Instrumental Variables with 2SLS

When a treatment $x$ is correlated with unobserved confounders, OLS is biased. An instrument $z$ affects $y$ only through $x$. Two-stage least squares:

1. regress $x$ on $z$ (with intercept) and take fitted values $\hat x$
2. regress $y$ on $\hat x$ (with intercept); the slope is the IV estimate