Unformatted text preview: 13.6 since there are the same number of men and women in
the sample.
(e) This equation cannot be estimated due to perfect multicollinearity. The data for the
constant term is 1’s and MALE = 1 – FE. Thus, the constant term is just a linear function of the
male and female variables:
(
). 4. (a)
̂ ∑
∑ (̂ ) ∑ ( ( ∑
∑ )
∑ ∑
∑ (b) We know that
If ( ∑
∑
∑ (∑ ) ) ∑
∑ ∑
(
∑ ) from the assumptions that ( ) then (∑ ) ) ( ∑
∑ ) ) ∑
(
∑ ) . , so (̂ )
Therefore, ̂ is unbiased.
(c) As in part (b), we have
(̂ ) ( ∑
∑ ∑
∑ The last term is still zero, but now since ∑
(
∑ )
( )
∑
(
∑ (̂ ) 3 we know that ∑
) . Thus, page 4
̂ is biased.
(d) From the previous part,
∑
(
∑ (̂ )
we know that ∑ . Thus, words, ̂ is biased downwards. ∑ (∑ ) 4 )
. This means that ( ̂ ) . In other...
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 Spring '08
 Staff
 Economics, Econometrics, Null hypothesis, $51,242

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