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A Solution Method for Linear Rational Expectation Models under Imperfect Information

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  • Katsuyuki Shibayama

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Abstract

This paper has developed a solution algorithm for linear rational expectation models under imperfect information. Imperfect information in this paper means that some decision makings are based on smaller information sets than others. The algorithm generates the solution in the form of k_t+1 = Hk_t + Jx^t,S f_t = Fk_t + Gx^t,S where k_t and f_t are column vectors of crawling and jump variables, respectively, while x^t,S is the vertical concatenation of the column vectors of past and present innovations. The technical breakthrough in this article is made by expanding the innovation vector, rather than expanding the set of crawling variables. Perhaps surprisingly, the H and F matrices are the same as those under the corresponding perfect information models. This implies that if the corresponding perfect information model is saddle path stable (sunspot, explosive), the imperfect model is also saddle-path stable (sunspot, explosive, respectively). Moreover, if the minimum information set in the model has all the information up to time t-S-1, then the direct effects on the impulse response functions last for only the first S periods after the impulse. In the subsequent dates, impulse response functions follow essentially the same process as in the perfect information counterpart. However, imperfect information can significantly alter the quantitative properties of a model, though it does not drastically change its qualitative nature. This article demonstrates, as an example, that adding imperfect information to the standard RBC models remarkably improves the correlation between labour productivity and output. Hence, a robustness check for information structure is recommended.

Suggested Citation

  • Katsuyuki Shibayama, 2007. "A Solution Method for Linear Rational Expectation Models under Imperfect Information," Studies in Economics 0703, School of Economics, University of Kent.
  • Handle: RePEc:ukc:ukcedp:0703
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    References listed on IDEAS

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    1. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 21-55, October.
    2. N. Gregory Mankiw & Ricardo Reis, 2002. "Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve," The Quarterly Journal of Economics, Oxford University Press, vol. 117(4), pages 1295-1328.
    3. John H. Boyd & Michael Dotsey, 1990. "Interest rate rules and nominal determinacy," Working Paper 90-01, Federal Reserve Bank of Richmond.
    4. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
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    Cited by:

    1. Anna Kormilitsina, 2013. "Solving Rational Expectations Models with Informational Subperiods: A Perturbation Approach," Computational Economics, Springer;Society for Computational Economics, vol. 41(4), pages 525-555, April.
    2. Carravetta, Francesco & Sorge, Marco M., 2013. "Model reference adaptive expectations in Markov-switching economies," Economic Modelling, Elsevier, vol. 32(C), pages 551-559.

    More about this item

    Keywords

    Linear rational expectations models; imperfect information;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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