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Multivariate Linear Rational Expectations Models

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  • Binder, Michael
  • Pesaran, M. Hashem

Abstract

This paper considers the solution of multivariate linear rational expectations models. It is described how all possible classes of solutions (namely, the unique stable solution, multiple stable solutions, and the case where no stable solution exists) of such models can be characterized using the quadratic determinantal equation (QDE) method of Binder and Pesaran (1995, in M.H. Pesaran & M. Wickens [eds.], Handbook of Applied Econometrics: Macroeconomics , pp. 139–187. Oxford: Basil Blackwell). To this end, some further theoretical results regarding the QDE method expanding on previous work are presented. In addition, numerical techniques are discussed allowing reasonably fast determination of the dimension of the solution set of the model under consideration using the QDE method. The paper also proposes a new, fully recursive solution method for models involving lagged dependent variables and current and future expectations. This new method is entirely straightforward to implement, fast, and applicable also to high-dimensional problems possibly involving coefficient matrices with a high degree of singularity.

Suggested Citation

  • Binder, Michael & Pesaran, M. Hashem, 1997. "Multivariate Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 13(06), pages 877-888, December.
  • Handle: RePEc:cup:etheor:v:13:y:1997:i:06:p:877-888_00
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    Cited by:

    1. Pesaran, M. H. & Xu, T., 2011. "Business Cycle Effects of Credit and Technology Shocks in a DSGE Model with Firm Defaults," Cambridge Working Papers in Economics 1159, Faculty of Economics, University of Cambridge.
    2. Massimo Franchi & Paolo Paruolo, 2015. "Minimality of State Space Solutions of DSGE Models and Existence Conditions for Their VAR Representation," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 613-626, December.
    3. Bennett T. McCallum, 2000. "Role of the Minimal State Variable Criterion," NBER Working Papers 7087, National Bureau of Economic Research, Inc.
    4. Bernd Funovits, 2014. "Implications of Stochastic Singularity in Linear Multivariate Rational Expectations Models," Vienna Economics Papers 1405, University of Vienna, Department of Economics.
    5. Tan, Fei & Walker, Todd B., 2015. "Solving generalized multivariate linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 95-111.
    6. McCallum, Bennett T., 1998. "Solutions to linear rational expectations models: a compact exposition," Economics Letters, Elsevier, vol. 61(2), pages 143-147, November.
    7. Seonghoon Cho, 2016. "Sufficient Conditions for Determinacy in a Class of Markov-Switching Rational Expectations Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 21, pages 182-200, July.
    8. Cologni, Alessandro & Manera, Matteo, 2013. "Exogenous oil shocks, fiscal policies and sector reallocations in oil producing countries," Energy Economics, Elsevier, vol. 35(C), pages 42-57.
    9. Alessandro Cologni & Matteo Manera, 2011. "Exogenous Oil Shocks, Fiscal Policy and Sector Reallocations in Oil Producing Countries," Working Papers 2011.55, Fondazione Eni Enrico Mattei.
    10. Binder, Michael & Pesaran, M. Hashem, 2001. "Life-cycle consumption under social interactions," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 35-83, January.
    11. Seonghoon Cho & Antonio Moreno, 2003. "A Structural Estimation and Interpretation of the New Keynesian Macro Model," Faculty Working Papers 14/03, School of Economics and Business Administration, University of Navarra.
    12. Majid M. Al-Sadoon, 2016. "The Linear Systems Approach to Linear Rational Expectations Models," Working Papers 875, Barcelona Graduate School of Economics.
    13. Lan, Hong & Meyer-Gohde, Alexander, 2014. "Solvability of perturbation solutions in DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 366-388.
    14. Hong Lan & Alexander Meyer-Gohde, 2012. "Existence and Uniqueness of Perturbation Solutions to DSGE Models," SFB 649 Discussion Papers SFB649DP2012-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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