Implementing the Modified Golden Rule? Optimal Ramsey Capital Taxation with Incomplete Markets Revisited

What is the prescription of Ramsey capital taxation in the long run? Aiyagari (1995) addressed the question in a heterogeneous-agent incomplete-markets (HAIM) economy, showing that a positive capital tax should be imposed to implement the so-called modified golden rule (MGR). In deriving the MGR result, Aiyagari (1995) implicitly assumed that the multiplier on the resource constraint of the Ramsey problem converges to a finite positive value in the limit. We first show that this implicit assumption has a strong implication for the shadow price of Ramsey taxation in the limit: it must go to zero. We next show that if the shadow price of Ramsey taxation remains positive rather than goes to zero in the limit, the results differ sharply, including (i) the multiplier on the resource constraint of the Ramsey problem must explode in the limit if a Ramsey steady state exists, (ii) Ramsey steady states may fail to exist, (iii) the MGR does not hold and the corresponding capital tax is non-positive even if a Ramsey steady state exists. The key to our results is embedded in the hallmark of the HAIM economy: the risk-free gross interest rate is lower than the inverse of the preference discount factor in steady state. We briefly explore which feature, convergent or divergent multiplier, is more plausible.