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ETC2410/BEX2410: Introductory Econometrics Group Assignment 1, Semester 2, 2022 Due: At or before 4:30 p.m. Australian Eastern Standard Time, on Friday September 16th, 2022 Instructions Regarding Assignment Submission and Presentation 1. This assignment is worth 20% of the marks for the unit. 2. Group Assignment 1 must be electronically submitted by 4:30 p.m. Australian Eastern Standard Time, on Friday September 16th., 2022. 3. The assignment must be submitted as a PDF document. 4. The file needs to be uploaded by only one member of each group. 5. 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. 6. Any assignment received after 4:30 p.m. on Friday, September 16th will be deemed late. 7. A penalty of 5% per day will be imposed on assignments that are submitted after the due date. For example, if a group receives a mark of 65% for an assignment that has been submitted one day late, the mark will be reduced to 60%. 8. Any assignment received after 4:30 p.m. Australian Eastern Standard Time on Friday, September 23rd will receive a mark of zero. 9. Your assignment must be typed. Please use Times New Roman font size 12. 10. When answering the assignment questions please impose the same structure on your answers that I have used in composing the assignment. For example, Q1, (a), i). 11. Please attach a number to any equation or diagram that you refer to when answering the assignment questions. 12. 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 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 coefficients: dwage 0.02 0. 163 1.75 20. 45 educ. 13. When instructed to do so, you must place relevant Eviews output in an appropriately labelled appendix. The material in the appendices will not be marked. It will only be used to check that the results reported in the main body of the assignment have been correctly reported. 14. Unless otherwise instructed, all hypothesis tests should be conducted at the 5% significance level. 15. A penalty of up to 10% will be imposed for careless presentation and/or failure to comply with the instructions above. 1 Peer Evaluation Survey Each group member will be required to complete an anonymous peer evaluation survey. The survey will be conducted via the TeamMates app which will email you a unique link to the survey (delivered to your Monash student email address).You will be asked to evaluate your group members’ participation and effort. The aim of the survey is to identify and address any dysfunctional groups as early as possible. The survey may also be used to adjust your assignment marks in the following manner: 1. 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 max0, 1 0. 4n0 0. 15n1GM. If n0 n1 2, then Arsene’s mark for the assignment will be equal to the GM. 2. 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. 2 Data Description for Question 1 The purpose of this question is to investigate the influence of various factors on the probability of an individual having private health insurance. An Eviews workfile containing the data for the assignment has been placed in the file Assignment 1 Data.wf1 which has been uploaded to the Assignment folder on Moodle. The data set contains observations on the following variables for a randomly selected sample of 3206 individuals: Variable Code Description private 1 for any individual who has private health insurance, 0 otherwise age age in years age2 age2 chronic number of chronic diseases an individual has educ years of schooling female 1 if individual is female, 0 otherwise hhincome a measure of household income hstatusg 1 if health status self-assessed as good, 0 otherwise white 1 if individual is white, 0 otherwise hisp 1 if individual is Hispanic, 0 otherwise 3 Question 1 (85 marks) (a) (20 marks) i) Assume that Eprivate|female 0 1female. The associated linear regression equation is given by private 0 1female u. (1) Estimate (1) by OLS. Report the estimated equation in equation form in the main body of your assignment. Report the estimated coefficients and standard errors to three decimal places. Place the Eviews output in Appendix (a). (2 marks) ii) Test the individual significance of the regressor female. 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) iii) Interpret 0. (2 marks) iv) Interpret 1. (2 marks) v) Do your results provide conclusive evidence that females are more/less likely than males to have private health insurance Briefly explain. (2 marks) vi) Derive a 95% confidence interval for 0. (2 marks) vii) Do you consider your point estimate of 0 to be precise Briefly explain (2 marks) viii) Use the confidence interval derived in vi) to determine whether or not 0 is statistically significant at the 5% significance level. (2 marks) 4 (b) 14 marks Assume that Eprivate|age,age2,chronic,educ, female,hhincome,hstatusg,white,hisp 0 1age 2age2 3chronic 4educ 5female 6hhincome 7hstatusg 8white 9hisp. (2) The associated linear regression equation is given by private 0 1age 2age2 3chronic 4educ 5female 6hhincome 7hstatusg 8white 9hisp u. (3) i) Estimate (3) by OLS. Place the Eviews output in Appendix (b1). (2 marks) ii) Are the regressors in (3) jointly significant Briefly explain. (2 marks) iii) Based on the reported p-values, are any of the regressors in (3) individually insignificant at the 10% significance level Briefly explain. (2 marks) iv) Test the joint significance of the regressors in (3) which were found to be individually insignificant in part iii). Conduct the test of joint significance at the 5% significance level. 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. Place the Eviews output for the restricted model in Appendix (b2) (8 marks) (c) (20 marks) i) Estimate the linear regression equation private 0 1age 2age2 3educ 4female 5hhincome 6hstatusg 7hisp u. (4) Place the Eviews output in Appendix (c). (2 marks) ii) Interpret 6. (2 marks) iii) How do you explain the sign of 6 (2 marks) iv) Derive the predicted probability of having private health insurance for a 40 years old, Hispanic female, who reports their health status as good, who has 10 years of education and an income of 30. (2 marks) 5 v) Test the null hypothesis that the probability of an individual having private health insurance is a linear function of age against the alternative hypothesis that it is a quadratic function of age. Test at the 10% significance level. 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) vi) Controlling for education, gender, income, health status and race, what is the predicted marginal effect of age on the probability of an individual aged 40 having private health insurance (2 marks) vii) Controlling for education, gender, income, health status and race, what is the relationship between the predicted probability of an individual having private health insurance and age Briefly explain. No marks will be awarded for an unsupported answer. (4 marks) (d) (11 marks) i) Derive a model to test the null hypothesis that the marginal effect of education on the response probability in private 0 1age 2age2 3educ 4female 5hhincome 6hstatusg 7hisp u (4) is the same as the marginal effect of income, against the alternative hypothesis that the marginal effect of education is greater. (5 marks) ii) Use the model you derived in part i) to test the null hypothesis specified in i). Test at the 5% significance level. State the null and alternative hypotheses, the unrestricted and restricted models, 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. Place any Eviews output that you generate in Appendix (d). (6 marks) (e) (4 marks) i) Extend the model given by private 0 1age 2age2 3educ 4female 5hhincome 6hstatusg 7hisp u (4) to allow for the possibility that the marginal effect of gender on the probability of having private health insurance may vary by race Report the extended model. (2 marks) ii) Does the data support the proposition that the marginal effect of gender on the response probability varies by race Briefly explain. (2 marks) 6 (f) 16 marks Consider once again the linear regression model given by private 0 1age 2age2 3educ 4female 5hhincome 6hstatusg 7hisp u. (4) i) Define population A to be the population of non-Hispanic females of a given age, with a given income and given level of education, who self-report their health status as good. Write down a theoretical expression for the probability of a randomly selected member of population A having private health insurance. (2 marks) ii) Define population B to be the population of Hispanic males, who self-report their health status as poor, who are the same age and have the same levels of income and education as the individuals in population A. Write down a theoretical expression for the probability of a randomly selected member of population B having private health insurance. (2 marks) iii) Derive the restriction(s) on the parameter(s) of (4) implied by the null hypothesis that the probability of having private health insurance is the same for a randomly selected member of population A as it is for a randomly selected member of population B, once we control for age, education and income. Report all steps in the derivation. No marks will be awarded for an unsupported answer. (2 marks) iv) Test the null hypothesis that the restriction(s) derived in iii) above is (are) true against the alternative hypothesis that the restriction(s) is (are) false. Test at the 5% significance level. Specify the null and alternative hypotheses, the unrestricted and the restricted models, 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.Place any Eviews output that you generate in Appendix (f). (10 marks) 7