Optimal Taxation without State‐Contingent Debt

TLDR

Lucas and Stokey’s model shows tax rates inherit the serial correlation of government expenditures, contradicting Barro’s random‑walk prediction, and the study builds on recent consumption‑smoothing advances. The authors modify Lucas and Stokey’s economy to allow only risk‑free debt in order to recover Barro’s random‑walk tax‑smoothing result. By restricting the economy to risk‑free debt, the Ramsey planner faces additional equilibrium constraints beyond those implied by complete markets, shaping the allocation outcomes. The resulting Ramsey outcome blends Barro’s and Lucas‑Stokey’s features, with exogenous expenditures driving deficit and taxes similarly to Lucas‑Stokey but introducing a near‑unit‑root component in debt and taxes, yet without asset‑holding limits the outcomes can diverge markedly from Barro’s predictions.

Abstract

In an economy studied by Lucas and Stokey, tax rates inherit the serial correlation structure of government expenditures, belying Barro's earlier result that taxes should be a random walk for any stochastic process of government expenditures. To recover a version of Barro's random walk tax‐smoothing outcome, we modify Lucas and Stokey's economy to permit only risk‐free debt. Having only risk‐free debt confronts the Ramsey planner with additional constraints on equilibrium allocations beyond one imposed by Lucas and Stokey's assumption of complete markets. The Ramsey outcome blends features of Barro's model with Lucas and Stokey's. In our model, the contemporaneous effects of exogenous government expenditures on the government deficit and taxes resemble those in Lucas and Stokey's model, but incomplete markets put a near–unit root component into government debt and taxes, an outcome like Barro's. However, we show that without ad hoc limits on the government's asset holdings, outcomes can diverge in important ways from Barro's. Our results use and extend recent advances in the consumption‐smoothing literature.