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Causality, Structure, and the Uniqueness of Rational Expectations Equilibria

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Author Info
Bennett T. McCallum
Abstract

Consider a rational expectations (RE) model that includes a relationship between variables xt and zt+1. To be considered structural and potentially useful as a guide to actual behavior, this model must specify whether xt is influenced by the expectation at t of zt+1 or, alternatively, that zt+1 is directly influenced (via some inertial mechanism) by xt (i.e., that zt is influenced by xt-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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15234.

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Date of creation: Aug 2009
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Handle: RePEc:nbr:nberwo:15234

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation

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  1. 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. [Downloadable!] (restricted)
  2. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer, vol. 20(1-2), pages 1-20, October. [Downloadable!]
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  3. 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, vol. 39(4), pages 1015-26, November.
  4. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, vol. 69(2), pages 114-18, May. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. McCallum, Bennett T., 2007. "E-stability vis-a-vis determinacy results for a broad class of linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1376-1391, April. [Downloadable!] (restricted)
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  7. Bennett T. McCallum, 2003. "Multiple-Solution Indeterminacies in Monetary Policy Analysis," NBER Working Papers 9837, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  8. John H. Cochrane, 2007. "Inflation Determination With Taylor Rules: A Critical Review," NBER Working Papers 13409, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  9. Zellner, Arnold, 1979. "Causality and econometrics," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 10(1), pages 9-54, January. [Downloadable!] (restricted)
  10. Calvo, Guillermo A., 1978. "On the indeterminacy of interest rates and wages with perfect foresight," Journal of Economic Theory, Elsevier, vol. 19(2), pages 321-337, December. [Downloadable!] (restricted)
  11. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 273-285, November. [Downloadable!] (restricted)
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