Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 221 / 4 / c / i / Solution

In the bivariate probit model for endogenous treatment, $U$ affects treatment through its threshold equation and $V$ affects the outcome through its threshold equation. When $\rho \ne 0$, the two disturbances are dependent, so treatment status carries information about the latent outcome disturbance even after conditioning on $X$. Consequentlyin general, and the no unmeasured confounding assumption fails.