Recursive Sequential Screening for State-Dependent Ex Post Types: How to Keep Customers from Cancelling Their Subscriptions

When do customers cancel subscription services, and can contract design change that decision? Tariff structure can cause what I call contract-induced churn. Profitable customers leave because pricing concentrates payment in low-usage periods. I develop a model of recursive sequential screening with posted tariffs, that is, fixed pricing schedules, in which customers decide whether to renew before observing their demand state. Because the same customer moves between demand states over time, the tariff screens a customer whose type changes period by period rather than a customer with fixed demand. Under a two-part tariff, the fixed fee loads payment onto low-usage periods, pushing customers toward exit when low demand persists. A three-part tariff reallocates payment from low-usage to high-usage months, raising continuation value and reducing exit.

I estimate the model on store-month panel data from a B2B delivery platform. Usage states are persistent (low-usage spells last 4.5 months on average), and exit risk is three times higher in low-usage states.

Switching to the best alternative three-part tariff raises customer lifetime value by 8.3 percent relative to an optimized two-part tariff and lowers the monthly exit probability in low-demand states from 22.1 to 19.9 percent. An out-of-sample implementation of a three-part tariff to a subset of customers supports the model's retention prediction. Tariff design can work as both a retention lever and a screening tool.