### Citations

715 |
Numerical Methods in Economics
- Judd
- 1998
(Show Context)
Citation Context ...the terms in y (x) t when ε = 0. are derivatives of [yt (ε)] with respect to ε For simplicity we consider the case of α = 1 although this might not be the best choice in general (see Holmes, 1995 and =-=Judd, 1998-=-, p. 516). Then, we take an expansion of f (·) around ε = 0 (assume that y (0) t = y0) f (ε, yt) ≈ f (0, y0) + fεε + fy (yt − y0) + 1 ( fεεε 2 2 + fyy (yt − y0) 2) + O ( ε 3) where for simplicity we h... |

487 | Recursive Macroeconomic Theory - Ljungqvist, Sargent - 2000 |

399 | Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function - Schmitt-Grohe, Uribe - 2004 |

334 |
Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model
- Klein
- 2000
(Show Context)
Citation Context ...stationary solution number of eigenvalues λ of the matrix pencil A1 − λA2 i.e. that the that lie inside the unit circle is equal to the number of predetermined variables (Blanchard and Kahn, 1980 and =-=Klein, 2000-=-) the system (13) will also be stationary. The Blanchard-Kahn stationarity conditions for this second-order linear system are identical to those of its companion rst-order system: if the latter is sta... |

216 | A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily.” Discussion Paper 101, Federal Reserve Bank of Minneapolis. - Uhlig - 1995 |

129 |
Introduction to Perturbation Methods
- Holmes
- 1995
(Show Context)
Citation Context ...ation. At present, Dynare version 4.2 o ers the pruning option for second order approximations. This option is not yet available to higher order. 6 ECB Working Paper Series No 1264 November 2010(e.g =-=Holmes, 1995-=-) to provide a formally consistent higher-order approximation to a non-linear model that is recursively linear as in Lombardo and Sutherland (2007). Using the standard neo-classical growth model we sh... |

113 | Dynare: a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm, CEPREMAP Working Papers No
- Juillard
- 1996
(Show Context)
Citation Context ...their paper the authors do not distinguish the order of the variables in the second order expansion. Widely used computer softwares that solve DSGE models to higher order, like Dynare (and Dynare++) (=-=Juillard, 1996-=-) or PerturbationAIM (Swanson et al., 2006) produce state space representations that are not pruned . 2 Part of the literature therefore o ers representations of the solution that are intrinsically no... |

83 | Solving Dynamic Equilibrium Models by a Method of Undetermined Coe¢cients”, - Christiano - 2002 |

72 | Perturbation Methods for General Dynamic Stochastic Models,” - Jin, Judd - 2002 |

57 | System Reduction and Solution Algorithms for Singular Linear Difference Systems under - King, Watson - 2002 |

41 | Second-order approximation of dynamic models without the use of tensors”. In: - Gomme, Klein - 2011 |

37 | Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Model. Working Paper, Federal Reserve Bank of San Francisco.
- Anderson, Levin, et al.
- 2006
(Show Context)
Citation Context ...nguish the order of the variables in the second order expansion. Widely used computer softwares that solve DSGE models to higher order, like Dynare (and Dynare++) (Juillard, 1996) or PerturbationAIM (=-=Swanson et al., 2006-=-) produce state space representations that are not pruned . 2 Part of the literature therefore o ers representations of the solution that are intrinsically non-linear and that, therefore, can generate... |

32 | Computing Second-Order-Accurate Solutions for Rational Expectation Models: Using Linear Solution Methods. - Lombardo, Sutherland - 2004 |

18 | Asymptotic methods for asset market equilibrium analysis. - Judd, Guu - 2001 |

17 | Perturbation Methods For Engineers and Scientists, - Bush - 1992 |

16 | Perturbation Methods with Nonlinear Changes of Variables”. Mimeo, Hoover Institution. - Judd - 2003 |

5 | How well-behaved are higher-order perturbation solutions?” Working Paper - Haan, Wind - 2009 |

1 | Perturbation theory of dynamical systems. Arxiv preprint math.HO/0111178 - Berglund - 2001 |

1 |
The Solution of Di erence Models under Rational Expectations
- Blanchard, Kahn
- 1980
(Show Context)
Citation Context ...vided that system (12) has a stationary solution number of eigenvalues λ of the matrix pencil A1 − λA2 i.e. that the that lie inside the unit circle is equal to the number of predetermined variables (=-=Blanchard and Kahn, 1980-=- and Klein, 2000) the system (13) will also be stationary. The Blanchard-Kahn stationarity conditions for this second-order linear system are identical to those of its companion rst-order system: if t... |

1 | 24 ECB Working Paper Series No 1264 November 2010 - F, Juillard - 2001 |

1 | Perturbation methods. Cambridge Univ Pr - Hinch - 1991 |

1 | erence equations: an introduction with ECB Working Paper Series No 1264 November 2010 25 - Di - 2008 |