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st: about dummy variables


From   Tae Hun Kim <thkim91@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: about dummy variables
Date   Wed, 16 Mar 2005 17:20:46 -0600

Hello.
I would be greatfull if someone helps me to understand dummy variables.

For example,
Y= a+b*X+c*dum+d*(X*dum)+e
where Y : income,  X : education(years),  dum=dummy variable (dum=1 if
male, dum=0 if female)

If I estimate this equation using OLS, recalulated coefficents are the
same regardless of whether dum=1 if male (0 otherwise) or  dum=1 if
female(0 otherwise).
i.e.  if I define a dummy variable as dum=1 if male, o otherwise 
     male(1) : E(Y)= (a+c)+(b+d)X,  female(1) : E(Y)=a+bX
      if I define a dummy variable as dum=1 if female, o otherwise 
     male(2) : E(Y)=a+bX,              female(2) : E(Y)= (a+c)+(b+d)X 
=>the coefficients of male(1) and male(2) equation are the same.  

(Question)
1. But when I estimate this equation using GMM or IV, the coefficients
of male(1) and male(2) equation are not the same. Why?
2. If the coefficient are different, what is the criteria to define a
dummy variable(male=1 or female=1) ?

Thanks in advance
TaeHun Kim
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