Optimal Long-Run Fiscal Policy with Heterogeneous Agents

How should a government that can fully commit to taxes and debt forever set long-run fiscal policy in an economy where households self-insure against uninsurable income risk by saving, as in Aiyagari (1995)? This paper introduces a new method for characterizing the long-run (“Ramsey”) steady state of such dynamic optimal-taxation problems, built on recently developed “sequence-space” representations of aggregate household behavior: household asset demand and labor supply at any date are written as functions of entire anticipated future paths of after-tax interest rates and wages, which lets the authors define “discounted elasticities” – present-value responses of household aggregates to a permanent, fully anticipated, one-time change in a price – as interpretable, potentially estimable sufficient statistics for the optimal-tax problem. Evaluating the resulting Ramsey steady-state optimality condition numerically for standard calibrations of a labor-only Aiyagari economy with the balanced-growth household preferences typically used in heterogeneous-agent macro models, the authors find that the condition is never satisfied at any finite tax rate: the marginal benefit of raising interest rates (providing more liquidity for precautionary saving) financed by higher labor taxes never turns negative, so optimal policy points toward “immiseration” – labor income taxes rising toward 100% and real consumption collapsing to zero – rather than converging to an interior steady state. Where a Ramsey steady state does exist under alternative parameterizations, it typically still involves near-confiscatory labor tax rates above 90%. The authors trace this result to a specific, counterintuitive channel: the discounted elasticity of labor supply with respect to the after-tax wage is negative in these calibrations, so households, anticipating that future taxes will keep rising, work more today rather than less, turning what is normally understood as the efficiency cost of labor taxation into an apparent benefit for the planner. This finding is robust across a wide range of income processes, initial government debt levels, government-spending levels, lump-sum-transfer and progressive-tax variants, and to extending the model to include capital and capital income taxes following Aiyagari (1995) directly, where the same near-immiseration or non-existence result reappears alongside a breakdown of the modified golden rule of capital accumulation. The one dependable escape route the paper identifies is a change in preferences: additively separable preferences with an elasticity of intertemporal substitution above 1, or Greenwood-Hercowitz-Huffman (GHH) preferences that eliminate wealth effects on labor supply altogether, both push the discounted labor-supply elasticity into positive territory and restore a reasonable interior Ramsey steady state. The authors are explicit that they regard the immiseration result as revealing an implausibly strong anticipatory response of household behavior to distant future tax changes, rather than a literal policy recommendation, and flag dampening these anticipation effects (in the spirit of Garcia-Schmidt and Woodford 2019 and Gabaix 2020) as a promising direction for future work.

Michael Cai | Macro Paper Warehouse

Optimal Long-Run Fiscal Policy with Heterogeneous Agents