Assignment 3

(For both 1 and 2) You are interested in analyzing the impact of laptop use on end-of course grades among Temple students, so you decide to run an experiment. You randomly divide half of the students in Econ 3580 and assign one half to take notes on their laptops/tablets and one half to use pen(cil)-and-paper.

1. Write down this experiment in regression form. Label the outcome variable and the treatment variable. Are there any other variables that you should include in the regression model?

2. Suppose instead that you were unable to randomly assign students to use their laptop. Is there selection bias in this (non-experimental) setting? If so, what other controls would you include in the regression model to help overcome the selection bias?

3. Suppose instead that the economics department asked all of its professors, starting in Fall 2016, to prohibit laptop use while in class. All other departments continued their existing laptop policies. (For an interesting real-world study similar to this, see Patterson and Patterson (2017) and https://www.brookings.edu/research/for-better-learning-in-college-lectures-laydown-the-laptop-and-pick-up-a-pen/amp/.)a. Who is in the treatment group of this study, and who is in the control group? b. Is the treatment variable randomly assigned in this study? c. Write down the difference-in-differences regression model to analyze this change in laptop policy. d. Fill in the missing blanks from the following difference-in-differences table, where "average GPA" is the outcome variable:

CONTROL TREATMENT DIFFERENCE

PRE-FALL 2016 X 2.95 -0.05

POAT-FALL 2016 2.90 3.00 X

DIFFERENCE -0.10 X 0.15

e. What is the interpretation of the policy effect?

f. Suppose you had more than two semesters of data wanted to control for different effects from different departments and semesters. You propose doing this by including separate fixed effects for each semester and department at Temple (instead of simply an effect for pre vs. post or Econ vs. all others). Write down the regression model corresponding to this new specification.

4. Some financial aid such as the Pell Grant is assigned on the basis of financial need. Suppose you examine the relationship between college completion and financial aid receipt by running a regression of college completion on aid receipt. Why might it be incorrect to interpret the coefficient on financial aid eligibility as a causal effect?

5. Explain why, in a difference-in-differences framework, it is not sufficient to label the treatment effect as the change in outcomes (post-minus-pre) among treated units.

6. You are interested in whether there is a causal impact of high school sports participation on one's likelihood of graduating from college. A number of researchers have examined this claim using instrumental variables.1 One popular instrument is a student's height as an adolescent. a. Identify the treatment, outcome, and instrument for this research setting. b. What is first condition of validity for instrumental variables as described in Lovenheim and Turner? Do you think this instrument satisfies it? Why or why not? c. What is second condition of validity for instrumental variables as described in Lovenheim and Turner? Do you think this instrument satisfies it? Why or why not? d. If you answered that the height does not satisfy either of the requirements in (b) and (c), how do you think that assuming validity of the instrument will affect the conclusions of the research?

7. Following the previous question, now suppose that the State of Missouri mandates that all high school students above a certain height (which differs by gender and school) will be given an offer to play on the basketball team (for boys) or basketball and volleyball teams (for girls). No student who is shorter than the gender- and schoolspecific mandated height is allowed to play on these teams. You imagine that this might be an ideal application for a regression discontinuity design. After crunching some numbers, you find that boys above the cutoff are 80% more likely to play on the team than those who are below the height cutoff, while girls above the cutoff are 65% more likely to play on one of the teams. a. Identify the forcing, treatment, and outcome variables in this RD. b. Is this a fuzzy or sharp RD? How can you tell? c. Do you think that this RD is subject to manipulation? Why or why not? d. Suppose that you verify that no one below the height cutoff is found on either the basketball or volleyball teams. Suppose also that you find that, at the cutoff, college graduation rates are 10 percentage points higher for both genders. Compute the local ATE for high school sports participation among the population of male Missouri high school students. What is the local ATE for female students? e. What can you conclude from this analysis about the college graduation prospects of students who are very short or very tall relative to the cutoff?