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Econ 1150 Mini-Exam 3

1. Suppose the true population regression is Yi = β0 +β1X1i +β2X2i +β3X3i +ui . We obtain an n-sized sample {(Yi , X1i , X2i , X3i)}, where i = 1, ..., n. However, we left out X2i and X3i in our sample regression estimation. That is, we estimated Yˆ i = βˆ 0 + βˆ 1X1i . Assume that E(ui |X1i , X2i , X3i) = 0.

(a) Using the formula  show that as n → ∞, βˆ 1 converges to a sum of the true population parameter β1 and omitted variable bias terms coming from leaving out X2i and X3i.

(b) Suppose β1 > 0, β2 > 0, β3 < 0, and cov(X1i , X2i) > cov(X1i , X3i) > 0. Is βˆ 1 biased? If so, what is the direction of the bias and how do you know that?

2. We’re interested in studying how choice of college degree field is associated to earnings. We have the following variables for each college-graduate i: income in dollars incwagei , work-experience in years experiencei , and binary variables sciencei and engineeringi .

❼ sciencei = 1 if i’s degree field is science and sciencei = 0 if i’s degree field is not science.

❼ engineeringi = 1 if i’s degree field is engineering and engineeringi = 0 if i’s degree field is not engineering.

The estimated regressions with their associated Stata output are as follows:

(a) In Regressions A and B, how should one interpret βˆ 1 A and βˆ 1 B? Do either of them differ signifi-cantly from zero at the 5% level?

(b) In Regression C, how should one interpret βˆ 1 C and βˆ 2 C? Do either of them differ significantly from zero at the 5% level?

(c) Using the appropriate regression, predict the income for a college graduate whose degree field is neither science nor engineering but has 10 years of work experience.

(d) By comparing the Stata output in Regressions A, B, and C, explain why it makes sense that βˆ 1 C > βˆ 1 A.

(Hint: Which individuals are you comparing science-graduates to in Regression A? What about in Regression C?)