Discussion Papers In Economics
And Business
Corruption, mortality rates, and development:
Policies for escaping from the poverty trap
Kiyoka Akimoto

Discussion Paper 18-10-Rev.
September 2019

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANCorruption, mortality rates, and development:
Policies for escaping from the poverty trap∗
Kiyoka Akimoto†
Graduate School of Economics, Kobe University

Abstract
We construct a three-period overlapping generations model in which corruption, mortality and fertility rates, and economic development are determined
endogenously. We consider a less developed economy suﬀering from a high degreeof corruption and high mortality and fertility rates in a poverty trap. We focus on
two policies: raising public sector wages as a means of reducing corruption andincreasing public health spending as a means of improving the mortality rate.
Our theoretical analysis shows that implementing both policies simultaneously isessential for less developed economies to escape from the poverty trap and achieve
economic development.

Keywords: Corruption, Public sector wage, Public health, Economic development.
JEL Classification: D73, I18, J38, O41.

∗

An earlier version of this study, titled “’Corruption, Mortality and Fertility Rates, and Development” (Discussion Papers In Economics And Business, Osaka University) was presented at a seminarat Kwansei Gakuin University, the 2018 China Meeting of the Econometric Society, the 2018 Asian
Meeting of the Econometric Society, and the 2018 European Summer Meeting of the Econometric Society. I am especially grateful to Koichi Futagami for helpful discussions and suggestions. I also thank
Ken Tabata, Takaaki Morimoto, and the participants in the seminars and conferences. The financial
support from the Grant-in-Aid for JSPS Fellows (Grant No. JP17J05419) is gratefully acknowledged.
There are no conflicts of interest to declare. Any errors are my responsibility.
†
Graduate School of Economics, Kobe University. Address: 2-1 Rokkodai, Nada, Kobe, Hyogo
657-8501, Japan. E-mail: akimoto1015@gmail.com.

1

Introduction

Both corruption and high mortality rates are considered major obstacles to economic
development. Studies have shown the negative eﬀects of each; see, for example, Mauro(1995) for evidence of the negative eﬀects of corruption and Lorentzen, McMillan, andWacziarg (2008) for the negative eﬀects of high mortality. In this study, we consider
two economic development policies: raising public sector wages as a means of reducing
corruption and increasing public health spending as a means of improving mortality
rates. Our aim is to examine what eﬀects each policy has on an economy and how
governments can achieve economic development using one, or both, of these policies.
Developing countries suﬀer from higher corruption and higher mortality rates thandeveloped ones. We use the Corruption Perception Index (CPI) published by Transparency International as the measure of corruption, male adult mortality rates, andper capita GDP (PPP, constant 2011 international dollars)1 to confirm the negative
correlation between corruption and development and between mortality rates and development, as shown in Figure 12 . The CPI uses a scale of 0 (highly corrupt) to 100(very clean). The figures show that less developed countries are associated with lower
CPI scores and higher mortality rates. In response to these facts, the need to takeaction, especially in these less developed countries, has been acknowledged worldwide.
For example, the United Nations’ Sustainable Development Goals, adopted in September 2015, propose reducing corruption substantially, reducing mortality from various
causes, such as hazardous air and water pollution, and achieving universal access toadequate and equitable sanitation and hygiene3 .
In the literature on demography and economic development, it is a well-establishedfact that mortality and fertility rates are strongly related, and changes in the two rates
influence development. Some studies develop theoretical models with endogenous mortality and fertility rates and focus on the role of public health expenditure in improving
1

The CPI is available at https://www.transparency.org. The data on mortality rates and on percapita GDP are available at https://data.worldbank.org/indicator.
2
Even if we plot the mortality rate of those under five or that of female adults as the mortality ratemeasure, the negative correlations between mortality rates and development can still be confirmed.
3
https://sustainabledevelopment.un.org.

1the mortality rate (e.g., Blackburn and Cipriani (1998), Hashimoto and Tabata (2005),
Blackburn and Sarmah (2008), Fanti and Gori (2014), and Agénor (2015))4 . Blackburn and Cipriani (1998) and Agénor (2015) conduct comparative statics analyses ofincreasing public health expenditure5 . According to their analyses, a policy that increases these expenditures can contribute to higher growth rates.
Although public spending can play a role in accelerating economic development,
some studies show that the level of corruption determines the eﬀectiveness of public
spending. Rajkumar and Swaroop (2008) provide empirical evidence that a one percentage point increase in the share of GDP spent on public health yields a smaller impact
if governance is weak6 . The finding concurs with the arguments by World Bank (2003),
which state that governments in developing countries struggle to translate public funds
into eﬀective services. These sources imply that it is not only essential to increase public
spending, but governments must also conduct policy in a way that reduces corruption.
The literature on corruption focuses on some methods of preventing corruption.
These methods include imposing severe punishment on corrupt behavior, rewarding alack of corruption, or improving the eﬀectiveness of monitoring systems. In line with
Becker and Stigler (1974), Besley and McLaren (1993), Acemoglu and Verdier (1998),
and Wadho (2016), we concentrate on the role of an eﬃciency wage. Becker and Stigler(1974) show that oﬀering public workers a higher wage than they can get elsewhere(i.e., an opportunity wage or a reservation wage) reduces corruption. At the empiricallevel, Goel and Nelson (1998), Van Rijckeghem and Weder (2001), and Di Tella andSchargrodsky (2003) provide evidence on the negative eﬀects of high public sector wages
on corruption.
4

Other studies determine the mortality rate using the level of human capital or private payments
for healthcare; for example, see Cigno (1998), Blackburn and Cipriani (2002), Kalemli-Ozcan (2002),
Lagerlöf (2003), Galor and Moav (2005), Hazan and Zoabi (2006), Cervellati and Sunde (2007), Fioroni(2010), and Futagami and Konishi (2019). To be exact, both private and public health expendituresaﬀect the mortality rate in Blackburn and Cipriani (1998) and Agénor (2015).
5
There are also studies that construct models in which public spending aﬀects mortality rate,
and these studies examine the eﬀects of increasing public spending. A few notable studies include
Chakraborty (2004), Aisa and Pueyo (2006), and Bhattacharya and Qiao (2007). However, they do
not take fertility rates into account.
6
Rajkumar and Swaroop (2008) measure governance by using two indicators: quality of bureaucracy
and level of corruption.

2

To the best of our knowledge, however, there is no theoretical study that examines
the eﬀects of a higher public sector wage on corruption and economic development byconstructing a dynamic general equilibrium model7 . This indicates that the questionof whether oﬀering a higher public sector wage can help an economy eradicate highlevels of corruption and move that economy beyond a less developed stage remains
unanswered.
The aim of our present study is to investigate what policy is eﬀective in helping
an economy escape from corruption and a high mortality rate and move toward development by constructing a dynamic general equilibrium model in which corruption,mortality and fertility rates, and development are determined jointly. To achieve thisaim, we first examine the eﬀects of raising public sector wages and increasing public
spending on public health.
We construct a three-period overlapping generations model in which agents live
through childhood, adulthood, and old age. In each period, newly born agents are divided into two groups, households and bureaucrats. Households decide their number ofchildren, and they work in the private sector. Bureaucrats are employed in the public
sector and produce public services by using public funds provided by the government.
They can engage in corruption by misallocating a share of public funds as illegal income. Public services contribute to the quality of public health, which determines themortality rate. The key assumption we impose is that households are subject to themortality rate in adulthood, while bureaucrats die at the end of adulthood. This makes
our model tractable since only households save a portion of their income, which simplifies the dynamic equations. In a dynamic general equilibrium model with endogenous
corruption and development, a policy often has both positive and negative eﬀects onan economy through a variety of channels. As such, it is diﬃcult to identify the net
eﬀects and each channel. This may be one of the reasons that previous theoretical
7

There are, however, theoretical studies that examine corruption and economic development in dynamic models, such as Ehrlich and Lui (1999), Sarte (2001), Alesina and Angeletos (2005), Blackburn,Bose, and Haque (2006, 2011), Blackburn and Forgues-Puccio (2007, 2009), Blackburn and Sarmah(2008), Eicher, Garcı́a-Peñalosa, and Van Ypersele (2009), Spinesi (2009), Blackburn (2012), Dzhumashev (2014a,b), and Varvarigos and Arsenis (2015).

3

studies have not fully explored the eﬀects of most policies, including the two policies
we consider in this paper. By imposing the assumption, our analysis can abstract froma few of the channels and eﬀects. However, it would still be interesting and importantto analytically clarify other eﬀects and their channels.
In an equilibrium, two stable steady states can exist. One steady state in the earlystage of development is characterized by a high degree of corruption and high mortality
and fertility rates, that is, a poverty trap. The other, the late stage of development, ischaracterized by no corruption and low mortality and fertility rates. In this study, we
consider an economy caught in the poverty trap. The economy needs to craft policythat will enable its escape from the trap and place it on a path toward the other steadystate. The government has two methods of accomplishing these goals, raising public
sector wages and increasing public health spending. Under a balanced-budget rule,both policies are financed by increasing the tax rate imposed on output.
We assume that the public sector wage is equal to the private sector wage andthe share of public spending to total output is low at the initial steady state. We,
then, demonstrate the following two cases. In the first case, only increasing public
spending is suﬃcient to escape from the trap. In the second case, it is necessary to
not only increase public spending but also to raise public sector wages. By doing so,
the economy escapes from the trap and takes a path that converges to a new steadystate. At the new steady state, no corruption, low mortality and fertility rates, andhigh development will be realized. In this case, merely increasing public spending is
not worthwhile and raising public sector wages plays an important role; that is, itheightens the eﬀectiveness of translating public funds into public services. By focusing
on certain structural parameters related to corruption, we discuss how the second casecan be applied to developing countries. Therefore, while previous studies have notfully explored the eﬀects of a policy meant to reduce corruption in a dynamic generalequilibrium model, our present study shows that raising public sector wages, as a way to
reduce corruption, is essential for developing countries to achieve economic development.
The remainder of this paper is organized as follows. Section 2 constructs the model.
Section 3 examines an equilibrium and derives the dynamics of an economy. Section 44

is the main part of this paper. In it, we conduct the comparative statics analysis andshow the eﬀects of raising public sector wages and increasing public spending on publichealth. After that, we explore what policy is eﬀective in helping an economy escapefrom the poverty trap. Section 5 presents concluding remarks.

2

Model

We construct a three-period overlapping generations model. The economy consists offirms, the government, and agents. Agents go through childhood, adulthood, and oldage. Children do not make any decisions. Adult agents work, consume goods, raisechildren, and save a part of their income. Old agents withdraw savings and consume
goods. Nt stands for the labor force in period t; in other words, Nt is the numberof adults in period t. In each period, newly born agents are divided into two groups,
bureaucrats and households. The population of each group in period t, NtB and NtH , isas follows:
NtB = λNt

and NtH = (1 − λ)Nt ,(1)

where λ ∈ (0, 1). In addition, two types of bureaucrats exist: corruptible and noncorruptible. The proportion, b ∈ (0, 1), is corruptible, while the remaining proportion,
1 − b, is non-corruptible. Corruptible bureaucrats can engage in corruption. We call acorruptible bureaucrat who is actually corrupt a dishonest bureaucrat and a corruptible
bureaucrat who is not corrupt an honest bureaucrat. Proportion σt become dishonest
bureaucrats, while proportion 1 − σt become honest bureaucrats. σt is an endogenous
variable. Households, corruptible bureaucrats, and non-corruptible bureaucrats are
represented by a superscript i ∈ {H, CB, N B}. All agents are endowed with one unitof labor, and they supply it inelastically. Households work for the private sector, while
bureaucrats work for the public sector. In addition, agents face the mortality rate inadulthood determined by the quality of public health.

5

2.1

Production

Firms produce final goods by using labor and capital. The production function is
Yt = AL1−α
Ktα , where α ∈ (0, 1). Yt , Lt , and Kt denote total output, labor, andtcapital, respectively. Output per capita is represented by
yt = Alt1−α ktα .

(2)yt , lt , and kt are Yt /Nt , Lt /Nt , and Kt /Nt , respectively. Profit maximizing yields thefirst order conditions:rt = (1 − τt )αAlt1−α ktα−1 ,(3)wt = (1 − τt )(1 − α)Alt−α ktα .

(4)rt , wt , and τt represent the interest rate, private sector wage, and tax rate, respectively.
The tax rate is imposed on output.

2.2

Government

The government has three roles in this model. The first is to supply public services
that aﬀect the quality of public health. The second is to determine a wage rate forbureaucrats. The third is to set a tax rate.
First, we explain the supply of public services and corruption. This follows Varvarigos and Arsenis (2015). The government devotes Gt units of public funds to public
services. This spending is proportional to total output:
Gt = θYt ,where θ ∈ (0, 1).

(5)

The government delegates the production and supply of public services to bureaucrats. Each bureaucrat is provided with Gt /NtB units of funds. When producing andsupplying public services, he or she can use two types of projects, Type-1 and Type-2.
6

The return of a Type-1 project is random, while that of a Type-2 project is constant.
If a bureaucrat invests one unit of funds in the Type-1 project, he or she obtains ξ > 1
units of public services with probability p and γ < 1 units with probability 1 − p.
Without loss of generality, the expected return is set to one; that is, pξ + (1 − p)γ = 1.
In contrast, if a bureaucrat invests one unit of funds in the Type-2 project, he or she
produces γ/δ units of services with probability 1. We assume that 0 < γ < δ < 1
so that γ/δ < 1. Since the Type-1 project creates higher expected returns than the
Type-2 project, the government instructs bureaucrats to operate the Type-1 project.
Non-corruptible bureaucrats comply with the instructions; that is, they invest all
their funds in the Type-1 project and supply (1 − b)Gt units of public services. On theother hand, corruptible bureaucrats can engage in corruption in the following steps.
Each dishonest bureaucrat invests δGt /NtB units of funds in the Type-2 project andsupplies γGt /NtB units of public services. Subsequently, dishonest bureaucrats insist
that they conducted the Type-1 project and unfortunately achieved a bad result because of an idiosyncratic shock. Finally, they obtain illegal income (1−δ)Gt /NtB . Thus,
γbσt Gt units of public services are supplied by dishonest bureaucrats. Conversely, honest bureaucrats who are not corrupt behave in the same manner as non-corruptible
bureaucrats. That is, they supply b(1 − σt )Gt units of public services. Then, the percapita public services supplied by all bureaucrats, ft , are as follows:
ft = [1 − σt b(1 − γ)]θyt .

(6)Second, the government oﬀers a wage contract to bureaucrats. Bureaucrats apply
for a job in the public sector if they can obtain a higher wage rate, ωt , than that in theprivate sector. Thus, to attract bureaucrats, the government oﬀers
ωt = ρwt ,where ρ ∈ [1, ∞).

(7)

Since the government cannot diﬀerentiate between bureaucrat types, it oﬀers the same7

contract to all bureaucrats8 .
Third, the government sets a tax rate to follow the balanced budget rule:τt Yt = Gt + ωt NtB .

(8)ρ and θ are important policy parameters in this model. Section 4 conducts comparative statics analyses to examine the eﬀects of raising public sector wages (i.e., anincrease in ρ) and increasing public spending on public health (i.e., an increase in θ).
τt is determined to keep the government’s budget balanced.

2.3

Public health and the mortality rate

The public services supplied by bureaucrats aﬀect the quality of public health. The
quality of public health is given by
ht =

ft
.
yt

(9)

Production activity has potential negative eﬀects on public health, such as air and waterpollution. Providing public services can mitigate these negative eﬀects. This idea iswidely supported in the existing literature. For instance, see Blackburn and Cipriani(1998), Osang and Sarkar (2008), and Dioikitopoulos (2014)9 .
The quality of public health determines the survival rate in period t, πt , as follows:
πt = Π(ht ),Π(ht ) ∈ [0, 1],8

Π′ (ht ) > 0.

(10)

If the government oﬀers ωt < wt , only corruptible bureaucrats who expect to receive compensation
through illegal income will apply for a job in the public sector and are identified as being dishonest.
Thus, oﬀering a lower public sector wage implies that the government accepts corruption. Since ouranalysis seeks to examine methods to escape from the poverty trap, we focus only on ρ ∈ [1, ∞).
9
As explained later, public health in (9) is an increasing function of per capita capital. Economic
development, represented by kt , has negative eﬀects on the quality of public health through greater
production and positive eﬀects through more public services. In equilibrium, the positive eﬀects
dominate. Thus, as capital accumulates, the quality of public health improves.

8

An improvement in the quality of public health in period t increases the survival ratein this period. That is, higher quality public health yields a lower mortality rate.

2.4

Agents

We consider agents born in period t − 1. We make the assumptions that bureaucrats
do not give birth and that they die at the end of adulthood10 . These assumptions allow
us to analytically clarify and examine the essential eﬀects of the government’s policies
on the economy.

2.4.1

Households

Households choose the number of children nt as well as their consumption in adulthoodHcHa,t and in old age co,t+1 to maximize the following expected utility:

Ha ln nt + (1 − a)[ln cH
a,t + βπt ln co,t+1 ].

They survive into old age with probability πt . β is the discount factor and a is theirpreference between children and consumption. High a implies a high preference toward
their children.
Households allocate their income between consumption, savings, and child rearing.
Following Fioroni (2010), we assume that raising each child requires e proportion ofincome. As such, the budget constraints of households are as follows:cH
a,t + st = wt − ent wt

and cHo,t+1 =

Rt+1
st ,
πt

where st is savings and Rt+1 is the gross interest rate. Maximizing the utility level
10

Similar assumptions are used in Blackburn and Sarmah (2008) and Varvarigos and Arsenis (2015).
The analysis of Blackburn and Sarmah (2008) assumes that households face a mortality rate, whereas
bureaucrats enjoy a whole lifetime. The analysis of Varvarigos and Arsenis (2015) assumes that only
households give birth and raise their children. However, as in the extended model of Varvarigos andArsenis (2015), our results and mechanisms hold qualitatively even if we consider a case in which bothhouseholds and bureaucrats raise their children.

9

subject to these two constraints yields the optimal level of consumption and savings:
cH
a,t =

1−a
wt ,
1 + (1 − a)βπt

cHo,t+1 =

(1 − a)βRt+1 wt ,1 + (1 − a)βπt

and
st =

(1 − a)βπtwt .
1 + (1 − a)βπt(11)The optimal number of children is given by
nt =

a
.
e[1 + (1 − a)βπt ](12)Equations (11) and (12) show that a decline of πt decreases st and increases nt . A highmortality rate implies that households have a low probability of living to old age. To
consume more in adulthood, they decrease their savings. In addition, to derive higher
utility in adulthood, they give birth to several children.

2.4.2

Bureaucrats

Bureaucrats derive their utility only from consumption in adulthood. Their utility is
as follows:
ln cia,t ,i ∈ {CB, N B}.

B
Non-corruptible bureaucrats consume cNa,t = ωt . Honest bureaucrats behave in thesame way as non-corruptible bureaucrats. Thus, their consumption level is ωt , and theirutility is given by
CB(honest)Ut= ln ωt .

(13)

In contrast, dishonest bureaucrats receive not only labor income ωt but also illegal
10income (1 − δ)Gt /NtB . Their consumption level is ωt + (1 − δ)Gt /NtB . In addition,
following Varvarigos and Arsenis (2015), we assume that dishonest bureaucrats face a
cost, and the cost is proportional to their utility. Therefore, their utility is given by
CB(dishonest)Ut= (1 − χ) ln[](1 − δ)Gt
ωt +
.
NtB

(14)

χ ∈ (0, 1) stands for the cost of engaging in corruption. It can be broadly interpreted.
One interpretation is that χ is the probability of being accused by the government. With
probability χ, dishonest bureaucrats are caught, and their utility becomes zero. With
probability 1−χ, they can avoid accusations and derive the utility. Thus, their expectedutility is represented by (14). Another interpretation is that χ represents psychologicaldistress related to the degree of severity of corruption in a society (i.e., cultural norms
against corruption). If the public tolerates corruption, dishonest bureaucrats would feelless psychological distress.
Last, we consider the maximization problem of a corruptible bureaucrat. A corruptible bureaucrat j becomes a dishonest bureaucrat with probability σjt ∈ [0, 1] andbecomes an honest bureaucrat with probability 1 − σjt . He or she chooses his or her
strategy, σjt , to maximize Ujt , which is defined by
CB(dishonest)

Ujt = σjt Ut

3

CB(honest)+ (1 − σjt )Ut.

Equilibrium

The labor market clearing condition is Lt = NtH = (1 − λ)Nt . Therefore, the per capita
labor force becomes constant:lt = l = 1 − λ.

11

(15)

Substituting (4), (5), (7), and (15) into the government’s balanced budget constraint,(8), we obtain the following tax rate:

τt = τ =θ(1 − λ) + ρλ(1 − α).
1 − λ + ρλ(1 − α)(16)Since θ ∈ (0, 1), τ ∈ (0, 1). We note that ∂τ /∂ρ > 0, limρ→∞ τ = 1, ∂τ /∂θ > 0, andlimθ→1 τ = 1. Substituting (15) and (16) into (2), (3), and (4), respectively, the percapita output, interest rate, and private sector wage are rewritten:y(kt ) = Al1−α ktα ,(17)r(kt ) = (1 − τ )αAl1−α ktα−1 ,(18)w(kt ) = (1 − τ )(1 − α)Al−α ktα .

(19)Since the government oﬀers contract ωt = ρwt , the public sector wage is given byω(kt ) = ρ(1 − τ )(1 − α)Al−α ktα .

(20)

We note that ∂ω(kt )/∂ρ > 0 and ∂ω(kt )/∂θ < 0.

3.1

Endogenous corruption and its eﬀects

We consider a strategy of corruptible bureaucrat j. He or she becomes honest if
CB(dishonest)

Ut

CB(honest)≤ Ut, or from (13) and (14),](1 − δ)Gt≤ ln ωt .
(1 − χ) ln ωt +
NtB
[

12

CB(honest)

However, he or she becomes dishonest if Ut

CB(dishonest)< Ut. Thus, from (1),(5), (17), and (20), he or she chooses σj,t = 1 for kt < k̂ where

k̂ ≡

{
[

ρ(1 − τ )(1 − α)Al

]
−α −1

[

θ(1 − λ)(1 − δ)1+ρλ(1 − τ )(1 − α)

} α1
] 1−χ
χ
.

(21)

In addition, σt = 1 is realized since all the other corruptible bureaucrats choose thesame strategy. For kt ≥ k̂, he or she chooses σjt = 0, and then σt = 0 is realized. Hence,solving the maximization problem of a corruptible bureaucrat yields1σ(kt ) =for kt < k̂,



0

(22)

for kt ≥ k̂.

σ(kt ), which represents the degree of corruption, has the following eﬀects in the economy. From (6), (17), and (22), the per capita public services supplied by bureaucrats
becomesf (kt ) =
[1 − b(1 − γ)]θy(k )for kt < k̂,θy(kt )for kt ≥ k̂.

t

(23)

In the early stage of development, kt < k̂, all corruptible bureaucrats behave dishonestly.
They take a proportion of public funds as illegal income, so the level of public services
is low. As capital accumulates, corruption stops occurring. Thus, all public funds are
devoted to public services. The level of per capita public services determines the qualityof public health. That is, from (9) and (23), ht is as follows:h(kt ) =[1 − b(1 − γ)]θfor kt < k̂,θfor kt ≥ k̂.

13

(24)

When the stock of per capita capital is small, the quality worsens because insuﬃcientpublic services are supplied. This results in a low survival rate, π. After the stock ofper capita capital exceeds the threshold, the survival rate reaches the maximum level,π̄. From (10) and (24), π(kt ) is given byππ(kt ) =for kt < k̂,



π̄

(25)

for kt ≥ k̂,

where π = Π ([1 − b(1 − γ)]θ), π̄ = Π (θ), and π < π̄. The fertility rate is also indirectly
aﬀected by corruption. From (12) and (25), the fertility rate is given by



n̄
n(kt ) =for kt < k̂,



n

(26)

for kt ≥ k̂,

where n̄ = a/{e[1 + (1 − a)βπ]}, n = a/{e[1 + (1 − a)β π̄]}, and n < n̄.
The preceding results can be summarized in the following proposition.
Proposition 1.
The equilibrium is described as follows.
1. For early stages of economic development, that is, kt < k̂, all corruptible bureaucrats engage in corruption, and the mortality and fertility rates are high.
2. For late stages of economic development, that is, kt ≥ k̂, no corruptible bureaucrats engage in corruption, and the mortality and fertility rates are low.
Our theoretical results replicate empirical facts on the relationships between corruption,mortality and fertility rates, and economic development. That is, developing countries
suﬀer from a higher degree of corruption and higher mortality and fertility rates.

14

3.2

Dynamics of the economy

The rest of this section derives the dynamics of per capita capital. The capital market
clearing condition is Kt+1 = st NtH . From (11) and (19), the condition is rewritten as
follows:
kt+1 =1−aeβ(1 − τ )(1 − α)Al−α π(kt )ktα .
a

To obtain the equation, we use Nt+1 = nt (1 − λ)Nt . By substituting (25) into the
dynamics, we obtain the following dynamics equations:
C
kt+1
=

1−a
eβ(1 − τ )(1 − α)Al−α πktαafor kt < k̂

(27)

NC
kt+1
=

1−a
eβ(1 − τ )(1 − α)Al−α π̄ktαafor kt ≥ k̂.

(28)

and

We note that ∂kt+1 /∂kt > 0 and ∂ 2 kt+1 /∂kt2 < 0 hold.
Drawing the two dynamics in the kt −kt+1 plane shows the transition of this economy
and steady states, as depicted in Figure 2. We show that two steady states can exist.
C
We denote the points at which the 45-degree line intersects with the dynamics kt+1
NC
and kt+1
as EC and EN C . These steady states are stable. Therefore, the economy will

converge to EC (EN C ) if its initial stock of per capita capital is less (higher) than k̂.
The stable steady states are characterized as follows: EC has corruption, low quality of
public health, and high mortality and fertility rates, whereas EN C has no corruption,high quality of public health, and low mortality and fertility rates.

15

4

Policies for escaping from the poverty trap

This section considers a less developed economy caught in a poverty trap at EC andstudies how the economy escapes from the trap and achieves economic development.
The government decides public sector wages, public health spending, and the tax rate:that is, ρ, θ, and τ . We first examine the eﬀects of raising the wage rate (i.e., increasedρ) and increasing public spending (i.e., increased θ). The tax rate is set to keep thebudget balanced. At the initial steady state, EC , the economy has the stock of percapita capital, k ∗ (ρ, θ). Equation (27) yields[

1−aπ(θ)(1 − θ)k ∗ (ρ, θ) =eβ(1 − λ)1−α (1 − α)Aa
1 − λ + ρλ(1 − α)

1
] 1−α

.

(29)

Substituting (15) and (16) into (21), the threshold under which all corruptible bureaucrats engage in corruption is given by{k̂(ρ, θ) =[] 1−χ } α11 − λ + ρλ(1 − α)θ(1 − δ)[1 − λ + ρλ(1 − α)] χ
1+.
ρ(1 − θ)(1 − λ)1−α (1 − α)Aρλ(1 − θ)(1 − α)(30)

We assume that the economy sets ρ = 1 and θ = θ0 at the initial steady state, EC .
In addition, we note that θ0 is suﬃciently small, so steady state EC exists. The initialstock of per capita capital is k ∗ (1, θ0 ), and the threshold is k̂(1, θ0 ).
First, we examine the eﬀects of ρ and θ on k̂(ρ, θ). From this, we can obtain thefollowing lemma.
Lemma 1.
k̂(ρ, θ) decreases with ρ and increases with θ. Moreover, when ρ approaches infinity,k̂(ρ, θ) converges to a finite value.
Proof. See appendix A. □Raising the public sector wage decreases the incentive for corruptible bureaucrats toengage in corruption. Since dishonest bureaucrats lose a part of their utility, a higher
16

wage increases the costs of corruption. Thus, the threshold decreases. However, evenif ρ goes to ∞, the threshold level does not approach to zero. This is because, as ρgoes to infinity, the public sector wage converges to a finite value; that is, limρ→∞ ωt =(1 − θ)λ−1 (1 − λ)1−α Aktα . Therefore, even if the government sets ρ at as high a value as
possible, corruptible bureaucrats still have incentive to engage in corruption. On theother hand, an increase in θ increases the threshold since it increases illegal income.
A high θ means that the government spends a large amount of public funds on publichealth and distributes the large funds to each bureaucrat. Thus, dishonest bureaucrats
obtain high illegal incomes since they illegally retain a certain proportion of the publicfunds for themselves.
Second, we examine the eﬀects of ρ and θ on k ∗ (ρ, θ). As is usual in the literature
on demography and development (e.g., Blackburn and Cipriani (2002), Hashimoto andTabata (2005), Fioroni (2010), and Fanti and Gori (2014)), we specify the survival rate
as follows:
πt = Π(ht ) =ht,
1 + htΠ′ (ht ) > 0, Π′′ (ht ) < 0, Π(0) = 0, and limht →∞ Π(ht ) = 1. From (25), π becomesπ(θ) =ϕθ
,1 + ϕθ

(31)

where ϕ = 1 − b(1 − γ). π ′ (θ) > 0, π ′′ (θ) < 0, π(0) = 0, and π(1) = ϕ/(1 + ϕ). Thus,
we can obtain the following lemma.
Lemma 2.
k ∗ (ρ, θ) decreases with ρ and is hump-shaped in θ.
Proof. See appendix B. □An increase in ρ aﬀects k ∗ (ρ, θ) by increasing τ . To keep the budget balanced, thegovernment must raise the tax rate. This decreases households’ after-tax income, wt ,and savings, st . Thus, k ∗ (ρ, θ) decreases. On the other hand, an increase in θ has
17

positive or negative eﬀects on k ∗ (ρ, θ). Through the same channel as a higher ρ does,a higher θ negatively aﬀects k ∗ (ρ, θ). At the same time, by setting θ at a higher value,
the government can improve the mortality rate, which causes a decline in the fertility
rate. As a result, households will save a larger portion of their income. If θ is lower
than θ̂, the positive eﬀect caused by improved survival rate is larger, and the increasein θ increases k ∗ (ρ, θ). In contrast, if θ is higher than θ̂, the negative eﬀect caused byan increased tax rate is larger, and the increase in θ decreases k ∗ (ρ, θ).
Next, we consider what policy is most eﬀective in helping the less developed economy
escape from the poverty trap in which corruption is rampant and the mortality andfertility rates are high. By enacting a policy, the economy can escape from the trap if
the threshold becomes lower than the steady state level of per capita capital. Figure 3
depicts k̂(1, θ), limρ→∞ k̂(ρ, θ), and k ∗ (1, θ). We focus on the following two cases. The
first case is that in which k ∗ (1, θ) intersects with both k̂(1, θ) and limρ→∞ k̂(ρ, θ). The
second case is that in which k ∗ (1, θ) intersects with limρ→∞ k̂(ρ, θ) but not with k̂(1, θ).
We explore a policy to escape from the poverty trap in each case11 .
Figure 4 shows the first case. We define the level of θ at each point that k ∗ (1, θ)intersects with limρ→∞ k̂(ρ, θ) as θ1 and θ4 . Furthermore, k ∗ (1, θ) intersects with k̂(1, θ).
We also define the level of θ at each point that these lines intersect as θ2 and θ3 . In thiscase, increasing just public health spending is suﬃcient. When the government raises θfrom θ0 to θ̃ ∈ [θ2 , θ3 ], k̂(1, θ̃) ≤ k ∗ (1, θ̃) holds true. That is, the economy escapes fromthe trap and converges to a new steady state. At the new steady state, no corruption,
low mortality and fertility rates, and high development are realized. In this case, while
increasing public spending increases bureaucrats’ incentives to engage in corruption,
the positive eﬀects on the level of per capita capital caused by the improved mortality
rate are much larger. Hence, only increasing public spending is enough to escape fromthe trap.
Figure 5 shows the second case. k ∗ (1, θ) intersects with limρ→∞ k̂(ρ, θ) twice. We
define the level of θ at each point that the two lines intersect as θ5 and θ6 . In this case,
The case in which k ∗ (1, θ) intersects with neither k̂(1, θ) nor limρ→∞ k̂(ρ, θ) is not considered sinceno policy will be eﬀective.
11

18

only increasing public spending is not worthwhile since given ρ = 1, k ∗ (1, θ) < k̂(1, θ)
holds for all θ ∈ (0, 1). To escape from the trap, the economy must not only increase
public spending but also raise public sector wages. We explain the transition of thiseconomy by drawing the phase diagrams in Figures 6 and 7. As depicted in FigureC6, when the government increases θ0 to θ̃ ∈ [θ5 , θ6 ], the dynamic equation kt+1
shiftsupward, and then the steady state level of per capita capital increases from k ∗ (1, θ0 ) tok ∗ (1, θ̃). However, increasing public spending oﬀers greater incentives for bureaucrats
to engage in corruption. Hence, the threshold also increases from k̂(1, θ0 ) to k̂(1, θ̃).
Thus, the economy converges to the new steady state, Ẽ. The economy still suﬀers
from the poverty trap at Ẽ since k ∗ (1, θ̃) < k̂(1, θ̃) holds. In this case, even if theeconomy increases public spending to improve the mortality rate, a large portion ofthat spending is not translated into public services. Thus, to heighten the eﬀectivenessof translating public spending into public services, a policy to reduce corruption must
be conducted. We show that there is ρ̂ that satisfies k̂(ρ̂, θ̃) = k ∗ (1, θ̃) in Figure 5.
This indicates that by increasing ρ from one to ρ̃ ∈ [ρ̂, ∞), k̂(ρ̃, θ̃) ≤ k ∗ (1, θ̃) holds, andthen the economy can escape from the trap. As shown in Figure 7, increasing ρ from
one to ρ̃ decreases bureaucrats’ incentives; that is, k̂(1, θ̃) decreases to k̂(ρ̃, θ̃). Then,the high public sector wage deters corruptible bureaucrats from engaging in corruption.
Accordingly, the economy jumps from Ẽ to E ′ , and the process of capital accumulationNC. Finally, the economy converges to the steady state,
follows the dynamic equation kt+1

EN C , at which the economy achieves no corruption, low mortality and fertility rates,
and high development12 .
The preceding results can be summarized in the following proposition.
Proposition 2.
Suppose that an economy is at initial steady state EC with ρ = 1 and a suﬃciently
small θ. Then, the following policies are eﬀective in helping the economy escape fromthe poverty trap.
1. If k ∗ (1, θ) intersects with both k̂(1, θ) and limρ→∞ k̂(ρ, θ), there is a range of θ that
We note that this result occurs in the first case when the government increases θ0 to θ̃ ∈ [θ1 , θ2 )or θ̃ ∈ (θ3 , θ4 ].
12

19

satisfies k̂(1, θ) ≤ k ∗ (1, θ); that is, the economy can escape from the trap only byincreasing public spending.
2. If k ∗ (1, θ) intersects with limρ→∞ k̂(ρ, θ) but not with k̂(1, θ), k ∗ (1, θ) < k̂(1, θ)
holds for all θ ∈ (0, 1); that is, the economy cannot escape from the trap only byincreasing public spending. However, there is a range of ρ and θ that satisfiesk̂(ρ, θ) ≤ k ∗ (1, θ); that is, the economy can escape from the trap by not only
increasing public spending but also raising the public sector wage.
We discuss when the first or second case occurs. The first (second) case is likely
to occur when k̂(1, θ) is lower (higher) or k ∗ (1, θ) is higher (lower) or both. We focus
on three parameters: δ, χ, and b. The parameters, δ and χ aﬀect k̂(1, θ), while b
aﬀects k ∗ (1, θ). A higher δ decreases k̂(1, θ); that is, ∂ k̂(1, θ)/∂δ < 0. A higher δ
indicates that the amount of illegal income is small since dishonest bureaucrats obtain1 − δ proportion of illegal income of public funds provided by the government. The
small benefits obtained by engaging in corruption diminish the incentives to be corrupt.
Similarly, as χ rises, k̂(1, θ) decreases; that is, ∂ k̂(1, θ)/∂χ < 0. Dishonest bureaucrats
lose χ proportion of their utility as costs of engaging in corruption. When χ is high andthe costs are high, corruptible bureaucrats are reluctant to engage in corruption. As
indicated earlier, χ can be broadly interpreted, such as the probability of being caught
by the government or psychological distress stemming from cultural norms against
corruption. If the probability or distress is high, engaging in corruption is not attractive
for bureaucrats. b is the share of corruptible bureaucrats. A higher b decreases k ∗ (1, θ),through which it causes a fall in the survival rate. In an economy at steady state EC ,all corruptible bureaucrats actually become dishonest. In other words, bNtB numberof bureaucrats engage in corruption. As b is high, public health spending does notcontribute to improvement in the quality of public health since a large portion of the
spending is stolen by the dishonest bureaucrats. This decreases the survival rate; thatis, dπ/db < 0. Households who face a low survival rate decrease their level of saving.
Thus, a high b decreases the stock of per capita capital at the steady state; that is,∂k ∗ (1, θ)/∂b < 0. Therefore, the first case can occur if δ or χ is high or b is low, or if20both conditions are true, and the second case can occur if δ or χ is low or b is high, orboth.
Last, we consider which case can be applied to developing countries. To do so, we
regard χ as the degree of psychological distress (e.g., cultural norms against corruption,social stigma, and peer reputation) and explore it in developing countries. The reason
why we focus on χ is that there are a large number of studies investigating the relationships between psychological costs and illegal activities (e.g., corruption, tax evasion,and crime). Barr and Serra (2010) find that in their experiment, individuals who grew
up in countries in which corruption is prevalent are likely to engage in bribery. They
state that social norms internalized during childhood determine individuals’ decisions
about bribery. Moreover, Dong, Dulleck, and Torgler (2012) and Lee and Guven (2013)use micro data sets and show that the higher the frequency of corruption, the higher
the justifiability of corruption. Hence, according to their findings, if the public tolerates
corruption, corruption is likely to occur; and, if corruption is rampant, the public arelikely to accept corruption. As we confirmed in the introduction (Figure 1), developing countries suﬀer from sever corruption. Thus, corrupt bureaucrats may feel lower
psychological distress when they engage in corruption; that is, χ is low in our model.
Therefore, the second case shown in Figure 5 can be applied to developing countries. As
summarized in Proposition 2, conducting a policy to prevent corruption is essential forthese countries to increase the eﬀectiveness of expanding public spending, and thereby
achieving economic development.

5

Concluding remarks

This paper builds an overlapping generations model by taking into account endogenous
corruption, mortality and fertility rates, and economic development. We consider a lessdeveloped economy suﬀering from corruption as well as high mortality and fertility rates
in a poverty trap. Our analysis examines how the economy can escape from the trap
and achieve economic development. In the analysis, we focus on two policies, raisingpublic sector wages as a way to reduce corruption and increasing public health spending21

to improve the mortality rate. We show that two cases exist. In the first case, increasing
public spending is suﬃcient. In the second, both policies must be implemented simultaneously. For developing countries, the second case can be applied; it may be essential
to increase both public spending and public sector wages. In particular, raising public
sector wages plays an important role in heightening the eﬀectiveness of transforming
public spending into public services. Thus, we can theoretically confirm the necessity ofa policy to prevent corruption, which is implied by the empirical finding of Rajkumar
and Swaroop (2008) and the arguments of World Bank (2003).
Finally, we must note that our analysis stands on the assumption that bureaucrats
die at the end of adulthood, whereas households only have a probability of surviving
to old age. Hence, we focus on only some of the many eﬀects that the policies haveon the economy. However, this study does contribute to the literature on corruption,
demography, and economic development in that the eﬀects and their mechanisms areanalytically clarified using the dynamic general equilibrium model.

22

Appendix
A

Proof of Lemma 1

By taking the partial derivatives of k̂(ρ, θ), represented by (30) with respect to ρ andθ, respectively, we obtain∂ k̂(ρ, θ)1−λk̂(ρ, θ)=−∂ραρ 1 − λ + ρλ(1 − α)

{

1−χ
1+
χ 1+

}

1
ρλ(1−θ)(1−α)θ(1−δ)[(1−λ)+ρλ(1−α)]<0andk̂(ρ, θ)∂ k̂(ρ, θ)=∂θα(1 − θ)

{

1−χ
1+
χ θ+

1
ρλ(1−θ)(1−α)(1−δ)[(1−λ)+ρλ(1−α)]}> 0.

In addition, we obtain{lim k̂(ρ, θ) =ρ→∞[] 1−χ } α1θ(1 − δ) χ
λ
1+
< ∞.
(1 − θ)(1 − λ)1−α A
1−θThus, k̂(ρ, θ) decreases with ρ and increases with θ. As ρ approaches infinity, k̂(ρ, θ)converges to a finite value. □B

Proof of Lemma 2

By taking the partial derivative of k ∗ (ρ, θ), represented by (29) with respect to ρ, we
obtain∂k ∗ (ρ, θ)k ∗ (ρ, θ)λ
=−
< 0.
∂ρ
(1 − λ) + ρλ(1 − α)23That is, k ∗ (ρ, θ) decreases with ρ. Similarly, by taking the partial derivative of k ∗ (ρ, θ)with respect to θ, we obtain∂k ∗ (ρ, θ)k ∗ (ρ, θ)=∂θθ(1 − α)

(

dπ θ
θ
−
dθ π 1 − θ).

(dπ/π)/(dθ/θ) represents the degree to which a change in θ leads to a change in thesurvival rate, π. Since the survival rate is given by (31), it has the following characteristics:
d
dθ

(

dπ θ
dθ π

)
< 0,

d2
dθ2

(

dπ θ
dθ π

)

dπ θ
= 1,
dθ π θ=0

> 0,

dπ θ
1
=
.
dθ π θ=1 1 + ϕOn the other hand, we can show that
d
dθ

(

θ
1−θ

)
> 0,

d2
dθ2

(

θ
1−θ

)

θ
= 0,
θ→0 1 − θ

> 0,

lim

θ
= ∞.
θ→1 1 − θlim

1Thus, there is a threshold, θ̂ = [−1 + (1 + ϕ) 2 ]/ϕ, that satisfies (dπ/π)/(dθ/θ)|θ=θ̂ =θ̂/(1 − θ̂). We also confirm θ̂ in Figure 8. If θ ∈ (0, θ̂), (dπ/π)/(dθ/θ) > θ/(1 − θ) holds.
On the contrary, if θ ∈ [θ̂, 1), (dπ/π)/(dθ/θ) ≤ θ/(1 − θ) holds. Thus, we obtain∗∂k (ρ, θ) > 0 if θ ∈ (0, θ̂),∂θ
≤ 0 if θ ∈ [θ̂, 1).

That is, k ∗ (ρ, θ) is hump-shaped in θ. □24

Figures

Figure 1: Negative correlation between corruption and development in 2015 (left) andnegative correlation between mortality rate and development in 2015 (right).

25

Figure 2: Multiple steady states.

26

Figure 3: k̂(1, θ), limρ→∞ k̂(ρ, θ), and k ∗ (1, θ).

27

Figure 4: First case, in which k ∗ (1, θ) intersects with both k̂(1, θ) and limρ→∞ k̂(ρ, θ).

28

Figure 5: Second case, in which k ∗ (1, θ) intersects with limρ→∞ k̂(ρ, θ) but not withk̂(1, θ).

29

Figure 6: The transition when the government only increases public health spending.

30

Figure 7: The transition when the government increases both public health spending
and public sector wages.

31

Figure 8: (dπ/π)/(dθ/θ) and θ/(1 − θ).

32

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