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The short-run dynamics of optimal growth models with delays

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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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Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico in its series Documentos de Trabajo del ICAE with number 0311.

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Length: 20 pages
Date of creation: 2003
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Handle: RePEc:ucm:doicae:0311

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Keywords: Time-to-build; Shooting method; DDEs.;

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  1. 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.).
  2. R. Boucekkine & F. del Rio & O. Licandro & Luis A. Puch, 2000. "Vintage Capital and the Dynamics of the AK Model," Econometric Society World Congress 2000 Contributed Papers 0436, Econometric Society.
  3. Boucekkine, R. & Germain, M. & Licandro, O., . "Replacement echoes in the vintage capital growth model," CORE Discussion Papers RP -1275, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  6. Jess Benhabib & Aldo Rustichini, 1990. "Vintage Capital, Investment and Growth," Discussion Papers 886, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
  8. 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.
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Cited by:
  1. 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.
  2. Raouf Boucekkine & David de la Croix & Omar Licandro, . "Modelling vintage structures with DDEs: Principles and applications," Working Papers 2004-07, FEDEA.
  3. José A. Herce, . "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
  4. 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.
  5. 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.
  6. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
  7. 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.
  8. 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).
  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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