IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Non-Local Solutions to Dynamic Equilibrium Models: the Approximate Stable Manifolds Approach

  • Viktors Ajevskis

    (Bank of Latvia)

This paper presents a method to construct a sequence of approximate policy functions of increasing accuracy on non-local domains. The method is based upon the notion of stable manifold originated from dynamical systems theory. The approximate policy functions are constructed employing the contraction mapping theorem and the fact that solutions to rational expectations models converge to a steady state. The approach allows us to derive the accuracy of the approximations and their domain of definition. The method is applied to the neoclassical growth model and compared with the perturbation method. Just the second approximation of the proposed approach yields very high accuracy of the approximate solution on a global domain. In contrast to the Taylor series expansions, the solutions of the method inherit globally the properties of the true solution such as monotonicity and concavity.

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.bank.lv/images/stories/pielikumi/publikacijas/petijumi/WP_3_2013_Ajevskis.pdf
Download Restriction: no

File URL: http://www.macroeconomics.lv/sites/default/files/wp_3_2013_ajevskis_0.pdf
Download Restriction: no

Paper provided by Latvijas Banka in its series Working Papers with number 2013/03.

as
in new window

Length:
Date of creation: 28 Dec 2013
Date of revision:
Handle: RePEc:ltv:wpaper:201303
Contact details of provider: Postal: K. Valdemara iela 2a, LV-1050 Riga
Phone: +371 702 2300
Fax: +371 702 2420
Web page: http://www.bank.lv/
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. Den Haan, Wouter J. & De Wind, Joris, 2012. "Nonlinear and stable perturbation-based approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1477-1497.
  2. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-85, July.
  3. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 21-55, October.
  4. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
  5. 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.
  6. Jules H. van Binsbergen & Jesús Fernández-Villaverde & Ralph S.J. Koijen & Juan F. Rubio-Ramírez, 2010. "The Term Structure of Interest Rates in a DSGE Model with Recursive Preferences," PIER Working Paper Archive 10-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. Martin M. Andreasen & Jesús Fernández-Villaverde & Juan Rubio-Ramírez, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," NBER Working Papers 18983, National Bureau of Economic Research, Inc.
  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. Lipton, David, et al, 1982. "Multiple Shooting in Rational Expectations Models [The Solution of Linear Difference Models under Rational Expectations]," Econometrica, Econometric Society, vol. 50(5), pages 1329-33, September.
  10. William T. Gavin & Benjamin D. Keen & Alexander W. Richter & Nathaniel A. Throckmorton, 2013. "Global Dynamics at the Zero Lower Bound," Auburn Economics Working Paper Series auwp2013-17, Department of Economics, Auburn University.
  11. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, June.
  12. Jinill Kim & Sunghyun Henry Kim, 2007. "Two pitfalls of linearization methods," Finance and Economics Discussion Series 2007-64, Board of Governors of the Federal Reserve System (U.S.).
  13. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
  14. Viktors Ajevskis & Kristine Vitola, 2011. "Housing and Banking in a Small Open Economy DSGE Model," Working Papers 2011/03, Latvijas Banka.
  15. 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.
  16. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Working Paper Series 1341, European Central Bank.
  17. Pablo Guerron & Martin Uribe & Juan Rubio-Ramirez & Jesus Fernandez-Villaverde, 2010. "Risk Matters: The Real Effects of Volatility Shocks," 2010 Meeting Papers 281, Society for Economic Dynamics.
  18. Robert Kollmann, 2004. "Welfare Effects of a Monetary Union: The Role of Trade Openness," Journal of the European Economic Association, MIT Press, vol. 2(2-3), pages 289-301, 04/05.
  19. Gomme, Paul & Klein, Paul, 2011. "Second-order approximation of dynamic models without the use of tensors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 604-615, April.
  20. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
  21. Kollmann, Robert, 2002. "Monetary Policy Rules in the Open Economy: Effects on Welfare and Business Cycles," CEPR Discussion Papers 3279, C.E.P.R. Discussion Papers.
  22. Gagnon, Joseph E. & Taylor, John B., 1990. "Solving stochastic equilibrium models with the extended path method," Economic Modelling, Elsevier, vol. 7(3), pages 251-257, July.
  23. Adjemian, Stéphane & Bastani, Houtan & Karamé, Fréderic & Juillard, Michel & Maih, Junior & Mihoubi, Ferhat & Perendia, George & Pfeifer, Johannes & Ratto, Marco & Villemot, Sébastien, 2011. "Dynare: Reference Manual Version 4," Dynare Working Papers 1, CEPREMAP, revised Jul 2014.
  24. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
  25. King, Robert G & Watson, Mark W, 2002. "System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 57-86, October.
  26. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
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:ltv:wpaper:201303. 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: (Ivars Tillers)

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.