Basic 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