Gender Wage Gap and Sample Selection Correction
with Risk Attitudes
S EEUN J UNG∗†
Paris School of Economics
January 2013
Abstract
This paper investigates a new way to decompose the gender wage gap with an introduction of individual risk attitudes using the Korean representative sample. We estimate
the wage gap with the correction of selection bias which leads overestimation of the wage
gap. Female workers are more risk averse, and, hence, they prefer working in the public sector where the wage is in general lower than in the private sector. Therefore, what
we observe from the gender wage differential in the normal Mincerian wage equation is
overestimated. Following Switching Regression Model and Lee’s polychotomous selection correction (1983), our (corrected) wage differential has significantly reduced. Hence
self-selection based on attitude towards risk explains, in part, what is popularly perceived
as gender discrimination.
JEL Classification: J24; J31; D81; C52
Keywords: Occupational Choice; Gender Wage Gap; Risk Preference; Selection Bias
∗
†
sejung (at) ens.fr
The author is grateful for comments by Andrew E. Clark, Luc Arrondel, Fabrice Etil´e, Thomas Dohmen,
Ronald Oaxaca, Chung Choe, seminar participants at ISER & GCOE Behavioral Economics Joint Seminar of
Osaka University, at CEPS/INSTEAD seminar in Luxembourg and the conference of EALE 2011. The financial
support of CEPREMAP is gratefully acknowledged.
1
1
Introduction
There are many factors which can affect an individual’s decisions regarding economic issues.
In human capital theory, risk is involved when students make educational decisions, such as
weighting random future income against an additional year of education. In the labor market,
some people choose to bear longer periods of unemployment in order to obtain better wages
and working conditions, while others prefer to exit unemployment sooner despite lower wages.
Others prefer lower wages and safer public-sector retirement and social security plans to higher
wages and private and riskier retirement and social security plans.
Several reasons may underlie these choices. First, markets might not clear so that firms do not
offer the same wage profiles to identical workers. Second, there could be individual heterogeneity in the decision making process. Even if all observable factors are controlled for - such
as gender, age, wealth, region, etc - there will still be significant differences in outcomes. This
suggests the presence of unobservable factors that make up individual heterogeneity and firm
behavior.
Murphy et al. (1987) and Moore (1995) showed that job sectors with both higher unemployment and risk tend to have higher wages. Hence, job sorting decisions may well vary with
individuals’ attitudes towards risk. Recent work such as Hartog et al. (2003) has also showed
that jobs with a greater level of risk are paid higher wages, contributing to the theory of compensating wage differentials. Workers who are more eager to exchange wages for risk are more
likely to choose to work in riskier jobs than are those who are less inclined to trade off wages
and risk. While job sector placement is sensitive to differences in attitudes towards risk, it is a
priori also strongly correlated with education decisions.
Measuring attitudes towards risks is, however, a delicate task, and there have been various attempts to find the right type of subjective self-reported variables to form a paradigm of risk aversion. Feinberg (1977) and Hersch and Viscusi (1990) studied the use of seat-belts and smoking
behavior. Ekelund et al. (2005) used a psychometric variable which measured harm avoidance
as an indicator of risk attitudes, and found that agents with a higher score of harm avoidance
(i.e., less risk averse) are more likely to become self-employed, which is considered riskier than
being employed. In an experimental study, Dohmen et al. (2005) showed that measures of subjective risk attitudes provide a valid predictor of actual risk behavior. Dohmen and Falk (2011)
built upon these results and used self-reported risk aversion in the German social-economic
panel to see whether risk preferences explain how individuals are sorted into occupations with
different earnings variability. Furthermore, Luechinger et al. (2007) and Pfeifer (2008) analyzed selection in public-sector employment, and Grund and Sliwka (2006) and Cornelissen
et al. (2011) studied pay-for-performance schemes. All concluded that risk-averse workers have
2
a greater preference for non-competitive working environments. Pissarides (1974) provided a
theoretical model which explains that risk-averse workers have lower reservation wages, which
relationship was demonstrated empirically by Pannenberg (2007). Similarly, Goerke and Pannenberg (2008) showed that there is a negative relationship between risk aversion and union
membership.
As job sorting matters for the position actually held in the labor market, it is legitimate
to wonder whether the job-sorting decision interacts with the gender disparity observed on
the labor market. As the gender bias in education has been reduced and the education gap
between men and women has narrowed over the last decades Arnot and Weiner (1999), it is
still a concern that there is a considerable wage gap as well as other kinds of labor market
discrimination between genders. To reconcile these findings, Croson and Gneezy (2009) and
Bertrand (2011) have argued that women may be more risk averse and less competitive than
men. More interestingly for our question, Gneezy et al. (2003), Niederle and Vesterlund (2007)
and Croson and Gneezy (2009) have all suggested that differences in risk attitudes might partly
explain the gender gap in labour market outcomes. In the same way, Barsky (1997), Dohmen
and Falk (2011) and Bonin et al. (2007) have shown that job sector selection and wages are
correlated with attitudes towards risk.
Then, here lies our interest. Gender wage gap is still an interesting issue for labor economists
and also for policy makers. In many countries, even in the developed countries like Sweden
where it is believed that the gender right is most equal in the world, we often observe the gender
wage differentials. Labor economists analyze this phenomenon and define the gender wage gap
as “discrimination” if it occurs for the equally productive workers (Becker (1993)). There have
been huge literature in this field, in order to look at the wage gap and discrimination, since one
of the most influential paper from Oaxaca (1973). The raw wage gap is decomposed with two
part; explained with human capital and endowments and unexplained which is often considered
as discrimination. When to estimate the wage with human capital empirically, the commonly
used method is Mincerian type wage equation (Mincer (1974)) in which the logarithmic wage
is regressed on observable socio-demographic variables such as gender, schooling, age, etc. In
this model, however, concerns may arise when we face selection issue or omitted variable bias;
what the level of wages would have been in the absence of discrimination? A number of studies have worked on this issue in order to correct this selection bias, mainly with the selection
of the labor market participation (Newman and Oaxaca (2004)). We, instead, look at sector
selection process (and also participation selection afterwards) to decompose the gender wage
gap correcting this selection issue with individual risk attitudes.
This paper shows how female workers seem to choose to work in the public sector, getting
paid less, and how individual risk attitudes may play a role in this decision-making process
3
and furthermore explain the reduced gender wage gap by developing an appropriate sample
selection model. The remainder of the paper is organized as follows. Section 2 will introduce
the simple conceptual framework of the idea, followed by the analytical framework with the
data description in Section 3. Section 4 presents the empirical results to test the impact of risk
aversion on job sorting and gender impact on wages with corrected selection bias. Last, Section
5 concludes.
2
Conceptual Framework
Public-sector jobs are often considered to be safer in terms of their associated benefits, job
stability and security. However, they also pay less than private-sector jobs where workers
obtain a wage premium for taking risks such as higher job separation rates and fewer or lowerquality benefits. For this reason, we might expect risk-averse workers to prefer public-sector
stability over private sector wage volatility and higher probability of unemployment. Also,
female workers are more sorted into the public rather than the private sector, which might be
explained by the risk attitude difference between genders.
In this section, I will introduce simple concepts of occupational self-sorting in terms of risk
attitudes.
2.1
Risk-Averse Workers’ Preferene on the Public Sector
We assume that there are two types of individuals whose risk attitudes are different: risk averse
and less risk averse (or risk neutral, risk loving). Also there are two types of firms. One is the
competitive firm (private sector) where the job separation rate is higher (job security is lower,
more likely to be fired) whereas the other is the non-competitive firm (public sector) with a
lower job-separation rate. In order to compensate for the job security risk, we assume there is
a wage premium for the competitive firms p > 0. Assume that in the non-competitive firms,
workers receive the risk free wage wpu while in the competitive firms workers obtain the riskfree wage plus a risk premium p (i.e. wpr = wpu + p). Here, we assume that the job separation
rate is higher for the competitive than for the non-competitive firms rpu < rpr . In the extreme
case, we could set rpu = 0 with no risk of being fired and rpr = r > 0. Setting the basic CRRA
preference utility with different risk aversion factor ρ : u(c) =
c1−ρ
,
1−ρ
we consider the different
risk aversion depending on individuals’ different attitudes towards risk (i.e. ρRA (risk averse
individuals)> ρRN ( less risk averse individuals) ). If a worker is fired, he receives a basic
governmental subsidy of b, with b < wpu < wpr . Setting the wage from the non-competitive
firms as w, the wage from the competitive firms would be w + p and the basic subsidy b could
4
also be rewritten as w − p0 for some positive value p0 . Under the condition that the risk wage
premium exceeds
r
p0 ,
1−r
the expected wage profile of the competitive firms is higher than that of
the non-competitive firms. We now turn to expected utility. Workers with higher risk aversion
would choose to work in non-competitive firms even though the wage is lower according to
their CRRA utility. With the same wage premium and job separation ratio, the expected utility
varies with the level of ρ. We are interested here in finding the condition which satisfies the
following:
◦ EU (wpu ) > EU (wpr ) for risk-averse workers with ρRA
◦ EU (wpu ) < EU (wpr ) for less risk-averse workers with ρRN
This is the case when the following condition holds:
r∈[
(w + p)1−ρRA − w1−ρRA
(w + p)1−ρRN − w1−ρRN
,
]
(w + p)1−ρRA − (w − p0 )1−ρRA (w + p)1−ρRN − (w − p0 )1−ρRN
Under this range of job separation rates of the competitive firms r, risk-averse workers are better
off choosing the non-competitive firms with the lower wage profiles. Also, within this range,
the market clears so that both risk-averse and less risk-averse workers maximize their utility. If
the ratio exceeds the upper (is less than the lower) bound, both workers would choose to work
in the non competitive (competitive) firms bearing lower wages (higher risks). This range of
the job separation ratio widens as the difference between ρRA and ρRN becomes larger, p0 is
larger (unemployment income is smaller), and the wage premium p is smaller.
Figure 1 shows the result from a simulation to compute the incentives to work in the public sector. The incentive function is simply the difference of the expected utility function of
working in the public sector and the expected utility function of working in the private sector.
The incentives is an increasing function of risk aversion variable under CRRA utility function.
Especially when workers are more risk averse (close to 1), the incentive is positive. Similarly,
Figure 2 gives the simulation result of the incentives to work in the public sector over the job
separation rate variation. The solid line represents a risk averse worker (ρ = 0.99) while the
dashed line is of a risk neutral worker (ρ = 0). This graph shows that the risk averse workers
get the positive incentive to work in the public sector in the lower job separation rate of the
private sector, while the risk neutral workers still get more incentives to work in the private
sectors with higher job separation rate. Also, the size of the incentives of working in the private
sector is higher for the risk neutral workers with the low job separation rate.1 These simulation
results support our research questions and give a reason for the empirical analyses.
1
Yet, over a certain job separation rate, the incentives to work in the public sector is higher for the risk neutral
workers compared to the risk averse workers (due to the steeper slope), extreme high job separation rate is unlikely
to happen in the reality.
5
2.2
Gender Difference in Expected Returns
Imagine again that there are two types of firms. One pays higher wages but the atmosphere
there is very competitive and the job is not secure . The other firm is relatively relaxed and the
job is more secure, but pays a lower wage than the competitive firm. Looking at the competitive
type of firms, we will show below that it pays male workers higher wages than female workers.
In the competitive firm, women’s return after child bearing is less guaranteed in comparison
to their return to the public sector, where maternity leave is more accepted. Assuming that
women’s quitting rates in competitive firms are higher than men’s due to their child bearing,
following which the competitive firms may not guarantee keeping their job positions open (i.e.
qf > qm ) (at least that is considered still to be true in most Asian countries), the expected return
for the one period after hiring by gender with productivity a and hiring cost of c, a > c > 0
(both identical by gender) in the competitive firms would be the following: Πf = a(1 − qf ) −
cqf < Πm = a(1 − qm ) − cqm . Therefore it makes sense for the competitive firm to prefer
to hire male workers (i.e. the male workers’ probability of being hired is greater than that of
female workers). More risk averse workers would set their reservation wage lower in order to
be hired Pissarides (1974), whereas less risk averse workers would have a lower probability
of being hired, though keeping their wage higher. This leads more risk averse female workers
to accept the lower wage offers in the competitive firms. Therefore, among female workers
in the competitive firm, the risk averse workers receives lower wages. This idea is alike the
“statistical discrimination”2 literature in a sense that there is different wage profile offering
from the demand sides (firms).
3
Analytical Framework
With the two stories in the previous section in mind, we now set up an analytical framework in
order to test them empirically. There are a number of studies that have investigated whether the
gender gap in risk taking preferences and competitiveness is significantly different and even
innate; Apicella et al. (2008) show that risk-taking in an investment game with potential for
real monetary pay-offs correlates positively with salivary testosterone levels and facial masculinity. More recently, Buser (2011) finds that women are less competitive both when taking
contraceptives that contain progesterone and estrogen and during the phase of the menstrual
cycle when the secretion of these hormones is particularly high. Beside hormone studies, Sutter (2010) examine compensation choices of 1,000 Austrian children and teenagers aged 3 to
2
Statistical discrimination is a theory of inequality between demographic groups based on stereotypes that do
not arise from prejudice or racial and gender bias (Phelps (1972))
6
18 years and find that the gender gap in competitiveness is already present by age three. We
therefore, in this paper, write risk aversion (showing individuals’ risk attitudes in general) as
a function of being female (F ) : RA = RA(F, ...). From section 2.1, the probability of
choosing to work in the Public Sector can be written as a function of being female and risk
aversion P ub = P ub(F, RA(F ), ...). Last, we extend the Mincerian-type wage equation as
w = w(F, P ub(F, RA(F )), ...).
Therefore, the wage gap across gender can be written as follows.
∆w
∂w
∂w ∆P ub
=
+
∆F
∂F
∂P ub ∆F
∂w
∂w ∂P ub ∂P ub ∆RA
=
+
(
+
)
∂F
∂P ub ∂F
∂RA ∆F
Female workers’ lower wages result from three factors: (1) being female on its own (this could
be interpreted as pure market discrimination); (2) female workers’ preference to work in the
public sector regardless of their risk attitudes or private firms preference on hiring male workers
leading women to work in the public (section 2.2), and (3) choosing to work in the public sector
due to women’s higher risk aversion.
3.1
Selection Issue
The concern often made when we use the Mincerian type wage equations is that the sector of
employment is endogenous to wages. Some omitted variables could both influence the wages
and also sector selections. Therefore, if we do not control for this selection issue, what we
observe from the wage equations could be biased. In our case, we use risk attitudes variable
so as to correct the selection issue and to get the modified estimates of the gender wage gap
as risk aversion could be one of the determinant when the workers to choose the sector of
employment.3
3.1.1
Switching Regression Model
Nakosteen and Zimmer (1980) suggest a model to deal with earnings of migrants and non migrants (move stay model). In our paper. we follow their method to cope with the self selection
issue. We separately estimate the earnings for workers in the public sector and workers in the
private sector.
0
wpub,i = αpub + Xpub,i
βpub + pub,i : P ublic W age Equation
3
As for the exclusion restriction, in Korean labor market, the wage is quite rigid after employed, and also not
often negotiable when entering the market. Therefore, we can assume that the impact of risk aversion could only
affect the wage by sector selection. However, we will discuss about this issue by using polychotomous choice
sample selection models in the followed section.
7
0
wpri,i = αpri + Xpri,i
βpri + pri,i : P rivate W age Equation
And, we have a sector selection function.
P ub∗i = δRAi + zi0 γ + ui : Sector Choice
P ubi = 1 if P ub∗i > 0 : In P ublic
where P ub∗i is a latent variable such that if P ub∗i > 0 then P ubi takes 1 (choosing the public
sector), otherwise Si takes 0 (choosing the private sector); RAi is the variable capturing the
individual risk attitudes (hereafter, risk aversion) and Zi is a vector of characteristics that influences the decision regarding employment sector. If we condition on P ubi = 1 (i.e. workers in
the public sector), the earning equation for workers in the public sector would be the following.
0
βpub + E(pub,i |ui > −δRAi − zi0 γ)
E(wpub,i |xpub , P ubi = 1) = αpub + Xpub,i
= αpub +
0
Xpub,i
βpub
φ(−δRAi − zi0 γ)
+ σpub ,u
1 − Φ(−δRAi − zi0 γ)
0
= αpub + Xpub,i
βpub + σpub ,u
φ(δRAi + zi0 γ)
Φ(δRAi + zi0 γ)
= E(ypub,i |xi ) + σpub ,u λ
where (pub,i , ui ) is joint normal and σpub ,u = Cov(pub,i , ui ). This covariance determines the
effect of selection on the conditional income of workers in the public sector. If ρpub ,u is significantly different from zero, it indicates that we can not ignore the unobservable characteristics
that could affect both the selection and the earnings. Then, the wage equation for workers in
the private sector would be similarly written as
0
E(wpri,i |xi , P ubi = 0) = αpri + Xpri,i
βpri + E(pri,i |ui ≤ −δRAi − zi0 γ)
0
= αpri + Xpri,i
βpri + σpri ,u [−
0
= αpri + Xpri,i
βpri − σpri ,u
φ(−δRAi − zi0 γ)
]
Φ(−δRAi − zi0 γ)
φ(δRAi + zi0 γ)
1 − Φ(δRAi + zi0 γ)
Furthermore, we can calculate the expected log wage for the hypothetical cases (i.e. public
sector workers’ expected wages if they worked in the private sector and private sector workers’
expected wages if they worked in the public sector).
0
E(wpub,i |xpub , P ubi = 0) = αpub + Xpub,i
βpub − σpub ,u
0
E(wpri,i |xi , P ubi = 1) = αpri + Xpri,i
βpri + σpri ,u
8
φ(δRAi + zi0 γ)
1 − Φ(δRAi + zi0 γ)
φ(δRAi + zi0 γ)
Φ(δRAi + zi0 γ)
3.1.2
Polychotomous Choice Sample Selection Model (Lee (1983))
Now, let’s consider the case where people are choosing among three alternatives; (1) employed
in the public sector, (2) employed in the private sector, and (3) otherwise (unemployed, inactive,
or self-employed). This allows us to take into account the possibility that risk aversion could
affect the wage through one more channel; reservation wage of entering the employed sector.4
Consider the following polychotomous choice model with three categories:
wk = αk + xk βk + ρk uk
s∗k = δRAk + zk γk + vk
where k = 1, 2, 3 and uk ∼ N (0, 1). McFadden (1974) shows that if vk is i.i.d with Gumbel
distribution, the probability of individual i choosing j is
P r(sij = 1) =
or =
exp(ηij )
if j > 1
P3
1 + k=1 exp(ηik )
1
1+
P3
k=1
exp(ηik )
if j = 1
where ηij = maxk=1,2,3k6=j s∗k − vj .
If we denote J = Φ−1 F and the transformed random variable ηj∗ = Jηs would be a standard
normal variable. Then, the bias-corrected wage equation would be
wj = αj + xj βj − σj ρj φ(Jj (δRAj + zj γ))/Fj (δRAj + zj γ) + j
with the assumption that uk and ηj∗ are joint normally distributed, E(j |jis chosen) = 0, φ is
standard normal density function, σj is the standard deviation of the disturbance uj , and ρj is
the correlation coefficient of uj and ηj∗ . The conditional variance of j is
V ar(j |l = j) = σj2 − (σj ρj )2 [Jj (δRAj + zj γ) + φ(Jj (δRAj + zj γ)/Fj (δRAj + zj γ)]
×φ(Jj (δRAj + zj γ)/Fj (δRAj + zj γ)
4
Data and Results
4.1
Data
In this paper, we use data from Korea, where the gender gap is still an important issue in
the labor market. Even though Korea’s economy has developed remarkably over the past few
4
Pissarides (1974)
9
decades, its gender wage gap remains the largest among the member countries of the Organization for Economic Cooperation and Development (OECD). Data from the OECD’s 2009
Annual report showed that male workers in Korea are paid 40 percent more than their female
counterparts, which is the widest gender pay gap of the 30 member economies of the OECD. It
was more than twice the OECD average of 18.8 percent.
Our data comes from the Korea Labor Income Panel Study published by the Korean Labor
Research Institute. This survey was initiated in 1998 and now has more than 10 waves, being
carried out once per year. It contains 5000 households and their members (11855 individuals in all) who currently live in Korea. One interesting aspect of this panel data is that there
are questions assessing risk attitudes and many different elements of job and life satisfaction.
For this paper, we restrict the sample to 4208 individuals in the one wave (2007) where the
risk questions are available, and also only consider individuals who are currently employed
and receiving wages in order to deal with the labor market sector selection issue. In the Korean sample, out of 13000 individuals, the composition of the occupation share is the following:
Mainly Working (in Public, in Private, and Self-Employed)
5927
50,0%
Domestic Work (child caring, looking after family)
2649
22,3%
Students
1396
11,8%
Doing Nothing and Others
1883
15,9%
Total
11855 100,0%
In our study, for the switching regression model, we use only wage earners (sample size 4208)
in order to look at sector selection between the public sector and the private. Then, we use the
full sample for the polychotomous selection model when to estimate the sector selection with
the labor market participation decision included. For individual risk attitudes, we construct a
measure based on the answers to five lottery-type questions as a proxy for risk aversion.
Table 1 shows the simple descriptive statistics for salaried workers. In Korea, in the salarypaying segment of the labor market, the proportion of female workers is about 40%. Figure
3 shows the female proportion among wage earners in different cohorts. In Korea, women
tend to enter the labor market earlier than do men as men have two years compulsory military
service before entering the labor market. Women’s labor market participation drops sharply
though by the age of thirty; this is the age at which they often get married (Figure 4). Figure
5 depicts the log wage difference between genders in the different cohort groups. At the time
of entry into the labor market, it seems that there is no difference in terms of wages. As
higher wages, with a break point at the age 25-30 which might be the age of ‘marriage’, male
workers start to earn more and the gap grows with age. Therefore, marital status in Korea
could be an interesting factor in explaining women’s labor market behavior including wages
10
and sectoral choices. However, this data set covers only employees, meaning that the selfemployed are missing where there are in general more men. Therefore, our data set here does
not represent the entirety of labor market participation. We can, first, look at the gender wage
differential. On average, women have lower wages (KRW130.61mil monthly)5 , fewer years of
schooling (12.39yrs), and are younger (age 39) than men (KRW227.57mil, 13.34yrs education,
age 41). This lower wage could be the result of not only gender discrimination but also the
characteristics of female workers, such as less education, and a higher proportion in the public
sector (47% of the public sector workers are women, as opposed to a figure of 36% in the private
sector) where wages in general are lower (KRW207mil in private, KRW140mil in public). In
addition, the risk aversion6 of public-sector workers is higher on average than that of those in
the private sector. Women are also found to be more risk averse. We now describe how risk
aversion is measured in our data.
4.2
Measuring Risk Aversion
The Korea Labor Income Panel Studies recently added several experimental questions regarding individual risk attitudes. We specifically use the 2007 wave, in which there are five questions involving lotteries which can help us to summarize individual risk-taking attitudes. Each
individual is asked to indicate whether they would accept the given lottery, take 100,000 KRW
(82 USD) in cash, or whether they are indifferent between the two. The details of the five
questions are shown below:
Number
Lottery characteristics
Expected Value
[Ni ]
Weight[αi ]
1
1/2 :KRW150000, 1/2 :KRW50000
KRW100000
363
0.155
2
1/2 :KRW200000, 1/2 :KRW0
KRW100000
314
0.179
3
1/5 : KRW500000, 4/5 :KRW0
KRW100000
226
0.249
L
3/5 :KRW200000, 2/5 :KRW0
KRW120000
389
0.145
H
2/5 :KRW200000, 3/5 :KRW0
KRW80000
207
0.272
Here the first three choices, which we call risk1, risk2, and risk3 have the same expected value
as the fixed amount of KRW100,000 but differ in their degree of riskiness. Taking risk2 as the
baseline, risk1 is lower risk than risk2, whiles risk3 is riskier. Meanwhile, RiskL and RiskH
have different expected values (KRW80,000 and KRW120,000 respectively). We used the answers to these five questions to construct a risk-aversion variable which may explain a part of
individual heterogeneity. Each question is assigned a value of 0 if the respondent prefers the
5
6
1 U.S. dollar is approximately 1100 Korean Won
We will discuss about risk aversion construction in the next section.
11
lottery that is regarded as risk taking, ‘indifferent’ is assigned a value of 0.5, while not choosing the lottery implies a value of 1. Higher numbers therefore indicate greater risk aversion.
However, we might want these figures to be different according to the lottery’s expected value.
For example, in riskL, saying ‘indifferent’ could also mean ‘risk averse’ as the expected value
is less than KRW100,000, because the distance between the expected value and KRW100,000
could be seen as a risk premium from choosing the lottery. Equally choosing the lottery in
risk1, 2, and 3, would above be assigned the same value of 1, but this does not mean that those
lotteries have the same associated levels of risk. With this idea in mind, we weight each risk
variable according to the inverse of the fraction of people choosing the lottery.
X
rai =
αi Riski , i = 1, 2, 3, L, andH 7
where Riski =0 (prefer lottery: less risk averse), 0.5 (indifferent: risk neutral), 1 (prefer cash:
risk averse), and αi is an ad hoc weight, which is higher for more risky lottery choice if that
P
lottery is chosen by fewer people, αi = bi / bi , where bi is the inverse of the proportion
P
of the number of lotteries chosen in each case (i.e. bi =
Ni /Ni , Ni in the table shows
the number of respondents who prefer each lottery i). The risk aversion measure, therefore,
has the range of [0, 1].8 Each lottery has its own weight which is calculated as the inverse
of the proportion of people who chose the lottery.9 The ascending order of risk amongst the
five lotteries as subjectively perceived by workers is L(the least risky) → 1 → 2 → 3 →
H(the most risky)).10
Table 2 shows risk aversion in various sub-samples: by gender, job sector, education, age,
and marital status. Female workers are more risk averse than male workers, and workers in
the public sector are more risk averse than those in the private sector. Also, highly educated
workers tend to be less risk averse than workers who hold a high school diploma. Older workers
(aged over 45) are more risk averse, while marital status is not associated with any significant
differences in risk aversion. We do indeed find a gender difference in attitude towards risk,
which is the basis for the work we undertake here. Figure 6 shows the relationship between
risk aversion and age profile across genders. Women have a tendency to be more risk averse
7
8
This method is introduced by Sung (2007)
A simple aggregation using the same weights for each question was also tested and yielded a fairly similar
picture to that from the method used above; these results are available upon request.
Alternatively, the Barsky (1997) method could be used. The first three questions would yield 27 categories of
different risk attitude-groups.
1
For example, α1 = 1 + 1 + 363
= 0.155
1
1
1
363
314
226 + 389 + 207
10
There is an issue of the inconsistency of respondent choice. For example, 53 respondents chose to take lottery
9
2 but not lottery 1 which is less risky. These inconsistency rates are, however, normally below 2.5% in this
sample and do not change the results much. We, therefore, have retained all of the observations regardless of their
inconsistency.
12
than men at all ages. There is also an increasing trend suggesting an age effect on risk aversion.
Figure 7 shows the risk aversion-age profile by sector. Similarly to what was found for gender,
public sector workers’ risk aversion is in general higher than that for private sector workers’
among most cohort groups. When we compare the risk aversion between the public sector and
the private sector, female workers continue to report greater risk aversion. However, the gender
difference in terms of risk aversion is larger among private sector workers (Figure 9) than in the
public sector (Figure 8), which might explain the difference in the gender wage gap between
sectors. This is what we now attempt to evaluate via a regression analysis.
4.3
Results
Table 3 gives the result of pairwise correlation matrices of the variables which we are interested.
The main variable risk aversion is significantly correlated with the wage, gender, employment,
sector selection, education, married, health, and also father’s education. The gender, public
workers, and also marital status are going in the same direction as risk aversion rises, while
wage, employment, education, health, and father’s education are in the opposite. This signs
and significance support the human capital theory and literature on the risk studies. The wage
is negatively correlated with female workers, and also the public workers, and without doubt,
female and public workers are positively correlated. All this correlation relationship can, therefore, give a clear start to our analyses.
Table 4 presents the results from various wage equations we used. Column 1 is the full sample
analysis without selection correction. In the Korean sample, female workers are, on average,
about 38% less paid compared to male workers controlled with other socio-demographic variables and public sector dummy. The return to schooling is about 8% which is quite standard.
Interesting point is that public workers are 25% less paid than the private company workers11 .
Column 2 and 4 give wage equations for workers in the public sector and workers in the private
sector, respectively. In the public sector, still female workers are paid less (32%) but the gap
is narrower than in the private sector (40%). The reason behind could be that in the public
sector, the discrimination is harder to be obvious by the policy and also the less competitive
atmosphere allows more equal working condition for men and women. On the other hand, the
private firms are more competitive to seek for the profit, which leads workers work harder;
female workers tend to be left behind in this working environment due to child care and less
competitive characteristics, that widens the gender gap. Also, the preference towards male
11
However, if we consider skilled work and unskilled work, the picture is slightly different. In the skilled work,
the private sector pays higher wage, whereas in the unskilled work, the public sector tend to pay higher wage. On
average, still the private sector pays more than the public sector
13
workers of the private firms may contribute to this wider gender wage gap in the private sector by offering higher wage to male workers. Besides, the return to schooling is higher in the
private sector. On average, the workers in the private sector earn more comparing the constant
terms (3.636 vs 3.35).
Now, we consider the selection model. First, we use the Switching Regression Model(Nakosteen
and Zimmer (1980)).12 The result from the selection step is presented in the second panel. The
binary dependant variable is working in the public sector. As we already presumed, female
workers tend to choose (or to be pushed to choose) in the public sector. Education does not
significantly correlate with the selection into public sector. Interestingly, the household income
is negatively correlated with working in the public sector (i.e. if you are richer, then you tend to
choose the private sector). This could be related to the risk taking behavior with initial wealth;
if you are initially richer, you are less risk averse in terms of relative risk aversion under CRRA.
Marital status is also negatively correlated with the public sector. Our variable of interest, risk
aversion is, indeed, positively correlated with the public sector choice; workers with higher
risk aversion tend to be found more often in the public sector. According to our framework,
risk aversion could be an important determinant in the sector selection step. With the selection
correction, we, now, see the difference in the gender wage gap in both sectors. Column 3 and
5 represent the wage equation results with the selection correction. In the public sector, the
gender gap which is not explained by other socio-demographics has reduced from 32% to 27%.
In the private sector, as well, the gender gap dropped by 5% (40% to 35%). This correction
seems meaningful as the rho is significantly different from zero which approves that there is,
indeed, a selection issue in the main wage equation. This supports our framework; if we control for the risk aversion, then it could correct the women’s self selection into public sector, and
reduce the pure gender gap which can not be explained and often defined as the market gender
discrimination.
Table 5 shows the prediction of the expected log wage based on the sample correction
method . Expected wages are calculated for the following: unconditional in the public sector, unconditional in the private sector, conditional in the public sector with workers currently
working in the public sector, conditional in the private sector with workers currently working in
the public sector, conditional in the public sector with workers currently working in the private
sector, conditional in the private sector with workers currently working in the private sector. As
rho1 is positive and significantly different from zero, the model suggests that individuals who
choose to work in the private sector with intention earn lower wages than a random individual
(or currently working in the other sector) from the sample would have earned (Row 4 vs Row
12
We use ‘movestay’ stata command developed by Lokshin and Sajaia (2006) in order to estimate the switching
regression.
14
6). On the other hand, as rho0 is also positive and significantly different from zero, individuals
who choose to work in the public sector with intention earn higher wages than a random individual (or currently working in the other sector) from the sample would have earned (Row 3 vs
Row 5).
Table 6 presents the result from various wage equations with two different selection correction method; the Switching Regression Model (Nakosteen and Zimmer (1980)) and Lee
(1983)’s polychotomous method13 . In this case, we dropped the working hour in the selection
step as it is not available for inactive and unemployed people. And also another instrument
‘father’s education’ has added in order to strongly support the selection step. The Switching
Regression Model we used (Column 3 and 6) is similar to the previous one (Table 4) except
the use of father’s education and the drop of working hour. The significance of risk aversion
estimates in the sector selection vanishes, possibly because father’s education could capture
some of the variation of risk aversion variable (in Table 3, we already saw father’s education is
negatively correlated with risk aversion). Though, the sign remains unchanged. In comparison
with the previous Table 4, after the sample selection correction by using the switching regression, the gender wage gap has narrowed from 32% to 28% in the public sector, and from 40%
to 35% in the private sector, which is similar. Then, Colume 4 and 7 give the wage equation
results corrected by Lee’s method. The second panel shows the multinomial logit model result
for (1) working in the public sector (in Column 4) and (2) working in the private sector (in Column 4), putting (3) self-employed or inactive people as the reference point. To be in the public
sector, both risk aversion and father’s education are not significantly influencing. However, to
be in the private sector, both of them are significant and crucial; the more risk averse you are,
the less found in the private sector, and if your father has higher education then you tend to
be found in the private sector. Noticing that all rhos are significantly different from zero, we
can now look at the corrected wage equations in the first panel. In the public sector, the model
correction increases the gender gap by 3.4% which is the opposite direction. However, if we
look at the selection step in the public sector, the risk aversion and father’s education did not
play a significant role. In the multinomial choice model, when people compare several alternatives, the estimates could be different from the binary choice model. In the three categorical
choice model, the results shows the alternative estimate comparison with the reference point; if
we look at the public sector estimation, the results show the comparison with self-employment
and inactive, not directly with the private sector. Therefore, when people compare the public
sector with self-employment or inactive, the risk aversion is not very important, and hence the
corrected wage gap may not go in the same direction. What is more important here is the pri13
We use ‘selmlog’ stata command developed by Bourguignon and Gurgand (2007) in order to estimate the
polychotomous choice selection model.
15
vate sector. In the selection step, the risk aversion and father’s education are key determinants.
This correction in the private sector make the gender wage gap drop even more than the switching regression model (from 40% to 29%). This results supports that the selection issue in the
private sector is indeed not negligible and also suggest that the gender wage gap in the private
sector is overestimated without correction. Because women are more risk averse in general, the
selection bias makes the gap seem much bigger.
5
Concluding Remarks
This paper provides some evidence on the impact of risk aversion on labor-market behavior.
Based on hypothetical lottery questions from Korean labor surveys, we control for risk attitudes. We especially look at job-sector choice between the private and public sectors, assuming
that the public sector has more incentives in terms of stability and job security relative to the
private sector. The results show that risk aversion is a significant and positive determinant of
the choice of working in the public sector. The tendency that women are more risk averse than
men gives a hint that there could be link the women’s self selection and its impact on wage.
We explain a part of gender labor market discrimination through the prism of workers’ risk
aversion. There are three channels that explain gender wage gap. A graphical illustration is as
follows.
Female
Risk Aversion
Public
Low Wage
This idea, therefore, support the reason why we should correct the wage equation for the selection bias. We show that individual risk attitudes could be an important determinant when to
choose the labor market participation, and also sector selection between public and private. Af16
ter using the switching regression model, the gender gap has dropped in both sector by abour
5%. In addition, when we extend our model to multinomial choice model for the selection
step, the gender gap in the private sector dropped sharply, although that in the public sector
surprisingly increased. This opposite direction, however, could be explained with the different mechanism when we use the multinomial model with the self-employment and inactive as
the reference category. These findings indicate that the wage gap is not simply a product of
the labor market environment, but also the choices made by women themselves based on their
risk aversion and other preferences. In other words, the wage gap is not only a result of pure
discrimination in the labor market, but also a result of intrinsic sorting based on preferences
formed by risk attitudes. This could be a new way to explain why female workers in Korea are
paid so much less than are male workers.
17
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20
Figures
Figure 1: Incentives to work in the public sector over Risk Aversion Variation
Figure 2: Incentives to work in the public sector over Job Separation Rate Variation
21
Figure 3: Female Participation
Figure 4: Marital Status over Age
Figure 5: Gender Wage Gap over Age
22
Figure 6: Risk Aversion Age Profile
Figure 7: Risk Aversion Age Profile by Sector
Figure 8: Risk Aversion Age Profile by gender in the Public Sector
23
Figure 9: Risk Aversion Age Profile by Gender in the Private Sector
24
Tables
Table 1: Descriptive Statistics
Age
Education
Female
Wage(mil won)
Public
Married
Risk Aversion
N
Full Sample
Male
Female
Diff
Private
Public
Diff
40.00
40.76
38.81
-1.95***
41.18
36.74
-4.43***
(11.50)
(11.11)
(12.01)
(10.96)
(12.31)
12.95
13.31
12.38
12.97
12.88
(3.19)
(3.01)
(3.37)
(3.25)
(3.01)
0.39
0.36
0.47
(0.49)
(0.48)
(0.50)
207.57
139.26
(208.56)
(105.80)
0.79
0.61
(0.41)
(0.49)
-0.94***
0.11***
189.37
227.15
130.58
(189.20)
(220.92)
(99.44)
0.27
0.23
0.32
(0.44)
(0.42)
(0.47)
0.74
0.76
0.71
(0.44)
(0.43)
(0.45)
0.927
0.904
0.963
0.06***
0.923
0.943
0.020**
(0.25)
(0.15)
(0.25)
(0.007)
(0.24)
(0.18)
(0.008)
4208
2563
1645
3085
1123
Notes. Standard errors in parentheses
*: p < 0.10, ** : p < 0.05, *** : p < 0.01
25
-96.57***
-0.09
-68.31***
0.09***
-0.05***
-0.17***
Table 2: Risk Aversion measures
Mean
SE
Obs
Full Sample
0.927
0.219
4208
Male
0.903
0.250
2563
Female
0.963
0.152
1645
0.060***
0.007
Private
0.922
0.229
3085
Public
0.942
0.189
1123
0.019**
0.008
Edu > 12yrs
0.935
0.213
2199
Edu ≤ 12yrs
0.919
0.225
2009
-0.015**
0.024
Age < 45
0.920
0.226
2879
Age ≥ 45
0.944
0.202
1329
0.024***
0.007
Not married
0.934
0.201
1101
Married
0.924
0.225
3107
diff
-0.009
0.008
diff
diff
diff
diff
Notes. *: p < 0.10, ** : p < 0.05, *** : p < 0.01
26
Risk Aversion
Risk Aversion
Table 3: Pairwise Correlation of Variables
Log Wage Female Employed In Public Education
Married
Health
1.0000
27
Log Wage
-0.1118*
1.0000
Female
0.1349*
-0.4100*
1.0000
Employed
-0.0771*
.*
-0.1907*
1.0000
In Public
0.0374*
-0.2555*
0.0989*
.*
1.0000
Education
-0.1172*
0.4410*
-0.2134*
0.2367*
-0.0143
1.0000
Married
0.0446*
0.1205*
0.0972*
-0.0089
-0.1769*
-0.2942*
1.0000
Health
-0.0635*
0.1628*
-0.1156*
0.1381*
-0.0366*
0.3388*
-0.2183*
1.0000
Father Edu
-0.0262*
0.0360*
-0.0213*
0.1012*
-0.1451*
0.0273*
0.0043
0.0069
Notes. *: p < 0.10
Father Edu
1.0000
Table 4: Switching Regression Model
Full Sample
Public
Private
Wage
Correction
Female
Education
Experience
Experience2
Married
Working Hours
In Public
No
No
Yes
No
Yes
-0,382***
-0,323***
-0,277***
-0,406***
-0,35***
(0,016
(0,03)
(0,032)
(0,019)
(0,021)
0,08***
0,060***
0,056***
0,085***
0,084***
(0,003)
(0,007)
(0,007)
(0,004)
(0,004)
0,234***
0,189***
0,214***
0,238***
0,26***
(0,023)
(0,042)
(0,041)
(0,028)
(0,028)
-0,049***
-0,047*** -0,051*** -0,047***
-0,049***
(0,004)
(0,007)
(0,007)
(0,005)
(0,005)
0,171***
0,161***
0,000
0,172***
0,047
(0,023)
(0,044)
(0,049)
(0,027)
(0,029)
0,063***
0,121***
0,127***
0,037***
0,034***
(0,005)
(0,009)
(0,01)
(0,006)
(0,081)
3,585***
3,35***
3,012***
3,636***
3,874***
(0,066)
(0,126)
(0,134)
(0,077)
(0,081)
-0,256***
(0,017)
Constant
Selection
Female
0,216***
(0,043)
Education
0,004
(0,007)
HH Income
-0,186***
(0,013)
Married
-0,525***
(0,047)
Working Hours
0,014
(0,015)
Risk Aversion
0,171*
(0,095)
rho0
0,749***
(0,023)
rho1
0,654***
(0,053)
wald chi2
Adj R 2
Obs
1568,84
0,4375
0,3930
4208
1123
Notes. Standard errors in parentheses
*: p < 0.10, ** : p < 0.05, *** : p < 0.01
28
0,4133
4208
3085
Table 5: Expected Log Wage with Selection
Expected lwage
Full Sample
Men
Women
Uncond in Pub
4,39
4,13
4,55
(0,373)
(0,329)
(0,298)
5,28
4,99
5,46
(0,364)
(0,301)
(0,268)
4,76
4,51
4,97
(0,393)
(0,331)
(0,308)
5,69
5,43
5,92
(0,388)
(0,3078)
(0,289)
4,24
3,95
4,41
(0,385)
(0,34)
(0,299)
5,12
4,78
5,31
(0,401)
(0,338)
(0,296)
0,28
0,32
0,25
(0,141)
(0,144)
(0,132)
Uncond in Pri
Cond in Pub w/ pub workers
Cond in Pri w/ pub workers
Cond in Pub w/ pri workers
Cond in Pri w/ pri workers
Prob to Choose Pub
Notes. Standard errors in parentheses
*: p < 0.10, ** : p < 0.05, *** : p < 0.01
29
Table 6: Switching Regression and Polychotomous Selection Model
Full Sample
Public
Private
Wage
Correction
Female
Education
Experience
Experience2
Married
Working Hour
In Public
No
No
Roy
Lee
No
Roy
Lee
-0,382***
-0,323***
-0,283***
-0,357***
-0,406***
-0,354***
-0,286***
(0,016
(0,03)
(0,032)
(0,053)
(0,019)
(0,021)
(0,036)
0,08***
0,060***
0,057***
0,098***
0,085***
0,084***
0,066***
(0,003)
(0,007)
(0,007)
(0,013)
(0,004)
(0,004)
(0,007)
0,234***
0,189***
0,214***
0,219***
0,238***
0,258***
0,239***
(0,023)
(0,042)
(0,042)
(0,045)
(0,028)
(0,028)
(0,028)
-0,049***
-0,047***
-0,05***
-0,051***
-0,047***
-0,049***
-0,047***
(0,004)
(0,007)
(0,007)
(0,008)
(0,005)
(0,005)
(0,005)
0,171***
0,161***
0,008
-0,136***
0,172***
0,056**
0,065*
(0,023)
(0,044)
(0,049)
(0,1)
(0,027)
(0,029)
(0,009)
0,063***
0,121***
0,122***
0,12***
0,037***
0,033***
0,037***
(0,005)
(0,009)
(0,009)
(0,011)
(0,006)
(0,006)
(0,009)
3,585***
3,35***
3,054***
1,017*
3,636***
3,873***
4,318***
(0,066)
(0,126)
(0,131)
(0,597)
(0,077)
(0,08)
(0,195)
0,212***
-0,286***
-0,788***
(0,043)
(0,066)
(0,047)
-0,256***
(0,017)
Constant
Selection
Female
Education
HH Income
Married
Risk Aversion
father edu
rho0
0,003
0,124***
0,139***
(0,007)
(0,010)
(0,007)
-0,188***
-0,063***
0,088***
(0,013)
(0,022)
(0,016)
-0,524***
-0,309***
0,643***
(0,048)
(0,071)
(0,055)
0,155
-0,15
-0,472***
(0,098)
(0,191)
(0,126)
-0,069***
-0,261
0,147***
(0,01)
(0,018)
((0,011)
0,723***
(0,026)
rho1
0,624***
-0,436***
(0,057)
(0,006)
rho2
0,513***
(0,063)
wald/LR chi2
Adj R 2
Obs
1602,55
0,4375
0,3930
4208
1123
1424,21
1424,21
0,4133
4208
Notes. Standard errors in parentheses
*: p < 0.10, ** : p < 0.05, *** : p < 0.01
30
3085