Double Selection in Causal Inference

Christian Alemán, Christopher Busch, Raül Santaeulàlia-Llopis and Tetyana Surovtseva

No 13035, CESifo Working Paper Series from CESifo

Abstract: 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.

Keywords: double Selection; difference-in-differences; causal inference; nonparametric identification (search for similar items in EconPapers)
JEL-codes: C14 C21 J38 (search for similar items in EconPapers)
Date: 2026
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