Statistical Analysis

1. 978-1-4673-7682-2/15/$31.00 ©2015 IEEE 1085
2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)
Statistical Analysis and Data Processing: A Case
Study of Employment Effects of Minimum Wages
Qiong Wang
Economics and Management school, Wuhan University,
Department of Economics, Hubei University of Economics,
Wuhan, China
Abstract—Different methods of sample collection, data processing
and model setting always bring about different results in
statistical studies. This article chooses the case of nine cities in
Hubei province to make a statistical analysis on the employment
effects of statutory minimum wages. After the indicators selection
and models setting, this article utilizes the weighted average
method to process the yearly data and make the nominal data
deflated by price index. Then by making two kinds of test
( Hausman test and Breusch-Pagan test) separately on the models
set, this article finally chooses the fixed effects model and the
results of estimation indicate that the changes of the minimum
wages have no significant negative effect on the employment in
the current period, but such effects may be significant in the
future period, inferring that the labor market in central China is
closer to the monopsony power theory. However, considering the
limitations of data collection in the domestic, it is also needed to
enlarge the range of samples to constitute the larger panel data
and explore the methods of data mining in the future.
Keywords-panel data; fixed effects model; data processing
I. INTRODUCTION
Sample collection, data processing and model selection are
now playing more and more important roles in the field of the
economic research, which directly influence the theory
verification and public policy making. However, due to the
different methods of sample collection, data processing and
model setting, the findings of research are often inconsistent
with each other. This is very common in the study of the
employment effects of statutory minimum wages nowadays.
Since the minimum-wage laws have been implemented in
many countries, the controversies of the employment effects
of statutory minimum wages have existed both in theories and
empirical studies.
There are two opposite theories that can explain the
employment effects of statutory minimum wages. One is the
competitive theory of labor market; the other is the
monopsony power theory of labor market. The competitive
model is based on the assumption of perfect competition and
believes that wages can adjust flexibly and timely to reach the
market equilibrium if there is no regulation on them. But after
the implementation of the minimum-wage laws, the flexibility
in the changes of wages has been violated. Wages become
rigid and cannot adjust with the changes of supply and
demand in a timely manner. Moreover, the minimum wages
prescribed by the government are often higher than the market
competitive wages, which will increase labor costs and cause
enterprises to reduce the demand for labor, or more likely to
replace labor with capital or technology. Therefore, the market
equilibrium may be broken with labor supply exceeding the
labor demand, suggesting that the minimum wage system may
bring a negative effect on employment.
The monopsony power model of the labor market indicates
that when there is only one “buyer” in a specific labor market
with the given labor supply, the one “buyer” can control the
equilibrium wages in the market by deciding the employment
himself. Thus, the employment will not necessarily decrease
with the changes of statutory minimum wages, suggesting that
the minimum wage system does not bring a negative effect on
employment.
In order to test which model is more realistic, a large
number of statistical studies have occurred over the past two
decades. These studies are based on the different data and
methods and have produced a wide range of results. Early
studies use time-series analysis to test the predictions of the
competitive model of labor market. Most estimates of these
studies indicate that the amount of employment decreases by 1
to 3 percent when the minimum wage is increased by 10
percent, suggesting smaller negative effects of the minimum-
wage laws. But time-series studies have several limitations.
The two main limitations are that the time-series observations
are not independent and that it is difficult to differentiate the
effects of a change in the minimum wage from the effects of
other structural changes, such as the changes in economic
conditions. Further, the negative effects of minimum-wage
increases tend to be magnified due to a publication bias in the
time-series studies. In particular, although the number of time-
series observations has increased over time, the standard errors
of the estimates do not decrease.
Then the researchers search for alternative methodologies.
One is the “natural experiments” methodology. It replicates
conditions of true experiments by comparing the effects of an
exogenous policy variable in two subsets of populations:
treatment and control groups. For minimum wage studies, the
treatment group is a state (or a city) with an increase in the
minimum wage, while the control group is a state (or a city)
where the minimum wage remains the same. If the minimum
wage has a negative effect on employment, then one would
expect that states with higher increases in the minimum wage

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would experience greater losses in employment. This
methodology is also referred to as a “differences-in-
differences” approach because it compares the changes in
employment levels, rather than the absolute levels of
employment in two groups. But this methodology still has
some limitations. The main limitation is that the control
groups cannot always been found in reality because the
minimum-wage laws in many countries are always
implemented across the country rather than being
implemented only in one state (or one city). Thus, this
methodology has not been widely used in fact.
Nowadays most of the studies utilize panel data analysis.
Some of them are even cross-country analysis. But the studies
focusing on the employment effects of minimum wages with
panel data analysis in China have still far from abundance.
Since the minimum-wage law has been enforced in China
from 1990s, it is meaningful to continue the study with more
workable methodologies. This article tries to use panel data
analysis to examine the employment effects of statutory
minimum wages in the local market of China. The next section
is the sample and model description. Data processing is
presented in section III. Section IV tests the models and
interprets the statistical outcomes. Section V gives the
conclusion and put forwards the possible improvements in the
future research.
II. SAMPLE AND MODEL DESCRIPTION
A. Selection of samples and Indicators
In order to better use statistical methods to analyze the
employment effects of minimum wages, this article chooses
the data of nine cities in Hubei province. These cities include
the city of Wuhan, the city of Huangshi, the city of Ezhou, the
city of Xiaogan, the city of Huanggang, the city of Xianning,
the city of Xiantao, the city of Qianjiang, and the city of
Tianmen. These cities have formed into the city circle in
Hubei province, which now is a core region in the central
China. The data of various economic indicators in those nine
cities can be found in the official database. Thus, the data
collected can be authoritative and systematic, which shall
build the first step of a high-quality statistical study.
The regulations of minimum wages in Hubei province
have been promulgated since 1995. The observations of nine
cities in one year constitute cross-sectional data. Thus, the data
of nine cities covering the period through 1995 to 2012 will
eventually be formed into panel data.
Based on the variables selected in previous studies and the
basic theory of labor market, the variables in this article shall
include Eit, MWit, MWi,t-1 and other control variables, Among
which Eit is the dependent variable and the others are
independent variables. The specific meanings of these
variables are as follows:
Eit refers to the amount of employment in the city of i and
the year of t. The employment effects of minimum wages
mean the impact of minimum wages on employment, which
can be measured by the absolute number of jobs or the relative
indicators such as employment rate, unemployment rate and
job flow, etc. This article chooses the absolute indicator--the
number of employees--as the amount of employment.
MWit refers to the minimum wages in the city of i and the
year of t. It is the crucial independent variable in the model,
because the changes of minimum wages may significantly
affect the employers’ demand for labor, thereby affecting the
number of jobs in the labor market.
MWi,t-1 refers to the minimum wages in the city of i and the
year lagged one period. Since it will take some time for
employers to adjust the input of factors, the lag effect of the
minimum wages should also be taken into account in the study.
There are many other factors that can affect the
employment. In order to increase the effectiveness of the
estimation, it is necessary to add other variables to control the
independent variables mentioned above. In this case, Gross
Domestic Product (GDP for short) has been used as the main
control variable to control the impact of the exogenous
economic shocks on employment.
In addition, all of the variables are converted into natural
logarithm form so as to better estimate and illustrate the values
of elasticity.
B. Description and Comparison of Fixed Effects Model and
Random Effects Model
Fixed effects model and random effects model can both be
used in the analysis of panel data. Fixed effects model restricts
the slope coefficients to be constant over both individuals and
time and allow for an intercept coefficient that varies by
individuals or by time. Considering the nine cities may have
some different properties with each other, the intercept
coefficient of fixed effects model in this study is likely to
vary over individuals, which causing the structure of model as
follows:
1 2 3 , -1 4ln ln ln lnit i it i t it itE MW MW GDPβ β β β ε= + + + + (1)
Where, β1i represents the intercept coefficient of city i. In
fact it is the 1 × 9 vector of intercept coefficients for the nine
cities. In order to take into account the different intercepts, the
eight dummy variables shall be used in this study besides the
original intercept. β2, β3, and β4 are separately the 1 × 9 vectors
of coefficients on lnMWit, lnMWi,t-1, and lnGDPit . In addition,
εit is the error term accordingly.
Random effects model specifies the individual effects as a
random draw that is uncorrelated with the independent
variables and the overall error item. The random effects model
can be transformed from the fixed effects model. In (1), β1i can
be assumed as an error item with the mean value of β1. Then,
the intercept coefficient of cross-section units can be written
as:
1 1i iuβ β= + (2)
The implication of this approach is that every cross-section
unit with individual properties has the same mean value, while

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the individual differences in intercept are reflected in the error
term. Put (2) into (1), we can get,
1 2 3 , -1 4ln ln ln ln iit it i t it itE MW MW GDP uβ β β β ε= + + + + + (3)
Defining it i itw u= + ε , where, wit is a composite error term.
The first half of it reflects the error from individuals (or cross-
section units), while the second half reflects the mixed error
from time-series and cross-section. Finally, put it i itw u= + ε
into (3), we can get the structure of the random effects model
as:
1 2 3 , -1 4ln ln ln lnit it i t it itE MW MW GDP wβ β β β= + + + + (4)
Both fixed effects model and random effects model have
some limitations. For the fixed effects model, when the
number of cross-section units is very large, more dummy
variables need to be used, thereby bringing about the big loss
of degree of freedom. In this study, we shall use eight dummy
variables for nine cities, so eight degree of freedom will be
lost. Compared to this, the random effects model can save the
degree of freedom, but it has a more stringent crucial
assumption that ui is uncorrelated with the independent
variables. If this assumption cannot be satisfied, the statistical
outcomes from the random effects model will be biased. In
fact, the satisfaction of this assumption needs the fact that
individuals (or cross-section units) are selected randomly from
a large sample. However, the case selection in this study
obviously shows that it cannot match the fact. Therefore, the
preliminary conclusion can be made that the fixed effects
model is more appropriate in this study.
III. DATA COLLECTION AND PROCESSING
A. Collection of Data
Based on the variables selected in section II, the number of
employees and the values of GDP in nine cities are collected
from the Statistical Yearbook of Hubei Province from the year
of 1996 to the year of 2013. But the data of GDP from those
databases are nominal indicators and cannot be used directly.
Thus, they need to be processed further.
The values of minimum wages in nine cities are collected
from the Statistical Bulletin of Hubei Province accordingly.
The regulations of minimum wages in Hubei province were
initially promulgated on May 22, 1995. Considering the
different economic growth in different regions, the minimum
wages prescribed by the government were divided into several
grades and raised every two or three years. Table I shows the
grades and dates of adjustment of minimum wages in Hubei
province since 1995. In the original legislation, the minimum
wages were divided into four grades. The highest grade was
200 Yuan per month, while the lowest grade was 140 Yuan
per month. In the year of 2002, the grades were adjusted into
five grades with the highest grade of 460 Yuan per month and
the lowest grade of 280 Yuan per month. Then the grades
were restored to four grades in 2008 and adjusted to three
grades in 2011 till now.
TABLE I. THE CHANGES OF MINIMUM WAGES IN HUBEI PROVINCE
Date of
Adjustment
Grades
Monthly Minimum Wages
（Chinese Yuan/month）
May,22,1995 4 200 180 160 140 —
Otc,19,1999 4 260 235 210 180 —
Jan, 1, 2002 5 400 340 310 280 240
Mar, 1, 2005 5 460 400 360 320 280
Mar, 1, 2007 5 580 500 460 420 380
Aug, 1, 2008 4 700 600 520 450 —
May, 1, 2010 4 900 750 670 600 —
Dec, 1, 2011 3 1100 900 750 — —
Sep, 1, 2013 3 1300 1020 900 — —
The data in the table are collected from the Statistical Bulletin of Hubei Province
There are two problems in using above data of minimum
wages in the statistical research. The first one is that, some of
the above nine cities have different districts, which have been
classified into different grades. For example, seven districts in
the city of Wuhan were classified into the highest grade with
the minimum wage of 1300 Yuan per month in 2013, while
the other four districts were classified into the middle grade
with the minimum wage of 1020 Yuan per month in the same
year. Thus, which grade of minimum wage should be chosen
for each city is needed to analyze further. The other problem is
that, there might be two types of values of minimum wages in
one year since the dates of adjustment of minimum wages
were not always from the beginning of the year or in the same
month of the year. Thus, a direct regression by year shall
result in a lack of comparability. Therefore, an appropriate
method needs to be used to solve this problem.
B. processing of Data
In view of the problem of incomparability of nominal GDP
between the nine cities in every year, it is necessary to
eliminate the factor of inflation. So the values of GDP
collected from the Statistical Yearbook are all deflated by
Consumer Price Index (CPI for short) of the same year.
In view of the different districts of one city having been
classified into different grades, this article chooses the value
of highest grade for the whole city. This is a commonly used
method in other studies now. Considering the inconsistencies
of adjustment date of minimum wages, this article chooses
weighted average method to process the yearly data. The
specific formula of weighted average method is as follows:
1 1 2 2 k kx f x f x f
x
n
+ + … +
= （5）
x1 to xk refer to the different values of minimum wages in
one year if the adjustment date was not set in the beginning of
the year. f1 to fk refer to the weights distributed to each value,
which are equal to the number of months the corresponding
value lasting. For example, the minimum wage in the city of
Wuhan was adjusted to 260 Yuan on October 19th, 1999.
Before that date the minimum wage in the city of Wuhan was

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still 200 Yuan. That means the value of 200 Yuan lasted ten
months in that year and the value of 260 Yuan lasted two
months. Thus, ten and two are the weights for the value of 200
and the value of 260 separately. The weighted average value
of minimum wage in the city of Wuhan in that year is 210
Yuan after calculation, see as follows:
200 10 260 2
210
12
× + ×
= (6)
Besides, in order to eliminate the impact of inflation, the
value of 210 is then deflated by CPI of the same year, thus
getting the value of 200 Yuan at last.
Relying on the above method, the minimum wages in the
city of Wuhan have been calculated and shown in table II,
which represent the real value of minimum wages in every
year. The values of minimum wages in other cities are all
converted by the same method.
TABLE II. THE VALUES OF MINIMUM WAGES IN THE CITY OF WUHAN
AFTER BEING PROCESSED
Year
Original
Value of
Minimum
Wages
Weighted
Average of
Minimum
Wages
CPI
Final Value
of Minimum
Wages
1995 200 200 100 200
1996 200 200 110.2 181.5
1997 200 200 113.1 176.8
1998 200 200 110.7 180.7
1999 260 210 107.6 195.2
2000 260 260 107.6 241.6
2001 260 260 107.9 241
2002 400 400 107.5 372.1
2003 400 400 109.9 364
2004 400 400 115.3 346.9
2005 460 450 118.6 379.4
2006 460 460 120.5 381.7
2007 580 560 126.3 443.4
2008 700 630 205.8 306.1
2009 700 700 133.7 523.6
2010 900 833 137.6 605.4
2011 1100 917 145.5 630.2
2012 1100 1100 149.8 734.3
2013 1300 1167 153.7 824.6
The unit of minimum wages in the table is Chinese Yuan.
IV. TESTS ON MODELS AND ANALYSIS OF FINAL
REGRESSION
A. Tests on Model Selection
Although the preliminary conclusion has been made that
the fixed effects model is more appropriate for the study, the
final judgments shall be made in this section by formal test
procedures.
Firstly uses Stata 11.0 to generate statistical results of two
models. As shown in table III and table IV, the statistical
results of two models are in general consistency. But there are
still some differences in the estimates of the coefficients. For
example, the estimate of the coefficient of MWit in the fixed
effects model is -0.1399, slightly higher than the estimate of -
0.2809 in the random effects model. Besides, the estimates of
coefficient of GDPit in two models are also slightly different
with each other. In order to determine which statistical result
shall be chosen, we then use some test procedures to make the
judgments.
TABLE III. THE MAIN RESULTS OF FIXED EFFECTS MODEL
Variables Coefficient
Standard
Deviation
T
Statistics
Probability
MWit -0.1399 0.3385 -0.88 0.381
MWi,t-1 1.033 0.3078 3.36 0.001
GDPit 0.7317 0.2495 2.93 0.004
constant -5.2605 0.7843 -6.71 0.002
TABLE IV. THE MAIN RESULTS OF RANDOM EFFECTS MODEL
Variables Coefficient
Standard
Deviation
T
Statistics
Probability
MWit -0.2809 0.2915 -0.96 0.335
MWi,t-1 1.0054 0.3057 3.29 0.001
GDPit 0.9243 0.8544 10.82 0.0003
constant -5.338 0.7794 -6.85 0.0001
Hausman test and Breusch-Pagan test are the most
common test procedures in determining the applicability of
fixed effects model and random effects model. Hausman test
focuses on the significance of the differences in the
coefficients between the two models. The null hypothesis is
that there is no essential difference in fixed effects model and
random effects model. Breusch-Pagan test focuses on the
correlation between the independent variables and the error
term. In the test, the square of OLS residual is regressed by the
independent variables first, and then determines whether to
reject the null hypothesis by examining the significance.
The results of Hausman test and Breusch-Pagan test are
shown separately in table V and table VI below. In table V,
the values in the fourth column and the fifth column can
indicate that the differences between the estimates of two
models are not significant on the given significance level of
5%. So the null hypothesis can be retained and the conclusion
can be made that it is the same no matter what kind of model
is used. In table VI, the probability of chi-square is 0.3873
meaning that it is not significant on the given significance
level of 5%. So the conclusion can be made that the random
effects model is inferior to the fixed effects model.
In conclusion, Hausman test indicate that there is no
substantive difference in the two models, while Breusch-
Pagan test indicate that the fixed effects model is better than
the random effects model. Combined with the analysis in

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section II, it can be thought that the fixed effects model is
more appropriate for this study.
TABLE V. THE RESULTS OF HAUSMAN TEST
Coefficient
Difference
(b)-(a)
Sqrt(diag(v_b-v_B))
S.E.
(a)
FEM
(b)
REM
MWit -0.1399 -0.2809 0.1409 0.172
MWi,t-1 1.033 1.0054 0.02756 0.3644
GDPit 0.7317 0.9243 -0.1926 0.2344
In this table, “FEM” represents the fixed effects model. “REM” represents the random effects model.
TABLE VI. THE RESULTS OF BREUSCH-PAGAN TEST
Var Sd=aqrt(Var)
lne 1.5313 1.2376
e 0.477 0.6907
u 0.0225 0.1501
In this table, “e” represents the error term. “u” represents the residuals. “Var” represents the variance.
B. Robust Regression and Analysis
Using the fixed effects model, the regression is carried out
again by Stata 11.0 and the final results are summarized in
table VII.
TABLE VII. THE FINAL RESULTS FROM FIXED EFFECTS MODEL
Variables Coefficient
Standard
deviation
T
Statistics
P
value
MWit -0.1399 0.1601 -0.89 0.3734
MWi,t-1 1.033 0.1488 6.94 0.0001
GDPit 0.7317 0.2205 3.32 0.0011
constant -5.2605 1.2186 -4.32 0.0003
Dhs -4.1568 0.8248 -5.04 0.0002
Dez -1.3194 0.6405 -2.06 0.0394
Dxg -2.6159 0.8520 -3.07 0.0022
Dhg -4.3352 1.5538 -2.79 0.0052
Dxn -0.7603 0.3953 -1.93 0.0536
Dxt -1.9375 0.6751 -2.87 0.0042
Dqj 3.6248 2.1198 1.71 0.0872
Dtm -2.7743 0.5816 -4.77 0.0002
R-sq: within: 0.495 between: 0.9396 overall: 0.6737
In this table, “constant” represents the intercept of the city of Wuhan. Dhs, Dez Dxg, Dhg, Dxn, Dxt, Dqj,
Dtm separately represent the intercept of the other cities besides the city of Wuhan.
R-square is used to judge the degree of explanation of
independent variables on the dependent variable, typically
ranging between 0 and 1. It shows a better fitting degree when
it’s close to 1. The R-square between the sample groups is
0.9396, indicating that the independent variables between the
different cities have made a strong explanation on the
dependent variable. The R-square in the whole samples is
0.6737, indicating that the model chosen above can meet the
degrees of explanation at approximately 67.37% on the whole.
However, the R-squares within the sample groups is 0.495,
relatively low, indicating that the model needs to be improved
in the explanation of the independent variables within the inner
regions of the different cities. In general, this model is a well
fitting model on the whole.
The estimate of β1 is -0.1399. It means if the minimum
wages in the current period grow one percent, the amount of
employment in the same period of nine cities will decrease
0.1399 percent. However, the value of t statistics of β1 is only -
0.89, which shows that this estimate of β1 is statistically
insignificant, that is to say, MWt, one of the core independent
variables, does not have great negative effects on the amount of
the employment.
Contrast to β1, the value of t statistics of β2 is 6.94, showing
that the estimate of β2 (that is 1.033) is quite significant. The
value of 1.033 means if the minimum wages of last year grow
one percent, the amount of employment in the current year will
increase 1.033 percent. That is to say, although the changes of
minimum wages in the current period have no significant effect
on the amount of employment in the current period, the
minimum wages lagged one period is not the same.
Unexpectedly, the latter has a strong positive effect on the
amount of employment in the current period.
The changes of GDP are also one of the reasons of the
changes of employment in the current period. The value of t
statistics of β3 is 3.32, showing that the estimate of β3 (that is
0.7317) is statistically significant. And if GDP grow one
percent, the amount of employment in the current period will
increase 0.7317 percent. This result is consistent with the
traditional theory.
The intercept coefficient of the city of Wuhan is -5.2605.
Taking into account the different dummy variables set for the
different cities, the estimates of intercept coefficients of other
eight cities can be calculated correspondingly. For example,
the estimate of intercept coefficient of the city of Huangshi is -
9.4173 (the value of -5.2605 being added to the value of -
4.1568). Except for the city of Qianjiang, the relatively high
values of t statistics of these estimates indicate that the fixed
effects in the nine cities are statistically significant.
V. CONLUSIONS
The statistical analysis in this article indicates that the
changes of the minimum wages have no significant effect on
the employment in the current period, but they do have
significant effects on the employment in the future period.
Such results are not entirely consistent with the conclusions of
competitive theory of labor market. However, it can be
inferred that the regional labor market in central China is
closer to the monopsony power theory.
Statistical analysis cannot ignore the theoretical and factual
basis behind it. The findings in the above statistical analysis
can be fully explained by the realistic conditions of labor
market in China today. In the domestic labor market nowadays,
the supply of labor has exceeded the demand of labor for quite
a long time, showing the market characteristics of monopoly,

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which is different from the basic hypothesis of competitive
labor market. Besides, the conclusion of competitive theory of
labor market is based on the facts that the minimum wages set
by the local government are always higher than the
competitive wages formed by the market itself. Since there is
the time interval in every adjustment of the minimum wages,
the following situation is likely to occur: the minimum wages
are higher than the competitive wages in the current period of
adjustment. But they may be basically consistent with the
competitive wages in the next period due to the inflation and
other factors. Therefore, the negative employment effects of
minimum wages may be probably lying in the long term rather
than lying in the short term. The statistical significance of β2
and β1 in the above analysis just illustrate these findings.
Generally speaking, the selection of indicators, the
methods of data processing and models test in this article are
robust. So the findings from the statistical analysis in this
article can be reliable to some extent. But the conditions and
individual behaviors in labor markets are very complex. The
samples in this article are not generally sufficient due to the
limitations of data collection in the domestic. Therefore, it is
also needed to enlarge the range of sample sources in China to
constitute the larger panel data with more observations and
explore the methods of data mining in the future.
ACKNOWLEDGMENT
Qiong Wang thanks Fang Wang for her great help in the
data processing and thanks the staff in the Bureau of Statistics
in Hubei Province for their help in the data collection.
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