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Causality, Structure And The Uniqueness Of Rational Expectations Equilibria

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  • BENNETT T. MCCALLUM

Abstract

Consider a rational expectations (RE) model that includes a relationship between variables x t and z t+1 . To be considered structural and potentially useful as a guide to actual behavior, this model must specify whether x t is influenced by the expectation at t of z t+1 or, alternatively, that z t+1 is directly influenced (via some inertial mechanism) by x t (i.e., that z t is influenced by x t-1 ). These are quite different phenomena. Here it is shown that, for a very broad class of multivariate linear RE models, distinct causal specifications involving both expectational and inertial influences will be uniquely associated with distinct solutions—which will result operationally from different specifications concerning which of the model’s variables are predetermined. It follows that for a given structure, and with a natural continuity assumption, there is only one RE solution that is fully consistent with the model’s specification. Furthermore, this solution does not involve “sunspot” phenomena.

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Bibliographic Info

Article provided by University of Manchester in its journal The Manchester School.

Volume (Year): 79 (2011)
Issue (Month): s1 (06)
Pages: 551-566

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Handle: RePEc:bla:manchs:v:79:y:2011:i:s1:p:551-566

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  1. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  2. Bennett McCallum, 2004. "On the Relationship Between Determinate and MSV Solutions in Linear RE Models," NBER Technical Working Papers 0297, National Bureau of Economic Research, Inc.
  3. Bennett T. McCallum, 2003. "Multiple-Solution Indeterminacies in Monetary Policy Analysis," NBER Working Papers 9837, National Bureau of Economic Research, Inc.
  4. Bennett T. McCallum, 2006. "E-Stability vis-a-vis Determinacy Results for a Broad Class of Linear Rational Expectations Models," NBER Working Papers 12441, National Bureau of Economic Research, Inc.
  5. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 28(2), pages 273-285, November.
  6. Zellner, Arnold, 1979. "Causality and econometrics," Carnegie-Rochester Conference Series on Public Policy, Elsevier, Elsevier, vol. 10(1), pages 9-54, January.
  7. John H. Cochrane, 2011. "Determinacy and Identification with Taylor Rules," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 119(3), pages 565 - 615.
  8. Calvo, Guillermo A., 1978. "On the indeterminacy of interest rates and wages with perfect foresight," Journal of Economic Theory, Elsevier, Elsevier, vol. 19(2), pages 321-337, December.
  9. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, American Economic Association, vol. 69(2), pages 114-18, May.
  10. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1305-11, July.
  11. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  12. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 24(10), pages 1405-1423, September.
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Cited by:
  1. Bennett T. McCallum, 2012. "A Continuity Refinement for Rational Expectations Solutions," NBER Working Papers 18323, National Bureau of Economic Research, Inc.
  2. Bennett T. McCallum, 2012. "Determinacy, Learnability, Plausibility, and the Role of Money in New Keynesian Models," NBER Working Papers 18215, National Bureau of Economic Research, Inc.
  3. Cho, Seonghoon & Moreno, Antonio, 2011. "The forward method as a solution refinement in rational expectations models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(3), pages 257-272, March.

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