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This is to certify that the
dissertation entitled

IMMIGRATION AND ECONOMIC INTEGRATION

presented by

ILKAY YILMAZ

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in ECONOMICS

 

 

Major Professor's Signature

JUNE 28, 2004

 

Date

MSU is an Afinnative Action/Equal Opportunity Institution

*v— ~

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LIBRARY

MiChiQan State
University

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIFIC/DatoDuo.p65—p.15

 

IMMIGRATION AND ECONOMIC INTEGRATION
By

Ilkay Yilmaz

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Economics

2004

ABSTRACT
IMMIGRATION AND ECONOMIC INTEGRATION
By

Ilkay Yilmaz

This dissertation contains four chapters, three of which are theoretical and the other is

empirical.

In the first chapter, by using a probabilistic static model, a possible relationship
between the desirability of economic integration and (illegal) immigration is studied.
Using the framework developed in Levy (1997), it is shown that migration from a labor
abundant country to a capital abundant country leads to economic integration between the
two countries. By reducing the median voter’s utility in the capital abundant country,
migration induces voters to support economic integration. In the second chapter the same
relationship is studied within the framework of a dynamic model. As in the first chapter,

it is shown that migration might lead to economic integration in the future.

The positive relationship between migration and economic integration suggests a
complementary relationship between factor movements and goods trade. Showing such a
relationship within a Heckscher-Ohlin setting indicates that supplementing the classical
Heckscher-Ohlin model with illegal immigration and political economy might render

invalid the earlier conclusions (starting with Mundell’s classical 1957 paper) that within

the standard Heckscher-Ohlin model factor movements and goods trade are undoubtedly

substitutes.

Both chapters also show that the possibility of economic integration is increasing
(decreasing) in income inequality in the relatively labor (capital) abundant country. This
result is compatible with Mayer’s (1984) prediction that an increase in inequality, holding
constant the economy’s overall relative endowments, raises trade barriers in capital-

abundant economies and lowers them in capital-scarce economies.

The third chapter incorporates smuggling to the two-good variant of the dynamic
model developed in the second chapter. It shows that the effect of smuggling on the time
of economic integration is ambiguous. It suggests that a higher (lower) detection rate of
smuggled goods tend to make the time of economic integration, i.e. free trade, later

(sooner).

In the last chapter I empirically test the prediction that the possibility of economic
integration is increasing (decreasing) in income inequality in the relatively labor (capital)
abundant country. I have found that only in democratic countries a positive (negative)
relationship exists between the income inequality level in the relatively labor-abundant

(capital-abundant) country and the possibility of the FTA.

to my parents and sister

iv

ACKNOWLEDGEMENTS

First of all, I would like to thank my advisor Dr. John D. Wilson. Without his help
and advice I could not have finished this dissertation. I also want to thank other members
of my committee, Dr. Steven J. Matusz, Dr. Susan C. Zhu, and Dr. Burt L. Monroe for

their valuable comments. However, I am responsible for any remaining mistakes.

Special thanks to my professors of Russian, Dr. David K. Prestel and Dr. Felix A.
Raskolnikov. Learning Russian and getting a Ph.D. degree in economics at the same time

was a challenging goal. With their help, I achieved my goal.

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

INTRODUCTION .............................................................................................................. 1

LITERATURE REVIEW ................................................................................................. 18
CHAPTER 1

Two Static Probabilistic Models of Migration and Integration ........................................ 27

1.1 Introduction ............................................................................................................ 27

1.2 One-Good Static Model . ....................................................................................... 29

1.2.1 The Setting ................................................................................................ 30

1.2.2 A Simple Model with Exogenous Immigration ........................................ 33

1.2.3 Static Probabilistic Model ......................................................................... 45

1.2.3.1 Results ........................................................................................... 48

1.3 Two-Good Static Model ....................................................................................... 52

1.3.1 A Numerical Example for Two-Good Model ........................................... 61

1.4 Conclusion ............................................................................................................ 67
CHAPTER 2

Two Dynamic Models of Migration and Integration ........................................................ 69

2.1 Introduction ............................................................................................................ 69

2.2 One-Good Dynamic Model .................................................................................... 72

2.2.1 Equilibrium Migration and Time of Integration ........................................ 77

2.2.2 Results ........................................................................................................ 82

2.2.3 Non-Integration Cases with High C(O) ...................................................... 86

2.3 Two-Good Dynamic Model ................................................................................... 88

2.3.1 Equilibrium Migration and Time of Free Trade ....................................... 89

2.3.2 Results ....................................................................................................... 94

2.3.3 Non-Integration (Autarky) Cases with High C(O) .................................... 98

2.4 Conclusion .......................................................................................................... 100

vi

CHAPTER 3

Extension with Smuggling ............................................................................................... 102
3.1 Introduction .......................................................................................................... 102
3.2 Literature Review ................................................................................................ 103
3.3 Two-Good Model with Smuggling ...................................................................... 111
3.4 Conclusion .......................................................................................................... 121

CHAPTER 4

The Effect of Income Inequality in the Determination of Free Trade Agreements ......... 122
4.1 Introduction .......................................................................................................... 122
4.2 Econometric Model and Estimation Method ...................................................... 124
4.3 The Data .............................................................................................................. 127
4.4 Results ................................................................................................................. 132
4.5 Conclusion .......................................................................................................... 135

CONCLUSION AND SUGGESTIONS F OR FURTHER RESEARCH ........................ 137

REFERENCES ................................................................................................................ 143

vii

A.1

A2

A3

A4

A5

A6

A.7

5.1

5.2

5.3

LIST OF TABLES

Stocks of foreign populations in selected European countries by nationality,
1978 and 1989 (thousands) ......................................................................................... 8

Inflows of foreign population into selected European countries, 1990-2000
(thousands) .................................................................................................................. 9

Inflows of asylum seekers into selected European countries, 1991-2001
(thousands) ................................................................................................................ 10

Stocks of foreign population in selected European countries, 1990-2000
(thousands and percentages) ..................................................................................... 11

Shares of US decennial population growth attributable to immigration,

1820-1990 (population in thousands) ....................................................................... 13
Estimates of the illegal immigrant population in the US, 1980-1998 ....................... 13
Undocumented immigrants in the US, by country of origin, 1998 ........................... 14
GINI and POLITY averages for 19605 ................................................................... 130
Summary statistics of the data ................................................................................ 131
Probit Results for the Probability of an FTA ......................................................... 133

viii

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

LIST OF FIGURES

Utility level of individual i with capital endowment ki .......................................... 33
Utility of the median voter when k ,’,""‘""" < kU < k m ............................................... 36
Utility ofthe median voter when kU < k gm" < E, < k,0 . ..................................... 37
Utility of the median voter when kU < k :Cd’“ < k m < [ER . ..................................... 37

Utility of the person who is indifferent between integration and non-integration....40

Immigration takes the capital-labor ratio in R from k m to k R‘, .............................. 41
Utility of the median voter when k 39‘1”" < kU < k R‘, < k M ....................................... 43
Utility of the median voter when kU < kged‘“ < k R, < ER < k m ............................... 44

Utility of the median voter when his capital-labor ratio increases from k 22‘1”"
to k 33“" ................................................................................................................... 49

1.10 ,6(T) and T ( ,8) curves determine the equilibrium number of immigrants and

the probability of economic integration .................................................................... 51

1.11 The strictly quasi-convex utility of an agent with a given capital-labor ratio

2.1

2.2

2.3

2.4

3.1

as a function of the economy’s capital-labor ratio .................................................... 53
Utility of the median voter when kU < k 36“” < k~R < k M ....................................... 73
Time line .................................................................................................................. 77
Migration rate as a function of time ......................................................................... 78
Migration rate for the case #2 . ................................................................................. 87
Smuggling reduces the utility level of the median voter ........................................ 115

ix

3.2

3.3

Utility of the median voter when smuggling immediately causes economic
integration ............................................................................................................... 1 1 8

Utility of the median voter when it takes longer to have free trade with
smuggling than without smuggling ......................................................................... 120

INTRODUCTION

The two major economic blocks, NAFTA and EU, seem to be centers of attraction for
immigration. It is not far-fetched to assume that in the absence of immigration costs and
restrictions, these economic blocks would have to absorb huge sizes of poor immigrants
who would change the economic and ethnic compositions of these blocks radically. It is
no wonder that the average citizen in these blocks is against immigration. It is also
reasonable to expect that illegal immigration from developing countries to the high-
income countries will intensify in the fiIture. In the case of economic blocks (especially
the EU), some of the source countries of these illegal immigration might be possible
candidates to these economic blocks. Then a natural question arises: “Does illegal
immigration from a candidate country to an economic block increase or decrease the
chance of being accepted to that block?” This thesis is an attempt to give an answer to

this question.

Europe has a long history of human migration, reasons of which were various such as
persecution of minorities, wars, dispossession of land, industrialization etc. In the 19th
and 20th centuries emigration to the New World was the dominant movement. Between
1820 and 1940, an estimated 55-60 million Europeans lefi for the New World. 38 million
of these ended up in the United States. Just before the First World War, at the peak of the
transatlantic migration) over 1 million people were migrating to the United States from

Europe annually.

Migrations within Europe were also important before 1940. Both economic and
political factors contributed to this phenomenon. Industrial countries like Britain, France

and Germany attracted workers from neighboring countries.

Two world wars caused tens of millions of people to move across borders and resettle
in countries where they were not born in. According to Kosinski (1970), the First World
War caused 7.7 million people to cross borders in Europe and the Second World War - 25
million. On this episode of European history especially the movements of German
speaking people were dominant. At the end of 1940’s there were 7.8 million refugees in
West Germany and 3.5 million in East Germany. Furthermore between 1950 and 1961, 3

million East Germans fled to the West (King 1995).

Even when political factors were the main cause of migration, i.e. when political
events forced people to move or created opportunities to move, people considered
economic perspectives and chose to move to places where they can materially live better,

as in the case of East German refugees to the West.

The migration of so called guest workers, on the other hand, was purely economic. It
started in the 19508, continued throughout 19605 and diminished in 1970’s. This mass
movement of workers helped rich North European countries to satisfy manpower needs.
At the beginning the idea was that foreign workers would migrate temporarily and they
would return to their countries after they gained experience in modern industries and

when their host country no longer needed them. In the 1950s Italy was the source of

migrant workers. Germany, the biggest economy in Europe, made a treaty with Italy in
1955 to recruit temporary guest workers. Similar treaties with Spain, Turkey, Morocco,
Portugal, Greece, Tunisia, Yugoslavia and South Korea were concluded in 19605.
Besides Germany, economies of emerging European Common Market, France, Belgium,

Holland and Luxemburg were the other main recruiting countries.

The general recession following the oil shocks in early 1970’s ended the demand for
foreign workers abruptly in 1974. As White (1986) and King (1995) pointed out many
migration flows continues until 1975. Afier that migration did not come to a bolt, rather
the character of the flows changed. The migration of single (mainly male) workers was
replaced by the migration of family members. Also, since Western European economies
no longer 5 ought foreign w orkers, for those w ho w ant to emigrate to Western E urope

illegal immigration and political asylum options become more important.

As it can be seen in table A], stocks of foreign populations in Western European

countries did not shrink through 19805, on the contrary they increased.

Following the collapse of the Communist block in Eastern Europe, a new wave of
migration from East to West emerged. Legal migration of ethnic minorities, like German
speaking people from former USSR, and illegal immigration from the former Communist
block countries caused by economic collapse took place. The humanitarian catastrophe
caused by civil wars in former Yugoslavia led to huge increases in the number of asylum

seekers into Western European countries especially in the early 19905.

Tables A.2, A.3 and AA present a statistical overview of immigration into European
countries, the number of asylum seekers and the stocks of foreign born populations
throughout the 19905. From these figures its easy to see the importance of migration
wave (mainly to Germany) in the early 19905 caused by the collapse of the USSR and the
civil war in former Yugoslavia. The mere fact that the influx of foreign populations into
Europe has never been less than 1 million annually throughout the 19905 indicates the

importance of immigration for Europe.

As mentioned above, in the 19th century and in the first decades of the 20th century
millions of Europeans moved to the United States in search of a new and better life. Also
10 to 20 million Africans were transported to the USA and other parts of the Americas as
slaves between 1700 and 1850 (when slavery was officially ended in the USA). These

people were mainly used in cotton and other plantations even after the Civil War.

During the long history of US immigration there were periods dominated by anti-
immigration sentiments, such as the campaigns against Chinese and other Asian
immigrants in 18805. The anti-immigrant feelings of 19205 and 19305 contributed to the
increasing number of restrictions and controls which were consolidated by the 1924
National Origins Act. A5 a result of this act and other anti-immigrant policies between
1931 and 1940 only about 500,000 new immigrants came to the United States. As it can
be seen in Table A5 this is the lowest such number in the recent history of United States

immigration.

Later in 1965 amendments to the Immigration and Nationality Act led to a system of
worldwide immigration by replacing earlier national origins quota arrangements. From
then on the ratio of non-Europeans to Europeans in the immigrant population

significantly increased.

The enactment of the Immigration Reform and Control Act of 1986, tried to improve
control over irregular immigration. By giving preference to family reunifications it
multiplied flows from particular source countries. One of the major components of this
act was an illegal immigrant amnesty program. As it can be seen from table A.6, the
number of illegal immigrants decreased about 2.4 million mainly due to the legalization

component of this act.

According to the Immigration and Naturalization Service (INS) in January 2000,
there were 7 million illegal aliens living in the United States. It is estimated that this
number is increasing by half a million a year. Therefore the illegal alien population in the
beginning of 2004 must be around 9 million. INS also reports a close link between legal
and illegal immigration, which is reflected by the fact that 1.5 million green cards were

given to illegal aliens in 19905.

The largest share of illegal immigrants comes from Mexico. As shown in table A.7, in
1998, 54% of all illegal immigrants in the US were from Mexico. Given this fact it is not

surprising that one of the aims of NAFTA was to reduce migration from Mexico to the

United States by stimulated economic growth. Although general agreements on migration
were e xplicitly n ot p art 0 f the N AF TA, leaders 0 f b oth M exico and the U nited S tates
supported NAFTA under the expectation that in the long run trade would substitute

migration.

The NAFTA debate emphasizes the question of whether free trade could stop
unwanted migration from less developed countries to developed ones. The standard
comparative statics analysis gives the answer that migration of labor without the
existence of trade tends to decrease and end because of the adjustment of wages.
Migration decreases wages in the receiving country and it increases wages in the sending
country. The Heckscher-Ohlin trade model concludes that trade and migration are

substitutes. Trade, by equalizing factor prices, eliminates the reason why people migrate.

An interesting question here is that if migration helps to lead to the creation of FTAs,
then should we regard migration and trade complements rather than substitutes? If the
Mexican immigration had not occurred over the years and if there were no threat of
further (illegal) immigration, would NAFTA get enough support in the United States? Or
in the European Union context, could the possibility of possible further unwanted
migration from Eastern Europe and Turkey be one of the reasons why these regions are in

the European enlargement perspectives?

The main idea of my thesis is that although unwanted migration hurts the median

voter in the receiving country, free trade with the sending country that will stop migration

might be preferable to further migration without free trade. The thesis constructs
Heckscher—Ohlin-Samuelson type models in which illegal migration from a labor
abundant country to a capital abundant country leads to economic integration (free trade)
between the two countries. The models suggest an ambivalent answer to the question of
whether goods trade and factor mobility are substitutes or complements. On the one hand,
the motivation for migration (factor mobility) is the absence of goods trade (if there were
goods trade, then we would have factor price equalization and no labor movement).
Furthermore, when countries switch from autarky to free trade, labor migration no longer
occurs. Thus, factor mobility and goods trade seem to be substitutes. On the other hand,
the reason for free trade is the labor migration, which suggests that factor movements and

goods trade are complements.

By conducting comparative statics analysis on the models, it is shown that the
probability of economic integration is increasing (decreasing) in income inequality in the
relatively labor (capital) abundant country. The econometric part of the thesis provides

evidence for this prognosis.

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12

Table A5: Shares of US decennial population growth attributable to

immigration, 1820-1990 (population in thousands)

 

Year

1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990

Source: Ghosh (1997)

Total US
population

9638
12866
17069
23192
31443
38558
50189
62721
76747
92198

106005
123197
132184
151291
179420
203302
226546
248710

Population
increase

in the

decade

3228
4203
6123
8251
7115
11631
12532
14026
15451
13807
17192
8987
19107
28129
23882
23244
22164

Immigrants
to the USA

143

599
1713
2598
2315
2812
5247
3688
8795
5736
4107

528
1035
2515
3322
4493
7338

AB Estimates of the illegal immigrant population in the US, 1980-1998

Source: Rivera-Batiz (2001)

 

Year

1980
1986
1987
1988
1990
1992
1994
1998

Number of
undocumented
immigrants

2100000
3200000
4800000
2200000
2600000
3400000
3750000
4700000

 

13

Immigrants
as 0/0

share of
the
increase

14
28
31
33
24
42
26
57
42
24

14
19
33

Table A.7: Undocumented immigrants in the US, by country of origin, 1998

 

Total Percentage

number of of total

undocumented undocumented

Country of origin immigrants population
Total 4,700,000 100.0
Mexico 2,538,000 54.0
El Salvador 315,000 6.7
Guatemala 155,000 3.3
Canada 1 13,000 2.4
Haiti 99,000 2.1
Philippines 89,000 1.9
Honduras 85,000 1 .8
The Bahamas 66,000 1.4
Nicaragua 66,000 1 .4
Poland 66,000 1 .4
Colombia 61,000 1 .3
Other 1,047,000 22.3

 

Source: Rivera-Batiz (2001)

14

The thesis is organized as follows:

In the following section, I discuss the related literature of illegal immigration,
substitutability and complementarity of factor movements and goods trade, and political

economy of economic integration.

The first chapter introduces a 2-factor, 2-country static probabilistic model of
migration and economic integration. Both countries have identical constant returns to
scale technologies; they differ in capital-labor ratios, i.e. wages are higher in the
relatively rich (capital abundant) country. I work with a one-good model, but the model is
later extended to include two goods, following the Heckscher-Ohlin set up. Decisions are
made by majority rule, which means that the chosen policy is the one most preferred by
the median voter. At the beginning (in the first stage) the median voter in the poor
country prefers economic union, whereas the median voter in the rich country does not.
In the first stage an illegal migration wave from the poor country to the rich country
occurs; in the second stage, people (excluding illegal immigrants) in the rich country vote
in order to determine whether to form an integrated economy including the two countries,
i.e. free movement of capital and labor in the case of one-good model and free trade in
the case of two-good model. In one-good model, it is assumed that in the case of
economic integration, a sufficient level of capital movement from the rich country to the
poor country occurs instantaneously, which equalizes factor prices in both countries
(factor-price equalization requires free movement of only one factor not both). In two-

good model, free trade in the two goods leads to factor price equalization. In these

15

models migration 0 fl abor from the p per country to the rich c ountry in the first stage
makes the median voter in the rich country indifferent between economic integration and
non-integration in the second stage. Then the probability of integration is determined by

the cost of migration and wage difference between the two countries.

In the second chapter, I set up two-country dynamic models to analyze the
relationship between immigration and economic integration decisions. I mainly show that
the movement of the poor from a relatively poor country to a relatively rich country
gradually increases the public support for the economic union between these two
countries in the rich country. The novelty of these models is their dynamic structure.
There is a continuous flow of immigrants from the poor country to the rich country. The
flow of immigrants decreases over time because of the decrease in the wage rate
difference c aused b y the p ast immigration. T he more immigrants there are in the rich
country the further the capital-labor ratio falls down, while the capital-labor ratio in the
poor country goes up. The decrease in the capital-labor ratio decreases the utility of the
median voter in the rich country, provided that the median voter’s capital-labor
endowment ratio is less than the country’s. In some cases this decrease in utility might be
big enough to compel him to prefer an economic union with the poor country, which will
give him a utility level no less than what he enjoys in his secluded country. In the second
part of this chapter, I switch from one-good model to two-good model and economic
integration means free trade in this case. As in the one-good model we will observe a

decrease in the real wage difference as a result of migration. Also the rich country’s

l6

median voter’s utility level once again will decrease exactly to the level which he would

enjoy under free trade and he will eventually vote for free trade.

The third chapter presents an extension to the 2-good dynamic model developed in
the second chapter. Smuggling is introduced to the model and it is shown that smuggling
has two opposing effects on the time of free trade. On the one hand it brings relative
prices closer in the two countries, which tends to slow down migration and tends to make
the time of free trade later. On the other hand it decreases the utility level of the median
voter in the capital abundant country, which decreases the necessary migration level for
free trade and tends to make the time of free trade earlier. The net effect of these two
opposing forces determines whether the model with smuggling makes free trade earlier or

later compared to the earlier model without smuggling.

In the fourth chapter combining a subset of the data used in Baier and Bergstrand
(2003) with GINI coefficients data from UN Development program and POLITY data
from POLITY IV project, I tested the relationship between income inequality and the
possibility of FTAs. I found evidence of a positive (negative) relationship between the
inequality level in the r elatively p oor (rich) country and the p ossibility of the F TA in
democratic countries, but I fail to find any relationship between the inequality level and

the possibility of the FTA in undemocratic countries.

The fourth chapter is followed by a small section in which the main conclusions of

the thesis and suggestions for further research are given.

17

LITERATURE REVIEW

There are three main dimensions of my dissertation, namely illegal immigration,
substitutability and complementarity of goods trade and factor movements, and finally

political economy within the context of economic integration.

To my knowledge, there is no earlier work about the linkage between economic

integration and illegal immigration.

Among the earlier works on the illegal immigration it is worth to mention Ethier
(1986), Bond and Chen (1987), Bucci and Tenorio (1996) and Yoshida (2000), all of

which include static models.

In Ethier (1986) the effects of border and internal enforcement policies in a one-
country, two-factor (skilled and unskilled labor), one good model are analyzed. He
defines the subject of illegal immigration by partially successful attempts to prevent that
migration. He models these attempts as border enforcement and internal enforcement. He
assumes that of those who illegally attempt to immigrate, a certain number are caught and
denied entry. The authorities’ success in preventing illegal entry depends upon the
resources devoted to border enforcement, which are financed by taxes. Internal
enforcement, on the other hand, is described as random inspections of firms. Again, the
number of illegal immigrants caught in the work place depends on the resources devoted

to internal enforcement which, again, are financed by taxes. The government policy

18

instrument in the model is the exogenous level of resources devoted to border and
internal enforcement efforts and it is used to control the internal distribution of income
between skilled and unskilled workers and also the level of illegal immigrants. But these
two policy targets are linked to each other technologically and cannot be unbundled. In
the model, illegal migration is motivated by the higher wage rate for unskilled workers in
the host country. Irnplicitly it is assumed that the ratio of unskilled labor to skilled labor
is higher at the outside world. The main conclusions of the paper are as follows: Border
enforcement policy will probably reduce national income even if the country has
monopoly power in the world market for unskilled workers. Nevertheless border
enforcement is an effective way of controlling the unskilled labor employment rate (if
there is a rigid wage rate in the unskilled labor market) or the wage of unskilled labor (if
wages are flexible). However if illegal immigrants are also taxed, the effects of border
enforcement on these are not predictable. Given an interdiction policy, varying the
number of legal immigrants will have no effect on the total number of immigrants (legal
and illegal together). In other words there is a perfect trade-off between the number of
legal immigrants and the number of illegal immigrants. If firms can distinguish illegal
immigrants, domestic enforcement policies will make illegal immigrants disadvantaged
relative to legal workers, otherwise such policies will harm all unskilled workers (native,
legal and illegal immigrants) relative to skilled workers. It is possible to reduce the cost
of immigration policy by mixing border and domestic enforcement methods instead of
using just one of them. Strangely, if illegal immigrants can pose as legal immigrants both

border and domestic enforcement seem to be more successful than they are.

19

By extending Ethier model, Bond and Chen (1987) constructed a standard, two-
country, one-good, two factor model and analyzed the effect of an internal enforcement
policy by the host country government on the host country’s welfare. In their work, they
hold the level of border enforcement constant and concentrate on internal enforcement
against firms that hire illegal workers. Firms produce one type of good by using capital
and labor. The optimal level of enforcement is examined and the effects of allowing
capital mobility are considered. They derive a formula for the optimal level of
enforcement against firms that hire illegal workers. They show that if terms of trade
effects are large enough and marginal cost of enforcement is sufficiently low, a non-zero
enforcement level that maximizes the national welfare may exist. On the other hand if
home country firms cannot distinguish illegal workers from legal workers, the optimum
level of enforcement is more likely to be zero. They also show that the enforcement
policy is less efficient than a wage tax because of enforcement costs. When capital
mobility is allowed, an increase in enforcement in home country benefits foreign workers
since it causes capital outflow. Finally it is shown that the optimal policy for home

country may be both penalizing illegal immigrants and allowing capital export.

Bucci and Tenorio (1996) on the other hand examined the effects of financing
internal enforcement on the host country’s welfare by introducing a government budget
constraint similar to Ethier’s into a small-country model. Yoshida by using Bond and
Chen (1987) and Bucci and Tenorio ( 1996) models reassessed the welfare effects of the
enforcement policy in terms of the welfare of the host country, the foreign country and

the world.

20

In my models I use the term illegal immigration by two reasons. First, median voter
in the rich country does not want migration, i.e. majority of the rich country does not
want these immigrants in their country. Second, immigrants from the poor country do not
posses voting rights in the rich country. They are not legal citizens of the rich country and
they are not allowed to participate in voting for a possible free trade agreement between

the country in which they live and the country from which they came.

Since my major aim is to capture the relationship between migration and economic
integration, rather than welfare effects of various enforcement policies as in most of the
illegal immigration literature, I do not follow the aforementioned papers to model illegal
immigration. In my models the illegal aspect of migration is represented by the high cost

of migration before the economic integration.

Before switching to the literature about the substitutability and complementarity
between goods trade and factor movements, 1 want to present the following four

meanings of these concepts given by Wong (1986 and 1995):

1. Quantitative-Relationship Sense: Goods trade and factor movements are
said to be substitutes (or complements) in the quantitative—relationship sense if an
increase in the volume of trade will diminish (or augment) the level of factor
movements and/or if an increase in the level of factor movements will diminish (or

augment) the volume of trade.

21

2. Price-Equalization Sense: Goods trade and factor movements are
substitutes if free trade in goods implies factor price equalization and/or free
trade in factors implies commodity price equalization.

3. World-efficiency Sense: ‘Substitutes here refers to the case where either
(trade or factor mobility) is sufficient to establish efficiency in world production,
and hence maximize potential world welfare’ (Purvis 1972), and they are
complements if both of them are required to establish world productive efliciency.

4. National—welfare Sense: Trade and factor mobility are substitutes If either
of them is sufficient to bring maximum welfare to the domestic economy, and

complements if both of them are required.

The question of whether goods trade and factor mobility are substitutes or
complements has been discussed since Mundel’s classical paper (1957), in which Mundel
showed that tariff-generated factor movements have the effect of reducing trade in the
Heckscher-Ohlin-Samuelson model. Markussen (1983) examined a number of situations,
such as differences in production technology and external economies of scale, and
showed that goods trade and factor mobility may be complements if the cause of trade is
not factor endowment differences. Generalizing Heckscher-Ohlin theorem, Svensson
(1984) compared the goods trade patterns with and without factor trade. He concluded
that factor trade and goods trade tend to be substitutes (complements) if traded and non-
traded factors are “cooperative” (“non-cooperative”). The definition of the terms
“cooperative” and “non-cooperative” are purely technical and they are given without a

clear intuition. In their joint paper, Markusen and Svensson (1985) developed a general

22

model of trade caused by international differences in production technology and examine
factor mobility within the context of this model. They showed that factor mobility leads
to an increase in the correlation between goods and factor trade, indicating a
reinforcement of the pattem of goods trade relative to the no-factor trade situation. Thus,
they concluded that factor trade and commodity trade are complements. Wong (1986) on
the other hand developed a 2x2x2 general equilibrium framework of the world which
allowed differences in tastes and technologies between the trading countries. He derived
the necessary and sufficient condition for substitutability and complementarity. Lately
Neary (1995) developed a two country model of trade and factor mobility in which
capital was sector-specific but internationally mobile. His model, unlike Heckscher-
Ohlin-Samuelson model, avoided the indeterminacy of the level of trade and factor flows

and the propensity to specialize in production and trade.

My political economy analyses on the first two chapters were mainly motivated by
Levy (1997). In this paper Levy compares the desirability of a bilateral trade agreement
with multilateral trade liberalization. He models countries’ decisions on trade relations as
binary choices. Countries first choose whether to join a free trade agreement with another
country or a group of countries, and then they choose whether to participate in a broader
multilateral agreement. Individuals in each country have different holdings of capital and
labor and for this reason they have different reactions to any given proposal. The
decisions of countries are characterized by the decisions of their median voters (the
individual with the median capital-labor ratio). Levy uses two models, Heckscher—Ohlin

and Differentiated Product, in his paper. In the former setting, he shows that there can be

23

no politically feasible bilateral trade agreements that would prevent a politically feasible
multilateral trade agreement. However in the latter, a bilateral free trade agreement can
weaken the support for a multilateral trade agreement by offering the median voter a huge
product variety gain with relatively small adverse price loss that will raise the utility of
the median voter above the one offered by the multilateral agreement. In my models, I
use the Heckscher-Ohlin framework of the first part of Levy’s paper. As in Levy’s paper
I allow individuals to have different holdings of capital so that their reactions to a free
trade agreement are different. I also retain the majority rule, i.e. the median voter’s

preference is the chosen policy.

Benhabib’s (1996) paper uses a similar setting to the models used here. He studies
how immigration policies that impose capital and skill requirements would be determined
under majority voting when native agents differ in their wealth holdings and vote to
maximize their income. He shows that the population will be polarized between those
who would want an immigration policy that will maximize capital-labor ratio and those
who would want an immigration policy that will minimize it. I used Benhabib’s notation
to describe population sizes and capital stocks in the two countries in my models.
Another similarity is the majority rule. In Benhabib’s paper, as in my models, natives
with high capital endowment in the capital abundant country benefit from labor

immigration whereas natives with low capital endowment suffer from it.

In a relatively new paper, Hansen and Kessler (2001) try to explain the stylized fact

that geographically small (big) countries tend to have low (high) tax rates. They argue

24

that immigration and democratically elected tax rates, together and interdependently, lead
to the mentioned stylized fact. They start with the reasonable assumption that high
income individuals, in general, prefer to live in countries with low taxation, and low
income individuals, on the other hand, prefer to live in countries with high taxation, i.e.
generous public spending. This causes the segregation of income classes across countries.
If this segregation is supported by national vote on tax level, then equilibrium at which
high income individuals live in low tax countries and low income individuals live in high
tax countries emerges. Here the geographical size of countries play a very important role
by providing the mechanism that prevents middle-class individuals from immigration into
countries with low tax rates. Scarcity of land in small countries causes such high property
prices that only rich people can immigrate to such countries. Unlike my model, this paper
does not use any factors of production. Individuals have constant exogenous income
rather than factors of production. Two other differences are that migration is costless and
not “illegal” in the sense I use this term, i.e. migrants become natives and they have

voting rights.

Surprisingly there is nothing much in the literature on what is behind the decision of a
group of countries to bilaterally liberalize factor flows. Giovanni Facchini’s (2002) paper
titled “ Why (1 oes a c ountry j oin an F TA?” represents a first attempt at answering this
question. It (1 evelops a theory 0 f the endogenous formation 0 f a common m arket in a
three country, n-factor model. Import restrictions/subsidies are determined by direct
democracy, i.e. by the decision of the median voter. The decision to join a common

market is modeled as a simultaneous move game between the two prospective members.

25

It is showed that differences in subsidies before the vote do not affect the decision of the
median voter. For a common market to be established the ex-post factor flows must be
balanced. In other words, if most of the factor flows are in one direction, then the median
voter in the country which receives most of the factor flows will be negatively affected.
Finally the possibility that a common market will be established increases in the number
of factors enjoying ex post enhanced protection, which indicates the potential tension

between social desirability and political feasibility of the common market.

This thesis tries to model the linkage between (illegal) migration and economic
integration. As we have seen above, almost all illegal immigration literature concerns
with welfare(s) of the host country and/or source country. Also no political economy
paper seems to have dealt with migration and free trade areas jointly. Although
Facchini’s (2002) model states the importance of ex-post factor flows in FT A decision, it
assumes no factor flow before the establishment of the common market. So far, to my
knowledge, there has been no attempt to model the linkage between (ex-ante) migration
and economic integration, which is surprising given the fact that one of the well known
reasons of NAFTA was to stop illegal migration from Mexico to the US by increasing
trade and economic growth in Mexico. By showing how the median voter's decision to
join an FTA is affected by unwanted migration from a relatively poor country, I provide a

model which links the decision to join an FTA directly to migration.

26

CHAPTER ONE

TWO STATIC PROBABILISTIC MODELS OF MIGRATION AND

ECONOMIC INTEGRATION

1.1 Introduction

This chapter presents two (one-good and two-good) two-country two-factor static
probabilistic models of migration and economic integration. These models aim to expose
a possible relationship between migration and economic integration. It is shown that by
changing the median voter’s utility level in the migrant-receiving capital abundant
country, migration of workers from a labor abundant country makes economic integration
possible b etween the two c ountries. T o m y k nowledge there is n o earlier w ork w hich
models migration as a determinant of free trade areas, although some authors, like Martin
(2001), acknowledge that s topping illegal immigration in the long run w as o ne 0 f the
goals of NAFTA. Explaining migration as a determinant of a free trade area has
important implications for the discussion about the substitutability and complementarity
between goods trade and factor movements. Migration causing free trade suggests that
factor mobility and goods trade are in a sense complements, rather than substitutes.
Although I use a Heckscher-Ohlin type model, the implication about the substitutability

and complementarity between goods trade and factor movements are different from the

27

usual interpretation of the Heckscher-Ohlin model, which clearly sees them as

substitutes.

It is also shown that a more egalitarian income distribution in the capital abundant
country increases the probability of economic integration whereas a more egalitarian
income distribution in the labor abundant country might prevent economic integration by
decreasing the number of possible migrants. These are compatible with Mayer’s (1984)
prediction that an increase in inequality, holding constant the economy’s overall relative
endowments, raises trade barriers in capital abundant economies and lowers them in

capital scarce economies.

It should be noted here that the probabilistic model that I use in this chapter of the
dissertation is different than the probabilistic voting model associated with Hinich (1977),
Coughlin and Nitzan (1981), and Ledyard (1981, 1984). In probabilistic voting models
basically voters do not vote with certainty for one particular policy or candidate, even if
that particular policy/candidate gives them higher utility than the a1ternative(s). For
example, when choosing between two political parties, say A and B, voters compare
utilities they would get under the two alternatives, A and B. Then the probability of
voting for the political party A is a smooth and continuous function of the two utility
levels, increasing in the utility the voter would get under the policy A and decreasing in
the utility the voter would get under the policy B. The probabilistic model which I use, on
the other hand, does not allow such a behavior. In the model used here, voters with

absolute certainty vote for the policy which gives them higher utility than the alternative,

28

and hence the policy preferred by the median voter is accepted with absolute certainty.
Only when median voter is indifferent between two alternatives, the outcome of voting

becomes probabilistic.

1.2 One-Good Static Model

This first part of the chapter presents a two-country static probabilistic model of
migration and economic integration. The two countries differ from each other in their
capital-labor ratios. The country with low capital-labor ratio and the wage rate is named
as the poor country, the other as the rich country. The poor country applies for an
economic integration (i.e. full movement of capital and labor) with the rich one; but the
majority of the rich country, characterized by the decision of its median voter, does not
prefer the integration. An important portion of the poor country’s labor stock consists of
workers without capital. These workers are potential migrants who may migrate to the
rich country if their expected wage differences cover the cost of migration. The migration
of workers without capital from the poor country to the rich country makes the median
voter in the rich country indifferent between economic union and non-union. The
possibility of economic union is determined by the cost of migration and the wage

difference between the two countries.

This part of the chapter is organized as follows. First the setting of the model is

introduced. Then, within a framework of a sub-model with exogenous immigration,

possible beginning equilibriums are presented. It is also shown here that the immigration

29

of the poor to the rich country increases the percentage of voters which are in favor of
integration in the rich country. Finally the probabilistic model is presented in detail. The
main results, i.e. the positive (negative) relationship between a better income distribution

in the rich (poor) country and the possibility of integration, are given at the end.

1.2.1 The Setting

There are two countries: relatively labor abundant poor country (P) and relatively
capital abundant rich country (R). R could be interpreted as an attractive economic block
and P as a candidate to this block. P and R produce one good by using the same
technology with capital and labor. Since here I use one-product model, naturally there is
no trade between countries. Wages are higher in R and interest rates are higher in P. In
this context, economic integration means free movement of factors (labor and capital).
Initially the only linkage between the two economies is illegal migration from P to R. I
assume that country P already applied for economic integration with R. Therefore
integration decision was made solely in R. I neglect the affect of illegal migration on the

decision of country P.

Each individual has one unit of labor and individuals are indexed by the units of

capital that they own, k. As in Benhabib (1996), the number of individuals is given by the

density function N]. (k), d efined o n [0,]?j ]. W e h ave two c ountries (poor and rich), so

j=P,R. The density function N J (k) is continuous in (0, IE] , but for the poor country at O

we allow a positive mass of individuals that have no capital (this assumption is necessary

30

to capture the potential immigrant stock in P). Call this number of individuals who do not

posses capital Z.

The initial capital stocks, K j. for j=P,R, are given by
if

((1.: INj(k)kdk. (1.1)
0

The initial population sizes, LP.0 and L“, are

1,.
L,,_0 = z + jN,(k) dk (1.2)
O

I?

L“, = [Ix/,0.) dk (1.3)
0
The country R is relatively capital abundant such that

r, r.
jN,(k) k dk [Npm k dk

or. > 0 r. - (1.4)
jN,(k)dk 2+ INP(k)dk

0 0

 

 

. . . K K . .
At time t capital-labor ratros are k P_, = 2—P— and k R', = —5- , where k j', rs the capital-
PJ R,’

labor ratio in country j at time t and Liar is the labor stock of country j at time t. Since P is

. . . K K
relatively labor abundant, at the beg1nnmg (when t=0) we have k m = L—”— <km = Z—"—.
P,0 R,0

We do not have time subscripts on K P and K R , since it is assumed that capital

endowments of the two countries are constant. The overall capital-labor ratio in P and R

31

together is kU , kU = (KP + 1(,,,)/(L,,‘O + L”) , which is between kj,‘0 and km. Again we
do not need time subscript for kU , since total number of individuals in both countries at
any time (L P', + L M) is equal to the total number of individuals in both countries at the

beginning (L1,.O + L”).

I assume the same constant-returns neoclassical production function

F(K,L)=L f (k), f'(k)>O and f”(k)<0for both countries. So wage rate is

w(k) = f(k) —f'(k) k and interest rate is r(k) = f'(k).

An individual’s income (Wi) is the sum of his wage and his earnings from his capital:

W’ =w(k)+r(k) ki (1.5)
where k is the capital-labor ratio of the economy in which individual i with capital
endowment k’ lives. Since every individual has only one unit of labor, individuals’
capital-labor ratios and their capital endowments are identical. The derivative of Wi is

dWi r i_

By the property of diminishing marginal productivity, r declines with k. In symbols,
r'(k) = f '(k) <0. As illustrated in Figure 1, the relation between an individual’s utility

and the economy’s capital-labor ratio is U-shaped. In particular,

dde<0 for k <k’ (1.7a)
dWi -

-————>0 or k>k' 1.7b
dk f ( >

32

%w for k=k’ (Me)

This equation characterizes the preference of the individual i in R with respect to the
capital—labor ratio of the economic entity in which he would like to live. So the welfare of

individual i roughly could be graphed as Figure 1.1.

utility

 

L---—-—--

 

economy K/L

a:

Figure 1.1: Utility level of individual i with capital endowment k’.

Horizontal axis in Figure 1.1 represents the capital-labor ratio of the economy in
which individual i lives. On the vertical axis his utility level is shown. He gets the

minimum utility when his capital-labor ratio is equal to the economy’s capital labor-ratio.

1.2.2 A Simple Model with Exogenous Immigration

Before introducing static model with endogenized immigration, let us examine a

simple median voter model with exogenous illegal immigration in a two-stage setting. At

33

the beginning, in the first stage (t=O), P applies for an economic union with R. People in
R go to the polls to determine in a referendum whether to establish an economic union
with P. The decision is made by majority vote, and the alternative most preferred by the
individual with the median capital-labor ratio is the winning alternative. We refer to this
individual as the “median voter” If this voter is indifferent between the two alternatives,
then there is a tie vote, in which case the chosen alternative is treated as random, with a

probability distribution endogenously determined below.

If the result of the referendum is positive, then the two countries economically unite
and capital move freely between the two countries causing the equalization of wages and
capital rents. If the result of the referendum is negative, then the only economic linkage
between the two countries is illegal immigration from P to R. The result of this illegal
immigration is an increase in the c apital-labor r atio in P and its d ecrease in R , which
might change the preferences of voters in R to such a degree that the result of another

majority voting in R at the second stage (t=1) might be positive.

Here, it is important to remember that I use “illegal immigration” instead of
“immigration” mainly by two reasons: First, the median voter in R would prefer to
eliminate immigration. Second, the immigrants do not have voting rights in R, since they

are not legal citizens of R.

To describe the possible equilibria at the beginning (t=O), we first define ”"4“" as the

median voter’s capital-labor ratio:

34

median
k R

jN,(k)dk

° = 0.5. (1.8)
LR,0

 

Assuming unequal society in which the relative capital endowment of the median
individual is less than the mean, we have kzed’“"<kR. The median voter’s preference

between two alternative economy capital-labor ratios is preferred by at least half of the
population in R. To see this, suppose that an integration agreement under consideration
would lead to a capital-labor ratio in the resulting integrated economy that was lower than
the alternative current capital-labor ratio. If this increases the utility of the median voter,
as illustrated in Figure 1.4, we can deduce from (1.7) that all voters with higher capital-

labor ratios than the median voter would also gain. The same reasoning applies if an
integration agreement would reduce the median voter’s utility. The symbol ER represents

the level of capital-labor ratio of R that is greater than kfed’“ and makes the median

voter indifferent between integration and non-integration, as illustrated in Figures 1.3,

1.4 and 1.7. So, it satisfies the following three conditions:

~

k, at kU, (1.9a)
it”, >k,’,"“”“" , ' (1 .9b)
w(kU ) + r(kU )kgedm" = w(k)) + r05, ) k zeta" . (1 .90)

Now we can describe the possible beginning conditions:

median
a) k, < kU < k,,'0

b) kU < kzed‘“ < 1?, < k,0

35

c) kl, < k,’;’“"‘”' < kR'0 < kR

In cases a and b, given by Figures 1.2 and 1.3, median voter enjoys a higher level of
utility in his home country than in the integrated economy. Therefore he opposes the
economic integration with P. On the other hand when we have case c, as in Figure 1.4,

median voter prefers the integrated economy with P to his own secluded R economy.

 

 

>-----------

b--------

 

k ”.../“m k economy K/L
R U kao

Figure 1.2: Utility of the median voter when k,’,""""’" < kU < kR_O .

Figure 1.2 illustrates the first case when k,’;’"""’" < k,, < k K0. Median voter’s utility in

his country is greater than the utility he would get living under the integrated economy.

Median voter opposes integration.

In Figure 1.3, as in Figure 1.2, median voter’s utility in his country is greater than the

utility he would get living under the integrated economy. Median voter opposes

36

integration. Unlike Figure 1.2, here we are able to define ER, since kU is less than

median
k, .

utility

    

 

I
I
l
I
I
I
I
I
I
I
I
L

 

~ economy K/L

k median

37'
E

Figure 1.3: Utility of the median voter when k,, < k;""’”" < k~R < k M .

l
utility

   

median
k R

------------fl-----

b--------—-

 

economy K/L

Pr“I

p;-
Q

km it

Figure 1.4: Utility of the median voter when kU < k ,’;"’ < k,o < k7,.

37

In Figure 1.4, the median voter’s utility in his country is less than the utility he would

get living under the integrated economy. Median voter supports integration.

Since median voter’s decision determines the result of the referendum, in the last case
(when kU < k fem" < k M < lg), ) the two countries establish an economic union in the first

stage, equalizing wages and rents by enough capital flow from R to P.

Now let us discuss the effect of an exogenous immigration wave to R from P in the
first two cases. The motivation for immigration is simply the wage difference between
the two countries. Since the result of the referendum in the first stage is negative, we are
dealing with two countries with different capital-labor ratios (R has a higher capital-labor

ratio, wages are higher in R than in P).

For analytical simplicity I assume that only those who do not have any capital in P are
potential immigrants, i.e. all immigrants are wage earners; they do not have any capital

earnings.

Assume that immigration level (number of illegal immigrants) is exogenous, say T.
To exclude unrealistic extreme situations, assume also that T is not big enough to make
kR less than kU in the second stage (such a “huge” level of immigration would cause

welfare decrease of the immigrants). In the first stage (t=0) for this case, T workers

illegally immigrate from P to R, and in the second stage (t=l) they work and earn wages

38

in R. Since they are not legal citizens of R they do not have voting rights in R in the

second stage.

The main effect of this immigration of T people on the voting shows itself through

the change in capital-labor ratio. In the second stage capital—labor ratio in R becomes

k R', = K R /(L 12.0 + T). Obviously this ratio is less than k R0 = K R / LR,0 in the first stage.

In the second stage, when they decide how to vote, citizens of R compare their

current eamings (from both capital and labor) in R to the would-be earnings under U, i.e.
w(kR)+r(kR) k’ vs. Mku)+r(ku)k’. If their would-be earnings under U are greater

than their current earnings in R, then they vote in favor of an economic integration with

P; otherwise they vote against it.

RESULT #1: Immigration of T number of people in the first stage increases the

percentage of votes which are in favor of integration with P.

To see this result define k as the capital endowment of the voter who is indifferent

between economic union and non-economic union as in Figure 1.5. k satisfies the

following equation:

w(kU)+r(kU)k=w(kR)+r(kR)k. (1.10)

39

utility

........................................

    

 

i------------

 

economy K/L

,3?-

7M
k-

x

C

Figure 1.5: The voter with capital endowment k is indifferent between economic union and
non-economic union.

Clearly k is between k,, and kR. Those citizens who have more capital than k will vote

for economic integration with P and the others, those with less capital than k , will vote

against it. Illegal immigration decreases kR which leads to a decrease in k . Since those

with capital endowment greater than k all vote for economic integration, the vote share
of economic integration necessarily increases. Formally this result could be obtained by

differentiating the both sides of the equation (1.10):

dk _ r’(kR)(k —k,,) >0
dk. ’ r(kui-rtkii

 

(1.11)

Since dk/dkR is positive, any decrease in kR makes k smaller, which indicates an

increase in the percentage of votes in favor of integration with P.

40

utility

  

 

p-----—--- -

..---------

 

economy K/L

3:-
3w
>-i
O
R‘-
27
P?
x
C

Figure 1.6: Immigration takes the capital-labor ratio in R from km to km.

In Figure l.6, immigration takes the capital-labor ratio in R from kR,0 to km. The
higher curve shows the utility of the person who is indifferent between integration and

non-integration, before the immigration. His capital endowment is he. All individuals

V

who have capital endowments greater than k0 support economic integration, since they
get higher utility under economic integration than under autarky. Others, with capital

endowments less than k0, are against it. After the immigration, another individual with

capital endowment kl becomes indifferent between economic integration and non-

integration. The lower curve shows the utility of this individual. Now, all those with

capital endowment higher than k, are in favor of economic integration, while those with

‘1

less capital endowment than kl are against it. Immigration increases the public support

for economic integration.

4]

In the second stage, we have voting for an integration agreement. If the median voter
prefers his own country’s capital-labor ratio to the integrated economy’s capital-labor
ratio, then the integration agreement is infeasible, i.e. it does not pass in the referendum.
If, on the other hand, the median voter prefers the integrated economy’s capital-labor
ratio to his own country’s capital-labor ratio, then he certainly votes for integration, i.e.

the integration agreement is feasible.

RESULT #2: a) Assuming k?”“" < kU <kR'0, integration is infeasible. b) Assuming

kU < kzed’“" < k~R < k m, there is a level of immigration T such that if T > T in the first

stage, economic integration becomes feasible in the second stage.

The first case (Result 2a) is obvious. Since we defined the level of exogenous

immigration, T, as something, not big enough to make kR less than kU in the second

stage, we will still have the same order of capital-labor ratios in the second stage, namely

median
kR < kU < km .

In Figure 1.7 we see the median voter’s utility level when we have kzedia" < kU < k M .

Before the immigration the median voter compares his current utility level at capital-

labor ratio kR‘0 to the utility level at capital-labor ratio kU. He prefers non-integration.

The immigration pulls the capital labor-ratio in R to k,“ at which the median voter still

42

gets higher utility than what he would get under integration. Therefore he still prefers

non-integration, i.e. the integration is infeasible.

utility

---------------------------

 

 

p----------------------

h------------

 

median
k R kU k R‘, economy K/L

>1:-
3’
C

Figure 1.7: Utility of the median voter when k,’,"""""' < kU < k,“ < km

When we have kU < k ,3’"""'" < k < k 12.0 as in the second case (Result 2b), we will have

the following inequality:

w(kt/ ) + r(kt/)k1:wdlan < w(kR,0) + r(kR,o)k1’:cdm - (1-12)
Now define AW R”:,"""'" as follows:
AWR”,"""’" = [w(kR', ) + r(kRJ ) k ,7“ ] — [w(kU ) + r(kl, )k,’;"’"""'] (1.13)

When we switch from the first stage to the second stage, the only changing variable in

AWR’Tdm" is km. Therefore AW R”f""’" could be interpreted as a function of km;

AWR”f""’” = Mk“). Now remember that E, is the level of capital-labor ratio of R which

43

makes the median voter indifferent between integration and non-integration. Formally
w(i) = o, i.e. E, = til-«0). T“ is then the level of immigration which will pull down it“,

from K R / LR.O (in the first stage) to 12;, (in the second stage). Since kR = K R /(LR,0 + T) ,

T=(K,, —/?,, L,,)/I?,,. (1.14)

utility

b----—--—----------------——-----------------——---

  

----------_-------J----
p.--——---—--—---——-—--——

I
I
I
I
I
I
I
I
I
I
I
I
l
I
I
I
I
l

p—-------

 

 

economy K/L

3%“
\.

median ~
kR k1“ k kR,O

Figure 1.8: Utility of the median voter when kU < k: “1”" < k Rj < KR < km

As in Figure 1.8, when we have kU <k,’,""""’" <de <kR'0, there is a level of
immigration T which pulls the capital-labor ratio in R from km to kR. At this capital-

labor ratio, lit), , the median voter is indifferent between integration and non-integration. If

we have an immigration level greater than T , then the capital labor ratio in R becomes
less than ER, such as km on the graph and the median voter prefers integration to non-

integration.

44

1.2.3 Static-Probabilistic Model

In this part we have the same setting and again two stages as in the simple exogenous
migration model, but now the number of migrants is endogenous, i.e. the number of
migrants in the first stage is determined within the model. Also, to exclude uninteresting
beginning situations, I assume that the median voter does not prefer economic integration

in the first stage, but immigration might change his preference, so

kU < kz'ed’“ < kk < km as in Figures 1.3 and 1.8.

The only equilibrium number of immigrants is the number which will make the

median voter in the rich country indifferent between economic integration and non-
integration, i.e. T . In other words, after the migration wave in the first stage, in the
second stage capital-labor ratio will be kR. The reason is simple: Any number of
migrants greater than T will make the probability of economic integration equal to 1,
since median voter will chose economic integration in this case. But if the possibility of
economic integration is one, no one would want to immigrate and incur migration costs

in the first place, since they can get all the benefits of economic integration by staying at

home and not incurring costs of migration. Similarly any number of migrants less than
T will make the probability of economic integration equal to 0. But if the probability of

economic integration is 0, then all workers (more than T ) would migrate to enjoy the

higher wages of R the second stage. This could not be an equilibrium, because if all

workers immigrate, the immigrant stock in R becomes bigger than T , which indicates

that the probability of economic integration is 1, not 0.

45

Then what is the possibility of economic integration when only T number of people
immigrates to R? We can find this by equating the cost of migration to the expected gains
from migrating. To keep the analysis simple, I use the “psychic” cost concept of Sjaastad
(1962). Migration involves a psychic cost, because people are often genuinely reluctant to
leave familiar surroundings, family, and friends. We might argue that in the case of
illegal immigration psychic cost becomes more relevant, since immigrants’ very presence
is not welcomed by the majority of the host country citizens. In our model median voter
is against immigration, since his real utility is decreasing because of immigration. Median
voter with at least half of the population in R is against immigration. Living in a foreign
country in which majority dislikes immigrants must not be very appealing to the potential

migrants. As Sj asstad explained, psychic costs do not represent real resource costs:

“...Rather they are of the nature of lost consumer (or producer) surplus on the
part of the migrant. Given the earnings levels at all other places, there is some
minimum earning level at location i which will cause a given individual to be
indifi’erent between migration and remaining at i. For any higher earnings at i, he
collects a surplus in the sense that part of his earnings could be taxed away and
that taxation would not cause him to migrate. The maximum amount that could be
taken away without inducing migration represents the value of the surplus. By
perfect discrimination, it would be possible to take away the full amount of the

surplus, but in doing so leave resource allocation unaflected (other than through

46

distributive eflects). Hence, the psychic cost of migration involve no resources for

the economy and should not be included as part of the investment in migration. "

Assuming that every immigrant incurs a constant psychic cost, C, we can find the
equilibrium level of migration and the probability of integration. Equilibrium level of
migration should make workers indifferent between staying in P without incurring the

cost C and migrating to R with incurring the cost C:

 

(I—fliwtimflw.)=(1mini/1'.)—Ci+fliw(kU)—Ci, (115a)
C=(1-/3)iw<17.)—w(/'Fp>i, (1.151»)
3 :1 C (1.15c)

- w(i. ) - will)
where endogenous variable [3 is the probability of a vote in favor of economic integration
and E, is the capital-labor ratio in P which corresponds to the capital labor ratio k~R in R.
In other words, when T number of people immigrates to R, the capital-labor ratio in P

becomes k P :

1?, = K, /(L,,,0 —T) (1.16)

Now we can restate the equilibrium conditions for the equilibrium number of
immigrants, T , and the equilibrium probability of economic integration, B:
i) The equilibrium number of immigrants, T , satisfies equation (1 . 14)

77:09, —k~,,L,,,,)/1?,. (1.14)

where k, is determined by conditions (1.9a), (1.9b) and (1.9c).

47

1?, e k,,, (1.9a)

1?, >k,’,’“"’“”' , (1 .9b)

we, ) + r(kU )k,’,"‘°"“”' = w(E, ) + r07, )k;“"’“" . (1 .9c)

ii) The equilibrium probability of economic integration, [3, is given by equation

(1.15c)

- ... C ~ (1.15c)
w(kR)—w(k,,)

 

fl=l

where E, is determined by equation (1.16).

12",, = K, /(L,,0 _r) (1.16)

1.2.3.1 Results

Here I will present the implications of the model about the effects of income

distribution and cost of migration on the probability of economic integration.

1) A more (less) equal income distribution in R, characterized by an increase

(decrease) in k 39”“ , leads to an increase (decrease) in the possibility of economic union.

To see this result, we need to take the derivative of kk with respect to kZ’ed’“.

Differentiating the both sides of the equation (1.7) will give us

d5. : raw—rd.) >0 (1 17)
dkged’“ r'(k,,)(k;'e""“" —k,) ’ '

48

kzed‘“ will lead to an

The positive sign of this derivative means that an increase in
increase in R, (as in Figure 1.9), which indicates decreases in Tand E. A higher kR
requires less migration from P than a lower it}, , which means T decreases. Decrease in
migration, T , on the other hand, means a decrease in E, . Since wage rate is increasing in

the economy capital-labor ratio, w(kR)—w(k,.)will increase. Then it is easy from

equation (1.15c) that B increases.A similar analysis shows that a decrease in k?“ will

cause a decrease in B.

utility

 
    

 

 

J

l
I

~

median median ~ econom K".
k. k... k... k... k... V

Figure 1.9: Utility of the median voter when his capital-labor ratio increases from kg?” to

median
k R ,1 .

49

median

Figure 1.9 shows that an increase in median voter’s capital-labor ratio from k m to

k:‘:""”' will lead to an increase in the capital-labor ratio at which the median voter is

indifferent between integration and non-integration (from km to E 11.1 ).

2) A more (less) equal income distribution in P, characterized by a decrease (increase)
in the number of workers without capital, may render infeasible an otherwise possible

economic integration.

Improvement of income distribution case:

Remember that Z the total number of workers without capital in P. These are the only

potential migrants by assumption. If we start with a situation of Z > T , there is a

possibility of economic integration since total number of immigrants required for
economic integration is T . Any income distributional change which decreases Z below
T makes economic union politically infeasible, since when all workers without capital
immigrate to R, R’s capital-labor ratio will still be greater than IE, and the median voter

in R will prefer non-integration with absolute certainty.

Worsening of income distribution case:

If we start with a situation of Z < T , there is no prospect for economic union. Since

even when all the potential workers immigrate, the capital-labor ratio in R will still be

higher than k~R and median voter will strictly prefer non-integration. In such a situation

50

any income distributional change which makes Z greater than T makes the total number

of immigrants equal to T and the possibility of economic integration arises.

3) Increase in the cost of migration will lead to a lower possibility of economic

integration. From equation (1.15c), it is very easy to see this.

13

l \ fl(T)

\TM)
7‘ T

Figure 1.10: Equilibrium number of immigrants and the probability of economic integration.

 

 

 

 

 

As illustrated in Figure 1.10, the number of immigrants depends on the probability of
integration, but the probability of integration depends on the number of immigrants. From
the ,B(T) curve we see that as long as the total number of immigrants is less than T , the
probability of integration will be 0, since median voter will prefer non-integration. An
immigration level above T will make median voter prefer integration, i.e. the possibility
of migration will be 1. On the other hand, if it is certain that in the second stage the two
economies will integrate, no one immigrates in the first stage (why should anyone pay for

the cost of migration if in the second stage wages are equal in both countries?) The lower

the probability of integration is, the higher the immigration will be. We can see this as we

51

go along the T ( ,6) curve. Therefore the only possible number of immigrants is T , which

is determined by the intersection of the two curves.

1.3 Two-Good Static Model

As in Levy (1997), this section will consider economic integration in a standard two
good, two—factor Heckscher-Ohlin trade model. By adding migration and probabilistic
features of the preceding section to the framework developed in Levy, I will show that

the results of the one- good model also hold true in the two-good model.

We keep all the assumptions of the previous one-good model except the number of
goods. Now, capital and labor are used in the constant returns to scale production of
goods OK and QL. The identical technologies in both countries are assumed to be such
that capital is used relatively intensively in QK (and labor in QL) with no factor-intensity

reversals. Perfect competition makes sure that profits are zero.

Individuals are assumed to have identical and homothetic preferences. People spend
their full income on goods OK and QL. Labor intensive good, QL, is the numeraire good;
p ,, is the price of QKin terms of QL in the poor country and p R is the price of QKin

terms of QL in the rich country.

In this two-good model integration is defined as a free trade agreement that will

equalize factor prices across the two economies. With free trade, the integrated economy

52

that would result from factor mobility will be achieved instead through trade flows. To
make things simple it is assumed that tariffs are either zero or prohibitive, so without free
trade both countries are in autarky. If two countries establish a free-trade area, the
resulting relative price will be between the autarky prices in the two countries and the

capital-abundant rich country will export OK and import QL,

Levy (1997) showed that in a standard two-good, two-factor Heckscher—Ohlin trade

model the utility of an agent i with a capital endowment k’ , can be depicted as a function
of k , the capital-labor ratio of the economy in which he lives. This function is strictly
quasi-convex in k and has a unique minimum when the agent’s capital-labor ratio is

equal to that of the economy.

utility

    

UA

   

 

b--—-—--—-----—--

_ L

E

"1‘

Autarky economy K/L

Figure 1.11: The strictly quasi-convex utility of an agent with a given capital-labor ratio as a
function of the economy’s capital-labor ratio.

Figure 1.11 shows the strictly quasi-convex utility of an agent with a given capital-
labor ratio as a function of the economy’s capital-labor ratio. Levy uses this figure to

illustrate his proposition. If this represented the median voter in a country, he would

53

reject trade agreements which resulted in economy capital-labor ratios in the range
(Autarky, E). Outside of that range, utility increases as the distance from Autarky

increases.

We can see the argument behind the U-shaped relationship between an individual’s
utility and the economy’s capital-labor ratio, by using indirect utility function and zero

profit condition of the economy. Differentiating indirect utility function of individual i,

V’ = V’(w+rk’,p), gives
,- ,- aVi
dV =/l(dw+drk )+—é—dp (1.18)
P

where dVi is the change in indirect utility, it is the marginal utility of income, dw is the

change in the wage rate, dr is the change in the interest rate, ki is the individual’s capital

endowment, —a—— is the marginal utility of a change in the price of the capital intensive

good and d p is the c hange in the p rice 0 f the c apital intensive good. Since the labor

intensive good’s price is numeraire, the change in its price is zero. Dividing both sides of

0V’

(1.18) by 7., and using Roy’s identity, i.e. i = —C‘ , where C i is the individual’s
l K K

 

consumption of the capital intensive good, we will have

i

ig—=dw+drk’—Cf(dp. (1.19)

Dividing both sides of the equation (1.19) by the individual’s income, w+ rk’ , allow us

to write

54

dVi _d_w w +1): rki _£lp pC}

———-—-—-——.——— . . . (1.20a)
A(w+rk‘) w (w+rk‘) r (w+rk’) p (w+rk')
or
dV’ - .
—————.-=w®' +f(~)‘ — “I“ 1.20b
xi.(W+rk’) L K P K ( )

where w: dw/w, f = dr/r, f; = dp/p , O; = w/(w+rk’), G); = rk’ /(w+rk’) and
I} = p C fr /(w+ rk’). In this notation, w is the proportional change in the wage rate, f
is the proportional change in the interest rate, I“) is the proportional change in the price of
the capital intensive good, (9’, is the share of labor in the income of individual i, O} is
the share of capital in the income of individual i, and finally I} is the share of spending

on capital intensive good in individual i’s total spending. We do not have superscript i in

FK, simply because of the fact that with homothetic and identical preferences all

individuals have the same FK. Since the marginal utility of income, 2., and the income of

individual i, w+ rk’ , are positive, we can conclude that if an increase in the economy’s

i

capital-labor ratio leads to an increase in ———.— ,
11(w + r k' )

then dV/dk is positive. Similarly

dVi

if an increase in the economy’s capital-labor r atio leads to a d ecrease in ———l.— ,
1(w + r k )

dV/ dk is negative.

i

To determine the sign of ————.—
2(w+rk')

w e c an u se the 2 cm profit c ondition for the

economy:

55

wL+rK—CL —pCK =0 (1.21)
In this equation L is the country’s labor stock, K is the country’s capital stock, CL is the
total consumption of labor intensive good in the economy and CK is the total consumption
of capital intensive good in the economy. Dividing everything by L, gives us

w—rk'm" —CZ‘"‘"’ —pC,’§"”“" =0. (1.22)
where k’"“" is the mean capital-labor ratio in the economy, C 2"“ is the mean

consumption of labor intensive good in the economy and C 2'8"” is the mean consumption
of capital intensive good in the economy. Differentiating equation (1.22) results in

dw — drk'm" — dpczm = 0. (1.23)

Dividing everything in (1.23) by the average income, w + rk'"""" , allows us to write

 

 

 

d7“) (w+:‘k""’“") —% (w:]:'k""’“") —(—15.(w1~i-€lkm”) = 0 (12421)
or

were“ + 1392“" — pl} = O (1.24b)
where w=dw/w, f=dr/r, p=dp/p, 82“" =w/(w+rk"'e‘"'),

62“" = rk’m” /(w+ rk’""“") and I} = p C 2“" /(w+ rkmea"). Once again, we do not have
superscript mean in FK , simply because of the fact that with homothetic and identical
preferences all individuals have the same FK. Equation (1.24b) indicates

pl} = were + F920“. (1.25)

Using equation (1.25) in (1 .20b) gives us

56

dVi

—.=w®’ —®"’""" +f' Oi —®"’"‘"’ . 1.26
Mw+rk,)(ii)(tx) ()

Since G); +9; =1 and 62’9“” +9?" =1, (9; —®2‘“") is equal to the negative of
(O: —®f“"). This would allow us to rewrite (1.25) as

dV‘
2(w+rki)

= (w—fxe", —e;'“"). (1.27)

From equation (1.27) we can easily see that the derivative of an individual’s utility with
respect to the economy’s capital-labor ratio is negative if the individual’s capital
endowment is greater than the economy’s capital-labor ratio. It is zero if the individual’s

capital endowment is equal to the economy’s capital-labor ratio and it is positive if the

individual’s capital endowment is lower than the economy’s capital-labor ratio.

Consider first, the situation where the individual i’s capital endowment is greater than
the economy’s. Then the individual i has a higher income than the individual with the
mean capital endowment which is equal to the economy’s capital-labor ratio. Since both
individuals have the same wage, the labor share of the income of the individual i must be

less than the labor share of the income of an individual with the mean capital endowment.
In other words (G): ‘9'an) is negative. An increase in the capital-labor ratio of the

economywill increase the real return on labor and decrease the real return on capital,
which indicates that w—f is positive. Therefore we conclude that when an individual’s
capital-labor ratio is greater than the economy’s, derivative of the individual’s utility with

respect to economy’s capital-labor ratio is negative:

57

dVi .
—<O ork' >k 1.28a
dk f ( )

where k is the capital-labor ratio of the economy and ki is the individual’s capital

endowment.

If the individual’s capital endowment is equal to the economy’s, then we will have
6); = 9'2“" , which indicates

Egg—=0 fork' =k. (1.28b)

If the individual i’s capital endowment, on the other hand, is less than the economy’s,
then the individual i has a lower income than the individual with the mean capital
endowment which is equal to the economy’s capital-labor ratio. Since both individuals
have the same wage, the labor share of the income of the individual i must be greater than

the labor share of the income of an individual with the mean capital endowment. In other
words ((9: —®’Z"‘"’) is positive. Therefore we conclude that when an individual’s capital-
labor ratio is less than the economy’s, derivative of the individual’s utility with respect to
economy’s capital-labor ratio is positive:

dV’ .
—>O k‘ <k 1.28c
dk for < )

Derivatives (1.28a), (1.28b) and (1.28c) together mean that the relationship between
an individual’s utility and the economy’s capital-labor ratio is U-shaped in the two-good

model just as it is in the one good model.

58

After having showed that the utilities of individuals are U shaped with minimums at
the individual’s capital—labor ratio, just like in the previous one-good model, now we turn
to the relationship between migration and economic integration, i.e. free trade. As in the
previous section, we have two stages and again the number of migrants in the first stage
is endogenous. Again we start with a situation where the median voter has lower capital-

labor ratio than his own country’s (inequality assumption) and he does not prefer
economic integration. So, we have kU <k;“’"’“" <kk <k,,‘o as in Figure 1.3. For
analytical purposes, we can use Figure 1.3 without any problem here, since it is U shaped

with a minimum at the median voter’s capital-labor ratio. Once again kU is the capital-

median
k R

labor ratio of the integrated economy, is the capital-labor ratio of the median voter

in R, k7, is the capital-labor ratio at which the median voter is indifferent between
economic integration (now free trade) and non-integration (autarky) and finally k 11.0 is

the capital-labor ratio in R in the first stage.

The argument developed in the one-good model that the only equilibrium number of

immigrants is the number which will make the median voter in R indifferent between

economic integration and non-integration, T , is also valid here, since median voter’s

decision determines the outcome of the referendum.

Again defining C as constant psychic costs of living in R (now C is in terms of the

indirect utility), we can find the equilibrium level of migration and the probability of

59

economic integration. Equilibrium level of migration should make workers indifferent
between staying in P without incurring the cost C and migrating to R with incurring the

cost C:

<1—,6)V(w?.),ptl?p»wan/cumin»

 

~ ~ (1.2%)
= (1— minurkkimikiii— C1 + fl[V(MkU),p(ki/))- C]
C = (1— mil/(Mi). 1,1206. » — Vin/”Fwd. ))I (1.291))
,8 = 1 C (1 .29c)

V(“(kR )a p(kR )) _ V(“(kp ),p(kp ))
where V(.) represents the indirect utility function. At equilibrium we have the equality

(1.29c). Figure 1.10 once again depicts the equilibrium number of immigrants and the

probability of integration.

Results of the previous section are also valid here. An increase in I; , caused by an

median
k R

increase in (as in Figure 1.8), will require lower migration level, since a decrease

in the equilibrium number of migrants will lead to a higher capital-labor ratio in R in the

second stage. Less migration will lead to an increase in the capital-labor ratio in P at the
equilibrium, kp. Since the indirect utility of a wage earner is increasing in the capital-
labor ratio of the economy in which he lives, V(w(kR ), p(kR )) increases and

V(w(kp), p(k,,)) decreases. Therefore the probability of free trade increases. So once
again we have seen that a more (less) equal income distribution in R, characterized by an
increase (decrease) in kz'ed’“, leads to an increase (decrease) in the possibility of

economic union.

60

The second result of the previous section, that is a more (less) equal income
distribution in P, characterized by a decrease (increase) in the number of workers
without capital, may render infeasible an otherwise possible economic integration, is also

valid here and the reasoning behind it is the same.

Finally the third result, that is an increase in the cost of migration will lead to a lower

possibility of economic integration, can easily be seen from equation (1.29c).

1.3.1 A Numerical Example for Two-Good Model

In this section, I will present a numerical example for the two-good model developed
above. In this example, the initial capital and labor endowments in the two countries and

in the integrated economy are as follows:

Economy: Poor Rich Integrated Economy
Capital: K, = 30 K, = 90 KU = 120

Labor: 1.,0 = 30 L” =10 LU = 40
Capital-labor ratio: k ,‘0 = l k 11.0 = 9 kU = 3

We have the following identical Cobb—Douglas production functions in both

countries:

Q1 = K161: (1-30)

61

Q. = Kit: (1.31)

Therefore, good-1 is capital intensive and the good-2 is labor intensive.

Consumer utility is also in the Cobb-Douglas form and identical in both countries:

U = Q15Q35° (1.32)
Defining I? and I? as total endowments of capital and labor in the economy allows us to
write, K 2 = I? - K I and L2 = T. — Ll . Plugging these into equation (1.31) gives

Q2 =(E—Ki)"(Z—L.)‘°. (1.33)
Plugging equations (1.30) and (1.33) into equation (1.32) gives

U = K,3L-,2(K' — Kl )'2(Z — L2 )3 (1.34)
Maximizing equation (1.34) indicates the following distribution of capital and labor

endowments across the production of labor intensive good-1 and the production of capital

intensive good-2.

=.6]?
.1?

....NW
II II
aha

.Z
.Z

Now we can write the revenue function by using these proportions of capital and

labor:
R = (.6'6)(.4"’)(p1?'°1-."’ + KT) (1.35)

where p is the price of the capital intensive good in terms of the numeraire labor intensive

62

good. Derivative of the revenue function with respect to the labor endowment gives the

wage rate:
_ 6R _ .6 .4 .6 .4
w — 5L: — (.6 )(.4 )(.4pk + .6k ) (1.36)

where k is the c apital-labor ratio, 1? / I_. , Similarly, d erivative o f t he revenue function
with respect to the capital endowment gives the interest rate:

6R .6 .4 —.4 -.6
r_—51?_(.6 )(.4 )(.6pk +.4k ). (1.37)

Zero profit conditions gives:

(.6‘6)(.4'4)pk'6 = .6rk + .4w (1.38)

(.6“")(.4"‘)k‘4 = .4rk + .6w. (1.39)
Plugging equations (1.36) and (1.37) either into equation (1.38) or into (1.39) results in

p=k"2. (1.40)
Plugging equation (1.40) into equations (1 .36) and (1.37) gives

w = (.6'6 )(.4'4 )k" (1.41)

r = (.6'°)(.4"‘)k"6 (1.42)

With these wage rate and interest rate we can calculate median voter’s income once
we know his capital endowment. Also individual utility maximization gives us quantities
of good-1 and good-2 in terms of individual income and the prices of goods:

income
Q1 =
2p

 

(1.43)

63

income
Q = 2 (1 -44)

 

Plugging equations (1.43) and (1.44) into consumer utility function (1.32) and using

(1 .40) gives us the indirect utility function:

 

income' k" w+ rk’

V' 5
2p' 2

(1.45)

Using equations (1.41) and (1.42), we can write the indirect utility of the median voter as
.6 .4
VRmedian : (6 )2('4 )(k: + k};.5k:edian) . (146)

Assume capital endowment of the median voter in R is 5. Then we can calculate his

utility under free trade and autarky at the beginning (t=0).

.6 .4
VJ""‘"" (kU = 3;k;;'"‘"’“" = 5) = (46—23205 + 3'55) 2 1.178187
.6 .4
V:""‘“" (k R = 9;k,',"""’“" = 5) = @5205 + 9“5 5) 2 1.190396
Since the utility of the median voter under autarky in R is greater than his utility under

free trade with P, he prefers autarky to free trade.

Median Voter is indifferent between economy capital-labor ratios 3 and 75/9, since

.6 .4 -5 --5
V,"""’“"(k,. = 795%....“ = 5) = WK?) +[7—93) 5] 51.178187.

The necessary migration for economic integration is .8, because ER = E = 90 means

~

9 10+T

 

T =.8. At this critical level of migration, capital-labor ratio in P is

22”,, = —39—- 3 1.027397
30-.8

Let the cost of migration to be .2, i.e. C=.2. To calculate the probability of free trade
agreement, we need to calculate the utilities of a worker without capital at this level of

critical migration under autarky in R and under autarky in P.

C
V(MEMOFRD—V(MEP),p(I?P»

 

,6 =1 (1.290)

(.6'6)(.4°“)(8.333333'5) ~

 

 

V(w(k~R ), poi”, )) = 2 = .736367
.6 .4 .5
V(w(k,,),p(k,))=('6 )(.4 )(;.027397 )2258556
.2
73:1 5.581424z58.1%

 

— .736367 — .258556

Now let us see that an increase in the cost of migration C, decreases the probability of
economic union. Let now C to be .25.

C=.25

fi :1. '25 E .476781 4 47.7%
.736367 - .258556

 

The decrease in the probability of free trade from 58.1% to 47.7% is due to the increase

in the cost of migration from .2 to .25.

To see that an increase in k,’,""‘““” increases the probability of economic union, let us

increase kz'edia" from 5 to 5.1.

65

kirenedian :51
median median (66 )(44) .5 —.5
VU (kU =3;k, =5.1)=—2——(3 +3 5.1)g1.192914

.6 .4
V,”d‘“"(k,, = 9;k;"'"""" = 5.1) = £9_12(-_4_)(9.s + 97-5 5.1); 1.198899

Again at the beginning (t=0) median voter prefers non-integration.

Median Voter is indifferent between economy capital-labor ratios 3 and 8.67, since
.6 .4
V,”“’"“”(k,, = 8.67;k;“’"’“" = 5.1) = 9—635-‘4—M8675 + 8.67"'5 5.1) 5 1.192914

The necessary migration for economic integration is 0.380623, because

ER =8.67 = 90~ indicates T =.380623. At this critical migration level, capital-labor
10+T

 

ratio in P is

l? 30

p = = 1.012850.
30—.380623

Again the cost of migration is .2, i.e. C=.2.

/3=1- ~ ~ C ~ ~ (1.290)
V(Mkk)ap(kk))—V(MkP):p(kP))

V(ME, ), p(k~R )) = ('6'6)('4;)(8'67'5) 2 .751094
V(MFPMUE» = (.6- )(.4- )(1.012850- ) ~

= .256719
2

 

p =1— '2 E .595449 z 59.5%
.751094-.256719

66

This increase in the probability of free trade from 58.1% to 59.5% is due to the

increase in the capital-labor ratio of the median voter from 5 to 5.1.

1.4 Conclusion

By presenting two (one-good and two-good) static probabilistic models of migration
and economic integration, this chapter provided an analytical basis for studying the
relationship between migration and economic integration. As it is stated earlier, to my
knowledge, there is no previous work in the literature which models migration as a cause
of free trade agreements. Therefore the models presented in this chapter seem to be the

first attempts in this direction.

It is shown that immigration might change the political economy equilibrium trade
policy from autarky to free trade, which implies a complimentary relationship between
factor movements and goods trade. This is an interesting result, because it conflicts with
Mundel’s (1957) classic conclusion that factor mobility in response to international factor
price differences leads to the elimination of trade via the elimination of the factor
proportions basis for trade, i.e. factor movements and goods trade are substitutes. This
important difference is because of the political economy and illegal immigration aspects
of my models. Illegal immigration changes the political economy equilibrium trade
policy by changing the median voter’s utility level and thus his preference about the trade

policy.

67

Results about the income distribution and the probability of free trade are given.
These results are in full compliance with Mayer’s (1984) prediction about the political
economy equilibrium trade policies in an unequal society (one in which the relative
capital endowment of the median individual is less than the mean). These policies will be
biased against capital owners. Mayer’s framework indicates that an increase in inequality
(the difference between the mean and the median capital-labor ratio), holding constant
the economy’s overall relative endowments, raises trade barriers in capital-abundant
economies and lowers them in capital-scarce economies. On this chapter, we have found
results that are analogous to Mayer’s in the context of free trade areas: An increase in
inequality in a capital rich country decreases the probability of free trade and an increase

in inequality in a labor rich country can make a free trade agreement feasible.

68

CHAPTER TWO

TWO DYNAMIC MODELS OF MIGRATION AND

ECONOMIC INTEGRATION

2.1 Introduction

This chapter presents two (one-good and two-good) two-country two-factor dynamic
models of migration and economic integration. As in the previous chapter, I aim to
expose a possible relationship between migration and economic integration. Once again it
will be shown that by changing the median voter’s utility level in the migrant-receiving
capital abundant country, migration of workers from a labor abundant country makes
economic integration possible between the two countries. The main difference in this
chapter from the previous one is the time dimension. Adding time dimension to the
framework developed in the previous chapter allows us to study the equilibrium time of
economic integration and the equilibrium time path of immigration instead of equilibrium
probability of economic integration of the first chapter. Also this new dynamic feature
makes it possible for us to asses the impact of the changes in income inequality on the

time of economic integration.

As in the previous chapter, implications for the discussion about the substitutability

and complementarity between goods trade and factor movements is that migration

causing free trade suggests that factor mobility and goods trade are in a sense

69

complements, rather than substitutes. Using a dynamic model rather than a static and
probabilistic one does not change this new complementarity feature of factor movements

and goods trade within a Heckscher-Ohlin type model.

It is also shown that a more egalitarian income distribution in the capital abundant
country makes the time of economic integration sooner whereas a less egalitarian income
distribution makes the time of economic integration later. This prediction is compatible
with the similar one in the previous chapter and with Mayer’s (1984) prediction that an
increase in inequality, holding constant the economy’s overall relative endowments,
raises trade barriers in capital abundant economies and lowers them in capital scarce
economies. Now the change in income inequality shows its effect on the time of

economic integration rather than the possibility of economic integration.

In the following section (2.2), I present the one-good model. A one-good model is
more suitable for pedagogical purposes, and the equalities and expressions are easier to
follow. In both models, we have two countries and two factors. The two countries differ
from each other in their relative factor endowments. The two factors are capital and labor.
The country with low capital-labor ratio and the wage rate is named as the poor country
(P), the other as the rich country (R). The poor country applies for an economic
integration with the rich one, i.e. free movement of both factors (for the factor price
equalization free movement of one factor is enough), but the majority of the rich country,
characterized by the decision of its median voter, does not prefer the integration. An

important portion of the poor country’s labor stock consists of workers without capital.

70

These workers are potential migrants who migrate to the rich country as long as the
present value of their future wage difference (the difference between the wage they get in
the rich country and the wage they would get in the poor country, if they had not
migrated) is non-negative (specifically 0). Naturally, the migration of workers without
capital from the poor country to the rich country increases the capital-labor ratio and the
wage rate in the former and decreases them in the latter. As capital-labor ratios get closer
and closer to each other, so do the wage ratios, i.e. the wage difference between the two
countries shrink. This shrinkage of wage difference coincides with a decreasing migration
rate. Migration continues until the median voter in the rich country becomes indifferent

between the economic integration of the two countries and the non-integration.

In the section (2.3) I switch to the two-good model. Since these two countries do not
trade at the time of autarky, we do not have exchange rates that would let us compare
wage rates in these countries. To see the motivation for migration, i.e. higher real wages
in R compared to P, we can use indirect utility functions of individuals. Assuming that
migrants do not have capital (as done in the previous section) and choosing the price of
the labor-intensive good as numeraire lets us define indirect utility only as a function of
wage and the price of the capital good. Then an increase in capital-labor ratio in P caused
by migration will increase wages and decrease the price of capital good, which
undoubtedly increase the utility of a wage earner. Similarly the decrease of capital-labor
ratio in R will decrease the real wage there. Therefore as in the one-good model we will
observe a decrease in the real wage difference as a result of migration. This result can

also be seen by using Rybczynski and Stolper-Samuelson theorems. By Rybczynski

71

theorem, holding product prices fixed, the decrease in P’s endowment of labor will
expand the capital-intensive industry and contract the labor-intensive industry, which

indicates an increase in QK /QL ratio (capital-intensive good production/labor-intensive

good production) in P. This will make the capital intensive good cheaper in terms of the
labor intensive good, which is numeraire. Now by using Stolper-Samuelson theorem we
can safely argue that the real wage in P will increase. A similar analysis for R shows that
the real wage will decrease in R as a result of migration, i.e. increase of labor endowment

in R.

In the last section (2.4) I present the conclusions.

2.2 One-Good Dynamic Model

The setting of this dynamic model is similar to the one on the previous model. The
main difference is the definition of migration costs. Now it is assumed that migrants need
some time to find “good jobs” at which they can exert their full labor and get the same
wage as native workers in the rich country. Until they find such jobs, they spend a time
period at bad jobs, C(M(t)), where M(t) is the total number of migrants at the time of
migration t. In these bad jobs they have low productivity (their individual labor is
lowered from 1 to a fraction, b) and therefore they got b fraction of the wage rate in the
rich country. We assume that b is low enough so that in this initial time period
(t,t+C(M(t))) migrants’ wage is less than what they would get in their hOme country.

Therefore the time period spent in bad jobs (t,t+C(M(t))) represents the cost of migration.

72

It is natural to assume that C(.) is increasing in M(t), since more migrants means more
competition among migrants for the same kind of jobs. Afier t+C(M(t)), migrants who
migrated at time t get used to the environment in the host country R and switch to good
jobs with full wages. The time spent in these good jobs until economic integration at time
t represents the benefits of migration. After economic integration, 1, wages will be
equalized across countries, i.e. there will be no benefits or costs after this time. The main
result is again the positive relationship between a more equal income distribution in R

and the closeness of integration.

utility

  

----------------------------------------

      

 

 

k k median economy K/L
U R

3:-
2:
a?
F
C

Figure 2.1: Utility of the median voter in the rich country when kU < k,’,""""’" < I?R < km-

median
kR

Now define as the capital-labor ratio of the median voter, and assume that

kU < k,’,""""’" < ER < k M , that is median voter’s capital-labor ratio is between the capital-

labor ratio of the integrated economy, k), , and the capital-labor ratio, ER , at which the

73

median voter is indifferent between economic integration and non-integration. Also at the
beginning the capital-labor ratio in R, km, is greater than R. Figure 2.1 shows an
illustration of this condition. As explained in the previous chapter, this is the case where
migration might cause economic integration. We need a reduction of the capital-labor

ratio of R from k”.0 to ER to make the median voter indifferent between economic

integration and non-integration.

In this d ynamic m odel we n 0 longer h ave two stages. Instead w e h ave continuous
time, i.e. t is in [0,oo). At the beginning (t=0), the median voter in R prefers no
integration. Therefore we have two economies linked to each other only by illegal
immigration. Immigration occurs continuously. Workers without capital in P immigrate
to R as long as the present value of their expected benefits from immigration covers the
cost. In R, on the other hand, voting for economic union occurs every instant of time, i.e.
whenever majority of the population in R prefers union, they vote for it and economic
union is established instantaneously. Again the median voter’s preference will determine

the result of any referendum.

Since wages are higher in R, there is a continuous flow of immigrants from P to R.

The labor stocks in the poor and rich countries are:

LP, = LP, — IM(s)ds (2.1)
0

L“ = LR.0 + :[bM(s)ds + :[(1— b)M(s) 1(s) ds (2.2)

74

where I(s) = O (1) if s+C(M(s)) >(<) t. The capital-labor ratios in the poor and rich
countries are:

km = K!“ = K" (2.3)

L 1
P-' LP.0 — [M(s)ds
0

 

k, = fl = KR (2.4)

‘ LR" LRO + :[bM(s)ds + :[(l —b)M(s)I(s)dS

 

K p , K R , L ,0 and L m are constants. Naturally immigration decreases L P, and k M ,

increases LR‘, and kP‘, overtime.

To decide whether to immigrate, workers look at the present value of their future
effective wage differences between the two countries. At any positive level of migration,

workers are indifferent about immigrating, as described by the following condition:

r+C‘(M(1)) r
je-P‘H’ [b w(kR‘S ) — w(kp', )]ds + few-0 Mk,“ ) — “(km )]ds = 0 (2.5)
r t+C(M(!))

where C(M (t)) is the period spent at bad jobs (this function’s value and its first

derivative are positive) and p is the discount rate. The Greek symbol 1 represents the time
when R decides to form an economic union with P. In the absence of such a union, 1
could be interpreted as infinity. I assume that as soon as R decides to form an economic
union with P, capital movements become possible instantaneously and that alone
equalizes factor prices in the two countries. Hence there is no wage difference between

the two countries after time T.

75

Since both countries use the same constant returns neoclassical production function,
wage rate in country j is Mk) 2 f (k j.) — f '(k j.) k j. It is assumed that b is low enough so
that in the initial time period (t,t+C(M(t))) migrants’ wage is less than what they would

get in their home country. The following condition satisfies this assumption:

Wow)
< _.___
w(kkn)

b (2-6)

The left hand side of the equation (2.5) represents the present value of their future
effective wage differences. The first integral gives the cost of migration in the form of
negative w age differences incurred in the initial w ork p eriod at b ad j obs, w hereas the
second integral gives the return 0 f m i gration in the form 0 f p ositive w age differences
after the workers switch jobs from bad ones to good ones. The summation of these two
integrals must be equal to 0 at the equilibrium. It is easy to see the reasoning behind this
equality. If the summation was negative, no one would immigrate to R. On the other
hand, if the summation was positive, more than M(t) number of workers would
immigrate to R, which would increase the cost of migration and decrease the benefits of it

until the summation would be equalized to 0.

Since the wage rate is increasing in the country’s capital-labor ratio, the wage rate in
R is always higher than in P, but the difference between them is decreasing as the
immigration flow from P to R continues. The reason is simple; as in the previous simple
model, the main effect of immigration is again to decrease the capital-labor ratio and the
wage rate in R and to increase them in P. Naturally as workers with no capital immigrate

from P to R, the wage difference between the two countries will decrease and eventually

76

the stock of immigrants in R will reach to a level where capital-labor ratio in R will be

such that median voter will be indifferent between integration and non-integration.

2.2.1 Equilibrium Migration and Time of Integration

First note that all migration occurs before the time of economic integration since there
is no point in migrating from P to R after wages are equalized. Also, if the lowest cost of
immigration C(O) is greater than 0, there must be a period of no migration before
economic integration occurs. When economic integration is in the very near future, there
will not be enough time with a positive wage difference to cover the cost of migrating.

Therefore we typically have the following time line:

I
l

‘—
—

N
H
N)
H
II
"I
N
II
N

(=0

Figure 2.2: Time line

As shown in Figures 2.2 and 2.3, we start at time 0. At time t=0, migration rate has its
maximum value. Migration continues by declining. The closer we are to the integration
time (t = r ), the lower the wage rate in R will be. Late workers will not have as much
time at good jobs to get high wages before the integration as the early ones. Therefore
their cost also must be lower. Since C(M(t)) declines only if M(t) falls, fewer and fewer

workers should migrate as time passes. Migration ends at t = f . So when 0 S t < f , we

77

have positive migration rate, i.e. M (I) > 0 , and we observe the equation (2.5). At time

t = f , M (t) = 0. After I = f , we don’t observe equation (2.5), instead we have,

”(7(0) r
je‘P‘H’ [b w(kR‘s ) — w(km )]ds + Ie'p‘H) [w(kR) — w(k,, )]ds < 0. (2.7)
1 1+('(0)
This inequality (2.7) show that after 1:? , if a worker migrated, he would not have
enough time at good jobs to cover the cost of migration period, C(O). Therefore he

doesn’t migrate. After I = f , we need C(O) time period, for the last migrant to find a good

job. So at t = 7 = f + C (0) , all the migrants find good jobs, i.e. when capital-labor ratio

in R reaches the critical level, ER at which the median voter in R is indifferent between

economic integration and non-integration. Finally at r = r , the median voter in R votes

for economic integration.

M(t)

 

I l l
t 7 r z

 

Figure 2.3: Migration rate as a function of time

Here we should note that for economic integration to occur eventually, C(O) must be

low enough to allow the necessary number of migrants to pull the capital-labor ratio of R

from k M to ER . The following expression satisfies this condition:

78

 

— [b w(k". ) - Wu; )1
(1- b)w(/7R)

p

ln[
OSC(O) <— (2.8)

 

To derive (2.8), one can look at condition necessary for the last immigrant to migrate to R

from P:
am co
- [W [b w(k) ) — “(17.)sz < ie‘p‘ two; > - w<IFP >14: (2.9)
0 C(0)

If (2.9) is not satisfied, for the last immigrant, the lowest cost possible with the
equilibrium level of ER (lefi hand side of 2.9) is not less than the highest possible benefit
with the equilibrium level of 16,, (right hand side of 2.9). Therefore the last migrant that

would make capital-labor ratio of R equal to k, will never migrate from P to R and

therefore economic integration will never occur. On section 2.2.3, I discuss the situations

where (2.8) is not satisfied.

In equation (2.5), wage differences, both [b w(kh ) — w(kp‘s )] and [w(k 12.: ) - w(k 1a., )] ,

depend on the total level of capital-labor ratios in the two countries, which are uniquely

determined by migration flow up to the time s, IM(t)dt. Then, given I, both the current
0

cost and the expected gains depend solely on the behavior of the immigration rate
through time. This fact implies why immigration is a function of time given 1:. Soon we
will see the equilibrium time of economic integration is endogenously determined, but for

the time being I will use the notation M (t;r) for immigration rate to emphasize that at

this stage t is a given number.

79

At the time of economic integration equilibrium, we will have a certain capital-labor
ratio, 1?, , w hich is d efined a s the level 0 f c apital-labor ratio 0 f R that is greater than

k few“ and makes the median voter indifferent between integration and non-integration.
So, ER satisfies the following three conditions:

1?, ¢ kU ,

a > kzredian ,

w(ku)+ r(ku)k;:""‘“" = w(I'ER>+ min/<17“ . (2.10)
If we call the number of migrants at the equilibrium T , then it is clear that with

T number of immigrants the capital-labor ratio in R becomes ER . We can express T in

terms of initial capital and labor endowments of R and ER :

 

12),: KR 2. (2.11)
LR.0+T

7:544“, (2.12)
k, '

Since the total number of immigrants equal to this constant T at the equilibrium, we

can write,

:[M(t;r)dt = f. (2.13)

80

Now we can restate the equilibrium conditions for M(t) and I. At the equilibrium,
M(t) = M(t,r) and r , together satisfy

(i) equality (2.5) fort such that M (t) > 0.

”C(MU» r
jig-P‘s") [b w(kR‘s ) — w(k,_, )]ds + Jew“) [Mkk's ) — “(km )]ds = 0 (2.5)
I l+C(M(I))

(ii) equality (2.13), where f is simply the lowest positive t such that M (t) = 0.
IM(t;r)dt = f (2.13)
0

Conditions (i) and (ii) together imply that at the equilibrium, we also observe (2.7) for

A

t >t .
I+C(O) 1’ ~ ~
jam“) [b w(k,” ) — w(kPJ )]ds + jaw" [w(kR ) — we, )]ds < o. (2.7)
I t+C(O)

To find the equilibrium value of r and migration function one can follow the

following steps:

1. For a given I use (2.5) to determine M(t,r) for 0 St < r.

i
2. Defining ? as the lowest positive I such that M (t, r) = 0 , calculate IM(t;r)dt .
0
3. If IM(t;r)dt > T , decrease r and go back to step 1.
0

4. If IM(t;r)dt < T , increase r and go back to step 1.
0

81

r
5. If IM(t;r)dt = T , current I is the equilibrium time of economic integration and
0

the current M (t,r) is the equilibrium path of the migration level.

2.2.2 Results

Here I will present the implications of the dynamic model about the effects of income

distribution and cost of migration on the time of economic integration.

1) Improvement (worsening) of income distribution in R, characterized by a increase

decrease in k’""""’" , causes economic inte ation to occur at an earlier later time.
R

median
kR

An increase in the capital endowment of the median voter, , i.e. a more equal

income distribution, increases k~R (as in Figure 1.8) and decreases k~,,. An increase in
[(1 and a decrease in k~,, means that less migration is needed for pulling the capital-labor
ratio in R from the initial k,,'O to 16,, at which the median voter in R is indifferent

between integration and non-integration. Therefore, the critical immigration stock

necessary for integration, T , decreases.

To see this result, first differentiate the equation (2.13):

M(f;r)a0+[j-ai4§fldz]dr=d'f. (2.14)
T

0

Then consider the last migrant’s costs and benefits of migration:

82

?+C(0) _ r _ ~ ~
Ie'MH) [b w(k,” ) — “(19.31813 + few”) [w(kR) — w(kP)]ds = o (2.15)
f 1+C(0)

Differentiating (2. 15) gives

{ble'pc‘m w(Z. > — w(k..;)1+1nrkp.- ) — 44“”an >114? (2 16)
+e‘P“""’[n(i€,)—w(i€,)]dr = 0. '

The coefficient of dr is obviously positive. We can determine the sign of the coefficient
of (If by using the knowledge that the time derivate of the migration rate,
dM(t)/ dt = M(t) < 0 , is negative. Remember that the closer we are to the integration
time (t = r ), the lower the wage rate in R will be. Late workers will not have as much
time at good jobs to get high wages before the integration as the early ones. Therefore

their cost also must be lower. Since COVl(t)) declines only if M(t) falls, fewer and fewer

workers should migrate as time passes. By differentiating equation (2.5), we can get the

expression for M (t):

[b w(kR.r ) - ”)(ka )] + (1 " b)e_pC(M(t))w(kR.r+C(M(r)))
C'(M(t)) (b '—1)e-K(M(!))W(kR.I+C(M(r)))

 

M(t) = (2.17)

Since the first derivative of the cost function is positive, the denominator in this fraction
is negative. Therefore the numerator has to be positive. This lets us to observe the

following inequality as long as the migration continues:

—pC(M( ))
w(kP', ) -— e I w(kR,r+(‘(M(r)))

b >
'- (M( )
w(kRJ) - e pC I) w(kR.r+C(M(t)))

 

for tin (0, r). (2.18)

Inequality (2.18) implies that the coefficient of d? in the equation (2.16) is negative.

83

When we rewrite the differentiated equations (2.14) and (2.16) in matrix form, we

have the following signs:

1’ illiHsl

Then both d? and dr are obviously negative.

Some intuition behind this result is that a better income distribution makes the median
voter wealthier and less oppose to the economic integration. To make the median voter
indifferent between integration and non-integration less migration is needed. Therefore,

the time of economic integration is closer.

2) Improvement (worsening) of income distribution in P, characterized by a decrease
(increase) in the number of workers without capital, may render infeasible an otherwise

feasible economic integration.

The reasoning behind this result is the same as in the first chapter. An improvement in

income distribution in P might make economic integration infeasible by decreasing the

number of workers without capital below the critical migration stock, T . Similarly a

worsening of income distribution might increase the number of workers without capital

from a level below 7: to a level above T . Thus, it might make it possible.

3) An increase (decrease) in the cost of migration causes economic integration to

occur at a later (earlier) time.

84

To see the effect of a change in the cost function, redefine the cost function as
C (M (1)) = aC (M (t)) , where a is a positive constant. The analysis up to this point may be

seen as a special case where a=l.

An increase in constant a will make equation (2.5) invalid, unless r , the time of
economic integration, increases. To see this consider the left hand side of equation (2.5)

with the new cost function:
l+aC(M(r)) r
je-W'” [b w(k“ ) — w(kp, )]ds + jam—0 [w(de ) — w(km )]ds (2.5a)
1 r+aC(M(r))
For any a>1 with the old path of M(t) (the equilibrium path of M(t) at the usual case
a=l) the value of this summation will be negative for every instant of time from t= 0 to
t=f , because a>1 indicates some increase in the cost of migration (first integral in

summation 2.5a) and some decrease in the benefit of migration (second integral in

summation 2.5a). Since the total migration stock compatible with economic integration

;
equilibrium is constant as equation (2.13), i.e. IM (t; r)dt = T , shows, without increasing
0

r , one cannot adjust the path of M(t) to make (2.5a) equal to zero for 0<t <f .
Therefore economic integration occurs at a later time. A similar analysis shows that a

decrease in constant a will cause economic integration to occur at an earlier time.

85

2.2.3 Non-Integration Cases with High C(O)

It is already stated that for the economic integration equilibrium, we need the

condition (2.8) derived from (2.9). Obviously if the cost of migration is too high

migration might stop before total immigrant stock reaches the critical level T or
migration might not occur at all. Now let us see different possibilities if the condition

(2.8) is not satisfied:

 

n _ [b w(kR.0) - w(kp,o )]
(1 —b)W(kR.o)
p

 

Case #1: C(0) > — [ (2.20)

No immigration occurs. The cost is simply too high for any person to immigrate from

P to R. This condition is another way of stating the following inequality:

C(O) co

— ie‘”1bw<k..o>—w(kp.o)idz > ie'51w(k...)—w(kp,.>1dz (2.21)
0 C(0)

Lefi hand side of (2.21) shows the present value of the cost of migration whereas the

right hand side represents the present value of the benefits. This inequality implies that

C(O) is so high that even one single worker will not migrate from P to R.

 

 

(I—biwua) (1—b>w(k.,o)
p p

-1bw<i€,.)-wu?.)1) ln[-1I)w(k,.,o)-Mk7...»
3 C(0) s -

ln[ ]
Case #2: — (2.22)

 

 

86

In this case, the cost of migration is not as high as in the first case. So, some
migration occurs. But the total number of immigrants never reaches T. Since the
capital-labor ratio in R will always be above k~R, R never decides to form an economic

union with P. The left part of this condition is derived from the following inequality:

(’(0) co
— [27" [b w(ER ) — w(k) )]dt 2 Ie'” [w(ER) — w(ic', )]dt (2.23)
(0

o (i )

This is just the opposite of inequality (2.9). It implies that the last immigrant necessary

for total immigrant stock in R to reach the critical level T , will never migrate to R.

M(t)

 

 

time
1 =0

Figure 2.4: Migration rate for the case #2

In Figure 2.4 we see the migration rate for the case #2. C(0) is not too high to prevent

some migration, but it is also not low enough to allow the immigrant stock in R to reach

the critical level T . Therefore free trade never occurs. In particular, if we have strict

inequality instead of (2.23), then the total immigrant stock in R will never even approach
to T. On the other hand if we have equality, then the total immigrant stock in R will

asymptotically approach to T as time goes to infinity, but it will always be below T to

allow free trade in real time:

87

 

 

 

 

ln(—1bw<I?R>—y(1?p>1]
T = IM(t)dt < f, if C(O) > — (1 7b)w(k”) (2.24)
o p
ln[ - [b w(k) ) 1861]
T = [Mam = f, if C(O) = - (1’ I’M“) (2.25)
o p

2.3 Two-Good Dynamic Model

In this section we switch from one-good model to two-good model. Now instead of a
one common good, we have two different goods, OK and QL. There are identical
technologies in the two countries. Capital is used relatively intensively in OK (and labor
in QL) with no factor-intensity reversals. Perfect competition makes sure that profits are
zero. As shown in the previous chapter, the U-shaped relationship between an

individual’s utility and economy’s capital-labor ratio is still valid in the two-good model.
The utility o f an agent i with a capital endowment ki is a function 0 f k , economy’s
capital-labor ratio. This function is strictly quasi-convex in k and has a unique minimum

when the agent’s capital-labor ratio is equal to that of the economy.

Although most of the features of the one-good model and the two-good model are the
same, there is one important feature of the two-good model that is particularly important
for us. To see the complementarity/substitutability relationships between the factor
movements and the goods trade we need to define economic integration as free trade

rather than free and full factor mobility of the previous one-good section. That is the main

88

reason why we are interested in the two-good model. Now non-integration is defined as
no-trade (autarky) and integration as free trade. For simplicity I assume that when free
trade is accepted good prices and factor prices are equalized across countries

instantaneously.

We have the basic Heckscher-Ohlin assumptions for the production of two goods in
the two countries, rich and poor as described in the previous sections; also consumers in

both countries have identical homothetic demands.

At the time t=0, I assume that kU < k:""’“" < I? < km as in Figure 2.1. Therefore we

start with a situation at w hich the m edian v oter in R does not p refer free trade at the
beginning. Since P is the labor abundant country the relative wage rate is lower and the
price of the capital intensive good is higher in P compared to R, which makes it certain
that the real wage is higher in R. Therefore workers in P have an incentive to migrate to

R.

As in the previous section the cost of migration, C (M (t)) , is the time spend at bad

jobs with labor supply b<l.

2.3.1 Equilibrium Migration and the time of Free Trade

When a worker decides to migrate to R from P, he looks at the present value of his

future real earnings. These are equal to 0 at equilibrium:

89

t+C(M(l))

Je_p(S—()[V(bwk,s 9 pR.s ) - V(WP.5 ’ pP.s )]dS
' (2.26)

+ Ie-p(S-I)[V(WR.5 ’ pR.s ) _ V(WP,3 ’ pP.s )]dS : 0'
l+C(M(1))
Here V(.) is the indirect utility function. It gives us the maximum utility achievable at

given prices and income. Since our immigrants do not have capital, their only income is

wage; w“ is the wage rate in country J at time 5. Everything is defined in terms of the
numeraire labor intensive good. Hence, p“ is the price of the capital intensive good in

country J at time s. We assume that b is low enough so that with the reduced wage a
migrant’s indirect utility in the rich country during the initial period is less than what it
would be in his home country. The necessary condition for this is

V(wa‘O, p M) < V(wp‘o, p R0) . If we have this initial inequality at the beginning, then we
can be sure that the inequality V (waJ, p M) < V (Wm, p M) will be satisfied throughout

the migration period, since migration will decrease (increase) the wage and increase
(decrease) the price of the capital intensive good in the rich (poor) country. This
necessary condition also guarantees that the reduced wage in terms of the numeraire good

in the rich country, wa‘, , during the initial “cost” period is less than the wage in terms of

the numeraire good in the poor country, w”; in other words, b < w“, /w,,‘o .

Equation (2.26) is analogous to the equation (2.5) of the one-good model. In (2.26)

t+C(M(1))
the first integral, je’”""’[V(wa.3, pm) — V(wPJ , pp'3)]ds , gives the cost of migration

I

in the form of negative indirect utility differences incurred in the initial work period at

90

bad jobs. The second integral, Ie'”"”’[V(wRJ , p 11.3 ) — V (wPJ , p p; )]ds , on the other
l+C(M(!))

hand, gives the return of migration in the form of positive wage differences after the

workers switch jobs from bad ones to good ones. The argument behind the equality to 0

is the same as in the previous section. If the summation was negative, people would not

migrate and if the summation was positive, all potential migrants would want to migrate.

Remember that we have infinite number of equations in the form of equation (2.26)
for t in (0,?) , where f is the end of migration wave as in the previous section. For a given

I, these equations imply that immigration rate is a function of time. So the notation for

immigration rate at this moment is M (t;r).

As in the previous section, after i migration no longer covers its costs, so for t > f ,

we have the following inequality:

r+C(M(r))
je‘”“"’1V<bw.,,.p.,.)—V(w.,.,pp,.>]ds
’ (2.27)

f

+ Ie-p(S—I)[V(WR.S ’ pR,s) - V(WP‘S 9 pp", )]ds < O.

t+C(M(t))

Defining T as the size of immigration stock in R necessary for making the capital-
labor ratio of R equal to the critical level k~R at which the median voter in R is indifferent

between autarky and free trade, we have once again equalities (2. 12) and (2.13):

KR

T'=~——L,,0 (2.12)
k, '

91

:[M(t;r)dt = T (2.13)

Also at the end of the migration period, T , we have the following equation:

1+C(M(0))

Ie—p(3—0 [V(bWR.3 ’ pR.s ) — V(M)P.s ’ pP.3 )]ds
' (2.28)

T

+ .i‘e—p(s-I)[V(WR ’ fills ) - V(WPJ ’ 17R: )]ds = 0'

E+C(M(0))
Equation (2.28) is analogous to equation (2.15) of the one-good section. Here, 1% is the

wage rate and [3} is the price of the capital intensive good in country I when the capital-

labor ratio of R reaches the critical level k~R .

As in the previous section, we need an upper bound for the minimum cost of

migration, C(0). We assume that

 

V(WR , I73 ) - V(bWR/fin)
p

~1V<bWR,ER)—V(wp,iip)1]

ln[
0 3 C(0) < -— (2.29)

 

This condition is analogous to the condition (2.8) of the one-good model. It is derived
from the condition necessary for the last immigrant to migrate to R from P in the two-

good model:

C(O) co
— ice—“Woman—mama< ie"“1V(wr.fiR)—V(wp.'fip)rds (2.30)
0 C(0)

The left hand side of the inequality (2.30) is the lowest possible equilibrium cost possible

with the critical capital-labor ratio RR and the right hand side is the highest possible

92

benefit with this capital-labor ratio of R. If inequality (2.30) is not satisfied, then the last
immigrant that would make the capital-labor ratio of R equal to k~R will never migrate

from P to R and free trade will never occur. In section 2.3.3, the situations where the

inequality (2.30) is not hold, will be discussed.

Now we can restate the equilibrium conditions for M(t) and r for the two-good
model. At the equilibrium, M (t) = M (t, r) and r , together satisfy

(i) equality (2.26) fort such that M (t) > 0 ,

1+C(M(!))

J‘e—p(S-I)[V(bwk.s ’ p8,: ) _ V(Wm a pm )]ds

f (2.26)
+ J‘e—ph—UIj/(WRJ ’ pR,5 ) _ V(WP.S ’ pP.s )]ds = 0'

t+C(M(!))

(ii) equality (2.13), where f is simply the lowest positive t such that M (t) = 0.
jM(t;r)dt = f. (2.13)
0

Conditions (i) and (ii) together imply that at the equilibrium, we also observe (2.27) for

A

t>t.

t+C(M(r))

le’”""’[V<wa..,pR,.>—V(wp..,pp,.)1ds

t

r (2.27)
+ jam—”Wm,“ pm) — V(wm , pp, )]ds < 0.

t+C(M(r))

To find the equilibrium value of r and migration function one can follow the

following steps:

93

1. For a given I use (2.26) to determine M(t,r) for 0 St < r.

i
2. Defining ? as the lowest positive t such that M (t, r) = 0 , calculate I M (t;r) dt .
0
3. If IM(t;r)dt > T , decrease r and go back to step 1.
0
4. If IM(t;r) dt < T , increase r and go back to step 1.
0

7
5. If IM(t;r)dt = T , current I is the equilibrium time of economic integration and
0

the current M (t, r) is the equilibrium path of the migration level.

2.3.2 Results

Since practically no difference between the one-good model and the two-good model

we have analogous results:

1) Improvement (worsening) of income distribution in R, characterized by a increase

median
kR

(decrease) in , causes economic integration to occur at an earlier (later) time.

An increase in the capital endowment of the median voter, kiwi“ , i.e. a more equal
income distribution, increases R}, (as in Figure 1.8) and decreases RP. Increase in k~R and
decrease in RP means that less migration is needed for pulling the capital-labor ratio in R

from the initial k R,0 to RR at which the median voter in R is indifferent between autarky

94

and free trade. Therefore, critical immigration stock necessary for free trade, T ,

decreases.

To see this result, first differentiate the equation (2.13):

M(f;r)cfi+[ I—a—A—gfi-th]dr = dT. (2.14)
T

0

Then consider the last migrant’s costs and benefits of migration:

E+C(0)

Ie~p(s—i)[V(wa‘S , pm ) _ V(Wm , pm )]ds

" f (2.28)
+ le‘”“""1V(wR,fiR. ) - V076,. , 5... )]ds = o.
5+C(0)
Differentiating (2.28) gives
{e‘pc‘°’[V(vaR , fir ) — V(VvR fig )1 - [V(wa; ,p; ) - V(Wp.; ’10,..- HW (2 31)

+ e‘”"‘”1V(WR,i5.)- V(wpndr = 0
The coefficient of dr is obviously positive. We can determine the sign of the coefficient

of (R by using the knowledge that the time derivate of the migration rate,
dM(t)/dt =M(t) <0, is negative. By differentiating equation (2.26), we can get the

expression for M (t). That gives us,

95

M(t) =2

where

4’ = V (bwkppk. ) - V(Wp.,,1)p.,) (2.32)
- e—MH) [V(bWRmeu» , pR.r+C(M(r)) ) - V(WR.1+C(M(1)) ’ pR.t+C(M(t)) )]

and

_ 100th
6 " C'(M(t))e [V(bWR.r+C(M(r))’pR.I+C(M(r))) _ V(WR.r+C(M(r))’pR.t+C(M(r)))]

Since M (t) itself and the denominator, 0, in the fraction is negative, the numerator, (p,

has to be positive:

¢ = V(bWR,r’pR.r)_V(WP,r9pP.r)

(2.33)
‘ ( ‘1)
‘e p 3 [V(bWR,r+C‘(M(r))’pR.r+C(M(r))) _ V(WR,r+C(M(r))’pR.r+C(M(t)))] > O

Inequality (2.33) implies that the coefficient of d? in the equation (2.31) is negative.

When we rewrite the differentiated equations (2.14) and (2.31) in matrix form, we

have the following signs:

1? illiHBl

Then both a? and dr are obviously negative.
Intuition behind this result is that a better income distribution makes the median voter

wealthier and less oppose to the free trade. To make the median voter indifferent between

autarky and free trade less migration is needed. Therefore, the time of free trade is closer.

96

2) Improvement (worsening) of income distribution in P, characterized by a decrease
(increase) in the number of workers without capital, may render infeasible an otherwise

feasible economic integration.
The reasoning behind this result is the same as in the first chapter.

3) An increase (decrease) in the cost of migration causes free trade to occur at a later

(earlier) time.

To see the effect of a change in the cost function, redefine the cost function as
6' (M (t)) = aC(M(t)) , where a is a positive constant. The analysis up to this point may be

Seen as a special case where a=1.

An increase in constant a will make equation (2.26) invalid, unless r , the time of free
trade, increases. To see this consider the left hand side of equation (2.26) with the new

Cost function:

t+aC(M(r))

je—p("’)[V(bWR,5 , pR‘S ) — V(wm , pm )]ds

1

, (2.26a)
+ je'P<‘-'>[V(w,, , p,.,)— V(wm, pp, )]ds = o.

”aC(M(t))
For any a>1 with the old path of M(t) (the equilibrium path of M(t) at the usual case
a=1) the value of this summation will be negative for every instant of time fiom 1 == 0 to

t = f , because a>1 indicates some increase in the cost of migration (first integral in

Summation 2.26a) and some decrease in the benefit of migration (second integral in

97

summation 2.26a). Since the total migration stock compatible with free trade equilibrium

1‘
is constant as equation (2.13), i.e. IM(t;r)dt = T , shows, without increasing 1 , one
0

cannot adjust the path of M(t) to make (2.26a) equal to zero for 0 <t < f . Therefore free
trade occurs at a later time. A similar analysis shows that a decrease in constant a will

cause free trade to occur at an earlier time.
2.3.3 Non-integration (Autarky) Cases with High C(O)

I have already stated that for free trade to occur at the end of the migration process,
we need the condition (2.29) derived from (2.30). We will not have free trade

equilibrium, if these conditions are not met. A high cost rate might not allow the total

Stock of immigrants in R to reach the critical number of immigrants, T , or if the cost of
immigration is too high there may not even be any migration at all. As we have done in
the previous one-good section, now let us see two possibilities if the condition (2.29) is

not satisfied.

 

n —[V(bwk.oapk,o)—V(wp,o,pp,o)]
V(WR.O’pR.0)_ V(wa,0’pR.0)
p

. l
Case#l: C(O) > — (2.35)

 

No immigration occurs. The cost is simply too high for any person to immigrate from

P to R. This condition is another way of stating the following inequality:

98

C(O)

- je‘“[V(bw..o,p,...>—V(w.,.,pp.0>]ds
° (2.36)

> Ie"‘“[V<w.,..p.,o>—V(wp_o,pp,o)]ds
(0

C )
The left hand side of (2.36) is greater than the right hand side, which indicates loss for

even one single migrant. That is why we do not observe any migration in this case.

Case#2:

 

 

ln{_[V(bwk’fiR)—V(Wp’fip)]] n[—[V(bwk'°’pk»°)-V(WP,09PP,0)]]
V(WR’fiR)_V(bWRnER) < C(O) < _ V(WR.O’pR,O)—V(bWR.O’pR.O)
’0 p

 

 

(2.37)
Although C(O) is not high enough to prevent any migration, it is too high to allow

enough immigration to cause the necessary drop in capital-labor ratio of R to ER.

Therefore total number of immigrants in R never reaches the necessary critical level T to

lead to free trade. The lefi part of this inequality comes from the opposite of the condition

(2-30):
C(O) co
— Je'“[V(bw,.,fi.)—V(mspnds2 Ie‘“[V(wR,fiR)—V(wp.fip)1ds (2.38)
0 am

This condition indicates that the C(O) is too high to allow the migration of the last

itl'ln‘ligrant that would make the total immigrant stock in R equal to f . Therefore free

t1‘adve never occurs. In particular, if we have strict inequality instead of (2.38), then the

total immigrant stock in R will never even approach to T . On the other hand if we have

99

equality, then the total immigrant stock in R will asymptotically approach to f as time

goes to infinity, but it will always be below 7 to allow free trade in real time.

 

 

 

 

n[—[V(bWR9fiR)_V(WP3fiP )]J
T: [Mam <f , if C(0)>— V(WR’p”)’V(bWR’pR) (2.39)
o p
ln[-[V(mefiR)-V(Wp,fip )1]
T = jM(t)dt = T if C(O) = — V(WR’pR)_ V(bwk’p”) (2.40)
o p

2.4 Conclusion

In this chapter dynamic models of migration and economic integration are developed.

The results of this chapter support the previous chapter’s results. Once again migration
Causes economic integration by lowering the median voter’s utility level. In the previous
chapter, the existence of economic integration was not certain, since I used probabilistic
In(>(iel. In this chapter migration leads to economic integration with certainty in a specific
time in the future, provided that the cost of migration is not very high. Therefore this
c1'1a13ter provides a more convincing argument of the complementarity of factor
Ir1<>\v'ements and goods trade. It is interesting to note that we have a basic Heckscher-
Ohl in model enriched with illegal migration and political economy, and yet we have the
oI’lbosite o f M undell’s classical c onclusion that factor m ovements and goods trade a re

SL1IDStitutes rather than complements in the Heckscher-Ohlin model.

100

Results about the income distribution and the probability of free trade are also very
much analogous to the ones in the previous chapter. One again, these results are in full
compliance with Mayer’s (1984) prediction about the political economy equilibrium trade
policies in an unequal society (one in which the relative capital endowment of the median
individual is less than the mean). These policies will be biased against capital owners.
Mayer’s framework indicates that an increase in inequality (the difference between the
mean and the median capital-labor ratio), holding constant the economy’s overall relative
endowments, raises trade barriers in capital-abundant economies and lowers them in
capital-scarce economies. The results of this chapter supports this prediction: An increase
(decrease) in inequality in a capital rich country makes the time of free trade later

(sooner) and an increase (decrease) in inequality in a labor rich country can make a free

trade agreement feasible (infeasible).

101

CHAPTER THREE

EXTENSION WITH SMUGGLING

3.1 Introduction

On this chapter, I incorporate smuggling into the model with two goods from chapter
three. To prevent unnecessary complexities, I use a very basic framework. Smuggling is
assumed to consist of transporting labor intensive goods from the poor country in
exchange for capital-intensive goods from the rich country. I assume that smuggling
industry is competitive and smugglers maximize profits, therefore the residence of the

smuggler clearly does not matter, since the smuggling profits under competition is zero.
Compared to the case without smuggling, introducing smuggling to the model have two
oPposing effects on the time of economic integration. On the one hand, we have price
effect. Smuggling makes the real wage difference between the two countries smaller by
bringing the relative prices in the two countries closer. This in return decreases the rate at
v"’l‘lich people migrate from the poor country to the rich one and tend to postpone the time
0 f economic integration. On the other hand, the median voter gets a lower utility because
of smuggling and therefore less migration is needed to switch his vote in favor of
eConomic integration, which tends to bring the time of economic integration closer. The
net effect of these two opposing effects determines whether the case with smuggling,
coIl'lpared to the case without smuggling, brings the economic integration closer in time

or not.

102

3.2 Literature Review

In the area of smuggling Bhagwati and Hansen (1973) is regarded as the seminal
paper, since it represents the first general equilibrium analysis of smuggling. By using a
version of Heckscher—Ohlin-Samuelson model, they implicitly assume that smuggling,
unlike legal trade with zero transport costs, has special real resource costs. These costs
are incurred in the form of the two tradables which enter the utility functions. The
analyses are done by using smuggling transformation (or offer) curve. They state that this
curve must be less favorable than the terms of trade, which imply smuggling costs. Thus

the country faces two terms of trade one in legal trade and the other in smuggling.
Furthermore they also implicitly assume that smuggling is riskless. By examining the
Welfare effects of smuggling under perfect competition and monopoly in a two-good
mOdel they find that smuggling would necessarily reduce welfare in a small open
economy only when smuggling coexisted with legal trade. The reason for this result is
that when both smuggling and legal trade exist, the domestic price is tariff inclusive
WOrld price, which indicates loss of tariff revenue, but no improvement in terms of trade.
Al so Bhagwati and Hansen assume that, in the monopolistic smuggling case, the
SI'l’luggler is a nonresident so that profits which he earns are not part of the country’s
Welfare. In the case of competitive smuggling the identities of the smugglers do not

rrlatter, since then profits are zero.

103

On the other hand, Kemp (1976) shows that if smuggling and legal trade have equal
transport costs, then for the welfare of the country, whether smuggling occurs or not is
not important, because fines and confiscations completely replace any reduction in the

tariff revenue.

In his alternative model to Bhagwati and Hansen model, Sheikh (1974) assumes that
smuggling requires real resources, in the form of a transportation commodity, T, which is
assumed to be produced with a constant returns to scale technology. Thus he has a three-
good (exportable, importable and T) and two-factor (capital and labor) model. To

smuggle one unit of the importable good, one unit of T is needed. Legal trade, on the
other hand, has no transportation costs. All goods are produced under perfect competition
and constant returns to scale. In this model, smugglers can smuggle any quantity at
Constant unit risk costs. Risk costs are confiscation of smuggled goods and fines in the
Case of detection. Thus, smuggling requires costs in two forms T and confiscations and
times. However, smuggling is also an increasing cost industry because of diseconomies,
i - e - a smuggler’s risk c osts increase i f o ther s mugglers increase their sm uggling level.
Sheikh, himself, acknowledges that such an increasing cost assumption is necessary for
so lution of the model. Sheikh’s model, unlike Bhagwati-Hansen model, implies that the
presence of smuggling, in requiring the use of a non tradable good using labor and
capital, affects the domestic transformation curve among the two tradable goods entering
tl'le utility function. Therefore smuggling can affect the domestic production of the two
t1‘adable goods even if the tariff-inclusive domestic price of the importable good is

Ill'lcTzlffected by smuggling. Also, smuggling and legal trade can co-exist in Sheikh’s model

104

and improve welfare, while Bhagwati-Hansen model indicates welfare loss when

smuggling coexists with legal trade.

Pitt (1981) provides a model in which legal trade, smuggling and price disparity (the
difference between the actual domestic price and the tariff inclusive world price of and
import good) exist simultaneously. In his model, illegal trade is carried on by the same
firms that engage in legal trade trough legal entry points rather than illegal entry points as
in Bhagwati and Hansen. Pitt's smuggling function, which is strictly concave and twice
differentiable, c ontinuous linear homogeneous function, g (l,s), relates a typical f irrn’s

smuggling to the level of its legal trade (1) and to the quantity (5) of input in terms of the
good being traded. Given this smuggling function firms are able to smuggle goods
Without making tariff payments and to sell them in the domestic market at a price below
the tariff inclusive world price. Smuggling costs could be interpreted either as real
transportation costs or as fines and confiscations. The welfare effect of smuggling is

alnbiguous in the former case and positive in the latter.

Martin and Panagariya (1984) explicitly model smuggling as an illegal act for which
he consequences are unknown ex ante by the trader. Firms engaging in smuggling take
the risk of being caught and punished. Therefore their behavior depends on the vigor with
which the authorities enforce the law. The probability of detection is increasing in the
r‘i‘iio of smuggled to legal imports. They also specify real resource costs attached to
srl'lllggling like special packing costs or payments to foreign firms for under-invoicing.

They analyze the real costs of smuggling as a choice variable of the firm. Transport costs

105

are, on the other hand, zero. They show that, as in Pitt, smuggling , legal trade and price
disparity may coexist. Actually at equilibrium there are no profits or rents and all firms
have the same ratio of smuggled to legal imports. Increased enforcement of laws against
smuggling raises real per unit costs of smuggling and the domestic price of importables
but lowers both the absolute quantity and the share of illegal imports in total imports.

They find that the net effect of smuggling on welfare is ambiguous.

Norton (1988) develops a model to explain smuggling of Common Agricultural
Policy (CAP) goods between neighboring EEC (now EU) countries. He particularly
thinks about the area between the Republic of Ireland and Northern Ireland (UK). Norton
considers a trader located within the EEC but outside the national border at a certain
distance from Home. Home is the country into which goods are smuggled. Trader has to
decide whether to keep his initial stock of goods to himself or to export them. If he
decides to export, then he must decide whether to sell his goods legally, to smuggle or
both. Norton assumes that smuggling requires domestic resources, which would
Otherwise be used for production. In his model he assumes that “smuggling of
agricultural goods is an increasing cost industry — not because of external diseconomies
Which cause upward shifts in the cost structures of firms as the industry expands, as in
some earlier models, but owing to increasing transport costs as the distance-margin for
sIn‘-lggling, i.e. the distance between the original place of the smuggled good and the
border, is extended”. Therefore smuggled goods originate within a certain distance from
the border between the countries. The greater distance the smuggled goods are carried,

the higher per unit smuggling costs. Also, a fraction of smuggled goods is detected and

106

confiscated at the border. Confiscations and fines represent the risk cost of smuggling.
The possibility of detection is decreasing in the quantity of goods legally exported by the
trader and it is increasing in the quantity of goods allocated to smuggling by the trader.
The model predicts that an increase in the tariff rate, reflecting price differentials between
contiguous countries, will induce increased contraband from existing smugglers. Also it
will enlarge the area in which smuggled goods originate. Norton’s model allows
smugglers, generally those close to the frontier, to earn large economic rents. This is due
to the assumptions that the locations of smugglers (traders) are exogenous and there is no

price disparity within the home country because of intervention agency transactions.

Thursby, Jensen and Thursby (1991) examine how market structure and enforcement
affect smuggling and welfare in a model where smuggling is camouflaged by legal sales.
'I‘hey model an import sector composed of firms in a Coumot industry. In this industry

both legal traders and firms that smuggle through camouflaging can survive if firms
differ in their excess cost of smuggling and have some market power. The probability of
successful smuggling of a firm depends on two things: the level of enforcement
mechanism and the fraction of smuggled goods to the total amount the firm imports.
There is also an additional cost of smuggling that firms incur regardless of whether the
Smuggling is successful or not. This cost could be a real cost like packaging and or a
bribe to customs officials. Increasing the number of firms in the industry increases the
tOtal volume of imports and it pulls the price down to the level which would prevail under
pure Competition. The conclusions of the paper are (i) that the price disparity that occurs

In n"lOdels where smuggled trade is camouflaged is directly related to the degree of

107

competition in the importing industry; (ii) the welfare effect of smuggling is also directly
related to the degree of competition in the importing industry, since this price disparity is
welfare improving; and (iii) an increase in enforcement may reduce welfare even when

enforcement is costless, since the quantity imported by a camouflager exceeds that of a

legal trader.

Lovely and Nelson (1995), unlike previous authors who used some versions of
Heckscher-Ohlin—Samuelson model, use a Ricardo-Viner type economy to analyze
smuggling. They consider a small open economy in which two goods (an exportable and
an importable) are produced from intersectorally mobile labor and sector-specific capital.
In their model the possibility of detection of 3 firms’ smuggling activity by the
government depends positively on the ratio of smuggled goods to legal imports and
negatively on the q uantity o f s muggling se rvices p urchased b y the importing firm p er
smuggled unit. Their conclude that smuggling need not reduce domestic welfare of a
tari ff-ridden economy, even when smuggling uses domestic resources that would
Otherwise be used for production. Smuggling decreases welfare if the value of productive

acti vity displaced by smuggling exceeds the benefit of the lower domestic price resulting

from smuggling.

Larue and Lapan (2002) extend Bhagwati’s (1965, 1969) analysis about the
non eq uivalence between tariffs and quotas when domestic production is monopolized and
the tenns of trade are exogenous, by allowing smuggling. The average cost in the

Smuggling industry is increasing in the total level of smuggling, but the average cost at

108

the individual smuggler’s level is constant, which implies that as total illegal imports
increase, individual smugglers must incur additional costs to avoid detection by the
government. The free entry and zero-profit conditions determine the total level of
smuggling. Laure and Lapan show that the dominance of tariff over quota is not robust:
When the price differential between domestic and world products falls below a certain
level, smuggling is irrelevant and the tariff remains a better instrument that the quota.
However, at lower levels of legal imports (higher tariffs), the quota is better than the

tariff. Also smuggling is welfare-improving (decreasing) when legal imports are

constrained by a quota (tariff).

As it is seen above, most of the smuggling literature try to explain welfare effects of
smuggling to the country into which goods are smuggled. From the earlier literature,

there is no clear answer to the effect of smuggling on welfare. In most papers the effect

on welfare is ambiguous.

Incorporating smuggling into the model which was developed in the previous chapter
Will allow us to see its effect on migration and economic integration. The effect of
smuggling on migration and economic integration, to my knowledge, has never been

analyzed.

As it will be seen in the next section, in my model, I assume an increasing detection
rate, i .e. the higher the volume of smuggling is, the higher the proportion of the detected

smuggled goods is. In the literature this increasing rate of detection is explained by two

109

approaches. One approach follows Bhagwati and Hansen (1973), which is lately
extended by Laure and Lapan (2002), where smuggling is conducted through illegal entry
points: There are real resource costs of smuggling and there are a large number of
smugglers. The average cost at the industry level is increasing but the average cost at the
individual smuggler’s level is constant. This congestion effect implies that, as total illegal
imports increase, individual smugglers must incur additional costs to avoid detection by
the enforcement authorities. Although this approach does not model detection explicitly,
it implicitly assumes that given a constant resource allocation of smuggling firms for

avoiding detection of smuggling activity, detection rate increases in the total level of

smuggling.

The other approach is by Martin and Panagariya (1983): They assume that firms
engage in both legal and illegal trade. So, smuggling is conducted through legal entry
points. The detection rate depends on two things, the ratio of legal to smuggled imports
and real costs of smuggling. Real costs of smuggling may be in the form of payments to

foreign firms for under-invoicing or of special packing costs necessary for concealing the

Sm uggled goods or of bribes paid to customs officials. The firms chooses a parameter [3

and for each unit of smuggled good it purchases l/B more of the same good, i.e. (1-B)/B

units “melt away” for each unit of smuggled good. With this interpretation, detection rate

increases in [3. Other than this [3, the detection rate also depends on the ratio of smuggled

to legal imports. The interpretation of this assumption is simple. If the firm imports 100

tons Of a good and declares 99 tons, it will probably succeed smuggling the 1 ton of

illegal imports. But if the firm declares 1 ton and tries to smuggle 99 tons, then it will

110

probably be detected. It is also implicitly assumed that the number of firms in the
industry is constant and all firms are identical, which implies that as the ratio of total
illegal imports to legal imports increase so does the detection rate. In the paper it is
explained how this m odel c an b e m odified to h andle Bhagwati-Hansen type 0 f i llegal
trade through illegal entry points. When smuggling is carried on through illegal entry
points, then the detection rate will depend on the absolute quantity of illegal imports and

legal imports will be equalized to zero.

Incorporating smuggling into the model with an increasing detection rate, gives an
ambiguous result. Depending on the parameters of the model, smuggling might increase
or slow the speed to free trade. If we interpret an earlier free trade agreement welfare
improving, then the result of this chapter supports the earlier findings in the literature: the

effect of smuggling on welfare is ambiguous.

3.3 Two-Good Model with Smuggling

I assume that there are no transportation costs, i.e. any amount of goods can be
transported between P and R free of charge. The poor country does not do anything to
Prevent illegal movement of goods (it is already assumed in previous sections that the
poor country already wants economic union, i.e. free trade, so it is unwilling to stop any
kind 0f trade). The rich country government can detect a portion of smuggled goods. It is
assumed, as in the most papers in the smuggling literature, this portion, q, is strictly

more asing in the amount of smuggled goods.

111

I try to model smuggling as simple as possible. I follow Bhagwati and Hansen’s
implicit assumption that the detection rate is increasing in the volume of total illegal
imports; also there are no legal imports. As in the previous chapters, following Levy

( 1997), we are trying to compare autarky (here with smuggling) and free trade.

q = q(SL) ; where S L is the amount of smuggled labor intensive good.

This function is an increasing (its first derivative is positive), non-negative function
(it takes values in (0,1) for positive S L ). For simplicity, as in Norton (1988), I assume

that all detected smuggled goods are confiscated and subsequently destroyed. In the
literature there are also papers which assume the distribution of confiscated goods to the
public in the same manner as tariff revenue. If such an assumption is adopted instead of
the destruction of confiscated goods, then the analysis virtually no different from legal
trade replacing tariff revenue with confiscated goods. The assumption of the
disappearance (destruction) of confiscated goods is also suitable for the alternative

“melting away” interpretation as in Martin and Panagariya (1983).

There are a large number of competitive smugglers. Entry to the smuggling industry

is fI‘ee. A typical smuggling activity 0 ccurs as follows: 1 unit 0 fl abor intensive good

bought in the poor country is smuggled into the rich country and exchanged for J— unit
PR

or the capital intensive good. This capital intensive good is then taken home and sold at

112

the unit price p ,, . With the detection rate q(SL ) , the revenue is [&][l — q(S,4 )]. By the

R

zero profit condition, this is equal to cost of one:

[&][1- (1(51. )1 =1 (3:13)

R

p: _ l
[ml-*2“)

This equality determines the total level of smuggling between the two countries.
Smuggling makes the capital intensive good more expensive in the poor country and
cheaper in the rich country. Therefore the more smuggling occurs, the lower the LHS
becomes and the higher the RHS b ecomes. This indicates that there is an equilibrium

level of smuggling which satisfies equation (3.1b).

Now we can look at the derivatives of prices in both countries and the total
equilibrium level of smuggling with respect to capital-labor ratios in both countries:

pp = pp(kp,k,.);%— < 0,dp—” > 0

k, dkR

 

dpR >0 dPR <0

p = k,k;
R “(P R)dk,, dkR

113

 

d5 d8
S =5 k ,k ;-¢<0, 1‘
L L( P R) dkP dkR

>0

The reasoning behind these derivatives is simple. As capital-labor ratios come closer
to each other (as k P increases and k R decreases) the prices of the capital intensive good

in these two countries come closer to each other and this, naturally, makes smuggling less

profitable.

To see the effect of migration within the framework of the dynamic model developed
in the previous section, we need to figure out how smuggling affects median voter’s
utility level in the rich country and the migration process between the two countries.
Remember that the median voter in the rich country has a lower capital-labor ratio than
the rich country’s overall capital-labor ratio and that he prefers autarky to free trade, i.e.
his utility from autarky at the country’s capital-labor ratio is higher than the utility he
would get under free trade. Smuggling reduces the welfare of the median voter in the rich

country by increasing the relative price of the capital intensive good.

Figure 3.1 illustrates how smuggling reduces the utility level of the median voter.
Note that smuggling reduces the median voter’s utility level when capital-labor ratio of
the country is far greater than the median voter’s. At these capital-labor ratios median
voter gains from being in a relatively capital abundant country. Smuggling reduces the
median voter’s utility by making the relative prices more like what they would be in a
less capital-abundant country. By providing smuggled labor intensive goods to the rich

country, smuggling decreases the relative demand for labor and it increases the relative

114

demand for capital in the rich country. This, naturally, increases the relative price of

utility .

without smuggling

      

   
 

----‘_---—--—----

  
   

UA - .......................................... with
UAS __________________________________________ smuggling
Uu , ......... i ...............................

 

 

-—--------------1-- ---- -----

q--------------—-

 

~

ku k [median kR kRS kR,0

Figure 3.1: Smuggling reduces the utility level of the median voter

capital and decreases the relative price of labor. On the other hand smuggling increases
median voter’s utility level when he lives in an economy in which the capital-labor ratio
is less than his own. That’s why his utility level increases because of smuggling when the

k :‘d'm . It is also

capital labor ratio of the economy in which he lives is between kU and
important to note that in the graph as we move from kU to further right along the

horizontal line, the level of smuggling is increasing, since price differences are becoming

more attractive for smugglers. At kU we have no smuggling and that’s why both utility

graphs overlap at this level. At the beginning, when the capital-labor ratio in R is km,

115

median voter’s utility is UA without smuggling. Smuggling reduces the median voter’s
utility by lowering the relative price of the labor intensive good. With smuggling median

voter gets the utility UAS. The case without smuggling requires the reduction of capital-

labor ratio from k M to k~R for free trade. With smuggling a smaller reduction from km

to if is needed.

As it could be seen from Figure 3.1, two opposing effects of the smuggling process
play role here. On the one hand less migration is needed for economic integration to

occur. The case without smuggling requires a migration level which will take the capital-

. . . K . .
Wthh indicates eel—Ll“) amount of migration; but
R

labor ratio from k”.O to ER,

smuggling requires a migration level w hich will take the c apital-labor r atio o nly from

~ . . . K . .
kR‘0 to k R" , which indicates :éi— LR.O amount of migratlon. On the other hand because
R

of Stolper-Samuelson effect, a lower relative price of the labor intensive good will lead to
a decrease in real wages in R, which will make migration from P to R less attractive. The
former effect tends to make the time of economic integration sooner, the latter effect —

later.

The negative effect through the change in prices can be seen from the following
equality. As it is explained in the previous section, when a worker decides to migrate to R
from P, at the equilibrium he is indifferent between staying in P and moving to R, i.e. the
present value of his expected future wage differences (between what he would get in P

and R) is zero.

116

l+C(M(!))

Ie‘pts—r)[V(bWRJ , PM ) - V(Wm , pm )]ds

' r (2.26)
+ Je"”(”"[V(wRJ ,pRJ ) — V(wp‘s , Pa: )]ds = 0.
t+C(M(t))
The effect of smuggling on these variables is as follows: for a given capital-labor I

ratio, now we have lower wk and pp, and higher wP and pk. If the same amount of

. . K . .
migration, :K—LR‘O , were requrred for free trade, then we would certainly have free _ «—

k R J

trade at a later time than the case without smuggling. But we now require less migration,

 

K

~—§ — L” , for free trade:

R

53.

jM(t;r)dt = f = [:5 —L,,‘0 (3.2)
0 R

Although the effect of smuggling on the time of free trade is ambiguous in general,
we can identify two extreme situations: One with immediate free trade, and one with a

time of free trade later than the case without smuggling.

Let us now see the first extreme case with immediate free trade. We have just seen
that smuggling reduces the welfare of the median voter at the beginning (t=0). It is easy
to see from equation 3.1 that the lower the q(SL) is, the higher the equilibrium level of SL
is. For a sufficiently low q(SL), we can get an S L sufficiently high so that the median

Voter’s utility falls below what he would get under free trade, as illustrated in Figure 3.2.

117

In such a situation median voter chooses free trade right away. Hence, smuggling alone

might cause free trade without any involvement of migration.

utility without smuggling

   
 

UA

........................................

with smuggling

-----y-------_--

 

Uu

 

.---------

 

~

median
kU k R k R k R ,0

Figure 3.2: Utility of the median voter when smuggling immediately causes economic
integration

Figure 3.2 shows the situation where smuggling immediately causes economic
integration. Without smuggling median voter’s utility is UA at the beginning (t=0). With
Smuggling he gets utility below UU. Therefore he chooses free trade immediately at the

beginning.

Formally we can easily find how low the detection rate must be in order to allow free
trade to occur immediately. Let S 1. be the level of smuggling which would make the
median voter indifferent between free trade and autarky with smuggling at the beginning

(t=0) when the capital-labor ratio is k M . If q(S ,) is such that

118

If?

 

p”: 1.. , (3.3)
pro 1—q(SL)

 

where ppoand pROare the prices of the capital intensive good in terms of the labor

intensive good in P and R respectively, then the median voter in R is indifferent between

autarky with smuggling and free trade. Therefore any detection rate function such that

pR.O (3.4)
pao

q('§L)-<-1_

 

leads to free trade immediately without any requirement for migration.

The second extreme example occurs when the detection rate is high enough so that
smuggling stops before median voter becomes indifferent between autarky and fiee trade,

as illustrated in Figure 3.3. Therefore in such a situation, to pull the capital-labor ratio

from k M, to k~R , we need exactly the same number of immigrants as in the case without

smuggling. Since smuggling makes relative prices for migration less appealing for

possible immigrants, compared to the case without smuggling, we will certainly need

more time for free trade.

119

utility

without smuggling

.------------’----------------.

with smuggling

-----.-----_--_-

    

   

L
i

 

 

)—--—-_-—--—-—
u-----------—-

h----.-.--

 

median
kU k R k R Z k R ,0

Figure 3.3: Utility of the median voter when it takes longer to have free trade with
smuggling than without smuggling

On the Figure 3.3, we see the median voter’s utility for the extreme case when it takes
longer to have free trade with smuggling than without smuggling. When the capital-labor
ratio is less than 2, smuggling is not profitable. For capital-labor ratios greater than 2,

price differences between the two countries are sufficient to allow smuggling. Both with
and without smuggling we need to reduce capital-labor ratio from kR,0 to It}, for free

trade. Since the case with smuggling has less attractive relative prices for migration, it

requires more time for free trade.

Formally, for the second extreme case we need detection rate to be high enough for

even “zero” number of smuggled goods such that

1-5isq(0)<1—p”'°, (3.5)

Pp pl’,0

 

Where ER and p, are the prices of the capital intensive good in R and P respectively,

120

when the capital-labor ratio in R is RR. For any detection rate function q(SL) which

satisfies inequality (3.5) we will have a longer waiting time for free trade compared to the

case without smuggling. If, on the other hand, q(0) is extremely high so that

pR.O

q(0) 2 1 — (3.6)

 

pP.0

then we would have no smuggling at all even at the beginning (t=0).

3.4 Conclusion

In this chapter, we have incorporated smuggling into the two-good, two-factor,
dynamic model of migration and economic integration developed in the previous chapter.
We have seen that introducing smuggling into the model has an ambiguous effect on the
time of economic integration depending on the parameters of the model, especially the
rate of detection. With high detection rates the model tends to lengthen the waiting time
between the beginning and free trade. With low detection rates the model tends to shorten
it. If we interpret a longer (shorter) waiting time as a loss (gain) of welfare, then we can
say that smuggling’s effect on welfare of both countries is ambiguous. In the literature
review we have seen that most of the papers in the smuggling literature imply that the

effect of smuggling on welfare is ambiguous. Here we have the same conclusion.

121

CHAPTER FOUR

THE EFFECT OF INCOME INEQUALITY IN THE DETERMINATION OF

FREE TRADE AGREEMENTS

4.1 Introduction

The goal of this chapter is to empirically investigate whether income inequalities in
country pairs could be one of the key economic factors influencing the possibility of an

FTA between the two countries.

The median-voter approach to trade policy determination as in Mayer (1984) in the
Heckscher-Ohlin framework indicates that an increase in inequality in a capital-abundant
(labor-abundant) economy raises (decreases) trade barriers. Dutt and Mitra (2002) find
support for this prediction using cross-country data on inequality, capital-abundance and
diverse measures of protection. For developing countries with lower capital-labor ratios,
greater inequality leads to lower tariffs. Conversely, for industrialized countries with
higher capital-labor ratios, greater inequality leads to higher tariffs. This provides support
for the median voter framework in the context of the Heckscher—Ohlin model. In addition,
Dutt and Mitra find that this relationship holds better in democracies than in

dictatorships.

122

In the models developed in the previous chapters we have also seen a similar
prediction that when migration is possible between country pairs, an increase in
inequality in the relatively poor (rich) country will tend to decrease (increases) the

possibility of economic integration between the two countries.

Although there is a large literature explaining empirically tariff and non-tariff barriers
between countries, the first econometric work that tries to explain empirically the
determinants of FTAs is a very recent one: Baier and Bergstrand (2004). My work on this
chapter basically follows their work. I added inequality variables (GINI coefficients in
the country pairs) to their explanatory variables to see whether they make a difference.
Their econometric model is based upon a general equilibrium theoretical model of world
trade with two factors of production, two monopolistically competitive product markets,
and explicit intercontinental and intracontinental transportation costs among multiple
countries on multiple continents. They find that trade —creating and trade-diverting
economic characteristics play an important role in explaining the probability of an FT A
between two governments. According to their results, two economies tend to form FT: (i)
the closer are two countries in distance; (ii) the more remote a pair of continental trading
partners is from the rest of the world; (iii) the larger in economic size are two trading
partners; (iv) the more similar in economic size are two partners; (v) the greater the
difference of capital-labor ratios between two partners (vi) the smaller the difference of
the members’ capital-labor ratios with respect to the rest of the world’s capital-labor

ratio; and (vii) the higher are the rest of the world’s tariffs. In their empirical model these

123

characteristics correctly predict 85 percent of the 286 FTAs existing in 1996 among 1431

pairs of countries and 97 percent of the remaining 1145 pairs with no FTAs.

The contribution of this chapter is to include income inequality in the analysis of the
economic determinants of the likelihood of FTAs between country pairs. Although Dutt
and Mitra (2002) find support for the prediction that an increase in inequality in a capital-
abundant (labor-abundant) economy raises (decreases) trade barriers, their work does not
say anything about FTAs. On the other hand Baier and Bergstrand (2004) did not
consider income inequality levels in their attempt to explain economic determinants of

FTAs.

My main finding is that in democratic countries a negative (positive) relationship
exists between the income inequality level in the relatively capital-abundant (labor-
abundant) country and the possibility of the FTA. I failed to find a similar relationship in

non-democratic countries.

4.2 Econometric Model and Estimation Method

As I mentioned above, my model is based on Baier and Bergstrand (2004)’s best

probit result. Therefore it includes their explanatory variables as well as inequality

variables (gini c oefficients) o f t he two c ountries in the p air and also interaction terms

124

between these inequality variables and dummy variables which indicate whether the
countries can be regarded as democratic:

P(FTA =1) = P(y* > 0)

4.1
= C(fl0 + XI) + 6, GINIP + (SZGINIR + 53GINIP.DEMP + 54 GINIR.DEMR) ( )

where y* denotes the (unobservable) difference in utility levels from the action of

forming of an FTA and
y* = ,60 + xii + 5, GINIP + 62 GINIR + 63GINIP.DEMP + 64 GINIR.DEMR + 2.
It is assumed that e is independent of x (the vector of explanatory variables from Baier

and Bergstrand), GIN IP, GINIR, GINIP.DEMP and GINIRDEMR and it has a standard

normal distribution. Since both countries’ consumers need to benefit from an FTA for

their representative countries to form one, formally y* = min(AU,., AU j ).

The dependent variable FTA gets the value 1 if there exists an FT A between the two

countries in 1996, which indicates y* > O , and 0 otherwise, which indicates y* S 0. Here

the standard n ormal c umulative d istribution function G (.) e nsures that P (FTA=l) i s i n

(0,1).

Parameters B = [,81 , ,6, , ,63, ,64, ,65 , ,66]' are the ones corresponding to the explanatory

variables from Baier and Bergstrand. The first one of these explanatory variables
NATURAL-j measures the geographical closeness of i and j. It is the natural logarithm of
the inverse of the distance between the economic centers i and j. The second one
REMOTE“, on the other hand measures the remoteness of a pair of continental trading

partners from the rest of the world. It takes the value 0 if the two countries are on

125

different continents. However if they are in the same continent then REMOTE-j measures
the simple average of the natural logarithms of the mean distance of country i from all of
its trading partners except j and the mean distance of country j from all of its trading
partners except i. While the third explanatory variable RGDPij simply measures the sum
of the logs o f real G DPs o f c ountries i and j in l 960, the fourth explanatory variable
DRGDPU- measures the absolute value of the difference between the logs of real GDPs of
countries i and j in 1960. The fifth explanatory variable DKLij measures the absolute
value of the difference between the logs of the capital-labor ratios of countries i and j in
1960. The sixth explanatory variable DROWKLU- measures the difference between the
capital-labor ratios of i and j and the rest of the world’s capital-labor ratio. It is the simple
average of two differences, which are between the natural logarithm of the combined
capital-labor ratio of i(j)’s all trading partners and the natural logarithm of the capital-

labor ratio of i(j).

The explanatory variable GINIP measures the income inequality in the relatively
labor abundant country in the pair. Similarly GIN IR measures the income inequality in
the relatively capital abundant country in the pair. These are the averages of gini
coefficients from the years 1960-69. The dummy variable DEMP takes the value 1 if the
relatively labor abundant country in the pair is democratic in the years 1960-69, it takes
the value 0 otherwise. Similarly DEMR takes the value 1 if the relatively capital-
abundant country in the pair is democratic in the years 1960-69 and it takes the value 0

otherwise.

126

Since it is not possible to find reliable gini coefficients and democracy data from
19605 for all the countries in B&B, the number of observations available for my model
shrank to 406 from 1431 observations used in B&B. To see whether this shrinkage in
data size causes any substantial change in the B&B model I also recalculated their model,
i.e.

P(FTA =1) = P(y* > 0) = G(,Bo + x0) (4.2)

by using only the 406 observations available for my model.

As in Baier and Bergstrand (2004), I use the maximum likelihood estimation (MLE)
method to estimate the parameters of the model. As stated in Wooldridge (2000), the
general theory of (conditional) MLE for random samples implies that, under very general

conditions, the MLE is consistent, asymptotically normal, and asymptotically efficient.

5.3 The Data

The data for B&B (Baier and Bergstrand [2004]) variables (FTAij, NATURAL),
REMOTE”, RGDPij, DRGDPU, DKlq'j, DROWKLU) were taken from Dr. Baier. For
further information about their sources, one can look at B&B. Here it should be
emphasized once more that although FTAij shows whether the pair has an FTA in 1996,
explanatory variables RGDPij, DRGDPij, DKLU- and DROWKhj are measurements

related to 1960. This time difference between the dependent variable and these

127

explanatory variables are due to potential endogeneity. B&B explains this choice by the

following lines:

Since an F TA formed several years prior to 1996 likely influenced
subsequent trade — which then influenced economic growth — incomes and capital
stocks in 1996 (variables in x) may well be endogenous to the dependent variable,
F T A. T 0 account for this, we used the earliest data on incomes, capital stocks,
and populations available in Baier, Dwyer, and T amura (2000) for a wide

' sample, namely, 1960 data. ”

The data for GINI coefficients are obtained from the UNU/WIDER — UNDP World
Income Inequality Database (WIID) which can be downloaded from the UNU/WIDER
web pages at

http://www.wider.unu.edu/wiid/wiid.htm

or from the UNDP/SEPED web pages at

http://www.undp.org/povery/initiatives/wider/wiid.htm.

To obtain a fairly reliable data subset of gini coefficients from this source, only those
data points with OKIN (“Reliable income or expenditure data referring to the entire
[national] population, not affected by apparent inconsistencies”) quality rating were
chosen. Since very few countries had gini coefficient data for the year 1960 for this
rating, averages of gini coefficients over the years from 1960 to 1969 are used. By this

way, gini variables are obtained for 30 countries out of 54 in B&B.

128

The data for dummy variables DEMP and DEMR are constructed by using data from
the Polity IV Project dataset. This dataset is easily available at the web at:

www.cidcm.umd.edu/inscr/polity

The indicator “POLITY” in the dataset ranges from -10 (full autocracy) to +10 (full
democracy). For each country average of POLITY scores from the years 1960-69 are
used. Those countries with positive average POLITY scores are regarded as democratic
and others with negative average POLITY scores are regarded as undemocratic. This
method allowed me to construct democracy dummy variables for the 29 countries out of
the 30 countries with gini variables. Table 5.1 gives GINI and POLITY averages of the

29 countries used in this chapter.

Subsequently GIN IP, G INIR, D EMP and D EMR v ariables are c onstructed for 4 06
pairs out of 1431 pairs in B&B. To determine the “poor” and the “rich” in each pair,
capital-labor ratios for the year 1960 are compared and the country with a higher capital-
labor ratio is labeled as “rich” and the other as “poor”. If the average POLITY score for
the relatively labor abundant country in the pair is positive (negative), then the variable
DEMP is unity (zero). Similarly, if the average POLITY score for the relatively capital

abundant country in the pair is positive (negative), the variable DEMR is unity (zero).

129

Table 5.1: GINI and POLITY averages for 19608

 

(OCDNOUIhOJN-t

NMNNNNNNNN-rr—n‘a—LAAAAA
comworcnowN-socomximorth-so

Argentina
Australia
BohWa
Brazil
Canada
Chne
Columbia
Costa Rica
Denmark
Ecuator

El Salvador
France
Germany
Honduras
Japan
Mexico
Netherlands
Norway
Panama
Peru
Philippines
South Korea
Spain
Sweden
Thailand
Turkey
United Kingdom
United States
Venezuela

GINI
average
(19603)

%

42.0
32.5
53.0
53.5
31.8
37.7
62.0
50.0
37.0
38.0
53.0
48.3
45.0
61.9
35.7
54.2
42.0
35.0
48.0
61.0
50.4
32.2
32.0
37.9
42.3
56.0
32.8
34.7
42.0

POLITY
average
(1 9608)

-4.2
10.0
-3.6
-2.9
10.0
5.6
7.0
10.0
10.0
0.5
-1.2
5.3
10.0
-1.0
10.0
-6.0
10.0
10.0
1.8
2.3
4.7
1.5
-7.0
10.0
-6.0
8.4
10.0
10.0
6.4

 

130

Table 5.2: Summary Statistics

 

Variable Mean Std. Dev. Min Max
FTA 0.1749 0.3803 0 1
NATURAL -8.51 86 0.8000 -9.6086 -5.0752
REMOTE 1 .8652 3.5769 0 9.1274
RGDP 34.9953 2.3018 28.8239 41 .0509
DRGDP 1.9203 1.4122 0.0071 6.9436
DKL 1.0145 0.7158 0.0076 2.8312
DROWDKL 0.8545 0.2780 0.1491 1 .6893
GINIP 46.8700 9.5700 31 .8 62
GINIR 41.5507 8.7985 31.8 62
DEMP 0.6650 0.4726 0 1
DEMR 0.8350 0.3717 0 1
GINIP.DEMP 30.3402 22.9238 0 62
GINIRDEMR 33.7943 16.8427 0 62

Number of observations: 406

 

On table 5.2 it is no surprise that minimum and maximum values of GINIP and
GINIR variables are the same. This is due to the fact that 27 out of 29 countries used in
the formation of 406 country pairs are labeled “poor” in some country pairs and “rich” in
others. Since we are considering relative country pairs, a given country is labeled “poor”
in a pair if the other country in the pair has higher 1960 capital-labor ratio and it is
labeled “rich” if the other country has lower 1960 capital-labor ratio. The two countries
that do not change their status of being “poor” or “rich” in all pairs are Thailand and
Australia. Thailand has the lowest 1960 capital-labor ratio whereas the Australia has the

highest among the 29 countries.

131

5.4 Results

Probit results indicate that the smaller data set of my model does not cause an
important distortion in the calculations of B&B coefficients. In Table 5.2, the first
column gives the results from B&B. The coefficient estimates of the same model
calculated with the smaller data set are given in the second column (2a). For each
explanatory variable coefficient estimates from both columns have the same sign and all
the coefficient estimates except the one for DROWKL in the second column are
statistically significant at 5% level. The coefficient estimates of the same model without
DROWKL are presented in the column 2b, where all variables are statistically significant

at 1% level.

The estimated coefficients of the model with gini coefficients and democracy
dummies from the third column show that the variables GINIP and GINIR are
statistically insignificant although interaction terms GINIP.DEMP and GINIR.DEMR are
statistically significant at 5% level with expected signs. This indicates that income
inequality has an effect on the formation of FTAs only in democratic countries. Also
once again we see that the variable DROWKL is insignificant at 5% level, although all
other B&B variables are statistically significant at 1% level. Therefore in column 3b the
version without DROWKL is presented. Taking DROWKL out of the regression does not
have any effect on the signs of the coefficient estimates. It only makes the variable DKL
statistically significant at 5% level instead of at 1% level. The variables GINIP and

GINIR stay statistically insignificant at 5% level.

132

Therefore another probit specification which includes only B&B variables and the
interaction terms GINIP.DEMP and GINIR.DEMR is estimated with the 406 pairs and
presented in c olumn 4 a of T able 5 .3. T he c oefficient e stimates o f the both interaction
terms have expected signs and they are statistically significant. The coefficient estimate
of the interaction term GINIP.DEMP is positive and it is statistically significant at 1%
level. The coefficient estimate of the other interaction term GINIR.DEMR is negative and
it is statistically significant at 5% level. Also, in column 4b the version without
DROWKL is presented. Taking DROWKL out of the regression does not have any effect

on the signs of coefficient estimates or on their statistical significances.

Table 5.3: Probit Results for the Probability of an FTA

 

Variable 1 (8881 2a 2b 3a 3b 4a 4b
CONSTANT 7.90 6.66 4.46 3.62 2.36 6.52 5.32
(4921* (2681* (2.15)** (1.07) (0.75) (2.43)" (2211**
[5401* [3431* [3041* [1 .48] [1 .011 [3001* [2851*
NATURAL 1.76 1.53 1.52 1.79 1.82 1.74 1.76
(13.43)* (6.41)* (6.57)* (6221* (6.39)* (6.38)* (6.54)*
[12.051* [6631* [7021* [7.34]* [7511* [6921* [2121*
REMOTE 0.18 0.18 0.18 0.21 0.21 0.20 0.20
(10.03)* (5.77)* (5801* (5781* (5801* (5741* (5761*
[10.041* [5601* [5531* [5501* [5751* [5501* [5671*
RGDP 0.17 0.15 0.19 0.25 0.28 0.20 0.22
(3671* (2.201“ (3.06)* (2891* (3421* (2661* (3231*
[4531* [2581* [3681* [3.76]* [4441* [3.1 11* [3.88]*
DRGDP -0.34 43.45 41.43 -0.59 .059 41.57 -0.56
(-5.45)* (4151* (4191* (4471* (4541* (4461* (4521*
[-5.46]* [-3.701* [-3.791* [4551* [4481* [4671* [4921*

133

DKL 0.85 0.59 0.44 0.70 0.64 0.65 0.59
(7.37)* (2.73)* (2.35)* (2.69)‘ (2.58)“ (2.84)* (2.70)*
[6.74]* [261]" [220]" [3.11]* [303]" [296]" [2.82]’
DROWKL -1 .29 -1.00 -0.68 -0.66
(-5.53)* (-1.83) (-1.16) (-1.14)
[-4.91]* [-2.22]*" {-1.24] {-1.23]
GINIP 0.02 0.02
(1.00) (0.93)
[1 .10] [1.02]
GINIR 0.02 0.02
(1.07) (1.12)
[1 .07] [1.13]
GINIP.DEMP 0.02 0.02 0.02 0.02
(2.42)" (2.50)" (2.70)* (2.80)‘
[2.61]* [2.66]"’ [3.02]* [3.08]*
GINIR.DEMR -0.02 -0.02 -0.02 -0.02
(-2.12)** (-2.42)** (-2.09)** (-2.38)**
{-2.1 1]" [-2.41]** (-2.05)** [-2.34]“
Pseudo qu 0.728 0.665 0.655 0.707 0.703 0.700 0.697
Log likelihood -194.4 -63.12 -64.86 -55.21 -55.89 -56.39 -57.04
# of observations 1431 406 406 406 406 406 406

 

Notes: The quantities in paranthesis below the estimates are z-statistics. The quantities in brakets
are robust z-statistics. *(**) denotes statistically significant z-statistic at 1 percent (5 percent) level
in two-tailed test.

The fact that the estimated coefficients of GINIP.DEMP and GINIR.DEMR are both
statistically significant with the expected signs also shows its effect on the goodness-of-
fit measure percent correctly predicted. The probit estimate of the model with B&B
variables and the interaction terms GINIP.DEMP and GINIR.DEMR (column 4a in Table
5.3) correctly predicts 81.69 percent of the 71 FTAs, and 97.01 percent of the remaining

335 pairs with no FTAs while the probit estimate of the model only with B&B variables

134

(column 2a in Table 5.3) correctly predicts 77.46 percent of the 71 FTAs and 96.72
percent 0 f the remaining 3 35 p airs with no F TAs. C omparisons o f the goodness-of-frt -
measure percent correctly predicted of the models without DROWKL also shows a
similar picture. The probit estimate of the model with B&B variables without DROWKL,
and with the interaction terms GINIP.DEMP and GINIR.DEMR (column 4b in Table 5.3)
correctly predicts 83.10 percent of the 71 FTAs, and 97.01 percent of the remaining 335
pairs with no FTAs while the probit estimate of the model only with B&B variables
without DROWKL (column 2b in Table 5.3) correctly predicts 74.65 percent of the 71

FTAs and 97.61 percent of the remaining 335 pairs with no FTAs.

5.5 Conclusion

The purpose of this study was to find evidence of the effect of income inequalities on
the formation of FTAs. It provides this evidence for democratic countries. The main
conclusion of the study is that in democratic countries the potential welfare gains and
likelihood of an FTA between a pair of countries is higher, the more (less) egalitarian the
income distribution in the relatively capital (labor) abundant country of the pair is. This
result is in full compliance with the predictions of the previous theoretical chapters of this
dissertation. The results of these chapters indicate that an increase in income inequality in
the relatively capital (labor) abundant country in a two-country pair decreases (increases)
the possibility of a free trade agreement between these two countries. One of the main

assumptions of these models was that decisions for joining an FTA were made by voting

135

in both countries. Therefore finding empirical evidence for this prediction only in
democratic countries and not in non-democratic countries is also compatible with these

models.

136

CONCLUSION
AND

SUGGESTIONS FOR FURTHER RESEARCH

This dissertation has shown that incorporating migration and median voter
approaches to the Heckscher-Ohlin setting leads to a complementary relationship
between factor movements and goods trade. Considering two non-trading countries
which differ from each other by their economy capital-labor ratios and assuming unequal
distribution of capital endowment within societies (those in which the relative capital
endowment of the median individual is less than the mean), we know that the median
voter in the labor abundant country would want his country to have a free trade
agreement with the capital abundant one, whereas the median voter in the capital
abundant country would oppose such an agreement. Migration of labor from the labor
abundant country to the capital abundant country changes the median voter’s decision in
the capital abundant country by lowering his utility level. When his utility level in the
autarky situation is lowered to the level he would get under free trade, the median voter
will be ready to prefer free trade to autarky. The absence of trade would mean further

migration and further decrease in the utility level of the median voter.

Thus, migration (factor mobility) causes free trade (goods trade). It is interesting to
note that migration occurs because of wage differences between the countries as a result
of the absence of trade. This indicates usual substitutability relationship of the

Heckscher-Ohlin model between the factor mobility and goods trade. However, since

137

4-1

 

migration eventually causes free trade through political economy, we observe the

complementary relationship in the big picture.

The models in this dissertation employ the median voter approach to trade policy
determination, as in Mayer (1986). In the static model, an increase in inequality in capital
abundant countries, holding constant the economy’s overall relative endowments of
factors, decreases the probability of free trade. In the dynamic model, this rise in
inequality postpones the time of free trade to a later date. An increase in inequality in
labor abundant countries, on the other hand, may render feasible an otherwise infeasible

free trade agreement.

One extension of the previous models would be to consider more than two countries.
For example, if we start with three different countries the pattern of immigration and its
result might be quite different than the two-country case. When modeling three-country

case, the cost of immigration function C(M(t)) could be different across the country

pairs. Such an enrichment of the models might allow us to understand more about the
directions of labor movements across countries by answering questions like, What are the
directions of migration between countries, i.e. which country or countries receive
immigrants and which country or countries are the source(s) of migration? Such a model
also might h elp u s p redict w hich c ountry p airs would b e m ore likely to e stablish free
trade agreements. Also we might be able to see whether a bilateral free trade agreement

could undermine political support for further multilateral trade liberalization.

138

Including illegal capital investment might also be an interesting extension. Citizens of
the capital abundant country might be allowed to invest in the labor abundant country
with a probability of detection and confiscation of their investment. It would be
interesting to see whether such a change would increase or decrease the probability of
free trade in the static model and whether it would make the time of free trade sooner or

later in the dynamic model.

Another possible extension is to include remittance payments to the model. One way
of doing this would be to assume that every migrant worker in the capital abundant
country sends a constant amount of remittance to the labor abundant country and total
amount of remittances are equally distributed among workers in the labor abundant
country. It should be noted that since there are impediments to trade, remittance
payments will also be subject to these impediments. Therefore these remittance payments

should include “melting away” type of cost. In this case migration rate, M (t), might

decrease since the future wage differences of migrant workers has to cover both the cost
of migration and the remittance payments. Naturally this might in the end lead to further

delay of free trade.

Delay in factor price equalization alter the free trade agreement might also be an
extension. If we assume that after free trade agreement it would take some time to
equalize wages and rents, then we might witness a higher migration rate at the beginning
and migration might c ontinue a fter the free trade a greement b ecause o f t he p revailing

wage differences. We might also witness a closer date of the free trade agreement,

139

although the full equalization of wages might be later than the normal case. A sharp
decrease in the cost of migration alter the free trade agreement might result in an increase
in the migration rate after the free trade agreement, which would be in accordance with
the real life experience as in the case of NAFTA. Martin (2001) draws attention to this
possibility of an increase in migration after the free trade agreement and reminds that “the
US Commission for the Study of International Migration and Cooperative Economic
Development, which embraced free trade as the best long term solution for unwanted
economically motivated migration, -‘expanded trade between the sending countries and
the United States is the single most important remedy’- nonetheless concluded that ‘the
economic development process itself tends in the short to medium term to stimulate
migration’. In other words, the same policies that reduce migration in the long run can
increase migration in the short run, creating ‘a very real short-term versus long-term
dilemma’ for a country such as the United States considering a free trade agreement as a
means to curb unauthorized immigration from Mexico.” Martin also mentions that
loosening the assumption that the adjustment to changes in international markets is
instantaneous c an p roduce a migration h ump, m caning that, when migration flows are
charted over time, migration first increases with closer economic integration and then

decreases.

The models of this dissertation ignore population growth. However, one can have the
same results by adding a constant population growth rate in both countries. This might
not give the exact same date of free trade unless C (M (t)) function is adjusted to allow a
proportional increase in the migration rate as the growth rate of population. However, the

complementary relationship and the effect of changes in income inequality results should

140

be the same even without any corresponding change in C (M (t)). Extending the model

by allowing populations of the labor abundant country, the capital abundant country and
migrants to grow at different rates might make it too complicated, but it might also lead
to interesting results. For example, if the illegal immigrants grow faster than the native
population in the capital abundant country, this increases the rate at which the capital-
labor ratio in the capital abundant country decreases and consequently makes the
economic integration sooner. On the other hand, if immigrants are given voting rights,
they will vote against economic integration in order to further enjoy high wages in the
capital abundant country. This might cause economic integration to occur at a later time
or even prevent it altogether. However if we assume that the migrants and their
descendents vote nationalistically (i.e. for economic integration with their original
country), rather than economically (i.e. against economic integration with their original

country), then the time of economic integration would be sooner.

Incorporating both the static and the dynamic models in one model might be more
realistic. One might remodel the dynamic model in such a way that starting with the time
when the median voter becomes indifferent between autarky and free trade for every
instant of time we have a constant probability of economic integration between 0 and 1
rather than either 0 or 1. A constant probability of free trade indicates a constant expected
waiting time for free trade, thus a poisson distribution. Then we can conjecture that if
people are risk neural, the equilibrium expected time of free trade is the same as the time

of free trade in the perfect foresight models of this dissertation. If, on the other hand,

141

people are risk takers (averse) the equilibrium expected time of free trade is sooner

(later).

As these various suggestions for further research indicate, this dissertation which
incorporates political economy and migration to the Heckscher-Ohlin model seems to

have laid a foundation for a fi'uitful research area. F

 

142

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