IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WP-CESifo_Working_Papers/wp-cesifo-2011/wp-cesifo-2011-04/cesifo1_wp3431.pdf
Download Restriction: no

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 3431.

as
in new window

Length:
Date of creation: 2011
Handle: RePEc:ces:ceswps:_3431
Contact details of provider: Postal:
Poschingerstrasse 5, 81679 Munich

Phone: +49 (89) 9224-0
Fax: +49 (89) 985369
Web page: http://www.cesifo-group.de
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
  2. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 353-360.
  3. Dale T. Mortensen & Rasmus Lentz, 2005. "An Empirical Model of Growth Through Product Innovation," 2005 Meeting Papers 910, Society for Economic Dynamics.
  4. R. Boucekkine & M. Germain & O. Licandro & A. Magnus, "undated". "Creative destruction, investment volatility, and the average age of capital," Working Papers 97-08, FEDEA.
  5. Patrick Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," UCLA Economics Working Papers 767, UCLA Department of Economics.
  6. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-51, March.
  7. 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.
  8. 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.
  9. repec:cor:louvrp:-1376 is not listed on IDEAS
  10. 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.
  11. 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.
  12. 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.
  13. 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 1042-1067, December.
  14. 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.
  15. Eric M. Aldrich & Jesús Fernández-Villaverde & Ronald Gallant & Juan F. Rubio-Ramírez, 2010. "Tapping the Supercomputer Under Your Desk: Solving Dynamic Equilibrium Models with Graphics Processors," PIER Working Paper Archive 10-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  16. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, Oxford University Press, vol. 105(1), pages 29-42.
  17. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
  18. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
  19. José Ramón Ruiz-Tamarit, "undated". "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  20. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
  21. Timo Trimborn & Karl-Josef Koch & Thomas Steger, 2006. "Multi-Dimensional Transitional Dynamics: A Simple Numberical Procedure," CESifo Working Paper Series 1745, CESifo Group Munich.
  22. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  23. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, "undated". "Numerical solution by iterative methods of a class on vintage capital models," Working Papers 97-26, FEDEA.
  24. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546, December.
  25. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  26. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-72, January.
  27. 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..
  28. 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.
  29. Merton, Robert C., 1973. "An asymptotic theory of growth under uncertainty," Working papers 673-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  30. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
  31. Chang,Fwu-Ranq, 2004. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521834063, October.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. Robert J. Barro, 2007. "Rare Disasters, Asset Prices, and Welfare Costs," NBER Working Papers 13690, National Bureau of Economic Research, Inc.
  37. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  38. 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.
  39. 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.
  40. Olaf Posch, 2010. "Risk Premia in General Equilibrium," CESifo Working Paper Series 3131, CESifo Group Munich.
  41. 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.
  42. 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.
  43. 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.
  44. 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.
  45. Stephen J. Turnovsky, 2000. "Methods of Macroeconomic Dynamics, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262201232.
  46. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  47. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
  48. 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.
  49. N. V. Quyen, 1991. "Exhaustible Resources: A Theory of Exploration," Review of Economic Studies, Oxford University Press, vol. 58(4), pages 777-789.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_3431. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Klaus Wohlrabe)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.