Gender Discrimination and Firm Proﬁt Eﬃciency:
Evidence from Brazil∗
Wenjun Liu†
Tomokazu Nomura‡
Shoji Nishijima§

Abstract
In this study, we investigated discrimination against women within
the Brazilian labor market using ﬁrm-level data. We based on employer
discrimination model proposed by Becker and considering the proportion of female employees as a proxy for the extent of discrimination.
Estimating the proﬁt eﬃciency of ﬁrms using data envelopment analysis, and regressing it on the proportion of female employees and otherﬁrm characteristics, we found that the proportion of female employees has positive eﬀect on ﬁrm proﬁt eﬃciency. Our ﬁnding provided
strong evidence of the existence of discrimination against female employees within the Brazilian labor market.

Keywords: Latin America, Brazil, gender discrimination, DEA∗

The authors thank Valentin Zelenyuk for helpful comments and providing his Matlab code for DEA. This work was supported by Grants-in-Aid for Scientific Research(No.21730228).
†
Graduate School of Economics, Kobe University.
‡
Graduate School of Economics, Kobe University. Email: nomura@econ.kobe-u.ac.jp§
Research Institute for Economics and Business Administration, Kobe University.

11

Introduction

It is well known that income distribution in Brazil is extremely unequal.
According to the United Nations Development Program (UNDP, 2006), thetop 20% of the Brazilian population earns an income that is 26 times larger
than that earned by the bottom 20%, yielding a Gini coeﬃcient of 0.58. Despite this fact, many argue that discrimination does not exist in Brazil, particularly discrimination against racial minorities. However, recent researchsuggests that there indeed exists discrimination against racial minorities andwomen in Brazil.
Discrimination within any society can lead to the distortion of resource
allocation, and may discourage economic growth. No less an authority thanthe World Bank (2001) claims that gender inequality disadvantages not only
women but also the entire society, while hidering economic development,
particularly in low-income countries.
Discrimination against women takes on numerous forms and exists inall sectors of society, including the labor market. Regarding the causes of
discrimination, inequality of educational opportunity is considered the root
cause of many other forms of inequality. In most countries, especially in developing countries, limitations on women’s access to education and inequality in education are the root causes of many aspects of gender inequality.
Despite this fact, the educational attainment of women in Brazil andseveral other Latin American countries is currently higher than that of men.
In one study, the Instituto Nacional de Estudos e Pesquisas Educacionais
Anı́sio Teixeira/Ministério da Eduçacão (Inep/MEC, 2004) found that in2

2001, Brazilian women had attained an average of 6.2 years of education
whereas Brazilian men had attained an average of 5.9 years. Despite womens higher educational attainment, discrimination exists within the Brazilian
labor market, a discrepancy that we investigated in this study.
The majority of the previous research on gender discrimination in Brazil
estimated the wage functions for men and women separately and considered
the diﬀerence between the coeﬃcients as a measurement of discrimination.
However, these estimated coeﬃcients reﬂected the bias that inevitably arises
due to the existence of unobservable factors that aﬀect productivity. If such
unobservable factors systematically diﬀer according to gender, the variableof “discrimination” as measured by this method would be little more thana measure of the gender diﬀerence in productivity. To address this concern,
we employed an approach that diﬀered from that of previous research todetermine whether discrimination exists within the Brazilian labor market.
Speciﬁcally, we assumed that if female employees are paid less than their productivity warrants due to the existence of discrimination, ﬁrms can increase
their proﬁtability by employing more women. Based on this assumption,
we employed data envelopment analysis (DEA) to analyze the relationshipbetween the proportion of female employees employed by a ﬁrm and the
ﬁrm’s proﬁt eﬃciency to test for the existence of discrimination.
The remainder of this paper is organized as follows. Section 2 reviews
the literature regarding gender discrimination while section 3 discusses thetheoretical background. Next, section 4 describes the empirical strategy
that we employed, and section 5 describes the data and the variables that3

we examined and our justiﬁcation for doing so. Section 6 discusses our
results before closing the study with concluding remarks.

2

Literature Review

Much research into male-female wage discrimination has been conductedusing the human capital approach. According to this approach, discrimination against women is considered to exist whenever the relative wage of men
exceeds the relative wage that would have prevailed if men and women had
been paid equally according to the same criteria (Oaxaca, 1973), with themarket discrimination coeﬃcient being deﬁned as the percentage wage differential between two types of perfectly substitutable labor (Becker, 1971).
Blinder (1973) and Oaxaca (1973) developed a simple means of decomposing wage diﬀerentials into the proportion of the diﬀerential arising from
diﬀerences in productivity and discrimination. To perform Blinder-Oaxaca
decomposition, suppose that the wages of each male and female employee
are determined by the following human capital earnings equations:ln wm = X m β m + um ,(1)

ln wf = X f β f + uf .

(2)Here, w denotes the wage, X denotes the vector of the labor characteristics
aﬀecting productivity, β the vector of the coeﬃcients of earnings functions,and u the error term. The superscripts

m

and

f

denote male andfemale, respectively. By estimating β m and β f by the ordinal least square4using individual-level data and deﬁning the estimated vectors of coeﬃcientsas β̂ m and β̂ f , we can decompose the wage diﬀerentials as follows:

ln wm − ln wf = X̄ m β̂ m − X̄ f β̂ f = (X̄ m − X̄ f )β̂ m + X̄ f (β̂ m − β̂ f ). (3)Here, ln w denotes the average of the log wage and X̄ the vector of the average value of the characteristics aﬀecting productivity. The ﬁrst term on theright side of the equation can be interpreted as the wage diﬀerential becauseof the diﬀerence in productivity between men and women and the second
term as the wage diﬀerential not explained by the diﬀerence in productivity,
i.e., discrimination.
Blinder-Oaxaca decomposition has been employed in many studies on
discrimination1 . Focusing on the Brazilian labor market, Lovell (2000) estimated the monthly wages of white, black, and mixed-race women andmen working in the states of São Paulo and Bahia using a sample of 1991
census data. She found that discrimination did indeed exist in Brazilian
labor market, with women and blacks working in São Paulo experiencing
greater discrimination compared to their counterparts in Bahia, but thatoccupational and wage distributions were more equal in São Paulo. Using data collected by the National Household Survey (PNAD) of 1992 and1998, Loureiro, Carneiro and Sachsida (2004) also tested for the existenceof racial and gender discrimination, accounting for sample selection bias bysimultaneously estimating the labor market participation function and thewage function following Heckman (1979). Even after controlling for sam-5

ple selection bias, they found that more than 50% of the male-female wage
diﬀerential could be attributed to discrimination, with the discrimination
diﬀerential being larger in urban areas.
In this study, we faced several limitations in using Blinder-Oaxaca decomposition to measure discrimination. First, we were unable to distinguishbetween discrimination due to unequal pay for equal work and discrimination due to unequal occupational distribution, i.e., occupational segregation.
Several researchers have addressed this challenge. When Birdsall and Fox(1985) analyzed the male-female wage diﬀerential of primary and secondary
Brazilian school teachers, they found evidence of only a low level of occupational segregation, and that the opportunity to be promoted to a secondary
school position, which paid a higher salary than did a primary school position, was relatively equal for men and women when the diﬀerences between
the observable characteristics of male and female teachers were taken into
account. When Nomura (2010) followed Brown, Moon and Zoloth (1980)
by including more comprehensive occupations in his analysis, he found thatwage discrimination for the same position was greater than was occupationalsegregation; this was consistent with the ﬁndings of Birdsall and Fox (1985).
A second limitation that we faced was the possible existence of unobservable factors aﬀecting productivity that systematically diﬀer according
to gender. Although Griliches (1977) and Card (1999) demonstrated thatthe impact of unobservable factors on wages was limited, the measurementsof discrimination using wage regression could have led them to overestimate
the extent of discrimination. To address this problem, Hellerstein, Neumark

6and Troske (2002) tested the discrimination hypothesis of Becker (1971)
more directly by using a “market testing” approach. Analyzing U.S. ﬁrmlevel data, they found a positive correlation between proﬁtability and the
proportion of female workers in the workforce. Since ﬁrms can earn more
proﬁt by employing more women when women are paid less than their productivity warrants, Hellerstein et al. (2002) considered the existence of thiscorrelation as evidence of gender discrimination. When Kawaguchi (2007)
performed market testing using Japanese ﬁrm-level panel data while maintaining a strong focus on unobservable productivity shocks, he identiﬁed
the existence of a positive correlation between female employment and ﬁrm
proﬁtability within the Japanese labor market. Since the costs of gender
discrimination and inequality are larger in less developed countries (World
Bank, 2001), market testing should be performed using data from developing countries as well. Nevertheless, no study before the present one has
performed market testing using Brazilian ﬁrm-level data.
This study, therefore, addressed a research gap by examining the relationship between the proportion of female employees and ﬁrm proﬁt eﬃciency using Brazilian ﬁrm-level data to test the discrimination hypothesis
proposed by Becker (1971). Although our research generally accords withthat of Hellerstein et al. (2002) and Kawaguchi (2007), we deﬁned proﬁt
eﬃciency as the distance from an actual point to the frontier identiﬁed by
non-parametric estimation, i.e., the DEA, and focused on estimating loss ineﬃciency due to gender discrimination.

7

3

Theoritical BackgroundWe based our method on the employer discrimination model proposed byBecker (1971), who assumed that an employer working for a ﬁrm prefers tomaximize his or her utility instead of the ﬁrm’s proﬁt taking wage as given.
Consider that a ﬁrm can produce an output Y using the inputs of malelabor M , female labor F , and other inputs OI = (OI1 , . . . , OIJ−2 ). The
utility function of an employer who prefers not to employ female workers
and thus pays a psychic cost when forced to employ women can be deﬁned
as(U = pY − wM M − wF F − d

F
M +F

)
− wOI OI,

(4)

where p is the price of the output; wM and wF are the wages of maleand female employees, respectively; wOI is the price of other inputs; andd is the discrimination coeﬃcient representing the extent of the employer’s
discrimination against women, which we assumed to vary across ﬁrms.
The employer’s utility maximization is given bydF= wM ,(M + F )2dM= wF ,M RPF −
(M + F )2

M RPM +

(5)
(6)

where M RPM and M RPF are the marginal revenue products of male andfemale workers, respectively. The marginal revenue product of female workers is set above their wages while that of male workers is set below their8

wage. Thus, only ﬁrms whose employers do not engage in discrimination(d = 0) can maximize their proﬁt, and the proﬁt decreases with an increasein d.
To investigate the existence of discrimination against female workers in
the Brazilian labor market, we employed a proﬁt eﬃciency model following
Färe and Grosskopf (2004). The proﬁt eﬃciency model begins with deﬁning
the notation of technology set T as

T = {(X, Y ) : X can produce Y } ,(7)where X = (M, F, OI) ∈ ℜJ+ is a nonnegative vector of inputs including
labor, Y ∈ ℜG
+ is a non-negative vector of outputs. Given output pricesJp ∈ ℜG+ and input prices w = (wM , wF , wOI ) ∈ ℜ+ , the maximum proﬁt fora ﬁrm can be deﬁned asΠ(p, w) = sup {pY − wX : (X, Y ) ∈ T } .

(8)The boundary of T is referred to as the technology or the production
frontier. The distance from the actual point of each ﬁrm in the production
set T to the frontier of T , which is considered as its level of ineﬃciency,
is determined by the ﬁrm’s environmental variables Z = (Z1 , . . . , ZQ ) ∈ℜQ+ . Depending on their speciﬁc environment, ﬁrms may operate along the
production frontier or at a point within the interior of their production
frontier, with the former being considered as eﬃcient ﬁrms and the latter9

being considered as ineﬃcient ﬁrms.
The Nerlovian proﬁt eﬃciency is deﬁned as

P E(p, w, Y, X; gY , gX ) =Π(p, w) − (pY − wX),
pgY + wgX

(9)where gX and gY are the directional vectors in which eﬃciency is evaluated.
This type of proﬁt eﬃciency is often regarded as aggregate eﬃciency as it
encompasses two types of eﬃciency: technical and allocative.
Under the condition that the output prices, wages, and eﬃciency directional vectors are identical across ﬁrms, the proﬁt eﬃciency of ﬁrms can be
estimated by examining their input and output values. Recognizing thatthe proﬁt eﬃciency of ﬁrms is determined by their speciﬁc characteristics,
we estimated the impact of ﬁrm-speciﬁc characteristics on eﬃciency. Amongthe many factors that likely impact proﬁt eﬃciency, we examined the impact
of discrimination against women using the proportion of female employees
as a proxy for the extent to which an employer engages in discrimination.
Since seeking to fulﬁll the goal of proﬁt maximization is a necessary condition for achieving proﬁt eﬃciency, only ﬁrms whose hiring managers do not
engage in discrimination against women can attain proﬁt eﬃciency. Thatis, assuming the existence of discrimination, a ﬁrm with a high proportionof female workers will have a higher level of proﬁt eﬃciency than will a ﬁrm
employing a low proportion of female workers.

10

4

Empirical Strategy

Our empirical procedure follows Simar and Wilson (2000) and Zelenyuk andZheka (2006) and cosists of two stages . In the ﬁrst stage, we estimate the
proﬁt eﬃciency of each ﬁrm by using DEA. Then in the second stage, we
analyze the determinant of ﬁrm eﬃciency by regressing the proﬁt eﬃciency
obtained in the ﬁrst stage on ﬁrm’s characteristics.

4.1

Proﬁt Eﬃciency Estimation

One challenge of researching proﬁt eﬃciency is that data regarding output
and input prices are usually unavailable as ﬁnancial information (e.g., labor,material, and energy costs) is typically reported at the ﬁrm level. To overcome this challenge, we employed an alternative DEA approach to measureproﬁt eﬃciency using ﬁnancial information. Speciﬁcally, we used input andoutput data aggregated with price data in the traditional DEA model tomeasure a proxy for proﬁt eﬃciency that encompassed both technical andallocative eﬃciency2 .
To measure such proﬁt eﬃciency, we employ the cost and revenue-based
eﬃciency index developed by Farrell (1957), which is deﬁned as{}
P Ei ≡ max θ (xi , θyi ) ∈ T ,θ

(10)where xi = wXi is a vector of aggregated inputs and yi = pYi is a vector of
aggregated outputs. When P Ei = 1, the ﬁrm is considered to be eﬃcient.
And when P Ei > 1, the ﬁrm is considered to be ineﬃcient, and the reciprocal

11

of P Ei , 0 < (1/P Ei ) ≤ 1, represents the percent level of the eﬃciency ofﬁrm i relative to the production frontier.
Since the true technology sets cannot be directly observed, we employed
the most common DEA procedure to estimate the best-practice frontier fromthe observed input-output combinations (xi , yi ), which is deﬁned as{T̂ =(x, y) yg ≤

n
∑

xj ≥

qi ygi ,i=1n∑qi x,ji

g = 1, . . . , G,
j = 1, . . . , J,

i=1
n
∑

qi = 1,qi ≥ 0,}i = 1, . . . , n, ,

(11)

i=1

where T̂ is the DEA estimate of the true production frontier of T and qi are
the intensity variables over which optimization is made. By employing thisprocedure, the DEA estimate of individual eﬃciency at any point (xi , yi )can be obtained by replacing T with T̂ in (10) and solving the following
linear programming problem:dP
E i = max

θ,q1 ,...,qn{}
θ|(xi , θyi ) ∈ T̂ .

(12)d
It is clear that T̂ ⊆ T , therfore P
E i is downward-biased estimator of
P Ei . To address this problem, we employ a bootstrap DEA procedure developed by several DEA researchers (e.g. Simar and Wilson, 2000; Henderson
and Zelenyuk, 2007; Simar and Zelenyuk, 2007).

12

4.2

Determinants of proﬁt eﬃciency

To investigate the dependency of ﬁrm eﬃciency on ﬁrm environmental variables, we regressed the proﬁt eﬃciency gained from the ﬁrst stage on several
environmental variables. The determinant model of eﬃciency is expressedasdP
E i = Zi β + εi
= β0 + β1 Z1i + β2 Z2i + β3 Z3i + β4 Z4i + indi β5 + vi + εi ,(13)dwhere PE i is the proﬁt eﬃciency of ith ﬁrm as deﬁned in (12); β is a vectorof the parameters that are being estimated; Zi is a vector of ﬁrm environmental variables that may aﬀect the eﬃciency of the ith ﬁrm. Z1i is the
proportion of female employees compared to total employees. If workplace
discrimination against women existed, then employing a higher proportionof female workers would result in higher proﬁt eﬃciency. Thus, a negative
β1 would lead to rejection of the null hypothesis that there is no gender discrimination3 . The variable of ﬁrm age, Z2i , may or may not have positiveeﬀect on ﬁrm performance; whereas ﬁrms tend to perform functions more
eﬀectively, which increases performance, with the experience that only canbe acquired with increased age, their level of bureaucracy (organizational
rigidity), which leads to increases in variable costs and overhead expenses,
and thereby decreases in performance, also increases with age. Z3i is an
output variable (the logarithm of total sales) that captures the scale eﬀect.
To account for the opportunity cost of capital, we included the ratio of

13

ﬁxed assets to total sales, Z4i , in the equation. We also introduced industry
dummies, indi , to control industrial heterogeneity; a proxy, vi , to capture
productivity or demand shocks; the idiosyncratic error term, εi . With regard to the proxy, vi , we employed the approach used by Kawaguchi (2007)
to control productivity or demand shocks, which he based on considerationof two types of proxy variables: one is investment following Olley and Pakes(1996) and the other is intermediate inputs following Levinsohn and Petrin(2003).
Assuming that current positive productivity shocks will aﬀect a ﬁrm’s
future level of investment, Olley and Pakes (1996) suggested that a ﬁrm’s
level of investment can be used as a proxy of unobserved productivity shocks
in the production function. When, according to their suggestion, the investment function is expressed as Ii = I(ki , vi ) and it is assumed that
∂Ii /∂vi > 0, where Ii is the amount of investment, ki is the capital stock,and vi is the productivity shock, productivity shock can be expressed as aninverse function of investment and capital. Following Kawaguchi (2007), we
speciﬁed the function as

Iivi = g (Ii , ki ) = λ1 + λ2
ki

(

Ii
Ii
−
ki ki

)2
.

(14)

At this point, we omitted from our sample those ﬁrms whose micro-level
data indicated that they made no investments. Levinsohn and Petrin (2003)
suggested using intermediate inputs as a proxy variable for productivity
shocks to avoid ommiting ﬁrms without reporting investments, explaining

14

that if the demand function of intermediate inputs is expressed as mi =m(vi , ki ), productivity shock can be expressed as a function of intermediate
inputs and capital stock. Again following Kawaguchi (2007), we speciﬁed
the function asmivi = h (mi , ki ) = δ1
+ δ2
Ci

(

mi mi
−
Ci
Ci

(

)2
+ δ3

mi mi
−
Ci
Ci

)
×

ki
, (15)
yi

where Ci is the total production cost, mi is the cost of intermediate inputs,
and ki /yi is the asset-to-sales ratio.
Traditional two-stage DEA models typically employ OLS or the Tobit
model to estimate (13). However, Simar and Wilson (2007) argued thatstandard DEA eﬃciency estimates are inappropriate because they do notprovide a coherent description of a data-generating process and because
they are serially correlated. Recognizing that the DEA estimation obtainedusing the traditional two-stage model is inconsistent in the second-stage
regression, they proposed the use of a two-stage bootstrap DEA approachto obtain a consistent result. In this study, our use of one of their bootstrap
procedures, Algorithm 24 , allowed us to replace the unobserved P Ei by
bc
bc
d
d
E i is deﬁned to be
its bias-corrected estimate, P
E i . In this procedure, P

equal or greater than one, the distribution of εi is restricted by the condition
εi ≥ 1 − Zi β, and the eﬃciency determinant model can be written asbcdP
E i ≈ Zi β + εi ,

15

(16)

whereεi ∼ N (0, σε2 ),5such that εi ≥ 1 − Zi β.

(17)

Data

We obtained the data that we analyzed in this paper from the World Bank
Investment Climate Survey, which used standardized survey instruments
and a uniform sampling methodology to analyze ﬁrm performance and thebusiness environment of developing countries5 . To conduct a survey on
Brazil, the Investment Climate Survey Group of the World Bank randomly
sampled 1,641 ﬁrms from nine manufacturing industries in 13 geographic
regions in the reference year 2002. After excluding observations with missing
values, our working sample consisted of 1,456 ﬁrms.
We used the variable of the value of total sales as the output and thevariables of labor, material, and energy costs as the inputs to estimate the
proﬁt eﬃciency score of each ﬁrm using a bootstrap DEA procedure. We
deﬁned the labor cost as the total annual cost of paying wages, salaries,
bonuses, and social security payments to employees; material cost as the total annual cost of raw materials and intermediate goods used in production;and energy cost as the total annual costs of fuel and electricity.
Such measurement of output and inputs enables us to extend the interpretation of technology to encompass more than simply engineering capacity,and gives us some justiﬁcation for pooling data over sub-industries to mea-16

sure eﬃciency of each ﬁrm using DEA (Zelenyuk and Zheka, 2006, p148).
A beneﬁt of pooling data over sub-industry was that it allowed us toincrease the sample size, which would prove to be very important in obtaining an estimation for the eﬃciency determinant model in the second stageof this study6 . Recognizing this beneﬁt, we pooled all the data collectedfrom ﬁrms within various sub-industries in manufacturing and estimatedthe meta-frontier of the entire manufacturing industry.
The descriptive statistics of our dataset are presented in Table 1.
[Table 1 is inserted here]

6

Empirical Results

6.1

Estimation of proﬁt eﬃciency

In the ﬁrst stage, we obtained the proﬁt eﬃciency score of each ﬁrm by solving the linear programming problem presented in Equation (10). When wethen used the kernel density estimator to obtain the density of the eﬃciency
scores in order to identify any outliers, our results suggested the existenceof several outliers in the sample. Zelenyuk and Zheka (2006) suggested that
there are mainly three reasons can give rise to eﬃciency outliers. First, ﬁrms
with eﬃciency outliers follow a diﬀerent distribution of eﬃciency; namely,
these ﬁrms operate under a diﬀerent production frontier. Second, although
all ﬁrms follow the same distribution pattern, experiencing external shocks(e.g., strikes or unexpected incidents) cause some ﬁrms to appear far within
the tail of the distribution. Finally, when ﬁrms commit errors when record-17

ing data regarding their output or input variables, such as by inserting extra
digits, their eﬃciency scores will be incorrect. We believe that outliers may
have arisen in our sample due to the last two factors, as the output and input data for several ﬁrms appeared unusual. As these outliers could disturb
our estimation of the frontier, we omitted 2.5% of the ﬁrms on both sides ofthe eﬃciency density distribution (5% of ﬁrms in total) from our sample.
We recognized that although our revised sample contained a distributionof eﬃciency scores that presented us with desirable properties for analysis,
it may not have been representative of the original sample. Fortunately, we
found that we could use the Simar-Zelenyuk adaption of the Li Test (Simarand Zelenyuk, 2007) to address this problem. We obtained a bootstrap Pvalue of 0.929 using the Simar-Zelenyuk-adapted Li Test and, thus, could
not reject the hypothesis that the distributions of the original and revised
samples are equal. Therefore, we used the revised sample in our two-stepestimations.
Examining the bootstrap bias-corrected eﬃciency scores that we had
obtained during the ﬁrst stage, we found that the aggregate of the eﬃciencies
obtained by our bootstrap bias-corrected estimation was larger than thatobtained by our original DEA estimation. Our result is thus consistent withthe bootstrap DEA literature, which asserts that the original DEA estimatesare biased downward.

18

6.2

Determinants of eﬃciency

In the second stage, we estimated the eﬃciency determinant model. We
obtain parameters and the conﬁdence intervals from performing 2,000 replications of the bootstrapping procedures. Speciﬁcally, we regressed the biascorrected eﬃciency scores that we obtained from the ﬁrst stage on ﬁrm environmental variables and industry dummies using Algorithm 2 of Simar andWilson (2007) and performed 2,000 replications of the bootstrapping procedures to both ensure bias correction and obtain the conﬁdence intervals of
the estimated coeﬃcients. Our results are presented in Table 2.
[Table 2 is inserted here]
As shown in Column (1), which reports the basic estimation result, thecoeﬃcient of the proportion of female employees is negative and statisticallysigniﬁcant at the 1% level according to the bootstrap conﬁdence intervals,
as we had expected. The negative coeﬃcient of the proportion of female
employees suggests that a proportion of female workers has a positive eﬀect
on ﬁrm proﬁt eﬃciency, and thus provides strong evidence for the existenceof gender discrimination.
In creating Column (2), which reports the result of the estimation using
Olley and Pakes (1996) proxy variables for productivity or demand shocks,
we omitted several observations from the sample shown in Column (1) because of the unavailability of investment data. As can be observed, thecoeﬃcients are statistically signiﬁcant, and suggest that investment captures productivity or demand shocks. Nevertheless, the coeﬃcient of the
proportion of female employees did not change signiﬁcantly after the proxy19

variables were included in the model.
As shown in Column (3), which reports the result of the estimation
including Levinsohn and Petrin (2003) proxy variables for productivity or
demand shocks, the coeﬃcients are also statistically signiﬁcant. However,when we used intermediate inputs as proxies, we found that the coeﬃcientof the proportion of female employees increased, a result that was contrary
to our expectation that the coeﬃcient of the proportion of female employees
would be upward biased7 .
Our ﬁnding that the logarithm of total sales has positive eﬀect on ﬁrm
proﬁt eﬃciency in all speciﬁcations suggests that larger ﬁrms tend to be more
eﬃcient than smaller ﬁrms within the Brazilian manufacturing industry. In
contrast, we found that the ratio of ﬁxed assets to total sales has negativeeﬀect on ﬁrm proﬁt eﬃciency in all speciﬁcations. Somewhat surprisingly,
we also found that ﬁrm age has negative eﬀect on ﬁrm proﬁt eﬃciency inall speciﬁcations. As discussed in Section 3, ﬁrm age may have positiveeﬀect on ﬁrm performance (greater age brings with it greater knowledge) or
negative eﬀect (greater age brings with it greater organizational rigidity).
We, therefore, interpreted our ﬁnding as the latter factor having a greater
impact on ﬁrm performance than the former factor does.

6.3

Proportion of female employees and total cost

If female employees are paid a lower wage than male employees due to theexistence of workplace discrimination, a ﬁrm can achieve higher allocativeeﬃciency by substituting male labor with female labor to decrease the labor20

cost. As discussed in the previous section, the proﬁt (aggregate) eﬃciency of
a ﬁrm can be decomposed into two forms of eﬃciency: technical and allocative. However, performing this decomposition empirically requires access todata regarding the prices of output and input that are typically unavailable.
Although it is diﬃcult to decompose the proﬁt eﬃciency into technical andallocative eﬃciency, it is worth to conﬁrm whether higher female proportion
leads to lower labor cost.
Following Kawaguchi (2007), we employed a total wage function to test
the hypothesis that employing a higher proportion of female employees leads
to lower labor cost. The total wage function is deﬁned aslog(wagei ) = γ0 + γ1 Z1i + γ2 log(output)i + γ3 indi + ui ,(18)

where wagei is the total labor cost of a ﬁrm and Z1i is the proportion of
female employees to total employees. If female employees are paid a lower
wage than male employees due to the existence of workplace discrimination, the proportion of female employees would have negative eﬀect on laborcost, given the same level of output. We estimated (18) by the ordinary
least square and tested the null hypothesis γ1 = 0 against the alternative
hypothesis γ1 < 0.
[Table 3 is inserted here]
As shown in Table 3, we found the coeﬃcient of the proportion of female employees to be negative and signiﬁcant at the 5% level, suggestingthat employing a higher proportion of female employees within the Brazil-

21

ian manufacturing industry leads to a lower labor cost. Therefore, we canconclude that employing a higher proportion of female employees leads tohigher allocative eﬃciency.

6.4

Robustness checks

As a robustness check, we also regressed proﬁtability on the proportion of
female employees following Hellerstein et al. (2002) and Kawaguchi (2007).
In parallel with (12), the speciﬁcation is as follows:

prof itabilityi = β0 + β1 Z1i + β2 Z2i + β3 Z3i + β4 Z4i + indi β5 + vi + εi , (19)where prof itabilityi is deﬁned as the ratio of total proﬁt (total sales - totalcost) to total sales and the explanatory variables on the right side are deﬁned
in the same manner as they are in (12).
The results of regression by the ordinal least square are reported inTable 4, with the results of the basic estimation for (19) in Column (1) andthe results of the estimation using Olley and Pakes (1996) and Levinsohn
and Petrin (2003) proxy variables for demand and productivity shocks in
Columns (2) and (3), respectively.
[Table 4 is inserted here]
As shown in Column(1), we found that the proportion of female employees has positive eﬀect on proﬁtability, which supports the results that we
obtained from the proﬁt eﬃciency model and provides further evidence thatgender discrimination exists within the Brazilian labor market.

22

As shown in Column (2), which reports the results when Olley and Pakes(1996) proxy variables are included in the regression, the coeﬃcient of the
proportion of female employees becomes more signiﬁcant when these variables are included, although the coeﬃcients of the proxy variables are insigniﬁcant. As shown in Column (3), which reports the result of the estimation including Levinsohn and Petrin (2003) proxy variables for demand andproductivity shocks, the coeﬃcients of the proxy variables are signiﬁcant.
Particularly noteworthy is that adding the proxy variables led the coeﬃcientof the proportion of female employees to decrease, a result that contrasts
with that obtained when using proﬁt eﬃciency determinant models.
Consistent with the results obtained using proﬁt eﬃciency determinantmodels, we found that ﬁrm size has positive eﬀect on proﬁtability in all
speciﬁcations. In contrast with the results obtained using proﬁt eﬃciency
determinant models, we found that ﬁrm age and the ratio of ﬁxed assets tototal sales have no signiﬁcant eﬀect on ﬁrm proﬁt ratio.
As each speciﬁcation resulted in diﬀerent conclusions, our results are notvery reliable, one reason for which may be the quality of the data, as thesurvey data that we used contained missing values or outliers. Although
we did our best to address these problems, we acknowledge the possibility
that our use of these data skewed our estimations. Despite this caveat, wefound that the proportion of female employees has positive eﬀect on proﬁt
eﬃciency and proﬁtability, regardless of the method or speciﬁcation used to
examine this eﬀect, a ﬁnding that provides strong evidence of the existenceof gender discrimination within the Brazilian labor market.

23

7

Conclusion

In this paper, we investigated gender discrimination in Brazil by employing
a two-stage bootstrap DEA approach to proﬁt eﬃciency, and testing the implication of the employer discrimination model proposed by Becker (1971).
Our results indicate that the proportion of female employees has positiveeﬀect on ﬁrm proﬁt eﬃciency, a ﬁnding that we found to be robust when
we used several diﬀerent methods and speciﬁcations. We consider this ﬁnding to be strong evidence of the existence of discrimination against female
employees within the Brazilian labor market. Although we were unable todecompose aggregated proﬁt eﬃciency into its components of technical efﬁciency and allocative eﬃciency, the results of our estimation of the total
wage function indicate that a ﬁrm employing a high proportion of female
workers incurs a lower labor cost while producing the same level of output compared with a ﬁrm employing a low proportion of female employees.
Our ﬁndings support those reported in previous studies (e.g, Lovell, 2000;
Loureiro et al., 2004; Nomura, 2010) that estimated workplace gender discrimination using Blinder-Oaxaca decomposition and that assumed that the
male-female wage diﬀerential which could not be explained by diﬀerences inindividual characteristics was due to discrimination.
Brazil has recently experienced very rapid economic growth, especiallyafter the implementation of the Real Plan in 1994. Nevertheless, income
inequality remains a serious concern, one that has been attributed to discrimination against women and racial minorities. As such, discrimination
impedes fair competition and confounds equality of opportunities and out-

24

comes, it likely distorts resource allocation and hinders economic growth,
negatively impacting not only women and discriminatory employers but also
Brazilian society as a whole.
The results of our analysis indicate that employer discrimination against
female employees leads to a loss of proﬁt eﬃciency. A serious concern remaining is to estimate the loss. We plan to address this concern, as well as
identify the ultimate bearers of discrimination, in our future research.

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Inep/MEC (2004) O desaﬁo de uma educação de qualidade para todos: educação no Brasil - 1990-2000, Brasilia: Instituto Nacional de Estudos e
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in the Telecommunications Equipment Industry,” Econometrica, Vol. 64,
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28

Notes

1 See Altonji and Blank (1999) for more details.

2 Färe and Grosskopf (1985), Färe and Zelenyuk (2002), and Färe and

Grosskopf (2004) have theoretically discussed aggregated inputs or outputs in DEA model. There are also many empirical studies using aggregated inputs and outputs in DEA formulation. See the discussion in
Zelenyuk and Zheka (2006).

3 Note that a larger eﬃciency score means larger ineﬃciency. Therefore,

the negative coeﬃcients in the regressions mean the positive eﬀect on
ﬁrm eﬃciency.

4 See Simar and Wilson (2007, p.42) for details.

5 For more information about the survey, see http://www.enterprisesurveys.org

6 Simar and Wilson (2007) argued that maximum likelihood often pro-duces biased estimates in small samples. Therefore, a large sample size
is preferred in the two-stage bootstrap DEA estimation.

7 The same result is obtained in Kawaguchi (2007).

diﬃcult to interpret these results.

29

Nevertheless, it isTable 1

Discriptive statistics of study dataset
Mean
Std. Dev. Mean
Std. Dev.
Variable
28.62
22.51
-65.2093.23
Profit ratio (%)
9.02
0.92
4.80
15.45
Log(wage)
Output variable (in thousands of R$):
Total sales
24700.00 134000.00
Input variables (in thousands of R$):
Labor cost
2490.78 10700.00
12300.00 73200.00
Material cost
561.543941.27
Energy cost

33.95

3670000.00

8.81
2.28
0.01

189000.00
2110000.00
90000.00

0.37
0.30
0.36
19.72
17.34
22.28
0.44
4.88
0.83
0.74
5.27
1.96
0.62
0.21
0.58
Material cost/Total cost
1456
Number of firms
Note: The number of observations of Investment/Fixed assets was 1338.

0.30
16.97
5.94
21.26
0.19

Explanatory variables:
Proportion of female employees
Firm age
Fixed assets/Total sales
Investment/Fixed assets

Table 2
Estimation results of the efficiency determinant model(1)(2)
Constant
12.96012.891
Proportion of female employees-0.211-0.211
Firm age
0.017
0.015
Log(output)-0.634-0.629Fixed assets/Total sales
0.009
0.008
Investment/Fixed assets-0.0222
0.306(I/FA-mean(I/FA)) /1000

Material cost/Total cost
2

(MC/TC-mean(MC/TC))(MC/TC-mean(MC/TC))*(FA/TS)
Industry dummiesσNumber of observations
Notes:

yes
1.599
1456

yes
1.603
1338

(3)
13.994-0.3180.007-0.387
0.002-4.919-19.839
0.079
yes
1.439
1456

1. Estimation according to Algorithm 2 of Simar and Wilson(2007), with 2000 bootstrap replication to correct bias and obtainconfidence intervals of the estimated regression coefficients.
2. The dependent variable was the bootstrap bias-corrected DEA
estimate of the efficiency score.
3. All the coefficients were statistically significant at 0.01
significance levels, according to the bootstrap confidence intervals.

Table 3
Determinantion of total wage
Constant
4.952***(0.181)
Proportion of-0.228**female employees(0.100)Log(output)
0.258***(0.010)Industry dummies
Yes
2
0.467
R
Number of observations
1456
Notes:
1. Standard errors in parenthesis.
2. ***,**,* represent 1%, 5%, 10% significance respectively.

Table 4
Estimation results of the profit determinant model
(1)
(2)
(3)
Constant-34.871***-34.150***-37.514***(5.764)(6.051)(5.745)
Proportion of female employee
5.286*
6.523** 4.264(3.139)(3.320)(3.124)
Firm age
0.026
0.049
0.019
(0.035)(0.037)(0.036)Log(output)
3.890*** 3.747*** 4.346***(0.339)(0.355)(0.385)
Fixed assets/Total sales-0.072-0.069-0.045(0.115)(0.115)(0.132)
Investment/Fixed assets
0.201(0.319)2-3.046(I/FA-mean(I/FA)) /1000(3.370)-8.590***Material cost/Total cost
(3.302)
2
34.483***(MC/TC-mean(MC/TC))(11.011)(MC/TC-mean(MC/TC))*(FA/TS)-0.351(0.993)
Industry dummies
yes
yes
yes
2
0.108
0.107
0.124
R
Number of observations
1456
1338
1456
Notes:
1. Standard errors in parenthesis.
2. ***,**,* represent 1%, 5%, 10% significance respectively.