The Ramsey steady-state conundrum in heterogeneous-agent economies

When macroeconomists solve for optimal capital and labor taxation in Aiyagari-style heterogeneous-agent, incomplete-markets economies, they routinely assume – without proving it – that the long-run “Ramsey steady state” exists and is well-behaved (interior), a step Aiyagari (1995) himself admitted was hard to justify. This paper proves that assumption is generally false in the standard Aiyagari model with constant-relative-risk-aversion preferences: for the empirically normal case of risk aversion sigma >= 1, no interior Ramsey steady state exists at all, and the only steady state the Ramsey planner can reach has aggregate consumption collapsing to zero and the labor tax rising to 100%, because the planner has a permanent incentive to borrow cheaply against a market interest rate that sits below the household discount rate, front-loading consumption until public debt becomes unsustainable. Using a modified, analytically tractable version of the Aiyagari model that nests the standard model as a limiting case, the authors then show that when an interior steady state does exist (under a feasibility condition on public debt capacity), it features a zero long-run capital tax – the opposite of Aiyagari’s celebrated positive-capital-tax result – with the modified golden rule instead satisfied purely through a high steady-state labor tax and public debt; for the alternative low-risk-aversion case (sigma < 1), an interior steady state can exist but only with a divergent Ramsey multiplier and a violation of the modified golden rule. The paper’s conclusions rest on a standard incomplete-markets model with CRRA power utility, ad hoc borrowing constraints, and a Ramsey planner maximizing time-zero discounted welfare; the authors are explicit that their results do not apply to Ramsey plans that instead maximize only steady-state welfare, where the incentive to front-load consumption disappears.

Yi Wen | Macro Paper Warehouse

The Ramsey steady-state conundrum in heterogeneous-agent economies