Basic Econometrics Individual Assignment
QUESTIONS:
1) Use R to run the following cross-sectional regression. (Please note the natural logs and construct these in R as needed):
𝐋𝐢𝐟𝐞𝐞𝐱𝐩 = 𝜷𝟎 + 𝜷𝟏𝐥𝐨𝐠(𝐆𝐃𝐏𝐩𝐜) + 𝜷𝟐𝐔𝐧𝐝𝐞𝐫𝐍𝐨𝐮𝐫𝐢𝐬𝐡𝐞𝐝 + 𝜷𝟑𝐃𝐫𝐢𝐧𝐤𝐢𝐧𝐠𝐖𝐚𝐭𝐞𝐫 + 𝜷𝟒𝐥𝐨𝐠(𝐓𝐁) + 𝜷𝟓𝒍𝒐𝒈(𝐈𝐦𝐦𝐮𝐧𝐢𝐳𝐚𝐭𝐢𝐨𝐧) + 𝒖
a) Present your regression results in a table below (R output):
2 marks
b) Interpret the constant (2.5 marks) and its p-value (1.5 marks).
4 marks
c) Interpret the coefficient on GDP per capita (2.5 marks) and its p-value (1.5 marks).
4 marks
d) Interpret the coefficient on the % of people using at least basic drinking water services (2.5 marks) and its p-value (1.5 marks).
4 marks
e) Interpret the coefficient on Incidence of tuberculosis (per 100,000 people) (2.5 marks) and its pvalue (1.5 marks).
4 marks
f) Interpret the coefficient on Immunization, DPT (% of children ages 12-23 months) (2.5 marks) and calculate its t-stat. Interpret the calculated t-statistic (1.5 marks).
4 marks
g) Interpret the R2 of the regression.
2 marks
h) One of the explanatory variables is in a functional form that is not usually recommended. Which one is it, and how would you change it?
2 marks
2) Specify if the Gauss-Markov assumptions are likely to hold for the regression in Question 1 or not and explain why (each assumption).
5 marks
3) Run the following regression with a quadratic drinking water term added to the original regression:
𝐋𝐢𝐟𝐞 𝐄𝐱𝐩𝐞𝐜𝐭𝐚𝐧𝐜𝐲 = 𝜷𝟎 + 𝜷𝟏𝐥𝐨𝐠(𝐆𝐃𝐏𝐩𝐜) + 𝜷𝟐𝐔𝐧𝐝𝐞𝐫𝐍𝐨𝐮𝐫𝐢𝐬𝐡𝐞𝐝 + 𝜷𝟑𝐃𝐫𝐢𝐧𝐤𝐢𝐧𝐠𝐖𝐚𝐭𝐞𝐫 + 𝜷𝟒𝐃𝐫𝐢𝐧𝐤𝐢𝐧𝐠𝐖𝐚𝐭𝐞𝐫𝟐 + 𝜷𝟒𝐥𝐨𝐠(𝐓𝐁) + 𝜷𝟓 𝐥𝐨𝐠(𝐈𝐦𝐦𝐮𝐧𝐢𝐳𝐚𝐭𝐢𝐨𝐧) + 𝒖
2 marks
a) Is the relationship U-shaped or inverted U shaped? Is this a significant relationship?
2 marks
b) Calculate the turning point of the quadratic relationship, and please analyse the result.
4 marks
4) Present a functioning R code reproducing the results below. This is a critical part of the assignment without which we’ll initiate a plagiarism check.
1 mark
Assignment Total: 40 marks
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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
𝑡 = 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 − ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 / 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟
Formula for a (1-α)% confidence interval
𝐶𝐼+,- = ^𝛽‘ − 𝑐-// ∗ 𝑠𝑒c𝛽‘d, 𝛽‘ + 𝑐-// ∗ 𝑠𝑒c𝛽‘df
Logarithmic/Quadratic/Interaction specifications
For the model 𝑙𝑜𝑔(𝑦) = 𝛽‘0 + 𝛽‘+𝑥+ + 𝛽‘/𝑥/, the exact effect of a change in explanatory variable x2 is: %∆𝑦k = 100nexpc𝛽‘/∆𝑥/d − 1r
For a quadratic specification of the form:
𝑦 = 𝛽0 + 𝛽+𝑥 + 𝛽/𝑥/ + 𝑢
The turning point (maximum/minimum) is given by:
𝑥∗ = s𝛽‘+/(2𝛽‘/)s
The approximation of the marginal effect of x on y is given by:
∆∆𝑦𝑥k ‘+ + 2𝛽‘/𝑥 ≈ 𝛽
For a interaction specification of the form:
𝑦 = 𝛽0 + 𝛽+𝑥+ + 𝛽/𝑥+ ∗ 𝑥/ + 𝑢
The approximation of the marginal effect of x1 on y is given by:
Δy/Δ𝑥/ ≈ 𝛽/ ∗ 𝛽/ 𝑥/
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