Start by acknowledging that when randomization is infeasible, we rely on observational causal inference methods, each with distinct assumptions. For each strategy, clearly state the identification assumption, propose empirical checks (e.g., pre-trends, covariate balance), and discuss potential violations and sensitivity analyses. Finally, compare the strategies in terms of feasibility, data requirements, and robustness to violations.
Pro tip: Emphasize that no single method is perfect; triangulating results across multiple identification strategies strengthens causal claims. Also, mention that Uber often uses switchback experiments or synthetic control for city-level promotions, showing practical awareness.
Use DiD when you have pre- and post-promotion data for treated and control groups. The key assumption is parallel trends: absent the promotion, the treated and control groups would have followed the same trajectory. Check by plotting pre-period trends and testing for differential pre-trends. Breakdown if trends diverge due to other shocks or if composition changes.
Match treated units (e.g., users exposed to promotion) with similar control units based on observed covariates. Assumption: conditional independence (no unmeasured confounders). Check covariate balance after matching and conduct sensitivity analysis for hidden bias. Breakdown if important confounders are unobserved or if overlap is poor.
Find an instrument that affects promotion exposure but not the outcome directly. Assumptions: relevance (instrument correlates with treatment) and exclusion restriction (instrument affects outcome only through treatment). Check relevance with first-stage F-statistic; exclusion is untestable but can be argued via context. Breakdown if instrument is weak or violates exclusion.
Exploit a cutoff (e.g., eligibility threshold) that determines promotion exposure. Assumption: units just above and below cutoff are comparable except for treatment. Check for manipulation of the running variable (e.g., McCrary test) and continuity of covariates at cutoff. Breakdown if units can manipulate the cutoff or if functional form is misspecified.
Construct a synthetic control from weighted combination of untreated units to mimic the treated unit's pre-promotion trajectory. Assumption: treated unit's post-promotion outcome would have followed the synthetic control's path absent treatment. Check pre-period fit and placebo tests. Breakdown if donor pool is contaminated or if there are idiosyncratic shocks.
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