Government Solvency, Ponzi Finance and the Redundancy and Usefulness of Public Debt

We investigate how the ability of the government to depart from budget balance and issue debt expands the set of equilibria that can be supported using lump-sum tax-transfer instruments. We show how this depends on the restrictions that exist on the capacity to tax and make transfer payments, and what these restrictions imply for the government's ability to issue debt. Central to our analysis is the definition of solvency for an infinite-lived government in an infinite-lived economy with overlapping generations of finite-lived households. Our specification is derived from the non-negativity constraints on the capital stock and on private consumption by all generations. Under fairly tight restrictions on the government's tax-transfer menu, our solvency constraint implies the conventional solvency constraint. With unrestricted taxes and transfers Ponzi finance is always possible but `unessential': it does not expand the set of equilibria that can be supported. Ponzi finance can be `essential' when taxes and transfers are restricted. The paper establishes a number of results that demonstrate how the government's ability to issue debt allows restricted tax-transfer schemes to support all equilibria attainable using unrestricted taxes and transfers.