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Transition Dynamics in Endogenous Recombinant Growth Models by Means of Projection Methods

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  • Fabio Privileggi

Abstract

This paper provides a step further in the computation of the transition path of a continuous time endogenous growth model discussed by Privileggi (2010) – based on the setting first introduced by Tsur and Zemel (2007) – in which knowledge evolves according to the Weitzman (1998) recombinant process. A projection method, based on the least squares of the residual function corresponding to the ODE defining the optimal policy of the 'detrended' model, allows for the numeric approximation of such policy for a positive Lebesgue measure range of values of the efficiency parameter characterizing the probability function of the recombinant process. Although the projection method's performance rapidly degenerates as one departs from a benchmark value for the efficiency parameter, we are able to numerically compute time-path trajectories which are sufficiently regular to allow for sensitivity analysis under changes in parameters' values.
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Suggested Citation

  • Fabio Privileggi, 2011. "Transition Dynamics in Endogenous Recombinant Growth Models by Means of Projection Methods," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 367-387, October.
    • Handle: RePEc:kap:compec:v:38:y:2011:i:3:p:367-387
    DOI: 10.1007/s10614-011-9278-7
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    1. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521898010, December.
    2. Martin L. Weitzman, 1998. "Recombinant Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 113(2), pages 331-360.
    3. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
    4. Privileggi, Fabio, 2008. "On the transition dynamics in endogenous recombinant growth models," POLIS Working Papers 120, Institute of Public Policy and Public Choice - POLIS.
    5. Alfonso Novales & Esther Fernández & Jesús Ruiz, 2022. "Economic Growth," Springer Texts in Business and Economics, Springer, edition 3, number 978-3-662-63982-5, June.
    6. Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc.
    7. Burkhard Heer & Alfred Maußner, 2024. "Dynamic General Equilibrium Modeling," Springer Texts in Business and Economics, Springer, edition 3, number 978-3-031-51681-8, June.
    8. Gian Italo Bischi & Carl Chiarella & Laura Gardini (ed.), 2010. "Nonlinear Dynamics in Economics, Finance and Social Sciences," Springer Books, Springer, number 978-3-642-04023-8, January.
    9. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, Decembrie.
    10. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521725200, December.
    11. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    12. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
    13. Tsur, Yacov & Zemel, Amos, 2007. "Towards endogenous recombinant growth," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3459-3477, November.
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    Cited by:

    1. Marchese, Carla & Marsiglio, Simone & Privileggi, Fabio & Ramello, Giovanni, 2014. "Endogenous Recombinant Growth through Market Production of Knowledge and Intellectual Property Rights," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201413, University of Turin.
    2. repec:uto:dipeco:201338 is not listed on IDEAS
    3. Burkhard Heer & Alfred Maußner, 2024. "Dynamic General Equilibrium Modeling," Springer Texts in Business and Economics, Springer, edition 3, number 978-3-031-51681-8, June.
    4. Marchese, Carla & Marsiglio, Simone & Privileggi, Fabio & Ramello, Giovanni B., 2019. "Endogenous Recombinant Growth And Intellectual Property Rights," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 2035-2067, July.
    5. Privileggi, Fabio & Marsiglio, Simone, 2014. "Dynamics and Welfare in Recombinant Growth Models with Intellectual Property Rights: a Computational Method," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201414, University of Turin.
    6. Privileggi, Fabio, 2015. "Takeoff vs. stagnation in endogenous recombinant growth models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 184-214.

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    More about this item

    Keywords

    Knowledge production; Endogenous recombinant growth; Transition dynamics; Projection methods; Least squares; C61; C63; O31; O41;
    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
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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