B. Unger Tackling ML 3.11.2007 1

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 2

Overview

1. Why I chose for the Walker Model

2. A Revised Walker Model Measured for the Netherlands

3. The Theoretical Underpinning of the Model: The Gravity Model

4. Lessons from modern trade theory

5. Future Challenges

B. Unger Tackling ML 3.11.2007 3

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 4

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

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2. A Revised Walker Model Percentage of World Criminal Money

Flowing into a country X (the Netherlands) 

),(

)(

),(

)(

1),(

1

i

i

n

i i

i

i yXdist

ynessattractive

yXdist

ynessattractiveyXP

Attractiveness=f(GDP per capita, BankSecrecy, AntimoneylaunderingPolicy, SWIFTmember, Financial Deposits,-Conflict,-Corruption,-Egmont Group.

Distance deterrence=f(Language,colonial background,trade,physical distance)

Country X, countries yi i=1...n

B. Unger Tackling ML 3.11.2007 6

1.LuxembourgBermudaSwitzerlandCaymen IslandsNorwayHong KongAustriaLiechtensteinBelgiumArubaJerseyIcelandCanadaIrelandSingapore

Walker 19951.Luxembourg

2.US

Switzerland

Caymen Islands

Austria

6.Netherlands

Liechtenstein

Vatican

9.UK

Singapore

Hong Kong

Ireland

Bermuda

Bahamas

Norway

Unger et al 2006

16. AustraliaIsle of ManVatican FranceSan MarinoGermany22.NetherlandsItalyFinlandGreeceJapanMaltaSweden29.USDenmark31.UK

Unger et al 200616. IcelandCanadaPortugalDenmarkSwedenMonacoJapanFinlandGermanyNew ZealandBelgiumItalyFranceCyprusCzech RepublicLatvia

Walker 1995

2. ATTRACTIVENESS top 31 out of 220 countries

B. Unger Tackling ML 3.11.2007 7

2.Flows of Dirty Money Into the NetherlandsOther Countries’ Criminal Money Flowing into the Netherlands

14,5 bill Euro

Netherlands

US

Germany

RussiaUK Dutch Antilles,

,

Laundering depends on Attractiveness and on ‘Distance’ Language,colonial background, trade, physical distance

US,

Russia,Italy

Germany,

UK,

France..

Netherlands Colombia

Turkey Spain

+ 4 bill

=18,5 bill

from Dutch

crime

+Through

flow

Money Laundering in the Netherlands about 5% of Dutch GDP

B. Unger Tackling ML 3.11.2007 8

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.

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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

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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).

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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

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3. The Theoretical Underpinning of the Walker Model:3.4. Walkers Model is a Modern Gravity ModelFij = 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-3CF-CRj+15) and Mj=(GNP/capita) j. He has divided the flow formula by Mi = (the proceeds of crime).

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• 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

4. Lessons from Modern Trade Theory

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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(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)

• Role of borders, overestimation of effective distance when one takes capital coordinates

4. Lessons from Modern Trade Theory

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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

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THANK YOU !

Prof. Dr. Brigitte UngerUtrecht School of EconomicsJanskerkhof 123512BL UtrechtThe Netherlands+31-(0)30-253-9809B.Unger@econ.uu.nl