Causal Effect Between Price and Expected Arrival Time (ETA) in a Real-Time Ride-Hailing Marketplace

Objective

Estimate the causal relationship between dynamic price and expected arrival time (ETA). Design an econometric strategy that identifies:

• The effect of price on ETA, and/or
• The effect of ETA on price, while addressing simultaneity and endogeneity.

Assume you observe request-level data with timestamps, geohashes/zones, posted price (or surge multiplier), predicted pickup ETA at request time, trip attributes, and rich context (weather, traffic, events, outages, regulations).

Tasks

1. Explain why OLS is biased due to simultaneity between price and ETA and outline a causal graph/intuition.
2. Propose valid instruments for:
   • Price → ETA (instruments that shift price but do not directly change ETA), and
   • ETA → Price (instruments that shift ETA but do not directly change price), drawing on exogenous supply shocks (e.g., weather or driver outages) and regulator-imposed price caps/floors where appropriate.
3. Write a 2SLS specification for each direction, including:
   • Functional form (recommend log or log–log),
   • Fixed effects (e.g., origin–destination, hour-of-week, date),
   • Clustering strategy for standard errors.
4. State the exclusion restrictions for each proposed instrument and discuss potential violations and how you would test them.
5. Show how to compute the ETA elasticity with respect to price under log–log and semi-log models.
6. Describe and interpret diagnostics:
   • Over-identification tests (e.g., Hansen J),
   • Weak-IV tests (e.g., first-stage F, Kleibergen–Paap rk statistic),
   • Stability and robustness checks (e.g., pre-trends, subsample stability, alternative instruments, local RDD around thresholds).
7. Explain how the estimated effects inform surge-pricing policy (e.g., trade-offs between wait times and price, SLA targeting, fairness/consumer protection).