ETF2100/5910 Introductory Econometrics Assignment 2, Semester 2, 2020 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, you can either find it using Eviews or use the statistical table. You should know how to do both. • This assignment is worth 20% of this unit’s total mark. • ETF2100 students must answer Question 1,2,3 and Question 5. • ETF5910 students must answer Question 1,2,3 and Question 4. • Total marks for ETF2100 and ETF5910 students are both 40. • 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 The dataset used for question 1, 2 and 3 is a dataset on pollution in Beijing, China and is available on Moodle in both EViews workfile format (.wf1) and in csv format (can be opened in Excel). The variables are measured daily at 6PM from 2nd January, 2010 until 31st December, 2015 (there are some days missing) and are as follows: • pm2 5 (in micrograms per cubic metre): The PM2.5 concentration is a measure of air pollution. More precisely it is the concentration in the air of particles which are less than 2.5 micrometres in diameter. • dewpoint (in degrees Celsius): The dew point is the temperature to which the air must be cooled to become saturated with water vapour. • humidity (in percentage points): A measure of the amount of water vapour in the air. • se: A dummy variable equal to 1 if the wind comes from the south east and 0 otherwise Page 1 of 11 • ne: A dummy variable equal to 1 if the wind comes from the north east and 0 otherwise • nw: A dummy variable equal to 1 if the wind comes from the north west and 0 otherwise • windspeed (in km/h): Measures the strength of the wind. Note: When the three wind direction dummies equal 0 the wind is calm or variable. Question 1: FOR ALL STUDENTS (13 Marks) *Please begin this question on a new page (a) Estimate the following regression model by least squares and include your EViews output in your answer (1 Marks) pm25 = β1 + β2humidity + β3dewpoint + β4se + β5ne + β6nw + β7windspeed + e (b) Interpret your estimate of β4. (2 Marks) (c) What is the estimated difference between the expected value of PM2.5 when the wind comes from a southeasterly direction compared to the case where the wind comes from a northeasterly direction, assuming humidity, dew point and wind speed are the same. Show your work and provide a full interpretation. (4 Marks) (d) Test at the 1% level of significance the null hypothesis that the southeasterly wind has the same effect on the expected value of PM2.5 concentration as the northeasterly wind, assuming all other variables remain constant, against the alternative hypothesis that the northeasterly wind reduces PM2.5 concentration more than the southeasterly wind. 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. (6 Marks) Question 2: FOR ALL STUDENTS (15 Marks) (a) We suspect that the relationship between humidity and PM2.5 concentration may be a quadratic relationship. We extend the model in Question 1 to allow for this relationship as follows. Es- timate this model and include your output. (1 Marks) pm25 = β1 + β2humidity + β3humidity 2 + β4dewpoint + β5se + β6ne + β7nw + β8windspeed + e (b) Using the F-test at 5% significance level, test whether humidity helps explain variation in PM2.5 concentration. You must write out the test in full including null and alternative hypotheses stated in terms of the parameters. Compute the F-statistic manually by estimating both the restricted and unrestricted model. Make sure to write down the restricted model and unrestricted model fully, and show the Eviews output for the restricted model. (7 Marks) Page 2 of 11 (c) What do the estimates for β2 and β3 tell you about the relationship between humidity and PM2.5 concentration, keeping all other variables constant. Hint: Think about the signs of these coefficients and what they say about the shape of the quadratic function. Make sure to explain your answer in the context of the question. (3 Marks) (d) For your model in question 2 (a), find and interpret the marginal effect of humidity on PM2.5 concentration when humidity is (i) 25 percentage points, and (ii) 80 percentage points. (4 Marks) Question 3: FOR ALL STUDENTS (5 Marks) (a) Starting from the model in Question 1, you suspect that the change in PM2.5 concentration associated with an increase in windspeed of 1 km/h depends on the direction from which the wind comes from. Extend the model in Question 1 to allow for this relationship. Estimate this model and include your output. (1 Marks) Hint: All wind direction dummies should be interacted. (b) For your model in question 3(a), find and interpret the marginal effect of windspeed when the wind comes from (i) a north western direction, and (ii) a south eastern direction. (4 Marks) Question 4: FOR ETF5910 ONLY (7 Marks) In this question, we examine the hours of work per week by married women (H) as a function of their earning per hour (W) measured in dollars, and number of children. [Note, you do not need a dataset or Eviews for this question.] Let ONEKID = 1 if a woman has one child, and zero otherwise. Let TWOKID=1 if a women has two children, and zero otherwise. Let MANY=1 if a women has three or more children, and zero otherwise. The regression model is: ln(Hi) = β1 + β2ln(Wi) + β3ONEKIDi + β4TWOKIDSi + β5MANYi + ei (1) The estimated model is: l̂n(Hi) = 3.60 + 0.02ln(Wi)− 0.025ONEKIDi − 0.041TWOKIDSi − 0.039MANYi (2) (a) Interpret the coefficient of TWOKID using both the “rough” calculation and the “exact” cal- culation. Report your answers to 2 decimal place. (4 Marks) (b) Find point prediction (using the natural predictor) for the hours of work of a woman earning 20 dollars an hour who has four children. (3 Marks) Page 3 of 11 Question 5: FOR ETF2100 ONLY(7 Marks) In this question, we examine the hours of work per week by married women (H) as a function of their earning per hour (W) measured in dollars, and education. [Note, you do not need a dataset or Eviews for this question.] There are four categories of education level: (i) Less than high school qualification, (ii) High school graduate (with no Bachelor’s degree), (iii) Bachelor’s degree, and (iv) Postgraduate degree Let POSTGRAD =1 if a woman has a postgraduate degree, and zero otherwise. Let BACH=1 if a woman has Bachelor’s degree, and zero otherwise. Let HIGH=1 if a woman has graduated high school (but has no Bachelor’s degree). The regression model is: ln(Hi) = β1 + β2ln(Wi) + β3POSTGRADi + β4BACHi + β5HIGHi + ei (3) The estimated model is: l̂n(Hi) = 3.71 + 0.01ln(Wi) + 0.073POSTGRADi + 0.046BACHi − 0.001HIGHi (4) (a) Interpret the coefficient of BACH using both the “rough” calculation and the “exact” calcula- tion. Report your answers to 2 decimal place. (4 Marks) (b) Find point prediction (using the natural predictor) for the hours of work of a woman earning 25 dollars an hour who has a postgraduate degree. (3 Marks) Page 4 of 11
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