MINISTRY OF EDUCATION AND SCIENCE, RUSSIAN FEDERATION
FEDERAL STATE AUTONOMOUS ORGANIZATION OF HIGHER EDUCATION
«NOVOSIBIRSK NATIONAL RESEARCH STATE UNIVERSITY»
(NOVOSIBIRSK STATE UNIVERSITY, NSU)
Faculty of Economics
Chair of Application of Mathematical Methods for Economics and Planning
Direction of Training: 38.04.01 Economics
Master Educational program: Quantitative Economics
GRADUATE QUALIFICATION PAPER
MASTER'S DISSERTATION
Alexandra Marie Febles Miranda
The Uprising of Terrorism:
an Econometric Approach for Africa and the Middle East
«Admitted to defense»
Scientific Supervisor,
The head of the chair:
Dr. of Economics, Prof.
Dr. of Economics, Prof.
Kolomak, E.A. /………...
Mkrtchyan G. /…………..
«……»………………2017
«……»………………2017
Date of defense: «……»………………2017
Novosibirsk, 2017
2
The Uprising of Terrorism:
an Econometric Approach for Africa and the Middle East
Alexandra Marie Febles Miranda
Master´s Degree Thesis
Novosibirsk, 2017
3
Table of Contents
Introduction…………………………………………………………………………………….
4
Chapter 1. Debates in the sphere of economics of terrorism…………………………………..
6
Chapter 2. Data and Methods for evaluating the perpetration of terror attacks………………..
9
2.1 Data description …………………………………………………………………… 9
2.2 Expected results ………………………………………………………………….... 11
2.3 Methods for the evaluation of terror attacks ……………………………………… 13
2.3.1
Evaluation of the socio-economic and political variables…………….. 13
2.3.1.1 The Fano Factor……………………..………………………… 15
2.3.1.2 The Negative Binomial Distribution……………………….….. 17
2.3.1.3 Panel Data regression model …………………………………. 23
2.3.2
Evaluation of the spatial variables…………………………………….. 24
2.3.2.1 Spatial contiguity weight matrix. ….…………………………. 24
2.3.2.2 Moran’s I index for spatial dependence ………………………. 25
2.3.2.3 Spatial distance matrix………….……………………………… 25
2.3.2.4 Stepwise Ordinary Least Squares Regression…………………. 26
Chapter 3. Analysis and Results ………………………………………………………………. 27
3.1 Panel Data Regression Model……………………………………………………… 27
3.2 Spatial Contiguity Weight Analysis……………………………………………….. 31
3.3 Spatial Distance Analysis………………………………………………………….. 32
Conclusions…………………………………………………………………………………….. 35
Bibliography …………………………………………………………………………………… 37
Appendix 1: Descriptive Statistics………………………………………………………………40
Appendix 2: Number of terror attacks by country………………………………………………43
Appendix 3: Spatial contiguity weight matrices ………………………………………………. 46
Appendix 4: Spatial distance matrices…………………………………………………………. 55
4
Introduction
Terrorism: “The premeditated use or threat of use of violence by individuals or subnational groups to
obtain a political or social objective through the intimidation of a large audience”.
United States Department of State
In recent years, terrorism has been one of the main topics throughout the world. It appears
constantly in the newspapers, on television; it has changed the way we travel, the places that we are
able to visit, it has been limiting our freedom of movement. Terrorism nowadays has no frontiers or
borders, it became a global threat and countries around the world are trying to prevent it. Terrorism is
sending our citizens to war zones; it has killed millions and, therefore, has a direct impact on multiple
countries’ political and economic policies.
Terrorism has been increasing in the last years. It does not only affect the countries where these
terrorist groups are located, but they are not being comprised to a specific area. It is affecting the world
economy and stability as a whole. Some studies point out that political situations are the ones that
increase the tensions and that it leads to more terrorist attacks. Other studies address that economic
instability and inequality, as well as other factors are the real root behind the political tensions that
have been conducting the terrorism to the levels of insecurity that we have nowadays.
However, there is no consensus on which variables truly explain the perpetration of terror
attacks. Moreover, most researches address social, political, economic and geographical factors as
separate issues and the application of spatial econometrics into economics of terrorism is, to our
knowledge, very limited. Other studies are done in different areas, but not taking Africa and the
Middle East as a whole. For those reasons, our novelty is to be able to do a joint research that
incorporates all these variables (socio-economic and political) as well as the inclusion of the spatial
econometrics area into the economics of terrorism studies for Africa and the Middle Eastern countries.
Our goal is to effectively evaluate the issues behind the perpetration of terrorist attacks through
the use of empirical and econometrical tools. In order to achieve our goal, we employ panel data
regression model with Poisson or negative binomial distribution to estimate the trend of perpetration of
terrorist attacks. Also, using spatial econometrics with a contiguity weight matrix and a spatial
distance matrix, we analyze the effect of neighboring countries and the distance between main
command centers of some terrorist groups and the perpetration of terrorist attacks in those regions.
Therefore, in order to effectively address all topics, we divided the work in two sections. The first
section deals with the socio-economic and political variables that might explain the terror incidents.
Herein, the following objectives are pursued:
5
1. To determine the appropriateness of the Poisson and negative binomial distribution using a
dispersion index (Fano factor).
2. To use panel-data regression analysis with Poisson or negative binomial distribution to measure
the impact of several socio-economic variables in the propensity of terrorism.
In the second section, we focus on applying spatial econometric techniques to measure their impact
on the propensity of terror attacks. In this section, the following objectives are pursued:
1. To construct a spatial contiguity weight matrix to determine the influence of other countries’
borders in the number of terror attacks.
2. To construct a spatial distance matrix between the command centers of the main worldwide
terror groups and the capitals of countries in Africa and the Middle East in order to measure the
impact of being nearer or farther in the propensity of terrorism.
The data on terrorism is obtained by the Global Terrorism Database, which is run by the National
Consortium for the Study of Terrorism and Responses for Terrorism, the University of Maryland and
the United States Department of Homeland Security. Other data is being obtained from international
organizations: The World Bank, the International Monetary Fund, the United Nations and others. The
time frame of this research is from 1994 to 2015.
This research consists of 3 main chapters, where each one of them contains several sections. In the
first chapter, we discuss the debates in the sphere of economics of terrorism and in what we based our
chosen variables. In the second chapter, we address the topic of the collection of data and the different
methods that will be used for each of our sections (socio-economic variables and spatial variables). In
the last chapter, we present the results obtained and analyze them. We finish our research with a
summary of the conclusions and some thoughts about possible areas of future research.
These results may be of interest of governments and international organizations who addresses
economic policy, public policy, terrorism and counter-terrorism measures as well as a step in terrorism
studies in economics and econometrics, as it will try to offer a more comprehensive view of terrorism,
in order to understand the economic, political and spatial causes of this fast-growing social problem.
6
Chapter 1: Debates in the sphere of economics of terrorism
Terrorism has been present in society in different ways throughout human history. It is not a
new form of war or social behavior. There is no exact definition of “terrorism”, the events that we
consider “terror events” may change over time and may be different between countries. The perception
of what constitutes a “terror attack” differs in the eye of the beholder. After the September 11 th terror
attacks in New York, United States; terrorism became one of the main issues in public policy and
attracted the attention of academicians and researchers. Understanding the roots and the effects of
terrorism around the world passed from being an entirely political issue to an economic one, as well as
to other areas. Even though this issue existed before, there was a lack of data that specifically address
this issue. Therefore, we can find more literature about terrorism after 2001 and there is still room for
developing and understanding it, as we have more data now than in that moment.
Reviewing the literature about terrorism, we find that there is a strong debate about which
variables are more important or predict in a better way the behavior of terrorists or why do they decide
to carry out terrorist attacks. Some of them argue that, in different ways, economic motifs are behind
the roots of terrorism (Schock (1996); Hamilton and Hamilton (1983); Azam and Thelen (2008)) while
others argue that political situations are the ones who influence someone to enter terrorism (Feldman
and Perälä (2004); Piazza (2007); Krueger and Maleckova (2003); Krueger and Laitin (2008)).
Even inside both ways of thinking, there is no consensus about which variables should be taken
into account. Therefore, in this research, we would like to take into account both ways of thinking, the
ones that incorporates economic variables and the ones what incorporates political factors, as we
understand that terrorism is a complex phenomenon that can not only depend on either one or the
other side. We will be using econometrical tools to evaluate those factors in relation to the data
available today. In addition, there will be a special section for spatial econometrics, where, to our
knowledge, we could not find studies related to the impact of neighboring countries and the distance of
major terrorist command centers to the increment on terrorist attacks.
As terrorism is considered a way of violent crime, we are including some basis of economics of
crime theory in our research. One of them is that the variable of population density or population size
within a jurisdiction may be a variable positively correlated with increments on criminal activities. A
study made by Nolan (2004) support this theory by establishing a correlation and regression analysis
between crime rates in different cities in the United States and the population size of those regions.
Also, Hawaii Department of the Attorney General (1984) used the Pearson correlation and simple
regression analysis to measure property crime and violent crime across with respect to population
density in different areas in the United States. In our research, we strive to determine if this variable is
7
also significant for Africa and the Middle East, with the incorporation of it in our panel data regression
model.
In term of economic variables, GDP per capita (by Purchasing Power Parity), the Gini
Coefficient, education and military expenditures will be used into the regression. Education is being a
controversial variable in terrorism studies, as some researchers suggest that it is not significant
(Krueger and Maleckova (2003); Krueger and Laitin (2008)), while others have found a positive
relation between these factors (Testas (2004), Azam and Thelen (2008)). However, the study by
Krueger and Maleckova (2003), where they did not found a relation between education and terrorism,
was done in a very specific setting, based on a survey in Palestine and Israel. Therefore, this variable
will be included in our research, as it is not done in a larger sample of countries and, therefore, cannot
be excluded.
Regarding the military expenditure, several studies pointed out that increasing the military
expenditure have a positive relation with economic growth (Alpetkin and Levin (2012), Dunne, Smith
and Willenbockel (2004)). However, Alpetlin and Levin (2012) state that this hypothesis is true for
developed countries and it is not supported for less developed countries and in general. Although it
also may be seen that an increase in military expenditure may lead to repression, some studies have
found a significant relationship between military expenditure and economic growth. Dunne, Smith and
Willenbockel in their paper “Models of Military Expenditure and Growth: A Critical Review”
distinguish and evaluate different models, the ones related to economic growth and other models
specified to the “defense economics” area. The authors argue that “while the mainstream growth
literature has not found military expenditure to be a significant determinant of growth, much of the
defense economics literature has found significant effects”1 and conclude that “military expenditure
has a positive effect on output when the threat is high and a negative effect when threat is low.” 2 Even
though this is a controversial variable, studies that have shown a negative relation between both factors
are not able to conclude that reducing levels of military expenditure lead to economic growth. One of
these authors is Jean Dreze, where in his study “Military expenditure and Economic Growth” states
that “it does not follow from these findings that a reduction in military expenditure can be expected to
generate swift and tangible economic benefits”3. Even more, the author addresses that “in some
countries, there is also a possibility that the haphazard reduction of military expenditure under pressure
in the 1990s has contributed to a surge in internal violence”4. Terrorism is a high threat criminal act
worldwide and, therefore, based on the combination of studies that find a positive relationship between
1,2
3
4
Dunne, Smith and Willenbockel (2004). Models of Military Expenditure and Growth: A Critical Review.
Dreze, J. (2006). Military expenditure and economic growth. Page 5
Dreze, J. (2006). Military expenditure and economic growth. Page 5
8
both variables with the fact that those who find negative effects are not able to prove a negative
correlation with economic growth, we will be using this approach from the “defense economics”
literature in our model. Hence, one of our goals is to understand the effect that increases in military
expenditure might have for Africa and the Middle East.
However, to evaluate repression, we will be using the variable “type of government” and the
Polity IV index of political stability. It will allow us to understand if democracies, anocracies or
autocracies have a significant effect in being prone to terrorist attacks. In this matter we may say that
the literature dedicated to this topic have found a positive relationship between democracy and
terrorism, arguing that “democratic regimes experience 62% more terrorism than nondemocratic
regimes”. 5 Other studies argue that “democracies in transition” or “partial autocracies” are more prone
to terrorist attacks, as several groups may want to obtain power within their country (Chenoweth
(2006), Chenoweth (2013)) and because they can be catalogued as “weak states” (Wilson and Piazza
(2013)). It seems, however, that most studies conclude that autocracies have lower levels of terrorism.
Chenoweth (2006) used intergroup competition, political regime competition and terror group
emergence to test the increase of terror groups, while in 2013 evaluated different political variables
like civil liberties and foreign policies and terrorism. In our research, we will use the Polity IV index
as an independent variable in conjunction with the other economic variables. This is a very tough and
sensitive topic for counter-terrorism measures, as democracy is highly valued in Western countries.
These findings lead us to add the last component of our research: spatial econometrics. In this
section, we would like to explore the possibility of the impact of the distance of the countries from
main command centers of terrorist groups and the dynamics of terrorist attacks, as well as a spatial
contiguity matrix to evaluate the effect to a country of sharing borders with the same increase in
terrorist attacks. The literature on spatial econometrics and terrorism is limited and the works found
evaluate the distance between the home country of the terrorist and the terror attack itself (Neumayer
and Plümper (2010)), but we were not able to find studies combining the proposed variables.
Therefore, the “spatial econometrics” part in this research will be one of the most innovative parts in
the studies on terrorism.
We may summarize that in this research, we will focus on a joint analysis of economic, socioeconomic, political and spatial economic variables to gain a better understanding of the factors that
might lead to terrorist attacks.
5
Piazza, James. (2004). Democracy and Terrorism: A Complex Relationship
9
Chapter 2: Data and methods for evaluating the perpetration of terror attacks
2.1 Data description
The methodology to be used is a panel data regression model with negative binomial
distribution to estimate the perpetration of terrorist attacks. The variables to be used in the research
are: GDP per capita as Purchasing Power Parity (PPP), Gini coefficient, military expense (as % of
government expenditure), education expenses (as % of government expenditure), Polity IV index for
political stability, years of compulsory education, population density (in square kilometers),
unemployment, and the incorporation of dummy variables for predominant religion (Christian or
muslim) and type of government (democratic, anocratic or autocratic). The component of spatial
regression will be used in 2 spatial contiguity matrices. The first matrix describes the neighboring
countries of each country in the study (see Appendix 3) and, the second one, describing the distance
from main terrorist groups’ command centers to each country’s capital in Africa and the Middle East
(see Appendix 4).
Data on terrorism is obtained by the Global Terrorism Database, which is run by the National
Consortium for the Study of Terrorism and Responses for Terrorism, the University of Maryland and
the United States Department of Homeland Security (see Appendix 2). The Polity IV index is taken
from the Political Instability Task Force (PITF), which is founded by the United States Central
Intelligence Agency and run by the Center for Systemic Peace. Other data is being obtained from
international organizations: The World Bank, the International Monetary Fund, the United Nations and
others. The time frame of this research will be from 1994 to 2015, for 66 countries in Africa and the
Middle East.
This geographical area has been chosen due to several reasons: (1) that most terrorist activities
originate from terrorist groups in these areas, (2) studies that have been done for the Middle East and
African countries does not combine all variables together, (3) others are done in a more limited set of
countries, (4) the researches that have used the same methodology have been done for South Asian,
Latin American and developed countries or (5) during other periods of time like the Cold War.
For simplicity, throughout the research we will be using specific codes to refer to each country.
The list of countries and their codes will be the following:
10
Table 1: List of countries and their codes
Code
AFG
DZA
AGO
BHR
BEN
BWA
BFA
BDI
CMR
CAF
TCD
COM
ZAR
COG
CIV
DJI
EGY
GNQ
ERI
ETH
GAB
GMB
GHA
GIN
GNB
IRN
IRQ
ISR
JOR
KEN
KWT
LBN
LSO
Country
Afghanistan
Algeria
Angola
Bahrain
Benin
Botswana
Burkina Faso
Burundi
Cameroon
Central African Republic
Chad
Comoros
Congo, Dem. Rep.
Congo, Rep.
Cote d'Ivoire
Djibouti
Egypt, Arab Rep.
Equatorial Guinea
Eritrea
Ethiopia
Gabon
Gambia, The
Ghana
Guinea
Guinea-Bissau
Iran, Islamic Rep.
Iraq
Israel
Jordan
Kenya
Kuwait
Lebanon
Lesotho
Code
LBR
LBY
MDG
MWI
MLI
MRT
MUS
MAR
MOZ
NAM
NER
NGA
OMN
QAT
RWA
SAU
SEN
SLE
SOM
ZAF
SSD
SDN
SWZ
SYR
TZA
TGO
TUN
TUR
UGA
ARE
YEM
ZMB
ZWE
Country
Liberia
Libya
Madagascar
Malawi
Mali
Mauritania
Mauritius
Morocco
Mozambique
Namibia
Niger
Nigeria
Oman
Qatar
Rwanda
Saudi Arabia
Senegal
Sierra Leone
Somalia
South Africa
South Sudan
Sudan
Swaziland
Syrian Arab Republic
Tanzania
Togo
Tunisia
Turkey
Uganda
United Arab Emirates
Yemen, Rep.
Zambia
Zimbabwe
11
2.2 Expected results
In a general setting, we know that economic conditions in African and Middle Eastern countries
are hard. Countries in these areas are characterized by high levels of inequality and instability. In this
research, we will be evaluating three different components: (1) socio-economic variables, (2) economic
variables and (3) spatial econometric variables to try to explain the changes in the terrorist attacks for
Africa and Middle Eastern countries that were mentioned before. The variables were selected by joining
the theories of “defense economics”, “economics of crime”, “economics of terrorism”, and the several
debates that were discussed in the previous section of Literature Review.
In the following tables, we show a summary of the variables that will be used for this study and the
expected relationships between them and our independent variable: number of terrorist attacks
perpetrated. The first two sets of variables (economic and socio-economic variables) will be evaluated
using panel data analysis. The last set of variables (spatial variables) will be evaluated in two separate
matrices in order to measure the impact of the geographical setting in the terrorism increases.
Table 2: Expected variable’s relations (Economic variables)
Variable
Expected
relation
Explanation
Economic Variables
GDP per capita (PPP)
-
Higher GDP’s per capita are expected to decrease the formation
of terrorist organizations, as there are less economic instability.
It is expected that a lower Purchasing Power Parity represents
economic hardship and, therefore, higher levels of terrorism.
Gini Coefficient
+
A higher level of inequality is expected to increase terrorist
organizations and attacks, as there is an economic discontent
and economic hardship.
Military expenditure
-
Countries with higher expenditure in military will have lower
levels of terrorism.
-
A lower investment in education may represent economic
instability in the future and, therefore, more likely to have
citizens which may engage in terrorist activities.
Education expenses
12
Table 3: Expected variable’s relations (Socio-economic variables)
Expected
relation
Variable
Explanation
Socio-economic variables
-
More years of education within the population may
represent lower levels of terrorism.
-
(POLITY IV)
More continuous changes in government, specially
unexpected represent political instability and a higher risk
of terrorism. Polity goes from -10 to +10 (instability to
stability). We expect that the more stable, less terrorism.
+
Population density
Higher population density, by other studies, is correlated
to economic hardship and higher criminal levels.
Therefore, a higher number of persons per square mile
may represent higher levels of terrorism.
+
Unemployment
An increase in unemployment rates might lead to an
increase in terror activity, due to the people being able to
receive money from those activities.
Predominant religion: Muslim
or Christian country
We want to know if being a Muslim or Christian country
has an impact on terrorism.
Type of government:
democratic, anocratic or
autocratic
It is expected that anocratic (neither autocratic nor
democratic) countries may have higher levels of
terrorism, as the basis of democracy is still forming.
Compulsory education years
Political Instability Index
Table 4: Expected variable’s relations (Spatial variables)
Variable
Expected
relation
Explanation
-
Countries closer to the main command centers of the biggest
terror groups will have higher levels of sub-groups formation and
terrorist attacks.
+
Countries that border main command centers will have higher
recruitment, therefore, new group formation and higher levels of
terror attacks.
Spatial variables
Distance from main
command centers
Influence of other
countries’ borders
13
2.3 Methods for the evaluation of terror attacks
2.3.1 Evaluation of the socio-economic and political variables
In this research, we will be dealing with what is called “count data”. Count data can be defined,
statistically, as data that can only take non-negative integer values and come from counting, instead of
ranking. This is the case of our dependent variable “terror attacks per year”. For such variables, the
econometric literature assumes that they come from a Poisson distribution. However, it imposes a very
strong restriction: that the variance should be equal to the mean. There are other measurements that come
from Poisson distribution, such as the binomial distribution and the negative binomial distribution. Each
of them is used to deal with a specific behavior of our count data, like under or over dispersion.
In order to determine the distribution from where our data comes from and, accurately, decide if a
Poisson distributed based regression is appropriate to use, we started looking at the “descriptive statistics”
of our data. In it, we were able to observe the p-values of the Jarque-Bera test for normal distribution (see
table 5). We can see that the vast majority of our data rejects the null hypothesis of having a normal
distribution. Therefore, we might proceed to the second stage.
Table 5: Jarque-Bera statistic for normal distribution
Country
Jarque-Bera statistic P-value
Afghanistan
8.082413 0.01758
Algeria
8.871705 0.01185
Angola
14.92996 0.00057
Bahrain
20.9607 0.00003
Benin
46.67705 0.00000
Bostwana
336.2441 0.00000
Burkina Faso
283.1185 0.00000
Burundi
11.94658 0.00255
Central Afr. Rep.
109.896 0.00000
Cameroon
68.85974 0.00000
Chad
103.2796 0.00000
Comoros
213.8039 0.00000
Congo
87.67818 0.00000
Congo Dem. Rep.
43.72091 0.00000
Ivory Coast
64.57313 0.00000
Djibouti
9.787178 0.00749
Egypt
37.76584 0.00000
Equatorial Guinea
336.2441 0.00000
Eritrea
5.710981 0.05753
Ethiopia
2.126009 0.34542
Gabon
22.15687 0.00002
Gambia
22.15687 0.00002
14
Country
Jarque-Bera statistic P-value
Ghana
75.63788 0.00000
Guinea Bissau
112.0476 0.00000
Iran
73.96376 0.00000
Iraq
9.015622 0.01102
Israel
96.39757 0.00000
Jordan
2.072811 0.35473
Kenya
11.83197 0.00270
Kuwait
4.601689 0.10017
Lebanon
53.65933 0.00000
Lesotho
98.79704 0.00000
Liberia
3.999903 0.13534
Libya
48.95551 0.00000
Madagascar
26.74541 0.00000
Malawi
336.2441 0.00000
Mali
54.965 0.00000
Mauritania
43.36794 0.00000
Morocco
32.82558 0.00000
Mozambique
47.27948 0.00000
Namibia
236.6697 0.00000
Niger
210.707 0.00000
Nigeria
13.56834 0.00113
Qatar
6.297532 0.04291
Rwanda
18.94911 0.00008
Saudi Arabia
278.4509 0.00000
Senegal
86.40961 0.00000
Sierra Leone
17.74608 0.00014
Somalia
47.81407 0.00000
South Africa
201.5535 0.00000
South Sudan
66.25951 0.00000
Sudan
38.37505 0.00000
Swaziland
39.58036 0.00000
Syria
26.77433 0.00000
Tanzania
30.14141 0.00000
Togo
313.2523 0.00000
Tunisia
32.05031 0.00000
Turkey
34.50585 0.00000
United Arab Emirates
15.08482 0.00053
Uganda
1.807548 0.40504
Yemen
21.83196 0.00002
Zambia
34.5914 0.00000
Zimbabwe
35.86618 0.00000
15
We computed the “Fano factor”, a statistical measurement for dispersion, also known as
“dispersion index” (see Table 6). We were able to corroborate the over-dispersion in our data. Hence, in
our regression model, we will start with a Poisson distributed panel data regression and examine if, after
the results, the residuals are still non-normally distributed and a less strict assumption regarding the mean
and variance of our data should be used. To evaluate this, we will be using the Wooldridge (1997) test for
negative binomial distribution.
2.3.1.1 The Fano Factor
The Fano factor (dispersion index) is:
𝐹=
2
𝜎𝑤
(1)
𝜇𝑤
Where 𝜎𝑤2 is the variance and 𝜇𝑤 is the mean of a random process in some time window W, for the
subsamples w. The result obtained can be divided in 4 dispersion measurements, where each one of them
describes a different distribution.
𝑖𝑓 𝐹 = 0
𝑖𝑓 0 < 𝐹 < 1
{
𝑖𝑓 𝐹 = 1
𝑖𝑓 𝐹 > 1
𝑛𝑜 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑖𝑜𝑛
𝑢𝑛𝑑𝑒𝑟 − 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑒𝑑
𝑃𝑜𝑖𝑠𝑠𝑜𝑛 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑
𝑜𝑣𝑒𝑟 − 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑒𝑑
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑟𝑎𝑛𝑑𝑜𝑚 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
𝐵𝑖𝑛𝑜𝑚𝑖𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝑃𝑜𝑖𝑠𝑠𝑜𝑛 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑏𝑖𝑛𝑜𝑚𝑖𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
In our case, our subsamples are each of our countries, in the time window 1994-2015. The results are
shown below.
Table 6: Fano Factor Index of dispersion
Mean
AFG 436.1818
DZA 112.2273
AGO 7.045455
BHR 8.136364
BEN 0.318182
BWA 0.045455
BFA 0.272727
22.5
BDI
CAF 8.863636
CMR 7.727273
TCD 3.181818
Std. Dev.
625.0262
76.29949
11.61886
14.43968
0.779888
0.213201
1.077113
28.10313
21.86603
21.78943
6.099464
Fano Factor
895.630562
51.8734049
19.1609921
25.6262329
1.91156411
0.99999266
4.25396977
35.1015963
53.9421145
61.4420197
11.692517
Dispersion
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
under-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
Distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
(1.1)
16
Mean
COM 0.181818
COG 0.909091
ZAR 20.86364
CIV 2.590909
DJI 0.363636
EGY 74.81818
GNQ 0.045455
ERI 0.454545
ETH 3.818182
GAB 0.136364
GMB 0.136364
GHA 0.409091
GNB 0.409091
IRN 9.227273
IRQ 849.8182
ISR 55.04545
JOR 1.818182
KEN 21.36364
KWT 0.636364
Std. Dev.
0.664499
1.849301
36.2022
3.620827
0.657952
149.7982
0.213201
0.738549
2.788349
0.35125
0.35125
0.959121
0.908116
8.917248
1093.826
61.31455
1.592732
33.12824
0.953463
Fano Factor
2.42857649
3.76190523
62.817384
5.06015
1.19047848
299.92043
0.99999266
1.20000138
2.03628066
0.90475905
0.90475905
2.24867595
2.01587097
8.61763946
1407.89562
68.2976348
1.39523723
51.3714089
1.42857184
Dispersion
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
under-dispersed
over-dispersed
over-dispersed
under-dispersed
under-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
Distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Binomial distribution
Negative binomial distribution
Negative binomial distribution
Binomial distribution
Binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
36.31818
0.272727
0.818182
74.27273
0.818182
0.045455
13.77273
0.636364
0.818182
2.681818
1.318182
4.181818
130.3182
0.227273
6.136364
8.181818
3.818182
3.818182
128.6818
16.54545
46.73572
0.7025
1.097025
194.5415
1.258736
0.213201
29.88061
1.255292
1.651446
5.890965
4.581395
8.671993
227.5588
0.428932
9.944108
21.63911
5.803417
7.235076
204.8289
37.28874
60.1414367
1.80952473
1.47089994
509.55977
1.9365084
0.99999266
64.8274419
2.47618974
3.33333401
12.9402773
15.9228241
17.9834375
397.358216
0.80952274
16.1146379
57.230689
8.82086
13.7097511
326.035836
84.0382178
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
under-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
under-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
LBN
LSO
LBR
LBY
MDG
MWI
MLI
MRT
MAR
MOZ
NAM
NER
NGA
QAT
RWA
SAU
SEN
SLE
SOM
ZAF
17
SSD
SDN
SWZ
SYR
TZA
TGO
TUN
TUR
ARE
UGA
YEM
ZMB
ZWE
5.045455
29.04545
0.409091
60.27273
2.136364
0.727273
3.727273
78.68182
0.318182
12.04545
116.7273
0.954545
1.318182
13.92318
43.82702
0.73414
133.5633
3.758108
2.763397
8.095747
101.9829
0.716231
9.863242
221.6549
2.298597
1.961204
38.4216966
66.1311043
1.31746125
295.973902
6.61094071
10.4999952
17.5842015
132.184435
1.61224345
8.07637263
420.903205
5.53514834
2.91789839
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
over-dispersed
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
Negative binomial distribution
2.3.1.2 The Negative Binomial Distribution
As seen above, the vast majority of our subsamples exhibit a negative binomial distribution. Therefore, in
order to proceed with the estimation of the Panel data regression using it, we will first briefly describe the
Negative binomial distribution, which is:
Pr{𝑌 = 𝑦|𝜆, 𝛼} =
Γ(𝑦+𝛼 −1 )
𝑦!Γ(𝑎−1 )
𝛼 −1
𝛼−1
(𝛼−1+𝜆)
λ
(𝛼−1+𝜆)
𝑦
(2)
Where 𝜆, 𝛼 > 0, 𝜆 is the mean of the distribution and 𝛼 is the over dispersion parameter. The variance is
𝛼 −1 (1 +
𝛼 −1
𝜆
), from where we can see that there is a negative relation between λ and α, and a decrease in
λ is an increase in dispersion α. As this is a slight modification of the Poisson distribution, we can arrive
to it if our dispersion, α=0.
Pr{𝑌 = 𝑦} =
𝑒 −𝜆 𝜆𝑦
(3)
𝑦!
As count models are estimated using maximum likelihood, the corresponding likelihood function for the
negative binomial model is:
𝑁
𝐿(𝛽|𝑦, 𝑋) = ∏𝑁
𝑖=1 Pr(𝑦𝑖 |𝑥𝑖 ) = ∏𝑖=1
Γ(𝑦+𝛼 −1 )
𝑦!Γ(𝑎−1 )
𝛼−1
𝛼 −1
(𝛼−1+𝜇 )
𝑖
𝜇
𝑖
(𝛼−1+𝜇
)
𝑖
𝑦𝑖
(4)
18
Where 𝜇𝑖 = 𝐸(𝑦𝑖 |𝑥𝑖 ) = exp(𝑥𝑖 𝛽)
And the corresponding likelihhod function for the Poisson restriction is:
𝐿(𝛽) = ∑𝑛𝑖=1{𝑦𝑖 𝑥𝑖 ′ 𝛽 − exp(𝑥𝑖′ 𝛽} − 𝑙𝑛𝑦𝑖 !}
(5)
We are able to triple check the appropriateness of the negative binomial subset of the Poisson
distribution graphically by observing its behavior in a random variable probability density function (PDF)
and comparing it to a graph showing our data behavior. The graphs are shown below.
Graph 1: Negative binominal distribution random variable Probability Density Function.
Obtained from: Negative Binominal Distribution. Boost Libraries (2008)6
6
Negative Binominal Distribution. Boost Libraries (2008) http://www.boost.org/doc/libs/1_36_0/
libs /math/doc/sf_and_dist/html/ math_toolkit/dist/dist_ref/dists/negative_binomial_dist.htm
19
24
20
24
20
12
8
16
Frequency
Frequency
16
12
8
4
4
0
-500
0
0
-500
500
0
1,000
500
1,000
1,500
1,500
AFGANISTAN Histogram
ALGERIA Histogram
AFGANISTAN Histogram BOTSWANA
ALGERIAHistogram
Histogram
BENIN Histogram
BENIN Histogram
BOTSWANA Histogram
C_AFR_REP_ Histogram
CAMEROON Histogram
C_AFR_REP_ Histogram
CAMEROON Histogram
CONGO Histogram
CONGO_DEM_
Histogram
CONGO Histogram
CONGO_DEM_
Histogram
EGYPT Histogram
EQUAT_GUIN_
Histogram
EGYPT Histogram
EQUAT_GUIN_
Histogram
GABON Histogram
GAMBIA
Histogram
GABON Histogram
GAMBIA
Histogram
IRAN Histogram
IRAQ Histogram
IRAN Histogram
IRAQ Histogram
KENYA Histogram
KUWAIT Histogram
KENYA Histogram
KUWAIT
Histogram
LIBERIA Histogram
LIBYA Histogram
LIBERIA Histogram
LIBYA
Histogram
MALI Histogram
MAURITANIA Histogram
MALI Histogram
Histogram
MOZAMBIQUE Histogram MAURITANIA
NAMIBIA Histogram
OMAN
Histogram
QATAR
Histogram
MOZAMBIQUE Histogram
NAMIBIA Histogram
SENEGAL Histogram
SERIES01 Histogram
OMAN Histogram
QATAR
Histogram
SOMALIA Histogram
SOUTH_AFRICA Histogram
SENEGAL Histogram
SERIES01
Histogram
SWAZILAND Histogram
SYRIA Histogram
SOMALIA Histogram
SOUTH_AFRICA
Histogram
TUNISIA Histogram
TURKEY Histogram
Histogram
SWAZILANDWEST_SAHARA
Histogram Histogram
SYRIAYEMEN
Histogram
TUNISIA Histogram
TURKEY Histogram
WEST_SAHARA Histogram
YEMEN Histogram
2,000
2,000
2,500
2,500
3,000
3,000
3,500
3,500
4,000
4,000
ANGOLA Histogram
BAHRAIN Histogram
ANGOLA HistogramHistogram BAHRAIN
HistogramHistogram
BURK__FASO
BURUNDI
BURK__FASO Histogram
BURUNDI Histogram
CHAD Histogram
COMOROS Histogram
CHAD Histogram
COMOROS Histogram
COTE_D_IV
OIRE
Histogram DJIBOUTI
DJIBOUTI
COTE_D_IV OIRE
Histogram
HistogramHistogram
ERITREA
Histogram
ETHIOPIA
ERITREA Histogram
ETHIOPIA
HistogramHistogram
GHANA Histogram
GUIN_BISSA
U Histogram
GHANA
Histogram
GUIN_BISSA
U Histogr
ISRAEL Histogram
JORDAN
HistogramHistogram
ISRAEL
Histogram
JORDAN
LEBANON Histogram
LESOTHO Histogram
LEBANON
Histogram
LESOTHO Histogram
MADA GA SCAR Histogram
MALAWI Histogram
MA
DA
GA
SCAR
Histogram
MALAWI
Histogram
MAURITIUS Histogram
MOROCCO
Histogram
MAURITIUS
Histogram
NIGER Histogram
NIGERIAMOROCCO
Histogram Histogram
RWANDA
Histogram
SAUDI_AR_
Histogram
NIGER
Histogram
NIGERIA
Histogram
SEYCHELLES Histogram
SIERRA_LEONE Histogram
RWANDA Histogram
SAUDI_AR_ Histogram
SOUTH_SUDA N Histogram
SUDAN Histogram
SEYCHELLES
Histogram TOGO Histogram
SIERRA_LEONE Histo
TANZANIA Histogram
SOUTH_SUDA
SUDAN
Histogram
U_A_E_ HistogramN Histogram UGANDA
Histogram
ZAMBIA Histogram
ZIMBABWE
Histogram
TANZANIA
Histogram
TOGO
Histogram
U_A_E_ Histogram
UGANDA Histogram
ZAMBIA Histogram
ZIMBABWE Histogram
Graph 2: Sample data on “terror-attacks” by year (1994-2015). Single graph frequency distribution.
20
Algeria
.00
1.0
0
Chad
2
4
6
20
30
0
Djibouti
1
2
3
-1
0
1
2
3
.000
-200
0
Gabon
0.5
1.0
1.5
0
-0.5
8
2
0.5
1.0
1.5
Density
120
-40
0.5
1.0
0
40
80
2
4
6
120
-5
0
5
10
15
20
Ethiopia
.2
.4
.1
.0
-1
0
1
2
3
-5
0
5
10
15
40
60
Iran
.08
1
0
0
80
.1
Guin.Bissau
.4
40
.2
120 160
2
-2
0
.0
-40
1.5
4
Cote d’Ivoire
.0
0.0
3
.1
Eritrea
.0
0.0
80
.02
12
2
.3
Ghana
Density
Density
0.0
4
1
.2
Congo Dem.
.8
1
40
.8
0
-0.5
200 400 600 800
2
1
0
Equat.Guin.
Gambia
2
0
-0.5
0
0
Cameroon
.00
-4
Density
Density
0
-1
.0
-40
4
.005
80
.04
Egypt
.010
60
.1
120
.4
4
.015
1
80
.0
-1
2
40
Density
Density
Density
10
40
.3
Congo
0.0
0
20
C.Afr.Rep.
.8
0.5
.0
-10
0
Comoros
.1
0
.0
-40
.4
.0
-20
.2
.02
8
1.0
.2
60
.00
-2
.3
40
Density
.4
1.5
20
Burundi
.0
0.5
0
.04
Density
Density
Density
2
0.0
.00
-20
.8
0
-0.5
Density
600
Burk.-Faso
4
Density
400
Density
Botswana
200
.04
Density
0
.8
Density
.000
-200
1,000 2,000 3,000
Density
0
.04
Density
.0000
-1,000
.004
Benin
.08
Density
.0005
Bahrain
.08
Density
Density
Density
.0010
Density
Angola
.008
Density
Afghanistan
.0015
.04
.00
-2
0
2
4
6
-20
0
20
Graph 3: Probability Density function Multiple Single graphs. Distribution of the number of terror attacks from 1994-2015. Afghanistan to Iran.
21
Israel
.0
100 200 300 400
200
0
1
Malawi
-1
.00
0.0
0.5
1.0
1.5
0
Namibia
50
100
.0
20
.1
30
-20
0
Saudi Ar.
20
40
60
.04
.00
40
80
120
Density
4
0
0
10
20
30
Density
Density
-2
0
10
20
30
2
4
6
.2
2
4
6
8
-10
0
30
.05
.00
0.0
0.5
1.0
1.5
-10
0
10
20
30
40
South Africa
.04
.002
.000
-400
20
.10
1
0
-0.5
10
Rwanda
Somalia
.1
4
Mozambique
.004
-10
0
Qatar
.0
-10
0
Sierra Leone
.1
3
.0
-2
200 400 600 800
2
.4
.4
6
.2
.0
0
200 400 600 800
2
.000
-200
Density
Density
.08
2
1
.4
Morocco
.005
.2
-40
0
0
.0
0
.0
Senegal
.12
.00
-200
4
.010
.0
10
3
Nigeria
Density
Density
.1
2
.8
-2
.2
0
1
Niger
.2
-10
0
.4
150
-1
Madagascar
.04
.0
-50
150
.8
Mauritania
.05
100
.08
.8
Density
2
0
-0.5
.4
4
.10
Density
Density
3
50
.12
Mali
4
Density
2
0
Libya
.0
-1
.4
.0
-50
Density
0.5
300
8
.8
0.0
100
4
Liberia
Density
Density
Density
.01
0
0
Lesotho
1.0
.00
-100
.00
-4
Density
0
Lebanon
.02
.02
Density
.000
-100
2,000 4,000 6,000
.1
.8
.04
Density
0
.004
.2
Density
.0000
-2,000
.008
Kuwait
.06
Density
.0002
Kenya
.3
Density
Density
Density
.0004
Density
Jordan
.012
Density
Iraq
.0006
.02
.00
0
400
800 1,200
-50
0
50
100 150 200
Graph 4: Probability Density function Multiple Single graphs. Distribution of the number of terror attacks from 1994-2015. Iraq to South Africa.
22
Sudan
.02
.02
.00
.01
.00
20
40
60
80
.0
-50
0
Tanzania
150
200
-1
.0
.2
.1
.0
0
4
8
12
16
0
Uganda
0
20
5
10
15
40
60
.00
-200
4
-10
0
10
20
30
.000
-200
40
600
200
400
600
Zimbabwe
.008
.2
.4
.1
.0
200 400 600 800 1,000
0
Zambia
.6
.004
400
.005
.3
0
200
.010
.012
.000
-200
0
Turkey
.2
20
Density
Density
.00
3
.05
.015
Yemen
.02
2
.0
-5
.04
-20
1
.4
Density
.2
-4
0
.10
Tunisia
.3
Density
Density
100
Togo
.4
Density
50
Density
0
.4
Density
-20
Sy ria
.15
Density
.04
Swaziland
.8
Density
.03
Density
Density
South Sudan
.06
.2
.0
-4
0
4
8
12
-2
0
2
4
6
8
10
Graph 5: Probability Density function Multiple Single graphs. Distribution of the number of terror attacks from 1994-2015. South Sudan to Zimbabwe.
23
2.3.1.3 Panel Data Regression Model
For the Panel Data regression, our dependent variable is number of terror attacks for Africa and the
Middle East. The variables are ordered based on their correlation coefficients shown before. We used the
Maximum likelihood method due to the fact that our dependent variables have negative binomial
distribution. The regression model is specified as follows:
𝑇𝐸𝑅𝑅𝐴𝑇𝑖𝑡 = 𝛼 + 𝛽𝐺𝐷𝑃𝑝𝑐𝑖𝑡 + 𝛽𝑀𝑖𝑙𝑖𝑡𝑎𝑟𝑦𝑔𝑜𝑣𝑖𝑡 + 𝛽𝐸𝑑𝑢𝑐𝑔𝑜𝑣𝑖𝑡 + 𝛽𝑃𝑜𝑝𝑑𝑒𝑛𝑠𝑖𝑡 +
+ 𝛽𝐸𝑑𝑢𝑐𝑦𝑒𝑎𝑟𝑠𝑖𝑡 + 𝛽𝐷𝑎𝑛𝑜𝑐𝑟𝑎𝑐𝑦𝑖𝑡 + 𝛽𝐷𝑚𝑢𝑠𝑙𝑖𝑚𝑖𝑡 + 𝛽𝐺𝑖𝑛𝑖𝑖𝑡 + 𝛽𝑃𝑜𝑙𝑖𝑡𝑦𝑖𝑡 +
+ 𝛽𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑎𝑟𝑟𝑖𝑡 + 𝛽𝐷𝑎𝑢𝑡𝑜𝑐𝑟𝑎𝑐𝑦𝑖𝑡 + 𝛽𝑈𝑛𝑒𝑚𝑝𝑙𝑖𝑡 + 𝜀𝑖𝑡
(6)
Where:
𝑇𝐸𝑅𝑅𝐴𝑇 = Number of terror attacks
𝐺𝐷𝑃𝑝𝑐 = Gross Domestic Product per capita (Purchasing Power Parity)
𝑀𝑖𝑙𝑖𝑡𝑎𝑟𝑦𝑔𝑜𝑣 = Military expenditure as total of government expenditures (%)
𝐸𝑑𝑢𝑐𝑔𝑜𝑣 = Education expenditure as total of government expenditures (%)
𝑃𝑜𝑝𝑑𝑒𝑛𝑠 = population density (in square kilometers)
𝐸𝑑𝑢𝑐𝑦𝑒𝑎𝑟𝑠 = compulsory years of education
𝐷𝑎𝑛𝑜𝑐𝑟𝑎𝑐𝑦 = Dummy variable for country with type of government “anocratic”. This type of
government is defined as an unstable government, where it is neither purely democratic nor autocratic.
𝐷𝑚𝑢𝑠𝑙𝑖𝑚 = Dummy variable for a country where the majority of its population practice Islam.
𝐺𝑖𝑛𝑖 = Gini coefficient for income inequality
𝑃𝑜𝑙𝑖𝑡𝑦 = Polity IV index (developed by Robert Gurr in the 1960’s). This index classifies governments
and political stability and ranges from -10 to +10 (from hereditary monarchies to consolidated
democracies). However, the range can be divided in 3 subsets (which has been used in our research to
determine the dummy variables for type of government): autocracies (from -10 to -6), anocracies (from -5
to +5) and democracies (from 6 to 10).
𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑎𝑟𝑟 = international tourism arrivals
𝐷𝑎𝑢𝑡𝑜𝑐𝑟𝑎𝑐𝑦 = dummy variable for “autocratic” government.
24
𝑈𝑛𝑒𝑚𝑝𝑙 = unemployment rates.
Our dependent and independent variables have subscripts 𝑖 and 𝑡, where 𝑖 = 1, 2, … , 𝑁 are the different
countries and 𝑡 = 1, 2, … , 𝑇 are the time periods.
2.3.2 Evaluation of the Spatial Variables
2.3.2.1 Spatial contiguity weight matrix
A spatial contiguity matrix 𝑊 will be a matrix containing all possible spatial relations between the
elements in the matrix. For the purpose of this research, a spatial relation, 𝑤𝑖𝑗 , is defined as all countries
that will be surrounding the country specified in our left axis. In order to avoid having “self-influence”,
the intersection of 𝑤𝑖𝑗 with itself will be 0. Therefore, we can describe our spatial contiguity matrix as:
𝑊 = (𝑤𝑖𝑗 : 𝑖, 𝑗 = 1, … , 𝑛)
(7)
Where:
𝑤𝑖𝑗 = {
1, 𝑏𝑛𝑑(𝑖) ∩ 𝑏𝑛𝑑(𝑗) ≠ ∅
0, 𝑏𝑛𝑑(𝑖) ∩ 𝑏𝑛𝑑(𝑗) = ∅
(7.1)
After the construction of the spatial contiguity matrix, we will normalize rows to 1. The purpose of
it is to understand if there is any influence of having border with certain countries and terrorism. The rownormalization can be defined as:
∑𝑛𝑗=1 𝑤𝑖𝑗 = 1 , 𝑖 = 1, … , 𝑛
(7.2)
Therefore, if 𝑤𝑖𝑗 = 1, after applying the row-normalization procedure, our spatial contiguity
1
weight matrix will be a matrix containing elements 𝑤𝑖𝑗 , where 𝑤𝑖𝑗 = 𝑘 , and k is the sum of all elements
in that row (the sum of all neighboring countries).
25
2.3.2.2 Moran’s I Autocorrelation Index for spatial contiguity dependence
Gittleman and Kot (1990) described the Moran’s I Autocorrelation Index, which is used to
measure the spatial dependence of a variable with a contiguity weight matrix. After the construction on
the contiguity weight matrix, this index will be used to measure if there is any spatial dependence or effect
of sharing a border with the propensity of terrorism of the different countries in Africa and the Middle
East.
The Moran’s I index is defined as follows:
𝑀𝑜𝑟𝑎𝑛′ 𝑠 𝐼 = ∑
𝑁
𝑖 ∑𝑗 𝑊𝑖𝑗
∑𝑖 ∑𝑗 𝑊𝑖𝑗 (𝑋𝑖 −𝑋̅)(𝑋𝑗 −𝑋̅)
(8)
2
∑𝑖(𝑋𝑖 −𝑋̅ )
Where:
𝑁 : the number of spatial units indexed by i and j
𝑋: our dependent variable (terror attacks by country)
𝑋̅: the mean of our dependent variable (terror attacks by country)
𝑊𝑖𝑗 : each element of the spatial weight matrix
2.3.2.3 Spatial distance matrix
A spatial distance matrix 𝑊 will be a matrix containing the distance, 𝑑𝑖𝑗 , between the command
centers of the main worldwide terror groups and the capitals of the countries in Africa and the Middle
East, 𝑤𝑖𝑗 . As in the spatial contiguity weight matrix, the intersection of 𝑤𝑖𝑗 with itself will be 0.
Therefore, we can define 𝑊 as:
𝑊 = (𝑤𝑖𝑗 : 𝑖, 𝑗 = 1, … , 𝑛)
(9)
Where:
𝑤𝑖𝑗 = {
𝑑𝑖𝑗 > 0
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(9.1)
26
2.3.2.4 Stepwise Ordinary Least Squares Regression
The Stepwise Ordinary Least Squares regression method will be used to calculate the relationship
between the distance from the main terror groups identified by the United States Department of Homeland
Security and the terror attacks in Africa and the Middle East. In our case, this method will allow us to
include the most significant terror groups and their relationship in the propensity of terrorism. We will be
using a forward stepwise regression, starting from the terror group with the higher correlation coefficient
and, step by step, in a bidirectional way, fitting the regression model.
27
Chapter 3: Analysis and Results
3.1 Panel Data Regression Model
First of all, we already showed that, due to the nature of our dependent variable, characterized by
being a “Count” variable, it is not normally distributed. Due to the fact that the Negative Binomial
distribution is a subset of the Poisson distribution, we started estimating our Panel Data model using the
Maximum Likelihood for general Poisson distribution (the most restrictive assumption).
Then, we
performed the Residual test for Poisson restriction by Wooldridge (1997), where the null hypothesis is that
the mean and variance are equal (see Table 7). Therefore, Poisson distributed Maximum Likelihood
Method should be used. On the other hand, if we reject the null hypothesis, we should re-estimate the
model using the Quasi-Maximum Likelihood method under the assumption of inequality of the mean and
variance, and using the coefficient parameter from the test as the fixed variance.
Analysis of Results
For the first regression using the Maximum Likelihood estimation, we can see that the adjusted Rsquared coefficient is 0.86, which means that 86% of the variations in terror attacks might be caused by
these socio-economic and political factors (see Table 8). However, we could see that the dummy variable
for Muslim countries appears to be non-significant. Therefore, we ran a second regression excluding this
parameter. The exclusion did not affected the relationships established by the first regression.
Based on the Arkaike information criterion, the second regression appears to be best fitted (5.59
for the first and 5.55 for the second regression). Also, the coefficient of determination is slightly better
(0.886). Therefore, we run the Wooldridge test for the Maximum Likelihood Poisson restriction on the
second regression and obtained a p-value of 0.5051, which lead us to not reject the null hypothesis. The
Maximum Likelihood approach is then appropriate.
Table 7: Wooldridge (1997) test for Poisson Restriction in Maximum Likelihood Regression
Dependent Variable: RESID^2-1
Method: Panel Least Squares
Variable
TERRATF
Coefficient
0.045473
Std. Error
0.067413
z-Statistic
0.674540
Prob.
0.5051
28
Table 8: Comparison between regressions using Panel Data Maximum Likelihood Method
Original Regression
New regression
50<Gini<60
Coefficient Prob.
Coefficient Prob.
Gini>60
Coefficient Prob.
40<Gini<60
Variable
Coefficient Prob.
C
13.28732 0.0000*** 13.51246 0.0000*** 6.003166 0.0008*** 5.821392 0.0004*** 6.626302 0.0001*** 6.123243 0.0004***
GDPPC
0.000112 0.0035*** 0.000102 0.0059*** 0.000193 0.0000*** 0.000139 0.0003*** 0.00014
MILITARYGOV 0.10716
Coefficient Prob.
40<Gini<50
0.0002*** 0.00018
0.0089*** 0.101892 0.0106** 0.107358 0.0113** 0.111756 0.0097*** 0.046494 0.2277
-0.071103 0.0650*
-0.07228
Coefficient Prob.
0.0602*
0.0000***
0.133132 0.0019***
EDUCGOV
-0.090918 0.0293** -0.089403 0.0321** -0.060364 0.1747
-0.061689 0.1512
POPDENS
0.005834 0.0017** 0.005286 0.0018*** 0.006286 0.0004*** 0.006621 0.0003*** 0.003831 0.0243** 0.007336 0.0001***
EDUCYEARS
-0.597159 0.0000*** -0.554333 0.0000*** -0.67981
0.0000*** -0.617333 0.0000*** -0.573987 0.0000*** -0.706795 0.0000***
DANOCRACY -5.845328 0.0003*** -5.911651 0.0002*** -4.683649 0.0020*** -4.334979 0.0015*** -4.984007 0.0011*** -4.533683 0.0027***
DMUSLIM
0.472979 0.3879
NA
NA
2.372242 0.0000*** 1.490059 0.0008*** 0.351719 0.5233
GINI
-0.141968 0.0000*** -0.146938 0.0000*** -0.798671 0.0000*** -0.815439 0.3125
POLITY
-0.562641 0.0002*** -0.575795 0.0001*** -0.36995
2.38702
0.0000***
-4.016731 0.0028*** -0.892406 0.0000***
0.0063*** -0.394127 0.0013*** -0.423342 0.0022*** -0.387553 0.0041***
DAUTOCRACY -7.923612 0.0000*** -7.801095 0.0000*** -6.432794 0.0003*** -6.247012 0.0001*** -6.596154 0.0003*** -6.551683 0.0002***
UNEMPL
0.125663 0.0038*** 0.136107 0.0008*** 0.02042
0.6204
0.07172
0.0433** 0.176842 0.0003*** 0.013139 0.7566
R-squared
0.911821
0.924015
0.93663
0.772683
0.865731
0.946192
Adjusted R2
0.860771
0.886022
0.899943
0.641079
0.787996
0.915039
Akaike crit.
5.595218
5.554666
5.65417
6.367326
6.014889
5.531467
29
Our regressions show that on average between all countries, terror attacks would be around 13 if
all other variables were 0. The GDP per capita is statistically significant, but the effect of its coefficient is
relatively small, suggesting that countries with higher GDP might experience slightly higher levels of
terrorism. This might be explained by the availability of more resources to buy weapons.
Regarding the military expenditure, we also have a positive relationship. It implies that increasing
military expenditure also increases the propensity of terrorism. Even though several studies point out that
there exists a positive relationship between military expenditure and economic growth, the situation for
countries in Africa and the Middle East is different. Based on our results, it helps to increase terrorism. It
might be due to the availability of firearms and military equipment, which can be quickly attainable by
terrorists. Increasing military expenditure might be helpful for economic growth in politically stable
countries and in developed economies, but not in countries with political instability, transitional
governments or undeveloped economies. It would be interesting for future research to evaluate if terrorism
is causing a never ending circle, where the government increases military expenditure, terror groups
increase and, again, military expenditure constantly increases and to study the relationship between
terrorism and military expenditure in countries with political instability or transitional governments.
In the case of education, expenditure in education and compulsory years in education appears to be
significant, but the effect of compulsory years of education in the reduction of terrorism is more.
Therefore, we cannot agree with Krueger, Maleckova and Laitin (Krueger and Maleckova (2003) and
Krueger and Laitin (2008)) where they did not found a relationship between education and terrorism.
However, our results show that even though expenditure in education is statistically significant,
compulsory years of education have more impact in the reduction of terrorism. Therefore, we agree with
Testas (2004), Azam and Thelen (2008) when they state that education is, indeed, important for reducing
terrorism. For these reasons, we might conclude that even though the allocations for education are
important, keeping or increasing retention of students or years of compulsory education might be a better
strategy in reducing the rates of terrorism.
In the case of population density, our variable has a positive relationship with terrorism. We might
say then, that our results agree with the basis of economics of crime theory, where it says that there may
be a positive correlation between population density and increments in criminal activities (terrorism in our
case). Therefore, countries with more persons per square kilometer were more prone to terrorism. One of
the possible intrinsic causes is the resource scarcity in such cases.
The next variables in our regression are the dummy variables for autocracy and anocracy
governments. The variable democracy was not included in the regression to avoid multicollinearity.
30
Therefore, we are evaluating those types of governments in relation to democracy (the dropped variable).
Both variables show a negative relationship, indicating that countries with such type of governments have
a decrease in terror attacks. For these variables, the coefficients are extremely important for interpretation.
For anocracy governments, we see a coefficient of -7.80 and a coefficient of -5.91 for autocratic
governments. This means that countries with autocratic regimes are less prone to terror attacks, followed
by countries with regimes that lie between autocratic and democratic. Lastly, our results show that
countries with democratic governments have more terror attacks than their counterparts. On the same
topic, our results for the Polity IV index reveal a negative relationship, suggesting that as we have more
political stability, terrorism decreases. Therefore, our results coincide with those of Piazza (2004), where
he found a positive relationship between democracy and terrorism and argued that “democratic regimes
experience 62% more terrorism than nondemocratic regimes”
7
and with other studies that conclude that
countries with autocratic regimes present lower levels of terrorism. Moreover, analyzing both results
together, it seems that countries with unstable democracies would be the ones with higher levels of
terrorism.
Unemployment rates are significant and positive, leading us to say that higher unemployment rates
might lead to terrorism. However, the effect of this variable seems to be small. This will be explained in
the future, after changing the Gini coefficient parameters. We will be back to this variable in the next
paragraphs.
The Gini coefficient is a parameter that caught our attention, as it is statistically significant but
negative. Due to this result, we decided to pursue a deeper study of this variable and establish dummy
variables at different levels of income inequality (between 40 and 50, 50 and 60 and more than 60). We
found out that the level of income inequality plays an important role in the dynamics of the other
coefficients.
The following variables were consistent in all the three different income inequality regressions:
GDP per capita, population density, years of education, political stability index, anocratic and autocratic
governments. The changes in the dynamics were present in: military expenditure, education expenditure,
dummy variable for Muslim countries, Gini coefficient and unemployment rates.
In the case for countries that lie between a Gini coefficient of 40 and 50, expenditure in education
and unemployment rates seem to be non-significant. It is important to state that countries in this range are
the ones that have less inequality in comparison from other groups. We might, then, relate these results to
7
Piazza, James. (2004). Democracy and Terrorism: A Complex Relationship
31
the idea that people will have more equal access to better schools and welfare programs, and that could be
the reason why these variables do not seem to have an impact in terrorism.
Most countries lie in the second group: countries with a Gini coefficient between 50 and 60. This
group exhibits the same relationships as the regression for the general case, with the entire sample. We
should notice, however, how the coefficient of Gini coefficient with respect to terror attacks decreases as
we move towards more unequal countries.
This led us to move to our third group: those countries with a Gini coefficient of more than 60. In this
group, the variables “military expenditure” and the dummy variable for Muslim countries are not
statistically significant, but both variables for education (education expenditure and compulsory years of
education) are significant. We might say then, that for these countries, more than for the others, having
accessible education is extremely important in contrast with other factors. Regarding the insignificance of
the dummy variable for Muslim country, we can say that for the group of countries with more inequality,
terrorism affect in the same way Christian and Muslim countries. When we compare the group with the
lower levels of inequality and this group, we can see how unemployment and education expenditure plays
a more important role in the latest, due to having more inequality and therefore, less welfare programs and
education allocations. Another difference between the groups is the Gini coefficient. As we mentioned
before, while we move towards more unequal countries, there is a reduction in the impact of the Gini
coefficient in terrorism. This is very interesting and explainable at the same time by the relative
deprivation theory. As we have poorer countries, there are other priorities than political ones.
3.2 Spatial Contiguity Weight Analysis
In order to measure the impact of spatial neighbors and the propensity of terrorism, we constructed a
spatial contiguity weight matrix (as defined in the Methodology section) in order to know if there is a
relationship between sharing a border with a country with a high rate of terror attacks and the propensity
of terrorism of the neighboring countries. (See Appendix for the spatial contiguity weight matrix). To this
purpose, we used the Moran’s I test and the results are presented:
Table 9: Moran’s I spatial dependence index
Results
Observed(computed) Moran’s I
0.005039
Expected value of Moran’s I under null hypothesis
-0.01538
Standard deviation of Moran’s I under the null hypothesis
0.058
P-value of Moran’s I test
0.7247
The null hypothesis of the Moran’s I index is that there is no spatial dependence between the variables.
In our case, the results obtained are 0.7247, which means that there is no evidence that sharing a border
with a country with high levels of terrorism will increase the propensity of terrorism in other countries.
3.3 Spatial Distance Regression Analysis
The following list shows the names of the terror groups that have been used for calculating the
spatial distance matrix (see Table 10). The matrix was constructed based on the List of Foreign Terror
Organizations by the United States Department of Homeland Security in 2015. The terror groups based on
Africa and the Middle East were selected, and we also recovered the data on the locations where these
terror groups usually operate. Based on this information, we constructed the spatial distance matrix from
this location to the capitals of the countries in Africa and the Middle East. See Appendix for the spatial
distance matrix itself.
After collecting the information, we ran a stepwise regression on the total number of terror attacks
from 1994-2015 for each country and the distance matrix from every terror group in the list. The
regression results are presented in Table 11.
Table 10: Terror groups, acronyms and locations
Name of the terror group
Abdallah Azzam Brigades (AAB)
Al-Aqsa Martyrs Brigade (AAMB)
Ansar al-Dine (AAD)
Ansar al-Islam (AAI)
Ansar al-Shari’a in Benghazi (AAS-B)
Ansar al-Shari’a in Darnah (AAS-D)
Ansar al-Shari’a in Tunisia (AAS-T)
Location Based
Lebanon
Gaza
lfora tribe, Tuareg, Mali
Kurdistan, Northern Iraq
Benghazi, Libya
Darnah, Libya
Tunisia
Army of Islam (AOI)
Asbat al-Ansar (AAA)
Boko Haram (BH)
Gama’a al-Islamiyya (IG)
Hamas
Haqqani Network (HQN)
Hizballah
Tzabra, Gaza Strip
Sidon, Lebanon
Borno, Nigeria
Egypt
Gaza, Palestinian Territory, West Bank
Loya Paktia, Kabul, Afghanistan
Bekaa Valley, South Beirut, Lebanon
33
Name of the terror group
Islamic State of Iraq and the Levant (ISIL)
ISIL Sinai Province (ISIL-SP)
Jama’atu Ansarul Muslimina Fi Biladis-Sudan
Jaysh
Rijal Al-Tariq Al-Naqshabandi (JRTN)
(Ansaru)
Jundallah
Kahane Chai
Kata’ib Hizballah (KH)
Kurdistan Workers’ Party (PKK)
Mujahidin Shura Council in the Environs of
Al-Mulathamun
Jerusalem (MSC)Battalion (AMB)
Location Based
Raqqa, Syria
Sinai Province, Egypt
Kano State, North-Central Nigeria
Kirkuk, Iraq
Sistan va Balochistan, Iran
Qiryat Arba, Hebron, Israel
Baghdad, Iraq
Kurdistan, Northern Iraq
Gaza Strip
Bamako, Mali
Al-Nusrah Front (ANF)
Palestine Islamic Jihad (PIJ)
Palestine Liberation Front – Abu Abbas Faction
Popular
(PLF) Front for the Liberation of Palestine
Popular
(PFLP) Front for the Liberation of PalestineAl-Qa’ida
(AQ) (PFLP-GC)
General Command
Al-Qa’ida in the Arabian Peninsula (AQAP)
Al-Qa’ida in the Islamic Maghreb (AQIM)
Al-Shabaab (AS)
Ildib Governorate, Syria
Gaza Strip
Ramallah, Palestine
Gaza Strip
Damascus, Syria
Khyber Pakhtunkhwa, Pakistani/Afghan
Zinjibar,
border Abyan Governorate, Yemen
Kabylie Region, Northeast Algeria
Barawe, Somalia
Analysis of Results
Even though Boko Haram appears to be non-significant in the regression individually, as a whole it
is significant and the exclusion of this group changes our R-squared dramatically. Therefore, we can
conclude that the inclusion of this terror group provides important information to our model.
From the 33 terrorist groups evaluated, 16 are part of the final stepwise regression. From the
statistically significant terror groups (with an arbitrary rule of 0.10), 7 out of 11 (63.6%) exhibit the
expected relationship. That is, being farther from the terror group decreases the number of terror attacks.
Another important result from this analysis is that these terror groups in our regression model and the
distance from them can have an impact of 80.8% in the propensity of terrorism.
34
Table 11: Regression results for number of terror attacks and distance from terror groups
Variable
C
AQ
AAI
ISIL
AAS_D
JUNDALLAH
AQ_AP
HQN
AMB
Coefficient
12294.53
-9.022804
14.70044
-9.490731
-3.113003
-4.548407
-0.942990
8.978972
0.615395
AQ_IM
AAS_B
AS
PFLP_GC
AAD
KH
AAS_T
BH
R-squared
-1.136475
3.359038
-0.188963
3.264723
-0.715976
-2.713491
0.565121
0.267386
0.861520
Adjusted R-squared
F-statistic
0.808765
16.33078
Std. Error
1857.201
2.977138
3.196813
2.920172
1.501345
0.721172
0.284461
3.087633
0.211219
t-Statistic
6.619924
-3.030697
4.598467
-3.250059
-2.073477
-6.306964
-3.315002
2.908043
2.913539
Prob.*
0.0000
0.0042
0.0000
0.0023
0.0443
0.0000
0.0019
0.0058
0.0057
0.418930
-2.712803
1.713643
1.960174
0.120882
-1.563204
2.079350
1.570069
0.374083
-1.913951
1.946624
-1.393947
0.429500
1.315767
0.210452
1.270529
Mean dependent var
0.0096
0.0566
0.1255
0.1239
0.0625
0.1707
0.1954
0.2109
548.3729
S.D. dependent var
Prob(F-statistic)
1410.050
0.000000
Such groups are: Boko Haram (BH), Al-Qa’ida (AQ), Islamic State of Iraq and the Levant (ISIL),
JundallahAl-Qa’ida in the Arabian Peninsula (AQAP), Haqqani Network (HQN), Al-Mulathamun
Battalion (AMB), Al-Qa’ida in the Islamic Maghreb (AQIM), Ansar al-Islam (AAI), Ansar al-Shari’a in
Benghazi (AAS-B), Ansar al-Shari’a in Darnah (AAS-D), Al-Shabaab (AS), Popular Front for the
Liberation of Palestine-General Command (PFLP-GC), Ansar al-Dine (AAD), Kata’ib Hizballah (KH)
and Ansar al-Shari’a in Tunisia (AAS-T).
Therefore, for the section of the spatial variables we are able to compare our results and conclude
that even though we might think that sharing a border with a country with terrorism might increase the
perpetration of terror attacks in the neighboring countries, the data proves the opposite. However, the
distance from the command centers of the main terror groups mentioned above does have an impact in the
number of terror attacks. The influence of those groups reaches farther than any border, being the nearer
countries the most affected.
35
Conclusions
From the Panel Data regression model, we can conclude that there are several common factors that
affect the propensity of terrorism between all countries in Africa and the Middle East: the GDP per capita,
population density, years of education, political stability index, anocratic and autocratic governments.
However, there are other factors than can be different depending on the level of income inequality in
which a country lies between.
Our results show that countries with higher GDP per capita by Purchasing Power Parity and
higher population density present slightly more levels of terrorism. From the education variables, we can
see that increasing years of compulsory education decreases terror attacks and although the effect of
education expenditure is important, maintaining accessible schools and increasing years of education seem
more important than expenditures in education.
However, education expenditure is a factor that becomes more important in countries with more
income inequality, while military expenditure is not significant for those countries. On the other hand, for
the group of countries with less income inequality, education expenditure and unemployment were not
significant. It can be explained by the availability of welfare programs and more equal education
programs, in contrast with higher inequality countries (where education expenditures and unemployment
are significant in the propensity of terrorism).
In our research, we also included a dummy variable representing Muslim-majority countries. Our
results show that for countries with more inequality (with a Gini coefficient of more than 60), being a
Muslim country is not statistically significant. However, for countries with lower and intermediate levels
of income inequality, Muslim countries exhibit more terror attacks. This can be explained by the relative
deprivation theory and by the list of priorities of the people in extreme poverty. However, in the general
setting, our results show that there is not a statistical difference between Muslim and non-Muslim
countries in terms of the propensity of terrorism. For future research, it can be interesting to study if there
is a threshold level of Christian/Muslim population ratio inside a country that might lead to political or
civil unrest and, therefore, to terrorism.
In the area of political variables, our research revealed that counties with autocratic regimes exhibit
less terror attacks, followed by countries with a mix of autocratic and democratic regimes and, lastly,
democracies are more prone to terrorism (8 less terror attacks for autocracies, 6 less terror attacks for
anocacies with respect to democracies). Based on the Political Stability Index, countries that are moving
36
towards more stable governments are less prone to terrorism. Therefore, from this section we can say that
countries with autocracies and stable governments have less terror attacks.
From the spatial analysis, we can conclude that being contiguous or sharing borders with a country
with high levels of terrorism does not imply that the neighboring country will also be a terrorist-prone
country. However, the distance from the main command centers of different terror groups does have an
impact in the number of terror attacks. These results are important in order to evaluate terrorism and
counter terrorism measures.
These results may be of interest of governments and international organizations who addresses
economic policy, public policy, terrorism and counter-terrorism measures. It is a step in terrorism studies
in economics and econometrics, as we try to offer a more comprehensive view of terrorism, incorporating
the economic, inequality, political and spatial causes into a single research. It is much more to be done, as
economics of terrorism is a still in development area.
For further research, it would be interesting to do a spatial clustering analysis for each of these
terror groups or to do some spatial contiguity matrix with its corresponding Moran’s I tests around those
terrorist groups identified as significant.
37
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