Card rewards: is there a 'Reverse-Robin-Hood-Effect'?

The main argument against interchange fees has always been that they are an anticompetitive instrument to raise the costs of card acceptance. In turn, high costs of card acceptance would lead to high retail prices harming consumers. Schuh, Scott, Oz Shy, and Joanna Stavins (2010) have added a new dimension to this critical view of interchange fees. One of the authors has dubbed this distributional effect as "Reverse-Robin-Hood-Cross- Subsidy." The main cause of this effect is the interaction of interchange fees and reward programs. Therefore, a model of product differentiation is used in this discussion to show that it may be much more difficult than is commonly assumed to estimate such distributional effects and that card users may, in fact, pay a large portion of their rewards themselves. This result is based on a form of "implicit surcharging." If merchants practice such implicit surcharging, they may recover card costs from card users without resorting to an explicit surcharge.