Using Econometrics to Aid in Choosing Schools for Your Sister

You have a young sister who will graduate in high school in next spring. Since you are the only person in your family that understands econometrics/statistics, they hope you can use expert knowledge to narrow down the list of colleges/universities that your sister will apply for. What makes your job challenging is the fact that different family members have different priorities. In other words, they define “good schools” using different criteria.

(A) The main concern of your sister is the difficulty level of getting accepted by a school. She understands that it is hard to get admitted by a school that is selective, but she is not sure how to measure selectiveness. Somebody tells her that maybe private schools are more selective than public schools, and she hopes you can provide statistical evidence for that argument. If what she hears turns out to be true, maybe she will apply for public schools only.

(B) Your mother is very cost-conscious, and she is primarily concerned with the monetary cost of college education. She would like to pay a high tuition only if it is justified by high quality. For example, she understands that a low student-teacher ratio may signal for high quality, and she is curious whether there are other signals for high quality. She also understands improving quality (such

as lowering the student-teacher ratio) entails raising tuition. Your mother would be very happy if you can present her some sort of quality-adjusted cost or quality-weighted tuition, based on which she can hunt for “bargain schools” for your sister. The school “with best value”, according to your mother, should be the one that charges tuition less than that implied by its quality.

(C) Your dad is an engineer, and he loves his job. So he hopes your sister can become an engineer as well. In terms of school choices, you dad hopes your sister can go to a school where the students on average have good math skill, which is needed by an engineer. For whatever reason, your dad would prefer your sister goes to a school outside Ohio. Finally, to show the support for your mother, your dad also wants to take the quality-adjusted tuition into account. To summarize, your dad would like to see a list of five schools that (i) are mostly reasonably priced, (ii) are outside Ohio, and (iii) put highest premium on the math skill.

Your job is to write a letter with three subsections. In each section you need to explain in detail to each family member how you use econometrics or statistics to address their concerns. In particular, you need to show them how the empirical results are linked to their questions. You need to convey your results so that a non-specialist audience can understand. Thus my suggestion is that in the letter

you need to try to minimize using jargons such as p-value and residual. Nevertheless, I hope to see how you take care of those econometric issues in the appendix of Stata commands and results. The data you will use for this project is called School data, which is posted on my webpage. The data file contains 718 colleges and universities in US. The variables and explanations are in Table 1 below:

Table 1: Variable Descriptions

school Name of a college or university

state The state in which the school is located

private =1 for a public school; =2 for a private school

mathsat The average SAT math score of newly enrolled students

verbalsat The average SAT verbal score of newly enrolled students

applications The number of applications received by a school

acceptance The number of accepted applications

newenrolled The number of students newly enrolled

fulltimeunder The number of full-time undergraduate students

parttimeunder The number of part-time undergraduate students

instatetuition The in-state tuition

outofstatetuition The out-of-state tuition

phdfal The percentage point of faculties who hold doctoral degrees

stufalratio The student-faculty ratio

Table 2: Tentative Rubric

Criteria Exceed Meet Fail

Is your letter well organized? Is the material ordered in a way that is

logical, clear and easy to follow?

Does the letter show high quality of econometric reasoning? Are

econometric methods properly chosen and implemented? Are the statistical

evidences adequate?

Do you explain the results so that a non-specialist can understand?

Is your letter free of grammatical or spelling problems?

Are the paragraphs and sentences cohesive? Is the writing

concise?

The rubric above is suggestive. It shows you roughly what I am looking at in your letter.

You can seek help from me, but not from your classmates. For instance, you can ask me for

clarification if you think some part of this project is unclear. You need to convince me that what you

do makes econometric sense, and are relevant to the concerns raised by your family numbers. There

are possibly multiple ways of conducting the empirical analysis. Please discuss fully if different

approaches produce different answers. Ultimately, the success of this project depends crucially on the

care and effort you put into it.

If you would like a feedback on a draft of your writing, please visit the Howe Writing Initiative in

FSB 3064. Appointments can be made online at www.miamioh.edu/hwi. They can only help your

writing, not econometrics!

Using Econometrics to Aid in Choosing Schools for Your Sister