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Department of Economics
Economics S3412
Summer 2019
Midterm Exam
Question 1 (30 points):
You wish to examine the relationship between the height of a person and his/her parents. You do this by collecting data from 310 individuals and their parents, and estimate the following relationship: height = 19.60 + 0.73×parh, (8.20) (0.10) with R²=0.45 and SER=2.0. Here, height is the height of students in inches, and parh is the average of the parental heights. Values in parentheses are standard errors.
(a) [6 pt] State formally the hypothesis that parents' heights have no impact on their child's height. Test the hypothesis at a 5% level and conclude.
(b) [6 pt] Interpret the values of R² and SER. Can you reject the null hypothesis that the regression R² is zero?
(c) [6 pt] Construct a 95% confidence interval of the expected impact of a two inches increase in the average of parental height.
(d) If children, on average, were expected to be of the same height as their parents, then this would imply two hypotheses, one for the slope and one for the intercept.
(i) [6 pt] What should the null hypothesis be for the intercept? Calculate the relevant t- statistic and carry out the hypothesis test at the 1% and 5% level. Conclude.
(ii) [6 pt] What should the null hypothesis be for the slope? Calculate the relevant t-statistic and carry out the hypothesis test at the 1% and 5% level. Conclude.
Question 2 (24 points):
Consider following data on average hourly earnings.
|
Variable name: |
Description:
|
Measurement unit: |
|
ahe |
Average Hourly Earnings |
$ per hour |
|
female |
=1 for females =0 for males |
binary variable |
|
age |
Age of the worker |
Years |
|
yreduc |
Education level of the worker |
Years |
|
northeast |
=1 if worker works in Northeast, =0 otherwise |
binary variable |
|
south |
=1 if worker works in South, =0 otherwise |
binary variable |
|
west |
=1 if worker works in West, =0 otherwise |
binary variable |
|
midwest |
=1 if worker works in Midwest, =0 otherwise |
binary variable |
Regression 1:
Regression 2:
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(a) [4 pt] Write regression 2 in an equation form (use 2 decimals points only)
(b) [4 pt] Interpret the coefficient on yrseduc.
(c) [4 pt] Is the binary variable south significant in Regression 1. Support your answer.
(d) [4 pt] South is significant in one regression and not significant in the other. What is the reason for this?
(e) [4 pt] Interpret RT in regression 2.
(f) [4 pt] There are 4 regional binary variables. What happens if we include all four in a regression? Explain your answer.
Question 3 (20 points):
Consider the following regression:
Y = β" + β1X1 + βTXT + β/X/ + u
Suppose you need to test the following hypotheses, write the “artificial regression” (fooling Stata) that you need to run for each case. Be specific in terms of new variables you need to generate and the null hypothesis you need to run
(a) H" :β1 + βT = 1
(b) H" :β1 = 3β/
Question 4 (26 points):
This dataset contains data from a random sample of high school seniors interviewed in 1980 and re-interviewed in 1986. In this exercise you will use this data set to investigate the relationship between the number of completed years of education for young adults and the distance from each student's high school to the nearest four-year college. The variable ed corresponds to years of education and dist is the distance to the nearest college and it is measured in tens of miles (For example dist = 3 means that the high school of the senior is 30 miles from the nearest college). Variables momcoll and dadcoll are binary variables that are equal to 1 if mom (dad) went to college and zero otherwise. Tuition is average tuition.
Regression 1:
Regression 2:
Regression 3:
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(a) [6p] Use regression 2: A student’s high school was 18 miles from the nearest college and both her parents went to college. Estimate the number of years of schooling completed.
(b) [6p] Use regression 1: Compute the 99% confidence interval for the difference in the predicted years of education between a high school senior who is 93 miles to the nearest college and another student who attends a high school that shares a campus with a college. Explain what your solution means in one sentence.
(c) [6p] Is tuition an important predictor of education? Support your answer.
(d) [8p] Is tuition jointly significant with parents education variables? How would you test this? Show your work. Be specific about which regression(s) you must use. (You can assume homoscedasticity here)