The topic and information on the dataset
This assignment involves the application of a range of econometric methods in analysing the effect of attending a private school on academic achievement. This topic has been the focus of a large research literature by economists, especially in the US, going back decades, and became known as the “school choice” debate. To quote Rouse (1998):
At the cornerstone of many school reform proposals lies the premise that private schools are more efficient than public schools… Proponents of school choice argue that governments should offer tuition vouchers to families who wish to send their children to private, rather than public, schools. If private schools are indeed more effective than public schools, a voucher program may offer a cost-effective way to improve the quality of education.
…
Critics of school choice programs have argued that private schools would not necessarily do a better job educating students who are currently attending public schools. Rather, they argue that the observed superiority of private school students arises from the selection process that leads higher-achieving students to attend private schools.
This quote comes from a published study by Rouse, Private School Vouchers and Student Achievement: An Evaluation of the Milwaukee Parental Choice Program (Quarterly Journal of Economics, May 1998, pp.553-602). It is available through the library. Reading the article is not required for this assignment (but if you are interested, I encourage you to take a look).The data used in our assignment is a subset of the data used in the paper. The data set is named ‘Assignment.dta’1.
Download the data from the Assignment tab in our Canvas site where you found these instructions.
Note: There are a few different versions of the data and each student will have a link to just one of these. I have edited the data slightly for each version, and by enough that you need to work on your own data. If you work on one of your classmate’s data sets, you may answer one or more questions in the quiz incorrectly and lose marks or be referred to the academic integrity office.
1 Assignment.csv is also available for those using software other than Stata.
The data, background and more info on key variables
The data is a cross-section of data from 1994 on 300 students. There are 300 rows – one for each student - and 9 columns. The columns correspond to the variables:
Variable name Description
studentid student identifier
black = 1 if Black or African America, 0 otherwise
hispanic = 1 if Hispanic, 0 otherwise
female = 1 if female, 0 otherwise
mnce Math NCE score, 1994 – more details are below.
selectyrs number of years selected to attend a choice school
choiceyrs number of years attended a choice school
mnce90 the student’s Math NCE score in 1990
appyear year of first application; 1990-1993
What we have called ‘choice’ schools here are private not-for-profit school. The sample is one of low income students from Milwaukee, Wisconsin. In 1990, Wisconsin ran a school choice lottery in Milwaukee. Available funding was limited – so the lottery was used to randomly select students who would receive a voucher (like a grant) that they could use to pay the fees to attend a choice (i.e. private) school. To be eligible to apply, the student’s family had to have a very low income at or below 1.75 times the national poverty line.
Our dataset includes students who applied to the voucher lottery and were accepted, applied to the lottery and were not accepted, and students who did not apply to the lottery.
Our variable choiceyrs is the number of years between 1991-1994 that a student attended a choice school.
Our variable selectyrs indicates the number of years a student was selected, via the lottery, for a voucher. If the student applied to the lottery in 1990 and received a voucher, then selectyrs=4, if she applied in 1991 and received a voucher then selectyrs=3, and so on.
The outcome variable of interest in mnce. This is a student’s percentile score on a maths test administered in 1994. The score takes values from 0-100, and is measured in percentile points.
We also have a mnce score from a test the students took 4 years earlier, in 1990, before they had the opportunity to enter a choice school.
Part A: Descriptive Statistics for the Sample [9 marks] Quiz questions 1-4: [5 marks]
Investigate the distribution of the variables:
mnce, black, hispanic, female, selectyrs, choiceyrs
For each, find the average, standard deviation, minimum, maximum and median of its sample distribution.
Construct and keep a copy of a histogram for mnce.
In the quiz you will be asked to report selected summary statistics either rounded to 2 decimal places or to the nearest whole number. You will also answer a multiple-choice question on the histograms.
Quiz questions 5: [2 marks]
Find out how many students in the sample of 300:
• never received a voucher
• had a voucher for four years
• never attended a choice school
• attended a choice school for four years. You will report each of these in the quiz.
Quiz question 6: [2 marks]
Pause and think about what you learn from these descriptive statistics. In the quiz you will be asked to briefly describe one useful, unusual or noteworthy thing you discovered from these descriptive statistics.
Part B: Simple & Multiple Regression Model - Estimation and Testing [27 marks] Quiz question 7: [3 marks]
(1) Estimate the simple regression model in (EQ.1):
ππππ = π½0 + π½1πβππππππ¦ππ + π’ (πΈπΈπΈ. 1)
In the quiz you will report selected coefficient estimates, standard errors and the R-squared, rounded to 4 decimal places.
Quiz questions 8-10: [5 marks]
If private school (i.e. what we are calling choice schools here) do indeed do a better job at educating students (at least as measured by test scores), what sign do we expect for the coefficient on choiceyrs? What is the sign of this relationship from your estimates of (EQ.1)? Based on the estimates, is attending a choice school associated with better academic achievement? Interpret the estimated slope coefficient.
Quiz questions 11-13: [3 marks] Is the estimated slope coefficient in (EQ.1) significantly different from zero at the 10% level of significance?
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