4.19 ATE: Identification Problem

• YES: \(\pi\) using E[D_i]

• YES: E[Y_i1|D_i = 1] using E[Y_i|D_i = 1]; E[Y_i0|D_i = 0] using E[Y_i|D_i = 0]

• NO: E[Y_i0|D_i = 1]): Average outcome under control (Y_i0) for those units in the treatment condition (D_i = 1)

• NO: E[Y_i1|D_i = 0]): Average outcome under treatment (Y_i1) for those in the control condition (D_i = 0)

• E[Y_i1 - Y_i0] = 2/6 \(\times\) (0.5 - ?) + 4/6 \(\times\) (? - 0.25)

	Y = 1	Y = 0
D = 1	0.5	?
D = 0	?	0.25

• Identification Problem: Two quantities are unobservable; We must rely on assumptions to identify ATE (fill em in)