Regress residuals in second regression

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: http://www.stata.com/statalist/archive/2008-03/msg00264.html

• are you talking about something along these lines? "In analysing multivariable datasets it is common that in looking at the effect of some variable ($x_1$) on a dependent variable of interest ($y$), the effects of a third continuous variable ($x_2$) are to be controlled for, for instance because its effects may confound those of $x_1$. In such circumstances it has become common to perform a regression of $y$ on $x_2$ and use the residuals from this regression in testing for the effects of $x_1$" found it here Jun 30 '15 at 22:41
• Yes, this should be helpful for background info - thank you.
– Z_D
Jul 1 '15 at 15:34
• Important to add here that the quote is only paraphrasing what other people say / do - the linked article explains why there is NO justification for this approach. Oct 27 '17 at 13:35