Table 2:

Weights for Constructing ATE, TT, TUT, PRTE, and MPRTE from $\widetilde{\text{MTE}}(p,u)$

Quantities of Interest	Weight
ATE(p)	hATE(p, u) = 1
TT(p)	$h_{\text{TT}}(p,u)=\frac{1(u<p)}{p}$
TUT(p)	$h_{\text{TUT}}(p,u)=\frac{1(u⩾p)}{1-p}$
PRTE(p, λ(p))	$h_{\text{PRTE}}(p,u)=\frac{1(p⩽u<p+\lambda (p))}{\lambda (p)}$
MPRTE(p)	hMPRTE(p, u) = δ(u − p)

Note: ATE=Average Treatment Effect; TT=Treatment Effect of the Treated; TUT=Treatment Effect of the Untreated; PRTE=Policy Relevant Treatment Effect; MPRTE=Marginal Policy Relevant Treatment Effect. δ(·) is the Dirac delta function.