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


From   Arthur Boman <boman@berkeley.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: how do we jointly test coefficients (fuller specification) from diff
Date   Tue, 19 Mar 2013 12:41:25 -0700

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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