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st: Interpreting a regression equation...


From   John Litfiba <cariboupad@gmx.fr>
To   statalist@hsphsun2.harvard.edu
Subject   st: Interpreting a regression equation...
Date   Thu, 22 Dec 2011 05:44:46 +0100

Dear Statalist,

I have a very simple question, but I would like to be sure...

I have a panel database, with repeated time values within the panel :
that is for example, individual i has many outcome values on the same
day t.

That is, I cannot really write the model as

(1)  Yits= constant +Alpha*Zi + beta* Xtc + gamma*BEFORE +eits

where Y is a financial return and X is the regressor which depends on
the stock S, Z is a regressor which depends on individual i, s is the
stock, e is the random noise and i indicates individual i, and BEFORE
is a dummy which equals 1 if day >01/01/2010 for instance

I cannot write it like that because if t represents a day (which is
the smallest time unit that I can have) then for the same day it can
happen that the same individual i trade on the same stock s
However, Stata does not understand the meaning of t (day), so my
question would be : im I correct to write the following Stata command
to estimate my model ?

regress Y Z X BEFORE, cluster(id)

And is (1)  conceptually equivalent to

(2)  Yins= constant +Alpha*Zi + beta* Xnc + gamma*BEFORE +enis

where n simply indicates the nth line in my database ? Of course the
dummy "before" willl still separate between those trades before and
after 01/01/2010

Moreover, let assume that now I run a fixed effects estimation,
indicating that id is the clustering variable for standard errors :

 xtset id
xtreg Y Z X BEFORE,  fe cluster(id)

In my model my errors have also a s (stock) subscript mainly because
one of the regressors (X) depend on the particular stock traded  on
day t...
what is the interpretation of the correction that I make with such
3way standands errors?
Standards errors are corrected for any correlation wthin an individual
... However if I fix a stock s, then (eits) are independent for any i
and any t ?

I hope that I have been clear enough...

Many, many thanks for your help

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