A dummy variable takes on only the values 0 and 1. It is used for categorical variables. Let D1 and D2 be vectors of 1’s and 0’s, with the i th element of D1 equaling 1 and that of D2 equaling 0 if the person is a man, and the reverse if the person is a woman. Suppose that there are n1 men and n2 women in the sample. Consider fitting the following three equations by OLS Y Æ ¹ÅD1®1 ÅD2®2 Åe (3.52)

Y ÆD1®1 ÅD2®2 Åe (3.53)

Y Æ ¹ÅD1ÁÅe (3.54)

Can all three equations (3.52), (3.53), and (3.54) be estimated by OLS? Explain if not.

(a) Compare regressions (3.53) and (3.54). Is one more general than the other? Explain the relationship between the parameters in (3.53) and (3.54).

(b) Compute 10 nD1 and 10 nD2, where 1n is an n £1 vector of ones.