I imagine that would be quite difficult to do. Something that is easier and is likely to address part of the problem is to simply adjust for household income.
I think it's wrong to effectively punish children for their parents being productive. And think of the logistics -- should an application to a public high school really require something like the parents' tax returns? To truly estimate "privilege" from household income you would need the income history since birth.
Smart people earn more, and since intelligence is highly heritable, rich people have children who are on average smarter than poor kids. Any regression of test scores on income is picking up this effect as well as the ability of affluent parents to provide a better environment. How do you separate these two effects?
