Population, Fertility and Health
1. Introduction.
a) Key facts
 Improvements in life expectancy
Figure 1
 Reduction in mortality rates
Figure 2
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 Decline in Birth rates lags behind Death rates
The demographic transition:
𝑔𝑃 = 𝐵𝑅 − 𝐷𝑅
Population growth follows an inverted-U relationship (first rises, then declines)
Figure 3
Source: Todaro & Smith (2015)
b) Relationship between population growth and economic growth
In the Solow growth model, a higher population growth rate retards economic
growth.
c) Causes of high population growth
In this topic, we’ll investigate:
- What are the principal determinants or causes of high fertility rates in
developing countries?
- Can these determinants of the "demand" for children be influenced by
government policy?
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To address these questions, we’ll develop two economics models and analyze
their economic implications:
- Macroeconomic perspective: Malthusian “population trap” model
- Microeconomic perspective: Household theory of fertility
Finally, we’ll provide insights for the role of government policy from randomized
studies:
- The effectiveness of financial incentives in improving vaccination rates.
2. Malthusian model.
a) Setup:
Population growth follows an inverted-U relationship (first rises, then declines)
𝑔𝑃 = 𝑎 + 𝑏𝑦 + 𝑐𝑦 2
with the following parametric restrictions 𝑏 > 0 and 𝑐 < 0.
Output growth must be consistent with the Solow model’s predictions about
convergence/divergence:
If divergence:
𝑔𝑌 = 𝑑
If convergence towards good equilibrium, where 𝑦 < 𝑦 ∗ :
𝑔𝑌 = 𝑒𝑦, where 𝑒 < 0.
b) Model's predictions:
 Equilbria
At equilibrium, 𝑔𝑃 = 𝑔𝑌 .
Since the 𝑔𝑃 and 𝑔𝑌 curves cross twice, there are two equilibria.
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 Stability of equilibria and transitional dynamics
If 𝑔𝑃 > 𝑔𝑌 , 𝑦 declines.
If 𝑔𝑃 < 𝑔𝑌 , 𝑦 increases.
These transition dynamic give rise to one stable equilibrium and one unstable
equilibrium.
The presence of two equilibria and the transitional dynamics give rise to a
Malthusian trap.
Figure 4
Source: Todaro & Smith (2015)
c) Implications for development:
 countries in middle-income range may be caught up in a Malthusian
trap;
 rich enough countries escape the Malthusian trap;
 countries that raise savings rate, productivity may escape the
Malthusian trap;
 effective government policies can only be big push policies.
Big push policies must be set such that 𝑔𝑌 > 𝑔𝑃 at a country’s current income
level.
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3. The Microeconomic Household Theory of Fertility.
a) Overview
Why do birth rates decline after death rates?
 Households’ choice of how many children to have.
In this section, we will explore whether the Malthusian predictions are consistent
with individual behavior.
The exposition of this theory is based on Todaro and Smith (2015), pp. 303 – 307.
b) Setup
 Goods
Households care about two goods: number of children (𝐶) and other goods (𝐺).
 Optimization behaviour
The conventional theory of consumer behaviour assumes that an individual with
given set of preferences for a range of goods (a utility function) tries to maximize
their own well-being from consuming these goods subject to their own budget
constraint.
In the application of this theory to fertility analysis, children are considered as a
special kind of consumption good relative to other goods. Parents enjoy benefits
of having kids, e.g., caring for them when old.
 Properties of goods
- Why is 'more children' better?
A higher probability that at least one child survives until adulthood to take care of
their parents when old.
- 𝐶 and 𝐺 are assumed to be normal goods.
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 Demand function for desired number of children 𝐶𝑑 = 𝑓(𝐼, 𝑃𝐶 , 𝑃𝐺 , 𝑎)
- The higher the household income, the greater the demand for
children (𝑀𝐶𝑌 =
𝜕𝐶𝑑
𝜕𝑌
> 0).
- The higher the net price of children, the lower the quantity demanded
(𝑀𝐶𝑃𝑐 =
𝜕𝐶𝑑
𝜕𝑃𝐶
< 0).
- The higher the prices of all other goods relative to children, the
greater the quantity of children demanded (𝑀𝐶𝑃𝐺 =
𝜕𝐶𝑑
𝜕𝑃𝐺
> 0).
- The greater the strength of tastes for goods relative to children,
the fewer children demanded (𝑀𝐶𝑎 =
𝜕𝐶𝑑
𝜕𝑎
< 0).
c) Model's predictions
Suppose that the initial optimal bundle is at pt. f on indifference curve 𝐼2 .
We will explore two alternatives that differ with respect to the introduction of a
government policy that raises the cost of raising children:
- Rising income but no change in prices
A pure income effect (IE) of rising income is depicted by a parallel shift of the
budget constraint from 𝑎𝑏 to 𝑎′𝑏′. As a result, both 𝐶 and 𝐺 increase since the
new optimal bundle is at pt. h.
This choice implies that higher income increases fertility.
- Rising income and increase in the price of raising children
A pure substitution effect (SE) resulting from a rising price of raising children is
depicted by a pivot of the budget constraint from 𝑎𝑏 to 𝑎𝑏". As a result, both 𝐶
and 𝐺 decrease since the new optimal bundle is at pt. e.
A pure income effect (IE) of rising income is depicted by a parallel shift of the
budget constraint from 𝑎′𝑏’ to 𝑐𝑑. As a result, both 𝐶 and 𝐺 increase at the new
optimal bundle at pt. g relative to the optimal bundle at pt. e.
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Combining the two effects, IE and SE, implies that the 𝐺 increases but
𝐶 decreases.
That is, an economic policy that increases the price of raising children while
incomes are rising implies a declining fertility.
Figure 5
Source: Todaro & Smith (2015)
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Income effect (IE):
A higher income implies that parents demand more children.
Substitution effect (SE):
A decrease in the opportunity cost of children rises (employment opportunities,
especially for females, increase), parents demand fewer children.
If IE dominates, the number of children demanded increases.
 This result conforms with the predictions of the Malthusian trap that
income growth increases population growth.
If SE dominates, the number of children demanded increases.
 This result implies that an economy might escape the “population trap”
without government intervention.
d) Implications for development
As income rises, the birth rate may even rise.
If pension plans are adopted during early stages of development, birth rates are
likely to decline faster.
4. Government policy.
There are three main directions, in which government policy could help a country
escape the Malthusian “population trap”.
a) Technological innovation
Big push policies in technological innovation are possible in the Ghatak and Jiang
model or the RR big push model.
b) Demographic restrictions
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Big push policies that temporarily restrict population growth, e.g. the one child
policy in China. To be effective, these policies must target all individuals or at least
a critical mass of them.
The policy implications of such policies produce benefits for future generations by
letting countries escape the Malthusian population trap. However, they come at a
cost for current generations subjected to the policy.
c) Preventative medical interventions, e.g. vaccines
The discussion is based on Benarjee et al (2012).
 Reducing child mortality rates
High mortality rates among children due to easily preventable diseases.
Immunization improves substantially the likelihood of surviving until adulthood.
“Immunisation is a highly cost effective way of improving survival in children in
developing countries. Every year throughout the world, however, an estimated 27
million children and 40 million pregnant women do not receive the basic package
of immunisations (as defined by WHO and Unicef), and two to three million
people die from diseases that can be prevented with vaccines.” ~ Benarjee et al
(2012)
While reducing child mortality rates is an end in itself, preventative policies
reduce fertility rates over time but may contribute to population increase in the
short-run.
 Policy effectiveness
- Availability of services vs. financial incentives
Financial incentives, such as in conditional cash transfer programmes, can be
effective in promoting the use of certain preventive healthcare services.
In settings with reliable immunisation services and a high pre-existing
immunisation rate such programmes have little impact on immunisation.
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In a setting with a low immunisation rate (under 6%), improving the reliability of
services modestly improved uptake of immunisation.
Small non-financial incentives, combined with improved reliability, have large
positive impacts on the uptake of immunisation and are more cost effective.
Provision of immunization services, even free of charge, typically results in
modest increases.
 Why randomized studies?
There are several sources of selection bias in rural areas. Some of them, listed in
the working paper version, include:
- Access to roads and proximity to a health post;
- Service availability is unpredictable (staff skips work on a regular basis or
health post is closed for an extended period of time).
How does each of these sources affect selection bias?
Example: Service availability
 Regression analysis
Design:
134 villages in rural India were randomized to one of 3 groups:
- a once-monthly reliable immunization camp (intervention A; 30 villages);
- a once-monthly reliable immunization camp with small incentives (lentils
and metal plates for completed immunization intervention B; 30 villages),
- control (no intervention, 74 villages).
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Surveys were undertaken in randomly selected households at baseline and
approximately 18 months after the interventions started (at endline). The primary
end point was the proportion of village children aged 1-3 at endline who were
partially or fully immunized.
Participants:
1640 children aged 1-3 at endline.
PRF:
𝑌𝑖 = 𝛽0 + 𝛽1 𝐷1𝑖 + 𝛽2 𝐷2𝑖 + 𝛽3 𝐷1𝑖 𝐷2𝑖 + 𝑢𝑖
𝑌𝑖 − immunization rate
𝐷1𝑖 − access to a reliable immunization camp
𝐷1𝑖 − financial incentives
Results:
able 2 | Effects of group allocation (A=immunisation, B=immunisation plus incentive).
Numbers are in absolute values
Mean (95% CI)
Control
Difference* (95% CI)
A
B
379
382
Relative risk† (95% CI)
A−control
B−control
B−A
—
—
—
A v control
B v control
—
—
BvA
End point cohort (aged 1-3 years)
No in group
860
—
No of immunisations
1.20
2.35
2.85
(0.94 to 1.46) (1.99 to 2.71) (2.44 to 3.25)
1.15
1.70
0.55
(0.95 to 1.35) (1.48 to 1.92) (0.26 to 0.83)
2.14
2.66
(1.84 to 2.44) (2.28 to 3.05)
1.22
(1.08 to 1.36)
≥1 immunisation
0.49
0.78
0.74
(0.40 to 0.57) (0.70 to 0.85) (0.67 to 0.82)
0.29
0.26
−0.03
(0.23 to 0.35) (0.20 to 0.33) (−0.09 to 0.04)
1.59
1.52
(1.35 to 1.83) (1.29 to 1.75)
0.96
(0.80 to 1.11)
Has BCG scar‡
0.28
0.50
0.50
(0.21 to 0.36) (0.41 to 0.59) (0.41 to 0.59)
0.22
0.22
0.00
(0.15 to 0.28) (0.15 to 0.28) (−0.08 to 0.08)
1.76
1.76
(1.41 to 2.12) (1.41 to 2.12)
1.00
(0.79 to 1.21)
Completely immunised
0.06
0.18
0.39
(0.03 to 0.09) (0.11 to 0.25) (0.30 to 0.47)
0.13
0.34
0.21
(0.09 to 0.16) (0.30 to 0.38) (0.15 to 0.28)
3.09
6.66
(1.96 to 4.21) (4.53 to 8.80)
2.16
(1.54 to 2.78)
Logbook cohort (aged 1-3 years)
No in group
—
—
—
—
—
—
—
Total No of immunisations
—
3.70
4.18
(3.39 to 4.01) (3.99 to 4.37)
—
—
0.59
(0.25 to 0.93)
—
—
1.15
(1.05 to 1.25)
Completely immunised
—
0.48
0.67
(0.38 to 0.59) (0.59 to 0.74)
—
—
0.22
(0.10 to 0.33)
—
—
1.43
(1.12 to 1.73)
407
725
*Estimated by fitting multilevel mixed effect linear model, with clustering at hamlet and household level.
†Estimated by fitting multilevel mixed effect Poisson regression, with clustering at hamlet and household
level.
‡For analysis with BCG scar as outcome, there were 790 observations in control group, 334 in treatment A
group, and 336 in treatment B group.
Source: Banerjee et al (2012)
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Interpretation: Improving reliability of services improves immunization rates, and
small, non-financial incentives have large positive impacts on the uptake of
immunization services in resource-poor areas.
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