VEC estimation: allow restrictions on the constant term?

[maxchen]

the "June 22, 2011" patch says : " Improvement to restricted VEC estimation to allow restrictions on the constant term."
so I try

Code: Select all

%ex7 = "\Example Files\EV7 Manual Data\" %ch32 = "Chapter 32 - Vector Autoregression and Error Correction Models" %wf = @evpath + %ex7 +%ch32 +"\var1.wf1" wfopen %wf var vec01.ec(c,1) 1 2 ff tb3 vec01.cleartext(coint) vec01.append(coint) b(1,1) = 1 vec01.append(coint) b(1,3) = 0 'error freeze(tb01r) vec01.ec(c,1,restrict) 1 2 ff tb3

hmm, it pops up with the following error
restriction syntax error: 'B(1,3)' is not a valid coefficient index ....
So, can I impose restrictions on the constant term in co-integrating Eq? note that if I use ec(a,1,restrict)， the intercept term in CE and each Eq all disappear.

[EViews Gareth]

Looks like that change might not have made it into the patch. I'll investigate tomorrow.

[EViews Gareth]

What restrictions are allowed on the deterministic terms depend on the ‘Deterministic Trend Specification’ choice.

If you choose ‘(3) Intercept (no trend) in CE and VAR’ the constant term is concentrated out before the cointegrating vector is estimated. It is not identified how much of the constant is ‘inside’ the cointegrating vector and how much is ‘outside’. EViews arbitrarily puts a constant inside the cointegrating vector (to make the sample mean of the cointegrating vector equal to zero?) and puts the rest outside.

At any rate, with option (3) a restriction on the constant is always non-binding because the constant is not identified. The error message isn’t all that obvious though.

So only option (2) and (4) have an extra term that can be restricted. In (2) it is the constant, in (4) it is the coefficient of the linear trend.

So, changing your program to be:

Code: Select all

%ex7 = "\Example Files\EV7 Manual Data\" %ch32 = "Chapter 32 - Vector Autoregression and Error Correction Models" %wf = @evpath + %ex7 +%ch32 +"\var1.wf1" wfopen %wf var vec01 vec01.cleartext(coint) vec01.append(coint) b(1,1) = 1 vec01.append(coint) b(1,3) = 0 'error freeze(tb01r) vec01.ec(b,1,restrict) 1 2 ff tb3

Appears to work (I changed the EC option from a C to a B).

[maxchen]

thanks for your kind explanation.

according to the following paper
Hansen, Peter Reinhard, 2005. Granger's Representation Theorem: A Closed-form Expression for I(1) Processes. Econometrics Journal, 8:23–38

I seems in situation C, the constant inside and outside is identified. The part inside the CE is (A'A)^(-1)*A'c, and the outside part is (C'C)^(-1)*C'c, where "c" is the constant in VAR/VEC form, and matrix C is the orthogonal complement of matrix A. For we have the identity
A(A'A)^(-1)*A'+C(C'C)^(-1)*C'=I