ETC2410/ETC5241: INTRODUCTORY ECONOMETRICS Assignment 1

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DEPARTMENT OF ECONOMETRICS AND BUSINESS STATISTICS
ETC2410/ETC5241: INTRODUCTORY ECONOMETRICS
SEMESTER 2, 2024
Assignment 1

Instructions

1. The assignment must be electronically submitted by 4:30pm Australian Eastern Standard Time, on Friday, 30 August 2024.

2. The file needs to be uploaded in PDF format by only one member of each group.

3. After Step 2, all members of the group must click the "Submit Assignment" button on Moodle and accept the University’s submission statement. This step is essential, so please make sure that you do this.

4. When instructed to do so, you must report your results in equation form, with standard errors reported in parentheses below the parameter estimates. Screen shots of EViews (or any other statistical package) output are not acceptable. For example, the estimated regression equation below is reported in equation form with standard errors reported in parentheses below the estimated coeffcients:

5. The assignment must be typed. Please use Times New Roman font size 12.

6. Please attach a number to any equation or diagram that you refer to when answering the assignment questions.

7. Unless otherwise instructed, all hypothesis tests should be conducted at the 5% significance level.

8. If an assignment is submitted late a penalty of 5% point deduction per 24hrs late applies.

9. If you are applying for special consideration for circumstances that may make you unable to engage in group work or to adhere to strict deadlines, please let Akanksha know as early as possible, so that alternative arrangements can be made in time.

10. A penalty of up to 10% will be imposed for failure to comply with the instructions above.

Peer Evaluation Surveys

• Consider hypothetical student called Arsene:

– Let n0 equal the number of (D) votes that Arsene receives from his teammates. A (D) indicates that in the opinion of his teammates Arsene has contributed nothing to the completion of the assignment.

– Let n1 equal the number of (C) votes that Arsene receives from his teammates. A (C) vote means that in the opinion of his teammates Arsene has contributed less than it was agreed by the group that he would contribute.

– Let GM equal Arsene’s group submission mark. If n0 + n1 ≥ 2, then Arsene’s mark for the assignment is 

max{0, 1 − 0.4n0 − 0.15n1} × GM

If n0 + n1 < 2, then Arsene’s mark for the assignment will be equal to the GM.

• If you fail to complete the survey by the deadline, we will assume that you have given everyone else in your group a (B) and that you have given yourself a (D).

Failure to complete the survey by the deadline will result in a loss of marks, so please complete the survey on time. It is important to communicate clearly with your group members and make sure that everyone understands what is expected from them.

Data Description

Place the Eviews output used for answering the questions in an Appendix. Note that there are various ways to transform a variable into a dummy variable in Eviews. For instance, @recode() can be used. Please consult the Eviews documentation for details.

Question 1 (20 marks)

1(a) Estimate the linear regression equation associated with (1) by OLS. Report the estimated equation in equation form with the estimated coefficients and standard errors to three decimal places. (4 marks)

1(b) Interpret βˆ 1 if expend increases by $100. (2 marks)

1(c) Does your interpretation for βˆ 1 align with what you would expect within the context? (2 marks)

1(d) Now, estimate a linear regression equation for math10 with expend, enroll, and lnchprg as explanatory variables. Report the estimated equation in equation form with the estimated coefficients and standard errors to three decimal places. (2 marks)

1(e) How does your interpretation for βˆ 1 in the regression equation estimated in Question 1(d) change compared to your interpretation for βˆ 1 in the regression equation estimated in Question 1(a)? (2 marks)

1(f) Now, interpret the coefficient on enroll in 1(d) if student enrolment increases by 1,000. Does the sign make sense to you? If yes, why? (4 marks)

Question 2 (20 marks)

Consider the linear regression equation for math10 with expend, enroll, and lnchprg as pre dictors. Conduct all tests at the 5% significance level.

2(a) Test the hypothesis that the percentage of students in school lunch program has no effect on average pass rates, once we control for school expenditure and school enrolment against the alternative that it has a negative effect. State the null and alternative hypotheses, the form and sampling distribution of your test statistic under the null, the sample and critical values of your test statistic, your decision rule and your conclusion. (6 marks)

2(b) Test the hypothesis that school enrolment and percentage of students in school lunch program have no effect on the math pass rates against the alternative that they have an effect. Specify the unrestricted and restricted models. State the null and alternative hypotheses, the form and sampling distribution of your test statistic under the null, the sample and critical values of your test statistic, your decision rule and your conclusion. (8 marks)

2(c) Test the joint significance of the regressors. State the null and alternative hypotheses, the form and sampling distribution of your test statistic under the null, the sample and critical values of your test statistic, your decision rule and your conclusion. (6 marks)

Question 3 (20 marks)

3(a) Derive a model to test the null hypothesis that expenditure per student has the same effect on math pass rates as school enrolment, against the alternative hypothesis that expenditure per student has a larger effect (5 marks).

3(c) Derive a model to test the null hypothesis that expenditure per student has the same effect on math pass rates as school enrolment, against the alternative hypothesis that the effects are different using an F-test. (3 marks).

3(d) Use the model you derived in Question 3(c) to test the null hypothesis specified in Question 3(c). State the null and alternative hypotheses, the form and sampling distribution of your test statistic under the null, the sample and critical value of your test statistic, your decision rule and your conclusion. (6 marks).

Question 4 (20 marks)

4(b) Estimate the extended linear regression equation by OLS. Report the estimated equation in equation form with the estimated coefficients and standard errors to three decimal places. (4 marks)

4(c) Test whether staff has an effect on math10 in the regression equation in question 4(b). Specify the unrestricted and restricted models. State the null and alternative hypotheses, the form and sampling distribution of your test statistic under the null, the sample and critical values of your test statistic, your decision rule and your conclusion. (8 marks)

4(d) Using the estimated extended regression model in 4(b), derive the predicted percentage of students passing 10th grade math exam for two schools: both spend an average of $5,332 per student, 4,046 student enrolment, with 5.5% of students receiving school lunch, and the first school has 90 staff members whereas the second school has 120 staff members. (4 marks)