From Tae Hun Kim 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) ?