Acta Oeconomica Pragensia 2014, 22(4):52-72 | DOI: 10.18267/j.aop.446

Alternative specification, estimation and identification of vector autoregressions

Roman Hušek, Tomáš Formánek
Vysoká škola ekonomická v Praze, Fakulta informatiky a statistiky (husek@vse.cz, formanek@vse.cz)

The article focuses on various aspects of specification, estimation and identification of vector autoregression (VAR) models. Key VAR-specific topics of verification of an estimated model are also covered, as well as the differences between a standard (unrestricted) and structural VAR model. Subsequently, we address theoretical properties and practical aspects of impulse response functions (IRFs) as calculated upon estimated VAR models. Topics such as Cholesky decomposition (CHD), orthogonalised and generalised IRFs are discussed. Properties of VAR models are compared against alternative econometric modelling tools, such as simultaneous equation models and dynamic stochastic general equilibrium (DSGE) models. The article is supplemented with an illustrative example: on an aggregated EMU-wide level, we estimate a VAR (2) model for real GDP, CPI and PPI inflation. IRFs are calculated using two different CHD orderings and compared to generalised IRFs. We find the IRFs from our illustrative model to be very robust against the chosen IRF calculation method and against equation ordering changes.

Keywords: Vector autoregression, impulse response functions, estimation, identification, specification
JEL classification: C32, E30, F41

Published: August 1, 2014  Show citation

ACS AIP APA ASA Harvard Chicago IEEE ISO690 MLA NLM Turabian Vancouver
Hušek, R., & Formánek, T. (2014). Alternative specification, estimation and identification of vector autoregressions. Acta Oeconomica Pragensia, 22(4), 52-72. doi: 10.18267/j.aop.446
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. AKAIKE, H. 1974. A new look at the statistical model identification. I.E.E.E. Transactions on automatic control. December 1974, vol. 19, no. 6, pp. 716-723. Go to original source...
    2. BLANCHARD, O.; DIAMOND, R 1989. The Beveridge curve. Brookings Papers on Economic Activity. 1989, vol. 1, pp. 1-60. Go to original source...
    3. BLANCHARD, O.; QUAH, D. 1989. The dynamic effects of aggregate demand and supply disturbances. The Americal Economic Review. September 1989, vol. 79, no. 4, pp. 655-673.
    4. BOX, G.; RIERCE, D. 1970. Distribution of residual autocorrelations in autoregressive moving average time series models. Journal of the American Statistical Association. December 1970, vol. 65, no. 332, pp. 1509-1526. Go to original source...
    5. BREITUNG, J.; CANDELON, B. 2006. Testing for short- and long-run causality: A frequency-domain approach. Journal of Econometrics. June 2006, vol. 132(2), pp. 363-378. Go to original source...
    6. BROWN, R. L.; DURBIN, J.; EVANS J. M. 1975. Techniques for Testing the Constancy of Regression Relationships Over Time. Journal of the Royal Statistical Society. Series B (Methodological), 1975, vol. 37, no. 2, pp. 149-192. Go to original source...
    7. COOLEY T; DWYER, M. 1998. Business cycle analysis without much theory: A look at structural VARs. Journal of Econometrics. January/February 1998, vol. 83, pp. 57-88. Go to original source...
    8. COOLEY T.; LE ROY S. 1985. Atheoretical macroeconometrics: A critique. Journal of Monetary Economics. November 1985, vol. 16, no. 3, pp. 283-308. Go to original source...
    9. DEJONG, D.; DAVE, C. 2007. Structural Macroeconometrics. Rrinceton : N.Y Rrinceton University Press, 2007. ISBN 978-0-691-12648-7.
    10. DICKEY D. A.; FULLER, W. A. 1979. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. 1979, vol. 74, pp. 427-431. Go to original source...
    11. DOLADO, J.; LUTKEROHL, H. 1996. Making Wald tests work for cointegrated VAR systems. Econometric Reviews. 1996, vol. 15, no. 4, pp. 369-386. Go to original source...
    12. EDGERTON, D.; SHUKUR, G. 1999. Testing autocorrelation in a system perspective. Econometric Reviews. 1999, vol. 18, no. 4, pp. 343-386. Go to original source...
    13. ENDERS, W. 1995. Applied econometric time series. New York : J. Wiley and Sons, 1995. ISBN 978-0471039419.
    14. GALÍ, J. 1992. How well does the IS-LM model fit postwar US data? Quarterly Journal of Economics. May 1992, vol. 107, no. 2, pp. 709-738. Go to original source...
    15. GEWEKE, J.; MEESE, R.; DENT, W. 1983. Comparing alternative tests of causality in temporal systems: Analytic results and experimental evidence. Journal of Econometrics. February 1983, vol. 21, no. 2, pp. 161-194. Go to original source...
    16. GRANGER, C. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica. July 1969, vol. 37, no. 3, pp. 424-438. Go to original source...
    17. HAMILTON, J. 1994. Time series analysis. Princeton : N.Y Princeton University Press, 1994. ISBN 978-0691042893. Go to original source...
    18. HANNAN, E.; QUINN, B. 1979. The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B. 1979, vol. 41, no. 2, pp. 190-195. Go to original source...
    19. IVANOV, V.; KILIAN, L. 2005. A practitioner's guide to lag order selection for VAR impulse response analysis. Studies in nonlinear dynamics and econometrics. March 2005, vol. 9, no. 1, pp. 1-36. Go to original source...
    20. JARQUE, C.; BERA, A. 1987. A test for normality of observations and regression residuals. International Statistical Review. August 1987, vol. 55, no. 2, pp. 163-172. Go to original source...
    21. KILLIAN, L. 1998. Small-sample confidence intervals for impulse response functions. Review of Economics and Statistics. May 1998, vol. 80, no. 2, pp. 218-230. Go to original source...
    22. KIM, S.; ROUBINI, N. 2000. Exchange rate anomalies in the industrial countries: A solution with a structural VAR approach. Journal of Monetary Economics. June 2000, vol. 45, no. 3, pp. 561-586. Go to original source...
    23. KOOP G. 1992. Aggregate shocks and macroeconomic fluctuations: A Bayesian approach. Journal of Applied Econometrics. October/December 1992, vol. 7, no. 4, pp. 395-411. Go to original source...
    24. KOOP G.; PESARAN, M.; POTTER, S. 1996. Impulse Response analysis in nonlinear multivariate models. Journal of Econometrics. September 1996, vol. 74, no. 1, pp. 119-147. Go to original source...
    25. LJUNG, G.; BOX, G. 1978. On a measure of a lack of fit in time series models. Biometrica. August 1978, vol. 65, no. 2, pp. 297-303. Go to original source...
    26. LÜTKEPOHL, H. 1996. Handbook of matrices. New York : J. Wiley and Sons, 1996. ISBN 0-471-96688-6.
    27. LÜTKEPOHL, H. 2004. Vector autoregressive and vector correction models. In LÜTKEPOHL, H.; KRÄTZIG, M. (eds.) Applied Time Series Econometrics. Cambridge : Cambridge University Press, 2004, pp. 86-158. ISBN 978-0-52154787-1. Go to original source...
    28. LÜTKEPOHL, H. 2005. New introduction to multiple time series analysis. Berlin : Springer Verlag, 2005. ISBN 3-540-40172-5. Go to original source...
    29. MARTIN, V.; HURN, S.; HARRIS, D. 2013. Econometric modelling with time series. Cambridge : Cambridge University Press, 2013. ISBN: 978-0-52113981-6.
    30. PERRON, P 1989. The great crash, the oil price shock and the unit root hypothesis. Econometrica. November 1989, vol. 57, no. 6, pp. 1361-1401. Go to original source...
    31. PESARAN, M.; SHIN, Y 1998. Generalized impulse response analysis in linear multivariate models. Economic Letters. 1998, vol. 58, no. 1, pp. 17-29. Go to original source...
    32. RAVENNA, F 2007. Vector autoregressions and reduced form representations of DSGE models. Journal of Monetary Economics. October 2007, vol. 54, no. 7, pp. 2048-2064. Go to original source...
    33. SIMS, C. 1980. Macroeconomics and reality. Econometrica. January 1980, vol. 48, no. 1, pp. 1-48. Go to original source...
    34. SIMS, C.; STOCK, J.; WATSON, M. 1990. Inference in linear time series models with some unit roots. Econometrica. January 1990, vol. 58, no. 1, pp. 113-144. Go to original source...
    35. SCHWARZ, G. 1978. Estimating the dimension of a model. Annals of Statistics. March 1978, vol. 6, no. 2, pp. 461-464. Go to original source...
    36. TODA, H.; PHILLIPS, P 1991. Vector autoregression and causality. Econometrica. May 1991, vol. 61, no. 6, pp. 1367-1393. Go to original source...
    37. UHLIG, H. 2005. What are the effects of monetary policy on output? Results from an asymptotic identification procedure. Journal of Monetary Economics. March 2005, vol. 52, no. 2, pp. 381-419. Go to original source...
    38. ZELLNER, A. 1962. An efficient method of estimating seemingly unrelated regressions and tests of aggregation bias. Journal of the American Statistical Association. June 1962, vol. 57, no. 298, pp. 348-368. Go to original source...

    This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content