Solving linear rational expectations models with lagged expectations quickly and easily - Alexander Meyer-Gohde (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2007)
A solution method is derived in this paper for solving a system of linear rational-expectations equation with lagged expectations (e.g., models incorporating sticky information) using the method of undetermined coefficients for the infinite MA representation. The method applies a combination of a Generalized Schur Decomposition familiar elsewhere in the literature and a simple system of linear equations when lagged expectations are present to the infinite MA representation. Execution is faster, applicability more general, and use more straight-forward than with existing algorithms. Current methods of truncating lagged expectations are shown to not generally be innocuous and the use of such methods are rendered obsolete by the tremendous gains in computational efficiency of the method here which allows for a solution to floating-point accuracy in a fraction of the time required by standard methods. The associated computational application of the method provides impulse responses to anticipated and unanticipated innovations, simulations, and frequency-domain and simulated moments.
Keywords: C32; C63; 330; Lagged expectations; linear rational expectations models; block tridiagonal; Generalized Schur Form; QZ decomposition; LAPACK; Rationale Erwartung; Lag-Modell; Mathematische Optimierung; Dekompositionsverfahren; Theorie