We contest the loss aversion theory of the endowment effect, in which the effect depends on the status of endowment alone. Instead, we propose that the nature of the trading process determines whether people resist or accept an exchange by affecting the responsibility people feel for their choice. The more they feel responsible for the decision, the more they expect experiencing regret over a negative outcome. Aversion to regret causes people to resist a rational trade and exhibit the endowment effect. In a series of experiments, we analyze two institutions that alter the trading process and reduce perceived responsibility --agency and markets. We find that both mute the endowment effect; moreover, participants intentionally use them to self-debias. Since many institutions shift responsibility, we conclude that the endowment effect is not present in many domains previously thought to implicate it. Institutional design often need not rely on paternalistic intervention.