Consider the population model

GPAi= Xi+SATi+Si+ei

where GPA is college GPA (in a semester), X is a vector of exogenous explanatory variables,

SAT is SAT score, S is total hours spent studying during the semester, and e is an error term.

You have access to a large random sample of students (indexed by i) from a single university .

Assume that X and SATare exogenous. Suppose that you are interested in estimating .

(a) What does represent in this model?

(b) Evaluate estimating the above relationship using OLS. Suppose that you are

primarily interested in estimating .

(c) Now, suppose that at this university , all students are are randomly assigned to

dorms. Dorms are varying distances (di) from the center of campus, where all classes

are held (in person only!). Explain how to use this variable to obtain a consistent es-

timate of , if it is possible. Clearly state any assumptions that you make. Be sure to

justify, in detail, why your approach is valid. If this new variable is not useful, simply

state that it is not useful.

(d) Now, suppose that you have access to data that tracks students over time, so

that GPAitrepresents the semester (not cumulative) GPA of student i in semester t,

and Sitrepresents hours studied by student i in semester t. The variables Xiand SATi

are constant over time. You don't have the distance variable anymore. The number of

students in the data is very large, and you have 8 semesters of data for each student.

Adapt the model in Equation (1) to make use of the new data. If possible, explain how

to obtain a consistent estimate of . Clearly state any assumptions that you make. If it's

not possible to get a consistent estimate of , simply state this.

(e) Suppose now that you have a new dataset from a large sample of graduates

from this university: wage at age 30, total hours studied during college, cumulative

college GPA at graduation, and Xiand SATias described above. In addition, you know

that all graduates with a GPA > 3.7 graduate with honors. This achievement is noted

prominently on their official transcript. Identify an interesting economic question that

you can answer using these data, and clearly state it. Write down an empirical model

and explain specifically how you would estimate it. Clearly state any assumptions that

you make.