How do you defend the parallel-trends assumption?

hard

Answer

$(1) Plot pre-treatment trends of treated and control — visually parallel?$
$(2) Event study: interact treatment indicator with lead / lag indicators; pre-treatment lead coefficients \approx 0.$
$(3) Placebo tests: pretend treatment happened at an earlier fake date — no effect should appear.$
$(4) Multiple control groups.$
$(5) Synthetic control if only one treated unit.$
$Rule: never present DID without explicit pre-trend evidence.$

Check yourself — multiple choice

Not needed
Plot pre-trends / event study (lead coeffs ≈ 0) / placebo dates / multiple controls / synthetic control — never present DID without pre-trend evidence
Random
Same as $R^{2}$

Parallel trends: event study + placebo + pre-trend plots + synthetic control.

#causal-inference#quasi-experimental

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