ArticlePDF Available
Corruption and Investment: Theory and Evidence from
China
Bingyong Zheng Junji Xiao
Abstract
We consider a principal-agent model to examine the conditions under which corruption
prompts investment. We also investigate three policies that can be used to combat corruption:
strengthening monitoring, increasing compensation, and enhancing accountability. Our theory
suggests that increasing monitoring intensity mitigates corruption at the cost of reduced invest-
ment. The most cost-effective policy to control corruption is to enhance accountability, which
reduces corruption without decreasing growth-enhancing investment. We test our theoretical
predictions using Chinese infrastructure investment and corruption data. The data show that
infrastructure investment is negatively correlated with anticorruption effort, as predicted by the
theoretical model.
Keywords: Corruption, investment incentive, infrastructure development, China.
JEL classification codes: D7, H4, O12, O53.
We are grateful to Shuaizhang Feng and Xiaolan Zhou for invaluable assistance. We thank Alberto Batinti,
Sambuddha Ghosh, Srihari Govindan, Dimitar Gueorguiev, James Heckman, Lars Lefgren, David Levine, Lance
Lochner, Francis T. Lui, Arunava Sen, Ling Shen, Andre Veiga, Xi Weng, Jan Werner, Zhiyong Yao, the associate
editor and two anonymous referees for comments. This work is supported by the Chinese National Science Foundation
(Project No. 71573168).
School of Economics, Shanghai University of Finance & Economics, Shanghai, China 200433. Email: bingy-
ongzheng@gmail.com
Economics Discipline Group, UTS Business School, University of Technology of Sydney, Australia. Email:
Junji.Xiao@uts.edu.au
1
Across China, more than 100,000 officials have been disciplined since President Xi Jinping’s
anticorruption drive began...As a result, many others are sitting on their hands...The problem
has become so severe it is ringing alarm bells at the top levels of government.
——— The Washington Post, Feb. 11, 2015
1 Introduction
Traditionally, corruption is considered a hurdle to investment and growth (e.g., Shleifer and
Vishny,1993;Mauro,1995;Fisman and Svensson,2007). China is one of the most corrupt coun-
tries in the world. Despite rampant corruption, however, China is thriving economically, posting an
average growth rate of 10% for three decades powered by investment, particularly infrastructure
investment.1The coexistence of rampant corruption and unprecedented infrastructure develop-
ment poses a serious question: why has rampant corruption not slowed infrastructure development
in China?
Some have suggested that corruption provides an incentive for Chinese officials to promote
infrastructure investment.2This view is not formalized or developed, however, and we therefore
lack an understanding of why and under what conditions corruption can increase investment. The
incentive effect of corruption on government investment is clearly important, especially for policy
evaluations. If corruption is found to be a major factor fueling Chinese officials’ insatiable appetite
for investment, the implications for China’s push for rebalancing and reconsidering the relationship
between corruption and development could be enormous.
This paper develops a principal-agent model to analyze the relationship between corruption
and investment and examines three policies that can be used to combat corruption. In this model,
the principal (the government in this case) hires agents (bureaucrats or officials) to implement
1According to the National Bureau of Statistics of China (NBS), investment accounted for more than 5% of China’s
10% average GDP growth rate during the period of 1984–2015.
2To explain the sharp slowdown in the Chinese economy in 2013 and 2014, for instance, Merrill Lynch, an
investment bank suggests that the major factor behind the slowdown was the “fiscal cliff” that resulted from the
anticorruption campaign initiated by President Xi Jinping and claims that “the room for potential corruption might be
greatly squeezed as a result of the anticorruption campaign, so some officials are disincentivized from starting new
projects.” (Fiscal cliff, Chinese style: why the slowdown in 1Q14? Bank of America Merrill Lynch: China Economic
Weekly, April 1, 2014.)
2
infrastructure investment. Each bureaucrat alone knows the benefit and cost of the project assigned
to him. He chooses costly effort to implement the investment project and the bribe amount to
take from the investment. Although unable to directly observe effort or corruption behavior, the
government can detect corruption and punish corrupt bureaucrats.
The model shows that an incentive to seek bribes can motivate self-interested bureaucrats to
exert costly effort to implement investment, thereby resulting in high investment driven by corrup-
tion. In addition, when facing the choice between stealing at no cost and implementing investment
at a cost, a bureaucrat may abstain from stealing and instead exert costly effort to implement invest-
ment. This occurs when the expected kickbacks from the investment are sufficiently large relative
to the amount that can be stolen and when stealing is easier to detect than bribery. Empirically,
this finding implies that there could be a decrease in nontransactional corruption (embezzlement)
and a simultaneous increase in transactional corruption (bribery in public asset transfers and public
contracts). The stylized facts of corruption behavior in China provide rare supporting evidence.
Furthermore, since investment decisions are made for the purpose of corruption gains, some in-
vestments are bound to be socially inefficient. In particular, corruption distorts government spend-
ing toward investments that feed corruption and away from investments that generate higher social
returns but provide fewer opportunities for corruption. As a consequence, officials’ endless pursuit
of large investment projects would result in wasteful investments. The policy implication of this
theoretical finding is crucial: if government officials attempt to create opportunities for corruption
in designing investment policies, for example, investment subsidies, such policies could lead to
capital market misallocation (see, e.g., Lien et al.,2016).
We consider three policies that can be used to combat corruption and improve investment ef-
ficiency: compensation policy, increased monitoring intensity, and political reforms to enhance
accountability. Our theory suggests that higher wages reduce the likelihood of a bureaucrat be-
ing corrupted but increase the bribe amount demanded by corrupt bureaucrats. In contrast, higher
monitoring intensity reduces not only the number of corrupt bureaucrats but also the bribe amount
under conditions that are realistic for many developing countries. Furthermore, increased moni-
toring intensity in general results in lower investments. An implication of this result is that it is
optimal to strengthen anticorruption enforcement as the marginal benefit of investment declines.
Finally, we find that enhancing accountability helps to reduce corruption and inefficient investment
while at the same time not slowing down growth.
3
Since the theoretical model has a number of predictions that can be tested empirically, we also
provide some empirical evidence in support of the theory. We apply a random effect model to panel
data on corruption and investment in China, and estimate the causal effect of anticorruption effort
on infrastructure investment using the feasible generalized least squares estimation method. Our
empirical findings suggest that anticorruption efforts reduce infrastructure investment, supporting
our major theoretical prediction.
This article contributes to a large literature on the impact of corruption on economic devel-
opment.3Some researchers (e.g., Leff,1964;Hutington,1968;Lui,1985) have suggested that
corruption may improve efficiency, as it allows entrepreneurs to bypass cumbersome regulations
in many developing countries. However, others (e.g., Myrdal,1968 and Bardhan,1997) have noted
that the distortions that corruption is assumed to mitigate are not exogenous and that corruption
may provide officials with an incentive to create more distortions.
Our paper differs from these studies in that the total amount of resources is endogenous and
increasing in efforts to promote investment, whereas the amount of resources for development
is assumed to be fixed in the literature. Thus, according to our model, corruption leads to an
increase in the quantity of investment and a decrease in the quality of investment, and the overall
effect of corruption on development may be ambiguous. This model helps reconcile the seemingly
contradictory findings in empirical studies. Whereas some empirical studies (e.g., Aidt,2009) have
uncovered a negative correlation between corruption and economic performance across countries,
others (e.g., Rock and Bonnett,2004;M´
eon and Weill,2010) have found evidence that corruption
can promote investment and growth, especially in countries with ineffective institutions and poor
governance.4This conflicting evidence prompts Svensson (2005, pp.39) to write the following in
his survey paper: “This finding seems to lead to a puzzle. Most of the theoretical literature as well
as case study and micro evidence suggest that corruption severely retards development. However,
to the extent we can measure corruption in a cross-country setting, it does not affect growth.” In our
model, while the authoritarian regime itself is an impediment to growth, mainly because officials
are not held accountable as their counterparts in democratic societies are, corruption can provide
3There is also a growing literature analyzing corruption in China, for example, Cai et al. (2013), Bai et al. (2014),
Fisman and Wang (2015), Batinti et al. (2019) and Lan and Li (2018).
4There are also studies, e.g., Ehrlich and Lui (1999), M´
eon and Sekkat (2005) and Swaleheen (2011), that report
evidence that the effect of corruption on economic growth is institution dependent.
4
them with an incentive to promote investment. As such, we offer a novel explanation for the so-
called East Asian Paradox—the coexistence of high levels of investment, rapid economic growth
and rampant corruption in China and some other East Asian countries (e.g., Rock and Bonnett,
2004).
In this sense, this paper is more closely related to those that emphasize the trade-off between
market failure and corruption. According to these studies, markets malfunction in many instances,
and corruption results as a byproduct of government intervention designed to correct market fail-
ures (e.g., Acemoglu and Verdier,2000). However, these studies seldom consider the role of
anticorruption policies; therefore, we lack an understanding of how different antigraft policies af-
fect the objectives of government interventions. Mookherjee and Png (1995) analyze the trade-off
among corruption, pollution and compensation policy but consider only the effect of compensation
policy on corruption.
By identifying corruption as an important driver of China’s investment boom, we also offer a
novel explanation of Chinese officials’ incentives to promote investment and therefore also con-
tribute to the literature on the Chinese economy. In this literature, Chinese officials’ addiction to
investment is usually associated with a promotion incentive (e.g., Li and Zhou,2005). However,
some recent studies also consider a corruption incentive, in addition to the promotion incentive, in
explaining China’s economic growth ( e.g., Wang and Zheng,2018;Huang and Zheng,2019;Xu
et al.,2019).
The remainder of the paper is organized as follows. Section 2provides some background
information on infrastructure investment and corruption in China. Section 3sets up the basic
model. Section 4explores the effects of different policies on corruption and investment. Section 5
considers some extensions of the basic model. Section 6presents the empirical evidence. Section
7concludes.
2 Background
Under China’s regionally decentralized authoritarian (RDA) regime, political and personnel
governance are centralized, but economic governance is regionally decentralized. The central gov-
ernment has control over personnel and uses appointment and promotion as tools to induce local
governments to follow the central government’s policies. Local governments, however, are the
5
major actors in the economy. Local government officials assume immense responsibilities for eco-
nomic development. They implement the country’s development agenda and “drive, influence, or
hamper regional/national economic development, macroeconomic conditions, environmental con-
servation or degradation, social stability, etc.” (Xu,2011, pp.1079) At the same time, these officials
also have control over substantial amounts of resources, including land, firms, financial resources,
and raw materials. For infrastructure development, it is usually up to local governments to make
project proposals, obtain approval from the Planning Department of the central government, and
secure the land and funding for investment. No wonder some researchers (e.g., Oi,1992;Walder,
1995;Mei et al.,2016) view local governments in China as “business corporations” and officials
as “entrepreneurs. For example, Oi (1992, pp. 100) wrote “local governments have taken on
many characteristics of a business corporation, with officials acting as the equivalent of a board of
directors. This merger of state and economy characterizes a new institutional development that I
label local state corporatism.
This governance structure begets the principal-agent problem. This arrangement works well
when conforming to the central government’s policies is in a local government’s own interests.
When doing so is not in their own interests, however, local governments frequently ignore or pas-
sively resist the central government’s policies. Indeed, leading officials in local governments often
push through dubious investment in defiance of central government directives and regulations, even
if doing so carries risks. One good example is the so-called “Tieben Incident” (see, e.g., Mei and
Pearson,2014). In 2002, when the central government was attempting to contain overinvestment
in the country’s steel industry, the local government in Jiangsu province helped a local firm, Tieben
Steel, bypass central government regulations to obtain land and loans in its ambitious expansion.
Eight officials, including the leading officials of the local government, were subsequently sacked
or disciplined for sabotaging the central government’s effort to contain overinvestment.
Their control over resources grants local leaders tremendous power, which brings them huge
benefits through corruption. When China began its transition to a market economy in the late
1970s, rigid central planning was in place, and the market did not exist. To obtain capital, land or
other resources, entrepreneurs had to offer bribes to bypass pervasive regulations and controls. In
this sense, corruption was a concurrent evil to encourage government officials to support promarket
reforms.
Even after 3 decades of reform and the implementation of numerous regulations governing
6
public works contracts and land transfers in recent years, leading officials of local governments
can easily bypass regulations and frequently assign contracts or land to favored businesses in return
for kickbacks. Since infrastructure investment creates numerous opportunities for bribes, it also
provides a direct incentive to mobilize government officials to pursue infrastructure investment.
Although corruption has played a role in motivating investment in economic liberalization and
reforms, China’s economic growth is now threatened by overinvestment in low-grade infrastruc-
ture. Many of the infrastructure projects are ill-conceived and have little return if they are not
pure wastes of resources. Based on Chinese provincial data for the period of 1995–2011, Shi and
Huang (2014) found that most of the western provinces in China overinvested in infrastructure in
2008 and that the nationwide large-scale infrastructure investment enacted by the government after
the 2008 financial crisis is not socially optimal. A report by two government researchers (Xu and
Wang,2014) went so far as to claim that since 2009, government stimulus measures and infrastruc-
ture investment had generated US $6.8 trillion in wasted investment, approximately 37% of total
investment. Fig. 1presents the ratio of investment to GDP and the incremental capital-output ratio
(ICOR). The ratio of investment to GDP for China is extremely high, and the return on investment
is deteriorating over time.5
An anti-corruption campaign began at the end of 2012, following the conclusion of the 18th
National Congress of the Communist Party of China. The campaign was notable for implicating
both incumbent and former national-level leaders, demonstrating the ambition of the central gov-
ernment to remove corrupt officials. Since then, more than 200,000 officials have been indicted for
corruption. To monitor local governments and incentivize their anticorruption inputs, the central
government has sent central inspection teams to the local governments, which has significantly
improved anticorruption enforcement.
5ICOR measures the extra investment needed to produce each additional unit of growth in an economy, with
investment as the numerator and the additional GDP as the denominator. The higher a country’s ICOR, the less
efficient its investment; that is, more investment is needed to produce an additional unit of economic output. Here,
as the measure of investment, we use gross capital formation, which, according to NBS, is much smaller than gross
investment in the last decade or so.
7
2 4 6 8
ICOR
.3 .35 .4 .45 .5
INV/GDP
1980 1990 2000 2010
year
INV/GDP ICOR
Fig. 1: The ratio of investment to GDP (INV/GDP) and the incremental capital output ratio (ICOR).
ICOR is a measure of how much investment it takes to produce each additional unit of growth in
an economy, with investment the numerator and additional GDP the denominator. Data source:
National Bureau of Statistics.
3 The basic model
3.1 The setup
There are three types of players in the game: a benevolent government, bureaucrats, and a
continuum of citizens of measure one.
Government: The aim of the government is to implement a set of infrastructure projects. How-
ever, as it lacks the information and expertise needed to implement any projects on its own, it
relies on bureaucrats (also called officials or agents) to collect information, make decisions, and
implement projects. Time is continuous with a common discount factor r.
Citizens: Citizens are risk-neutral and maximize expected payoffs. They care about the private
benefit that can be obtained from a project. Let θibe citizen i’s private valuation of the project
and τibe the lump-sum tax individual ineeds to pay for the investment. Thus, the net payoff
for iis vi=θiτiwhen the project is completed and zero otherwise. The valuation θifollows
the distribution G(·)on [0,
θ]. Apart from the private benefit θi, the investment also generates a
positive externality W0that is not internalized by individual citizens. The cost of the project
is c(0,). However, citizens do not know the true cost c; instead they learn the total b+c
from the announcement of the bureaucrat, where b0is the amount to be taken by the bureaucrat
responsible for the project.
8
There is no practical mechanism that can be used to induce individuals to truthfully report
private valuations θiand charge them accordingly. We assume that when an investment is made,
the cost is equally borne by all citizens and, thus, the lump-sum tax levied on individual iis
τi=c+b. Hence, ex ante, an average citizen expects to receive ¯
θcbfrom the investment,
where ¯
θis the mean of θi. To obtain a closed-form solution, we assume that θifollows a uniform
distribution, and so ¯
θ=
b
θ
2.
After observing his private benefit θiand the sum c+bto be paid for the project, an individual
citizen idecides whether to support or oppose the investment. The proportion of citizens who
oppose the investment over the total population, denoted by M, affects the bureaucrat’s effort cost
in implementing the project and, in turn, the time at which the project will be completed (as we
will describe further momentarily).
Bureaucrats: There are nobservationally identical bureaucrats who differ only in the degree
to which their interests are aligned with those of citizens. Specifically, let ϕkbe a bureaucrat ks
encompassing interest parameter, with ϕk[0,1] for all kn. Below we sometimes omit the
subscript kfor convenience. The non-pecuniary benefit that bureaucrat kobtains from successfully
implementing the project equals ϕk(ivi+W). In general, the encompassing interest parameter ϕ
can be affected by two factors: the institutional mechanism that induces bureaucrats to act in the
interest of citizens (accountability) and a bureaucrat’s intrinsic preference for development.6
A bureaucrat receives a flow payoff V0from working for the government. Here, Vcan
be interpreted as his wage income minus his reservation wage. After observing the characteristics
of a project (W,
θ, c), the bureaucrat chooses the bribe amount bto take from the investment and
the costly effort e[0,)to expend to implement the project. The time tat which the project
is completed depends stochastically on the bureaucrat’s effort e. Specifically, assume that time t
follows an exponential distribution F(t)with mean equal to 1/h(e):
F(t) = t
0
h(e) exp(h(e)s)ds,
where h(e) = δe with δ > 0. When e= 0, the project is not implemented. At the time the project
6Economists and sociologists (see, e.g., Benabou and Tirole,2003 and Akerlof and Kranton,2005) have high-
lighted the importance of intrinsic motivations in incentive provision. According to Besley and Ghatak (2005), the
production of collective goods is mission-oriented since workers in this sector typically perceive an intrinsic bene-
fit from their work. In our model, the mission for bureaucrats is to promote investment and development, and the
successful implementation of socially beneficial investments provides them with an intrinsic benefit.
9
6 6 6 6 -
Government:
announce σI
Bureaucrat:
observe (W,
b
θ, c)
choose (e, b)
announce (b+c)
Citizens:
observe (θi, b +c)
oppose/not
Government:
audit
payoff realized
time
Fig. 2: Timing of events
is completed, the bureaucrat obtains a nonpecuniary benefit that equals ϕtimes the social benefit
of the project in addition to the bribe amount b.
To implement the project, the bureaucrat incurs a private cost C(e), which depends on his effort
level eand the proportion of citizens opposed to the project. Specifically, assume that C(e) =
αe
(1M), where α(0,)is an insulation parameter indicating how costly a given fraction of
opposition is. One interpretation of αis that it reflects the ability of the society to resolve collective
action problems and bear the short-run cost of long-term beneficial projects. A high αindicates
that the society has high cost and therefore that even an urgently needed infrastructure investment
with large Wmay not be made if a sufficiently large proportion of individuals in the economy
oppose the investment. Another interpretation is that αreflects institutional features of the society,
for example, how easy it is to increase taxes to fund an investment, whether land for infrastructure
projects can be acquired and so forth.
The government does not observe the characteristics (W,
θ, c) of a project. However, it can
conduct an audit to determine whether corruption has occurred after the investment, as a result of
which, corruption is detected with probability σI[0,1) (monitoring intensity). For simplicity, we
assume that the government can commit to the monitoring intensity σIto avoid dynamic incentive
problems. When corruption is detected, the bureaucrat is punished by the loss of band the flow
payoff V. Bureaucrats know the monitoring intensity σIbefore making decisions. The timing of
events is summarized in Fig. 2.
Denote by ¯vthe benefit of the project to the economy, ¯v= (¯
θcb+W). Note that when
corruption is not detected, the bureaucrat receives a payoff of ϕ¯v+b, in addition to the flow payoff
V. This occurs with probability 1σI. In the event that corruption is detected, he still obtains the
10
nonpecuniary payoff ϕ¯vbut forfeits band Vfrom the point of detection, which is assumed to be
the same instant that the project is completed. Thus, the expected payoff for the bureaucrat from
choices (e, b) for a project (W,
θ, c) is:
Ub=σI
0
exp(rt)h(e) exp(h(e)t)ϕ¯vdt +
0t
0
Vexp(rs)dsh(e) exp(h(e)t)dt+
(1 σI)
0
exp(rt)h(e) exp(h(e)t)(ϕ¯v+b)dt +V
rαe
1M.(1)
Note that only individuals with θicb0would oppose the investment and, thus, M=(b+c)
b
θ
and C(e) = α
b
θe
(
b
θcb).
Before proceeding, we discuss some of the assumptions. First, we have assumed positive
externalities from infrastructure investment that are not internalized by citizens. This is consistent
with a broad consensus among economists and policy makers. For example, many researchers
(e.g., Aschauer,1989) have noted that infrastructure investment has large positive externalities in
the form of increased productivity, enhanced competitiveness, reduced consumer prices and job
creation. However, there is a large and growing gap between demand and actual spending on
infrastructure globally. Hence, it is reasonable to assume that individual citizens do not internalize
the positive externalities of infrastructure investment.
Second, by incorporating the encompassing interest parameter ϕ, we are assuming that some
bureaucrats may operate in the interests of society. Some discussion of this assumption is worth-
while. Note that the bureaucrats we have in mind are governors and mayors (and also party sec-
retaries in China’s case). In a democratic society, the principal would be the electorate, and the
bureaucrats would be elected officials. In that case, since their re-election usually depends on their
performance in office, it is reasonable to assume that the interests of elected officials are partially
aligned with those of citizens, i.e., ϕ > 0. In an authoritarian regime such as China, this may not
be obvious. In this case, the principal is the central government, and the bureaucrats would be
appointed officials at various levels of government. While local government officials are de facto
dictators in their jurisdiction and not held accountable to citizens, their performance is evaluated
by higher-level governments that decide their career paths. If local government officials want to
have a reasonably good record of GDP growth and social welfare is positively correlated with GDP
growth, then ϕwould not be zero. Judging by the widespread corruption and inefficient investment
as discussed in Section 2, one can tell that on average, ϕis very low for Chinese officials.
Next, citizens can oppose investments that increase the private cost to officials in implementing
11
a project. Government officials face various types of opposition to infrastructural investment, even
in some developed countries. By pushing through projects that are opposed by citizens, elected
officials usually incur some personal cost in terms of its effect on their future election prospect.
Even in China, local governments frequently face resistance, which can cause delays or cancel-
lations.7Moreover, infrastructure investment project usually involves farmland acquisition, and
seizing farmland for development in China sometimes leads to sharp conflicts between farmers
and local governments. Therefore, opposition from citizens carries personal risks to leading of-
ficials of local governments in China, as petitions by locals to higher-level government or social
unrest resulting from land requisition usually have a negative impact on their careers. In addition,
it is usually true that the stronger the opposition is, the higher the personal risk is.
Finally, we assume that citizens know the cost c+b. This is plausible, at least in some cases.
In China, for example, local officials often seize rural land with little compensation in the name
of development. They can then sell the requisitioned land at a market price that is usually much
higher than the acquisition price, use the land as collateral to secure bank loans or assign it to
favored businesses. For the farmers who lose their land, the difference between the requisitioned
price and market price of their land is the cost c+bthat they have to pay for the development.
3.2 No anticorruption in infrastructure development
We first analyze a bureaucrat’s optimization problem in the case of σI= 0. This allows us to
focus on the key point of the paper: corruption incentives lead to investment. The method proceeds
in two steps. In the first step, we fix the bribe amount band find the bureaucrat’s optimal effort
level eas a function of the bribe amount. In the second step, we determine the optimal bribe
amount bfor the bureaucrat.8
When σI= 0, the bureaucrat chooses effort eand bribe amount bto maximize his expected
7As one example, the planned maglev train from Shanghai to Hangzhou was first postponed and then scrapped due
to opposition by the public.
8From the bureaucrat’s perspective, he understands that his choice of bdetermines M, the opposition to the invest-
ment, which in turn affects his effort cost C(e). Hence, optimal effort eis a function of b, suggesting a backward
induction approach to the problem.
12
payoff:
Ub=δe(ϕ¯v+b)
δe +r+V
rαe
θ
θcb.
Here, ¯v=¯
θcb+W. To simplify the notation, let u=ϕ(¯
θc+W)+b(1ϕ),ˆv= (
θcb)
and λ=αr
b
θ
δ. We have the following result:
Proposition 1. (1) Under the condition that λ < uˆv, optimal effort
e=r
δuˆv
λ1
2
1>0.(2)
(2) The expected time for the project to be completed is equal to 1
[r(uˆv/λ1)] .
According to this result, therefore, two almost identical economies but with different insulation
parameters αmay have different development outcomes. This prediction is in accord with obser-
vations from many developing countries. For example, one factor frequently cited to explain the
difference in infrastructure development between China and India is that Chinese society is more
homogeneous and more capable of resolving collective action problems than Indian society. The
parameter αcan also be interpreted as reflecting the coercive power of the government. In gen-
eral, authoritarian regimes are less constrained by citizen opposition than democratic regimes. For
example, whereas local governments can usually appropriate rural land without much difficulty
in China, land for infrastructure projects or factories is often impossible to acquire at any price
in India. As we will show in Section 5, this difference may also affect the types of corruption in
different countries.
When λuˆv, however, optimal effort would be zero, and no investment would be made. In
what follows, we therefore consider only the case that investment is made, λ < uˆv, and determine
the bureaucrat’s optimal bribe amount bfrom the investment.
Inserting einto the expected payoff function, we then differentiate Ubwith respect to b, which
yields
∂Ub
∂b =1λ
uˆv1
2(1 ϕ)(λu)1
2
ˆv3
2.(3)
Under the condition λ<uˆv,∂Ub
∂b <0when ϕ= 1. Kuhn-Tucker conditions then imply that the
optimal bribe amount b= 0; that is, a bureaucrat whose interest is completely aligned with the
13
interest of the society would take no bribe. The intuition for the result is straightforward. The
marginal benefit from any bribe b > 0is zero, while the marginal cost is strictly positive for a
bureaucrat with ϕ= 1; thus, a bureaucrat with ϕ= 1 will voluntarily choose zero bribe. A
continuity argument would then indicate that one with ϕsufficiently close to 1 would also choose
b= 0. The result below shows that this is indeed true.
Let
p=λ
(1 ϕ), q =λ[(1 ϕ)(
θc) + ϕ(¯
θc+W)]
(1 ϕ)2,
and ∆ = q
22+p
33. We make the following assumption:9
Assumption 1. λ < (¯
θc+W)(
θc).
Proposition 2. Suppose that Assumption 1holds. (1) There exists ϕ0(0,1) such that when
ϕϕ0, the optimal bribe amount b= 0, and when ϕ < ϕ0,
b=q
2+ ∆1
21
3+q
21
21
3+ (
θc).(4)
(2) The optimal bis decreasing in ϕand W.
In the Appendix, we provide the formula for ϕ0(equation (A.2)) and show that bis positive
but less than (
θc)if ϕ < ϕ0(see Lemma 3).
Before proceeding, we elaborate on some of the results. A bureaucrat’s effort eis positively
related to the bribe amount bwhen ϕis small. Indeed, one implication of Proposition 1is that a
bureaucrat who does not care about social welfare or is not held accountable (ϕ= 0) would exert
no effort unless he can personally benefit from the investment. This is true even if the project
under consideration could generate a substantial benefit (high W) for society and the majority
would support the investment (small M). In fact, it is not difficult to see that, absent the gain from
corruption as a bonus, socially beneficial projects would not be implemented by bureaucrats with
positive but relatively small ϕ, which is typically the case in societies with low accountability but
high effort cost (large α).
This, however, does not mean that corruption is good for economic development. By siphoning
off part of the gains that might have been realized from the investment, corruption undermines the
9Recall the definitions of uand ˆv. Note that when ϕ= 1,u=¯
θc+Wand ˆv=
θc. Thus, Assumption 1
helps rule out the case that λis so large that the optimal effort would be zero even for a bureaucrat with ϕ= 1.
14
very purpose of government intervention. Moreover, unbridled corruption gives rise to inefficient
investment. To illustrate the last point, consider a project with ¯
θ < c and W= 0, indicating
negative returns even absent corruption. However, under certain conditions, the project will still
be implemented.
Proposition 3. Suppose that ¯
θc+W < 0and λ < (
b
θc)2
4. Then, a bureaucrat with sufficiently
low ϕwould exert positive effort (e>0) to implement the inefficient project.
That is, a self-interested bureaucrat may make an investment that has little social value simply
because it affords him an opportunity to take kickbacks. Therefore, we would expect the govern-
ment to institute some mechanisms to prevent corruption and resource misallocation. This is the
focus of the next section.
4 Government policies to combat corruption
4.1 Bureaucrat’s choices
For a given monitoring intensity σI, the optimization problem facing a bureaucrat who takes a
bribe is:
max
e,b Ub=δe[ϕ(¯
θc+W) + (1 σIϕ)bσIV/r]
(δe +r)
θ
θcb+V
r
s.t. e 0, b > 0.
From the above discussion, we know that under certain conditions, a bureaucrat may choose
not to take any bribe. For the discussion to be non-trivial, we make the following assumption:
Assumption 2. σIV
r(1σI)<(
θc).
Assumption 2ensures that at least some bureaucrats will take a bribe. To see this, recall that the
maximum bribe the bureaucrat can take is no more than
θc, so the right-hand side of the inequality
is the upper bound of the benefit from bribe taking. The left-hand side is the expected cost from
bribe taking, which is increasing in σI. When σIis sufficiently close to 1 such that σIV
r(1σI)>
θc,
no bureaucrat would find it profitable to take any bribes. To exclude this uninteresting case, we
therefore make this assumption.
15
Let ˜u=ϕ(¯
θc+W) + (1 ϕσI)bσIV/r,ˆv=
θcb, and let
˜p=λ
(1 σIϕ),˜q=λ[ϕ(¯
θc+W)σIV/r + (1 σIϕ)(
θc)]
(1 σIϕ)2,
˜
∆ = ˜q
22+˜p
33. We can solve for the bureaucrat’s optimal choices of effort and bribe amount
when government anticorruption enforcement exists. This is given in the following result.
Proposition 4. Suppose Assumptions 1and 2holds. (1) There exists ϕσsuch that when ϕϕσ,
˜
b= 0, and when ϕ < ϕσ,˜
b=˜q
2+˜
1
21
3+˜q
2˜
1
21
3+ (
θc). (2) Optimal effort
˜e= ( r
δ)˜uˆv
λ1
21if λ < ˜uˆv, and ˜e= 0 otherwise.
Note that ϕσ=ϕ0when σI= 0, but ϕσ< ϕ0when σI>0.
4.2 Comparative statics
Next, we analyze how government policies affect corruption and the bureaucrats’ efforts on
investment. While there are other tools that the government could use to combat corruption, we
consider only three instruments: monitoring intensity σI, compensation policy Vand enhanced
accountability ϕ.
First, we look at the effect of monitoring intensity on corruption and investment.
Proposition 5. Suppose Assumptions 1and 2hold and that σIgoes up. (1) ϕσdecreases. (2) ˜
b
increases under the condition
V
r[(1 σIϕ)(
θc)+2ϕ(¯
θc+W)]
1ϕ+σI
,(5)
and decreases under the condition 10
V
r<[(1 σIϕ)(
θc)+3ϕ(¯
θc+W)]
22ϕ+σI
.(6)
(3) ˜edecreases under the condition
(1 σIϕ)
θc+2V
r+σIV
rϕ(¯
θc+W).(7)
10The two cutoffs are not equal mainly because the magnitudes of ϕand Wcan also affect the effect of changes in
σon b. Note that σI<1ϕimplies that [(1σIϕ)(
b
θc)+2ϕ(¯
θc+W)]
1ϕ+σI>ϕ(¯
θc+W)]
1ϕ, and thus,
[(1 σIϕ)(
θc)+3ϕ(¯
θc+W)]
22ϕ+σI
<[(1 σIϕ)(
θc)+2ϕ(¯
θc+W)]
1ϕ+σI
.
16
According to Proposition 5, an increase in monitoring intensity reduces the extent of corrup-
tion by preventing minor corruption. The effect of increases in monitoring intensity on the bribe
amount, however, can be positive or negative depending on the wages of bureaucrats. When wages
are low, such that (6) holds, increases in monitoring intensity result in a lower bribe amount. When
wages are high, such that (5) is satisfied, however, increases in monitoring intensity lead to a
higher bribe amount. As discussed above, the bureaucrat’s wage V/r is actually the difference
between his legal income and reservation wage, the alternative wage he can obtain in the market.
In many developing countries, the average pay for officials is low and therefore it is more likely
that condition (6) holds.
Next, we consider the effect of compensation policy on corruption and investment.
Proposition 6. Suppose Assumptions 1and 2hold. An increase in Vleads to a decrease in ϕσ, an
increase in ˜
band a decrease in ˜e.
An increase in wages reduces minor corruption and this helps lower extent of corruption in
the economy. Meanwhile, an increase in wages leads to a higher bribe amount demanded by
corrupted bureaucrat. At first glance, this may appear somewhat surprising; however, the intuition
is simple. Since the bureaucrat trades off the benefit against the expected cost of taking bribes,
he will naturally demand a higher bribe amount when higher wages increase the expected cost of
corruption. Moreover, higher fixed pay also lowers bureaucrats’ incentive to implement investment
for corruption gains.
Finally, we analyze how government can affect corruption by enhancing accountability. From
the above discussion, we see that the encompassing interest parameter ϕcan affect the impact of
anticorruption enforcement on government intervention and corruption. In addition, the following
result shows that an increase in ϕresults in more socially beneficial investment and less corruption.
Proposition 7. Suppose Assumptions 1and 2hold. An increase in ϕleads to a decrease in ˜
b, and
an increase in ˜ein any project with ¯
θc+W0.
Above, we also show in Proposition 3that bureaucrats with a high ϕhave no incentive to imple-
ment socially inefficient investment. Together, the two results (Propositions 3and 7) demonstrate
the importance of increasing the encompassing parameter to simultaneously reduce corruption and
promote investment. Therefore, if developing countries can successfully institute accountability
17
mechanisms to increase ϕ, they may be able to promote infrastructure development and economic
growth while simultaneously mitigating corruption. This is perhaps why development economists
have devoted so much attention to the reform of bureaucracies and institution building in develop-
ing countries (e.g., Xu,2011).
There are several ways for the government to enhance accountability to better align the in-
terests of bureaucrats with those of society. First, the government can use screening to select
bureaucrats with higher ϕks to fill positions, “matching on mission preferences” as suggested in
Besley and Ghatak (2005). Next, this screening mechanism needs to be reinforced with political
reforms that help improve the monitoring and evaluation of bureaucrats, such as separating moni-
toring and law enforcement mechanisms from local governments. Currently, many regulatory and
law enforcement agencies in China are part of local governments. Thus, officials are evaluated by
and accountable to their superiors, who face inherent and difficult informational problems in as-
sessing their performance. An independent press and independent judiciary would be much more
effective at monitoring officials and should greatly enhance the latter’s accountability. Moreover,
a more effective monitoring mechanism will also reduce the difficulty in matching candidates to
government jobs: More effective monitoring decreases the expected payoffs of bureaucrats with
a low encompassing parameter ϕand therefore discourages them from seeking government jobs
with large non-pecuniary payoffs but low monetary compensation. Ultimately, however, the so-
lution should be political reforms that allow citizens to choose officials and play an active role
in decision-making on local developments. The government faces inherent and difficult informa-
tion problems in evaluating the benefits of investments and in monitoring officials’ performance.
However, the information problem will be less severe for citizens, especially in evaluating the per-
formance of local officials. If the prospect of re-election is closely linked to performance, then
the interests of officials are more likely to be aligned with those of citizens than if officials are
appointed from above.
18
5 Extension
5.1 Allow stealing
In this section, we assume that each bureaucrat needs to simultaneously perform two tasks. The
first is to implement infrastructure investment at a cost as described in the basic model, while the
second is to administer a government-spending program E. We assume that fulfilling this task is
costless and, thus, the only choice for a bureaucrat is how much to steal, denoted by s. Stealing
will be detected with probability σE(0,1). For simplicity, we assume that the probability of
detection σEdoes not depend on s. Suppose that the maximum that a bureaucrat can steal is ¯s.
Further assume that σI< σE, i.e., it is easier to detect the misappropriation of government funds
or embezzlement than to detect bribe taking.
In this case, without stealing, a bureaucrat expects to obtain U
b=Ube,˜
b)from the infras-
tructure investment, which equals V/r if ˜e= 0 and is greater than V/r if ˜e>0; with stealing s,
his total payoff would be (1 σE)(s+U
b). This is the case because once he is caught stealing
public funds, he not only needs to return the amount sthat he stole but also forfeits his job and,
with it, opportunities to obtain kickbacks from infrastructure investment. Hence, he would have no
incentive to steal if (1 σEsσEU
b. Since U
bis decreasing in both σIand αbut increasing in
(¯
θc)and V, we have the following result:
Proposition 8. Given (V , σI, α), there exists ˆσE<1such that the optimal s= 0 if σEˆσE. In
addition, ˆσEis increasing in σIand αbut decreasing in Vand (¯
θc).
That is, the easier it is to implement infrastructure projects (smaller α) from which substantial
bribes can be collected, the less likely a bureaucrat is to steal public funds. Additionally, when a
large bribe can be taken from investment (bis increasing in ¯
θc), a bureaucrat would have no
incentive to steal. This perhaps sheds some light on the paradox that countries ranked similarly on
Transparency International’s Corruption Perception Index may have totally different development
outcomes: In some developing countries, corruption mainly takes the form of stealing, which
impedes development. In contrast, in some East Asian countries, including China, while corruption
still entails inefficiency and the misallocation of resources, it at least provides officials an incentive
to promote investment and economic growth.
Of course, this type of corruption-promoted development may be infeasible in other developing
19
countries, as other governments may not be able to seize privately owned land that they can resell
for a profit or use as collateral to secure bank loans, as is typically done in China. Even in China,
this type of practice became possible only in the early 1990s, when the central government allowed
local governments to requisition rural land for development to give them an additional source of
revenue. Therefore, it is not surprising that corruption in the form of stealing was more common
before then. Data show that most corruption cases involving government officials in China before
the 1990s consist of embezzlement and misappropriation (see Section 6).
5.2 Choice of projects
In Section 3, we assumed that a bureaucrat can work on one project only. In this section, we
consider a scenario in which the optimal decisions for the bureaucrat also include choosing among
multiple projects.
To illustrate how corruption incentives affect the types of investment that will be made, we
assume that there are two different projects and that a bureaucrat chooses only one of the two to
implement. For simplicity, assume that the two projects differ only in the positive externality W
and the probability of corruption being detected. In particular, let the two projects be denoted by
(W1, σI1) and (W2, σI2). Assume that W1> W2and σI1> σI2. Then, it is true that a self-interested
bureaucrat, one with ϕ= 0, always chooses (W2, σI2) over (W1, σI1). Furthermore, the same is
true of bureaucrats who do not care much about social welfare, i.e., those with low ϕ. We present
the result as follows:
Proposition 9. Suppose that there are two projects with W1> W2and σI1> σI2that are oth-
erwise identical. There exists ϕsuch that bureaucrats with ϕϕimplement project (W2, σI2)
instead of (W1, σI1).
Thus, bureaucrats with low ϕwould choose projects with low social benefit over those with
high benefit simply because the corruption is less likely to be detected in the former than in the lat-
ter. Previous studies, for example, Shleifer and Vishny (1993), note that officials in poor countries
may import goods on which bribes are easy to take without being detected rather than goods that
are the most profitable for firms or for the country. Our result is consistent with their prediction.
20
6 Empirical evidence
The theoretical model provides several testable predictions. In this section, we use provincial-
level macrodata from China to provide some empirical evidence consistent with the theoretical
model.
6.1 Data
We apply data on infrastructure investment to test our theory. According to the report on the most
corrupted industries by Charney Research in 2014,11 investment in infrastructure is one of the
categories most susceptible to corruption in China. For example, the incidence of corruption is
42% in transport infrastructure construction among all their surveyed investment projects.
Infrastructure investment refers to investment in the utilities and facilities that provide essential
services and help drive economic growth and productivity. Infrastructure can be divided into three
major sectors: 1) utilities, such as electricity, gas, communications and water; 2) transport, such as
airports, roads, seaports and rail; and 3) social services, such as education facilities, hospitals and
other community facilities.
For our empirical analysis, we use provincial data on fixed-asset investment in infrastructure.
The data on fixed investment are available from the China Statistical Yearbook 2000–2016 pub-
lished by the National Bureau of Statistics (NBS). NBS reports the fixed investment by sector of
the national economy. For infrastructure investment, we use the sum of fixed investments from 10
sectors in the period of 2004–2016.12
The data on anticorruption efforts are collected from provincial Senior Procuratorate’s Reports.
In annual reports, provincial Chief Procurators report the numbers of officials involved in corrup-
tion in their provinces in the previous year.13 We can obtain two variables for this measurement:
11Corruption in China: What Companies Need to Know, by Craig Charney and Shehzad Qazi, 2015.
12These sectors include (1) electricity, gas and water supply; (2) transportation; (3) information and software;
(4) water resources and environmental management; (5) scientific research and geological investigation; (6) services
to citizens and other services; (7) education; (8) health and social security; (9) culture and sports; and (10) public
administration and social organization.
13The Procuratorate’s Yearbook of China includes the annual Senior Procuratorate’s Report of each province. For
2004–2010, the data can be obtained from the Procuratorate’s Yearbook. For 2011–2016, provincial procuratorates’
reports are collected from their websites or local newspapers.
21
the total number of corrupted officials and the number of corrupted senior officials (those holding
leadership positions at or above the county level). Unfortunately, some provinces report only one
or two numbers randomly in our sample periods; consequently, there are many missing values for
these variables. Of a total of 403 observations, 27 observations are missing for the number of
corrupted officials and 31 are missing for the number of corrupted senior officials.
We propose to use the number of corrupted officials as a proxy for the anticorruption efforts
(denoted anticorr) of the local government since it is closely related to the monitoring intensity σI
in the theoretical model: when the local government spends more efforts on anticorruption activity,
this number increases because conviction rates will increase. However, one problem with anticorr
is that the anticorruption efforts are entangled with corruption forces. Formally,
anticorr =#(corrupted)
#(off icials)×#(charged)
#(corrupted)
where the first part of the right-hand side of this equation measures the incidence of corruption and
the second part measures the conviction rates determined by σI. As the corruption incidence is
unobservable and may be correlated with investment decisions,14 we have to resort to our theory to
tease it out from our proxy measurement of σI. We will discuss this in Section 6.2. In practice, we
standardize this number by the number of government employees. Specifically, our measurement
of anticorruption efforts (denoted anticorr) is the ratio of corrupted officials to 10,000 government
employees.
To control for provincial heterogeneities, we also collect the following macro-economic data
from the China Statistical Yearbooks (2000–2016). First, Proposition 1suggests that optimal ef-
forts depend on the insulation parameter α, which measures the government’s cost of collective
actions. In our study, a crucial cost factor of effort input into infrastructure investment is the land
acquisition costs, which vary across provinces and over time. We collect the total sizes and values
of land purchased by the real estate development enterprises in various ways to obtain land-use
14We thank an anonymous reviewer for comments on this issue of the potential correlation that could be due to
selection effects regarding the officials who are caught. For example, when officials have lower income, they are more
likely to make greater investments to secure larger bribes, thereby generating a positive correlation between corruption
incidence and investment.
22
rights;15 then, we define the unit cost of land acquisition (luc) as
luc =Total value paid for land acquired
Area of land acquired .
This is the cost the real estate developers pay the government and, thus, it is a proxy of the land
acquisition cost of the government from the original land users because the government usually
sets its transfer price to real estate developers by just adding a markup over its acquisition cost.16
Second, we collect the investment in real estate. We need this variable to control the endogene-
ity issue with luc in our analysis of infrastructure investment: real estate investment will increase
house prices, which are correlated with the land acquisition costs (luc), and induce infrastructure
investment. Therefore, we must isolate the real estate investment from the error terms of the re-
gression of infrastructure investment on luc; otherwise, omitted variable bias will arise. Third, we
collect the data on the average wage of employees in the sectors of public management and social
organization. Proposition 6suggests that the incidence of corruption decreases with the wage of
employees in administrative sectors; therefore, we use the wage data to disentangle the corruption
forces entwined in variable anticorr (see section 6.2 for details). Here, wage is the average annual
wage of employees working in public administration and social organizations. Finally, to measure
the development level of each province, we also collect the per capita GDP of each province.
Table 1presents the summary statistics of the variables in our analysis. Note that we have
divided investment and GDP by population to obtain their per capita measurement at the province
level (e.g., infra inv for infrastructure investment and real inv for real estate investment). All
pecuniary values are measured in RMB. In total, we have 375 observations for empirical analysis.
The data show different patterns of bribery cases and embezzlement cases.17 One implication
of our theory is that an increase in investment can lead to a decrease in nontransactional corruption
(embezzlement) and an increase in transactional corruption (bribery in public assets transfers and
15The total values paid for land acquisition include: (1) the land compensation fees, land attachments and young
crops compensation, resettlement and land compensation fees, and collection and management fees for lands obtained
through land-use-rights allocation; (2) premiums charged by the government for lands obtained through the sale of
land-use rights; and (3) the value bid for lands obtained through procurement auction.
16The government is the land owner in China; however, the government usually compensates land users for the
transfer of usage rights.
17The Procuratorate’s Yearbook of China reports national corruption cases by categories. Unfortunately, no such
information is available at the province level. Note also that embezzlement here is a sum of 2 categories: embezzlement
cases and misappropriation cases as reported.
23
.35 .4 .45 .5
INV/GDP
.2 .3 .4 .5 .6
Ratio of Bribery/embezzlement to corruption cases
1999 2004 2009 2013
year
embezzlement bribery INV/GDP
Fig. 3: Ratios of bribery and embezzlement to total corruption cases & investment/GDP ratio
(INV/GDP). Data sources: The Procuratorate’s Yearbook of China.
public contracts) since embezzlement offsets part of infrastructure investment while transactional
corruption increases the volume of infrastructure investment. Fig. 3presents the ratios of bribery
and embezzlement cases to total corruption cases and the ratio of infrastructure investment to
GDP.18 While the ratio of bribery cases to total corruption cases is increasing, following closely
the trend in the ratio of investment to GDP, the ratio of embezzlement to the total is decreasing.
These patterns are consistent with our prediction that more opportunities for kickbacks reduce
officials’ incentives to steal.
6.2 Strategy of the empirical test
The primary prediction of our theory is that an increase in monitoring intensity (σI) has a neg-
ative impact on investment susceptible to corruption (Proposition 5).19 All else being equal, an
18The Procuratorate’s Yearbook of China reports national corruption cases by categories. Unfortunately, no such in-
formation is available at province level. Further note that embezzlement here is a sum of two categories: embezzlement
cases and misappropriation cases as reported.
19The inequality condition (7) must hold in China’s case for the following reason. Recall that parameter ϕindicates
to what extent officials’ interests are aligned with those of society. While some officials may care greatly about citizens’
interests (high ϕ), on average, the parameter ϕshould be close to zero. Local government officials are appointed from
above and many have to bribe their superiors to be promoted. As discussed in Section 2and the discussion following
the model setup in Section 3.1, it is highly likely that they would not care much about the interest of the society, so
ϕis very low. Meanwhile, before the current anticorruption campaign, corrupted officials were seldom caught and
24
increase in anticorruption intensity decreases the effort taken by local government officials to pro-
mote such investment and therefore reduces investment.
To test the theoretical predictions, we will apply our data to an empirical model given by
I=f(A, X)
where Iis the infrastructure investment, Ameasures the anticorruption intensity and Xconsists
of other control variables. If our empirical analysis supports the theoretical prediction, we should
have ∂I
∂A <0.
One concern with our regression analysis is the measurement of anticorruption monitoring
intensity (σI). The proxy variable we will use is the number of corrupted officials reported by
the Procuratorate’s Yearbook (anticorr), which actually represents both anticorruption intensity
and corruption incidence. To tease out the factor of corruption incidence, we apply the equilib-
rium bribery conditions as summarized in Proposition 6. Basically, the equilibrium bribery should
be negatively correlated with wage in the public sector. By the Frisch-Waugh-Lovell theorem
(Frisch and Waugh,1933;Lovell,1963), we can incorporate the major determinants of corrup-
tion forces into the regression of infrastructure investment on the reported number of corrupted
officials (anticorr). The coefficient of anticorr then measures the marginal effect of the anticor-
ruption intensity since the corruption forces are teased out by the most related determinants, such
as wage.
To test if wage is the most important determinant of corruption, we run a regression of anticorr
on wage. A hypothesis test is conducted to check whether our theory (Proposition 6) can be
supported and whether our proposed method of teasing out the twisted force of corruption from
anticorr is justified. In addition, to provide some evidence that anticorr is the product of both
corruption incidence and anticorruption intensity, we also run a regression of anticorr on both
wage and an anticorruption campaign dummy. We expect anticorr to be negatively correlated
with wage but positively correlated with anticorruption force. Empirical findings consistent with
our prediction imply that anticorr consists of these two components and justify our use of wage to
control the component of corruption incidence in anticorr (details will be reported in section 6.3).
We also control other confounding factors in our analysis of infrastructure investment following
punished, implying a low σIat least before the anticorruption campaign. Thus, a low ϕand low σItogether should
ensure that the inequality holds in China’s case.
25
the theoretical predictions. Proposition 1suggests that optimal efforts depend on the insulation
parameter α; therefore, as discussed in the last section, we use the unit cost of land acquisition as
the proxy for this parameter and control the provincial heterogeneity in this dimension.
6.3 Evidence of anticorruption enforcement and investment
We first test the relationship between infrastructure investment and its determinants as suggested
by Proposition 1. Our empirical model is given by equation (8) as follows,
ln inf ra invi,t =ρ0+ρ1luci,t +ln real invi,t +Di+Dt+εi,t (8)
where ln inf ra inv is the logarithmic per capita investment in infrastructure, as defined in Sec-
tion 6.1.luc is the unit cost of land acquisition. ln real inv is the logarithmic per capita investment
in real estate. This variable is controlled to avoid the omitted variable bias since infrastructure in-
vestment is to some extent a derived investment following real estate investment. Subscripts iand
tare indexes for province iand time t, respectively. The fixed effects Diand Dtcapture other
heterogeneity across provinces and over time, respectively. We assume the error term ϵi,t satisfies
the assumptions of strict exogeneity of the panel data, that is, E(ϵi,t|xi) = 0, where xiis a vector
of covariates for province i, and there is no autocorrelation among the errors across provinces and
over time, i.e., cov(ϵit, ϵj s) = 0, if i̸=j, or i=jbut t̸=s. The strict exogeneity assumption
ensures that the feasible generalized least squares estimator (FGLS) is consistent when Diis inde-
pendent of luc and ln real inv, which makes equation (8) the random effect model. However, a
contemporaneous correlation between the error term and real estate investment could exist since a
common shock could influence the investment in both the infrastructure and real estate sectors. To
solve this problem, we use a one-period lag of real estate investment as our independent variable
in the regression.
Table 2reports the results from regression (8).20 Column (1) corresponds to the same model
specification as equation (8), while column (2) corresponds to a modified specification with a one-
period lag of infrastructure investment in the regressors to capture the time trends of investment
changes. The results are consistent with the theoretical prediction that infrastructure investment
efforts are negatively correlated with the cost of resolving collective action problems, represented
20 Estimates of province fixed effects are not reported in the table since they are not our primary interest.
26
by the insulation parameter α. In addition, the results suggest that part of the infrastructure in-
vestment is derived from real estate investment. Usually, real estate developers negotiate with the
local government for infrastructure construction when they develop real estate projects, and thus,
these two types of investments are usually positively correlated. The estimates of time fixed effects
demonstrate obvious time trends over sample periods, which justifies the inclusion of lagged in-
frastructure investment in the regressors. The coefficient of the lagged infrastructure investment is
positive and significant, indicating an upward growth trend of infrastructure investment; however,
the coefficient is less than one, suggesting that the growth rate is decreasing over time.
Before adding the measurement of anticorruption efforts to the baseline model, we have to test
if the wage in the public administration sector is a valid instrument to tease out the confounding
factor of corruption incidence in the variable anticorr following Proposition 6. Our empirical
model for this test is given by
anticorr =wag+Di+Dt+µit (9)
Table 3reports the results of this regression. For the dependent variable, anticorr, we have
two measurements: 1) the logarithmic number of corrupted officials (anticorr1, with correspond-
ing results reported in columns 1-2) and 2) the logarithmic number of corrupted senior officials
(anticorr2, with corresponding results reported in columns 3-4). Columns (1) and (3) correspond
to the specification given by equation (9), while columns (2) and (4) correspond to the specifica-
tions with the addition of the anticorruption campaign dummy (but dropping the year fixed effects).
The anticorruption campaign started in 2013 and continued until the last period of our sample.
Our results show that the coefficients of wage are negative and statistically significant in all
specifications, supporting Proposition 6. The time effects are insignificant for the number of offi-
cials (anticorr1) but are significant for the number of senior officials (anticorr2) over periods ex
post campaign. Consistently, the magnitude of the campaign coefficient in the anticorr2regression
is larger than that in the anticorr1regression. This finding confirms the belief of many people that
the campaign targets high-ranking officials and has political purpose. The coefficient of campaign
is positive and significant, suggesting that it could identify the anticorruption efforts twisted in the
variables of anticorr. Overall, the model fitness is good as the coefficient of determination (R2) is
high.
Based on our baseline model equation (8) and our findings from equation (9), we further add
27
the anticorruption effort measurement and wage into the model and test Proposition 5. The full
regression model is given by
ln inf ra invi,t =ρ0+ρ1luci,t +ρ2ln real invi,t +ρ3anticorrit +ρ4wageit +Di+Dt+εi,t (10)
By the FWL theorem, this regression amounts to running two-stage regressions: First, we
regress infrastructure investment and anticorr on wage and the other control variables, respec-
tively, generating the residuals of these two regressions (ˆeinv
it and ˆeanti
it , respectively). Second, we
regress ˆeinv
it on ˆeanti
it , and the estimator from this regression should be the same as the estimator
of ρ3in the full regression model (10). However, this two-stage regression offers us more insight
into the meaning of the coefficient of anticorr in equation (10) since wage is an instrument to
disentangle the corruption incidence entwined in anticorr.ˆeanti
it largely measures the anticorrup-
tion intensity, and thus, its coefficient in the second-stage regression reveals the causal relationship
between anticorruption intensity and ˆeinv
it , which is the part of infrastructure investment that is not
explained by economic variables such as wage and other real estate investment. The estimator of
ρ3should have the same meaning.
Table 4presents the results from the regression of the full model. We use the number of cor-
rupted officials as the measurement of anticorruption monitoring intensity (anticorr1) in columns
(1)-(3) and use the number of senior corrupted officials (anticorr2) as the proxy for the same mea-
surement in columns (4)-(6). Columns (1) and (4) use the binary variable campaign to measure
the exogenous national shocks in anticorruption intensity, while columns (2) and (5) capture these
shocks using year fixed effects. Furthermore, columns (3) and (6) capture the time trend in anti-
corruption intensity by using a one-period lag of the anticorruption measurement. The provincial
fixed effects are included, but their coefficients are omitted. All other control variables are the
same as those in the baseline models.
The coefficients of anticorr1are negative and significant in all model specifications, supporting
our theoretical prediction. By controlling the wage in the administrative sectors, this variable
measures the anticorruption intensity, and thus, our results suggest that infrastructure investment
decreases with anticorruption intensity; in other words, when corruption cost is lower, there will be
more corruption and, simultaneously, more infrastructure investment. The coefficient of anticorr2
is negative and significant in columns (5) but not in the other specifications. However, as we
have explained above, anticorr2is also confounded by political factors and is not a very good
28
instrument for anticorruption intensity. Hereafter, therefore, we will use the first three columns to
interpret our results.
The coefficients of the other variables are also as expected and are similar to the results for the
baseline model. The results in column (3) with the lagged dependent variable differ from those in
the first two columns. For example, the coefficients of both the unit cost of land acquisition and
wage are not significant. This difference could be caused by a multicollinearity problem due to the
correlation between the lagged dependent variable and these two variables.
7 Conclusion
This paper analyzes the links between corruption and government infrastructure investment.
The model demonstrates that corruption incentives can drive public infrastructure investment and
predicts that increased anticorruption enforcement in general reduces investment. Moreover, it
shows that the ability of a society to resolve collective action problems may not only affect its
development outcome but also determine the types of corruption that it faces. Empirical tests
using Chinese provincial data provide evidence in support of the theoretical predictions.
Compared with previous studies based on promotion incentives, this paper provides a novel
explanation for Chinese officials’ obsession with large investments. For policy makers, under-
standing the effect of corruption incentives is important. If promotion incentives alone lead to
overinvestment, then terminating the practice of promoting officials on the basis of GDP growth
or evaluating officials using more comprehensive measures that include social development in ad-
dition to economic growth should be effective. However, if corruption incentives are important,
then such measures will not be enough. In this case, anticorruption enforcement can be a useful
tool to rein in excessive investment. It may not be a pure coincidence that the government headed
by President Xi is clamping down on corruption while simultaneously attempting to rebalance
the Chinese economy and shift from investment-driven toward consumption-based growth. Thus
far, the campaign has caught more than 180 “tigers, senior officials at the ministerial level or
above, and as a result, investment has declined significantly. Our results suggest that China may
need to implement far more serious measures than punishing corrupt officials. In particular, if it
is to succeed in the goal of eliminating corruption and promoting balanced growth, institutional
reform must accompany the anticorruption struggle to hold officials accountable and increase the
29
transparency of government decisions.
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33
Appendix A. Empirical results
Table 1
Summary statistics: 31 provinces from 2004–2016
obs. mean sd min max
Infrastructure Investment 375 0.65 0.48 0.08 2.80
(RMB 10 thousands per capita)
Real estate Investment 375 0.51 0.44 0.03 2.14
(RMB 10 thousands per capita)
Reported Corrupted Officials 375 1477.26 902.87 36.00 4523.00
(anticorr)
GDP per capita 375 3.15 2.15 0.43 10.69
(RMB 10 thousands per capita)
Financial Investment 375 0.01 0.01 0.00 0.14
(RMB 10 thousands per capita)
Tourism Investment 375 0.03 0.03 0.00 0.21
(RMB 10 thousands per capita)
Ratio of College Graduates (per 10 thousand people) 375 0.02 0.01 0.00 0.04
Openness 375 0.31 0.39 0.04 1.72
Wage (RMB 10 thousands) 375 3.73 1.90 1.11 11.18
34
Table 2
The determinants of infrastructure investment
(1) (2)
Variables ln(Infrastructure Investment) ln(Infrastructure Investment)
lagged ln(Infrastructure Investment), 0.7249***
(19.70)
unit cost of land acquisition -0.0168*** -0.0034*
(-6.81) (-1.87)
lagged ln(real estate investment), 0.4079*** 0.1314***
(12.55) (5.04)
year = 2005 0.1416*** 0.0629**
(3.86) (2.50)
year = 2006 0.2586*** 0.0755***
(6.81) (2.77)
year = 2007 0.2873*** 0.0420
(6.85) (1.36)
year = 2008 0.3556*** 0.0920***
(7.51) (2.65)
year = 2009 0.5924*** 0.2553***
(11.16) (6.42)
year = 2010 0.6672*** 0.1435***
(11.34) (3.00)
year = 2011 0.5576*** 0.0006
(8.40) (0.01)
year = 2012 0.6330*** 0.1277**
(8.45) (2.25)
year = 2013 0.7168*** 0.1679***
(8.89) (2.74)
year = 2014 0.8839*** 0.2099***
(10.03) (3.06)
year = 2015 1.0481*** 0.2311***
(11.01) (3.02)
Constant -0.5739*** -0.1096**
(-9.72) (-2.36)
Provincial FE Yes Yes
Observations 370 370
R-squared 0.963 0.983
t-statistics in parentheses
*** p<0.01, ** p<0.05, * p<0.1
35
Table 3
Decomposition of the variable anticorr
(1) (2) (3) (4)
Variables anticorr1anticorr1anticorr2anticorr2
Wage -0.0532*** -0.0408*** -0.0736** -0.0721***
(-2.80) (-5.12) (-2.21) (-4.58)
year = 2005 -0.0336 0.0281
(-0.72) (0.36)
year = 2006 -0.0683 0.0524
(-1.47) (0.64)
year = 2007 -0.0661 0.0978
(-1.29) (1.12)
year = 2008 -0.0444 0.0599
(-0.82) (0.63)
year = 2009 -0.0479 0.0415
(-0.83) (0.41)
year = 2010 0.0043 0.0009
(0.07) (0.01)
year = 2011 -0.0116 -0.0713
(-0.17) (-0.59)
year = 2012 0.0310 -0.1317
(0.42) (-0.98)
year = 2013 0.0614 0.0105
(0.79) (0.08)
year = 2014 0.1239 0.3549**
(1.48) (2.38)
year = 2015 0.1576 0.5991***
(1.57) (3.35)
Campaign 0.1060*** 0.3007***
(3.87) (5.27)
Constant 2.7340*** 2.6473*** 1.1669*** 1.1683***
(29.01) (41.47) (7.52) (9.56)
Provincial FE Yes Yes Yes Yes
Observations 376 376 371 371
R-squared 0.868 0.862 0.723 0.659
t-statistics in parentheses
*** p<0.01, ** p<0.05, * p<0.1
36
Table 4
Estimation results for the full model
(1) (2) (3) (4) (5) (6)
Variables ln(Infrastructure Invest) ln(Infrastructure Invest) ln(Infrastructure Invest) ln(Infrastructure Invest) ln(Infrastructure Invest) ln(Infrastructure Invest)
anticorr1-0.1045* -0.1022** -0.0757*
(-1.65) (-1.96) (-1.76)
anticorr20.0038 -0.0545** 0.0216
(0.13) (-1.97) (1.09)
unit cost of land acquisition -0.0081*** -0.0135*** -0.0020 -0.0078*** -0.0135*** -0.0018
(-2.83) (-5.59) (-1.02) (-2.61) (-5.37) (-0.88)
ln(real estate invest) 0.6358*** 0.4398*** 0.1990*** 0.6370*** 0.4308*** 0.1783***
(26.89) (13.25) (6.84) (25.46) (12.20) (6.12)
Wage 0.0431*** -0.0655*** 0.0136 0.0534*** -0.0654*** 0.0147
(2.72) (-3.66) (1.24) (3.31) (-3.45) (1.36)
Campaign 0.0413 0.0148
(1.35) (0.43)
lag ln(Infrastructure Invest) 0.6855*** 0.7173***
(18.34) (19.04)
year = 2005 0.1405*** 0.1606***
(3.84) (4.28)
year = 2006 0.2526*** 0.2948***
(6.62) (7.07)
year = 2007 0.3080*** 0.3446***
(6.62) (7.02)
year = 2008 0.4159*** 0.4225***
(7.47) (7.00)
year = 2009 0.6436*** 0.6701***
(9.89) (9.55)
year = 2010 0.7446*** 0.7758***
(10.13) (9.72)
year = 2011 0.6367*** 0.6660***
(7.46) (7.16)
year = 2012 0.7280*** 0.7640***
(7.40) (7.16)
year = 2013 0.8381*** 0.8653***
(7.85) (7.49)
year = 2014 1.0132*** 1.0609***
(8.66) (8.42)
year = 2015 1.2280*** 1.2880***
(9.16) (8.90)
Constant -0.2923 -0.0838 0.0502 -0.6099*** -0.3152*** -0.1473**
(-1.53) (-0.51) (0.39) (-6.44) (-3.50) (-2.23)
Provincial FE Yes Yes Yes Yes Yes Yes
Observations 354 354 354 339 339 339
Number of regions 31 31 31 31 31 31
R-squared 0.950 0.969 0.976 0.946 0.966 0.976
z-statistics in parentheses
*** p<0.01, ** p<0.05, * p<0.1
37
Appendix B. Proof of main results.
Proof of Proposition 1.For a given b, the first-order condition for the optimal eis
∂Ub
∂e =δr(ϕ¯v+b)
(δe +r)2α
θ
θcb0.
Under the condition that λ<uˆv, we can solve for eas given in (2). In addition, since 2Ub
∂e2=
2δ2r(ϕ¯v+b)
(δe+r)3<0, this optimal solution is also unique.
Lemma 1. When interior solutions for the bureaucrat’s optimization problem exist, i.e., e>
0, b>0, then it must be true that, at b,(1 ϕvu < 0.
Proof. From Proposition 1, we know that to have positive effort, it is necessary that uˆv > λ. If
b>0, then (3) is satisfied with equality, and hence,
(1 ϕv3
2(λu)1
2= 0.(A.1)
Combining the two conditions, we have (1 ϕv < u.
Lemma 2. If ϕϕ0,b= 0.
Proof. The result requires that for all ϕϕ0,∂Ub
∂b |b=0 0,21 indicating
(1 ϕ)
1λ
ϕ(
θc)(¯
θc+W)1
2
λ
(
θc)2
ϕ(
θc)(¯
θc+W)
λ1
2
1
.
This is equivalent to (1 ϕ)2(
θc)3ϕλ(¯
θc+W). Solving for ϕ0produces the following:
ϕ0= 1 1
2
λ(¯
θc+W)
(
θc)32
+4λ(¯
θc+W)
(
θc)3
1
2
λ(¯
θc+W)
(
θc)3
.(A.2)
Clearly, ϕ0(0,1) under Assumption 1. For all ϕϕ0,b= 0.
Proof of Proposition 2.The first part is shown in Lemma 2. The second part proceeds in three
steps.
21This follows from standard textbook results on maximization with nonnegative constraint. For a reference, see,
for example, Mathematical Appendix of Advanced Microeconomic Theory by Jehle and Reny.
38
First, we show that there is a unique solution in real numbers for the first-order condition (3).
From equation (A.1) we have
b33(
θc)b2+3(
θc)2+λ
(1 ϕ)b+λϕ(¯
θc+W)
(1 ϕ)2(
θc)3= 0.
We use Cardano’s method to solve the equation: for x3+kx2+mx +n= 0, let x=tk/3to
obtain t3+pt +q= 0, where p=mk2
3, and q=n+2k39km
27 . To do so, we first transform
the equation such that we can directly apply the formula. In this case, k=3(
θc),m=
3(
θc)2+λ
1ϕ, and n=λϕ(¯
θc+W)
(1ϕ)2(
θc)3. Thus, we have p, q and as defined in the
text. Since ∆ = λ2[ϕ(¯
θ+W) + (1 ϕ)
θc]2/4(1 ϕ)4+λ3/27(1 ϕ)3>0, there is only one
solution in real numbers. Cardano’s formula yields bas in (4).
Next, we show that bindeed maximizes Ub. To do so, we show that under the condition that
λuˆv,2Ub/∂b20. Note that 2Ub
∂b2=λ1
2
v5
2u3
2[(1 ϕvu]22λ
ˆv3ˆvu
λ1
21.Using equality
(A.1) and simplifying yields 2Ub
∂b2=(1ϕ)
vu2[u+ (1 ϕv][(1ϕ)ˆv+ 3u], which is strictly negative
since at b,u > (1 ϕvby Lemma 1. So bis the unique solution to the maximization problem.
Taking the derivative of equation (A.1) with respect to ϕand rearranging terms, we have
∂b
∂ϕ =2ˆv5
2u1
2λ1
2ˆv(¯
θcb+W)]
λ1
2[3u+ (1 ϕv].
Again, using the condition that λ1
2= (1 ϕ)ˆv3
2u1
2for b>0, we have
∂b
∂ϕ =ˆvu[2u+ (1 ϕ)( ¯
θcb+W)]
(1 ϕ)[3u+ (1 ϕv]0.
In a similar way, we can show that ∂b/∂W 0.
Lemma 3. When ϕ= 0 and σI= 0, the optimal b>
b
θc
2. For any ϕ[0,1] and σ0,
b<
θc.
Proof. Lemma 1shows that (1 ϕv < u, which is equivalent to 2(1 ϕ)b>(1 ϕ)(
θc)
ϕ(¯
θc+W). Thus, when ϕ= 0,b(
θc)/2. To show the second part, note that q > 0by
assumption. Thus, b<
θc.
Proof of Proposition 3.Note that when uˆv < λ, optimal effort e>0. However, when λ <
(
θc)2/4, there exists bsuch that b(
θcb)> λ, indicating that a bureaucrat with ϕ= 0
chooses positive effort. A continuity argument implies that under this condition, there exists ϕ
39
such that [b(1 ϕ) + ϕ(¯
θc+W)](
θcb) = λ. Thus, for any bureaucrat with ϕ<ϕand
optimal choice b(ϕ),[b(ϕ)(1 ϕ) + ϕ(¯
θc+W)](
θcb(ϕ)) > λ. Therefore, the bureaucrat
chooses positive effort in implementing the project.
Proof of Proposition 4.Note that the cutoff ϕσequals ϕ0as defined in (A.2) if σI= 0. When
σI>0,ϕσis implicitly determined by the equality
(1 σIϕσ)b=σIV
r.(A.3)
One should not take a bribe at all if the bthat maximizes Ubis such that (1 σiϕ)bσV /r.
Next, assume that σIand ϕσare such that the optimal b>0. We simply take first-order
condition and identify the optimal band e. The proof for Part (1) is similar to the Proof of
Proposition 2. The proof for Part (2) is similar to the Proof of Proposition 1.
Proof of Proposition 5.First, as discussed in the previous proof, the cutoff ϕσis determined by
equation (A.3), and apparently, an increases in σIlowers ϕσ.
We show result (2) in two steps. In the first step, we prove the first part of (2). Note the
derivatives pσ=λ/(1 σIϕ)2,
qσ=λ[(1 σIϕ)(
θc) + 2ϕ(¯
θc+W)(1 + σIϕ)V/r]
(1 σIϕ)3
Differentiating bwith respect to σIand rearranging terms, we have
˜
b
∂σI
=1
2˜
1
2+˜q
4qσ+˜p2
18 pσ˜q
2˜
1
22
3+1
2˜
1
2˜q
4qσ˜p2
18 pσ˜q
2+˜
1
22
3
˜p2˜
1
2/3
Thus, the sign of ˜
b/∂σIis the same as the numerator:
Π =A˜p6
18 ˜
1
2+˜p6˜q
36 q3
σ+˜p8
54q2
σpσ˜p7˜q
36 +˜p7
18 ˜
1
2p2
σqσ+˜p6˜q2
36 +˜p6˜q
18 ˜
1
2+˜p9
486p3
σ1
3
+A˜p6
18 ˜
1
2+˜p6˜q
36 q3
σ˜p8
54q2
σpσ+˜p7˜q
36 ˜p7
18 ˜
1
2p2
σqσ˜p6˜q2
36 ˜p6˜q
18 ˜
1
2+˜p9
486p3
σ1
3
where A=3
1
182. Let
˜
Π = ˜p6
18 ˜
1
2+˜p6˜q
36 q3
σ+˜p8
54q2
σpσ˜p7˜q
36 +˜p7
18 ˜
1
2p2
σqσ+˜p6˜q2
36 +˜p6˜q
18 ˜
1
2+˜p9
486p3
σ
˜p6
18 ˜
1
2+˜p6˜q
36 q3
σ˜p8
54q2
σpσ+˜p7˜q
36 ˜p7
18 ˜
1
2p2
σqσ˜p6˜q2
36 ˜p6˜q
18 ˜
1
2+˜p9
486p3
σ
=˜
1
2˜p6
9q3
σ˜p7
9p2
σqσ+˜p6˜q
9p3
σ.
40
Note that ˜
Π>0implies that Π>0, which in turn indicates that ˜
b/∂σI>0. Thus, all we
need to show is that ˜p6q3
σ
9˜p7p2
σqσ
9+˜p6˜qp3
σ
9>0, which is equivalent to
˜p6
9
λ3
(1 σIϕ)8[(1 σIϕ)(
θc)+2ϕ(¯
θc+W)(1 + σIϕ)V/r]3
1σIϕ
+λ[ϕ(¯
θc+W) + (1 ϕ)V/r]>0.
First, under condition (5), the first term inside the bracket is nonnegative. Next, we show
that this condition also implies that the second term is nonnegative. Recall that we previously
showed that a positive amount of corruption requires that σIV/r < (1 σIϕ)b. However,
b <
θc, and thus, σIV
r<(1 σIϕ)(
θc). Plugging the inequality into condition (5), we
have (1ϕ)V
r> ϕ(¯
θc+W). Hence, we conclude that ˜
bis increasing in σIunder condition (5).
In step two, we prove the second part of (2). Note that (1 σIϕv˜u < 0is equivalent to
(1 σIϕ)˜
b>(1 σIϕ)(
θc)ϕ(¯
θc+W) + σIV/r
2.(A.4)
Taking the derivative of equation (A.1) with respect to σIand simplifying yields
˜
b
∂σI
=v5
2˜u1
2+λ1
2ˆv(˜
b+V/r)
λ1
2(3˜u+ (1 σIϕv)
The first-order condition for the optimal ˜
bimplies that λ= (1 σIϕ)2ˆv3˜u1. Thus, we have
˜
b
∂σI
=
ˆv[2˜u+ (1 σIϕ)˜
b+V
r]
(1 σIϕ)[3˜u+ (1 σIϕv].(A.5)
u+ (1 σIϕ)˜
b+V
r=2ϕ(¯
θc+W)(1 σIϕ)˜
b+(1 + σIϕ)V
r
<(1 σIϕ)(
θc)+3ϕ(¯
θc+W)
2+(1 + σI/2ϕ)V
r,
which is negative under the condition on V.
To show result (3), we differentiate ˜ew.r.t. σI:
˜e
∂σI
=1
2r
δα
θ˜uˆv1
2ˆv˜
bV
r+ ((1 σIϕv˜u)˜
b
∂σI.
Plugging the expression for ˜
b/∂σ into the equation and simplifying yields
˜e
∂σI
=(r˜uˆv)1
2[2(1 σIϕ)(˜
b+V
r)(1 σIϕv+ ˜u]
(δα
θ)1
2(1 σIϕ)[3˜u+ (1 σIϕv],
41
which is non-positive under the condition specified in the proposition.
Proof of Proposition 6.First, equation (A.3) implies that the cutoff ϕσis decreasing in V.
Next, we differentiate ˜
bwith respect to V:
˜
b
∂V =˜qv
6∆1
2(1
2˜q+ ∆1
2)
[1
2˜q+ ∆1
2]2/3
1
2˜q+ ∆1
2
[1
2˜q1
2]2/3
=˜qv
6∆1
2[1
2˜q+ ∆1
2]1
3[1
2˜q+ ∆1
2]1
3.
The term inside the curly bracket is negative, and
˜qv=σI
r(1 σIϕ)2<0.
Hence, we conclude that ˜
b
∂V >0.
Lastly, we differentiate ˜ewith respect to V:
˜e
∂V =r
2δ˜u1
2ˆ
V
λ1
2˜u
∂V =σI
2δ˜u1
2ˆ
V
λ1
2
<0.
This concludes the proof.
Proof of Proposition 7.To show the first part, we take derivatives of the first-order condition for
optimal bwith respect to ϕ. After rearranging terms and using the condition that λ1
2= (1
ϕv3
2˜u1
2, we have
˜
b
∂ϕ =ˆv˜u[2˜u+ (1 σIϕ)(¯
θcb+W)]
(1 σIϕ)[3˜u+ (1 ϕv]0.
To show the second part, we take the derivative of ˜ewith respect to ϕ:
˜e
∂ϕ =r
2δ1
λ˜uˆv1
2(
θc+W)u(1 σIϕv)˜
b
∂ϕ .
We have shown previously that ˜u(1 σIϕ)ˆv > 0if ˜e>0and ˜
b>0, and ˜
b/∂ϕ < 0.
Hence, ˜e/∂ϕ > 0if
θc+W0.
Proof of Proposition 9.Denote the optimal payoff for the bureaucrat from implementing projects
1 and 2 as U1and U2, respectively, with
Uj=δe
j[ϕ(¯
θc+Wj) + (1 σIj ϕ)bj]
δe
j+rσIj V
re
jα
θ
θcbj
+V
r.
42
To prove the result, we first note that Ujis increasing in Wand decreasing in σI j . Second, note
that for e>0, it is true that ϕ(¯
θc+Wj) + (1 σIj ϕ)bj>0, which implies that Ujis also
increasing in ϕ.
Next, observe that when ϕ= 0,U1< U2. According to Proposition 4, there exists ϕσsuch
that for ϕϕσ,b
1=b
2= 0, in which case,
U1=δe
1ϕ(¯
θc+W1)
δe
1+re
1α
θ
θc+V
r> U2=δe
2ϕ(¯
θc+W2)
δe
2+re
2α
θ
θc+V
r.
Since Ujis increasing in ϕ, there must exist ϕsuch that for ϕϕ,U1U2, and thus, bureaucrats
with ϕ < ϕ choose project 2 over project 1. This concludes the proof.
43
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