I am wondering if anyone can point me to a paper/lecture notes on the rationale behind first running an OLS on a set of variables, and then in a second regression using the residuals of that regression as the dependent variable to regress on several new (but related) independent variables. To specify, this is not aiming for an IV/2SLS approach - there's no instrument here that's uncorrelated with the dependent variable in the "first stage." Instead, it aims to kind of set a standard across the sample set with the first result, and then attribute the differences from the market-wide (ie the residuals) on the 2nd set of variables.
First off, wouldn't this approach by definition limit the first regression to one independent variable for a regular OLS? Otherwise the dependent variable in the 2nd would be an nx2 matrix...
Overall, is there any purpose to such a process? I believe I have seen it done before, but my searches have come up mostly fruitless. Closest conversation I've found is this Stata thread: