The Cass criterion, the net dividend criterion, and optimality

Abel, Mankiw, Summers, and Zeckhauser [Assessing dynamic efficiency: theory and evidence, Rev. Econ. Stud. 56 (1989) 1-20] propose the net dividend criterion as an easy to use sufficient condition for optimality in general stochastic overlapping generations economies with production. We provide examples based on the criterion due to Cass [On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization, J. Econ. Theory 4 (1972) 200-223] and its extensions, the usual tools for such problems, to show that the net dividend criterion need not give the right answer. We identify the flaw in their proof. We also provide an alternative condition which, by an argument unrelated to theirs, is a sufficient condition for optimality when dividends are nonnegative and then argue that the condition is not innocuous since it cannot be verified in actual economies.