Debt, Deficits, and Finite Horizons

This paper builds a tractable model of an economy populated by finitely lived agents – each facing a constant instantaneous probability of death p, with new cohorts continuously born – and uses it to show that government debt and the timing of taxes have real, lasting effects on interest rates, capital accumulation, and consumption, in contrast to the Ricardian-equivalence result that holds when agents are infinitely lived (p = 0). Because each agent’s expected horizon is finite while the economy as a whole survives forever, the model can be aggregated into a simple closed-form consumption function – aggregate consumption is a linear function of financial wealth plus human wealth – while still differing sharply from the infinite-horizon permanent-income model: non-interest income is discounted at a rate (r+p) above the interest rate, so a decrease in current taxes financed by a future tax increase raises human wealth and current consumption unless p = 0, with the effect growing the longer taxes are deferred. In the closed economy, finite horizons by themselves lower the steady-state capital stock relative to the infinite-horizon (modified-golden-rule) benchmark, though this is offset, ambiguously, by a “saving for retirement” effect if labor income declines over an agent’s life. In the open economy, government debt displaces foreign assets in private portfolios – one-for-one when the steady-state interest rate is zero, and more than one-for-one otherwise – so the government can use debt policy to choose any steady-state level of private consumption. The paper also shows that the effect of a historically realistic policy of early deficits followed by surpluses builds up over time rather than disappearing, and that debt policy can, in principle, be used to smooth aggregate consumption across generations in the face of output fluctuations.

Olivier J. Blanchard | Macro Paper Warehouse

Debt, Deficits, and Finite Horizons