This article studies the structural differences between implicit and explicit government debt in a two-generations-overlapping model with stochastic factor-prices. If a government can issue safe bonds and new claims to wage-indexed social security to service a given initial obligation, there exists a set of Pareto-efficient ways to do so. This set is characterized by the conflicting interests of the current young and the yet unborn generations regarding the allocation of factor-price risks. However, it is shown that there will always exist a simple intertemporal compensation mechanism which allows to reconcile these conflicting interests. This compensation mechanism narrows the set of Pareto-efficient debt structures until only one remains. This result hinges on the double-incomplete markets structure of stochastic OLG models where households can neither trade consumption-loans nor factor-price risks privately.