An Introductory Review of a Structural VAR-X.pdf - Revista Colombiana de Estadística Diciembre 2012 volumen 35 no 3 pp 479 a 508 An Introductory Review

An Introductory Review of a Structural VAR-X.pdf - Revista...

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Revista Colombiana de Estadística Diciembre 2012, volumen 35, no. 3, pp. 479 a 508 An Introductory Review of a Structural VAR-X Estimation and Applications Una revisión introductoria de la estimación y aplicaciones de un VAR-X estructural Sergio Ocampo 1 , a , Norberto Rodríguez 2 , 3 , b 1 Research Department, Inter-American Development Bank, Washington, DC, United States of America 2 Macroeconomic Modeling Department, Banco de la República, Bogotá, Colombia 3 Statistics Department, Universidad Nacional de Colombia, Bogotá, Colombia Abstract This document presents how to estimate and implement a structural VAR-X model under long run and impact identification restrictions. Esti- mation by Bayesian and classical methods are presented. Applications of the structural VAR-X for impulse response functions to structural shocks, multiplier analysis of the exogenous variables, forecast error variance decom- position and historical decomposition of the endogenous variables are also described, as well as a method for computing higher posterior density re- gions in a Bayesian context. Some of the concepts are exemplified with an application to US data. Key words : Econometrics, Bayesian time series, Vector autoregression, Structural model. Resumen Este documento cubre la estimación e implementación del modelo VAR-X estructural bajo restricciones de identificación de corto y largo plazo. Se pre- senta la estimación tanto por métodos clásicos como Bayesianos. También se describen aplicaciones del modelo como impulsos respuesta ante choques estructurales, análisis de multiplicadores de las variables exógenas, descom- posición de varianza del error de pronóstico y descomposición histórica de las variables endógenas. Así mismo se presenta un método para calcular regiones de alta densidad posterior en el contexto Bayesiano. Algunos de los conceptos son ejemplificados con una aplicación a datos de los Estados Unidos. Palabras clave : econometría, modelo estructural, series de tiempo Baye- sianas, vector autoregresivo. a Research Fellow. E-mail: [email protected] b Principal Econometrist and Lecturer. E-mail: [email protected] 479
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480 Sergio Ocampo & Norberto Rodríguez 1. Introduction The use of Vector Autoregression with exogenous variables (VAR-X) and struc- tural VAR-X models in econometrics is not new, yet textbooks and articles that use them often fail to provide the reader a concise (and moreover useful) descrip- tion of how to implement these models (Lütkepohl (2005) constitutes an exception of this statement). The use of Bayesian techniques in the estimation of VAR-X models is also largely neglected from the literature, as is the construction of the historical decomposition of the endogenous variables. This document builds upon the Structural Vector Autoregression (S-VAR) and Bayesian Vector Autoregres- sion (B-VAR) literature and its purpose is to present a review of some of the basic features that accompany the implementation of a structural VAR-X model.
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