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Economy 
ISSN: 2313-8181 
Vol. 1, No. 1, 15-19, 2014 
www.asianonlinejournals.com/index.php/Economy 

 

 

 

 

 

15 

 

Median Regression Analysis of Gender-wise Income Gap in 

Punjab, Pakistan 
 

Muhammad Aslam
1
 --- Arslan Saeed

2 
--- Saima Altaf

3
 

 
1,3

Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan  
2
Govt. Science College, Multan, Pakistan 

 

Abstract 
 

 

 

 

 

 

 

 

 

 
 

 

 
This work is licensed under a Creative Commons Attribution 3.0 License 

Asian Online Journal Publishing Group 

 

 

1. Introduction 
Income is the central motivating factor of human activities. According to the classical and modern economists, 

materialistic life is the game of income earning and spending. According to Robbins (1945) “economics is the study 

of human behavior adopted between unlimited end and scare means”. Every human tries to satisfy his end with his 

scare resources. The main head of resource is income that is the reward of man’s mental and physical effort. Income 

and income related issues are very important for study to a research scholar.  The most relevant income related issues 

are unemployment, inflation, income inequality and poverty etc. 
Income is one of the vast fields of study. So, how much research is made about income or its related issues 

(development, poverty, inflation, and living standard etc.) is insufficient due to dynamic changes in the world. 

However, the study of income gap is one of the important areas for the researchers.  

Various researchers have analyzed the income gap in different forms. For instance,  Falaris (2003) has analyzed 

the wage differences between males and females at various quantiles of income in Panama. Machado and Mata 

(2005) have analyzed the wage gap or wage changes over various periods of time in their study.  

A number of studies have also been conducted about the income gap in Pakistan. For example,  Hyder and Reilly 

(2005) have analyzed the public and private sector wage gap in Pakistan.  Sabir and Aftab (2007) have also given the 

study about dynamism in the gender wage gap. Some other important studies are given by  Ali et al. (1999),  Ahmad 

(2000), Shahbaz et al. (2007) and Cheema and Sial (2012) etc. 

The present article is also about the income related issues focusing the province of Punjab in Pakistan. We 

primarily aim to discuss the gender-wise gap in income. However, the impact of area (urban or rural), education, and 

job type on income of the people of Punjab are also being targeted in this study. 

It is common to use the ordinary least squares (OLS) method to estimate the values of dependent variable, 

depending on different covariates. But sometimes the conditional mean of response variable is not desirable when 

one wants to obtain a good estimate that satisfies the location and shape properties better than the ordinary mean as 

found in the OLS. Koenker and Bassett (1978) argued that the OLS estimators may be seriously deficient in linear 

models with non-Gaussian errors. They introduced the quantile regression for this situation. 

The traditional regression analysis is focused on mean. The conditional mean models have certain attractive 

properties under ideal conditions (assumptions). The conditional mean models have some deficiencies i.e. (a) these 

models are not extendable for non central location (b) the assumptions of conditional mean modeling are not always 

met in the real world (c) the conditional mean models do not go beyond location. They do not cover all 

This paper primarily examines the impact of gender on the monthly income of the working 

class in Punjab, Pakistan. The relevant data have been obtained from Pakistan Labour Force 

Survey (2008-9). A special case of quantile regression i.e. the median regression is used for 

the desired investigation. In addition to gender, the other covariates are marital status, area 

of residence, level of education, job type and status etc. As in many other regions and 

countries, the male workers in Punjab tend to have higher average income and the income 

tend to increase with increase in level of education. The workers with permanent jobs earn 

more as compared to temporary job holders. 

 
Keywords: Income gap, Labour force survey, Median income, Poverty, Quantile, Quantile regression. 

http://creativecommons.org/licenses/by/3.0/


Economy, 2014, 1(1): 15-19 

 

 

 

 

16 

 

characteristics (like scale, skewness and other higher order properties) of relationship between response distribution 

and explanatory variables.  

When we study the distribution of income, it is found to be highly skewed and invites the quantile regression to 

be used. When the distribution is highly skewed then mean is not good representation of location as median. The 

conditional median regression model is used in modeling the location and shape of distribution of response variable 

which is specific type of quantile regression. Therefore, in the present study, we aim to use the median regression 

model. The upcoming section elaborates the structure of such model. We are not the first who are using this 

approach. Many researchers used the same in their studies about income or wages e.g., see Buchinsky (1997), Tasi 

and Kuan (2003),  Falaris (2003), Machado and Mata (2005) among many others. Similarly, a number of studies 

about the income modeling in Pakistan can also be found in  Hyder and Reilly (2005) and  Sabir and Aftab (2007) 

etc.. However, the present work addresses the income gap focusing of the largest province of Pakistan i.e. Punjab.  

 

2. Material and Methods 
Our analysis based on the secondary data taken from “Pakistan Labor Force Survey” (PLFS) 2008-09 conducted 

by the Federal Bureau of Statistics, Pakistan. Previously, Hyder and Reilly (2005), among many others, have also 

used the PLFS Data in their research.  Such data give detailed and comprehensive characteristics of employed 

persons of age greater than 10 years. 
In our study, the data of earning persons in Punjab consist of 7070 individuals whose monthly incomes are given.  

2.1. Variables and Description 
For our study, we used the variable as given in Table 1. 

 
Table-1.Variables and Coding 

Variable  Notation Definition 

Income  Y Natural logarithm of the monthly income of a person. 

Gender                           G = 1 if a person is male; = 0 if female. 

Age                                 X1                         Age of a person in years. 

Area  X2 = 1 if a person belongs to urban area; = 0, otherwise. 

Marital status  X3 = 1 if a person is married; = 0, otherwise. 

Primary                         

Education 

level and 

Training 

E1 = 1 if a person has primary level education but below middle; 

= 0, otherwise. 

Middle E2  = 1 if a person has middle level education but below 

matriculation; = 0, otherwise.         

Matric E3 = 1 if a person has matric level education but below 

intermediate; = 0, otherwise.         

Intermediate E4 = 1 if a person has intermediate level education but below 

graduation; = 0, otherwise.         

Graduate E5 = 1 if a person has ordinary graduate level education but 

below masters; = 0, otherwise.      

Profdeg E6 = 1 if a person has a professional degree in engineering, 

medicine, computer and agriculture etc.; = 0, otherwise. 

Postgraduate E7 = 1 if a person is postgraduate or has higher degree; = 0, 

otherwise. 

Training E8 = 1 if a person has received any on/off job training; = 0, 

otherwise. 

Job status                      

Job nature 

and Status 

J1 = 1 if a person has a permanent job; = 0, otherwise. 

LSOM J2 = 1 if a person is legislator, senior official or manager etc.; = 

0, otherwise. 

Professionals               J3 = 1 if a person is professional doctor, engineer etc.; = 0, 

otherwise. 

TASP                          J4 = 1 if a person is technician or associate                                            

professional etc.; = 0, otherwise. 

Clerks                          J5 = 1 if a person is clerk; = 0, otherwise. 

SWSMSW                  J6 = 1 if a person is service worker, sale’s person etc.; = 0, 

otherwise. 

SAFW                         J7 = 1 if a person is skilled agricultural or fishery worker etc.; = 

0, otherwise. 

CTW                           J8 = 1 if a person is craft or  related trade worker; = 0 otherwise. 

PMOA                         J9 = 1 if a person is plant or machine operator or assembler etc.; 

= 0, otherwise. 

EO                                J10 = 1 if a person belongs to elementary occupation; = 0, 

otherwise. 

 

Although  Hyder and Reilly (2005)  also used the majority of such variables in their studies but we added few 

variables, displaying the job type and status. 

 

2.2. Median Regression 
For the empirical analysis of our study, the relationship between response variable and covariates is established. 

In statistics, we know that the basic descriptive aspects of any data are location (average) and shape (dispersion). In 

analysis our concern lies in the both aspects of the distribution of response variable with the connection of covariates 

effects i.e. how the covariates affect the location and shape of response variable. Thus, we chose to use the quantile 

regression model. The concept of quantile regression has given by Koenker and Bassett (1978). They have explained 

the significance of the quantile regression approach when the distribution of response variable is non-Gaussian. In 



Economy, 2014, 1(1): 15-19 

 

 

 

 

17 

 

statistics, for non-Gaussian distribution the suitable descriptive statistic for location is median rather than mean. So 

the median regression which is a special case of a quantile regression, gives the estimates of median of response 

variable distribution with the connection of covariates effects. One more advantage of such regression approach is 

that it is robust technique in handling the extreme values and outliers. 

Consider a real valued random variable Y characterized by the following distribution function, 

F(y) = Prob (Y  y),       

the -th quantile of Y is defined as the inverse function 

Q() = inf {y: f(y)  },       

where 0 <  < 1. In particular, the median is Q(1/2). 

The -th sample quantile )(ˆ  , which is an analogue of Q(), may be formulated as the solution of the optimization 

problem, 

),(min
1







y
i

n

iR

       

where ,10)),0(()(  
zIzz  is usually called the check function. 

When covariates X are considered, the linear conditional quantile function, )()|(  xxXQ  , can be estimated 

by solving, 

)(minarg)(ˆ
1


 xy ii

n

i




,                    (1) 

for any ).1,0(  The quantity )(ˆ   is called the regression quantile. The case 0.5  , which minimizes the 

sum of absolute residual, is usually known as median regression. For more details and use of the median regression, 

see Koenker and Hallock (2001), Buhai (2004) ,  Martins and Pereira (2004), Chen and Wei (2005) and Aslam et al. 

(2010) . 

Our model of interest is  
3 8 10

0
1 1 1

( ) ,i i j ji k ki m mi i
j k m

Q y G X E J           
  

               (2) 

where ( )iQ y is the desired  -th quantile of the log-income of the ith individual,  i is the random error with 

zero mean and constant variance and rest are the respective coefficients and covariates defined in Table 1. However, 

for 0.5,  we have the model of interest, the median regression model. 

 

3. Results and Discussion 
There are 7,070 individuals of the Punjab, whose monthly incomes are given in the data (PLFS, 2008- 09). Out 

of 7,070 persons 4,848 (68.57%) belong to the urban and 2,222(31.43%) belong to the rural areas of Punjab. There 

are 85.40% males and 14.60% females. It seems that the working class of men is greater than five times of that of 

women in Punjab. Mean age of the respondents is 33.29   12.43(standard deviation: SD). In the data, there are 

76.40% literate and 23.6% illiterate persons and this shows that literacy rate in employed community is high. Only 

32.57% of the individuals have permanent job. 

The average monthly income is reported to be Rs. 8,293.72  8,405.26 (95% C.I: Rs. 8,097.76, 8,489.67).  The 

median of monthly income is found to be Rs. 6,000. It means than 50% of the working class in Punjab earns just Rs. 

6,000 or below per month.  

It is noted that the distribution of income is positively skewed the mean is far from median and close to the upper 

quartile. It is also evident from Fig. 1.  
 

 

 

 

 
 

Fig-1.Histogram of Monthly Income 

 
From Table 2, it is reported that the average income of males and females in Punjab are Rs. 8,554 and Rs. 6,770, 

respectively (using PLFS 2008-9). Thus, the average income gap is Rs. 1,784 which is also statistically significant.  

 
Table-2.Comparison of Average Income of Males and Female 

Gender N Mean Std. Deviation Std. Err. t p-value 

Male 6038 8554.09 8413.23 108.27 
6.32 0.00 

Female 1032 6770.31 8198.33 255.20 

 

Table 3 presents the median regression estimates which are the chief targets of the present study. All the 

regression coefficients are found to be statistically significant at 1% or 5% level of significance. Since the 

logarithmic income is used in Model (2), the coefficients in Table 3 are directly interpretable. They merely tell the 

0 50000 100000

0

500

1000

1500

Income

F
re

q
u
e
n
c
y



Economy, 2014, 1(1): 15-19 

 

 

 

 

18 

 

percent change in the median monthly income of an individual in Punjab. It is reported if a person in Punjab is male 

he can earn 46.77% more income as compared to female for just being male. In other words, if the 50% of the 

females in Punjab earn monthly income Rs. 10,000 then 50% of their male counterparts will earn Rs. 14,677. 

However, when we compare our result with that given in Hyder and Reilly (2005), this figure is 21.28% for the 

entire country (using LFS 2001-02). Thus, the income gap between males and females almost double in Punjab when 

compared with entire Pakistan. Being married can increase 9.53% of income and it is evident due to change in the 

responsibilities after getting married. Moreover, if we compare the urban and rural residents of Punjab, the gap in 

income is found to be 9.87%. The urban workers tend to earn more. However, it should be noted that in PLFS (2008-

9), the area means the area of residence not the work area so we cannot assess the true income gap between the rural 

and urban workers. It may possible that a rural resident works in some urban area and vice versa.  

When we focus on the education level of the workers in Punjab, we note expectedly that with the increase in the 

education, there is increase in the income.  Professional degree holders earn at highest rate as compared to the others. 

According to Hyder and Reilly (2005) , the change in the median income is 6.83% if a person has primary level of 

education in Pakistan. This figure is almost double i.e. 11.35% in Punjab. It shows that there are fair available 

sources of income for low educated persons in Punjab as when compared with entire Pakistan.  

If we focus on the job status and nature in Punjab, we report that after having a permanent job, the median monthly 

income can be increased as much as 41.17%. The median income of is legislators, senior officials or managers is at 

the highest level in Punjab. 

Now we elaborate the results of the estimated median regression model with the help of hypothetical information 

of a working individual of Punjab. Suppose, if we consider a graduate married male (E5 =1, G =1, X3 =1) worker of 

age 30 (X1 = 30) who lives in an urban area (X2 = 1) and is a clerk (J5 = 1) on permanent (J1 = 1) basis. The median 

monthly income of the persons in Punjab having such characteristics can be computed to be Rs. 11,762. In other 

words, 50% of the male workers with the above stated characteristics will have monthly income more than Rs. 

11,762 and 50% less than this amount. If such person is a female then the median income is Rs. 7,368. Thus, there is 

a gap of Rs. 4,394 between the males and females of the same cadre and status as stated above.  

 

4. Conclusion 
A data set of 7,070 individuals of the Punjab, whose monthly incomes are given in PLFS (2008-09) is 

considered. In addition to income, several other variables are included in the study whose impacts are being 

measured on the monthly income. These covariates are gender, age, marital status, education level and job status etc. 

It is found that the female labour force participation is very low (14.60%) in Punjab. More than 75% of the working 

class is literate 68.57% belongs to the urban areas. Majority of the employers do not have permanent jobs. The 

average monthly income is reported to be Rs. 8,293.72. Moreover, 50% of the employees in Punjab earn less than 

Rs. 6,000 per month according to the information available in PLFS (2008-9). Similarly, from the distribution of 

income, it is depicted that a huge working class has low income. The average monthly income of males and females 

are reported to be Rs. 8,554 and Rs. 6,770, respectively (using PLFS 2008-9). The males tend to earn Rs. 1,784 more 

income, on average, as compared to their female counterparts in Punjab. The median regression analysis has the 

following main findings:  

a)  A male can increase 46.77% in the median monthly income as compared to working female in Punjab; b) The 

factor of marriage increases 9.53% in the monthly income; c) The people with urban origin can earn 9.87% more; d) 

Permanent job is prime factor in the increase of income.  
 

Table-3.The Median Regression Estimates 

Variable Coef. Std. Err. T p-value [95% Conf. Interval] 

Constant 7.1111 0.03821 186.10 0.0000 7.0362 7.1860 

Age 0.0097 0.0007 13.89 0.0000 0.0083 0.0111 

Gender 0.4677 0.0207 22.60 0.0000 0.4272 0.5083 

Marital Status 0.0953 0.0185 5.15 0.0000 0.0590 0.1315 

Area 0.0987 0.0146 6.76 0.0000 0.0701 0.1274 

Primary 0.1135 0.0488 2.33 0.0296 0.0179 0.2092 

Middle 0.1758 0.0525 3.35 0.0029 0.0729 0.2787 

Matriculation 0.2768 0.0521 5.31 0.0000 0.1747 0.3789 

Intermediate 0.4510 0.0553 8.15 0.0000 0.3426 0.5593 

Prof. Degree 1.0322 0.0682 15.13 0.0000 0.8985 1.1659 

Graduation 0.5280 0.0316 16.71 0.0000 0.4661 0.5899 

Post Graduation 0.8989 0.0364 24.69 0.0000 0.8275 0.9702 

Training 0.0634 0.0206 3.08 0.0055 0.0230 0.1037 

Job Status 0.4117 0.0165 24.95 0.0000 0.3794 0.4440 

LSOM 0.7308 0.0369 19.80 0.0000 0.6584 0.8031 

Professional 0.4715 0.0376 12.54 0.0000 0.3978 0.5452 

TASP 0.2965 0.0322 9.21 0.0000 0.2334 0.3596 

Clerk 0.3685 0.0372 9.91 0.0000 0.2956 0.4414 

SWSMSW                  0.3087 0.0287 10.75 0.0000 0.2524 0.3649 

SAFW                         0.2601 0.0541 4.81 0.0001 0.1540 0.3661 

CTW                           0.3977 0.0238 16.71 0.0000 0.3510 0.4443 

PMOA                         0.4673 0.0305 15.32 0.0000 0.4075 0.5270 

EO                                0.2705 0.0238 11.36 0.0000 0.2238 0.3171 

 



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