in with technical tools that help us pursue goals that used to be very difficult. Schelling stated

Violence and Migrations:

The goals or purposes or objectives relate directly to other people and their behavior

An Agent-Based Model

explains clearly that we are not alone in the economic system and the use of homogeneous agents is to begin with incorrect.

Juan Tom´as Sayago G´omez∗ (Preliminary Version) 21st July 2007

2 Abstract

Migrations

I want to show how agents behave according to their status and their land status. First of all I have to define migration, as the process when a person or a family leave his or their place of residence and move to another one. For more simplicity I suppose that there are only two kinds of places or sectors as described by Harris and Todaro (HT from now) (Harris and Todaro, 1970), for this model the difference is more related to place, because people move to the better place.

The Displacement is a problem that is transforming the state of societies in the whole world as it was stated on the Internally Displaced People bye Global project and their consequences may last for a long time, even though after many years we’ll see displaced people that is trying to fit or get a living. This paper presents a model to help us understand how violence affects the composition of the population inside societies.

There are different reasons for agents to migrate from one place to another: economic 1 Introduction reasons are related to wage conditions and The societies are the background of the eco- resources, HT developed a simple model nomic system, we are interested in review where agents migrate from the rural side of how the agents are not alone in the eco- the country to the urban side of the country, nomic system, when we think of them as fam- when the expected wage in the urban zone 1 ilies or persons and each decision affects an- is more than the wage in the rural zone ; other. The recently developed Agent-based social reasons like the ones I am looking into, Computational Economics (ACE) allows us agents migrate because of the conflict that is to study complex macroeconomic systems being held in their country and they look for safer places; and last there are migrations ∗ [email protected]. Student at the Universidad Nacional de Colombia and active member of Macr´ opolis y GIERU, I would like to thank professors Luis Lorente and Michael Greenwood for their comments. All remaining errors are my own.

1 This

model was complemented by Silveira, Espindola and Penna, 2005, when they set a model of migrations through agent behavior. It was a starting point for me to do my analysis.

1

originated by health reasons, which can be explained for moments when there was risk of illness and people moves away to places where there are less risk.2

flee their homes by fear of being target of future attacks. The central characteristic of colombian displacement is that generally from rural areas - where state presence is weak and armed insurgents and paramilitary I attempt to explain how do economic agents groups are active - to urban and semi-urban behave in presence of violence and they mi- centres (Global IDP Project, 2002). grate to a different place, where there is less violence.

2.2

Each year hundreds of thousands of people in different corners of the world are forced from the safety of their homes and compelled to take flight

IDP in Guatemala

The displacement problem in Guatemala was caused by the civil war that finished on 1996. The IDP were scattered throughout the country and the majority of people went to the capital or the southern coast and the (Global IDP Project, 2002), this pheindigenous people flee to areas where state nomenon is called Internally Displaced presence was not active, because they were People (IDP). IDP is described as the most considered as supporters of the insurgency. demanding difficulties in our time, because it has really complex and irreversible consequences, so it became a worldwide problem and affects some of the undeveloped 2.3 IDP en Algeria countries like Angola, Colombia, Lebanon, Over the last ten years Algeria has been Sierra Leone and Sudan. I will introduce one of most violent countries, where there some of the countries where displacement has been armed attacks, massacres and has occurred and the way it happened. large scale rights abuses. It is unknown the

2.1

number of Algerians displaced by political violence, because all major international human rights organization has been prohibited from visiting the country. Although data about this doesn’t exist, some reports state that movements of displaced persons are from rural areas to safer metropolitan areas, and the level of actual population displacement is lower than in previous years.

IDP in Colombia

The displacement of populations in Colombia is a phenomenon that has been present for almost 40 years. The conflict showed armed groups against one another, each with different interests. The armed factions have changed over the years, they are described as: insurgents, paramilitary groups and the official military and police. During the course of the conflict, people are forced to

3

2 Nowadays

its not a very important cause of migrations, because there has been a great advance in modern medicine.

The basic model setup

I followed HT first intuition in order to understand the basic way of reasoning of 2

the agents in the system, they used the differential between expected wage in the urban area and wage in the rural area as the main reasons for them to migrate. So when people see violence and using the difference mortality rate between the rural and the urban areas as the way of stimulate agents to migrate. Additionally Silveira et al argue that it should be considered the existence of interactions between agents and its effects on ”socioeconomic phenomena” (Silveira et al, 2005, 6) and they propose an agent based computational model to describe the rural-urban migratory process. They presented a formalization of the influence that individuales receive from their neighbors. Finally I take their tools and adding a factor that signals the properties that are left behind on the migration.

asks in the box 1. VMR changes between MRC and MRU if the neighbor is living at the Rural area or the Urban Area.

I1 I4 I6

Box 1 I2 I3 Ind I5 I7 I8

The different values that D can take depend of its value when I assume α = 0:  1 D= −1

if D > α if D < α

(2)

Now we have described the main equation that defines the dynamic of the migration. We just have to describe the behavior of the mortality rates, because if we don’t initiate changes in its behavior it will tend to leave us with people only at one area. Equation (3) shows a simple pattern that should be followed by the MRC and makes our system stable, which means that we won’t get to the place where there is no people in one area.

First we describe that an agent can only be in one specific area, so when the individual is at the urban area he is denoted with an 1 or at the Rural area he is marked with a -1. This way an agent can only be in one place at every moment.

M RC = γ + β · PopC D =P M RC(t) − M RU (t) − Loss + n i=1 V M R(t) · Ii (1) n−1

4

The variables used are: D is referring to the decision made by the individual, MRC and MRU represent Mortality Rates for Rural and Urban, VMR is a variable that changes according to where is the individual that is asked and the Lo∫ ∫ is a small fraction to create the impression, that the individual considers the value of his belongings. This reflects that the individual asks to his acquaintances about the reality in the neighbors area. I show the way, that the agent

(3)

Methodology

We will create spatial dispersion matrices in MATLAB, where the an agent who is placed at the urban area is marked with one or if he is at the rural area with 0. The order spy helps us show the location of the agents in an understandable way. The figure 1 is a simple example of the location of the agents, when the point is blue, then the individual is living at the urban area and it’s white when he lives in the rural area.

3

0

0

2 4

0

0

50

50

50

100

100

100

6 8

0

10

50 100 nz = 5898

0

50 100 nz = 5639

0

0

0

50

50

50

0

50 100 nz = 5859

0

50 100 nz = 6916

12 14 16

100 18 20 0

2

4

6

8

10 12 nz = 209

14

16

18

0

100

50 100 nz = 6273

0

50 100 nz = 6631

100

0

0

0

50

50

50

20

Figure 1: Matrix for spatial dispersion

100

0

100

50 100 nz = 7144

0

50 100 nz = 7365

100

0

50 100 nz = 7585

0

Figure 3: Behavior of the population when there is a higher mortality rate at the rural area

10 20 30 40

8000

50 60 7000

70 80 6000

90 100 0

20

40 60 nz = 6008

80

5000

100

4000

Figure 2: First moment when half the people lives in each area

3000

2000

5

Simulation

1

2

3

4

5

6

7

8

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Figure 4: Behavior of the population I begin the simulation process by studying the problem of migration caused by violence when there is bigger mortality rate in the rural areas. It must be noted that at first the population is divided by almost half people in each side. First, I can say that at first all agents tend to generate clusters and also the loss value makes the population in the rural area increase. Second, after the second period, I see that the population in the rural are decrease and the population in the urban area increase. Figures 3 and 4 show how is the behavior of the population, when the mortality

rate is higher at the rural area than at the urban area.

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A special case

Its interesting to analyze what happens when there is war, and I observe that this should be the case when the mortality rate is higher in the urban area than in the rural area. So the first way of thinking tells us to make a little change in equation (1) 4

0

0

0 50

50

50

50

50

100

100

100

0

50

0

nz = 1059

50

0

0

nz = 1070

0

0

50 100 nz = 1962

0 50

0

0

50 100 nz = 4688

0

0

50

50

100 50

50 0

50

0

nz = 978

100

50

0

nz = 967

50 100 nz = 8379

50 100 nz = 10481

0

0

0

0

0

20

50

50

50

50 nz = 825

Figure 5: wartime

100

40 0

0

50

100 0

nz = 720

50 100 nz = 11894

50 100 nz = 6927

0

50 100 nz = 11040

100 0

20 40

0

100 0

50 100 nz = 12762

0

50 100 nz = 13670

Behavior of the population at Figure 6: First moment when 20% of the people lives in the urban area

and it can be seen in equation (4). The result is viewed at figure 5, where I see that the people will leave the metropolitan centre.

14000

12000

10000

8000

D= P8 M RU (t)−M RC(t)−Loss+ i=1 V M R(t)·Ii (4)

6000

4000

2000

7

0

Migration with demographical dynamics

1

2

3

4

5

6

7

8

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Figure 7: Behavior of the population with demographical dynamics

To complete the model, it is important to introduce demographical behavior and population growth in a simple way in order to understand that everything related to population dynamics is never stable. It makes us understand how it will never get to an equilibrium because the addition of demographical dynamics tips off the destabilizes the society as there is a new generation growing up. The ways to include demographical dynamics were taken from the work done by Galor and Weil in 2000, when they explained the pass from a regime of malthusian stagnation to

a modern growth regime and see the importance of schooling in the development process in the countries.

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Conclusion

This paper develops a model of migration caused by violence and the results are consistent with a theoretical explanation that people migrates from rural to urban areas. The conflict makes people migrate 5

with their families, even though they will lose everything. It is just a starting point in the search for ways to study dynamics in undeveloped countries that have been affected by inside conflicts. It explain something that John Steinbeck stated ”Maybe we can start again, in the new rich land” (Steinbeck, 1939).

ment: A Two Sector Analysis. The American Economic Review Vol 60 No.1. 1970. 5. Schelling, Thomas. Micromotives and Macrobehavior. W.W. Norton and Company. 1978. 6. Silveira, Jaylson, Thadeus Penna and Aquino Espindola. An Agent Based Model to Rural-Urban Migration Analysis. Physica A 364. 2006.

It is interesting to see how the behavior of the population at wartime is contrary and according to the way it was supposed, giving the basic model a certain degree of reliance and making it more useful to observe other characteristics and consequences related to conflicts.

7. Steinbeck, John. Grapes of Wrath. Bantam Books. 1939. 8. Thorngate, Warren. Teaching social simulation with MATLAB. http://jasss.soc.surrey.ac.uk/3/1/forum/1.html

It should be interesting to introduce unemployment and informal economy in the urban area and explain the formation and consolidation of this phenomenon that is very important for undeveloped countries, and their conclusions can help us understand how they are affecting underdeveloped countries and think about new ways to reduce their effects.

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Bibliography

1. Defensor´ıa del Pueblo. Desplazamiento forzado en Colombia. 2003. 2. Galor, Oded and David Weil. Population, Technology and Growth: From the Malthusian Regime to The Demographic Transition and Beyond. American Economic Review 90. 2000. 3. Global IDP Project. Internally Displaced People. Earth Scan Publications Ltd. Second Edition. 2002. 4. Harris, John and Michael Todaro. Migration, Unemployment and Develop6