Basic Econometrics Individual Assignment: Cross-Sectional Regression Analysis, Model Interpretation, and Gauss-Markov Assumptions

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):

𝐋𝐢𝐟𝐞_𝐞𝐱𝐩 = 𝜷_𝟎 + 𝜷_𝟏𝐥𝐨𝐠(𝐆𝐃𝐏𝐩𝐜) + 𝜷_𝟐𝐔𝐧𝐝𝐞𝐫𝐍𝐨𝐮𝐫𝐢𝐬𝐡𝐞𝐝 + 𝜷_𝟑𝐃𝐫𝐢𝐧𝐤𝐢𝐧𝐠𝐖𝐚𝐭𝐞𝐫 + 𝜷_𝟒𝐥𝐨𝐠(𝐓𝐁) + 𝜷_𝟓𝒍𝒐𝒈(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 = 𝜷_𝟎 + 𝜷_𝟏𝐥𝐨𝐠(𝐆𝐃𝐏𝐩𝐜) + 𝜷_𝟐𝐔𝐧𝐝𝐞𝐫𝐍𝐨𝐮𝐫𝐢𝐬𝐡𝐞𝐝 + 𝜷_𝟑𝐃𝐫𝐢𝐧𝐤𝐢𝐧𝐠𝐖𝐚𝐭𝐞𝐫            + 𝜷_𝟒𝐃𝐫𝐢𝐧𝐤𝐢𝐧𝐠𝐖𝐚𝐭𝐞𝐫^𝟐        + 𝜷_𝟒𝐥𝐨𝐠(𝐓𝐁) + 𝜷_𝟓                      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 

FORMULA SHEET

Critical values for the standard normal distribution (z)

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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