Using the generalized Schur form to solve a multivariate linear rational expectations model

By Paul Klein. 2000

685 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/062d4b1415169c387e565f050eee91251419097d

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Citations in the corpus

Perturbation Methods for Markov-Switching DSGE Models (2014, methodology): “2For the theory of Gröbner bases and its application to economics, see Kubler and Schmedders (2010a) and Kubler and Schmedders (2010b) for finding multiple equilibria in general equilibrium models and Datta (2010) for finding all Nash equilibria.”
Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models (2016, background): “4.1 Solving polynomial equations When there are no Markov-switching parameters, the system of quadratic polynomial equations (see system (A.4) in Appendix A) collapses to a special form that can be solved by using the generalized Schur decomposition (Klein (2000)).”
Anticipated Alternative Policy-Rate Paths in Policy Simulations (2011, methodology): “Assuming a linear model (a linearized DSGE model), we provide an alternative simple and convenient algorithm that allows a stochastic interpretation more precisely a standard state-space representation of a stochastic linear model with forward-looking variables, the solution of which can be express”
A Small-Sample Study of the New-Keynesian Macro Model (2006, background): “Panel D reports the Jarque-Bera tests for normality of the residuals, with their corresponding probability values. the analysis in Taylor (1999) and Leeper and Zha (2000) showing that monetary policy shocks during the 1990s were small.”
Dynamic Identification of Dynamic Stochastic General Equilibrium Models (2011, neutral): “Solution algorithms include Anderson and Moore (1985), Uhlig (1999), Klein (2000), King and Watson (2002), and Sims (2002), among others.”
Evaluating the strength of identification in DSGE models. An a priori approach (2010, methodology): “There are several algorithms for solving linear rational expectations models (see for instance Blanchard and Kahn (1980), Anderson and Moore (1985), King and Watson (1998), Klein (2000), Christiano (2002), Sims (2002)).”
Oil and the Great Moderation (2010, neutral): “We approximate our model to …rst-order and solve it with a standard method for linear rational expectations models (e.g. Sims 2002, and Klein, 2000).”
Efficient Perturbation Methods for Solving Regime-Switching DSGE Models (2015, neutral): “In many cases, they also use the type of notation used in Klein (2000), Schmitt-Grohe and Uribe (2004) and by Gensys.”
Financial Openness and Business Cycle Volatility (2002, methodology): “In a second step, we use the algorithm developed by Klein (2000) to simulate the model numerically.”
A New Keynesian Perspective on the Great Recession (2011, methodology): “Hence, the value ψ = 0.10 is also fixed prior to estimation; as explained in Ireland (2004, 2007), this setting for ψ can be interpreted based on the fact that it implies an amount of sluggishness in nominal goods prices equivalent to what is produced by the alternative, but closely related, specifi”
Search, Liquidity and the Dynamics of House Prices and Construction (2014, background): “(1 + )ft = (1 ) G Wt + (1 f )ft 1 (33) (1 + )bt = G Wt + [1 (!t 1)] bt 1 + (1 n)nt 1 (34) (1 + )nt = (1 )(1 n)nt 1 + (!t 1)bt 1 (35) (1 + )ht+1 = ht + (nt + bt + ft) ( EtVt+1 qt) : (36)”
Monetary Policy Rules for an Open Economy (2003, methodology): “20 substitute foreign bond holdings out of the model and concentrate on the movements of the other variables, as in McCallum and Nelson (1999). 2.”