Conventionally, mobile network operators charge users for data plan subscriptions. To create new revenue streams, some operators now also incentivize users to watch ads with data rewards and collect payments from advertisers. In this work, we study two such rewarding schemes: a Subscription-Aware Rewarding (SAR) scheme and a Subscription-Unaware Rewarding (SUR) scheme. Under the SAR scheme, only the subscribers of the operators' existing data plans are eligible for the rewards; under the SUR scheme, all users are eligible for the rewards (e.g., the users who do not subscribe to the data plans can still get SIM cards and receive data rewards by watching ads). We model the interactions among a capacity-constrained operator, users, and advertisers by a two-stage Stackelberg game, and characterize their equilibrium strategies under both the SAR and SUR schemes. We show that the SAR scheme can lead to more subscriptions and a higher operator revenue from the data market, while the SUR scheme can lead to better ad viewership and a higher operator revenue from the ad market. We provide some counter-intuitive insights for the design of data rewards. For example, the operator's optimal choice between the two schemes is sensitive to the users' data consumption utility function. When each user has a logarithmic utility function, the operator should apply the SUR scheme (i.e., reward both subscribers and nonsubscribers) if and only if it has a small network capacity.