When Are 2 Observations Sufficient?: Revisiting the Method of Difference

• In Event: Advances in Causal Inference

Abstract

We derive novel sufficient conditions for making causal inferences from the comparison of binary cross-sectional observations on two units (N = 2, T = 1) or on a single unit before and after treatment (N = 1, T = 2). We show that when (a) there is a monotonic effect for the treated unit, (b) the baseline potential outcomes for the two observations are exchange- able, and (c) the association between baseline potential outcomes is monotonic in the same direction as the effect, the false positive rate (FPR) can be bounded above in terms of the prior odds for the alternative hypothesis and a prior prognostic score. We also show that the FPR bound can be lowered with the inclusion of post-treatment information. Finally, we demonstrate that synthetic controls can be constructed to satisfy these conditions and that the FPR bounds are robust to monotonic forms of interference and non-exchangeability. This methodology is demonstrated in the re-evaluation of a contested claim that Sekou Toure’s public opposition to the proposed French constitution was likely essential for Guinean independence from France in 1958.

Authors

• Adam Glynn, Emory University

• Nahomi Ichino, Emory University