[Gretl-users] VEC Question

Ricardo Gonçalves Silva ricardogs at terra.com.br
Mon Jun 1 10:56:32 EDT 2009


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 at gmail.com>
Sent: Sunday, May 31, 2009 7:59 PM
To: "Gretl list" <gretl-users at 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 at 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 at univpm.it>
>> Sent: Sunday, May 31, 2009 8:46 AM
>> To: "Gretl list" <gretl-users at 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 at univpm.it
>>> http://www.econ.univpm.it/lucchetti
>>
>>
>>
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>>
>>
>>
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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 at tcd.ie
> mailto:frainj at gmail.com
>
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