Hyperbolic discounting and the sustainability of rotational savings arrangements

People across the developing world join rotational savings and credit associations (roscas) to fund repeated purchases of nondivisible goods. When the scope for punishment is weak, there is a natural question about why agents do not defect from these groups. I model a rosca as a commitment savings device for hyperbolic discounters. Roscas are attractive for two reasons: the possibility of getting the nondivisible good early (the standard reason), and the fixed saving requirement (valued only by time-inconsistent agents). I find explicit conditions under which an agent strictly prefers to remain in a rosca, even in the absence of formal contracting or social punishment. I show why, unlike with standard commitment products, a hyperbolic discounter will not postpone entry into a rosca. Finally, this paper makes predictions about the relative survival of random and fixed roscas. Random roscas are more resilient and beneficial than fixed roscas when information is limited and matching for new roscas is fast.