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∆Y 1,3(0)⊥ ⊥D2, D3 |X 1, X3(0,0), D 1 = 0⇒AT T(2,3) isnotidentified, S 2,3(0) ={X 1, X3(0,0)}, S2,3 ={X 1, X3} Figure H

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econ.EM 1

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2026 1

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Causal Graphs for Conditional Parallel Trends

econ.EM · 2026-04-14 · unverdicted · novelty 7.0

Δ-SWIGs allow d-separation to imply conditional parallel trends for DiD, showing that post-treatment controls are required when time-varying covariates affect outcomes while pre-treatment trends only partially justify post-treatment effects.

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  • Causal Graphs for Conditional Parallel Trends econ.EM · 2026-04-14 · unverdicted · none · ref 5

    Δ-SWIGs allow d-separation to imply conditional parallel trends for DiD, showing that post-treatment controls are required when time-varying covariates affect outcomes while pre-treatment trends only partially justify post-treatment effects.