Estimating Demand for Subscriptions: Identifying Willingness to Pay without Price Variation

We demonstrate how to obtain the distribution of consumer willingness to pay (WTP) for digital subscription products, where consumers pay a fixed price each period for potentially unlimited usage, for example, music streaming like Spotify. Typically, in such applications, usage data are observed and is critically valuable for the method here. We demonstrate how variation in usage and subscription choice together can identify the WTP distribution in the absence of price variation. Our framework accommodates and builds upon a range of utility specifications for usage, which is related to subscription decisions. We provide the conditions required on exogenous variation impacting usage, and prove how these lead to identification of the WTP distribution. We also investigate the conditions under which usage variation is not equivalent to price variation. We apply our method to an empirical application using the data from a music streaming service. Using the estimated WTP distribution, we obtain the revenue maximizing prices for different consumer segments.