Apply instrumental variables under interference
Overview
This question evaluates understanding of causal inference with instrumental variables in the presence of interference, testing skills in defining units and aggregation levels for market‑level spillovers, articulating IV assumptions (relevance, exclusion restriction, independence, monotonicity), and formulating estimation frameworks such as two‑stage least squares. Commonly asked in Statistics & Math interviews for data scientist roles because networked marketplaces invalidate simple A/B tests, it sits in the econometrics/causal inference domain and primarily assesses practical application of IV methods while requiring conceptual understanding of identification, robustness diagnostics, and sensitivity analysis.
IV estimation for a ride‑sharing feature when A/B testing is infeasible due to interference
Context
You need to estimate the causal effect of a new ride‑sharing feature on trip volume. A clean A/B test is not feasible because users (drivers/riders) interact within a marketplace, creating interference/spillovers across units (e.g., one driver's treatment can affect other drivers' and riders' outcomes in the same market/time).
Task
- Propose an instrumental‑variables (IV) strategy to identify the causal effect of feature exposure/adoption on trip volume in the presence of interference.
- Clearly define the unit of analysis, treatment, outcome, and the level at which interference is addressed (e.g., market × time clustering/aggregation).
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State and justify all IV assumptions precisely:
- Relevance
- Exclusion restriction
- Independence (as‑if random)
- Monotonicity (if you claim a LATE interpretation)
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Provide at least two concrete, plausibly exogenous instruments and justify them. Examples to consider include:
- Staggered driver app version eligibility (e.g., forced update schedule, app‑store review lags)
- An encouragement design (e.g., hash‑bucket canary eligibility) or a weather‑based interaction that shifts usage only among eligibles
- Write the first‑stage and second‑stage (2SLS) equations, including controls and fixed effects.
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Describe how you will:
- Diagnose weak instruments (first‑stage F‑statistics; Kleibergen‑Paap for robust/clustered settings)
- Run over‑identification tests (Sargan/Hansen J)
- Handle heteroskedasticity and clustering (e.g., two‑way clustering by market and time; wild cluster bootstrap if few clusters)
- Assess and mitigate violations of exclusion in the presence of marketplace spillovers
- Discuss whether an effectively unlimited supply environment makes the exclusion restriction more or less credible, and why.
- If assumptions partially fail, outline sensitivity analyses or bounds (e.g., Conley‑type plausibly exogenous bounds, Anderson‑Rubin tests).
Solution
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