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Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty

  • Olaf Posch
  • Timo Trimborn

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.

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File URL: http://degit.sam.sdu.dk/papers/degit_16/c016_044.pdf
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Paper provided by DEGIT, Dynamics, Economic Growth, and International Trade in its series DEGIT Conference Papers with number c016_044.

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Length: 36 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:deg:conpap:c016_044
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  1. Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," UWO Department of Economics Working Papers 8904, University of Western Ontario, Department of Economics.
  2. Klaus Wälde, 2005. "Endogenous Growth Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(3), pages 867-894, 08.
  3. Turnovsky, Stephen J, 1993. "Macroeconomic Policies, Growth, and Welfare in a Stochastic Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(4), pages 953-81, November.
  4. Sandmo, Agnar, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Wiley Blackwell, vol. 37(3), pages 353-60, July.
  5. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  6. Walde, Klaus, 1999. "A Model of Creative Destruction with Undiversifiable Risk and Optimising Households," Economic Journal, Royal Economic Society, vol. 109(454), pages C156-71, March.
  7. Chang, Fwu-Ranq & Malliaris, A G, 1987. "Asymptotic Growth under Uncertainty: Existence and Uniqueness," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 169-74, January.
  8. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper 2003-27, Federal Reserve Bank of Atlanta.
  9. Rasmus Lentz & Dale T. Mortensen, 2005. "An Empirical Model of Growth Through Product Innovation," Boston University - Department of Economics - Working Papers Series WP2005-004, Boston University - Department of Economics.
  10. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
  11. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
  12. Miller, Marcus H & Weller, Paul, 1990. "Currency Bubbles Which Affect Fundamentals: A Qualitative Treatment," Economic Journal, Royal Economic Society, vol. 100(400), pages 170-79, Supplemen.
  13. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
  14. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper Series, Macroeconomic Issues WP-97-15, Federal Reserve Bank of Chicago.
  15. Karl-Josef Koch & Timo Trimborn & Thomas M. Steger, 2005. "Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure," Volkswirtschaftliche Diskussionsbeiträge 121-05, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
  16. Turnovsky, Stephen J. & Smith, William T., 2006. "Equilibrium consumption and precautionary savings in a stochastically growing economy," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 243-278, February.
  17. Robert J. Barro, 2007. "Rare Disasters, Asset Prices, and Welfare Costs," NBER Working Papers 13690, National Bureau of Economic Research, Inc.
  18. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-72, January.
  19. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  20. Eric M. Aldrich & Jesus Fernandez-Villaverde & A. Ronald Gallant & Juan F. Rubio-Ramirez, 2010. "Tapping the Supercomputer Under Your Desk: Solving Dynamic Equilibrium Models with Graphics Processors," Working Papers 10-89, Duke University, Department of Economics.
  21. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  22. Kevin Salyer & Victor Dorofeenko & Gabriel Lee, 2005. "A New Algorithm for Solving Dynamic Stochastic Macroeconomic Models," Working Papers 62, University of California, Davis, Department of Economics.
  23. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
  24. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
  25. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
  26. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
  27. 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.
  28. John B. Taylor & Harald Uhlig, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  29. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  30. Stephen J. Turnovsky, 2000. "Methods of Macroeconomic Dynamics, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262201232, June.
  31. Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, vol. 62(3), pages 635-56, May.
  32. Patrick K. Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," NBER Technical Working Papers 0211, National Bureau of Economic Research, Inc.
  33. R. Boucekkine & M. Germain & O. Licandro & A. Magnus, . "Creative destruction, investment volatility, and the average age of capital," Working Papers 97-08, FEDEA.
  34. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546, March.
  35. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," Levine's Bibliography 122247000000000849, UCLA Department of Economics.
  36. Olaf Posch, 2009. "Risk premia in general equilibrium," CREATES Research Papers 2009-58, School of Economics and Management, University of Aarhus.
  37. Alejandro Justiniano & Giorgio E. Primiceri, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," NBER Working Papers 12022, National Bureau of Economic Research, Inc.
  38. Quyen, N V, 1991. "Exhaustible Resources: A Theory of Exploration," Review of Economic Studies, Wiley Blackwell, vol. 58(4), pages 777-89, July.
  39. Weil, Philippe, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 29-42, February.
  40. Merton, Robert C., 1973. "An asymptotic theory of growth under uncertainty," Working papers 673-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  41. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
  42. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-67, December.
  43. repec:cup:cbooks:9780521834063 is not listed on IDEAS
  44. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  45. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, . "Numerical solution by iterative methods of a class of vintage capital models," Working Papers 98-20, FEDEA.
  46. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  47. Olaf Posch & Juan F. Rubio-Ramírez & Jesús Fernández-Villaverde, 2011. "Solving the new Keynesian model in continuous time," 2011 Meeting Papers 829, Society for Economic Dynamics.
  48. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  49. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
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