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Numerical solution of continuous-time DSGE models under Poisson uncertainty

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  • Posch, Olaf
  • Trimborn, Timo

Abstract

We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We then use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary differential equations by standard methods and fix-point iteration. Analytical solutions are provided as a benchmark from which our numerical method can be used to explore broader classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We find that, even for non-linear policy functions, the maximum (absolute) error is very small.

Suggested Citation

  • Posch, Olaf & Trimborn, Timo, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Hannover Economic Papers (HEP) dp-450, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  • Handle: RePEc:han:dpaper:dp-450
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    1. 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.
    2. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    3. 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.
    4. 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.
    5. 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 635-656, May.
    6. Wen Yao & Juan Rubio Ramirez & Jesus Fernandez Villaverde & Dario Caldara, 2009. "Computing Models with Recursive Preferences," 2009 Meeting Papers 1162, Society for Economic Dynamics.
    7. 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.
    8. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, Oxford University Press, vol. 105(1), pages 29-42.
    9. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    10. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    11. 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.
    12. Dario Caldara & Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Wen Yao, 2009. "Computing DSGE Models with Recursive Preferences," NBER Working Papers 15026, National Bureau of Economic Research, Inc.
    13. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    14. Rasmus Lentz & Dale T. Mortensen, 2008. "An Empirical Model of Growth Through Product Innovation," Econometrica, Econometric Society, vol. 76(6), pages 1317-1373, November.
    15. 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.
    16. 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.
    17. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-264, March.
    18. Posch, Olaf, 2011. "Risk premia in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1557-1576, September.
    19. 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.
    20. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, Oxford University Press, vol. 121(3), pages 823-866.
    21. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 353-360.
    22. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    23. 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.
    24. 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.
    25. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 375-393.
    26. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    27. 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.
    28. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-172, January.
    29. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    30. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    31. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    Cited by:

    1. Poudel, Diwakar & Sandal, Leif K., 2014. "Stochastic Optimization for Multispecies Fisheries in the Barents Sea," Discussion Papers 2014/2, Norwegian School of Economics, Department of Business and Management Science.
    2. Poudel, Diwakar & Sandal, Leif K. & Steinshamn, Stein I. & Kvamsdal, Sturla F., 2012. "Do Species Interactions and Stochasticity Matter to Optimal Management of Multispecies Fisheries?," Discussion Papers 2012/1, Norwegian School of Economics, Department of Business and Management Science.

    More about this item

    Keywords

    Continuous-time DSGE; Optimal stochastic control; Waveform Relaxation;

    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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