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

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Abstract

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.

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  • Yunmin Chen & YiLi Chien & C.C. Yang, 2017. "Implementing the Modified Golden Rule? Optimal Ramsey Capital Taxation with Incomplete Markets Revisited," Working Papers 2017-003, Federal Reserve Bank of St. Louis, revised 01 Oct 2020.
  • Handle: RePEc:fip:fedlwp:2017-003
    DOI: 10.20955/wp.2017.003
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    Cited by:

    1. Chien, YiLi & Wen, Yi, 2021. "Time-inconsistent optimal quantity of debt," European Economic Review, Elsevier, vol. 140(C).
    2. YiLi Chien & Yi Wen, 2020. "Optimal Fiscal Policy under Capital Overaccumulation," Working Papers 2020-002, Federal Reserve Bank of St. Louis, revised 30 Aug 2021.
    3. Chien, YiLi & Wen, Yi, 2022. "The determination of public debt under both aggregate and idiosyncratic uncertainty," Journal of Economic Theory, Elsevier, vol. 203(C).
    4. Krueger, Dirk & Ludwig, Alexander & Villalvazo, Sergio, 2021. "Optimal taxes on capital in the OLG model with uninsurable idiosyncratic income risk," Journal of Public Economics, Elsevier, vol. 201(C).
    5. YiLi Chien & Yi Wen, 2022. "Optimal Ramsey Taxation in Heterogeneous Agent Economies with Quasi-Linear Preferences," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 46, pages 124-160, October.
    6. YiLi Chien & Yi Wen & HsinJung Wu, 2020. "Are Government Bonds Net Wealth or a Liability? ---Optimal Debt and Taxes in an OLG Model with Uninsurable Income Risk," Working Papers 2020-007, Federal Reserve Bank of St. Louis, revised 03 Jan 2021.

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    More about this item

    Keywords

    Capital Taxation; Modified Golden Rule; Ramsey Problem; Incomplete Markets; heterogeneous agent;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • H30 - Public Economics - - Fiscal Policies and Behavior of Economic Agents - - - General

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