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Solving Reduced-form Linear Rational Expectations


  • Jae Won Lee


  • Woong Yong Park



This paper proposes an improvement on popular solution methods for linear rational expectations models (for example, Sims 2002) in terms of computational performance: When a model can be transformed into a reduced form, the QZ decomposition to decouple the dynamics of the stable and unstable block of the model can be replaced with the Schur decomposition. The latter runs faster. The new method is applicable to a wide class of models in the literature. It is especially useful for a large-scale model such as a multisector model and a heterogeneous agent model that are increasingly popular recently. Compared to the method that uses the QZ decomposition, the new method that uses the Schur decomposition reduces computing time by 33.0% for a medium-scale model with 39 equations and 91.3% for a large-scale model with 1,908 equations.

Suggested Citation

  • Jae Won Lee & Woong Yong Park, 2020. "Solving Reduced-form Linear Rational Expectations," Working Paper Series no132, Institute of Economic Research, Seoul National University.
  • Handle: RePEc:snu:ioerwp:no132

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    solution methods for linear rational expectational models; QZ decomposition; Schur decomposition; multisector model; heterogeneous agent model;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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