Hostage Taking: Understanding Terrorism Event
Patrick T. Brandt, Todd Sandler∗
School of Economic, Political and Policy Sciences
800 W. Campbell Road
The University of Texas at Dallas
Richardson, Texas 75080-3021
This paper employs advanced time series methods to identify the dynamic properties of three
hostage taking series. The immediate and long run multipliers of three covariates — success-
ful past negotiations, violent ends, and deaths — are identified. Each hostage series responds
differently to the covariates. Past concessions have the strongest impact on generating future kid-
napping events, supporting the conventional wisdom to abide by a stated no-concession policy.
Each hostage series has different changepoints caused by a variety of circumstances. Skyjack-
ings and kidnappings are positively correlated, while skyjackings and other hostage events are
negatively correlated. Policy recommendations are offered.
JEL classification: C22; D74; H56
Key words: Kidnappings, Skyjackings, No-concession policy, Impact multipliers, Poisson
autoregressive model, Changepoint models, reversible-jump Markov chain Monte Carlo methods
From the seizure of the Israeli athletes during the 1972 Munich Olympics to the four
simultaneous skyjackings on September 11, 2001 (henceforth, 9/11), hostage events have
been some of the most spectacular and newsworthy attacks during the modern era of
Email addresses: email@example.com, firstname.lastname@example.org (Patrick T. Brandt, Todd
Preprint submitted to Elsevier 14 July 2008
international terrorism. In fact, this modern era is traced to the July 22, 1968 hijacking of
an Israeli El Al flight by the Popular Front for the Liberation of Palestine (PFLP) (Hoff-
man, 2006). During the incident, the PFLP terrorists gained significant media coverage
and forced the Israelis to negotiate with the Palestinians (Hoffman, 1998, 68). After the
incident, terrorists increasingly staged attacks at foreign venues to capture the world’s
attention. Other high-profile hostage events include: the PFLP’s abduction of eleven Or-
ganization of Petroleum Exporting Countries (OPEC) ministers on December 21, 1975;
the students’ takeover of the U.S. embassy in Tehran, Iran on November 4, 1979; and the
Chechen rebels’ seizure of over a thousand hostages at a middle school in Beslan, Russia
on September 1, 2004.
Terrorist hostage incidents fall into four categories: kidnappings, skyjackings, barri-
cade and hostage taking missions (i.e., the takeover of a building with hostages), and
the capture of a nonaerial means of transportation (e.g., a boat, train, or bus). Kidnap-
pings are the least risky hostage events owing to their unknown location and, as such,
account for over two-thirds of the hostage incidents (1318 of 1941 incidents in our data
set). Skyjackings are less risky than barricade and hostage taking missions and other
forms of hijackings, since it is more difficult for authorities to approach a plane unseen
than to approach buildings or other means of transport. Terrorists engage more often
in skyjackings than in other forms of nonkidnapping hostage events (see below). Even
though hostage taking incidents are among some of the most dangerous missions, terror-
ists resort to such attacks because they can result in high payoffs in terms of publicity,
recruitment, and ransoms. Hostage events comprise 15% of all terrorist events for the
1968-2005 sample period (Mickolus et al., 2006). Terrorists choose their mix of attacks
according to perceived risks, engaging in riskier modes less often (Sandler et al., 1983),
which is borne out by the frequency of the four kinds of hostage missions.
For hostage events, the conventional wisdom is that past concessions to terrorists en-
courage additional seizures owing to terrorists’ updated priors of high payoffs. If, instead,
terrorists know beforehand that they have nothing to gain from hostage taking due to
a government’s announced no-concession stance, then they will never abduct hostages.
Thus, many governments — including the United States — have adopted a no-concession
policy in the hopes of reducing hostage taking (U.S. Department of State, 2003). Lapan
and Sandler (1988), however, demonstrate that the efficacy of the no-concession stance
hinges on some unstated assumptions, which often do not hold (e.g., credibility of the gov-
ernment’s pledge and the absence of terrorist gains from a negotiation failure). Terrorists
believe that, if they capture a sufficiently valuable hostage, the government will renege
on its no-concession pledge. There have been many instances of this in the past—e.g., a
large ransom was paid to the PFLP for the release of the OPEC ministers in 1975—that
foster this belief. Each concession made to hostage taking terrorists by one government
makes the terrorists change their beliefs about the likelihood of other governments’ giving
into their demands. For example, the Reagan administration’s arms-for-hostages deal to
release Rev. Benjamin Weir, Rev. Lawrence Jenco, and David Jacobsen encouraged the
terrorists to capture other academics and journalists in Beirut (e.g., Robert Polhill, Al-
lan Steen, Jesse Turner, Mithileshwar Singh, and Roger Augue) to replace those released
(Enders & Sandler, 2006, 172–173). In 2004, terrorists in Iraq took other countries’ cit-
izens hostage once South Korea and the Philippines made concessions. Apparently, one
country’s concession causes a negative influence or externality on the perceived credibility
of other target countries’ pledges. Although the influence of past concessions on generat-
ing future hostage incidents is an important policy question, the essential no-concession
wisdom has never been tested empirically.
There has also been no dynamic test of whether the use of force to end a hostage mission
discourages future incidents, thereby justifying the associated loss of life including that
of some of the hostages. Up until now, there has not been a sufficiently long time series of
hostage events to test important dynamic propositions including how policy statements
and past actions generate or discourage future hostage incidents. In addition, advanced
time series methods have not been applied to disaggregated hostage events to identify
important changepoints resulting from policies and/or exogenous shocks.
This paper has a number of purposes. First, it employs sophisticated time series tech-
niques to quantify how past concessions encourage future hostage events; similarly, it
applies these methods to quantify how violent actions (e.g., the authorities storming a
hijacked plane) influence future hostage missions. Second, we use advanced methods to
identify past changepoints in the hostage taking series where the arrival rates increase or
decrease. Once these changepoints are identified, we can match them, in most cases, with
the precipitating shock or event. By using only exogenously given policy interventions,
past analyses miss many changepoints. Third, we ascertain how hostage events differ
when the location is unknown or known. If, for example, the dynamics associated with
kidnappings (unknown location) differs from that of other kinds of hostage events, then
policy recommendations must also differ between types of hostage events. Fourth, we
determine the temporal level of aggregation (i.e., days, months, or quarters) or the unit
of analysis that is most appropriate.
In the course of the study, we establish significant empirical support for the conven-
tional wisdom with respect to maintaining a no-concession policy. For kidnappings, each
concession to the terrorists results in two to three additional abductions. A smaller num-
ber of additional skyjackings and other hostage incidents follows concessions granted.
Unexpectedly, violent ends or deaths are associated in many instances with more, not
fewer, hostage incidents. Thus, decisive actions by the authorities to end a hostage event
with force did not always deter future actions, except for skyjackings. The level of ag-
gregation can make a difference in identifying the impact of these covariates. Moreover,
alternative types of hostage events are associated with different changepoints. The esti-
mated arrival rates of kidnappings and skyjackings are negatively correlated, indicative
of substitution effects; the arrival rates of kidnappings and nonskyjacking hostage events
are uncorrelated; and the arrival rates of skyjackings and nonkidnapping hostage events
are positively correlated, indicative of complementarity.
The body of the paper contains four sections. Section 2 presents preliminaries including
essential definitions, concepts, and brief review of the relevant literature. The data is
discussed in Section 3. This is followed by the empirical analysis in Section 4. The final
section contains concluding remarks and further policy implications.
Terrorism is the premeditated use or threat to use violence by individuals or subna-
tional 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 crucial ingredients are violence and the political/social motive; violent acts without
such motives are merely criminal acts and do not constitute terrorism. Other essential
aspects of terrorism that have been subject to debate concern the identity of the victim
(i.e., noncombatant or otherwise), perpetrator (e.g., states as terrorists), and audience
(Hoffman, 1998; Enders & Sandler, 2006). Our definition is closely akin to that of the
U.S. Department of State (2003) and captures many features of the myriad definitions in
the literature. Moreover, this definition is consistent with that of the data set described
in the next section. Terrorists utilize different modes of attack — e.g., bombings, assassi-
nations, armed attacks, skyjackings, kidnappings, and barricade missions — to pressure
a government into conceding to their political demands. Our focus is on hostage events
since we are interested in how past concessions or violent actions by governments influ-
ence the arrival rate of future incidents. Such a study informs governments as to whether
their independent policy responses work to curtail or encourage future hostage taking
incidents. The analysis here assists governments learn best practices.
Terrorism is further subdivided into domestic and transnational events. Domestic ter-
rorism is homegown (i.e., home financed, planned, and executed) and has consequences
for just the host country, its institutions, citizens, property, and policies. The kidnapping
of a German industrialist, Hanns Martin Schleyer, in 1977 by the Red Army Faction
is a domestic terrorist incident. In contrast, transnational terrorism involves perpetra-
tors, victims, institutions, governments, or citizens from at least two countries. Incidents
funded or planned abroad are transnational terrorist events, as are incidents where the
terrorists cross a national border to engage in the attack. The January 2002 kidnapping
of Wall Street Journal reporter Daniel Pearl in Pakistan is a transnational terrorist event.
A skyjacking of a plane that originates in Rome and is made to fly to Beirut is a transna-
tional incident. The kidnappings of Westerners and other foreign nationals in Lebanon
during the 1980s, as well as the kidnappings of foreign contractors and aid workers in Iraq
following the Abu Ghraib prison scandal on April 6, 2004, are examples of transnational
hostage missions. The four simultaneous skyjackings on 9/11 are transnational because
the hijackers were foreigners, the victims came from many countries, and the financial
implications were global. In general, transnational terrorist incidents have ramifications
that transcend the host country’s soil.
The past literature on terrorist hostage taking includes both theoretical and empirical
contributions. The theoretical literature is primarily interested in the desirability (Islam
& Shahin, 1989) and the practicality (Lapan & Sandler, 1988) of the no-concession policy
in discouraging future hostage taking. These papers provide some casual evidence, but do
not present any empirical test of the propositions put forward. The empirical literature
focuses on the effectiveness of metal detectors in airports and other counterterrorism poli-
cies (e.g., sky marshals, UN conventions outlawing skyjackings, and longer jail sentences
to convicted skyjackers) to inhibit subsequent skyjackings (Enders & Sandler, 1993; En-
ders et al., 1990a,b; Landes, 1978). These past studies prespecify the changepoints in
hostage events rather than allow the data to uncover them. Moreover, the dependent
variable — say, the number of skyjackings — were not related to covariates about the
(past) events, such as past concessions. Another set of articles investigates the determi-
nants of hostage taking success (Gaibulloev & Sandler, 2009; Sandler & Scott, 1987) and
bargaining aspects (Atkinson et al., 1987). Like this study, Poe (1988) examines whether
a tough stance against hostage takers limits future abductions. This earlier study uses
multiple regression and cannot capture the true dynamics of past hostage taking inci-
dents, in contrast to the Poisson autoregressive and changepoint models in this paper.
Poe finds that a tough stance did not deter future hostage missions.
In a recent paper, Enders & Sandler (2005) examine prespecified (e.g., 9/11) and
unspecified changepoints in hostage events time series. Unlike the current study, which
disaggregates hostage incidents into three distinct classes, Enders & Sandler (2005) aggre-
gate all hostage events to quarterly series. These authors apply Bai-Perron (1998, 2003)
methods rather than the changepoint models employed here. In this study, we identify a
much richer set of changepoints that differ among alternative hostage missions.
Finally, Lee et al. (2008) use an alternative estimation method (sequential importance
sampling) rather than a reversible jump Markov chain Monte Carlo method, but apply
it to nonhostage incidents for a truncated time period that ends prior to 9/11. Like
the current study, these authors use monthly data. Their main concern is whether past
patterns in the data could have predicted 9/11.
We use event data on terrorist hostage incidents drawn from International Terrorism:
Attributes of Terrorist Events (ITERATE), which was originally devised by Mickolus
(1982) and later updated by Mickolus et al. (2006). ITERATE records just transnational
terrorist incidents using a host of sources, including the Associated Press, United Press
International, Reuters tickers, New York Times, Washington Post, the Foreign Broadcast
Information Services (FBIS) Daily Reports, ABC, NBC, and CBS evening news. 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 complete source
for foreign coverage of terrorist incidents. ITERATE currently includes 12,942 terrorism
incidents from 1968 to 2005. An overlap of coders ensures a consistency of coding as the
data are updated.
ITERATE’s COMMON file records a host of general observations about each terrorist
event including the incident date, incident type, and the total number of individuals
(i.e., terrorists, victims, or bystanders) killed. In addition, ITERATE’s HOSTAGE file,
which has been recently updated to run from 1968 to 2005, includes a negotiation success
variable that indicates whether the terrorists received none, some, or all of their demands.
The HOSTAGE file also includes the response of the target — shoot-out with terrorists
or something else (e.g., capitulation, Bangkok solution [i.e., a plane to a safe haven], no
compromise, or no shoot-out). These two variables allow us to construct two important
covariates. We have merged the hostage events with those in the COMMON file so
that we have common and hostage attributes of 1941 hostage events, made up of 1318
kidnappings, 380 skyjackings, and 243 other hostage events (i.e., barricade missions and
nonaerial hijackings).1For hostage events without a fully specified date (either missing a
month or a day), events were assigned a modal date. Missing days were assigned the 15th
of the month (if a month were supplied) and missing months were assigned to June. All
observations with a missing month have a missing day. Using this data, we constructed
1These are ITERATE incident types 1 (kidnapping), 2 (barricade and hostage seizure), 9 (aerial hi-
jacking) and 10 (takeover of nonaerial means of transportation).
three time series — a KIDNAP series, a SKYJACK series, and an OTHER hostage events
series (known henceforth as OTHER) for the 1968-2005 period.2
Figure 1 presents the KIDNAP time series and their autocorrelation functions at
monthly and quarterly levels of aggregation. The dashed vertical line in each graph is
for 9/11. Visual inspection of these series reveal two immediate properties: 1) the series
are cyclical (around an AR(1-4) processes depending on the level of aggregation), and 2)
the variance of the series increases over time. The latter property is especially evident in
the quarterly data. The right column in Figure 1 are the autocorrelation functions for
the three series.3Time scales in these ACFs are based on the periodicity of the data, so
the “1” on the x-axis in the monthly data is 12 months, and 4 quarters in the quarterly
data. The y-axis are the autocorrelations.
Figures 2 and 3 present the same information as Figure 1 for the SKYJACK, and
OTHER series. Note that the SKYJACK and OTHER series appear to have negative
trends, descending from high points in the 1980s and 1990s. The KIDNAP event series
display higher volatility in more recent periods. particularly post 9/11 where the series
reaches its historical maximum. An upward trend since 1990 is evident for the quarterly
KIDNAP series, except for a drop prior to 9/11.
4. Testing for cycles and changes in hostage taking events
We are particularly interested in two questions about hostage events: are they cyclical
and have there been structural changes in the hostage taking series. The former are moti-
vated by previous findings such as Enders & Sandler (2005) where hostage taking events
are shown to be both cyclical and subject to structural shifts. However, these earlier
analyses can be refined by careful modeling of the KIDNAP, SKYJACK and OTHER
series. In the literature, cycles are attributed to a cat-and-mouse game between the au-
thorities and the terrorists as defensive breakthroughs (e.g., metal detectors at airports)
are countered by operational innovations (e.g., plastic guns or flammable liquids). In
other cases, cycles may stem from demonstration effects of success or failure (see Enders
& Sandler, 2006, 2005; Enders et al., 1992; Im et al., 1987). Whatever their cause, we
must account for cycles and structural breaks to identify the true dynamics of the time
The refinements we employ here are threefold. First, we work with more disaggregated
data (also see Barros & Gil-Alana, 2006). This is important since 1) aggregating to
quarterly data can mask cyclical components (at frequencies less than a quarter), and 2)
may confound inferences about structural shifts since they may be “lost” in a quarter.
Second, we employ event count time series methods rather than ARIMA or (normal)
linear regression models. Event count models based on Poisson and negative binomial
2These data are sparse. For the January 1, 1968 to December 31, 2005 period, 8.6% of the days have
one or more KIDNAP event, 2.6% of the days have one or more SKYJACK event, and 1.7% of the
days have one or more OTHER event. For a monthly aggregation of the data, 85% of the months have
some KIDNAP events, 47% of the months have some SKYJACK events, and 35% of the months have
an OTHER event.
3These ACFs are computed using the standardized hostage counts. They are computed using zt=yt−¯ y
where ¯ y and σ are the mean and standard deviation, respectively of the series. This method is suggested
by Cameron & Trivedi (1998).
Monthly KIDNAP Events
ACF for Monthly KIDNAP Counts
Quarterly KIDNAP Events
ACF for Quarterly KIDNAP Counts
Fig. 1. ITERATE KIDNAP events time series, 1968–2005.
data generation processes provide less biased and more consistent estimates of cyclical
and structural components for data like those presented here. Brandt et al. (2000), Brandt
& Williams (2001) and Park (2007) all present models for count data that produce less
biased inferences about cyclical components and structural shifts. This is important, since
incorrect data generation process assumptions will potentially invalidate tests for cycles
and shifts. Finally, we employ more robust methods for checking for structural changes
in the disaggregated data. Such methods check for possibly incorrect assumptions about
the number and timing of structural breaks in the three hostage (event count) series. The
methods used here — event count time series regressions and a Bayesian reversible-jump
changepoint model — allows us to combine prior beliefs about the number of changepoints
and the data to produce robust inferences about changepoints, without indefensible data
aggregation or exogenously limiting the number of changepoints in the data (see, e.g.,
Barros, 2003; Barros & Gil-Alana, 2006; Enders et al., 1990a,b). The remainder of this
section presents two alternative models of the three hostage event series.
Monthly SKYJACK Events
ACF for Monthly SKYJACK Counts
Quarterly SKYJACK Events
ACF for Quarterly SKYJACK Counts
Fig. 2. ITERATE SKYJACK events time series, 1968–2005.
4.1. PAR(p) analyses
One can look at the cyclical properties of the data using the Poisson autoregressive
model (PAR(p)) of Brandt & Williams (2001). This model is based on an extended
Kalman filter for the count process. Let ytbe the observed number of hostage events at
time t, and xtbe a 1 × k vector of covariates. The basic model for the counts has two
equations, a measurement equation and a transition equation that describe the evolution
of the counts via an autoregressive process and some initial conditions:
Monthly OTHER Events
ACF for Monthly OTHER Counts
Quarterly OTHER Events
0.01.0 2.0 3.0
ACF for Quarterly OTHER Counts
Fig. 3. ITERATE OTHER events time series, 1968–2005.
Pr(mt|yt−1,...,yt−p) = Γ(σt−1mt−1,σt−1)
where mtis the mean of the Poisson process at time t, ρi’s are the autoregressive param-
eters for the lagged counts, β is a k×1 vector of regression coefficients for the covariates,
and σt is the scale of the transition equation at time t. The measurement equation is
a Poisson density for the number of events yt at time t, while the transition equation
describes how the (latent) mean number of events evolves via an autoregressive process.
The initial conditions determine the probability density for the autoregressive process
in each time period, whose mean is gamma distributed with a scale parameter of σt.
The resulting predictive distribution of the counts is a negative binomial (for details see
Brandt & Williams, 2001), which accounts for the overdispersion of the data due to the
serial correlation in the counts.
The analysis here includes three covariates for each of hostage series. The first covariate
indicates past negotiation success of the hostage missions, in which the terrorists obtain
some or all of their demands. Because terrorists are apt to ask for as much as possible
to maximize concessions paid, gaining their full demands is too stringent a condition
for negotiation success. Based on conventional wisdom (previously discussed), successful
negotiations in one type of hostage incident is likely to generate more incidents of the
same type as terrorists raise their priors for expected gains. From the HOSTAGE file, the
negotiation success covariate is coded as 1 if the terrorists received some or all of their
demand and 0 otherwise. The second covariate derives from the “response of the target”
from the HOSTAGE file of ITERATE, where the constructed variable of a violent end
is coded as 1 for “shoot out with terrorists” and 0 otherwise. We anticipate that such a
forceful end to an incident will deter future incidents of that type unless the terrorists are
motivated by martyrdom or publicity. The third covariate is from the COMMON file of
ITERATE and indicates whether deaths are associated with a hostage incident. Incidents
with one or more deaths are coded as 1 and those with no deaths are coded as 0. Such
bloodshed is anticipated to deter future incidents of that type unless the perpetrators are
more bent on murder than on other gains. All three covariants are recorded as within-
period sums of the relevant variable for the specific kind of hostage event.
There are two issues that must be addressed in specifying the PAR(p) model with
these covariates. The first is the number of lags of the count series in the model. We fit
a series of these PAR(p) models for each of the three hostage time series. In so doing,
we tested for the lag length of each PAR model using successive models with higher lags
and selected the most parsimonious model with statistically significant lag coefficients.
The second issue is the distributed lag specification for the exogenous variables. We
looked at models with contemporaneous covariates and lags up to two periods. Based
on hypothesis tests and Akaike information criteria (AIC) values, we selected the most
parsimonious distributed lag specification. Table 1 summarizes the results of the models
for both quarterly and monthly aggregations of the data.4
These results generate four main insights into the hostage data. First, the hostage
events are not independent of each other. The joint hypothesis for ρi= 0,i = 1,...p for
the PAR(p) is a test of whether the autoregressive process is jointly zero and the data
are better explained by a Poisson regression, where the hostage events are independent
of each other. This test is rejected for each of the models. Thus, there is a dependent,
autoregressive process among the hostage events in each time series. Second, this temporal
dependence among the series is generally positive, which means that hostage taking
events generally are correlated positively over time. Third, the equilibration of additional
new hostage events is rather rapid, since the sum of the AR coefficients tends to be
bounded away from 1. This is interpreted as meaning that the impact of each hostage
taking event on subsequent events occurs over a short period of time (approximately
8-12 months at most). Finally, negotiation successes, violent endings, and incidents with
deaths have statistically significant effects in predicting each of the hostage series. This
last conclusion is based on the statistically significant covariates in the latter rows of
the table. The positive influence of negotiation success agrees with our priors, while the
positive influence of violent end and deaths does not agree with our priors, except when
martydom or publicity are motivators. By calculating the multipliers for each covariate
for each of the three series, we are better able to quantify their impacts.
This latter result can be seen by computing the impact and long run multipliers of a
one unit change in each of the covariates (holding the others at their means). These are
found by the following (see Brandt and Williams 2001 for details):
4There are fewer observations in some of the series because the PAR(p) model cannot be estimated
with initial observations of zero. Truncating the data series to the first nonzero observation produces the
Table 1. PAR(p) results for monthly and quarterly KIDNAP, SKYJACK and OTHER series 1968–2005.
0.23 (0.04) 0.18 (0.05) 0.25 (0.07) 0.30 (0.07) 0.19 (0.05) 0.21 (0.09)
0.13 (0.05) 0.14 (0.05) 0.17 (0.08) 0.16 (0.08)
0.06 (0.07) -0.13 (0.05)
0.13 (0.07) 0.11 (0.06)
0.27 (0.06) 0.22 (0.04) 0.67 (0.07) 0.33 (0.06) 0.34 (0.19) 0.43 (0.15)
0.37 (0.06) 0.24 (0.05) 0.87 (0.14) -0.16 (0.16) 0.66 (0.16) 0.07 (0.20)
Incidents with Deathst
0.36 (0.04) 0.16 (0.02) 0.87 (0.09) 0.53 (0.10) 0.93 (0.14) 0.52 (0.13)
Incidents with Deathst−1
0.73 (0.07) 1.65 (0.08) -0.52 (0.16) 0.20 (0.18) -0.83 (0.11) 0.06 (0.13)
χ2, H0: Poisson model (p-value)107 (<0.01) 29 (<0.01) 98 (<0.01) 51 (<0.01) 13 (<0.01)
Note: Standard errors are in parentheses. The ρiterms are the autoregressive lag coefficients at lag i. All of the Wald tests for a
reduction to a Poisson model have p degrees of freedom (the number of lagged counts) and have p-values generally less than 0.01.
exp(γzt+ β1xt+ β2xt−1)β1
Long run multiplier : exp(γzt+ β1xt+ β2xt−1)(β1+ β2)
where βiand γ are a partition of the coefficients, xt−iare a given shock to exogenous
variables and ztare the fixed variables (typically held at their sample means). The impact
multiplier finds the instantaneous effect of a one unit change in an xtvariable at time
t+1. The total multiplier computes the total effect of the one unit change in the covariate.
Tables 2 and 3 show the computed multipliers as well as a Monte Carlo estimate of their
68% confidence regions (approximately one standard deviation around the mean). These
multipliers show the impact or change in the KIDNAP, SKYJACK, or OTHER series for
a one unit changes in one of the independent variables (specified in the columns) holding
all of the other variables at their sample means. The first rows in each table give the
impact (next month or quarter) effect, while the final rows give the total impact.
A comparison of the two tables shows that the level of data aggregation makes a differ-
ence in subsequent conclusions. For the monthly data, the effects of one more negotiation
success, violent end, or deaths incident are more hostage events. For the monthly KID-
NAP series, the impact of a negotiation success, violent end, or deaths incident is 0.44
to 0.61 new kidnappings. The total (long run) impacts of one more negotiation success,
violent end, or deaths incident on KIDNAP is 0.75 to 1.03 new kidnappings. In the case
of SKYJACK, the three covariates are associated with much weaker impacts that vary
between 0.21 and 0.28 new incidents for the immediate effect and between 0.56 and
0.73 new incidents for the total impact. Compared with the KIDNAP series, OTHER
hostage events also display smaller impact and total multipliers. Generally, we see that
an unknown location for hostage incidents means that the covariates, such as negotiation
success, have a greater impact initially and over time than for known locations. This
implies that the no-concession policy is particularly important for kidnappings, which
will also be borne out for quarterly data. For all monthly hostage series, the effect of the
three covariates is to raise hostage events.
The quarterly data PAR(p) multipliers are given in Table 3 and differ from the monthly
results. For the quarterly data, a one unit increase in each of the covariates has a posi-
tive effect on KIDNAP. These results are approximately two to three times the monthly
effects of the covariates for four of the six multipliers. These multiples are consistent
with the quarterly data aggregation. Most notable, conceding to kidnappers’ demands is
associated with 2.62 additional abductions, lending strong support for the conventional
wisdom. Neither violent ends nor deaths during the incident are a deterrent to kidnap-
pings, probably because hostage takers believe that better efforts to keep their location
unknown will not result in a shoot-out with authorities even if a recent incident concluded
this way. Past violence in kidnappings may encourage future events owing to the promise
of increased media coverage. Moreover, deaths of a hostage may still result in a ransom,
provided that the death is discovered after payment. The quarterly SKYJACK multipli-
ers associated with negotiation success and deaths are positive and somewhat larger than
their monthly counterparts. These slightly larger multipliers are not consistent with the
quarterly data aggregation. For quarterly data, a violent end deters future skyjackings
immediately and in the long run. Although this influence is not large, it greatly differs
from the monthly data and supports past actions to end a skyjacking forcefully (e.g.,
Table 2. Impact and long run impact multipliers for one unit increases in each of the independent variables for the monthly PAR(p) models.
(0.33, 0.55) (0.51, 0.71) (0.52, 0.65) (0.18, 0.25) (0.23, 0.33) (0.24, 0.32) (0.07, 0.23) (0.22, 0.36) (0.34, 0.48)
(0.57, 0.93) (0.87, 1.20) (0.90, 1.09) (0.47, 0.65) (0.61, 0.84) (0.63, 0.84) (0.08, 0.29) (0.27, 0.45) (0.44, 0.59)
Note: The 68% confidence regions included in parentheses under each multiplier.
Table 3. Impact and long run impact multipliers for one unit increases in each of the independent variables for the quarterly PAR(p) models.
(0.97, 1.33) (1.00, 1.41) (0.75, 0.94) (0.27, 0.39) (−0.31, −0.01) (0.43, 0.63) (0.33, 0.62) (−0.14, 0.31) (0.44, 0.73)
(2.19, 3.06) (0.72, 1.65) (0.27, 0.67) (0.49, 0.69) (−0.57, −0.02) (0.81, 1.11) (−0.32, 0.34) (0.45, 1.30) (0.04, 0.70)
Note: The 68% confidence regions included in parentheses under each multiplier.
Operation Thunderbolt by Israeli commandos at Entebbe Airport in Uganda to free the
hostages from Air France flight 139 in June 1976). Data aggregation also makes a dif-
ference for OTHER hostage events, where instead of the net positive multipliers of the
monthly data, the quarterly data’s impact and long run multipliers are more complex
when the confidence intervals are consulted. The total multiplier is nonzero for only the
violent end and death covariates; thus, the immediate impact of negotiation success on
OTHER events is ameliorated in the long run.
In sum, we find that negotiation success generates more kidnappings regardless of the
unit of analysis. Moreover, kidnappings with violent ends or deaths do not deter future
incidents. When examined quarterly, violent ends deter skyjackings but deaths do not.
The latter finding is likely due to past events where the skyjackers murdered a passenger
— e.g., TWA flight 847 on June 14, 1985 — to make the authorities take their demands
seriously. Such tactics were often associated with concessions eventually being made. For
OTHER hostage events, the three covariates generally resulted in more hostage taking.
The magnitude and, for skyjackings, the direction of the covariate’s influence is time-
One reason for the differing results for the monthly versus quarterly data is that there
may be structural changes in the three hostage series. The next section looks at this
4.2. Bayesian multiple changepoint model analysis
The PAR(p) models assume that the data have a unique equilibrium, which is violated
if there are structural changes in the number of average events per period or a noninde-
pendent arrival time between hostage events. This could be the result of the data being
better explained by a clustered or time-dependent Poisson process, such as a negative bi-
nomial process. In fact, the PAR(p) models results show that the predictive distribution
for this model is a negative binomial.
The PAR(p) model does not allow one to test for the presence of structural changes
in the inter-arrival times of hostage events. One could do this by fitting a sequence of
models and using tests analogous to those for structural breaks in regression models.
Such a task, however, requires the analyst to know or specify the number and timing of
the possible structural breaks. This would be an ad hoc task and is largely self-fulfilling
because of analysts’ biases in looking for or “confirming” changes (cf., Park, 2007).
Alternatively, one could use a Bai-Perron test for structural breaks. But this test
depends on an assumption that the data are normally distributed, which is not the case
for event count data at low frequencies unless the mean number of counts is “large.”
Thus, we adopt a different model that uses a multiple changepoint model, which looks
for changes in the arrival of events in a Poisson process. The assumption here is that each
individual event is a draw from a cumulative counting process where the timing between
the events is a time-dependent rate.5The model is referred to as “multiple” changepoint
model because it allows for an endogenous set of changes or shifts to occur in the rate of
events. At each point in time one evaluates whether there should be a changepoint to a
new level (a birth) or a changepoint back to a previous level (a death), a change in the
5Such models are commonly used to model disasters, such as coal mining accidents (Raftery & Akman,
1986; Green, 1995).
height or probability of each changepoint, or a change in the location of the position of a
changepoint. For these four options, one estimates the endogenously determined number
of breaks or shifts in the arrival rate. These shifts can be to higher or lower hostage event
arrival rates. This procedure surmounts the problem of pre-specifying the changepoints
and biasing the results.
An additional complication with specifying a multiple changepoint model for frequen-
tist inference is that an analyst would need to pre-specify the maximal number of breaks.
Since a priori the number of changepoints is unknown, one must find a robust method
for evaluating whether to add or eliminate a changepoint from the model. This problem
has been solved in a Bayesian approach by the development of reversible jump Markov
chain Monte Carlo (RJ-MCMC) methods. These methods allow one to sample whether
the posterior distribution of the data (and parameters) are better characterized by a
model with either k−1, k, or k+1 changepoints. The choice of the value of k is a model
determination or order issue: the choice of k determines the number of parameters in the
The Bayesian model for the changepoints is provided by Green (1995). The model
uses daily data on the hostage events, since any aggregation of the data would only
rescale the arrival rate of the events by the periodicity of the data. Thus, for determining
breaks, the level of aggregation often has little consequence. Let the data points for the
Poisson process of number of hostage events per day be yi,i = 1,2,...,n ∈ [0,L]. The
daily arrival rate for the Poisson process for the events varies over time according to the
arrival rate function w(t). The likelihood for these Poisson events is
where n is the number of events and L is the total elapsed days of the hostage events.
The multiple changepoint aspect enters the model by assuming there are step functions
that describe the jumps in the rate function w(t). Suppose there are k steps at intervals
0 < s1< s2< ... < sk< L and the steps take a value or height of hjbetween [sj,sj+1]
for j = 0,1,2...,k. The number of possible steps is assumed to be Poisson distributed
p(k) = exp(−λ)λk
where k ≤ kmax and kmax is the arbitrary maximum number of breaks. Under these
assumptions, the steps are even-numbered order statistics from 2k + 1 points over a
uniform interval [0,L]. The heights of the steps, h0,h1,...,hk(which describe the density
of changepoints) are independent draws from a Γ(α,β) density. These assumptions define
a model where up to kmax breaks are possible, with a uniform density for the break
locations. The latter is computationally expensive and possibly leads to selecting too
This model could be implemented by classical (i.e., maximum likelihood) methods if
one were to pre-specify k, but this presupposes knowing the number of changepoints.
One instead can take a Bayesian approach and condition the model on the choice of
k, which requires comparing the posterior probability of adding or subtracting from k.
This is the “reversible” part of the estimation since it changes the dimension of the
number of changepoints in w(·) from either 1) k to k − 1 (a death step), 2) k to k + 1
(a birth step), 3) changing the step height, or 4) changing the position of a step. In this
situation, classical likelihood theory breaks down because the changepoint models for k
versus k ±1 are nonnested, but Bayesian estimation (even with a diffuse prior about the
number of changepoints and their arrival times) provides a solid basis for inference (see
Bayesian RJ-MCMC changepoint models for the daily KIDNAP, SKYJACK, and
OTHER series were fitted with a diffuse prior.6The RJ-MCMC sampler consisted of
400,000 burn-in iterations (which were discarded to remove the initial conditions from
the sampler) and a final posterior sample of one million draws, which were thinned from
a total of twenty million draws from the posterior density.7
Figure 4 shows the plot of the cumulative number of events, the arrival rate of new
events and the changepoints in the KIDNAP series, while Table 4 shows the ten estimated
breaks in the KIDNAP series. The solid line in the figure is the cumulative number of
KIDNAP events over the period while the dashed line is the estimated arrival rate of new
events. Changes in the slope of the arrival rate are identified as the changepoints which are
presented in Table 4. The table’s columns display the median date for the changepoints,
their 68% credible intervals, and the direction of change. In the right-most column of
Table 4, we have matched, based on detailed historical accounts (e.g., U.S. Department of
State, various years and ITERATE writeups), the precipitating events. Thus, changepoint
1 is attributed to the rise in transnational terrorism that followed Israeli occupation after
the Arab-Israeli wars. For changepoint 2, there is no clearly defined cause. Changepoint
3 is attributed to the arrival of Lebanon multinational (peacekeeping) force (MNF) that
triggered a rise in kidnappings in Lebanon and throughout the Middle East. The eventual
fall in these kidnappings by 1988 results in changepoint 4. At times, certain countries
or regions were plagued with a spate of kidnappings — see changepoints 5 and 7. An
important recent changepoint followed the Abu Ghraib revelations at the start of April
2004 that resulted in myriad kidnappings of foreign contractors and aid workers in Iraq
(Enders & Sandler, 2006, Table 7.3, 174). Thus, changepoints 1, 3, and 9 followed from
policy decisions with unintended awful consequences. Many of the breaks in Table 4
have not been identified previously, thus underscoring the importance of our procedure.
Notably, 9/11 is not a changepoint.
Figure 5 shows the SKYJACK series results, where there are eight breaks in the series,
indicated by the vertical lines. Once again, the solid line is the cumulative number of
SKYJACK events and the dashed line is the estimated arrival rate of new events. The
information on the changepoints from Figure 5 is summarized in Table 5, along with
confidence intervals, direction of change, and precipitating events. Two important con-
trasts between the KIDNAP and SKYJACK series are worth highlighting: SKYJACK
6The prior sets kmax= 50, α = 1, β = L/n, which is the elapsed days from the first event divided by the
total number of events, or a very low prior step height for changes, λ = 2 or a prior of two changepoints.
This prior is consistent with the Bai-Perron breakpoint analysis results of Enders & Sandler (2005).
Using a larger prior number of changepoints merely generates clusters of changepoints around those
7The posterior sample of the parameters passes standard diagnostic tests for convergence (Gelman and
Rubin potential scale reduction factors computed using multiple chains are all one, traceplots show good
mixing and convergence, and the acceptance rates of the acceptance rates for the Hasting steps for the
number of changepoint are between 35-55%.)
Cumulative number of kidnap events
Posterior mean arrival rate of kidnap events
Fig. 4. Cumulative number of KIDNAP events and the posterior arrival rate of kidnap events, 1968–2005.
Table 4. KIDNAP event changepoint dates and their 68% credible intervals, 1968-2005.
Changepoint Median Date
68% credible set
1970-02-17 (1970-01-28, 1970-02-25)
Rise of transnational terrorism
1977-10-25 (1971-08-19, 1983-06-21)
Small decline in kidnappings
1983-07-27 (1983-04-22, 1988-03-17)
Lebanon MNF, rise in Middle East kidnappings
1988-07-27 (1987-09-16, 1991-10-26)
Downturn in Middle East kidnappings
1993-05-22 (1992-09-01, 1994-01-17)
1998-01-09 (1997-12-20, 1998-04-02)
Drop in transnational terrorism
1998-12-21 (1998-12-01, 1999-01-05)
African / Latin American kidnappings
2000-10-14 (2000-09-19, 2000-11-24)
Pre 9/11 drop
2004-04-05 (2004-03-30, 2004-04-07)
Abu Ghraib revelations
2004-11-06 (2004-11-02, 2004-11-15)
Reduction in Iraqi kidnappings
has fewer changepoints, and the changepoints differ between the two series. This last
observation means that past studies — e.g., Enders & Sandler (2005) — that aggregate
all hostage events miss important breaks in the series. In Table 5, changepoint 1 corre-
sponds to a number of well-publicized PFLP skyjackings that demonstrated to terrorists
worldwide that well-executed seizures with lives hanging in the balance not only capture
media attention, but may also yield concessions. The introduction of metal detectors
at the start of 1973 led to a fall in skyjackings as the U.S. lead on January 3, 1973
was gradually followed by other countries over the next six months. Changepoint 3 is
attributed to Cuban exiles commandeering U.S. planes to Cuba, a practice that finally
ended (changepoint 4) once Castro dished out 40-year sentences to hijackers upon arrival
and passengers started to take matters into their own hands. Changepoint 5 is associated
with a large number of skyjackings in the Soviet Union prior to its collapse in 1991. The
reduction in state-sponsored terrorism after the Cold War is matched to changepoint 6,
while the decline of all forms of terrorism in 1996 may explain changepoint 7. Finally,
increased airport security is tied to changepoint 8.
Figure 6 shows the cumulative number of OTHER hostage events and their arrival
rate. The four changepoints are marked with vertical lines that match the entries in
Table 6. Note that these breaks are much more spaced out — there are roughly six to
eight years between each break. Large shifts in the arrival rate occur from late 1975
through 1985. Barricade missions and nonaerial hijackings lost their popularity in the
late 1980s, thus explaining the paucity of changepoints after 1985. In Table 6, the four
changepoints are matched to precipitating causes. Efforts to secure airports and other
actions to protect business people from kidnappings resulted in a substitution into other
kinds of hostage events — changepoint 2. As embassies were fortified in 1985, there was
a drop in barricade missions (Enders & Sandler, 1993, 2006). Finally, the post-Cold War
reduction in state-sponsored terrorism is tied to changepoint 4.
It is noteworthy that as hostage taking missions become more difficult (e.g., skyjackings
are more difficult than kidnappings) that the number of changepoints fall from Table 4
to Table 6. Quite simply, innovations and shocks are more difficult to achieve for more
difficult missions. The arrival rate changes are plotted together in Figure 7. The KIDNAP
and SKYJACK events are negatively correlated (r = −0.12), which is indicative of
substitutes. Thus, as metal detectors cut down on skyjackings, terrorists substituted into
kidnappings, not protected by these detectors. The arrival rates of KIDNAP and OTHER
hostage events are uncorrelated (r = −0.01). In contrast, these arrival rates are positively
correlated (r = 0.15) for SKYJACK and OTHER hostage events, where the location is
known to authorities. This positive correlation is indicative of complements.
The identification of substitute and complement modes of hostage taking is essential to
informed and effective policymaking. Policymakers must anticipate that actions to reduce
one attack mode will be somewhat offset by greater reliance by terrorists on a substitute
mode. Thus, the authorities must also protect against this anticipated substitution with
foresight. In the case of complementary modes, a single policy intervention is apt to
reduce both forms of hostage taking. If hostage models are uncorrelated, then a policy
intervention for one mode is unlikely to have repercussions on the other attack mode.
Cumulative number of skyjack events
Posterior mean arrival rate of skyjack events
Fig. 5. Cumulative number of SKYJACK events and the posterior arrival rate of skyjack events, 1968–2005.
Table 5. SKYJACK event changepoint dates and their 68% credible intervals, 1968-2005.
Changepoint Median Date
68% credible set
1969-08-02 (1969-05-09, 1973-03-12)
PFLP skyjackings demonstration effect
1973-04-17 (1972-10-18, 1979-11-10)
1980-01-02 (1979-06-04, 1981-10-12)
1981-11-24 (1981-06-09, 1987-08-03)
Castro 40-yr sentences
1990-04-29 (1986-01-15, 1990-06-15)
1991-01-02 (1990-05-21, 1995-04-10)
End of Cold War
1996-09-03 (1994-12-15, 1998-08-08)
Low terrorism year
2003-04-23 (1999-07-10, 2003-06-27)
Increased airport security
Cumulative number of other events
Posterior mean arrival rate of other events
Fig. 6. Cumulative number of OTHER hostage events and the posterior arrival rate of nonkidnap events, 1968–2005.
Table 6. OTHER event changepoint dates and their 68% credible intervals.
Changepoint Median Date
68% Credible Set
1972-06-26 (1969-11-17, 1972-09-04)
1979-10-01 (1972-08-14, 1981-10-31)
Substitution into other hostage events
1985-02-10 (1981-02-28, 1991-09-10)
1993-06-10 (1991-05-26, 2001-02-11)
Post-Cold War reduction
0.000.05 0.100.15 0.200.25
Fig. 7. Estimated arrival rates for each type of hostage event, based on the RJ-MCMC changepoint model, 1968-2005
5. Concluding remarks
This paper investigates the dynamic properties of three hostage taking series — kid-
nappings, skyjackings, and other hostage events. Based on the Poisson autoregressive
model, we identify the lag structure of these three series for monthly and quarterly data,
as well as the impacts of three covariates (i.e., successful negotiations, violent ends, and
deaths). These impacts are expressed in terms of an impact and a long run multiplier.
In the latter half of the paper, we apply a changepoint model estimated using reversible
jump Markov chain Monte Carlo methods to identify the changepoints for the three series
and to relate these breaks to the precipitating event.
This study shows that the level of aggregation — monthly or quarterly — makes a
difference in the inferences about the dynamics of the series and the impacts of covari-
ates. Moreover, we show that the covariates have different impacts on various hostage
series. This indicates that policy recommendations for, say, kidnappings do not necessar-
ily apply to skyjackings or other hostage events. For example, past concessions granted
have the strongest impact on inducing future kidnapping events. For quarterly data, each
successful negotiation results on average in 2.62 additional abductions over time. In fact,
violent ends encourage further kidnappings and other hostage events, a disturbing and
When changepoints are investigated, we find that each type of hostage event has dif-
ferent changepoints. The more risky the event, the fewer are the number of changepoints.
These differences again underscore that policy recommendations must distinguish among
the various types of hostage incidents. Another disturbing finding is that some policies —
e.g., Lebanon MNF and Abu Ghraib abuses — have unintended negative consequences
that generate a wave of kidnappings. Thus, changepoints may result from policies, polit-
ical events, or terrorism hotspots. Past studies that only used counterterrorism policies
to identify changepoints will miss many such points.
Kidnappings and skyjackings estimated arrival rates are negatively correlated so that
policies that discourage skyjackings — e.g., airport metal detectors — may encourage
kidnappings. This negative correlation, thus, alerts policymakers to account for such po-
tential substitutions, which may call for multiple policy interventions to head off policy-
induced transference of attacks. Since skyjackings and other hostage events estimated
arrival rates are positively correlated, a single policy intervention may have a double div-
idend by curbing more than one terrorist tactic. When making allocation decision among
alternative counterterrorism actions, policymakers need to account for such negative and
Our methods can be fruitfully applied to other terrorist tactics for policy and forecast-
Patrick Brandt appreciates the support of the National Science Foundation (grants
SES-0351205 and SES-0540816). The code used to estimate the models in this paper
(written in R and Fortran), replication materials, and additional results are available
Todd Sandler gratefully acknowledge research support from the Vibhooti Shukla en-
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