ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E06-1

Causes, effects, and prevention of agent corruption
in Chinese SOEs
by
DAPENG CAI and JIE LI

February 2006

ECONOMIC RESEARCH CENTERSCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Causes, effects, and prevention of agent corruption in Chinese SOEsg
DAPENG CAI¾ & JIE LI¾¾
Abstract: This article analyzes agent corruption in a state-owned enterprise (SOE) in a
duopoly model, in which an SOE competes with a private enterprise. The manager of
the SOE contemplates to embezzle, and is caught and subject to punishment at aprobability. The comparative statics of the compensation to the manager, the legal
loopholes in the SOE, the unit transaction cost of corruption, and the government’s
concern for employment are examined, and their effects on outputs, social welfare andthe value of the government’s objective function are considered. The conditions underwhich corruption may be socially good are also presented.
Keywords: Agent corruption; Information asymmetry; State-owned enterprises (SOEs);
Transitional economy
JEL classification code: P20; L32; L13g

We thank Ryuhei Okumura, Hikaru Ogawa, Yasuhiro Sato, Yuan Shu, Gregory G. Chow, and other participants at
research seminars at Nagoya University and Sun Yat-Sen University, and the 4th International Conference of the Japan
Economic Policy Association. The usual disclaimers apply.
¾
Research Associate, Graduate School of Economics, Nagoya University, Email: cai@soec.nagoya-u.ac.jp.
¾¾
Corresponding author. Lecturer, Department of Economics, Lingnan (University) College, Sun Yat-Sen University,
Email: lijie@lingnan.net.

1.

Introduction

The severest problem encountered during the state-owned enterprise (SOE) reform in
China has been increasingly pervasive corruption by SOE managers, especially in largeand medium-sized SOEs. As more and more Chinese SOEs start to meet their massive
capital demands by accessing global capital markets, corruption in SOEs is an issue ofabundant political and economic implications not only to China, but also to the global
economy.1 In this article, we intend to examine the causes, consequences and theprevention of corruption in SOEs, from the perspectives of both a social planner thataims at maximizing social welfare and a government that is pressured to provide
employment opportunities.
Corruption, defined as illegitimate use of public office for private gains, has been
more rampant and endemic in transitional economies due to the withdrawal or absenceof government authority, economic collapse and political instability, underdeveloped
legislature and legal loopholes, inefficiency of state institutions, and weakly establishedcivil society, democratic political traditions, and judiciary (He, 2000; Levin and Satarov,2000). There has been a proliferation of literature on corruption in transitional
economies.2 Corruption in transitional economies can be roughly classified into thefollowing types: The administrative monopoly, the state capture, influence, and theadministrative corruption (Abed and Davoodi, 2000; Hellman et al., 2000; Guo and Hu,
2004). The first three are “grand” corruption, in that they capture the situation in which
the formation of legislation and ordinances, or public policies is influenced throughbribes to public officials.3 Undervalued sales of SOEs by managers and officials tofriends and family belong to this category. On the other hand, the administrative
corruption is rather “petty,” as it denotes the situation in which public officials extract
dirty money from the abuse of their daily discretionary power. The agent corruption we
consider in this paper belongs to this category: The managers of SOEs, being agents
dispatched by the government, corrupt in the forms of the embezzlement of the firms’
assets, or kickbacks in procurement.
It has long been suggested in the literature that corruption could conceivably be
1

According to China Securities Regulatory Commission, by December 2005, there are 100 Chinese firms listed in
Hong Kong Stock Exchange, 12 jointly in US and Hong Kong Stock Exchange, 5 jointly in London and Hong Kong
Stock Exchange, and 2 in Singapore Stock Exchange (www.csrc.gov.cn). With a few exceptions, Chinese firms listed
overseas are all SOEs.
2
He (2000), Nakagane (2003), and Guo and Hu (2004) contain good reviews of the literature.
3
Recent theoretical analyses on the grand corruption include Ventelou (2002) and Damania et al. (2004). Ventelou(2002) incorporates the grand corruption into the analysis of economic growth, whereas Damania et al. (2004)
considers the persistence of corruption in a model in which a firm seeks to evade regulation through either bribery or
lobbying.

2socially good (Leff, 1964; Huntington, 1968).4 However, the vast empirical studies in
the literature seem to confirm that corruption damages economic development, reduces
social welfare, and induces social polarization (Treisman, 2000; Hu and Guo, 2001;
Vinod, 2003).5 The fact that China has been able to grow fast while being ranked among
the most corrupt countries then appears to be an apparent paradox, leading Svensson to
ask “Is corruption less harmful in China?” in his survey article on corruption (Svensson,2005). Corruption may take a variety of different forms, and there is no reason tobelieve that similar types of corruption may exert equal impact on the economy.6 In thispaper, we focus on agent corruption in SOEs, and examine its effects and prevention in
the Chinese context. Questions we intend to address include: Will the Leff-Huntington
hypothesis that agent corruption may be socially good be espoused when it is “costly,”in the sense that it is accompanied by a transaction cost and a penalty? And if so, underwhat conditions? Moreover, do higher salaries for managers reduce corruption? We also
consider the impacts of corruption from the perspective of a government like that ofChina, whose objective differs substantially from that of a social planner as it tends tovalue employment opportunities. Will such a government tend to prefer a different levelof law enforcement to fight corruption than that of a social planner? How will suchdifference, if it ever exists, affect social welfare? Furthermore, we also investigate theeffects of the anti-corruption measures on both government payoffs and social welfare
and ponder their implications for the prevention of corruption.
There has been a sizeable theoretical literature on corruption using game-theoretic,
imperfect information and principal-agent models (see, for example, Klitgaard, 1988;
Laffont and Tirole, 1991; Murphy et al., 1991; Mauro, 1995; Laffont and N’Guessan,
1999; Fisman, 2001; Polinsky and Shavell, 2001; Rauch, 2001; Celetani and Ganuza,
2002; Li, Smyth, and Yao, 2005). The literature mainly characterizes the cases of grandcorruption, in which a bribe is contributed to change the rules of the game. This paper
expands the literature by applying a game-theoretic duopoly competition model toaddress the effects of the petty corruption by examining the agent corruption in Chinese
SOEs. Specifically, we consider a duopolistic market, in which an SOE coexist with a4

Leff (1964) stresses the grease effect of corruption and argues corruption can be socially good as it may improve
efficiency. Hunington (1968) also maintains similar views and argues that corruption may surmount obstacles that
hamper economic expansion. The grease effect is later verified by Lui (1985) with a queuing model of bribery.
However, as Myrdal (1968) argues, corruption may instead lead to more inefficiency. Klochko and Ordeshook (2003)
also show that corruption may lead to under-investment.
5
There has been a vast empirical literature that contemplates to test the Leff-Huntington hypothesis. The hypothesis
has been largely reputed at the micro level, however, the marco evidence seems to be inconclusive (thorough reviewsof the empirical studies can be found in Davoodi, 2001; Nakagane, 2003; and Svensson, 2005).
6
There is a surging literature that considers various aspects of corrtuption in the Chinese context (see, for example,
Liew, 1993; Manion, 1996; Yao, 1997; Chen, 2004; Chow, 2005; Li, Smyth, and Yao, 2005).

3

private firm, where the manager of the SOE has the opportunity to embezzle. We
examine a two-stage model, where in the first stage the government or the social
planner chooses the appropriate level of anti-corruption measures to maximize its own
payoff. In the second stage, the SOE competes against a private firm in the productmarket, á la Cournot. While the private firm is a pure profit maximizer, the manager of
the SOE maximizes her expected illicit gains. We find that at least under ourformulation of the model, under certain conditions, the Leff-Huntington hypothesis that
corruption may increase social welfare is espoused even when it is “costly.” This is so
as corruption generates a pro-competitive effect that induces the SOEs to increase
production, which partially corrects the oligopoly distortion. When the pro-competitiveeffect dominates the deadweight loss associated with the transaction cost, corruption issocially good, and vice versa. Moreover, a government under the pressure to provide
employment opportunities tends to prefer a different level of law enforcement from thatof a social planner, with the difference of the two depends on a comparison between theexaggerated average cost of SOE and the sum of the employment effect and themarginal transaction costs of corruption. Finally, we also present the comparative static
effects of changes in the parameters on social welfare and the government’s payoff.
The rest of the article is organized as follows. In the next section, we first provide abrief background of the agent corruption in Chinese SOEs. In Section 3, we set up thebasic model. In Section 4, we characterize the comparative static properties of themodel. In Section 5, we examine the government’s and the social planner’s optimallevels of law enforcement and their impacts on social welfare. Our concluding remarks
are given in Section 6, in which we ponder the implications of our findings for China’s
crusade against corruption. The proofs of our results are collected in Appendix.
2.

The SOE reform and the agent corruption in SOEs

Our model formulation intends to capture the following features of the contemporary
Chinese economy: First, after a series of reform, SOEs emerge as profit-maximizing
enterprises with modern corporate governance; second, corruption by SOE managers
are pervasive as there lacks sufficient supervision over their discretionary power, due tothe de facto none-existence of principals; third, the prevalent market structure may be anoligopoly in which state firms and private ones compete with each other; and fourth, thegovernment may confront an employment pressure.
2.1

The SOE reform
4The reform of the state-owned enterprises (SOEs) has been at the core of social agendas
in China. Under the previous central planning system, the industrial sector was
dominated by SOEs, which served mainly as cost centers to fulfill government-specified
production quotas and to provide lifelong employment. The aim of the initial reforms
was to “revitalize” SOEs through decentralization, improvement of internal managerial
and incentive systems, and introduction of market competition, with the aim totransform SOEs to economic units responsible for profit targets (Wu, 1999). Startingfrom the mid-1990s, through a policy termed zhuada fangxiao, or “retain control of thelarge and let loose of the small,” small and medium-sized SOEs were transformed intolargely private share-holding companies and the shares were sold to the management,
staff, and workers of the enterprises, whereas large enterprises were restructured into
limited liability companies or joint stock companies in which the shares are mostly heldby government organizations. The “successful” large enterprises are listed in stock
markets, with the corporate governance within which closely resembles that of theirwestern counterparts. The shareholder conference, the board of directors, and the boardof supervisors have been introduced as new governance structures into SOEs.7
Meanwhile, the heavy ideological and social burdens once shouldered under theprevious central planning system have been gradually peeled off from the SOEs throughthe implementation of a policy termed xiagang fenliu, or “rearrange layoffs.” Together
with the reform measures such as bankruptcies, sales, and acquisitions and mergers,
remaining SOEs are increasingly like free market players, with the ratio of
profit-making SOEs improving over the years.8
Despite intensive reforms, SOEs are still intrinsically different from private
enterprises (Zhang, 1999; Zhou and Wang, 2000; Garnaut, et al, 2005). First, theincentive system within SOEs to reward managerial achievements remains to be largely
inflexible and insufficient. Although the managers’ incomes have been linked to theperformance of the firms, they are still at relatively low levels as compared to those withsimilar positions in private enterprises. Moreover, to SOEs, the principal is virtuallynone-existent. As noted in Zhou and Wang (2000), the principal is the government that
represents people, but there lacks sufficient incentives for the government to ensure that7

Chow (2005) points out that good corporate governance “may be good on paper, but it may not govern actual
behavior,” and as exemplified by the Enron case, “smart managers and accountants can cook the books even in theUS.”
8Although SOEs’ performance is still in inferiority as compared with those of foreign funded and private enterprises.
SOEs’ rate of return on net fixed assets is 12% in 2004, whereas the same index is 21.9% to foreign funded
enterprises and 15.8% to all large and medium sized enterprises, the ratio of loss-suffering enterprises to allstate-owned and state-controlled industrial enterprises was 41.5% in 1998, which declined to 35.0% in 2004 (2005
China Statistical Yearbook).

5

SOEs pursue profit maximization. The property rights of SOEs remain largely
ambiguous and under state-dominance, and the control rights rest with bureaucrats who
have only an indirect interest in profit (World Bank, 1992; Schleifer and Vishny, 1997;
Zhang, 1997; Zhang, et al., 2002).
On the other hand, managers, being agents appointed by the government to be incharge of daily management, have considerable discretionary power. According to asurvey conduced by Garnaut, et al. (2005), managers are placed in strong positions in
the new governance structures: “Not only was the firm’s manager often the board
chairman, but, on the average, the top management took 53 percent of the seats on theboard and the middle management took another 17 percent” (p. 122). Moreover, “themanager played the most important role in decisions related to employment and thedaily operation of the firm” (p. 134).
2.2

Agent corruption in SOEs

It has been widely argued that corruption in SOEs originated from the aforementioned
characteristic structure of SOEs. Under the previous central planning system, themanagers’ main task was the management of the production process. As both theprocurement of raw materials and the sales of outputs were taken care of by thegovernment via means of orders, there is little room for them to embezzle. 9Contemporary Chinese SOEs, however, have a relatively high degree of autonomy toparticipate in the market process. As independent accounting, auditing, and property
evaluation institutions are still underdevelopment in China, there is a high moral hazard
that agents may take advantage of the information asymmetry by abusing theirdiscretionary power for personal benefits by for example, entering into contracts thatmaximizes their personal interests (Lin, et al., 2002). These factors have combined toaggravate corruption in SOEs, and have transformed SOEs into “corruption centers.” In
March 2005, in his annual work report delivered to the China’s National People’s
Congress, China’s top prosecutor of Supreme People’s Procuratorate reported thatduring 2004, cases involving SOEs’ managers account for 41.5% of all cases ofcorruption under investigation, exemplifying the graveness of corruption in Chinese

9

As noted in Chow (2005), corruption does not exist in the initial stage of the reform, the introduction of the“responsibility system,” as the responsibility system is essentially a leasing arrangement and there is noprinciple-agent problem. The privatization of small and medium sized SOEs also leads to no corruption as bydefinition, “a manager of a private enterprise cannot be called corrupt if he takes his own money” (Chow, 2005, p.13).
In the reform of the large and medium-sized SOEs, however, the problem of agent corruption emerges as there exists
opportunities for corruption in the institutional framework.

6

SOEs (Supreme People’s Procuratorate of China, www.spp.gov.cn).10
Common practices of agent corruption include zuo jiazhang, or “cook the books,”in which the manager directly embezzles resources from SOEs by either overstating thecosts of raw materials or under-reporting the sales revenue in accounting documents;
and chi huikou, or “acquire kickbacks or bribes in public biddings, procurement, or
sales,” in which the manager colludes with the bidders, suppliers, or buyers, to enter
into contracts that are unfavorable to the firm (for example, overpricing the costs of the
raw materials or under-pricing the firm’s products). A portion of the price differences islater (or beforehand) remitted back to the manager’s private accounts by theaccomplices.11 Arguably, these types of misuse of corporate assets by managers can also
be spotted in private firms, however, reflecting an underlying institutional framework
aforementioned, they are routine in SOEs. Hence, the objective of the managers of
SOEs may be different from those of the government and the private enterprises: Rather
than profits, the managers value the public assets that can be embezzled, as well as thesize of the sales volume, which contributes to the increment of her embezzlement
revenue.
2.3

Market structure in China

Private-owned firms have emerged to serve the deregulated domestic markets, and haveexperienced rapid growth for the past two decades. By the end of 2004, only 35.2% of
the gross national industrial value was produced by the state-owned and state-controlled
enterprises, whereas the rest are attributable to the private sector (2005 China Statistical
Yearbook).
2.4

Chinese government’s concern for employment

The employment pressure has been particularly striking in China due to its huge
population, abundant labor resources, and economic restructuring. Research conductedby the RAND Corporation shows that when taken into account of the “disguised” rural
unemployment

andthe “unregistered” urban

unemployment,

China’sactualunemployment rate is estimated to be as high as 23% of the total labor force (Wolf,
2004). For political and social as well as economic reasons maintaining a high rate of
10

China’s national ranks in the annual corruption perceptions index, issued by Transparency International, have also
been declining steadily from 58 in 2001 to 78 in 2005 (www.transparency.org).
11
It may also be provided to the managers or their relatives in other forms of favors such as free trips or meals.

7job creation is no less important than achieving a high rate of economic growth (Wolf,
2004). According to the Ministry of Labor and Social Security, Chinese government
regards generating ample employment opportunities as a major strategic task ineconomic and social development, and controlling the rate of unemployment as a main
target in macro-economic regulation and control (Ministry of Labor and Social Security,
www.molss.gov.cn).
On the other hand, as a result of the SOE reform, SOEs’ ability to assimilate
employment has diminished dramatically. By the end of 2004, a large portion of theemployment positions were provided by the private sector, for example, in the mining,
manufacturing, and electricity industries, SOEs employees only account for 32.2% of
the labor employed (2005 China Statistical Yearbook).
3.

The model formulation

The market we consider consists of an SOE and a private firm, both produce ahomogenous product with output being Q and Q , respectively. The market’s inverse
1

2

demand function is given by P(Q) , where Q = Q1 + Q2 and P '(Q ) < 0 . We assume that thereal marginal cost of both the SOE and the private firm to be zero so as to exclude theeffects of the discrepancy of productive efficiency on corruption. We consider the casein which an SOE’s manager contemplates to embezzle the SOE’s assets by exaggerating
the average cost of production.
The reform on SOEs has so far succeeded in introducing into SOEs a managementcompensation scheme that consists of both a basic salary and a performance-based
bonus. 12 As aforementioned, due to a lack of sufficient incentives to monitor
management performance and a shortage of information on the SOE’s daily operation,
the government’s supervision is inadequate and the SOE managers can easily allocate
the firm’s internal assets according to their own interests. As incentive contracts only
work when there are “measurable targets used and performance information is easily
available, corruption occurs even in their presence (World Bank, 1997, p. 55).” Hence,as argued in Zhang (1999) and Wen (2004), the real income and other benefits of the
SOEs’ managers come from three sources: First, a fixed basic salary; second, ticheng, or“a bonus that is a proportion, t (0 < t < 1) , of the accounting profit;” and finally, an
exaggeration of average cost by γ (γ > 0) . Here ticheng represents an incentive contractthat is used to induce the managers to focus on profits, whereas γ is the ratio of
12
As noted in Garnaut, et al. (2005), legal and regulatory barriers to the introduction of modern compensation
mechanisms still persist. For instance, there is no juridical basis for the issuance of share options to the managers.

8embezzlement to the accounting profit. We assume that the manager embezzles to the
maximum extent possible, so γ also represents the magnitude of legal loopholes
within the SOE. To simplify the analysis, we normalized the fixed salary income into
zero. Hence, the manager’s income is t ( PQ1 − γ Q1 ) + γ Q1 , with t ( PQ1 − γ Q1 ) denotes herlegal income and γ Q1 her illicit income.
In reality, due to its secretive and uncertain nature, corruption can be costly as theembezzlement of public assets always mandates lobbying, bribing, and in many cases,
money laundering. We assume such transaction costs are proportional to the manager’s
illicit income and equal τγ Q1 , where τ is a constant that measures the unit transaction
cost. These transaction costs generate a deadweight loss for the whole society, as they
are often simply squandered, or like the money laundering case, paid to foreign brokers.
Finally, on the basis of Martin and Panagariya (1984) and Klittgaard (1988), there exists
a risk for the managers of SOEs to be caught and subject to punishment, captured as theprobability of being caught α ( 0 ≤ α ≤ 1 ) and the associated punishment is represented
by a twice continuously differentiable function ϕ (γ Q1 ) , with ϕ ′(⋅) > 0 , ϕ ′′(⋅) > 0 and
ϕ (0) = 0 . The punishment function ϕ (⋅) , being an increasing convex function of theamount embezzled, can be any combination of confiscation and imprisonment.
Furthermore, to ensure that the manager of the SOE does not corrupt when α = 1 , we
impose the following assumption: ϕ ( x ) > (1 − τ ) x , which is equivalent to assume that the
net illicit income of the SOE’s manager is smaller than the punishment, in the casewhen corruption is detected at possibility 1. On the other hand, we assume that t < 1 − τ ,i.e., the incentive system within SOEs to reward managerial achievements remains to belargely insufficient, and the manager of the SOE has a strong incentive to corrupt when
α = 0 . The objective function of the manager in SOE is then specified as follows:
S1 = (1 − α )[t ( PQ1 − γ Q1 ) + γ Q1 ] + α [t ( PQ1 − γ Q1 ) + γ Q1 − ϕ (γ Q1 )] − τγ Q1 ,(1)which can be simplified as
S1 = t ( PQ1 − γ Q1 ) + γ Q1 − αϕ (γ Q1 ) − τγ Q1 .

(1’)

It should be noted that when γ = 0 or α = 1 , equation (1’) is reduced to S1 = tPQ1 ,which implies that the objective of the SOE’s manager is equivalent to that of a profit
maximizer. This formulation of the SOEs’s objective function differs substantially fromthose in the literature of mixed oligopoly markets, in which SOEs also taken into
account government’s concerns, such as employment pressure.13 We argue that after theintensive SOE reform, especially reform like “corporatization,” SOEs have been
restructured to profit-maximizing limited liability companies or joint stock companies
13

Sun, et al. (2005) contains a good reference to the literatures concerning mixed oligopolies.

9that have internal organizations closely resembles those of their western counterparts.14
However, due to a lack of the principal and insufficient supervision over the managers’
discretionary power, they do retain a salient feature of abundant legal loopholes that the
managers can take advantage of. More precisely, we argue that modern Chinese SOEs,
especially large- and medium-sized ones, are better labeled as “distorted”
profit-maximizing firms, distorted by the manager’s routine corruption.
On the other hand, the private firm simply maximizes its profit,(2)π 2 (Q1 , Q2 ) = PQ2 .

As usual, the social welfare function W , defined as the sum of producer surplus(the real profits of the two firms) and consumer surplus, is used to measure theeconomic efficiency of the whole society. Managers’ corruption incurs a transaction cost,which is a deadweight loss to the society. The social planner takes into account such aloss, and the social welfare is defined as
Q + Q2W (Q1 , Q2 ) = π 1 + π 2 + CS − τγ Q1 = ∫0 1

15

Pdq −τγ Q1 .

(3)

However, the governments in transitional economies may not be social-welfare
maximizers as they are pressured by heavy employment burden. To reflect the
government’s concern for employment, we incorporate the total output of the SOE andthe private firm as an argument into the government’s objective function, denoted byθ (Q1 + Q2 ) , where θ (0 ≤ θ ≤ 1) is a constant that measures the degree of employmentpressure.16 Furthermore, we assume that when the government determines the optimallevel of law enforcement, she also cares about the nominal social welfare. Moreover,since the transaction costs of corruption is less visible and is not explicitly promulgatedby the government, we excluded such a cost from the government’s objective function.
Hence, the government’s payoff has as arguments the nominal social surplus, as well as
total output of the SOE and the private firm. It equals the sum of the SOE’s reported
nominal profit, PQ1 − γ Q1 , the private firm’s profit, PQ2 , consumer surplus,∫

Q1 + Q20

Pdq − P (Q1 + Q2 ) , and the employment pressure, θ (Q1 + Q2 ) , i.e.,

14

As aforementioned, the reform has separated SOEs from the governmental bureaucracy and reorganized them into
private capitalist corporations. Recognizing this transformation, the 8th National People’s Congress (1993) changed
the appellation used to describe SOEs from guoying qiye, or “state-run enterprises” to guoyou qiye, or “state-owned
enterprises.” During the report delivered by former Prime Minister LI Peng to that congress, the objective of thereform on SOE has been proclaimed to be “transforming SOEs into self-managed, self-developing, andself-restrictive market players responsible for both profits and losses.”
15
Here π 1 = PQ1 is the real profit of the SOE.
16
In our model formulation, to better reflect the fact that in China, private sector has becoming increasingly
important in absorbing labors, the government takes into account of the whole output. This differs from thegovernment’s objective specified in Sun, et al. (2005), which uses the SOE’s output to denote the government’s
concern for employment. Moreover, it is assumed that in the industry under consideration, the employment
opportunities are increasing in the total output.

10G (Q1 , Q2 ) =∫Q1 + Q20

Pdq − γ Q1 + θ (Q1 + Q2 ) .

(4)

We consider a two-stage game among the government, the SOE and the private
firm: In the first stage, the government chooses α (at no cost) to maximize its own
payoff; whereas in the second stage, the two firms engage in quantity competition, á la
Cournot, by choosing their outputs, respectively.17
Let us first analyze the second stage of the game, taken as given the level of law
enforcement, α . Firms simultaneously choose their outputs to maximize their payoffs.
The Cournot equilibrium is determined by the following first-order conditions,t ( P′Q1 + P − γ ) +Marginal Legal Income

18−αγϕ ′(γ Q1 )(1 − τ )γ



=0,



(5)

Net Marginal Illicit Income Expected Marginal Punishment

P ′Q2 + P = 0 ,(6)

and the second-order conditions ∂ 2 S1 / ∂Q12 < 0 and ∂ 2π 2 / ∂Q22 < 0 . We assume that the2stable equilibrium condition is satisfied, i.e., ∆ ≡2∂ S1 ∂Q1
2∂ π 2 ∂Q2 ∂Q1

2∂ S1 ∂Q1∂Q2
2

2∂ π 2 ∂Q2

> 0 . Equations(5) and (6) implicitly define the reaction functions for the SOE and private firms,
denoted by R1 (Q2 ) and R2 (Q1 ) :R1 (Q2 ) ≡ arg max S1 (Q1 , Q2 ; α , γ , t ,τ ) , R2 (Q1 ) ≡ arg max π 2 (Q1 , Q2 ;α , γ , t ,τ ) .
Q1 ≥ 0Q2 ≥ 0As is common in the literature (see, for example, Dixit, 1986), the outputs of thetwo firms are assumed to be “strategic substitutes,” i.e., one firm’s marginal revenue
declines when the output of the other firm rises, which is equivalent to the holding of
the following two inequalities
P + P Q2 < 0,
'

''

(7)

P + P Q1 < 0,'''

for 0 < α < 1 and 0 < t < 1 . Condition (7) ensures that the slope of each firm’s reaction
function is negative, i.e., Ri' (Q j ) < 0 and Ri' (Q j ) < 1 , here i = 1, 2, and j = 1, 2 . For
example,17

As in Martin and Panagariya (1984), the “costless law enforcement” can be interpreted in two ways. Either “themachinery for law enforcement already exists, and all that is required to make enforcement more vigorous is a
decision by the authorities to ‘get tough’”, or, it is the result of a “technological improvement in the enforcement
activity” (Martin and Panagariya 1984, pp. 210-211).
18
Under our formulation of the model, the book profit of the SOE is positive when P > γ , and negative whenP < γ . From equation (5), it is easy to see that depending on the values of t , τ , α , and ϕ (⋅) , it is possible for the
manager to embezzle to a certain extent even when the book profit is negative. It should be noted that under such a
circumstance, the first term of equation (5) is negative, which implies that the manager has to shoulder part of thenominal loss of the SOE. However, in reality, although the managers are rewarded for their successes, they are notcredibly punished for their failures, and normally, when P < γ , t equals zero.

11

−1 < R2' (Q1 ) = −P ' + P ''Q2
2 P ' + P ''Q2

<0,

(8)

as 2P ' + P''Q2 < 0 by the second-order condition, and P ' + P''Q2 < 0 by (7).
4. A comparative static analysis
We first consider the condition under which the manager corrupts.
Lemma 1. Given the ticheng, t , the legal loopholes in SOE, γ , the unit transaction
cost, τ , and the punishment function, ϕ (⋅) , there exists some α * ∈ (0,1) such that the
manager of the SOE embezzles when α < α * ; otherwise, she chooses not to corrupt.
Lemma 1 shows that under certain circumstances, corruption indeed occurs under ourmodel formulation. To make the analysis more interesting, in what follows, we restrict
our focus to the case in which corruption occurs, i.e., α < α * . Based on the first orderconditions specified by equations (5) and (6), we first consider the comparative static
effects of a change in the probability of detection, α , on the equilibrium outputs,
denoted E1 (α ) and E2 (α ) , and the price, which are summarized as Proposition 1:
Proposition 1. An increase in the probability of detection decreases the SOE’s output,
increases the private firm’s output, but nevertheless decreases total output and, hence,increases price. Formally,

∂E1
∂α

<0,

∂E2
∂α

> 0,

∂ ( E1 + E2 )∂α

< 0 , and

∂P
∂α

>0.

There is a straightforward interpretation to Proposition 1. From the first order condition(5), we see that a decline in α generates a positive effect on the manager’s payoff as it
reduces her expected marginal punishment. Output should then rise to restore theequilibrium. Given that the firms’ products are strategic substitutes, such a commitment
would induce a decrease in the private firm’s output. However, as

dR2 / dQ1 = R2' (Q1 ) < 1 ,the output decrease of the private firm is smaller than the output increase of the state
firm, thus leading to a rise in total output, and hence, a decline in price. As augmented
output intensifies competition and partially corrects the distortions that accompany the
duopoly market structure, it is not surprising to see that the manager’s corruption
generates a pro-competitive effect, or more specifically, a rise in consumer surplus.
The effect of law enforcement level on output has important implications for the12equilibrium book profit of the SOE, π 1* , as the well-being of the SOE’s employees ispositively correlated to the book profit. Specifically, we have:
∂π 1

*

∂α

=

∂[( P − γ ) E1 ]
∂α

=

∂P
∂α

E1 + ( P − γ )From Proposition 1, we see that
∂π 1

∂P
∂α

∂E1
∂α

.

E1 > 0 , whereas sign[( P − γ )*sign( P − γ ) . If P − γ < 0 ,

∂α

∂π 1

∂E1
∂α

] depends on*> 0 ; otherwise, sign(∂α) is ambiguous. When P − γ < 0 ,the book profit of the SOE is negative, and a severer law enforcement level improves
the well-being of the SOE employees. On the other hand, when the book profit of the
SOE is positive, the effect of a severer law enforcement level on the welfare of the
SOE’s employees remains ambiguous. Moreover, the effect of severer law enforcementlevel on the profit of the private firm is quite straightforward. From Proposition 1,
*

∂π 2
∂α

=

∂P
∂α

E2 + P∂E2∂α> 0 , i.e., a stricter law enforcement level is beneficial to the private

firm, as both the price and her output increase as a result. The above findings can besummarized as the following corollary:
Corollary 1. A stricter level of law enforcement benefits the employees of theloss-suffering SOEs and private firms, whereas its effect on the nominally profit-making∂π 1*

SOEs remains ambiguous. Formally,∂α> 0 if P − γ < 0 , otherwise, it is ambiguous;

*

∂π 2
∂α

> 0.

Next, we consider the comparative static effects of changes in ticheng, t , theabundance of legal loopholes in SOE, γ , and the unit transaction cost, τ , on theequilibrium outputs, which are given as Propositions 2, 3 and 4, respectively.
Proposition 2. When the marginal revenue is larger than the exaggerated average cost,or when the expected marginal punishment is larger than the net marginal illicit income,a rise in ticheng augments the SOE’s equilibrium output, decreases the private firm’s
output, but nevertheless increases the total output and hence, lowers price, and viceversa. Formally, when

P ′E1 + P > γ (orαγϕ ′(γ E1 ) > (1 − τ )γ ),

13

∂E1
>0 ,
∂t

∂E2
<0 ,
∂t

∂ ( E1 + E2 )∂E1
∂E2
∂ ( E1 + E2 )∂P∂P
> 0 , and< 0 , and< 0 . Otherwise,
< 0,
>0,
> 0.
∂t
∂t
∂t
∂t
∂t
∂t

Proposition 2 can be interpreted in a similar manner as Proposition 1. From the firstorder condition (5), we see that when the marginal revenue, P′E1 + P , is larger than theexaggerated average cost (which is also the marginal loss of being dishonest), γ , i.e.,
P ′E1 + P > γ (or αγϕ ′(γ E1 ) > (1 − τ )γ ), a rise in t generates a positive effect on the
manager’s payoff as it raises her expected marginal legal income, t ( P′E1 + P − γ ) . To
maintain the expected payoff unchanged, SOE’s output should rise to raise the expectedmarginal transaction cost of corruption and lower her marginal legal income. Moreover,as indicated above, the output decrease of the private firm is smaller than the output
increase of the SOE, thus leading to a rise in total output, and hence, a fall in price. Insum, a rise in t also generates a pro-competitive effect as it induces a rise in consumer
surplus.
One message arising from Proposition 2 is that when the marginal revenue issmaller than the exaggerated average cost, increasing t may reduce the embezzlementof the manager. This is so as given γ , the manager’s embezzlement is denoted by γ E1 .
When E1 decreases, the illicit income also falls.
Proposition 3. When the sum of ticheng, t , and the marginal impact of the legal
loopholes on the marginal punishment in the case of detection, ∂[αγϕ (γ E1 )] ∂γ , is larger
than the net marginal illicit income, a rise in the availability of legal loopholes inside
SOE decreases the SOE’s output, increases the private firm’s output, lowers the total
outputandhence,t + ∂[αγϕ (γ E1 )] ∂γ > 1 − τ ,raisestheprice,

andvice

versa.

Formally,

when

∂E1
∂E2
∂ ( E1 + E2 )∂P
>0 ,< 0 , and> 0 . Otherwise,
<0 ,
∂γ
∂γ
∂γ
∂γ

∂E1
∂E2
∂ ( E1 + E2 )
∂P
<0.
> 0,
< 0,
> 0 , and
∂γ
∂γ
∂γ
∂γ

Proposition 3 can be interpreted in the following manner. The first order condition (5)characterizes the state in which the manager’s expected marginal revenue equals her
marginal cost of corruption. When t + ∂[αγϕ (γ E1 )] ∂γ > 1 − τ , we see that a rise in γ
breaks the equilibrium and marginal illicit income is smaller than the sum of marginal
legal income and expected marginal punishment. Accordingly, SOE’s output has todecrease to restore the equilibrium, i.e.,∂E1< 0 . The rest of Proposition 3 can be∂γ

14explained in a similar manner as that of Proposition 1 and 2.
Proposition 4. An increase in the unit transaction cost contributes to a fall in SOE’s
output, a rise in the private firm’s output, a decrease in total output, and a rise in price.
Formally,∂E1∂E2∂ ( E1 + E2 )
∂P
< 0,
>0,
< 0 , and
> 0.
∂τ
∂τ
∂τ
∂τ

The intuition behind Proposition 4 can be given in a similar way as that of Proposition 3
by exploring the first order condition (5).
Next, we move back to the first stage of the game and analyze the determination of
the optimal levels of law enforcement chosen by the social planner and the government.
We take as a benchmark a situation in which a social planner chooses the optimal levelof law enforcement. Taking the second stage equilibrium outputs into account, the social
planner selects an optimal α * that maximizes her payoff W E (α ) ≡ W ( E1 (α ), E2 (α )).
With the assumption of the existence of an interior solution, i.e., Wαα ≡ ∂ 2W ∂α 2 < 0 ,some derivations lead to the following lemma:

Lemma 2. The optimal level of law enforcement chosen by the social planner, αW* ,should satisfy the following condition
P (1 + R2′ )

Margianl Consumer Surplus Effect

=

τγ
N

.

(9)

Marginal Corruption Deadweight Loss EffectLemma 2 shows that the social planner’s optimal choice involves balancing two
effects. First, there is a consumer surplus effect (the LHS of equation (9)), which
represents the impact of the law enforcement level on consumers. A looser level of law
enforcement generates a positive pro-competitive effect that is beneficial to theconsumers. However, there is also a marginal corruption deadweight loss effect (theRHS of equation (9)), as the looser level of law enforcement also induces the manager
to embezzle more, which leads to a higher level of transaction costs, and hence, moresocial welfare loss. Lemma 2 shows that it is optimal for the social planner to choose alevel of law enforcement that equalizes these two effects.
Next, assuming the existence of an interior solution, i.e., Gαα ≡ ∂ 2G ∂α 2 < 0 , we get
the following result regarding the government’s optimal choice:15

Lemma 3. The optimal level of law enforcement α G* that maximizes the government’s
payoff G E should satisfy the following condition:
P(1 + R2′ )
Marginal Consumer Surplus Effect+θ (1 + R2′ )Employment Effect

=

γN

.

(10)

Nominal Productivity Efficiency

Lemma 3 characterizes how the government determines the optimal level of law
enforcement by balancing three effects. First, like the choice of the social planner, there
is a consumer surplus effect (the first term of the LHS of equation (10)). Second, there
is an employment effect (the second term of the LHS equation (10)), as the government
values employment opportunities. A looser level of law enforcement creates a
pro-competitive effect, and the augmented output as a result implies a higher consumer
surplus level and more employment opportunities. Third, there is a nominal productivity
effect (the RHS of equation (10)), since the government also cares about the average
cost reported by the manager. Lemma 3 shows that when choosing the optimal level oflaw enforcement, the government should balance in such a way that the sum of theconsumer surplus effect and the employment effect exactly matches the nominal
productivity of the SOE.
It should be noted that the condition listed in Lemma 2 differs substantially fromthat in Lemma 3. This is so precisely because of the difference in the objectives of thetwo: Unlike the government, the social planner does not consider the employment
burden. A comparison of Lemma 2 and 3 immediately leads to the following
proposition:
Proposition 5. Whether the government prefers a severer level of law enforcement than
the social planner depends on the comparison between (1 − τ )γ and θ (1 + R2′ ) , namely,
the expected marginal illicit income of the manager and the employment burden effect.
When the former dominates the latter, the government prefers a severer level of law
enforcement, and vice versa. Formally, α G* > αW* if (1 − τ )γ > θ (1 + R2′ ) ; otherwise,
α G* ≤ αW* .

The mechanism behind Proposition 5 can be explained as follows. Condition(1 − τ )γ > θ (1 + R2′ ) implies P (1 + R2′ ) − τγ > P (1 + R2′ ) + θ (1 + R2′ ) − γ . In such a case,applying the optimal α G* chosen by the government to the optimal problem of the16social planner generates a positive net effect to the social planner. The maximization ofsocial welfare mandates the social planner to loosen the level of law enforcement, until
P (1 + R2′ ) − τγ reaches zero, hence α G* > αW* . As aforementioned, Chinese government
confronts a heavy employment pressure. Proposition 5 thus implies that there is apossibility that the government may adopt a less severe law enforcement level than thatof the social planner. In what follows, we explicitly characterize the impacts of optimallevels of law enforcement on social welfare.
5.

Optimal levels of law enforcement and their impacts

In this section, we further explore the properties of the model and show how changes inticheng, legal loopholes in SOEs, and the unit transaction cost affect the government’s
and social planner’s optimal choices of law enforcement. In addition, we consider the
impact on social welfare of the optimally levels of law enforcement chosen by thegovernment and the social planner. Our discussion is based on the following linear
demand function:
P = 1 − Q1 − Q2 ,(11)

and the punishment function:
1

ϕ (γ Q1 ) =2(γ Q1 ) .

(12)

2

From first-order conditions (5) and (6), the equilibrium outputs can be calculatedasE1 (α ) =(1 − 2γ )t + 2(1 − τ )γ
3t + 2αγ

2, andE2 (α ) =equilibrium price, on the other hand, is P E =t (1 + γ ) + αγ − (1 − τ )γ2

3t + 2αγ 2,respectively. The

t (1 + γ ) + αγ − (1 − τ )γ 19
2.

3t + 2αγ 2We first analyze how the government chooses her optimal level of law enforcement.
TakingE1 (α )andE2 (α )
into account, the government maximizes
G E (α ) ≡ G ( E1 (α ), E2 (α )) , giving rise to:αG =*(5γ − 1 − 3θ )t + (1 − τ )γγ (1 + 2θ )
2

.

(13)

On the other hand, the optimal level of law enforcement that maximizes social
welfare, denoted as αW* , can be expressed as
19

In this numerical example, the critical point α*

where the manager is indifferent between corruption and being

integrity is implicitly determined by the following function:t [t (1 − 2γ ) − αγ + (2 + τ )γ ] + 2αγ −
2

3

αγ

2

t (3t + 2αγ )2[(1 − 2γ ) t + 2(1 − τ )γ ] − τγ (3t + 2αγ ) =2

2

As in Section 3, we only consider the case where α < α .
*

17

2

9[(1 − 2γ )t + 2(1 − τ )γ ]

.

αW =
*

(1 + γ − 3τγ )t − (1 − τ )γ

γ (2γτ − 1)
2

.

(14)

Next, we turn to analyze how changes in ticheng, the unit transaction cost and legal
loopholes affect the government’s and social planner’s optimal choices of law
enforcement. In addition, the effect of the employment pressure on government’s
optimal choice is also considered.
The comparative static properties of government’s optimal law enforcement levelcan be summarized as follows:
Result 1. Given the demand and the punishment specifications in equations (11) and∂α G*(12), we have (1)if t >∂t∂α G> 0 if γ >1 + 3θ
5*(1 − τ )γ2(1 + 3θ ) − 5γ

,

∂γ

*

∂α G
*

> 0 , otherwise,∂α G, otherwise,∂γ∂t< 0 ; (4)Result 1 is easy to interpret. Noting that γ >

∂α G

∂α G
*

≤ 0 ; (2)

∂τ

∂α G
*

< 0 ; (3)

∂γ

>0

*

∂θ

< 0.

1 + 3θ
5

implies P′E1 + P > γ , from

Proposition 2, we see that a rise in t leads to a rise in P , resulting a fall in marginal
consumer surplus effect (the first term of the LHS of equation (10)). As shown in the
Proof of Lemma 3,∂E1< 0 implies that P (1 + R2′ ) + θ (1 + R2′ ) − γ∂αis an increasing

function in α G* , a larger α G* is then mandated to restore the equilibrium. The case forγ ≤1 + 3θ
5can be explained conversely. Similarly, from Proposition 4, we see a rise inτ increases P , which leads to a rise in marginal consumer surplus effect in equation(10), calling for a fall in α G* to restore the equilibrium. On the other hand, noting thatt>

(1 − τ )γ2(1 + 3θ ) − 5γ

implies t + ∂[αγϕ (γ E1 )] ∂γ > 1 − τ , from Proposition 3, we see that a risein γ leads to a rise in P and results in an increase in marginal consumer surplus
effect, as can been seen from equation (10), which generates a negative impact on thegovernment’s payoff, and to restore the equilibrium, the government is forced tostrengthen the law enforcement. The case for t ≤(1 − τ )γ2(1 + 3θ ) − 5γ

can be explained in an

opposite manner. In addition, a rise in θ increases the employment effect in equation18

(10), which mandates a smaller α G* to restore the equilibrium. Intuitively, as theemployment pressure increases, the government has to resort to a less severe law
enforcement level as it generates a pro-competitive effect to increase total output,
resulting in more employment opportunities.
Next, we consider the comparative static properties of the optimal law enforcementlevel chosen by the social planner. Although we cannot prove theoretically, thefollowing result shows these effects within our choice of the relevant parameters.
Result 2. Given the demand and the punishment specifications in equations (11) and(12), and choosing t = 0.2, γ = 0.4, τ = 0.5, then the comparative static effects of a change∂α W*of t , γ , or τ on αW can be obtained by fixing the rest two:
*

∂α W

∂τ

∂α W
*

< 0,

> 0 , and

∂γ

*

∂t

< 0.

Result 2 can be interpreted by resorting first order condition (9) and Proposition 2, 3,
and 4, similarly to that of Result 1.
Next, we move on to consider the effects of ticheng, the unit transaction cost andlegal loopholes on the government payoff and that of the social planner. In addition, theeffect of the employment pressure on government’s optimal choice is also explored.
Using G* and W * to denote the equilibrium government payoff and social planner’s
payoff, respectively, we have the following two results:
Result 3. Given the demand and the punishment specifications in equations (11) and (12)and choosing t = 0.2, γ = 0.4, τ = 0.5, θ = 0.5, the comparative static effects of a change∂Gof t , γ , τ , or θ on G* can be obtained by fixing the rest three: (1)
∂G

*

∂t

∂G
∂γ

if t < 0.4 , otherwise,

>0

∂G
∂t

*

≤ 0 ; (3)

∂G
∂τ

*

< 0 ; (4)

∂G
∂γ

*

> 0 if γ <

∂θ

1
9

*

>0;

(2)

, otherwise,*≤0.

The effect of θ on G * can be directly explained from the objective function of
the government. Noting that t < 0.4 corresponds to P(1 + R2′ ) + P > γ in Proposition 2,

19

we see that when t < 0.4 , an increase in t generates a pro-competitive effect, resulting
a rise in the government’s payoff. On the other hand, when t ≥ 0.4 , a rise in t leads to acompetition reduction effect, and the total payoff of the government falls as a result.
From Proposition 4, we see a rise in τ generates a competition reduction effect, which
lowers the payoff of the government. Finally, noting that γ <t + ∂[αγϕ (γ E1 )] ∂γ < 1 − τ19corresponds tofrom Proposition 3, we see that a rise in γ generates a

pro-competitive effect, which dominates the productivity efficiency loss, γ E1 , resulting
1

in a rise in government's payoff. Conversely, in the case γ ≥ , an increase in γ leads
9

to a fall in the government’s payoff.
Result 4. Given the demand and the punishment specifications in equations (11) and (12)and choosing t = 0.2, γ = 0.4, τ = 0.5, the comparative static effects of a change oft , γ or τ , on W*

can be obtained by fixing the rest two: (1)t < 0.5349 , otherwise

∂W
∂t

*

≤ 0 ; and (3)

∂W

∂W
∂τ

*

< 0 ; (2)∂W*

> 0 if

∂t

*

∂γ

<0.

Result 4 can be interpreted by resorting to Proposition 2, 3, and 4, similarly to thatof Result 3.
Finally, we consider the validity of the Leff-Huntington hypothesis that corruption
may augment social welfare. It can be easily shown that the social welfare under nocorruption is4. We use WG* to denote the social welfare achievable under the optimal
9level of law enforcement chosen by the government. We find that there exists a
possibility that corruption can be socially good, even for a government facing heavy
employment burden. This argument is illustrated by the following two results:
Result 5. Given the demand and the punishment specifications in equations (11) and (12)and choosing t = 0.2, γ = 0.4, θ = 0.5, there exists some τ * ∈ (0,1) such that W >
*

G

4
9

if

τ <τ*.
Result 6. Given the demand and the punishment specifications in equations (11) and (12)20and choosing t = 0.2, τ = 0.5, θ = 0.5, there exist γ 1* , γ 2* ∈ (0,1) with γ < γ , such that
WG >
*

4
9

*

*

1

2

if γ ∈ (γ 1* , γ 2* ) .

Result 5 and Result 6 specify two cases under which corruption can be sociallygood, for a government that faces employment pressure. Specifically, when the unittransaction cost is small, or when there are moderate legal loopholes in the SOE,
corruption can be socially good. The underlying mechanism of the above two results is
attributable to the tradeoff between the pro-competitive effect and the deadweight loss
effect. When the pro-competitive effect generated from corruption dominates thedeadweight loss effect, as the conditions given above, corruption can be socially goodby increasing social welfare.
6.

Concluding remarks

Out of the above analysis, there are a couple of messages worth to be stressed. First, atleast under our formulation of the transaction costs, under certain conditions, thepro-competitive effect of corruption is verified, and hence, the Leff-Huntington
hypothesis is espoused even when corruption is “costly.” Second, the literature has
examined the relationship between the competitiveness of the economy and the corrupt
incentives. Rose-Ackerman (1996) maintains that a rise in competitiveness reduces thecorrupt incentives, whereas Celentani and Ganuza (2002) argue that corruption may be
increasing in competition. Our results show that competition and corruption are also
related in a reverse fashion: Under certain conditions, corruption may also increase
competition. In particular, corruption may generate a pro-competitive effect in an
oligopolistic market, which partially corrects the market distortion. Third, a government
under the pressure to provide employment opportunities tends to prefer a different levelof law enforcement from that of a social planner, with the difference of the two depends
on the comparison between the exaggerated average cost of SOE and the sum of theemployment burden effect and the marginal transaction cost of corruption. Fourth, asshown in Proposition 2, under certain conditions, higher wages for managers may
reduce corruption. These insights, we believe, are highly relevant to the ongoing
discourse on SOE reform and the anti-corruption campaign in transitional economies.
Without a doubt, the way we conceptualize and model agent corruption in Chinese
SOEs is not the uniquely best approach. Our approach may not capture all the essential
21

features of agent corruption and the Chinese SOEs. For example, we have used theequilibrium book profit of the SOE as a proxy for the well-being of the employees. An
arguably more satisfactory indicator for this purpose might be the labor cost. However,
the examination of labor cost mandates the introduction of a production function thatallows both labor and capital as inputs, which may complicate analysis, but neverthelessremains to be an interesting topic for future research. Moreover, to emphasize the factthat after a series of reform, many Chinese SOEs have been transformed into largely
profit-maximizers, we have excluded the government’s concerns from the SOE’s
objective. However, in reality, the government does retain certain control powers over
the SOEs, and our specification is admittedly rather shortcut. A promising extension
would be to reformulate the present specification of the SOE’s objective into a weighted
average of the present setting and the government’s payoff. It would be interesting to
see under which conditions the pro-competitive effect might be stronger. In addition, it
would also be interesting to consider the case in which both firms engage in pricecompetition, á la Bertrand. As the reaction functions are upward sloping in a price game(rather than downward sloping in a quantity game), the results may be reversed. Finally,
we have assumed that ticheng, t , the legal loopholes, γ , and the unit cost ofcorruption, τ , are exogenously given in our model. It is also necessary to examine thecases in which they are endogenously determined.
The most natural way to advance the current analysis would be to study an
extended model in which these insufficiencies are addressed. It would be interesting to
examine whether our conclusions could be carried over to such an extended model.

22

Appendix
Proof of Lemma 1. Given α , equations (5) and (6) jointly determine the equilibrium
outputs E1 and E2 . Substituting E1 and E2 , back into equation (1’), we get theequilibrium expected payoff for the SOE’s manager, S . By the envelope theorem,*

1∂S1 ∂α = −ϕ (γ E1 ) < 0 . From the manager’s objective function, we know that when α = 0 ,*the manager inevitably embezzles the public assets, whereas she chooses to be integrity
when α = 1 . Therefore, there exists some α * ∈ (0,1) such that the manager of the SOE
embezzles if α < α * ; otherwise, she chooses not to corrupt.

□

Proof of Proposition 1. By differentiating the first-order conditions (5) and (6) withrespect to α and collecting the terms, we obtain:∂E1 γϕ ′(γ E1 ) [ P '' E2 + 2 P ']
,
=
∂α
∆

(A1)

γϕ ′(γ E1 ) [ P '' E2 + P ']
∂E2
,
=−
∂α
∆

(A2)

where K ≡ t ( P′′E1 + 2 P′) − αγ 2ϕ ′′(γ E1 ) , H ≡ t ( P '' E1 + P′) , and ∆ ≡KHP '' E2 + P ' P '' E2 + 2 P '.

From the second-order conditions and the stability condition, P ′′E2 + P′ < 0 ,P ′′E2 + 2 P ′ < 0 and ∆ > 0 . Together with the assumption of ϕ ′(⋅) > 0 ,∂E2> 0 . Furthermore, from equation (8),∂αdownward-sloping demand curve,∂E1 ∂E2>, hence,
∂γ
∂γ

∂E
dP
= P'
> 0.
dα
∂α

∂E1
< 0 and∂α∂E< 0 . With a∂α□Proof of Proposition 2. By differentiating the first-order conditions (5) and (6) withrespect to t and collecting the terms, we obtain:∂E1 [γ − ( P ' E1 + P) ][ P '' E2 + 2 P ']
,
=
∂t
∆

(A3)

[γ − ( P ' E1 + P )][ P '' E2 + P ']
∂E2
.
=−
∂t
∆

(A4)

1
t

From (5), P′E1 + P −γ = − [(1 − τ )γ − αγϕ ′(γ E1 )] , so we have two cases: P′E1 + P > γ (or23(1 − τ )γ < αγϕ ′(γ E1 ) ) and P ′E1 + P < γ

Proposition 1 yield the result.

(or (1 − τ )γ > αγϕ ′(γ E1 ) ). Similar derivations like□

Proof of Proposition 3. By differentiating the first-order conditions (5) and (6) withrespect to γ and collecting the terms, we obtain:∂E1 [t − (1 − τ ) − ∂[αγϕ ′(γ E1 )] ∂γ ][ P '' E2 + 2 P ']
=
,
∂γ
∆

(A5)

[t − (1 − τ ) − ∂[αγϕ ′(γ E1 )] ∂γ ][ P '' E2 + P ']
∂E2
=−
.
∂γ
∆

(A6)

Similar to the proof of Proposition 2, sign(∂E1∂E) and sign( 2 ) depend on∂γ∂γ

sign[t − (1 − τ ) − ∂[αγϕ ′(γ E1 )] ∂γ ] .

Similar arguments like the proof of Proposition 1 and 2 yield the result.

□

Proof of Proposition 4. By differentiating the first-order conditions (5) and (6) withrespect to τ and collecting the terms, we obtain:∂E1 γ [ P '' E2 + 2 P ']
=
,
∂τ
∆

γ [ P '' E2 + P ']
∂E2
.
=−
∂γ
∆

Similar arguments like Proposition 1 generate the result.

□

Proof of Lemma 2. By differentiating W E (α ) ≡ W ( E1 (α ), E2 (α )) with respect to α at E1
and E2 , we get∂E1
dW E ∂E1 ⎡ ∂W ∂W ∂E2 ∂α ⎤ ∂E1< 0 , it=+[ P(1 + R2′ ) − τγ ]. Since⎢⎥=∂α ⎣ ∂Q1 ∂Q2 ∂E1 ∂α ⎦ ∂αdα∂αfollows that P(1 + R2′ ) − τγ = 0 .

□Proof of Lemma 3. By differentiating G E (α ) ≡ G ( E1 (α ), E2 (α )) with respect to α at E1
and E2 , we get:dG E ∂E1 ⎡ ∂G ∂G ∂E2 ∂α ⎤ ∂E1=+[ P(1 + R2′ ) + θ (1 + R2′ ) − γ ].
⎢⎥=∂α ⎣ ∂Q1 ∂Q2 ∂E1 ∂α ⎦ ∂α
dα

Since

∂E1
< 0 , it follows that P(1 + R2′ ) + θ (1 + R2′ ) − γ = 0 .
∂αProof of Proposition 5. When (1 − τ )γ > θ (1 + R2′ ) , we have24□

P (1 + R2′ ) − τγ > P (1 + R2′ ) + θ (1 + R2′ ) − γ , ∀α ∈ (0,1) .

∂E1
∂E1
∂E1
[ P (1 + R2′ ) − τγ ] <[ P (1 + R2′ ) + θ (1 + R2′ ) − γ ] , ∀α ∈ (0,1) .
< 0 implies that
∂α
∂α
∂α

Inserting α = α G* into the above inequality and from Lemma 1, we get∂E1∂α[ P (1 + R2′ ) − τγ ]<0.
α =α G*

From Lemma 2, Wα (α W* ) ≡∂E1

Therefore,

∂α

∂E1
∂α

[ P (1 + R2′ ) − τγ ][ P (1 + R2′ ) − τγ ]

∂E1

<

∂α

*

α =α G

Since Wαα < 0 , we have=0.
*α =α W.

[ P (1 + R2′ ) − τγ ]*α =α Wα G* > αW* .

When (1 − τ )γ ≤ θ (1 + R2′ ) , α G* ≤ αW* can be shown in a similar way.

□

Proof of Result 1. Differentiating equation (13) with respect to t , τ , γ and θ ,respectively, we have:
∂α G
*

=

∂t
∂α G

(5γ − 1 − 3θ )γ (1 + 2θ )
2

*

=−

∂θ

∂α G

*

γ (1 + 2θ )2t>

(1 − τ )γ

if γ >

>0

∂t

∂τ

=−

γ (1 + 2θ )

∂α G

2

1 + 3θ
5

2(1 + 3θ ) − 5γ

∂γ

< 0,

∂γ

=

2(1 + 3θ )t − 5tγ − (1 − τ )γγ (1 + 2θ )
3

2α G
*

3t

γ (1 + 2θ )
2

=−

∂α G

(1 + 2θ )−

3t

γ (1 + 2θ )
2

,

< 0.

*

; otherwise,

*

,

−

∂α G
*

1

2[(5γ − 1 − 3θ )t + (1 − τ )]*Obviously,

∂α G

,

∂α G
*

> 0 ; otherwise,∂γ∂t≤ 0 . It is also obvious if

< 0.

□

Proof of Result 2. Differentiating equation (14) with respect to t by choosing∂α W(1 + 0.4 − 3 × 0.5 × 0.4)*

γ = 0.4, τ = 0.5 we have∂t=

0.16(2 × 0.4 × 0.5 − 1)

=−

25
3

<0.

Similarly, differentiating equation (14) with respect to τ by choosing t = 0.2, γ = 0.4 ,∂α G*

we have∂τ=−

0.01246(0.108τ − 0.16)

2

< 0.

Differentiating equation (14) with respect to γ by choosing t = 0.2, τ = 0.5 , we get:
∂α W
*

∂γ

2(3γ − 3γ + 1)
2=

5γ (1 − γ )
3

2

.

25

∂α W
*

Since 3γ 2 − 3γ + 1 > 0 ,

∂γ

> 0.

□

0.04 − 0.06θ

Proof of Result 3. Choosing t = 0.2, γ = 0.4, τ = 0.5 , then α G* =0.16(1 + 2θ ).

Substituting it into the expressions for E1 (α ) and E2 (α ) , we have*

0.08 + 0.16α G*

0.44

E1 (α G ) =, E2 (α G* ) =*0.6 + 0.32α G, E1 (α G* ) + E2 (α G* ) =0.6 + 0.32α G*

0.56 + 0.44θ
0.68.

Hence,G (α G ) =**0.384 + 0.648θ + 0.44θ

2

−

0.68

1 ⎛ 0.56 + 0.44θ ⎞

⎜

2⎝

2

∂G

*

= 0.591 + 1.01θ > 0 .
⎟,
∂θ
⎠

0.68

Similarly, choosing θ = 0.5, γ = 0.4, τ = 0.5 , we have
G (α G ) =**0.29 + 1.945t−

0.2 + 2.5t

Hence, when t < 0.4 ,∂G∂t

1 ⎛ 0.3 + 1.35t ⎞

2

∂G

⎜
⎟ ,
2 ⎝ 0.2 + 2.5t ⎠> 0 ; Otherwise,

=

∂t

∂G

*

*

0.192(0.4 − t )(0.2 + 2.5t )

3

.

*

∂t

≤0.

By choosing θ = 0.5, γ = 0.4, t = 0.2 , the expression of G * is denoted as
0.969 − 0.58τ

1 ⎛ 0.87 − 0.6τ ⎞

2

∂G

⎜
⎟,
0.9 − 0.4τ
2 ⎝ 0.9 − 0.4τ ⎠Choosing θ = 0.5, τ = 0.5, t = 0.2 , we have
G (α G ) =**G (α G ) =
*

∂G

*

*

∂γ

Here, sign(
γ <

1
9

−

1.5(0.15 + 1.05γ )1.5γ + 0.1(0.2γ + 0.6γ )1.5γ + 0.1

=−

∂t

2

−

*

−

(0.1921 + 0.232τ )(0.03 + 0.2τ )(0.9 − 0.4τ )1 ⎛ 0.15 + 1.05γ ⎞

3

< 0.

2

⎟ ,

⎜

2 ⎝ 1.5γ + 0.1 ⎠(0.9γ + 3.2625γ + 0.1945)(0.45γ − 0.05)
2

=−
∂G

(1.5γ + 0.1)

3

.

*

∂γ

, we have) depends on the sign of the term (0.45γ − 0.05) . Obviously, when
∂G
∂γ

*

> 0 ; when γ ≥1
9, we have

∂G
∂γ

*

≤0.

Proof of Result 4. Choosing t = 0.2, γ = 0.4 , then αW* =20τ − 1516τ − 20□.

Substituting it into the expressions for E1 (α ) and E2 (α ) , we have
E1 (α W ) =*0.44

0.08 + 0.16α W*, E2 (αW* ) =*0.6 + 0.32α W

0.6 + 0.32α W*

Hence,

26, E1 (αW* ) + E2 (α W* ) =71τ − 52.5 − 20τ
50τ − 52.5

2.

(71τ − 52.5 − 20τ )2W (α W ) =
*

∂W
∂τ

*

*

2(50τ − 52.5)

2

,

2

(71τ − 52.5 − 20τ )(50τ − 52.5)(1000τ − 2100τ + 1102.5)
2

=−

2

(50τ − 52.5)

4.

Since τ ∈ [0,1] , it can be easily shown that(71τ − 52.5 − 20τ )(50τ − 52.5)(1000τ − 2100τ + 1102.5) > 0 .
2∂WTherefore,

2

*

∂τ

<0.

Similarly, when choosing τ = 0.5, γ = 0.4 , we have
W (α W ) =**(65t + 29)(76 − 44t )625(5 + t )It can be shown that

∂W
∂t

∂W

,

*

=

∂t

16116 − 28600t − 2860t
625(5 + t )

2

∂W

*

*

if t < 0.5349 , otherwise

>0

∂t

2

.

≤0.

When choosing τ = 0.5, t = 0.2 , we get(5γ + 2 − 3γ )2W (α W ) =**8(3γ + 1)

∂W

2

,

2

*

(5γ + 2 − 3γ )(3γ + 1)
2

=−

∂γ

4(3γ + 1)

3

4

< 0.

□

Proof of Result 5. Choosing θ = 0.5, γ = 0.4, t = 0.2 , we have
EG = E1 (α G ) + E2 (α G ) =**87 − 60τ

1(87 − 60τ )(93 − 92τ + 32τ )22(90 − 40τ )2, WG* = EG* (1 − EG* − τγ ) =90 − 40τ

48019 − 64656τ + 61936τ − 17280τ

918(90 − 40τ )Hence, WG − =
*

*

2

2

2

.

3

.

Let F (τ ) ≡ 8019 − 64656τ + 61936τ 2 − 17280τ 3 , we can show that
F (0) > 0, F (1) < 0, F ′(0) < 0, F ′(1) > 0, F ′′(τ ) > 0 .
Thus there exists some τ ** ∈ (0,1) , such that F ′(τ ) < 0 if τ < τ ** and F ′(τ ) > 0 if
τ >τ

**

. Since F (0) > 0 and F (1) < 0 , there must exists some τ * ∈ (0, τ ** ) such that

F (τ ) > 0

if τ < τ * .

□Proof of Result 6. Choosing θ = 0.5, τ = 0.5, t = 0.2 , we have
EG = E1 (α G ) + E2 (α G ) =***3 + 21γ
2 + 30γ

4700γ − 5 − 1827γ − 1134γ

918(2 + 30γ )Hence, WG* − =

2

2

1

3 + 132γ + 597γ − 126γ22(2 + 30γ ), WG* = EG* (1 − EG* − τγ ) =

2

2

3

.

3

.

Let G (γ ) ≡ 700γ − 5 − 1827γ 2 − 1134γ 3 , we can show that
G (0) < 0, G (1) < 0, G ′(0) > 0, G ′(1) < 0, G ′′(γ ) < 0 .
Thus there exists some γ ** ∈ (0,1) , such that G ′(τ ) > 0 if γ < γ ** , G ′(τ ) < 0 if γ > γ **27

and G ′(γ ** ) = 0 . By solving the equation G ′(γ ** ) = 700 − 3654γ − 3402γ 2 = 0 , we getγ**= 0.166 . Since G (γ ) = G (0.166) = 55.623 > 0 , there exist γ 1 , γ 2 ∈ (0,1)
*

**

4

*

with γ 1* < γ 2* ,such that G (γ ) > 0 if γ ∈ (γ 1* , γ 2* ) . As sign(WG* − ) depends on sign(G (γ )) , we
9immediately get the result.

□28

References

Abed, G.T. and Davoodi, H.R. (2000). Corruption, structural reform, and economic
performance in the transition economies. IMF Working Paper WP/00/132.
International Monetary Fund.
Celentani, M. and Ganuza, J. (2002). Corruption and competition in procurement.
European Economic Review 46: 1273-1303.

Chen, K. (2004). Fiscal centralization and the form of corruption in China. European
Journal of Political Economy 20: 1001-1009.

Chow, G. (2005). Corruption and China’s economic reform in the early 21st century.
CEPS Working Paper No. 116, Princeton University.
Damania, R. Fredriksson, P.G. and Mani, M. (2004). The persistence of corruption andregulatory compliance failures: Theory and evidence. Public Choice 121:363-390
Dixit, A. (1986). Comparative statics for oligopoly. International Economic Review 27:
107-122.
Fisman, R. (2001). Estimating the value of political connections. American Economic
Review 91: 1095-1102.

Gamboa-Cavazos, M. Garza-Cantu, V. and Salinas, E. (2005). The organization ofcorruption. Mimeo.
Garnaut, R. Song, L. Tenev, S. and Yao, Y. (2005). China’s ownership transformation:
Process, outcomes, prospects. Washington, D.C.: The World Bank.

Guo, Y., and Hu, A. (2004). The administrative monopoly in China’s economictransition. Communist and Post-Communist Studies 37: 265-280.
He, Z. (2000). Corruption and anti-corruption in reform China. Communist andPost-Communist Studies 33: 243-270.

Hellman, J.S. Jones, G. and Kaufmann, D. (2000). ‘Seize the state, seize the day’: State
capture, corruption, and influence in transition. Working Paper 2444. The WorldBank.
Huntington, S. (1968). Political order in changing societies. New Haven: Yale
University Press.
Klitgaard, R. (1988). Controlling corruption. Berkeley: University of California Press.
Klochko, M.A. and Ordeshook P.C. (2003). Corruption, cooperation and endogenous
time discount rates. Public Choice 115: 259-283.
Laffont, J.J. and N’Guessan, T. (1999). Competition and corruption in an agency
relationship. Journal of Development Economics 60: 271-295.
29Laffont, J.J. and Tirole, J. (1991). Auction design and favoritism. International Journalof Industrial Organization 9: 9-42.

Leff, N. (1964). Economic development through bureaucratic corruption. American
Behavioral Scientist 8: 8-14.

Levin, M. and Satarov, G. (2000). Corruption and institutions in Russia. European
Journal of Political Economy 16: 113-132.

Li, K. Smyth R. and Yao, S. (2005). Institutionalized corruption and privilege in China’s
socialist market economy: A general equilibrium analysis. Pacific Economic
Review 10: 341-360

Liew, L. (1993). Rent-seeking and the two-track price system in China. Public Choice
77: 359-377.
Lin, J.Y. Cai, F. and Li, Z. (2002). The Chinese miracle: Development strategy andeconomic reform. Shanghai: Sanlian Press (in Chinese).

Lui, F. (1985). An equilibrium queuing model of bribery. Journal of Political Economy
93: 760-781.
Manion, M. (1996). Corruption by design: Bribery in Chinese enterprise licensing.
Journal of Law, Economics and Organization 12: 167-195.

Martin, L. and Panagariya, A. (1984). Smuggling, trade, and price disparity: A
crime-theoretic approach. Journal of International Economics 17: 201-217.
Mauro, P. (1995). Corruption and growth. Quarterly Journal of Economics 110:681-712.
Murphy, K. Shleifer, A. and Vishney, R. (1991). The allocation of talent: Implication forgrowth. Quarterly Journal of Economics 105: 503-530.
Myrdal, G. (1968). Asian drama. New York: Random House.
Nakagane, K. (2003). Economics on corruption in development and transitional process.
Ajia Keizai (Asian Economy) 44: 27-46 (in Japanese).

Polinsky, A.M. and Shavell, S. (2001). Corruption and optimal law enforcement.
Journal of Public Economics 81: 1-24.

Rauch, J.E. (2001). Leadership selection, internal promotion, and bureaucratic
corruption in less developed polities. Canadian Journal of Economics 34:
240-258.
Rose-Ackerman, S. (1996). Redesigning the state to fight corruption. Public Policy for
Private Sector, World Bank.
Schleifer, A. and Vishny, R.W. (1997). A survey of corporate governance. Journal of
Finance 52: 737-783.

Sun, Q. Zhang, A. and Li, J. (2005). A study of optimal state shares in mixed oligopoly:30

Implications for SOE reform and foreign competition. China Economic Review
16: 1-27.
Svensson, J. (2005). Eight questions about corruption. Journal of Economic Perspective
19: 19-42.
Treisman, D. (2000). The causes of corruption: A cross-national study. Journal of Public
Economics 76: 399-457.

Ventelou, B. (2002). Corruption in a model of growth: Political reputation, competitionand shocks. Public Choice 110: 23-40.
Vinod, H.D. (2003). Open economy and financial burden of corruption: Theory andapplication to Asia. Journal of Asian Economics 13: 873-890.
Wen, M. (2004). Bankruptcy, sale, and mergers as a route to the reform of Chinese
SOEs. China Economic Review 15: 249-267.
Wolf, C. (2004). China’s rising unemployment challenge. Asian Wall Street Journal,
July 7, 2004.
World Bank (1992). Reform in 1990 and the role of planning. Washington, D.C.
World Bank (1997). Shareholding experiment, modern enterprise reform system, andstate-owned enterprise reform. Washington, D.C.

Wu, J. (1999). China’s contemporary economic reform: Strategies and implementations.
Shanghai: Far Eastern Press (in Chinese).
Yao, S. (1997). Corruption and the anti-corruption movement: The modelling andanalysis of the situation in China. Australian Economic Papers 36: 156-165.
Zhang, A. Zhang, Y. and Zhao, R. (2002). Profitability and productivity of Chinese
industrial firms: Measurement and ownership implications. China Economic
Review 13: 65-88.

Zhang, W. (1997). Decision rights, residual claim and performance: A theory of how the
Chinese state enterprise reform works. China Economic Review 8: 67-82.
Zhang, W. (1999). Firm theory and SOE reform in China. Beijing: Peking University
Press (in Chinese).
Zhou, M. and Wang, X. (2000). Agency cost and the crisis of China’s SOE. China
Economic Review 11: 297-317.

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