International Studies Perspectives (2007) 8, 287–302.
Applying Analytical Methods to Study
Terrorism*
Todd Sandler
University of Texas at Dallas
Walter Enders
University of Alabama
This paper presents a perspective on the application of theoretical and
empirical methods to the study of domestic and transnational terrorism. The use of such methods can lead to informed policy making. On
the theoretical side, both choice-theoretic and game-theoretic methods
are examined. For empirical applications, the paper focuses on the
study of trend, cycles, and forecasting. Additionally, the use of intervention analysis in various forms is reviewed with to regards to evaluating
policy effectiveness and quantifying the economic impact of terrorism.
Although this paper is not intended as a literature review, some key
studies are highlighted for readers to pursue in greater depth.
Keywords: terrorism, game theory, intervention analysis, forecasting, policy effectiveness
The four hijackings on September 11, 2001 (henceforth, 9 ⁄ 11), was a wake up
call to the world, which had viewed terrorism as an annoyance in a globalized
world. The unprecedented 9 ⁄ 11 incidents resulted in a death toll greater
than the total number killed from all transnational terrorist attacks (incidents
impacting more than one nation) during the prior decade when 2,695
people perished.1 Moreover, this single incident resulted in losses estimated in the
$80–100 billion range (Kunreuther and Michel-Kerjan 2004). Even beyond these
losses, at-risk countries lost essential freedoms as civil liberties were sacrificed for
enhanced security. This loss of freedoms is underscored by the current restrictions on liquids, creams, and gels in carry on luggage following British authorities stopping an alleged plot in August 2006 to blow up trans-Atlantic U.S.-bound
passenger planes with improvised bombs. In the United States, tens of billions of
dollars are now spent on homeland security to protect against terrorist threats
1
This figure comes from Figure 5 in Sandler and Enders (2004:303), which is based on U.S. Department of
State data published in annual reports entitled, Patterns of Global Terrorism. The National Counterterrorism Center’s
(NCTC) ‘‘Report on Incidents of Terrorism 2005’’ is not a consistent replacement for Patterns of Global Terrorism,
insofar as NCTC inflates the number of events by including many domestic events. By including domestic events
worldwide, NCTC reduces the proportion of fundamentalist-based terrorist attacks.
*
Sandler’s research was partially supported by the U.S. Department of Homeland Security (DHS) through the
Center for Risk and Economic Analysis of Terrorism Events (CREATE) at the University of Southern California,
grant number N00014-05-0630. However, any opinions, findings, and conclusions or recommendations are solely
those of the authors and do not necessarily reflect the views of the DHS. We have profited from the comments of
three reviewers.
2007 International Studies Association.
Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road, Oxford OX4 2DQ , UK
288
Applying Analytical Methods to Study Terrorism
that now include biological, chemical, and radiological agents. The DHS budget
for 2006 is approximately $41 billion, of which 61% guards against terrorism on
U.S. soil (Enders and Sandler 2006:231–235). This enhanced expenditure
on homeland security does not include the tens of billions of dollars spent on
terrorism-related military operations. Antiterrorism actions redirect government
funds away from social welfare, education, highways, and scientific research. On
9 ⁄ 11, a traumatized public began to appreciate the risks posed by today’s fundamentalist-based terrorism. Subsequent attacks at a Bali nightclub on October 12,
2002, against Madrid commuter trains on March 11, 2004, and on the London
transport system on July 7, 2005, underscored the continued threat of terrorism.
With the creation of DHS, the Science and Technology directorate funded
Centers of Excellence for the study of terrorism at the University of Southern
California, Texas A & M University, the University of Minnesota, the University
of Maryland, and elsewhere. In part, these centers apply various theoretical and
empirical techniques to the study of terrorism. The use of analytical techniques
dates back to a study by Landes (1978) that measured the deterrent effects of
airport metal detectors (introduced in January 1973), air marshals, and prison
sentences for skyjackings. Well before 9 ⁄ 11, numerous studies used analytical
techniques as a way of predicting terrorist behavior and improving governments’
responses.2 DHS Centers of Excellence need to tap into these earlier studies.
Terrorism is a powerful weapon that exploits crucial asymmetries between governments and terrorists to governments’ disadvantage and terrorists’ advantage.
The purpose of this article is to provide a perspective for international studies’
students, researchers, and practitioners on how analytical methods—both empirical and theoretical—can inform policy makers and enlighten governments
about the challenges that terrorism poses to a globalized society, where borders
are porous. Counterterrorism actions at home have far-reaching implications, as
augmented fortifications can displace attacks to foreign venues, while foreign
countermeasures can shift an attack to home territory.
What Is Terrorism?
Terrorism is the premeditated use or threat to use violence by individuals or subnational groups against noncombatants to obtain political or social objectives
through the intimidation of a large audience, beyond that of the immediate victims. In this definition, two essential ingredients are violence and the political ⁄ social motive; violent acts without such motives are merely criminal. Much has
been written on the definition of terrorism, with the debate centering on the identity of the victim, perpetrator, and audience (Hoffman 1998; Wilkinson 2001). For
example, some definitions (U.S. Department of State) exclude attacks against an
occupying army as terrorism, while others (U.S. Department of Defense) do not.
Our definition is the nearest to that of the U.S. Department of State, whose data
are only for transnational attacks (see below). Alternative definitions influence the
number of events and, hence, the need for policy makers to allocate resources to
counterterrorism. By making their acts appear random and disperse, terrorists
seek to cause anxiety to the widest possible audience. These acts are not random,
but are aimed at exploiting the targeted society’s least defended venues—that is,
protective measures for government officials made the general public a more
attractive target. Terrorists succeed when the targeted audience pressures its policy
2
Early empirical studies include Brophy-Baermann and Conybeare (1994), Enders and Sandler (1993), Enders,
Sandler, and Cauley (1990), Im, Cauley, and Sandler (1987), Nelson and Scott (1992), and Poe (1988), while early
theoretical studies include Islam and Shahin (1989), Lapan and Sandler (1988, 1993), Lee (1988), Overgaard
(1994), Sandler and Lapan (1988), Sandler, Tschirhart, and Cauley (1983), and Selten (1988).
Todd Sandler and Walter Enders
289
makers to concede to terrorist demands and they cave in to this pressure, because
the cost of holding firm becomes greater than that of conceding.
Terrorism is further subdivided into domestic and transnational. Domestic
terrorism is homegrown and has consequences for just the host country, its institutions, citizens, property, and policies. In contrast, a transnational terrorist
event, such as 9 ⁄ 11, involves perpetrators, victims, institutions, governments, or
citizens from at least two countries. Attacks that kill foreign visitors or include
terrorists from abroad are transnational. Additionally, the kidnapping of a foreign journalist in Baghdad for political demands (e.g., releasing all women prisoners) is a transnational terrorist incident. Although domestic incidents
outnumber transnational incidents almost eight to one,3 the latter poses the
greatest risks to the developed world, whose assets (people and property) are
vulnerable worldwide. In recent years, relatively few domestic attacks have
occurred in developed countries (except for Israel); most domestic attacks have
taken place in conflict-ridden developing countries. Globalization has, however,
blurred the distinction between domestic and transnational terrorist events,
because some homegrown incidents may have international ramifications. For
instance, long-term domestic terrorist campaigns may destabilize neighboring
countries, resulting in transnational implications.
Methods Used
Appropriate theoretical methods include game theory in which strategic behavior among rational players is assumed that allows a player to anticipate the
response of others to its own actions.4 Each player tries to outguess the other
players’ behavior by imagining how he or she would respond when in the other
players’ shoes. Thus, a government that installs metal detectors in airports
should not be surprised when terrorists respond by abducting hostages at other
venues. Games are played between terrorists and a government, among targeted
governments, among terrorist groups, or among factions within terrorist groups.
Economists and political scientists who model terrorists as rational players judge
their rationality based on an appropriate (predictable) response to changes in
their constraints as they seek objectives. Researchers do not brand terrorists as
irrational because their goals or techniques are repugnant to most people. Moreover, engaging in risky, even deadly, activities is not indicative of irrationality, as
firefighters and ordinary people assume such risks daily (e.g., driving to work).
Game theory is appropriate because it captures the strategic interplay among
adversaries and allies, characteristic of terrorist campaigns. Moreover, game theory
allows adversaries to issue threats and promises for strategic advantage—for example, the issuing of a never-to-negotiate pledge by governments to discourage hostage taking. Game theory also incorporates uncertainty and learning relevant
when, for instance, a government is uninformed about the terrorists’ true strength
and must update its beliefs based on terrorists’ past actions. Additionally, game
theory includes bargaining behavior, germane to terrorist negotiation scenarios.
As a weak adversary, terrorists must behave strategically to be a formidable
threat against a vastly stronger government opponent. Terrorists exploit many strategic asymmetries to obtain an advantage. For example, they gain a second-mover
advantage by identifying soft targets after the government has allocated a limited
3
This statement is based on comparing data for domestic and transnational terrorist incidents as reported in
the National Memorial Institute for the Prevention of Terrorism (2006) website at http://www.mipt.org.
4
Sandler and Arce (2007) provide an up-to-date survey of game-theoretic papers on terrorism. There is
currently a lot of interest in applying game theory to the study of terrorism with recent contributions by Arce and
Sandler (2007), Bueno de Mesquita (2005), Heal and Kunreuther (2005), and Siqueira (2005).
290
Applying Analytical Methods to Study Terrorism
defensive budget among alternative potential targets. By always identifying a weakness or vulnerable target, terrorists can force governments to spend ever-greater
amounts on defense, thereby being a costly nuisance. Nations are target-rich; terrorists are target-poor. The latter is heightened by locating operatives (i.e., sleeper
cells) among the general population where governments must be restrained in
their actions. Terrorists overcome collective action barriers and form networks.
Terrorist groups’ weakness gives them little choice but to join forces, while leaders’ lifetime tenure means that they view their interactions with other leaders as
infinitely repeated games. As such, they are able to overcome prisoner’s dilemmas
and other collective action concerns. In contrast, governments’ perceived strength
and limited office periods hamper their ability to cooperate. The withdrawal of
Spanish forces from Iraq and Afghanistan following the Madrid train bombings
and the election of the socialist Zapatero government in 2004 is a case in point.
Other theoretical methods include choice-theoretic models where an agent is
viewed as maximizing some objective subject to a constraint. For instance, policy
makers allocate a fixed counterterrorism budget among alternative terrorismthwarting activities to achieve the greatest reduction in terrorism. Another
instance concerns how a terrorist group allocates its resources among various
attack modes, each with its own risks and costs. In doing so, terrorists must balance net expected benefits at the margin. A wide range of empirical tools can
be applied to test theoretical predictions and to forecast terrorism patterns.
These analytical tools have investigated the effectiveness of counterterrorism
policies (e.g., metal detectors and U.N. conventions). Policy choices between
preemptive and defensive action have also been studied. Lapan and Sandler
(1988) applied game theory to show the pitfalls of implementing a never-tonegotiate policy whose effectiveness hinges on unstated assumptions (e.g., the
value of a future hostage is not too high or the government’s pledge is believed)
that do not hold in practice.
Data and Patterns
Much of the empirical work on terrorism has relied on events data that draw
information from the media. Information on each terrorist event—for example,
the number of terrorists, the type of event, number of deaths, and venue—are
coded for researchers. The most used data set is International Terrorism: Attributes of
Terrorist Events (ITERATE), which was originally devised by Mickolus (1982) and
later updated by Mickolus, Sandler, Murdock, and Flemming (2006). An overlap
of coders has maintained coding consistency for ITERATE, which contains information on about 15,000 transnational terrorist incidents from 1968 to 2005. ITERATE relies on a host of sources, including the Associated Press, United Press
International, Reuter tickers, New York Times, Washington Post, the Foreign Broadcast
Information Service (FBIS) Daily Reports, ABC, NBC, and CBS evening news. Up
through 1996, the regional FBIS Daily Reports have been invaluable: these reports
draw from hundreds of world print and electronic media services and are the
most comprehensive source for foreign coverage of terrorist incidents. The
biggest drawback of ITERATE is that it only records transnational terrorist events.
Another data set is the National Memorial Institute for the Prevention of
Terrorism (2006), which was jointly gathered by RAND and researchers at
St. Andrews University, Scotland. Up until 1997, National Memorial Institute for
the Prevention of Terrorism (MIPT) only recorded transnational terrorist incidents. Beginning in 1998, it includes domestic and transnational terrorist incidents (http://www.mipt.org). A third data set for transnational terrorist events
had been maintained by the U.S. Department of State and reported in Patterns
of Global Terrorism through 2004 when the Bush administration abolished this
Congress-mandated report. Time series plots of these data sets are quite similar
Todd Sandler and Walter Enders
291
(Enders 2007) when inclusion of terrorist events are made homogeneous—
for example, leaving out domestic incidents for MIPT. A fourth terrorism data
set—Terrorism in Western Europe: Events Data (TWEED)—concerns ‘‘internal’’ terrorist events in 18 Western European countries for 1950–2004 (Engene 2004).
This data set excludes transnational terrorists incidents if the terrorist came
from outside of Western Europe—for example, spillover terrorism from the Middle East, such as the Madrid train bombings. The data include some transnational events where, say, Irish terrorists engage in a terrorist attack in Spain;
however, the overwhelming majority of incidents in TWEED are domestic. This
data can be downloaded at http://www.uib.no/people/sspje/tweed.htm and are
useful for investigating the impact of European terrorism on tourism, foreign
direct investment, and local economies.
Based on ITERATE data, Figure 1 displays quarterly totals for all transnational
incidents and bombings for the 1968–2005 period. Transnational terrorist events
display peaks and troughs, suggestive of cycles. Bombings are terrorists’ favorite
types of attack, accounting for about half of all transnational terrorist incidents.
In addition, the bombings time series tracks the all-incident series rather well
and generally imparts its pattern to that of the overall series. From the early
1990s to about 2002, there is a downward trend to both series due to fewer states
sponsoring terrorism in the post–Cold War era (Hoffman 1998). The fall of
Communist regimes also meant that Leftist groups experienced trouble in
attracting supporters and adherents, which eventually resulted in the demise of
some groups—for example, Red Army Faction and April 19. Efficient police
operations ended other Leftist groups—Italian Red Brigades, Combatant Communist Cells, and 17 November (Alexander and Pluchinsky 1992; Hoffman
1998). Other long-standing terrorist campaigns—in Northern Ireland—cooled
down during this period. An upturn occurs in 2002 about the time that the United States launched its ‘‘war on terror.’’ A new downturn in transnational terrorism takes place in 2005; ironically, this downturn has not been publicized
because Patterns of Global Terrorism is no longer published. A display of the quarterly time series for assassinations and hostage-taking events (e.g., skyjackings
and kidnappings) for 1968–2005 would also show cycles. The quarterly totals for
assassinations and hostage events are smaller compared with bombings. This is
consistent with terrorists, as rational actors, responding to risk and engaging less
frequently in more dangerous and logistically complex attacks.
350
All
Bombings
Incidents per quarter
300
250
200
150
100
50
0
1968 1970 1973 1975 1978 1980 1983 1985 1988 1990 1993 1995 1998 2000 2003 2005
FIG. 1. All Incidents and Bombings.
292
Applying Analytical Methods to Study Terrorism
1
0.9
0.8
Proportion of total
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1968
1970
1973
1975
1978
1980
1983
1985
1988
1990
1993
1995
1998
2000
2003
2005
FIG. 2. Proportion of Casualty Incidents.
Until the start of the 1990s, Left-wing terrorist organizations that wanted to
win the hearts and minds of the people were the dominant influence. Such
terrorists tried to avoid casualties, except for individuals characterizing the establishment or the ‘‘enemy.’’ Beginning in 1979, Left-wing and secular terrorist
groups began to be replaced by religious fundamentalist groups. The number of
such fundamentalist groups increased as a proportion of active groups: 2 of 64
groups in 1980; 11 of 48 groups in 1992; 16 of 49 groups in 1994; and 25 of 58
in 1995 (Hoffman 1998). Rapoport (2004) calls the dominance of fundamentalist terrorists in recent years as the ‘‘Fourth Wave.’’ With the rise of al-Qaeda and
other fundamentalist terror groups, terrorists purposely sought out greater casualties, viewing anyone not sharing their beliefs as a legitimate target, as 9 ⁄ 11
underscored. In a statistical analysis, Enders and Sandler (2000) established that
a significant rise in casualties from transnational terrorism can be traced back to
the takeover of the U.S. embassy in Tehran and the Soviet invasion of Afghanistan in the last quarter of 1979, which marked the start of fundamentalist terrorism.5 In Figure 2, we display the quarterly proportion of transnational terrorism
incidents with casualties (i.e., injuries or deaths) for 1968–2005. The fundamentalist impact is unmistakable as the proportion of casualty incidents trends
upward from the 1990s once the fundamentalist terrorists became the dominant
influence (Rapoport 2004). From 2002 on, the drift is upward after a brief
downturn following 9 ⁄ 11. Today’s terrorists mean business—incidents with casualties almost always now involve deaths.
Forecasting Terrorism
The key ingredient in forecasting is to relate statistically the current number of
terrorist incidents to their past values, time, and potential shocks or interventions (events such as a policy change or the rise in fundamentalism). There
are some important forecasting insights. First, observed patterns in the time
series can be used for forecasting purposes. Second, short-run forecasts are more
5
Enders and Sandler (2000) time-series test supported Hoffman’s (1998) informed hypothesis that the fundamentalists changed the nature of terrorism in late 1979. A test for structural changes at quarters on either side of
1979 pinpointed the maximum alteration at the fourth quarter of 1979.
Todd Sandler and Walter Enders
293
accurate than long-run forecasts—for example, it is easier to forecast the weather tomorrow than to forecast it 2 weeks or a year hence. Because a time series
of terrorist events that relates today’s incidents to past incidents and other influences is not completely regular, the cumulated errors mean that long-term forecasts will be associated with rather large errors. Third, a time series of terrorist
incidents can be forecast without knowing precisely why the numbers of incidents change in a particular regular pattern. Fourth, the ability to forecast patterns of, say, skyjackings does not mean that one can predict a particular
catastrophic event such as 9 ⁄ 11. Enders and Sandler’s (2000) forecast in 2000
cautioned about the rising severity of transnational terrorism, but did not foresee 9 ⁄ 11. Only intelligence or infiltrating a terrorist group can do that.
A typical time-series model, given by equation (1) for skyjackings (SKY), might
have the following functional form:
SKY t ¼ a0 þ a1 t þ b1 SKY t1 þ b2 SKY t2 þ et
ð1Þ
where SKYt is the number of skyjackings in period t ; a0 + a1t denotes a linear
trend; b1SKYt)1 + b2SKYt)2 represents the short-run dynamics based on the
number of skyjackings in the two previous periods; and et stands for an error
term. Every time series of terrorist events can be broken down into at least
three primary ingredients: trend, cyclical components, and noise. Trend refers
to long-run movements in a time series that can be predicted far into the
future. The standard technique for estimating trend is to fit a polynomial
involving time (t)—i.e., t + t2 + …—to describe the current value of incidents.
Time terms are added until they are no longer statistically significant. If, for
example, the only significant time term is t, then the event series possesses a
linear trend as in equation (1) indicating that it either rises or declines at a
constant rate over time. If, instead, a quadratic time term is significant, then
the trend is parabolic representing a hill or a valley. Although most commentators and experts describe terrorism trend in linear terms, past research
shows that no terrorist time series shows linear trend; rather, time series display parabolic (hill or valley shaped), or more complex patterns (Sandler and
Enders 2004:306).
Any series will temporarily diverge from its long-run trend. This can be seen
in Figure 1, shown earlier, where the all-incident series displays a positive jump
at the end of 1998 and appears to depart from its trend for several quarters.
Such departures are part of the short-run dynamics of the series, known as its
irregular or cyclical component. If the nature of these short-run movements is
known, the observed discrepancies from trend facilitate forecasting. Cycles in
terrorism can be attributed to various factors that result in the bunching of
incidents on a regular basis. A successful event can induce others to copy the
attack’s strategy until the authorities devise the means and acquire the resources
for effective countermeasures. As new antiterrorism measures block more
attacks, terrorists hold off until they develop ways to circumvent these measures—for example, metal detectors induced terrorists to use ground crews to
plant guns on planes. This cat-and-mouse game can induce cycles. Enders and
Sandler (2006) argued that each kind of attack mode has its own characteristic
cycle, where logistically complex modes (e.g., skyjacking, kidnapping, and assassination) have longer cycles than simpler events (e.g., threat) as the cat-andmouse game takes longer to play out.
To test this conjecture, Enders and Sandler (2006:72) applied spectral analysis, which fits sine and cosine terms to the detrended time series for various
types of transnational terrorist events. They found that threats had a primary
cycle of just under a year, while incidents with deaths had a primary cycle of
almost 10 years. Hostage events had a primary cycle of seven and a half years,
and assassinations had a primary cycle of 4 years. Moreover, the length of cycles
294
Applying Analytical Methods to Study Terrorism
associated with various types of attack modes generally increased with logistical
complexity. A knowledge of these cycles allows officials to know when to augment defenses, say, against skyjackings after a lull. In essence, authorities would
have the means to allocate resources more efficiently by raising them during
anticipated peaks and reducing them during expected troughs. As cycles among
types of attacks are often out of sync, counterterrorist resources can be allocated
to thwart various events with a minimal outlay.
Finally, the noise component reflects the portion of the time series that cannot be predicted. But even this component can guide forecasting. Enders and
Sandler (1999) showed that the noncasualties terrorism series is white noise with
no deterministic information or predictive value. By purging these incidents
which include threats and nuisance bombings, forecasting improves with the
residual casualty time series. This insight improves forecasting and can guide
countermeasure resource allocations over time.
Counterterrorism Effectiveness
Intervention analysis is a statistical technique that indicates whether an abrupt
change in the pattern of time series is due to a particular policy or to an outside force. In essence, this analysis relates the current value of a series
(e.g., today’s skyjackings) to its lagged values and to intervention variables. The
latter can capture not only the magnitude and significance of a policy’s impact,
but also its temporal nature—for example, was its effectiveness immediate and
ephemeral or gradual and enduring. In particular, intervention variables are
added to equation (1) that reflect either an ephemeral impact—say, lasting one
period following the policy action—or a continuous impact. In the latter case,
the impact is felt in all periods after the action or event. Other temporal patterns for the intervention are possible. In January 1973, the introduction of
metal detectors in the United States had an immediate and enduring effect of
decreasing the number of U.S. hijackings by 5.62 attacks per quarter (Enders
et al. 1990). Transnational skyjackings decreased from three incidents per quarter to just over one per quarter following the installation of metal detectors.
Moreover, these detectors’ long-run effectiveness exceeded their short-run
effectiveness. Unfortunately, metal detectors were also associated with an
increase in terrorist events with casualties as terrorists substituted into more
deadly attacks, an unintended consequence (Enders and Sandler 2006:82).
Intervention investigation also showed that U.N. conventions and resolutions to
outlaw attacks against diplomats, hostage taking, and even bombings had no
impact. This is noteworthy because some terrorist experts view these U.N.
responses as the most effective means for thwarting terrorism (Wilkinson 2001).
Retaliatory raids—for example, the U.S. bombing of Libya on the morning of
April 15, 1986, in retaliation for the La Belle discotheque bombing—had the
unintended consequence of temporarily increasing attacks against U.S. and U.K.
interests, followed by a short-lived decrease as terrorists paused to build
up depleted resources (Enders et al. 1990). A subsequent study by BrophyBaermann and Conybeare (1994) found similar surprising results for Israeli retaliatory raids. Although these reactive raids have no demonstrated ameliorating
effect on terrorism, they do have a political effect by showing the electorate that
the government is lashing back at the terrorists. This political benefit needs to
be modeled in future studies.
In a subsequent work, Enders and Sandler (1993) applied a more sophisticated intervention analysis that accounts for the interdependency among various
terrorist series. This newer technique is vector-autoregression (VAR) intervention
analysis. Because terrorists will react to barriers, such as metal detectors, by
switching their mode of attack, a proper evaluation of the effectiveness of these
Todd Sandler and Walter Enders
295
detectors requires ascertaining the effects of metal detectors on related modes
of attacks—for example, attacks against protected persons (including diplomats),
other hostage events (e.g., kidnappings), and other terrorist incidents. This technique also permits a researcher to investigate the impact of more than one intervention—for example, metal detectors in January 1973, embassy fortification in
1976 and 1985, and the Libyan retaliatory raid in 1986.
Figure 3 illustrates the results of this VAR intervention study. The four panels measure the number of incidents per quarter for four types of terrorist
attacks, in which the vertical lines in each panel correspond to the four interventions. The irregular dashed lines denote the actual time paths, while the
solid lines are the estimated time paths that account for the effects of the various interventions. In the figure, there are abrupt changes in the skyjacking,
other hostage-taking and protected-person attacks series with the installation of
metal detectors. Skyjackings dropped precipitously; however, other hostage-taking attacks rose abruptly. This rise greatly limits the true effectiveness of metal
detectors as terrorists substituted to softer targets. With a lag, attacks against
protected persons fell as metal detectors were placed in embassies after their
introduction in airports. Subsequent fortification of embassies in 1976 and
1985 did not have a marked effect on the time series displayed. The VAR-intervention method has been used for alternative time series representations. In
particular, Enders and Sandler (1993) found that securing embassies resulted
in more assassinations and attacks against embassy officials in nonsecure
venues. VAR analysis revealed the unintended consequences of well-intended
policies. By only examining skyjackings, Landes (1978) never identified the
unintended negative impacts of metal detectors and thus overestimated their
benefits.
Economic Impacts of Terrorism
The techniques used to measure policy effectiveness have also been applied with
other methods to calibrate the impact of terrorism on the economy and by sectors (e.g., commercial air travel—see Ito and Lee 2005). Impacts come in two
varieties: direct and indirect costs. Direct costs can be calculated by summing
the replacement costs of damaged goods, equipment, structures, and inventories. In addition, economists have procedures—lost wages or the value of a statistical life—for evaluating the cost of lives lost. Indirect costs are trickier to
measure and include lost commerce, security costs, workman’s compensation,
raised insurance premiums, and other losses. Direct and indirect costs of the
unprecedented 9 ⁄ 11 attacks are estimated to be in the $80–100 billion range for
the United States—a high terrorist payback for an operation that cost less than
half a million dollars.
Past studies have generated some general principles. First, some sensitive
sectors (e.g., transportation, tourism, and foreign direct investment) can be
affected if the terrorists specifically target these sectors. For example, Enders
and Sandler (1996) calculated that two terrorist campaigns during 1979–1981
and 1985–1987 cost Spain $1.8 billion and $3 billion of its foreign direct investment, respectively, as money was redirected to safer countries. Second, the transfer of activities among sectors, based on perceived risk, allows large diversified
economies to withstand terrorism without displaying much overall impact on the
countries’ overall income or consumption. Moreover, these countries are able to
deploy security measures quickly to regain confidence. Third, small countries
can be greatly affected by intense terrorism campaigns. Eckstein and Tsiddon
(2004) applied a VAR model and estimated that terrorism during 2003–2005
cost Israel about 10% of its per-capita income. Similar declines were found
for the Basque Country by Abadie and Gardeazabal (2003). Fourth, with the
296
Applying Analytical Methods to Study Terrorism
Skyjackings
40
35
30
25
20
15
10
5
0
1970
1972
1974
1976 1978 1980
Interventions
1982 1984
Actual
1986
1988
1986
1988
Hostage incidents
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
1970
1972
1974
1976 1978 1980
Interventions
1982 1984
Actual
Protected-person attacks
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988
Interventions
Actual
Other incidents
200
180
160
140
120
100
80
60
40
1970
1972
1974
1976
1978
Interventions
1980
1982
1984
1986
1988
Actual
FIG. 3. Substitutions Between Attack Modes.
exception of 9 ⁄ 11, most significant terrorist incidents were shown to have an
impact of just 1–4 days on stock exchanges by Chen and Siems (2004)—this is
good news for markets. The attacks of 9 ⁄ 11, however, took the world stock
Todd Sandler and Walter Enders
297
exchanges 30–40 days to rebound. Economies that are most vulnerable to terrorism are in less-diversified developing countries, especially when terrorism hits
their main export sectors, such as tourism or shipping (e.g., the bombing of the
USS Cole and the Limburg in Yemen resulted in a 50% decrease in its port activity—a main export sector). Greece and Spain sustained large foreign direct
investment losses in the 1980s from tourism that hurt these countries’ gross
domestic product (GDP) (Enders and Sandler 1996); however, France’s terrorism had little effect on foreign direct investment or GDP.
Advanced economies can insulate themselves from terrorism-induced economic impacts for at least three reasons: significant security response, rapid intersector reallocation of resources, and effective economic policy. The last point is
illustrated for the United States in Figure 4. In Panel 1, we see that U.S. GDP
fell prior to 9 ⁄ 11 owing to a recession. The vertical axis indicates an indexed
GDP level, where the third quarter of 2001 (2001:Q3) is assigned an index of
100. As shown, GDP grew immediately following 9 ⁄ 11 despite the fall in industrial production (see Panel 2). In fact, the latter did not recover until 2002. In
times of uncertainty, investors usually seek highly liquid assets. To address this
anticipated surge in liquidity demand that would have choked off investment,
the Federal Reserve sharply decreased the federal funds rate following 9 ⁄ 11 (the
interest rate that banks charge one another for very short-term loans) (see Panel
3). This increased liquidity and reduced interest rate encouraged borrowing
for investment and enhanced economic activity. Fiscal policy also played a supportive role owing to a tax cut that fortuitously was signed into law in May 2001,
months before 9 ⁄ 11. In Panel 4, we see that real disposable income (the after-tax
income of households) grew at the start of 2002. A Congress-approved $40 billion
in emergency spending also bolstered disposable income and spending. The message is that advanced economies possess powerful tools to offset adverse economic
effects from a large terrorist attack, which, is not true for developing countries.
Game Theory and Counterterrorism
As mentioned at the outset, game theory is an appropriate tool for understanding the strategic interactions associated with terrorists and those charged
with counterterrorism. To illustrate the usefulness of this tool, we report on a
couple of applications of game theory to the study of counterterrorism.6
We first examine a simple preemption game played by two countries—A and
B, targeted by the same terrorist group. This game is represented by the 2 · 2
bold-bordered matrix in the northwest corner of the 3 · 3 matrix of Figure 5.
Both countries have two strategies: preempt a common terrorist threat or do
nothing (i.e., maintain the status quo), indicated by the two rows for country A
and the two columns for country B. The payoffs are chosen to capture the freerider problem that such a game often presents, because weakening a common
threat is a pure public good for all at-risk countries. That is, actions by either
country would decrease the threat to both countries, so that a country would
gain the most by doing nothing and free riding on the efforts of the other
country. Suppose that each preemptor confers benefits of six on itself and on the
other country at a cost of eight to itself, where the units of measurement are billions of dollars. In the matrix, the first payoff is that of country A and the second is that of country B. If no country preempts, then the payoffs are 0. When
country A preempts and B free rides, country A receives a net gain of )2 as its
costs of eight are deducted from its benefits of six, while B gets six in benefits
6
This first analysis is based on Arce and Sandler (2005). Other game-theoretic investigations are mentioned in
footnotes 2 and 4.
298
Applying Analytical Methods to Study Terrorism
Panel 1: Real GDP
120
(2001:Q3 = 100)
115
110
105
100
95
90
1999
2000
2001
2002
2003
2004
Panel 2: Industrial production
120
(2001:Q3 = 100)
115
110
105
100
95
90
1999
2000
2001
2002
2003
2004
Panel 3: Federal funds rate
7
Percent per year
6
5
4
3
2
1
1999
2000
2001
2002
2003
2004
Panel 4: Real disposable income
120
(2001:Q3 = 100)
115
110
105
100
95
90
1999
2000
2001
2002
2003
FIG. 4. Macroeconomic Variables and 9 ⁄ 11.
2004
299
Todd Sandler and Walter Enders
Country A
Preempt
Country B
Status quo
Defend
Preempt
4, 4
–2, 6
–8, 8
Status quo
6, –2
0, 0
6, –2
Defend
8, –8
–2, 6
–4, –4
FIG. 5.
Preemption-defensive Game.
with no cost. If roles were interchanged, then the payoffs would also be
switched. Mutual action gives each country a net gain of four as its costs of eight
are deducted from the benefits of 12, received from the two preemption efforts
(i.e., 2 · 6).
The underlying game is a prisoner’s dilemma where self-interested actions
result in an equilibrium with disappointing payoffs. Each country is motivated to
maintain the status quo insofar as the payoffs associated with this strategy are
greater than the corresponding payoffs of preempting—that is, 6 > 4 and
0 > )2. Thus, this strategy is said to be dominant for both players. As they play
their dominant strategy, they end up with 0 payoffs. Ironically, this outcome is a
Nash equilibrium, from which neither player would unilaterally want to move,
because preempting alone results in a worse outcome of )2. This equilibrium is
shaded in gray. If this game were generalized to n targeted countries whose individual preemption costs exceed the associated benefits from each country’s perspective, then the outcome would be no action by any country. This follows
because the dominant strategy for every country is not to preempt in the hope
of free riding on the actions of others.
Next, we consider a simple defensive game where the roles of costs and benefits are switched. Suppose that defensive efforts cost a nation six but provide
eight in benefits to just the defender. Further, suppose that the defender’s effort
makes the other country a softer target for the terrorists. If, say, the defender
costs the other country six in losses from its increased risk, then defensive
actions have a potential negative consequence on others. The associated boldbordered 2 · 2 matrix game is displayed in the southeast corner of the 3 · 3
matrix in Figure 5. If country A defends alone, then it nets two as costs of six
are deducted from benefits of eight, while B receives )6 from its enhanced vulnerability. The other payoffs are computed as before by allowing each unit of
defense to give eight in benefits to defender and six in costs to both countries.
This defensive game is also a prisoner’s dilemma with a dominant strategy to
defend mutually. The Nash equilibrium for this 2 · 2 game is mutual defense
with losses of )4 for both countries. We should stress that less extreme losses
from mutual defense will also result in mutual defense at the equilibrium.
Finally, we allow the two-targeted nations to have three choices—preempt, do
nothing (status quo), and defend—in the 3 · 3 matrix. The cost and benefit
from preempting or defending are unchanged for the two embedded 2 · 2
games. To complete the payoffs, we must compute the payoffs when one nation
defends and the other preempts for the upper right-hand and lower left-hand
cells. The defender receives a net gain of two from its action and an additional
free-rider benefit of six from the other country’s preemption for a total gain
of eight. In contrast, the preemptor loses two from its actions and incurs an
additional loss of six from the defender’s action for a payoff of )8. By comparing country A’s (or B’s) payoff in the bottom row (right-hand column) to the
respective country’s corresponding payoffs in the other rows (or columns), we
see that each country’s dominant strategy is to defend, which gives the lower
300
Applying Analytical Methods to Study Terrorism
right-hand shaded Nash equilibrium of mutual defense for the combined preemption-defensive game. Ironically, the countries wind up with the least desirable
of the competing equilibriums. In fact, this equilibrium possesses the lowest
summed payoff in the game! Thus, the countries’ actions lead to an unsafe
world that is overly defended.
Arce and Sandler (2005) showed that this dilemma can be escaped if one
country is a prime target of the terrorists, and thus gains sufficiently from preemption to orchestrate an offensive against a common terrorism threat as others
defend. This scenario is descriptive of the post-9 ⁄ 11 era where U.S. interests are
the target of 40% of all transnational attacks. The 9 ⁄ 11 attacks gave the United
States little choice but to strike back at al-Qaeda, joined by the United Kingdom,
whose 9 ⁄ 11 losses were second to those of the United States.
Game theory shows how terrorists exploit asymmetric warfare to their strategic
advantage. Terrorist networks allow terrorists to deploy their ‘‘best-shot’’ effort
against targeted countries whose lack of cooperation means that there are always
soft targets or the weakest links for terrorists to attack for maximum gain. In
addition, terrorists choose an optimal risk-minimizing network structure, where
infiltrators learn only a few identities as terrorist cells maintain limited linkages
with other cells. This is possible because terrorist operations are generally small
scale with the need of few operatives. British authorities’ ability to infiltrate the
August 2006 plot against U.S.-bound planes is largely due to the need for so
many terrorists to attack multiple planes simultaneously. As a terrorist operation
grows in complexity, it becomes more vulnerable to intelligence. As terrorists
seek more mass-casualty attacks, they sacrifice one of their greatest advantages—secrecy.
Many other counterterrorism measures can be addressed with game theory.
Bandyopadhyay and Sandler (2006), for example, developed a two-stage preemption-defensive game, where countries can both preempt and defend. In the first
stage, the targeted countries decide preemption levels, while, in the second
stage, they decide defensive measures to deflect the attack. These authors found
that the preemptor is apt to be the high-cost defender with the greatest foreign
interests; surprisingly, the preemptor need not be the low-cost preemptor. Preemptive efforts limit the overall level of terrorism and are more advantageous to
a targeted country that has high-defense cost owing to long exposed borders
and foreign interests. Even more surprising, these authors showed that changing
the order of the stages—that is, defense before preemption—does not change
the nature of the solution. In addition, these authors found that foreign interests and being a prime target also encourage preemption. Such studies will assist
governments in allocating tens of billions of dollars between offensive and
defensive counterterrorism measures.
Many other counterterrorism choices can benefit from game-theoretic analysis.
For instance, future game-theoretic studies must allow the terrorists to be active
players (see, e.g., Rosendorff and Sandler 2004; Siqueira 2005). Often, the terrorists are treated as passive agents who merely react to counterterrorism policies. What is required are more three-agent games that include the terrorists
and two targeted governments as active players whose decision calculus is displayed. Also, domestic politics must be added so that agents include the electorate and government in at-risk countries, along with the terrorists. In some
instances, an outside terrorist sponsor (e.g., state sponsors) may be relevant as
an active agent in a strategic framework. Clearly, there are many interesting avenues to pursue. Most recent game-theoretic analyses involve continuous variables, where game matrices are eschewed for mathematical approaches (see, e.g.,
Bueno de Mesquita 2005; Rosendorff and Sandler 2004). Future investigations
will address dynamic optimization—differential games—where decisions today
influence decisions tomorrow and a plan of action must be chosen.
Todd Sandler and Walter Enders
301
Conclusion and Further Future Directions
Technology allowed modern-day terrorism to assume insidious forms. The
extreme advantage that terrorism provides to the weak against powerful governments means that terrorism is here to stay. The application of analytical techniques is a way for targeted countries to level the playing field. By identifying
the roadblocks to cooperation and more effective policy, analytical studies can
empower governments to engage in more informed counterterrorism. Empirical
methods permit governments to evaluate policy effectiveness and gauge economic impacts of terrorism. Much can be learned from these studies. Thus far,
they have yielded surprising results.
There are many future empirical applications that would cast light on terrorism and its impact on society. First, improved quantification of the economic
impact on developing economies is needed to understand aid and security policies. In doing so, cross-country studies must group more homogeneous nations,
both in terms of their economies and the extent of terrorism, to achieve a more
informative average viewpoint. Second, further studies on the microeconomic
impact for sectors other than airlines and tourism would add to our knowledge
of the costs of terrorism. If we better understand this cost, then policy makers
can exercise more informed judgments on how much to spend to defend
against terrorism. Third, novel VAR studies must investigate the influence of
policies and other events on terrorism time series. These studies would improve
greatly if both domestic and transnational terrorist incidents are included.
Fourth, statistical analyses are needed to investigate how different types of terrorist groups—for example, fundamentalist versus Left-wing terrorists—operate and
respond to policy. Fifth, there needs to be a better melding of theory and empirics, so that the empirical models follow from clearly derived behavioral models.
References
Abadie, Alberto, and Javier Gardeazabal. (2003) The Economic Cost of Conflict: A Case Study
of the Basque Country. American Economic Review 93: 113–132.
Alexander, Jonah, and Dennis Pluchinsky. (1992) Europe’s Red Terrorists: The Fighting Communist
Organizations. London: Frank Cass.
Arce, Daniel G., and Todd Sandler. (2005) Counterterrorism: A Game-Theoretic Analysis. Journal
of Conflict Resolution 49: 183–200.
Arce, Daniel G., and Todd Sandler. (2007) Terrorist Signalling and the Value of Intelligence. British Journal of Political Science 37. (Forthcoming).
Bandyopadhyay, Subhayu, and Todd Sandler. (2006) The Interplay between Preemptive and Defensive
Counterterrorism Measures: A Two-Stage Game. Unpublished manuscript, School of Economic, Political & Policy Sciences, Richardson, TX: University of Texas at Dallas.
Brophy-Baermann, Bryan, and John A. C. Conybeare. (1994) Retaliating against Terrorism:
Rational Expectations and the Optimality of Rules Versus Discretion. American Journal of Political
Science 38: 196–210.
Bueno de Mesquita, Ethan. (2005) Conciliation, Commitment and Counterterrorism: A Formal
Model. International Organization 59: 145–176.
Chen, Andrew H., and Thomas F. Siems. (2004) The Effects of Terrorism on Global Capital Markets. European Journal of Political Economy 20: 249–266.
Eckstein, Zvi, and Daniel Tsiddon. (2004) Macroeconomic Consequences of Terror: Theory and
the Case of Israel. Journal of Monetary Economics 51: 971–1002.
Enders, Walter. (2007) Terrorism: An Empirical Analysis. In Handbook of Defense Economics Vol. 2,
edited by T. Sandler and K. Hartley. Amsterdam: North-Holland.
Enders, Walter, and Todd Sandler. (1993) The Effectiveness of Anti-Terrorism Policies: A VectorAutoregression-Intervention Analysis. American Political Science Review 87: 829–844.
Enders, Walter, and Todd Sandler. (1996) Terrorism and Foreign Direct Investment in Spain
and Greece. Kyklos 49: 331–352.
302
Applying Analytical Methods to Study Terrorism
Enders, Walter, and Todd Sandler. (1999) Transnational Terrorism in the Post-Cold War Era.
International Studies Quarterly 43: 145–167.
Enders, Walter, and Todd Sandler. (2000) Is Transnational Terrorism Becoming More Threatening: A Time-Series Investigation. Journal of Conflict Resolution 44: 307–332.
Enders, Walter, and Todd Sandler. (2006) The Political Economy of Terrorism. Cambridge: Cambridge University Press.
Enders, Walter, Todd Sandler, and Jon Cauley. (1990) U.N. Conventions, Technology, and
Retaliation in the Fight against Terrorism: An Econometric Evaluation. Terrorism and Political
Violence 2: 83–105.
Engene, Jan Oskar. (2004) Terrorism in Western Europe: Explaining the Trends Since 1950. Cheltenham,
UK: Edward Elgar.
Heal, Geoffrey and Howard Kunreuther. (2005) IDS Model of Airline Security. Journal of Conflict
Resolution 49: 201–217.
Hoffman, Bruce. (1998) Inside Terrorism. New York: Columbia University Press.
Im, Eric I., Jon Cauley, and Todd Sandler. (1987) Cycles and Substitutions in Terrorist Activities:
A Spectral Approach. Kyklos 40: 238–255.
Islam, Muhammad Q., and Wassim N. Shahin. (1989) Economic Methodology Applied to Political
Hostage-Taking in Light of the Iran-Contra Affair. Southern Economic Journal 55: 1019–1024.
Ito, Harumi, and Darin Lee. (2005) Assessing the Impact of the September 11th Terrorist Attacks
on U.S. Airline Demand. Journal of Economic and Business 57: 75–95.
Kunreuther, Howard, and Erwann Michel-Kerjan. (2004) Dealing with Extreme Events: New Challenges for Terrorist Risk Coverage. Unpublished manuscript, Philadelphia, PA: Wharton, University
of Pennsylvania.
Landes, William M. (1978) An Economic Study of U.S. Aircraft Hijackings, 1961-1976. Journal of
Law and Economics 21: 1–31.
Lapan, Harvey E., and Todd Sandler. (1988) To Bargain or Not To Bargain?: That Is the Question. American Economic Association Paper and Proceedings 78: 16–20.
Lapan, Harvey E., and Todd Sandler. (1993) Terrorism and Signalling. European Journal of Political
Economy 9: 383–397.
Lee, Dwight R. (1988) Free Riding and Paid Riding in the Fight against Terrorism. American Economic Association Papers and Proceedings 78: 22–26.
Mickolus, Edward F. (1982) International Terrorism: Attributes of Terrorist Events, 1968-1977 (ITERATE
2). Ann Arbor, MI: Inter-University Consortium for Political and Social Research.
Mickolus, Edward R., Todd Sandler, Jean M. Murdock, and Peter Flemming. (2006) International
Terrorism: Attributes of Terrorist Events, 1968-2005 (ITERATE 5). Dunn Loring, VA: Vinyard Software.
National Memorial Institute for the Prevention of Terrorism. (2006) M.I.P.T. Terrorism Knowledge Base. Available at http://www.mipt.org. (Accessed September 11, 2006).
Nelson, Paul S., and John L. Scott. (1992) Terrorism and the Media: An Empirical Analysis.
Defence Economics 3: 329–339.
Overgaard, Per B. (1994) The Scale of Terrorist Attacks as a Signal of Resources. Journal of Conflict
Resolution 38: 452–478.
Poe, Steven C. (1988) Nations’ Responses to Transnational Hostage Events: An Empirical Evaluation. International Interactions 14: 27–40.
Rapoport, David C. (2004) Modern Terror: The Four Waves. In Attacking Terrorism: Elements of a Grand
Strategy, edited by A. K. Cronin and J. M. Ludes. Washington DC: Georgetown University Press.
Rosendorff, B. Peter, and Todd Sandler. (2004) Too Much of a Good Thing? The Proactive
Response Dilemma. Journal of Conflict Resolution 48: 657–671.
Sandler, Todd, and Daniel G. Arce. (2007) Terrorism: A Game-Theoretic Approach. In Handbook
of Defense Economics Vol. 2, edited by T. Sandler and K. Hartley. Amsterdam: North-Holland.
Sandler, Todd, and Walter Enders. (2004) An Economic Perspective on Transnational Terrorism.
European Journal of Political Economy 20: 301–316.
Sandler, Todd, and Harvey E. Lapan. (1988) The Calculus of Dissent: An Analysis of Terrorists’
Choice of Targets. Synthe`se 76: 245–261.
Sandler, Todd, John Tschirhart, and Jon Cauley. (1983) A Theoretical Analysis of Transnational
Terrorism. American Political Science Review 77: 36–54.
Selten, Reinhard. (1988) A Simple Game Model of Kidnappings. In Models of Strategic Rationality,
edited by R. Selten. Boston: Kluwer Academic.
Siqueira, Kevin. (2005) Political and Militant Wings within Dissident Movements and Organizations.
Journal of Conflict Resolution 49: 218–236.
Wilkinson, Paul. (2001) Terrorism versus Democracy: The Liberal State Response. London: Frank Cass.