1Inter-American Development Bank, Research Department, Washington, DC, United States of America. Research Fellow. Email: socampo@iadb.org
2Banco de la República, Macroeconomic Modeling Department, Bogotá, Colombia. Universidad Nacional de Colombia, Statistics Department, Bogotá, Colombia. Principal Econometrist and Lecturer. Email: nrodrini@banrep.gov.co
This document presents how to estimate and implement a structural VAR-X model under long run and impact identification restrictions. Estimation 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 decomposition and historical decomposition of the endogenous variables are also described, as well as a method for computing higher posterior density regions in a Bayesian context. Some of the concepts are exemplified with an application to US data.
Key words: Econometrics, Bayesian time series, Vector autoregression, \linebreak Structural model.
Este documento cubre la estimación e implementación del modelo VAR-X estructural bajo restricciones de identificación de corto y largo plazo. Se presenta 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, descomposición 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 Bayesianas, vector autoregresivo.
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References
]]>1. Amisano, G. & Giannini, C. (1997), Topics in Structural VAR Econometrics, Springer. [ Links ]
2. Bauwens, L., Lubrano, M. & Richard, Jean-Francois (2000), Bayesian Inference in Dynamic Econometric Models, Oxford University Press. [ Links ]
3. Bianchi, C., Carta, A., Fantazzini, D., Giuli, M. . D. & Maggi, M. (2010), 'A Copula VAR-X Approach for Industrial Production Modelling and Forecasting', Applied Economics 42(25), 3267-3277. [ Links ]
4. Blanchard, O. J. & Quah, D. (1989), 'The Dynamic Effects of Aggregate Demand and Supply Disturbances', American Economic Review 79(4), 655-73. [ Links ]
5. Burbidge, J. & Harrison, A. (1985), 'A Historical Decomposition of the Great Depression to Determine the Role of Money', Journal of Monetary Economics 16(1), 45-54. [ Links ]
]]>6. Canova, F. (2007), Methods for Applied Macroeconomic Research, Princeton University Press, Nueva Jersey. [ Links ]
7. Canova, F. & De Nicolo, G. (2002), 'Monetary Disturbances Matter for Business Fluctuations in the G-7', Journal of Monetary Economics 49(6), 1131-1159. [ Links ]
8. Canova, F. & Pappa, E. (2007), 'Price Differentials in Monetary Unions: The Role of Fiscal Shocks', Economic Journal 117(520), 713-737. [ Links ]
9. Casella, G. & George, E. I. (1992), 'Explaining the Gibbs Sampler', The American Statistician 46(3), 167-174. [ Links ]
10. Chen, Ming-hui & Shao, Qi-man (1998), 'Monte Carlo Estimation of Bayesian Credible and HPD Intervals', Journal of Computational and Graphical Statistics 8, 69-92. [ Links ]
]]>11. Chiu, C. W. (., Eraker, B., Foerster, A. T., Kim, . B. & Seoane, H. D. (2011), Estimating VAR's Aampled at Mixed or Irregular Spaced Frequencies : a Bayesian Approach, Research Working Paper RWP 11-11, Federal Reserve Bank of Kansas City. [ Links ]
12. Christiano, L. J., Eichenbaum, M. & Evans, C. . (1999), Monetary Policy Shocks: What Have We Learned and to What End?, 'Handbook of Macroeconomics', Vol. 1 of Handbook of Macroeconomics, Elsevier, chapter 2, p. 65-148. [ Links ]
13. Galí, J. (1999), 'Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?', American Economic Review 89(1), 249-271. [ Links ]
14. Geman, S. & Geman, D. (1984), 'Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images', IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741. [ Links ]
15. Hyndman, R. J. (1996), 'Computing and Graphing Highest Density Regions', The American Statistician 50, 120-126. [ Links ]
]]>16. Jeffreys, H. (1961), Theory of Probability, International Series of Monographs on Physics, Clarendon Press. [ Links ]
17. Kadiyala, K. R. & Karlsson, S. (1997), 'Numerical Methods for Estimation and Inference in Bayesian VAR-Models', Journal of Applied Econometrics 12(2), 99-132. [ Links ]
18. Kilian, L. (1998), 'Small-Sample Confidence Intervals For Impulse Response Functions', The Review of Economics and Statistics 80(2), 218-230. [ Links ]
19. King, T. B. & Morley, J. (2007), 'In Search of the Natural Rate of Unemployment', Journal of Monetary Economics 54(2), 550-564. [ Links ]
20. Kociecki, A. (2010), 'A Prior for Impulse Responses in Bayesian Structural VAR Models', Journal of Business & Economic Statistics 28(1), 115-127. [ Links ]
]]>21. Koop, G. (1992), 'Aggregate Shocks and Macroeconomic Fluctuations: A Bayesian Approach', Journal of Applied Econometrics 7(4), 395-411. [ Links ]
22. Litterman, R. B. (1986), 'Forecasting with Bayesian Vector Autoregressions - Five Years of Experience', Journal of Business & Economic Statistics 4(1), 25-38. [ Links ]
23. Lütkepohl, H. (1990), 'Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models', The Review of Economics and Statistics 72(1), 116-25. [ Links ]
24. Lütkepohl, H. (2005), New Introduction to Multiple Time Series Analysis, Springer. [ Links ]
25. Moon, H. R., Schorfheide, F. & Lee, E. G. . M. (2011), Inference for VARs Identified with Sign Restrictions, NBER Working Papers 17140, National Bureau of Economic Research, Inc. [ Links ]
]]>26. Mountford, A. & Uhlig, H. (2009), 'What are he Effects of Fiscal Policy Shocks?', Journal of Applied Econometrics 24(6), 960-992. [ Links ]
27. Nicholls, D. F. & Pope, A. L. (1988), 'Bias in the Estimation of Multivariate Autoregressions', Australian Journal of Statistics 30A(1), 296-309. [ Links ]
28. Rodriguez, A. & Puggioni, G. (2010), 'Mixed Frequency Models: Bayesian Approaches to Estimation and Prediction', International Journal of Forecasting 26(2), 293-311. [ Links ]
29. Runkle, D. E. (1987), 'Vector Autoregressions and Reality', Journal of Business & Economic Statistics 5(4), 437-42. [ Links ]
30. Sims, C. A. (1980), 'Macroeconomics and Reality', Econometrica 48(1), 1-48. [ Links ]
]]>31. Sims, C. A. & Zha, T. (1999), 'Error Bands for Impulse Responses', Econometrica 67(5), 1113-1156. [ Links ]
32. Smets, F. & Wouters, R. (2007), 'Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach', American Economic Review 97(3), 586-606. [ Links ]
33. Uhlig, H. (2005), 'What are the Effects of Monetary Policy on Output? Results From an Agnostic Identification Procedure', Journal of Monetary Economics 52(2), 381-419. [ Links ]
34. Zellner, A. (1996), An Introduction to Bayesian Inference in Econometrics, Wiley Classics Library, John Wiley. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv35n3a09, ]]>
AUTHOR = {Ocampo, Sergio and Rodríguez, Norberto},
TITLE = {{An Introductory Review of a Structural VAR-X Estimation and Applications}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2012},
volume = {35},
number = {3},
pages = {479-508}
}