Problem 5 1. Explain what it means for an estimator to be consistent. How is it different from the property of unbiasedness? 2. Give an example of an estimator that is consistent but biased.

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3. Add the variable abil (a measure of cognitive ability) to the regression from
part (2), and report the results in equation form. Does ability help to explain
variations in education, even after controlling for parents' education? Explain.
4. Now estimate the equation where abil appears in quadratic form:
educ Bo + Bimotheduc + B₂ fathedu+Bsabil +Babil² + u
Assuming all else fixed, find the value of abil where educ is minimized (notice
that abil is measured so that negative values are permissible).
5. Argue that only a small fraction of men in the sample have "ability" less than
the value calculated in part (4). Why is this important?
6. Using the estimated equation in (4), test the null hypothesis that educ is linearly
related to abil against the alternative that the relationship is quadratic.
7. Add the two college tuition variables to the regression from part (4) and deter-
mine whether they are jointly statistically significant.
8. What is the correlation between tuit 17 and tuit18? Explain why using the
average of the tuition over the two years might be preferred to adding each
separately. What happens when you do use the average?
9. Do the findings for the average tuition variable in part (8) make sense when
interpreted causally? What might be going on?
Problem 5
1. Explain what it means for an estimator to be consistent. How is it different
from the property of unbiasedness?
2. Give an example of an estimator that is consistent but biased.
Transcribed Image Text:3. Add the variable abil (a measure of cognitive ability) to the regression from part (2), and report the results in equation form. Does ability help to explain variations in education, even after controlling for parents' education? Explain. 4. Now estimate the equation where abil appears in quadratic form: educ Bo + Bimotheduc + B₂ fathedu+Bsabil +Babil² + u Assuming all else fixed, find the value of abil where educ is minimized (notice that abil is measured so that negative values are permissible). 5. Argue that only a small fraction of men in the sample have "ability" less than the value calculated in part (4). Why is this important? 6. Using the estimated equation in (4), test the null hypothesis that educ is linearly related to abil against the alternative that the relationship is quadratic. 7. Add the two college tuition variables to the regression from part (4) and deter- mine whether they are jointly statistically significant. 8. What is the correlation between tuit 17 and tuit18? Explain why using the average of the tuition over the two years might be preferred to adding each separately. What happens when you do use the average? 9. Do the findings for the average tuition variable in part (8) make sense when interpreted causally? What might be going on? Problem 5 1. Explain what it means for an estimator to be consistent. How is it different from the property of unbiasedness? 2. Give an example of an estimator that is consistent but biased.
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