The Economic Foundation of the Walker Model: The Gravity
Model
by Prof. Dr. Brigitte Unger
Presentation prepared for the Conference on Tackling Money Laundering,
organized by the Utrecht University School of Economics, 2nd and 3rd November
2007
B. Unger
Tackling ML 3.11.2007
1
Overview
1.
2.
3.
4.
5.
Why I chose for the Walker Model
A Revised Walker Model Measured for the Netherlands
The Theoretical Underpinning of the Model: The Gravity Model
Lessons from modern trade theory
Future Challenges
B. Unger
Tackling ML 3.11.2007
2
1. The Walker Model
•
A pioneer study from 1994
•
Allows for a framework to measure money laundering per country and worldwide
•
Is a positive example for interdisciplinary work between criminology and
economics
•
Recently updated (Walker 2005)
•
Is based on a solid model of economic theory
B. Unger
Tackling ML 3.11.2007
3
1. The Walker Model
consists of two parts of which the second part is the controversial one in the
debate on money laundering
1. The proceeds from domestic crime that are being laundered
2. The proceeds from foreign crime that flow into a country for laundering
B. Unger
Tackling ML 3.11.2007
4
2. A Revised Walker Model
Percentage of World Criminal Money Flowing into a country X
(the Netherlands)
attractiveness ( yi )
1
P( X , y i ) 

n
dist ( X , yi )
 attractiveness ( yi ) 



dist
(
X
,
y
)
i 1 
i

Country X, countries yi i=1...n
Attractiveness=f(GDP per capita, BankSecrecy,
AntimoneylaunderingPolicy, SWIFTmember, Financial Deposits,-Conflict,Corruption,-Egmont Group.
Distance deterrence=f(Language,colonial background,trade,physical
distance)
B. Unger
Tackling ML 3.11.2007
5
2. ATTRACTIVENESS top 31 out of 220 countries
Unger et al 2006
1.Luxembourg
Bermuda
Switzerland
Caymen Islands
Norway
Hong Kong
Austria
Liechtenstein
Belgium
Aruba
Jersey
Iceland
Canada
Ireland
Singapore
B. Unger
Walker 1995
Unger et al 2006
1.Luxembourg 16. Australia
2.US
Isle of Man
Switzerland
Vatican
Caymen Islands France
San Marino
Austria
6.Netherlands Germany
Liechtenstein 22.Netherlands
Italy
Vatican
Finland
9.UK
Greece
Singapore
Japan
Hong Kong
Malta
Ireland
Sweden
Bermuda
29.US
Bahamas
Denmark
Norway
31.UK
Tackling ML 3.11.2007
Walker 1995
16. Iceland
Canada
Portugal
Denmark
Sweden
Monaco
Japan
Finland
Germany
New Zealand
Belgium
Italy
France
Cyprus
Czech Republic
Latvia
6
2.Flows of Dirty Money Into the Netherlands
Other Countries’ Criminal Money Flowing into the Netherlands
Laundering depends on Attractiveness and on ‘Distance’ Language,colonial
background, trade, physical distance
14,5 bill Euro
fromUS
Dutch
US,
UK Dutch Antilles,
crime
Russia,Italy
+ 4 bill
Russia
Netherlands
Colombia
Netherlands
Germany,
,
Germany
+Through Turkey Spain
UK,
=18,5 bill
flow
France..
Money Laundering in the Netherlands about 5% of Dutch GDP
B. Unger
Tackling ML 3.11.2007
7
3. The Theoretical Underpinning of the Walker Model:
3.1. Newton’s Apple
Fij = G* Mi*Mj/ (Dij)2
Fij...Attractive Force between object i and j
Mi....Mass of object i
Mj ..Mass of object j
Dij...Distance between object i and object j
G...Gravitational constant
In 1687, Newton proposed the “Law of Universal Gravity”, which held that the attractive force
between two objects i and j depends on their masses, the square distance between these objects
and a gravitational constant.
B. Unger
Tackling ML 3.11.2007
8
3. The Theoretical Underpinning of the Walker Model:
3.2. Tinbergen’s Old Gravity Model of 1962
Fij = G* Mi α * Mj β / Dij θ
The export flows from country i to country j depend on the GDP of both the
exporting and importing country and the distance between them.
Note that if α, β = 1and θ =2, then this is the same as the original Newton
formula:
Fij = G* Mi*Mj/ (Dij)2
B. Unger
Tackling ML 3.11.2007
9
3. The Theoretical Underpinning of the Walker Model:
3.3. The Gravity Model in Modern Trade Theory
The trade flows from country i to country j Fij = sij*Mj
Where sij is the share of country j’s income Mj spent for goods from country i.
sij = g(mi, ni, Dij) / Σ g (ml, nl, Dlj) mi……quality of goods of country I
ni….variety of goods of country i
Dij…distance between country I and j
This share increases if country i produces a greater variety of goods (ni) or a higher quality of goods (mi). This share
also decreases with distance.
Depending on the trade theory used, either mi=1 (which means all products from a country have the same average
quality) or ni=1 (each country exports only one single good).
Under the assumption that mi=1 and that all firms q are of the same firm size, the number of products ni = Mi/q. The
higher the income of the country, the more products will be produced, and the larger the firms size in the country,
the less variety will be produced (monopolistic trade models, Dixit Stiglitz).
B. Unger
Tackling ML 3.11.2007
10
3. The Theoretical Underpinning of the Walker Model:
3.3. The Gravity Model in Modern Trade Theory contd
If mi=1 and all firms q are of the same firm size, the number of products ni = Mi/q.
The higher the income of the country, the more variety of products, the larger the
firms size in the country, the less variety (monopolistic trade models).
After some modification, follows
sij = Mi Dij – θ Rj where Rj = 1/ Σ l (Ml, Dlj – θ) and
from this follows Newton’s-Tinbergen’s formula
Fij = Rj * Mi*Mj / Dij θ
B. Unger
Tackling ML 3.11.2007
11
3. The Theoretical Underpinning of the Walker Model:
3.4. Walkers Model is a Modern Gravity Model
Fij = Rj* Mi α * Mj β / Dij θ
Fij/Mi = Attractiveness j /Distance ij2 where
Fij/Mi = (GNP/capita)j * (3BSj+GAj+SWIFTj-3CFj –CRj +15)/ Distance ij2
Where GNP/capita is GNP per capita, BS is Banking Secrecy, GA is Government Attitude, SWIFT is
SWIFT member, CF is Conflict, CR is Corruption.
If one compares this to the original gravity model, Walker assumes, Rj= (3BSj+GAj+SWIFTj-3CFCRj+15) and Mj=(GNP/capita) j. He has divided the flow formula by Mi = (the proceeds of crime).
B. Unger
Tackling ML 3.11.2007
12
4. Lessons from Modern Trade Theory
•
•
•
•
•
Tinbergen’s ad hoc formula was progressively micro-founded.
Anderson (1979), showed that the gravity model was evident in expenditure share models
Helpman (1984) and Bergstrand (1985) demonstrated that the gravity model could also be
derived from models of trade in differentiated products.
Deardorff (1998) showed that a suitable modelling of transport costs produces the gravity
equation as an estimation, even for the Heckscher-Ohlin model.
Helliwell (2000), Head (2003) role of distance, colonial background, language
B. Unger
Tackling ML 3.11.2007
13
4. Lessons from Modern Trade Theory
The role of distance
• It is a proxy for transport costs
• it indicates the time elapsed between shipment
- damage or loss of the good (ship sinks in the storm)
- spoiling of the good
- loss of the market (purchaser unable to pay once it arrives)
•
•
It stands for transaction costs (searching for trading opportunities, establishment of trust between
partners)
It stands for cultural distance
•
Role of borders, overestimation of effective distance when one takes capital coordinates
(clashes in negotiation style, language) ‘Countries that speak the same language will trade twice to
three times as much as pairs that do not share a common language” (Helliwell 2000)
B. Unger
Tackling ML 3.11.2007
14
4. Future Challenges
•
•
•
•
•
better micro-foundation of the Walker model
cooperation with criminologists for studying criminal behavior
Variables in the attractiveness indicator still arbitrary
weights of variables in attractiveness and distance indicator still arbitrary
It was a long way from Tinbergen’s ad hoc formula to the micro foundation by modern
trade theory. Similar is needed for criminal flows
B. Unger
Tackling ML 3.11.2007
15
THANK YOU !
Prof. Dr. Brigitte Unger
Utrecht School of Economics
Janskerkhof 12
3512BL Utrecht
The Netherlands
+31-(0)30-253-9809
B.Unger@econ.uu.nl
B. Unger
Tackling ML 3.11.2007
16