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Unformatted text preview: Midterm Answers Fall 2006 Question 1 & Part A: One point for each assumption & SLR1: y = & + B 1 x + u (Model is linear in & ;B 1 ) & SLR2: Our data f x i ;y i g constitute a random sample from y = & + B 1 x + u & SLR3: E ( u i j x i ) = 0 8 i & SLR4: x i 6 = c 8 i (some variation in x i ) & SLR5: V ( u i j x i ) = ¡ 2 8 i & Part B: E ( u i j x i ) = 0 ! cov ( x;u ) = 0 & Part C: I was looking for a concrete example that violates cov ( x;u ) = 0 & For example, you could have described a common example used in class: ln( wage ) = & + B 1 ( educ ) + u & What&s in u ? Innate ability, parent&s education & We must be assuming that the distribution of u s is the same for each level of x ¡ Or we could phrase it as the mean of all other factors is the same regardless of the amount of education attained & However, we are likely to violate the assumption because these unobservables in u are likely correlated with education & Part D: Formula for least squares estimator of & and & 1 & Slope: c &...
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