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Federal Reserve Bank of Chicago

Fertility Transitions Along the
Extensive and Intensive Margins
Daniel Aaronson, Fabian Lange, and
Bhashkar Mazumder

REVISED
June 2012
WP 2011-09

Fertility Transitions Along the Extensive and
Intensive Margins
Daniel Aaronson, Fabian Lange, Bhashkar Mazumder∗

Abstract
By augmenting the standard quantity-quality model with an extensive
margin, we generate sharp testable predictions of causes of fertility transitions. We test the model on two generations of Southern black women
affected by a large-scale school construction program. Consistent with
our model, women facing improved schooling opportunities for their
children became more likely to have at least one child but chose to have
smaller families overall. By contrast, women who themselves obtained
more schooling due to the program delayed childbearing along both the
extensive and intensive margins and entered higher quality occupations,
consistent with education raising opportunity costs of child rearing.

1

Introduction

All societies that embark on a sustained path of economic development experience a decline in fertility concurrent to other important societal changes, such
as increases in schooling and declines in mortality. Many different forces are
plausible explanations for fertility transitions, including skill-biased technical
∗

Federal Reserve Bank of Chicago, Yale University, and Federal Reserve Bank
of Chicago. Comments welcome at daaronson@frbchi.org, fabolange@gmail.com, or
bmazumder@frbchi.org. We thank seminar participants at various universities and conferences for their comments and especially Jon Davis for his valuable research assistance.
The views expressed in this paper are not necessarily those of the Federal Reserve Bank of
Chicago or the Federal Reserve System.

1

change, a decline in the cost of contraception, an increase in the relative wages
of women, an increase in life expectancy, and a decline in the value of child
labor.1 But the importance of these different factors remains unsettled.
One reason is that it is impossible to separately identify the different proposed causes of the transition using the standard implementation of the workhouse model used to study fertility patterns, the quantity-quality model of
Becker and Lewis (1973). In order to obtain tractable results, researchers impose auxiliary assumptions on the quantity-quality model to ensure that fertility is always positive. This simplifies the analysis because it focuses exclusively
on the intensive margin. But along the intensive margin, every explanatory
cause of the fertility transition has the same prediction that quantity and
quality of children are substitutes.
However, we argue that there is scope for identification along the extensive margin the option to remain childless. Take, for example, a change
that causes a decrease in the price of investing in child quality, say because
of expanded access to high-quality schools or increased rates of return to education. An augmented quantity-quality model that allows for an extensive
margin predicts an increase in the probability that a woman will have a first
child. Intuitively, it is necessary to have at least one child in order to invest
in the quality of children. Consequently, fertility along the extensive margin
increases as the opportunity to invest in child quality expands. We refer to
this complementarity at the extensive margin as “essential complementarity.”
Note that this prediction stands in contrast to the well-known response along
the intensive margin, where a positive educational shock causes fertility to
decline.
Next, consider an increase in the cost of raising children, say through improved labor market conditions and consequently an increase in the opportunity cost of women’s time. In this scenario, our augmented quantity-quality
model predicts that women will reduce fertility along both the extensive and
intensive margin. Therefore, our refinement of the standard quantity-quality
model generates sharp testable predictions of how variation in different vari1

For a recent critical survey on the evidence, see Galor (2012).

2

ables affect fertility along the extensive margin that we can use to test the
model and improve our understanding of the forces that shape demographic
transitions.
Our empirical application examines fertility along the extensive and intensive margins for two generations of women in the American South in response
to a large-scale school-building program.2 The Rosenwald Rural Schools Initiative (Aaronson and Mazumder, 2011) prompted the construction of almost
5,000 new schools, potentially easing significant constraints on the cost of educating children. Schools were targeted to one particular demographic group,
rural blacks, allowing the formation of control groups such as urban blacks and
rural whites within the same county. Moreover, the building occurred over two
decades between 1913 and 1932 providing variation in access to schooling
across cohorts.
From the decennial Censuses, we construct two distinct samples of women.
The first sample includes women who were of childbearing age when the schools
were built but too old to have attended themselves. For rural black women in
this cohort, the schooling opportunities for their prospective children expanded
and therefore the price of child quality declined. Consistent with the idea that
parents substitute quality for quantity, we show that these women’s fertility
declined along the intensive margin. We also show that the share of rural black
women who had any children increased (fertility increased along the extensive
margin), consistent with our extension of the standard quantity-quality model.
Overall, we find that the effects along the two margins roughly cancel each
other out. We therefore conclude that the evidence from the introduction
of the Rosenwald schools supports the idea of essential complementarity in
response to a decline in the price of child quality. Further, models that abstract
from the extensive margin will fail to capture the full effect of the change in
2

Other studies that test the quantity-quality model include Schultz (1985), Bleakley and
Lange (2009), Becker, Cinnirella, and Woessmann (2010), and Qian (2009). However, none
explicitly distinguishes between the extensive and the intensive fertility margin. There have
also been many empirical studies examining the effects of women’s education on fertility
more generally including Strauss and Thomas (1995), Black, Devereux and Salvanes (2008)
and McCrary and Royer (2011).

3

opportunities on fertility decisions and may lead to incorrect inferences.
The Rosenwald Initiative also provides insight into the role of the opportunity cost of women’s use of time as a factor in the fertility transition. To
investigate this hypothesis, we use a second sample of women who were of
school-going age at the time the schools were built. Aaronson and Mazumder
(2011) document the substantial impact the schools had on the human capital
accumulation of these women. Our model predicts that as the value of female
time increases, fertility will decline along both the extensive and the intensive
margin. We show that by the ages of 18-22, rural black women who were exposed to the Rosenwald schools during childhood were more likely to work in
a higher paying occupation, less likely to have children, and less likely to have
larger families if they did have children. These effects are quantitatively meaningful, statistically significant, and consistent with the hypothesis that the
per-child time cost of childrearing increases with the education and work opportunities of mothers. Therefore, the evidence from the Rosenwald-educated
women suggests a strong direct effect of increasing schooling opportunities on
fertility.
Although it is common to see fertility declines along both the extensive
and the intensive margin during 20th century demographic transitions, most
studies have focused solely on the intensive margin. We believe that emphasizing the extensive margin is a novel and useful contribution to the literature
and, importantly, is a relevant aspect of the fertility transition. Although the
preponderance of our empirical evidence supports such an extension of the
standard quantity-quality model, we acknowledge that in some cases our results are mixed or not as precisely estimated as one might like. Therefore,
we think it would be particularly useful if future work explores our findings in
other contexts.3
Section 2 describes a simple model of the fertility transition based on Galor (2012). The discussion centers on how essential complementarity and the
3
One potential example is Lucas (2011), who finds that women of childbearing age around
the time that malaria was eradicated in Sri Lanka experienced an increase in fertility, whereas
those who were born post-eradication experienced an improvement in education and a reduction in fertility.

4

extensive margin provide additional explanatory evidence on the fertility transition. Sections 3 and 4 introduce the Rosenwald Rural Schools Initiative and
the data that provide the empirical evidence reported in section 5. Section 6
concludes with thoughts on the relevance of the extensive fertility margin in
developing economies.

2

The Extensive and the Intensive Margin in
Fertility Choices

Our framework relies on Galor (2012). Households maximize preferences
U (c, n, e) subject to the budget constraint:
n (τ q + τ e e) + c ≤ I.

(1)

Household income I is spent on consuming goods and services c, raising n
children, and investing e in the quality of those n children.4 The cost of
rearing and investing into children depends on the parameters τ q and τ e . The
parameter τ q represents a fixed cost of rearing children that is independent of
the investments made into these children. The parameter τ e affects the costs
of investing in the quality of children. Both costs depend on the quantity n of
children.
At an interior solution (n∗ , e∗ ), the shadow prices of quantity and quality
are:
pn = τ q + τ e e ∗

(2)

pe = n∗ τ e .

(3)

Because the shadow price of quantity pn increases in the quality of children e∗ ,
increased investments in quality will tend to reduce the quantity of children.
Likewise, the shadow price of quality pe increases in the number of children n∗ ,
4

We denote the quality of children using the letter e because quality investment is typically associated with education. However, e can also represent investment into the health
and general well-being of children.

5

so additional children reduce investment in child quality. It is this substitution
between quality and quantity at the interior solution that generates a fertility
transition (Becker, Murphy, and Tamura 1990; Galor and Weil 1996, 2000).
It is common in the literature to impose an Inada condition
lim+

n→0

∂U (c, n, e)
=∞
∂n

(4)

of preferences over fertility, ensuring that fertility levels are always positive.5
However, this assumption removes important behavioral distinctions operating during the transition from high to low fertility levels. At high fertility
levels, the interaction of quality and quantity in the budget constraint (1)
leads to the familiar quality-quantity tradeoff. But the quantity and quality
of children are necessarily complements around the extensive margin, or at low
fertility levels, simply because it is essential to have children in order to consume the complementary good child quality, an idea that we label “essential
complementarity.”
In particular, note that the value of remaining childless V0 (I) is independent of the cost of rearing children or investing into child quality. By contrast,
the value function capturing optimal fertility conditional on having children
V (I, τ q , τ e ) depends negatively on the child cost parameters (τ q , τ e ). A woman
will choose to have children if V (I, τ q , τ e ) exceeds V0 (I).
Now suppose there is a decline in the price of child quality τ e . The value
of having children V (I, τ q , τ e ) rises without impacting the value of remaining
childless V0 , implying that more women will choose to have a child. But as
fertility increases along the extensive margin, it will decline along the intensive
margin as women substitute out of quantity into quality. Thus, a decline
in τ e will compress the distribution of family size from both sides. The
impact on total fertility depends on the magnitude of these offsetting effects.
5

Such an assumption is imposed by Barro and Becker (1989), Becker, Murphy, and
Tamura (1990), Galor and Weil (2000), Doepke (2004), Galor (2012), and many others. The
exceptions that we are aware of are Gobbi (2011), who analyzes the dynamics of voluntary
childlessness during the demographic transition and Baudin, de la Croix and Gobbi (2012),
who consider the relationship between childlessness and education in the U.S. in a modern
setting.

6

By contrast, an increase in the direct cost of rearing children τ q results in
fertility declines along both margins, leading to an unambiguous decline in
total fertility. Thus, observed declines in fertility along the extensive margin
cannot be attributed exclusively to factors that lower τ e .
This simple model illustrates the value of examining fertility along both
the extensive and intensive margins. However, to make the example more
concrete, consider how some of the hypotheses advanced as explanations for
the fertility transition roughly map into our stylized model. Some argue that
improved access to schooling, increased returns to education because of skillbiased technical change, or increased life expectancy lead to observed declines
in fertility. We can think of these factors as reductions in τ e because they imply
the cost of acquiring additional lifetime earnings through increased investments
into child quality decline. As we argued above, declines in τ e would not just
lower fertility along the intensive margin but would also raise fertility along the
extensive margin. Alternatively, improved access to labor markets for women
raises the opportunity cost of rearing children, represented in our model as an
increase in τ q .6 An increase in τ q should lower fertility along both the extensive
and the intensive margin. Observing fertility along both margins allows us to
empirically distinguish explanations of the fertility transition that map into
reductions in τ e and explanations that map into increases in τ q . Examining
only the intensive margin precludes this distinction.

3

The Rosenwald Schools

Our empirical test draws on the Rosenwald Rural Schools Initiative, a matching grant program that partly funded the construction of almost 5,000 schoolhouses for rural blacks in 14 southern states between 1913 and 1932.7 Figure
6

Improvements in contraceptive technology, which reduce the costs of averting births,
could also be viewed as an increase in τ q .
7
Briefly, the Rosenwald Initiative was a response to inadequate support for southern
rural black education at the turn of the 20th century (see, for example, Bond 1934, Myrdal
1944, and Margo 1990). The Rosenwald program originated in Alabama in 1913 and spread
through the remainder of the south by the early 1920s. When the Initiative closed in 1932,
roughly 92% of rural black children in the 14 states with Rosenwald presence lived in a

7

1 displays the fraction of school-age black children in a county who could have
been seated in a Rosenwald school when the program closed in 1932. The
across-county variation in access to Rosenwald schools, in concert with variation in the timing of construction over the two decades, provides the basis of
our main identification strategy.
We consider the effect of the Rosenwald schools on the fertility decisions
of two distinct samples of women. The first group (“older cohorts”) includes
women who were of childbearing age when the schools were built but were too
old to attend the schools themselves. For these older cohorts, the introduction
of the program provided lower cost access to high-quality schools for their
children; in the model, we interpret this development as a decline in the price
of child quality τ e , which is expected to increase fertility along the extensive
margin and decrease fertility along the intensive margin.
Our second group (“younger cohorts”) are women who were of school-going
age when Rosenwald schools were open. For these younger cohorts, Aaronson
and Mazumder (2011) demonstrate that exposure to Rosenwald schools improved school attendance, increased years of completed education, and raised
cognitive ability as measured by military exams. As adults, these women faced
an increase in the opportunity cost of rearing children τ q , which we predict to
cause their fertility to fall along both the extensive and intensive margin. In
addition, the introduction of the program lowered the cost of access to highquality schools for the children of the younger cohort. That is, the younger
cohort also face a decline in τ e . Observing declines in fertility along the extensive margin therefore underestimate the strength of the opportunity cost
effect and declines along the intensive margin overstate the same.
county with at least one Rosenwald school. Rosenwald schools could accommodate roughly
36% of all rural black children in these states. Detailed descriptions of the Rosenwald
program are available in McCormick (1934), Ascoli (2006), and Hoffschwelle (2006).

8

4

Data and Empirical Specification

4.1

Fertility

Our sample of southern women is drawn from the 1910, 1920, and 1930 decennial Censuses using the Integrated Public Use Microdata Series (IPUMS,
see Ruggles et al. 2010). We use the 1.4% sample for 1910, the 1% sample
for 1920, and a 6% sample for 1930. The 1930 data combines the publicly
available 1% IPUMS with an early version of the 5% sample, with duplicate
observations discarded.
For the older cohorts, women from all three IPUMS who were between the
ages of 25 and 49 at the time of the Census are included. As we discuss below,
we track their fertility over the 10 years before the Census interview. For
example, we measure the fertility experience of the 1930 sample as they move
from the ages of 15—39 in 1920 to 25—49 in 1930. The 1920 sample allows us
to include women who were of childbearing age when the earliest schools were
built. It also provides us with a large sample of women from a “control” group
who were living in non-Rosenwald counties. We ensure that no women in our
sample of older cohorts could have attended a Rosenwald school themselves.
Recall that this allows us to generate a clear prediction that the fertility effects
should differ between the extensive and intensive margins.
For our sample of younger cohorts, only women who were between the ages
of 18 and 22 in the 1930 IPUMS are included.8 A clear limitation of this part
of the analysis is that we cannot observe completed fertility, or later fertility,
for these women with available data. This concern is addressed in more detail
in section 5.2.
Fertility measures are constructed using counts of surviving children under
the age of 10 who can be linked to their biological mothers in the Census years.9
8

Few women above the age of 22 in 1930 were exposed to the schools and few women
below the age of 18 have children. The results are qualitatively similar to expanding our age
range by a year or two in either direction. Note that we cannot include 18- to 22-year-old
women in the 1920 Census because these women would have been part of our older cohort
sample (they would have faced a reduction in τ e as a result of Rosenwald schools available
at the time).
9
The 1910 to 1930 Censuses do not ask women about the total numbers of children that

9

We limit the analysis to children under 10 because we wish to avoid problems
associated with children leaving their parents’ household. We construct three
measures of fertility total fertility, total fertility conditional on at least one
child, and an indicator of whether a woman had at least one child under the
age of 10 to correspond to decisions on the intensive and extensive margins.
Summary statistics of the fertility measures are available in Table 1. The
10-year fertility rates vary substantially by race and rural status and over
time. For the older cohort, we can roughly approximate the better known
total fertility rate (TFR) by multiplying these 10-year fertility rates by 3.5.
This approximate TFR declined rapidly between 1910 and 1930 for rural blacks
(5.3 to 3.9) and rural whites (5.8 to 4.6). The urban TFR is much lower but
also trends downward by a comparable 25% during these two decades.

4.2

Rosenwald Exposure

Women are linked to the Rosenwald schools through county of residence, rural
status, and birth year. We obtained information on the schools from files
that the Rosenwald Fund used to track their construction projects. Each file
includes, among other information, the location (state and county), year of
construction, and number of teachers. Our analysis uses 4,932 schools with the
capacity to hold 13,746 teachers in 888 counties. See Aaronson and Mazumder
(2011) for more details.
We use different measures of exposure to the Rosenwald schools for each
of our two samples. In each case, we start by measuring the coverage of
the schools for each cohort in each county. Specifically, we calculate the
ratio of the Rosenwald Fund’s count of Rosenwald teachers in county c in
were ever born. We merge our sample of women with children under 10 via their household
ID (serial) and the mother’s ID within the household (pernum for the mother, momloc
for the child). The links are summarized in the IPUMS variable momrule, which is equal
to 1 when there is a clear and convincing mother-child link (a son/daughter linked to a
wife/spouse) and greater than one when there are various ambiguities in the relationship.
Using this procedure, we can perfectly replicate the IPUMS reported count of children
(nchild). However, we use our procedure for three reasons: (1) we can construct fertility for
the 5% 1930 sample that does not include nchild; (2) we can drop nonbiological relationships;
and (3) we can drop ambiguous matches.

10

year t multiplied by an assumed class size of 4510 relative to the estimated
number of rural blacks between the ages of 7 and 13 in the county in each
year.11,12 Denote this ratio by Tt,c . For the older cohorts, exposure is defined
10
P
1
as Etc = 10
Tt−k,c , the 10-year average of Ttc between Census year t − 1 and
k=1

t − 10 in county c. This measure reflects the expanded schooling opportunities
that women of childbearing age might expect for their children based on the
Rosenwald schools they observe in their community. For the younger cohorts,
7
P
we use Ebc = 17
Tb+6+k,c , the average coverage during the years when these
k=1

birth cohorts b were aged 7—13. This measure reflects how the Rosenwald
program affected educational opportunities when these women were of school
age.
Table 1 presents summary statistics of the Rosenwald exposure measures
for both cohorts. Over this period of declining fertility, there was a rapid
increase in exposure to Rosenwald schools among the older cohorts, rising
from 0 in 1910 to roughly 19.3% among rural black women in 1930. Almost all
of this increase occured after 1920. The exposure measure averages 7.6% for
our younger cohorts of rural black women who were between 18 and 22 years
old in 1930. Again, both measures exhibit significant cross-county dispersion,
as in Figure 1.
10

An average class size of 45 is consistent with surveys of rural black southern schools in
state and county education board reports at the time. It was also the standard assumption
in internal Rosenwald Fund documents.
11
We confine our analysis to the effects of exposure during the ages of 7—13 because
we cannot distinguish which schools (among those built after 1926) included high school
instruction. However, our results are robust to defining exposure over the ages of 7—17.
In a small minority of cases, our exposure measure exceeds 1. In such cases, we topcode
values at 1.
12
The population counts in the denominator are computed from the digitized 100% 1920
and 1930 Census manuscript files available through ancestry.com and interpolated for 1919
and 1921 through 1929.

11

4.3

The Empirical Specification

The key empirical challenge we face is that the Rosenwald schools were not
randomly located. Indeed, the Rosenwald Fund’s refrain is clear on this point:
“Help only where help was wanted, when an equal or greater amount of help
was forthcoming locally, and where local political organizations co-operated”
(McCormick, 1934). The matching grant aspect of the program further assured nonrandom placement of schools. Aaronson and Mazumder (2011)
discuss a number of tests to quantify the extent of the selection bias and find
that it is small. In particular, they show that black socioeconomic characteristics do not predict the location of the Rosenwald schools13 and, further, levels
and trends in black schooling before the program were similar in counties that
never had a Rosenwald school to those that did. They also show that the
effects on human capital are similar when they only use variation arising from
the first schools that were built in Alabama for plausibly idiosyncratic reasons.
To deal with endogenous selection, we follow Aaronson and Mazumder’s
main empirical strategy of controlling for a rich set of covariates, including
county-fixed effects and time trends, and applying differencing estimators that
exploit that the program was targeted at one demographic group. The basic
statistical model for the older cohort is:
yibct = f (blacki , rurali , Xit , ageit , t, c) +

(5)

(γ0 + γ1 blacki + γ2 rurali + γ3 (blacki ∗ rurali )) × Etc + εibct
which relates a fertility outcome yibct for individual i born in year b living in
county c in Census year t to a flexible function in black and rural indicators,
controls Xit , age, calendar-year dummies, county-fixed effects, and Etc , the
exposure to Rosenwald schools in county c at time t. We interact our Rosenwald exposure measure with race and rural status to take advantage of the
explicit targeting of the treatment to rural blacks while allowing other groups,
13
They do find that white literacy levels predict the location of the schools, consistent
with the Rosenwald Fund’s approach to locating in areas where white backlash could be
minimized.

12

particularly rural whites and urban blacks, to serve as controls.
This approach provides four different estimators of the effect of school
exposure on fertility. The sum of the OLS estimators γ
b0, γ
b1, , γ
b2 , and γ
b3 provides
an “undifferenced” estimate of the effect on rural blacks. To the extent that
there were other factors that may have affected the fertility of all blacks in
a county, including urban blacks, that were unrelated to the introduction of
the schools, we can difference out such effects by using γ
b2 + γ
b3 . There may
be actual effects on blacks living in areas classified as urban according to the
Census to the extent that the Rosenwald Fund and the Census Bureau had
different definitions of rural counties. A third estimator uses the difference
between rural blacks and rural whites in order to remove any common “rural”
effect that both blacks and whites shared. This is represented by γ
b1 + γ
b3 .
Finally, the “triple difference estimator” γ
b3 differences out both rural and race
effects and is therefore our preferred estimator. Any alternative explanation
for the result estimated by γ
b3 must reflect confounding factors that affected
only rural blacks and not rural whites or urban blacks in the same county.
We construct an analogous cross-sectional specification for the younger
cohort of women who were between the ages of 18 and 22 in 1930. In this case,
we modify equation (5) as follows: we (1) drop the time dummies, (2) replace
Etc with Ebc , and (3) replace the county-fixed effects with state-fixed effects.
Because both Etc and Ebc can take on values between 0 and 1, we interpret the
coefficients in equation 5 as the effect of going from no Rosenwald exposure in
one’s county to complete exposure.

5
5.1

Results
Fertility Among the Older Cohorts

Table 2 shows the results for our older cohort of women. Recall that these
women were too old to have gone through the Rosenwald schools themselves
but their children were potentially exposed to the schools. Column (1) shows
the effect of Rosenwald exposure on overall fertility in the last 10 years. Using
13

the triple difference estimator (b
γ3 ), we find that going from no exposure to
complete exposure results in an increase of 0.019 children with a standard error
of 0.051. The three alternative estimators (black rural - black urban, black
rural - white rural, black rural) reveal larger, though generally statistically
insignificant, positive point estimates. On their own, these results appear to
contradict the prediction of the standard quantity-quality model that relaxing
the constraints to invest into education leads to lower fertility rates.
The results on overall fertility, however, conflate opposing effects along the
extensive and intensive margins. Along the extensive margin (column 2), our
preferred estimator indicates that complete exposure to the schools increases
the probability that a woman had a child in the preceding 10 years by 3.2
(1.8) percentage points.14 The effects are similar for the black rural minus
black urban estimator and slightly larger and statistically significant if we use
the black rural minus white rural difference or the undifferenced estimator.
Column (3) reports results along the intensive margin. Among women who
had at least one child in the preceding 10 years, full exposure leads to 0.151
(0.085) fewer children, a result that is marginally statistically significant. The
alternative estimators show the same signed effect but are smaller in absolute
value and therefore broadly statistically insignificant.
Columns (4) to (6) repeat this exercise for a subsample of married women.
Childbearing was relatively less common among unmarried women in the early
20th century compared to today. The results are, unsurprisingly, stronger for
married women, especially along the extensive margin. Complete exposure to
Rosenwald raised the probability of having a child by 5.8 (1.6) to 6.8 (1.5)
percentage points, depending on the estimator. Along the intensive margin,
our preferred (b
γ3 ) estimator suggests a decline of 0.183 (0.092) children, although other estimators tend to be smaller and not statistically different from
zero.15 We see the evidence broadly suggesting that fertility for all women
aged 25—49 rose by a little more than 5% along the extensive margin and fell
14

The baseline 10-year probability of having children among rural blacks is 45.6%.
There is no statistically significant effect on either the intensive or extensive margin for
unmarried women and no effect on the probability of marriage.
15

14

by slightly less along the intensive margin in response to the availability of
higher quality schooling for all rural black children in a county. 16 On balance, the response along the extensive margin slightly dominates the response
along the intensive margin and thus average fertility increases somewhat with
exposure, particularly for married women. Our results imply that the number
of black children growing up in small families increased as the distribution of
the number of children was “compressed” from both sides. Indeed, the (unreported) probability that a woman had exactly one child under 10 increased
by 3.8 (1.3) percentage points in counties with complete Rosenwald coverage.
These findings are consistent with essential complementarity. For our older
cohorts, the Rosenwald initiative can be viewed as representing a decline in
the price of the quality of education τ e , as the program led to improvements
in both school access and school quality. This, in turn, led parents to invest
more heavily into the quality of children. Indeed, Aaronson and Mazumder
(2011) find that exposure to the schools led to large improvements in the
human capital of students. Our model predicts that this decline in τ e raised
fertility along the extensive margin because of essential complementarity. The
model also predicts that fertility will decline along the intensive margin because
quantity and quality substitute for each other at higher levels of fertility. Both
predictions are confirmed by the data. Importantly, the results based on
total fertility, combining fertility across both margins, might have led one to
mistakenly conclude that the schools had no, or even a paradoxical positive,
effect on the fertility of the older cohorts. However, enhancing the model
to distinguish between the separate effects of essential complementarity and
the quantity-quality tradeoff enables us to reconcile the empirical patterns in
fertility among this cohort of women.

5.2

Fertility Among the Younger Cohorts

In Table 3, we present the results for the younger cohorts. Aaronson and
Mazumder (2011) show that exposure to the Rosenwald schools during child16

Typical Rosenwald exposure in 1930 was roughly one-third, suggesting actual average
effects along the extensive and intensive margins on the order of 2%.

15

hood had a significant positive effect on the average level of human capital of
girls. As adults, increased access to higher quality schooling as children likely
raised the opportunity cost of procreation τ q . In response, fertility should
decline along both the intensive and extensive margins.
We start by showing the overall effect of Rosenwald exposure at ages 7—13
on fertility at ages 18—22 in column (1). Using our preferred specification,
full exposure to the Rosenwald schools leads to a 0.238 (0.092) decline in the
number of children per woman. For a county that goes from 0 to complete
Rosenwald exposure, the magnitude of the effect is roughly 60% of the mean
fertility rate of 0.39 for rural black women in this age group. The point
estimates range from -0.12 to -0.37 across alternative estimators but are all
statistically significant at conventional levels.
In columns (2) and (3), we demonstrate that this overall decline is due to
a reduction in fertility along both the extensive and intensive margins. The
evidence is especially strong along the intensive margin as all four estimators
show large and statistically significant negative effects of school exposure on
fertility. The triple difference estimator suggests that full exposure leads to a
0.793 (0.402) decline in the number of children among women who have at least
one child. The evidence along the extensive margin is more mixed: the point
estimate for our preferred estimator is negative and economically meaningful
but not statistically significant. The estimator when differencing across rural
and urban blacks delivers the economically and statistically strongest evidence
for a decline in fertility along the extensive margin. It is worth reemphasizing
that the negative effect along the extensive margin may be attenuated by
the potentially offsetting effect of a decline in τ e , as experienced by the older
cohorts. Moreover, the negative effect along the intensive margin is enhanced
by the same decline in τ e .
In columns (4) to (6) of Table 3, we focus on women between the ages of 20
and 22, among whom fertility rates are much higher and potential effects of exposure on fertility are therefore easier to detect. Indeed, we find notably larger
negative effects for total fertility and along both the extensive and intensive
margins. For example, the triple difference estimator suggests that complete
16

exposure to Rosenwald schools on average leads to more than one-half fewer
children for women in this age group (or 0.22 fewer children at the average
Rosenwald exposure rate). Overall, the response in fertility behavior among
the younger cohorts is larger than that among the older cohorts, suggesting
that changes in the opportunities for women due to increased education can
have an important impact on the onset of fertility.
Table 4 breaks out marriage and fertility outcomes among the 18- to 22year olds. Complete exposure to Rosenwald appears to delay marriage and
childbearing among married women but not childbearing among unmarried
women. By age 22, full exposure to Rosenwald schools as school children
led to a reduction in the probability of marriage by age 22 of -6.9 (4.3) to
-13.3 (4.6) percentage points (column 1). These are economically large, albeit
sometimes statistically insignificant, effects that have a direct impact on overall
fertility because of the close connection between marriage and childbearing.
We also observe a decline in fertility within marriage: average fertility among
married women by age 22 declined by about 0.40 (0.23) children. Again, the
(unreported) effects are larger among the more fecund 20—22 population.
Finally, consistent with the opportunity cost view, Table 5 reports evidence
that the occupational standing of women educated in Rosenwald schools rose
compared to those that did not go through the schools. Because of data
limitations on education and earnings in Censuses before 1940, we use the
Census-derived occscore measure, which assigns an occupation to the median
income of all individuals working in that occupation in 1950. We find that in
most specifications, exposure to Rosenwald schools at ages 7—13 significantly
raises the occscore of the younger cohort (columns 1 and 2), consistent with the
view that Rosenwald-educated women had better opportunities in the labor
force than those who did not go through the schools themselves. We also
find (unreported) that edscore, which is based on a measure of occupational
educational attainment in 1950, rose for the younger cohort. No such effect
on occscore or edscore is found among the older cohorts who were too old to
have obtained Rosenwald educations themselves (column 3).
Because we cannot extend the analysis beyond the 1930 Census with cur17

rent data, we cannot determine how much our results on the Rosenwaldeducated women reflect changes to timing of fertility or completed fertility.17
That said, we find a strong association between fertility at young and old
ages in general. In particular, we constructed a data set of the average number of children under 10 by state of birth, race, and birth cohort from the
1900—1950 Censuses. The correlation between the fertility of 18- to 22-yearold black women and 38- to 42-year-old black women from the same state of
birth and birth cohort is 0.54. Adjusted for sampling error, this correlation
rises to 0.87.18 For Rosenwald-only states, the adjusted correlation is 0.81.
Therefore, we view our measure of fertility as a useful proxy for completed
fertility.

6

Discussion

This paper explores the implications of using an augmented quantity-quality
model to explain fertility choices along the extensive and intensive margin after
a wholesale change in the availability of higher quality schools. We show that
the predictions of essential complementarity are largely consistent with how
women of childbearing age adapted their fertility behavior when faced with
an increase in schooling opportunities for their children. In particular, among
17

In due course, as the 1940 Census geographic data becomes available, we will be able
to consider fertility for these women up to age 32 and thus learn whether the Rosenwald
intervention primarily delayed the onset of fertility or whether the intervention reduced
fertility up through the early 30s as well.
18
To compute the sampling error-adjusted correlation between the fertility of the young,
y
φg , and old, φog , among group g, let Ngy and Ngo be the number of individuals of group g for
which we observe fiy and fio , the fertility of individual i at a young or at an old age. Note that
the Censuses do not allow us to observe the same individual at both young and old ages. It
cd
ov (fgy ,fg0 )
can be shown that corr(φyg , φog ) =


!1/2
!1/2
where sb2y,i∈g =

1
Ngy −1

P
g

eyi∈g

1
vd
ar(fgy )− G


2 

P
g

1
y
Ng

s
b2y,i∈g

1
vd
ar(fpy )− G

P
g

1
y
Ng

s
b2o,i∈g

is the sampling variance for the young, derived from

the sample residuals within group. An analogous formula applies to the sampling variance
of the old, sb2o,i∈g . A derivation is available from the authors on request.
Note that we remove group cells with fewer than five observations.

18

our older cohorts, the probability of having a child rose and the number of
children, conditional on having children, fell in response to the introduction
of Rosenwald schools. These two competing effects roughly offset each other.
We also find that the expansion of Rosenwald schools caused those women
who were educated in the Rosenwald schools, our younger cohorts, to change
their fertility behavior substantially. The increase in education among these
women was accompanied by a substantial decline in early fertility (along both
the extensive and the intensive margin), a delay in marriage, and an increase
in the quality of their chosen occupations. This behavior is consistent with
the notion that education raised the opportunity costs of fertility.
It is common to see fertility declines along both the extensive and the
intensive margin during demographic transitions. Over the first half of the
20th century, childlessness became more prevalent among southern black and
white American women, at the same time that large families became less
common (see Figure 2). Developing countries today display the same pattern.
Figure 3 shows the fraction of women without children against the average
number of children in families with children among developing countries in the
Demographic Health Surveys over the last 30 years. Similar to the American
South a century ago, modern-day developing countries with high fertility along
the intensive margin are simultaneously those with high fertility along the
extensive margin.
Introducing an extensive margin within a standard quantity-quality model
generates additional tests of hypotheses regarding the channels driving demographic transitions. For example, skill-biased technical change or improvements in longevity will act analogous to a decline in the price of investing
in the quality of children. Therefore, these explanations fail to generate the
simultaneous decline in fertility along both the intensive and the extensive
margin that is typical during demographic transitions. These explanations are
therefore unlikely to be the sole driving forces behind the transition. Instead,
we tentatively propose that increases in the opportunity cost of childbearing
induced by increased schooling attainment among young women play an important role in the demographic transition. One plausible interpretation of the
19

time-series evidence in Figures 2 and 3, along with the more detailed findings
of the Rosenwald era, would be that improved schooling opportunities induce
greater schooling investments, which subsequently raise the opportunity cost
of childbearing and lower fertility along all margins.

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[9] Bleakley, H., and Lange, F. (2009). Chronic disease burden and the interaction of education, fertility, and growth. Review of Economics and
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[17] Lucas, A. (2011). The impact of malaria eradication on fertility. Economic
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[21] Myrdal, G. (1944). An American dilemma: The negro problem and modern democracy. New York: Harper and Row.
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22

Table 1: Summary Statistics

Fertility Measures
Total fertility
Total fertility, 1910
Total fertility, 1920
Total fertility, 1930
Extensive margin
Extensive margin, 1910
Extensive margin, 1920
Extensive margin, 1930
Intensive margin
Intensive margin, 1910
Intensive margin, 1920
Intensive margin, 1930
Rosenwald Measures
Own exposure to Rosenwald
Rosenwald exposure in last 10 years
Rosenwald exposure last 10 years, 1910
Rosenwald exposure last 10 years, 1920
Rosenwald exposure last 10 years, 1930

Other Measures
Married
Labor force status
Literate
Occscore (hundreds of 1950$)

N

Black,
Rural

Older Cohort
Black,
White,
Urban
Rural

White,
Urban

Black,
Rural

Younger Cohort
Black,
White,
Urban
Rural

White,
Urban

1.216
[1.645]
1.509
[1.729]
1.344
[1.662]
1.126
[1.613]
0.456
[0.498]
0.551
[0.497]
0.512
[0.50]
0.425
[0.494]
2.664
[1.440]
2.739
[1.433]
2.624
[1.426]
2.648
[1.444]

0.484
[1.061]
0.607
[1.125]
0.509
[1.052]
0.463
[1.050]
0.234
[0.423]
0.299
[0.458]
0.258
[0.438]
0.221
[0.415]
2.073
[1.233]
2.028
[1.161]
1.972
[1.184]
2.095
[1.253]

1.397
[1.482]
1.666
[1.580]
1.519
[1.503]
1.320
[1.449]
0.599
[0.490]
0.656
[0.475]
0.634
[0.482]
0.582
[0.493]
2.331
[1.221]
2.541
[1.260]
2.395
[1.211]
2.269
[1.206]

0.760
[1.128]
0.959
[1.303]
0.801
[1.159]
0.718
[1.085]
0.406
[0.491]
0.453
[0.498]
0.418
[0.493]
0.395
[0.489]
1.873
[1.025]
2.116
[1.139]
1.917
[1.037]
1.817
[0.990]

0.388
[0.839]

0.207
[0.616]

0.391
[0.762]

0.213
[0.558]

0.388
[0.839]
0.226
[0.418]

0.207
[0.616]
0.131
[0.337]

0.391
[0.762]
0.258
[0.438]

0.213
[0.558]
0.154
[0.361]

0.226
[0.418]
1.716
[0.914]

0.131
[0.337]
1.581
[0.850]

0.258
[0.438]
1.514
[0.739]

0.154
[0.361]
1.383
[0.640]

1.716
[0.914]

1.581
[0.850]

1.514
[0.739]

1.383
[0.640]

0.000
[0.000]
0.139
[0.177]
0.000
[0.000]
0.006
[0.015]
0.193
[0.183]

0.000
[0.000]
0.198
[0.247]
0.000
[0.000]
0.005
[0.015]
0.248
[0.254]

0.000
[0.000]
0.145
[0.214]
0.000
[0.000]
0.005
[0.016]
0.198
[0.228]

0.000
[0.000]
0.166
[0.234]
0.000
[0.000]
0.003
[0.012]
0.218
[0.247]

0.076
[0.107]

0.080
[0.123]

0.074
[0.134]

0.068
[0.121]

0.789
[0.408]
0.465
[0.499]
0.728
[0.445]
8.100
[5.296]

0.652
[0.476]
0.636
[0.481]
0.845
[0.362]
8.802
[6.876]

0.851
[0.356]
0.127
[0.333]
0.940
[0.237]
16.717
[9.805]

0.763
[0.425]
0.230
[0.421]
0.972
[0.164]
21.372
[8.275]

0.490
[0.50]
0.376
[0.484]
0.877
[0.328]
7.154
[5.093]

0.442
[0.497]
0.531
[0.499]
0.945
[0.227]
9.781
[6.795]

0.476
[0.499]
0.189
[0.391]
0.978
[0.148]
17.408
[9.244]

0.402
[0.490]
0.422
[0.494]
0.993
[0.082]
20.869
[6.153]

70,555

39,178

190,725

107,267

20,623

9,659

46,661

24,119

The older cohort includes 25-49-year-old women from the 1910, 1920, and 1930 IPUMS. The younger cohort includes women
aged 18-22 from the 1930 IPUMS. The extensive margin is the probability that a woman has at least one child. The intensive
margin is the number of children a woman has, conditional on having at least one child. Refer to the text for details on how the
variables are constructed.

Table 2: The Effect of Rosenwald Exposure on the Fertility of the Older Cohorts

(1)

(3)

(4)

Total
Fertility

(2)
All, 25-49
Extensive
Margin

(5)
(6)
Married, 25-49
Extensive
Intensive
Margin
Margin

Intensive
Margin

Total
Fertility

γ0

-0.010
[0.029]

0.002
[0.011]

0.001
[0.038]

-0.035
[0.034]

-0.010
[0.012]

0.006
[0.039]

γ1

0.034
[0.028]

0.008
[0.012]

0.108*
[0.064]

0.043
[0.038]

0.004
[0.015]

0.142**
[0.071]

γ2

0.038
[0.027]

-0.006
[0.010]

0.041
[0.034]

0.055*
[0.031]

-0.000
[0.011]

0.043
[0.035]

0.032*
[0.018]

Triple Difference
-0.151*
0.085
[0.085]
[0.062]

0.064***
[0.021]

-0.183**
[0.092]

Difference in Difference
-0.110
0.140**
[0.082]
[0.059]

0.063***
[0.019]

-0.140
[0.089]

-0.043
[0.057]

0.068***
[0.015]

-0.041
[0.060]

Undifferenced Effect of Exposure
-0.001
0.148***
0.058***
[0.060]
[0.054]
[0.016]

0.009
[0.063]

Preferred Estimator
B-W Rural - B-W Urban
(γ3)

0.019
[0.051]

Alternative Estimators
Black, Rural-Urban
(γ2 + γ3)

0.057
[0.048]

0.026
[0.016]

B-W Rural
(γ1 + γ3)

0.054
[0.044]

0.041***
[0.014]

Rural black
(γ0 + γ1+γ2 + γ3)

0.081*
[0.046]

0.037**
[0.015]

0.128**
[0.050]

407,725
407,725
199,150
N
325,150
325,150
189,585
0.134
0.116
0.112
R2
0.157
0.141
0.113
Sample includes women aged 25-49 from the 1910, 1920, and 1930 IPUMS. The dependent variables are:
columns 1 and 4: the number of 0-9 year olds at the time of the Census; columns 2 and 5: an indicator of having
at least one child between the age of 0 and 9; columns 3 and 6: the number of children conditional on at least one
child. All specifications contain county fixed effects, state-specific time trends, race and rural specific trends, a
full sets of age and year dummies and literacy. Robust standard errors, clustered at the county level, are in
brackets. Stars indicate probability values: *** p < 0.01, ** p < 0.05, * p < 0.10.

Table 3: The Effects of Rosenwald Exposure on the Fertility of Younger Cohorts

(1)
Sample
Overall
Fertility

(2)
(3)
18-22 year olds
Extensive
Intensive
Margin
Margin

(4)
Overall
Fertility

(5)
(6)
20-22 year olds
Extensive
Intensive
Margin
Margin

γ0

0.134***
[0.036]

0.045*
[0.026]

0.080
[0.101]

0.022
[0.082]

0.011
[0.052]

-0.097
[0.153]

γ1

0.120
[0.074]

0.073*
[0.041]

0.344
[0.380]

0.382*
[0.218]

0.132
[0.089]

0.963
[0.625]

γ2

-0.135***
[0.046]

-0.039
[0.031]

-0.064
[0.108]

0.038
[0.104]

0.037
[0.062]

0.094
[0.174]

-0.065
[0.052]

Triple Difference
-0.793**
-0.673***
[0.402]
[0.259]

-0.195*
[0.113]

-1.583**
[0.669]

Difference in Difference
-0.857**
-0.635***
[0.393]
[0.239]

-0.158*
[0.096]

-1.489**
[0.668]

-0.449***
[0.150]

-0.063
[0.070]

-0.620**
[0.302]

-0.015
[0.068]

-0.623**
[0.281]

Preferred Estimator
B-W Rural - B-W Urban
(γ 3)

-0.238***
[0.092]

Alternative Estimators
Black, Rural-Urban
(γ 2 + γ 3)

-0.372***
[0.085]

-0.104**
[0.044]

B-W Rural
(γ 1 + γ 3)

-0.118**
[0.059]

0.008
[0.034]

Rural black
(γ 0 + γ 1+γ 2 + γ 3)

-0.119**
[0.056]

0.014
[0.033]

-0.291**
[0.147]

Undifferenced Effect of Exposure
-0.433***
-0.231
[0.138]
[0.142]

N
101,062
101,062
21,669
59,231
59,231
16,450
2
R
0.069
0.062
0.075
0.038
0.036
0.049
The full sample includes women aged 18-22 from the 1930 1 and 5% IPUMS. The table displays coefficient
estimates from a regression of the indicated fertility measure on the own age 7 to 13 exposure variable described
in the text. All specifications include race and rural dummies and their interaction, age dummies, and state fixed
effects. Robust standard errors, clustered by county, are in brackets. *** p < 0.01, ** p < 0.05, * p < 0.10.

Table 4: Marriage Rates, Marital and Extramarital Fertility Among the Younger Cohorts
(1)

(2)

(3)

All
Probability
of Marriage

Overall
Fertility

Married
Extensive
Margin

γ0

0.066
[0.043]

0.010
[0.082]

γ1

-0.056
[0.055]

γ2

-0.002
[0.045]

(4)
18-22 years old

(5)

(6)

(7)

Intensive
Margin

Overall
Fertility

Unmarried
Extensive
Margin

Intensive
Margin

-0.065
[0.060]

0.081
[0.101]

0.004
[0.005]

0.000
[0.003]

-0.322
[2.107]

0.388**
[0.197]

0.200*
[0.105]

0.320
[0.401]

-0.023
[0.017]

-0.014
[0.009]

0.898
[2.355]

-0.039
[0.092]

0.056
[0.066]

-0.062
[0.108]

0.002
[0.006]

0.004
[0.003]

-0.003
[2.494]

-0.395*
[0.230]

Triple Difference
-0.069
-0.776*
[0.128]
[0.424]

-0.007
[0.024]

0.002
[0.013]

-0.676
[2.685]

-0.079
[0.062]

-0.434**
[0.212]

Difference in Difference
-0.013
-0.838**
-0.004
[0.102]
[0.412]
[0.025]

0.006
[0.013]

-0.679
[1.139]

-0.133***
[0.046]

-0.007
[0.137]

0.131*
[0.075]

-0.030*
[0.018]

-0.012
[0.009]

0.222
[1.262]

-0.036
[0.128]

Undifferenced Effect of Exposure
0.122*
-0.437***
-0.023
[0.072]
[0.139]
[0.018]

-0.008
[0.009]

-0.104
[0.633]

Preferred Estimator
γ3
(B-W Rur - B-W Urb)

-0.077
[0.068]

Alternative Estimators
Black, Rural-Urban
(γ 2 + γ 3)
B-W Rural
(γ 1 + γ 3)

Effect on Rural Blacks
(γ 0 + γ 1 + γ 2 + γ 3 )

-0.069
[0.043]

-0.456***
[0.153]

N
100,992
46,255
46,255
21,370
54,737
54,737
299
R2
0.066
0.066
0.054
0.075
0.007
0.008
0.140
The estimates are based on the same specification as that used in Table 3. For details refer to the notes in that table. Robust
standard errors, clustered by county, are in brackets. *** p < 0.01, ** p < 0.05, * p < 0.10.

Table 5: The Effect of the Rosenwald Schools Initiative on Occupational Score, by Cohort
(1)

(2)

(3)

18-22

Age
20-22

25-49

γ0

0.245***
[0.088]

0.174
[0.118]

0.024
[0.026]

γ1

0.061
[0.130]

-0.059
[0.184]

0.092***
[0.022]

γ2

-0.483***
[0.148]

-0.588***
[0.221]

0.052*
[0.030]

0.326
[0.214]

Triple Difference
0.680**
[0.290]

-0.109***
[0.041]

Black, Rural-Urban
(γ 2 + γ 3)

-0.156
[0.176]

Difference in Difference
0.092
[0.225]

-0.057*
[0.033]

B-W Rural
(γ 1 + γ 3)

0.387**
[0.163]

0.621***
[0.233]

-0.017
[0.035]

Effect on Rural Blacks
(γ 0 + γ 1 + γ 2 + γ 3 )

0.150
[0.119]

Undifferenced Effect of Exposure
0.207
[0.177]

0.059*
[0.033]

N

27,449

17,526

97,788

Preferred Estimator
γ3
(B-W Rur - B-W Urb)
Alternative Estimators

2

0.419
R
0.433
0.432
The table displays coefficient estimates from a regression of log(occupational score) on Rosenwald
exposure. The first two columns use age 7 to 13 Rosenwald exposure, the third column uses average
exposure over the previous decade. The specification for column 1 and 2 mirror that used in Table 3. The
column 3 specification is the same as that used in Table 2. For details refer to the notes in those tables.
Robust standard errors, clustered by county where appropriate, are in brackets. *** p < 0.01, ** p < 0.05,
*p < 0.10.

Figure 1
Ros enwald C o v erage by 1931

•

..

*

Covera ge

*

Montgomery, AL
H ampton, VA
c = 0 (508)
0 .0 < c <0.1 (84)
0 .1 <= c < 02 (1 ~1 )
0 .2 <= c < 0.3 (111 )
0 .~ <= c < 0.4 (11 2)

0 .4 <= c < 0.5 (82)
0 .5 <= c < 0.6 (71 )
0 .6 <= c < 0.7 (:38)
-

0 .7<= c < 0.8 (40)

-

0 .8 <= c < 0.9 (:34)

c >= 0.9 (154)

0

100

Ivlile s

200

Figure 2
Distribution of Number of Children Ever Born,
Black Married Southern Women, aged 40-44
0.8
0.7
average 1900-1910
average 1940-1950

0.6

Sha
Share

0.5
0.4
0.3
0.2
0.1
0
0

1

2

Number of children

3+

Figure 3: Changes in Fraction Childless vs. Avg. Fertility
Avg Fertility measured conditional on having at least 1 child
Panel B: Changes
.15

Panel A: Levels
.15

Jordan
Morocco

Change in Fraction without Kids
0
.05
.1

Fraction of Women without Kids
.05
.1

Jordan

Peru
Nigeria
Zambia
Egypt
Colombia
SenegalPakistan
Ghana
Rwanda
Namibia
Bangladesh
Kenya
Indonesia
Bolivia Haiti
ZimbabweTanzania
Ecuador
India
Malawi
El
Salvador
Guatemala
Dominican
Republic
Paraguay
Madagascar Mali
Niger
Cameroon
Liberia
Uganda

0

-.05

Philippines
AzerbaijanVietnam
Sri Lanka
Philippines
Trinidad
and Tobago
Thailand
Armenia
Brazil
Cambodia
Vietnam
Colombia
Brazil
CAR
Cambodia
Tunisia
Mauritania Sudan
Pakistan
Armenia
Egypt
Peru Colombia
Haiti
Mexico Cameroon
Uganda
Paraguay
Haiti
Pakistan
Madagascar
Kazakhstan
Indonesia
Indonesia
Morocco
Ecuador
Senegal
Kazakhstan
Dominican
Republic
Eritrea
Paraguay
Turkey Botswana
South
Ecuador
Africa
Comoros
ElGuatemala
Salvador
Namibia
Niger Yemen
Dominican
Republic
Egypt
Mozambique
BoliviaMadagascar
Bolivia
El
Salvador
Chad
Senegal
Moldova
India Guatemala
Zambia
Jordan
TurkeyNepal
Cameroon
Namibia
Honduras
Congo
Mali
Democratic
Republic
IndiaLesotho
Liberia
Nigeria
Angola
Cote
d'Ivoire
Maldives
Swaziland
Peru
Mozambique
Kyrgyz
Republic
Eritrea
Gabon
Nicaragua
Nepal
Guinea
Nicaragua
Niger
Ethiopia
Turkmenistan
Ghana
Kenya
Uganda
Tanzania
Zimbabwe
Mali
Cote
d'Ivoire
Zimbabwe
Guinea
Kenya
Tanzania
Yemen
Bangladesh
Benin
Benin
Chad
Sierra
Rwanda
Leone
Uzbekistan
Congo
Burkina
Ethiopia
Malawi
FasoFaso
Bangladesh
Burundi
Burkina
Ghana
Togo
Zambia
Malawi Rwanda
Togo
Liberia
Nigeria

Morocco

2

4
6
Avg Number of Children|positive

8

Using the first and the most recent surveys available from DHS

-3
-2
-1
0
1
Change in Avg Number of Children|positive

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
A Leverage-based Model of Speculative Bubbles
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WP-08-01

Displacement, Asymmetric Information and Heterogeneous Human Capital
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BankCaR (Bank Capital-at-Risk): A credit risk model for US commercial bank charge-offs
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Bank Lending, Financing Constraints and SME Investment
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Global Inflation
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Scale and the Origins of Structural Change
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New Vehicle Characteristics and the Cost of the
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Thomas Klier and Joshua Linn

WP-08-13

Realized Volatility
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WP-08-14

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WP-08-15

1

Working Paper Series (continued)
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Una Okonkwo Osili and Anna Paulson

WP-08-17

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WP-08-18

Remittance Behavior among New U.S. Immigrants
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WP-08-19

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Marco Bassetto

WP-08-21

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WP-09-01

Why do the Elderly Save? The Role of Medical Expenses
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-09-02

Using Stock Returns to Identify Government Spending Shocks
Jonas D.M. Fisher and Ryan Peters

WP-09-03

Stochastic Volatility
Torben G. Andersen and Luca Benzoni

WP-09-04

The Effect of Disability Insurance Receipt on Labor Supply
Eric French and Jae Song

WP-09-05

CEO Overconfidence and Dividend Policy
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WP-09-06

Do Financial Counseling Mandates Improve Mortgage Choice and Performance?
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WP-09-07

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Pay for Percentile
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WP-09-09

The Life and Times of Nicolas Dutot
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WP-09-10

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WP-09-11

2

Working Paper Series (continued)
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WP-09-12

WP-09-13

WP-09-14

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WP-09-15

Estimation of a Transformation Model with Truncation,
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WP-09-16

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WP-09-17

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WP-09-18

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WP-09-22

WP-09-23

The Economics of “Radiator Springs:” Industry Dynamics, Sunk Costs, and
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WP-09-24

On the Relationship between Mobility, Population Growth, and
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WP-09-26

3

Working Paper Series (continued)
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WP-10-03

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Mortgage Choices and Housing Speculation
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WP-10-16

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WP-10-17

4

Working Paper Series (continued)
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Simple Markov-Perfect Industry Dynamics
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WP-10-21

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WP-10-22

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Federal Reserve Policies and Financial Market Conditions During the Crisis
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The Financial Labor Supply Accelerator
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Survival and long-run dynamics with heterogeneous beliefs under recursive preferences
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A Leverage-based Model of Speculative Bubbles (Revised)
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Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation
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WP-11-08

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WP-11-09

5