Optimal Timing in Rotten Kid Families

In a family context with endogenous timing, multiple public goods and alternative parental instruments, we show that the optimal timing for the sequential-action game played by rotten kids and a parent depends crucially on whether the kids are homogeneous or heterogeneous. For homogeneous kids, the rotten kid theorem holds irrespective of the parental policy instrument, implying that it is optimal to let the kids to be action leaders. If the kids are heterogeneous, however, parental leadership yields a first best outcome and, hence, it is optimal whenever the kids are economically dependent and agree on the tradeoff between public goods.