AUTHOR Marco Steenbergen PUBLISHED May 5, 2024 Table of contents Instructions Problems Set 1 Set 2 References Instructions This homework covers IVs and RDDs. It is due on May 20 at 23.59 hours. The homework is to be completed in groups of 3 students. You should submit: The answers in the quiz tool on OLAT. This will provide instant feedback on your performance. An R syntax file via email to [email protected]. Without this file, you will not receive any points for the homework. Good luck! Problems Set 1 A university discovers that many students have to work while studying. It fears that the combination of work and study negatively affects scholastic performance. For this reason, the university administration decides to make available stipends to students. The policy is limited to students with parental incomes at 30 percent of the median or less. Since this still leaves too many students for the available budget, the administration also makes eligibility contingent on a standardized test and sets a minimum score of 80 out of 100 points. Those indigent students who score at least 80 receive a stipend, whereas others do not.1 The minimum test score is advertised ahead of the start of the stipend program. The university administration has asked you to evaluate the effect of stipends on performance, as measured by student’s GPA at the end of the year.2 It has collected the following data, which can be found in stipend.Rda: test is the standardized test score that was used to determine who is eligible to receive a stipend. motivation is a survey measure of student’s motivation that was taken in the summer before the academic year started and before the standardized test was taken. Higher scores mean that students are more motivated to succeed in their studies. gpa is the grade point average at the end of the academic year and serves as the outcome measure. Now answer the following questions. Using the approach of Imbens and Kalyanaraman (2012), what is the bandwidth you should use? Using a polynomial regression of order 3 and controlling for motivation, what is the estimate of the treatment effect? Based on appropriate tests, which of the following conclusions can you draw? Which of the following statements best describes when we perform a placebo test on the location of the minimum test score? The students at this university are an altruistic lot. Someone discovers that a subset of students share their stipends with peers who did not meet the test score but still need the money. What assumption would this violate? Set 2 A team of scholars performs the following experiment on the effects of voting advice applications (VAAs) on voting behavior, specifically voting correctly (Lau and Redlawsk 1997). A random sample of 1000 respondents is drawn. Half of the sample is randomly assigned to the treatment, which means they receive a letter encouraging them to use a VAA. The other half do not receive such encouragement. Voting correctly is coded 1 if someone’s vote corresponds to what it would have been under full information. Among those who were encouraged to use a VAA, the proportion of people who voted correctly was 0.35. Among those who were not, that proportion was 0.30. Since encouragement does not equate actual treatment intake, the team of scholars also recorded whether someone had actually used a VAA. The team obtains the following information: Of those encouraged to take the treatment, 250 did use a VAA. Of those assigned to the control group, 300 individuals did not use a VAA. Based on the information and what you know from the lecture, please answer the following questions. What is the intention-to-treat effect? How many always-takers are “hiding” among those who used a VAA and were encouraged to do so? What is the compliance rate? What is the LATE? The authors find that those encouraged to use a VAA also tended to watch more news about the election. What, if any, assumption is being violated here? References Imbens, Guido, and Karthik Kalyanaraman. 2012. “Optimal Bandwidth Choice for the Regression Discontinuity Estimator.” The Review of Economic Studies 79 (3): 933–59. https://doi.org/10.1093/restud/rdr043. Lau, Richard R., and David P. Redlawsk. 1997. “Voting Correctly.” American Political Science Review 91 (3): 585–98. https://doi.org/10.2307/2952076. Footnotes You may assume that everyone who is eligible to take the stipend also does and that no one who is not eligible can receive the money.↩︎ GPA = grade point average. For this exercise, we assume the university is located in the United States and uses a grading scale from 0 to 4. On this scale, 0 means F (fail), 1 corresponds to a grade of D, 2 to a grade C, 3 to a grade of B, and 4 to a grade of A.↩︎
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likesAnswer to a math question AUTHOR Marco Steenbergen PUBLISHED May 5, 2024 Table of contents Instructions Problems Set 1 Set 2 References Instructions This homework covers IVs and RDDs. It is due on May 20 at 23.59 hours. The homework is to be completed in groups of 3 students. You should submit: The answers in the quiz tool on OLAT. This will provide instant feedback on your performance. An R syntax file via email to [email protected]. Without this file, you will not receive any points for the homework. Good luck! Problems Set 1 A university discovers that many students have to work while studying. It fears that the combination of work and study negatively affects scholastic performance. For this reason, the university administration decides to make available stipends to students. The policy is limited to students with parental incomes at 30 percent of the median or less. Since this still leaves too many students for the available budget, the administration also makes eligibility contingent on a standardized test and sets a minimum score of 80 out of 100 points. Those indigent students who score at least 80 receive a stipend, whereas others do not.1 The minimum test score is advertised ahead of the start of the stipend program. The university administration has asked you to evaluate the effect of stipends on performance, as measured by student’s GPA at the end of the year.2 It has collected the following data, which can be found in stipend.Rda: test is the standardized test score that was used to determine who is eligible to receive a stipend. motivation is a survey measure of student’s motivation that was taken in the summer before the academic year started and before the standardized test was taken. Higher scores mean that students are more motivated to succeed in their studies. gpa is the grade point average at the end of the academic year and serves as the outcome measure. Now answer the following questions. Using the approach of Imbens and Kalyanaraman (2012), what is the bandwidth you should use? Using a polynomial regression of order 3 and controlling for motivation, what is the estimate of the treatment effect? Based on appropriate tests, which of the following conclusions can you draw? Which of the following statements best describes when we perform a placebo test on the location of the minimum test score? The students at this university are an altruistic lot. Someone discovers that a subset of students share their stipends with peers who did not meet the test score but still need the money. What assumption would this violate? Set 2 A team of scholars performs the following experiment on the effects of voting advice applications (VAAs) on voting behavior, specifically voting correctly (Lau and Redlawsk 1997). A random sample of 1000 respondents is drawn. Half of the sample is randomly assigned to the treatment, which means they receive a letter encouraging them to use a VAA. The other half do not receive such encouragement. Voting correctly is coded 1 if someone’s vote corresponds to what it would have been under full information. Among those who were encouraged to use a VAA, the proportion of people who voted correctly was 0.35. Among those who were not, that proportion was 0.30. Since encouragement does not equate actual treatment intake, the team of scholars also recorded whether someone had actually used a VAA. The team obtains the following information: Of those encouraged to take the treatment, 250 did use a VAA. Of those assigned to the control group, 300 individuals did not use a VAA. Based on the information and what you know from the lecture, please answer the following questions. What is the intention-to-treat effect? How many always-takers are “hiding” among those who used a VAA and were encouraged to do so? What is the compliance rate? What is the LATE? The authors find that those encouraged to use a VAA also tended to watch more news about the election. What, if any, assumption is being violated here? References Imbens, Guido, and Karthik Kalyanaraman. 2012. “Optimal Bandwidth Choice for the Regression Discontinuity Estimator.” The Review of Economic Studies 79 (3): 933–59. https://doi.org/10.1093/restud/rdr043. Lau, Richard R., and David P. Redlawsk. 1997. “Voting Correctly.” American Political Science Review 91 (3): 585–98. https://doi.org/10.2307/2952076. Footnotes You may assume that everyone who is eligible to take the stipend also does and that no one who is not eligible can receive the money.↩︎ GPA = grade point average. For this exercise, we assume the university is located in the United States and uses a grading scale from 0 to 4. On this scale, 0 means F (fail), 1 corresponds to a grade of D, 2 to a grade C, 3 to a grade of B, and 4 to a grade of A.↩︎
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