Bequests, Golden-age Capital Accumulation and Government Debt

Abstract

The purpose of this paper is to examine the golden ages of an infinite time horizon economy in which individual families have finite life-spans but are connected with other generations through bequests. We construct a model of family bequest behaviour based on utility maximization and combine it with a simple, aggregative description of production. We then show that the overall model always has at least one steady-state equilibrium. Although we do not argue that bequest-motivated saving must necessarily play a major role in total capital accumulation, we do derive the following result: bequests will become an overwhelmingly important source of capital in situations in which the steady-state interest rate approaches a level P 1 derived in our analysis. Thus, at minimum, bequest behaviour has a safety value role, preventing a steady-state interest rate too much above the golden rule level and, hence, putting a lower bound on potential steady-state capital-to-labour ratios. We also present a second, somewhat different, application of our steady-state model: we show that the government can always change the steady-state interest rate with a properly designed shift between tax and debt financing of its spending. This result conflicts with the argument that government debt is not a component of private aggregate net worth since the discounted value of future debt service should exactly counterbalance the value now of any new government bonds issued. The organization of this paper is as follows. The first section sets up our bequest model for families. The second establishes the existence of at least one steady state and derives a lower bound for the aggregate capital-to-labour ratio. The third discusses government debt. All proofs for the propositions of this paper are in a separate appendix at the end.