Hi John,
This also was my intuition. I estimating the model as:
D(y1) = A(1,1)*(B(1,1)*y1(-1) + B(1,2)*y2(-1)) + C(1,1)*D(y1(-1)) +
C(1,2)*D(y1(-12)) + C(1,3)*D(y2(-1)) + C(1,4)*D(y2(-12))
D(y2) = A(2,1)*(B(1,1)*y1(-1) + B(1,2)*y1(-1)) + C(2,1)*D(y1(-1)) +
C(2,2)*D(y1(-12)) + C(2,3)*D(y2(-1)) + C(2,4)*D(y2(-12))
and doing exactly as you describe. The results appears to be consistent, but
I already don't know how I will prove the results.
Rick
--------------------------------------------------
From: "John C Frain" <frainj(a)gmail.com>
Sent: Sunday, May 31, 2009 7:59 PM
To: "Gretl list" <gretl-users(a)lists.wfu.edu>
Subject: Re: [Gretl-users] VEC Question
It may be possible to do maximum likelihodd estimation by a
variation
of the Johansen methodology. In the general case with no exclusions
one starts with two auxiliary regressions.
1. \Delta y_t on \Delta y_{t-1} ... \Delta y_{t-11}
2. y_{t-1}t on \Delta y_{t-1} ... \Delta y_{t-11}
In your case the auxiliary regressions will be on the sum of the
lagged first differences. Calculate the residuals from these
regressions and proceeding as in Johansen (See Hamilton pages 636 et
seq.). As far as I can tell this should give you your ML estimates.
I suspect that many of the Johansen tests may remain valid but you
will need a bit of work to prove this.
I would be interested to hear if anyone else has established some
results (confirming or contradicting my intuition).
Best regards
John
2009/5/31 Ricardo Gonçalves Silva <ricardogs(a)terra.com.br>:
> Hi Jack,
> t
> Very nice explanation. I'm sure this point is obscure for most of the
> applied econometricians..
> I really understand the problem but this is exactly the kind of model I
> wa
> to explore.
> I'm now working in writing a general procedure for this kind of
> estimation
> using Gauss.
> If it's work nicely I believe I can translaansente the code to GRETL and
> post it.
>ition
> Cheers
>
> Rick.two auxiliary regressions
>
> --------------------------------------------------
> From: "Riccardo (Jack) Lucchetti" <r.lucchetti(a)univpm.it>
> Sent: Sunday, May 31, 2009 8:46 AM
> To: "Gretl list" <gretl-users(a)lists.wfu.edu>
> Subject: Re: [Gretl-users] VEC Question
>
>> On Fri, 29 May 2009, Ricardo Gonçalves Silva wrote:
>>
>>> Hi Sven,
>>>
>>> Nice. I need the estimates and the impulses responses.
>>>
>>> Thanks
>>>
>>> Ricardo
>>
>> I'm sorry if this is obvious to you, but since it isn't obvious in
>> general
>> I thought I'd post it to the list. The difficulty with this from an
>> econometric viewpoint is that if you want to estimate a model like
>>
>> \Delta y_t = \alpha \beta' y_{t-1} + \Gamma y_{t-12} + u_t
>>
>> the problem of estimating \beta via ML is not trivial: the VAR
>> representation of the above is a 13-order VAR which not only contains
>> "holes", but also other constraints:
>>
>> y_t = A_1 y_{t-1} + A_2 y_{t-2} + ... + A_{13} y_{t-13} + u_t
>>
>> where
>>
>> (1) A_1 = I + alpha \beta'
>> (2) A_{i} = 0 for i=2..11
>> (3) A_{12} = -A_{13}
>>
>> The theoretical construction for the Johansen estimator assumes that the
>> only constraint to the VAR representation is (1) (ok, deterministic
>> terms
>> aside), and the code is written on that basis.
>>
>> Riccardo (Jack) Lucchetti
>> Dipartimento di Economia
>> Università Politecnica delle Marche
>>
>> r.lucchetti(a)univpm.it
>>
http://www.econ.univpm.it/lucchetti
>
>
>
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--
John C Frain
Economics Department
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.html
mailto:frainj@tcd.ie
mailto:frainj@gmail.com
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