support@essaywritingexpert.orgBasic Econometrics
Individual Assignment
This is an individual assignment where you must work alone. You must submit an
electronic copy of your assignment in Canvas in pdf, doc or docx format. Hard copies and
submission via email will not be accepted. Show your calculations (if any) as well as
answering the questions in clear full sentences. Log referrers to natural logarithm.
QUESTION 1)
We model the salary of the average inhabitant of Pinkland. Salaries are a function of
education (expressed in years), working hours (expressed in hours), firm sales (expressed in
millions of pinkies) and sector. There are 3 sectors in Pinkland, namely agriculture, industry
and service.
Salaries are expressed in pinkies (currency of Pinkland). The model is estimated as follows:
Log(salary) = 1.2 + 0.166*educ + 0.76*log(hours) + 0.16*log(sales) + 0.35*service –
0.13*agriculture
N=800
R2 = 0.63
1) Interpret the coefficient on education. What type of relationship is this?
2 marks
2) Interpret the coefficient on “hours” and “sales”. What type of relationship are these?
4 marks
1 mark
3) What is the base category for the categorical variable?
4) Interpret the coefficient on “service” and “agriculture”.
4 marks
5) Calculate the degrees of freedom for the regression and explain if standard normal critical
values can be used or not.
2 marks
Don’t forget: Log referrers to natural logarithm!
Subtotal: 13 marks
QUESTION 2
Use the dataset: Energy.RData,
Use R to run a cross sectional regression on energy use per capita for the listed countries as
follows:
lntpes_pc = 𝜷𝜷𝟎𝟎 + 𝜷𝜷𝟏𝟏𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝜷𝜷𝟐𝟐𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝜷𝜷𝟑𝟑𝐥𝐥𝐧𝐧𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠 + 𝜷𝜷𝟒𝟒𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟 +
𝜷𝜷𝟓𝟓𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝜷𝜷𝟔𝟔𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝒖𝒖
The variables are defined as follows:
lntpes_pc = log of total primary energy consumption per capita (ktoe)
lnypcpenn =log of GDP per capita (USD)
lnypcpenn2 = square of log of GDP per capita (USD)
ln_gasprice = log of pump price for gasoline (USD/liter)
ln_annualprecip= log of annual precipitation (mm)
ffrents = Fossil Fuel Rents (% of GDP)
lnpop = log of population (in millions)
lnland = log of land area (in km2)
I_Incomegroup = refers to income groups “1” , “2” and “3”, low, mid and high income
countries.
*”Log” always refers to natural logs or “ln” here.
Log referrers to natural logarithm!
1) Present your regression results in a table below (R output):
5 marks
2) Interpret the constant and its p-value.
3 marks
3) Interpret the coefficient on gas price and its p-value.
3 marks
4) Interpret the coefficient on ln land and carry out (meaning: calculate with the official
formula) a t-test to determine the significance of the coefficient.
3 marks
5) Interpret the coefficient on ff-rents and its p-value.
3 marks
6) The above model belongs to the class of nonlinear equations. Calculate the turning
point of the nonlinear relationship.
3 marks
7) Is this a U-shaped or inverted U-shaped relationship?
1 mark
8) Interpret the adjusted R2 of the regression.
`2 marks
9) a) Please define MLR 3 and describe if MLR 3 is likely to hold or not?
b) Please define MLR 4 and describe if MLR 4 is likely to hold or not? What other
variables might be in the error term?
2 x2=4 marks
Subtotal: 27 marks
Assignment Total: 40 marks
FORMULA SHEET
Critical values for the standard normal distribution (z)
Confidence
level
(1-α)
Level of
Significance
(α)
Two–Sided
Critical Value
cα/2
One-Sided,
Upper-Tail
Critical Value
cα
One-Sided,
Lower-Tail
Critical Value
-cα
90% 10% 1.645 1.28 -1.28
95% 5% 1.96 1.645 -1.645
99% 1% 2.58 2.33 -2.33
Formula for a t-statistic
𝑡𝑡 = 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 − ℎ𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
Formula for a (1-α)% confidence interval
𝐶𝐶𝐼𝐼1−𝛼𝛼 = �𝛽𝛽̂ − 𝑐𝑐𝛼𝛼/2 ∗ 𝑠𝑠𝑠𝑠�𝛽𝛽̂�, 𝛽𝛽̂ + 𝑐𝑐𝛼𝛼/2 ∗ 𝑠𝑠𝑠𝑠�𝛽𝛽̂��
Logarithmic/Quadratic/Interaction specifications
For the model 𝑙𝑙𝑙𝑙𝑙𝑙(𝑦𝑦) = 𝛽𝛽̂
0 + 𝛽𝛽̂
1𝑥𝑥1 + 𝛽𝛽̂
2𝑥𝑥2, the exact effect of a change in explanatory
variable x2 is:
%∆𝑦𝑦� = 100�exp�𝛽𝛽̂
2∆𝑥𝑥2� − 1�
For a quadratic specification of the form:
𝑦𝑦 = 𝛽𝛽0 + 𝛽𝛽1𝑥𝑥 + 𝛽𝛽2𝑥𝑥2 + 𝑢𝑢
The turning point (maximum/minimum) is given by:
𝑥𝑥∗ = �𝛽𝛽̂
1/(2𝛽𝛽̂
2)�
The approximation of the marginal effect of x on y is given by:
∆𝑦𝑦�
∆𝑥𝑥 ≈ 𝛽𝛽̂
1 + 2𝛽𝛽̂
2𝑥𝑥
For a interaction specification of the form:
𝑦𝑦 = 𝛽𝛽0 + 𝛽𝛽1𝑥𝑥1 + 𝛽𝛽2𝑥𝑥1 ∗ 𝑥𝑥2 + 𝑢𝑢
The approximation of the marginal effect of x1 on y is given by: ∆𝑦𝑦�
∆𝑥𝑥1
≈ 𝛽𝛽̂
1 + 𝛽𝛽̂
2𝑥𝑥2