ETF2100/5910 Introductory Econometrics Assignment 2, Semester 2, 2021 IMPORTANT NOTES: • Type your answers using Microsoft Word or write your answers CLEARLY. You must submit a PDF file to Moodle. Other file formats are not accepted. • Notation used in the assignment needs to be typed or written correctly and properly. Marks are also awarded for presentation. • When doing calculation, keep at least 4 decimal in each step for precision. For final answer, 3 decimal point is sufficient, unless specified otherwise in the question. • In this assignment, when you need to use t or F critical value, if the question does not specify, you can either find it using Eviews or use the statistical table. If the question specifies, use that method. • This assignment is worth 15% of this unit’s total mark. • ETF2100 students must answer Question 1, Question 2, Question 3, and Question 4. • ETF5910 students must answer Question 1, Question 3, Question 4, and Question 5. • Total marks for both ETF2100 and ETF5910 students is 45. • Marks will be deducted for late submission on the following basis: 5 marks off for each day late, up to a maximum of 3 days. Assignments more than 3 days late will not be marked. Data and context for Questions 1, 2 and 3 You will use the data file br5 available in csv and Eviews format (.wf1) on Moodle to answer these question. The data provides prices and characteristics of a sample of houses. The variables are as follows: • price: Selling price in thousand dollars • baths: Number of bathrooms • bedrooms: Number of bedrooms • sqft: Total living area (total size) of the house in hundreds of square feet • age: age of each house in years Page 1 of 4 Question 1 (7 marks) (a) (2 marks) Estimate the following model using least squares. Report the result in full AND provide Eviews output. pricei = β1 + β2sqfti + β3agei + β4bathsi + ei (1) (b) (5 marks) Interpret the estimated coefficient for sqft, age and baths. Is the sign of each coefficient what you expected? Why? Question 2 (6 marks): FOR ETF2100 ONLY Based on the model in question 1(a) above, test at the 5% level of significance the null hypothesis that a decrease in total living area by 100 square feet has the same effect on house price as a 10 year increase in the house age, other things being constant. Use a t-statistic approach and write down all the steps used to conduct your test. You can use Eviews to calculate the test statistic and obtain the t-critical value. Question 3 (15 marks) (a) (2 marks) You suspect that the change in price associated with an extra square feet of house size depends on how old the house is. Extend the model in question 1(a) to allow for this (write the new model down). Estimate this model and include your Eviews output. (b) (2 marks) Comment on the significance of all the coefficients in the extended model you just estimate for question 3(a) using the p-value appraoch. (Don’t forget to state the significance level at which the coefficients are significant, e.g. 1, 5 or 10 percent) (c) (3 marks) Using this extended model, write down the expressions for the marginal effect ∂ ̂E(price|X) ∂sqft where X denote all observations on sqft and age. Interpret this expression for a house with age equal to a particular level, say age0. Note, there is no need to put in any numbers here and you can use bk to denote estimate for βk. (d) (8 marks) Find point estimates AND 95% interval estimates for the marginal effect of an extra hundred square feet of total living area on house price for houses that are (i) 2 years old, and (ii) 45 years old. How do these estimates change as age increases? [You can use Eviews to find the appropriate standard errors]. Page 2 of 4 Data and context for questions 4 and 5 In these questions, we are interested in studying whether a mother’s smoking affects the birthweight of her baby. The data for this question is birthweight.csv available on Moodle. The variables you need are as follows: • bweight:infant birthweight (grams) • smoke2: 1 if mother smokes 1-5 cigarettes per day, 0 otherwise • smoke3: 1 if mother smokes 6-10 cigarettes per day, 0 otherwise • smoke4: 1 if mother smokes 11 or more cigarettes per day, 0 otherwise • mmarried: 1 if mother married, 0 otherwise • mage: mother’s age Question 4 (17 marks) (a) (1 marks) Estimate the following regression model by least squares. Provide Eviews output. No need to report the result in full in equation form. bweighti = β1 + β2smoke2i + β3smoke3i + β4smoke4i + β5magei + β6mmariedi + ei (2) (b) (3 marks) Interpret the estimated coefficients of smoke2, smoke3 and smoke4 (c) (6 marks) Using the F-test at 1% significance level, test the hypothesis that mother’s smoking behavior does not affect the birthweight of her baby. [Hint: All smoking dummies should be considered here.] You must write out the test in full including all the steps. Don’t forget to write down the restricted model. Compute the F-statistic using the Wald test function in Eviews and show the Eviews Wald test output screenshot (no need to manually estimating both the restricted and unrestricted models separately here). Also use Eviews to find the exact F critical value. (d) (3 marks) What is the estimated difference in the expected birthweight of a baby whose mother is not married and smokes 1-5 cigarettes a day relative to that of a baby whose mother is of the same age, married, and smokes 11 or more cigarettes a day? Interpret your answer in full. (e) (1 marks) Now consider a similar model but with log of birthweight as dependent variable. Estimate this model and provide Eviews output. No need to report the result in full in equation form. ln(bweight)i = β1 + β2smoke2i + β3smoke3i + β4smoke4i + β5magei + β6mmariedi + ei (3) (f) (3 marks) Using the results from part (e), interpret the coefficient of smoke4 using both the “rough” calculation and the “exact” calculation. Report your answers to 2 decimal place. Page 3 of 4 Question 5 (6 marks): FOR ETF5910 ONLY Based on the model in question 3(e), test at 5% significance level the null hypothesis that smoking 11 or more cigarettes per day reduces birthweight by no more than smoking 6-10 cigarettes per day, against the hypothesis that smoking 11 or more cigarettes per day reduces birthweight by more than smoking 6-10 cigarettes per day. Use a t-statistic approach and write down all the steps used to conduct your test. You can use Eviews to calculate the test statistics and obtain the critical value. Page 4 of 4