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484—Chapter 32. Vector Autoregression and Error Correction Models

If the restrictions are binding, EViews will report the LR statistic to test the binding restrictions. The LR statistic is reported if the degrees of freedom of the asymptotic x2 distribution is positive. Note that the restrictions can be binding even if they are not identifying, (e.g. when you impose restrictions on the adjustment coefficients but not on the cointegrating vector).

Options for Restricted Estimation

Estimation of the restricted cointegrating vectors b and adjustment coefficients a generally involves an iterative process. The VEC Restrictions tab provides iteration control for the maximum number of iterations and the convergence criterion. EViews estimates the restricted b and a using the switching algorithm as described in Boswijk (1995). Each step of the algorithm is guaranteed to increase the likelihood and the algorithm should eventually converge (though convergence may be to a local rather than a global optimum). You may need to increase the number of iterations in case you are having difficulty achieving convergence at the default settings.

Once you have filled the dialog, simply click OK to estimate the VEC. Estimation of a VEC model is carried out in two steps. In the first step, we estimate the cointegrating relations from the Johansen procedure as used in the cointegration test. We then construct the error correction terms from the estimated cointegrating relations and estimate a VAR in first differences including the error correction terms as regressors.

A Note on Version Compatibility

The following changes made in Version 4 may yield VAR results that do not match those reported from previous versions of EViews:

The estimated residual covariance matrix is now computed using the finite sample adjustment so the sum-of-squares is divided by T p where p is the number of esti-

mated coefficients in each VAR equation. Previous versions of EViews divided the sum-of-squares by T .

The standard errors for the cointegrating vector are now computed using the more general formula in Boswijk (1995), which also covers the restricted case.

References

Amisano, Gianni and Carlo Giannini (1997). Topics in Structural VAR Econometrics, 2nd ed, Berlin: Springer-Verlag.

Blanchard, Olivier and Danny Quah (1989). “The Dynamic Effects of Aggregate Demand and Aggregate Supply Disturbances,” American Economic Review, 79, 655-673.

Boswijk, H. Peter (1995). “Identifiability of Cointegrated Systems,” Technical Report, Tinbergen Institute.

References—485

Christiano, L. J., M. Eichenbaum, C. L. Evans (1999). “Monetary Policy Shocks: What Have We Learned and to What End?” Chapter 2 in J. B. Taylor and M. Woodford, (eds.), Handbook of Macroeconomics, Volume 1A, Amsterdam: Elsevier Science Publishers B.V.

Dickey, D.A. and W.A. Fuller (1979). “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, 74, 427–431.

Doornik, Jurgen A. (1995). “Testing General Restrictions on the Cointegrating Space,” manuscript.

Doornik, Jurgen A. and Henrik Hansen (1994). “An Omnibus Test for Univariate and Multivariate Normality,” manuscript.

Engle, Robert F. and C. W. J. Granger (1987). “Co-integration and Error Correction: Representation, Estimation, and Testing,” Econometrica, 55, 251–276.

Fisher, R. A. (1932). Statistical Methods for Research Workers, 4th Edition, Edinburgh: Oliver & Boyd.

Johansen, Søren (1991). “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models,” Econometrica, 59, 1551–1580.

Johansen, Søren (1995). Likelihood-based Inference in Cointegrated Vector Autoregressive Models, Oxford: Oxford University Press.

Johansen, Søren and Katarina Juselius (1990). “Maximum Likelihood Estimation and Inferences on Coin- tegration—with applications to the demand for money,” Oxford Bulletin of Economics and Statistics, 52, 169–210.

Kao, C. (1999). “Spurious Regression and Residual-Based Tests for Cointegration in Panel Data,” Journal of Econometrics, 90, 1–44.

Kelejian, H. H. (1982). “An Extension of a Standard Test for Heteroskedasticity to a Systems Framework,”

Journal of Econometrics, 20, 325-333.

Lütkepohl, Helmut (1991). Introduction to Multiple Time Series Analysis, New York: Springer-Verlag.

Maddala, G. S. and S. Wu (1999). “A Comparative Study of Unit Root Tests with Panel Data and A New Simple Test,” Oxford Bulletin of Economics and Statistics, 61, 631–52.

MacKinnon, James G., Alfred A. Haug, and Leo Michelis (1999), “Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration,” Journal of Applied Econometrics, 14, 563-577.

Newey, Whitney and Kenneth West (1994). “Automatic Lag Selection in Covariance Matrix Estimation,”

Review of Economic Studies, 61, 631-653.

Osterwald-Lenum, Michael (1992). “A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics,” Oxford Bulletin of Economics and Statistics, 54, 461–472.

Pedroni, P. (1999). “Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors,” Oxford Bulletin of Economics and Statistics, 61, 653–70.

Pedroni, P. (2004). “Panel Cointegration; Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis,” Econometric Theory, 20, 597–625.

Pesaran, M. Hashem and Yongcheol Shin (1998). “Impulse Response Analysis in Linear Multivariate Models,” Economics Letters, 58, 17-29.

Phillips, P.C.B. and P. Perron (1988). “Testing for a Unit Root in Time Series Regression,” Biometrika, 75, 335–346.

Said, Said E. and David A. Dickey (1984). “Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order,” Biometrika, 71, 599–607.

Sims, Chris (1980). “Macroeconomics and Reality,” Econometrica, 48, 1-48.

486—Chapter 32. Vector Autoregression and Error Correction Models

Urzua, Carlos M. (1997). “Omnibus Tests for Multivariate Normality Based on a Class of Maximum Entropy Distributions,” in Advances in Econometrics, Volume 12, Greenwich, Conn.: JAI Press, 341358.

White, Halbert (1980).“A Heteroskedasticity-Consistent Covariance Matrix and a Direct Test for Heteroskedasticity,” Econometrica, 48, 817–838.

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