They aren't, after all, variables (dependent nor otherwise). They are just two constants.

If, however, you are interested in the effects of the class variable on something else, and you believe those effects are, in turn, dependent on the values of some other variables, then what you need to do is estimate a model in which class is interacted with those other variables. And, once again, to really get answers that are not artifacts of the choice of a reference category, you would need to follow your regression with an appropriate -margins- command.

Without more information about what your actual goal is, it isn't possible to give you more specific advice how to proceed.