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Optimal policy and consumption smoothing effects in the time-to-build AK model

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  • Bambi, Mauro
  • Fabbri, Giorgio
  • Gozzi, Fausto

Abstract

In this paper the dynamic programming approach is exploited in order to identify the closed loop policy function, and the consumption smoothing mechanisms in an endogenous growth model with time to build, linear technology and irreversibility constraint in investment. Moreover the link among the time to build parameter, the maximum capital reproduction rate, and the magnitude of the smoothing effect is deeply investigated and compared with what happens in a vintage capital model characterized by the same technology and utility function. Finally we have analyzed the effect of time to build on the speed of convergence of the main aggregate variables.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17128.

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Date of creation: 27 Aug 2009
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Handle: RePEc:pra:mprapa:17128

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Keywords: Time-to-build; AK model; Dynamic programming; optimal strategies; closed loop policy.;

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References

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  1. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, 2003. "Vintage capital and the dynamics of the AK model," Documentos de Trabajo del ICAE, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico 0310, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  2. Fabrice Collard & Omar Licandro & Luis A. Puch, 2003. "The short-run dynamics of optimal growth models with delays," Documentos de Trabajo del ICAE, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico 0311, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  3. Patrick K. Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," NBER Technical Working Papers 0211, National Bureau of Economic Research, Inc.
  4. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, Elsevier, vol. 143(1), pages 331-373, November.
  5. Hippolyte d’Albis & Emmanuelle Augeraud-Véron, 2007. "Balanced cycles in an OLG model with a continuum of finitely-lived individuals," Economic Theory, Springer, Springer, vol. 30(1), pages 181-186, January.
  6. Akiomi Kitagawa & Akihisa Shibata, 2005. "Endogenous growth cycles in an overlapping generations model with investment gestation lags," Economic Theory, Springer, Springer, vol. 25(3), pages 751-762, 04.
  7. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006, Society for Computational Economics 77, Society for Computational Economics.
  8. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, Econometric Society, vol. 40(6), pages 1137-46, November.
  9. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, . "Vintage capital and the dynamics of the AK model," Working Papers 2000-01, FEDEA.
  10. Ortigueira, Salvador & Santos, Manuel S, 1997. "On the Speed of Convergence in Endogenous Growth Models," American Economic Review, American Economic Association, American Economic Association, vol. 87(3), pages 383-99, June.
  11. Rochelle M. Edge, 2000. "Time-to-build, time-to-plan, habit-persistence, and the liquidity effect," International Finance Discussion Papers, Board of Governors of the Federal Reserve System (U.S.) 673, Board of Governors of the Federal Reserve System (U.S.).
  12. Mauro Bambi, 2008. "Unifying time-to-build theory," CER-ETH Economics working paper series 08/98, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  13. Fabrice Collard & Omar Licandro & Luis A. Puch, . "The short-run dynamics of optimal growth models with delays," Working Papers 2004-05, FEDEA.
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Citations

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Cited by:
  1. Raouf Boucekkine & Giorgio Fabbri & Patrick-Antoine Pintus, 2011. "On the optimal control of a linear neutral differential equation arising in economics," Working Papers halshs-00576770, HAL.
  2. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
  3. repec:hal:journl:halshs-00786419 is not listed on IDEAS
  4. Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M., 2010. "Delay equivalence in capital accumulation models," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1243-1246, November.
  5. Emmanuelle Augeraud-Veron & Mauro Bambi, 2012. "Does habit formation always increase the agents' desire to smooth consumption?," Discussion Papers, Department of Economics, University of York 12/12, Department of Economics, University of York.
  6. Mauro Bambi & Omar Licandro, 2011. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.
  7. Giorgio Fabbri & Salvatore Federico, 2014. "On the infinite-dimensional representation of stochastic controlled systems with delayed control in the diffusion term," Working Papers hal-01038088, HAL.

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