Loyalty programs are increasingly popular. According to the 2017 Colloquy Loyalty Census, in the United States alone consumers hold 3.8 billion loyalty program memberships (2.6 billion in 2012) that cover a wide array of industries, including retail, airlines, hotels, restaurants, car rentals, and financial services. The value of rewards earned in 2011 was $47.9 billion. This may sound too good to be true and indeed about one third of these claims remained unredeemed. But why would people sign up for a better deal but give up profiting from it later on?
In BSE Working Paper No. 1196 “Time-limited loyalty rewards,” Ramon Caminal argues that the main reason behind these unredeemed benefits is the time limits commonly used in loyalty programs. The paper then aims to understand the motivation behind tight restrictions on the timing of redemption of rewards as well as its implications.
Perhaps surprisingly, the paper provides a favorable view of loyalty programs. It reasons that the commitment to discount prices on repeat purchases may help to reduce the inefficiency generated by market power. Moreover, it shows that consumers also benefit from loyalty programs, which is compatible with the evidence.
A new way to tackle the issue
Most loyalty programs include various time restrictions on the collection and redemption of rewards. For example, frequent-flyer programs were introduced in the early-1980s and a few years later airlines introduced point (miles) expiration dates, which since then has become the industry standard. Similarly, in other industries accumulated points or coupons also typically expire after a certain date. But do firms benefit from them? Are consumers harmed by them? Should time limits be regulated?
To address these questions, the present paper extends the existing literature on loyalty rewards and introduces a new theoretical framework with two key features: the heterogenous degree of impatience of firms and consumers, and the cyclical consumer behavior induced by such membership programs.
In an infinite-horizon model, a monopolist sells a non-durable good to a continuum of repeat buyers whose preferences are subject to temporary shocks. Such shocks foster consumers with relatively low valuations to purchase the good at discount prices and hence it motivates the introduction of loyalty programs. At any point in time, the monopolist can offer a bundle that includes one unit of the current good plus the option of purchasing the good in the future at a reduced price (which is set equal to marginal cost). To highlight the role of time limits on the redemption of rewards two scenarios are considered: when the option to purchase the good at the reduced price expires after one period (i.e., time-limited rewards); and when this option never expires (i.e., time-unlimited rewards).
A crucial implication of this characterization is that purchases at regular prices are followed by the redemption of rewards (i.e., purchases at discount prices), after which a new cycle begins. Thus, both consumers and the firm must take into account how the timing of reward redemptions affects subsequent purchases at regular prices.
The case for time-limited rewards
Consumers holding a current time-limited reward face a straightforward decision problem: since these rewards expire at the end of the period, it is optimal to purchase the good whenever their valuation exceeds the discount price. Since such a price is set equal to marginal cost, reward redemption implies ex-post efficiency by temporarily eliminating the inefficiency associated with monopoly power.
However, the introduction of these rewards may or may not be optimal for the monopolist because they involve costs and benefits. On one hand, the consumers anticipate the additional future rents associated with the loyalty reward, and so increase their willingness to pay for the current purchase which then raises firm’s current profits. On the other hand, the reward also involves a liability. Some consumers that would have also purchased the good at the regular price will end up redeeming the reward and hence monopoly rents are foregone. The firms’ willingness to introduce time-limited rewards depends on the relative strength of these two effects. The first effect (the benefit) depends positively on consumers’ discount factor, whereas the second effect (the cost) depends on the firm’s discount factor. Thus, an immediate implication is that the firm will introduce time-limited rewards provided consumers’ discount factor is sufficiently high relative to the firm’s discount factor.
Lifting time restrictions generates similar a trade-off. On one side, it raises the value of the rewards for consumers by allowing them to engage in intertemporal substitution. On the other, it induces consumers to excessively delay the redemption of rewards, and hence all future purchases.
In most of the scenarios examined in the paper the second effect dominates and hence time-limited rewards are adopted by firms. Moreover, the interests of consumers and the firm tend to be aligned and hence there is little room for public intervention exclusively concerned with the time dimension of rewards.
The paper finds that time-limits are indeed necessary to discipline consumers in loyalty rewards programs. In the absence of such constraints, buyers would tend to excessively delay the redemption of rewards, and consequently all future purchases. Hence, time-limited rewards are optimal.
Not only that, but the paper suggests that optimality of the time limits is quite a robust result. Time-unlimited rewards may be optimal if the consumers intrinsically value time flexibility and both the consumer and the firm are less concerned about the impact of their actions on future purchases. In particular, the author shows that if consumers experience satiation (i.e., with a certain probability they leave the market after a consumption episode), then they more carefully choose the timing of their purchase and will care less about their future purchases. If the degree of satiation is sufficiently high, then lifting time restrictions allows consumers to redeem the reward whenever it is (approximately) efficient.