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q2 only but with explanatons

Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Group Assignment (45%) Graded Assignment Descriptions, Rubrics and Guidelines Units Covered 1 – 8 Weighting: 45% of your grade Final mark Computation: */ x 45 = Opens: Sunday June 27, at 5:00 am ECT Closes: Tuesday, July 20, at 11:55 pm ECT Answer all questions and show all your work for full marks. Only (1) member of the group submits the assignment and the cover page should identify all group member by name and ID numbers. Plagiarism will be penalized. Upload your assignment as a Word document. The submitted Microsoft Word document should consist of the following: 1.5-line spacing, 12-point font, and scholarly references. You are expected to use Microsoft equation tool where needed to show all equations or notations. Accuracy in referencing using the APA style is paramount. Question 1 is worth 20 marks Question 2 is worth 30 marks Question 3 is worth 20 marks Question 4 is worth 30 marks Total marks 100 marks Related Course Objectives: • All units Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Question 1 (20 marks) Using a sample of 1801 black individuals, the following earnings equation has been estimated: ??(????????̂ ) = 7.059 + 0.147???? + 0.049?????????? − 0.201?????? (0.135) (0.008) (0.007) (0.036) ?2 = 0.179; ? = 1801 a) Interpret the coefficient estimate on female b) Test the hypothesis that there is no difference in expected earnings between black women and black men. Test the hypothesis against a two-sided alternative, using a 5% significance level. c) Dropping experience and female from the equation gives: ??(????????̂ ) = 6.703 + 0.151???? (0.182) (0.012) ?2 = 0.153 ? = 1801. Are experience and female jointly significant in the original equation at the 5% significant level? Question 2 (30marks) 1. The estimation of a Cobb-Douglas production function for 20 firms of a given industry yields: ?�̂� = 16.907 + 0.322?? + 2.777?? ?2 = 0.915 ?? = 2.032 ??? = 0.461 ??? ? = 5% ??? �̂� = ( 0.166070 0.031857 0.216639 −0.857446 −0.057229 4.939971 ) where ?�̂�: fitted values of naturals logaritrhms of output (output express in 1000 tons); ??: ??????? logaritrhms of capital output (output express in 1000 tons) ??: ??????? logaritrhms of labour (labour is in hours) ???: ???????? ??? ?? ??????? ?: ???? ????? ??? �̂�: ???????? − ?????????? ?????? ?? ????????? a. Evaluate the statistical significance of the coefficients. b. A regression on the original regressors, �̂�t2 and a constant term yields the following statistics: R2 = 0.296041 F = 1.177507 coeff of �̂�t2 has a t-statistic of 2.876 (i) With this information, which test can you implement to deal with the problem omitted variables and why? Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 (ii) Implement the test as stated in b(i) and interpret the results. (iii) What is (are) five consequence(s) of omitted variables in a regression model? Question 3 (20marks) State whether the statements in (i)-(x) are true or false, and explain why. i. Heteroskedasticity implies that ???(?/×) = ???(?/×) . True by definition ii. The goodness of fit ?2 or the coefficient of determination is always between 0 and 1. True by definition iii. The goodness of fit having a ?2 that is nearly equals to zero indicates that very little of the variation in ?? is captured by the variation in the ?? True by definition iv. A white noise process is a non-stationary process for which all autocorrelations are equal to zero. v. If our series are non-stationary, it is safe to use OLS as our estimation method. vi. Heteroscedasticity occurs when the disturbance term in a regression model is correlated with one of the explanatory variables vii. In the presence of heteroscedasticity, ordinary lease squares (OLS) is an inefficient estimation technique and this causes t tests and F tests to be invalid. viii. Heteroscedasticity can be detected with the Chow test. ix. In the presence of autocorrelation, ordinary lease squares (OLS) produce unbiased estimates and hence t tests and F tests are still valid. x. One problem with the use of a lagged dependent variable as an explanatory variable is that it always gives rise to autocorrelation. Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Question 4 (30marks) Let ECON10 denote the percentage of econometric students at UWI who need to receive a passing score on a standardized econometrics exam. The government wish to estimate its efforts of the local funded tertiary econometrics analysis software on students’ performance. In fact, the government expect the analysis software to have a positive ceteris paribus effect performance, all other things being equal, if the student who is under-privilege to purchase the software becomes eligible for the government funded tertiary assistance software program, his or her performance should improve by 10% points in the error term in UWI and students’ characteristics that effect the school program. Given that tertiary denotes % of the students who is eligible for the software program and ? – error term. 1. Write a simple regression model? 2. UWI for 2019 – 2020 academic year obtain the following: ?????? = ??. ?? − ?. ?????????? ? = ??? ?? = ?. ??? What does the equation predict? 3. Do you agree / disagree with the prediction. Briefly Give two (2) reasons for your answer. 4. Is the regression biased or unbiased? Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Group Assignment Rubric Question Distribution of Marks Total Marks 1a 1b 1c Interpret the coefficient estimate on female Test the hypothesis that there is no difference in expected earnings between black women and black men. Are experience and female jointly significant in the original equation 4 marks 8 marks 8 marks 20 2 Evaluate the statistical significance of the coefficients which test can you implement to deal with the problem omitted variables and why Five consequence(s) of omitted variables in a regression model? 10 marks 10 marks 10 marks 30 3 Explain with reason whether the following statements are true, or false. 2 marks each 1 mark for correct response (i.e. true, false) 1 mark for justified explanation 20 4 Write a simple regression model? What does the equation predict? Do you agree / disagree with the prediction. Give 2 reasons why Is the regression biased or unbiased? 4 marks each 6 marks each 12 marks 8 marks 30 Total 100 END of Group Assignment QUESTION PAPER

Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Group Assignment (45%) Graded Assignment Descriptions, Rubrics and Guidelines Units Covered 1 – 8 Weighting: 45% of your grade Final mark Computation: */ x 45 = Opens: Sunday June 27, at 5:00 am ECT Closes: Tuesday, July 20, at 11:55 pm ECT Answer all questions and show all your work for full marks. Only (1) member of the group submits the assignment and the cover page should identify all group member by name and ID numbers. Plagiarism will be penalized. Upload your assignment as a Word document. The submitted Microsoft Word document should consist of the following: 1.5-line spacing, 12-point font, and scholarly references. You are expected to use Microsoft equation tool where needed to show all equations or notations. Accuracy in referencing using the APA style is paramount. Question 1 is worth 20 marks Question 2 is worth 30 marks Question 3 is worth 20 marks Question 4 is worth 30 marks Total marks 100 marks Related Course Objectives: • All units Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Question 1 (20 marks) Using a sample of 1801 black individuals, the following earnings equation has been estimated: ??(????????̂ ) = 7.059 + 0.147???? + 0.049?????????? − 0.201?????? (0.135) (0.008) (0.007) (0.036) ?2 = 0.179; ? = 1801 a) Interpret the coefficient estimate on female b) Test the hypothesis that there is no difference in expected earnings between black women and black men. Test the hypothesis against a two-sided alternative, using a 5% significance level. c) Dropping experience and female from the equation gives: ??(????????̂ ) = 6.703 + 0.151???? (0.182) (0.012) ?2 = 0.153 ? = 1801. Are experience and female jointly significant in the original equation at the 5% significant level? Question 2 (30marks) 1. The estimation of a Cobb-Douglas production function for 20 firms of a given industry yields: ?�̂� = 16.907 + 0.322?? + 2.777?? ?2 = 0.915 ?? = 2.032 ??? = 0.461 ??? ? = 5% ??? �̂� = ( 0.166070 0.031857 0.216639 −0.857446 −0.057229 4.939971 ) where ?�̂�: fitted values of naturals logaritrhms of output (output express in 1000 tons); ??: ??????? logaritrhms of capital output (output express in 1000 tons) ??: ??????? logaritrhms of labour (labour is in hours) ???: ???????? ??? ?? ??????? ?: ???? ????? ??? �̂�: ???????? − ?????????? ?????? ?? ????????? a. Evaluate the statistical significance of the coefficients. b. A regression on the original regressors, �̂�t2 and a constant term yields the following statistics: R2 = 0.296041 F = 1.177507 coeff of �̂�t2 has a t-statistic of 2.876 (i) With this information, which test can you implement to deal with the problem omitted variables and why? Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 (ii) Implement the test as stated in b(i) and interpret the results. (iii) What is (are) five consequence(s) of omitted variables in a regression model? Question 3 (20marks) State whether the statements in (i)-(x) are true or false, and explain why. i. Heteroskedasticity implies that ???(?/×) = ???(?/×) . True by definition ii. The goodness of fit ?2 or the coefficient of determination is always between 0 and 1. True by definition iii. The goodness of fit having a ?2 that is nearly equals to zero indicates that very little of the variation in ?? is captured by the variation in the ?? True by definition iv. A white noise process is a non-stationary process for which all autocorrelations are equal to zero. v. If our series are non-stationary, it is safe to use OLS as our estimation method. vi. Heteroscedasticity occurs when the disturbance term in a regression model is correlated with one of the explanatory variables vii. In the presence of heteroscedasticity, ordinary lease squares (OLS) is an inefficient estimation technique and this causes t tests and F tests to be invalid. viii. Heteroscedasticity can be detected with the Chow test. ix. In the presence of autocorrelation, ordinary lease squares (OLS) produce unbiased estimates and hence t tests and F tests are still valid. x. One problem with the use of a lagged dependent variable as an explanatory variable is that it always gives rise to autocorrelation. Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Question 4 (30marks) Let ECON10 denote the percentage of econometric students at UWI who need to receive a passing score on a standardized econometrics exam. The government wish to estimate its efforts of the local funded tertiary econometrics analysis software on students’ performance. In fact, the government expect the analysis software to have a positive ceteris paribus effect performance, all other things being equal, if the student who is under-privilege to purchase the software becomes eligible for the government funded tertiary assistance software program, his or her performance should improve by 10% points in the error term in UWI and students’ characteristics that effect the school program. Given that tertiary denotes % of the students who is eligible for the software program and ? – error term. 1. Write a simple regression model? 2. UWI for 2019 – 2020 academic year obtain the following: ?????? = ??. ?? − ?. ?????????? ? = ??? ?? = ?. ??? What does the equation predict? 3. Do you agree / disagree with the prediction. Briefly Give two (2) reasons for your answer. 4. Is the regression biased or unbiased? Econometrics (ECON3049) Course Assessments. Academic Year 2020/2021, Semester 3 Group Assignment Rubric Question Distribution of Marks Total Marks 1a 1b 1c Interpret the coefficient estimate on female Test the hypothesis that there is no difference in expected earnings between black women and black men. Are experience and female jointly significant in the original equation 4 marks 8 marks 8 marks 20 2 Evaluate the statistical significance of the coefficients which test can you implement to deal with the problem omitted variables and why Five consequence(s) of omitted variables in a regression model? 10 marks 10 marks 10 marks 30 3 Explain with reason whether the following statements are true, or false. 2 marks each 1 mark for correct response (i.e. true, false) 1 mark for justified explanation 20 4 Write a simple regression model? What does the equation predict? Do you agree / disagree with the prediction. Give 2 reasons why Is the regression biased or unbiased? 4 marks each 6 marks each 12 marks 8 marks 30 Total 100 END of Group Assignment QUESTION PAPER

Jul 20, 2021

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