How to account for a regressand affecting a regressor?

Question

I forget the terminology, but this happens when you regress, say, $Y$ on a list of variables, and you suspect that $Y$ affects, say, $x_3$ in addition to $x_3$ affecting $Y.$ I forget how this is called, and how to deal with it -- something along the lines of adding an extra variable? Thanks!

Answer 1

You probably mean reverse causality. That is a form of endogeneity. For a nice discussion, see page 146 here. Broadly, you deal with it the same way you deal with endogeneity in general, using either instrumental variables, or finding a natural experiment.