Math for Causal Inference
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Event Studies & Pre-Trends

Event-study coefficients with pre-trends, anticipation and a sensitivity interval for bounded violations.

Day 68: Parallel Trends & Event Studies
02-5-4-3-2-101234event time kcoefficient
β at k = 2
1.95
true effect 2.00
sensitivity interval (M = 1)
[0.92, 2.98]

Event-study coefficients (dots, with 95% intervals) are DiDs relative to the reference period. Grey squares show the true effect plus any pre-existing trend gap. Add a linear pre-trend, anticipation or noise and see what the pre-period coefficients reveal, and how a sensitivity interval that allows post-period violations up to M times the largest pre-period one changes the conclusion at k = 2.