Computational Economics

, Volume 40, Issue 3, pp 265–291 | Cite as

On Boundary Conditions Within the Solution of Macroeconomic Dynamic Models with Rational Expectations

  • Frank HespelerEmail author


This article develops a solution method, which integrates a transversality condition representing the terminal condition of a dynamic model with an infinite horizon into the solution of a macroeconomic rational expectations model. Thus this transversality condition can be used to decrease the potential degree of indeterminacy within the model by reducing the degrees of freedom. Conditions which assess the relevance of the method, are derived and discussed. Numerical simulations of example models substantiate the potential of the transversality condition to lower the degree of indeterminacy in their solutions.


Transversality condition Rational expectations models Indeterminacy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aseev S. M., Kryazhimskii A. V. (2008) On a class of optimal control problems in mathematical economics. Proceedings of the Steklov Institute of Mathematics 262: 10–25CrossRefGoogle Scholar
  2. Binder M., Pesaran M. H. (1995) Multivariate rational expectations models and macroeconomic modelling: A review and some new results. In: Pesaran M. H., Wickens M. R. (eds) Handbook of applied econometrics: Macroeconomics. Basil Blackwell, Oxford, pp 139–187Google Scholar
  3. Binder M., Pesaran M.H. (1997) Multivariate linear rational expectations models: Characterization of the nature of the solutions and their fully recursive computation. Econometric Theory, 13: 877–888CrossRefGoogle Scholar
  4. Blanchard O. J., Kahn C. M. (1980) The solution of linear difference models under rational expectations. Econometrica 48(5): 1305–1311CrossRefGoogle Scholar
  5. Calvo G. A. (1983) Staggered prices in a utility-maximizing framework. Journal of Monetary Economics 12(3): 383–398CrossRefGoogle Scholar
  6. Camerer C. F., Loewenstein G. (2004) Behavioral economics: Past, present and future. In: Loewenstein G., Camerer C. F., Matthew R. (eds) Advances in behavioral economics, chap. 1. Princeton University Press, Princeton, pp 3–51Google Scholar
  7. Cho, S. & Moreno, A. (2008). The forward solution for linear rational expectations models. Technical report.Google Scholar
  8. Driskill R. (2006) Multiple equilibria in dynamic rational expectations models: a critical review. European Economic Review 50: 171–210CrossRefGoogle Scholar
  9. Evans G., Honkapohja S. (1998) Economic dynamics with learning: New stability results. Review of Economic Studies 65(1): 23–44CrossRefGoogle Scholar
  10. Gray, J. A. & Salant, S. W. (1981). Transversality conditions in infinite horizon models. International Finance Discussion Papers 172 Board of Governors of the Federal Reserve System.Google Scholar
  11. Hespeler F. (2008) Solution algorithm to a class of monetary rational equilibrium macromodels with optimal monetary policy. Computational Economics 31(3): 207–223CrossRefGoogle Scholar
  12. Honkapohja S., Mitra K. (2004) Are non-fundamental equilibria learnable in models of monetary policy?. Journal of Monetary Economics 51: 1743–1770CrossRefGoogle Scholar
  13. King R. G., Watson M. W. (2002) System reduction and solution algorithms for singular linear difference systems under rational expectations. Computational Economics 20(1–2): 57–68CrossRefGoogle Scholar
  14. Klein P. (2000) Using the generalized Schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control 24(10): 1405–1423CrossRefGoogle Scholar
  15. Kowal, P. (2005). An algorithm for solving arbitrary linear rational expectations Model. EconWPA.Google Scholar
  16. Lewis F. L., Metzios B. G. (1990) On the analysis of discrete linear time-invariant singular systsems. IEEE Transactions on Automatic Control 35(4): 506–511CrossRefGoogle Scholar
  17. McCallum, B. T. (1983). On non-uniqueness in rational expectations models: An attempt at perspective. NBER Working Papers 0684. Cambridge: National Bureau of Economic Research, Inc.Google Scholar
  18. McCallum B. T. (1998) Solutions to linear rational expectations models: A compact exposition. Economics Letters 61(2): 143–147CrossRefGoogle Scholar
  19. Onatski A. (2006) Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models. Journal of Economic Dynamics and Control 30(2): 323–345CrossRefGoogle Scholar
  20. Shea P. (2011) Are Sunspots Stabilizing?. Theoretical Economics Letters 1(3): 111–113CrossRefGoogle Scholar
  21. Sims C. A. (2002) Solving linear rational expectations models. Computational Economics 20(1–2): 1–20CrossRefGoogle Scholar
  22. Yongge T. (2005) Special form of generalized inverses of row block matrices. Electronic Journal of Linear Algebra 15: 249–261Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Institute for Forecasting and Macroeconomic ResearchTashkentUzbekistan

Personalised recommendations