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Labor Market Signaling and Self-Confidence:
Wage Compression and the Gender Pay Gap
∗
Luís Santos-Pinto
†
Faculty of Business and Economics, University of Lausanne
This version: December 12, 2011
Abstract
I extend Spence’s (1973) signaling model by assuming some workers are
overconfident—they underestimate their marginal cost of acquiring education—
and some are underconfident. Firms cannot observe workers’ productive
abilities and beliefs but know the fractions of high-ability, overconfident, and
underconfident workers. I find that biased beliefs lower the wage spread and
compress the wages of unbiased workers. I show that gender differences
in self-confidence can contribute to the gender pay gap. If education raises
productivity, men are overconfident, and women underconfident, then women
will, on average, earn less than men. Finally, I show that biased beliefs can
improve welfare.
JEL Codes: D03; D82; J24; J31.
Keywords: Signaling; Education; Self-Confidence; Wage Compression;
Gender Pay Gap.
⋆
I am thankful to Miguel Costa-Gomes, Robert Dur, Lorenz Goette, Hans Hvide,
Bettina Klaus, David Myatt, Joel Sobel, Michael Waldman, and an anonymous
referee for helpful comments and suggestions.
†
Faculty of Business and Economics, University of Lausanne, Internef 53, CH-1015,
Lausanne, Switzerland. Ph: 41-216923658. Fax: 41-216923435. E-mail address:
LuisPedro.SantosPinto@unil.ch.
1
1 Introduction
This paper explores the implications of worker self-confidence in the classic
labor market signaling model by Spence (1973). Firms are perfectly compet-
itive and cannot observe workers’ productive abilities, which may be either
high or low. Unbiased workers know their marginal cost of acquiring edu-
cation. Overconfident (underconfident) workers believe that their marginal
cost of acquiring education is low (high) when, in fact, it is high (low). Firms
cannot observe workers’ beliefs but know the fraction of high-ability, over-
confident, and underconfident workers in the labor market.
I start by showing that workers’ biased self-evaluations can lead to wage
compression. Wage compression, i.e., the fact that there are lower wage
differences across workers than differences in productivity, is a key feature
of many labor markets and has important consequences for labor market
performance. While a compressed wage structure is generally believed to
reduce labor market efficiency and welfare, it has also been used to explain
why firm sponsored training of employees can arise.
1
My first result shows that biased beliefs compress wages in the sense that
the wage spread with biased workers is smaller than the wage spread with
rational workers. In a separating equilibrium, overconfident low-ability work-
ers and unbiased high-ability workers choose a high education level whereas
underconfident high-ability workers and unbiased low-ability workers choose
a low education level. The optimal response of firms to the fact that over-
confidence raises the proportion of low-ability workers in the high education
group whereas underconfidence raises the proportion of high-ability workers
in the low education group is to lower the wage of the high education group
and raise the wage of the low education group.
I also find that the presence of biased workers in the labor market com-
presses the wages of unbiased workers in the sense that the wage spread
across unbiased workers is less than the productivity spread. In contrast, the
model predicts that the wage spread across biased workers is greater than
the productivity spread.
Next, I study the impact of gender differences in self-confidence on the
gender pay gap, i.e., the fact that men earn, on average, more than women.
1
The economics literature has proposed several explanations for wage compression,
ranging from labor market institutions, to incentives not to sabotage colleagues competing
in a tournament, to fairness considerations in wage-setting decisions by firms. I review the
relevant literature in Section 3.
2
I show that if education raises productivity, males are overconfident, and
females underconfident, then there is a gender pay gap.
2
The intuition behind
this result is as follows. Before making any educational investments, men
and women are equally productive. However, if men are overconfident and
women underconfident, the proportion of men among the male population
who acquire a high education level will be higher than the proportion of
women among the female population who acquire a high education level. If
education raises productivity, then men will be, on average, more productive
than women. This generates the gender pay gap.
Finally, I show that if the fraction of overconfident workers is not too
high and workers are sufficiently similar in terms of productivity and cost
of education, then biased beliefs can improve welfare. When all workers are
unbiased, Spence’s (1973) model shows that if the two groups of workers are
sufficiently similar in terms of productivity and cost of education, then there
exist separating equilibria with overinvestment in education by the more
productive group. In this case private information about productive ability
reduces welfare. However, Spence (2002) shows that it is possible to improve
market efficiency with an optimal tax-subsidy schedule that consists of a
rising tax on education which reduces the level of education of high-ability
workers combined with a lump-sum transfer to low-ability workers so that
net tax revenues are zero.
The reasons why workers’ biased beliefs raise welfare are similar to those
why a tax-subsidy schedule raises welfare. Overconfidence is like a “tax” on
the education of unbiased high-ability workers because it lowers their wage
and their education. When the fraction of overconfident workers is not too
high, the education level of unbiased high-ability workers will be close to the
optimal. Underconfidence is like a “subsidy” for unbiased low-ability workers
because it raises their wage for a given education level. This result is consis-
tent with the theory of the second best. According to this theory, introducing
a new distortion–workers’ biased beliefs–in an environment where another
distortion is already present–private information about skill–, may increase
welfare.
Of course, welfare does not always rise when workers have biased beliefs
and are sufficiently similar in terms of productivity and cost of education.
If the fraction of overconfident workers is too high, unbiased high-ability
workers are “overtaxed” and end up with an education level far from the
2
Section 4 contains a brief discussion of the large literature on the gender pay gap.
3
optimal. In this case there is a transfer of utility from unbiased high-ability
to unbiased low-ability workers.
One policy implication of the welfare analysis is that improving workers’
self-evaluations will reduce welfare when the fraction of overconfident workers
is not too high and workers are sufficiently similar in terms of productivity
and cost of education. In contrast, if either (i) workers are sufficiently differ-
ent or (ii) a significant fraction of workers is overconfident and workers are
sufficiently similar, then improving self-evaluations increases welfare.
The assumption that some workers are overconfident and others under-
confident is supported by robust empirical evidence on patterns of over- and
underestimation in self-evaluation of skills. Overconfidence is a staple find-
ing in psychology and has been shown to be present in individuals’ self-
assessments of performance in their jobs. According to Myers (1996), a
textbook in social psychology, “(...) on nearly any dimension that is both
subjective and socially desirable, most people see themselves as better than
average.”
3
Kruger and Dunning (1999) find that it is the poorest performers who
hold the least accurate evaluations of their skills and performances, grossly
overestimating how well their performances stack up against those of their
peers. They observe that students performing in the bottom 25% among
their peers on tests of grammar, logical reasoning, and humor tend to think
that they are performing above the 60% percentile. They also find that top
performers consistently underestimate how superior their performances are
relative to their peers. In Kruger and Dunning (1999) studies, the top 25%
tended to think that their skills lay in the 70-75% percentile, although their
performances fell roughly in the 87% percentile.
4
This paper is an additional contribution to the growing literature on the
impact of behavioral biases on markets and organizations. DellaVigna and
Malmendier (2004) and Gabaix and Laibson (2006) study market interac-
3
Baker, Jensen and Murphy (1988) cite a survey of General Electric Company employ-
ees according to which 81 percent of a sample of white-collar clerical and technical workers
rated their own performance as falling within the top 20 percent of their peers in similar
jobs. Myers (1996) cites a study according to which, in Australia, 86 percent of people
rate their job performance as above average.
4
These patterns have been replicated among undergraduates completing a classroom
exam (Dunning et al., 2003), medical students assessing their interviewing skills (Hodges,
Regehr, and Martin, 2001), clerks evaluating their performance (Edwards et al., 2003), and
medical laboratory technicians evaluating their on-the-job expertise (Haun et al., 2000).
4
tions between sophisticated firms and biased consumers. They find that in
competitive markets, biased consumers may be indirectly exploited by so-
phisticated consumers.
Sandroni and Squintani (2007) investigate the policy implications of over-
confidence in insurance markets. They find that compulsory insurance fails
to make all agents better off because it is detrimental to low-risk agents.
Thus, behavioral biases may weaken asymmetric information rationales for
government intervention in insurance markets.
My paper is closely related to literature on the impact of overconfidence
on labor market choices. Squintani (1999) studies overconfidence and on-the-
job signaling. He finds that overconfident workers choose tasks that are too
onerous, fail them, and, dejected by such a failure, settle down for a position
inferior to their potential. Hvide (2002) shows that worker overconfidence
about productivity outside the firm improves worker welfare. Santos-Pinto
(2008, 2010) shows how firms can design optimal contracts to take advantage
of worker overconfidence about productivity inside the firm.
Dubra (2004) and Falk, Huffman, and Sunde (2006) study the impact of
self-confidence on job search. Dubra (2004) finds that if searchers are not pa-
tient, a slightly overconfident one may fare better than unbiased ones because
he will search longer. Falk et al. (2006) show that unemployment duration
erodes self-confidence and the willingness to continue search. This implies
that falling self-confidence can be a complementary mechanism leading to
negative duration dependence.
Fang and Moscarini (2005) study the implication of worker overconfi-
dence on the firm’s optimal wage-setting policies using the principal-agent
approach. Wage contracts provide incentives and affect workers’ confidence
in their own skills by revealing private information of the firm about work-
ers’ skills. They find, using numerical examples, that overconfidence is a
necessary condition for a firm to choose a non-differentiation wage policy
(the most extreme form of wage compression). This happens because, when
ability and effort are complements, a non-differentiation wage policy pre-
serves worker overconfidence which in turn induces higher effort, offsetting
the moral hazard inefficiency.
The paper is organized as follows. Section 2 sets-up the model. Section
3 shows that biased beliefs lower the wage spread and compress the wages of
unbiased workers. Section 4 shows that gender differences in self-confidence
can contribute to the gender pay gap. Section 5 analyzes the impact of
biased beliefs on welfare. Section 6 explains how the paper contributes to
5
the existing literature on labor market signaling and discusses extensions of
the model. Section 7 concludes. Proofs of all results are in the Appendix.
2 The Model
For each worker there are two possible productive abilities: low, θ
L
, and high,
θ
H
, with 0 < θ
L
< θ
H
. Nature determines a worker’s productive ability and
beliefs about marginal cost of acquiring education. The worker chooses a
level of education, e ≥ 0, based on her beliefs. Two firms, 1 and 2, observe
the worker’s education and then simultaneously make wage offers w
1
and w
2
,
with w
i
≥ 0, i = 1, 2. The worker accepts the highest of the two wage offers,
flipping a coin in case of a tie.
The payoff of a firm that employs a worker with ability θ and education
e is π(w, e, θ) = y(e, θ) −w, where y(e, θ) is the worker’s output. The payoff
of a firm that does not employ a worker is zero. High-ability workers are
more productive: y
θ
(e, θ) > 0. Education does not reduce productivity, i.e.,
y
e
(e, θ) ≥ 0 where y
e
(e, θ) is the marginal productivity of education for a
worker of ability θ at education e. The marginal productivity of education is
non-increasing with education: y
ee
(e, θ) ≤ 0. The marginal productivity of
education is non-decreasing with ability: y
eθ
(e, θ) ≥ 0.
There are four types of workers in the labor market. Unbiased high-ability
workers have marginal cost of acquiring education c
e
(e, θ
H
) and know it. Un-
biased low-ability workers have marginal cost of acquiring education c
e
(e, θ
L
)
and know it. Overconfident low-ability workers believe their marginal cost
of acquiring education is c
e
(e, θ
H
) when in fact it is c
e
(e, θ
L
). Underconfi-
dent high-ability workers believe their marginal cost of acquiring education
is c
e
(e, θ
L
) when in fact it is c
e
(e, θ
H
). Let λ = Pr(θ = θ
H
) ∈ (0, 1) be
the fraction of high-ability workers, ν ∈ [0, λ] be the fraction of underconfi-
dent high-ability workers, and κ ∈ [0, 1 − λ] be the fraction of overconfident
low-ability workers. Firms cannot observe a worker’s productive ability and
beliefs, but know λ, κ and ν.
The utility of an employed worker is u(w, e, θ) = w − c(e, θ), where w is
the wage offer made by a firm and c(e, θ) is the cost to a worker with ability θ
to obtaining education e. The utility of an unemployed worker is normalized
to zero. The cost of no education is zero: c(0, θ) = 0. The cost of education
increases with education: c
e
(e, θ) > 0, where c
e
(e, θ) is the marginal cost of
education for a worker of ability θ at education e. The cost of education
6
decreases with ability: c
θ
(e, θ) < 0. The marginal cost of education increases
with education: c
ee
(e, θ) > 0. The marginal cost of education decreases with
ability: c
eθ
(e, θ) < 0. This assumption is critical since it means that low-
ability workers find signaling more costly than high-ability workers, i.e., for
every e, c
e
(e, θ
L
) > c
e
(e, θ
H
). The assumption is also known as the Spence-
Mirrlees single-crossing condition since it implies that the indifference curves
of low- and high-ability workers only cross once.
In a separating equilibrium, education choices are determined by work-
ers’ beliefs about their marginal cost of acquiring education: underconfident
high-ability workers and unbiased low-ability workers choose a low educa-
tion level, e
LU
, whereas overconfident low-ability workers and unbiased high-
ability workers choose a high education level, e
HO
, with e
HO
∈ [ˆe
B
, ¯e
B
], and
e
HO
> e
LU
. Firms cannot distinguish between underconfident high-ability
workers and unbiased low-ability workers because, at the time wage offers
are made, both types of workers have the same education level: e
LU
. Simi-
larly, firms cannot distinguish between overconfident low-ability workers and
unbiased high-ability workers because both types of workers display the same
education level e
HO
. However, firms know λ, κ and ν.
Among all workers who choose an education level e
LU
firms know that
fraction α =
ν
1−λ−κ+ν
has high ability and fraction 1 − α =
1−λ−κ
1−λ−κ+ν
has low
ability. Among all workers who choose an education level e
HO
firms know
that fraction β =
κ
λ+κ−ν
has low ability and fraction 1 − β =
λ−ν
λ+κ−ν
has high
ability. Hence, the firms’ posterior belief that a worker has high ability after
observing education level e is
µ(θ
H
|e) =
α, for e < e
HO
1 − β, for e ≥ e
HO
.
The firms’ strategy is then
w(e) =
(1 − α)y(e, θ
L
) + αy(e, θ
H
), for e < e
HO
βy(e, θ
L
) + (1 − β)y(e, θ
H
), for e ≥ e
HO
. (1)
The firms’ strategy is derived from the assumption that firms make zero
profits in equilibrium and that firms know λ, κ and ν. Competition between
firms implies that the wage offered to each group of workers (those who
choose e
LU
and those who choose e
HO
) must be a weighted average of the
productivities of each type of worker in the group.
In a separating equilibrium the wage of overconfident low-ability workers
and unbiased high-ability workers is higher than the wage of underconfident
7
high-ability workers and unbiased low-ability workers. It follows from (1)
and e
LU
< e
HO
that this condition is satisfied if α + β ≤ 1, or, using the
definitions of α and β,
(1 − λ)ν + λκ ≤ (1 −λ)λ. (2)
Condition (2) says that if the fractions of overconfident and underconfi-
dent workers are sufficiently small, education can serve as a signal of produc-
tive ability. When the fraction of biased workers is too high, condition (2) is
violated and separating equilibria may no longer exist.
5
I assume from now
on that condition (2) is satisfied.
In a separating equilibrium underconfident high-ability workers and un-
biased low-ability workers do not envy overconfident low-ability workers and
unbiased high-ability workers, that is
(1 − α)y(e
LU
, θ
L
) + αy(e
LU
, θ
H
) − c(e
LU
, θ
L
)
≥ βy(e
HO
, θ
L
) + (1 − β)y(e
HO
, θ
H
) − c(e
HO
, θ
L
), (3)
and overconfident low-ability workers and unbiased high-ability workers do
not envy underconfident high-ability workers and unbiased low-ability work-
ers, that is
βy(e
HO
, θ
L
) + (1 − β)y(e
HO
, θ
H
) − c(e
HO
, θ
H
) ≥
(1 − α)y(e
LU
, θ
L
) + αy(e
LU
, θ
H
) − c(e
LU
, θ
H
). (4)
Let e
∗
(σ, β) be the solution to max
e
[βy(e, θ
L
) + (1 − β)y(e, θ
H
) − c(e, θ
H
)] ,
where σ = (θ
L
, θ
H
). Let the wage and utility associated with e
∗
(σ, β) be
w
∗
(σ, β) = βy(e
∗
(σ, β), θ
L
) + (1 −β)y(e
∗
(σ, β), θ
H
) and u
∗
(σ, β) = w
∗
(σ, β) −
c(e
∗
(σ, β), θ
H
)), respectively. Additionally, let e
∗
(σ, α) be the solution to
max
e
[(1 − α)y(e, θ
L
) + αy(e, θ
H
) − c(e, θ
L
)] . Finally, let the wage and utility
associated with e
∗
(σ, α) be w
∗
(σ, α) = (1−α)y(e
∗
(σ, α), θ
L
)+αy(e
∗
(σ, α), θ
H
)
and u
∗
(σ, α) = w
∗
(σ, α) − c(e
∗
(σ, α), θ
L
)).
There are two qualitatively different kinds of separating equilibria. If
workers are sufficiently similar in terms of productivity and cost of acquiring
5
There are always pooling equilibria where all types of workers choose the same educa-
tion level e. The firms’ posterior belief about a worker’s productive ability after observing
e must be the prior belief, µ(θ
H
|e) = λ, which in turn implies that the equilibrium wage
is w = λy(e, θ
H
) + (1 − λ)y(e, θ
L
).
8
education and the fraction of biased workers is not too high, separation re-
quires “overeducation” by the overconfident low-ability workers and unbiased
high-ability workers. This happens when underconfident high-ability workers
and unbiased low-ability workers prefer the wage w
∗
(σ, β) and the education
level e
∗
(σ, β) of overconfident low-ability workers and unbiased high-ability
workers, that is,
w
∗
(σ, α) − c(e
∗
(σ, α), θ
L
) < w
∗
(σ, β) − c(e
∗
(σ, β), θ
L
). (5)
When inequality (5) is satisfied, overconfident low-ability workers and unbi-
ased high-ability workers must choose an education level greater than e
∗
(σ, β)
to distinguish themselves from underconfident high-ability workers and un-
biased low-ability workers, i.e., e
HO
∈ [ˆe
HO
, ¯e
HO
], with ˆe
HO
> e
∗
(σ, β).
6
If workers are sufficiently different in terms of productivity and cost of
education or if the fraction of biased workers is sufficiently high, separation
does not require “overeducation” by the overconfident low-ability workers
and unbiased high-ability workers. In this case it is too expensive for un-
derconfident high-ability workers and unbiased low-ability workers to ac-
quire education e
∗
(σ, β), even if doing so would make firms believe that
they are overconfident low-ability workers or unbiased high-ability work-
ers and cause them to pay the wage w
∗
(σ, β), thus violating inequality (5):
w
∗
(σ, α) − c(e
∗
(σ, α), θ
L
) > w
∗
(σ, β) − c(e
∗
(σ, β), θ
L
).
3 Wage Compression
A key feature of many labor markets is the presence of wage compression
across skills (see Garibaldi, 2006, pp. 21). Wage compression refers to a
tendency of wages to be equalized across the skill distribution.
Campbell and Kamlani (1997) conducted a survey of 184 US firms and
found that pay differentials represented about one half of the productivity
differential between any two workers identical in all respects but productiv-
ity. Frank (1984a) examined wages and productivities of sales workers and
university professors, and found that the more productive workers were paid
6
Inequality (5) is satisfied if workers are sufficiently similar in terms of productivity
and cost of acquiring education and the fraction of biased workers is not too high. Indeed,
supposing y(e, θ) = θe and c(e, θ) = e
2
/2θ, then e
∗
(σ, α) = θ
L
(θ
L
+ αρ), e
∗
(σ, β) =
θ
H
(θ
H
−βρ), where ρ = θ
H
−θ
L
, and (5) becomes
θ
H
θ
L
< 2 −
θ
L
(θ
L
+αρ)
2
θ
H
(θ
H
−βρ)
2
.
9
less than their marginal product, while the least productive were paid more
than their marginal product.
Mourre (2005) provides evidence that there is a compressed wage dis-
tribution in Europe. Wage compression mainly occurs in continental and
southern countries, whilst no compression is detected in Anglo-Saxon coun-
tries and mixed evidence is found in Northern European countries. She also
finds that the compression of wages is not uniform across wage levels: there
is more wage compression at the lower end of the earnings distribution.
Wage compression has important consequences for labor market out-
comes. Lindquist (2005) shows that even low degrees of wage compres-
sion lead to large welfare losses from costly unemployment among low-skilled
workers. Acemoglu and Pischke (1999) demonstrate that wage compression
may encourage employers to offer and pay for general training. By making
the firm a residual claimant of productivity increases, a compressed wage
structure increases the willingness of firms to finance training of their em-
ployees.
Economic theory offers two main explanations for wage compression. The
first one identifies exogenous labor market frictions and institutions like mo-
bility costs, trade-unions, efficiency wages, wage floors, or any institution
which contributes to raise the reservation wage (e.g., generous unemploy-
ment benefits), as sources of wage compression. Freeman (1982) shows that
unionized firms appear to have less wage dispersion than non—unionized ones.
The second type of explanations identifies endogenous causes for wage
compression. Frank (1984b) shows that if workers value status, then those
who put a highest value on prestige will be willing to work for a wage that
is lower than their marginal product in return for having lower-level workers
around who in return are paid more than their marginal product. In contrast,
Lazear (1989) and Milgrom and Roberts (1990) argue that wage inequalities
may give rise to rent-seeking behavior within firms when workers change their
behavior with the aim of ensuring wage increases. Wage compression reduces
uncooperative behavior and may be efficient. Akerlof and Yellen (1990) posit
that large wage differentials between groups may be perceived as unfair and
lead to reduced effort.
In this section I start by showing that biased beliefs compress wages in
the sense that the wage spread with biased workers is smaller than the wage
spread with rational workers. After that I show that biased beliefs compress
the wages of unbiased workers, i.e., wage differences across unbiased workers
are smaller than differences in productivity.
10
Since the wage spread is the difference between the wages of high and low
education workers and these in turn depend on their education investments,
I must start by characterizing the impact of biased beliefs on education in-
vestments and wages. Proposition 1 characterizes the wage and education
levels of low education workers and applies to any separating equilibrium.
Proposition 1: In a separating equilibrium: (i) the education level of
underconfident high-ability workers and unbiased low-ability workers is at
least the first-best education level of low-ability workers—e
LU
= e
∗
(σ, α) ≥
e
∗
(θ
L
)—, (ii) the wage paid to underconfident high-ability workers and un-
biased low-ability workers is greater than the first-best wage of low-ability
workers—w(e
LU
) = w
∗
(σ, α) > w
∗
(θ
L
)—, and (iii) the utility of unbiased low-
ability workers is greater than the first-best utility of low-ability workers—
u(w(e
LU
), e
LU
, θ
L
) = u
∗
(σ, α) > u
∗
(θ
L
).
The intuition behind Proposition 1 is as follows. Underconfident high-
ability workers think (mistakenly) they have a high marginal cost of acquiring
education and, like unbiased low-ability workers, choose a low education level.
Firms observe this low education level but since they are unable to distinguish
each type of worker, they pay a wage that is equal to the average product of
underconfident high-ability workers and unbiased low-ability workers. This
implies that, for a given education level, the marginal benefit of education is
higher for underconfident high-ability workers and unbiased low-ability work-
ers than it would be for low-ability workers if everyone were rational. Since
the perceived marginal cost of education is the same, the education level of
underconfident high-ability workers and unbiased low-ability workers is at
least the first-best education level of low-ability workers. Thus, underconfi-
dent high-ability workers and unbiased low-ability workers are paid a higher
wage than the first-best wage of low-ability workers since they have a higher
average product and at least the same education. Finally, the utility of un-
biased low-ability workers is higher than the first-best utility of low-ability
workers because the positive direct effect of underconfidence on the wage is
larger than the negative effect of shifting the education level away from the
optimal one.
Proposition 2 characterizes the wage and education levels of high educa-
tion workers when the model has a unique separating equilibrium.
Proposition 2: If workers are sufficiently different in terms of productivity
and cost of acquiring education or the fraction of biased workers is sufficiently
high—inequality (5) is violated—, then: (i) the education level of overconfident
11
low-ability workers and unbiased high-ability workers is at most the first-
best education level of high-ability workers—e
HO
= e
∗
(σ, β) ≤ e
∗
(θ
H
)—, (ii)
the wage paid to overconfident low-ability workers and unbiased high-ability
workers is less than the first-best wage of high-ability workers—w(e
HO
) =
w
∗
(σ, β) < w
∗
(θ
H
)—, and (iii) the utility of unbiased high-ability workers is
smaller than the first-best utility of high-ability workers—u(w(e
HO
), e
HO
, θ
H
) =
u
∗
(σ, β) < u
∗
(θ
H
).
When workers are sufficiently different in terms of productivity and cost
of education or the fraction of biased workers is sufficiently high, there is
a unique separating equilibrium. Overconfident low-ability workers think
(mistakenly) they have a low marginal cost of acquiring education and, like
unbiased high-ability workers, choose a high education level. Firms observe
this high education level but since they are unable to distinguish each type of
worker, they pay a wage that is equal to the average product of overconfident
low-ability workers and unbiased high-ability workers. This implies that,
for a given education level, the marginal benefit of education is lower for
overconfident low-ability workers and unbiased high-ability workers than for
high-ability workers if everyone were rational. Since the perceived marginal
cost of education is the same, overconfident low-ability workers and unbiased
high-ability workers will, at most, acquire the first-best education level of
high-ability workers. Thus, overconfident low-ability workers and unbiased
high-ability workers are paid a lower wage than the first-best wage of high-
ability workers since they have a lower average product and at most the
same education. Finally, the utility of unbiased high-ability workers is lower
than the first-best utility of high-ability workers because overconfidence has
a negative direct effect on the wage and shifts the education level away from
the optimal one.
I will now characterize the set of equilibria wage and education levels
of high education workers when the model has a continuum of separating
equilibria.
Proposition 3: If workers are sufficiently similar in terms of productivity
and cost of acquiring education and the fraction of biased workers is suf-
ficiently small—inequality (5) is satisfied—, then: (i) the education level of
overconfident low-ability workers and unbiased high-ability workers belongs
to [ˆe
HO
, ¯e
HO
], with ˆe
HO
< ˆe
H
and ¯e
HO
< ¯e
H
, and (ii) the wage paid to
overconfident low-ability workers and unbiased high-ability workers belongs
to [ ˆw
HO
, ¯w
HO
], with ˆw
HO
< ˆw
H
and ¯w
HO
< ¯w
H
.
12
If workers are sufficiently similar in terms of productivity and cost of ed-
ucation and everyone is rational there is a continuum of separating equilibria
where high-ability workers overinvest in education to distinguish themselves
from low-ability workers.
7
In this case e
H
∈ [ˆe
H
, ¯e
H
] with ˆe
H
> e
∗
(θ
H
). These
various separating equilibria can be Pareto ranked. In all of them a high-
ability worker’s utility is y(e
H
, θ
H
) − c(e
H
, θ
H
), a low-ability worker’s utility
is u
∗
(θ
L
), and firms earn zero profits. However, a high-ability worker does
strictly better in equilibria where she gets a lower level of education (and a
lower wage) since this brings her utility closer to the complete information
utility u
∗
(θ
H
). Thus, the separating equilibrium in which the high-ability
worker gets education level ˆe
H
Pareto dominates all others and is called the
least cost separating equilibrium. The separating equilibrium in which the
high-ability worker gets education level ¯e
H
is called the most cost separating
equilibrium.
Proposition 3 shows that if inequality (5) is satisfied, then the educa-
tion and wage of overconfident low-ability workers and unbiased high-ability
workers in the least (most) cost separating equilibrium with biased workers
is smaller than the education and wage, respectively, of high-ability workers
in the least (most) cost separating equilibrium with rational workers. Thus,
the set of equilibria education-wage levels of high-ability workers is higher
than (in the strong set order sense) the set of equilibria education-wage levels
of overconfident low-ability workers and unbiased high-ability workers.
8
The intuition behind the result is as follows. In the least cost separating
equilibrium with rational workers, low-ability workers are indifferent between
getting their education-wage contract and that of high-ability workers, i.e.,
u
∗
(θ
L
) = u(ˆe
H
, θ
L
). Similarly, in the least cost separating equilibrium with
biased workers, underconfident high-ability workers and unbiased low-ability
workers are indifferent between getting their education-wage contract and
that of overconfident low-ability workers and unbiased high-ability workers,
i.e., u
∗
(σ, α) = u(ˆe
HO
, θ
L
).
We know from Proposition 1 part (iii) that the utility of underconfident
high-ability workers and unbiased low-ability workers is higher than the first-
7
In this case inequality (5) is satisfied when α = β = 0, that is, w
∗
(θ
L
)−c(e
∗
(θ
L
), θ
L
) <
w
∗
(θ
H
) − c(e
∗
(θ
H
, θ
L
).
8
A set M ⊆ R is as high as another set N ⊆ R (in the strong set order), written
M
S
N, if for every x ∈ M and y ∈ N, y ≥ x implies both x ∈ M ∩ N and y ∈ M ∩ N.
A set M is higher than N, written M ≻
S
N if M is as high as N but N is not as high as
M.
13
best utility of a low-ability worker, i.e., u
∗
(σ, α) > u
∗
(θ
L
). This implies that,
in the least-cost separating equilibrium with biased workers, the utility of
underconfident high-ability workers and unbiased low-ability workers of the
education-wage contract (ˆe
HO
, ˆw
HO
) is higher than the utility of (ˆe
H
, ˆw
H
),
i.e., u(ˆe
HO
, θ
L
) > u(ˆe
H
, θ
L
). But this can only be true if ˆe
HO
is lower than
ˆe
H
, i.e., overconfident low-ability workers and unbiased high-ability workers
choose a lower education level than high-ability workers would if everyone
were rational.
The wage of overconfident low-ability workers and unbiased high-ability
workers in the least cost separating equilibrium with biased workers is smaller
than the wage of high-ability workers in the least cost separating equilibrium
with rational workers because the education and productive ability of over-
confident low-ability workers and unbiased high-ability workers are smaller
than those of high-ability workers.
We are now ready to summarize the impact of workers’ biased beliefs on
the wage spread.
Corollary 1:
(i) If workers are sufficiently different in terms of productivity and cost of
education—inequality (5) is violated when α = β = 0—, then the equilibrium
wage spread with biased workers is smaller than that with rational workers,
i.e., △w
∗
(α, β) < △w
∗
;
(ii) If workers are sufficiently similar in terms of productivity and cost of
education and the fraction of biased workers is not too high—inequality (5) is
satisfied—, then the wage spread in the least (most) cost separating equilibrium
with biased workers is smaller than the wage spread in the least (most) cost
separating equilibrium with rational workers, i.e., △ˆw
B
< △ˆw
R
( △ ¯w
B
<
△¯w
R
).
The intuition behind Corollary 1 is as follows. The presence of under-
confident high-ability workers in the low-education group implies that the
average product of a worker in that group is higher than the product of a
low-ability worker. So, for the same education level, firms must pay a higher
wage to workers in the low-education group than they would to low-ability
workers if everyone were rational. This implies that the marginal benefit of
education is higher for underconfident high-ability workers and unbiased low-
ability workers than for low-ability workers if everyone were rational. Given
that the perceived marginal cost of education is the same, underconfident
high-ability workers and unbiased low-ability workers will acquire at least
14
the first-best education level of low-ability workers. Since underconfident
high-ability workers and unbiased low-ability workers have a higher aver-
age product and have acquired at least the education level that low-ability
workers would acquire if everyone were rational, they must be paid a higher
wage.
If workers are sufficiently different in terms of productivity and cost of ed-
ucation, the model has a unique separating equilibrium. In this equilibrium,
workers in the high-education group do not need to overinvest in educa-
tion. The presence of overconfident low-ability workers in the high-education
group implies that the average product of a worker in that group is lower
than the product of a high-ability worker would be if everyone were rational.
So, for the same education level, firms must pay a lower wage to workers in
the high-education group than they would to high-ability workers if everyone
were rational. This implies that the marginal benefit of education is lower
for overconfident low-ability workers and unbiased high-ability workers than
it would be for high-ability workers if everyone were rational. Given that the
perceived marginal cost of education is the same, overconfident low-ability
workers and unbiased high-ability workers will acquire at most the first-best
education level of high-ability workers. Since overconfident low-ability work-
ers and unbiased high-ability workers have a lower average product and have
acquired at most the education level high-ability workers would acquire if
everyone were rational, they must be paid a lower wage. Hence, when work-
ers are sufficiently different in terms of productivity and cost of education,
the equilibrium wage spread with biased workers is smaller than the one with
rational workers.
If workers are sufficiently similar in terms of productivity and cost of
education and the fraction of biased workers is not too high, the model has
a continuum of separating equilibria where workers in the high-education
group overinvest in education to distinguish themselves from those in the
low-education group. In the least cost separating equilibrium, the incentive
compatibility condition of underconfident high-ability workers and unbiased
low-ability workers is binding. This can only happen if overconfident low-
ability workers and unbiased high-ability workers acquire less education than
high-ability workers would if everyone were rational. The lower education
and lower average product imply that overconfident low-ability workers and
unbiased high-ability workers are paid a lower wage than high-ability workers
would be if everyone were rational. Hence, the wage spread in the least cost
separating equilibrium with biased workers is smaller than that in the least
15
cost separating equilibrium with rational workers.
9
Corollary 1 shows that biased beliefs compress wages in the sense that
the wage spread with biased workers is smaller than the wage spread with
rational workers. When all workers are rational (κ = ν = 0) workers’ wages
are equal to their productivity, i.e., w
H
= y(e
H
, θ
H
) and w
L
= y(e
L
, θ
L
). In
the model with biased workers (κ, ν > 0) we have four groups of workers
with different productivities. Unbiased high-ability workers have productiv-
ity y(e
HO
, θ
H
), overconfident low-ability workers y(e
HO
, θ
L
), underconfident
high-ability workers y(e
LU
, θ
H
), and unbiased low-ability workers y(e
LU
, θ
L
).
The wage spread across high and low paid workers (or equivalently, high and
low education workers) just equals the difference in average productivities
across these groups.
The wage spread with biased workers is smaller than that with ratio-
nal workers because the existence of overconfident low-ability workers lowers
the average productivity of the high-education group and the existence of
underconfident high-ability workers raises the average productivity of the
low-education group. This is a weak form of wage compression because it
says nothing about differences in wages across workers relative to differences
in productivity.
The existence of workers with biased beliefs compresses the wages of
unbiased workers relative to their productivity. This happens because the
wage of unbiased high-ability workers is smaller than productivity, w
HO
=
βy(e
HO
, θ
L
) + (1 −β)y(e
HO
, θ
H
) < y(e
HO
, θ
H
), whereas the wage of unbiased
low-ability workers is greater than productivity, w
LU
= (1 − α)y(e
LU
, θ
L
) +
αy(e
LU
, θ
H
) > y(e
LU
, θ
L
). Hence, the wage spread across unbiased workers
is less than the productivity spread: w
HO
− w
LU
< y(e
HO
, θ
H
) − y(e
LU
, θ
L
).
The model also predicts that the wage spread across biased workers, i.e.,
the difference in productivities of overconfident low-ability and underconfi-
dent high-ability workers, is greater than the productivity spread: w
HO
−
w
LU
> y(e
HO
, θ
L
) − y(e
LU
, θ
H
). This happens because the wage of overcon-
fident low-ability workers is greater than productivity, w
HO
> y(e
HO
, θ
L
),
whereas the wage of underconfident high-ability workers is smaller than pro-
ductivity, w
LU
< y(e
LU
, θ
H
). This is one sense in which wage compression
does not hold in this model.
9
In the most cost separating equilibrium the intuition is similar with the difference
that it is the incentive compatibility constraint of overconfident low-ability workers and
unbiased high-ability workers that binds.
16
4 Gender Pay Gap
Empirical evidence shows that, on average, women are paid less than men.
This is known as the gender pay gap.
10
The gender pay gap may be statis-
tically decomposed into two components: one due to gender differences in
measured characteristics, and the other due to “unexplained” and potentially
due to discrimination.
Various explanations have been offered to justify the existence of a gender
pay gap. The gender pay gap may be due to differences in human capital of
men and women (see Mincer and Polachek, 1974). This is consistent with
empirical evidence which shows that, on average, men acquire more college
education than women and men have more full-time labor market experience
than women. According to Eckel and Grossman (2003) the gap might be
due to gender differences in risk aversion. Experimental studies have shown
that women are less willing than men to take risks or to enter a competitive
environment such as a tournament (see Niederle and Vesterlund, 2007).
Labor market discrimination may also affect women’s wages. Becker
(1971) shows how a preference for men over women, either on the part of
employers, employees or costumers, can lead to women being paid less than
men. Rothschild and Stiglitz (1982), explain discrimination as arising due
to differences in the noise of productivity signals across gender. If output
depends upon matching a worker’s quality type with a job and women have
noisier signals than men, then their quality is more difficult to ascertain and
they should be paid a lower wage.
In this section I show that gender differences in self-confidence can con-
tribute to the gender pay gap. I do not pretend to capture the “full picture”
about the gender pay gap, but rather show the possibility of a link between
psychological differences between men and women and labor market out-
comes.
11
10
In the US, the gender pay gap is measured as the ratio of female to male median
earnings among full-time, year-round workers. According to the Bureau of Labor Statistics
(2010), women who worked full time in wage and salary jobs had median weekly earnings
of $657 in 2009. This represented 80 percent of men’s median weekly earnings ($819).
At EU level, the gender pay gap is defined as the relative difference in the average gross
hourly earnings of women and men within the economy as a whole. Eurostat (2011) found
a gender pay gap of 17.5 percent on average in the 27 EU Member States in 2009.
11
Waldman (1994) provides an evolutionary explanation for gender differences in self-
confidence. He considers an environment where individuals compete in wealth accumula-
tion, utility depends on wealth and disutility from effort, and males can overestimate or
17
Gender differences in self-confidence have been extensively documented
in a variety of settings. Numerous psychology studies purport to show that
men are more (over-)confident than women (see references in Barber and
Odean, 2001). For example, testing for the perception of competence on
various tasks, Beyer (1990) finds that men tend either to be accurate or to
over-estimate their ability, whereas women tend to be either accurate or to
under-estimate their ability.
Paglin and Rufolo (1990) report that the propensity of women to choose
less mathematical college majors can account for the entire gender wage
differential among college graduates. Correll (2001) finds that males are
more likely to perceive that they are good at math than are those females
with equal math grades and test scores. She also finds that self-assessments
of task competence influence career-relevant decisions, even when controlling
for commonly accepted measures of ability. For males and females, the higher
they rate their mathematical competence, the greater the odds that they will
continue on the path leading to careers in the quantitative professions.
Bengtsson, Persson and Willenhag (2005) use the structure of the Eco-
nomics I exam at Stockholm University to look for gender differences in
self-confidence. By answering an extra, optional question, the students can
aim for a higher mark. They find that there are striking differences between
male and female students in terms of choices and outcomes. They find a
clear gender difference in that male students are more inclined than female
students to take this opportunity. They also find that female students are
slightly better at passing the exam, but male students are much better at
getting the highest grade.
To study the impact of gender differences in self-confidence on the gen-
der pay gap I assume that labor supply is composed of males and females.
Let λ denote the proportion of high-ability workers in the male and female
populations. Thus, before any educational investments are made, men and
women are equally productive.
Among the low-ability males, proportion κ
m
is overconfident and, among
the high-ability males, proportion ν
m
is underconfident. Among the low-
ability females, proportion κ
f
is overconfident and, among the high-ability
females, proportion ν
f
is underconfident. Firms know λ, κ
m
, ν
m
, κ
f
and ν
f
.
underestimate their own abilities. He finds that if there is sexual inheritance of the traits
disutility from effort and perception of ability, then males exhibiting both disutility from
effort and overestimation of abilities can be an evolutionary stable strategy.
18
The mean wage paid to males is equal to
w
m
= (1 − λ − κ
m
+ ν
m
)w
LU
m
+ (λ + κ
m
− ν
m
)w
HO
m
. (6)
and mean wage paid to females to
w
f
= (1 − λ − κ
f
+ ν
f
)w
LU
f
+ (λ + κ
f
− ν
f
)w
HO
f
. (7)
If all men and women have correct beliefs there is no gender pay gap since
ν
m
= κ
f
= κ
m
= ν
f
= 0 implies w
m
= w
f
.
To analyze the impact of gender differences in self-confidence on the gen-
der pay gap I assume y(e, θ) = e + θ and c(e, θ) = e
2
/2θ. In this case edu-
cation and productive ability are independent since y
eθ
= 0. I also assume
some males are overconfident—κ
m
∈ (0, 1−λ]—and no male is underconfident—
ν
m
= 0. Finally, I assume some females are underconfident—ν
f
∈ (0, λ]—and
no female is overconfident—κ
f
= 0.
Proposition 4: Let y(e, θ) = e + θ, c(e, θ) = e
2
/2θ, κ
m
∈ (0, 1 − λ], ν
f
∈
(0, λ], and ν
m
= κ
f
= 0.
(i) If workers are sufficiently different in terms of productivity and cost of
education, i.e.,
θ
H
θ
L
> 3 − 2 min {α
f
, β
m
}, then w
∗
f
< w
∗
< w
∗
m
;
(ii) If workers are sufficiently similar in terms of productivity and cost of
education, i.e.,
θ
H
θ
L
< 3 − 2 max {α
f
, β
m
}, and λ ≤
2
3
, then ˆw
f
≤ ˆw < ˆw
m
;
(ii) If
θ
H
θ
L
< 3 − 2 max {α
f
, β
m
}, λ >
2
3
, and male overconfident is high
relative to female underconfidence, i.e.,
κ
m
ν
f
>
3λ−2
1−λ
, then ˆw < ˆw
f
< ˆw
m
;
(iv) If
θ
H
θ
L
< 3 − 2 max {α
f
, β
m
}, λ >
2
3
, and male overconfidence is low
relative to female underconfidence, i.e.,
κ
m
ν
f
<
3λ−2
1−λ
, then ˆw < ˆw
m
< ˆw
f
.
Part (i) of Proposition 4 characterizes the impact of gender differences
in self-confidence on the gender pay gap when workers are sufficiently dif-
ferent in terms of productivity and cost of education. It shows that if some
males are overconfident and some females are underconfident then males will,
on average, earn more than females. The intuition behind this result is as
follows.
Male overconfidence has two effects on the mean wage of men. First, over-
confident low-ability men believe they have a low marginal cost of education
and so acquire a high education level. Since education increases productivity,
the higher education level of overconfident low-ability men implies that firms
pay them a higher wage than the wage firms would pay to low-ability work-
ers if everyone were rational. Second, unbiased high-ability men acquire less
19
education than they would if everyone were rational because firms cannot
distinguish between them and overconfident low-ability men and therefore
pay them their average productivity. So, unbiased high-ability men are paid
a lower wage than would be paid to high-ability workers if everyone were
rational. The increase in the wage of overconfident low-ability men is of
first-order whereas the decrease in the wage of unbiased high-ability men is
of second-order and therefore the mean wage of males is greater than it would
be if everyone were rational.
Female underconfidence has two effects on the mean wage of women.
First, underconfident high-ability women believe they have high marginal
cost of education and so acquire a low education level. Since education in-
creases productivity, the lower education level of underconfident high-ability
women implies that firms pay them a lower wage than the wage firms would
pay to high-ability workers if everyone were rational. Second, unbiased low-
ability women acquire more education than they would if everyone were ratio-
nal because firms cannot distinguish between them and underconfident high-
ability women and therefore pay them their average productivity. Hence,
unbiased low-ability women are paid a higher wage than would be paid to
low-ability workers if everyone were rational. The decrease in the wage of
underconfident high-ability women is of first-order whereas the increase in
the wage of unbiased low-ability women is of second-order and therefore the
mean wage of females is lower than it would be if everyone were rational.
Parts (ii)-(iv) of Proposition 4 refer to the case when workers are suf-
ficiently similar in terms of productivity and cost of education.
12
Part (ii)
shows that if some males are overconfident, some females underconfident,
and the fraction of high-ability workers is at most 2/3, then males will, on
average, earn more than females. Part (iii) shows that if λ > 2/3 and male
overconfidence is high compared to female underconfidence, then males will
earn, on average, more than females. Finally, part (iv) shows that if λ > 2/3
and male overconfidence is low compared to female underconfidence, then
females will earn, on average, more than males.
As before, male overconfidence raises the wage of overconfident low-ability
males in relation to the wage low-ability workers would get if everyone were
12
Cho and Kreps’ (1987) intuitive criterion selects the least cost separating equilibrium
as the unique prediction of Spence’s signaling model. Therefore, when workers are suf-
ficiently similar in terms of productivity and cost of education, I focus on the impact of
gender differences in self-confidence on the least cost separating equilibrium mean wages
paid to males and to females, ˆw
m
and ˆw
f
, respectively.
20
rational and lowers the wage of unbiased high-ability males in relation to the
wage high-ability workers would get if everyone were rational. The first effect
is of first-order whereas the second effect is of second-order and therefore the
mean wage of males is greater than it would be if everyone were rational.
Also, female overconfidence lowers the wage of underconfident high-ability
females in relation to the wage high-ability workers would get if everyone
were rational and raises the wage of unbiased low-ability females in relation
to the wage low-ability workers would get if everyone were rational. However,
when workers are sufficiently similar in terms of productivity and cost of
education, female underconfidence has an additional effect on female wages.
In the least cost separating equilibrium, unbiased low-ability females must be
indifferent between acquiring their low education level and the high education
level acquired by unbiased high-ability women. Since female underconfidence
raises the wage of unbiased low-ability females in relation to the wage low-
ability workers would get if everyone were rational, unbiased high-ability
women must overinvest more in education than high-ability workers would if
everyone were rational. The higher (over)investment in education increases
the productivity of unbiased high-ability females and, therefore, their wage.
When the fraction of high-ability workers is at most 2/3, the mean wage
of women is at most the mean wage workers would get if everyone were ratio-
nal because the decrease in the wage of underconfident high-ability females
dominates the increase in the wages of unbiased low- and high-ability females.
When λ > 2/3 and male overconfidence is high compared to female under-
confidence, the mean wage of males raises by more than the mean wage of
females relative to the mean wage workers would get if everyone were rational.
Hence, males will, on average, earn more than females. When λ > 2/3 and
male overconfidence is low compared to female underconfidence, the mean
wage of males raises by less than the mean wage of females relative to the
mean wage workers would get if everyone were rational. Hence, females will,
on average, earn more than males.
My next result characterizes the impact of gender differences on the gen-
der pay gap when y(e, θ) = eθ and c(e, θ) = e
2
/2θ. In this case education
and productive ability are complements since y
eθ
> 0.
Proposition 5: Let y(e, θ) = eθ, c(e, θ) = e
2
/2θ, κ
m
∈ (0, 1 − λ], ν
f
∈
(0, λ], ν
m
= κ
f
= 0, µ
f
=
(θ
L
+α
f
ρ)
2
θ
2
H
, µ
m
=
θ
2
L
(θ
H
−β
m
ρ)
2
, φ =
θ
2
H
−θ
2
L
+θ
L
θ
H
θ
2
H
−θ
2
L
−θ
L
θ
H
, and
Φ =
ρ
√
θ
2
H
−θ
2
L
+θ
2
H
+θ
L
θ
H
+
λ
1−λ
θ
2
L
ρ
√
θ
2
H
−θ
2
L
−(θ
2
L
+θ
L
θ
H
−θ
2
H
)
.
21
(i) If 2 −
θ
L
θ
H
min {µ
f
, µ
m
} <
θ
H
θ
L
≤
1+
√
5
2
, then ˆw
f
< ˆw ≤ ˆw
m
;
(ii) If
θ
H
θ
L
> max
2 −
θ
L
θ
H
min {µ
f
, µ
m
},
1+
√
5
2
and
κ
m
ν
f
< φ, then w
∗
f
<
w
∗
m
< w
∗
;
(iii) If
θ
H
θ
L
> max
2 −
θ
L
θ
H
min {µ
f
, µ
m
},
1+
√
5
2
and
κ
m
ν
f
> φ, then w
∗
m
<
w
∗
f
< w
∗
;
(iv) If
θ
H
θ
L
< min
√
2, 2 −
θ
L
θ
H
max {µ
f
, µ
m
}
, then ˆw
f
≤ ˆw < ˆw
m
;
(v) If
√
2 <
θ
H
θ
L
< 2 −
θ
L
θ
H
max {µ
f
, µ
m
} and
κ
m
ν
f
< Φ, then ˆw
f
< ˆw
m
< ˆw;
(vi) If
√
2 <
θ
H
θ
L
< 2 −
θ
L
θ
H
max {µ
f
, µ
m
} and
κ
m
ν
f
> Φ, then ˆw
m
< ˆw
f
< ˆw.
Parts (i)-(iii) of Proposition 5 characterize the impact of gender differ-
ences in self-confidence on the gender pay gap when workers are sufficiently
different in terms of productivity and cost of education. Parts (iv)-(vi) refer
to the case when workers are sufficiently similar in terms of productivity and
cost of education.
Proposition 5 shows that the main qualitative findings in Proposition
4 also apply when education and productive ability are complements: for
most parameter configurations, gender differences in self-confidence imply
that males will, on average, earn more than females.
The main qualitative difference between the two propositions is that part
(iii) of Proposition 5 shows that if workers are sufficiently different in terms of
productivity and cost of education, and male overconfidence is high relative
to female underconfidence, then females might earn more, on average, than
males.
13
This model only explains a gender pay gap due to measured character-
istics: differences in educational investments of males and females. The as-
sumption that education raises productivity, y
e
> 0, is critical to this result.
If education has no direct effect on productivity, y
e
= 0, then biased beliefs
do not lead males’ educational investments to differ from those of females
and there is no gender pay gap.
Gender differentials in educational investments are well documented. In
the US women have recently surpassed men in terms of completing secondary
and post-secondary education.
14
Gender differences in field of study compo-
13
To see this let φ(r) =
r
2
−1+r
r
2
−1−r
where r =
θ
H
θ
L
. The inequality
κ
m
ν
f
> φ(r) is only satisfied
when the proportion of overconfident males is high relative to that of underconfident
females since φ(r) > 1 for all r > 1 and φ(2) = 5.
14
In 2007, the Current Population Survey (2007) estimated that 18,423,000 males ages
22
sition are larger (more unequal) than those for college attainment. While
women are now more likely to complete a college degree than men, the dis-
tribution of college majors among college graduates remains unequal with
women about 2/3 as likely as men to major in science, mathematics, engineer-
ing, business or economics. In contrast, women are much more likely than
men to major in humanities, social sciences and teaching (see Gemici and
Wiswall, 2011). My model shows how gender differences in self-confidence
can contribute to gender differences in educational investments across fields
of study which in turn lead to the gender pay gap.
5 Welfare Impact of Biased Beliefs
In this section I characterize the impact of biased beliefs on welfare. To do
that I compare welfare levels with biased and rational workers. In both cases
firms make zero profits so welfare is equal to the weighted average of the
utilities of each group of workers.
To evaluate the utility of a biased worker I take the perspective of an
outside observer who knows the worker’s actual marginal cost of acquiring
education.
15
Hence, welfare with biased workers is
W
B
= (λ − ν)u(w(e
HO
), e
HO
, θ
H
) + νu(w(e
LU
), e
LU
, θ
H
)
+ κu(w(e
HO
), e
HO
, θ
L
) + (1 − λ − κ)u(w(e
LU
), e
LU
, θ
L
). (8)
When all workers are unbiased, Spence’s (1973) model shows that if the
two groups of workers are sufficiently different, then there is a unique sepa-
rating equilibrium where investments in education are the efficient ones and
the outcome is as if there was perfect information in the market place. Thus,
the existence of workers with biased beliefs acts as a distortion which lowers
welfare when workers are sufficiently different.
Let us then focus on the interesting case where workers are sufficiently
similar in terms of productivity and cost of education. One of the main results
eighteen and over held a bachelor’s degree, while 20,501,000 females ages eighteen and over
held one. Fewer males held a master’s degree, as well: 6,472,000 males had received one
and 7,283,000 females had. However, more men held professional and doctoral degrees
than women. 2,033,000 males held professional degrees and 1,079,000 females did and
1,678,000 males had received a doctoral degree, while 817,000 females had.
15
This is the “hardest” test. An alternative would be to measure the utility of biased
workers according to their perceived utility function.
23
of Spence’s (1973) model is that in this case private information about ability
reduces welfare. This happens because high-ability workers must overinvest
in education (by comparison with the complete information education level)
to distinguish themselves from low-ability workers.
My first welfare result shows that if workers are sufficiently similar in
terms of productivity and cost of education and all biased workers are over-
confident, then biased beliefs reduce welfare.
Proposition 6: If all biased workers are overconfident and workers are
sufficiently similar in terms of productivity and cost of acquiring education—<