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The Short-Run Dynamics of Optimal Growth Models with Delays

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  • Collard, Fabrice
  • Licandro, Omar
  • Puch, Luis

Abstract

Differential equations with advanced and delayed time arguments may arise in the optimality conditions of simple growth models with delays. Models with delayed adoption of new technologies, habit formation or learning-by-using lie in this category. In this paper we present new insight on the role of advanced time arguments to mitigate the echo effects induced by lag structures. In so doing we use optimal control theory with delays, and 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 implement these methods 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 C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5414.

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Date of creation: Dec 2005
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Handle: RePEc:cpr:ceprdp:5414

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

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References

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  1. 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.
  2. BOUCEKKINE, Raouf & LICANDRO, Omar & PUCH, Luis A. & DEL RIO, Fernando, . "Vintage capital and the dynamics of the AK model," CORE Discussion Papers RP -1757, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Patrick Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," UCLA Economics Working Papers 767, UCLA Department of Economics.
  4. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
  5. Benhabib, Jess & Rustichini, Aldo, 1990. "Vintage Capital, Investment And Growth," Working Papers 90-22, C.V. Starr Center for Applied Economics, New York University.
  6. Jody Overland & Christopher D. Carroll & David N. Weil, 2000. "Saving and Growth with Habit Formation," American Economic Review, American Economic Association, vol. 90(3), pages 341-355, June.
  7. 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.
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Cited by:
  1. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
  2. José A. Herce, . "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
  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. Simon Sosvilla-Rivero & Pedro N. Rodríguez, . "Linkages in international stock markets: Evidence from a classification procedure," Working Papers 2004-23, FEDEA.
  5. Raouf Boucekkine & David De La Croix & Omar Licandro, 2004. "MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 151-179.
  6. 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.
  7. 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.
  8. Bambi, Mauro & Fabbri, Giorgio & Gozzi, Fausto, 2009. "Optimal policy and consumption smoothing effects in the time-to-build AK model," MPRA Paper 17128, University Library of Munich, Germany.
  9. Mauro Bambi & Omar Licandro, 2011. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.

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