ECON1066

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 along with your R-code. Hard copies will not be accepted. Show your calculations (if any) as well as answering the questions in clear full sentences. Log referrers to natural logarithm!

Use the dataset: LifeExpectancy.RData

Estimating the driving factors of life expectancy internationally provides valuable insights into the factors  influencing  the  health  and  longevity  of populations  across  different  countries.  It  enables researchers to identify socio-economic, environmental, and healthcare-related variables that contribute to disparities in life expectancy, helping governments and organizations design targeted policies to improve public health. Moreover, understanding these determinants aids in forecasting future trends, assessing the effectiveness of current health interventions, and promoting equitable access to healthcare resources. By analysing these factors through econometric models, we can develop a comprehensive understanding of the complex interplay between economics and health, ultimately contributing to global well-being and development strategies.

You are a newly hired analyst tasked to model national life expectancy worldwide. Assume that the outgoing research officer had started working on the econometric model to assess some of the drivers of life expectancy. Now as an incoming research officer your job is to finish this research. Your variables of interest, which originate form the World Development Indicators (World Bank), for the year 2023 are:

•    Life_exp = Life expectancy at birth, total (years) [SP.DYN.LE00.IN]

•    GPPpc = GDP per capita, PPP (constant 2021 international $) [NY.GDP.PCAP.PP.KD]

•    UnderNourished = Prevalence of undernourishment (% of population) [SN.ITK.DEFC.ZS]

•    DrinkingWater = People using at least basic drinking water services (% of population) [SH.H2O.BASW.ZS]

•    TB= Incidence of tuberculosis (per 100,000 people) [SH.TBS.INCD]

•    Immunization = Immunization, DPT (% of children ages 12-23 months) [SH.IMM.IDPT]

Dependent variable:

Life expectancy at birth, total (years): We would like to estimate the relationship of other factors with this variable. It is defined as the number of years a newborn infant would live if prevailing patterns of mortality at the time of its birth were to stay the same throughout its life.

Explanatory variables:

GDP per capita (GDPpc): The richer a country is, some scholars expect higher life expectancy, due to several factors, among others higher hygiene, better access to services etc. This variable is likely to be highly multicollinear with other explanatory variables.

Prevalence of undernourishment (% of population): Undernourishment is expected to be in a negative relationship with life expectancy.

People using at least basic drinking water services (% of population): It is expected that as higher percentage of the population has access to basic drinking water services, life expectancy will increase at an accelerating rate, because the initial benefits from reduced waterborne diseases are amplified by improvements in related factors such as sanitation and healthcare.

Incidence of tuberculosis (per 100,000 people): Higher incidence of tuberculosis directly reduces life expectancy due to increased mortality from the disease and reflects underlying health vulnerabilities that shorten lives.

Immunization, DPT (% of children ages 12-23 months): Immunisation at early ages against diphtheria, pertussis, and tetanus, is a key scientific achievement aimed at reducing childhood mortality. We expect a positive relationship with life expectancy and a high correlation with GDPpc.

All data originate from the World Bank (WDI). Please assess whether the above variables are truly associated with life expectancy, and if yes, how. Answer the following questions:

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 = β0  + β1 log(GDPPc) + β2 underNourished + β3 Drinkingwater + β4 log(TB) + β5 Immunization + u    (Equation 1)

a.     Present your regression results in a table below (R output): 4 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 and its p-value (1.5 marks each). 3 marks

d.    Interpret the coefficient on the % of people using at least basic drinking water services and its p- value (1.5 marks each). 3 marks

e.     Interpret the coefficient on Incidence of tuberculosis (per 100,000 people) and its p-value (1.5 marks each). 3 marks

f. Interpret the coefficient Immunization, DPT (% of children ages 12-23 months) and calculate its t-stat. Interpret the calculated t-statistic (1.5 marks each). 3 marks

g.    Interpret the R2 of the regression. 2 marks

h.     Several explanatory variables would be in a multicollinear relationship with each other. Explain perfect and imperfect multicollinearity and present a correlation matrix between the independent variables in Equation 1. 2 marks

2)   Describe each of the Gauss-Markov assumptions and specify if they are likely to hold for the regression in Question 1 or not. 5 marks

3) Run the following regression with a quadratic drinking water term added to the original regression:

Life ExPectancy = β0  + β1 log(GDPPc) + β2 underNourished + β3 Drinkingwater + β4 Drinkingwater2   + β4 log(TB) + β5 Immunization + u      (Equation 2)

a.  Present your regression results in a table below (R output): 3 marks

b.  Is the relationship U-shaped or inverted U shaped? Is this a significant relationship? 2 marks

c.  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 (not in a separate file). This is a critical

part of the assignment without which we’ll initiate a plagiarism check. 2 marks

Assignment Total: 40 marks