WPS6930
Policy Research Working Paper 6930
Comparative Advantage, International Trade,
and Fertility
Quy-Toan Do
Andrei Levchenko
Claudio Raddatz
The World Bank
Development Research Group
Macroeconomics and Growth Team
June 2014
Policy Research Working Paper 6930
Abstract
This paper analyzes theoretically and empirically the intensive goods are characterized by lower fertility. This
impact of comparative advantage in international trade is because female wages and therefore the opportunity
on fertility. It builds a model in which industries differ in cost of children are higher in those countries. The paper
the extent to which they use female relative to male labor demonstrates empirically that countries with comparative
and countries are characterized by Ricardian comparative advantage in industries employing primarily women
advantage in either female labor or male labor intensive exhibit lower fertility. The analysis uses a geography-based
goods. The main prediction of the model is that instrument for trade patterns to isolate the causal effect of
countries with comparative advantage in female labor comparative advantage on fertility.
This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger
effort by the World Bank to provide open access to its research and make a contribution to development policy discussions
around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors
may be contacted at qdo@worldbank.org, alev@umich.edu, or craddatz@bcentral.cl.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
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its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Comparative Advantage, International Trade, and
Fertility⇤
Quy-Toan Do Andrei A. Levchenko Claudio Raddatz
The World Bank University of Michigan Central Bank of Chile
NBER and CEPR
Keywords: Fertility, trade integration, comparative advantage.
JEL Codes: F16, J13, O11.
⇤
We are grateful to Raj Arunachalam, Martha Bailey, Francesco Caselli, Francisco Ferreira, Elisa Gam-
beroni, Gene Grossman, David Lam, Carolina Sanchez-Paramo, and seminar participants at various insti-
¸ gatay Bircan, Aaron Flaaen, Dimitrije Ruzic, and Nitya Pandalai Nayar
tutions for helpful suggestions. Ca˘
provided outstanding research assistance. The project has been funded in part by the World Bank’s Research
Support Budget. The views expressed in the paper are those of the authors and need not represent either
the views of the World Bank, its Executive Directors or the countries they represent, or those of the Central
Bank of Chile or the members of its board. This document is an output from a project funded by the
UK Department for International Development (DFID) and the Institute for the Study of Labor (IZA) for
the benefit of developing countries. The views expressed are not necessarily those of DFID or IZA. Email:
qdo@worldbank.org, alev@umich.edu, craddatz@bcentral.cl.
1 Introduction
Attempts to understand population growth and the determinants of fertility date as far back
as Thomas Malthus. Postulating that fertility decisions are influenced by women’s oppor-
tunity cost of time (Becker, 1960), choice over fertility has been incorporated into growth
models in order to understand the joint behavior of population and economic development
throughout history (see e.g. Barro and Becker 1989; Becker et al. 1990; Kremer 1993; Galor
and Weil 1996, 2000; Greenwood and Seshadri 2002; Doepke 2004; Doepke et al. 2007; Jones
and Tertilt 2008). The large majority of existing analyses examine individual countries in a
closed-economy setting. However, in an era of ever-increasing integration of world markets,
the role of globalization in determining fertility can no longer be ignored.
This paper studies both theoretically and empirically the impact of comparative advan-
tage in international trade on fertility outcomes. Our conceptual framework is based on
three assumptions. First, goods di↵er in the intensity of female labor: some industries em-
ploy primarily women, others primarily men. This assumption is standard in theories of
gender and the labor market Galor and Weil (1996); Black and Juhn (2000); Qian (2008);
Black and Spitz-Oener (2010); Rendall (2010); Pitt et al. (2012); Alesina et al. (2013), and
as we show below finds ample support in the data. In the rest of the paper, we refer to goods
that employ primarily (fe)male labor as the (fe)male-intensive goods. Second, women bear a
disproportionate burden of raising children. That is, a child reduces a woman’s labor market
supply more than a man’s. This assumption is also well-accepted (Becker, 1981, 1985; Galor
and Weil, 2000), and is consistent with a great deal of empirical evidence (see, e.g., Angrist
and Evans, 1998; Guryan et al., 2008). Finally, di↵erences in technologies and resource en-
dowments imply that some countries have a comparative advantage in the female-intensive
goods, and others in the male-intensive goods. Our paper is the first to both provide em-
pirical evidence that countries indeed di↵er in the gender composition of their comparative
advantage, and to explore the impact of comparative advantage in international trade on
fertility in a broad sample of countries.
The main theoretical result is that countries with comparative advantage in female-
intensive goods exhibit lower fertility. The result thus combines Becker’s hypothesis that
fertility is a↵ected by women’s opportunity cost of time with the insight that this opportu-
nity cost is higher in countries with a comparative advantage in female-intensive industries.
We then provide empirical evidence for the main prediction of the model using industry-
level export data for 61 manufacturing sectors in 145 developed and developing countries
over 5 decades. We use sector-level data on the share of female workers in total employment
to classify sectors as female- and male- intensive. The variation across sectors in the share
1
of female workers is substantial: it ranges from 8-9 percent in industries such as heavy
machinery to 60-70 percent in some types of textiles and apparel. We then combine this
industry-level information with data on countries’ export shares to construct, for each country
and time period, a measure of its female labor needs of exports that captures the degree to
which a country’s comparative advantage is in female-intensive sectors. We use this measure
to test the main prediction of the model: fertility is lower in countries with a comparative
advantage in female-intensive sectors.
The key aspect of the empirical strategy is how it deals with the reverse causality prob-
lem. After all, it could be that countries where fertility is lower for other reasons export
more in female-intensive sectors. To address this issue, we follow Do and Levchenko (2007)
and construct an instrument for each country’s trade pattern based on geography and a
gravity-like specification. Exogenous geographical characteristics such as bilateral distance
or common border have long been known to a↵ect bilateral trade flows. The influential
insight of Frankel and Romer (1999) is that those exogenous characteristics and the strong
explanatory power of the gravity relationship can be used to build an instrument for the
overall trade openness at the country level. Do and Levchenko (2007)’s point of departure
is that the gravity coe cients on the same exogenous geographical characteristics such as
distance also vary across industries – a feature of the data long known in the international
trade literature. This variation in industries’ sensitivity to the common geographical vari-
ables allows us to construct an instrument for trade patterns rather than the overall trade
volumes. Appendix B describes the construction of the instrument and justifies the identi-
fication strategy at length. As an alternative approach, we supplement the cross-sectional
2SLS evidence with panel estimates that include country and time fixed e↵ects.
Both cross-sectional and panel results support the main empirical prediction of the model:
countries with a higher female-labor intensity of exports exhibit lower fertility. The e↵ect is
robust to the inclusion of a large number of other covariates of fertility, and is economically
significant. Moving from the 25th to the 75th percentile in the distribution of the female-
labor needs of exports lowers fertility by as much as 20 percent, or about 0.36 standard
deviations of fertility across countries.
Our paper contributes to two lines of research in fertility. The first is the empirical testing
of Becker’s hypothesis that fertility is a↵ected by women’s opportunity cost of time. The key
hurdle in this literature is to identify plausibly exogenous variation in this opportunity cost.
While the negative correlation between women’s wages and fertility is very well-documented
(Jones et al., 2010), it cannot be interpreted causally, since wages are only observed for
women who work.1 Some authors have used educational attainment as an instrument for
1
While some studies have argued – implicitly or explicitly – that levels of female labor force participation
2
female wages after estimating a Mincer equation (Schultz, 1986) or directly as a proxy for
productivity (Jones and Tertilt, 2008). However, as emphasized by Jones et al. (2010),
education and occupational choices are potentially endogenous to fertility: women with a
preference for large families might decide to invest less in education or choose occupations
with lower market returns. Alternatively, to avoid using endogenous individual characteris-
tics, some studies use median and/or mean female wages to proxy for women’s opportunity
cost of time (Fleisher and Rhodes, 1979; Heckman and Walker, 1990; Merrigan and St.-
Pierre, 1998; Blau and van der Klaauw, 2007). Still, when the wage statistics are computed
from the selected sample of working women, they may not be representative of women’s
opportunity cost of time when it comes to fertility decisions.2 Our approach avoids these
limitations. By constructing country-level measures of female labor needs of exports, and
instrumenting these using exogenous (and arguably excludable) geographical variables, we
build a proxy for women’s opportunity cost of time that is exogenous to individual fertility,
education, or labor force participation.3 Our paper thus provides novel empirical evidence
on Becker’s influential hypothesis.
The second is the (still sparse) literature on fertility in the context of international in-
tegration. Schultz (1985) shows that the large changes in world agricultural prices and the
gender division of labor in agriculture a↵ected fertility in 19th-century Sweden. Galor and
Mountford (2009) study the impact of initial comparative advantage on the dynamics of
fertility and human capital investments. Saur´ e and Zoabi (2011a,b) examine how trade af-
fects female labor share, wage gap, and fertility in a factor proportions framework featuring
complementarity between capital and female labor. Rees and Riezman (2012) argue that
when foreign direct investment improves work opportunities for women, fertility will fall.
Our framework is the first to combine the Ricardian motive for trade with di↵erences in
female-labor intensity across sectors.
Our paper also relates to the small but growing literature on the impact of globalization on
gender outcomes more broadly (Black and Brainerd, 2004; Oostendorp, 2009; Aguayo-Tellez
et al., 2010; Marchand et al., 2013; Juhn et al., 2014). Closest to our paper is Ross (2008), who
shows empirically that oil-abundant countries have lower FLFP. Ross (2008)’s explanation
are “high enough” in the U.S. so that censoring is not a significant issue (Cho, 1968; Fleisher and Rhodes,
1979), this assumption would be more problematic to make in the context of low and middle-income countries,
that typically exhibit low levels of female labor force participation and for which data on female wages are
scarce and imprecise in part due to the large size of the informal sector (World Bank, 2012).
2
Heckman and Walker (1990) argue that “[i]t is plausible that in Sweden the wage process is exogenous
to the fertility process. Sweden uses centralized bargaining agreements to set wages and salaries” (p.1422).
Since this institutional feature is specific to Sweden, this approach is di cult to extend to other contexts.
3
Our methodology is thus similar in spirit to Alesina et al. (2013), who also use a geography-based variable
(soil crop suitability in this case) as an instrument for the adoption of a female-labor-intensive technology:
the plough.
3
for this empirical pattern is that Dutch disease in oil-exporting countries shrinks the tradable
sector, and expands the non-tradable sector. If the tradable sector is more female-intensive
than the non-tradable sector, oil lowers demand for female labor and therefore FLFP. Our
theoretical mechanism relies instead on variation in female-labor intensity within the tradable
sector. On the empirical side, the e↵ect we demonstrate is much more general: it is present
when excluding natural resource exporters, as well as excluding the Middle East-North Africa
region.
The rest of the paper is organized as follows. Section 2 presents a simple two-country
two-sector model of comparative advantage in trade and endogenous fertility. Section 3 lays
out our empirical strategy to test the predictions of the model. Section 4 describes the data,
while section 5 presents estimation results. Section 6 concludes. All the proofs are collected
in Appendix A.
2 Theoretical Framework
2.1 The Environment
Consider an economy comprised of two countries indexed by c 2 {X, Y }, and two sectors
c c
indexed by i = {F, M }. The representative household in c values consumption CF and CM
of the two goods, as well as the number of children N c it has according to the utility function
c c c ⌘ c 1 ⌘
u ( CF , CM , N c ) = ( CF ) ( CM ) + v (N c ) ,
with v (.) is increasing and concave. To guarantee interior solutions, we further assume that
limN !0 v 0 (N ) = +1.4
We adopt the simplest form of the gender division of labor, and assume that production
in sector F only requires female labor and capital, while sector M only requires male labor
and capital. Technology in sector i is therefore given by
Yic (Ki , Li ) = ic Ki↵ L1
i
↵
,
where Li is the sector’s employment of female labor (in sector F ) and male labor (in sector
c2{X,Y }
M ), Ki is the amount of capital used by sector i, and {ic }i2{M,F } are total factor productivities
in the two sectors and countries. Formally, this is the specific-factors model of production
4
The assumption that utility is quasi-linear in income is made for analytical tractability. It shuts down
the income e↵ect and allows us to focus solely on the substitution e↵ect. For discussions on conditions for
the substitution e↵ect to dominate the income e↵ect under more general assumptions, see Jones et al. (2010)
and Mookherjee et al. (2012).
4
and trade (Jones, 1971; Mussa, 1974), in which female and male labor are specific to sectors
F and M respectively, while K can move between the sectors. Thus, we take the arguably
simplistic view that men supply “brawn-only” labor, while women supply “brain-only” labor,
and men and women are not substitutes for each other in production within each individual
sector. Of course, there is still substitution between male and female labor in the economy
as a whole, since goods F and M are substitutable in consumption.5
The key to our results is the assumption that countries di↵er in their relative productiv-
ities F c /M c . For convenience, we normalize
(F c )⌘ (M c )1 ⌘
=1 (1)
in both countries. Since the impact of relative country sizes is not the focus of our analysis,
and the aggregate gender imbalances in the population tend to be small, we set the country
endowments of male and female labor and capital to be L ¯c = L ¯ c = 1 and K ¯ c = 1 for
M F
c 2 {X, Y }. Capital can move freely between sectors, and the market clearing condition
c c
for capital is KF + KM = 1. Men supply labor to the goods production sector only, and
hence supply it inelastically: Lc
M = 1. On the other hand, childrearing requires female labor,
and women split their time between goods production and childrearing. N c children require
⇥ ⇤
spending N c units of female labor at home, so that N c 2 0, 1 . Female market labor force
participation is then LcF = 1 N c.
All goods and factor markets are competitive. International trade is costless, while capital
and labor cannot move across countries.6 In country c, capital earns return rc and female
c c
and male workers are paid wages wF and wM , respectively. Let the price of goods i 2 {M, F }
be denoted by pi , and set the price of the goods consumption basket to be numeraire:
p⌘ 1 ⌘
F pM = 1. (2)
5
The necessary condition for obtaining our results is that in equilibrium, women’s relative wages are
higher in the country with a Ricardian comparative advantage in the female-intensive good. This plausible
equilibrium outcome obtains under more general production functions in which both types of labor are used
in both sectors (see, for instance, Morrow, 2010). On the other hand, our result is inconsistent with models
that feature Factor Price Equalization (FPE). FPE is ruled out in our model by cross-country productivity
di↵erences in all sectors, which implies that generically FPE does not hold in our model.
6
The assumption of no international capital mobility is not crucial for our results. In fact, our results
can be even more transparent with perfect capital mobility. When capital is internationally mobile, relative
female wages in the two countries depend only on the relative Total Factor Productivities in the female sector
X Y 1/(1 ↵)
(when the solution is interior): wF /wF = F X /F Y . This expression relates relative female wages
to absolute advantage in the female-intensive sector. Thus, as long as a country’s Ricardian comparative
advantage is the same as its absolute advantage (that is, as long as M X /M Y is such that F X /F Y Q 1 )
F X /F Y M Y /M X Q 1), it will have higher female wages, and the rest of the results follow.
5
It will be convenient to express all the equilibrium outcomes of the economy (prices and
KFc
quantities) as functions of ✓c ⌘ K c c
instead of KF .
M
c2{X,Y }
A competitive equilibrium in this economy is a set of prices {pi , rc , wi c
}i2{M,F } , capital
c 2 { X,Y } c 2 { X,Y }
allocations {✓c } , and fertility levels {N c } , such that (i) consumers maximize
utility; (ii) firms maximize profits; (iii) goods and factor markets clear.
Fertility in both countries and production/consumption allocations are thus jointly de-
termined in equilibrium, making it more di cult to handle than the typical model of inter-
national exchange in which factor supplies are fixed. For expositional purposes, we describe
the equilibrium in two steps. We first characterize the global production and consumption
allocations for a given fertility profile {N c }c2{X,Y } . We then endogenize households’ decisions
over fertility.
2.2 Production and Trade Equilibrium
We first characterize the production and trade equilibrium under a fixed female labor supply
⇥ ⇤
Lc
F = 1 N c , for a given N c 2 0, 1 .
Firms’ optimization In each of the two sectors i 2 {M, F }, firms rent capital and hire
labor to maximize profits:
max pi ic K ↵ L1 ↵
rc K c
wi L.
K,L
The necessary and su cient first-order conditions with respect to Kic yield the following
⇣ c ⌘1 ↵
c
c Li
expression for the return to capital: rpi
= ↵ i c
Ki
. Equalizing the returns to capital
across sectors and assuming that labor markets clear pins down relative prices of the two
pF c ✓c 1 ↵
goods: p M
=M F c 1 Nc
. Under the choice of numeraire (2), prices are equal to
8
1 indicates that country c has a comparative advantage in the female-
.
intensive good F . The comparative advantage can be decomposed into a technological or
Nc
Ricardian component c and an occupational or “factor-proportions” component 11 N c,
which can exacerbate or attenuate technological di↵erences. We rewrite the two equations
(7) and (8) as a system of two equations with two unknowns {✓c , ✓ c } given exogenous model
parameters and “pre-determined” values {N c , N c }:
⌘ (1 ⌘ ) ✓c ↵) ⌘ (1 ⌘ ) ✓ c
c ↵ + ( c )⌘(1 = 0 (9)
(1 + ✓ ) (1 + ✓ c )↵
✓ c
⇢c c = 1 (10)
✓
7
Equation (9) implicitly defines a downward-sloping “goods market-clearing curve” in the
space (✓ c , ✓c ) and is just⇣a rearrangement
⌘⌘ of equation (7), keeping in mind that normalization
M c F cM c ⌘
(1) implies that M c = M c F c = ( c ) (1 ↵) . Since goods produced by the two countries
are perfect substitutes, market clearing implies a negative relationship between the size ✓c
of the F -sector in country c and its size ✓ c in country c. On the other hand, the upward-
sloping “factor market-clearing curve” in the space (✓ c , ✓c ), defined by (10), implies that
F -sectors have to be of comparable size in the two countries (i.e. the larger sector F gets in
country c, the larger it needs to be in country c as well), otherwise the return to capital will
diverge across the F - and M -sectors in each country. Thus, allocations of capital between
two sectors in the two countries {✓c }c2{X,Y } are uniquely determined by the system of two
equations (9) and (10).
Proposition 1: Production and trade equilibrium Consider the endowment struc-
ture K ¯ c , Lc c2{X,Y } = {1, 1, 1
¯ c, L N c }c2{X,Y } . The unique production and consump-
M F
c c2{X,Y }
tion equilibrium is characterized by the vector of prices {pi , rc , wi }i2{M,F } defined by (3)-(6),
2 { }
and capital allocations {✓c } c X,Y
that solve (9)-(10).⌅
The proof of Proposition 1 establishes existence of an intersection of the two “factor
market-clearing” and “goods market-clearing” curves, which is therefore unique since the two
curves have opposite slopes.
2.3 Fertility Decisions
The analysis above is carried out under an exogenously fixed fertility rate or, equivalently,
an exogenously fixed level of female labor force participation. We now turn to endogenizing
households’ fertility decisions. To pin down equilibrium fertility N c , we proceed in two steps.
c
First, for a given N c , wF and N c are jointly determined by labor supply and demand. Thus,
we must ensure that labor supply is upward-sloping and the female labor market equilibrium
is well defined. Second, fertility in the other country a↵ects the labor market equilibrium by
shifting female labor demand and hence fertility in country c. We therefore look for a fixed
point in {N c , N c } such that the female labor markets are in equilibrium in both countries
simultaneously.
Fertility choices and female labor supply Taking N c as given and anticipating the
production equilibrium prices and quantities, households make fertility decisions accordingly.
8
Namely, they take prices as given and choose N c to maximize their indirect utility:
c
V c (N ) = r c + wF (1 c
N ) + wM + v (N ) . (11)
The first-order condition for the representative household’s fertility decision is necessary and
su cient and given by 8
0 . ⌅
Thus, an increase in female labor supply in country c increases c’s comparative advantage
in the female-labor intensive good (the factor-proportions e↵ect). This will increase ✓c , the
size of the F -sector in country c and exert a downward pressure on female wages. By the same
token, country c0 s comparative advantage in the female-labor intensive good is reduced,
decreasing ✓ c , the size of the F -sector in that country, which in turn will put additional
downward pressure on female wages in country c. The female labor demand curve is therefore
downward-sloping.
Lemma 2: Fertility in partial equilibrium For a given level of the other country’s
fertility level N c , there exists a unique N c satisfying both (12) and (13).⌅
In the proof of Lemma 2, we establish that the female labor supply and demand curves
either intersect at the corner, i.e. N c = 1 , or in the interior and the solution is also unique
since labor supply and demand curves have opposite slopes.
Equilibrium fertility Lemma 2 and the labor demand equation (13) imply that the female
labor demand curve in country c shifts down when female labor supply in country c goes
up. Thus N c (N c ) , the equilibrium fertility rate in country c when that rate in country
c is N c , is decreasing; so is N c (N c ) . The following proposition formally establishes that
these two “reaction functions” intersect and therefore defines the complete equilibrium of the
economy.
Proposition 2: Full characterization of the equilibrium Equations (3) to (6),
c i2{M,F }
(10), and (12) define a vector of prices {pi , rc , wi }c2{X,Y } , capital allocations {✓c }c2{X,Y } and
fertility decisions {N c }c2{X,Y } that form the unique equilibrium of the economy.⌅
Comparative statics and cross-sectional comparisons We now consider (✓c , N c ) and
˜c , N
(✓ ˜ c ), two equilibrium capital allocations and fertility decisions of the economy when the
Ricardian comparative advantage of country c takes values c and ˜ c , respectively. The
objective of this section is to compare fertility and the allocation of capital across sectors in
these two parameter configurations.
10
Lemma 3: Comparative statics in general equilibrium An increase in compara-
˜ c .⌅
˜ c and N c N
tive advantage exacerbates fertility di↵erences: if c ˜ c , then N c N
From Lemma 3, the main result of the paper is stated in the theorem below:
Theorem 1: Cross-sectional comparison If country c has a Ricardian comparative
Fc F c
advantage in the female-labor intensive sector ( M c > M c ), it will exhibit lower equilibrium
fertility: N c < N c .⌅
Theorem 1 is the main theoretical prediction of the model, and one that will be tested
empirically. The intuition for this result is as follows. Female wages will be higher in the
country with the comparative advantage in the female-intensive sector because of higher
relative productivity further exacerbated by a flow of capital to the sector with comparative
advantage. Since a higher female wage increases the opportunity cost of childbearing in
terms of goods consumption, equilibrium childbearing drops.
The theoretical exposition above makes clear what are the measurement and identifica-
tion challenges for the empirical work. First, in order to test for the impact of gender-biased
comparative advantage on fertility, we must develop a measure of comparative advantage in
(fe)male sectors. Fortunately, the model presents us with a way of doing this: observed trade
flows. Countries with a comparative advantage in the female-intensive good will export that
good. Our empirical strategy thus starts by building a measure of the female intensity of
exports based on observed export specialization. Second, the model shows quite clearly that
observed specialization patterns, trade flows, and fertility levels are jointly determined. In
particular, countries with higher technological comparative advantage in the female sector
can potentially accentuate that comparative advantage with a higher female labor supply
and will thus e↵ectively exhibit relative factor proportions that also favor exports in the
female-intensive sectors. Thus, in order to provide evidence for the causal impact of compar-
ative advantage on fertility, we must find an exogenous source of variation in comparative
advantage. We describe all parts of our empirical strategy and results below.
3 Empirical Strategy
To test for the impact of comparative advantage on fertility, we must first construct a measure
of the degree of female bias in a country’s export pattern. We begin by classifying sectors
according to their female intensity. Let an industry’s female-labor intensity F Li be measured
as the share of female workers in the total employment in sector i. We take this measure
as a technologically determined industry characteristic that does not vary across countries.
11
We then construct for each country and time period a measure of the “female-labor needs of
exports”:
XI
X
F LN Xct = !ict F Li , (14)
i=1
X
where i indexes sectors, c countries, and t time periods. In this expression, !ict is the share
of sector c exports in country c’s total exports to the rest of the world in time period t. Thus,
F LN Xct in e↵ect measures the gender composition of exports in country c. This measure is
meant to capture the female bias in each country’s comparative advantage. It will be high
if a country exports mostly in sectors with a large female share of employment, and vice
versa.7
Using this variable, we would like to estimate the following equation in the cross-section
of countries:
N c = ↵ + F LN Xc + Zc + "c . (15)
The left-hand side variable N c is, as in Section 2, the number of births per woman, and Zc
is a vector of controls. The main hypothesis is that the e↵ect of comparative advantage in
female-intensive sectors F LN Xc on fertility is negative ( < 0). The potential for reverse
causality is immediate here: higher fertility will reduce women’s formal labor force partic-
ipation and therefore could also a↵ect the country’s export pattern. To deal with reverse
causality, we implement an instrumentation strategy that follows Do and Levchenko (2007),
and exploits exogenous geographical characteristics of countries, together with how those
exogenous characteristics a↵ect international trade in di↵erent industries di↵erentially. The
construction of the instrument is described in detail in Appendix B.
We also exploit the time variation in the variables to estimate a panel specification of the
type
Ntc = ↵ + F LN Xct + Zct + c + t + "ct , (16)
where country and time fixed e↵ects are denoted by c and t respectively. The advantage of
the panel specification is that the use of fixed e↵ects allows us to control for a wide range of
time-invariant omitted variables that vary at the country level, and identify the coe cient
purely from the time variation in comparative advantage and fertility outcomes within a
country over time.
The baseline controls include PPP-adjusted per capita income, overall trade openness,
and, in the case of cross-sectional regressions, regional dummies. (We also check robustness
of the results to a number of additional control variables.) The cross-sectional specifications
7
The form of this index is based on Almeida and Wolfenzon (2005) and Do and Levchenko (2007), who
build similar indices to capture the external finance needs of production and exports.
12
are estimates on long-run averages for the period 1980-2007. The panel specifications are
estimated on non-overlapping 5-year and 10-year averages. As per standard practice, we take
multi-year averages in order to sweep out any variation at the business cycle frequency. The
panel data span 1962 to 2007 in the best of cases, though not all variables for all countries
are available for all time periods.
4 Data Sources and Summary Statistics
The key indicator required for the analysis is the share of female workers in the total em-
ployment in each sector, F Li . This information comes from the UNIDO Industrial Statistics
Database (INDSTAT4 2009), which records the total employment and female employment
in each manufacturing sector for a large number of countries at the 3-digit ISIC Revision 3
classification (61 distinct sectors), starting in the late 1990s. We compute F Li as the mean
share of female workers in total employment in sector i across the countries for which these
data are available and relatively complete. This sample includes 11 countries in each of
the developed and developing sub-samples: Austria, Cyprus, Ireland, Italy, Japan, Lithua-
nia, Korea, Malta, New Zealand, Slovak Republic, United Kingdom; and Azerbaijan, Chile,
Egypt, India, Indonesia, Jordan, Malaysia, Morocco, Philippines, Thailand, Turkey. Table
1 reports the values of F Li in our sample of sectors. It is clear that there is wide variation
in the share of women in sectoral employment. While the mean is 27 percent, these val-
ues range from the high of 71 percent in Wearing Apparel and 62 percent in Knitted and
Crocheted Fabrics to the low of 8 or 9 percent in Motor Vehicles, Bodies of Motor Vehicles,
Building and Repairing of Ships, and Railway Locomotives.8 One may be concerned that
F Li could simply be a proxy for skill intensity (since women supply relatively more “brain”
than “brawn” labor input compared to men). However, it turns out that F Li is uncorrelated
with skill intensity.9
8
One may be concerned that these values are very di↵erent across countries in general, and across devel-
oped and developing countries in particular. However, it turns out that the rankings of sectors are remarkably
similar across countries. The values of F Li computed on the OECD and non-OECD samples have a correla-
tion of 0.9. The levels are similar as well, with the average F Li in the OECD of 0.29, and in the non-OECD
of 0.27 in this sample of countries. Pooling all the countries together, the first principal component explains
77 percent of the cross-sectoral variation across countries, suggesting that rankings are very similar. We also
experimented with taking alternative averages: medians instead of means across countries; and dropping
outlier values of female shares in individual sectors. The results were very similar. Another concern is that
F Li is measured based on data from the last 10-15 years, whereas our estimation sample goes back several
decades. We are not aware of similar data for earlier periods. Our measure of F Li can be combined with
data for earlier time periods as long as there are no “gender-intensity reversals” over time, that is, the ranking
of industries by female intensity is stable.
9
The correlation between F Li and the share of skilled workers in the total wage bill is 0.06, and the
correlation between F Li and the share of skilled workers in total industry employment is -0.06. The skill
13
X
The export shares !ict are calculated based on the COMTRADE database, which contains
bilateral trade data starting in 1962 in the 4-digit SITC revision 1 and 2 classification. The
trade data are aggregated up to the 3-digit ISIC Revision 3 classification using a concordance
developed by the authors.
Table 2 reports some summary statistics for the female labor needs of exports for the
OECD and non-OECD country groups. We observe that for the OECD, the measure is
relatively stable across decades, with an average of about 0.25. For the non-OECD countries,
the female labor needs of exports is higher, between 0.27 and 0.30, and, if anything, rising
over time. Notably, the dispersion in F N LX among the non-OECD countries is both much
greater than among the OECD, and increasing over time. In the OECD sample, the standard
deviation is stable at 0.03-0.04, whereas in the non-OECD sample it rises monotonically from
0.08 to 0.12 between the 1960s and the 2000s.
Tables 3 reports the countries with the highest and lowest F LN X values. Typically,
countries with the highest values of female content of exports are those that export mostly
textiles and wearing apparel, while countries with the lowest F LN X are natural resource
exporters.
Equally important for our empirical strategy are changes over time. Table 4 reports
the countries with the largest positive and negative changes in F LN X between the 1960s
and today. We can see that relative to the cross-sectional variation, the time variation
is also considerable. For the countries with the largest observed increases in F LN X , the
common pattern is that they change their specialization from agriculture-based sectors to
wearing apparel. For instance, in the 1960s 80% of exports from Cambodia were in the food
products sectors (ISIC 151 through 154). By the 2000s, 85% of Cambodian exports are in
ISIC 181, “Wearing apparel.” The other countries in the top 10 largest positive changes in
F LN X follow this pattern as well. Since food products sectors are right in the middle of
the F Li distribution, and “Wearing apparel” is the most female-intensive sector, this type of
specialization change will lead to large increases in F LN X .
The largest observed decreases in F LN X are driven by the discovery of natural resources.
For instance, Niger was an agricultural exporter in the 1960s, with nearly 80% of exports
in ISIC 151, “Meat, fish, fruit, vegetables, oils and fats.” By the 2000s, over 60% of Niger’s
exports were in “Refined petroleum products” (ISIC 232) and “Nuclear fuel” (ISIC 233).
The natural resource-based sectors are among the least female-intensive, with F Li of 0.11-
0.13, which accounts for why countries with major shifts towards natural resources exhibit
intensity data come from Autor et al. (1998), who compute these measures for the U.S.. Unfortunately, we
cannot compute skill intensity measures from the UNIDO data used to compute F Li , as these data do not
include employment breakdowns by education level.
14
reductions in their F LN X .
It turns out that these two groups of countries experienced very di↵erent changes in
fertility. Among the 10 countries with the largest increases in F N LX , fertility fell on average
by 3.5 children per woman, from 6.5 to 3 between the 1960s and the 2000s. By contrast,
in the 10 countries with the largest decreases in F N LX , fertility fell by only 1.3 children
per woman over the same period, from 6.9 to 5.6. Remarkably, while these two groups had
similar fertility levels in the 1960s (6.5 and 6.9), their subsequent paths were very di↵erent.
This is of course only an illustrative example, and we explore these patterns formally in the
next section.
Data on fertility are sourced from the World Bank’s World Development Indicators. The
baseline controls – PPP-adjusted per capita income and overall trade openness – come from
the Penn World Tables. Table 2 presents the summary statistics for fertility (number of births
per women) in each decade and separately for OECD and non-OECD countries. There is
considerable variation in fertility across countries: while the median fertility after 1980 is
3.3 births per woman in our sample of countries, the standard deviation is 1.8, and the
10th-90th percent range spans from 1.4 to 6.3. The table highlights the pronounced cross-
sectional di↵erences between high- and low-income countries, as well as the secular reductions
in fertility over time in both groups of countries. Our final dataset contains country-level
variables on up to 145 countries.
5 Empirical Results
5.1 Cross-sectional results
Table 5 reports the results of estimating the cross-sectional specification in equation (15).
Both left-hand side and the right-hand side variables are in natural logs. All of the specifica-
tions control for income per capita and overall openness. Column 1 presents the OLS results.
There is a pronounced negative relationship between the female-labor need of exports and
fertility, significant at the one percent level. By contrast, the coe cient on overall trade
openness is zero to the second decimal point and not significant. As is well known, income
per capita is significantly negatively correlated with fertility. These three variables absorb a
great deal of variation in fertility across countries: the R2 in this regression is 0.63. Column
2 repeats the OLS exercise but including the regional dummies.10 The R2 increases to 0.86,
10
The regional dummies correspond to the o cial World Bank region definitions: East Asia and Pacific,
Europe and Central Asia, Latin America and the Caribbean, Middle East and North Africa, North America,
South Asia, and Sub-Saharan Africa.
15
but the female labor need of exports remains equally significant. Figure 1 displays the partial
correlation between fertility and F N LX from Column 2 of Table 5.
Column 3 implements the 2SLS procedure. The bottom panel displays the results of the
first stage. As expected, the instrument is highly significant with a t-statistic of 9.4, and
the F -statistic for the excluded instrument of 43 is comfortably within the range that allows
us to conclude that the instrument is strong (Stock and Yogo, 2005). Figure 2 presents the
partial correlation plot from the first stage regression between F N LX and the instrument.
There is a clear positive association between the two variables that does not appear to be
driven by a few outliers. As expected, the variation in the instrument is much smaller than
the variation in the actual F N LX . The instrument is predicting F N LX while throwing out
a great deal of country-specific information, and thus the instrument’s predictions for the
country-specific F N LX vary much less across countries than do actual values.
In the second stage, the main variable of interest, F N LX , is statistically significant at the
one percent level, with a coe cient that is about one-third larger in absolute value than the
OLS coe cient. Column 4 repeats the 2SLS exercise adding regional dummies. The second-
stage coe cient of interest both increases in absolute value and becomes more statistically
significant.
The OLS and 2SLS results described above constitute the main cross-sectional finding
of the paper. Countries that have a comparative advantage in the female-intensive sectors
exhibit lower fertility. The estimates are economically significant. Taking the coe cient in
column 4 as our preferred estimate, a 10 percent change in F N LX leads to a 4.7 percent
lower fertility rate. In absolute terms, this implies that moving from the 25th to the 75th
percentile in the distribution of the female content of exports lowers fertility by as much as
20 percent, or about 0.36 standard deviations of average fertility across countries. Applied
to the median of 3.3 births per woman in this sample of countries, the movement from the
25th to the 75th percentile in F LN X implies a reduction of 0.64 births per woman.
5.2 Panel Results
The cross-sectional 2SLS results are informative, and allow us to make the clearest case for
the causal relationship between comparative advantage and fertility. However, because they
do not allow the use of country fixed e↵ects, the cross-sectional results may still su↵er from
omitted variables problems. As an alternative empirical strategy, we estimate the panel
specification (16) on non-overlapping 5-year and 10-year averages from 1962 to 2007. The
gravity-based instrumentation strategy is not feasible in a panel setting with fixed e↵ects.
On the other hand, country e↵ects allow us to control for a wide range of unobservable time-
16
invariant country characteristics, and identify the coe cient of interest from the variation in
F N LX and fertility within a country over time.
The results are presented in Table 6. To control for autocorrelation in the error term,
all standard errors are clustered at the country level. Column 1 reports the results for
the pooled specification without any fixed e↵ects. The coe cient is remarkably similar to
the OLS coe cient from column 1 of Table 5. Column 2 adds country fixed e↵ects. The
coe cient on F N LX is nearly unchanged, and significant at the one percent level. Column 3
adds time e↵ects to control for secular global trends, while column 4 adds female educational
attainment. The results continue to be highly significant. Columns 5–8 repeat the exercise
taking 10-year averages instead.11 The coe cients are very similar in magnitude and equally
significant.
5.3 Robustness
We now check the robustness of the cross-sectional result in a number of ways. The first set
of checks is on how the instrument construction treats zero trade observations. As detailed in
Appendix B, the baseline instrument estimates the standard log-linear gravity specification
that omits zeros in the trade matrix, and predicts trade only for those values in which
observed trade is positive. We address the issue of zeros in two ways. The first is to predict
trade values for the observations in which actual trade is zero based on the same log-linear
regression. The second is to instead estimate a Poisson pseudo-maximum likelihood model on
the levels of trade values, as suggested by Santos Silva and Tenreyro (2006). In this exercise,
the zero trade observations are included in the estimation sample. The results of using those
two alternative instruments are presented in columns 5 and 6 of Table 5. It is clear that very
little is changed. The instruments continue to be strong, and the second-stage coe cients of
interest are similar in magnitude and significant at the one percent level. We conclude from
this exercise that the way zeros are treated in the construction of the instrument does not
a↵ect the main results.
Another concern is that the instrument is constructed based on variables – such as pop-
ulation – that do not satisfy the exclusion restriction. Note that the instrument relies on
the di↵erential impact of each gravity variable across sectors, as determined by the sectoral
variation in non-country-specific gravity coe cients. To further probe into the importance of
the country-specific gravity variables, column 7 of Table 5 implements the instrument with-
out the exporter population (the population of each particular trading partner is plausibly
exogenous to the exporting country’s fertility). The instrument remains strong, as evidenced
11
To be more precise, these are decadal averages for the 1960s, 1970s, and up to 2000s. Since our yearly
data are for 1962-2007, the 1960s and the 2000s are averages over less than 10 years.
17
by the first stage diagnostics, and the main result is robust. Alternatively, column 8 controls
for area and population directly. Area is insignificant as a determinant of fertility, and popu-
lation comes in with the right sign, but the size of the coe cient, interpreted as an elasticity,
is small. The coe cient of interest remains significant and of similar magnitude.
Table 7 performs a number of additional specification checks. All columns report the
2SLS results controlling for openness, income, and regional dummies. First, we may expect
the impact of F N LX to get stronger with openness. Column 1 checks this by adding
an interaction term between F N LX and overall openness. As expected, the interaction
coe cient is significant: in more open countries the e↵ect we highlight is more pronounced.12
Next, it might be that what matters is the female labor need of net exports. That is,
perhaps a country imports a lot of the female-labor intensive goods, in which case its domestic
demand for female labor will be lower. This is unlikely to be a major force on average, as
import baskets tend to be more similar across countries than export baskets. Most countries
specialize in a few sectors, but import a broad range of products. Indeed, in our data the
standard deviation of the “female labor need of imports ” (F N LI ) is 3.6 times smaller than
the standard deviation of F N LX . Nonetheless, to check the robustness of the results, we use
the female labor need of net exports, F N LX F N LI , as the independent variable. Since
it can take negative values, we must use levels rather than logs. As the instrument, we use
the level of predicted F N LX , rather than log. Column 2 of Table 7 reports the results, and
shows that they are robust to using this alternative regressor of interest.
Next, we check whether the results are robust to including additional controls. Column 3
controls for female schooling, to account for the possible relationship between education and
fertility. Female schooling is measured as the average number of years of schooling in the
female population over 25, and is sourced from Barro and Lee (2000). While higher female
schooling is indeed associated with lower fertility, the coe cient on F N LX changes little
and continues to be significant at the one percent level. Column 4 controls for the prevalence
of child labor, since fertility is expected to be higher when children can contribute income to
the household. Child labor is measured as the percentage of population aged 10-14 that is
working, and comes from Edmonds and Pavcnik (2006). While the prevalence of child labor
is indeed positively associated with fertility, the main coe cient of interest remains robust.
Column 5 controls for infant mortality, sourced from the World Bank’s World Development
12
The main e↵ect of F N LX is now positive, but of course the overall e↵ect is a combination of the main
e↵ect and the coe cient on openness times openness. The distribution of openness in this sample of countries
is such that the point estimate of the combined e↵ect of F N LX , which is equal to 1.68 0.49⇥Log (Openness),
is positive for all but the bottom 5% least open countries. The table does not report the first-stage coe cients
and diagnostics in order to conserve space since there are now two variables being instrumented. The F -
statistics associated with both instrumented variables are in excess of 35.
18
Indicators. Countries with higher infant mortality have higher fertility, but our coe cient
of interest remains robust.
Next, column 6 controls for income inequality, using the Gini coe cient from the World
Bank’s World Development Indicators. Higher inequality is associated with higher fertility,
but once again the main result is robust. Finally, column 7 controls for the extent of democ-
racy, using the Polity2 index from the Polity IV database. The extent of democracy is not
significantly associated with fertility, and F N LX is still significant at the one percent level.
Table 8 checks whether the finding is driven by particular countries. Column 1 drops
outliers: the top 5 and bottom 5 countries in the distribution of F N LX . Column 2 drops
the OECD countries, to make sure that our results are not driven simply by the distinction
between high-income countries and everyone else.13 Column 3 drops the Middle East and
North Africa region, and column 4 drops Sub-Saharan Africa. It is clear that the results are
fully robust to dropping outliers and these important country groups. The coe cients are
similar to the baseline and the significance is at one percent throughout. Finally, column 5
drops mining exporters, defined as countries that have more than 60% of their exports in
Mining and Quarrying, a sector that includes crude petroleum.14 The results are una↵ected
by dropping these countries.
The women’s opportunity-cost-of-time hypothesis has a natural counterpart in another
use of time, namely female labor force participation (FLFP). We should expect that an
increase in comparative advantage in female-intensive sectors, as it lowers fertility, should
also increase FLFP. Appendix C discusses this issue at length and estimates the relation-
ship between comparative advantage in female-intensive sectors and FLFP. It appears that
comparative advantage in female-intensive sectors increases FLFP, but only for countries
with lower levels of income and female educational attainment and higher fertility. We argue
that this type of conditional relationship should be expected, given that there is no simple
relationship between fertility and FLFP, either in theory or in the data. The results with
respect to FLFP are nonetheless supportive of the main hypothesis in the paper.
Finally, one may be concerned that our sample includes only manufacturing sectors. To
the extent that some countries export significant amounts of agricultural and mining raw
materials, our manufacturing-based F N LX may not accurately reflect the gender bias of
a country’s specialization pattern. To address this coverage issue, we also constructed F Li
13
OECD countries in the sample are: Australia, Austria, Belgium, Canada, Denmark, Finland, France,
Germany, Greece, Iceland, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Swe-
den, Switzerland, the United Kingdom, and the United States. We thus exclude the newer members of the
OECD, such as Korea and Mexico.
14
These countries are Algeria, Angola, Republic of Congo, Gabon, Islamic Republic of Iran, Kuwait,
Nigeria, Oman, Saudi Arabia, and Syrian Arab Republic.
19
based on data for a single country – the U.S. – using the Labor Force Statistics database of the
U.S. Bureau of Labor Statistics (BLS). The BLS has published “Women in the Labor Force:
A Databook” on an annual basis since 2005. It contains information on total employment
and the female share of employment in each industry covered by the Census, sourced from
the Current Population Survey. The data are available at the 4-digit U.S. Census 2007
classification (262 distinct sectors, including both manufacturing and non-manufacturing).
In order to construct the share of female workers in total sectoral employment F Li , we
take the mean of this value across the years for which the data on the female share of
employment are available (2004-2009). After dropping non-tradables, the sector sample
includes 78 manufacturing and 15 non-manufacturing sectors. An earlier working paper
version of our paper (Do et al., 2012) replicates all of the empirical analysis using this
alternative measure of F Li , and shows that the results are robust. Thus, we do not report
them here to conserve space.15
6 Conclusion
Fertility is an economic decision, and like all economic decisions has long been considered
an appropriate – and important – subject of analysis by economists. As trade integration
increased in recent decades, there is growing recognition that the impacts of globalization are
being felt well beyond the traditional market outcomes such as average wages, skill premia,
and (un)employment. This paper makes the case that international trade, or more precisely
comparative advantage, matters for this key non-market outcome: the fertility decision.
Our results thus emphasize the heterogeneity of the e↵ects of trade on countries’ industrial
structures and gender outcomes. At a more conjectural level, to the extent that comparative
advantage impacts fertility, it may also impact women’s human capital investments, occu-
pational choice, and bargaining power within the household. From a policy perspective, our
results suggest that it will be more di cult for countries with technologically-based compar-
ative advantage in male-intensive goods to undertake policy measures to reduce the gender
gap, potentially leading to a slower pace of women’s empowerment. In an increasingly inte-
grated global market, the road to female empowerment is paradoxically very specific to each
15
While the U.S.-based alternative F Li measure has the advantage of extending the set of sectors to
agriculture and mining, it has two important drawbacks. First, the data are compiled based on individual-
level surveys rather than firm- or plant-level data, and thus relies on workers self-reporting their industry of
occupation. If the number of individuals in the survey who report working in a particular sector is small, or
if workers make mistakes in reporting their industry of employment, the data will be measured with error.
And second, the U.S. is only one, very special country, and thus its values of F Li may not be representative
of the average country’s experience. For our UNIDO-based measure, averaging the share of female workers
across a couple of dozen countries helps alleviate both of these problems.
20
country’s productive structure and exposure to international trade. At the same time, since
our paper points to comparative advantage as a determinant of women’s opportunities, a
potential policy lever to a↵ect the gender gap could be through industrial policy promoting
female-intensive sectors.
Appendix A Proofs
Proof of Proposition 1
The “goods market-clearing curve” and “factor market-clearing curve” have opposite slopes.
We therefore need to show that they intersect at least once, since if they do, such intersection
is unique. A necessary and su cient condition for the two curves to intersect is that the
“goods market-clearing curve” be above the “factor market-clearing curve” for low values of
f c and below for larger values of ✓c .
• As ✓c gets arbitrarily close to 0, equality (9) implies that the “goods market-clearing”
curve is bounded below by 1 1 ⌘ , while (10) indicates that the “factor market-clearing”
curve converges to 1 < 1 1 ⌘ , and therefore lies below the “goods market-clearing” curve.
• On the other hand, when ✓c grows arbitrarily large, the “goods market-clearing” curve
converges to 1 1 ⌘ , while the “factor market-clearing” diverges, and hence lies above the
“goods market-clearing” curve.
Thus, the “goods market-clearing” curve is above the “factor market-clearing” curve in the
neighborhood of 1, while the opposite holds for large values of ✓c . Continuity of the two
curves implies existence of an intersection.⌅
Proof of Lemma 1
From equation (9), let’s try to characterize the behavior of ✓c when the patterns of compar-
ative advantage ⇢ are changing.
Dropping the country reference and substituting for ✓ c , f is implicitly defined for every
⇢ by:
✓ ◆↵
✓ c ⌘ (1 ↵) ↵ ✓
+ 1 [⌘ (1 ⌘ ) ✓] + ( ) (1 + ✓) ⌘ (1 ⌘ ) = 0
⇢ ⇢
that is denoted x (✓, ⇢) = 0. On the one hand,
✓ ◆↵ 1
@ x (✓, ⇢) ↵✓ ✓ (1 ⌘) ✓
= +1 [⌘ (1 ⌘ ) ✓] + ( c )⌘(1 ↵)
(1 + ✓)↵
@⇢ ⇢2 ⇢ ⇢2
and since x (✓, ⇢) = 0, we can rewrite
@ x (✓, ⇢) (1 + ✓)↵ ✓ ✓
= ( c )⌘(1 ↵)
↵⌘ + (1 ⌘ ) + (1 ↵) (1 ⌘)
@⇢ ⇢ ⇢+✓ ⇢
21
On the other hand, similar derivation yields
✓ ◆⇢
@ x (✓, ⇢) c ⌘ (1 ↵) ↵ ⇢ 1 ↵ [⌘⇢ ✓(1 ⌘ )] ⌘ (1 ⌘)
= ( ) (1 + ✓) +
@✓ ⇢ (1 + ✓) (✓ + ⇢) [⌘ (1 ⌘ ) ✓]
The implicit function theorem indicates that ✓ (⇢) is well defined and continuously di↵er-
entiable around ⇢ such that x(✓(⇢), ⇢) = 0; we can now compute the derivative of ✓ with
respect to ⇢ :
h i
✓
(1 ⌘ ) ✓ ⌘ ✓ (1 + ✓) ↵⌘ + (1 ⌘ ) + (1 ↵) (1 ⌘ ) ⇢
✓ 0 ( ⇢) =
⇢ 1 ⌘⇢ [↵ + (1 ↵) (1 ⌘ ) (1 + ✓)] + ✓ (1 ⌘ ) [↵✓ + (1 ↵) ⌘ (1 + ✓)]
The second term of the equation is always positive; by virtue of (9) and (10), the first term
(1 ⌘ )✓ ⌘
⇢ 1
> 0. We thus have
✓0 (⇢) > 0.
⌅
Proof of Lemma 2
Having established that the female labor demand curve is downward sloping for every level
of country c’s female labor force participation and that the female labor supply curve is
upward sloping, we have shown uniqueness of an intersection. We now need to show existence
of an intersection.
• As N c goes to zero (i.e. female labor supply goes to 1), the labor supply curve defined
by (12) diverges given that lim0 v 0 (.) = +1, by assumption. The labor demand curve
is on the other hand bounded above since it is downward sloping; it therefore lies below
the labor supply curve.
• Let’s now let N c get arbitrarily close to 1 , so that ⇢c converges to zero. Equation (10)
implies that ✓c will converge to 0, so that, by virtue of (9), ✓ c will converge to some
⇥ ⇤
¯ c > 0 such that ⌘ + ( c )⌘(1 ↵) ✓
✓ ¯ c + 1 ↵ ⌘ (1 ⌘ ) ✓ ¯ c = 0. Thus, the labor
c
demand curve converges to some positive wage w ¯F . Two cases arise:
v0 ( 1 ) c
– if 0, such that N c (0) = 1 "c . Next, and
given that N c (.) is decreasing, we have N c (N ) 2 [0, 1 "c ] , a compact set. Suppose now
that N c is set arbitrarily close to 1 . Then, (10) implies that ✓ c converges to 0, uniformly
with respect to N c ; (9) in turn implies that ✓c converges towards some ✓ ¯c < 1 such that
⇥ ⇤
⌘ + ( c )⌘(1 ↵) ✓¯c + 1 ↵ ⌘ (1 ⌘ ) ✓ ¯c = 0. Equation (5) indicates that female wages in
country c remain bounded above, so that lim 1 N c (.) > 0. Thus, the curve N c (.) cuts N c (.)
at least once, and “from above,” as shown in Figure A2 below. This establishes the existence
of an equilibrium N X , N Y .
Uniqueness To show uniqueness, we look at the labor market equilibrium. For an interior
solution, we note that {(✓c , N c )}c2{X,Y } are implicitly defined by the intersection of labor
supply and demand, i.e.
✓ ◆↵ ✓ ◆1 ⌘ (1 ↵)
v 0 (N c ) 1 ✓c
= (1 ↵) . (A.1)
1 + ✓c 1 Nc
N c can thus be expressed as a function N (.) of ✓c and exogenous parameters only such that
N (.) is continuously di↵erentiable and simple algebra yields for an interior solution:
1
dN (✓) 1 N (✓ ) 1 1 ⌘ (1 ↵) 1+✓
↵ ✓
= v ”[N (✓ )] 1 N (✓ )
0 (A.2)
d✓ ✓
v 0 [N (✓ )] 1 ⌘ (1 ↵)
We now turn to the system of equilibrium conditions (9) and (10) that are conditional on la-
bor endowments 1 NX, 1 N Y . On the one hand, (9) defines a negative unconditional
relationship between ✓c and ✓ c ; on the other hand, we rewrite (10) as
✓c c ✓ c
= (A.3)
1 Nc 1 N c
that can be written uc (✓c ) = c u c (✓ c ) , where uc (✓) = 1 ✓ N (✓ )
. Inequality (A.2) implies
c
that u (.) is increasing, so that (A.3) defines a positive unconditional relationship between
✓c and ✓ c . Thus, the two equilibrium conditions for capital define two curves with opposite
slope, implying a unique intersection, given that existence was established above. Uniqueness
of capital allocation across sectors implies uniqueness of fertility decisions.⌅
23
Proof of Lemma 3
The ratio of female wages in the two countries and use (10) to obtain the following equality:
✓ ◆↵
v 0 (N c ) 1 + ✓c
0 c c
= ( c )1 ⌘(1 ↵) . (A.4)
v (N ) 1 + ✓
v 0 (N˜ c)
c v 0 (N c ) 1+✓ c 1+✓˜c
Equality (A.4) implies that if ˜ c then either v 0 (N c ) v (N
0 ˜ c) or 1+✓ c 1+✓˜ c, or
both. In other words, a change in comparative advantage triggers either a change in fertility
choices in either or both countries (N c N ˜ c and/or N c N˜ c ), or a reallocation of
capital across sectors in either or both countries (✓ c ˜ and/or ✓ c ✓
✓ c ˜ c ). However,
since c = 1/ c , a stronger comparative advantage in the F -good in country c is associated
with a weaker comparative advantage in country c, vice and versa. Therefore, if a change
in comparative advantage positively (resp. negatively) a↵ects fertility in country c, it will
simultaneously negatively (resp. positively) a↵ect fertility in country c. The same holds
for capital allocation. Thus, we can state the following:
⇣ ⌘ ⇣ ⌘
c
˜ c =) N c N ˜ c and N c N ˜ c or ✓c ✓ ˜c and ✓ c ✓˜ c (A.5)
Finally, to see that both fertility and capital allocation respond to an exogenous change in
comparative advantage, we note that the right-hand side of (A.1) is increasing in ✓c , while
the left-hand side is decreasing in N c . The following equivalence therefore holds:
✓c ˜c () N c N
✓ ˜ c. (A.6)
That is, a higher inflow of capital in the F -sector is associated with higher female labor force
participation and hence lower fertility in equilibrium. Equivalence (A.6) implies that the last
term in (A.5) is therefore redundant and we can simply write
⇣ ⌘
c
˜ c =) N c N ˜ c and N c N ˜ c . (A.7)
⌅
Proof of Theorem 1
To move from comparative statics to cross-sectional comparisons, we set ˜ c = 1.
Interior solutions Equilibrium conditions (9) and (10) and labor market clearing equa-
˜ c = N 0,
˜c = N
tions (A.1) are thus symmetric in both (N c , N c ) and (✓c , ✓ c ), implying N
˜ c=
˜c = ✓
where N 0 satisfies (A.1) with ✓ 1
. Implication (A.7) becomes for ˜ c = 1:
1 ⌘
c
1 =) N c N 0 N c
.
Corner solutions Finally, since the arguments leading to Proposition 4 assume interior
solutions for equilibrium fertility in both countries, we now address the cases in which the
24
1
labor market equilibrium is at a corner (i.e. N c = or N c
= 1 ). Without loss of generality,
suppose that c 1.
• If N c = 1 , i.e. the F -sector in country c disappears, then N c < 1 (since N c = 1
implies that ✓c = 0, and (9) does not hold for ✓c = ✓ c = 0), and the proposition
trivially holds. Indeed, if c0 s comparative advantage in the F -sector is large enough,
then c will end up producing all the F -goods in the economy.
1
• Alternatively, suppose that N c = and N c
< 1 . Female wages are given by
✓ c
◆1 ⌘ (1 ↵) ✓ ◆
c c ✓ 1 0 1
wF = (1 ↵) c
v
1 N
✓ c
◆1 ⌘ (1 ↵)
✓ 1
c
wF = (1 ↵) c
= v0 N c
1 N
and since N c < 1 , and v 0 (.) is decreasing, we have v 0 (N c
)>v 1
so that wF c > wF
c
.
This implies
c
< 1,
a contradiction.
• Finally, N c = N c = 1 cannot be an equilibrium since no production would take place,
thus pushing female wages in both countries to infinity.
This concludes the proof.⌅
Appendix B The Instrument
This Appendix describes the steps necessary to build the instrument for the female labor
needs of exports. The construction of the instrument follows Do and Levchenko (2007),
and exploits exogenous geographic characteristics of countries together with the empirically
observed regularity that trade responds di↵erentially to the standard gravity forces across
sectors. The exposition in this Appendix draws on, and extends, the material in Do and
Levchenko (2007).
For each industry i, we estimate the Frankel and Romer (1999) gravity specification,
which relates observed trade flows to exogenous geographic variables:
1 2
LogXicd = ↵i + ⌘i ldistcd + ⌘i lpopc + ⌘ 3 4 5
i lareac + ⌘i lpopd + ⌘ i laread + (B.1)
⌘6 7 8
i landlockedcd + ⌘i bordercd + ⌘i bordercd ⇥ldistcd +
⌘9 10 11
i bordercd ⇥ popc + ⌘ i bordercd ⇥areac + ⌘i bordercd ⇥popd +
12
⌘i bordercd ⇥aread + ⌘ 13i bordercd ⇥landlockedcd + ✏icd ,
where LogXicd is the log of exports as a share of GDP in industry i, from country c to country
d. The right-hand side consists of the geographical variables. In particular, ldistcd is the log
of distance between the two countries, defined as distance between the major cities in the
25
two countries, lpopc is the log of population of country c, lareac log of land area, landlockedcd
takes the value of 0, 1, or 2 depending on whether none, one, or both of the trading countries
are landlocked, and bordercd is the dummy variable for common border. The right-hand
side of the specification is identical to the one used by Frankel and Romer (1999). We use
bilateral trade flows from the COMTRADE database, converted to the 3-digit ISIC Revision
3 classification. To estimate the gravity equation, the bilateral trade flows Xicd are averaged
over the period 1980-2007. This allows us to smooth out any short-run variation in trade
shares across sectors, and reduce the impact of zero observations.
Having estimated equation (B.1) for each industry, we then obtain the predicted logarithm
of industry i exports to GDP from country c to each of its trading partners indexed by d,
\ icd . In order to construct the predicted overall industry i exports as a share of GDP
LogX
from country c, we then take the exponential of the predicted bilateral log of trade, and sum
over the trading partner countries d = 1, ..., C , exactly as in Frankel and Romer (1999):
C
X
ˆ ic = \
X eLogX icd . (B.2)
d=1
d 6= c
That is, predicted total trade as a share of GDP for each industry and country is the sum
of the predicted bilateral trade to GDP over all trading partners.
The instrument for F N LX is constructed using the predicted export shares in each
industry i, rather than actual ones, in a manner identical to equation (14):
I
X
F\
LN X c = X
bic
! F Li ,
i=1
X
bic
where the predicted share of total exports in industry i in country c, ! , is computed from
ˆ
the predicted export ratios Xic :
ˆ ic
X
X
bic
! = PI . (B.3)
X ˆ ic
i=1
Note that even though X ˆ ic is exports in industry i normalized by a country’s GDP, every
sector is normalized by the same GDP, and thus they cancel out when we compute the
predicted export share.
Discussion
We require an instrument for trade patterns, not trade volumes, and thus our strategy will
only work if it produces di↵erent predictions for X bic across sectors for the same exporter.
All of the geographical characteristics on the right-hand side of (B.1) do not vary by sector.
However, crucially for the identification strategy, if the vector of estimated gravity coe cients
bic across sectors i within the same
⌘ i di↵ers across sectors, so will the predicted total exports X
country. The strategy of relying on variation in coe cient estimates for the same geographical
variables bears an a nity to Feyrer (2009), who uses the di↵erential e↵ect of gravity variables
26
on ocean-shipped vs. air-shipped trade to build a time-varying instrument for overall trade
openness, and to Ortega and Peri (2014), who exploit the fact that the same gravity variables
a↵ect goods trade and migration flows di↵erently to build separate instruments for overall
trade openness and immigrant population. This subsection (i) discusses the intuition for
how the instrument works; (ii) reviews the existing sector-level gravity literature to provide
reasons to expect the gravity coe cients to vary across sectors; (iii) describes the variation
in our own gravity coe cients from estimating (B.1) by sector.
The following simple numerical example illustrates the logic of the strategy. Suppose that
there are four countries: the U.S., the E.U., Canada, and Australia, and two sectors, Wearing
Apparel and Motor Vehicles. Suppose further that the distance from Australia to either the
U.S. or the E.U. is 10,000 miles, but Canada is only 1,000 miles away from both the U.S.
and the E.U. (these distances are not too far from the actual values). Suppose that there are
only these country pairs, and that trade between them is given in Table A1. Let the gravity
model include only bilateral distance. The trade values have been chosen in such a way that
a gravity regression estimated on the entire “sample” yields a coe cient on distance equal
to -1, a common finding in the gravity literature. The gravity model estimated separately
for each of the two sectors yields the distance coe cient is -0.75 in Wearing Apparel and
-1.25 in Motor Vehicles (this amount of variation in the distance coe cients is reasonable,
as we show below). Using these “estimates” of the distance coe cients, it is straightforward
to take the exponent and sum across the trading partners as in (B.2), and to calculate the
predicted shares of total exports to the rest of the world in each of the two sectors, as in
(B.3). Now let the share of female labor in Wearing Apparel be F LAP P = 0.71, and of Motor
Vehicles, F LM V = 0.09 (these are the actual values of F Li for these two industries). Then,
the predicted female labor need of exports of Canada is F\ N LX CAN = 0.18, which is some
40% lower than the predicted value for Australia of F\ N LX AU S = 0.31.
The key intuition from this example is that countries located far away from their trading
partners will have relatively lower predicted export shares in goods for which the coe cient
on distance is higher, compared to countries located close to their trading partners. This
information is combined with cross-industry variation in female employment to generate pre-
dicted F\N LX . There are several important points to note about this procedure. First, while
this simple example focuses on the variation in distance coe cients along with di↵erences
in distances between countries, our actual empirical procedure exploits variation in all 13
regression coe cients in (B.1), along with the entire battery of exporting and destination
country characteristics. Thus, to the extent that coe cients on other regressors also dif-
fer across sectors, variation in predicted F\ N LX will come from the full set of geography
variables. Second, while this simple four-country illustrative example may appear somewhat
circular – actual exports and distance a↵ect the gravity coe cient, which in turn is used to
predict trade – in the real implementation we estimate the gravity model with a sample of
more than 150 countries, and thus the trade pattern of any individual country is unlikely to
a↵ect the estimated gravity coe cients and therefore its predicted trade. Third, it is crucial
for this procedure that the gravity coe cients (hopefully all 13 of them) vary appreciably
across sectors. Below we discuss the actual estimation results for our gravity regressions,
and demonstrate that this is indeed the case.
Can we support the notion that the gravity coe cients would be expected to di↵er across
27
sectors? Most of the research on the gravity model focuses on the e↵ects of trade barriers on
trade volumes. Thus, existing empirical research is most informative on whether we should
expect significant variation in the coe cients on distance and common border variables,
which are meant to proxy for bilateral trade barriers. Anderson and van Wincoop (2003,
2004) show that the estimated coe cient on log distance is the product of the elasticity of
trade flows with respect to iceberg trade costs (commonly referred to as simply the “trade
elasticity”) and the elasticity of iceberg trade costs with respect to distance. Thus, the
distance coe cient will di↵er across industries if either or both of those elasticities di↵er
across industries.
A number of papers estimate trade elasticities by sector (see, among many others, Feen-
stra, 1994; Broda and Weinstein, 2006; Caliendo and Parro, 2012; Imbs and M´ ejean, 2013).
Imbs and M´ ejean (2013) – the most recent and the most comprehensive study – reports
sector-level trade elasticity estimates using both of the principal estimation methods pro-
posed in the literature. The conservative range of trade elasticities across sectors reported in
that paper is from 2 to 20, consistent with the other studies undertaking similar exercises.
There is less direct evidence on whether the elasticity of iceberg trade costs with respect
to distance varies across sectors. Trade costs do vary significantly across industries. Hummels
(2001) compiles freight cost data, and shows that in 1994 these costs ranged between 1% and
27% across sectors in the U.S..16 Hummels (2001, 2007) further provides evidence that the
variation in freight costs is strongly related to the value-to-weight ratio: it is more expensive
to ship goods that are heavy. Thus, it is plausible that the elasticity of trade costs with
respect to distance is heterogeneous across sectors as well.
To summarize, there are strong reasons to expect the coe cients in (B.1) to vary across
sectors. It is indeed typical to find variation in the gravity coe cients across sectors, though
studies di↵er in the level of sectoral disaggregation and specifications (see, e.g. Rauch, 1999;
Rauch and Trindade, 2002; Hummels, 2001; Evans, 2003; Feenstra et al., 2001; Berthelon and
Freund, 2008). For instance, Hummels (2001) finds that the distance coe cients vary from
zero to -1.07 in his sample of sectors, while the coe cients on the common border variable
range from positive and significant (as high as 1.22) to negative and significant (as low as
-1.23).
Table A2 reports the cross-sectoral variation in the gravity coe cients in our estimates.
For each coe cient, it reports the mean, standard deviation, min, and max in our sample
of sectors. The variation in all of the gravity coe cients across sectors is considerable. The
distance coe cient, as expected, is on average around 1, but the range across sectors is
from -1.65 to -0.53. The common border coe cient has a mean of 1.4, and a standard
deviation of 2.5 across sectors. Our instrumentation strategy relies on this variation in
sectoral coe cients.
There is another potentially important issue, namely the zero trade observations. In our
gravity sample, only about two-thirds of the possible exporter-importer pairs record positive
exports, in any sector. At the level of individual industry, on average only a third of possible
16
In addition to the simple shipping costs, trade costs di↵er across industries in other ways. For in-
stance, trade volumes in di↵erentiated and homogeneous goods sectors react di↵erently to informational
barriers (Rauch, 1999; Rauch and Trindade, 2002), and to importing country institutions such as rule of law
(Berkowitz et al., 2006; Ranjan and Lee, 2007).
28
country-pairs have strictly positive exports, in spite of the coarse level of aggregation.17
We follow the Do and Levchenko (2007) procedure, and deal with zero observations in two
ways. First, following the large majority of gravity studies, we take logs of trade values, and
thus the baseline gravity estimation procedure ignores zeros. However, instead of predicting
in-sample, we use the estimated gravity model to predict out-of-sample. Thus, for those
observations that are zero or missing and are not used in the actual estimation, we still predict
trade.18 In the second approach, we instead estimate the gravity regression in levels using
the Poisson pseudo-maximum likelihood estimator suggested by Santos Silva and Tenreyro
(2006). The advantage of this procedure is that it actually includes zero observations in the
estimation, and can predict both zero and non- zero trade values in-sample from the same
estimated equation. Its disadvantage is that it assumes a particular likelihood function, and
is not (yet) the standard way of estimating gravity equations found in the literature. The
main text reports the results of implementing all three approaches. It turns out that all
three deliver very similar results, an indication that the zeros problem is not an important
one for this empirical strategy.
Appendix C Female Labor Force Participation
The theoretical model in Section 2 connects comparative advantage to fertility through the
opportunity cost of women’s time. This mechanism is related to female labor force participa-
tion (FLFP). This section presents a set of empirical results on how comparative advantage
a↵ects FLFP. To clarify the connections between these and the baseline results, we preface
the empirics with a theoretical discussion of the relationship between fertility and FLFP.
C.1 Theoretical Discussion
In the simple model of Section 2, fertility is perfectly negatively correlated with FLFP,
which, if taken literally, conveys the impression that comparative advantage a↵ects fertility
“through” FLFP. However, the notion that fertility is a↵ected by the opportunity cost of
women’s time is distinct from women’s labor supply for a series of reasons.
First, the elasticity of FLFP with respect to women’s wage is not simply the negative of
the elasticity of fertility with respect to the wage. Suppressing the country superscripts, let
N , as before, be the number of children, and denote FLFP by LF = 1 N . Denote the
@ x wF
elasticity of a variable x with respect to the female wage by "x ⌘ wF x . It is immediate
that "LF = "N 1 NN . Thus, for a finite "N , the elasticity of FLFP with respect to the wage
approaches zero as childrearing time goes to zero, either because of low or low N . This
suggests that in countries with already low fertility, or in countries with low (for instance,
due to easily accessible childcare facilities, as in many developed countries) the impact of
(log) opportunity cost of women’s time on (log) FLFP may not be detectable.19
17
These two calculations make the common assumption that missing trade observations represent zeros
(see Helpman et al., 2008).
18
More precisely, for a given exporter-importer pair, we predict bilateral exports out-of-sample for all 61
sectors as long as there is any bilateral exports for that country pair in at least one of the 61 sectors.
19
To give a stark example, suppose that v (.) is CES: v (N ) = N 1 1/⇣ /(1 1/⇣ ), so that the elasticity of
29
Second, even in levels the negative linear relationship between fertility and labor supply
is an artifact of the assumption that working in the market economy and childrearing are
the only uses of women’s time. More generally, suppose that there is another use of women’s
time, Q, which can stand for leisure, investments in quality of the children (as opposed to
quantity N ), or non-market housework. Suppose further that the indirect utility, instead of
(11), is now represented by:
V (N, Q) = r + wF (1 N µQ) + wM + v (N ) + z (Q) , (C.1)
where µ is number of units of a woman’s time required to produce one unit of Q.
On the one hand, this addition leaves unchanged the first-order condition with respect
to fertility, (12), embodying the notion that fertility is a↵ected by the opportunity cost of
women’s time.
On the other hand, there is now another first-order condition that relates women’s op-
portunity cost of time to Q:
z 0 ( Q)
wF = . (C.2)
µ
Thus, the relationship between FLFP and wF is now
LF = 1 (v 0 ) 1 ( wF ) µ(z 0 ) 1 (µwF ),
and the elasticity of FLFP with respect to the wage is
N µQ
"L F = "N "Q .
1 N µQ 1 N µQ
It is immediate that FLFP and fertility are no longer inversely related one-for-one. Depending
on the curvatures of v (.) and z (.), FLFP could be more or less concave in wF than N , even as
(12) continues to hold and the wage-fertility relationship is una↵ected. When "Q is di↵erent
from "N , and µQ is high relative to N , "LF can look very di↵erent from negative "N even
when women’s labor supply is far away from 1.20
Third, the simple model above assumes that the marginal utility of income is always
constant at 1. Departing from that assumption and introducing diminishing marginal utility
c
of income will make the relationship between FLFP and wF even more complex, and possibly
non-monotonic, due to income e↵ects. While in all of the cases above, FLFP and fertility were
still negatively correlated, with income e↵ects it is possible to generate a positive relationship
between FLFP and fertility at high enough levels of income, for instance through satiation
in goods consumption.
Finally, when it comes to measurement of FLFP, an additional challenge is that the
model is written in terms of the intensive margin (i.e. hours), whereas the FLFP data
fertility with respect to the wage is simply constant: "N = ⇣ . In this case, we will always be able to detect
the e↵ect of (log) wage on (log) fertility at all levels of fertility or income, whereas the impact of (log) wage
on (log) FLFP will go to zero as income rises/fertility falls.
20
As an example, when v (.) and z (.) are CES: v (N ) = N 1 1/⇣ /(1 1/⇣ ) and z (Q) = Q1 1/⇠ /(1 1/⇠ ),
N µQ
"Q and "N are simply constants, and "LF = ⇣ 1 N µQ + ⇠ 1 N µQ , which can obviously be very di↵erent
from ⇣ .
30
are recorded at the extensive margin (binary participation decision). This implies that,
especially for countries with already high FLFP, in which in response to fertility women
adjust hours worked rather than labor market participation, our data will not be able to
accurately capture the interrelationships between FLFP and fertility.21
To summarize, the insight that fertility is determined by the opportunity cost of women’s
time does not have a one-to-one relationship to FLFP. One can easily construct examples in
which the wage elasticities with respect to fertility and FLFP are very di↵erent.22 In addition,
even the simple baseline model above implies that the elasticity of female labor supply with
respect to the opportunity cost of women’s time is not constant, and approaches zero as
time spent on childrearing falls. This suggests that the impact of comparative advantage
in female-intensive goods on FLFP will be attenuated, and potentially di cult to detect in
countries with high income and low fertility.
C.2 Empirical Results
With those observations in mind, Table A3 explores the relationship between F N LX and
FLFP. FLFP data come from the ILO’s KILM database, and are available 1990-2007. All
shown specifications include controls for per capita income and openness, and regional dum-
mies. Column 1 presents the OLS regression. The coe cient on FLFP is positive but not
significant. Column 2 reports the 2SLS results. The coe cient becomes larger, but not
significant at conventional levels (p-value of 11%). However, as argued above the elasticity
of FLFP with respect to F N LX should not be expected to be constant across a wide range
of countries. Thus, in columns 3 and 4 we re-estimate these regressions while letting the
impact of F N LX vary by income. The di↵erence is striking. Both the main e↵ect and the
interaction with income are highly significant, and the impact of F N LX is clearly less pro-
nounced for higher-income countries. Column 5 reports the 2SLS results in which F N LX is
interacted with fertility, and column 6 with female educational attainment. In both cases,
all of the coe cients of interest are highly significant.23
Of course, the main e↵ect of the F N LX is now not interpretable as the impact of F N LX
on FLFP. To better illustrate how the impact of F N LX on FLFP varies through the distri-
bution of income, fertility, and educational attainment, we re-estimate the specification with
quartile-specific F N LX coe cients, rather than the interaction terms (that is, we discretize
income, fertility, or female educational attainment into quartiles, and allow the F N LX co-
e cient to di↵er by quartile). Figure A3 reports the quartile-specific coe cient estimates,
with the bars depicting 95% confidence intervals. The top panel presents the results by
quartile of income. There is a statistically significant positive e↵ect of F N LX on FLFP in
the bottom quartile of countries, with the coe cient estimate of 0.53. In the second quartile,
21
Unfortunately, data on hours worked are not available for a large sample of countries.
22
Indeed, in the data there is no simple negative relationship between fertility and FLFP. For instance,
Ahn and Mira (2002) show that it is not stable even among the OECD countries: FLFP was was negatively
correlated with fertility until the 1970s and 1980s, and but since then the correlation changed sign, and
fertility is now positively correlated with FLFP.
23
In order to conserve space, Table A3 does not report the first-stage coe cients and diagnostics. With
the income, fertility and educational attainment interactions, two variables are being instrumented, which
would require reporting multiple coe cients and F -statistics. All of the F -statistics in these specifications
are above 25.
31
the coe cient is positive at 0.36, but no longer significant. In the top half of the income
distribution, the coe cient estimates are close to zero and not significant.
The second panel presents the same result with respect to fertility. As expected, the
impact of F N LX on FLFP is most pronounced at high levels of fertility. The top quartile
estimate is statistically significant at the 1% level, and the third quartile coe cient is signif-
icant at the 10% level. Finally, the bottom panel presents the results with respect to female
educational attainment quintiles. The impact of F N LX is strongly positive in the bottom
quartile, and close to zero elsewhere.
To summarize, the results with respect to FLFP are suggestive that the impact of com-
parative advantage on fertility is concomitant with a female labor supply response, but only
in some countries. As argued above, this is should be expected, given that the relationship
between FLFP and fertility is not straightforward.
32
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37
Table 1. Share of Female Workers in Total Employment, Highest to Lowest
ISIC Code Sector Name F Li
181 Wearing apparel, except fur apparel 0.71
173 Knitted and crocheted fabrics and articles 0.62
192 Footwear 0.49
172 Other textiles 0.47
321 Electronic valves and tubes and other electronic components 0.46
332 Optical instruments and photographic equipment 0.45
191 Leather and leather products 0.43
323 TV and radio receivers, sound or video apparatus 0.43
333 Watches and clocks 0.42
319 Other electrical equipment n.e.c. 0.42
182 Fur and articles of fur 0.41
154 Other food products 0.39
331 Medical appliances and instruments 0.38
369 Manufacturing n.e.c. 0.38
322 TV and radio transmitters; telephony and telegraphy apparatus 0.38
171 Spinning, weaving and finishing of textiles 0.37
242 Other chemical products 0.36
151 Meat, fish, fruit, vegetables, oils and fats 0.36
223 Reproduction of recorded media 0.35
315 Electric lamps and lighting equipment 0.34
300 O ce, accounting and computing machinery 0.34
160 Tobacco products 0.33
221 Publishing 0.33
311 Electric motors, generators and transformers 0.32
313 Insulated wire and cable 0.32
312 Electricity distribution and control apparatus 0.30
222 Printing and service activities related to printing 0.29
293 Domestic appliances n.e.c. 0.28
252 Plastics products 0.27
314 Accumulators, primary cells and primary batteries 0.26
152 Dairy products 0.25
372 Recycling of non-metal waste and scrap 0.25
155 Beverages 0.23
251 Rubber products 0.23
210 Paper and paper products 0.23
243 Man-made fibres 0.22
359 Transport equipment n.e.c. 0.21
38
Table 1 (cont’d). Share of Female Workers in Total Employment, Highest to Lowest
ISIC Code Sector Name F Li
343 Parts and accessories for motor vehicles and their engines 0.21
153 Grain mill, starch products, and prepared animal feeds 0.20
361 Furniture 0.20
261 Glass and glass products 0.19
289 Other fabricated metal products 0.19
202 Products of wood, cork, straw and plaiting materials 0.18
371 Recycling of metal waste and scrap 0.17
201 Sawmilling and planing of wood 0.16
291 General purpose machinery 0.16
269 Non-metallic mineral products n.e.c. 0.16
241 Basic chemicals 0.15
353 Aircraft and spacecraft 0.15
292 Special purpose machinery 0.14
231 Coke oven products 0.14
232 Refined petroleum products 0.13
272 Basic precious and non-ferrous metals 0.13
273 Casting of metals 0.12
281 Structural metal products, tanks, reservoirs, steam generators 0.12
233 Nuclear fuel 0.11
271 Basic iron and steel 0.10
341 Motor vehicles 0.09
351 Building and repairing of ships and boats 0.09
352 Railway and tramway locomotives and rolling stock 0.08
342 Bodies for motor vehicles; trailers and semi-trailers 0.08
Mean 0.27
Min 0.08
Max 0.71
Notes: This table reports the share of female workers in total employment by sector, averaged across coun-
tries.
39
Table 2. Summary Statistics for Female Labor Need of Exports and Fertility
OECD NON-OECD
Panel A: Female Labor Need of Exports
Mean St. Dev Countries Mean St. Dev Countries
1960s 0.263 0.043 20 0.275 0.077 102
1970s 0.256 0.044 20 0.274 0.082 103
1980s 0.255 0.047 20 0.284 0.100 103
1990s 0.261 0.042 21 0.302 0.109 123
2000s 0.256 0.032 21 0.293 0.122 128
Panel B: Fertility Rates
Mean St. Dev Countries Mean St. Dev Countries
1960s 2.80 0.460 20 6.15 1.367 102
1970s 2.13 0.457 20 5.75 1.593 103
1980s 1.74 0.261 20 5.13 1.758 103
1990s 1.63 0.248 21 3.99 1.847 123
2000s 1.64 0.254 21 3.38 1.704 128
Notes: This table reports the summary statistics for F N LX and fertility, by country group and decade.
Table 3. F N LX : Top 10 and Bottom 10 Countries, 1980-2007
Highest F N LX Lowest F N LX
Lesotho 0.650 Algeria 0.146
Haiti 0.572 Angola 0.144
Bangladesh 0.557 Kazakhstan 0.141
Mauritius 0.528 Venezuela, RB 0.140
Sri Lanka 0.525 Saudi Arabia 0.138
Honduras 0.486 Kuwait 0.138
Cambodia 0.485 Nigeria 0.137
El Salvador 0.471 Gabon 0.137
Nepal 0.465 Iraq 0.135
Dominican Republic 0.461 Libya 0.134
Notes: This table reports the 10 countries with the highest, and 10 countries with the lowest F N LX .
40
Table 4. F N LX : Top 10 and Bottom 10 Changers since 1960s
Largest Increase in F N LX Largest Decrease in F N LX
Cambodia 0.410 Mozambique -0.097
Honduras 0.311 Rwanda -0.112
Haiti 0.269 Sudan -0.112
Sri Lanka 0.225 Ecuador -0.129
Tunisia 0.211 Congo, Rep. -0.132
Albania 0.210 Chad -0.147
Morocco 0.196 Angola -0.159
El Salvador 0.186 Yemen, Rep. -0.160
Madagascar 0.182 Niger -0.170
Nicaragua 0.169 Timor-Leste -0.281
Notes: This table reports the 10 countries with the largest increases and the largest decreases in F N LX .
Change is calculated as the di↵erence between the F N LX in the 2000s and that in the 1960s.
41
Table 5. Cross-Sectional Results, 1980-2007
(1) (2) (3) (4) (5) (6) (7) (8)
OLS OLS 2SLS 2SLS 2SLS 2SLS 2SLS 2SLS
Dependent Variable: (Log) Fertility Rate
(Log) Female Labor -0.29*** -0.20*** -0.37*** -0.47*** -0.57*** -0.56*** -0.28*** -0.38***
Need of Exports (0.080) (0.057) (0.128) (0.085) (0.131) (0.137) (0.095) (0.115)
(Log) Openness -0.00 0.01 -0.01 0.01 0.01 0.01 0.01 -0.01
(0.037) (0.032) (0.037) (0.032) (0.034) (0.034) (0.030) (0.037)
(Log) GDP per capita -0.39*** -0.26*** -0.40*** -0.27*** -0.28*** -0.28*** -0.26*** -0.27***
(0.020) (0.023) (0.020) (0.023) (0.024) (0.025) (0.022) (0.022)
Log (Area) 0.02
(0.016)
Log (Population) -0.04***
(0.017)
Constant 5.48*** 4.17*** 5.81*** 5.23*** 5.61*** 5.57*** 4.47*** 5.18***
(0.296) (0.314) (0.480) (0.362) (0.514) (0.540) (0.436) (0.766)
42
R2 0.630 0.859
First Stage
Dependent Var. (Log) FLNX
(Log) Predicted FLNX 3.23*** 3.04*** 3.32***
(0.342) (0.373) (0.548)
(Log) Predicted FLNX 2.43***
(out of sample) (0.469)
(Log) Predicted FLNX 1.00***
(Poisson) (0.201)
(Log) Predicted FLNX 3.03***
(No Population) (0.547)
F-test 43.02 34.69 32.21 27.24 24.77 29.78
First Stage R2 0.400 0.534 0.402 0.392 0.461 0.548
Region Dummies no yes no yes yes yes yes yes
Observations 145 145 145 145 145 145 145 145
Notes: Robust standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%. All variables are
averages over the period 1980-2007 and in natural logs. Variable definitions and sources are described in detail in the text.
Table 6. Panel Results, 1962-2007
(1) (2) (3) (4) (5) (6) (7) (8)
Five-Year Averages Ten-Year Averages
Dependent Variable: (Log) Fertility Rate
(Log) Female Labor -0.37*** -0.34*** -0.22*** -0.22*** -0.38*** -0.36*** -0.24*** -0.23***
Need of Exports (0.067) (0.077) (0.058) (0.061) (0.069) (0.093) (0.069) (0.072)
(Log) Openness -0.02 -0.18*** -0.02 -0.00 -0.02 -0.18*** -0.02 -0.00
(0.028) (0.041) (0.031) (0.034) (0.028) (0.049) (0.036) (0.039)
43
(Log) GDP per capita -0.38*** -0.35*** -0.18*** -0.18*** -0.38*** -0.37*** -0.20*** -0.19***
(0.019) (0.051) (0.043) (0.047) (0.019) (0.059) (0.048) (0.051)
(Log) Female -0.00 -0.01
Educational Attainment (0.038) (0.041)
Country FE no yes yes yes no yes yes yes
Year FE no no yes yes no no yes yes
R2 0.576 0.885 0.937 0.936 0.584 0.895 0.943 0.942
Observations 1,247 1,247 1,247 1,102 627 627 627 554
Notes: Standard errors clustered at the country level in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%.
All of the variables are 5-year averages (left panel) or 10-year averages (right panel) over the time periods spanning 1962-2007, and in
natural logs. Variable definitions and sources are described in detail in the text.
Table 7. Alternative Specifications and Controls: Cross-Sectional 2SLS Results, 1980-2007
(1) (2) (3) (4) (5) (6) (7)
Dependent Variable: (Log) Fertility Rate
(Log) F N LX 1.69** -0.41*** -0.40*** -0.30*** -0.34*** -0.42***
(0.820) (0.092) (0.096) (0.089) (0.089) (0.093)
(Log) F N LX ⇥(Log) -0.49**
Openness (0.192)
F N LX F N LI -0.02***
(0.004)
(Log) Openness 1.66** 0.01 0.03 0.07 -0.00 -0.03 0.01
(0.651) (0.034) (0.041) (0.044) (0.028) (0.042) (0.034)
(Log) GDP per capita -0.26*** -0.31*** -0.25*** -0.27*** -0.13*** -0.29*** -0.26***
(0.023) (0.027) (0.032) (0.033) (0.036) (0.031) (0.030)
(Log) Female -0.11**
Educational Attainment (0.046)
Child Labor Indicator 0.01***
(0.002)
44
(log) Infant Mortality 0.20***
(0.047)
Gini Coe↵ 0.78***
(0.302)
Polity 2 Indicator 0.00
(0.005)
Constant -2.27 4.23*** 4.88*** 4.55*** 2.77*** 4.72*** 4.97***
(2.883) (0.295) (0.438) (0.449) (0.702) (0.372) (0.439)
First Stage
(Log) Predicted F LN X 2.97*** 2.99*** 3.07*** 3.12*** 3.04***
(0.362) (0.457) (0.449) (0.507) (0.427)
Predicted F LN X 2.77***
(0.493)
F-test 22.52 31.74 29.45 35.39 20.98 35.05
First Stage R2 0.531 0.558 0.513 0.538 0.527 0.548
Region Dummies yes yes yes yes yes yes yes
Observations 145 145 125 103 144 102 144
Notes: Robust standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%. All variables are averages
over the period 1980-2007. Variable definitions and sources are described in detail in the text.
Table 8. Subsamples: Cross-Sectional 2SLS Results, 1980-2007
(1) (2) (3) (4) (5)
Sample: no no no Sub- no Middle East No mining
outliers OECD Saharan Africa & North Africa exporters
Dependent Variable: (Log) Fertility Rate
(Log) Female Labor -0.48*** -0.47*** -0.59*** -0.42*** -0.47***
Need of Exports (0.121) (0.082) (0.161) (0.087) (0.102)
(Log) Openness 0.02 0.04 0.01 0.01 0.01
(0.034) (0.037) (0.053) (0.031) (0.033)
(Log) GDP per capita -0.26*** -0.32*** -0.29*** -0.29*** -0.28***
(0.025) (0.026) (0.030) (0.024) (0.024)
45
Constant 5.17*** 5.44*** 5.85*** 5.27*** 5.35***
(0.499) (0.348) (0.713) (0.365) (0.433)
First Stage
(Log) Predicted FLNX 2.69*** 3.14*** 2.55*** 2.94*** 2.85***
(0.400) (0.407) (0.398) (0.400) (0.406)
F-test 32.81 30.62 32.84 35.59 34.24
First Stage R2 0.439 0.547 0.542 0.497 0.474
Region Dummies yes yes yes yes yes
Observations 135 125 104 129 135
Notes: Robust standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%. All variables are averages
over the period 1980-2007. Variable definitions and sources are described in detail in the text.
Figure 1. Partial Correlation Between Fertility and F N LX
TKM
.5
TJK OMN
SAU GTM
MYS IRL
AGO LAO TUR
NOR
PNG
AFG PAK PHL GIN KHM
LBY ARE
FRA
GAB SWE GBR HND
KAZ BOL PRY KGZ DNK
FIN
NER IRQ TCD CIV
VEN NLD
SEN USA ALB
COG
CMR CHE HTI
NGA ZMB KWT
Ln(Fertility)
BEN
MEX KEN UGA
ZWE
RWA MLI
MWI
BFA
AZE
ECU PER UZB AUT SLE
JOR
MOZ NZL MRT SLV
NIC DOM
MNG
YEMAUSARG NPL ETH GMB GRC
0
IDN SWZ
PRT
POL
ESP
DEU MKD CRI
SDN
PAN
LBR TGO COL
BRA VNM BDI JAM MDG
HUN
ZAF ARMITA
SOM
NAM
RUS IRN IND
GHA
CAN BGD
CAF
DZA SYR TZAROM ISR
CHL SGP
SVKCZE SVN
TTO GNB EST
BLR
THA URY BWA
GEO JPN EGYLTU HRV
BGR ERI
KOR MAR
LVA
MDALKA HKG LBN TUN LSO
UKR CHN
BIH
−.5
MUS
CUB
−1 −.5 0 .5 1
Ln(FNLXc)
Notes: This figure displays the partial correlation between F N LX and fertility, in logs, after controlling for
openness, per capita income, and regional dummies (see Column 2 of Table 5).
46
Figure 2. First Stage: Partial Correlation between F N LXc and F\
LN X c
1
LSO
MUS
TUN
MAR
HTI
ISR
.5
LBN
HND BWA SWZMDGDOM SLV
CRI
TUR
GTM GRC PRT
JAM
Actual Ln(FNLXc)
ALB HKG
NIC KHM
MNG IRL
CAF
MRT JORBGD MKDSLE CHE
MWI
GMB
MLI
URY GIN BFA
HRV ROM DNK
ETH
CUB LKA
NAM
ITA
USA BDI SOM
PHLUGA
HUNARM ERI
CHN BIH BLR NLD
SVN MDA
EST THA KGZ
FRA TZALTU
GBR
KOR AUT
BGR
FIN PAK
CIV LAO KEN
ZAF
ZWESEN POL
EGY NPL RWA
GNB
0
MYS PRYDEU VNM
ESP
SWE
SDN PAN NZL SVK SYR CZE SGP
ARGBEN TCDUZBARE
COL
LVA
AUS OMN GHA
CAN
BRAMOZ MEX
IND JPN
AFG PNG PER
NOR IRN YEM KWT
DZA SAU
LBY TGO IDN
TJK CHL
UKR
ECUGEO
RUS TKM BOL IRQ AZE
−.5
COG CMRLBR
ZMB
GAB KAZ AGO
NER TTO
NGA
VEN
−1
−.2 −.1 0 .1 .2
Instrument (Predicted Ln(FNLXc))
Notes: This figure presents the partial correlation plot from the first stage regression between the actual
value of F N LXc and the instrument.
47
Table A1. An Illustration of the Instrumentation Strategy
Sector Exporter Destination Distance Exports F Li
Apparel Canada EU 1000 2500 0.71
Apparel Canada US 1000 4500 0.71
Apparel Australia EU 10000 850 0.71
Apparel Australia US 10000 415 0.71
Motor Vehicles Canada EU 1000 25000 0.09
Motor Vehicles Canada US 1000 15000 0.09
Motor Vehicles Australia EU 10000 1000 0.09
Motor Vehicles Australia US 10000 1150 0.09
48
Table A2. Variation in Gravity Coe cients Across Sectors
Coe cient Mean Std. Dev. Min Max
Ln(Distancecd ) -1.115 0.238 -1.651 -0.532
Ln(P opc ) -0.083 0.359 -0.986 0.367
Ln(Areac ) -0.138 0.226 -0.507 0.393
Ln(P opd ) 0.723 0.227 0.404 1.424
Ln(Aread ) -0.144 0.120 -0.568 0.050
Landlockedcd -0.538 0.439 -2.590 0.644
Bordercd 1.398 2.520 -6.814 5.957
Bordercd ⇥ Ln(Distancecd ) 0.200 0.236 -0.462 0.674
Bordercd ⇥ Ln(P opc ) 0.239 0.178 -0.236 0.665
Bordercd ⇥ Ln(Areac ) -0.194 0.150 -0.542 0.158
Bordercd ⇥ Ln(P opd ) -0.214 0.193 -0.596 0.364
Bordercd ⇥ Ln(Aread ) 0.019 0.119 -0.360 0.283
Bordercd ⇥ Landlockedcd 0.398 0.281 -0.290 1.180
49
Table A3. FLFP: Cross-Sectional Results, 1980-2007
(1) (2) (3) (4) (5) (6)
OLS 2SLS OLS 2SLS 2SLS 2SLS
Dependent Variable: (Log) FLFP
(Log) F N LX 0.07 0.20 1.63*** 2.53*** -0.94*** 1.34***
(0.078) (0.126) (0.580) (0.913) (0.346) (0.489)
(ln) F LN X *(ln) GDP per capita -0.18*** -0.27***
(0.070) (0.103)
(ln) F LN X * (ln) Fertility 0.88***
(0.248)
(ln) Fertility -2.95***
(0.869)
(ln) F LN X * (ln) Fem. Educ. Attainment -0.67**
50
(0.269)
(ln) Fem. Educ. Attainment 2.34**
(0.927)
(Log) Openness 0.03 0.04 0.63*** 0.92*** 0.04 -0.01
(0.029) (0.031) (0.227) (0.342) (0.043) (0.038)
(Log) GDP per capita -0.02 -0.02 -0.01 -0.01 0.00 -0.08
(0.053) (0.054) (0.056) (0.060) (0.060) (0.048)
Constant -0.80* -2.00*** -5.98*** -9.83*** 1.68 -4.69***
(0.465) (0.671) (1.929) (3.149) (1.292) (1.738)
R2 0.577 0.599
Region Dummies yes yes yes yes yes yes
Observations 145 145 145 145 145 125
Notes: Robust standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%. All variables are
averages over the period 1980-2007, except FLFP, which is averaged over 1990-2007. Variable definitions and sources are described
in detail in the text.
Figure A1. Female Formal Labor Market Equilibrium
wF wF
Labor& Labor&
supply&& supply&&
Labor& Labor&
demand& demand&
1 - λN 1 - λN
Interior&solu3on& Corner&solu3on&
51
Figure A2. Equilibrium Female Labor Force Participation
Nc
1
λ
N −c (N c )
N c (N −c )
1 Nc
λ
52
Figure A3. Impact of F N LX on FLFP by Quartile
1
Coefficient on FNLX
0 −.5 .5
First Second Third Fourth
Income Quartile
(a) By Income
1 .5
Coefficient on FNLX
0 −.5
−1
First Second Third Fourth
Fertility Quartile
(b) By Fertility
2
1.5
Coefficient on FNLX
.5 0
−.5 1
First Second Third Fourth
Female Educational Attainment Quartile
(c) By Educational Attainment
Notes: This figure displays the quartile-specific coe cients on F N LX in the 2SLS regressions with log
FLFP as the dependent variable, and the controls/regional dummies as in Table A3. Panel (a) displays the
coe cients by income quartile, panel (b) by fertility quartile, and panel (c) by female educational attainment
quartile.
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