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If the Johansen tests say that there are 3 cointegrating relationships (All 5 tests) for a 4 variable system, is it allowed/accepted to use less than 3 cointegrating equations for the VECM? Thanks!

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A VECM with not all cointegrating relationships accounted for will suffer from omitted variable bias; one or more error correction terms will be missing from the model's equations. This is similar to the case of not including the error correction term in a bivariate VECM, turning it into a VAR on first differences.

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  • $\begingroup$ Hi Richard, Thanks for your response. In addition to this, one of the problems in my dataset is that 3 of my variables are I(1) whereas the last variable is I(2) - how may this affect cointegration? $\endgroup$
    – John
    Mar 27, 2020 at 13:42
  • $\begingroup$ @John, there may only be cointegration between the three variables and the first difference of the fourth one: $x_1, x_2, x_3, \Delta x_4$. $x_4$ by itself will not be cointegrated with any of $x_1, x_2, x_3$ or their linear combination. $\endgroup$ Mar 27, 2020 at 13:57
  • $\begingroup$ Does this mean that the Johansen test would be run on x1, x2, x3, ∆x4 and then the subsequent VECM would include these four variables and omit x4? $\endgroup$
    – John
    Mar 27, 2020 at 15:49
  • $\begingroup$ @John, yes, indeed. $\endgroup$ Mar 27, 2020 at 16:06
  • $\begingroup$ Continuing on this line of thought, the lag length which minimises SIC for x1, x2, x3, ∆x4 is d - should the Johansen test use d or (d-1)lags? $\endgroup$
    – John
    Mar 28, 2020 at 9:19

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