Re: Re: st: robust estimation SUREG

[Jorge Eduardo Pérez Pérez <perez.jorge@ur.edu.co>]

Not really, it was only an idea. You might find this reference useful though:

Robust Estimation of the SUR Model
Martin Bilodeau and Pierre Duchesne
The Canadian Journal of Statistics / La Revue Canadienne de Statistique
Vol. 28, No. 2 (Jun., 2000), pp. 277-288

http://www.jstor.org/pss/3315978


_______________________
Jorge Eduardo Pérez Pérez




On Mon, May 30, 2011 at 3:14 PM, pierrick.jan@art.admin.ch
<pierrick.jan@art.admin.ch> wrote:
> Dear M. Pérez,
>
> As I have compared a manually computed SUR with
> a SUR performed using the geometric average of the weights
> generated when estimating independently each equation
> using robust regression, I have been looking for literature
> using (or advocating for the use) of a geometric average of the weights.
> However I could not find any literature related to this issue.
> Would you have any references?
>
> Thanks in advance for your answer!
>
> Best regards from Switzerland!
>
> ------------------------------
>
> Date: Sun, 29 May 2011 18:41:18 -0400
> From: =?ISO-8859-1?Q?Jorge_Eduardo_P=E9rez_P=E9rez?= <perez.jorge@ur.edu.co>
> Subject: Re: Re: st: robust estimation SUREG,
>
> Very clever solution. It is not clear for me how to adjust the
> standard errors in the final step though. Maybe someone else in the
> list has ideas.
>
> _______________________
> Jorge Eduardo Pérez Pérez
>
>
> On Sun, May 29, 2011 at 2:14 PM, pierrick.jan@art.admin.ch
> <pierrick.jan@art.admin.ch> wrote:
>> Dear M. Pérez,
>>
>> Thanks a lot for your prompt reply and your very helpful suggestions and the corresponding stata code!
>> As you mentioned the rreg does not have any "hascons" option, which is critical as the constant
>> of the first model is dropped (due to perfect multicollinearity). To circumvent this problem, I first of all
>> performed a robust regression for each equation taken independently.
>> Then I generated the weights in a matrix and used these weights in the final step.
>> The adapted program is shown below (the parts I added are marked with an @ at the end).
>>
>> Regards,
>>
>> Pierrick Jan
>>
>> - -- Begin code ----
>>
>> sysuse auto, clear
>> * Robust regression and weights generation @
>> rreg price weight trunk, genwt (w1) @
>> rreg length trunk, genwt (w2) @
>> * Benchmark
>> sureg (price weight trunk) (length trunk)
>> est store sur
>> * Obtain errors
>> reg price weight trunk
>> predict e1, resid
>> reg length trunk
>> predict e2, resid
>> * Obtain covariance
>> cor e1 e2, cov
>> mat s = r(C)
>> mat i = I(_N)
>> mat v = s#i
>> * Generating a weights vector*@
>> mkmat w1, matrix (W1) @
>> mkmat w2, matrix (W2) @
>> matrix W = W1\W2 @
>> * Stack dependent
>> gen zero=0
>> stack price weight trunk zero length zero zero trunk, into(y weight
>> trunk trunk2) clear
>> gen cons1 =(_stack==1)
>> gen cons2 =(_stack==2)
>> * Transform variables
>> mkmat weight trunk cons1 trunk2 cons2, matrix(X)
>> drop weight trunk cons1 trunk2 cons2
>> matrix Xa=(cholesky(inv(v))'*X)
>> svmat Xa, names(col)
>> mkmat y
>> drop y
>> matrix ya=(cholesky(inv(v))'*y)
>> svmat ya, names(col)
>> * Introducing the weights of the robust regressions in the dataset @
>> svmat W, names(wrreg) @
>> reg y weight trunk cons1 trunk2 cons2, hascons
>> * Which is same as SUR, se needs adjustment
>> est replay sur
>> * Now run robust instead, does not have nocons option. Would have to
>> modify the call to -reg- in rreg.ado
>> rreg y weight trunk cons1 trunk2 cons2
>> * Alternative: perform a regression using the reg command and introduce the weights of the initial robust regressions @
>> reg y weight trunk cons1 trunk2 cons2 [aweight = wrreg], hascons @
>>
>> - -- End code ----
>> _______________________
>>
>> -----------------------------
>>
>> Date: Sat, 28 May 2011 14:19:49 -0400
>> From: =?ISO-8859-1?Q?Jorge_Eduardo_P=E9rez_P=E9rez?= <perez.jorge@ur.edu.co>
>> Subject: Re: st: robust estimation SUREG
>>
>> A geometric mean might be more appropiate, so the final weight is zero
>> if any of them is zero.
>>
>> An alternative is to run the SUR manually, stacking the variables,
>> correcting for the error covariance and estimating with -reg- at the
>> end. In this case, you could do the last step with -rreg- instead of
>> - -reg-. -rreg- does not allow a -nocons- option, so you would have to
>> modify its call to -reg-. See the code below.
>>
>> - -- Begin code ----
>>
>> sysuse auto, clear
>> * Benchmark
>> sureg (price weight trunk) (length trunk)
>> est store sur
>> * Obtain errors
>> reg price weight trunk
>> predict e1, resid
>> reg length trunk
>> predict e2, resid
>> * Obtain covariance
>> cor e1 e2, cov
>> mat s = r(C)
>> mat i = I(_N)
>> mat v = s#i
>> * Stack dependent
>> gen zero=0
>> stack price weight trunk zero length zero zero trunk, into(y weight
>> trunk trunk2) clear
>> gen cons1 =(_stack==1)
>> gen cons2 =(_stack==2)
>> * Transform variables
>> mkmat weight trunk cons1 trunk2 cons2, matrix(X)
>> drop weight trunk cons1 trunk2 cons2
>> matrix Xa=(cholesky(inv(v))'*X)
>> svmat Xa, names(col)
>> mkmat y
>> drop y
>> matrix ya=(cholesky(inv(v))'*y)
>> svmat ya, names(col)
>> reg y weight trunk cons1 trunk2 cons2, hascons
>> * Which is same as SUR, se needs adjustment
>> est replay sur
>> * Now run robust instead, does not have nocons option. Would have to
>> modify the call to -reg- in rreg.ado
>> rreg y weight trunk cons1 trunk2 cons2
>>
>> - -- End code ----
>> _______________________
>> Jorge Eduardo Pérez Pérez
>>
>>
>>
>>
>> On Sat, May 28, 2011 at 9:27 AM, pierrick.jan@art.admin.ch
>> <pierrick.jan@art.admin.ch> wrote:
>>> Thanks a lot for your answer!! I have also tried to perform a SUREG by introducing
>>> the three sets of weights generated by the rreg command but I realized that it was not
>>> possible. As you mention I would have to combine them somehow. However it is for me
>>> not clear how to combine them. An arithmetic average is definitely not appropriate. I was
>>> wondering if it would not be more appropriate to proceed as described hereafter. In a first step,
>>> on the basis of each robust regression performed, I determine outliers (i.e. observations under a
>>> certain threshold in terms of weight height). In a second step I exclude these outliers from the data set
>>> and  then perform the SUR regression. I am however not really satisfied with this solution.
>>>
>>> Pierrick Jan
>>> __________________________________________________________________________
>>>
>>> Date: Fri, 27 May 2011 12:47:38 -0400
>>> From: =?ISO-8859-1?Q?Jorge_Eduardo_P=E9rez_P=E9rez?= <perez.jorge@ur.edu.co>
>>> Subject: Re: st: robust estimation SUREG
>>>
>>> You could use the -genwt- option in -rreg- to generate the weights
>>> used in the robust regression, then use those weights in -sureg-. You
>>> will have three sets of weights from your first three regressions, and
>>> - -sureg- will only allow a set of weights, so you would have to combine
>>> them somehow.
>>> _______________________
>>> Jorge Eduardo Pérez Pérez
>>
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