Problem Description

This is a further analysis of the public-private pay gap for individuals with similar productive characteristics in the Australian population. Mahuteau et al. (2017) report that (1) on average public sector workers earn about 5.1% more hourly wages than those in the private sector and (2) that this wage premium (comparatively higher wages in public sector) is slightly higher for females than males. Systematic remuneration differences for employees with similar productive capabilities potentially has both efficiency and equity consequences.

In order to estimate the extent of discrimination in the job market where public servants with identical labor market characteristics as their private counterparts receive different wages, you will estimate a set of linear regression models. Since this is an additional analysis of the public-private pay gap, the content in the Introduction section of your report may overlap with the one in the Group Assignment submitted earlier. However, you are encouraged to develop/source new background materials. You will use the same dataset as in Assignment

2. The data are drawn from the 2019 Household, Income and Labour Dynamics in Australia (HILDA) survey. The sample used for analysis comprises 219 full-time Australian workers in the age group 21-65. The dataset values can be interpreted and be used to create appropriate variables as follows:

1. Worker’s Wages: the variable wage records hourly earnings in AU dollars of full-time workers

2. Sector: Public and private sector identification data can be converted into a dummy variable named as “public”, with 1 representing public employee else 0 for private employee.

3. Gender: using the gender identification data, create a dummy variable male that identifies male employee as 1 and female as 0.

4. Educational attainment: the dummy variable degree = Yes (1) if the individual has a bachelor’s degree or higher qualification, and = No (0) for lower than degree qualifications.

5. Age: is the numerical data type reflecting the age of an employee.

REQUIREMENT:

1. Before estimating the regression equation, conduct an overall preliminary analysis of the relationship between workers’ wages and

a. sector,

b. gender,

c. educational attainment,

d. age and

e. 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)

2. 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:

a) Write down the estimated regression equation,

b) Interpret the slope coefficient,

c) 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. d) Interpret your hypothesis test results.

3. 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:

a) Write down the estimated regression equation,

b) Interpret the slope coefficients,

c) Carry out any relevant two-tailed hypothesis tests for each individual slope coefficient using the p-value approach, at the 5% significance level.

d) Carry out an overall significance test using the p-value approach.

e) Carefully interpret your hypothesis test results.

f) Are your regression findings with regards to public-private wage gap broadly consistent with those reported in the study of Mahuteau et al. (2017)?

4. 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.

5. 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

6. 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.

7. Another conclusion from Mahuteau et al. (2017) is that the wage premium (comparatively higher wages) for 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