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A Complete Characterization of ARMA Solutions to Linear Rational Expectations Models

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Abstract

Linear rational expectations models with expectations of future endogenous variables have multiple equilibria. For a scalar model with k forward expectational lags and l backward lags, this paper characterizes the complete set of ARMA solutions. It is shown that the maximum degree solutions are ARMA (k + l, k), that the solutions of maximum degree are obtained directly from the characteristic polynomial but have arbitrary MA parameters, and that all lower degree ARMA solutions are obtained by deleting common factors in the AR and MA lag polynomials. The results are applied to several macroeconomic examples.

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  • George Evans & Seppo Honkapohja, 1986. "A Complete Characterization of ARMA Solutions to Linear Rational Expectations Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 227-239.
    • Handle: RePEc:oup:restud:v:53:y:1986:i:2:p:227-239.
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    File URL: http://hdl.handle.net/10.2307/2297648
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    Cited by:

    1. Behzad T. Diba & Herschel I. Grossman, 1985. "The Impossibility of Rational Bubbles," NBER Working Papers 1615, National Bureau of Economic Research, Inc.
    2. Bjorn Wahlroos & Tom Berglund, 1984. "Stock Returns," Discussion Papers 598, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Heinemann, Maik, 1997. "Convergence of Adaptive Learning and the Concept of Expectational Stability in Linear Rational Expectations Models with Multiple Equilibria," Hannover Economic Papers (HEP) dp-207, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    4. Marco M. Sorge, 2013. "A Note on Information Flows and Identification of News Shocks Models," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 56(1), pages 28-38.
    5. Fanelli, Luca, 2012. "Determinacy, indeterminacy and dynamic misspecification in linear rational expectations models," Journal of Econometrics, Elsevier, vol. 170(1), pages 153-163.
    6. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    7. Schaefer, Daniel & Singleton, Carl, 2018. "Unemployment and econometric learning," Research in Economics, Elsevier, vol. 72(2), pages 277-296.
    8. Evans, George W. & Honkapohja, Seppo, 2003. "Expectational stability of stationary sunspot equilibria in a forward-looking linear model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 171-181, October.
    9. C. R. McKenzie & Michael McAleer, 2001. "Comparing Tests of Autoregressive Versus Moving Average Errors in Regression Models Using Bahadur's Asymptotic Relative Efficiency," ISER Discussion Paper 0537, Institute of Social and Economic Research, Osaka University.
    10. Duffy, John & Xiao, Wei, 2007. "Instability of sunspot equilibria in real business cycle models under adaptive learning," Journal of Monetary Economics, Elsevier, vol. 54(3), pages 879-903, April.
    11. Evans, George W. & McGough, Bruce, 2005. "Stable sunspot solutions in models with predetermined variables," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 601-625, April.
    12. Luis-Felipe Zanna, 2004. "PPP rules, macroeconomic (In)stability and learning," International Finance Discussion Papers 814, Board of Governors of the Federal Reserve System (U.S.).
    13. Luis-Felipe Zanna, 2009. "Ppp Exchange Rate Rules, Macroeconomic (In)Stability, And Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(4), pages 1103-1128, November.
    14. John H. Boyd & Michael Dotsey, 1990. "Interest rate rules and nominal determinacy," Working Paper 90-01, Federal Reserve Bank of Richmond.
    15. George W. Evans & Seppo Honkapohja, 2001. "Expectational Stability of Resonant Frequency Sunspot Equilibria," CESifo Working Paper Series 497, CESifo.
    16. Wenzelburger, Jan, 2006. "Learning in linear models with expectational leads," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 854-884, November.

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