dear,
how to conduct the VEC Granger Causality Test/ Block Exogeneity Wald Test?

Hi, I'm interpreting your question as being about strong exogeneity of, say, x with respect to y, such that no (lagged) terms involving x should appear in the equation with y (or \Delta y) on the LHS.

I don't think this is natively available in the VECM context, and probably for good reasons. Quoting Kilian & Lütkepohl (the SVAR book): "Granger causality may be assessed within the VEC framework [...] but the asymptotic distributions depend on nuisance parameters. [...] an easy cure for this problem is to add a further lag to the VAR process and perform the test on the first p lags of the lag-augmented VAR." (p. 49)

So I would recommend to just run a single-equation OLS regression for y with p+1 lags of all involved variables (x as well as other conditioning variables Z), and then perform an omission restriction on the lags 1...p of x.

Of course this test will in practice be sensitive to the lag choice p, but that is a general problem not specific to this question.

cheers

sven