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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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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. 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.
  2. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
  3. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  4. R. Boucekkine & M. Germain & O. Licandro & A. Magnus, . "Creative destruction, investment volatility, and the average age of capital," Working Papers 97-08, FEDEA.
  5. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for Solving Dynamic Models with Occasionally Binding Constraints," NBER Technical Working Papers 0218, National Bureau of Economic Research, Inc.
  6. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Departmental Working Papers 200106, Rutgers University, Department of Economics.
  7. Aldrich, Eric M. & Fernández-Villaverde, Jesús & Ronald Gallant, A. & Rubio-Ramírez, Juan F., 2011. "Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 386-393, March.
  8. 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.
  9. Olaf Posch, 2011. "Risk premia in general equilibrium," Post-Print hal-00851860, HAL.
  10. Rasmus Lentz & Dale T. Mortensen, 2008. "An Empirical Model of Growth Through Product Innovation," Econometrica, Econometric Society, vol. 76(6), pages 1317-1373, November.
  11. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," Levine's Bibliography 122247000000000849, UCLA Department of Economics.
  12. 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.
  13. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, Junio.
  14. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, . "Numerical solution by iterative methods of a class on vintage capital models," Working Papers 97-26, FEDEA.
  15. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
  16. Olaf Posch, 2007. "Structural estimation of jump-diffusion processes in macroeconomics," CREATES Research Papers 2007-23, Department of Economics and Business Economics, Aarhus University.
  17. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 353-360.
  18. Trimborn, Timo & Koch, Karl-Josef & Steger, Thomas M., 2008. "Multidimensional Transitional Dynamics: A Simple Numerical Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 12(03), pages 301-319, June.
  19. 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.
  20. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  21. repec:cor:louvrp:-1376 is not listed on IDEAS
  22. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, March.
  23. Stephen Turnovsky & William Smith, 2004. "Equilibrium Consumption and Precautionary Savings in a Stochastically Growing Economy," Working Papers UWEC-2006-01-P, University of Washington, Department of Economics, revised Oct 2004.
  24. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
  25. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-64, March.
  26. 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.
  27. Klaus Wälde, 2009. "Production Technologies in Stochastic Continuous Time Models," CESifo Working Paper Series 2831, CESifo Group Munich.
  28. Klaus, WAELDE, 2003. "Endogenous growth cycles," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 15 Mar 2004.
  29. Fwu-Ranq Chang & A. G. Malliaris, 2005. "Asymptotic Growth under Uncertainty: Existence and Uniqueness," World Scientific Book Chapters, in: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays, chapter 1, pages 3-8 World Scientific Publishing Co. Pte. Ltd..
  30. 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.
  31. Dorofeenko, Victor & Lee, Gabriel S. & Salyer, Kevin D., 2010. "A new algorithm for solving dynamic stochastic macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 388-403, March.
  32. 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.
  33. 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.
  34. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
  35. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  36. N. V. Quyen, 1991. "Exhaustible Resources: A Theory of Exploration," Review of Economic Studies, Oxford University Press, vol. 58(4), pages 777-789.
  37. 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.
  38. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, Oxford University Press, vol. 105(1), pages 29-42.
  39. Stephen J. Turnovsky, 2000. "Methods of Macroeconomic Dynamics, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262201232, March.
  40. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 82(3), pages 465-473.
  41. 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.
  42. 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.
  43. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-72, January.
  44. 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.
  45. Merton, Robert C., 1973. "An asymptotic theory of growth under uncertainty," Working papers 673-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  46. 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.
  47. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
  48. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546, December.
  49. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
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