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The short-run dynamics of optimal growth models with delays

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  • Fabrice COLLARD
  • Omar LICANDRO
  • Luis A. PUCH

Abstract

Differential equations with advanced and delayed time arguments may arise in the optimality conditions of simple growth models with delays. Models with investment gestation lags (time-to-build), consumption gestation lags (habit formation) or learning by using lie in this category. In this paper, we propose a shooting method to deal with leads and lags in the Euler system associated to dynamic general equilibrium models in continuous time. We introduce the discussion describing the dynamics that emerge under various assumptions on learning by using and gestation lags. Then, we implement the numerical method we propose to solve for the short run dynamics of a neoclassical growth model with a simple time-to-build lag.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2004/04.

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Date of creation: 2004
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Handle: RePEc:eui:euiwps:eco2004/04

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Keywords: time-to-build; shooting method; DDEs;

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References

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  1. Boucekkine, Raouf & Del Rio, Fernando & Licandro, Omar, 2000. "Vintage capital and the dynamics of the AK model," CEPREMAP Working Papers (Couverture Orange) 0003, CEPREMAP.
  2. Patrick Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," UCLA Economics Working Papers 767, UCLA Department of Economics.
  3. 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.
  4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  5. Raouf, BOUCEKKINE & David, DE LA CROIX & Omar, LICANDRO, 2006. "Vintage Capital," Discussion Papers (ECON - Département des Sciences Economiques) 2006014, Université catholique de Louvain, Département des Sciences Economiques.
  6. Raouf Boucekkine & Omar Licandro & Christopher Paul, . "Differential-Difference Equations in Economics: On the Numerical Solution of Vintage Capital Growth Models," Computing in Economics and Finance 1996 _036, Society for Computational Economics.
  7. Christopher D. Carroll & Jody Overland & David N. Weil, 1995. "Saving and growth with habit formation," Finance and Economics Discussion Series 95-42, Board of Governors of the Federal Reserve System (U.S.).
  8. Jess Benhabib & Aldo Rustichini, 1990. "Vintage Capital, Investment and Growth," Discussion Papers 886, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. BOUCEKKINE, RAOUF & de la CROIX, David & LICANDRO, Omar, 2004. "Modelling vintage structures with DDEs : principles and applications," CORE Discussion Papers 2004047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Mauro Bambi & Omar Licandro, 2011. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.
  3. BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, . "On the optimal control of a linear neutral differential equation arising in economics," CORE Discussion Papers RP -2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes P. Schlöder, 2006. "Numerical solution of optimal control problems with constant control delays," CER-ETH Economics working paper series 06/59, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  5. Simon Sosvilla-Rivero & Pedro Rodriguez, 2010. "Linkages in international stock markets: evidence from a classification procedure," Applied Economics, Taylor & Francis Journals, vol. 42(16), pages 2081-2089.
  6. José A. Herce, . "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
  7. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer, vol. 50(3), pages 635-669, August.
  8. F. Ricci, 2004. "Environmental Policy and Growth when Inputs are Differentiated in Pollution Intensity," THEMA Working Papers 2004-23, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  9. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.

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