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ORM2010 Mechanisms for corruption suppression
Alexander Vasin Pavel Nikolaev Anton Urazov Lomonosov Moscow State University

The research was supp orted by Grant of the President of the Russian Federation #693.2008.1 and by Grant of Russian Foundation for Basic Research for project #08-01-00249 #693.2008.1 #08-01-00249

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Introduction

Government agencies and large corporations meet similar problems related to control of agents dealing with outsiders: citizens under audit of the agency or clients of the company. In such interaction there typically exists a possibility of collusion. In order to prevent it, agencies and corporations usually organize hierarchical controlling structures. The present pap er considers game-theoretic models of such structures and examines a problem of their optimal organization.

, : , , . . , , . - .

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There are two main directions of the state inspections' activities:
1

Collection of payments to the state budget. Inspection's task is to control the payment's values and check the exemptions from the payment. The aim is to prevent evasion but not interfere with the agents eligible for exemption from the payment.

2

The second direction is concerned with prevention of the law infringement. Police, sanitary, firework inspection deal with this task.

:
1

. : . : , , , .

2

: , - (, , , ).

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Corruption in Russia

Corruption is one of the most imp ortant problems in the government inspections' organization. In broad terms, corruption is the abuse of public office for private gain. From the beginning of 2000's Russian leaders demonstrate willingness to restrict corruption, but p ositive shifts were not achieved.

( ). 2000- , .

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Corruption Perceptions Index by Transparency International (Novemb er 17, 2009): The most corruption-free country is New Zealand with 9.4 p oints of 10 possible. The first ten also included Denmark, Singapore, Sweden, Switzerland, Finland, Netherlands, Australia, Canada and Iceland. Russia app eared in 146th place of 180 with 2.2 points. The same score got Ukraine, Zimbabwe, Kenya, Cameroon, Ecuador, Sierra Leone, Timor-Leste.

Transparency International 17 2009 : C ( 9,4 10 ) . , , , , , , - , . 2,2 , 146 180 . , , , , , -, .

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In 2005 Indem Foundation published the results of the second survey, devoted to the corruption in Russia (the first one took place in 2001). Annual volume estimate of the business corruption market reached $316 billion and exceeded budget revenues 2.6 times. The most corrupted organizations are non-financial organizations and sup ervising bo dies (they were mentioned by 39% of resp ondents). The highest readiness to bribe indicator was found in road p olice services: 68.9%, but in 2001 it made 86.0%. According to the National Anticorruption Committee, annual volume of corruption in Russia for 2009 is about 300 billion. Thus, the situation has not improved.

2005 . "" , ( 2001 ): $316 ., 2,6 . "" : , C, ., 39%. : 68,9%, 2001 . 86,0%. , 2009 $300 . , .
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There are 2 main forms of corruption:
1

Brib ery. Happens when an inspector provides some privileges to the agent who has no rights on it or allows or supposes illegal activity favorable to the agent. Extortion. Happ ens when an inspector demands a reward for granting a privilege to the agent who has legitimate rights to it.

2

Remark 1 (on the metho dology of our research) An economic damage caused by corruption can not b e measured merely by the number and size of brib es. Corruption causes hundreds billions rubles of underpayed taxes and customs duties, thousands of p eople killed and injured in fires, accidents, etc.

:
1

. , , , . . , .

2

1 ( ) , , . , , , , , .
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Literature review

Corruption and its impact on the efficiency of government agencies has b een widely discussed in theoretical literature (see reviews in Satarov (2004), Levin, Tsirik (1998)). In some features, our mo del is close to the works by Chander, Wilde (1992), Hindriks, Keen, Mutho o (1999), that take corruption in tax inspection into account. The important difference: in these mo dels brib ery is revealed with a certain exogenously given probability, while we focus on centralized mechanisms of corruption suppression, and in our models the probability of revealing corruption depends on the strategy of insp ection organization.

(. (2004), , (1998)). , Chander, Wilde (1992) Hindriks, Keen, Muthoo (1999), . , , , .
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Another relevant research direction examines optimal hierarchies (Keren, Levhari, 1983, Qian, 1994). However, these pap ers do not take collusion into account. Our previous results see in Vasin, Panova (2000), Vasin (2005), Vasin, Morozov (2005). The purp ose of the research The purp ose of the present research is to find an answer to the question: How to construct an efficient controlling system that suppresses corruption and provides law enforcement? We consider a country where a b enevolent leader aims to organize an efficient controlling system (for instance, tax inspection) and to suppress corruption.

(Keren, Levhari, 1983, Qian, 1994). , . Vasin, Panova (2000), Vasin (2005), Vasin, Morozov (2005). : c , ( ) ? , (, ) .
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We assume that 0-level agents (taxpayers) choose correct action depending on the realization of random factor (in particular, pay a tax according to their income and tax schedule). In order to provide honest b ehavior, the leader creates a pyramidal structure in which 1-level inspectors control 0-level agents, 2-level insp ectors revise audits of the 1-st level, etc. The leader has a limited numb er of associates, whose time is very expensive, and he can hire a necessary numb er of agents, who maximize their own expected income, that is they behave honestly if such b ehavior is optimal.

, 0- () ( ). , 1- 0- , 2- 1- .. , , , , , .

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The formal model

N 0 (). ( ) T0 . t0 . t (Ia ) 0 () Ia [I ). t0 (Tmin , T
min

,I

max

] (, t (I ) 0
min

max

), Tmin = t (I 0

), Tmax = t (Imax ). 0

Ia F (I ), . 2 :
, , , .

, Ia .

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: 0 p1 (t0 ). t0 < t , 0 f0 (t (I ) - t0 (I )), f0 > 1. 0 c1 . . 2- . p2 (t0 , t1 ) 0 1. ... k pk (t0 , t1 , . . . , tk
-1

).
l-1

l tl > t

, r
-1

(r = 0, 1, . . . , l - 1) fr (tl - tl 2

).

, ( ). .
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The inspection strategy

P : k p1 (t0 ), . . . , pk (t0 , . . . , tk
-1

).

: f0 , . . . , fk c1 , . . . , ck . , , . 2 .
-1

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The coalitional approach (cooperative game theory) ( )

Cl , 0 1, . . . , l, l < k, . Cl t0 (I ), t1 (I ), . . . , tl (I ), i = 0, . . . , l - 0 . P Cl , , .. t0 (I ) = t (I ), 0 tr (I ) = t (I ), r = 1, . . . l, 0 l + 1, . . . , k - 1. 1 P Cl , p1 (·) · . . . · ps (·) 1 f0 + . . . + f , s l + 1.
s-1

()

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The non-cooperative approach (subgame perfect equilibrium) ( )
P , 0, 1, . . . , k - 1. , s l - 1 0 (tl-1 < t ). 0 0, 1, . . . , l, ? , tl [tl-1 , t (I )) 0 : 8 > pl+1 (t0 , . . . , tl ) · fi + bil < fi , < X bil > pl+1 (t0 , . . . , tl ) · fl . > :
i
, i = 0, . . . , l - 1

b

il

, i l

(t (I ) - tl ). 0 I , l = 1, . . . , k - 1 t0 . . . tl < t (I ) , 0 , P , .
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2 P , , , p1 (·) · . . . · ps (·) s k. , P , (*) s k. , . : Z (p1 (c1 + p2 (c2 + . . . + pk-1 (ck-1 + pk ck ) . . .)dF (I ),
I
1 f0 + . . . + fs

,
-1

( )

pi = pi (t (I ), . . . , t (I )). 3 , , s- 2 P fi 1 f0 i=0 p1 = p1 = ^ , p2 = p2 = ^ , ps = ps = ^ , s = 2, . . . , k, s- 1 f0 f0 + f1 P fi
i=0

t0 , . . . , t

k -1

max

.
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Other punishment schemes

, , . , . , , , . ?

K (l) {0, 1, . . . , l - 1}, l - 1 K (l) , , l . , (bil 0, i K (l)) : 8 > pl+1 fi + bil < fi , i K (l) K (l + 1) > > > < bil < fi , i K (l)\K (l + 1) >X > > bil > pl+1 fl . > :
iK (l)
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4 (K (l), l = 0, . . . , k - 1), P , , , P fi ps
iK (s-1)

P
iK (s)

f

s k.
i

S = (K, P ), K P . , .

5 , , S (K (l) = {0, . . . , l - 1}, l = 1, . . . , k) p, 3. ^

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The optimal salaries of inspectors

fi , . , . (si - s , s , = . l [1, . . . , k - 1] sl . ck . sl fl (sl ) = (sl - salt )/(tmax - tmin ).
1- alt alt

), si

, ,

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3 5, , : . s s s

C (s) =

1 0

f

+

2

f0 + f1 (s1 ) c
k

+ ... +

k-1 k-2

f0 + f1 (s1 ) + . . . + f - min

(s

k-2

)

+

+

f0 + f1 (s1 ) + . . . + f

k -1

(s

k-1

)

s1 ,...,sk-1

,

si sa ,

i = 1 , . . . , k - 1.

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ta = s · ^ , t 1 = s1 · , . . . , tk = tk = ck · , f0 (tmax - tmin ) f0 (tmax - tmin ) f0 (tmax - tmin ) (1) i-1 X ui = 1 + tj - (i - 1)ta , i = 1, . . . , k + 1 (2)
j =1

alt

:
k X ui i=1 +1

G(u) = u1 = 1, u
k+1

+ ta

ui

-

u2 ,...,uk+1

min

(3)

^ = uk - tk + ta , u

i+1

ui , i = 1, . . . , k - 1.

(4)

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6 u , i = 2, . . . , k - 1 : i ui =
-1

-1

u2 i ui
+1

+ ta

,

i = 2, . . . , k .

(5)

s1 , . . . , sk (1)-(2)

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An Example (Taxation of small enterprises)

Ia [0, Im ] E [I ] = I
av g

. Ia

t0 (Ia ) = tIa . : R = N (tIavg - C (s)) (6)

: I
m

= 1 000 000$, I

av g

= 400 000$, = 0.0018 (

annual

= 0.1), = 570

t = 0.2, f0 = 4 ck = 100 000$ s
alt

= 140$ (700$

). 5 (60 ).

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Numerical results

, , C /(C + R), Z = C /C
min

, C

min

=s

alt

/f0 ,

, , k = 3, . . . , 7 :
k C R C /(C + R) Z s1 s2 s3 s4 s5 s6 p1 p2 p3 p4 p5 p6 p7 0,2500 0,2404 0,2418 0,2500 0,3407 0,3447 0,3460 0,2500 0,4178 0,4252 0,4284 0,4298 0,2500 0,4766 0,4876 0,4932 0,4960 0,4974 3 3 710 76 290 0,0464 106 4 582 18 475 4 3 080 76 920 0,0385 88 2 861 7 988 22 770 5 2 777 77 223 0,0347 79 2 099 4 689 10 699 24 647 6 2 602 77 398 0,0325 74 1 684 3 240 6 358 12 608 25 139 7 2 490 77 510 0,0311 71 1 430 2 473 4 351 7 738 13 846 24 863 0,2500 0,5216 0,5361 0,5442 0,5487 0,5513 0,5527
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Discussion

. 4 , 4% . k = 4 100 000 559 - 17 ( k = 7, , 868 11). 0.56. , .

, . .

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A model with secret signals

1, . . . , k - 1 . s Is , I Is I . , , , . 3 P (): p1 = p2 = 1 f
0 s-1

,

ms {0, 1}, ms = 1

f0 , m1 = 0, p2 = 1 - 1 , m1 = 1. f0 + f1 (s1 ) p3 (m1 , m2 ) = 2 > 0, , p3 (m1 , m2 ) = 1 - 3 , , .. max(m1 , m2 ) = 1.
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7 1 , 2 , 3 > 0 P () . 0 (t0 = t (I )), 1 2 0 . 0- 1- . : 0 1 N f0 @s1 + s2 A + O(). f0 f0 + f1 (s1 ) (140$ ). , , 70$ 80 000$. , , .

(7)

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On practical implementation of specified strategy. Singapore's example . .
In the proposed mo del of organizing tax insp ection we tried to formalize the approach, which was successfully applied in Singapore: The Corrupt Practices Investigation Bureau (CPIB) was founded to prevent corruption. The CPIB derives its p ower from legislation that grants it remarkable discretion. Among the CPIB's unique features are its strict hierarchical structure and small size. The officials are paid high salaries, but are subject to intensive control.

, : . . . , .
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In case of negligent work the employee is fired without the possibility get a job in public services again. About 50% of employees of tax and customs services were fired during the initial stages of the reform. Singap ore is among the ten least corrupt rated countries according to Transparency International at the moment. It to ok about 20 years to achieve this result.

. 50% . 10- Transparency International. 20- , .

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Possible anti-corruption measures in Russia

Strict regulation of officials' actions and simplification of bureaucratic pro cedures. Successful suppression of the corruption is p ossible in areas which have unambiguously interpreted, comprehensive and verifiable rules defining right b ehavior of controlled agents. Formulation of such rules is the first necessary step for corruption suppression. Tightening of insp ections and p enalties. Such approach do esn't always lead to efficient results. In some cases, increased p enalties only lead to increasing the amount of brib es. But even the optimal audit strategy with excessively strict punishment of taxpayers and insp ectors can have a negative impact and lead to more serious crimes.

, . , , , . - . . . . , .
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Mandatory declaration of prop erty and income by officials has been widely discussed in Russia recently. The introduction of such rule may be reasonable in terms of limiting so cial inequality and strengthening of public control over the exp enditure of public funds. However, it will reveal only unexp erienced and stupid corrupt officials. Most of the brib etakers are ready for the intro duction of the rule and will definitely find someone to rewrite their income and assets to. Moreover, such law creates the p otential for discredit of honest officials.

. . , . , . , .

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Hot lines and whistle-blower protection. Our analysis shows that secret signals about the attempts of bribery can significantly reduce the costs of checking and allow to organize an insp ection more effectively. In Hong Kong, for instance, the Indep endent Commission Against Corruption runs a hot line and guarantees that every allegation is investigated. However, in cases where anonymity cannot be guaranteed, those who protest corruption often place themselves at risk. For this reason, anti-corruption efforts need legislation to protect whistle blowers from official sanctions or even to reward them.

. , . , , . , , , j . : .
32 / 34

Limiting the maximum numb er of audits to one or two for the annual rep orting p eriod seems quite wrong. The p otential for rep eated audit is a critical factor for preventing corruption. Note that the mechanism of random selection should b e controlled by the center. Otherwise, a situation of corruption development will be created. Regular staff replacement. Annual dismissal of ab out 3% of the employees. If the dismissal is not directly related to the audit results, then this measure will increase costs for corruption suppression.

. . , . , . . 3% . , .
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[2]

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[3]

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[4]

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[5]

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[6]

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http://www.transparency.org/policy_research/surveys_indices/cpi/2009/cpi_2009_table. [7] [8] Vasin A., Panova E. Tax Collection and Corruption in Fiscal Bo dies. 2000. .: , "",

. / . . . . 2004.

[9]

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[10]

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[11]

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