Why Do The Rich Have So Few Kids?
Jeff Ely and Adriana Lleras-Muney
May 5, 2012
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Two Puzzles
World’ total fertility rate TFR (births per women) is declining: 5 in
1950, 2.7 in 2000 (Lee 2003)
Developed countries started their “fertility transition” around 1800,
and TFR fell slowly.
Developing countries started post WWII and TFR fell rapidly
This decline coincided with large increases in GDP
Income and fertility are negatively correlated today
Across countries, and within countries across individuals.
Income and fertility were positively correlated prior to transition
Some historical evidence for England and Wales (Guinnane 2011),
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Figure 1: Fertility declines around the world
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Figure 2: Fertility and male income (proxied by education)
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Figure 3: Fertility and female income (proxied by height)
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
What do the data suggest?
Fertility trends unambigously point to a world decline
Income proxies are negatively related to fertility, and the association is
larger in richer countries
There is a suggestion of a positive association at low levels of GDP
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Evolution and Fertility Preferences
If natural selection could be expected to impact our preferences over any
decision, it would be fertility.
How to allocate resources toward reproduction.
Quality/quantity tradeoff.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Model Summary
Asexual reproduction
Perfect inheritance
Each generation begins with some resources
Gene determines how to allocate those resources
quantity of offspring.
“quality”
What gene maximizes the long-run size of its population?
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Setup
An individual begins life with an endowment of resources
B = e +q
e is the exogenous endowment, constant across generations.
Subject to infrequent shocks.
q is the investment made by the parent. (inheritance for example)
She allocates this budget between production r and investment B − r
in offspring.
Spending r on reproduction produces O (r ) offspring.
C (n ) cost function.
The remainder B − r will be divided equally among the O (r ) offspring
(becoming their q.)
Then dies.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
A Gene
A gene is a function
g :R→R
where
g (B ) ≤ B
g (B ) is the amount of resources that a bearer of gene g allocates to
reproduction when her budget is B.
Hence O (g (B )) is the number of children.
And
B − g (B )
Γ (B |g ) = O g e +
· O (g (b ))
O (g (B ))
is the quantity of grandchildren with quality
B − g (B )
O (g (b )) B − g (B )
β (B |g ) =
−g e +
Γ(B |g ) O (g (B ))
O (g (B ))
etc.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Optimal Genes
A gene is optimal if for every initial budget B it maximizes the number of
descendants after sufficiently many generations.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Necessary Condition
If g is optimal then for every B
Γ(B |g ) = max k · l
s.t. B − C (k ) − k (C (l ) − e ) = kl β(B |g )
Because if not
There is another gene which is a “two-shot” deviation from g starting
with resources B
And produces strictly more grandchildren of equal quality
And therefore has more descendants at every subsequent generation.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
“First-order” Condition
The area of the rectangle represents the number of grandchildren
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
“First-order” Condition
Suppose we reduce the number of kids by 1. Resources in the amount of
C 0 (k ) + C (l ) − e are saved.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
“First-order” Condition
To restore the original number of grandchildren, the offspring must collectively produce l additional (grand)children.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
“First-order” Condition
To a first-order approximation this costs lC 0 (l ).
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
“First-order” Condition
If k and l were optimal then this re-arrangement must not save resources:
C 0 (k ) + C (l ) − e ≤ lC 0 (l )
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Necessary Condition
If k is the number of kids and l is the number of kids per kid then at an
optimum
C 0 (k )
≤ Ō + γ(l )
C 0 (l )
with equality when k < O (B ) where
γ (l ) =
C 0 (l ) [l − Ō ] − [C (l ) − e ]
C 0 (l )
measures the difference between the marginal and average cost of
reproduction.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Concave Reproduction Technology
When O is concave we have γ(l ) > 0 so that when parents invest in
quality
C 0 (k )
> Ō > 1
C 0 (l )
i.e. fertility is declining monotonically.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Concave Reproduction Technology
C'(n)
O(e)
Jeff Ely and Adriana Lleras-Muney
n
Why Do The Rich Have So Few Kids?
Is there any evidence for the shape of the production
function?
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Qualitative Results
Quantity and quality are both normal goods.
At low income levels there is a corner solution at zero quality.
No demand for contraception.
Fertility
incentives will have no effect at the margin.
Fertility caps are different.
This reflects the inherent “impatience” arising from the arithmetic of
reproduction.
And it is therefore essentially a no-borrowing constraint.
At large enough income levels there is a demand for quality.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Corner Solution
Effect of forced reductions in fertility (like One Child Policy) is to
increase savings (transfers)
Banarjee et al (2011) find that 1972 fertility policies resulted in an
increase in savings
in their model this is due to needs for old age, in our model savings
increase to increase child quality.
Harbuagh (2004) reports that other Asian countries experienced similar
fertility declines around the same time without government-imposed
constraints and did not see the same increases in savings.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
One Child Policy
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
One Possible Resolution of Both Puzzles
If given access to borrowing, the poor will borrow to increase quantity
and reduce quality.
The next generation is even poorer.
Etctera.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
How The Rich Get Rich By Having Few Kids
q
q
n
(a) The poor
n
(b) The Rich
Figure: Gains From Trade
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Limitations of the Model
Implementation via preferences: U (n, q ).
Only identified for “legacy” budget sets.
How granular?
direct taste for n and q?
utility increasing in expected great great . . . grandchildren?
Could have suboptimal behavior at novel budget sets.
inferior goods
wrong quality-quantity tradeoff due to novel relative prices.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Other Theories
Decline in infant mortality.
Availability of contraception.
The rise of social insurance.
Increase in the cost of quantity.
Increase in the returns to quality.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Infant Mortality Declines
Could possibly explain decline in births but harder to explain a decline
in surviving offspring.
Infant mortality declines do not precede fertility declines in several
countries (US, France most notably)
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Ideal Number of Kids
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Availability of contraception
Fertility fell before introduction of modern contraception
However the evidence is not strong.
“Traditional” contraception methods can have a substantial effect on
fertility (age at marriage, abstinence, coitus interruptus)
We do see greater demand for contraception among the rich.
However, this is entirely consistent with the model and the conclusion
that fertility increases with income.
Is the desire for sex (rather than children) what is selected by
evolution?
Presence/demand for fertility clinics suggests otherwise
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Use of contraception by GDP
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Fertility Services
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Social Insurance
Care in old age as a motivation for having children is hard to
understand from a biological point of view. (Lee and Miller 1994
Bergstrom 1996)
fertility decline precedes SI programs
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Costs of Quantity and Quality
The cost of quantity.
Urbanization
Higher opportunity cost for women.
From a biological point of view these cannot explain the puzzle so long
as it is possible to replicate whatever old “technology” yielded lower
costs of fertility
The returns to quality, e.g. schooling.
Can explain a short-run decline in fertility.
But only because it results in a compensating increase in fertility in the
long run.
Kaplan, Lancaster and Johnson (1995): within a generation fewer but
more educated children results in fewer grandchildren.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
The Cost of Quality
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Relative income (Easterlin 1966)
”I believe that an important factor affecting a young couple’s willingness
to marry and to have children is their outlook for supporting their material
aspirations. If the couple’s potential earning power is high in relation to
aspirations, they will have an optimistic outlook and will feel freer to
marry and have children. If their outlook is poor relative to aspirations,
the couple will feel pessimistic and, consequently, will be hesitant to marry
and have children. . . . Note that two elements enter into the judgment
about the couple’s economic prospects. One is their potential earning
power; the other is their material aspirations.”
”By life-style, I mean how the material standards of young adults are
formed—why one generation, say, views a car as a luxury and the next, a
necessity. My argument is that the material expectations of young adults
are largely the unconscious product of the environment in which they grow
up. . . . And this environment is very largely shaped by the economic
circumstances, or income, of one’s parents.” (Easterlin 1980, p. 39-41)
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Data and identification issues
do not have exogenous variation in income
children might be “normal” goods but OV masks relationship:
empirical evidence mixed
OV must be possitively correlated w GDP/income but negatively affect
fertility: question remains what OV is
fertility is reported by women: a non-trivial fraction of births are to
fathers in other households
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Are there an alternative explanations consistent with EB?
Introduce heterogeneity in preferences for q and n: patient have
fewer/better kids (as in Galor and Weil 2002)
can explain cross-section: those who don’t like children get rich
cannot explain trends
”Race to the bottom model”
individuals invest in q thinking it will increase # descendants by giving
offpsring advantage in marriage market
all individuals do the same–zero sum game
Another possibility: human race will disappear
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?
Data Description
1
GDP data: PPP-adjusted GDP per capita from the Penn World
Tables version 7.0.
2
Fertility trends: World Bank data obtained from multiple sources
3
Micro data on fertility: Demographic and Health Surveys (DHS)
113 surveys from waves III, IV and V spanning 1993-2009
54 countries with anthropometric data for women and education of
spouses in addition to fertility histories.
Jeff Ely and Adriana Lleras-Muney
Why Do The Rich Have So Few Kids?