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ECOM20001 Final Exam
This is a preview of the draft version of the quiz. Started: Oct 11 at 16:20 Quiz Instructions Academic Integrity Declaration By commencing and/or submitting this assessment I agree that I have read and understood the University’s policy on academic integrity. I also agree that: 1. The work I submit will be original and solely my own work (cheating); 2. I will not seek or receive any assistance from any other person (collusion); and, 3. I will not use any sources without proper acknowledgment or referencing (plagiarism). Semester Two Assessment, 2021 Faculty/Dept: Faculty of Business and Economics, Department of Economics Subject Number: ECOM20001 Subject Name: Econometrics 1 Writing Time: 3 hours Reading: 30 minutes Start and End Times (for students without an Alternative Exam Arrangement (AEA)) Exam Start: 3:00 PM Australian Eastern Standard Time (AEST) on Tuesday 09/11/2021 Exam End: 6:30 PM Australian Eastern Standard Time (AEST) on Tuesday 09/11/2021 You must start and submit your exam within this 3:00 PM - 6:30 PM AEST time window. The exam will end automatically at the 6:30 PM cut-off time Students in different time zones are reminded to be mindful of relevant time zone differences Start and End Times (for students with an Alternative Exam Arrangement (AEA)) Refer to your AEA for the the Exam Start and End times. Open Book Status: Open Book Additional Information 11/10/2021, 16:20 Quiz: ECOM20001 2021 S2 Final Exam 2/20 Exam timetable information can be found on my.unimelb.edu.au Instruction to Students This examination contributes 70% to the final subject mark for ECOM20001 The exam includes 4 sections, 25 questions, and 100 marks in total. Answer all questions using the Canvas LMS quiz tool. Section A: multiple choice Sections B, C, D: type in answers directly into the text boxes provided for each question Questions overview Section A (20 marks) 10 questions (Q1 to Q10). Each question carries 2 marks. Section B (36 marks) 3 questions (Q11, Q12, Q13). Each question carries 12 marks. Section C (22 marks) 6 questions (Q14, Q15, Q16, Q17, Q18, Q19). Section D (22 marks) 6 questions (Q20, Q21, Q22, Q23, Q24, Q25). Exam Conditions All exams will be moderated. Please contact 13MELB (+61 3 9035 5511) for assistance during the exam if you are experiencing technical difficulties. They will be able to contact your examiner during the duration of the examination. You may consider using the Exam Support Chat Tool in LMS Canvas. You will find the Exam Support chat tool in your subject menu where an 'Exam Support' link is set up specifically for your exam. Do not contact your lecturer during the examination period. Students with an Alternative Exam Arrangement (AEA) that is held outside teaching hours should be aware that support may not be available outside teaching times. The University has recommended Google Chrome as a reliable browser due to technical issues with Safari users. Firefox has also been shown to be reliable. Suggest Ethernet instead of WiFi connection if possible and save your exam answers often. DO NOT press the SUBMIT QUIZ button unless you are ready to submit. Once you click on submit, you won't be able to submit again. (Hint: give yourself some buffer time and submit at least several minutes before the exam ends.) After you have answered and checked your answers to all of the questions, click on the SUBMIT QUIZ button at the bottom of the LMS quiz window to 3/20 submit your exam for grading. Attachments for the Exam Please download the following PDF attachment before starting the exam by clicking on the link. formulas.pdf (formula sheet) Good luck! SECTION A: MULTIPLE CHOICE (20 points) This section contains 10 questions (Q1-Q10). 2 ptsQuestion 1 H0: B1=B2 vs. H1: B1!=B2 (where != means “not equals”) H0: B3=0 vs. H1: B3!=0 H0: B1=B2=0 vs. H1: at least one of B1!=0 or B2!=0 None of the above Consider the following regression: Y_i = B0 + B1 X1_i + B2 X2_i + B3 (X1_i * X2_i) + u_i. Suppose we wanted to test whether the partial effect of X1_i is the same as the partial effect of X2_i. What are the correct null and alternative hypotheses? 2 ptsQuestion 2 In a sample with n=61 observations you run a regression with k=5 regressors and obtain a standard error of the regression (SER) of SER=12. The sample variance of Y is 132. What of the following statement about the R-squared (R2) is correct? 4/20 R2 = 0 0 < R2 < 0.5 R2 = 0.5 R2 > 0.5 2 ptsQuestion 3 0.2 0.8 0.08 none of the above Suppose we are interested in the relationship between weather (X=0 means no rain; X=1 means rain) and stock market performance (Y=0 means stock market falls; Y=1 means stock market rises). Suppose the joint distribution of X and Y is given as P(X=0, Y=0)=0.32, P(X=0, Y=1)=0.48, P(X=1, Y=0)=0.08, P(X=1, Y=1)=0.12. What is the probability of raining conditional on a stock market fall? 2 ptsQuestion 4 Reject null at the 1% significance level Reject null at the 5% significance level, but not at the 1% significance level Reject null at the 10% significance level, but not at the 5% significance level Not reject null at the 10% significance level Suppose you estimate a single linear regression of Y on X and obtain a slope estimate of B1=-12 with a standard error of SE(B1)=2. Suppose that you wanted to test the null hypothesis that the true value of B1 is -16 against the alternative that it is not equal to -16. Which of the following is correct? 11/10/2021, 16:20 Quiz: ECOM20001 2021 S2 Final Exam 5/20 2 ptsQuestion 5 The OLS estimator is the best linear unbiased estimator The variance of the error term is the same for any X A linear regression model fits better than a nonlinear regression model The variance of the OLS estimator can be estimated Which of the following statements are wrong under homoskedasticity? 2 ptsQuestion 6 An additional bar per 10,000 population is associated with an increase of 10 infected individuals per 1,000 population An additional bar per 10,000 population is associated with an increase of 1 infected individual per 1,000 population An additional bar per 10,000 population is associated with an increase of 0.1 infected individuals per 1,000 population An additional bar per 10,000 population is associated with an increase of 0.01 infected individuals per 1,000 population Suppose you run a single linear regression of Infect_i = B0 + B1 Barden_i + u_i where Infect_i is the number of infected individuals per 10,000 population in area i and Barden_i is the number of bars per 1,000 population in area i. If you obtained a B1 estimate of 10, which of the following would be the correct interpretation? 2 ptsQuestion 7 The slope estimate must be positive Suppose X is the regressor and Y is the dependent variable. Suppose there is classical measurement error in X. When we regress Y on X, which of the following statement is correct? 6/20 The slope estimate must be close to zero The slope estimate may be negative or positive None of the above 2 ptsQuestion 8 Yes No We need to know the sample mean to answer the question There is not enough information Suppose we carry out hypothesis testing on the population mean of a random variable. Suppose from a random sample with a very large sample size you compute a 95% confidence interval for the population mean of [-1, 3.9]. Further, suppose that you wanted to test the null hypothesis that the population mean equals 4 against the alternative that it is not equal 0. Would you reject the null at the 1% level of significance? 2 ptsQuestion 9 It is the elasticity of Y_i with respect to X_i A 1-unit increase in X_i yields a 100B1% increase in Y_i A 1-unit increase in X_i yields a B1% increase in Y_i A B1 unit increase in X_i yields a 1% increase in Y_i Consider the following regression: ln(Y_i)=B0 + B1 X_i + u_i. Which of the following is the correct interpretation of B1? 2 ptsQuestion 10 11/10/2021, 16:20 Quiz: ECOM20001 2021 S2 Final Exam 7/20 X and Y are statistically independent because raining cannot affect the stock market X and Y are statistically independent X and Y are not statistically independent X has a causal effect on Y if X and Y are not statistically independent Suppose we are interested in the relationship between weather (X=0 means no rain; X=1 means rain) and stock market performance (Y=0 means stock market falls; Y=1 means stock market rises). Suppose the joint distribution of X and Y is given as P(X=0, Y=0)=0.32, P(X=0, Y=1)=0.48, P(X=1, Y=0)=0.08, P(X=1, Y=1)=0.12. Which of the following is correct? SECTION B (36 points) This section contains 3 questions (Q11, Q12, Q13). 12 ptsQuestion 11 We are interested in estimating casual effect of yoga exercise on health. Answer the following questions. Show your working. Wherever relevant, you should write down the estimation equation, define all the variables that you would use, and briefly describe the hypothesis test involved. (Hint: when conducting the test, do not impose restrictions on the sign of the effect.) (a)(3pts) Suppose we have a data set for all residents in Melbourne. There are two variables: individual’s health score (SCORE); individual’s number of hours of yoga exercise per week (YOGAHRS). Suppose individuals who regularly do yoga exercise also tend to eat more unhealthy food (e.g., they indulge themselves after exercising). Assume that eating more healthy food results in better health, all else being equal. Write down the equation for the single linear regression of SCORE on YOGAHRS, and then explain what the direction of the omitted variable bias would be for the slope coefficient on YOGAHRS. 11/10/2021, 16:20 Quiz: ECOM20001 2021 S2 Final Exam 8/20 p 0 words (b)(3pts) Suppose someone in a health organization suggests a randomized controlled trial, which randomly selects half of the Melbourne residents to be given a free yoga mat. Suppose you have data on all Melbourne residents' health scores and whether each individual is given a free yoga mat. Explain how you would evaluate the effect of this policy using regression. (c)(6pts) Suppose the manager thought that the experiment was too expensive. Instead, the manager held free yoga lessons in five suburbs of Melbourne (Carlton, Parkville, Southbank, Docklands, Flemington) in February 2021. Suppose you have data on all Melbourne residents' health scores in January 2021 and February 2021. Explain how you would use a differences-in-differences model to evaluate the effect of this policy. You should also describe how you define the treatment and control groups and pre- and post-policy periods in the data.
12 ptsQuestion 12 Consider the following population linear regression model of individual consumption: Y = 30 + 0.2X + u, where Y is yearly consumption (in thousand dollars), X is the individual’s yearly income (in thousand dollars), and 30+0.2X is the population regression line. Suppose we generate artificial data for 3 Edit View Insert Format Tools Table 12pt Paragraph 9/20 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Observation X Y E(Y|X) u Predicted value of Y (Yhat) Residual (uhat) 1 30 50 V1 V2 45 5 2 70 V4 44 ? V3 -10 3 110 ? ? ? ? V5 Suppose we know that in this artificial sample, the sample mean of Y is 60, the sample variance of Y is 300, the sample variance of X is 1600, and the sample covariance between X and Y is 600. Assume these summary statistics hold in all parts of this question. Answer the following questions. Show your working. (a)(2pts) What are the values of V1 and V2? (b)(3pts) Compute the OLS regression line of the regression of Y on X. (Hint: Assume the OLS regression line continue to hold in parts (c)-(e).) (c)(2pts) What are the values of V3 and V4? (d)(2pts) Compute the value of V5 using the information given by the table alone. Briefly explain how you obtain this result. (e)(3pts) Compute the R-squared of the regression in part (b). Show your working. Edit View Insert Format Tools Table 12pt Paragraph 11/10/2021, 16:20 Quiz: ECOM20001 2021 S2 Final Exam 10/20 p 0 words 12 ptsQuestion 13 Consider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to test the null hypothesis H0: B1 + 2 B2 = 0, versus the alternative hypothesis H1: B1+ 2 B2 != 0 (!= means "not equal to"). The data set consists of 300 observations. Answer the following questions. Show your working. In all places that are relevant, you should describe the test statistic and critical-value (or p-value) used. (a)(6pts) Describe TWO different ways of transforming the regression to conduct the test. (b)(2pts) Suppose we use an F-statistic to conduct the test. What are the degrees of freedom associated with this test statistic? (c)(2pts) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b). Denote the actual F-statistic by F_act. Suppose G(F_act)=0.07. Do you reject the null hypothesis at the 10% significance level? Briefly explain why. (d)(2pts) Suppose you find that the F-test in part (b)-(c) and the test in part (a) yield identical p-values. Do you think this result is correct? Briefly explain your reasoning. Edit View Insert Format Tools Table 12pt Paragraph 11/10/2021, 16:20 Quiz: ECOM20001 2021 S2 Final Exam 11/20 p 0 words SECTION C (22 points) This section contains 6 questions (Q14, Q15, Q16, Q17, Q18, Q19). A data set of 5,000 workers contains the following variables: LNEARN: logarithm of annual earnings AGE: age in years AGE_SQ: square of AGE LNAGE: logarithm of AGE Regression output with HC standard errors is shown below: Dependent variable: LNEARN (1) (2) LNAGE 0.491 (0.040) AGE 0.098 (0.007) AGE_SQ -0.001 (0.0001) CONSTANT 8.955 8.572 (0.150) (0.152) R2 0.037 0.069 Answer the following questions. Show your working. (Hint: You may want to take a screenshot of the regression output so you don't have to scroll up and down when you answer the questions.) 12/20 4 ptsQuestion 14 p 0 words Discuss the result in regression (1) by interpreting the coefficient estimate on LNAGE and discussing its statistical significance. Then, based on regression (1), compute the 95% confidence interval for the coefficient on LNAGE.