Debt Cycles with Endogenous Interest Rate

In the course of economic development, nations may find it optimal to go through a cycle of debt. A recent theoretical paper by Long and Siebert (1989) gives sufficient conditions for this, under the assumption that the country is small and faces an exogenously given and time-independent world rate of interest. This raises an interesting question: would debt cycles be optimal (under certain conditions) if the country is large enough to influence the world rate of interest? In addition, is it possible that a debt cycle repeats itself indefinitely with the same frequency and magnitude? Can debt cycles exhibit the property of a converging spiral?