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Computing Sunspots in Linear Rational Expectations Models


  • Thomas Lubik
  • Frank Schorfheide


We provide computationally simple methods of analyzing the effects of fundamental and sunspot shocks in linear rational expectations models when the equilibrium is indeterminate Under indeterminacy sunspots can affect model dynamics through endogenous forecast errors that do not completely adjust to fundamental shocks alone Moreover the effect of fundamental shocks on forecast errors is not uniquely determined We characterize the full set of equilibria and show that some solution methods only generate subsets of all the rational expectations equilibria by imposing specific restrictions on the forecast errors However in most cases it is possible to recover the full set of equilibria from the output of these methods The solution algorithms are illustrated with a New Keynesian dynamic stochastic equilibrium model that can be solved analytically We show that under a passive interest-rate rule the response of output and inflation to an unanticipated interest rate cut is ambiguous: while output rises there are some equilibria in which inflation increases and other in which prices fall
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Suggested Citation

  • Thomas Lubik & Frank Schorfheide, 2002. "Computing Sunspots in Linear Rational Expectations Models," Computing in Economics and Finance 2002 138, Society for Computational Economics.
  • Handle: RePEc:sce:scecf2:138

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    References listed on IDEAS

    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, vol. 39(4), pages 1015-1026, November.
    2. Lubik, Thomas A. & Marzo, Massimiliano, 2007. "An inventory of simple monetary policy rules in a New Keynesian macroeconomic model," International Review of Economics & Finance, Elsevier, vol. 16(1), pages 15-36.
    3. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    4. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    5. Perli, Roberto, 1998. "Indeterminacy, home production, and the business cycle: A calibrated analysis," Journal of Monetary Economics, Elsevier, vol. 41(1), pages 105-125, February.
    6. Weder, Mark, 2000. "Animal spirits, technology shocks and the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 24(2), pages 273-295, February.
    7. Farmer Roger E. A. & Guo Jang-Ting, 1994. "Real Business Cycles and the Animal Spirits Hypothesis," Journal of Economic Theory, Elsevier, vol. 63(1), pages 42-72, June.
    8. 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.
    9. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
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    Cited by:

    1. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
    2. Pedro Pablo Álvarez Lois, 2003. "Capacity utilization and Monetary Policy," Working Papers 0306, Banco de España;Working Papers Homepage.

    More about this item


    Sunspots; Indeterminacy; Rational Expectations; Computational Methods;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E00 - Macroeconomics and Monetary Economics - - General - - - General


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