Long-Term Contracting with Time-Inconsistent Agents∗

In many contractual relationships, consumers are allowed to terminate agreements at will. We study how removing commitment power from consumers affects equilibrium contracts and welfare when consumers have self-control problems. We show that removing commitment power is welfare improving when consumers are sufficiently dynamically inconsistent. Controlling for impatience, it is easier to sustain long-term contracts when consumers are timeinconsistent than when they are dynamically consistent. Moreover, because naive consumers overestimate the surplus from keeping a long-term contract, it is easier to sustain long-term contracts with them than with sophisticates. In fact, we show that the welfare loss from timeinconsistency of naifs vanishes as the number of periods grows (with or without commitment). As a result, naive agents get a higher welfare than sophisticates if the contracting horizon is large. We also show that limiting the fees that companies can charge actually hurts naive consumers. JEL: D03, D81, D86 ∗Preliminary version; comments are especially welcome. We thank Marina Halac, George Mailath, Philipp Strack, Jeremy Tobacman, and Edward Van Wesep for helpful comments. †Washington University in St. Louis, [email protected] ‡University of Colorado at Boulder, [email protected]. 1