I am estimating a dependent variable as a function of a regressor using Ordinary Least Squares regression. If I add a control variable that is (partly) an outcome of my dependent variable, how do I then interpret the estimated coefficient for my regressor? I know that we would not normally do this, but I would like to know how the interpretation changes if we do.
It is totally problematic, because if you do that, you have an endogeneity problem. Not only that coefficient, but, in general, the rest of the coefficients will be inconsistent/biased.
At best, in some cases, one can interpret the coefficients of the rest of variable (not the variable you have just introduced) as the effect of those variables conditioned on the control variable you have just introduced. For instance, I have seen that in the context of the labour demand: the labour demand conditioned on output.
I hope it helps.
All the best,
José-Ignacio
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