Instagram plans a new Shopping tab but cannot observe off-app purchases. Design a rigorous end-to-end plan. Part A — Verify the hypothesis that users see purchase-inspiring posts on Instagram but buy on third-party sites: What measurable in-app signals would you use as proxies for off-app purchase intent (e.g., outbound merchant-link clicks, profile->bio link navigations, saves/shares with commerce hashtags, search-after-view patterns)? How would you quantify potential bias (e.g., selection, novelty, confounding from seasonality) and construct counterfactuals (e.g., synthetic controls, matched cohorts)? Part B — Pre-launch opportunity sizing: Assume DAU = 50M, 10% show intent weekly (as defined by a defensible in-app proxy), each intentor averages 0.2 purchases/week off-platform with AOV = $45, and a future platform take rate of 5%. Merchants are expected to spend ads/placement fees equal to $0.002 per impression for Shopping-tab surfaces with an estimated 6 impressions per intentor per week. Estimate weekly gross revenue impact by component (transaction fee vs. ads). What sensitivity analyses would you run and which 3 assumptions most dominate the estimate? Part C — Launch readout: You ship the tab and observe high click-through into merchant flows but purchases are far below forecast. Build a metric tree and investigation plan that (i) localizes drop-offs across the funnel (Discovery -> Product View -> Deep Link -> Cart -> Purchase), (ii) evaluates cannibalization of existing commerce surfaces (e.g., Marketplace) vs. true incrementality (design a geo or user-level holdout), (iii) distinguishes product/UX frictions from supply/quality issues (relevance, price, shipping), and (iv) rules out instrumentation/data-quality problems. Specify primary success metrics, guardrails (e.g., session length, feed CTR, ad revenue lift, complaint rate), required segmentation cuts, and what evidence would trigger a rollback.