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ECMT2150 S2 2021, Quiz 2

Part A (15 marks)

Questions 1-4 are short answer and should be answered in reference to the following:

A group of academic advisors at the University of Sydney is investigating the relationship between students’ WAM (Weighted Average Mark) and the hours they are employed in work each week. To investigate the issue, they surveyed 5,000 first-year and second-year students and gathered data on their WAMs, year-level, age and average weekly time spent studying. They also asked: “How many hours are you employed in work in a typical week?”.

Note: It is important that you define any variables you use in answering the questions below.

1) [3 marks] Write an equation that would allow you to estimate the associated effects of employment on students’ WAMs, while controlling for other factors. You should be able to make statements such as “Being employed for one more hour per week is estimated to change a student’s WAM by x points.”

2) [4 marks] Propose a regression model that would allow you to test whether employment is associated with different effects on the WAMs of first-year vs. second-year students. How would you test the hypothesis that employment is estimated to affect first-year and second-year students differently?

3) [4 marks] You believe students might not be correctly reporting the amount of time they are employed. To overcome this problem, someone proposes classifying students into three categories: Not employed (no employment at all); Part-time Employed (employed 1 – 22 hours each week); and Full-time employed (employed 23 or more hours per week). Using those categories, write a model that allows you to estimate the effects of employment on students’ WAM.

4) [4 marks] Using the model in part (3), explain in detail how you would test the null hypothesis that employment is not estimated to have any effect on students’ WAMs. Be very specific and include a careful listing of degrees of freedom.

PART B (30 marks)

Empirical Exercise Using STATA: Estimation, Interpretation and Inference

Questions related to this part will be worth 30 points. There will be a mix of multiple choice, numerical answer, and short answer questions.

REMINDER: I encourage you to work through the following analysis of the data in STATA or another software package before doing the quiz. There are no trick questions, so if you have completed each of the following questions, kept a copy of your output and made a note of your answers, there will be no surprises when you are taking the quiz. You should not need to use STATA during the quiz at all. The quiz is not timed, so you can leave and come back to the quiz if you need to.

Accessing the data: You can download the data from the ‘Quiz 2 Instructions’ page where you found these instructions. Head to the ‘Assignments’ area on our Canvas site:

https://canvas.sydney.edu.au/courses/35741/assignments

Note: there are multiple versions of the dataset. Each student will have a link to just one of these datasets. I have edited the data for each version to make them different enough to prevent collusion. You need to answer the questions using your own data. If you answer questions using one of your classmate’s datasets, you will answer questions in the quiz incorrectly and you will lose marks or be referred to the academic integrity office.

Data and research question description

Housing prices in Sydney have been increasing strongly for several years. This brings with it issues related to housing affordability and concerns about the sustainability of rising debt levels. We will investigate some potential drivers of house prices to help policy makers better understand what might be causing rising housing prices in Sydney. To do this, we will use observations on housing prices and housing characteristics collated from different suburbs in Sydney in the mid-1990. This is when housing prices in Sydney first started rising. The dataset, ‘syd_hprice.dta’, contains a sample of 88 observations on the following variables:

● price = house price, $1000s

● assess = assessed value, $1000s

● bdrms = number of bedrooms

● lotsize = size of the property in square metres

● sqrm = size of house in square metres

● fed = indicator variable, 1 if home is federation style, 0 otherwise

Questions:

a) [3 marks] Compute the mean and standard deviation of price, assess, lotsize and sqrm.

b) [3 marks] Create (and keep a copy of) two scatterplots. One with a plot of price (y-axis) against lotsize (x-axis) and the second one with a plot of the natural log of price (y-axis) against the natural log of lotsize (x-axis). Discuss the differences you observe in the two scatterplots.

c) [4 marks] Consider the following model of housing prices:

Create the new explanatory variables in the model and estimate the model and report the results. Comment on the individual coefficient estimates and whether these are statistically significant and/or economically significant.

d) [3 marks] Interpret the estimated coefficient on the federation indicator (dummy) variable in the model. What does it suggest about the price of Federation-styled homes in Sydney?

e) [3 mark] What share of the variation in the log of housing prices across the sample of suburbs does the model explain? What does the R² tell us about the reliability of our results?

f) [3 marks] Instead of, or in addition to, the R², how should we assess the reliability of our results in the model?

g) [4 marks] Test the null hypothesis:

Against the alternative hypothesis that at least one of the restrictions is not valid. Show the F-statistic and p-value. What do you conclude about the model for housing prices?

h) [4 marks] Based on the results from g) we decide to estimate the following alternative model for Sydney housing prices:

Report and interpret the results for this alternative model. What is the implication of this model for housing prices in Sydney?

i) [3 marks] Create a document in STATA or in Word that documents your work (commands and output) in STATA. This should be no more than 2 pages long. You will need to upload it during the quiz – as a Word document or a PDF. Quizzes that are missing this file may be penalized.

There are lots of ways to do this:

● You could use a STATA log file that you could later save as a PDF to upload

● You can copy paste from the log file into a Word doc

● You can highlight the relevant output in the Results window, then right clicking to copy either as text or as a picture. Then paste into a word document.

Whatever method you use, save the Word or PDF document somewhere you can find it, so you can easily upload it while you are taking your quiz.