Wage is one of the most important factors in motivating employees.
Because wage depends on a variety of determinants, the existence of
the wage gap is inevitable. According to economic theory, the wage
gap can be decomposed into two main components. The first
component is due to the difference in endowments of the workers. The
second one is due to the difference in the coefficients or due to market
returns to the endowments. The second component is statistical
evidence of discrimination that can lead to inequality in society.

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MINISTRY OF EDUCATION AND TRAINING
UNIVERSITY OF ECONOMICS OF HO CHI MINH CITY
--------------
TRẦN THỊ TUẤN ANH
QUANTILE REGRESSION
DECOMPOSITION OF THE WAGE GAP
IN VIETNAM
DISSERTATION SUMMARY
HO CHI MINH CITY, 2015
ii
MINISTRY OF EDUCATION AND TRAINING
UNIVERSITY OF ECONOMICS OF HO CHI MINH CITY
------------
TRẦN THỊ TUẤN ANH
QUANTILE REGRESSION
DECOMPOSITION OF THE WAGE GAP
IN VIETNAM
Major : Probability and Statistics.
Major code : 62.46.01.06
DISSERTATION SUMMARY
SUPERVISORS:
1. ASSOC. PROF. PH.D. LÊ VĂN PHI
2. PH.D. BÙI PHÚC TRUNG
iii
The research is completed at University of Economics Ho Chi
Minh City:
................................................................................
Supervisors:
1. Assoc. Prof. Ph.D. Lê Văn Phi
2. Ph.D. Bùi Phúc Trung
Examiner 1: ............................................................
Examiner 2: ............................................................
Examiner 3: ............................................................
The dissertation will be defended at dissertation
councils, meeting at: University Of Economics
Hồ Chí Minh City
at .............................................................................
...............................................................................
You can find more information about the dissertation at:
National Library or the Library of the University of
Economics Ho Chi Minh City.
INTRODUCTION
1. The necessary of the topic
Wage is one of the most important factors in motivating employees.
Because wage depends on a variety of determinants, the existence of
the wage gap is inevitable. According to economic theory, the wage
gap can be decomposed into two main components. The first
component is due to the difference in endowments of the workers. The
second one is due to the difference in the coefficients or due to market
returns to the endowments. The second component is statistical
evidence of discrimination that can lead to inequality in society.
Therefore, the main purposes of this study are (1) to estimate
the wage regression in Vietnam, (2) to examine the existence of gender
and urban/rural wage gap, and (3) to decompose these wage gaps to
clarify whether there are wage discrimination in Vietnam throughout
the wage distribution. These are the reasons that lead to this doctoral
dissertation which is titled as “Quantile regression decomposition of
the wage gap in Vietnam”
2. Research objectives
This dissertation aim to fulfill the following objectives:
1) Briefly summarizing the background of quantile regression and
decomposition method based on quantile regression to analyze the
wage gap.
2) Applying advanced quantile regression which account for sample
selection bias and the endogeneity of explanatory variables to
2
estimate wage equations for men/women and urban/rural groups
in Vietnam across their wage distribution.
3) Determining the gender wage gap in Vietnam and decomposing
this gap into the explained and unexplained components during
the period from 2002- 2012.
4) Determining the urban/rural wage gap in Vietnam and
decomposing this gap into the explained and unexplained
components during the period from 2002-2012.
5) Examine the change of wage distribution over the years by
comparing quantiles of wage in 2002 with that in 2012. This
difference in wage is also decomposition into two components:
the one that caused by the change in labor force’s characteristics
and the other due to the change in the return of these
characteristics.
3. The theoretical and empirical contributions
Along with these research objectives this dissertation have some
following theoretical and empirical contributions:
(a) This dissertation briefly introduces the definition and features
of quantile regression method which was first suggested by
Koenker & Bassett (1978) and has been used widely around
the world but still not popular in Vietnam. There is a few of
studies in Vietnam applied quantile regression techniques,
especially in the area of wage inequality. None of them cover
fully features of quantile regression.
3
(b) Using the advanced quantile regression, this study estimates the
wage equations in Vietnam which help examine the determinants
of real hourly wage in domestic labor market. The quantile
regression techniques applied in this studies was adjusted to
account for the problem of sample selection bias and endogeneity
that leads to unbiased and consistent estimators.
(c) This study constructs the wage equations across the quantiles for
each following groups: men, women, urban, and rural. These
results are compared in pairs to clarify the difference in their wage
structures.
(d) This study confirms the existence and estimates the magnitude of
gender wage differentials in Vietnam (for the entire sample and
for each male/female and urban/rural group of workers). In
addition, this study also shows the declined trends of gender wage
gap over time in Vietnam.
(e) After showing the existence of gender wage differential, this
research use Machado – Mata method to decompose this gap into
two components: the first component represents difference in
average characteristics between men and women; the second
component represents differences in returns to these
characteristics which may be interpreted as possible gender
discrimination.
(f) This study demonstrates the urban - rural wage differential and the
change of this gap over time by comparing the estimation in the
year 2002 with that in the year 2012.
4
(g) This dissertation decomposes the urban/rural wage
differential in order to determine the proportion of this
disparity which caused by the difference in endowments
between urban and rural workers and the proportion of this
gap caused by the difference in the market returns to the
endowments.
(h) After all, this research illustrates in details the change in wage
equation over time and shows the decreasing trends in these
wage gap over time.
CHAPTER 1 THE BACKGROUND OF QUANTILE
REGRESSION AND MACHADO – MATA DECOMPOSITION
1.1. Mincerian wage model and some extensions
The Mincerian wage equation may be written as
2ln ,tw s z z
where w: real hourly wage; s: years of schoolings, and z: worker’s
years of experience.
Card (1994) extended the standard Mincer’s wage equation as
2ln ,tw s z z X u (1.1)
where X represents for control variables such as gender, race,
region, marriage status, and so on.
After Card D. (1994), many studies also augmented the
Mincerian wage model by including various explanatory variables into
the equation to examine the determinants of compensation and to
conduct the ceteris paribus analysis of partial effects on wage.
5
1.2. Quantile regression
Quantile regression which was introduced by Koenker &
Bassett in 1978 is a method for describing the causality relationship
variables at different points in the conditional distribution of the
dependent variable. Considering the linear regression model
i i iY X u , the quantile regression estimator for each quantile τ ϵ
(0, 1) minimizes the objective function
1
1
( ) (
n
i i
i
V Y X
n
In the other word,
1
1ˆ arg min ( ).
k
n
i i
R i
Y X
n
The quantile regression for quantile τ is written as
ˆ( | )i i iQ Y X X (1.14)
1.3. Sample selection bias correction
The problem of sample selection bias correction for linear
regression with the pioneering work of Heckman (1979) has been
extensively studied in econometrics and in labor economics.
Buchinsky (1998a and 2001) was the first to consider the difficult
problem of estimating quantile regression in the presence of sample
selection and to propose the correction for this bias in the quantile
regression.
1.4. Endogeneity and the method of two - stage quantile regression
(2SQR)
6
Chevapatrakul et al (2009) suggested the method named 2SQR
(two-stage quantile regression) in order to account for the problem of
endogeneity in the quantile regression.
1.5. The decomposition method based on quantile regression
A decomposition analysis is a standard approach to examine the
wage differential between male and female workers. According to
Oaxaca - Blinder (1973)’s approach, the mean wage differential is
decomposed into one component capturing differences in
characteristics and another component referring to different returns
using the estimates of male and female wage equations). Analogous to
the linear regression case, Machado and Mata (2005) proposed a
similar decomposition which combines a quantile regression and a
bootstrap approach in order to estimate counterfactual density
functions.
CHAPTER 2 LITERATURE REVIEW
2.1. Previous studies around the world
Some representative studies in investigating the determinants of
wage and the wage gap decomposition before the appearance of
quantile regression are Edgewort (1922); Becker (1957); Dunlop
(1957); Slichter (1950); Cullen (1956); Dalton & Ford (1977); Long
& Link (1983); Dickens & Katz (1987); Krueger & Summers (1988);
Groshen (1991); Ferber & Green (1982); Lindley, Fish & Jackson
(1992); Blackaby et al (2005)
7
Buchinsky (1994) initiated the application of quantile regression
in estimating wage regression. This led to a trend of using quantile
regressions in order to decompose the gender wage gap at different
points of the wage distribution. It can be listed some noticeable studies
as Fortin and Lemieux (1998); Ajwad et al (2002); Albrecht et al
(2003); Machado & Mata (2005); Melly (2006); Gunawardena (2006);
Arulampalam et al (2007); Nestic (2010); Del Río, Gradín & Canto
(2011).
2.2. Previous studies in Vietnam
Very few studies in Vietnam applied quantile regression to
investigate wage differentials as well as decompose these wage
differentials into explained and unexplained parts. The typical studies
can be listed are Hung et al (2007a) and Hung Ho et al (2007b).
However, these studies which used the VHLSS 2002 did not account
for the problem of endogeneity.
CHAPTER 3 DATA AND METHODOLOGY
3.1. Data
This study uses the VHLSS 2002 and 2012 to estimate the wage
equation in Vietnam labor market and conduct an empirical
investigation of wage differentials between the male and female
workers as well as the urban and rural areas. In order to dispose of the
wage change due to inflation, the data was deflate to obtain the
comparable real wages.
8
By comparing the kernel density estimation of wage distribution
between male and female worker as well as urban and rural areas, the
results demonstrate that the wage distributions in 2002 and 2012 had
both location shift and shape shift. This provided evidence that
quantile regression is appropriate for the usage of quantile regression-
based method in examining wage differentials in Vietnam economy.
3.2. METHODOLOGY
This study estimates the following regression:
1 2 3 4
5 6
6 5
1 1
3 5
1 1
lnWage + +
_
+
Region
i i i i
i i
i i i i
i i
Married Male Urban
Experience Experience sq
Degree Occupation
Type u
.i
Schooling is defined into seven categories: no schooling (base
category), completed primary, completed secondary, completed high
school, vocational, college and postgraduate. Dummy variables for
occupations, marital status, regions, and ethnicity are also included as
control variables.
First, this equation was estimated throughout the wage distribution
using all observations in the sample to obtain the overall wage
regression. After that, it was estimated again over male/female and
urban/rural groups. In order to acquire the unbiased and consistent
9
estimators, this study applied the two stage quantile regression in
combination with sample selection bias correction.
In addition, this study decomposes the wage differentials between
male/female, urban/rural and 2002/2012 by using the method of
Machado - Mata (2005).
CHAPTER 4 RESULTS AND DISCUSSION
4.1. The estimated wage equations in Vietnam
The estimated wage equations across the 0.1 – 0.25 – 0.5 – 0.75 –
0.9 quantiles in Vietnam are briefly reported in Table B.2 and Table
B.4 along with 2SLS estimation. As we can see, most of the coefficient
estimates are statistically significant. The estimates of return to
education are positive and increasing along with the qualification
levels. This indicates generally that workers with higher qualifications
would receive higher real hourly wage. Skilled workers who complete
undergraduate or postgraduate course are expected to have
substantially higher wage in comparison with the others.
Men and women’s wage equations
This study conducts the analysis separately for men and women in
the year of 2002 and 2012. An intuition of the results in 2012 can be
seen from Table B.2, which demonstrates the differences in pattern of
wage for the two groups of workers. In 2012, for the lower
qualifications (such as primary, secondary, and high school) the
10
returns to women’s education are higher than men’s regression.
However, for higher qualifications, the situation is quite opposite.
Urban and rural wage equations
The trend that higher qualifications higher returns still be stable in
both urban and rural wage equations. The education returns in the
urban area are higher than the rural area, especially at the bottom of
the wage distribution. With workers who complete primary, secondary
and high school in rural areas, the returns to education seem to
decrease as quantiles increase. In contrary, in urban areas workers with
higher qualifications have higher education returns at higher quantiles.
On the other hand, there is no clear pattern in the estimation for other
cases.
Extraction of Table B.2: Wage equations for men and women on 2012
Men’s wage equation in 2012 Women’s wage equation in 2012
Independent
variables
2SLS 2SQR 2SLS 2SQR
10% 25% 50% 75% 90% 10% 25% 50% 75% 90%
Primary 0.0788*** 0.126** 0.0780** 0.0797*** 0.0116 0.0273 0.138*** 0.0948 0.141*** 0.166*** 0.155*** 0.0524
[2.690] [2.385] [1.963] [2.672] [0.338] [0.572] [3.631] [1.102] [3.128] [4.568] [3.871] [0.869]
Secondary 0.121*** 0.169*** 0.132*** 0.107*** 0.0475 0.0845* 0.179*** 0.169* 0.194*** 0.183*** 0.175*** 0.122*
[4.013] [3.099] [3.238] [3.488] [1.349] [1.719] [4.497] [1.878] [4.110] [4.800] [4.174] [1.925]
High school 0.212*** 0.233*** 0.199*** 0.172*** 0.148*** 0.203*** 0.294*** 0.198* 0.242*** 0.268*** 0.259*** 0.310***
[5.884] [3.588] [4.072] [4.678] [3.519] [3.461] [6.285] [1.869] [4.373] [5.971] [5.257] [4.167]
Vocational 0.306*** 0.275*** 0.233*** 0.251*** 0.283*** 0.404*** 0.288*** 0.218* 0.274*** 0.305*** 0.340*** 0.296***
[9.123] [4.533] [5.106] [7.340] [7.213] [7.375] [5.843] [1.949] [4.690] [6.449] [6.564] [3.782]
Colleges 0.636*** 0.580*** 0.542*** 0.530*** 0.562*** 0.700*** 0.532*** 0.476*** 0.537*** 0.511*** 0.547*** 0.576***
[15.590] [7.862] [9.785] [12.748] [11.776] [10.513] [9.823] [3.878] [8.365] [9.836] [9.593] [6.680]
Postgraduate 1.047*** 0.934*** 0.969*** 0.925*** 1.066*** 1.193*** 0.778*** 0.888*** 0.816*** 0.757*** 0.735*** 0.649***
[12.302] [6.074] [8.384] [10.661] [10.705] [8.589] [7.424] [3.733] [6.564] [7.519] [6.663] [3.889]
Control
variables
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
t-stat in brackets *, **, *** : significant at 10%, 5%, 1% Source : Author’s calculations
12
Extraction of Table B.4: Wage equations in the urban and rural areas in 2012
Urban wage equation in 2012 Rural wage equation in 2012
Components 2SLS
2SQR
2SLS
2SQR
10% 25% 50% 75% 90% 10% 25% 50% 75% 90%
Primary 0.000577 -0.0693 0.0173 0.0761 0.000257 -0.0479 0.148*** 0.176*** 0.183*** 0.143*** 0.102*** 0.0604
[0.012] [-0.773] [0.280] [1.431] [0.004] [-0.506] [5.585] [3.113] [5.242] [5.535] [3.558] [1.544]
Secondary 0.0556 0.0402 0.0755 0.116** 0.0509 0.0308 0.190*** 0.294*** 0.227*** 0.153*** 0.148*** 0.101**
[1.125] [0.440] [1.196] [2.132] [0.805] [0.318] [6.878] [4.972] [6.236] [5.665] [4.953] [2.467]
High school 0.176*** 0.0512 0.159** 0.218*** 0.137** 0.235** 0.301*** 0.343*** 0.290*** 0.217*** 0.245*** 0.279***
[3.317] [0.521] [2.345] [3.735] [2.017] [2.264] [8.732] [4.656] [6.394] [6.462] [6.568] [5.495]
Vocational 0.242*** 0.0799 0.153** 0.269*** 0.328*** 0.394*** 0.345*** 0.331*** 0.326*** 0.282*** 0.313*** 0.355***
[4.636] [0.826] [2.297] [4.680] [4.908] [3.856] [10.249] [4.606] [7.347] [8.597] [8.605] [7.149]
College 0.484*** 0.349*** 0.380*** 0.431*** 0.518*** 0.765*** 0.591*** 0.577*** 0.569*** 0.479*** 0.530*** 0.574***
[8.419] [3.278] [5.162] [6.831] [7.033] [6.795] [14.053] [6.416] [10.271] [11.687] [11.650] [9.257]
Postgraduate 0.766*** 0.736*** 0.656*** 0.686*** 0.851*** 0.994***
[8.911] [4.622] [5.974] [7.265] [7.729] [5.909]
Control
variables
yes yes yes yes yes yes yes yes yes yes yes yes
t-stat in brackets; *, **, *** : significant at 10%, 5%, 1% Source : Author’s calculations
4.2. Decomposition results
Now we turn to the Machado – Mata technique to decompose
the urban/rural wage gap across quantiles into two components – one
due to urban – rural differences in the distributions of covariates and
the other due to urban-rural differences in the distributions of returns
to those covariates. The decomposition of the gender wage gap based
on Machado – Mata method is reported in Table C.1. As we can see
from Table C.1, real hourly wages seem to be always greater for men
than for women at all considered quantiles. This wage gap is smaller
at higher wage. The largest gap is found at quantile 0.1. The gender
wage differential declines over the time. However, in each year, using
the male wage structure as a reference, the gender wage gap is totally
due to the differences in returns, which are traditionally interpreted as
discrimination.
Table C.1 Decomposition of gender wage differential
Components
All sample By areas
2002 2012
In urban In rural
2002 2012 2002 2012
Quantile 0.1
Raw differential 0.2947*** 0.2173*** 0.1760*** 0.1516*** 0.3941*** 0.2854***
[18.04] [17.48] [8.87] [7.45] [22.98] [13.44]
Due to endowments -0.0858** -0.070*** -0.0348 -0.0503** -0.071*** -0.061**
[-3.16] [-2.92] [-1.46] [-1.52] [-2.88] [-1.16]
Due to returns 0.3805*** 0.287*** 0.2109*** 0.2046*** 0.4655*** 0.3465***
[14.22] [21.81] [8.83] [8.61] [20.82] [12.77]
Quantile 0.25
Raw differential 0.2306*** 0.1690*** 0.1595*** 0.1589*** 0.3312*** 0.2071***
[30.73] [19.89] [11.65] [9.29] [29.21] [18.20]
Due to endowments -0.075*** -0.076*** -0.046*** -0.051*** -0.064*** -0.068***
[-5.51] [-5.11] [-2.77] [-2.44] [-4.91] [-2.75]
Due to returns 0.3059*** 0.2453*** 0.2055*** 0.2101*** 0.3957*** 0.2755***
14
[23.49] [33.98] [11.65] [12.19] [29.70] [16.96]
Quantile 0.5
Raw differential 0.1569*** 0.121*** 0.1565*** 0.1477*** 0.2167*** 0.1471***
[30.37] [15.70] [14.18] [8.10] [35.87] [19.48]
Due to endowments -0.084*** -0.085*** -0.073*** -0.033* -0.053*** -0.063***
[-8.000] [-5.81] [-4.47] [-1.70] [-6.27] [-4.01]
Due to returns 0.2416*** 0.207*** 0.2295*** 0.1813*** 0.2702*** 0.2106***
[22.81] [23.65] [15.58] [9.57] [35.91] [14.34]
Quantile 0.75
Raw differential 0.0912*** 0.086*** 0.1590*** 0.1413*** 0.1287*** 0.1076***
[17.30] [9.10] [11.30] [7.05] [16.75] [9.46]
Due to endowments -0.119*** -0.098*** -0.071*** -0.004 -0.067*** -0.095***
[-9.36] [-5.73] [-4.07] [-0.23] [-6.32] [-4.28]
D