From Physical to Human Capital Accumulation:
Effects of Mortality Changes
Keiya Minamimura
Daishin Yasui
April 2016
Discussion Paper No.1614

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANFrom Physical to Human Capital Accumulation:
Effects of Mortality Changes
Keiya Minamimura∗ and Daishin Yasui†
April 5, 2016

Abstract
This paper develops a growth model à la Galor and Moav (Review of Economic Studies
71(4):1001–1026, 2004) that captures the replacement of physical capital accumulation byhuman capital accumulation as the prime engine of growth. We show that (i) decreased
mortality promotes this replacement, and (ii) the effect of a decrease in mortality on percapita income differs across the phases of the development process. A notable predictionof our theory is that the higher the level of education in an economy, the more likely it isthat a decrease in mortality will increase income per capita. Using finite mixture models,
we show that this prediction is supported by the data.

∗ Graduate School of Economics, Kobe University. keiya.minami@gmail.com† Kobe University. yasui@econ.kobe-u.ac.jp1

1

Introduction

Does a decrease in mortality raise income per capita? An influential paper by Acemoglu andJohnson (2007) provoked a controversy over this question. In contrast to studies based on crosscountry variation (e.g., Lorentzen et al., 2008), Acemoglu and Johnson (2007) use instruments
for mortality changes to solve the endogeneity problem, and obtain a surprising result: improved life expectancy has a positive effect on population growth, but a negative effect on GDP
per capita. This result is somewhat shocking because it implies a trade-off between health improvement and economic growth. Theoretically, their result is justified by the dilution effect intraditional growth theories: population growth decreases land per capita (the Malthus channel)
and physical capital per capita (the Solow channel), thus reducing income per capita. On theother hand, recent growth literature suggests the increasing importance of human capital overland and physical capital as an engine of growth, particularly in developed countries (e.g., Jonesand Romer, 2010). Here, we develop a growth model in which the replacement of physical capital accumulation by human capital accumulation is endogenous and mortality changes affect the
replacement process. Furthermore, we theoretically and empirically investigate how a decreasein mortality affects income per capita.
We extend the model of Galor and Moav (2004) that captures the replacement of physicalcapital accumulation by human capital accumulation as a prime engine of growth to consider theeffect of mortality changes on the development process. Our model derives two key results: (i)decreased mortality promotes this replacement, and (ii) the effect of a decrease in mortality on
per-capita income differs across the phases of the development process. As in Galor and Moav
(2004), we shed light on the portfolio choice between physical and human capital. However,
our focus differs from theirs. We focus on an asymmetry between physical and human capital:
human capital is inherently embodied in people and thus human capital yields a return only when
the investor survives, whereas physical capital returns belong to a spouse and offspring even if
the investor dies. This asymmetry implies that in environments with higher mortality, it might2

be riskier for households to concentrate their assets in human capital. A decrease in mortality
stimulates the incentive to invest in human capital and promotes the replacement of physicalcapital accumulation with human capital accumulation.1
Many studies already establish the theoretical result that a decrease in mortality promotes
human capital investment (e.g., de la Croix and Licandro, 1999; Kalemli-Ozcan et al., 2000;
Boucekkine et al., 2002, 2003; Soares, 2005; Cervellati and Sunde, 2005).2 The difference
from prior studies is that we shed light on the cooperative behaviour among family members
in asset formation, rather than the behaviour of a single agent.3 Most prior studies focus on aproperty of human capital that human capital continues to yield a return as long as agents are
able-bodied workers once they form human capital, while physical capital investment yields a
one-time-only return. Thus, a higher mortality shortens the working life over which investments
in human capital pay off, thereby negatively affecting human capital investment. In contrast, we
focus on the property that human capital cannot be carried over to surviving family members
if the investor dies because human capital is embodied in the original investor. On the other
hand, physical capital can be left to surviving family members. Thus, a higher mortality induces
agents to substitute physical capital for human capital in case of death.4
In our model, an economy switches from a regime where only physical capital is accumu-

1 Galor and Moav (2004) focus on a different asymmetry between physical and human capital: in contrast tophysical capital, human capital is inherently embodied in people, and human capital investment exhibits diminishingreturns at the individual level. Based on this asymmetry, they show that income inequality, through capital-market
imperfection, affects economic growth differently in the various stages of the development process.
2 Jayachandran and Lleras-Muney (2009) empirically show that longer life expectancy increases educational attainment.
3 It is generally agreed that the family institution serves as an insurance device for individuals (e.g., Weiss, 1997).
For example, Kotlikoff and Spivak (1981) find that consumption and bequest-sharing arrangements in marriages
and larger families can significantly substitute for complete and fair annuity markets, suggesting the importance ofcooperation among family members in asset formation. An advantage of our approach focusing on family cooperationis that it does not contradict a finding of Hazan (2009). Hazan (2009) finds that the expected total hours worked overa lifetime for males has decreased because of a decrease in hours worked per year and early retirement, insisting thatan increase in the expected length of working life should not be responsible for increasing education. On the other
hand, the total lifetime hours worked for married couples has not decreased owing to increased female labour force
participation (Ramey and Francis, 2009).
4 Our mechanism might be justified in terms of family member altruism (e.g., a spouse, siblings, or offspring).
The presence of altruism has been shown by many studies and is assumed in a large number of growth theories (e.g.,
Loury, 1981; Galor and Zeira, 1993).

3

lated to a regime where both physical and human capital are accumulated during the development process. In the former regime, a decrease in mortality depresses income per capita by the
dilution effect on physical capital, especially in the short run. In the latter regime, however, two
additional effects improve the average amount of human capital in the labour market. First, adecrease in mortality induces agents to substitute human capital for physical capital by the mechanism mentioned above. This shift in assets not only improves human capital, but also weakens
the dilution effect because physical capital is vulnerable to the dilution effect compared to human capital.5 Second, a decrease in mortality raises the average age of the working population.
Since older workers have more human capital because of human capital accumulation, such achange in the age composition of the workforce increases the average amount of human capital in the workforce. In the determination of per-capita output, the human capital improvement
effect acts in the opposite direction to the physical capital dilution effect. Our model predicts
that a decrease in mortality is more likely to increase GDP per capita in an economy with moreeducation because the human capital improvement effect dominates the dilution effect, while theopposite is true in an economy with less education.
Figure 1 depicts wage profiles of workers in high- and low-education countries, illustrating
the intuition behind our mechanism.6 If the wage rate reflects the amount of human capital,
the wage profile represents human capital accumulation over a lifetime. The wage profile forhigh-education countries is steeper and has a higher peak than that for low-education countries,
implying that the gap in human capital between young and adult workers is larger in high-

5 The following example captures the vulnerability of physical capital to the dilution effect. Suppose that parents

leave $10,000 to their two children and there are two measures of asset maintenance, physical and human capital
investment, both of which have the same gross rates of return, 100%. First, consider the case where $10,000 isinvested in physical capital. If the two children survive, each child gets physical capital of $5,000. If one child dies,
the other gets physical capital of $10,000. Next, consider the case where $10,000 is invested in human capital. If
both children survive, each child gets human capital of $5,000. If one child dies, the other gets human capital of$5,000. The amount of assets per capita halves by the dilution effect when it is invested in physical capital, whereas
it does not change when invested in human capital because human capital is embedded in individuals and disappears
with their death.
6 The classification between high- and low-education countries is based on the empirical result in Section 3 and is
the same as the classification in panel (b) of Figure 4. Due to limited data availability, however, the sample in Figure
1 consists of 15 out of 47 countries used in the empirical analysis.

480Percentage Wage Increase
20
40
60
0

0

5

10

15
20
25
Potential Experience
Low education

30

35

40

High education

Source: Lagakos et al. (2015)

Figure 1: Wage profile in high- and low-education countries
education countries than that in low-education countries. A decrease in mortality has two effects:
a direct effect and a composition effect. First, it lifts the profile from the low-education typeto the high-education type by increasing educational investment. This directly improves theaverage amount of human capital because each agent has more human capital. Second, it shifts
the weight on the workforce from young to adult workers, and thus has the effect of improving
the average amount of human capital. This composition effect is larger in higher-education
countries because they have a larger gap in the amount of human capital between older andyounger workers.
A notable implication of our theory is heterogeneity in the effects of mortality on per-capita
income among countries. The higher the level of education in a country, the more likely it is thata decrease in mortality will increase income per capita. To test this hypothesis, we use the samedata and identification strategy as Acemoglu and Johnson (2007), though our approach differs
in that we relax the assumption that all countries are in the same growth regime. Using a finite
mixture model (FMM) approach, we investigate whether the effects of mortality on per-capita
income differ between countries in high- and low-education regimes.7
7 See Frühwirth-Schnatter (2006) for details about FMM, and Bloom et al. (2003), Owen et al. (2009), andCervellati and Sunde (2011a) for applications to growth regressions.

5

Cervellati and Sunde (2011a, 2011b) share our motivation to reinterpret the analysis of Acemoglu and Johnson (2007). Cervellati and Sunde (2011b) split the sample of Acemoglu andJohnson (2007) between pre- and post-demographic-transition countries based on the classification criteria used in demography literature. They show that improved life expectancy has a negative effect on per-capita GDP in pre-transition countries, but a positive effect in post-transition
countries. Cervellati and Sunde (2011a) use an FMM approach without imposing any ex-anteclassification, obtaining similar results to those of Cervellati and Sunde (2011b). Cervellati andSunde (2011a, 2011b) base their studies on demographic-transition theory to investigate the roleof population growth in determining the effect of mortality on per-capita income. Here, we focus on the role of education in determining the effect of mortality on per-capita income basedon human-capital theory. Since the demographic-transition and human capital theories are twopillars in the literature on long-run growth, our study is a natural development of this literature.
The empirical part of our study shows that both education and population growth are importantin determining the effect of mortality on per-capita income.
The remainder of this paper is organized as follows. Section 2 presents the model andanalyses the effect of mortality changes on income per capita. In Section 3, we confront the
testable implications of the model with empirical evidence. Section 4 concludes the paper.

2

Model

Consider an overlapping generations model in which agents live for at most two periods, youth
and adulthood. Some agents die at the beginning of adulthood and cannot enter the labour market in adulthood.8 In both periods, agents inelastically supply one unit of time to the labour
market. The efficiency units of labour per unit of time of young agents are normalized to 1 (i.e.,the basic skill level), while those of adult agents can increase with an educational investment intheir youth. At the end of the youth period, agents receive an inheritance from their ancestors
8 We here concentrate on the role of adult mortality. See Subsection 2.6 for the effect of introducing child mortality
into our model.

6

Time
Generation t + 1

Generation t
Start life
Work
Receive inheritance
Allocate asset

Period t

Have children
Survive with probability ρWorkReceive labour and asset income
Consume and leave bequest

Start life
Work

Period t + 1

Receive inheritance
Allocate asset

Table 1: Timing of eventsand allocate it between savings and an educational investment. Savings and educational investment increase asset income and labour income in adulthood, respectively. In the second period(adulthood), surviving agents supply their efficiency units of labour and allocate the household’s
labour and asset income between their own consumption and transfers to their offspring. Table
1 depicts the timing of events.
The basic unit of our analysis is a household consisting of a continuum of individuals.
Household members of the same generation jointly choose their behaviour to maximize joint
utility. We impose this assumption mainly with couples in mind. In the real world, married couples would make consumption and investment decisions jointly and with concern for the other’sliving standards after their own death. The assumptions of joint utility and joint decision-making
are intended to capture this reality.9

9 The assumption of the continuum is for simplification. If we use a couple consisting of two persons as the basic

unit, then heterogeneity arises between households (i.e., both parents survive, one parent survives, or both parentsdie) and the model becomes too complex to solve analytically. However, the essence of the proposed mechanism
does not depend on whether we employ a household consisting of continuous or discrete members as the basic unit.

7

2.1

Production

Production occurs according to Cobb-Douglas production technology. The output produced inperiod t is given by Yt = Ktα Ht1−α , where Kt and Ht are the quantities of physical capital andlabour (measured in efficiency units), respectively, employed in production, and α ∈ (0, 1) is thecapital share of income. The factor markets are competitive and physical capital fully depreciates
in one period. The wage rate and the gross rate of return to physical capital are:wt = (1 − α ) ktα ≡ w (kt ) and Rt = α ktα −1 ≡ R (kt ) ,(1)

respectively, where kt ≡ Kt /Ht is the capital-labour ratio.

2.2

Households

There is a continuum of households of measure 1. In every period, a continuum of individuals of
measure 1 is born into a household as young members. They survive and enter the labour market
in adulthood with probability ρ ∈ (0, 1). Thus, each household has 1 + ρ members (i.e.,1 young
members and ρ adult members) in every period. Since the measure of households is 1, the total
population size of this economy is 1 + ρ .
Household members of the same generation jointly choose their behaviour to maximize joint
utility. The preferences of generation t (born in t) of household i are defined over consumption
i , and transfers to their offspring, bi . The variables ci
iin adulthood, ρ ct+1
t+1
t+1 and bt+1 are con-sumption per surviving adult member and transfer per young member, respectively. Since ρ out
i . Onof 1 adult members survive until the time of consumption, their total consumption is ρ ct+1
i . The preferences
the other hand, since the size of young members is 1, the total bequest is bt+1

are given by:ii
γ ln ρ ct+1
+ (1 − γ ) ln bt+1,

where γ ∈ (0, 1) denotes the relative weight given to consumption.

8(2)

In period t, generation t of household i receives an inheritance, bti , from generation t − 1 ofhousehold i, which is allocated between savings, sti , and education expenditure, eti : sti + eti = bti .
The budget constraint of generation t of household i is:
(
)
i
i
i
ρ ct+1+ bt+1= wt+1 + ρ wt+1 ht+1
+ Rt+1 bti − eti ,(3)iwhere ht+1
denotes the efficiency units of labour (i.e., the level of human capital) per adult mem-ber. The LHS is the adult-period expenditure, namely their own consumption and transfers totheir offspring. The RHS is the adult-period wealth: the first, second, and third terms are thewage income earned by young members, the wage income earned by surviving adults, and thereturn on savings from the previous period, respectively. Note that we assume that adult members control the young members’ wage income. One may argue that this patriarchal assumption
does not fit the description of developed countries, though is suitable for some developing nations. However, this assumption is not as restrictive as it may seem. In the real world, people
have some degree of control over the wealth of their offspring because the transfer is usuallyieither positive or negative. In this model, the net transfer to offspring, bt+1
− wt+1 , can be either

positive or negative: the larger the amount of adult members’ human capital, the more likely it isthat the net transfer will be positive. Therefore, our model can capture the reality that there is an
exploitation of child labour in underdeveloped countries, whereas in advanced countries, many
people transfer a positive amount of wealth to their children, although they can leave a debt.
Furthermore, this patriarchal assumption simplifies the dynamics because we need not consider
the decisions of two generations simultaneously.
i , is a function of the real expenditure on eduThe level of human capital in adulthood, ht+1

cation in childhood t, eti :i
ht+1= 1 + µ eti ,(4)where µ > 0 represents the efficiency of education. Without capital investment in education,9the level of human capital in adulthood is equal to the basic level during youth.10 For analyticalconvenience, we assume a linear human capital production technology.11
Generation t of household i maximizes (2) subject to (3) and (4). The solution to this problem
is given by




0



eti =
[0, ∞)




 ∞

if

ρ µ wt+1 < Rt+1 ,if

ρ µ wt+1 = Rt+1 ,if

ρ µ wt+1 > Rt+1 ,

and
[
(
)
(
)]
i
bt+1
= (1 − γ ) wt+1 + ρ wt+1 1 + µ eti + Rt+1 bti − eti .

(5)

There is a threshold level of capital-labour ratio, k̃, below which households do not invest in human capital, that is, k̃ is defined by ρ µ w(k̃) = R(k̃). It follows from (1) that k̃ = α / [(1 − α ) ρ µ ].
If the capital-labour ratio in the next period is expected to be below k̃, agents do not acquire nonbasic skills.
Before moving to the equilibrium analysis, we should mention two points. First, the optimallevel of human capital investment depends on the rate of return and is independent of the level ofincome. Since there are no credit constraints in this model, the rate of return is the investor’s only
concern. Second, as mortality declines, households are more likely to invest in human capitalthan in physical capital (i.e., k̃ decreases with ρ ). Since human capital is inherently embodied inpeople, human capital yields returns in adulthood for surviving members only, whereas physicalcapital does not have this property. With higher mortality, it is riskier for households to con-

10 We are aware that the opportunity cost as well as the pecuniary cost constitutes a major part of the education costsin the real world (e.g., Bils and Klenow, 2000), and that time devoted to education matters in determining educational
attainment. Following the spirit of Galor and Moav (2004), however, we assume that there is no difference in the time
agents devote to education, enabling us to concentrate on the portfolio choice between physical and human capital
investments.
11 If we assume a strictly concave human capital production technology, perpetual growth (Pattern III in Figure2) does not arise. However, all comparative-static results in Propositions 1 and 2, except for those in the balanced
growth path, still hold. Since the emergence of perpetual growth is not essential in this study, we assume linear
technology to obtain a closed-form solution.

10

centrate their assets in human capital. Thus, human capital investment becomes more profitablecompared to physical capital investment as mortality declines.

2.3

Aggregate physical and human capital

Assume that all households have identical initial capital ownership. We then focus on a symmetric equilibrium where sti = st and eti = et for all t and i.12 Given the inheritance received
by households of generation t, the optimization of these households in period t determines thelevel of physical capital, Kt+1 , and human capital, Ht+1 , in period t + 1: Kt+1 = st = bt − et andHt+1 = 1 + ρ (1 + µ et ). It follows that the capital-labour ratio in period t + 1 is:

kt+1 =

bt − et.
1 + ρ (1 + µ et )(6)First, suppose that the capital-labour ratio in the next period is expected to be below k̃.
Since et = 0 in this case, kt+1 = bt / (1 + ρ ). The resultant capital-labour ratio is consistent withhouseholds’ expectation if and only if bt / (1 + ρ ) ≤ k̃, that is,bt ≤α (1 + ρ )≡ b̃.
(1 − α ) ρ µ(7)

In the case of bt > b̃, on the other hand, et > 0. Note that when et > 0, kt+1 = k̃ must hold. If
kt+1 < k̃, then no one invests in human capital (i.e., et = 0). If kt+1 > k̃, then no one invests inphysical capital and, thus, kt+1 = 0, which is inconsistent with kt+1 > k̃. When et > 0, using(6) and kt+1 = k̃, we obtain et = [(1 − α ) ρ µ bt − α (1 + ρ )] / (ρ µ ). Therefore, we can write the

12 It is also possible that some households specialize in physical capital accumulation and others specialize inhuman capital accumulation, and that the ratio between the two is determined in equilibrium. However, our results
do not change in that situation because the aggregate variables in the asymmetric equilibrium are the same as thosein the symmetric equilibrium by households’ arbitrage behaviour.

11equilibrium educational investment as a function of bt :

et =



 0

if bt ≤ b̃, (1−α )ρ µ bt −α (1+ρ )ρµif bt > b̃.

This implies that a higher ρ and larger bt induce a larger educational investment. Although thelevel of inheritance does not affect the investment decision at the household level, it matters at
the aggregate level because of the general-equilibrium effect: the greater the resources available,
the higher the level of human capital investment such that the marginal returns on physical andhuman capital are equalized.
Then, it follows from (1), (5), and (6) that the evolution of inheritance is:bt+1 (bt ) = (1 − γ ) (1 + ρ )1−α bα ≡ Ψ1 (bt )t

if bt ≤ b̃, (1 − γ ) α α (1 − α )1−α ρ −α µ −α (1 + ρ + ρ µ bt ) ≡ Ψ2 (bt ) if bt > b̃,(8)which governs the dynamics of this economy. The difference equation (8) implies Ψ1 (b̃) =′′′′ (b ) < 0Ψ2 (b̃), Ψ′1 (b̃) = Ψ′2 (bt ), bt+1 (0) = Ψ1 (0) = 0, bt+1
(bt ) > 0, bt+1(0) = Ψ′1 (0) = ∞, bt+1
t′′ (b ) = 0 if b > b̃. Therefore, depending on the parameter configuration, we
if bt ≤ b̃, and bt+1
tt

can classify the dynamic system into three patterns (see Figure 2). In Pattern I (panel (a)),
there exists a steady state where physical capital investment is the only method of capital accumulation. In Pattern II (panel (b)), there exists a steady state with both physical and humancapital investments. In Pattern III (panel (c)), the economy shows persistent growth, and both
physical and human capital investments exist along the growth path. For Pattern I to arise,1b∗1 = (1 − γ ) 1−α (1 + ρ ) ≤ b̃, where b∗1 is a fixed point of Ψ1 (·). For Pattern II to arise, b∗1 > b̃and Ψ′2 (bt ) = (1 − γ ) α α (1 − α )1−α ρ 1−α µ 1−α < 1. For Pattern III to arise, Ψ′2 (bt ) ≥ 1.
The pattern to arise depends on some parameters. According to the value of the survival rate,

12

bt+1

bt+1

45

45

bt

b̃

bt

b̃

(a) Pattern I(b) Pattern II

bt+1

bt+1

45

bt

b̃

45

b̃

b̃

bt

b̃

(d) Eﬀects of rises in ρ(c) Pattern III

Figure 2: Dynamics

ρ , the main parameter of interest, the patterns of the dynamics of this economy are classified asPattern IPattern II Pattern III

where ρ̃1 ≡ifρ ≤ ρ̃1 ,ifρ̃1 < ρ < ρ̃2 ,ifρ̃2 ≤ ρ ,αα1(1 − γ ) 1−α (1 − α ) µand ρ̃2 ≡α − 1−α1(1 − γ ) 1−α (1 − α ) µ.

(9)A rise in ρ shifts Ψ1 (·) and Ψ2 (·) upward and decreases b̃. A decrease in mortality increases
the steady-state value of bt , if it exists. Otherwise, it raises the growth rate of bt . Panel (d) in

13

Figure 2 illustrates this effect. Decreases in mortality induce the economy to move to the patternwith higher education.
We conclude this subsection by presenting the steady-state inheritances in Patterns I and II(the fixed points of Ψ1 (·) and Ψ2 (·), respectively):
1 b∗ = (1 − γ ) 1−α (1 + ρ )in Pattern I,1

α b∗2 = (1−γ )α (1−α α )1−α

ρ −α µ −α (1+ρ )
1−(1−γ )α (1−α )1−α ρ 1−α µ 1−α2.4

in Pattern II.

Effect of mortality changes on per-capita output

It follows from the results obtained in the previous subsection that given bt , bt+1 increases withρ (panel (d) in Figure 2). Then, what about the effect on per-capita output? The answer is notclear, because a higher survival rate increases the population and dilutes physical capital per
capita. This subsection attempts to answer this question.
Our analysis distinguishes between the short- and long-run effects of mortality changes on
per-capita output: the short- and long-run effects refer to the effects on per-capita output of thecurrent generation and the per-capita output in the steady state (or that for the balanced growthpath), respectively. Here we impose an additional assumption:

α<

1
,
1+ρ

(10)

which means that human capital has a sufficiently large contribution to production. This assumption seems empirically reasonable. The value of 1/ (1 + ρ ) is in [1/2, 1] because the valueof ρ is in [0, 1], whereas it is widely accepted that the capital share, α , is less than 1/2.
First, we obtain the following proposition regarding the short-run effect of a change in thesurvival rate on per-capita output.13
13 Although we here analyse the effect of the ‘expected’ mortality change, it is also possible to analyse the effectof the ‘unexpected’ mortality change. The difference between the effects of the expected and unexpected changes
is only quantitative. The negative effect on per-capita output is stronger in the case of unexpected change becausehouseholds do not react optimally in response to a mortality change.

14

Proposition 1. In the short run, (i) in the case without human capital investment (i.e., bt ≤ b̃), a
rise in ρ decreases per-capita output, and (ii) in the case with positive human capital investment(i.e., bt > b̃), the effect of a rise in ρ on per-capita output can be either positive or negative: alarger value of bt is more likely to make the effect positive.
Proof. Given bt , output per capita in period t + 1, yt+1 ≡ Yt+1 / (1 + ρ ), is

yt+1 = [bt / (1 + ρ )]αif bt ≤ b̃, α α (1 − α )1−α µ −α (1 + ρ + ρ µ bt ) / [(1 + ρ ) ρ α ] if bt > b̃.

(11)(i) It follows that ∂ yt+1 /∂ ρ < 0 when bt ≤ b̃.
(ii) When bt > b̃, we obtain the following:∂ yt+1 α α (1 − α )1−α
=
∂ρ
µα
]
[
(1 + µ bt ) (1 + ρ ) ρ α − (1 + ρ + ρ µ bt ) ρ α + α (1 + ρ ) ρ α −1
×,[(1 + ρ ) ρ α ]2
and

(12)

∂ 2 yt+1 α α (1 − α )1−α µ 1−α [1 − α (1 + ρ )]=.
∂ bt ∂ ρ(1 + ρ )2 ρ αUnder the assumption (10), ∂ 2 yt+1 /∂ bt ∂ ρ > 0: a higher value of ρ is more likely toincrease per-capita output as bt rises. We denote the inheritance level such that a changein ρ has no effect on per-capita output by b̂ (i.e., ∂ yt+1 (b̂)/∂ ρ = 0). Using (12), we obtainb̂ = α (1 + ρ )2 /{ρ µ [1 − α (1 + ρ )]}. We can easily confirm that b̂ > b̃. Therefore, whenbt > b̃, ∂ yt+1 /∂ ρ > 0 if and only if bt > b̂. ■When physical capital investment is the only method of capital accumulation, a decrease inmortality decreases per-capita output in the short run. Since bt is given, the assets available to thegeneration with declining mortality do not change. Thus, the quantity of labour input increases,
while the quantity of physical capital does not change, as a result of the decrease in mortality.
15

The average labour productivity decreases by the diminishing marginal productivity of labour,and thus per-capita output decreases.
In the case with positive human capital investment, the short-run effect is positive if bt is sufficiently large. The intuition behind this result is as follows. As in the case of bt ≤ b̃, a decreasein mortality increases labour inputs and decreases the return per unit of human capital. However,in contrast to the case of bt ≤ b̃, a decrease in mortality increases the average amount of humancapital in the labour market, which is the weighted average of young and adult agents’ humancapital: 1/ (1 + ρ ) × 1 + ρ / (1 + ρ ) × ht+1 . There are two effects of a decrease in mortality on
the average amount of human capital. First, a decrease in mortality induces households to invest
in human capital (i.e., ∂ et /∂ ρ > 0) and, thus, ht+1 increases. Second, a decrease in mortality
raises the proportion of adult workers, ρ / (1 + ρ ), in the labour market. Since adult workers
have more human capital than young workers (i.e., ht+1 > 1), a rise in the proportion of adult
workers increases the average amount of human capital. Therefore, the negative effect on physical capital and the positive effect on human capital coexist, and thus the total effect can be either
positive or negative. If bt is large, then the educational investment is large, so the growth rate ofhuman capital from youth to adulthood is high. Then, the higher weight of adult human capital
resulting from a decrease in mortality has a greater effect on increasing the average amount of
human capital. Therefore, as bt rises, a higher value of ρ is more likely to make the positiveeffect dominant.
Next, we obtain the following proposition regarding the long-run effect of a change in thesurvival rate on per-capita output.
Proposition 2. In the long run, (i) in Pattern I, a rise in ρ has no effect on per-capita output,(ii) in Pattern II, a rise in ρ increases per-capita output, and (iii) in Pattern III, a rise in ρ raises
the growth rate of per-capita output.
α

Proof. (i) In Pattern I, output per capita in the steady state is y∗ ≡ Y ∗ / (1 + ρ ) = (1 − γ ) 1−α . It
follows that ∂ y∗ /∂ ρ = 0.

16

(ii) In Pattern II, the output per capita in the steady state isy∗ =This implies

α α (1 − α )1−α

ρ α µ α − (1 − γ ) α α (1 − α )1−α ρ µ.

∂ y∗
α α +1 (1 − α )1−α ρ α −1 µ α Ω (ρ )
= −[
]2 ,
∂ρ
ρ α µ α − (1 − γ ) α α (1 − α )1−α ρ µwhere Ω (ρ ) ≡ 1 − (1 − γ ) α α −1 (1 − α )1−α ρ 1−α µ 1−α .

Note that Ω′ (ρ ) < 0 and Ω (ρ̃1 ) = 0. Since we now consider the case of ρ > ρ̃1 , we obtain∂ y∗ /∂ ρ > 0.
(iii) In Pattern III, since there is no steady state, we analyse the long-run growth rateinstead. Using (8) and (11), we obtain the following per-capita output growth rate:
yt+1 − ytρ µ bt−1= (1 − γ ) α α (1 − α )1−α ρ 1−α µ 1−α −.
yt
1 + ρ + ρ µ bt−1
Since bt grows persistently, bt−1 → ∞ as t → ∞. Thus, in the long run, the growth rate
converges to (1 − γ ) α α (1 − α )1−α ρ 1−α µ 1−α − 1, which rises with ρ . ■In the long run, in contrast to the fixed inheritance in the short run, the future generation’s
inheritance increases because an increase in the survival rate increases labour inputs and thus
output. This effect offsets the diluting effect of an increase in population size. Since physicalcapital per capita does not decrease, output per capita does not decrease, even if there is no
positive effect on human capital investment. In the case with positive human capital investment,a rise in the survival rate necessarily increases output per capita by enhancing human capital
investments.
In summary, the above analysis generates the following predictions: (i) the effect of a decrease in mortality on per-capita income is ambiguous; (ii) the effect of a decrease in mortality
on per-capita output is more likely to be positive in the long run than in the short run; and (iii) the17higher a country’s education level, the more likely it is that a decrease in mortality will increase
output per capita.

2.5

Numerical illustration

This subsection presents numerical examples to illustrate our key results. The productivity parameter in education, µ , is set to unity, and the value of physical capital share, α , is set to 1/3.
The parameter related to preferences on own consumption, γ , is specific to the analysis at hand,and little is known about its magnitude. Thus, we specify a value of γ to ensure that the regime
switch occurs at a reasonable survival rate and such that ρ̃1 = 0.75 when α = 1/3 and µ = 1.
Note that ρ̃1 represents the threshold survival rate given by (9), below which Pattern I arises.
This procedure leads to γ ≈ 0.237.
Heterogeneity in ρ

We demonstrate how a once and permanent increase in the survival rate, ρ ,affects per-capita output. Suppose that the economies are initially in steady states, with ρ = 0.6,

ρ = 0.7, and ρ = 0.8. We now increase the value of ρ from 0.6 to 0.7, from 0.7 to 0.8, and from
0.8 to 0.9. Since ρ̃1 (the threshold survival rate between Patterns I and II) is 0.75, the economy
with an initial survival rate of 0.6 is in Pattern I, both before and after the change, the economy
with an initial survival rate of 0.7 switches from Pattern I to Pattern II as a result of the change,
and the economy with an initial survival rate of 0.8 is in Pattern II, both before and after thechange. Panel (a) in Figure 3 depicts the responses in per-capita output in these simulations.
The per-capita output steeply decreases immediately after the change due to the dilution effecton physical capital. Subsequently, per-capita output starts increasing due to physical capital
accumulation by the larger working population, returning to the initial steady-state level in Case
1. Per-capita output increases further by increases in the average amount of human capital,
converging to the new steady-state levels above the initial levels in Cases 2 and 3.

18

y

y

Case 1: From Pattern I to Pattern I
Case 2: From Pattern I to Pattern II
Case 3: From Pattern II to Pattern II
−1

1

3

5
t

7

9

Case 1: From Pattern I to Pattern I
Case 2: From Pattern I to Pattern II
Case 3: From Pattern II to Pattern II

11

−1

1

(a) Heterogeneity in ρ

3

5
t

7

9

11

(b) Heterogeneity in µ

Figure 3: Simulation results
Heterogeneity in µ

Next, we examine the differential effects of mortality changes between

economies with different education systems. We model the development of an education system
as an increase in µ : a higher value of µ implies a more efficient education system. Here,
we examine the responses in per-capita output to mortality changes for different values of µ ,along with the same values of α and γ used above. Suppose the economies are initially in steadystates, with µ = 0.5, µ = 1.5, and µ = 2.5. Then, the respective threshold survival rates between
Patterns I and II are 1.5, 0.5, and 0.3. Now, we increase the value of ρ from 0.4 to 0.8. The
economy with µ = 0.5 is in Pattern I, both before and after the change; the economy with µ = 1.5
switches from Pattern I to Pattern II as a result of the change; and the economy with µ = 2.5 isin Pattern II, both before and after the change. Panel (b) in Figure 3 displays the responses of
per-capita output in these simulations, which decreases steeply immediately after the change dueto the dilution effect on physical capital. Subsequently, the per-capita output starts increasing,returning to the initial steady-state level in Case 1 and converging to the new steady-state levels
above the initial levels in Cases 2 and 3. The mechanisms behind these dynamics are the sameas the simulations with heterogeneity in ρ .
19Panels (a) and (b) in Figure 3 capture the feature that we want to emphasize: the higher acountry’s education level, the more likely it is that a decrease in mortality will increase income
per capita. Regardless of the cause of lower education levels (i.e., lower ρ or lower µ ), a risein the survival rate is more likely to have a negative effect on per-capita output in an economy
with a lower level of education: the size of the initial drop is larger, the pace of the subsequent
recovery is slower, and the steady-state level attained finally is lower.14

2.6 Child Mortality
We have thus far focused on adult mortality and ignored child mortality. However, life expectancy generally reflects both adult and child mortality, and child mortality has a key role inits determination. This subsection introduces child mortality into our model, showing that suchan extension has only a minor effect on the results obtained above.
We assume that δ ∈ (0, 1) out of 1 young members survive and enter the labour market inyouth, that is, new-born agents die at the beginning of their lives with probability 1 − δ . Since
the sizes of adult and young members change from ρ to δ ρ and from 1 to δ , respectively, theutility function (2) becomes:ii
γ ln δ ρ ct+1
+ (1 − γ ) ln δ bt+1.

(13)

The budget constraint remains the same as that in the model without child mortality, (3), because
all arguments in equation (3) are multiplied by δ when we introduce child mortality, and it thus
has virtually no effect on the equation. Generation t of household i maximizes (13) subject to(3) and (4). The solution to this problem is the same as that in the model without child mortality.
That is, introducing child mortality does not change the household’s behaviour. The dynamic
14 We here assume a parameter configuration such that per-capita output decreases in the short run in response to arise in ρ (i.e., the initial steady-state value of bt is smaller than b̂). For a simulation of Case 3 where an economy isinitially in Pattern II, we can choose a parameter configuration that makes the short-run effect positive, as shown in
Proposition 1.

20

equation of the capital-labour ratio also remains the same as that in the model without childmortality, (6), because both the numerator and the denominator in the RHS of equation (6)are multiplied by δ if child mortality is introduced, and thus, it has virtually no effect on theequation. It follows that introducing child mortality does not change the dynamics of the statevariable. Therefore, there is no change in the effect of a rise in the adult survival rate, ρ , in
Propositions 1 and 2 after introducing child mortality.
In the real world, new drug development and improvements in nutrition and sanitation usually decrease both child and adult mortality. Here, let us consider the effect of a simultaneouschange in child and adult mortality. Suppose the child and adult survival rates rise from δ to

δ ′ and ρ to ρ ′ , respectively. As mentioned above, the effect of a change in ρ does not dependon the presence of child mortality, and thus, the response of per-capita output is similar to the
responses depicted in Figure 3. The only difference after adding child mortality changes is in
the short-run effect. In the period when mortality changes, the proportion of young members in
the population becomes δ ′ / (δ ′ + δ ρ ′ ), which is larger than the proportion in the case withoutchild mortality change, 1/ (1 + ρ ′ ). However, the proportion becomes 1/ (1 + ρ ′ ) in one period
and remains the same from then on. This temporary change in the age composition of the population strengthens the dilution effect on physical capital and decreases the average amount of
human capital. Therefore, the size of the initial drop is larger in the case associated with a fall inchild mortality than in the case without, but there is no qualitative difference in the response of
per-capita output with respect to mortality changes between these two cases, and is negligible in
the long run.

3

Empirical analysis

A notable implication of our theory is heterogeneity in the effects of mortality on per-capita
income among countries: a higher education level increases the likelihood that a decrease inmortality will increase income per capita. In this section, we use data to test this implication.

21

3.1

Empirical framework and identification

The dependent variable is the change in log GDP per capita, and the main explanatory variable
is the change in predicted mortality. Our estimations are based on the following estimation
framework:∆ ln yi = C + π ∆mi + ui ,where ∆ ln yi and ∆mi are the changes in log GDP per capita and the (instrumented) predictedmortality of country i between 1940 and 1980, respectively. Following Cervellati and Sunde(2011a), we use the change in predicted mortality rather than life expectancy as the regressor.
Note that a negative coefficient π implies that a decrease in mortality promotes growth.
To estimate the causal effect of mortality on per-capita income, we follow the identification
strategy proposed by Acemoglu and Johnson (2007). The instrument for the change in mortality is the reduction in mortality from 15 infectious diseases (e.g., tuberculosis, malaria, andpneumonia), following the international epidemiological transition in the 1940s.15 The basic
idea behind this choice of instrument is as follows.16 There were no appropriate treatments forthese diseases in 1940 and the international epidemiological transition enabled the worldwide
dissemination of treatment and prevention by 1980. Thus, the change in mortality resulting fromthese diseases between 1940 and 1980 was exogenous to each country, and we can assume thatthe exclusion restriction holds.
The departure from Acemoglu and Johnson (2007) is that we relax the assumption that all
countries are in the same growth regime to allow for heterogeneous effects of mortality on percapita income between regimes. For this purpose, we use a finite-mixture approach, jointly
estimating the probability of being in a distinct growth regime and the effect of mortality changes
in each regime. Compared to the approach that assigns observations into groups a priori, our
15 The international epidemiological transition consists mainly of three factors: a wave of global drug and chemical

innovations, the establishment of the WHO and UNICEF, and the change in international values leading to a fastdissemination of medical knowledge. The international epidemiological transition caused a dramatic improvement
in life expectancy in much of the world, particularly in less developed areas.
16 See Acemoglu and Johnson (2007) for more detail.

22

approach has the advantage of being entirely data driven because the country groupings into
regimes as well as the growth regression parameters for each regime is estimated.
We assume that growth processes can be classified into two discrete regimes.17 We referto these as “Low” and “High.” As will become apparent later, education level is a significant
predictor of regime membership. The labels “Low” and “High” refer to low- and high-education
regimes, respectively. The probability structure for a given country is:
)
(
)
(
)
(
f ∆ ln y| ∆m; π Low , π High , ϕ Low , ϕ High = ϕ Low f ∆ ln y| ∆m; π Low + ϕ High f ∆ ln y| ∆m; π High ,()
where ϕ j is the probability of membership in latent regime j, and f ∆ ln y| ∆ ln m; π j is the
distribution of growth rates conditional on membership in latent regime j. The probabilities areparameterized as:

ϕ Low =

exp (θ X)
1and ϕ High =,1 + exp (θ X)
1 + exp (θ X)

where X represents the determinants of regime membership, and θ is the coefficient that captures
the effect of X on the probability of being in the Low regime. Based on the prediction derived
in the theoretical part, we use variables related to the level of education as covariates X.
We estimate the model via maximum likelihood. Assume that the error term in the growthequation comes from a normal distribution with standard deviation σ j . The log-likelihood function is:
N { [
(
)
(
)]}
ln L = ∏ ln ϕ Low f ∆ ln yi | ∆mi ; π Low + ϕ High f ∆ ln yi | ∆mi ; π High
,
i=1

where
(

f ∆ ln yi | ∆mi ; π

j

)

[ (
)2 ]
∆ ln yi −C j − π j ∆mi
=√
.
exp −
j )2
2
2
(
σ
j
2π (σ )
1

17 Although it is possible to assume more than two regimes, we select the two-regime model based on the resultsof the likelihood-ratio test.

23

We estimate this finite mixture model using the Stata package fmm (Deb, 2012).

3.2

Data

The dependent variable is the change in log GDP per capita between 1940 and 1980, and themain explanatory variable is the change in predicted mortality between 1940 and 1980. We use
Maddison (2003) and Acemoglu and Johnson (2007) as data sources for these variables. We use
the same base sample of 47 countries as in Acemoglu and Johnson (2007), for which all relevant
data on these variables are available for 1940 and 1980.
We use education level as a predictor of regime membership. Specifically, we use variables
related to tertiary education as regime membership predictors. Recall that our theory addresses
agents’ decisions about their own education, rather than education provided by parents. It isreasonable to focus on variables related to higher levels of education for consistency with thetheory. Further, we check robustness by using the proportion of no-schooling among persons as
another measure of education. The data on education comes from Barro and Lee (2013).
This study focuses mainly on the role of education in the heterogeneous effects of mortality
on income per capita based on human capital theory, though other studies focus on the roleof population growth based on demographic-transition theory (Cervellati and Sunde, 2011a,
2011b). Our baseline estimations only use variables related to education as regime-membershippredictors, but we also estimate models that include variables related to both education andpopulation as regime-membership predictors for comparison with previous studies. Our data
source for the population variables is Maddison (2003).
Table 2 provides the summary statistics.

3.3

Results and implications

Table 3 presents the main estimation results. The results reported in column [1] are qualitatively
the same as the results obtained in Acemoglu and Johnson (2007). With the full sample, theeffect of mortality on income per capita is positive (a positive coefficient of predicted mortality
24

Variables
Change of log GDP per capita (1940–1980)
Change of predicted mortality (1940–1980)
Years of tertiary schooling : 30–39 (1950)
Years of tertiary schooling : 30–49 (1950)
Tertiary complete (%) : 30–39 (1950)
No schooling (%) : 30–39 (1950)
Log of GDP per capita (1940)
Change of log population (1930–1940)

Obs
47
47
47
47
47
47
47
47

Mean
0.884
−0.473
0.095
0.090
1.824
32.6857.739
0.130

Std. Dev.
0.388
0.280
0.124
0.115
2.380
29.410
0.725
0.072

Min
−0.086−1.126
0.002
0.001
0.038
0.2
6.332
-0.015Max
1.606−0.1210.604
0.548
11.957
86.7
8.855
0.303

Table 2: Summary statistics
change), that is, the effect of life expectancy on income per capita is negative.
Columns [2]-[9] present estimates of the finite mixture models. In columns [2] and [3],as the baseline estimation, we use the average number of years of tertiary schooling in the
population between the ages of 30 and 39 in 1950 as covariate X to predict the latent regime
membership. To draw accurate conclusions about country characteristics that sort countries into
regimes, we should use membership predictors that are uncorrelated with the error term in thegrowth model. Since people over 30 years of age in 1950 completed their education by the onsetof the international epidemiological transition, it seems reasonable to use a measure of tertiary
schooling in the population between the ages of 30 and 39 in 1950 as the covariate. The estimatesin columns [2] and [3] indicate the existence of two different regimes with opposite effects ofmortality on income growth. Countries with a higher level of education are less likely to beclassified into the Low regime (a negative coefficient of covariate). A decrease in mortality tends
to increase income per capita in the High regime (a negative coefficient of predicted mortalitychange) and decrease income per capita in the Low regime (positive coefficient). This result is
consistent with our theory.
In the estimations reported in columns [4]-[9], we use different education criteria to thoseused in columns [2] and [3] as predictors of regime membership to check the robustness of ourresults. The estimations reported in columns [4] and [5] use the average number of years oftertiary schooling in the population between the ages of 30 and 49, rather than between 30 and
39, as covariates. The estimations reported in columns [6] and [7] use the proportion of the

25

OLS
Covariate
Age group
RegimePredicted mortality change
Constant

30–39[1]0.585∗∗∗[0.147]1.160∗∗∗[0.069]Probability of regime Highσ
Coefficient of covariate
Constant
AIC
BIC
SABIC
Number of countries

Finite Mixture Model
Tertiary complete
30–49
30–39
Low
High
Low
High
[4]
[5]
[6]
[7]
0.590∗∗∗−0.5320.559∗∗−0.497[0.224][0.332][0.242][0.330]1.071∗∗∗
1.007∗∗∗
1.033∗∗∗
1.022∗∗∗[0.253][0.080][0.269][0.087]0.324
0.357
0.341∗∗∗
0.159∗∗∗
0.332∗∗
0.163∗∗[0.08][0.041][0.08][0.038]−18.879∗∗−1.077∗∗[9.329][0.430]2.286
2.274[1.951][1.525]42.36541.37
57.16656.17232.07531.08147
47

Years of tertiary

47

Low
High
[2]
[3]
0.574∗∗∗−0.525∗[0.207][0.315]1.052∗∗∗
1.014∗∗∗[0.213][0.081]
0.338
0.335∗∗∗
0.163∗∗∗[0.064][0.034]−17.537∗∗[7.032]
2.154[1.332]42.45257.25432.16347

No schooling
30–39
Low
High
[8]
[9]
0.495∗∗∗−0.445[0.143][0.419]0.972∗∗∗
1.068∗∗∗[0.163][0.070]0.362
0.311∗∗∗
0.156∗∗∗[0.069][0.061]
0.041∗[0.022]−0.548[1.081]40.21455.01529.92447

OLS (Column [1]) and FMM with two components (Columns [2]-[9]). All regressions are long-difference specifications with two
observations per country, for 1940 and 1980. The dependent variable is the log of GDP per capita. The independent variable
is predicted mortality. Regressions in columns [2]-[5] and [6]-[7] use years of tertiary schooling and tertiary completed in 1950
as covariates, respectively. Regressions in columns [8]-[9] use no schooling in 1950 as covariates. The samples correspond tothe base sample of Acemoglu and Johnson (2007). AIC, BIC, and SABIC are Akaike, Bayesian, and Sample Adjusted Bayesian
information criteria, respectively. Robust standard errors are in brackets. ∗∗∗ , ∗∗ , ∗ indicate significance at the 1-, 5-, and 10-%levels, respectively.

Table 3: Estimation results I
population that completed tertiary education, rather than the average number of years of tertiary
schooling, as covariates. The estimations reported in columns [8] and [9] use the proportion of
no-schooling among persons as covariates. The results reported in columns [4]-[9] demonstratethat the choice of measures of education has only minor effects compared to the main finding ofheterogeneous effects of mortality on growth.
Figure 4 intuitively captures the difference between our results and those of Acemoglu andJohnson (2007). Panel (a) in Figure 4 shows that in the full sample, as reported by Acemoglu
and Johnson (2007), a decrease in mortality depresses income per capita. In panel (b) in Figure
4, we assign countries into two groups based on the estimations in columns [2] and [3] in Table
3. In the first group, the countries have an estimated probability of being in the “High” regime ofmore than 50% (High group), and the second group consists of all other countries (Low group).
It follows from panel (b) in Figure 4 that a decrease in mortality boosts income per capita in the26

Covariate
Age group
RegimePredicted mortality change
Constant
Probability of regime Highσ
Coefficient of covariate
Constant
AIC
BIC
SABIC
Number of countries

Finite Mixture Model
Years of tertiary/Log of GDP per capita
Years of tertiary/Population Growth
30–39
30–39
Low
High
Low
High
[1]
[2]
[3]
[4]
0.549∗∗∗−0.527∗0.449∗∗∗−0.632∗∗[0.207][0.301][0.169][0.286]1.029∗∗∗
1.017∗∗∗
0.970∗∗∗
1.012∗∗∗[0.135][0.070][0.137][0.070]0.354
0.362
0.332∗∗∗
0.164∗∗∗
0.335∗∗∗
0.155∗∗∗[0.063][0.036][0.051][0.026]−13.323∗ / − 0.568−15.454∗ /22.896∗∗[7.926]/[0.775][8.473]/[10.804]
6.176−0.808[5.722][1.219]44.11138.86360.76255.51432.53527.287
47
47

FMM with two components. All regressions are long-difference specifications with two observations per country: 1940 and 1980.
The dependent variable is the log of GDP per capita. The independent variable is predicted mortality. The regression reported incolumns [1] and [2] uses years of tertiary schooling in 1950 and the log of GDP per capita in 1940 as covariates. The regression
reported in columns [3] and [4] uses tertiary education completed in 1950 and the change in the log of population between 1930 and
40 as covariates. Robust standard errors are in brackets. ∗∗∗ , ∗∗ , ∗ indicate significance at the 1-, 5-, and 10-% levels, respectively.

Table 4: Estimation results II
High group, but depresses income per capita in the Low group.
One may argue that the effect of education only captures the effect of GDP per capita, andthat our estimation results suggest that the degree of economic development, not education,
influences the effect of mortality on per-capita income. We conduct the estimation reported incolumns [1] and [2] in Table 4 to address this problem. The estimation uses not only education
criterion but also log GDP per capita in 1940 as covariates. The result shows that education
remains a significant predictor of regime membership after controlling for the effect of GDP per
capita, whereas log GDP per capita is not a significant predictor after controlling for the effectof education.
The estimation reported in columns [3] and [4] in Table 4 uses not only education criteria but
also demographic criteria as predictors of regime membership. The result shows that both criteria are significant predictors of regime membership. Countries with higher levels of educationand lower population growth are more likely to be classified into the regime in which a decrease

27

PRT
BRA

ITA
MEX
PAN

CRI

ECU

VEN

PER

FIN
NOR
AUT
BEL
SWE
NLD
MYS KORCANIRLCHE DNK
DEU
AUS

USA

PRY CHN
CHL
PAK

PHL

ESP
GRC
FRA

COL

SLV

IND

THA

Change in Log GDP per capita 1940-1980
0
.5
1
1.5

Change in Log GDP per capita 1940-1980
1
1.5
0
.5

PRT

IDN

HND
LKA

URY

ARG
NZL
GBR

NIC

GTM
MMR
BGD

-1.2

-1

-.8
-.6
-.4
Change in Predicted mortality 1940-1980

-.2

0

BRA
ITA
MEX

VEN

PER

DEU
AUS

USA

PRY CHN
CHL
PAK

PHL

FIN
NOR
AUT
BEL
SWE
NLD
MYS KORCANIRLCHE DNK

COL

SLV
HND

IDN

IND

LKA

URY

ARG
NZL
GBR

NIC

GTM
MMR
BGD

-1.2

(a) Full sample

PAN

CRI

ECU

THA

ESP
GRC
FRA

-1

Low group

High group

Fitted line for Low group

Fitted line for High group

-.8
-.6
-.4
Change in Predicted mortality 1940-1980-.20(b) Classification by education level

Figure 4: Change in log GDP per capita and change in predicted mortality, 1940-1980.
in mortality increases income per capita. This is consistent with the results of Cervellati andSunde (2011a, 2011b).
The estimates are quantitatively similar across specifications. Overall, the findings support our hypothesis that education level plays an important role in the heterogeneous effects
of mortality on income per capita, even after controlling for the effects of income level anddemographic factors.

4

Conclusion

This paper developed a growth theory in which the replacement of physical capital accumulation
by human capital accumulation is endogenous and mortality changes affect the replacement
process. A testable prediction drawn from the theory is the heterogeneous effects of mortality
on per-capita income among countries: the higher a country’s education level, the more likely
it is that a decrease in mortality will increase income per capita. We applied an FMM approachto the causal estimation of Acemoglu and Johnson (2007), and confirmed that the prediction is
supported by the data. Although our analysis is mainly descriptive, our findings have relevant28policy implications. Simply introducing policies to improve health in poor regions where theeducation system is underdeveloped might decrease per-capita income. Policies that promote
education and improve health are needed to put economies stuck in poverty onto a growth path.
The theoretical part of this study assumed mortality as an exogenous parameter and analysed the effect of exogenous changes in mortality. The empirical part of this study used an event
where mortality changed exogenously (the international epidemiological transition) to test ourtheoretical predictions. Whether exogenous mortality has high validity depends on the situation.
A decrease in mortality by new drug development is exogenous, especially for developing countries. However, a decrease in mortality via improved nutrition and sanitation is endogenous formany countries to some extent. Human capital accumulation seems to play a key role in life
expectancy improvements. Endogenizing mortality in our framework in which the replacementof physical capital accumulation by human capital accumulation is endogenous would be aninteresting direction for future research.

5

Acknowledgments

We thank Zheng Fang, Yu Liu, Yoichi Matsubayashi, Tamotsu Nakamura, and seminar and conference participants at Kobe University, Kwansei Gakuin University, Kyoto University, Nanyang
Technological University, Sophia University, and the Japanese Economic Association Autumn
Meeting 2015 for useful comments. We also thank David Lagakos for providing data. Yasui isgrateful for financial support from JSPS KAKENHI Grant Number 15K17022.

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