A. Bias in self-reported voter turnout
Surveys are frequently used to measure political behavior such as voter turnout (whether a voter voted or not), but some researchers are concerned about the accuracy of self-reports. In particular, they worry about the potential for social desirability bias. In this context, social desirability bias occurs when, in postelection surveys, respondents who did not vote in an election lie about not having voted because they feel that they should have voted. Is such a bias present in the American National Election Studies (ANES)? ANES is a nationwide survey that has been conducted for every election since 1948. ANES is based on face-to-face interviews with a nationally representative sample of adults. Table 1 displays the names and descriptions of variables in the turnout.csv data file.
Table 1: US Election Turnout Data
Variable Description
year election year
VEP voting eligible population (in thousands)
VAP voting age population (in thousands)
total total ballots cast for highest office (in thousands)
ANES ANES estimated turnout rate felons total ineligible felons (in thousands) noncitizens total noncitizens (in thousands)
overseas total eligible overseas voters (in thousands)
osvoters total ballots counted by overseas voters
The following code loads this dataset into R:
turnout <- read.csv("~/shared/Problem sets/Problem Set 1/turnout.csv")
1. [5 points] How many rows are in the dataset? How many columns are in the dataset? What is the range of years covered in this data set?
2. [5 points] Turnout (the turnout rate) is a ratio that is calculated by:
# of votes cast # of possible voters
Calculate the turnout rate using the voting age population as the denominator. Note that for this data set, we must add the total number of eligible overseas voters (overseas) since the VAP variable does not include these individuals in the count.
3. [5 points] Calculate the turnout rate using the voting eligible population or VEP as a denominator. What difference do you observe from to your answer to #2? What do you think accounts for this difference?
4. [5 points] Compute the differences between the VAP and ANES estimates of turnout rate. How big is the difference on average? What is the range of the differences? Conduct the same comparison for the VEP and ANES estimates of voter turnout. Briefly comment on the results.
5. [5 points] Compare the average VEP turnout rate with the average ANES turnout rate in presidential elections (1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008) and in midterm elections (1982, 1986, 1990, 1994, 1998, 2002). Note that the data set excludes the year 2006. Does the bias in the ANES estimates vary across election types?
6. [5 points] Subset the data into two periods: early (1980-1992) and late (1994-2008). Calculate the difference between the VAP turnout rate and the ANES turnout rate separately for each year within each period. Has the bias of ANES increased over time?
7. [5 points] ANES does not interview prisoners or overseas voters. Calculate an adjustment to the 2008 VAP turnout rate. Begin by subtracting the total number of ineligible felons and noncitizens from the VAP to calculate an adjusted VAP. Next, calculate the turnout rate using this adjusted VAP as the denominator, taking care to subtract the number of overseas ballots counted from the total ballots in 2008. Compare the adjusted VAP turnout with the unadjusted VAP, VEP, and the ANES turnout rate. Briefly discuss the results.
B. Potential Outcomes #1:
Does visting the hospital make people healthier? You are interested in estimating the causal effect of visiting a hospital on individuals’ health status. Note that individuals are indexed by i.
The National Health Interview Survey (NHIS) collected data on hospital visits and health conditions of individuals. Health conditions are measured based on 5-scale (1, 2, 3, 4, 5 with higher numbers = better health conditions) index. Table 2 summarizes the survey results.
Table 2: Hospital Visits and Health Conditions
Group Sample Size Mean Health Status Visited a hospital 7,774 3.21
Did not visit a hospital 90,049 3.93
1. [5 points] What is the treatment (Ti) here? What is the outcome variable (Yi)?
2. [5 points] As we have discussed in class, with a binary treatment as in the motivation for this case, each respondent has two potential outcomes Yi(Ti = 0) and Yi(Ti = 1). (To aid in typing out notation, you can just call these “Y0” and “Y1”.) Which potential outcome is revealed for those that visited the hospital? Which potential outcome is revealed for those that did not visit the hospital?
3. [5 points] Taken at face value, the measures in Table 2 suggests that going to the hospital makes people sicker. Is there a problem with this conclusion? Briefly explain your reasoning, making reference to the potential outcomes you discuss in #2.
C. Potential Outcomes #2:
Public health guidance following the COVID-19 question has led to widespread use of remote learning. New York City Public Schools have adopted a blended remote/in-person plan (for the moment) that allows parents to select one of the following options for their children:
• Blended: 1-3 days per week “in person” in school, remote learning at home on the other days
• All remote: all remote learning
Is all remote learning as effective as in-person learning? Suppose that we define the treatment as any in-person learning. Consider one outcome: math scores at the end of the 2021 academic year.
1. [5 points] Suppose that at the end of the 2020-2021 academic year, math scores are higher for students in remote-only learning. Does this mean that remote learning is more effective than in-person learning? Briefly explain why or why not? For reference, this article may be helpful.
2. [5 points] Suppose you were to design an experiment to test in-person versus remote learning. Briefly explain how an experiment would look different from what NYC public schools are currently doing.
3. [5 points] Now, suppose that in an alternate universe, NYC public schools were to run the experiment you describe in #2. At the conclusion of the experiment (at the end of the 2020-2021 academic year), math scores are higher for students in remote-only learning. Can we conclude that remote learning is more effective than in-person learning? Would you recommend all-remote learning to another city on the basis of this finding?
D. The Mark of a Criminal Record:
In this exercise, we analyze the causal effects of a criminal record on the job prospects of white and black job applicants. This exercise is based on Devah Pager’s 2003 article, “The Mark of a Criminal Record,” published in American Journal of Sociology. To isolate the causal effect of a criminal record for black and white applicants, Pager ran an audit experiment. In this type of experiment, researchers present two similar people that differ only according to one trait thought to be the source of discrimination.
To examine the role of a criminal record, Pager hired a pair of white men and a pair of black men and instructed them to apply for existing entry-level jobs in the city of Milwaukee. The men in each pair were matched on a number of dimensions, including physical appearance and self-presentation. As much as possible, the only difference between the two was that Pager randomly varied which individual in the pair would indicate to potential employers that he had a criminal record. Further, each week, the pair alternated which applicant would present himself as an ex-felon. To determine how incarceration and race influence employment chances, she compared callback rates among applicants with and without a criminal background and calculated how those callback rates varied by race.
In the data you will use, criminalrecord.csv nearly all these cases are present, but 4 cases have been redacted. As a result, your findings may differ slightly from those in the paper. The names and descriptions of variables are shown below in Table 3. You may not need to use all of these variables for this activity. We’ve kept these unnecessary variables in the dataset because it is common to receive a dataset with much more information than you need.
Table 3: Criminal Record Dataset
Variable Description
jobid election year
callback 1 if tester received a callback, 0 if the tester did not receive a callback
black 1 if the tester is black, 0 if the tester is white
crimrec 1 if the tester has a criminal record, 0 if the tester does not
interact 1 if tester interacted with employer during the job application, 0 if tester does not interact with employer
city 1 is job is located in the city center, 0 if job is located in the suburbs
distance job’s average distance to downtown
custserv 1 if job is in the customer service sector, 0 if it is not
manualskill 1 if job requires manual skills, 0 if it does not
The following code loads the data into R:
cr <- read.csv("~/shared/Problem sets/Problem Set 1/criminalrecord.csv")
1. [5 points] What is the sample size of the experiment? In what proportion of observations is the tester Black? In what proportion of observations did the tester present as an “ex-felon”?
2. [6 points] This study has two different randomized treatments that are “crossed”. First, T1 is the tester’s race where T1 = 1 means that the tester was Black and T1 = 0 means the tester was White. Second T2 is the tester’s criminal record where T2 = 1 means that the tester presented as an “ex-felon” and T2 = 0 indicates that the tester did not present as having a criminal record. Our outcome of interest, Y , is whether or not a subject got a callback. In words, describe each of the following potential outcomes:
• Yi(T1 = 0, T2 = 0)
• Yi(T1 = 1, T2 = 0)
• Yi(T1 = 0, T2 = 1)
• Yi(T1 = 1, T2 = 1)
3. [6 points] Now we examine the central question of the study. Calculate the callback rate for white applicants with and without a criminal record. Then calculate the callback rate for black applicants with and without a criminal record. Note that the R function mean() may be helpful for calculating callback rates. How do these callback rates relate to the potential outcomes you described in #2?
4. [6 points] What is the difference in callback rates between individuals with and without a criminal record within each race? This is the ATE of (presenting with) a criminal record for each race. What do these specific results tell us?
5. [6 points] Compare the callback rates of whites with a criminal record versus blacks without a criminal record. What do we learn from this comparison?
6. [6 points] When carrying out this experiment, Pager made many decisions. For example, she opted to conduct the research in Milwaukee; she could have done the same experiment in Dallas or Topeka or Princeton. She ran the study at a specific time: between June and December of 2001. But, she could have also run it at a different time. Pager decided to hire 23-year-old male college students as her testers; she could have done the same experiment with 23-year-old female college students or 40-year-old male high school drop-outs. Further, the criminal record she randomly assigned to her testers was a felony conviction related to drugs (possession with intent to distribute, cocaine). But, she could have assigned her testers a felony conviction for assault or tax evasion. Now you should pick one of these decisions described above or another decision of your choosing. Speculate about how the results of the study might (or might not) change if you were to conduct the same study but alter this specific decision. This is part of thinking about the external validity of the study.
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