IDEAS home Printed from https://ideas.repec.org/a/kap/jeczfn/v124y2018i3d10.1007_s00712-017-0567-z.html
   My bibliography  Save this article

Stochastic continuous time growth models that allow for closed form solutions

Author

Listed:
  • Francesco Menoncin

    (University of Brescia)

  • Stefano Nembrini

    (University of Brescia)

Abstract

We find a closed form solution that maximises the expected utility of an agent’s inter-temporal consumption subject to a stochastic technology, which is a linear combination of AK and Cobb–Douglas technologies. Additionally, we consider two cases of agent preferences: (i) Constant Relative Risk Aversion (CRRA) preferences, which treat optimal consumption as a linear function of capital, and (ii) Hyperbolic Absolute Risk Aversion (HARA) preferences, which treat optimal consumption as an affine function of capital. By establishing a minimum (subsistence) level of consumption in the HARA model, we are able to create a framework that more accurately represents real-world circumstances than previous studies have done. Furthermore, for both the CRRA and HARA cases we show the suitable, consistent stochastic differential equation which describes the capital dynamics. Finally, we perform a numerical simulation based on the CRRA case and calibrate US data for the HARA case.

Suggested Citation

  • Francesco Menoncin & Stefano Nembrini, 2018. "Stochastic continuous time growth models that allow for closed form solutions," Journal of Economics, Springer, vol. 124(3), pages 213-241, July.
    • Handle: RePEc:kap:jeczfn:v:124:y:2018:i:3:d:10.1007_s00712-017-0567-z
    DOI: 10.1007/s00712-017-0567-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00712-017-0567-z
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00712-017-0567-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Carolina Achury & Sylwia Hubar & Christos Koulovatianos, 2012. "Saving Rates and Portfolio Choice with Subsistence Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(1), pages 108-126, January.
    2. Carolina Achury & Sylwia Hubar & Christos Koulovatianos, 2012. "Saving Rates and Portfolio Choice with Subsistence Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(1), pages 108-126, January.
    3. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
    4. Growiec, Jakub & Mućk, Jakub, 2020. "Isoelastic Elasticity Of Substitution Production Functions," Macroeconomic Dynamics, Cambridge University Press, vol. 24(7), pages 1597-1634, October.
    5. Sethi, Suresh P. & Taksar, Michael I. & Presman, Ernst L., 1992. "Explicit solution of a general consumption/portfolio problem with subsistence consumption and bankruptcy," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 747-768.
    6. Luc Arrondel & Hector Calvo Pardo & Xisco Oliver, 2010. "Temperance in Stock Market Participation: Evidence from France," Economica, London School of Economics and Political Science, vol. 77(306), pages 314-333, April.
    7. Growiec, Jakub, 2013. "A microfoundation for normalized CES production functions with factor-augmenting technical change," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2336-2350.
    8. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    9. Jakub Growiec, 2008. "A new class of production functions and an argument against purely labor‐augmenting technical change," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 483-502, December.
    10. Weinbaum, David, 2005. "Subsistence consumption, habit formation and the demand for long-term bonds," Journal of Economics and Business, Elsevier, vol. 57(4), pages 273-287.
    11. Levaggi, Rosella & Menoncin, Francesco, 2013. "Optimal dynamic tax evasion," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2157-2167.
    12. Jones, Larry E & Manuelli, Rodolfo E, 1990. "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 1008-1038, October.
    13. Joseph Eisenhauer & Luigi Ventura, 2003. "Survey measures of risk aversion and prudence," Applied Economics, Taylor & Francis Journals, vol. 35(13), pages 1477-1484.
    14. Strulik, Holger, 2010. "A Note On Economic Growth With Subsistence Consumption," Macroeconomic Dynamics, Cambridge University Press, vol. 14(5), pages 763-771, November.
    15. Yisheng Bu, 2006. "Fixed capital stock depreciation in developing countries: Some evidence from firm level data," Journal of Development Studies, Taylor & Francis Journals, vol. 42(5), pages 881-901.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    2. Liao, Zhong-Wei & Shao, Jinghai, 2024. "Stability and mean growth rate of stochastic Solow model driven by jump–diffusion process," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    3. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    4. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.

    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. Levaggi, Rosella & Menoncin, Francesco, 2013. "Optimal dynamic tax evasion," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2157-2167.
    2. Gamannossi degl’Innocenti, Duccio & Levaggi, Rosella & Menoncin, Francesco, 2022. "Tax avoidance and evasion in a dynamic setting," Journal of Economic Behavior & Organization, Elsevier, vol. 204(C), pages 443-456.
    3. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    4. Armando Sánchez-Vargas & José Manuel Márquez-Estrada & Eric Hernández-Ramírez, 2023. "Uncovering the Link Between the Theoretical and Probabilistic Models of the Global Production Function: A Copula Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 289-315, June.
    5. Antony, Jürgen & Klarl, Torben, 2022. "Poverty and sustainable development around the world during transition periods," Energy Economics, Elsevier, vol. 110(C).
    6. Antony, Jürgen & Klarl, Torben, 2023. "Subsistence consumption and natural resource depletion: Can resource-rich low-income countries realize sustainable consumption paths?," Journal of Macroeconomics, Elsevier, vol. 77(C).
    7. Wang, Hao & Siu, Tak Kuen & Hu, Shujie & Wang, Ning, 2024. "Life-cycle model with subsistence consumption constraint and state-dependent utilities," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    8. Antony, Jürgen & Klarl, Torben, 2019. "Resource depletion in a Ramsey economy with subsistence consumption, exogenous technical change and capital depreciation: A full characterization," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203640, Verein für Socialpolitik / German Economic Association.
    9. Jürgen Antony & Torben Klarl, 2019. "Non-Renewable Resources in a Ramsey Economy with Subsistence Consumption, Human and Physical Capital Accumulation: A full Characterization," Bremen Papers on Economics & Innovation 1904, University of Bremen, Faculty of Business Studies and Economics.
    10. Antony, Jürgen & Klarl, Torben, 2019. "Non-renewable resources, subsistence consumption, and Hartwick's investment rule," Resource and Energy Economics, Elsevier, vol. 55(C), pages 124-142.
    11. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    12. Ricardo Bebczuk & Leonardo Gasparini & Noelia Garbero & Julian Amendolaggine, 2015. "Understanding the Determinants of Household Saving: Micro Evidence for Latin America," CEDLAS, Working Papers 0189, CEDLAS, Universidad Nacional de La Plata.
    13. Studer, Sabrina & Falkinger, Josef & Zhao, Yingnan, 2015. "Explaining structural changes towards and within the financial sector," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113004, Verein für Socialpolitik / German Economic Association.
    14. Hlouskova, Jaroslava & Fortin, Ines & Tsigaris, Panagiotis, 2019. "The consumption–investment decision of a prospect theory household: A two-period model with an endogenous second period reference level," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 93-108.
    15. Antosiewicz, Marek & Witajewski-Baltvilks, Jan, 2021. "Short- and long-run dynamics of energy demand," Energy Economics, Elsevier, vol. 103(C).
    16. Carolina Achury & Sylwia Hubar & Christos Koulovatianos, 2012. "Saving Rates and Portfolio Choice with Subsistence Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(1), pages 108-126, January.
    17. Guimarães, Luís & Mazeda Gil, Pedro, 2022. "Explaining the Labor Share: Automation Vs Labor Market Institutions," Labour Economics, Elsevier, vol. 75(C).
    18. J. François Outreville, 2015. "The Relationship Between Relative Risk Aversion And The Level Of Education: A Survey And Implications For The Demand For Life Insurance," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 97-111, February.
    19. Jacek Osiewalski & Justyna Wróblewska & Kamil Makieła, 2020. "Bayesian comparison of production function-based and time-series GDP models," Empirical Economics, Springer, vol. 58(3), pages 1355-1380, March.
    20. Growiec, Jakub, 2015. "On the modeling of size distributions when technologies are complex," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 1-8.

    More about this item

    Keywords

    Dynamic stochastic general equilibrium models; Closed-form solution; HARA preferences; CRRA preferences; Autonomous consumption;
    All these keywords.

    JEL classification:

    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

    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:kap:jeczfn:v:124:y:2018:i:3:d:10.1007_s00712-017-0567-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.