National Debt in a Neoclassical Growth Model

This 1965 American Economic Review paper by Peter Diamond extends Samuelson’s pure consumption-loan model by adding a produced, durable capital good, so that people can provide for retirement either by lending to other people or by holding physical capital, and asks what happens to the economy’s long-run competitive equilibrium once a government issues debt. Working with two-period-lived overlapping generations, a constant-returns aggregate production function, and a population growing at a constant rate n, Diamond first characterizes the “Golden Rule” capital-labor ratio that would maximize steady-state per-capita consumption for a central planner, then shows that the decentralized competitive equilibrium – in which the young lend their unconsumed wages to entrepreneurs at an interest rate equal to capital’s marginal product – need not coincide with it. His central theoretical result is that the free-market solution can settle at a capital-labor ratio permanently above the Golden Rule level, meaning the interest rate falls permanently below the population growth rate; in that case the economy is dynamically inefficient, since it would be possible to make every future generation better off simply by holding less capital, even though the model has no monopoly power, taxes, externalities, or any other conventional source of inefficiency. Diamond then introduces government debt into this framework and shows that externally held debt reduces long-run individual welfare (in the efficient case) purely through the taxes needed to service it, while internally held debt does so by an even larger amount, because it additionally substitutes government paper for productive physical capital in individual portfolios, further shrinking the capital stock. In the dynamically inefficient case, by contrast, both forms of debt can raise welfare by moving the interest rate closer to the growth rate.

Peter A. Diamond | Macro Paper Warehouse

National Debt in a Neoclassical Growth Model