Chapter 2:
Fertility decisions, demographic change and development
Harvard Kennedy School
PED 365, Spring 2011
(Harvard Kennedy School)
Hillel Rapoport
PED 365, Spring 2011
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Plan
1
Introduction
2
Fertility and the old-age security hypothesis
3
Trading o¤ quantity for quality of children: a generic model
4
Fertility choices in context: India and France
5
Fertility choices in historical perspective
6
Conclusion: "love thy children"
(Harvard Kennedy School)
Hillel Rapoport
PED 365, Spring 2011
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Introduction
As we have seen, the demographic transition is one from high to low
birth and death rates, with birth rates decreasing (sometimes long)
after death rates started decreasing.
Why do birth rates decrease long after death rates?
Macro inertia: has to do with the age distribution of the population
(with high birth and deaths rates, the population is young; even if
today’s fertile women start having less children, they will soon be
joined by many additional mothers).
Micro inertia: in takes time for fertility behavior (and, hence, to
natality) to adjust to the lower death rates. Social norms evolve
slowly, information on death rates, longevity and risks may di¤use
very slowly or be processed with cognitive biases.
(Harvard Kennedy School)
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Introduction
In this chapter:
We …rst discuss in more depth the "micro-inertia" in connection to
the "old age security" hypothesis
We then present a generic model of parental choice between fertility
and education (i.e., quality/quantity tradeo¤) in the spirit of Becker
and Lewis (1973)
We the examine evidence on such a tradeo¤ in a di¤erent contexts
(India and France) and in historical perspective
(Harvard Kennedy School)
Hillel Rapoport
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Plan
1
Introduction
2
Fertility and the old-age security hypothesis
3
Trading o¤ quantity for quality of children: a generic model
4
Fertility choices in context: India and France
5
Fertility choices in historical perspective
6
Conclusion
(Harvard Kennedy School)
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Fertility and the old-age security hypothesis
Children are not only a "consumption good" (people love to have
children) but also an "investment good" in a context of missing
institutions (social security) and markets (credit, insurance); in
particular, children are a form of investment for old-age security.
Couples decide on the number of children anticipating that some will
be unable to support them in their old age due to death, insu¢ cient
income earning capacity, or opportunistic behavior (be a "bad child")
Assume these di¤erent risks are captured by a probability p that a
given child grows up to look after the parents in their old age; assume
also the parents want to secure a probability q that at least one of
their children supports them when they get old: how many children
should they have?
(Harvard Kennedy School)
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Fertility and the old-age security hypothesis
The answer is given by a simple formula: with n children, the
probability that none of them supports you is (1 p )n . You will
therefore choose n so that:
1
(1
p )n > q
Numerical examples: assume p = 1/2 (realistic in the context of
developing countries given mortality tables), then with q = 0.9 you
will want n = 4 children; if you are more risk-averse and want
q = 0.95 then you will choose to have n = 5 children
Gender bias: if support must come from sons, for whatever reason
(social norms, land ownership norms), this will double the number of
desired children.
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Fertility and the old-age security hypothesis
We can now explore the implications of this model in terms of
micro-inertia in fertility behavior: why do fertility rates remain high
(for some time) in the face of rapidly falling death rates?
Information and cognitions: death rates fell in developing countries in
the 40s and 50s at unprecedented rates; however people have
adaptative expectations (e.g., myopic: they expect what happened in
the previous generation to hold for them), and it is only after the fact
that things are known.
Hoarding versus targeting: the former holds to a higher extent if
death rates fall for adults (hoarding) rather than for younger children
(infant mortality and sequential decisions or targeting)
p is a composite probability; the risks associated with a surviving
child not caring for his/her parents remain and can go up
(urbanization, emigration – Williamson, 1985)
(Harvard Kennedy School)
Hillel Rapoport
PED 365, Spring 2011
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Plan
1
Introduction
2
Fertility and the old-age security hypothesis
3
Trading o¤ quantity for quality of children: a generic model
4
Fertility choices in context: India and France
5
Fertility choices in historical perspective
6
Conclusion: "love thy children"
(Harvard Kennedy School)
Hillel Rapoport
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Trading o¤ quality for quantity of children
Utility function – parents enjoy having more children and more
educated ones:
U = U (e, n)
where n = number of children, e = education level per child and
U 0 > 0, U”< 0
Budget constraint:
(1
fn )w m + w f = en
where f is the time required to have a child and w m , w f are the mother’s
and father’s wages.
(Harvard Kennedy School)
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Trading o¤ quality for quantity of children
n
1/f
U(n,e)=U°
f wm
e
(Harvard Kennedy School)
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Trading o¤ quality for quantity of children
Initial situation where women’s wages are low and there is a strong
preference for quantity (due e.g. to lack of social security)
Result: maximal fertility
n
1/f
fw
(Harvard Kennedy School)
f
e
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Trading o¤ quality for quantity of children
What happens if women’s wages go up?
Opportunity cost of children rises, education is relatively cheaper – as
drawn the substitution e¤ect dominates
n
e
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Trading o¤ quality for quantity of children
What if men’s wages go up (or households receive lump-sum
transfers)?
Pure income e¤ect – both quantity and quality should rise
n
e
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Trading o¤ quality for quantity of children
With education subsidies at subsidy rate s, the budget constraint
becomes (1 fn )w m + w f = (1 s )en
Uncertain e¤ect on fertility, education goes up
n
f wm / (1-s)
e
(Harvard Kennedy School)
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Trading o¤ quality for quantity of children
With a possibility of child labor (productivity p), the budget
constraint becomes (1 fn )w m + w f + pn = en
Fertility increases, uncertain e¤ect on education (opposite if ban on
child labor)
n
(Harvard Kennedy School)
Hillel Rapoport
e
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Trading o¤ quality for quantity of children
Let us summarize the predictions from this simple model:
Introduction of social security institutions, and less gender-bias in
preferences, should result in less fertility and more education
Fertility and education should both go up if men’s wages increase (or
households receive lump-sum transfers such as child allowances)
Fertility should go down and education up if women’s wages (and
women’s labor force participation) increase
Education subsidies increase education and have an uncertain e¤ect
on fertility
Child-labor laws (bans, sanctions) should reduce fertility and have an
uncertain e¤ect on education
(Harvard Kennedy School)
Hillel Rapoport
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Plan
1
Introduction
2
Fertility and the old-age security hypothesis
3
Trading o¤ quantity for quality of children: a generic model
4
Fertility choices in context: India and France
5
Fertility choices in historical perspective
6
Conclusion: "love thy children"
(Harvard Kennedy School)
Hillel Rapoport
PED 365, Spring 2011
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Fertility choices in context: India and France
Paper on India: "Estimating the e¤ect of fertility decisions on child
labor and schooling", by Furio Rosati and Partha Deb (Working
Paper, Understanding Children’s Work Project, ILO, Unicef and
World Bank 2004).
Context: Rural India in 1994, 35000 households in 1765 villages.
Descriptive statistics (mean and standard deviation) – see next slide
Complex econometric model; important features: …rst endogenizes
fertility (…rst stage) and then looks at how fertility a¤ects children’s
time use and outcomes.
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Fertility choices in context: India and France
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Fertility choices in context: India and France
We focus on the marginal e¤ects of di¤erent variables on fertility.
Results (1): e¤ect of parents’education as expected (positive for
fathers, negative for mothers); note the gender bias....
(Harvard Kennedy School)
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Fertility choices in context: India and France
Results (2): cultural and social norms matter (positive e¤ect of
"Muslim", negative for "Christian")
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Fertility choices in context: India and France
Results (3): membership in a lower caste ("poor") decreases fertility,
having assests such as cattle increases fertility; school infrastructure
and cost of education not signi…cant
(Harvard Kennedy School)
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Fertility choices in context: India and France
Is it so di¤erent from developed countries?
Not really: same e¤ects of male and female income, of female
education, of localisation patterns, and important role of cultural
values and norms
Example: analysis of French Women Survey in "Religion and Fertility:
the French Connection" by Thomas Baudin (CORE WP, Université
Catholique de Louvain, 2010)
(Harvard Kennedy School)
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Fertility choices in context: India and France
(Harvard Kennedy School)
Hillel Rapoport
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Plan
1
Introduction
2
Fertility and the old-age security hypothesis
3
Trading o¤ quantity for quality of children: a generic model
4
Fertility choices in context: India and France
5
Fertility choices in historical perspective
6
Conclusion: "love thy children"
(Harvard Kennedy School)
Hillel Rapoport
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Fertility choices in historical perspective
Strong, robust relationship between fertility and mothers education:
true for micro data, as seen, and for cross-country comparisons:
(Harvard Kennedy School)
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Fertility choices in historical perspective
The economic literature on the demographic transition is generally
silent on the cross-sectional implications of the fertility model
employed.
To some degree, this is because many studies rely on
representative-agent models which do not generate cross-sectional
predictions.
Another, maybe more important, reason is that little historical data is
available on fertility across income groups.
Solution: learn from "precursors", i.e. groups that experienced
substantial fertility decline decades or even centuries before the mass
of the population.
(Harvard Kennedy School)
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Fertility choices in historical perspective
A source of information that is available for very long time periods are
the genealogical records of the high aristocracy; such data have been
exploited by Peller for Europe and y Hollingsworth for England.
Fragmented evidence is also available for other social groups, notably
the Jews, and the urban population
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Fertility choices in historical perspective
An index of marital fertility for England and Wales shows that fertility
has been nearly constant between 1500 and 1850, at which point it
dropped dramatically
To be compared with the fertility rate of British peerage families
(26000 individuals over more than three centuries): fertility in this
social class …rst falls, then rises in the eighteenth century, then falls
again.
The gap between the aristocratic and the overall fertility rates in
England widens in the 19th century and then narrows in the 20th
century
(Harvard Kennedy School)
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Fertility choices in historical perspective
Marital fertility - England
8
7
6
5
4
3
England and Wales
2
British peerage
1
0
155074
(Harvard Kennedy School)
160024
165074
170024
175074
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180024
185074
190024
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Fertility choices in historical perspective
Livi Bacci provides the same type of evidence comparing the birth
rates in Roman Jewish families (Jews are well-known precursors in
fertility control)
Birth rate (per 1000)
50
45
40
35
Italy
30
Jews in Rome
25
1751(Harvard Kennedy School)1775
17761800
180118261825Rapoport
1850
Hillel
18511875
18761900
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Fertility choices in historical perspective
Finally, we have excellent data for two important European cities,
Rouen and Geneva, with a breakdown by social classes.
Rouen: Ia= highest ranked notables, I="notables", II=merchants,
III=craftsmen, IV=workers
Ia
1670-99
1700-29
1730-59
1760-92
(Harvard Kennedy School)
I
4.66
4.53
3.87
2.71
II
6.23
4.87
4.84
3.77
Hillel Rapoport
III
6.53
5.51
4.81
3.28
IV
7.19
6.29
5.48
4.84
7.21
6.06
5.67
4.84
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Fertility choices in historical perspective
Geneva: I=notables, II=craftsmen, III=workers
I
1675-96
1700-4
1741-5
1770-4
(Harvard Kennedy School)
II
6.70
6.70
4.70
2.80
Hillel Rapoport
III
7.10
7.30
5.70
5.20
6.20
5.50
4.20
4.70
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Fertility choices in historical perspective
Precursors in the fertility decline have many things in common.
Urban connection
Also, mortality among the forerunners was generally moderate and
lower than in the general population, though doubts remain for the
urban populations (again, example of the Jews – black death,
Gibraltar)
Finally, the precursors were characterized by above average economic
level.
Have they reduced their fertility simply because mortality fell more
rapidly in these groups, or is it because they shifted towards
promoting education instead of quantity of children in the face of
better skill premiums? Or both?
(Harvard Kennedy School)
Hillel Rapoport
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Plan
1
Introduction
2
Fertility and the old-age security hypothesis
3
Trading o¤ quantity for quality of children: a generic model
4
Fertility choices in context: India and France
5
Fertility choices in historical perspective
6
Conclusion: "love thy children"
(Harvard Kennedy School)
Hillel Rapoport
PED 365, Spring 2011
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Love thy children? On the rise of parental altruism
Source: Hillel Rapoport and Jean-Pierre Vidal: "Economic Growth and
Endogenous Intergenerational Altruism", Journal of Public Economics,
2007.
The models we have seen so far explain changes in the demand for
quality and quantity of children by changes in incentives (rise in
women’s wages, child labor laws, higher skill premiums), holding
preferences constant.
However it could be that changes in the economic environment
(growth, higher incomes) also modify the demand for children (and
their quality), through two potential mechanisms: non-homothetic
preferences (higher income elasticity for "quality" than for
"quantity") (analogy with wine); or the evolution of altruism
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Love thy children? On the rise of parental altruism
The evolution of altruism, in turn, can take a number of forms:
Darwinian selection (Galor and Moav, QJE2002; Galor, 2005):
"The theory suggests that during the epoch of Malthusian stagnation that
had characterized most of human existence, traits of higher valuation for
o¤spring quality generated an evolutionary advantage and their
representation in the population gradually increased. This selection process
and its e¤ect on investment in human capital stimulated technological
progress and initiated a reinforcing interaction between investment in human
capital and technological progress that brought about the demographic
transition and the state of sustained economic growth" (Galor, 2005: 266)
intergenerational taste externalities, cultural transmission (Bisin and
Verdier, 2000)
Endogenous formation of parental altruism (Rapoport and Vidal,
2007)
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Main ingredients in Rapoport and Vidal (JPubE2007)
Changes in parental behavior, in particular in terms of time and
resources devoted to child rearing activities and education, are
attributed to the endogenous reinforcement of altruistic traits beyond
an endogenously given degree of economic development.
At earlier stages of economic development, individuals are constrained
with respect to spending on child-oriented goods; both their
consumption patterns and intergenerational transfers only depend on
their "natural" degree of altruism.
Along the growth path, the endogenous formation of altruism starts
once economic development exceeds a threshold level, at which
individuals have satis…ed their own physiological constraints and can
devote resources to the shaping of their own altruistic preferences.
This in turn increases their "social" degree of altruism beyond its
natural level, which leads to larger spending on "children oriented
goods" (investments in child quality) and bequests and speeds up the
pace of capital accumulation and economic development.
(Harvard Kennedy School)
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Historical evidence
Spending time with one’s children is a relatively recent phenomenon.
Example: Philippe Ariès (1960) analyzed the dramatic evolution of
attitudes towards children in 17th and 18th century France. During
that period, children became increasingly considered as ”persons” and
represented as such in the arts and literature of the time.
At the same time, the development of pediatrics and of child
psychology brought about increased awareness of the medical and
psychological needs of children. And yet, it is only well after the
industrial revolution that concerns for children’s well-being
materialized in terms of parental time spent interacting with children.
A striking example of such discrepancy between knowledge and
behavior is given by Jean-Jacques Rousseau, philosopher and among
other things author of education treatises such as Emile (1762).
Rousseau abandonned his …ve children to foundling homes.
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Historical evidence
Evolution of the institution of wet nursing, an institution common to
many European countries but most developed in France during the
pre-industrial era.
French historian and demographer Jacques Dupaquier (1995): child
mortality rates in the late 18th century were more or less equal across
social classes, a …nding he attributes to the higher propensity of the
richer classes to send out children for nursing:
”the practice of wet nursing, on which aristocrats and bourgeois relied
systematically, tends to reduce the advantages inherent to birth ... The
social practice of wet-nursing plays a role of child mortality accelerator in
the a- uent classes and of moderator in the poor classes where it is far less
common” (Dupaquier, 1995, T2, pp. 227 and 229).
(Harvard Kennedy School)
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Historical evidence
Out of the 21,000 children born each year in Paris circa 1780, 18,000
were sent away to a wet nurse and more than two-thirds did never
return.
Another important cause of child mortality is the practice of
abandoning children. The total number of abandoned children was
estimated for France at 40,000 in 1784 and 63,000 in 1801. Note that
mortality …gures available for Paris at the turn of the nineteenth
century show mortality rates of abandoned children of 98 percent for
those in foundling homes and of 79 percent for those sent out for
nursing (Dupaquier, 1995, T3, p. 447).
(Harvard Kennedy School)
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Historical evidence
Such practices did not disappear with the industrial revolution but did
so very slowly and gradually throughout the 19th century.
For example, according to Brochard, a rural physician, nearly 20,000
children were “exported” from Paris to the neighboring rural district
of Nogent-le-Rotrou during the year 1860, either through placement
agencies (for the majority of them) or directly by the parents
themselves or by public authorities; Brochard sets the survival rate of
these children at 25 percent. The French moralist Sarcey reaches the
same estimate for the 1850s.
Finally, it is noteworthy that the number of abandoned children in
France started decreasing only during the last decades of the
nineteenth century, and it is estimated that 30 to 40 percent of the
children born in the largest cities of France were still sent out to a
wet-nurse in the early 1900s.
(Harvard Kennedy School)
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Evidence from (today’s) developing countries
In today’s developing countries, there isevidence that parents-children
relationships do not involve the type of preferences which are
conducive to the joint accumulation of concern and wealth
Brown and Haddad (1995): the time spent with children does never
exceed two hours per day and is in most cases lower than one hour a
day for women, while few men - if any - engage in child rearing
activities in all seven countries studied (extended family)
Causes of gender di¤erences: allocation of time along gender lines, or
di¤erences in the concern for children between mothers and fathers?
Intrahousehold resource allocation literature: the relative bargaining
power of women is of considerable importance for children’s health
and other outcomes.
Famous "policy experiments" with child allowances in the UK (1970s)
and South Africa (2000s).
(Harvard Kennedy School)
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Evidence from (today’s) industrialized countries
Gender di¤erences in parental behavior tend to narrow in more
economically advanced societies, as if fathers and mothers’preferences
were converging towards a higher and equally shared level of altruism.
Corroborated by many recent studies showing that the time spent
interacting with one’s children represents a substantial and increasing
fraction of parents’time.
Total time spent by mothers has remained almost constant since the
1920s (despite the rise in women’s labor force participation and the
sharp reduction in fertility rates, resulting in mothers spending twice
as much time per child on primary care)
Fathers’s time spent with children increased gradually since the 1950s
and nearly trippled over the last half-century, resulting in an overall
increase in the total time dedicated by parents to their children.
These studies agree this is due to more concern for children’s
well-being rather than to income e¤ects.
(Harvard Kennedy School)
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Historical evidence: child labor
Finally, the historical evidence on the rise and fall of child labor is also
suggestive of the formation of altruism.
Parsons and Goldin (EI1989) report that in late nineteenth-century
America, ”nonaltruistic behavior by parents was pervasive”: more
than 50 percent of teenage children living in textile districts used to
work against only ten percent for children in nontextile ones.
Parents voted with their feet: child labor in the textile industry
induced large immigration from nontextile districts in spite of the fact
that earnings of adult males in the child-labor intensive textile sector
were 32% below those of adult males in nontextile industries.
No migration in the opposite direction, which rules out migration
decisions based on di¤erences in parental altruism.
Humphries (2003) for 19th century England: the bene…ts from child
labor were appropriated by parents through increased leisure time and
personal consumption.
(Harvard Kennedy School)
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Historical evidence: child labor
Manacorda’s (AER2006) study, on the other hand, takes place in
post-WWI America, a few decades after the period studied by Parsons
and Goldin (1989).
Manacorda takes advantage of the existence at the time of
State-speci…c child labor laws as a source of exogenous variation in
child labor to identify the e¤ect of a rise in the proportion of working
children on household members’labor-supply.
The results suggest that the bene…ts from increased children
participation in the labor force were not appropriated by the parents,
whose labor-supply was basically una¤ected, but by the children
themselves in the form of lower labor-supply and higher school
attendance per child, which is fully consistent with intrahousehold
allocation of resources under full parental altruism.
(Harvard Kennedy School)
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Endogenous altruism or non-homothetic preferences?
Key question: do people spend more time with their children as they
become richer because they enjoy spending time with them
(non-homothetic preferences) or because they want to care more
about them in the future (endogenous altruism)?
Since altruistic preferences are not directly observable, there is an
obvious identi…cation issue which is not easy to confront.
What are the distinctive predictions of the endogenous preferences
model?
1. Timing: altruism manifests itself through more time spent with
children, investment in their education, prohibition of child labor and
general concern for children’s well-being long after incomes start to rise
(threshold e¤ect) and knowledge about children’s needs is di¤used
(Harvard Kennedy School)
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Endogenous altruism or non-homothetic preferences?
2. Nature and timing of the relationship between "children oriented
goods" and bequests:
the very purpose of spending on children oriented goods is to increase
bequests; complements vs substitutes.
the relationship is causal in the case of endogenous altruism: the
historical evidence for the last century suggests that altruism has
gradually emerged as the dominant drive of bequests.
DeLong (2005): bequests are now motivated primarily by ”individuals’
desires to see their children – all their children – lead better lives”
while they were previously motivated primarily by ”the desire to see
the power and wealth of future male lineage heads grow”; which leads
him to conclude: ”a historical look back at the pattern of inheritance
in the Anglo-Saxon world over the past several hundred years has to
reinforce one’s sense of how mutable human motivations are.”
(Harvard Kennedy School)
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