Double Selection in Causal Inference

• Authors: Christian Alemán-Pericón, Christopher Busch, Raül Santaeulàlia-Llopis and Tetyana Surovtseva
• BSE Working Paper: 1604 | October 2026
• Keywords: differences-in-differences, double selection, causal inference, nonparametric identification
• JEL codes: C14, C21, J38

We introduce a unified double selection framework accommodating group-specific additive and multiplicative shifters of an unobserved common time trend (CTT). Under double selection, the CTT does not manifest as a parallel trend; the resulting non-constant selection bias is a linear combination nesting standard difference-in-differences (DiD) in levels and logs. Opposing shifters can yield patterns structurally impossible under standard DiDs, such as a ranking reversal of the groups over time. We establish that in the presence of double selection bias treatment effects are non-parametrically identified by the change of the ratio of within-group outcome changes over time. The double selection structure induces a stable linear relationship in the outcome-on-outcome space, grounding a simple two-step estimator operating in levels. Revisiting Card (1992), double selection uncovers valid counterfactuals where standard DiD fails.