Material for “ Identification of Average Effects under Magnitude and Sign Restrictions on Confounding ” Karim

Appendix B.1 extends the results in Section 4 on the identification of average exogenous random coeffi cients to study a panel structure and proxies included in the Y equation. Appendix B.2 characterizes the OVB of nonparametric regression and IV methods when U enters the Y and W equations additively separably. Appendix B.3 characterizes the nonparametric regression bias for β̄(x, x∗|x∗, s) and β̄(x|x, s) in the nonseparable case with discrete U , yielding analogous results to Theorem 5.1 with continuous U .