IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v12y2012i1n9.html
   My bibliography  Save this article

Strict Concavity of the Value Function for a Family of Dynamic Accumulation Models

Author

Listed:
  • Bobenrieth Eugenio S.A.

    (Pontificia Universidad Católica de Chile, ebobenrieth@uc.cl)

  • Bobenrieth Juan R.A.

    (Universidad del Bío-Bío, jbobenri@ubiobio.cl)

  • Wright Brian D.

    (University of California, Berkeley, bwright@berkeley.edu)

Abstract

We prove strict concavity of the value function for liquidity constrained dynamic accumulation models without adopting at least one of the following restrictive assumptions: zero response of productive effort, bounded marginal value of accumulated balances, or strictly convex cost of holding accumulated balances. Thus we extend well known theoretical results to more general models of saving with liquidity constraints and of commodity storage with non-negativity constraints on stocks. Our results provide a foundation for estimation of a homogeneous markovian process for consumption in models of saving, or for price in commodity storage models, under more realistic assumptions.

Suggested Citation

  • Bobenrieth Eugenio S.A. & Bobenrieth Juan R.A. & Wright Brian D., 2012. "Strict Concavity of the Value Function for a Family of Dynamic Accumulation Models," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-11, April.
    • Handle: RePEc:bpj:bejtec:v:12:y:2012:i:1:n:9
    DOI: 10.1515/1935-1704.1838
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1935-1704.1838
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/1935-1704.1838?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
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. José A. Scheinkman & Jack Schechtman, 1983. "A Simple Competitive Model with Production and Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(3), pages 427-441.
    2. Eugenio S. A. Bobenrieth H. & Juan R. A. Bobenrieth H. & Brian D. Wright, 2002. "A Commodity Price Process with a Unique Continuous Invariant Distribution Having Infinite Mean," Econometrica, Econometric Society, vol. 70(3), pages 1213-1219, May.
    3. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    4. Allen B. Paul, 1970. "The Pricing of Binspace—A Contribution to the Theory of Storage," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 52(1), pages 1-12.
    5. Deaton, Angus & Laroque, Guy, 1996. "Competitive Storage and Commodity Price Dynamics," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 896-923, October.
    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. Juan R. A. Bobenrieth & Eugenio S. A. Bobenrieth & Andrés F. Villegas & Brian D. Wright, 2022. "Estimation of Endogenous Volatility Models with Exponential Trends," Mathematics, MDPI, vol. 10(15), pages 1-27, July.
    2. Bobenrieth H., Eugenio S.A. & Bobenrieth H., Juan R.A. & Wright, Brian D., 2008. "A foundation for the solution of consumption-saving behavior with a borrowing constraint and unbounded marginal utility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 695-708, March.
    3. He, Zhechun & Simmons, Peter, 2022. "The impact of the minimum housing scale constraint on life-cycle risky asset and housing investment," Journal of Housing Economics, Elsevier, vol. 55(C).
    4. Zhechun He & Peter Simmons, 2018. "A Life Cycle Model with Housing Tenure, Constrained Mortgage Finance and a Risky Asset under Uncertainty," Discussion Papers 18/18, Department of Economics, University of York.

    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. Eugenio S. A. Bobenrieth & Juan R. A. Bobenrieth & Brian D. Wright, 2014. "Bubble Troubles? Rational Storage, Mean Reversion, and Runs in Commodity Prices," NBER Chapters, in: The Economics of Food Price Volatility, pages 193-208, National Bureau of Economic Research, Inc.
    2. Christophe Gouel, 2012. "Agricultural Price Instability: A Survey Of Competing Explanations And Remedies," Journal of Economic Surveys, Wiley Blackwell, vol. 26(1), pages 129-156, February.
    3. Nishimura, Kazuo & Stachurski, John, 2009. "Equilibrium storage with multiple commodities," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 80-96, January.
    4. Christophe Gouel, 2013. "Comparing Numerical Methods for Solving the Competitive Storage Model," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 267-295, February.
    5. Juan R. A. Bobenrieth & Eugenio S. A. Bobenrieth & Andrés F. Villegas & Brian D. Wright, 2022. "Estimation of Endogenous Volatility Models with Exponential Trends," Mathematics, MDPI, vol. 10(15), pages 1-27, July.
    6. Jaime Casassus & Pierre Collin-Dufresne & Bryan R. Routledge, 2005. "Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technology," NBER Working Papers 11864, National Bureau of Economic Research, Inc.
    7. Dalheimer, Bernhard & Fiankor, Dela-Dem Doe, 2022. "Food Production Shocks and Agricultural Supply Elasticities in Sub-Saharan Africa," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322168, Agricultural and Applied Economics Association.
    8. Roberts, Michael J. & Tran, A. Nam, 2013. "Conditional Suspension of the US Ethanol Mandate using Threshold Price inside a Competitive Storage Model," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150717, Agricultural and Applied Economics Association.
    9. Kelley, Clare & Lanot, Gauthier, 2002. "Consumption Patterns Over Pay Periods," Economic Research Papers 269469, University of Warwick - Department of Economics.
    10. Colin A. Carter & Gordon C. Rausser & Aaron Smith, 2017. "Commodity Storage and the Market Effects of Biofuel Policies," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 99(4), pages 1027-1055.
    11. Michaelides, Alexander & Ng, Serena, 2000. "Estimating the rational expectations model of speculative storage: A Monte Carlo comparison of three simulation estimators," Journal of Econometrics, Elsevier, vol. 96(2), pages 231-266, June.
    12. Zhu, Xiaohong, 2016. "New models to estimate costs of US farm programs," ISU General Staff Papers 201601010800006209, Iowa State University, Department of Economics.
    13. Kelly, Clare & Lanot, Gauthier, 2003. "Analytical results for a Model of Periodic Consumption," Economic Research Papers 269486, University of Warwick - Department of Economics.
    14. Tore S. Kleppe & Atle Oglend, 2019. "Can limits‐to‐arbitrage from bounded storage improve commodity term‐structure modeling?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(7), pages 865-889, July.
    15. repec:vuw:vuwscr:19065 is not listed on IDEAS
    16. Evans, Lewis & Guthrie, Graeme, 2007. "Commodity Price Behavior With Storage Frictions," Working Paper Series 19065, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    17. Ing-Haw Cheng & Wei Xiong, 2014. "Financialization of Commodity Markets," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 419-441, December.
    18. Nicolas Legrand & Christophe Gouel, 2022. "The Role of Storage in Commodity Markets: Indirect Inference Based on Grains Data," Working Papers hal-03809825, HAL.
    19. Guerra Vallejos, Ernesto & Bobenrieth Hochfarber, Eugenio & Bobenrieth Hochfarber, Juan & Wright, Brian D., 2021. "Solving dynamic stochastic models with multiple occasionally binding constraints," Economic Modelling, Elsevier, vol. 105(C).
    20. Zhu, Xiaohong, 2016. "New models to estimate costs of US farm programs," ISU General Staff Papers 3547, Iowa State University, Department of Economics.
    21. Ehsan Ahmed & J. Rosser & Jamshed Uppal, 2014. "Are there nonlinear speculative bubbles in commodities prices?," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 36(3), pages 415-438.

    More about this item

    Keywords

    consumption; savings; strict concavity; value function;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • Q11 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Aggregate Supply and Demand Analysis; Prices

    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:bpj:bejtec:v:12:y:2012:i:1:n:9. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.