Before estimating the regression equation, conduct an overall preliminary analysis of the relationship between workers’ wages and
sector,
gender,
educational attainment,
age and
marital status.
Use tables and/or appropriate graphs for the categorical variables (male, public, degree, married) and the numerical variable (age).
Interpret your findings by comparing and contrasting the earnings of the counterparts based on each of these dummy variables and also explain the kind of relationship you observe between workers’ earnings and age?
(5 marks)
Use a simple linear regression to estimate the relationship between workers’ earnings and the variable public (Model A). You may use the Data Analysis Tool Pack. Based on the Excel regression output:
Write down the estimated regression equation,
Interpret the slope coefficient,
Carry out any relevant two-tailed hypothesis test of the slope coefficient using the critical value approach, at the 5% significance level, showing the step by step workings/diagram in your report.
Interpret your hypothesis test results.
(4 marks)
Use a multiple regression model to explore the relationship of workers’ earnings with variables related to sector, gender, educational attainment, age and marital status (Model B). You may use Data Analysis Tool Pack for this. Based on the Excel regression output:
Write down the estimated regression equation,
Interpret the slope coefficients,
Carry out any relevant two-tailed hypothesis tests for each individual slope coefficient using the p-value approach, at the 5% significance level.
Carry out an overall significance test using the p-value approach.
Carefully interpret your hypothesis test results.
Are your regression findings with regards to public-private wage gap broadly consistent with those reported in the study of Mahuteau et al. (2017)?
(8 marks)
Interpret the R-squared in Model A and adjusted R-squared in Model B. Which one is a better model? Explain why, relating your answer to the interpretations.
(2 marks)
Compare the coefficients of public variable in Model A and Model B. Explain carefully why the results are different, relating your discussion to sector wage discrimination.
(4 marks)
Predict the earnings of a 40-year-old male, university qualified and married public worker. Next, predict the earnings of a female worker with the same characteristics.
(2 marks)
Another conclusion from Mahuteau et al. (2017) is that the wage premium (comparatively higher wages) for the workers in the public sector is slightly higher for females than males. Conduct appropriate regression analyses to examine whether your findings based on 2019 data are broadly consistent with those reported in the study.
(4 marks)
If you could request additional data to study the factors that influence workers’ earnings, what extra variables would you request? Discuss two such variables, explaining why you choose them and how each of your proposed variables could be measured in the regression model. [You could draw evidence from journal articles, newspapers, etc]
(3 marks)