Cointegration

 

When this box is checked, the Bartlett correction factors given in Corollary 2 of Johansen (2002b) are applied to the trace statistics. For this option to be used, SVAR requires that you don't have any exogenous stochastic variables or any deterministic variables other than constant, trend, or seasonal dummies. Please note that for large models, this computation can take some time.

 

By default, SVAR uses a simple criterion for restricted β convergence, namely, the relative change in the log-likelihood function. By checking this option, the software will use the gradient for the free parameters of β as measure of convergence.

 

When this option is selected, all exogenous I(0) variables will be accumulated and moved to the group of exogenous I(1) variables. This allows for inference on the cointegration rank in partial systems without nuisance parameters introduced through the exogenous I(0) variables; see Rahbek and Mosconi (1999) for details.

 

This allows SVAR to find a higher maximum for the likelihood function than the default, i.e. to first estimate β under restrictions and then to estimate α, the C or the B matrix under the restrictions specified for these parameters. The alternative method will continue from the last step in the default estimation by re-estimating β given the new values for the other parameters, conditional on the new value for β again estimate the other parameters, and continue in this fashion until convergence has been achieved.

 

When check marked SVAR normalizes the i:th cointegration vector on the i:th variable. By default SVAR does not normalize unrestricted β. In that case, the variance of the corrected relations are normalized to have unit variance. The choice for this option does not have any effect when β is (generically) identified; see Johansen (1995).

 

When check marked SVAR can decompose parameters on the constant and linear trend terms (when present) given that they are unrestricted. Hence, the option does not affect models with a restricted constant. The decompositions are based on models without additional deterministic terms other than centered seasonal dummies and no exogenous I(1) or I(0) variables. For a model with an unrestricted constant, the decomposition of the parameter on the constant is into one part which equals the mean of the cointegration relations, and another part which equals the mean of the first differences.

 

The weak exogeneity tests with respect to α and β are computed and written to output when this option is selected.

 

Tests for common cycles are computed when the number of cointegration relations is less than the number of endogenous variables for reduced form models; see, e.g, Vahid and Engle (1993). Tests for common cycles in structural form models have not yet been implemented.

 

Calculates LR-tests that a variable (endogenous, exogenous I(1), and any deterministic variable restricted to the cointegration space) can be excluded from the cointegration space (zero coefficients in a row of β), and LR-tests of the null hypothesis that an endogenous variable is stationary. For models with a constant or a linear trend that is restricted to the cointegration space, the stationarity test allows the coefficient on that deterministic variable to be nonzero for the restricted cointegration vector. Hence, zero restrictions are only imposed on the other endogenous variables and all exogenous I(1) variables; see Johansen (1996, Chapter 7.2) for details on the algorithms for estimating β under (i) the same restrictions on all β vectors, (ii) some known β vectors, and (iii) individual restrictions on the β vectors.

 

Allows you to choose whether a critical value for a particular quantile or a p-value should be shown with the trace tests (see Cointegration Rank Tests). This option requires that you don't use a mixture of I(0) and I(1) exogenous variables and that you don't use any deterministic variables other than a constant, a linear trend, or centered seasonal dummies. The only exception to this is when all your exogenous variables are I(1) and the model has an unrestricted constant or an unrestricted linear trend. In those cases the limiting distribution of the trace test depends on a nuisance parameter. For the I(0) exogenous regressors cases, the asymptotic distribution is approximated with a gamma distribution and based on estimates of the nuisance parameters as discussed by, e.g., Boswijk and Doornik (2005).