IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v101y2019icp62-81.html
   My bibliography  Save this article

Optimal timing of decisions: A general theory based on continuation values

Author

Listed:
  • Ma, Qingyin
  • Stachurski, John

Abstract

By extending a methodology dating back to Jovanovic (1982), we develop a comprehensive theory of optimal timing of decisions based on continuation value functions and operators that act on them. Rewards can be bounded or unbounded. One advantage of this approach over standard Bellman methods is that continuation value functions are smoother than value functions. Another is that, for a range of problems, the continuation value function exists in a lower dimensional space than the value function. We exploit these advantages to obtain a range of new results on optimality, optimal behavior and efficient computation.

Suggested Citation

  • Ma, Qingyin & Stachurski, John, 2019. "Optimal timing of decisions: A general theory based on continuation values," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 62-81.
  • Handle: RePEc:eee:dyncon:v:101:y:2019:i:c:p:62-81
    DOI: 10.1016/j.jedc.2019.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188919300284
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jedc.2019.02.003?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Giuseppe Moscarini & Fabien Postel-Vinay, 2013. "Stochastic Search Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1545-1581.
    2. Rui Albuquerque & Hugo A. Hopenhayn, 2004. "Optimal Lending Contracts and Firm Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(2), pages 285-315.
    3. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09j003nctkn is not listed on IDEAS
    4. A. Kerem Co?ar & Nezih Guner & James Tybout, 2016. "Firm Dynamics, Job Turnover, and Wage Distributions in an Open Economy," American Economic Review, American Economic Association, vol. 106(3), pages 625-663, March.
    5. Le Van, Cuong & Vailakis, Yiannis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Journal of Economic Theory, Elsevier, vol. 123(2), pages 187-209, August.
    6. Hamish Low & Costas Meghir & Luigi Pistaferri, 2010. "Wage Risk and Employment Risk over the Life Cycle," American Economic Review, American Economic Association, vol. 100(4), pages 1432-1467, September.
    7. Satyajit Chatterjee & Esteban Rossi‐Hansberg, 2012. "Spinoffs And The Market For Ideas," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 53-93, February.
    8. Jesper Bagger & Fran?ois Fontaine & Fabien Postel-Vinay & Jean-Marc Robin, 2014. "Tenure, Experience, Human Capital, and Wages: A Tractable Equilibrium Search Model of Wage Dynamics," American Economic Review, American Economic Association, vol. 104(6), pages 1551-1596, June.
    9. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09j003nctkn is not listed on IDEAS
    10. Jean‐Marc Robin, 2011. "On the Dynamics of Unemployment and Wage Distributions," Econometrica, Econometric Society, vol. 79(5), pages 1327-1355, September.
    11. Jeremy Lise, 2013. "On-the-Job Search and Precautionary Savings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 1086-1113.
    12. Lars Ljungqvist & Thomas J. Sargent, 2008. "Two Questions about European Unemployment," Econometrica, Econometric Society, vol. 76(1), pages 1-29, January.
    13. Gomes, Joao & Greenwood, Jeremy & Rebelo, Sergio, 2001. "Equilibrium unemployment," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 109-152, August.
    14. Boyan Jovanovic & Rafael Rob, 1989. "The Growth and Diffusion of Knowledge," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 569-582.
    15. J. J. McCall, 1970. "Economics of Information and Job Search," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(1), pages 113-126.
    16. Enrique G. Mendoza & Vivian Z. Yue, 2012. "A General Equilibrium Model of Sovereign Default and Business Cycles," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(2), pages 889-946.
    17. Timothy Dunne & Shawn D. Klimek & Mark J. Roberts & Daniel Yi Xu, 2013. "Entry, exit, and the determinants of market structure," RAND Journal of Economics, RAND Corporation, vol. 44(3), pages 462-487, September.
    18. Markus Poschke, 2010. "The Regulation of Entry and Aggregate Productivity," Economic Journal, Royal Economic Society, vol. 120(549), pages 1175-1200, December.
    19. Ryan Kellogg, 2014. "The Effect of Uncertainty on Investment: Evidence from Texas Oil Drilling," American Economic Review, American Economic Association, vol. 104(6), pages 1698-1734, June.
    20. Russell Cooper & John Haltiwanger & Jonathan L. Willis, 2007. "Implications of Search Frictions: Matching Aggregate and Establishment-level Observations," NBER Working Papers 13115, National Bureau of Economic Research, Inc.
    21. Satyajit Chatterjee & Burcu Eyigungor, 2012. "Maturity, Indebtedness, and Default Risk," American Economic Review, American Economic Association, vol. 102(6), pages 2674-2699, October.
    22. Juan Carlos Hatchondo & Leonardo Martinez & César Sosa-Padilla, 2016. "Debt Dilution and Sovereign Default Risk," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1383-1422.
    23. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    24. Cristina Arellano, 2008. "Default Risk and Income Fluctuations in Emerging Economies," American Economic Review, American Economic Association, vol. 98(3), pages 690-712, June.
    25. Bental, Benjamin & Peled, Dan, 1996. "The Accumulation of Wealth and the Cyclical Generation of New Technologies: A Search Theoretic Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 687-718, August.
    26. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    27. Pablo D. Fajgelbaum & Edouard Schaal & Mathieu Taschereau-Dumouchel, 2017. "Uncertainty Traps," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1641-1692.
    28. Emin M. Dinlersoz & Mehmet Yorukoglu, 2012. "Information and Industry Dynamics," American Economic Review, American Economic Association, vol. 102(2), pages 884-913, April.
    29. Jesse Perla & Christopher Tonetti, 2014. "Equilibrium Imitation and Growth," Journal of Political Economy, University of Chicago Press, vol. 122(1), pages 52-76.
    30. Marcus Asplund & Volker Nocke, 2006. "Firm Turnover in Imperfectly Competitive Markets -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(2), pages 295-327.
    31. Guido Menzio & Nicholas Trachter, 2018. "Equilibrium Price Dispersion Across and Within Stores," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 205-220, April.
    32. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, July.
    33. Menzio, Guido & Trachter, Nicholas, 2015. "Equilibrium price dispersion with sequential search," Journal of Economic Theory, Elsevier, vol. 160(C), pages 188-215.
    34. Cooper, Russell & Haltiwanger, John & Willis, Jonathan L., 2007. "Search frictions: Matching aggregate and establishment observations," Journal of Monetary Economics, Elsevier, vol. 54(Supplemen), pages 56-78, September.
    35. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
    36. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
    37. Timoshenko, Olga A., 2015. "Product switching in a model of learning," Journal of International Economics, Elsevier, vol. 95(2), pages 233-249.
    38. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    39. Jesper Bagger & Francois Fontaine & Fabien Postel-Vinay & Jean-Marc Robin, 2014. "Tenure, Experience, Human Capital, and Wages," Post-Print hal-01301431, HAL.
    40. Edouard Schaal, 2017. "Uncertainty and Unemployment," Econometrica, Econometric Society, vol. 85(6), pages 1675-1721, November.
    41. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, May.
    42. repec:hal:spmain:info:hdl:2441/7rep5mp5ij95l94ec64n5tdclp is not listed on IDEAS
    43. Kenneth Burdett & Tara Vishwanath, 1988. "Declining Reservation Wages and Learning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 655-665.
    44. Jovanovic, Boyan, 1987. "Work, Rest, and Search: Unemployment, Turnover, and the Cycle," Journal of Labor Economics, University of Chicago Press, vol. 5(2), pages 131-148, April.
    45. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    46. Michael Pries & Richard Rogerson, 2005. "Hiring Policies, Labor Market Institutions, and Labor Market Flows," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 811-839, August.
    47. Matthew F. Mitchell, 2000. "The Scope and Organization of Production: Firm Dynamics Over the Learning Curve," RAND Journal of Economics, The RAND Corporation, vol. 31(1), pages 180-205, Spring.
    48. Emin M. Dinlersoz & Mehmet Yorukoglu, 2012. "Information and Industry Dynamics," American Economic Review, American Economic Association, vol. 102(2), pages 884-913, April.
    49. repec:hal:spmain:info:hdl:2441/22qd4iha9ql84kd2t534hdeb is not listed on IDEAS
    50. Cuong Le Van & Yiannis Vailakis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Post-Print halshs-00101201, HAL.
    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. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2022. "Unbounded dynamic programming via the Q-transform," Journal of Mathematical Economics, Elsevier, vol. 100(C).

    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. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2022. "Unbounded dynamic programming via the Q-transform," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    2. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    3. Qingyin Ma & John Stachurski, 2019. "Dynamic Optimal Choice When Rewards are Unbounded Below," Papers 1911.13025, arXiv.org.
    4. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    5. Roldan-Blanco, Pau & Gilbukh, Sonia, 2021. "Firm dynamics and pricing under customer capital accumulation," Journal of Monetary Economics, Elsevier, vol. 118(C), pages 99-119.
    6. Andrew B. Bernard & Stephen J. Redding & Peter K. Schott, 2006. "Multi-Product Firms and Product Switching," NBER Working Papers 12293, National Bureau of Economic Research, Inc.
    7. Alessandro Gavazza & Simon Mongey & Giovanni L. Violante, 2018. "Aggregate Recruiting Intensity," American Economic Review, American Economic Association, vol. 108(8), pages 2088-2127, August.
    8. Florin Maican & Matilda Orth, 2017. "Productivity Dynamics and the Role of ‘Big-Box’ Entrants in Retailing," Journal of Industrial Economics, Wiley Blackwell, vol. 65(2), pages 397-438, June.
    9. Lucia Foster & Cheryl Grim & John Haltiwanger, 2016. "Reallocation in the Great Recession: Cleansing or Not?," Journal of Labor Economics, University of Chicago Press, vol. 34(S1), pages 293-331.
    10. Pau Roldan & Sophia Gilbukh, 2017. "Firm Dynamics and Pricing under Customer Capital Accumulation," 2017 Meeting Papers 1235, Society for Economic Dynamics.
    11. A. Kerem Co?ar & Nezih Guner & James Tybout, 2016. "Firm Dynamics, Job Turnover, and Wage Distributions in an Open Economy," American Economic Review, American Economic Association, vol. 106(3), pages 625-663, March.
    12. G. Jacob Blackwood & Lucia S. Foster & Cheryl A. Grim & John Haltiwanger & Zoltan Wolf, 2021. "Macro and Micro Dynamics of Productivity: From Devilish Details to Insights," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 142-172, July.
    13. Roman Fossati, 2011. "Outsourcing versus Vertical Integration: A Dynamic Model of Industry Equilibrium," 2011 Meeting Papers 1421, Society for Economic Dynamics.
    14. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2018. "On Temporal Aggregators and Dynamic Programming," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01437496, HAL.
    15. Ouyang, Min, 2009. "The scarring effect of recessions," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 184-199, March.
    16. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2018. "On temporal aggregators and dynamic programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 787-817, October.
    17. Kersting, Stefan & Hüttel, Silke & Odening, Martin, 2015. "Structural change in agriculture under capacity constraints: An equilibrium approach," Thuenen-Series of Applied Economic Theory 140, University of Rostock, Institute of Economics.
    18. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2015. "On Aggregators and Dynamic Programming," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01169552, HAL.
    19. John Stachurski & Junnan Zhang, 2019. "Dynamic Programming with State-Dependent Discounting," Papers 1908.08800, arXiv.org, revised Oct 2020.
    20. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2015. "On Aggregators and Dynamic Programming," Post-Print halshs-01169552, HAL.

    More about this item

    Keywords

    Continuation values; Dynamic programming; Optimal timing;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

    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:eee:dyncon:v:101:y:2019:i:c:p:62-81. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.