ECON2280: Introductory Econometrics
Assignment 1 (Due Monday Feb. 19, 2024)
February 2, 2024
Guidelines
You are free to work on this assignment in groups (of up to 3 students) but
you are strongly encouraged to work out these problems individually before
discussing answers with your group. Each group should submit a single copy of
answers to these questions onto Moodle. Write your student ID and the names of
any student you worked with on this assignment. Names cannot be added after the
assignment is submitted. The whole assignment must be typed. Equations must be
typed with software for typing equations, such as the Equation Editor in MS Word.
Late submission or handwritten assignments will not be accepted and a zero score
will be given.
Questions
1 [20pts] You are provided with the following descriptions of data collected for different research studies. For each description, identify the type of dataset it represents
(e.g., cross-sectional, time series, panel data, or pooled cross-sectional).
(a) Researchers collected annual GDP growth rates for the United States from
1990 to 2020.
(b) A survey was conducted in 2021 where 500 individuals from various cities were
asked about their monthly household income and expenditure.
(c) Data was compiled on the annual sales and number of employees for 50 technology companies over the last ten years.
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(d) A health study gathered information on the weight and blood pressure of 1000
participants in January and then again in July of the same year.
(e) HKU conducts annual surveys of its graduating students from 2010 to 2020,
gathering data on first job salary, job field, and searching time.
2 [15pts] Consider the following linear regression model with no explanatory variable other than the constant regressor:
Topic 2 P23
y = β0 + u
. Show that the OLS estimator is βˆ0 = ȳ, where ȳ =
1
n
n
P
yi .
i=1
3 [40pts] The Provost of the University of Hong Kong is interested in understanding how class size may affect student performance.
(a) Formulate a simple regression model for answering this question. [Hint: Write
down the variable names explicitly instead of x and y] [2pts]
(b) What is the dependent variable in your model? What is the independent
variable in your model? [2pts]
(c) How many parameters are there in the model? What are they? [1pts]
(d) The Provost hypothesized a negative correlation between class size and student performance. Why might this hypothesis be true? [2pts]
Clement has collected data on class size and student performance (Average Grade)
for five classes in the Faculty of Business and Economics:
Table 1: Class size and student performance
Index
1
2
3
4
5
Code
ECON1210
ECON1220
ECON1280
ECON2262
ECON2280
2
Size Grade
20
88
40
82
50
75
60
73
80
57
(e) Calculate the following statistics using the data: (i) mean of class size, (ii)
mean of student performance, (iii) variance of class size, (v) covariance between class
size and student performance [10pts]
(f) Use the Ordinary Least Squares (OLS) method to estimate the parameters in
ˆ
, β0 = ȳ − β1 x̄] [10pts]
the model. [Hint: Recall the OLS estimators: β1 = Cov(x,y)
V ˆar(x)
(g) What is the interpretation of the slope parameter in this model? [2pts]
(h) What is the interpretation of the intercept parameter in this model? Is it
meaningful? [2pts]
(i) What is the predicted grade for a class with 70 students? [2pts]
(j) Do students in ECON2280 perform better than expected? [2pts]
(k) Based on the data, the Provost concluded that smaller class sizes lead to better
student performance. Do you agree with this conclusion? Why or why not? [5pts]
4 [15pts] Richard is interested in understanding the factors that affect the hourly
wage of workers in Hong Kong. He collects data on 500 workers and estimates the
following linear regression model:
wage
[ = −45.2 + 27.1educ
where wage is the hourly wage in HKD, and educ is the number of years of education.
(a) Interpret the coefficients on educ. [2pts]
(b) Anson has 12 years of education. What is the predicted hourly wage for Anson? [2pts]
(c) Anson’s actual hourly wage is 250 HKD. Is Anson overpaid or underpaid? By
how much? [2pts]
Richard also estimated the following model:
wage
[ = −169.5 + 32.2educ + 3.5exper
where exper is the number of years of work experience.
(d) Interpret the coefficient on exper. [2pts]
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(e) Anson has 5 years of work experience. Will your conclusion to question (c)
change? [2pts]
(f) Consider the following regression:
d = δ̂0 + δ̂1 exper
educ
. Without estimating the model, can you tell whether the coefficient δ̂1 will be positive or negative? Explain. [5pts]
5 [10pts] Consider the estimation of the log-log model:
ln\
salary = 4.822 + 0.257 ln sales
where salary is the annual salary of the CEO in thousands of dollars, and sales is
annual firm sales in millions of dollars.
(a) Interpret the coefficient 0.257 [2pts]
(b) Interpret the intercept 4.822 [2pts]
(c) How much does CEO salary increase if firm sales increase by 10%? [2pts]
(d) A CEO with a salary of 200 thousand dollars is hired by a firm with sales of
100 million dollars. How much will be the CEO’s salary if the firm sales increase by
50 million dollars? [2pts]
(e) Now we measure salary in dollars instead of thousands of dollars:
salarydol = 1, 000salary
. Without re-estimating the model, what is the new coefficient on ln sales? Explain.
[2pts]
*** END OF ASSIGNMENT 1 ***
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