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Types of Minority Discrimination and Terrorism
Manuscript Forthcoming in Conflict Management and Peace Science, 2012, 29(5)
James A. Piazza
Associate Professor
Department of Political Science
The Pennsylvania State University
330 Pond Lab
University Park, PA 16802
814.867.4429
Keywords: Terrorism, Minorities, Minorities at Risk, Discrimination,
Abstract
Qualitative research suggests that discrimination against minority groups precipitates terrorism in
countries. This study adds to this body of research by determining which specific manifestations
of minority discrimination – political, socioeconomic or cultural – are important and substantive
predictors of terrorist activity. To do so, I conduct a series of negative binomial estimations and
substantive effects simulations on a cross-national dataset of terrorist attacks and the treatment of
minority groups in four specific areas: political participation and representation, economic status,
and religious language rights. The results indicate that socioeconomic discrimination against
minorities is the only consistently significant and highly substantive predictor of terrorism. The
study concludes by discussing the implications of these findings to the scholarly literature on
terrorism.
Acknowledgements: The author would like to thank the three anonymous reviewers, Justin
Conrad, Bryan Arva, Will Moore, Kathleen Deloughery and Victor Asal for their helpful
comments on drafts of the manuscript.
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Case studies of individual terrorist movements and campaigns frequently depict
discrimination against minority groups to be an important motivating factor for terrorist activity.
(see for example Bradley 2006; Buendia 2005; Van de Voorde 2005; Whittaker 2001; Ergil
2000; Laqueur 1999; O’Hearn 1987). These findings are compatible with the results of cross-
national empirical studies on the precipitants of civil war onset, rebellions and other episodes of
mass political violence that yield, albeit inconsistent, evidence that minority discrimination, and
the targeting of minority populations for repression by states, fuels small-scale intra-state armed
conflict. (Regan and Norton 2005; Bonneuil and Ariat 2000; Moore 1998; Lichbach) More
generally, the phenomenon of ethnic, racial and class discrimination in societies has been
empirically linked to violent crime, aggression and antisocial behavior in the criminology and
sociology literatures. (see, for example, Simons et. al 2006; Dubois et al. 2002; McCord and
Ensminger 2002) It is then curious that with the exception of one recent study by Piazza (2011)
revealing a robust relationship between economic discrimination and domestic terrorism and
aside from being inserted as controls in studies focusing on other structural predictors (Eubank
and Weinburg 1994; Wade and Reiter 2007; Lai 2007), minority discrimination and minority
status has been largely overlooked as a potential predictor in the current generation of cross-
national empirical literature on the root causes of terrorism.
In this study I examine the effects of discrimination against minority groups on patterns
of terrorism afflicting countries and delve deeper to find out the relationship between specific
manifestations of minority discrimination and terrorist attacks. I make two key findings: First,
that countries containing minority groups that face general discrimination experience higher rates
of transnational and domestic terrorist attacks. This provides empirical backing to the case study
literature and reinforces the scant findings existent in the empirical literature. Second, I find that
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only some types of discrimination precipitate terrorism. Across all models, economic
discrimination against minorities – explained in detail below as formal and informal barriers
preventing minorities from full access to economic opportunities – significantly and
substantively increases the likelihood that a country will experience terrorist attacks. Political
discrimination – formal and informal barriers preventing minorities from participating in or
being represented in governance – is significant in some of the models, but is rendered
insignificant when evaluated next to economic discrimination and bears a much smaller
substantive effect on terrorism. The analysis also reveals that cultural discrimination – formal
and informal restrictions on minority group religious practice and linguistic rights – are neither
significant nor substantive predictors of terrorism.
The organization of this study is as follows: In the next section I trace the theoretical link
between general discrimination against minorities and terrorism and focus on what the terrorism,
comparative politics and larger conflict literatures say about the effects of economic, political
and cultural manifestations of minority group discrimination on terrorist activity. I then move on
to my empirical analyses, which involve a series of negative binomial regression models using
data from the Minorities at Risk database (Minorities at Risk 2009) and data on terrorist
incidents from the Global Terrorism Database. I then produce and discuss the substantive effects
of the four different types of minority group discrimination on terrorist attacks using Monte
Carlo simulations. I conclude with a brief discussion of the theoretical import of these findings.
Discrimination Against Minorities as a Cause of Terrorism?
Why, generally speaking, should we expect discrimination against minorities to produce
terrorism, and how might specific manifestations of discrimination precipitate terrorist activity?
I answer this question by examining three theoretical arguments, grounded in various social
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science literatures, for why societies in which discrimination against minorities is a prominent
feature might experience and produce more terrorism. All three theoretical arguments are
premised on the assumption that experience of discrimination by minority groups both produces
and reinforces a sense of collective identity among group members that is distinct from the
majority population or majority culture – fostering a sense of alienation or “otherness” – while
defining and making salient grievances among group members. When alienated and aggrieved
minority groups are able to overcome collective action problems and mobilize, which is often
facilitated by elites within the communities who can channel grievances, then political violence
is more likely to occur. (Gurr 1998) While Gurr’s model linking otherness, grievance and
mobilization is mainly adapted to higher-intensity manifestations of mass political violence, like
rebellions and riots, Crenshaw (1981), Ross (1993) and Piazza (2011) explicitly link it to
terrorism, and depict minority group marginalization and grievance as a crucial ingredient of
terrorist group formation and terrorist activity.
This summary of the relevant literature leads to the first hypothesis tested in the study:
H1. Countries containing minority groups facing discrimination will experience higher levels of
terrorism.
In theory, however, alienation, grievance and minority group engagement in political
violence can be triggered by different types of discrimination. I briefly describe each below.
Political Discrimination and Terrorism
This argument utilizes a rational-choice framework and also helps to make a case that
political discrimination, in particular, is likely to prompt terrorist activity. Subgroups of citizens
are assumed to be rational actors and discrimination a structural barrier to citizens’ use of
nonviolent, legal means to redress grievances and enact policy change. When a political system
denies subgroups channels to seek redress, they have a higher probability of engaging in political
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behavior outside of the formal, legal system and to engage in political violence. (Crenshaw
1981, 1990; DeNardo 1985) This theoretical argument is state-centered, meaning that it
considers qualities of the state, whether it is democratic or not, whether its leaders are responsive
and accessible or not, as the key predictors of the likelihood of terrorism, and it also assumes that
the terrorists will hail from aggrieved minority group communities.
Crenshaw (1981: 383-384) offers an explicit description of the process where
discrimination produces preconditions under which terrorist groups develop and become active.
Population subgroups with concrete grievances – she specifically uses the example of “ethnic
minorities” that are “discriminated against by the majority population” – develop social
movements which then agitate for policies to remedy their grievances. Typically, Crenshaw
maintains, these demands involve either granting equal rights to all citizens or providing political
autonomy to the aggrieved minority group. Out of these social movements come radical fringe
elements that may resort to terrorist violence to achieve their goals. Whether or not they do so is
also determined, according to Crenshaw, by whether or not they lack access to avenues for
participation in the political process, and by what she terms “precipitating events.” In the
situation that government institutions prove to be unresponsive to the minority group’s demands
for redress, and when this intransigence is met with, for example, a sharp government crackdown
or some sort of atrocity committed by government agents or majority group members, terrorism
is more likely to ensue.
Empirical studies of terrorism have not, to date, tested Crenshaw’s (1981, 1990) theories
linking discrimination and lack of opportunity for minority groups to redress grievances within
the political system and the incidence of terrorism. However, the conflict literature has
thoroughly investigated the effects of minority grievances on political violence. Gurr’s (1968)
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work on intra-state armed conflicts revealed that relative political deprivation, the inability of
society to meet the expectations for political influence that subgroups acquire, was, among other
predictors, a significant positive correlate for aggregate civil strife. In later works (1993, 1996,
2000) Gurr further developed his theory on this relationship arguing that grievances lead to
group mobilization which then leads to violent rebellion. In this context, Gurr also explains that
in properly-functioning democratic regimes, rebellion is avoided because grievances are
channeled into nonviolent political participation, and has seen this prong of his argument
validated in several empirical studies.1 (see for example Muller and Weede 1990)
In summary, this literature provides some evidence of a relationship between political
discrimination against minority groups and general political violence. It leads to the second
hypothesis tested in the analysis:
H2. Countries exhibiting political discrimination against minority groups will experience more
terrorism.
Socio-Economic Discrimination and Terrorism
The stream of literature on which this argument rests explains that exclusion from the
mainstream socio-economic life of a country, either as a result of discriminatory public policy or
more informal barriers that relegate minorities to second-class citizen status, breeds radicalism
and a predilection for violence, including support for terrorism. Gurr’s (1970; 1993) use of
1 It should be noted that Gurr’s (1968) earlier empirical findings on political deprivation have not been
consistently reproduced. Regan and Norton (2005) also find political discrimination to be a significant
predictor of civil war, but Gurr and Duvall (1973), Ellina and Moore (1990) and Gurr and Moore (1997).
Furthermore, a third set of studies find a more complex relationship between political discrimination and
conflict that often depends on the interaction between political discrimination and other factors.
(Bonneuil and Ariat 2000; Lichbach 1987; Moore 1998)
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relative deprivation – a phenomenon similar to the mechanism explained in the link between
political discrimination and terrorism above whereby individuals become aggrieved when their
material status does not match to their expectations, partially set by the higher socioeconomic
status of others in society – to explain the occurrence of political violence undergirds much of
the broad theoretical framework linking socioeconomic deprivation suffered by minorities and
terrorism. And, like the link between political discrimination and terrorism above, there is some
evidence linking relative deprivation to general political violence (see Ellina and Moore 1990).2
However, a rich qualitative case study literature illustrates that members of economically-
marginalized ethnic, racial and social minority groups are prey to radical ideologies, are more
likely to support political violence as solution to their problems and are more likely to be
recruited into terrorist activity if they experience severe discrimination. There are many
examples of this. Systematic employment, social welfare and housing discrimination against
Catholics in Northern Ireland through the 1960s and 1970s aided Irish Republican Army
recruitment efforts and prompted higher levels of terrorist attacks. (O’Hearn 1987) Formal
systems of apartheid and white rule in South Africa and Zimbabwe (Rhodesia), which created
high unemployment levels among blacks, helped to mold the early strategies of the African
National Congress and the Zimbabwe Africa National Union, which involved terrorist
campaigns. (Rich 1984) Scholars of Latin American politics have maintained that along with
socioeconomic marginalization through discrimination against indigenous people in countries
like Brazil, Colombia, Ecuador, Mexico, Nicaragua and Peru is a factor in producing conditions
2 Though Gurr (2000, 1996, 1993) does not find a significant relationship between measures of
economic discrimination, relative deprivation and political violence.
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under which terrorism and political violence occurs. (see Cleary 2000)3 Finally, studies of
Muslims living in Europe draw strong links between experiences of employment discrimination,
lack of access to educational opportunities and social marginalization and terrorism. Both Cesari
(2005) and Pauly (2004) demonstrate that socioeconomic marginalization of Muslim youths in
France has increased the popularity of radical Islam and its attendant violent jihadist movements
both in Europe and abroad, noting that experience of personal economic discrimination was a
motivating factor for 9/11 conspirator Zacharias Moussaui. These case studies, in addition to
broader theoretical expectations grounded in the relative deprivation literature, lead to the third
hypothesis of the study:
H3. Countries exhibiting economic discrimination against minority groups will experience more
terrorism.
Cultural Discrimination and Terrorism
Only some work has been done on the subject of ethnic, cultural, linguistic and religious
identity grievances as a predictor of terrorism. Goodwin (2006) argues that “revolutionaries” or
“insurgents” generally attack what they take to be “complicitious civilians” – civilians seen by
the armed movements to be beneficiary constituents of states that they oppose – with whom they
do not share similar languages, religious traditions or have experienced territorial segregation.
Agnew (2010: 1) makes a similar finding: that terrorism is more likely when populations
experience “collective strains” that are high magnitude, impact noncombatants, are perceived as
unjust and are, “inflicted by significantly more powerful others, including ‘complicit’ citizens,
3 Although Cleary’s (2000: 1146) empirical analysis itself fails to provide clear support for
political discrimination in the 1980s against minority groups as a significant predictor of
rebellion.
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with whom the members of the strained collectivity have weak ties.” For Agnew, “otherness”
refers to cultural identity-based perceptions of difference. Fox (2000; 1999) adapts Gurr’s basic
model to demonstrate how religious and cultural discrimination against minorities produces
identity-based grievances that can lead to mobilization and engagement in political violence.
Fox (2004; 2002; 2000) uses work by Wentz (1987) to argue that non-material identities, such as
religious identity, are fundamental building blocks in the psychological makeup of people, their
communities and their daily lives. When they are threatened through discrimination, very strong
grievances are produced which are especially likely to motivate violence. He finds validation in
this process, and that it can motivate terrorism in particular, in work by Jurgensmeyer (1993) and
Rapoport (1991).
As was the case for economic discrimination and terrorism, experience of cultural
discrimination my minority groups is frequently depicted as a key precipitant of terrorist group
formation and terrorist activity in qualitative case studies. A couple of examples: Restrictions
on Kurdish dress, celebration of traditional holidays and bans on the use of the Kurdish language
in schools and in media in Turkey is commonly cited as a motivator for severe grievances that
facilitated the development of the Kurdish Workers Party (PKK) terrorism movement in the
1980s and 1990s, and more recent accommodation of Kurdish cultural autonomy by succeeding
Turkish governments is credited as an important factor damping PKK activity. (see Ergil 2000;
Uslu 2007) A similar process of forced assimilation and repression of Basque cultural autonomy
fueled the development and activities of ETA under the Franco dictatorship. (Clark 1984)
Chinese religious and cultural restrictions imposed upon Muslim minority groups in Western
China are regarded to be an exacerbating factor contributing to Uighur terrorism and the
activities of the East Turkestan Islamic Movement. (Wang 2003) Repression of Basque cultural
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autonomy during the Franco dictatorship produced sentiments exploited by ETA. Finally,
Wiktorowicz (2005) demonstrates, through personal interviews with members of radical Muslim
groups in Great Britain, that extremist movements have capitalized off of widespread feelings of
identity crisis that are the product of discrimination and ethnic exclusion among European-born,
relatively well-acculturated Muslims.
This, therefore, leads to the fourth and fifth hypotheses tested in the study:
H4. Countries exhibiting religious restrictions against minority groups will experience more
terrorism.
And,
H5. Countries exhibiting linguistic restrictions against minority groups will experience more
terrorism.
Finally, the results of the study can help to shed light on the relative importance or
significance of the different types of minority discrimination as precipitants of terrorism. Is it the
case that manifestations of minority discrimination that are linked to materialist conceptions of
oppression – such as denying minorities the right to freely participate in political life or affording
minorities unequal access to job opportunities – are more likely to produce terrorist activity than
those that depicted in post-materialist depictions of minority status – such as those denying
cultural and religious autonomy or cultural and religious respect to minority groups? To account
for this possibility, the study tests the following hypothesis:
H6. Countries exhibiting political and economic discrimination against minorities are more
likely to experience terrorist attacks than countries exhibiting religious or linguistic
discrimination against minorities.
Validation of this hypothesis would be consistent with findings in the conflict literature
that that political factors, in particular stability and accountability of political institutions, and
economic factors, including poverty and socioeconomic inequality, are more important
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predictors of political violence than ethnic, religious or cultural factors. (e.g. Fearon and Laitin
2003) There are also theoretical reasons to expect that manifestation of identity-based
discrimination is a less directly-linked precipitant of terrorism. I suspect that of the four types of
discrimination that minorities can suffer in society, political and economic discrimination,
especially if they are acute, are more intrusive and dislocating than religious or linguistic. This is
primarily due to the different degree of enforceability surrounding political and economic
discrimination. In this conception, formal or informal barriers to voting, running for political
office, getting a job or securing housing are easier for governments or majorities to implement,
apply effectively and unambiguously sustain than are prohibitions against worship or use of
language. The latter two can, and in countries where governments try to ban them are, subverted
by the afflicted groups. This makes political or economic discrimination more provocative.
Analysis
I subject the six hypotheses to a battery of cross-national empirical tests. The study is
executed through two types of analyses: a set of multiple regression models and a set of
simulations to determine the first difference substantive effects of the four main independent
variables in the study. The regression models determine whether or not the general presence of
discrimination and specific manifestations of minority discrimination are causally related to the
incidence of terrorism. The substantive effects identify which of the specific types have the
greatest impact on terrorist activity. The first part of the study executes a set of negative
binomial regression estimations on the incidence of aggregated domestic and transnational
terrorism occurring within countries using a database that includes country-year observations of
166 countries for the years 1991 to 2006. The latter represent the most complete,
chronologically-contiguous time series available for the main independent variables in the
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study.4 Due to missing data for some years of observations resulting in list-wise deletion, the
number of observations per model ranges from 1,990 to 2,406.
Because the distribution of values for the dependent variable, incidents of domestic and
transnational attacks occurring in a country each year, are unevenly distributed spatially and
temporally, because the values of dependent variable observations may not, in theory, be
independent of one another and because in no case can the dependent variable assume negative
values, I employ negative binomial regression models rather than standard ordinary least squares
(OLS) models or Poisson count models. (see Brandt et. al. 2000; Cameron et. al 1998; King
1988). Moreover, the results of Vuong tests conducted during robustness checks, explained in
detail below, do not indicate that zero-inflated negative binomial estimations are more efficient
than negative binomial estimations. I also note that in addition to these justifications, negative
binomial models, rather than OLS or other models, have become an industry standard in studies
of terrorism. (see for example Dreher and Gassebner 2008; Wade and Reiter 2007; Drakos and
Gofas 2006; Li 20050) In all models, I calculate robust standard errors that are clustered on
country. The second analytical component of the study uses the Clarify freeware statistical
package developed by Tomz, Wittenberg and King (2001) to generate simulated values of the
dependent variable – incidents of terrorism – produced by first difference increases in the four
types of minority discrimination while holding all covariates in the negative binomial regression
constant.
4 Data in the Minorities at Risk Database for the minority discrimination indicators (ECDIS,
POLDIS, CULPO1 and CULPO2) is available for the years 1970 and 1981 and then annually
1991 through 2006. Robustness specifications including observations for 1970 and 1981
produce the same results as those in the main models.
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Variables
A list of the variables used in the study along with their descriptions, operationalization
and sources is published in Table 1.
(insert Table 1 about here)
The dependent variable in the study is a country-year tally of all incidents of terrorism
occurring within a country and is derived from the Global Terrorism Database (GTD) maintained
by the National Consortium for the Study of Terrorism and Responses to Terrorism.5 The GTD
affords researchers several advantages. It includes counts of domestic terrorism, a type of
terrorism that Abadie (2006) notes is woefully under-examined in empirical studies but is a
significantly more frequent occurrence than transnational terrorism. The Global Terrorism
Database also allows researchers to set inclusion criteria for incidents. In this analysis, I opt to
balance minimum and maximum degrees of inclusion in line with the most commonly used
definitions of terrorism as defined by Rapoport (2006).6
There are five independent variables in the study that operationalize minority group status
and experience of discrimination. All of them are derived from data from the Minorities at Risk
Database coded by the Minorities at Risk project (2009). Minorities at risk groups are ethnic,
linguistic and religious communities in countries that, “…collectively suffer or benefit from
systematic discriminatory treatment vis-à-vis other groups in society…” (Minorities at Risk
5 Access to the database, along with descriptions of count methods and operationalization of
terrorism, is available online at: http://www.start.umd.edu/gtd/.
6 Specifically, I opted to for GTD’s “Criterion I” – event has a political goal and intends to
convey a message to a larger audience – and “Criterion II” – the event is directed against
civilian, rather than military, targets. (Global Terrorism Database 2009: 5)
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Project 2009: 1) The Minorities at Risk (MAR) database aims to be as comprehensive as
possible, collecting data on all prominent minority groups in countries and publishing data on
282 separate minority at risk groups. Because the MAR database publishes its data on a group
by group basis, I reshape it to a country-year format for the purposes of this analysis. This leaves
many countries with more than one minority at risk group within it and it is frequently the case
that the groups experience different degrees of discrimination. In these cases, noting that I need
to distill all minority group discrimination into a single value for the country-year observation, I
adopt the method used by Lai (2007) and Caprioli and Trumbore (2003) and code the highest
measurement of discrimination across all national minority groups. In my database, 115 out of
166 countries contain at least one minority at risk community in the average year, and
approximately 66.6 percent of all country-years observed contain at least one minority at risk
group.
After reconfiguring the MAR database to a country-year format, I take four of its
indicators – “POLDIS, Political Discrimination Index,” “ECDIS, Economic Discrimination
Index,” “CULPO1, Restrictions on Religion” and “CULPO2, Restrictions on Use of Language or
Language Instruction” – and recode them into the main independent variables of the study. It is
necessary to recode these indicators, rather than inserting them raw into the model, for two
reasons. First, in the raw, POLDIS and ECDIS are pseudo-categorical indicators rather than
clear ordinal scales. The codes of these two variables in MAR are zero, indicating that the
minority group in question does not experience political or economic discrimination, one,
indicating that the group suffers from a legacy of discrimination but benefits from official
remediation policies, and two, three and four, indicating increasing degrees of discrimination,
exclusion and government neglect, and overt government repression in the highest code.
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CULPO1 and CULPO2 are more unambiguously ordinal scales: zero indicates no discrimination,
one indicates informal discrimination, two and three indicate somewhat and sharp discrimination
and restriction of minority group religious and linguistic rights. Second, reshaping the MAR
database to a country-year format creates observations – 33.3 percent of all observations in the
dataset – without a minority at risk community to code values for. This complicates the zero
code, which is the default code for all cells, for the four MAR discrimination variables; the non-
recoded zero therefore indicates both an observation where minority groups are not discriminated
against and observations where there is no minority group to be discriminated against.
My solution is to produce five recoded variables measuring both the presence of minority
groups in countries that experience some level of discrimination and the different aspects of
minority status vis-à-vis discrimination in countries. The first independent variable is a simple
dummy coded one for all observations where 1) a minority at risk group is present; and 2) where
that minority group experiences some level of any type – political, economic, religious or
linguistic – discrimination. The next four independent variables code, on an ordinal scale,
experience and intensity of the specific types of discrimination. These recoded variables,
summarized in Table 2 below, are built by addressing the two concerns about the raw data: the
need to produce a true ordinal scale of minority economic discrimination and the need to address
observations lacking a minority at risk group.
(insert Table 2 about here)
The types of minority group discrimination variables are correlated with one another,
though not in a uniform manner. Table 3 presents results of Pearson’s r correlation coefficients
for the four different types of minority discrimination. All of the coefficients are significant, but
Minority Political Discrimination and Minority Economic Discrimination are much stronger
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predictors of one another than they are of Minority Linguistic and Minority Religious
Discrimination. Minority Linguistic and Minority Religious Discrimination are significant
predictors of one another, but, again, bear smaller coefficients than that for political and
economic discrimination against minorities within countries. I discuss more fully the
implications of patterns of correlation between the types of discrimination, as well as the
possibility of simultaneous effects, in a subsequent section.
(insert Table 3 about here)
In all models I also include an array of standard control variables that are frequently
included in empirical studies of terrorism. (See for example Wade and Reiter 2007; Li 2005;
Eyerman 1998) I include natural logs of gross national income per capita, national population,
national geographic area, national GINI coefficients and the number of years the current political
regime has been in power. Noting that Li (2005) found that different aspects of political regime
type have different effects on terrorism experienced by a country, I also control for the degree to
which a country’s executive branch is constrained and level of political participation in a
country. Finally, because Walsh and Piazza (2010) found that countries with poor human rights
records experienced more frequent incidents of terrorism, I control for both the level of physical
integrity rights protections in a country.
Reverse Causation
All independent variables in the study are lagged one period. This, of course, helps to
capture delayed effects of changes in the predictors and further helps to parse out direction of
causation. As a further precaution against problems of endogeneity between the discrimination
variables and terrorism, I produced a set of ordered logit models testing for a possible
relationship between terrorist attacks in t0 and change in the four types of minority discrimination
17
in t1; essentially flipping the main model dependent and independent variables. In none of these
checks are terrorist attacks significant predictors of discrimination. This is consistent with the
different rates of change over time of the two sets of variables. While counts of terrorist attacks
can widely vary from year to year, change in discrimination status is slow and rare in the sample.
Summary statistics of all variables are published in Table 4.
(insert Table 4 about here)
Model Results
The results of the four regression models are presented in Table 4:
(insert Table 5 about here)
Table 5 reveals some interesting patterns which generally identify economic
discrimination – as opposed to political, religious or linguistic – as the most consistently
significant predictor of terrorist attacks in countries. These findings are interesting for a couple
of reasons, not the least of which is that they deviate from some of Gurr’s findings (2000, 1996,
1993) on minority economic discrimination and other forms of political violence, like rebellion
and civil war.7 First, model 1 demonstrates that presence of minorities at risk groups that
experience some level of discrimination of any kind is a significant positive predictor of
terrorism, thus supporting my first hypothesis. When delving deeper, however, it becomes clear
that only certain types of discrimination significantly contribute to terrorism. In model 2,
minority group political discrimination is a significant positive predictor of terrorism, and in
model 3 minority group economic discrimination is also a significant positive predictor of
terrorism. However, as evidenced in models 4 and 5, neither religious discrimination nor
7 A nontrivial difference, though, between this study and Gurr’s work is the quite different
dependent variable we use.
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linguistic discrimination are significant predictors of terrorism at all. Finally, model 5, which
compares the relative effects of all four different types of minority group discrimination,
demonstrates that only economic discrimination is a significant predictor of terrorist attacks.
Realizing that many countries feature more than one type of minority group discrimination and,
in theory, the different types of discrimination may predict one another, I ran traditional
collinearity diagnostics.8 These do not indicate significant multicollinearity distortions and
coupled with the findings in models 2 through 5, where the different types of discrimination are
run individually, the conclusion that religious and linguistic discrimination are not significant
predictors of terrorism can be reported with confidence. Overall, the results suggest that
countries that permit informal or formal discrimination against their minority communities can
expect to experience more domestic and transnational terrorist attacks, but that this is
conditioned on the type of minority discrimination that prevails in the country.
Across all models several of the control variables are significant, many of them at the
highest level, demonstrating that the core findings in the analysis – that political and economic
discrimination in countries produces more terrorism – is robust to the inclusion of important
covariates. The natural log of gross national income per-capita is a consistently significant
positive predictor of terrorism across the models, while GINI coefficient is significant in only
some of the models. This suggests that wealthy countries are more likely to experience terrorism
than poorer countries; a finding consistent with some of the empirical literature and with the
theoretical argument that wealthy countries afford more targeting opportunities for terrorist
movements . The argument that terrorism is more likely in countries with uneven distribution of
income is not as consistently supported by the results. The results in Table 5 suggest that more
8 Results available from author.
19
populous countries experience more terrorism, which is an expected finding, but in none of the
models is the geographic size of the country a significant predictor of terrorism. The covariates
in the models also conform to the expectation formed by Li (2005) that mature regimes,
measured by Durable, and regimes with high levels of political participation experience
significantly less terrorism. However, executive constraints, the other measure of regime type, is
not significant. Finally, reproducing the findings of Walsh and Piazza (2010), in all models
countries affording their citizens poor human rights protections (Physical Integrity Rights Index)
experience less terrorism.
Robustness Specifications
I conduct a series of robustness checks on the main results and find them to reinforce the
main findings of the study that among different types of minority discrimination, economic
discrimination is the significant driver of terrorism. The results of these checks, discussed in
more detail below, are summarized in Table 6
(insert Table 6 about here)
To check the results produced using the main negative binomial models I first reran the
main models using three alternative estimation techniques: 1) Zero-inflated negative binomial
estimations, in order to account for the possibility of two different types of zero values in the
dependent variable; 2) Country and year-fixed effects negative binomial estimations, to address
omitted variable bias; and 3) Rare events logistical regression models, in which the dependent
variable is truncated into a dummy coded “1” for any observation in which at least one terrorist
attack occurred, to reduce the impact of outliers cases on the overall results. These alternative
modeling technique specifications produce mostly the same results as found in the main models
of the study. In the zero-inflated models, the exact same pattern is reproduced: economic
20
discrimination against minorities is the only consistently significant positive predictor of
terrorism in countries. However, in both the rare-events logit and fixed-effects negative
binomial models, both political and economic discrimination are found to be consistently
significant, while religious and linguistic discrimination are not. In these models, mere presence
of minority groups facing some sort of discrimination is significant, except for in the fixed-
effects model. While the results of the alternative estimation technique specifications due
underscore the main findings, they themselves are marred by limitations. As previously noted,
Vuong tests for the zero-inflated models do not demonstrate higher levels of efficiency than
standard negative binomial models. The rare-event logits do address the issue of outlier effects
in the dependent variable, but they do not cluster on country, leaving open the possibility of
omitted variable bias. Finally, while the fixed effects models do address country and year-
specific observation factors that could affect the results, they eliminate around 15 country cases
per model due to lack of variation in one or more indicators. However, taken together they
increase confidence that the results of the main models are not dependent on the selection of the
modeling technique.
I also undertook several other robustness specifications. To determine if the results in the
study are driven by extreme, rather than mild, manifestations of minority discrimination I
truncated the discrimination indicators into dummy variables and reran the main negative
binomial models. Noting also that Li (2005) controlled for previous terrorist activity, I also reran
the models including a one-year lagged measure of attacks on the right-hand side of the
equation.9 To determine whether or not the effects of minority discrimination mostly drive
9 However, Brandt and Williams (2001) and Brandt, Williams and Fordham (2000) illustrate the
complications associated with including a lagged dependent variable as a covariate in event-
21
domestic, as opposed to transnational, terrorism I also reran the models using data on domestic
terrorism derived from Enders, Sandler and Gaibulloev’s (2011) database of transnational and
domestic terrorist attacks decomposed from the Global Terrorism Database. Gurr (2000, 1996,
1993) found ethnic minority group legacy of separatism to be a significant predictor of violent
conflict in countries, so as a further check I have also rerun the main models including the
Minorities at Risk index of separatism (“SEPX”) as a control. Finally, noting the potential
limitations associated with aggregating acuteness levels of minority discrimination to the
country-year level for countries containing more than one minority at risk group – the technique
that Lai (2007) and Caprioli and Trumbore (2003) use but a larger research design issue raised
by Young and Finley (2011) and Rustad et al. (2011) – I also rerun the models including a count
variable for the number of minority groups within the country. In all of these robustness
specifications, the same results as those featured in the main analysis are reproduced.
Simultaneous Effects
As previously noted, the different types of minority discrimination are correlates of one
another. Furthermore, minority at risk groups in countries are frequently afflicted by multiple
types of discrimination: in 22.1 percent of observations in the data, minority groups experience
two types of discrimination; in 8.4 percent of observations they experience three types and in 2.4
percent they experience all four. This could potentially complicate interpretation of the main
results if different types of discrimination affect one another. To shed light on this possible
complication, I pair together the four different measures of minority discrimination, political,
economic, religious and linguistic, in all possible two, three and four grouping combinations and
count time series models. I therefore only use this specification as a robustness check and
observe that it does not change the main results of the study.
22
create ten new dummy variables. I then rerun these as predictors of terrorism using the same
covariates as in the main models. The coefficients for these models – coefficients for the other
covariates are not reported for simplicity – are presented in Table 7.
(insert Table 7 about here)
None of the combinations of types of discrimination are found to be significant predictors
of terrorism, at least using the standard .05 p-value level threshold. Only one of the combined
discrimination dummy variables, “Political and Economic Discrimination,” approaches
significance with a p-value of .104 (z = 1.62). This later finding provides a good test of
hypothesis six – that countries exhibiting “traditional-materialist” minority discrimination, like
economic and political discrimination, are more likely to experience terrorism than those
exhibiting “post-materialist” minority discrimination like religious or cultural discrimination –
but, given the marginal significance of the coefficient, produces rather weak results.10
Taken
along with the results of model 7 in the main analysis presented in Table 5 which demonstrate
that when pooled together in the same model only economic discrimination is a significant
predictor of terrorism, these results suggest that the types of discrimination affecting minorities
bear distinct effects on patterns of terrorism within countries, and that their specific impacts are
10
However, when a combined political and economic minority discrimination dummy variable
and a combined religious and linguistic minority discrimination dummy variable are run together
in the same model , with all covariates, the political-economic discrimination indicator is a
significant (p≤ .05) positive predictor of terrorism, while the religious-linguistic discrimination
variable is not. This perhaps further suggests support for hypothesis six, but is inconsistent with
other specifications, namely those showing marginal significance when political-economic
discrimination is run alone with covariates.
23
seen in isolation rather than in simultaneous effects. Of the types of discrimination coded by
Minorities at Risk, it is economic discrimination that is the strong and consistent precipitant of
terrorist activity.
Substantive Effects
Table 8 reports the substantive effects of discrimination on terrorism.
(insert Table 8 about here)
These are produced using Monte Carlo simulations of the expected effects of first-difference
changes in the intensity level of discrimination on terrorist attacks. The patterns revealed in the
simulations are consistent with the main model results and help to elucidate the nature of the
relationship between discrimination and terrorism. First, Table 8 demonstrates that increases in
intensity of discrimination does not bear a uniform effect on amount of terrorism produced
across the types of discrimination. While average one-intensity-level increases in economic and
political discrimination produce higher levels of terrorist attacks, increases in religious and
linguistic discrimination have mixed effects. Indeed, the confidence interval / error estimates for
terrorist attacks produced by increasing religious and linguistic discrimination dip into the
negative range. This further suggests that these two manifestations of minority discrimination
are not clearly linked to higher propensity for terrorist activity.
Second, Table 8 clearly demonstrates that between political and economic discrimination
against minorities, it is the former that is the more substantive driver of terrorism. An average
one-level-increase in the intensity of political discrimination suffered by minorities produces, in
the simulations, just .6 more attacks while a similar increase of economic discrimination
produces nearly one and a half more incidents of terrorism. Looking at the upper ranges of the
24
confidence intervals for the simulations, economic discrimination produces more than double the
amount of terrorist attacks than does political discrimination against minorities.
Conclusion
The overall findings of this study that discrimination against minorities in countries is
positively associated with higher levels of terrorist attacks, but that this relationship is confined
to and most evident in economic, and to a lesser degree political, discrimination rather than
religious and linguistic discrimination, are highly preliminary and they recommend further
investigation. In particular, while the study shows that countries featuring discrimination,
specifically economic discrimination, against minority groups are more likely to produce and
sustain terrorist attacks, they do not explain the mechanisms of the relationship between
discrimination and terrorism. They, therefore, do not shed light on which component of the
theoretical argument prevalent in the literature – alienation and social exclusion, construction of
grievances, opportunities to mobilize, etc. – is the empirically substantiated explanation linking
discrimination to terrorism. One of the key problems is that the measurements used in the
analysis are still over-aggregated. Future studies that are able to “drill-down” to the subnational
group or individual levels might be better able to establish a more satisfactory explanation of
how the experience of generalized or economic discrimination propels individuals to join
terrorist groups or support terrorism.
Despite this, the results of the study are striking given the direction that the “root causes”
of terrorism literature has taken after the September 11th
2001 terrorist attacks in the United
States. Generally speaking, as scholars have failed to establish consistent and unambiguous
statistical links between democratic rule, poverty and socioeconomic inequality and terrorism,
indicators of individual’s economic statuses have taken a back seat to religion, cultural identity,
25
as potential predictors of terrorism. (See Moore 2008 for a brief survey of these trends) The
results of this study suggest that a reconsideration of more nuanced or targeted measurements of
political opportunities available to all segments of society and economic status or inequality as
root causes of terrorism are in order. This recommendation is consistent with qualitative
research on root causes of terrorism conducted by scholars like Von Hippel (2009) who argue
that quantitative studies that fail to find a link between economic conditions and terrorism have
cast too narrow a net and have not fully examined the often indirect process by which economic
deprivation leads to radicalization and the creation of a lucrative pool of recruits for terrorist
movements in places like Pakistan and Afghanistan.
Finally, as noted by Rustad et al. (2011) and Young and Findley (2011), cross-national
analysis using highly aggregated measurements of country features are the norm in the current
generation – 2001 to present – of empirical studies investigating the root causes of terrorism.
Young and Findley argue that this methodological tendency is really more of a product of data
convenience, as much of the statistical data used in the earlier conflict literature relied on
aggregate measurements denominated in country-year format, rather than growing out of a
serious consideration of whether or not root causes of terrorism may register at the national level
or not. This study suggests that the next generation of quantitative terrorism studies should
differentiate the effects of features of marginal actors within society on patterns of terrorism
rather than the mean or modal actor, which is more likely to be accurately captured in aggregate,
national statistics.
26
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Table 1. Variables, Operationalization and Sources
Variable Operationalization Source
Incidents of Terrorism (GTD)
Number of incidents of domestic and transnational terrorism
occurring in a country in a given year.
Global Terrorism Database, National Consortium for
the Study of Terrorism and Responses to Terrorism
(START). Retrieved from:
http://www.start.umd.edu/gtd/ , July 2009
Minority Group Facing
Discrimination
Dummy variable coded “1” for all country years in which a
minority at risk group is present and it faces some level of
discrimination. (Where “POLDIS” or “ECDIS” or
“CULPO1” or “CULPO2” are greater than 1.)
Minorities at Risk Project (2009). “Minorities at Risk
Database.” College Park, MD: Center for International
Development and Conflict Management. Retrieved
from http://www.cidcm.umd.edu/mar on June 8, 2009.
Political Discrimination Against
Minorities
Transformation of “POLDIS Political Discrimination Index”
into an ordinal measure coded:
0 = No Minorities at Risk present in country
1 = Minorities at Risk in country either currently experience
no discrimination or benefit from remediation policies for
legacy of discrimination
2 = Minorities at Risk in country suffer from informal
discrimination with no remedial policies
3 = Minorities at Risk in country suffer from informal
discrimination and social exclusion with no remedial
policies
4 = Government adopts repressive discriminatory policies
against Minorities at Risk groups.
Ibid.
Economic Discrimination
Against Minorities
Transformation of “ECDIS Economic Discrimination Index”
into an ordinal measure coded:
0 = No Minorities at Risk present in country
1 = Minorities at Risk in country either currently experience
no discrimination or benefit from remediation policies for
legacy of discrimination
2 = Minorities at Risk in country suffer from informal
discrimination with no remedial policies
3 = Minorities at Risk in country suffer from informal
discrimination and social exclusion with no remedial
policies
4 = Government adopts repressive discriminatory policies
Ibid.
31
against Minorities at Risk groups.
Religious Discrimination
Against Minorities
Transformation of “CULPO1 Restrictions on Religion
Index” into an ordinal measure coded:
0 = No Minorities at Risk present in country
1 = Minorities at Risk in country experience no religious
discrimination
2 = Practitioners of minority religions suffer from
widespread but informal discrimination
3 = Minority religious activity somewhat restricted
4 = Minority religious activity sharply restricted
Ibid.
Linguistic Discrimination
Against Minorities
Transformation of “CULPO2 Restrictions on Use of
Language or Language Instruction Index” into an ordinal
measure coded:
0 = No Minorities at Risk present in country
1 = Minorities at Risk in country experience no linguistic
discrimination
2 = Minority language speakers suffer from widespread but
informal discrimination
3 = Minority use of language somewhat restricted
4 = Minority use of language sharply restricted
Ibid.
log Gross National Income per
cap
Natural log of gross national income per capita in U.S.
dollars at current prices.
United Nations Statistical Division, “National Accounts
Main Aggregates Database.” 2009. Retrieved from:
http://unstats.un.org/unsd/snaama/dnllist.asp on May
30, 2009.
log Population Natural log of national mid-year population. U.S. Census Bureau “International Database.” 2009.
Retrieved from: http://www.census.gov/ipc/www/idb/
on May 30, 2009.
log Area Natural log of surface area of country. Ibid.
GINI Coefficient GINI Coefficient, measurement of income inequality in
country.
United Nations Development Program (UNDP).
Human Development Report. Various years.
32
Durable “DURABLE” measurement. Number of years current
political regime in country has been in place.
Polity IV Project: Political Regime Characteristics and
Transitions, 1800-2008. (Marshall and Jaggers 2009)
“Polity IV Data Series v.2007.” 2009. Retrieved from:
http://www.systemicpeace.org/polity/polity4.htm on
May 30, 2009
Executive Constraints (Polity
IV)
Average of XRCOMP (Competitiveness of Executive
Recruitment), XROPEN (Openness of Executive
Recruitment), XCONST (Constraints on Chief Executive)
from Polity IV database.
Ibid.
Political Participation (Polity
IV)
Average of PARREG (Regulation of Political Participation)
and PARCOMP (Competitiveness of Political Participation)
from Polity IV database.
Ibid.
Physical Integrity Rights
Protections
“PHYSINT” Physical Integrity Rights Index. Additive
index constructed from Torture, Extrajudicial Killings,
Political Imprisonment and Disappearance indicators
ranging from 0, no government respect, to 8, full
government respect.
CIRI Human Rights Data Project. (Cingranelli and
Richards 2008). Retrieved from
http://ciri.binghamton.edu/ on July 20, 2009.
33
Table 2. Recoding Scheme for Minority Discrimination Variables
Original MAR Indicator Recoded Discrimination Variable
POLDIS, Political Discrimination Index
ECDIS, Economic Discrimination Index
Political Discrimination Against Minorities
Economic Discrimination Against Minorities
= 0 No Minority Group Present
= 0 No Discrimination = 1 Minority Group Present, No Discrimination
= 1 Legacy of Discrimination, Remediation Policy = 1 Minority Group Present, Legacy and Remediation
= 2 Neglect with No Remediation Policy = 2 Minority Group Present, Neglect with No Remediation
= 3 Social Exclusion = 3 Minority Group Present, Social Exclusion
= 4 Repression = 4 Minority Group Present, Repression
CULPO1, Restrictions on Religion
CULPO2, Restrictions on Language
Religious Discrimination Against Minorities
Linguistic Discrimination Against Minorities
= 0 No Minority Group Present
= 0 No Restrictions = 1 Minority Group Present, No Restrictions
= 1 Activity Informally Restricted = 2 Minority Group Present, Activity Informally Restricted
= 2 Activity Somewhat Restricted = 3 Minority Group Present, Activity Somewhat Restricted
= 3 Activity Sharply Restricted = 4 Minority Group Present, Activity Sharply Restricted
34
Table 3. Correlation Coefficients for Types of Minority Discrimination
Political Discrimination Economic Discrimination Religious Discrimination Linguistic Discrimination
Political Discrimination .690 .264 .294
Economic Discrimination .690 .225 .275
Religious Discrimination .264 .225 .223
Linguistic Discrimination .294 .275 .223
n 2,495 2,495 2,495 2,495
Pearson’s r tests, one-tailed.
35
Table 4. Summary Statistics
Variable Obs. Mean St. Deviation Min Max
Terrorist Incidents (GTD) 5,761 12.2 46.6 0 817
Minority Group Facing Discrimination 2,666 .56 .49 0 1
Political Discrimination Against Minorities 3,299 1.79 1.60 0 4
Economic Discrimination Against Minorities 3,309 1.66 1.49 0 4
Religious Discrimination Against Minorities 2,669 .91 .94 0 4
Linguistic Discrimination Against Minorities 2,666 1.02 1.03 0 4
Log Gross National Income per cap 3,282 7.5 1.6 3.7 14.1
Log Population 3,282 1.9 1.7 -2.8 7.1
Log Area 3,310 11.7 2.2 5.7 16.6
GINI Coefficient 5,813 43.4 8.9 17.8 84.8
Durable 5,808 21.9 27.4 0 197
Political Participation (Polity IV) 5,701 3.2 .9 .5 5.0
Executive Constraints (Polity IV) 5,813 3.4 1.5 .5 5.0
Physical Integrity Rights Protections 3,837 4.8 2.3 0 8
Cold War 6,364 .57 .49 0 1
36
Table 5. Types of Discrimination and Incidents of Terrorism, 1991 to 2006
model 1 2 3 4 5 6
Minority Group Facing Discrimination .486 (.142)**
Political Discrim. vs. Minorities .115 (.046)* .048 (.090)
Economic Discrim. vs. Minorities .148 (.051)** .209 (.091)*
Religious Discrim. vs. Minorities .036 (.092) -.144 (.107)
Linguistic Discrim. vs. Minorities .079 (.080) -.075 (.096)
log Gross National Income per cap .340 (.068)*** .345 (.068)*** .345 (.068)*** .305 (.075)*** .301 (.076)*** .273 (.071)***
log Population .518 (.070)*** .528 (.073)*** .529 (.074)*** .548 (.078)*** .549 (.078)*** .536 (.083)***
log Area -.083 (.052) -.072 (.051) -.074 (.049) -.073 (.053) -.082 (.054) -.069 (.053)
GINI Coefficient .016 (.009) .020 (.009)* .019 (.009)* .019 (.010) .018 (.010) .012 (.010)
Durable -.008 (.002)*** -.006 (.002)** -.007 (.002)** -.006 (.002)* -.005 (.002)* -.005 (.002)*
Executive Constraints (Polity IV) .008 (.057) -.011 (.058) -.016 (.058) -.014 (.058) -.016 (.058) -.048 (.059)
Political Participation (Polity IV) -.200 (.070)** -.220 (.075)** -.237 (.072)** -.259 (.085)** -.268 (.082)** -.290 (.080)***
Physical Integrity Rights Index (CIRI) -.277 (.041)*** -.280 (.045)*** -.268 (.041)*** -.277 (.042)*** -.274 (.042)*** -.239 (.042)***
Constant .287 (.803) .159 (.796) .229 (.770) .707 (.910) .830 (.895) 1.047 (.889)
n 2,406 2,386 2,387 1,993 1,990 1,990
Wald χ2 305.37*** 300.01*** 305.36*** 239.82*** 240.85*** 248.36***
n. Countries (clusters) 166 166 166 166 166 166
Dependent variable: Country-year counts of terrorist incidents (GTD). All models negative binomial regression estimations. Robust, country-clustered standard errors in
parentheses. *p ≤ .05, **p ≤ .01, ***p ≤ .001, one-tailed tests.
37
Table 6. Summary of Robustness Specifications
Variable:
Specification Minority Group
Facing
Discrimination
Minority
Political
Discrimination
Minority
Economic
Discrimination
Minority
Religious
Discrimination
Minority
Linguistic
Discrimination
Zero-Inflated Negative Binomial Model1 +++
2 n/s +++ n/s n/s
Rare Events Logit Model +++ ++ ++ n/s n/s
Country and Year Fixed Effects NBREG Model n/s ++ ++ n/s n/s
NBREG Dichotomized MAR Discrimination Variables3 n/s + n/s n/s
NBREG with Lagged Terrorist Attacks + n/s ++ n/s n/s
NBREG using Enders et al. (2011) Domestic-only Attacks +++ n/s +++ n/s n/s
NBREG including Legacy of Separatism (SEPX) +++ n/s +++ n/s n/s
NBREG with Count Variable for no. of MAR Groups +++ n/s ++ n/s n/s
+++ indicates significant and positive at .000 level; ++ indicates significant and positive at .01 level; + indicates significant and positive at .05 level; “n/s” indicates no significant
relationship found.
1 Inflated logit equation includes regime-type indicator, Executive Constraints, as the theoretical predictor of “certain zero” observations, following the assumptions of Drakos and
Gofas (2006) that certain zero countries are those with state-controlled media. Note that Vuong tests do not indicate that a zero-inflated negative model is a more efficient model. 2 Significant across all model specifications (isolated and combined models). 3 All ordinal MAR variables truncated down to dichotomized variables where values 0,1 = 0 and values 2,3,4 = 1.
38
Table 7. Coefficients Simultaneous Effects Negative Binomial Models (Summary)
model
7
8
9
10
11
12
13
14
15
16
Political and Economic Discrim. .283 (.174)
Political and Religious Discrim. -.051 (.301)
Political and Linguistic Discrim. -.431 (.260) Economic and Religious Discrim. .026 (.337)
Economic and Linguistic Discrim. -.470 (.284)
Religious and Linguistic Discrim. -.115 (.482) Econ., Pol., and Rel. Discrim. .034 (.350)
Econ., Pol., and Ling. Discrim. -.463 (.289)
Pol., Rel., and Ling. Discrim. -.546 (.525) Econ., Pol., Rel. and Ling. Discrim. -.510 (.531)
n 2,614 2,111 2,108 2,111 2,108 2,108 2,108 2,108 2,111 2,111 Wald χ2 309.83*** 242.82*** 245.43*** 244.56*** 244.79*** 242.09*** 243.94*** 244.79*** 245.44*** 245.18***
No. of Countries 167 166 166 166 166 166 166 166 166 166
Dependent variable: Country-year counts of terrorist incidents (GTD). All models negative binomial regression estimations. Results for covariates (log Gross National Income per cap.; log Population;
log Area; GINI; Durable; Executive Constraints; Political Participation; Physical Integrity Rights; Cold War Dummy) are not reported for simplicity. Robust, country-clustered standard errors in
parentheses. *p ≤ .05, **p ≤ .01, ***p ≤ .001, one-tailed tests.
39
Table 8. Substantive Effects of Types of Discrimination on Terrorist Attacks
Unit Change Predicted
Terrorist Attacks
[95% Confidence
Interval]
Minority Political Discrimination 0-1-2-3-4 .623 [.463 — .925]
Minority Economic Discrimination 0-1-2-3-4 1.401 [.867 — 1.972]
Minority Religious Discrimination 0-1-2-3-4 .469 [-.366 — 1.555]
Minority Linguistic Discrimination 0-1-2-3-4 .067 [-.111 — 1.670]
Monte Carlo simulations of first-difference expected values using Clarify software package (Tomz et al. 2003)
