Estimating a Promotion's Causal Effect Without an Experiment
Context
You need to estimate the causal impact of a marketing promotion on engagement (e.g., trips, bookings, revenue) when a randomized experiment is not feasible. You have longitudinal data at user/geo × time granularity, with information on promotion eligibility/exposure, outcomes, covariates, and rollout timing that may be staggered across units.
Task
Propose and justify at least three distinct identification strategies to estimate the promotion’s causal effect. For each strategy, clearly state:
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Identification setup and estimator(s)
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Key assumptions
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Diagnostics and robustness checks
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Failure modes and how you would detect/mitigate them
You may choose from (or add to) the following:
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Difference-in-Differences (DiD) / Event Study with staggered rollout using modern estimators (avoid naive TWFE bias), including parallel-trends checks and placebo tests.
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Synthetic Control at the geo level with pre-period fit metrics and sensitivity to donor pool/regularization.
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Instrumental Variables exploiting exogenous variation (e.g., eligibility rules, random delivery outages), with relevance/exclusion checks and weak-IV diagnostics.
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Regression Discontinuity if eligibility thresholds exist (e.g., tenure ≥ 30 days), with bandwidth/functional-form sensitivity and McCrary density tests.
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Propensity-score or doubly-robust learners (IPW/AIPW, causal forests) with overlap checks and covariate balance.
Additionally, explain how you would:
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Report ATE/ATT with uncertainty
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Account for interference/network effects (spillovers)
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Control for seasonality and concurrent campaigns