BUSINESS STATISTICS
Assessment 3: Individual Assignment
Instructions:
This is an individual assignment with a total of 40 marks. The allocation of marks is as follows:
Statistical Analysis with Excel File: 32
Professional Report: 8
Total: 40
Report Structure
The response must be provided in the form of a professional report with no more than 10 pages (excluding the cover page).
The structure of your professional report must include:
A Title,
An Executive Summary,
An Introduction,
Analysis, and
Conclusions.
Submission
You must submit an electronic copy of your assignment on Canvas. See the attached Template of your submission for more details.
Excel Work
This assignment requires the use of Microsoft Excel. Using Data Analysis Tool-Pack will Help tremendously in getting through the assignment requirements.
You need to submit the Excel file along with your report. The excel file needs to be clear and carefully organized and must show all workings underlying the Professional report and associated statistical analysis. It will be treated as an appendix to your report, i.e., not included in the page count.
DO NOT leave references to the excel workbook within the Professional report as responses to the questions. You will need to take relevant results from your Excel workbook and incorporate them into your report. The report needs to be standalone.
Presentation Instructions:
Your written professional report should comply with the following presentation standards:
Typed using a standard professional font type (e.g. Times Roman), 12-point font size.
1.5-line spacing, numbered pages, and clear use of titles and section headings.
Delivered as a Word (.doc or .docx) or PDF (.pdf) file.
Checked for spelling, typographical and grammatical errors. Where relevant, round to 3 decimal places.
With all relevant tables and charts, the report should be no more than 10 pages long.
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 the identical labour market characteristics as their private counterparts receive different wages, you will estimate a set of linear regression models.
Since this is an additional analysis on 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:
Worker’s Wages: the variable wage records hourly earnings in AU dollars of full-time workers [note the unit of measurement]
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.
Gender: using the gender identification data, create a dummy variable male that identifies male employee as 1 and female as 0.
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.
Age: is the numerical data type reflecting the age of an employee.
Marital Status: the dummy variable married = Yes (1) if the individual is married and No (0), otherwise.
Locate the data file (IndividualBusStats.xls) on CANVAS.
REQUIREMENT:
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 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,
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.
(3 marks)
Use the following multiple regression model to explore the relationship of workers’ earnings with variables related to sector, gender, educational attainment, age and marital status
Model B: Wages=ß_0+ß_1 public+ß_2 male+e
Model C: Wages=ß_0+ß_1 public+ß_2 male+ß_3 age+e
Model D: Wages=ß_0+ß_1 public+ß_2 male+ß_3 age+ß_3 education+e
Model E: Wages=ß_0+ß_1 public+ß_2 male+ß_3 age+ß_4 education+ß_5 married+e
Based on the Excel regression outputs, select the best model and explain why it is the best.
Write down the estimated equation for the best model and interpret the slope coefficients,
Based on the best model, 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 in c) and d).
Are your regression findings with regards to public-private wage gap broadly consistent with those reported in the study of Mahuteau et al. (2017)?
(9 marks)
Compare the coefficients of public variable in Model A and Model E. Explain carefully why the results are different, relating your discussion to sector wage discrimination.
(4 marks)
Based on the Model E, 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.
(2.5 marks)
Based on the result in Question 5, how will your result in Question 5 change if the male/female worker is 50 years old? Explain without any calculation.
(2.5 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]
(2 marks)
(5 + 3 + 9 + 4 + 2.5 + 2.5 + 4 + 2 = 32 marks)
(Professional report = 8 marks)
Reference:
Mahuteau, S, Mavromaras, K, Richardson, S & Zhu, R 2017, Public–private sector wage differentials in Australia, Economic Record, vol. 93, pp. 105-121.
