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):

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 p-value (1.5 marks). 4 marks  

f) Interpret the coefficient on Immunisation, 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

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/