State border corruption is still a problem for Belarus, Ukraine and Moldova. In a theoretical model, it is shown how a border guard authority should optimally allocate budgetary resources to oblasts in presence of corruption, so as to minimise the general average number of illegal migrants.corruption; border guard authority; illegal migration; illegal immigration; undocumented migration; border corruption; border guards; people smuggling; people smugglers; human smuggling; border region; state border corruption; border crossings; bribes; resource allocation

Lappo, Petr

Lundgren, Ted

English

Research Papers in Economics

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BhrnyCK 2 
PROBABILITY THEORY, 

MATHEMATICAL STATISTICS 

AND THEIR APPLICATIONS 

THE COLLECTION OF SCIENTIFIC PAPERS 

Number 2 

MI1HCK 
Pl1Blll 
2009 STATE  BORDER  CORRUPTION  AND  ILLEGAL 

MIGRATION: A  MODEL 

Ted Lundgren, Petr Lappo 
Moldova State University, departments ofWorld Economics 

and Mathematical Modeling 

G6teborg, Sweden 

E-mail: wLlundgren@hotmail.com 

Belarusian State University, Probability Theory 

and Mathematical Statistics Department 

Minsk, Belarus 

E-mail: LappoPM@bsu.by 

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Keywords:  Illegal  migration,  irregular  migration,  people  smuggling,  illegal  border 
crossings, syndicates, corruption, border administration, state border corruption 
In recent years, a number of authors have pointed out the relationship between irregular 
migration and state border corruption. The critical variable seems to be the interaction between 
the governments and organised crime syndicates [1,  p.  149]. There is  a  direct relationship be­
tween the regimes that organise and regulate migratory movements, and the scope of irregular 
migration [6, p.  78]. As syndicates have become more sophisticated and profitable - as a conse­
quence of the higher demand and cost for their services - their capacity and means to corrupt 
have also grown [3, p.  121]. Corruption is now a key element in human smuggling and traffick­
ing because it makes it easier to get the migrants across the borders [1, p. 149] and should there­
fore  be viewed as an essential cog in the wheel of labour trafficking [5, p.  148]. Without em­
ployees at border checkPoints turning a blind eye, often after the payment of  a significant sum of 
money, this form of  organised crime could not proceed [7, p.  55]. Payment of bribes in money, 
goods, or kind can persuade an official to turn a blind ~ye to  improper documentation or protec­
tion against scrupulous checking of vehicles, cargo holders,  or v,essels holding smuggled mi­
grant workers [9, p.157]. 
In the Western Newly Independent States - WNIS - thereis a lot of anecdotal evidence 
about state border corruption. As an.example, it has been pointed out that Ukraine's ability to 
address irregular migration has been limited by widely acknowledged but as yet unsubstantiated 
corruption of consular, border guard, law enforcement and state officials [6, p. 79]. In addition, 
the results from a  survey carried out in Ukraine in 2001  showed that many people were con­
cerned about corruption within customs and border services [4, p.  12]. 
There  is  also  actual  evidence of corruption.  The European Union's  Border Assistant 
Mission to Ukraine and Moldova - EUBAM - points out that even though border conuption has 
been decreasing in recent years, it is still present in the two countries [2, p.13]. Measures have 
been taken to  improve the situation. At the field level, EUBAM has been able to  advice on im­
102  . 
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t proving proceaure-s-ih-order to  reduce the opportunities for  conuption:--A-jointoperation has 
been created in which border guards and the police have begun to operate more closely together. 
A special system, ASYCUDA, has been introduced in order to restrict direct payments made to 
customs officers_ ·  In addition, a directive has been implemented limiting the amount of  money to 
be carried by officers and prohibiting the use of mobile phones [ibid]. 
In the Republic of Moldova, during the first  10 months of 2008, disciplinary measures 
were taken against 183 border officials, of which 36 were sacked for corrupt acts and behaviour. 
10 files were passed on to the public prosecutor and 6 people were arrested. As a comparison, in 
the year before, 179 were punished and one person sacked. In 2006, 143  employees were fined 
and no-one sacked [9] . 
To date, the economic modelling of state border corruption is basically non-existent. One 
reason is that data more detailed than the above is extremely hard to come by, due to the clan­
destine nature of the subject and the  authoriti~s' lack of willin'gness to share information. Using 
data from court cases is a difficult approach as well, since there would be no way of adjusting 
the parameters in the model without knowing the shadow size of true cases and the prosecution 
intensity. However, for a purely theoretical context, there are several approaches that one could 
think of.  ' 
In a  game  theoretical  setting,  one  approach would  be  to  construct a  regular  auditing 
model with mixed strategy equilibria and regular observation.  Contrary to Nash equilibria, such 
models do  not predict that auditors react only to  incentives faced  by their counterpart, but they 
also react to own incentives (at least in a lab environment). See, for example [8] 
Another possibility would be to study state border corruption within a framework of re­
source allocation. The following model assumes that the task of the border guard service is to 
minimise the number of illegal border crossings, in presence of corruption. We start out with the 
following designations: 
N - the general number of border guards, 
L - the number of oblasts protected by the Border Guard Service, 
N, -the number of  border guards in  i  - th oblast,  L~ = l N, - N , 
~,- the  average number of migrants in  i  - th oblast, trying to cross the border with the 
help of  conupt border guards for the defined period, 
a, - the level of  cOlTuption in i  - th oblast, 
B,  - budgetary funds p.llocated to border protection in i  - th oblast, 
B - general budgetary expenses allocated to the protection of  the state bord~r. 
We  assume that the .level of corruption is inversely proportional to  the  level  Of budgetary in­
vestments. The higher the wage of the border guard, the less likely it is that he or she will be in­
clined to COlTUpt behavior. We therefore assume that 
eN. 
a.=--'  ,  B  , 
where c is a coefficient of proportionality, as a first general approximation for all oblasts. Coef­
ficient  a, is the share of corrupt border officials. Furthermore, it is clear that even in presence of 
corrupt border guards, a risk of  disclosure still exists for the group of illegal migrants. It is there­
fore natural to introduce the probability  p,  for a successful border crossing of the group of ille­
gal migrants, which is proportional to the share of  COlTUpt border guards. That is: 
103 p; =c;ap  o<c; <1 
One of the purposes of the Border Guard Service is to minimize the number of illegal migrants 
crossing the state border.  Out of this  purpose, a problem of optimally distributing budgetary 
funds to areas so as to minimize the general average of illegal migrants, arises. Mathematically, 
this can be formulated in the following way: 
MLI.~ ·  )  LL~  N;  .  =  ' =  cc . -~  (1) ;=)  ;P,  ;=);' B  mIn, 
i  8/ 
under constraints 
(2) 

The magnitude M is the average number of illegal migrants who have successfully overcome the 
border.  Having expressed  B) ,from the relationship (2) and having equated the partial deriva­
tives  M  and  B,  to zero,  i=  2, 3, """' L, we get 
aM _ .  - ~)ccINl 
(3) 
aBi - (B - L~=2  B[ )2 
After reduction to a common denominator, we have 
- ~ICCINIBi2 -~iJcc;N;(B- L;~2 B[)2 =0 
(4)
(B-"L B)2B2 L....J[ = 2  , I 
i=2,3, ... ,L 

The system (4) can be solved numerically. However, for the case L=2 it can be solved analyti­

cally. In t.~is case the equations of the system (4) are transformed into one quadratic equation: 

k)(N -NJB; -k2N 2(B-B2)2  =0, 
where  k;  = ~,C ; C, i =1,2. 
Its positive solution looks as follows: 
- k2N2B + B~klk2NIN2  B  = --------'- - - ­
2  kiN) -k2N2 
That is, taking into account (2) 
Thus the average number of illegal migrants who have successfully-overcome the border equals 
=k N  kINI  - k2N2  k N  ·  kIN)  - k2N2  . M min  I)  I  T  +  2  2  I k]NIB - RV.klk)\  )N2  - k2N 2B + B-yk.k2N IN2 
We investigate the dependence of  this magnitude on the level of  corruption. Considering that 
ai = C;i  and k; =  ~ i C j C, we see that M mm  =  ~]c]a] + ~2c 2 a 2' 
, 
In this equality,  aj  has been calculated at the optimum ?istribution of resources  B j  Put differ­ • 
ently, in the above model the minimum average of migrants who have successfully overcome 
the border linearly depends on the corruption levels in oblasts at an optimum allocation of the 
104 
budget and afixed distribution of the nwnber of border guards. The above model shows how to 
allocate  budgetary resources if the  levels  of corruption and the  number of border guards  are 
known for each oblast.  For the two-oblast case, the solution was written out explicitly. Possibly, 
a model closer to  reality would be one in which the number of border guards per oblast were not 
fixed, but ought to be allocated according to. the budget. The local budgets of  each oblast would 
in that case be subject so some lower constraint. However, a model of this kind could only be 
solved numerically. 
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105 


Global human smuggling: comparative perspectives. /

Human trafficking

international migration and asylum

Irregular and Illegal Migration through Ukraine.

Report 2005/2006. The European Union Border Assistance Mission

Republicii Moldova,

Strategic errors and audit quality: An experimental investigation.

The Trafficking of Migrant Workers: \Vhat are the Links Between Labour Trafficking and Corruption? I Richards,

State border corruption and illegal migration: A model

State border corruption and illegal migration: A model

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