# Hostage taking: Understanding terrorism event dynamics

**ABSTRACT** 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--successful 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 kidnapping 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. Skyjackings and kidnappings are negatively correlated, while skyjackings and other hostage events are positively correlated. Policy recommendations are offered.

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Page 1

Hostage Taking: Understanding Terrorism Event

Dynamics

Patrick T. Brandt, Todd Sandler∗

School of Economic, Political and Policy Sciences

GR 31

800 W. Campbell Road

The University of Texas at Dallas

Richardson, Texas 75080-3021

Abstract

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

1. Introduction

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

∗Corresponding author.

Email addresses: pbrandt@utdallas.edu, tsandler@utdallas.edu (Patrick T. Brandt, Todd

Sandler).

Preprint submitted to Elsevier14 July 2008

Page 2

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-

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Page 3

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.

2. Preliminaries

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

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Page 4

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.

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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.

3. Data

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).

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Page 6

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

series.

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).

σ

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Monthly KIDNAP Events

Date

1970198019902000

0

5

10

15

0.00.2 0.40.60.81.0

0.0

0.4

0.8

Lag

ACF

ACF for Monthly KIDNAP Counts

Quarterly KIDNAP Events

19701980 19902000

0

10

20

30

0.01.02.03.0

?0.2

0.2

0.6

1.0

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.

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Monthly SKYJACK Events

Date

1970198019902000

0

2

4

6

8

10

0.00.20.40.60.81.0

0.0

0.4

0.8

Lag

ACF

ACF for Monthly SKYJACK Counts

Quarterly SKYJACK Events

1970 1980 19902000

0

5

10

15

20

0.01.0 2.03.0

?0.2

0.2

0.6

1.0

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:

Measurement equation:

Pr(yt|mt) =myt

texp(−mt)

yt!

Transition Equation:

mt=

p

?

i=1

ρiyt−i+

?

1 −

p

?

i=1

ρi

?

exp(xtβ)

Initial Conditions:

8

Page 9

Monthly OTHER Events

Date

1970 198019902000

0

2

4

6

8

0.00.2 0.40.60.8 1.0

0.0

0.4

0.8

Lag

ACF

ACF for Monthly OTHER Counts

Quarterly OTHER Events

19701980 19902000

0

2

4

6

8

10

0.01.0 2.03.0

?0.2

0.2

0.6

1.0

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

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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

smaller samples.

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Table 1. PAR(p) results for monthly and quarterly KIDNAP, SKYJACK and OTHER series 1968–2005.

KIDNAP

SKYJACK

OTHER

Parameters

Monthly

Quarterly

Monthly

Quarterly

Monthly

Quarterly

ρ1

0.23 (0.04) 0.18 (0.05) 0.25 (0.07) 0.30 (0.07) 0.19 (0.05) 0.21 (0.09)

ρ2

0.13 (0.05) 0.14 (0.05) 0.17 (0.08) 0.16 (0.08)

ρ3

0.02 (0.04)

0.06 (0.07) -0.13 (0.05)

ρ4

-0.02 (0.04)

0.13 (0.07) 0.11 (0.06)

ρ5

0.002 (0.04)

ρ6

0.12 (0.04)

ρ7

0.03 (0.04)

ρ8

-0.12 (0.04)

Negotiation Successt

0.27 (0.06) 0.22 (0.04) 0.67 (0.07) 0.33 (0.06) 0.34 (0.19) 0.43 (0.15)

Negotiation Successt−1

0.12 (0.04)

-0.42 (0.24)

Violent Endt

0.37 (0.06) 0.24 (0.05) 0.87 (0.14) -0.16 (0.16) 0.66 (0.16) 0.07 (0.20)

Violent Endt−1

-0.08 (0.06)

0.53 (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

-0.10 (0.03)

-0.26 (0.18)

Intercept

0.73 (0.07) 1.65 (0.08) -0.52 (0.16) 0.20 (0.18) -0.83 (0.11) 0.06 (0.13)

Log likelihood

-862

-405

-503

-265

-399

-218

AIC

1747

827

1019

544

806

450

χ2, H0: Poisson model (p-value)107 (<0.01) 29 (<0.01) 98 (<0.01) 51 (<0.01) 13 (<0.01)

6 (0.02)

d.f.

437

140

446

144

425

135

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.

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Impact multiplier:

?

1 −

p

?

i=1

ρi

?

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.,

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Table 2. Impact and long run impact multipliers for one unit increases in each of the independent variables for the monthly PAR(p) models.

KIDNAP

SKYJACK

OTHER

Negotiation

Violent

Incidents Negotiation

Violent

Incidents Negotiation

Violent

Incidents

Success

End

with Deaths

Success

End

with Deaths

Success

End

with Deaths

Impact

0.44

0.61

0.58

0.21

0.28

0.28

0.15

0.29

0.41

(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)

Total

0.75

1.03

0.99

0.56

0.72

0.73

0.19

0.36

0.51

(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.

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Table 3. Impact and long run impact multipliers for one unit increases in each of the independent variables for the quarterly PAR(p) models.

KIDNAP

SKYJACK

OTHER

Negotiation

Violent

Incidents Negotiation

Violent

Incidents

Negotiation

Violent

Incidents

Success

End

with Deaths

Success

End

with Deaths

Success

End

with Deaths

Impact

1.15

1.20

0.84

0.33

−0.16

0.53

0.48

0.09

0.59

(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)

Total

2.62

1.18

0.47

0.59

−0.29

0.96

0.01

0.87

0.37

(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.

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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-

frame dependent.

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

posssibility.

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).

15

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