Abstract
Vector autoregressive (VAR) models are capable of capturing the dynamic structure of many time series variables. Impulse response functions are typically used to investigate the relationships between the variables included in such models. In this context the relevant impulses or innovations or shocks to be traced out in an impulse response analysis have to be specified by imposing appropriate identifying restrictions. Taking into account the cointegration structure of the variables offers interesting possibilities for imposing identifying restrictions. Therefore VAR models which explicitly take into account the cointegration structure of the variables, so-called vector error correction models, are considered. Specification, estimation and validation of reduced form vector error correction models is briefly outlined and imposing structural short- and long-run restrictions within these models is discussed.
I thank an anonymous reader for comments on an earlier draft of this paper that helped me to improve the exposition.
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References
Amisano, G., Giannini, C. (1997). Topics in Structural VAR Econometrics. 2nd ed., Springer, Berlin.
Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis. John Wiley, New York.
Benkwitz, A., Lütkepohl, H., Neumann, M. (2000). Problems related to bootstrapping impulse responses of autoregressive processes. Econometric Reviews19 69–103.
Benkwitz, A., Lütkepohl, H., Wolters, J. (2001). Comparison of bootstrap confidence intervals for impulse responses of German monetary systems. Macro economic Dynamics5 81–100.
Boswijk, H. P. (1996). Testing identifiability of cointegrating vectors. Journal of Business & Economic Statistics14 153–160.
Breitung, J., Brüggemann, R., Lütkepohl, H. (2004). Structural vector autoregressive modeling and impulse responses. In Applied Time Series Econometrics (H. Lütkepohl, M. Krätzig, eds.), pp. 159–196, Cambridge University Press, Cambridge.
Engle, R. F., Granger, C.W. J. (1987). Cointegration and error correction: Representation, estimation and testing. Econometrica55 251–276.
Fisher, L. A., Huh, H. (1999). Weak exogeneity and long-run and contemporaneous identifying restrictions in VEC models. Economics Letters63 159–165.
Gonzalo, J., Ng, S. (2001). A systematic framework for analyzing the dynamic effects of permanent and transitory shocks. Journal of Economic Dynamics & Control25 1527–1546.
Granger, C. W. J. (1981). Some properties of time series data and their use in econometric model specification. Journal of Econometrics16 121–130.
Granger, C. W. J., Newbold, P. (1974). Spurious regressions in eonometrics. Journal of Econometrics2 111–120.
Hubrich, K., Lütkepohl, H., Saikkonen, P. (2001). A review of systems cointegration tests. Econometric Reviews20 247–318.
Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control12 231–254.
Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica59 1551–1581.
Johansen, S. (1995). Likelihood-based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press, Oxford.
Kilian, L. (1998). Small-sample confidence intervals for impulse response functions. Review of Economics and Statistics80 218–230.
King, R. G., Plosser, C. I., Stock, J.H., Watson, M.W. (1991). Stochastic trends and economic fluctuations. American Economic Review81 819–840.
Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer, Berlin.
Lütkepohl, H., Krätzig, M. (eds.) (2004). Applied Time Series Econometrics. Cambridge University Press, Cambridge.
Saikkonen, P. (1999). Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes. Econometric Reviews18 235–257.
Sims, C. A. (1980). Macroeconomics and reality. Econometrica48 1–48.
Vlaar, P. J. G. (2004). On the asymptotic distribution of impulse response functions with long-run restrictions. Econometric Theory20 891–903.
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Lütkepohl, H. (2006). Structural Vector Autoregressive Analysis for Cointegrated Variables. In: Hübler, O., Frohn, J. (eds) Modern Econometric Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32693-6_6
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DOI: https://doi.org/10.1007/3-540-32693-6_6
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