How can I define this restriction in R 545 observations of young working males in the U.S. with some
professional and personal characteristics Variables are as follows:
logwage: logarithm of per hour wage rate;
union: dummy variable, 1 if union member;
mar: dummy variable, 1 if married;
school: year of schooling;
exper: experience in years;
black: dummy variable, 1 if black;
hisp: dummy variable, 1 if Hispanic.
logwagei = 0 + school + exper + union + mar + black + hisp + e
We would like to explain log wages from other variables using the model below:
We extend the model by allowing for the possibility that black union members benefit more
from union membership than non-black union members. How can I Estimate this extended model and
test this hypothesis?

All you need to do is add another variable called an interaction term, which is the product between union and black, called, e.g. union*black, and if its regression coefficient value is positive and it's significant (p-value<0.05), then black union members benefit more than non-union blacks.  In fact, the average log(wage) for union blacks will be equal to $\beta_0 + \beta_{black} + \beta_{union*black}$, whereas the average loq(wage) for non-union blacks will simply be $\beta_0 + \beta_{black}$.
