## Generalized Impulse Response Analysis in Linear Multivariate Models (1997)

Citations: | 115 - 7 self |

### BibTeX

@MISC{Pesaran97generalizedimpulse,

author = {M. Hashem Pesaran and Yongcheol Shin},

title = {Generalized Impulse Response Analysis in Linear Multivariate Models },

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

Building on Koop, Pesaran and Potter (1996), we propose the `generalized' impulse response analysis for unrestricted vector autoregressive (VAR) and cointegrated VAR models. Unlike the traditional impulse response analysis, our approach does not require orthogonalization of shocks and is invariant to the ordering of the variables in the VAR. The approach is also used in the construction of order-invariant forecast error variance decompositions.

### Citations

1102 |
Cointegration and error correction: Representation, estimation and testing. Econometrica 55:251–276
- Engle, Granger
- 1987
(Show Context)
Citation Context ...y collinear. Under Assumption 2.2, xt would be covariance-stationary, and (2.1) can be rewritten as the in¯nite moving average representation, xt = 1X Ai"t¡i + i=0 1X Giwt¡i; t=1;2; :::; T; (2.2) i=0 =-=[1]-=-where the m £ m coe±cient matrices Ai can be obtained using the following recursive relations: Ai = ©1Ai¡1 + ©2Ai¡2 + ¢¢¢+©pAi¡p;i=1;2;:::; (2.3) with A0 = Im and Ai = 0 for i<0, and Gi = Aiª. An imp... |

579 |
Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Advanced Texts in Econometrics
- Johansen
- 1995
(Show Context)
Citation Context ...ave GIx(n; ±j; t¡1) =E(xt+nj"jt = ±j;t¡1) ¡ E (xt+njt¡1): (2.8) 1This history invariance property of the impulse response is speci¯c to linear systems and does not carry over to non-linear models. =-=[2]-=-Assuming that "t has a multivariate normal distribution, it is now easily seen (see also Koop et al. (1996)) that 2 E ("tj"jt = ±j) =(1j;2j; :::; mj) 0 ¡1 jj ±j = §ej ¡1 jj ±j: Hence, the m £ 1... |

247 |
Impulse Response Analysis in Nonlinear Multivariate Models
- Koop, Pesaran, et al.
- 1996
(Show Context)
Citation Context ...To deal with unit roots and cointegration, we replace Assumption 2.2 by 4Proposition 3.1 also applies to the relationship between the generalised and the orthogonalised forecast error decompositions. =-=[4]-=-Assumption 4.1 The roots of jIm ¡ P p i=1 ©iz i j =0satisfy jzj > 1 or z =1. In this case (2.1) can be transformed into the VEC form: p¡1 X ¢xt = ¡¦xt¡1 + ¡i¢xt¡i + ¦¤wt + "t; t=1;2;:::;T; (4.1) i=1 ... |

59 |
Cointegration and speed of convergence to equilibrium
- Pesaran, Shin
- 1996
(Show Context)
Citation Context ...), the ML estimators of the short-run parameters (¡ and ®) andof the long-run parameters (¯) are p T-consistent and T -consistent, respectively. For a proof see, for example, Pesaran and Shin (1997). =-=[9]-=-and by the Taylor series expansion e 0 j ^§ej ´ 1 2 = ¡ e 0 j §ej ¢ 1 1 ¡ ¢ 1 2 0 ¡ ¡ 2 0 + ej §ej e 2 je 0 ¢ j vec(^§ ¡ §)+R; (A.10) where R is a scalar remainder term which in view of the consis... |

42 |
Impulse Response Analysis of Cointegrated Systems
- Lutkepohl, Reimers
- 1992
(Show Context)
Citation Context ...rices of coe±cients, and t is running from 1948(1) to 1988(4). 5 Notice that B1 = C(1); and therefore ¯ 0 B1 = 0: 6 For more details see LÄutkepohl and Reimers (1992) and Pesaran and Shin (1996). j=1 =-=[6]-=-After estimating the parameters in (5.1) consistently by OLS, we turn to estimate the orthogonalized and the generalized impulse response functions with respect to one standard error shock to the out... |

19 |
Stochastic trends and economic ¯uctuations
- King, Plosser, et al.
- 1991
(Show Context)
Citation Context ... by resampling techniques if the distribution of errors is not known. 3For a further discussion of the generalised forecast error variance decompositions see Pesaran and Pesaran (1997, Section 19.5). =-=[3]-=-are unique and fully take account of the historical patterns of correlations observed amongst the di®erent shocks. The relationship between the two impulse responses are set out in the following prop... |

10 |
Long run structural modelling, Unpublished manuscript
- Pesaran, Shin
- 1995
(Show Context)
Citation Context ... James Mitchell and Ron Smith for helpful comments. Partial ¯nancial support from the ESRC (grant No. L116251016) and the Isaac Newton Trust of Trinity College, Cambridge, is gratefully acknowledged. =-=[8]-=-A Appendix: Proofs of (4.11) and (4.12) Let ^¡, ^®, ^¯ and ^§ be the maximum likelihood estimators of ¡, ®, ¯ and § in the VEC model (4.1). Using the results in LÄutkepohl and Reimers (1992) and Pesa... |

5 |
Introduction to Multiple Time Series Analysis
- LÄutkepohl
- 1993
(Show Context)
Citation Context ...egration is given by ¯ 0 C(1) = 0, where C(1) = P1 i=0 Ci with rank[C(1)] = m ¡ r (see Engle and Granger (1987)). Then, the cointegrating relations can be written as zt = ¯ 0 xt = 1X ¯ 0 Bi"t¡i + i=0 =-=[5]-=- 1X ¯ 0 Bi¦¤wt¡i: (4.7) i=0Hence, the generalized impulse response functions of zt with respect to a shock in the jth equation is given by Ã g z;j 2 (n) =¡1 jj ¯0Bn§ej; n=0;1;2; ::: : (4.8) Similarl... |

4 |
Working with Micro®t 4.0: Interactive Econometric Analysis
- Pesaran, Pesaran
- 1997
(Show Context)
Citation Context ...e ¯rst variable in the VAR. See Proposition 3.1. 9For more details on the choice of intercepts and trends in cointegrated VAR models see Pesaran and Pesaran (1997) and Pesaran, Shin and Smith (1997). =-=[7]-=-where the asymptotic standard errors are given in bracket, and LL is the maximized loglikelihood. Imposition of the full set of restrictions implied by two great ratios yields the maximized log-likel... |

2 | Structural analysis of vector autoregressive models with exogenous - Pesaran, Shin, et al. - 1997 |