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Gender Pay Gap in Australia: Microeconomics Report and Analysis

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Added on 2021/06/17

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This report presents an analysis of the gender pay gap among highly educated individuals in Australia, focusing on those with graduate degrees. The study utilizes data from the Australian Household Survey of 2015-2016, employing OLS estimators to assess wage differentials. The report examines various factors, including age, gender, marital status, and occupation, to determine their impact on wages. The methodology involves initial model development, testing assumptions such as multicollinearity and normality, and refining the model to address heteroskedasticity. Results indicate little to no gender pay gap among the highly educated population, though limitations exist due to the use of OLS estimators with complex panel data. The report provides detailed data summaries, including descriptive statistics and scatter plots, and concludes with an overview of the findings and potential areas for further research. Tables and figures are used to illustrate the findings of the research.

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Question 2: Microeconomics – Wages
Executive Summary
The given report is an estimation of the gender pay gap among the highly educated
population of Australia i.e. the population that has at least a graduate degree. Gender pay
gap is a hotly debated topic worldwide with almost every field of work showing a Gender
Pay Gap. This report has observed little to no gender pay gap among the highly educated
population in Australia. However, there might be shortcomings to these results as OLS
estimators are very weak predictors of variables in complex Panel Data.

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Contents
1. Introduction................................................................................................................................... 1
2. Data............................................................................................................................................... 1
2.1. Data Description.................................................................................................................... 1
2.2. Data Summary....................................................................................................................... 2
3. Methodology................................................................................................................................. 8
3.1. Initial Model........................................................................................................................... 8
3.2. Testing Assumptions..............................................................................................................8
3.3. Final Model and Estimation Technique.................................................................................. 8
4. Results......................................................................................................................................... 10
5. Conclusion................................................................................................................................... 12
6. Appendix...................................................................................................................................... 13
7. References................................................................................................................................... 13
Figure 1 Summary Statistics for the Industry of the Main Job of the Respondent = Accommodation
and Food Services,................................................................................................................................. 2
Figure 2 Scatter Plot of Wages Earned Per Hour Against Age................................................................6
Figure 3 Scatter Plot of Wages Earned Per Hour Against Number of Hours worked per week..............7
Table 1 Variables’ Name, Description and Type/Units..........................................................................1
Table 2 Summary Statistics for Log of Wages, female respondents, respondents who are working and
married, the total number of children in the household, and the square of the age of the respondent
...............................................................................................................................................................2
Table 31 Figure 1 Summary Statistics for the Industry of the Main Job of the Respondent =
Accommodation and Food Services,......................................................................................................2
Table 4 Summary Statistics for the Industry of the Main Job of the Respondent = Accommodation
and Food Services; Administrative and Support services, ; Agriculture, Forestry and Fishing..............3
Table 5 Summary Statistics for the Industry of the Main Job of the Respondent = Arts and Recreation
Services; or Construction; or Education and Training............................................................................3
Table 6 Summary Statistics for the Industry of the Main Job of the Respondent = Electricity, Gas,
Water and Waste Services; or Financial and Insurance Services or Health Care and Social Assistance.3
Table 7 Summary Statistics for the Industry of the Main Job of the Respondent = Information Media
and Telecommunications; or Manufacturing; or Mining.......................................................................4
Table 8 Summary Statistics for the Industry of the Main Job of the Respondent = Other Services; or
Professional, Scientific and Technical Services; Public Administration and Safety or Rental, Hiring and
Real Estate Services...............................................................................................................................4
Table 9 Summary Statistics for the Industry of the Main Job of the Respondent = Retail Trade; or
Transport, Postal and Warehousing; or Wholesale Trade.....................................................................4
Table 10 Summary Statistics for the Occupation of the Main Job of the Respondent = Community and
Personal Service Workers; or Labourers; or Machinery Operators and Drivers....................................5
Table 11 Summary Statistics for the Occupation of the Main Job of the Respondent = Machinery
Operators and Drivers; or Professionals................................................................................................5

Table 12 Summary Statistics for the Occupation of the Main Job of the Respondent = Sales Workers;
or Technicians and Trade Workers........................................................................................................ 6
Table 13 Scatter Plot (Years_with_children_in_the Household) and (ln_wages)..................................9
Table 15 OLS Estimates of Model A..................................................................................................... 11
Table 16 OLS Estimates of Model B..................................................................................................... 11
Table 17 Mean Comparison between Independent Variable for Male and Female Workers.............11
Table 18 Normality Test (Jarque –Bera Test).......................................................................................13

1. Introduction
OLS Estimators or regressions are used to make forecasts to understand the importance of a given
variable in determining a dependent variable. Gender parity is a hotly debated topic currently as
Australian industries too seem to have a gender pay gap. (Organization for Economic Co-operation
and Development, 2017). This report is an attempt to analyse the gender pay gap among the highly
educated population (i,e population that has at least a graduate degree). In order to do so, OLS
estimation has been used on a sample collected from the Household Survey of Australia, 2015-2016.
(Australian Bureau Of Statistics, 2017)
2. Data
The Data for taken from the Australian Household Survey for 205-2016. (Australian Bureau Of
Statistics, 2017)This Panel data survey respondents on a variety of demographic indicators such as
age, education, wage, number of house works. The given data is a sample from this database. The
data contains sample for only those workers who have at least a graduate degree. The data for
cleaned before analyses, in order to remove outliers. Accordingly, the top 1% earners i,e those
earning more than 183.03 AUD and the bottom 1% earner i.e. those earning less than 7.61AUD were
removed as observations. Similarly, average wages are not a good statistic to consider since the
wage differentials can be a result of the cost of living in a region. Hence, the log of wages or ln wages
has been used as dependent variable in the OLS estimator. The log of a variable considers the
elasticity of a variable, given a change in another variable, instead of the absolute value.
(Wooldridge, 2015)
2.1. Data Description
Table 1 Variables’ Name, Description and Type/Units
Name Description Type/Units
Unique household
number
Assigned Unique Identification number for every
Member surveyed
String Variable (ID
number) / None
Person number within
each income unit
Position in income
unit (relationship to
the IU reference
person)
The number of people within the household
Whether the member of the family is the head of the
household or the spouse of the head of the household
Ordinal Number eg,
1.2.3
Descriptive.
Variables can eother
take values “
Head of the income
unit” or
Spouse of the head
of the income unit
Age Age of the respondent Years (rounded off)
1

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Wage Hourly wage earned by the person Dollars
Female Indicates whether the person is female or not 1,0 (dummy
variable)
Ft/pt Indicates whether the person is employed full time or part
time.
1,0 (dummy
variable)
Ind Indicates the industry that a person is employed in, from a
pre-drawn list of industries
Categorical string
data, pre selected
categories
OCC Indicates the occupation that the person is employed in Categorical string
data, pre selected
categories
2.2. Data Summary
Figure Summary Statistics for Log of Wages, female respondents, respondents who are working
and married, the total number of children in the household, and the square of the age of the
respondent
Table 21 Figure 2 Summary Statistics for the Industry of the Main Job of the Respondent =
Accommodation and Food Services,
2

Table 3 Summary Statistics for the Industry of the Main Job of the Respondent = Accommodation
and Food Services; Administrative and Support services, ; Agriculture, Forestry and Fishing
Table 4 Summary Statistics for the Industry of the Main Job of the Respondent = Arts and
Recreation Services; or Construction; or Education and Training
Table 5 Summary Statistics for the Industry of the Main Job of the Respondent = Electricity, Gas,
Water and Waste Services; or Financial and Insurance Services or Health Care and Social
Assistance
3

Table 6 Summary Statistics for the Industry of the Main Job of the Respondent = Information
Media and Telecommunications; or Manufacturing; or Mining
Table 7 Summary Statistics for the Industry of the Main Job of the Respondent = Other Services;
or Professional, Scientific and Technical Services; Public Administration and Safety or Rental,
Hiring and Real Estate Services
Table 8 Summary Statistics for the Industry of the Main Job of the Respondent = Retail Trade; or
Transport, Postal and Warehousing; or Wholesale Trade
4

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Table 9 Summary Statistics for the Occupation of the Main Job of the Respondent = Community
and Personal Service Workers; or Labourers; or Machinery Operators and Drivers
Table 10 Summary Statistics for the Occupation of the Main Job of the Respondent = Machinery
Operators and Drivers; or Professionals
5

Table 11 Summary Statistics for the Occupation of the Main Job of the Respondent = Sales
Workers; or Technicians and Trade Workers
 EXPLAIN THE RELATIONSHIPS (+VE or –VE), WHAT GRAPHS ARE TRYING TO SHOW?
Figure 3 Scatter Plot of Wages Earned Per Hour Against Age
10
20
30
40
50
60
70
80
0 40 80 120 160 200
Wage ($/hour)
Age (years)
The Residuals are concentrated negatively towards the lower wages, implying the model is not a
good fit for lower wages. Additionally, the residuals seem to show a lower bias, implying that they
are less than estimated. However, the slope of the line is positive.
6

Figure 4 Scatter Plot of Wages Earned Per Hour Against Number of Hours worked per week
0
10
20
30
40
50
60
70
0 40 80 120 160 200
Wage ($/hour)
Hours (hour/week)
The regression line is almost parallel with a very light downward trend. The Residuals are
concentrated negatively towards the lower wages, implying the model is not a good fit for lower
wages. The model is a better fit when the wages are higher.
7

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Figure 3: Bar Diagram of the Average Wage Plotted Against every Occupation
The highest number of graduate respondents are professionals with the lowest number of
reposndents being technicians and trade workers. However, the wages per house do not change
much based on the occupation. However, they seem to be the highest for occupations “managers”
and “Clerical and Administrative Workers”.
3. Methodology
3.1. Initial Model
The initial model records the of of the hourly wages, regressed on the gender, years with children in
the household, married or not, age, full time or part time, number of hours,
Ln(wagei) = f (femalei; marriedi, kidyrsi, agei, , agei,2, ftpti, hoursi, , indi, occi) -- > model A
Ln(wagei) = f (female Xmaried, female x kidyears, age, hours, occ) -- > model B
3.2. Testing Assumptions
Testing for Multicollinearity: It is assumed that there is no collinearity. This assumption is tested
using multicollinearity tests. Generally, the VIF tests is used after an OLS Regression is generated.
However, since an OLS regression was not generated, the correlation statistics of the entire group
was checked, manually. The variables age and age2 had a high correlation for model 1. Hence, age2
was dropped. (Wooldridge, 2015). Additionally, a special co-relation test was performed to see the
Normality: It is assumed that the data is normally distributed. This is tested using the normality test
called Jarque Bera Test in eviews. ( IHS Global Inc., 2017) The null hypothesis is that data is normally
distributed. The p-value was 0.00. Hence, the test was rejected. (Wooldridge, 2015)
Hetereskedascity: Normally, a test would be conducted to detect Homoskedascity. However, a
variety of software packages (microfit, Gretl, Eviews, Oxmetrics) were used but the results could not
be detected since no OLS regression was generated. However, we understand that heteroskedascity
occurs when the residuals do not show a homogenous trend. The scatter plots in Figure 1 and 2
show heteroskedascity as the residuals around the fiited line do not show a homogenous trend.
Hence, there is heteroskedascity, at least for these two variables. (Lambert, 2013).
3.3. Final Model and Estimation Technique
Since, not other test could be performed, a bar diagram of the variable “indutsry of main job” was
taken and each industry seems to have an equal weight. Hence, this variable was dropped.
8

Further, the regression of variable “Years with children in the household” was examined using a
scatter plot
Table 12 Scatter Plot (Years_with_children_in_the Household) and (ln_wages)
Given the heteroskedasticity , the variables
9

Ln_age = log (Age(years) )
Ln_hours = log (Hours (hour/week))
Ln_kd_years = log (Years with children in the household)
The final model is estimated as below
The regression model A is as below:
Ln(wagei) = α + β1 female+ β2married + β3 Years with children in the household + β3 Age (years)+ β4
ftpt + β5 Occupation of the Main Job of the Respondent, Clerical and Administrative Workers+ β6
Occupation of the Main Job of the Respondent, Community and Personal Service Workers+ β7
Occupation of the Main Job of the Respondent, Labourers + β8 Occupation of the Main Job of the
Respondent, Machinery Operators and Drivers + β9 Occupation of the Main Job of the Respondent,
Managers+ β10 Occupation of the Main Job of the Respondent.’ Professionals+ β11 Occupation of the
Main Job of the Respondent, Managers + β12 Occupation of the Main Job of the Respondent, Sales
Workers + β13 Occupation of the Main Job of the Respondent, Technicians and Trades Workers + u
Model B remained the same
Ln(wagei) = α + β1 (female Xmaried) + β2 female xkidyears, + u -- > model B
4. Results
a) Model A is not a good fit since the R-Square is small. Moreover, the probability of the
occupations of the main job are not significant is the main job is not a labourer or a
machinery operation job. The two occupations that are significant are labourers and
machinery operant jobs. Hence, these jobs are the only significant jobs that regress the
wages. The standard errors of the model are small. But the R squared was very low. Hence,
this model was not good fit. Additionally, no variables has any testing significance, since p-
values hovered around zer. This model is not a good model and should be dropped in favour
of model B.
However, the hours per week and whether female or not are negatively related, implying
that women are likely to have lower wages and the increase in wages in lower, if the number
of hours go high (Intuitively, this makes sense as labourers tend to have greater working
hours and lower wages).
However, the results obtained were as below
In this model, no variable is significant.
b) For Model B, both being married and having children or being married and the age of the
kids in the household are not significant regressors, since the probability of both of these
variables is 0. However, noth co-efficient of regression were positive regressors.
c )The mean of the log of wages is greater for males, implying that men tend to earn more on an
average.
10

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Table 13 OLS Estimates of Model A
Table 14 OLS Estimates of Model B
Dependent Variable: LN_WAGES
Method: Least Squares
Date: 05/18/18 Time: 16:29
Sample (adjusted): 1 2043
Included observations: 2043 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
FEMALE_X_MARRIED 3.029430 0.121508 24.93191 0.0000
FEMALE_X_KIDYEARS 0.084108 0.010844 7.756149 0.0000
R-squared -34.100537 Mean dependent var 3.564541
Adjusted R-squared -34.117735 S.D. dependent var 0.475784
S.E. of regression 2.819507 Akaike info criterion 4.911980
Sum squared resid 16225.18 Schwarz criterion 4.917484
Log likelihood -5015.587 Hannan-Quinn criter. 4.913999
Durbin-Watson stat 0.908536
Table 15 Mean Comparison between Independent Variable for Male and Female Workers
ln_wages (female)
Mean 3.509849
Standard Error 0.012946
12

Median 3.51631
Mode 3.218876
Standard Deviation 0.43903
Sample Variance 0.192747
Kurtosis 0.884741
Skewness 0.185265
Range 3.178218
Minimum 2.029463
Maximum 5.207681
Sum 4036.326
Count 1150
Ln_wages (male)
Mean
3.63497
342
Standard Error
0.01709
9679
Median
3.64675
4488
Mode
3.21887
5825
Standard
Deviation
0.51099
1523
Sample
Variance
0.26111
2337
Kurtosis
0.19455
751
Skewness
0.06916
9781
Range
3.15564
0226
Minimum
2.03731
6625
Maximum
5.19295
6851
Sum
3246.03
1264
Count 893
5. Conclusion
The results are in line with a study by Morgan ( 2008) who found virtually no differences in pay for
recent graduates based on gender, in USA. Nevertheless, Gender Pay Gap exists. (Blau & Kahn,
2007) (Arulampalam, Arulampalam, & Bryan, 2007) The reason for the opposing results may be due
to a variety of factors such as bias in sample selection (only graduates were considered) or due to
the estimation technique.
13

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The OLS estimates given in the table are not reliable as OLS regression may not be a good technique
for Panel Data. Plenty of the regressors have probabilities close to zero. Hence, it is important to use
more sophisticated and current methods. (Schmidheiny, 2016)
14

6. Appendix
Table 16 Normality Test (Jarque –Bera Test)
LN_WAGES FEMALE MARRIED YEARS_WI... AGE__YEARS_ AGE2 INDUSTRY... INDUSTRY... INDUSTRY... INDUSTRY...
Mean 3.564541 0.562898 0.698483 5.687714 40.32795 1771.633 0.035732 0.020558 0.005384 0.026432
Median 3.559055 1.000000 1.000000 0.000000 38.00000 1444.000 0.000000 0.000000 0.000000 0.000000
Maximum 5.207681 1.000000 1.000000 24.00000 75.00000 5625.000 1.000000 1.000000 1.000000 1.000000
Minimum 2.029463 0.000000 0.000000 0.000000 20.00000 400.0000 0.000000 0.000000 0.000000 0.000000
Std. Dev. 0.475784 0.496150 0.459029 7.384775 12.05656 1051.418 0.185666 0.141934 0.073197 0.160455
Skewness 0.178263 -0.253605 -0.865005 0.888692 0.465399 0.944215 5.002335 6.757503 13.51787 5.904277
Kurtosis 3.520540 1.064316 1.748233 2.315982 2.340770 3.209845 26.02336 46.66385 183.7327 35.86048
Jarque-Bera 33.88599 340.8521 388.1575 308.7464 110.7451 307.3187 53643.09 177842.0 2842769. 103788.9
Probability 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
Sum 7282.357 1150.000 1427.000 11620.00 82390.00 3619446. 73.00000 42.00000 11.00000 54.00000
Sum Sq. Dev. 462.2487 502.6676 430.2653 111360.3 296826.3 2.26E+09 70.39158 41.13656 10.94077 52.57269
Observations 2043 2043 2043 2043 2043 2043 2043 2043 2043 2043
INDUSTRY... INDUSTRY... INDUSTRY... INDUSTRY... INDUSTRY... INDUSTRY... INDUSTRY...
0.061185 0.184533 0.025942 0.046500 0.012237 0.018111 0.138522
0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
0.239727 0.388013 0.159002 0.210617 0.109969 0.133384 0.345531
3.661854 1.626465 5.964378 4.307439 8.873127 7.227355 2.092816
14.40917 3.645389 36.57380 19.55403 79.73239 53.23466 5.379877
15646.48 936.2117 108065.8 29644.96 528012.4 232600.6 1973.480
0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
125.0000 377.0000 53.00000 95.00000 25.00000 37.00000 283.0000
117.3519 307.4312 51.62506 90.58248 24.69408 36.32991 243.7983
2043 2043 2043 2043 2043 2043 2043
7. References
IHS Global Inc. (2017, October 25). Residual Diagnostics. Retrieved from eviews:
http://www.eviews.com/help/helpintro.html#page/content/testing-
Residual_Diagnostics.html
Arulampalam, W., Arulampalam, W., & Bryan, M. L. (2007). Is There a Glass Ceiling over Europe?
Exploring the Gender Pay Gap across the Wage Distribution. ILR Review, 60 (2), 163-186.
Australian Bureau Of Statistics. (2017, October 27). Household Income and Wealth, Australia, 2015-
16. Retrieved from Australian Bureau Of Statistics: http://abs.gov.au/household-income
Blau, F. D., & Kahn, L. M. (2007). The Gender Pay Gap: Have Women Gone as Far as They Can?
Academy of Management Perspectives, 21(1), 58-63.
Lambert, B. (2013, June). Heteroscedasticity: as a symptom of omitted variable bias - part 1.
Retrieved from YouTube: https://www.youtube.com/watch?v=sFOtuCKQztc
Lambert, B. (2013, June 3). Heteroskedasticity summary. Retrieved from YouTube:
https://www.youtube.com/watch?v=zRklTsY9w9c&t=185s
Lambert, B. (2013, June 18). Interpreting Regression Coefficients in Linear Regression. Retrieved from
YouTube.com: https://www.youtube.com/watch?v=JwGaos2Y9bM
Morgan, L. A. (2008). Major Matters: A Comparison of the Within‐Major Gender Pay Gap across
College Majors for Early‐Career Graduates. A Journal of Economy and Society, 47 (4), 625-
650.
Schmidheiny, K. (2016). Panel Data: Fixed and Random Effects. Retrieved from
http://www.cantab.net/users/bf100/pdf/pd_slides_fingleton.pdf
Wooldridge, J. M. (2015). Introductory Econometrics: A Modern Approach : Sixth Edition (pg 75).
online: Cengage Learning.
15