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ECMT6007/6702: Econometric Applications Problem Set 4
发布时间：2022-11-10
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ECMT6007/6702: Econometric Applications
Problem Set 4
Semester 2 2022
Question 1. Computer Exercise: Student Literacy and School Resources
This problem set analyses a dataset that has been used to assess the effect of school resources (mea- sured by school spending per student) on student literacy (measured by the percentage of Year 5 students who pass a reading test). The dataset is a random sample of schools across Australia from
2012.
(i) Download the dataset student_literacy.dta from the Course Canvas site. Generate the following variables that will be used in the following analysis:
• lnSchoolExpendPP which is the natural logarithm of school expenditure per stu- dent enrolled
• lnEnroll which is the natural logarithm of the total student enrolment
Report the sample mean, minimum and maximum values for the variables: Read5YR,
lnSchoolExpendPP, lnEnroll, and Poverty.
Read5YR = β0 + β1 lnSchoolExpendPP + β2 lnEnroll + u (1)
by OLS and report the results in the standard way (i.e. estimates, standard errors, and model fit).
(iii) What is the interpretation of β1 ? What is the expected sign of β1 ? Explain.
(iv) Test H0 : β 1 = 0 against H1 : β 1 
0 using a 10% significance level. What do you conclude?
Does your conclusion change if you use a 1% significance level?
Read5YR = β0 + β1 lnSchoolExpendPP + β2lnEnroll + β3 Poverty + u (2)
which now includes a control variable for the socio-economic status of the school community. Report the results in the standard way.
(vi) What happens to the coefficient on lnSchoolExpendPP when the additional explanatory variable Poverty is added to the model? Explain the reason for the difference in estimates for β 1 in models (1) and (2).
(vii) From model (2), obtain the predicted Read5YRwhen lnSchoolExpendPP = 8.5, lnEnroll = 5.9 and Poverty = 39. Estimate a regression model which allows you to put a 95% confidence interval around the predicted value (this is a‘conditional’ or ‘within sample’prediction). Re- port the confidence interval.
(viii) Now consider a prediction for an individual. Construct the 95% confidence interval for the predicted Read5YR for a school where lnSchoolExpendPP = 8.5, lnEnroll = 5.9 and Poverty = 39 (this is an ‘unconditional’prediction). Comment on the width of this confi- dence interval compared to that in constructed in (vii).
(ix) Generate a new variable which is equal to lnEnroll2, and add it to the model (2). Estimate this new model and compute the turning point in the quadratic.
(x) In your assessment, does model (2) measure the causal effects of lnSchoolExpendPP on Read5YR? Explain your reasoning.
The dataset school_literacy .dta contains the following four variables:
1. Read5YR: per cent of Year 5 students who pass a common reading test
2. SchoolExpend: school expenditure
3. Enroll: total student enrolment
4. Poverty: per cent of the student population from low socio-economic backgrounds
