Re: st: RE: how do we jointly test coefficients (fuller specification) from diff

[Arthur Boman <boman@berkeley.edu>]

David Urbain and Jorge,

I have done further research.  All of your comments were helpful.  Thank
you.  I think all four ways work.

It is true that the specification below contains truly unrelated (not just
seemingly unrelated) regressions.  However, sureg (exactly as proposed by
Jorge) still works, it just saves much time in correcting for standard
errors of the 25 different tests.  It doesnt pick up any added benefit by
relating the regressions, but it does the calc quickly and easily. 
Liklihood as David mentioned works fine as well.  

All the Best,
Arthur


On Tue, 19 Mar 2013 12:41:25 -0700, Arthur Boman <boman@berkeley.edu>
wrote:
> David (Jorge can check first part and think if it jives with the code he
> sent),
> ____
> 
> Thank you.  This got me thinking more about the model.  Here is my
model:
> 
> y1= a*x1 + f*x2 + e1
> y2= b*x1 + g*x2 + e2  
> y3= c*x1 + h*x2 + e3
>  
> e1, e2, e3 are independent, normal, and mean-zero.  They have different
> variances, but it would be okay to assume the variances do not change
with
> time.
> 
> Then the null is a=b=c=0.  
> 
> ( When I say independent I mean both cross-sectionally (e1 at any time
is
> independent of e2 at any time) and independent across time as well, no
> serial correlation.  
> 
> Constant variance across time is okay, i.e. not heteroscedastic. If it
is
> easy to allow heteroscedasticity and correct for this, then okay. )
> 
> ____
> 
> Bonferroni:  Yes I had thought of this but I am not sure whether it is
> accurate.  It seems like it should not be far off, or maybe it is
accurate.
> What I wondered is whether the x's can be considered predetermined for
> subsequent models, as they are the same for all.  I also wonder if I did
> the tests separately and allowed for heteroscedasticity, would
Bonferroni
> work same way?
>  
> ____
> 
> The fact that "3" is actually 25 makes all of this more "interesting."
> 
> ( -:
> 
> ____
> 
> Don't worry about the priced factor thing.  Testing if coeff on x1's are
> all zero with the other x's in there.  
> 
> Yes, there are x2, x3, and x4.
> 
> ____
> 
> Sounds complicated:
> 
>> The suggestion of stacking y1, y2, and y3 into a column vector seems
>> to be headed toward a multiple regression (in which the "design"
>> matrix also stacks x1 and x2 for each of the y's) and then perhaps a
>> likelihood-ratio test.  It may be appropriate (or necessary) to take
>> into account correlation among y1, y2, and y3; that would turn the
>> analysis into a multivariate regression with (y1, y2, y3) as the
>> vector dependent variable.  Even without correlation, y1, y2, and y3
>> may not have the same variance.
>> 
>> The fact that "3" is actually 25 makes all of this more "interesting."
>>  And maybe your asset-pricing model involves other factors besides x2.
>> 
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