understanding wage characteristics

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Statistical Research Project MBA (IB) 2009-2012 (PT) BUSINESS STATISTICS

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Statistical Research Project

Understanding

Wage CharacteristicsMBA (IB) 2009 2012 (PT)

October 7, 2009

Rajesh Kumar Garg (Roll no. 30)

Ravi Ganesh (Roll no. 33)

Saurabh Agarwala (Roll no. 44)

Siddharth Sikka (Roll no. 48)

Ujjwal Malik (Roll no. 59)


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Table of Contents

The Need for Understanding Wages Setting the Background ......................................................................3

Data Integrity ...................................................................................................................................................3

Problem Statement ..........................................................................................................................................4

Method ............................................................................................................................................................4

Sample Characteristics .....................................................................................................................................5

Detailed Statistics.............................................................................................................................................7

Conclusions ................................................................................................................................................... 13

Recommendations ........................................................................................................................................ 13

References .................................................................................................................................................... 13


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The Need for Understanding Wages Setting the Background

In the United States, work is often more rewarding for men than women. Men earn more there is a gap

between wages paid to women who perform the same job as men. Additionally, the so-called marriagetax penalizes secondary earners, usually women. Not surprisingly, women quit working at rates far

greater than those of men, especially once they have children.

Research by Alberto Alesina of Harvard University and Andrea Ichino of the University of Bologna has

shown that a solution to these gender-based labour inequities is by means of Gender Based Taxation. In

order to encourage women to work, and to even out the stubborn gender-based pay gap, these two

economists suggest taxing every woman's earnings at a significantly lesser rate than men.

Every year, the Income Tax department seeks information on wage characteristics of the population in

order to set discriminatory taxation policies. Not just gender, wage differences are common across

multiple other characteristics including years of experience, sector or nature of occupation.

This project is an attempt to develop an understanding of differences in wage characteristics across a few

variables of interest. Insights from such an analysis could come in handy to income tax policy makers or to

the various human resource consultants, who attempt to benchmark wages across sectors.

Data Integrity

The dataset that has been used comprises 534 observations on selected variables sampled from the

Current Population Survey. The Current Population Survey (CPS) is used to supplement census

information between census years. Sampled data contains information on gender, years of experience,nature of occupation and sector of occupation in addition to wages.


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Problem Statement

Application of descriptive statistics to develop an understanding of the relationship between wage and

other characteristics of workers such as gender, years, of experience, nature of occupation and sector ofemployment.

Method

1. The sample data is sorted in an ascending order on the basis of wages.2. The population characteristics have been described based on the following variables:

o Gender distributiono Sectoro Occupationo Years of Experience (with appropriate intervals )

The results for this are highlighted in Section 1 of the Results Section

3. The descriptive statistics are carried out on the sample data including the 5-N summary. These consistof :

o Minimumo Maximumo 1st Quartileo 3rd Quartileo Mediano Modeo Standard deviationo Meano Cumulative Wageso Kurtosiso Varianceo Range, etc.

The results for the above are highlighted in Section 2 of the Results Section

4. Graphical representation of data is done using Box-plots to help understand wage characteristicsacross the four chosen parameters. The results for the above are highlighted in Section 3 of the

Results Section

5. Wage characteristics are modelled against the Years of Experience. The results for the above arehighlighted in Section 4 of the Results Section

6. Hypothesis testing is utilized to carry out 4 different tests to ascertain certain conclusions from thedata


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Sample Characteristics

Section 1: A series of the pie-charts given below have been used to describe the sample distribution

amongst the following characteristics

1. Gender : The distribution of male and females working population in the geography is 54 % and46 % respectively

2. Sector: More than Two-thirds of the jobs in the area are concentrated in the non-manufacturing and non-construction sectors


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3. Occupation: Other category of options form the highest concentrated occupation followedby Professional and Sales related occupations

4. Years of Experience: Equitable distribution of years of experience amongst different sectors.This provides a insights into the strengths and accuracy of the sample data


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Detailed Statistics

Section 2: This section makes use of descriptive statistics to provide a view of the mean and cumulative

wage

1. Mean Wage: The graph and the table below provide a view of the descriptive statistics. Themean wage is $9 an hour with a standard

0

10

20

30

40

50

60

70

1 3 5 7 9 11 1 3 1 5 17 19 2 1 23 2 5 27 2 9 31 3 3 35 37 3 9 41 4 3 45

Number of people

Wage ($ per hour)

Mean

Statistic Valu e

Mean 9.0

Standard Error 0.2

Median 7.8

Mode 5.0

Standard Deviation 5.1

Sample Variance 26.4Kurtosis 5.0

Skewness 1.7

Range 43.5

Minimum 1.0

Maximum 44.5

Sum 4818.9

Count 534.0

2. Cumulative Wage: The cumulative wage graph provides the view of the wages as distributedover the complete sample population.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

Cumulative Wage Distribution

Wage ($ per hour)


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Section 3: This section makes use of box plots to plot the wages against all the different parameters

including: Gender, Sectors, Occupations and Years of Experience

1. Summary statistics for the wages across genders and sectors

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

TOTAL POPULATION

MALES

FEMALES

SECTOR : CONSTRUCTION

SECTOR : MANUFACTURING

SECTOR : OTHERS

2. Summary statistics for the wages across Occupations

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

TOTAL POPULATION

OCCUPATION: CLERICAL

OCCUPATION : PROFESSIONALS

OCCUPATION : SALES

OCCUPATION : SERVICE

OCCUPATION: MANAGEMENT

OCCUPATION : OTHERS


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3. Summary statistics for the wages across years of experience

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

TOTAL POPULATION

EXP : 0-6 yrs

EXP : 13-18 yrs

EXP : 19-28 yrs

EXP : 28+ yrs

EXP : 7-12 yrs

4. Summary statistics for the wages of the total population- It can be surmised that majority ofthe population has wages lying between $5 - $11 an hour

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48


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Section 4: In this section wage has been plotted against the Years of experience. A logarithmically fitted

curve provides best fit between wages and years of experience with the least average error

Experience

Wage


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Section 5: In this section, hypothesis testing has been used to arrive at specific conclusions regarding the

wage behaviour of the population

TEST 1

H0: Average wage of female employees is same as overall average

H1: Average wage of female employees is not equal to overall average

Type of test z test

x bar 7.9

Mu 9.0

Sigma 4.5

N 245.0

z value -3.5

Conclusion: H0 rejected with 99% confidence. There is a difference in average wage of females from the

overall average

TEST 2

H0: Average wage of employees in manufacturing sector is same as overall average

H1: Average wage of employees in manufacturing sector is not equal to overall average

Type of test z test

x bar 9.6

mu 9.0

sigma 4.5

n 99.0

z value 1.1

Conclusion: H0 not rejected at even 90% confidence level. There is no difference in average wage of

manufacturing sector employees from the overall average


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TEST 3

Test whether variance in wage of management is higher, lower or equal to that of total sample

Sample Size 55 n

Sample Variance 57.34 s2

Test Statistic 117.242 2

Null hypothesis p-value 1%

H0: 2 = 26.41 0.0 Reject

H0: 2 >= 26.41 1.0

H0: 2


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Conclusions

Sample wage distribution is positively skewed, with a mean of $9 and an IQR of $6. (Q1=$5 andQ3 = $11).

Average wage per hour of females is lower than that of males Wage difference across sectors manufacturing, construction and others is not significant Management wages tend to be higher and also have a higher variance Wages of clerical and service professions are least dispersed (IQR of $5 ($5-$10) for clerks and $4

($4-$8) for service employees).

However, proportion of females working in clerical / service sectors is also higher than overallsample proportion by more than 10%

Entry level (0-6 experience) salaries are low. However, beyond that level of experience, salariesremain more or less constant accounting for a logarithmic fit between wages and years of

experience

Recommendations

Based on the above conclusions, policy makers can design income tax policies that favour lower taxation

for females. A taxation policy based on the sector of occupation is not feasible as glaring differences are

not evident. As the variances in the management salaries are higher than most others, slabs can be

defined in income tax policies that increase the tax rate in proportion to the salary earned. Also, policies

directed at providing subsidies can be extended to entry level employees (0-6 years).

Human resource consultants can make use of the trend equation to determine appropriate level of wage

rates for years of experience that a candidate can bring to the table.

References

Data has been used from the Current Population Survey (CPS) from the Economics Web Institute -

http://www.economicswebinstitute.org
http://www.economicswebinstitute.org/http://www.economicswebinstitute.org/http://www.economicswebinstitute.org/

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