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Computing Sunspots in Linear Rational Expectations Models

  • Thomas A 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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Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 456.

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Date of creation: Oct 2001
Date of revision: Jun 2002
Handle: RePEc:jhu:papers:456
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  1. Roberto Perli, . "Indeterminacy, Home Production, and the Business Cycle: a Calibrated Analysis," CARESS Working Papres 97-4, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  2. 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.
  3. Thomas Lubik & Massimiliano Marzo, 2003. "An Inventory of Simple Monetary Policy Rules in a New Keynesian Macroeconomic Model," Economics Working Paper Archive 500, The Johns Hopkins University,Department of Economics.
  4. James Bullard & Kaushik Mitra, 2002. "Learning about monetary policy rules," Working Papers 2000-001, Federal Reserve Bank of St. Louis.
  5. Roger E.A. Farmer & Jang Ting Guo, 1992. "Real Business Cycles and the Animal Spirits Hypothesis," UCLA Economics Working Papers 680, UCLA Department of Economics.
  6. 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.
  7. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  8. 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.
  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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