4.17 ATE: Naive Estimate

• Naive estimate of ATE: Difference between expected values in treatment and control
  • Equate E[Y_i1] - E[Y_i0] with (0+1)/2 - (1+0+0+0)/4 = 0.5 - 0.25 = 0.25
  • Q: What is the problem with the naive estimate of the treatment effect? Can we interpret 0.25 as causal effect? Why (not)?¹⁹

Unit	Di (Aspirin: Yes/No)	Yi (Pain: Yes/No)	Yi1 (Pain | YesAspirin)	Yi0 (Pain | NoAspirin)
Simone	1	0	0	?
Julia	1	1	1	?
Paul	0	1	?	1
Trump	0	0	?	0
Fabrizio	0	0	?	0
Diego	0	0	?	0

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19. Selection into treatment or control, e.g., males smuggle themselves into the treatment group.↩