Skill-biased Technological Change, Fertility Choice and Gender Inequality

Henry Tam*

Abstract

This paper develops a model to explain why the female-male earnings gap keeps narrowing in recent

decades, despite the general trend of widening earnings inequality ever since the 80s among many developed

countries. The model integrates the theory of skill-biased technological change (SBTC) with the theory of

households’ sexual division of labor and fertility choice into a unified framework to shed light on the wage

inequality and employment patterns between the genders in the last two decades. Using a Mincerian earnings

function, the model finds that the combined effects of SBTC on the education premium and the experience

premium affect fertility choice, whereas the differential impacts of SBTC on the education premium and the

experience premium determine the time allocation toward schooling and labor participation given fertility choice.

Because the fertility choice affects female and male education attainment and average experience asymmetrically,

gender gaps in education attainment and experience narrow, which contribute to the continued decline of gender

earnings inequality. The model can also explain several other labor market patterns between the genders in the last

two decades, including: the rise in female labor participation in the midst of slightly declining male labor

participation and the narrowing of the gender gaps in schooling, experience and measured experience premium.

JEL classification: E24, J13, J16, J22, J24, J31, O33

Keywords: skill-biased technological change; gender inequality; fertility choice; sexual division of labor; female

and male labor participation; education and experience premiums

*York University and Texas A&M University. Visiting Professor, SASIT Economics Program, York

University, Toronto, ON, Canada M3J 1P3; Assistant Professor, Department of Economics, Texas A&M

University, College Station, TX 77843-4228, USA. Contact information: TEL 1-416-736-2100 x30112; EMAIL

thenry@yorku.ca.

2

1. Introduction

In the U.S., as well as in many OECD countries, although overall wage dispersion decreased in

the 60s and 70s, the 80s and 90s witness a reversal in the earnings inequality trend.1 In particular, the

wage differential between skilled and unskilled labor has widened. However, while many demographic

groups that are traditionally relatively unskilled therefore suffer from escalating inequality, women, who

are traditionally among such demographic groups, are largely unaffected by the recent events. Despite

the general trend of widening inequality, the earnings gap between male and female keeps narrowing.

In light of the rising earnings dispersion since the 80s, empirical research on changes in wage

inequality “has literally exploded in the past decade” (Katz and Autor 2000). Theoretical models have

also emerged since the late 90s and have mainly focused on skill-biased technological change (SBTC) as

the driving force behind such rising wage inequality.2 The focus on SBTC prevails because SBTC could

not only account for the overall increase in wage dispersion and the increase in skill premiums, but also

the increase in skill intensity in almost all sectors.3,4 Since the first canonical models by Acemoglu

(1998), Aghion and Howitt (1998 Ch.9) and Caselli (1999), the theoretical literature in SBTC has

burgeoned in various directions.5 On wage inequality, the theoretical literature has since been pre-

1 Key studies documenting the recent evolution of wage distribution in the U.S. include Davis and Haltiwanger (1991), Bound and Johnson (1992), Katz and Murphy (1992), Levy and Murnane (1992), Murphy and Welch (1992), Juhn et al (1993), Karoly (1993) and Gottschalk (1997). A non-exhaustive list of studies for OECD countries includes Davis (1992), Freeman and Katz (1994), Gottschalk and Smeeding (1997), Berman et al (1998) and Katz and Autor (2000). 2 Three prominent alternative explanations that have been offered as causes of the overall pattern of increasing wage inequality and the rise in skill premiums are trade liberalization, deindustrialization and changing labour institutions. However, these alternatives are incompatible with the observation that skill intensity increased in almost all sectors. 3 Berman et al (1994), Doms et al (1997) Machin (1996) Autor et al (1998) and Berman et al (1998) documented that skill intensity increased in almost all sectors, including both traded goods and non-traded goods sectors , in various OECD countries since the 80s. 4 In order for both the skill premiums and the skill intensity to rise, the shift in demand for skill due to the technological advance since the 80s has to be greater than the shift in the supply of skill. This could happen either because the rate of increase in the supply of skill slowed down (Katz and Murphy 1992; Topel 1997; Lloyd-Ellis 1999; Card and Lemieux 2001) or because the rate of increase in the demand for skill accelerated. However, Krusell et al (2000) provided a convincing piece of evidence using calibration method that the rise of the college premium could largely be attributed to an increase in the rate of capital-embodied skill-biased technological change. 5 Outside of the literature on wage inequality, the development of the theory of SBTC has also been prolific in the growth literature: to understand disparity in productivity and economic growth experiences across different countries in recent decades (Acemoglu and Zilibotti 2001; Thoenig and Verdier 2003), as well as to shed light on the episode of productivity

3

occupied with whether the theory of SBTC could also address some additional stylized facts concerning

the labor market. These stylized facts include the increase in wage dispersion within skill groups, the

decline in real wages for low-skill workers and the change in workplace organization.6 Neither the

increase in within-group wage dispersion, nor the decline in wages of low-skill workers, is a natural

prediction of the theory of SBTC. As a result, many extensions of the first models are developed to shed

light on them.7 Several models have also been put forth to understand how SBTC could affect changes

in firms’ organizational forms, which ramify the pure technological effect on wage inequality.8

The anomaly of the declining gender wage inequality amidst the general trend of increasing

wage dispersion, however, has so far been neglected in the flourishing theoretical literature in SBTC. No

theoretical model has yet been developed to understand why SBTC does not give rise to widening

gender inequality.9 The current research contributes to bridge such an important gap.

The puzzle posed by the continued decline in gender inequality alongside with rising level of

wage inequality in general is multi-layered. On the surface, the seeming contradiction is that, since

women on average have less education and experience than men, the increase in education premium and

experience premium in the past two decades due to SBTC would therefore cause the gender pay gap to

widen, not to narrow. At first glance, to resolve such an apparent paradox is not difficult. One solution

would be that some outside factors such as reduction in discrimination were more than sufficient to

counterbalance the adverse effects of SBTC on gender inequality. However, the timing of such events

slowdown among developed countries since the 70s (Hornstein and Krusell 1996; Greenwood and Yorukoglu 1997; Acemoglu 1998; Galor and Moav 2000). 6 Juhn et al (1993) documented that only about one-third of overall wage variation was due to between-group wage differential whereas about two-third was attributed to within-group wage dispersion, as well as the decline in real wages for low-skill workers. Bresnahan (1999), Caroli and van Reenen (2001), Bresnahan et al (2002) and Autor et al (2003) documented that firm organization has become less hierarchical and increasingly focused on team work since the 80s. 7 Galor and Moav (2000), Gould et al (2001), Aghion et al (2002) and Violante (2002) developed models to explain such increase in within-group wage dispersion. Beaudry and Green (1998), Acemoglu (1999), Caselli (1999), Galor and Moav (2000) and Acemoglu et al (2001) developed models to understand the decline in wages of low-skill workers. 8 These include Kremer and Maskin (1996), Acemoglu (1999) and Thesmar and Thoenig (2000). 9 For instance, there is simply no mention of any theoretical model that purports to explain such anomaly in the three prominent surveys of the theoretical literature on the relation between SBTC and wage inequality (Aghion et al 1999; Acemoglu 2002a; Aghion 2002).

4

did not quite match the trend in gender inequality. In the U.S., for example, gender pay gap was

narrowing from the beginning of the twentieth century until 1960, but was almost constant during the

60s and 70s, and then continued to decline in the 80s and 90s from its long-run trend. The expansion of

women’s movement and the passage of major anti-discrimination legislation, however, took place

during the 60s and 70s, exactly when the gender gap failed to narrow.10 Another trivial hypothesis would

be that technological change since the 80s has been biased more toward female skills than male skills in

nature, but the empirical bases for such a premise would be hard to verify.

Instead, the current paper makes the following argument: to explain the continued decline in

gender inequality since the 80s, one has to understand the impacts of SBTC in a framework with fertility

choice and sexual division of labor.

That SBTC would widen the gender gap in earnings is based on the presumption that women’s

relative levels of education and experience have remained unchanged. If women’s levels of education

and experience have increased relative to men’s, SBTC could cause gender gap to narrow. Although the

theoretical literature has so far been silent about the underlying causes for the continued decline in

gender earnings inequality since the 80s, several empirical studies (e.g. O’Neill and Polachek 1993;

Blau and Kahn 1997, 2000; Blau 1998) have indeed documented that the contributing components of

such decline include the narrowing of gender gaps in education and in experience in the last two

decades. At a deeper level, therefore, the question is: could SBTC lead to the narrowing of gender

education and experience gaps in theory and could such narrowing of gender gaps in education and

experience more than compensate for the aforementioned widening effect of SBTC on the gender pay

gap? The current research proposes that the answer is yes. However, the “genderless” approach in the

recent burgeoning theoretical literature on SBTC is simply not appropriate to analyze gender

differences. To this end, the current paper develops an original theoretical framework to bring into the

10 For comparison, we could also juxtapose the case of black-white wage convergence in the 60s and 70s, which coincided with the passage of major anti-discrimination acts (e.g. Card and Krueger 1992), and the lack of such convergence since the 80s, which coincided with the IT revolution (e.g. Juhn et al 1991; Bound and Freeman 1992).

5

theory of SBTC the additional ingredient: the theory of sexual division of labor and households’ lifetime

allocation problem including fertility choice.

The first step of the present model involves building a theory of sexual division of labor within

households to determine the lifetime allocation decisions of the female and male parents including time

used to rear children. The model thus departs from most models of fertility choice that make use of the

argument of quantity versus quality of children in a “genderless” household setting to understand how

fertility rate correlates with the level of economic development.11 Instead, this model builds on the

specialized role of women in child-rearing and how changes in the relative wages of women affect

fertility decisions. In this respect, the modeling strategy is similar to Galor and Weil (1996) and Zhang

et al (1999). There are two major differences. One is that while Galor and Weil (1996) has an earnings

function in which wages increases linearly with level of schooling, the present model adopts a Mincerian

earnings function in which log wages increase with the quadratics of schooling and experience.12 The

implications on fertility choice is that while Galor and Weil (1996) studies how the price of having

children affects fertility choice in a linear pricing framework, the present model studies such effect in a

non-linear pricing framework. Another important difference is that both Galor and Weil (1996) and

Zhang et al (1999) assume male has absolute advantage in certain production respects (in physical

abilities for Galor and Weil 1996 and in initial endowment in mental abilities for Zhang et al 1999). The

present model, on the other hand, makes the assumption that male and female do not differ in any

productive abilities, but female has comparative advantage in rearing children. Like its predecessors,

however, the present model demonstrates, as Becker (1985) shows, that tiny difference in gender

endowment lead to specialization and large differences in earnings. In the model, the female parent will

bear the whole responsibility of rearing children, which has large time cost. Her time over her lifespan 11 The literature is voluminous. Seminal papers include Becker and Barro (1988), Barro and Becker (1989), Becker et al (1990), Tamura (1996, 2002), Galor and Weil (2000), Hansen and Prescott (2002) and Lucas (2002). 12 The recent empirical growth literature also uses the Mincerian earnings function in growth accounting regressions to shed light on why previous research (e.g. Benhabib and Spiegel 1994), which use earnings function in which wages increase linearly with schooling, could not find any effect of changes in human capital on economic growth, but more current research that uses Mincerian earnings function could (e.g. Topel 1999; Krueger and Lindhal 2001; Pritchett 2001).

6

for getting educated and participating in labor force is therefore much less than the male counterpart. As

a result, the schooling and experience of a woman are lower than those of a man, thus giving rise to

disparity in gender earnings.

The second step of the model addresses how SBTC influences households’ allocation of time of

each gender differentially toward getting educated, participating in workforce and rearing children and

therefore how SBTC affects the evolution of gender inequality through time. The main innovation here

is that while all models of SBTC so far have emphasized either the direction of technology change or the

magnitude of overall technological advancement in affecting wage inequality, the present model stresses

the importance of the relative quantitative impacts of SBTC on different skills. In the typical literature

of SBTC, the current technological change is biased toward observable skills (education and experience)

as well as unobservable skills (innate ability) and such general skill-biasedness is sufficient to account

for the rise in education premium, experience premium and wage dispersion within observed-skill

groups. The relative magnitude of increase in the premiums of different skills is immaterial. In the

present model, however, the quantitative impacts of SBTC on the education premium versus experience

premium are crucial and substantive. This is so because the effect on education premium directly affects

the incentive to get educated whereas the impact on experience premium directly affects the incentive to

participate in workforce. Thus, the combined effect of SBTC on education premium and experience

premium determines the lifetime allocation toward rearing children, whereas the differential effect of

SBTC on the different skill premiums determines how the remaining time is divided into schooling and

workforce participation.

This, together with the sexual division of labor and hence the predominant role of female in

child-rearing, is able to explain not only the anomaly of declining gender earnings inequality amidst

rising overall earnings dispersion since the 80s, but also several other empirical observations, including:

female labor participation rate continued to increase in the last two decades, while male labor

participation rate slightly decreased (e.g. Goldin 1990, 2002; Blau and Ferber 1992; Juhn 1992; Blau

7

1998); both female and male years of schooling, particularly college graduate rates, continued to

increase in the 80s and 90s (e.g. Goldin 1992; Blau 1998); and the average number of children a couple

has, hence the fertility rate, continued to decline in the 80s and 90s.

The basic logic of the model is as follows. First, because the male parent does not spend time

rearing children in the model, if SBTC affects the education premium more than the experience

premium, the incentive for male to get educated will increase while male labor participation will fall.

Second, though such differential effects of SBTC will affect the female decisions similarly, female labor

participation and education decisions depend also on the fertility choice of the household, which in turns

depends on the combined effect of SBTC on the different skill premiums. Female education, which is

positively affected by both the differential and combined effects of SBTC on the different skill

premiums, will certainly increase. Moreover, if the combined effect of SBTC on the different skill

premiums is more than sufficient to counterbalance the differential impact of SBTC on the different skill

premiums, female labor force participation will, unlike the male counterpart, also rise.

Because the increase in male education is due to the differential effect of SBTC on the education

premium and experience premium, while the increase in female education is due to both the combined

and differential effects on the different skill premiums, the rate at which female schooling increases

would be faster than that of male. This explains the narrowing of gender education gap. Furthermore,

because male labor participation rate is decreasing due to the differential effect of SBTC, whereas

female labor participation rate is increasing due to the premise that the combined effect of SBTC

overwhelms its differential impact on the different skill premiums, the average experience of female

workers will increase relative to that of male workers. This explains the narrowing of gender experience

gap. The narrowing of the gender education and experience gaps will tend to increase the relative wages

of women. This feeds back into the reduction in fertility rate.

The theoretical framework developed by this model is therefore potentially capable of explaining

the reduction in gender inequality in spite of the general trend of widening earnings inequality, as well

8

as various labor market patterns between the genders in the last two decades, by applying the theory of SBTC

and the theory of sexual division of labor and fertility choice together. In what follows, Section 2 sets up

the model specification for the partial equilibrium analysis that takes economic growth as given. Section

3 provides the analysis of that model and discusses the model empirical implications. Section 4

discusses how the model could also shed light on the additional stylized fact that measured experience

premium was rising faster for female than for male since the 80s (O’Neill and Polachek 1993). Section 5

provides numerical simulation of the model. The penultimate section provides a general equilibrium

analysis of the model in an endogenous growth framework. Section 7 concludes.

2. Model Specification

We consider a closed economy with overlapping generations of couples. Time is discrete. For

each generation t, half the population is male and half female. Marriage is monogamous. Every one in

each generation is married and there are no singles in any generation. Economic activities of each

generation take place in two periods. In the first period, each couple decides on the allocation of time to

rear children, to invest in education and to work. There is no consumption when young. Thus, couples

save all their earnings. In the second period, they retire and consume their savings.

Because the present paper models fertility choice by focusing on the theory of sexual division of

labor, couples are, by construct, not altruistic, nor have any old-age support motive. Similar to Jones

(2001), utility depends only on consumption of the parents and number of children, but not on the

consumption or utility of the children. Utility is additive in the log, following Galor and Weil (1996).

Thus, the representative couple maximizes the per couple utility ut given by

( ) 1ln 1 lnt t tu n cγ γ += + − , (1)

where nt is the number of children and ct+1 is the couple’s consumption when old.

The time constraint per person when young is given by

1 where or i i it t tp s x i m f+ + = = .

9

The superscript i refers to the male (m) and female (f) parents in each couple. itp is i’s time spent in

rearing children (parenting), sti is i’s time spent in schooling and xt

i is i’s time spent in working (which

determines the average experience of i).

Unlike Galor and Weil (1996) and Zhang et al (1999), who also model fertility choice by

building on the specialized role of women in child-rearing but assume gender difference in productive

endowment, the present model assumes that there is no difference in the productive endowment between

the female and male parents.13 Instead, women are assumed to have comparative advantage in rearing

children. For women, child-rearing requires a fixed time cost z per child. For men, child-rearing requires

a larger fixed time cost zm>z per child.

Following the labor literature, we use a Mincerian earnings function (Mincer 1974).14 Log wages

is a function of schooling and its square, of experience and its square and of an interaction term between

schooling and experience. We assume that skills generated by experience are driven by some learning-

by-doing mechanism. Thus, the more time one spends on working, the higher the skill level according to

experience. Because each couple owns no physical capital when young, the earnings per parent when

young are given by

( ) ( )2 2

0 where or i i i i i i

t t t t t t t t t t ts s s x x xit tw w e i m f

λ φ ϕ µ η− + + −= = ,

where λt, φt, ϕt, µt, ηt are positive parameters, wti is the wages of individual i at time t, w0t is the wages

for raw labor (i.e. unskilled wages) and wages increases exponentially with schooling and its square,

with experience and its square and with an interaction term between schooling and experience in

accordance with the Mincerian specification. The log “skill premium” is therefore

13 It can be shown that while the difference in endowments between female and male is unnecessary in the current setup with a Mincerian earnings function in order for the model implications to be compatible with the data, such difference might be necessary in a setup with a different earnings function. In particular, if the current model uses an earnings function in which wages (not log wages) increase linearly with schooling as in Galor and Weil (1996), the assumption of some initial difference in endowments between the genders is necessary for female force participation to increase with technological improvement. This might explain the modeling choice of Galor and Weil (1996) and Zhang et al (1999). 14 More recently, Klenow and Rodriguez-Clare (1997) and Hall and Jones (1999) have also used the Mincerian earnings function for level accounting exercises in macroeconomics.

10

( ) ( )2 2i i i i i it t t t t t t t t t ts s s x x xλ φ ϕ µ η− + + − for an individual with st

i years of schooling and xti years of

experience. Expressed in the more familiar “earnings regression” form, we have

( ) ( )2 2

0ln lni i i i i i it t t t t t t t t t t t tw w s s s x x xλ φ ϕ µ η= + − + + − . (2)

In empirical labor economics, the interest in (2) is to estimate the regression coefficients

λt, φt, ϕt, µt, ηt in cross-section micro data at given time t. Here, the interest is to understand how, when

SBTC leads to changes in these parameters, it will affect a typical couple’s decisions on schooling, labor

participation and fertility choice over time.

In the partial equilibrium analysis under the next section, we shall abstract from knowledge

generation and physical capital accumulation, but take the rates of technological improvement and

physical capital accumulation as given. We shall complete the general equilibrium analysis by modeling

knowledge generation and physical capital accumulation in an endogenous growth model in Section 6.

In essence, the utility function, which is additively separable in the log, allows us to analyze the problem

in a partial equilibrium framework without changing the main empirical implications of the present

theory in the general equilibrium set-up.15 Suppose the real interest rate is rt+1, the optimization problem

in (1) of the representative couple at time t is to maximize

( ) ( ) ( ) ( ) ( ) ( )2 2 2 2

1 0ln 1 ln 1m m m m m m f f f f f f

t t t t t t t t t t t t t t t t t t t t t ts s s x x x s s s x x x

t t tn r w e eλ φ ϕ µ η λ φ ϕ µ η

γ γ− + + − − + + −

+

+ − + + . (3)

Although rt+1 and w0t depend on the state variables such as the level of physical capital stock and the

state of technology, they will not alter the first order conditions of the representative couple. Therefore,

the time allocation problem of the households is independent of rt+1 and w0t.

Technological change is assumed to be skill-biased in the present model. In the theoretical

literature of SBTC, the modeling of SBTC comes in two strands. In Aghion and Howitt (1998), Caselli

(1999) and Galor and Moav (2000), for example, the nature of technology is general purpose but skilled

15 In fact, a utility function that is additively separable in nt and ct+1 and log in ct+1 will work. The log in nt is not necessary.

11

workers can adapt to changing environment more quickly a al Nelson and Phelps (1966). According to

this type of SBTC, any technological change is temporarily skill-biased and the faster the technological

change the higher the degree of skill-biasedness.

The present modeling of SBTC follows the second formulation as in Acemoglu (1998, 2002b)

and Kiley (1999).16 Under this formulation, technological change can be skill-biased or unskilled-biased

or skill-neutral in nature. Goldin and Katz (1998), for example, documented that technological change

was largely unskilled-biased in the early part of the Industrial Revolution but became skill-biased at the

turn of the twentieth century and increasingly so in the last few decades.

We shall let At be (un)skill-biased technology and Bt be skill-neutral technology. In essence, rt+1

and w0t depend on both At and Bt (and the physical capital stock), but the parameters in the Mincerian

earnings function λt, φt, ϕt, µt, ηt depend only on At. Technological change is skill-biased if the increase

in At leads to changes in λt, φt, ϕt, µt, ηt that increase the skill premiums (education premium and

experience premium).

3. Analysis of the model and the model implications

3.1. The household optimization problem

For simplicity, in this section, we shall suppress the time subscript, unless it is necessary to do

so. Because the female parent has lower time cost per child (z<zm) in rearing children, the opportunity

cost to rear children is lower for the female parent than for the male parent even if both earn the same

hourly wages. Thus, the female parent will at least be responsible for rearing the first marginal child.

Furthermore, because wages increase with schooling and experience, the male parent will be earning

more than the female parent in hourly earnings because of the female time cost in rearing the first

marginal child. As a result, the opportunity cost for rearing the second marginal child is again lower for

16 Although the present paper adopts this latter approach in modeling SBTC, the set-up here is different from the previous literature. In Acemoglu (1998, 2002b), the classification of skilled and unskilled labour is discrete. In the present model, there is a continuous skilled-unskilled spectrum.

12

the female parent. Consequently, if zn<1, only the female parent will take care of children. We shall

assume such interior solution.17

Given the parameters restriction, pm=0 and pf=zn. Besides, because of the log utility, the time

allocation problem of the households is independent of r and w0. The optimization problem of the

representative couple in (3) therefore becomes:

( ) ( ) ( ) ( ) ( )2 2 2 2

max ln 1 lnm m m m m m f f f f f fs s s x x x s s s x x xfp e e

λ φ ϕ µ η λ φ ϕ µ ηγ γ − + + − − + + − + − + ,

subject to 1 and 1m m f f fs x p s x+ = + + = .

Substituting xtm and xt

f into the utility function, the optimization problem can be rewritten as:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2 2 2 21 1 1 1 1 1

max ln 1 lnm m m m m m f f f f f f f f fs s s s s s s s s p s s p s pfp e e

λ φ ϕ µ η λ φ ϕ µ ηγ γ − + − + − − − − + − − + − − − − − + − + . (4)

3.2. Female and male schooling and labor participation decisions

Let , , , , m m f f fs x s x p be the optimal choices of the representative couple. We shall first

analyze the couple’s schooling and labor participation decisions, taking the fertility choice as given. The

first order conditions 0 and 0m f

u u

s s

∂ ∂= =∂ ∂

imply

2 2 where or i i i is x x s i m fλ φ ϕ µ η ϕ− + = − + = .

Substituting the time constraints, we obtain for the male and female parents respectively:

17 The condition for interior solution is µ ( )( )µµ

2 42 1

1 2 2

pp p

p

γ ζ ε εζ ε

γ ζ ε ε+ −

+ − < +− + −

, where µp solves the implicit

equation µµ

µ µ( )( )22 412 2

p ppe

p

ζ εζ ε ε γγζ ε ε

+ −+ −=

−+ −,

( )2ϕηλ φη λ η

ζφ η ϕ

+ + +≡

+ + and

2

4ϕ φη

εφ η ϕ

−≡

+ +. Essentially, the weight on

children (γ) has to be sufficiently low in order for women not to spend all their time rearing children.

13

( ) ( )

( ) ( )

2;

2 2Male:

2.

2 2

m

m

s

x

η ϕ λ µφ η ϕ φ η ϕ

φ ϕ λ µφ η ϕ φ η ϕ

+ − = + + + + + + − = − + + + +

(5)

( ) ( ) ( ) ( )

( ) ( ) ( )

21 ;

2 2Female:

21 .

2 2

f f f

f f f

s p p

x p p

η ϕ λ µφ η ϕ φ η ϕ

φ ϕ λ µφ η ϕ φ η ϕ

+ − = − + + + + + + − = − − + + + +

(6)

The schooling and labor participation decisions of male and female are very similar. For both

male and female, years of schooling are positively dependent onλ µ− , the difference between (the

linear term of) education premium and experience premium. Intuitively, the incentive to go to school

rather than to participate in labor earlier depends on how large the education premium is relative to the

experience premium. If the education premium is high relatively, one will rather spend more time in

school to reap such high marginal benefits in earnings. Similarly, years to spend on working depend

negatively onλ µ− : one would decide to join the labor force earlier rather than to pursue higher

education if the experience premium is high relatively.

The difference between the male and female decisions on schooling and labor participation is

that there is an additional term (1-pf) for female. This is so because the female parent has to spend time

rearing children. The total time available for schooling and labor participation is therefore her time

endowment when young minus her time spent on parenting (pf).

3.3. The couple’s fertility choice

Let ym and yf denote the “skilled component” of the male and female earnings. That is, let

( ) ( )2 2ln i i i i i i iy s s s x x xλ φ ϕ µ η= − + + − . Substituting in the optimal schooling and labor participation

decisions of the couple in (6) given the fertility choice, we obtain the derived skilled components

( ) and m f fy y p as

14

( ) ( )

( ) ( ) ( ) ( )

2 2

2 2 2

1 1 12 4 4

1 1 11 1

2 4 4

;

.f f

m

p pf

y e

y e

ϕηλ φµ ϕ λ µ φη λ µ

φ η ϕ

ϕηλ φµ ϕ λ µ φη λ µ

φ η ϕ

+ + + + − + − + +

+ + + − + − − + − + +

=

=

(7)

Note that the female derived skill component of wages depends on fertility choice (pf).

Using the derived skill components of the male and female wages in (7), we could rewrite the

couple’s optimization problem in (4) using the derived utility ( ) ( )( ), ,f m f f fv p u s s p p= as

( ) ( )( )max ln 1 lnf

f m f f

pp y y pγ γ+ − + . (8)

The first order condition 0f

v

p

∂ =∂

implies

( )( )

( ) 11

f

f ff m

ff f f f

p

y pp y

py p y p

γγ

∂ − = + ∂ −

. (9)

The R.H.S. of (9) is a function of the relative earnings of male versus female. The L.H.S. of (9) is the

negative of the elasticity of the female derived skill premium with respect to fertility choice at the

optimal fertility decision. Therefore, the optimal fertility rate depends on the relative earnings of male

versus female, as in Galor and Weil (1996).

Substituting the expressions of the derived skill premiums in (7) into the first order condition in

(9), we obtain the optimal fertility rate in an implicit equation:

( )( ) ( )( )( )2

2 1 1 11 1

f fm p pf f

f f

yp p e

y p

ζ εγ γζ εγ γ

+ − + − = + = + − −

, (10)

where

2

4ϕ φη

εφ η ϕ

−≡

+ + and

( )2ϕηλ φµ λ µ

ζφ η ϕ

+ + +≡

+ +. Fertility choice is therefore pinned down by the

preference parameter γ and the parameters in the Mincerian earnings functions. To understand how the

optimal fertility choice changes with the Mincerian regression coefficients, we have to turn to the second

15

order conditions for local maximum: 2

20

f

u

p

∂ <∂

and 22 2 2

2 2 0f f f f

u u us p s p

∂ ∂ ∂− > ∂ ∂ ∂ ∂ . These second order

conditions imply

( ) ( ) ( )2 2 2 41

mf f

f f

yp p

y p

γ ζ ε ε ζ ε εγ

+ − < + −−

. (11)

Let’s focus on changes in the linear terms (λ and µ) in the education premium and experience premium.

That is, we assume ε is unchanged. Taking derivative of (10) with respect to ζ, we obtain

( )

( ) ( ) ( )( )

11

2 4 2 21

mf

f ff

f

mf f

f f

yp

y ppp

yp py p

γγ

ξζ γζ ε ε ζ ε ε

γ

− −

∂ = ≡∂

+ − − + −−

. (12)

By the second order condition, fertility decreases with ζ insofar as ( )1m

f f

y

y p

γγ−

< . If the initial female-

male earnings gap is too large relative to the relative weights on consumption versus children, SBTC

will in fact have strong “income” effect on having more children. But if initial female-male earnings gap

is not too large relative to the relative weights on consumption versus children, SBTC will have stronger

“substitution” effect to induce couples to have fewer children. A sufficient, though not necessary,

condition for fertility to decrease with ζ is ε>0. In this case, the second condition in (11) will guarantee

that the condition ( )1m

f f

y

y p

γγ−

< holds. To be compatible with evidence, we shall assume this is the

case: the substitution effect overwhelms the income effect. Because ζ is a weighted sum of the linear

terms (λ and µ) in the education premium and experience premium, the household’s chosen fertility rate

decreases as the weighted sum of the linear terms in education premium and experience premium

increases.

16

3.4. The model implications

When technology is skill-biased, the parameters in the Mincerian earnings function will change

in such a way to increase the skill premiums. For illustration, we shall assume the second order terms in

the Mincerian earnings function φ, ϕ and η are unchanged by SBTC, but the first order terms λ and µ

increase with SBTC. That is, 0d

dA

λ > and 0d

dA

µ > . With SBTC, 1t tA A+ > . Therefore, 1t tλ λ+ > and

1t tµ µ+ > with SBTC.

We would like to know how the present model of SBTC with sexual division of labor and

fertility choice is capable of explaining the declining gender inequality in earnings amidst overall

increase in wage dispersion in the last two decades, as well as the following stylized facts in the 80s and

90s: (i) fertility rate continued to decline in the last two decades; (ii) male years of schooling was high

relative to the female counterpart and kept increasing in the 80s and 90s; (iii) male labor force

participation slightly decreased; (iv) female years of schooling was lower than the male counterpart but

increased at a faster rate; (v) as a result of (iv), the gender gap in education, particularly gender gap in

the percentage of college graduates, narrowed significantly in the past two decades; (vi) female years of

experience were lower than the male counterpart but female labor participation continued to increase in

the last two decades, and, unlike the rise in female labor participation before the present era, in which

women worked as rather unskilled labor, the recent decades witness the rise in professional women; (vii)

as a result of increasing female labor participation and slightly declining male labor participation, the

gender gap in working experience also narrowed.

3.4.1. How SBTC affects fertility choice

From the previous subsection, we find that time allocated toward parenting (pf) decreases as the

weighted sum of λ and µ increases. From the theoretical result in (12), we obtain

( )

02

ff f pd p p d d d d d

dA dA dA dA dA dA

ξζ λ µ ϕ λ µη φζ φ η ϕ

∂ = = • + + + < ∂ + + , (13)

17

because ( ) 0fpξ < insofar as ( )1m

f f

y

y p

γγ−

< . The model, therefore, predicts that fertility decreases

with SBTC as in stylized fact (i).

3.4.2. How SBTC affects male education and labor participation choice

To account for the continued increase in male education attainment in (ii) but the decrease in

male labor participation in (iii), the results in (5) show that male schooling and labor participation

decisions respond to the differential impacts on the education premium and experience premium. If the

education premium is rising faster than the experience premium, i.e. d d

dA dA

λ µ> , then male would choose

to stay longer in school rather than joining the labor force earlier. Topel (1997, Figure 2 in p. 58), for

example, illustrates that the college wage premium, as measured by the wage ratio for college versus

high school graduate, has been rising at an amazing rate since the late 70s. On the other hand, the

experience wage premium, as measured by the wage ratio for high experience (25-35 years of

experience) versus low experience (0-10 years of experience) workers, has risen since the 70s but at a

slower pace. There is, therefore, empirical evidence concerning the relative changes of the education

premium and the experience premium in the recent decades that is in agreement with the hypothesis that

d d

dA dA

λ µ> . (14)

Given this assumption, we obtain

( )

( )

10;

2

10.

2

m

m

ds d d

dA dA dA

d x d d

dA dA dA

λ µφ η ϕ

λ µφ η ϕ

= − > + +

= − − < + +

(15)

The model is therefore capable of generating the stylized facts in (ii) and (iii) concerning the male

schooling and labor force participation choices in the last couple of decades as well.

18

3.4.3. How SBTC affects female education choice and gender education gap

Moreover, by comparing the expressions in (5) and (6), the model implies, in accordance with

the stylized fact in (iv), that female years of schooling is lower than the male counterpart ( )f ms s< ,

because of the time spent by female in parenting (pf). Regarding the trend in female schooling as

described in (iv), the model also predicts that female years of schooling increase with SBTC.

Furthermore, the rate of increase is faster than that of male years of schooling. From the results in (6)

and (13), the rate of increase in female years of schooling is given by

( ) ( )

( ) ( )( ) ( )2

2 12 2

2 1.

2 22

f f

f

ds d p d ddA dA dA dA

p d d d d d d

dA dA dA dA dA dA

η ϕ λ µφ η ϕ φ η ϕ

η ϕ ξ λ µ ϕ λ µ λ µη φ

φ η ϕφ η ϕ

+ = − + − + + + +

+ = − + + + + − + + + +

(16)

Like the male schooling decision in (15), female schooling is increasing with the differential increase in

the education premium versus the experience premium (the second term in (16), which is positive). In

addition, female schooling choice is dependent on the rate of change in the fertility rate, which in turn

responds to the combined effect of the increase in the education premium and the experience premium

(the first term in (16), which is positive). As a result, in accordance with stylized fact (v), the gender gap

in education ( )m fs s− narrows:

( )( )

( ) ( )( )

22

20.

2 2

m ff

f

d s s d p

dA dA

p d d d ddA dA dA dA

η ϕφ η ϕ

η ϕ ξ λ µ ϕ λ µη φφ η ϕ

− +=+ +

+ = + + + < + +

(17)

3.4.4. How SBTC affects female labor participation choice and gender experience gap

Similarly, because of the time spent by female in parenting (pf), the model implies, in accordance

with the stylized fact in (vi), that female years of experience is lower than the male counterpart (again by

comparing the expressions in (5) and (6)). Besides, unlike the declining male labor participation in (15),

19

which results because of the differential magnitudes of the increase in the education premium versus that

in the experience premium, female labor participation decision responds to changes in fertility choice as

well. Female labor participation would, therefore, increase insofar as the combined effect of the increase

in the education premium and experience premium in releasing time from parenting more than

counterbalances the substitution effect of the differential increase in the education premium versus the

experience premium against female labor participation. That is,

( ) ( )

( ) ( )( ) ( )2

2 12 2

2 10,

2 22

f f

f

d x d p d ddA dA dA dA

p d d d d d d

dA dA dA dA dA dA

φ ϕ λ µφ η ϕ φ η ϕ

φ ϕ ξ λ µ ϕ λ µ λ µη φ

φ η ϕφ η ϕ

+ = − − − + + + +

+ = − + + + − − > + + + +

(18)

provided that ( ) ( )

( )2

2 2

fp d d d d d ddA dA dA dA dA dA

φ ϕ ξ λ µ ϕ λ µ λ µη φφ η ϕ

+ − + + + > − + + . The model also predicts, in

agreement with stylized fact (vii), that the gender gap in experience ( )m fx x− narrows:

( )( )

( ) ( )( )

22

20.

2 2

m ff

f

d x x d p

dA dA

p d d d ddA dA dA dA

φ ϕφ η ϕ

φ ϕ ξ λ µ ϕ λ µη φφ η ϕ

− +=+ +

+ = + + + < + +

(19)

3.4.5. How SBTC affects gender earnings gap

Although SBTC would induce gender pay gap to widen if women’s relative skill level were

unchanged, gender inequality in earnings could decline in face of SBTC provided that women’s skills

increase faster than the rate at which men’s skills increase. Because the gender gaps in education and in

experience do narrow in the present model, due to declining fertility rate in face of SBTC, the model is

capable of explaining declining gender pay gap in the midst of the increase in overall wage dispersion in

the 80s and 90s. With the expressions in (7), in the present model, the log male-female earnings ratio is

given by

20

( ) ( )( )ln 2m

f f

f f

yp p

y pζ ε= + − . (20)

Taking derivative of (20) with respect to A, we obtain

( )( ) ( )( )ln ln 2 1f

m f f f fd d d py y p p p

dA dA dAζ ζ ε− = + + − . (21)

The expression in (21) has an intuitive interpretation. From the results in (17) and (19), the

gender gaps in schooling and experience would be unchanged if and only if 0fd p

dA= . The first term on

the R.H.S. of (21), f dp

dA

ζ, therefore measures the change in relative earnings of male versus female if

the gender gaps in schooling and experience remained unchanged, i.e. 0fd p

dA= . With the increase in

the education premium 0d

dA

λ > and in the experience premium 0

d

dA

µ > due to SBTC, 0

d

dA

ζ > and

gender inequality in earnings would therefore widen in face of SBTC, should the gender gaps in

schooling and experience remain unchanged, because men have higher levels of education and

experience than women (as indicated by the difference in time available for schooling and working, i.e.,

the multiplicative term fp ). This logic would apply to the widening of wage differentials by skills

between any skilled-unskilled groups with fixed skill disparity.

The difference between the evolution of gender earnings inequality and the trend of earnings

inequality among any skilled-unskilled groups with fixed skill disparity lies in the second term on the

R.H.S. of (21): ( )( )2 1f

f d pp

dAζ ε+ − . This second term measures the effect of changes in gender gaps

in schooling and experience on the relative earnings of male versus female. Because 0fd p

dA≠ , the

21

relative skill levels between male and female do not remain fixed in face of SBTC. Indeed, 0fd p

dA< .

Hence, the gender gaps in schooling and experience narrow.

The net effect of SBTC on the gender pay gap depends on the relative magnitudes of the first

“fixed relative levels” effect and the second “relative change” effect on the R.H.S. of (21). Substituting

the expression for fd p

dA as given in (12) and (13) into (21), we obtain

( ) ( )( ) ( ) ( )

2

2

2ln ln 0

2 4 2 21

f f

f

m f

p pf f

pdy y

dA p p eζ ε ε

ε

γζ ε ε ζ ε εγ

+ −

− = − < + − − + − −

, (22)

insofar as ε>0, given the second order condition in (11). Therefore, in the present model, with a

Mincerian earnings function, gender gap in earnings would narrow with SBTC. Notwithstanding the

effect of SBTC to widen wage differentials among skilled-unskilled groups with fixed skill disparity, the

effect of SBTC to narrow the gender gaps in schooling and experience via the reduction in fertility rate

could more than compensate for this “fixed relative levels” effect on gender pay gap and lead gender

inequality in earnings to decline despite the general increase in overall wage dispersion.

4. The female-male experience premium gap

Like the empirical results obtained by O’Neill and Polachek (1993), Blau and Kahn (1997, 2000)

and Blau (1998) among others, the present theory therefore attributes the anomaly of declining gender

inequality in earnings to the narrowing of gender gaps in education and experience. O’Neill and

Polachek (1993), however, also documented a third component that contributed to the narrowing of

gender pay gap: that the female-male experience premium gap narrowed during the 80s.

At first sight, the present theory does not seem to predict such third contributing factor.

According to the above analysis, the experience premiums for both male and female change at the same

rate 0d

dA

µ > . However, in practice, “measured” experience is only a proxy to actual experience. Many

22

data sets used by empirical researchers, for example, the Current Population Surveys (CPS), do not

contain a measure of actual years of work experience. The standard proxy for actual years of experience

is a measure of potential experience (typically, age-schooling-6), which is a much weaker proxy for

women than for men. Even in data sets that use actual years of experience, such as the National

Longitudinal Surveys (NLS) and the Panel Study of Income Dynamics (PSID), the actual number of

hours worked year is imperfectly measured. If we believe that the experience of women is badly

measured, the current theory could, in fact, also account for the empirical stylized fact that the measured

female experience premium has been rising faster than the male counterpart.

To illustrate how, we shall look at an extreme example. Suppose, after obtaining the optimally

chosen years of schooling ( )fs , each year women devote f

f f

p

p x+ fraction of time to child-rearing and

1f

f f

p

p x

− +

fraction of time to working. Suppose measured female experience, denoted by ¶fx , is

determined by the number of years worked. Then, we have

¶ 1f

f f

f f

px x

p x

= − +

(23)

On the other hand, suppose, after obtaining the optimally chosen years of schooling ( )ms , men devote

100% of time working each year. Then, measured male experience, denoted by ¶mx will be the same as

actual experience mx . As a result, in Mincerian earnings regressions, we would obtain

( ) ¶ ¶( )( ) ¶

¶ ¶( )

22

0

2

0

22

Male: ln( ) ln ;

Female: ln( ) ln 1

1 1 .

m m m m m m m

ff f f f f

f f

f ff f

f f f f

w w s s s x x x

pw w s s s x

p x

p px x

p x p x

λ φ ϕ µ η

λ φ ϕ

µ η

= + • − • + • + • − •

= + • − • + − • +

+ − • − − • + +

(24)

23

The estimated first order terms of the experience premiums for male and female are respectively µ and

1f

f f

p

p xµ

− +

. As a result, the ratio of the estimated male experience premium to the estimated female

experience premium is given by

estimated male experience premium 1

estimated female experience premium1

f

f f

p

p x

=−

+

. (25)

As fp decreases with SBTC and fx increases with SBTC, the “measured” male-female experience

premium gap narrows.

Even though the above example is extreme and the measurement error in experience is likely to

be smaller in actual datasets such as the NLS and PSID than the example suggests, to the extent that

such smaller measurement error does correlate with the fertility choice similar to (23), the present theory

is capable of producing the narrowing of gender experience premium gap in similar veins to what

equation (25) suggests.

Such measurement error argument could shed further light on the narrowing in measured gender

pay gap. If measured female hourly earnings is by similar argument ¶ 1f

f f

f f

py y

p x

= • − +

, the log

measured male-female earnings ratio is given by

¶ln ln 1m m f

f ff

y y p

y xy

= +

.

Taking derivative with respect to A, we obtain

¶

( )( ) ( ) ( )2 2

ln

2 1

m

f f f f f ff f

f f f f

yd

y d d p x d p p dxp p

dA dA dA dA dAp x p x

ζ ζ ε

= + + − + −

+ +. (26)

24

The first two terms of (26) is the same as the R.H.S. of (21), but the last two terms contribute further to

the decline in measured male-female earnings ratio.

5. Numerical simulation of the model

(to be completed)

6. An endogenous growth model

To complete the model, we shall bring in the determination of economic growth in a general

equilibrium framework. We consider an overlapping generation model. Each generation t consists of a

continuum of individuals with population measure Nt. Marriage is monogamous and every one is

married. There are therefore 2

tN couples for generation t. For convenience, we assume that production

takes place at the end of each period, after all human capital (education and experience) has been

accumulated. Production function is Cobb-Douglas:

( )1

t l t tY K Hαα −= Γ ,

where Kt is physical capital stock, Ht is human capital stock and Γt is the state of technology. Ht is given

by htNt , where ht is the average human capital per individual in accordance with the Mincerian earnings

function given by 2

m fy y+ and Nt is raw labor.18 Physical capital depreciates completely after one

period. The wages per unit of human capital usage and the real interest rate are therefore given by

1

1-0 = and 1t t t t t

t t tt t t t

Y K Y Hw r

H H K K

α α

α

− ∂ ∂ Γ= Γ + = = ∂ ∂

.

For a couple in generation t, the physical capital investment it at time t and the consumption ct+1

at time t+1 are given by

( ) ( )0 1 1 and 1m ft t t t ti w y y c r i+ += + = + .

18 The formulation here is therefore similar to Klenow and Rodriguez-Clare (1997), Hall and Jones (1999) and Jones (2002).

25

The overlapping generation set-up has the aggregate physical capital stock and human capital stock at

time t given by

( )1 and 2 2

m ft tt t t

N NK i H y y−= = + .

We shall follow Lucas (1988) and Romer (1990) to allow for knowledge generation to depend on

existing technology and human capital, but modify their formulation following Jones (1995) to get rid of

the unpleasant “scale” effect of population level on economic growth. In discrete time, we have

1 1 1t t t tHθ β− − −Γ = Γ + Γ ,

where 0<θ<1 and β>0. Suppose technological change is skill-neutral, i.e. we have t tBΓ = . Then, the

parameters in the Mincerian earnings function are constant. As a result, the endogenous fertility rate

given by (10) is invariant with time. So are the skill premium parts of earnings and m fy y . Let gBt

denote the growth rate of skill-neutral technology Bt. Then, we have

11 1

1

1

, 1 1 1

, 1 2 2

1.

t tBt t t

t

Bt B t t t

B t t t

B Bg B H

B

g g B H

g B H

θ β

θ β

−− −

−

−− − −

− − −

−= =

− ⇒ = −

The standard non-scale endogenous growth results. There exists a steady state with economic growth

equal to *Bg . Such steady state is achieved when , 1

, 1

0Bt B t

B t

g g

g−

−

−= . This happens when

1

1 1

2 2

t t

t t

B HB H

θ β−

− −

− −

=

. This implies that at steady state ( )1* * * *11 1B Bg n g n

βθ β θ−

−+ = ⇒ = − . Therefore, with

skill-neutral technology, the present model obtains the same result of endogenous non-scale economic

growth as in Jones (1995), but with endogenous (gross) population growth rate *fp

nz

= , where fp is

determined endogenously by the preference parameter γ and the Mincerian earnings function

parameters.

26

With skill-biased technology, t tAΓ = . In this case, the Mincerian earnings function parameters

change with At. As a result, , and f m fp y y change with At. But suppose the parameters in the

Mincerian earnings function are bounded above. Then, eventually , and f m fp y y will reach these

steady state values. Steady state economic growth will again be given by some *Ag that depends on the

steady state endogenous fertility rate, which depends on the preference parameter γ and the bounded

values of the parameters in the Mincerian earnings function following (10). The present model is

therefore capable of generating steady state non-scale economic growth as well as explaining the gender

wages and employment patterns as observed in the recent decades.

7. Concluding remarks

Building upon the current burgeoning theoretical and empirical literature on the effects of SBTC

on wage inequality, the present paper resolves theoretically the puzzle of declining gender earnings

inequality amidst the general increase in wage dispersion among many developed countries in the last

two decades. By integrating the theory of SBTC with the theory of sexual division of labor and fertility

choice, the present model address (I) how the combined and differential impacts of SBTC on the

education and experience premiums affect parents’ allocation of time toward getting educated,

participating in workforce and rearing children, (II) how the fertility choice then affects the choice of the

female parent in developing her skills asymmetrically and hence the female-male education and

experience gaps, and (III) how the skill-biased nature of technological change affects the gender gap in

earnings given the changes in gender gaps of education and experience. Not only can the model explain

the anomaly of the declining gender pay gap in the 80s and 90s, it can also corroborate several other labor

market patterns between the genders in the la st two decades, including: the rise in female labor participation in the

midst of declining male labor participation and the narrowing of the gender gaps in schooling, experience and

measured experience premium.

27

The current paper can be extended in a number of fruitful directions. First, the empirical

implications of the model could be quantified. The next logical step is, therefore, to calibrate the model

using the estimates of the Mincerian earnings regressions produced by previous empirical research to

infer the rate of change in the education and experience premiums in the previous decades. Having

parameterized the model, we could run numerical simulations of the model to assess how much of the

observed changes in the gender gaps of earnings, education and experience, in male and female labour

participation, and in the fertility rate can be explained by the quantitative model. Moreover, since there

are differences in cross-country experience in terms of changes in education and experience premiums

(Gottschalk and Smeeding 1997; Katz and Autor 2000), numerical simulations could be run for each

country where data is available. The results could then be compared to the observed differences in cross-

country experience in gender employment and inequality patterns.

Another promising extension is to endogenize the direction of technological change as in

Acemoglu (2002b) in the general equilibrium framework. In the present paper, though we model the rate

of technological change in an endogenous growth framework in Section 5, we take the skill-biased

nature of technological change in recent decades as given. By modeling directed technical change in the

present framework, we will likely obtain some interesting dynamics in terms of the supply and demand

of skills of the two genders. On the one hand, the rapid increase in the female years of schooling and

experience during the modern era could be key to the acceleration of SBTC in the recent decades due to

the market size effect. On the other hand, SBTC that arises before the rise of professional women in the

present era might be the cause of the rapid increase in female years of schooling and experience in the

first place.

Moreover, although the current model could in principle account for the narrowing in gender

gaps of measured experience premium in the previous decades (O’Neill and Polachek 1993), two

extensions of the current model would further help explain this additional stylized fact. First, returns to

experience in the present model are treated as the consequence of some unintentional learning-by-doing

28

mechanism. But one important implication of the human capital theory pioneered by Becker (1962,

1964), Pen-Porath (1967) and Mincer (1974) is that years of work experience increase earnings in part

because of costly on-the-job training. As women’s anticipated years of experience increase, they are

likely to have greater incentive to invest in on-the-job training. Second, the effort provided by workers

and hence the quality of hours worked cannot be measured directly. If child-rearing does not only cost

time but also effort, the actual increase in quality-inclusive experience of women in recent decades is

therefore likely understated in the “measured” increase in experience. This will again induce the

“measured” increase in experience premium for women to be biased upward. Thus, broadening the

current model to include costly on-the-job training and unobservable effort choice will shed further light

on this additional empirical observation.

References

Acemoglu, Daron (1998), “Why do new technologies complement skills? Directed technical change and

wage inequality,” Quarterly Journal of Economics 113:4, pp.1055-89.

Acemoglu, Daron (1999), “Changes in unemployment and wage inequality: an alternative theory and

some evidence,” American Economic Review 89:5, pp. 1259-78.

Acemoglu, Daron (2002a), “Technical change, inequality, and the labor market,” Journal of Economic

Literature 40:1, pp. 7-72.

Acemoglu, Daron (2002b), “Directed technical changes,” Review of Economic Studies 69, pp. 781-809.

Acemoglu, Daron, Philippe Aghion and Gianluca Violante (2001), “Technical change, deunionization

and inequality,” Carnegie-Rochester Conference Series on Public Policy 55:1, pp.229-64.

Acemoglu, Daron and Fabrizio Zilibotti (2001), “Productivity differences,” Quarterly Journal of

Economics 116:2, pp. 563-606.

Aghion, Philippe (2002), “Schumpeterian growth theory and the dynamics of income inequality,”

Econometrica 70:3, pp.855-82.

29

Aghion, Philippe, Eve Caroli and Cecilia Garcia-Penalosa (1999), “Inequality and economic growth: the

perspective of the new growth theories,” Journal of Economic Literature 37:4, pp.1615-60.

Aghion, Philippe and Peter Howitt (1998), Endogenous Growth Theory. M.A.: MIT Press.

Aghion, Philippe, Peter Howitt and Giovanni Violante (2002), “General purpose technology and within-

group inequality,” Journal of Economic Growth 7:4, pp. 315-45.

Autor, David H., Lawrence F. Katz and Alan B. Krueger (1998), “Computing inequality: have

computers changed the labor market?” Quarterly Journal of Economics 113:4, pp. 1169-213.

Autor, David H., Frank Levy and Richard J. Murnane (2003), “The skill content of recent technological

change: an empirical exploration,” Quarterly Journal of Economics 118:4, pp. 1279-1334.

Barro, Robert J. and Gary S. Becker (1989), “Fertility choice in a model of economic growth,”

Econometrica 57:2, pp. 481-501.

Becker, Gary S. (1962), “Investment in human capital: a theoretical analysis,” Journal of Political

Economy 70, pp. 9-49.

Becker, Gary S. (1964), Human Capital: A Theoretical and Empirical Analysis, with Special Reference

to Education. New York: Columbia University Press.

Becker, Gary S. (1985), “Human capital, effort, and the sexual division of labor,” Journal of Labor

Economics 3:1, pp. S33-58.

Becker, Gary S. and Robert J. Barro (1988), “A reformulation of the economic theory of fertility,”

Quarterly Journal of Economics 108:1, pp. 1-25.

Becker, Gary S., Kevin M. Murphy and Robert F. Tamura (1990), “Human capital, fertility, and

economic growth,” Journal of Political Economy 98:5, pt. 2, pp. S12-S37.

Benhabib, Jess and Mark M. Spiegel (1994), “The role of human capital in economic development:

evidence from aggregate cross-country data,” Journal of Monetary Economics 34:2, pp. 143-74.

Ben-Porath, Yoram (1967), “The production of human capital and the life cycle of earnings,” Journal of

Political Economy 75, pp. 352-65.

30

Berman, Eli, John Bound and Zvi Griliches (1994), “Changes in the demand for skilled labor within

U.S. manufacturing industries: evidence from the annual survey of manufactures,” Quarterly

Journal of Economics 109, pp. 367-97.

Berman, Eli, John Bound and Stephen Machin (1998), “Implications of skill-biased technological

change: international evidence,” Quarterly Journal of Economics 113, pp.1245-80.

Beaudry, Paul and David Green (1998), “What is driving U.S. and Canadian wages: exogenous technical

change or endogenous choice of technique?” NBER Working Papers no. 6853.

Blau, Francine D. (1998), “Trends in the well-being of American women: 1970-1995,” Journal of

Economic Literature 36:1, pp. 112-65.

Blau, Francine D. and Marianne A. Ferber (1992), “Women’s work, women’s lives: a comparative

economic perspective,” in Women’s Work and Women’s Lives: The Continuing Struggle Worldwide.

Hilda Kahne and Janet Z. Giele, ed. Boulder and Oxford: Westview Press.

Blau, Francine D. and Lawrence M. Kahn (1997), “Swimming upstream: trends in the gender wage

differential in 1980s,” Journal of Labor Economics 15:1, pp. 1-42.

Blau, Francine D. and Lawrence M. Kahn (2000), “Gender differences in pay,” Journal of Economic

Perspectives 14:4, pp. 75-99.

Bound, John and Richard B. Freeman (1992), “What went wrong? The erosion of relative earnings and

employment among young black men in the 1980s,” Quarterly Journal of Economics 107:1, pp.

201-32.

Bound, John and George Johnson (1992), “Changes in he structure of wages in the 1980s: an evaluation

of alternative explanations,” American Economic Review 82, pp. 371-92.

Bresnahan, Timothy F. (1999), “Computerization and wage dispersion: an analytical reinterpretation,”

Economic Journal 109, pp. F390-F415.

31

Bresnahan, Timothy F., Erik Brynjolfsson and Lorin M. Hitt (2002), “Information technology,

workplace organization and the demand for skilled labor: firm-level evidence,” Quarterly Journal of

Economics 117:1, pp. 339-76.

Card, David and Alan B. Krueger (1992), “School quality and black-white relative earnings: a direct

assessment,” Quarterly Journal of Economics 107:1, pp. 151-200.

Card, David and Thomas Lemieux (2001), “Can falling supply explain the rising return to college for

younger men?” Quarterly Journal of Economics 116:2, pp. 705-46.

Caroli, Eve and John van Reenen (2001), “Skill-biased organizational change? Evidence from a panel of

British and French establishments,” Quarterly Journal of Economics 116:4, pp. 1449-92.

Caselli, Francesco (1999), “Technological revolution,” American Economic Review 89:1, pp. 78-102.

Davis, Steven J. (1992), “Cross-country patterns of changes in relative wages,” NBER Macroeconomics

Annual 7, pp. 239-300.

Davis, Steven J. and John Haltiwanger (1991), “Wage dispersion within and between manufacturing

plants,” Brookings Papers on Economic Activity: Microeconomics, pp. 115-180.

Doms, Mark, Timothy Dunne and Kenneth R. Troske (1997), “Workers, wages, and technology,”

Quarterly Journal of Economics 112:1, pp. 253-90.

Freeman, Richard B. and Lawrence F. Katz (1994), “Rising wage inequality: the United States vs. other

advanced countries,” in Differences and Changes in Wage Structures, Richard Freeman and

Lawrence Katz, eds. Chicago, IL: University of Chicago Press and NBER.

Galor, Oded and Omer Moav (2000), “Ability biased technological transition, wage inequality and

economic growth,” American Economic Review 87, pp. 363-82.

Galor, Oded and David N. Weil (1996), “The gender gap, fertility, and growth” American Economic

Review 86:3, pp. 374-87.

Galor, Oded and David N. Weil (2000), “Population, technology, and growth: from Malthusian

stagnation to the demographic transition and beyond” American Economic Review 90:4, pp. 806-28.

32

Goldin, Claudia (1990), Understanding the Gender Gap: An Economic History of American Women.

Oxford: Oxford University Press.

Goldin, Claudia (1992), “The meaning of college in the lives of American women: the past one-hundred

years,” NBER Working Papers no. 4099.

Goldin, Claudia (1994), “The U-shaped female labor function in economic development and economic

history,” NBER Working Papers no. 4707.

Goldin, Claudia (2002), “The rising (and then declining) significance of gender,” NBER Working

Papers no. 8915.

Goldin, Claudia and Lawrence F. Katz (1998), “The origins of technology-skill complementarity,”

Quarterly Journal of Economics 113:3, pp. 693-732.

Gottschalk, Peter (1997), “Inequality in income, growth and mobility: the basic facts,” Journal of

Economic Perspectives 11, pp. 21-40.

Gottschalk, Peter and Timothy M. Smeeding (1997), “Cross-national comparisons of earnings and

income inequality,” Journal of Economic Literature 35:2, pp. 633-87.

Gould, Eric D., Omer Moav and Bruce Weinberg (2001), “Precautionary demand for education,

inequality and technological progress,” Journal of Economic Growth 6:4, pp. 285-316.

Greenwood, Jeremy and Mehmet Yorukoglu (1997), “1974,” Carnegie-Rochester Conference Series on

Public Policy, pp. 342-62.

Hall, Robert E. and Charles I. Jones (1999), “Why do some countries produce so much more output per

worker than others,” Quarterly Journal of Economics 110:3, pp. 83-116.

Hansen, Gary D. and Edward C. Prescott (2002), “Malthus to Solow,” American Economic Review 92:4,

pp. 1206-17.

Hornstein, Andres and Per Krusell (1996), “Can technology improvements cause productivity

slowdown?” NBER Macroeconomics Annual, pp. 209-59.

33

Jones, Charles I. (1995), “R&D-based models of economic growth,” Journal of Political Economy 103,

pp. 759-84.

Jones, Charles I. (2001), “Was an Industrial Revolution inevitable? Economic growth over the very long

run,” Advances in Macroeconomics 1:2, pp. 1-43.

Jones, Chales I. (2002), “Sources of U.S. Economic Growth in a World of Ideas,” American Economic

Review 92:1, pp. 220-39.

Juhn, Chinhui (1992), “Decline of male labor market participation: the role of declining market

opportunities,” Quarterly Journal of Economics 107:1, pp. 79-121.

Juhn, Chinhui, Kevin M. Murphy and Brooks Pierce (1991), “Accounting for the slowdown in black-

white wage convergence,” in Workers and Their Wages: Changing Patterns in the United States.

Marvin H. Kosters, ed. Washington, DC: AEI Press.

Juhn, Chinhui, Kevin M. Murphy and Brooks Pierce (1993), “Wage inequality and the rise in returns to

skill,” Journal of Political Economy 101, pp. 410-42.

Karoly, Lynn (1993), “The trend in inequality among families, individuals and workers in the United

States: a twenty-five years perspective,” in Uneven tides. S. Danziger and P. Gottschalk, eds. New

York: Russell Sage.

Katz, Lawrence F. and David H. Autor (2000), “Changes in the wage structure and earnings inequality,”

in Handbook of Labor Economics vol. III. Orley Ashenfelter and David Card, eds. Amsterdam:

Elsevier Science.

Katz, Lawrence F. and Kevin M. Murphy (1992), “Changes in relative wages: supply and demand

factors,” Quarterly Journal of Economics 107:1, pp. 35-78.

Klenow, Peter and Andres Rodriguez-Clare (1997), “The neoclassical revival in growth economics: has

it gone too far?” NBER Macroeconomics Annual, pp. 73-103.

Kremer, Michael and Eric Maskin (1996), “Segregation by skill and the rise in inequality,” NBER

Working Papers no. 5718.

34

Krueger, Alan B. and Mikael Lindahl (2001), “Education for growth: why and for whom?” Journal of

Economic Literature 39, pp. 1101-36.

Krusell, Per, Lee Ohanian, Victor Rios-Rull and Giovanni Violante (2000), “Capital-skill

complementarity and inequality: a macroeconomic analysis,” Econometrica 68, pp. 129-54.

Levy, Frank and Richard J. Murnane (1992), “U.S. earnings levels and earnings inequality: a review of

recent trends and proposed explanations,” Journal of Economic Literature 30, pp. 1333-81.

Lucas, Robert E. Jr. (1988), “On the mechanics of economic development,” Journal of Monetary

Economics 22, pp. 3-42.

Lucas, Robert E. Jr. (2002), “The Industrial Revolution: past and future,” in Lectures on Economic

Growth. Cambridge, MA: Harvard University Press.

Lloyd-Ellis, Huw (1999), “Endogenous technological change and wage inequality,” American Economic

Review 89:1, pp. 47-77.

Machin, Stephen (1996), “Changes in the relative demand for skills,” in Acquiring Skills, Market

Failures, their Symptoms and Policy Responses. A. L. Booth and D. J. Snower, eds. Cambridge, UK:

Cambridge University Press.

Mincer, Jacob (1974), Schooling, Experience and Earnings. New York: NBER.

Murphy, Kevin M. and Finis Welch (1992), “The structure of wages,” Quarterly Journal of Economics

107, pp. 255-85.

Nelson, Richard R. and Edmund S. Phelps (1966), “Investment in humans, technological diffusion, and

economic growth,” American Economic Review 56:2, pp. 69-75.

O’Neill, June and Solomon Polachek (1993), “Why the gender gap in wages narrowed in the 1980s,”

Journal of Labor Economics 11:1, pp. 205-228.

Pritchett, Lant (2001), “Where has all the education gone?” The World Bank Economic Review 15:3, pp.

367-91.

35

Romer, Paul (1990), “Endogenous technological change,” Journal of Political Economy 94, pp. S71-

S103.

Tamura, Robert F. (1996), “From decay to growth: a demographic transition to economic growth,”

Journal of Economic Dynamics and Control 20, pp. 1237-61.

Tamura, Robert F. (2002), “Human capital and the switch from agriculture to industry,” Journal of

Economic Dynamics and Control 27: pp. 207-42.

Thesmar, David and Mathias Thoenig (2000), “Creative destruction and firm organization choice: a new

look into the growth-inequality relationship,” Quarterly Journal of Economics 115:4, pp. 1209-38.

Thoenig, Mathias and Thierry Verdier (2003), “A theory of defensive skill-biased innovation and

globalization,” American Economic Review 93:3, pp. 709-28.

Topel, Robert H. (1997), “Factor proportions and relative wages: the supply-side determinants of wage

inequality,” Journal of Economic Perspectives 11:2, pp. 55-74.

Topel, Robert H. (1999), “Labor markets and economic growth,” in Handbook of Labor Economics.

Orley Ashenfelter and David Card, eds. Amsterdam: North Holland.

Violante, Giovanni L. (2002), “Technological acceleration, skill transferability and the rise in residual

inequality,” Quarterly Journal of Economics 117:1, pp. 297-338.

Zhang, Junsen, Jie Zhang and Tianyou Li (1999), “Gender bias and economic development in an

endogenous growth model,” Journal of Development Economics 59:2, pp. 497-525.