Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/61603.html
   My bibliography  Save this paper

Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model

Author

Listed:
  • Lin, Hwan C.
  • Shampine, L.F.
Abstract
The statutory patent length is 20 years in most countries. R&D-based endogenous growth models, however, often presume an infinite patent length. In this paper, finite-length patents are embedded in a non-scale R&D-based growth model, but any patent’s effective life may be terminated prematurely at any moment, subject to two idiosyncratic hazards of imitation and innovation. This gives rise to an autonomous system of mixed-type functional differential equations (FDEs). Its dynamics are driven by current, delayed and advanced states. We present an algorithm to solve the FDEs by solving a sequence of standard BVPs (boundary value problems) for systems of ODEs (ordinary differential equations). We use this algorithm to simulate a calibrated U.S. economy’s transitional dynamics by making discrete changes from the baseline 20 years patent length. We find that if transitional impacts are taken into account, optimizing the patent length incurs a welfare loss, albeit rather small. This suggests that fine-tuning the world’s patent systems may not be a worthwhile effort.

Suggested Citation

  • Lin, Hwan C. & Shampine, L.F., 2014. "Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model," MPRA Paper 61603, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:61603
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/61603/1/MPRA_paper_61603.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/66479/1/MPRA_paper_66479.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Furukawa, Yuichi, 2007. "The protection of intellectual property rights and endogenous growth: Is stronger always better?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3644-3670, November.
    2. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    3. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    4. Fabrice Collard & Omar Licandro & Luis A. Puch, 2008. "The short-run Dynamics of Optimal Growth Model with Delays," Annals of Economics and Statistics, GENES, issue 90, pages 127-143.
    5. Eicher, Theo S. & Turnovsky, Stephen J., 2001. "Transitional dynamics in a two-sector non-scale growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 85-113, January.
    6. Charles I. Jones, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(2), pages 495-525.
    7. Jones, Charles I & Williams, John C, 2000. "Too Much of a Good Thing? The Economics of Investment in R&D," Journal of Economic Growth, Springer, vol. 5(1), pages 65-85, March.
    8. Bambi, Mauro & Gozzi, Fausto & Licandro, Omar, 2014. "Endogenous growth and wave-like business fluctuations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 68-111.
    9. repec:pra:mprapa:52608 is not listed on IDEAS
    10. Grossmann, Volker & Steger, Thomas & Trimborn, Timo, 2013. "Dynamically optimal R&D subsidization," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 516-534.
    11. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    12. Grossman, Gene M & Helpman, Elhanan, 1990. "Trade, Innovation, and Growth," American Economic Review, American Economic Association, vol. 80(2), pages 86-91, May.
    13. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    14. Peretto, Pietro F, 1998. "Technological Change and Population Growth," Journal of Economic Growth, Springer, vol. 3(4), pages 283-311, December.
    15. Grossman, Gene M & Helpman, Elhanan, 1990. "Comparative Advantage and Long-run Growth," American Economic Review, American Economic Association, vol. 80(4), pages 796-815, September.
    16. Kwan, Yum K. & Lai, Edwin L. -C., 2003. "Intellectual property rights protection and endogenous economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 853-873, March.
    17. Helpman, Elhanan, 1993. "Innovation, Imitation, and Intellectual Property Rights," Econometrica, Econometric Society, vol. 61(6), pages 1247-1280, November.
    18. Norrbin, Stefan C, 1993. "The Relation between Price and Marginal Cost in U.S. Industry: A Contradiction," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1149-1164, December.
    19. Guido Cozzi & Silvia Galli, 2014. "Sequential R&D and blocking patents in the dynamics of growth," Journal of Economic Growth, Springer, vol. 19(2), pages 183-219, June.
    20. Thomas M. Steger, 2003. "The Segerstrom Model: Stability, Speed of Convergence and Policy Implications," Economics Bulletin, AccessEcon, vol. 15(4), pages 1-8.
    21. Grinols, Earl & Lin, Hwan C., 2006. "Global patent protection: channels of north and south welfare gain," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 205-227, February.
    22. Francisco L. Rivera-Batiz & Luis A. Rivera-Batiz, 2018. "Economic Integration and Endogenous Growth," World Scientific Book Chapters, in: Francisco L Rivera-Batiz & Luis A Rivera-Batiz (ed.), International Trade, Capital Flows and Economic Development, chapter 1, pages 3-32, World Scientific Publishing Co. Pte. Ltd..
    23. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 71-102, October.
    24. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    25. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
    26. repec:adr:anecst:y:2008:i:90:p:05 is not listed on IDEAS
    27. Lin, Hwan C., 2010. "Technology diffusion and global welfare effects: Imitative R&D vs. South-bound FDI," Structural Change and Economic Dynamics, Elsevier, vol. 21(4), pages 231-247, November.
    28. Chu, Angus C. & Cozzi, Guido & Galli, Silvia, 2012. "Does intellectual monopoly stimulate or stifle innovation?," European Economic Review, Elsevier, vol. 56(4), pages 727-746.
    29. Futagami, Koichi & Iwaisako, Tatsuro, 2007. "Dynamic analysis of patent policy in an endogenous growth model," Journal of Economic Theory, Elsevier, vol. 132(1), pages 306-334, January.
    30. Caballero, Ricardo J & Hammour, Mohamad L, 1994. "The Cleansing Effect of Recessions," American Economic Review, American Economic Association, vol. 84(5), pages 1350-1368, December.
    31. Angus Chu, 2009. "Effects of blocking patents on R&D: a quantitative DGE analysis," Journal of Economic Growth, Springer, vol. 14(1), pages 55-78, March.
    32. Diego Comin, 2004. "R&D: A Small Contribution to Productivity Growth," Journal of Economic Growth, Springer, vol. 9(4), pages 391-421, December.
    33. Norrbin, Stefan C, 1993. "The Relation between Price and Marginal Cost in U.S. Industry: A Contradiction," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1149-1164, December.
    34. Angus Chu, 2010. "Effects of patent length on R&D: a quantitative DGE analysis," Journal of Economics, Springer, vol. 99(2), pages 117-140, March.
    35. Alwyn Young, 1998. "Growth without Scale Effects," Journal of Political Economy, University of Chicago Press, vol. 106(1), pages 41-63, February.
    36. Segerstrom, Paul S, 1998. "Endogenous Growth without Scale Effects," American Economic Review, American Economic Association, vol. 88(5), pages 1290-1310, December.
    37. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    38. Tatsuro Iwaisako & Koichi Futagami, 2013. "Patent protection, capital accumulation, and economic growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 631-668, March.
    39. Lai, Edwin L. -C., 1998. "International intellectual property rights protection and the rate of product innovation," Journal of Development Economics, Elsevier, vol. 55(1), pages 133-153, February.
    40. Guido Cozzi & Giammario Impullitti, 2010. "Government Spending Composition, Technical Change, and Wage Inequality," Journal of the European Economic Association, MIT Press, vol. 8(6), pages 1325-1358, December.
    41. Segerstrom, Paul S & Anant, T C A & Dinopoulos, Elias, 1990. "A Schumpeterian Model of the Product Life Cycle," American Economic Review, American Economic Association, vol. 80(5), pages 1077-1091, December.
    42. Judd, Kenneth L, 1985. "On the Performance of Patents," Econometrica, Econometric Society, vol. 53(3), pages 567-585, May.
    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. Hwan C. Lin & L. F. Shampine, 2018. "R&D-based Calibrated Growth Models with Finite-Length Patents: A Novel Relaxation Algorithm for Solving an Autonomous FDE System of Mixed Type," Computational Economics, Springer;Society for Computational Economics, vol. 51(1), pages 123-158, January.
    2. Lin, Hwan C., 2016. "The switch from patents to state-dependent prizes for technological innovation," Journal of Macroeconomics, Elsevier, vol. 50(C), pages 193-223.
    3. repec:pra:mprapa:52608 is not listed on IDEAS
    4. Angus C. Chu, 2022. "Patent policy and economic growth: A survey," Manchester School, University of Manchester, vol. 90(2), pages 237-254, March.
    5. Angus C. Chu, 2024. "Macroeconomic effects of intellectual property rights: an updated survey," Chapters, in: Walter G. Park (ed.), Handbook of Innovation and Intellectual Property Rights, chapter 2, pages 13-26, Edward Elgar Publishing.
    6. Chu, Angus C. & Furukawa, Yuichi, 2011. "On the optimal mix of patent instruments," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1964-1975.
    7. Iwaisako, Tatsuro, 2020. "Welfare Effects Of Patent Protection In A Semi-Endogenous Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 24(3), pages 708-728, April.
    8. Hu, Mei-Ying & Lu, You-Xun & Lai, Ching-chong, 2023. "Patent term extensions and commercialization lags in the pharmaceutical industry: A growth-theoretic analysis," Journal of Macroeconomics, Elsevier, vol. 76(C).
    9. Angus Chu & Guido Cozzi & Chih-Hsing Liao, 2013. "Endogenous fertility and human capital in a Schumpeterian growth model," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(1), pages 181-202, January.
    10. Angus Chu, 2009. "Effects of blocking patents on R&D: a quantitative DGE analysis," Journal of Economic Growth, Springer, vol. 14(1), pages 55-78, March.
    11. Sener, Fuat, 2008. "R&D policies, endogenous growth and scale effects," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3895-3916, December.
    12. Guido Cozzi & Silvia Galli, 2014. "Sequential R&D and blocking patents in the dynamics of growth," Journal of Economic Growth, Springer, vol. 19(2), pages 183-219, June.
    13. Lu, You-Xun & Lai, Ching-Chong, 2021. "Effects of patent policy on growth and inequality: A perspective of exogenous and endogenous quality improvements," MPRA Paper 111183, University Library of Munich, Germany.
    14. Angus Chu & Guido Cozzi, 2018. "Effects of Patents versus R&D subsidies on Income Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 68-84, July.
    15. Akimoto, Kiyoka & Morimoto, Takaaki, 2020. "Examination and Approval of New Patents in an Endogenous Growth Model," Economic Modelling, Elsevier, vol. 91(C), pages 100-109.
    16. Angus C. Chu & Yuichi Furukawa & Lei Ji, 2016. "Patents, R&D subsidies, and endogenous market structure in a schumpeterian economy," Southern Economic Journal, John Wiley & Sons, vol. 82(3), pages 809-825, January.
    17. Hwan C. Lin, 2015. "Creative Destruction and Optimal Patent Life in a Variety‐Expanding Growth Model," Southern Economic Journal, John Wiley & Sons, vol. 81(3), pages 803-828, January.
    18. Guido Cozzi & Silvia Galli, 2009. "Upstream Innovation Protection: Common Law Evolution and the Dynamics of Wage Inequality," Working Papers 2009_20, Business School - Economics, University of Glasgow.
    19. Chu, Angus C., 2009. "Macroeconomic Effects of Intellectual Property Rights: A Survey," MPRA Paper 17342, University Library of Munich, Germany.
    20. Yibai Yang, 2018. "On the Optimality of IPR Protection with Blocking Patents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 27, pages 205-230, January.
    21. Furukawa, Yuichi, 2010. "Intellectual property protection and innovation: an inverted-U relationship," Economics Letters, Elsevier, vol. 109(2), pages 99-101, November.

    More about this item

    Keywords

    Patent Length; Innovation; Delay Differential Equation; Advance Differential Equation; Transitional Dynamics; Endogenous Growth;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • O34 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Intellectual Property and Intellectual Capital

    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:pra:mprapa:61603. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.