VECM Causality 2 CIVs

[victor]

Hello,

I am trying to do causality test for VECM. Using VECMCAUSE.RPF as an example, let's say we have 5 variables: tb3mo tb6mo A B C
after cointegration test I find 2 cointegrating vectors.
following description in VECMCAUSE.RPF

(1) I estimate cointegrating vectors z1 and z2
(2) I run

linreg d3mo

# z1{1} z2{1} d3mo{1 to nlags-1} d6mo{1 to nlags-1}.... C{1 to nlags-1}

(3) Is this a right way for short run causality?

exclude(title="Test for 6MO causing 3MO")

# z{1} z2{1} d6mo{1 to nlags-1}

(4) Is this a right way for long-run causality?

exclude(title="Test for 6MO long-run causing 3MO")

# z{1} z2{1}


5) Continuing this way, I want to test C cause 3MO

Should I do ?
exclude(title="Test for C causing 3MO")

# z{1} z2{1} C{1 to nlags-1}

exclude(title="Test for C long-run causing 3MO")

# z{1} z2{1}

But now long-run for 6MO and C are same?

Please help.

[TomDoan]

Hello,

I am trying to do causality test for VECM. Using VECMCAUSE.RPF as an example, let's say we have 5 variables: tb3mo tb6mo A B C
after cointegration test I find 2 cointegrating vectors.
following description in VECMCAUSE.RPF

(1) I estimate cointegrating vectors z1 and z2
(2) I run

linreg d3mo

# z1{1} z2{1} d3mo{1 to nlags-1} d6mo{1 to nlags-1}.... C{1 to nlags-1}

(3) Is this a right way for short run causality?

exclude(title="Test for 6MO causing 3MO")

# z{1} z2{1} d6mo{1 to nlags-1}

(4) Is this a right way for long-run causality?

exclude(title="Test for 6MO long-run causing 3MO")

# z{1} z2{1}


5) Continuing this way, I want to test C cause 3MO

Should I do ?
exclude(title="Test for C causing 3MO")

# z{1} z2{1} C{1 to nlags-1}

exclude(title="Test for C long-run causing 3MO")

# z{1} z2{1}

But now long-run for 6MO and C are same?

Please help.

This all gets very complicated when you have more than two variables (which is true even of causality in a regular VAR) and even more complicated when you have multiple cointegrating vectors since the individual cointegrating vectors aren't statistically identified. If variable X doesn't enter one of the cointegrating vectors, then you can have a non-zero alpha on that without it meaning that X long-run causes a target variable. You can also have non-causality even with both alpha's being non-zero if the cointegrating vectors have the correct structure. Combine that with the fact that excluding one variable out of five doesn't really tell you anything very interesting in the first place (as described in the link above) means that this just really isn't a statistically useful exercise.

[victor]

Thank you so much for your detailed explanation.