Solution
= 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 $\rho\ne0$, the two disturbances are dependent, so treatment status carries information about the latent outcome disturbance even after conditioning on $X$. Consequently
$$
Y(a)\not\!\perp A\mid X
$$
in general, and the <no unmeasured confounding assumption> fails.