Content uploaded by Bingyong Zheng

Author content

All content in this area was uploaded by Bingyong Zheng on Mar 24, 2021

Content may be subject to copyright.

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=θi−τiwhen 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 W≥0that 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 b≥0is 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 ¯

θ−c−bfrom 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 k’s

encompassing interest parameter, with ϕk∈[0,1] for all k≤n. 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 V≥0from 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

(1−M), 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= (¯

θ−c−b+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 1−σI. 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

r−αe

1−M.(1)

Note that only individuals with θi−c−b≤0would oppose the investment and, thus, M=(b+c)

b

θ

and C(e) = α

b

θe

(

b

θ−c−b).

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 e∗as a function of the bribe amount. In the second step, we determine the optimal bribe

amount b∗for 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 e∗is a function of b, suggesting a backward

induction approach to the problem.

12

payoff:

Ub=δe(ϕ¯v+b)

δe +r+V

r−αe

θ

θ−c−b.

Here, ¯v=¯

θ−c−b+W. To simplify the notation, let u=ϕ(¯

θ−c+W)+b(1−ϕ),ˆv= (

θ−c−b)

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/λ−1)] .

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 λ≥uˆv, 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 b∗from the investment.

Inserting e∗into the expected payoff function, we then differentiate Ubwith respect to b, which

yields

∂Ub

∂b =1−λ

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)(

θ−c) + ϕ(¯

θ−c+W)]

(1 −ϕ)2,

and ∆ = q

22+p

33. We make the following assumption:9

Assumption 1. λ < (¯

θ−c+W)(

θ−c).

Proposition 2. Suppose that Assumption 1holds. (1) There exists ϕ0∈(0,1) such that when

ϕ≥ϕ0, the optimal bribe amount b∗= 0, and when ϕ < ϕ0,

b∗=−q

2+ ∆1

21

3+−q

2−∆1

21

3+ (

θ−c).(4)

(2) The optimal b∗is decreasing in ϕand W.

In the Appendix, we provide the formula for ϕ0(equation (A.2)) and show that b∗is positive

but less than (

θ−c)if ϕ < ϕ0(see Lemma 3).

Before proceeding, we elaborate on some of the results. A bureaucrat’s effort e∗is 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=¯

θ−c+Wand ˆv=

θ−c. 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 ¯

θ−c+W < 0and λ < (

b

θ−c)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(¯

θ−c+W) + (1 −σI−ϕ)b−σIV/r]

(δe +r)−eα

θ

θ−c−b+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(1−σI)<(

θ−c).

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

θ−c, 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(1−σI)>

θ−c,

no bureaucrat would ﬁnd it proﬁtable to take any bribes. To exclude this uninteresting case, we

therefore make this assumption.

15

Let ˜u=ϕ(¯

θ−c+W) + (1 −ϕ−σI)b−σIV/r,ˆv=

θ−c−b, and let

˜p=λ

(1 −σI−ϕ),˜q=λ[ϕ(¯

θ−c+W)−σIV/r + (1 −σI−ϕ)(

θ−c)]

(1 −σI−ϕ)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 ϕ≥ϕσ,

˜

b∗= 0, and when ϕ < ϕσ,˜

b∗=−˜q

2+˜

∆1

21

3+−˜q

2−˜

∆1

21

3+ (

θ−c). (2) Optimal effort

˜e∗= ( r

δ)˜uˆv

λ1

2−1if 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 −σI−ϕ)(

θ−c)+2ϕ(¯

θ−c+W)]

1−ϕ+σI

,(5)

and decreases under the condition 10

V

r<[(1 −σI−ϕ)(

θ−c)+3ϕ(¯

θ−c+W)]

2−2ϕ+σI

.(6)

(3) ˜e∗decreases under the condition

(1 −σI−ϕ)

θ−c+2V

r+σIV

r≥ϕ(¯

θ−c+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<1−ϕimplies that [(1−σI−ϕ)(

b

θ−c)+2ϕ(¯

θ−c+W)]

1−ϕ+σI>ϕ(¯

θ−c+W)]

1−ϕ, and thus,

[(1 −σI−ϕ)(

θ−c)+3ϕ(¯

θ−c+W)]

2−2ϕ+σI

<[(1 −σI−ϕ)(

θ−c)+2ϕ(¯

θ−c+W)]

1−ϕ+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 ˜

b∗and 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 ˜e∗in any project with ¯

θ−c+W≥0.

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=Ub(˜e∗,˜

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 s∗that 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 −σE)¯s≤σEU∗

b. Since U∗

bis decreasing in both σIand αbut increasing in

(¯

θ−c)and V, we have the following result:

Proposition 8. Given (V , σI, α), there exists ˆσE<1such that the optimal s∗= 0 if σE≥ˆσE. In

addition, ˆσEis increasing in σIand αbut decreasing in Vand (¯

θ−c).

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 ¯

θ−c), 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 ϕ≤ϕimplement 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 =wageβ +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.

References

Acemoglu, D., Verdier, T., 2000. The choice between market failures and corruption. American

Economic Review 90, 194–211.

Aidt, T., 2009. Corruption, institutions, and economic development. Oxford Review of Economic

Policy 25, 271–91.

Akerlof, G., Kranton, R., 2005. Identity and the economics of organizations. Journal of Economic

Perspectives 19, 9–32.

Aschauer, D., 1989. Is public expenditure productive? Journal of Monetary Economics 23, 177–

200.

Bai, C.-E., Hsieh, C.-T., Song, Z., 2014. Crony capitalism with Chinese characteristics, working

paper.

Bardhan, P., 1997. Corruption and development. Journal of Economic Literature 35, 1320–346.

Batinti, A., Lee, Y. T., Zheng, B., 2019. Anticorruption and corporate investment in China: Evi-

dence from a quasi-natural experiment, working paper.

Benabou, R., Tirole, J., 2003. Intrinsic and extrinsic motivation. Review of Economic Studies 70,

489–520.

Besley, T., Ghatak, M., 2005. Competition and incentives with motivated agents. American Eco-

nomic Review 95, 616–36.

Cai, H., Henderson, V., Zhang, Q., 2013. China’s land market auction: evidence of corruption?

The Rand Journal of Economics 44, 488–521.

Ehrlich, I., Lui, F. T., 1999. Bureaucratic corruption and endogenous economic growth. Journal of

Political Economy 107, 270–293.

30

Fisman, R., Svensson, J., 2007. Are corruption and taxation really harmful to growth? ﬁrm level

evidence. Journal of Development Economics 83, 63–75.

Fisman, R., Wang, Y., 2015. Corruption in Chinese privatizations. Journal of Law, Economics, and

Organization 31, 1–29.

Frisch, R., Waugh, F. V., 1933. Partial time regressions as compared with individual trends. Econo-

metrica 1, 387–401.

Huang, L., Zheng, J., 2019. The winner takes it all: A tournament model with endogenous prefer-

ential treatment, working paper.

Hutington, S. P., 1968. Political order in changing societies. New Haven: Yale University Press.

Lan, X., Li, W., 2018. Swiss watch cycles: evidence of corruption during leadership transition in

China. Journal of Comparative Economics 46, 1234–52.

Leff, N. H., 1964. Economic development through bureaucratic corruption. American Behavior

Scientist 82, 337–41.

Li, H., Zhou, L., 2005. Political turnover and economic performance: the incentive role of person-

nel control in China. Journal of Public Economics 89, 1743–1762.

Lien, a. W., Wang, W., Zheng, J., 2016. A model of capital allocation, education and job choice in

China. Chinese Economy 49, 307–26.

Lovell, M. C., 1963. Seasonal adjustment of economic time series and multiple regression analysis.

Journal of the American Statistical Association 58, 993–1010.

Lui, F. T., 1985. An equilibrium queuing model of bribery games. Journal of Political Economy

93, 760–781.

Mauro, P., 1995. Corruption and growth. Quarterly Journal of Economics 110, 681–712.

Mei, C., Chen, K., Wu, X., 2016. Introduction: Local government entrepreneurship in China: A

public policy perspective. China: An International Journal 14, 3–15.

31

Mei, C., Pearson, M. M., 2014. Killing a chicken to scare the monkeys? deterrence failure and

local deﬁance in China. The China Journal 72, 75–97.

M´

eon, P.-G., Sekkat, K., 2005. Does corruption grease or sand the wheels of growth? Public

Choice, 69–97.

M´

eon, P.-G., Weill, L., 2010. Is corruption an efﬁcient grease? World Development 38, 244–59.

Mookherjee, D., Png, I., 1995. Corruptible law enforcers: how should they be compensated? Eco-

nomic Journal 105, 145–59.

Myrdal, G., 1968. Asian Drama. Vol. II. New York: Random House.

Oi, J. C., 1992. Fiscal reform and the economic foundations of local state corporatism in China.

World Politics 45, 99–126.

Rock, M. T., Bonnett, H., 2004. The comparative politics of corruption: accounting for the East

Asian paradox in empirical studies of corruption, growth and investment. World Development

32, 999–1017.

Shi, H., Huang, S., 2014. How much infrastructure is too much? a new approach and evidence

from China. World Development 56, 272–286.

Shleifer, A., Vishny, R. W., 1993. Corruption. Quarterly Journal of Economics 108, 599–617.

Svensson, J., 2005. Eight questions about corruption. Journal of Economic Perspectives 19, 19–42.

Swaleheen, M., 2011. Economic growth with endogenous corruption: an empirical study. Public

Choice 146, 23–41.

Walder, A. G., 1995. Local governments as industrial ﬁrms: An organizational analysis of China’s

transitional economy. American Journal of Sociology 101, 263–301.

Wang, B., Zheng, Y., 2018. A model of tournament incentives with corruption, working Paper.

Xu, C., 2011. The fundamental institutions of China’s reforms and development. Journal of Eco-

nomic Literature 40, 1076–1151.

32

Xu, C., Wang, Y., 2014. Prevent resource waste due to inefﬁcient investment, Shanghai Security

Journal (Shanghai Zhengjuan Bao), November 20, 2014.

Xu, X., Huang, S., Shi, F., 2019. The economics of political connection: Local bureaucrats’ career

concern versus the corrupt incentive, working paper.

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 e∗is

∂Ub

∂e =δr(ϕ¯v+b)

(δe +r)2−α

θ

θ−c−b≤0.

Under the condition that λ<uˆv, we can solve for e∗as 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 −ϕ)ˆv−u < 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 −ϕ)ˆv3

2−(λu)1

2= 0.(A.1)

Combining the two conditions, we have (1 −ϕ)ˆv < u.

Lemma 2. If ϕ≥ϕ0,b∗= 0.

Proof. The result requires that for all ϕ≥ϕ0,∂Ub

∂b |b=0 ≤0,21 indicating

(1 −ϕ)

1−λ

ϕ(

θ−c)(¯

θ−c+W)1

2

≤λ

(

θ−c)2

ϕ(

θ−c)(¯

θ−c+W)

λ1

2

−1

.

This is equivalent to (1 −ϕ)2(

θ−c)3≤ϕλ(¯

θ−c+W). Solving for ϕ0produces the following:

ϕ0= 1 −1

2

λ(¯

θ−c+W)

(

θ−c)32

+4λ(¯

θ−c+W)

(

θ−c)3

1

2

−λ(¯

θ−c+W)

(

θ−c)3

.(A.2)

Clearly, ϕ0∈(0,1) under Assumption 1. For all ϕ≥ϕ0,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

b3−3(

θ−c)b2+3(

θ−c)2+λ

(1 −ϕ)b+λϕ(¯

θ−c+W)

(1 −ϕ)2−(

θ−c)3= 0.

We use Cardano’s method to solve the equation: for x3+kx2+mx +n= 0, let x=t−k/3to

obtain t3+pt +q= 0, where p=m−k2

3, and q=n+2k3−9km

27 . To do so, we ﬁrst transform

the equation such that we can directly apply the formula. In this case, k=−3(

θ−c),m=

3(

θ−c)2+λ

1−ϕ, and n=λϕ(¯

θ−c+W)

(1−ϕ)2−(

θ−c)3. Thus, we have p, q and ∆as deﬁned in the

text. Since ∆ = λ2[ϕ(¯

θ+W) + (1 −ϕ)

θ−c]2/4(1 −ϕ)4+λ3/27(1 −ϕ)3>0, there is only one

solution in real numbers. Cardano’s formula yields b∗as in (4).

Next, we show that b∗indeed maximizes Ub. To do so, we show that under the condition that

λ≤uˆv,∂2Ub/∂b2≤0. Note that ∂2Ub

∂b2=λ1

2

2ˆv5

2u3

2[(1 −ϕ)ˆv−u]2−2λ

ˆv3ˆvu

λ1

2−1.Using equality

(A.1) and simplifying yields ∂2Ub

∂b2=(1−ϕ)

2ˆvu2[−u+ (1 −ϕ)ˆv][(1−ϕ)ˆv+ 3u], which is strictly negative

since at b∗,u > (1 −ϕ)ˆvby Lemma 1. So b∗is 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

2−λ1

2ˆv(¯

θ−c−b+W)]

λ1

2[3u+ (1 −ϕ)ˆv].

Again, using the condition that λ1

2= (1 −ϕ)ˆv3

2u−1

2for b∗>0, we have

∂b∗

∂ϕ =−ˆvu[2u+ (1 −ϕ)( ¯

θ−c−b+W)]

(1 −ϕ)[3u+ (1 −ϕ)ˆv]≤0.

In a similar way, we can show that ∂b∗/∂W ≤0.

Lemma 3. When ϕ= 0 and σI= 0, the optimal b∗>

b

θ−c

2. For any ϕ∈[0,1] and σ≥0,

b∗<

θ−c.

Proof. Lemma 1shows that (1 −ϕ)ˆv < u, which is equivalent to 2(1 −ϕ)b∗>(1 −ϕ)(

θ−c)−

ϕ(¯

θ−c+W). Thus, when ϕ= 0,b∗≥(

θ−c)/2. To show the second part, note that q > 0by

assumption. Thus, b∗<

θ−c.

Proof of Proposition 3.Note that when uˆv < λ, optimal effort e∗>0. However, when λ <

(

θ−c)2/4, there exists bsuch that b(

θ−c−b)> 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(¯

θ−c+W)](

θ−c−b) = λ. Thus, for any bureaucrat with ϕ<ϕand

optimal choice b∗(ϕ),[b∗(ϕ)(1 −ϕ) + ϕ(¯

θ−c+W)](

θ−c−b∗(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 −σI−ϕσ)b=σIV

r.(A.3)

One should not take a bribe at all if the bthat maximizes Ubis such that (1 −σi−ϕ)b≤σV /r.

Next, assume that σIand ϕσare such that the optimal b∗>0. We simply take ﬁrst-order

condition and identify the optimal b∗and 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 −σI−ϕ)2,

qσ=λ[(1 −σI−ϕ)(

θ−c) + 2ϕ(¯

θ−c+W)−(1 + σI−ϕ)V/r]

(1 −σI−ϕ)3

Differentiating b∗with 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 −σI−ϕ)8−[(1 −σI−ϕ)(

θ−c)+2ϕ(¯

θ−c+W)−(1 + σI−ϕ)V/r]3

1−σI−ϕ

+λ[−ϕ(¯

θ−c+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 −σI−ϕ)b. However,

b <

θ−c, and thus, σIV

r<(1 −σI−ϕ)(

θ−c). Plugging the inequality into condition (5), we

have (1−ϕ)V

r> ϕ(¯

θ−c+W). Hence, we conclude that ˜

b∗is increasing in σIunder condition (5).

In step two, we prove the second part of (2). Note that (1 −σI−ϕ)ˆv−˜u < 0is equivalent to

(1 −σI−ϕ)˜

b∗>(1 −σI−ϕ)(

θ−c)−ϕ(¯

θ−c+W) + σIV/r

2.(A.4)

Taking the derivative of equation (A.1) with respect to σIand simplifying yields

∂˜

b∗

∂σI

=−2ˆv5

2˜u1

2+λ1

2ˆv(˜

b∗+V/r)

λ1

2(3˜u+ (1 −σI−ϕ)ˆv)

The ﬁrst-order condition for the optimal ˜

b∗implies that λ= (1 −σI−ϕ)2ˆv3˜u−1. Thus, we have

∂˜

b∗

∂σI

=

ˆv[−2˜u+ (1 −σI−ϕ)˜

b∗+V

r]

(1 −σI−ϕ)[3˜u+ (1 −σI−ϕ)ˆv].(A.5)

−2˜u+ (1 −σI−ϕ)˜

b∗+V

r=−2ϕ(¯

θ−c+W)−(1 −σI−ϕ)˜

b∗+(1 + σI−ϕ)V

r

<−(1 −σI−ϕ)(

θ−c)+3ϕ(¯

θ−c+W)

2+(1 + σI/2−ϕ)V

r,

which is negative under the condition on V.

To show result (3), we differentiate ˜e∗w.r.t. σI:

∂˜e∗

∂σI

=1

2r

δα

θ˜uˆv1

2ˆv−˜

b−V

r+ ((1 −σI−ϕ)ˆv−˜u)∂˜

b∗

∂σI.

Plugging the expression for ∂˜

b∗/∂σ into the equation and simplifying yields

∂˜e∗

∂σI

=(r˜uˆv)1

2[−2(1 −σI−ϕ)(˜

b+V

r)−(1 −σI−ϕ)ˆv+ ˜u]

(δα

θ)1

2(1 −σI−ϕ)[3˜u+ (1 −σI−ϕ)ˆv],

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 ˜

b∗with 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˜q−∆1

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 −σI−ϕ)2<0.

Hence, we conclude that ∂˜

b∗

∂V >0.

Lastly, we differentiate ˜e∗with 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 b∗with respect to ϕ. After rearranging terms and using the condition that λ1

2= (1 −

ϕ)ˆv3

2˜u−1

2, we have

∂˜

b∗

∂ϕ =−ˆv˜u[2˜u+ (1 −σI−ϕ)(¯

θ−c−b+W)]

(1 −σI−ϕ)[3˜u+ (1 −ϕ)ˆv]≤0.

To show the second part, we take the derivative of ˜e∗with respect to ϕ:

∂˜e∗

∂ϕ =r

2δ1

λ˜uˆv1

2(

θ−c+W)−(˜u−(1 −σI−ϕ)ˆv)∂˜

b∗

∂ϕ .

We have shown previously that ˜u−(1 −σI−ϕ)ˆv > 0if ˜e∗>0and ˜

b∗>0, and ∂˜

b∗/∂ϕ < 0.

Hence, ∂˜e∗/∂ϕ > 0if

θ−c+W≥0.

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(¯

θ−c+Wj) + (1 −σIj −ϕ)bj]

δe∗

j+r−σIj V

r−e∗

jα

θ

θ−c−bj

+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(¯

θ−c+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 ϕ≥ϕσ,b∗

1=b∗

2= 0, in which case,

U1=δe∗

1ϕ(¯

θ−c+W1)

δe∗

1+r−e∗

1α

θ

θ−c+V

r> U2=δe∗

2ϕ(¯

θ−c+W2)

δe∗

2+r−e∗

2α

θ

θ−c+V

r.

Since Ujis increasing in ϕ, there must exist ϕsuch that for ϕ≤ϕ,U1≤U2, and thus, bureaucrats

with ϕ < ϕ choose project 2 over project 1. This concludes the proof.

43