IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/24006.html
   My bibliography  Save this paper

Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings

Author

Listed:

Abstract

Using the second order Taylor expansion of the Lagrangian of the Ramsey model of optimal savings, wealth is included in the quadratic loss function, and not only consumption. Its weight is given by the degree of concavity of the decreasing returns to scale production function times the marginal utility of consumption. The weight of consumption is given by the degree of concavity of the utility function. This quadratic loss function implies that the speed of convergence is explicitly driven by the trade-off between wealth smoothing (fostering convergence, related to technology) versus consumption smoothing (delaying convergence, related to preferences). By contrast, the second order Taylor expansion of the utility instead of the Lagrangian leads to a quadratic loss function with a weight of wealth equal to zero, which is false for a decreasing returns to scale production function

Suggested Citation

  • Jean-Bernard Chatelain & Kirsten Ralf, 2024. "Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings," Documents de travail du Centre d'Economie de la Sorbonne 24006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:24006
    as

    Download full text from publisher

    File URL: http://mse.univ-paris1.fr/pub/mse/CES2024/24006.pdf
    Download Restriction: no
    File URL: https://shs.hal.science/halshs-04612845
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Pascal Michaillat & Emmanuel Saez, 2021. "Resolving New Keynesian Anomalies with Wealth in the Utility Function," The Review of Economics and Statistics, MIT Press, vol. 103(2), pages 197-215, May.
    2. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    3. Havranek, Tomas & Horvath, Roman & Irsova, Zuzana & Rusnak, Marek, 2015. "Cross-country heterogeneity in intertemporal substitution," Journal of International Economics, Elsevier, vol. 96(1), pages 100-118.
    4. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    5. Salemi, Michael K, 1995. "Revealed Preference of the Federal Reserve: Using Inverse-Control Theory to Interpret the Policy Equation of a Vector Autoregression," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 419-433, October.
    6. Michau, Jean-Baptiste, 2018. "Secular stagnation: Theory and remedies," Journal of Economic Theory, Elsevier, vol. 176(C), pages 552-618.
    7. Campbell, John Y., 1994. "Inspecting the mechanism: An analytical approach to the stochastic growth model," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 463-506, June.
    8. Kinnunen, Maarit & Wood, Emma H. & Li, Yanning & Moss, Jonathan, 2022. "Self-recorded conversations in tourism memory research," Annals of Tourism Research, Elsevier, vol. 96(C).
    9. Levine, Paul & Pearlman, Joseph & Pierse, Richard, 2008. "Linear-quadratic approximation, external habit and targeting rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3315-3349, October.
    10. McGrattan, Ellen R, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 41-44, January.
    11. Chow, Gregory C., 1997. "Dynamic Economics: Optimization by the Lagrange Method," OUP Catalogue, Oxford University Press, number 9780195101928.
    12. Michael Kremer & Jack Willis & Yang You, 2022. "Converging to Convergence," NBER Macroeconomics Annual, University of Chicago Press, vol. 36(1), pages 337-412.
    13. Levine, Paul & Pearlman, Joseph, 2011. "Computation of LQ Approximations to Optimal Policy Problems in Different Information Settings under Zero Lower Bound Constraints," Dynare Working Papers 10, CEPREMAP.
    14. Magill, Michael J. P., 1977. "Some new results on the local stability of the process of capital accumulation," Journal of Economic Theory, Elsevier, vol. 15(1), pages 174-210, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Etro, Federico, 2017. "Research in economics and macroeconomics," Research in Economics, Elsevier, vol. 71(3), pages 373-383.
    2. Valentina Ciriotto & José Noguera-Santaella, 2023. "The Catching up in Steady State per Capita Income: Latin America and the Caribbean," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 51(1), pages 71-82, March.
    3. Thomas Aronsson & Sugata Ghosh & Ronald Wendner, 2023. "Positional preferences and efficiency in a dynamic economy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 311-337, August.
    4. Levine, Paul & Pearlman, Joseph, 2011. "Computation of LQ Approximations to Optimal Policy Problems in Different Information Settings under Zero Lower Bound Constraints," Dynare Working Papers 10, CEPREMAP.
    5. Lars Lochstoer & Harjoat S. Bhamra, 2009. "Return Predictability and Labor Market Frictions in a Real Business Cycle Model," 2009 Meeting Papers 1257, Society for Economic Dynamics.
    6. Evren Ceritoglu, 2017. "The effect of house price changes on cohort consumption in Turkey," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 17(3), pages 1-99–110.
    7. Yulei Luo & William T. Smith & Heng-fu Zou, 2009. "The Spirit of Capitalism and Excess Smoothness," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 281-301, November.
    8. Silvia Bertarelli, 2006. "Public capital and growth," Politica economica, Società editrice il Mulino, issue 3, pages 361-398.
    9. Julian Thimme, 2017. "Intertemporal Substitution In Consumption: A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 31(1), pages 226-257, February.
    10. Pablo A. Cuba-Borda & Sanjay R. Singh, 2019. "Understanding Persistent Stagnation," International Finance Discussion Papers 1243, Board of Governors of the Federal Reserve System (U.S.).
    11. Hashimoto, Ken-ichi & Ono, Yoshiyasu & Schlegl, Matthias, 2023. "Structural unemployment, underemployment, and secular stagnation," Journal of Economic Theory, Elsevier, vol. 209(C).
    12. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, April.
    13. Pascal Michaillat & Emmanuel Saez, 2022. "An economical business-cycle model [Breaking through the zero lower bound]," Oxford Economic Papers, Oxford University Press, vol. 74(2), pages 382-411.
    14. Georgios Karras, 1999. "Taxes And Growth: Testing The Neoclassical And Endogenous Growth Models," Contemporary Economic Policy, Western Economic Association International, vol. 17(2), pages 177-188, April.
    15. David Staines, 2023. "Stochastic Equilibrium the Lucas Critique and Keynesian Economics," Papers 2312.16214, arXiv.org, revised Jun 2024.
    16. Qichun He & Yulei Luo & Jun Nie & Heng-fu Zou, 2023. "Money, Growth, and Welfare in a Schumpeterian Model with the Spirit of Capitalism," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 47, pages 346-372, January.
    17. Ken-ichi Hashimoto & Yoshiyasu Ono & Matthias Schlegl, 2020. "Structural Unemployment, Underemployment, and Secular Stagnation," CESifo Working Paper Series 8318, CESifo.
    18. Zhiheng He & Yang You, 2024. "Convergence in Financial Development and Growth," Open Economies Review, Springer, vol. 35(4), pages 779-799, September.
    19. Martin Lettau & Harald Uhlig, 2000. "Can Habit Formation be Reconciled with Business Cycle Facts?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(1), pages 79-99, January.
    20. Klein, Alexander & Crafts, Nicholas, 2023. "Unconditional Convergence in Manufacturing Productivity across U.S. States: What the Long-Run Data Show," CEPR Discussion Papers 18065, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    Linear quadratic approximation; wealth; consumption; savings; negative feedback; speed of convergence;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:24006. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.