Principal-Agent Problems and Control

This section discusses principal agent theories of terrorist groups. According to such theories, counterterrorism threatening to expose a terrorist leader may diminish leaders’ control over their operatives. Depending on the preferences of leaders and operatives, this could increase terrorist violence.

Both Shapiro (Reference Shapiro2013) and Abrahms and Potter (Reference Abrahms and Potter2015) model terrorist groups as nonunitary organizations, subject to principal-agent problems. Principal-agent problems arise because leaders and operatives within terrorist organizations have different preferences regarding how many and what type of terrorist attacks to commit. Unless the leader can exert control over operatives, operatives might not act as the leader wants. Control refers to efforts by the leader to determine the actions of operatives, specifically, (1) communication—the leader telling operatives what to do—and (2) punishment—the leader penalizing operatives that do not follow orders or rewarding those that do (Shapiro Reference Shapiro2013).

Counterterrorism that threatens to expose the terrorist leader is predicted to decrease the degree of control a leader is able or willing to exert (Shapiro Reference Shapiro2013). Engaging in communication and punishment makes a leader more vulnerable to detection by counterterrorism agencies, so leaders may opt to exert less control as scrutiny by counterterrorism agencies intensifies. Mir (Reference Mir2018) illustrates qualitatively how drone strikes affect control within terrorist organizations in FATA: to avoid detection by drones, leaders eschewed use of communication devices, quit meetings, and were out of contact with operatives for months. A drone strike that hits a terrorist leader plausibly decreases control more steeply than a drone strike that misses a terrorist leader. The new leader is likely less capable of exerting control, at least initially. If the new leader were better than the old leader at exerting control, presumably he would already be the leader. The new leader may also be less willing to exert control. The old leader evidently revealed enough information about themselves to be killed by drone. The new leader might not yet have, giving them an incentive to trade off control for secrecy.

The predicted effect of a decrease in control on terrorist violence is ambiguous: this depends on the relative preferences of the leader and the operative (Shapiro Reference Shapiro2013). If the operative has a greater preference for violence than the leader, decreasing the leader’s control within the terrorist group is predicted to lead to more violence.

There are theoretical reasons to believe that terrorist operatives indeed have a greater preference for violence than terrorist leaders. The main theoretical argument is that leaders, having had longer tenure within the organization, know better that particular terrorist attacks harm the group’s long-term prospects by decreasing public support (Abrahms and Potter Reference Abrahms and Potter2015; Shapiro Reference Shapiro2013). Attacks that are harmful in the long term likely include attacks on civilians (Abrahms Reference Abrahms2012; Fortna Reference Fortna2015). Alternative theoretical arguments include a selection effect—operatives are selected for their tendency towards violence—whereas leaders have other qualities (Shapiro Reference Shapiro2013)—or greater benefits to violence for operatives—for example in the form of pillage or promotion within the organization (Abrahms and Potter Reference Abrahms and Potter2015).

Empirical evidence also suggests that terrorist leaders prefer less violence than operatives, especially violence against civilians. In a study of over 1,300 individual members of radical groups in the US, Jasko and LaFree (Reference Jasko and LaFree2019) find that leaders have a lower propensity for violence than followers. Anecdotal evidence and qualitative case studies suggest a similar pattern. Intercepted letters from Al-Qaida suggest that its leaders repeatedly admonish subsidiary groups to commit less violence against Muslim civilians (Crenshaw Reference Crenshaw2012). Al-Qaida in Iraq in particular ignored orders to halt beheadings and other tactics that eventually eroded its popular support base (Price Reference Price2019; Jordan Reference Jordan2019). Price (Reference Price2019) details how the imprisonment of a Hamas leader eroded checks on who could execute suicide bombings, resulting in more attacks. Abrahms and Mierau (Reference Abrahms and Mierau2017) provide a detailed case study of how leaders of the Taliban tried but on various occasions failed to stop lower level members from perpetrating indiscriminate violence against civilians. The death of TTP leader Hakimullah Mehsud reportedly sparked a debate within the group about whether civilians were legitimate targets, and terrorist attacks by the TTP spiked (Crenshaw Reference Crenshaw2012). Leaders of the TTP and Haqqani network publicly denied involvement in attacks that members of their respective organizations likely did commit, including attacks after TTP had signed a peace agreement with the Pakistani governmentFootnote ⁹ and an attack on a funeral.Footnote ¹⁰

The latter examples illustrate that leaders who cannot exert sufficient control to prevent operatives from executing attacks harmful to the group’s long-term interests may still try to do damage control by not claiming these attacks. See Abrahms and Conrad (Reference Abrahms and Conrad2017) for a formal theory of such strategic credit claiming.

Principal-agent models thus give the following hypotheses. Drone strikes that kill terrorist leaders are predicted to lead to a decrease in control of leaders over operatives (H1.1). A decrease in control may be expressed empirically by an increase in terrorist attacks on civilian and private targets (H1.1a) or an increase in terrorist attacks committed but not claimed by the organization (H1.1b).

The degree of control leaders exert affects the organizational structure of terrorist groups. Abrahms and Potter (Reference Abrahms and Potter2015) note that group structure is a standard proxy for leadership control. Groups with higher degrees of control are more centrally organized—that is, have more ties between leaders and operatives. Robustness of central control is one of two defining characteristics in Staniland’s (Reference Staniland2014) classification of armed group organizational structure. A group with robust central control has an effective bureaucracy to discipline members and socialize them into the “party line.”

This gives us a further set of hypotheses. Drone strikes undermining control may lead to a change in organizational structure: if all ties between terrorist leaders and operatives break down, parts of the group may form splinter groups (H1.1c) or fight among each other (H1.1d). Furthermore, groups that rely more on central control may be affected more strongly by drone strikes than groups that do not (H1.2a). If a group has no central control to begin with, control cannot be further undermined by killing its leader, and we would expect drone strikes to have little effect.

Finally, the effect of drone strikes on violence may be stronger for the first leader killed (H1.2b). The first leader targeted decided how much information to reveal about themselves prior to the existence of drones, and it may be too late to hide this information through decreasing control. The subsequent leader is possibly better able to trade off control for secrecy. Hence, we may expect the drop in control to be greatest after the first leader of each group is killed.

Capacity

A drone strike can be considered an example of a proactive counterterrorism policy aiming to eliminate terrorist capacity: resources needed for the execution of terrorist attacks. Consider a production function of terrorist attacks. Several resources can be inputs to this production function, for example, leadership, financial capital, or operatives’ labor. Assume that terrorist groups maximize the number of terrorist attacks committed subject to their resource constraints. Drone strikes eliminating leadership tighten this resource constraint, leading to a predicted decrease in the frequency of terrorist attacks (see for example Powell Reference Powell2007; Sandler and Arce Reference Sandler and Arce2003).

However, capacity models considering that terrorist groups may choose between different types of attacks can predict an increase in the frequency of terrorist attacks as a result of proactive counterterrorism (Enders and Sandler Reference Enders, Sandler and Silke2004). Imagine that terrorist groups maximize the political impact of their attacks. They can commit some number of low-impact attacks (requiring fewer resources) or high-impact attacks (requiring more resources). If proactive counterterrorism policies disproportionately eliminate terrorist resources that are required for high-impact attacks, terrorist groups may substitute away from high-impact attacks into low-impact attacks. If the increase in the number of low-impact attacks is larger than the decrease in the number of high-impact attacks, the frequency of terrorist attacks increases, despite lower capacity and lower political impact of the terrorist group.

Hence, capacity models predict that a decrease in terrorist group capacity due to a drone hit on its leader may lead to a substitution of high-impact with low-impact attacks (H2.1). This could manifest in more “failed” terrorist attacks, smaller terrorist attacks in terms of number of victims, or substitution of attacks on military targets and US citizens or attacks abroad, with attacks on private and civilian targets or attacks in Pakistan.

Signaling

A drone strike that hits a terrorist leader may introduce uncertainty about a terrorist group’s ability or resolve to continue terrorist attacks, which in turn may give terrorist groups an incentive to commit more attacks in the periods after the drone strike by way of a signal. Imagine a government must decide whether to make concessions to a terrorist group but is uncertain about the resolve or resources commanded by the terrorist group. Terrorist groups then have an incentive to commit more or larger terrorist attacks in the period soon after this uncertainty arises, in an attempt to convince the government of their strength or resolve and induce concessions (Arce and Sandler Reference Arce and Sandler2007; Lapan and Sandler Reference Lapan and Sandler1993).

Signaling models thus hypothesize that a drone strike hitting a terrorist leader leads to an increase in terrorist attacks that send a strong signal (H3.1). The strongest signal arguably consists of terrorist attacks that immediately follow the drone strike hitting a terrorist leader that hit a “hard” target, such as a military target or a US citizen, and that are claimed by the terrorist organization. Furthermore, we might hypothesize that these effects are stronger for more prominent leaders (H3.2): the more prominent the leader killed by drone, the stronger the signal required to convince others of the organization’s resolve.

Signaling as a theoretical explanation is difficult to empirically distinguish from revenge or retaliation. If a terrorist group wishes to avenge the death of its leader, the resulting pattern of terrorist attacks is plausibly similar to that suggested in H3.1 and H3.2.

Backlash and Recruitment

Proactive counterterrorism policies may cause “backlash” if they result in civilian collateral damage, thereby spurring terrorist recruitment. Conceptually, backlash is distinct from the effect of targeted leader killing, but in practice the two might be related if operations killing leaders disproportionately kill civilians. In this respect, drone strikes are distinct from other methods of targeted leader killing, such as special operations, which may present a lower risk of civilian casualties.

Backlash could occur if terrorist organizations use civilian casualties to foment ideological opposition (Bueno de Mesquita Reference Bueno de Mesquita2005). Alternatively, Kalyvas (Reference Kalyvas2000) suggests that those facing indiscriminate violence by the hands of one party to a violent conflict may protect themselves by joining the other. If violence is completely indiscriminate, joining does not pose additional risk, but provides the new recruit with information on when and where such indiscriminate violence might occur. A fully informed government may still wish to engage in counterterrorism creating backlash—if it trades off an increase in future attacks for a decrease in current attacks (Jacobson and Kaplan Reference Jacobson and Kaplan2007) or if it does not fully internalize the global costs of proactive counterterrorism because this increases recruitment, but displaces terrorist attacks to softer foreign targets (Rosendorff and Sandler Reference Rosendorff and Sandler2004).

Backlash need not remain limited to the terrorist organization subject to proactive terrorism policies; it may extend to terrorist groups generally. Siqueira and Sandler (Reference Siqueira and Sandler2007) provide a model in which proactive counterterrorism measures against one terrorist group trigger reprisal attacks by other groups.

Theoretical models considering backlash predict that drone strikes that hit civilians may lead to increased terrorist attacks by the terrorist organization that was the target of the drone strike or by terrorist groups in general (H4.1).

Data

This paper uses a newly constructed panel dataset of successful and failed targeted leader killings, capturing variation across 13 terrorist groups over a period of 12 years (2004–2015). The unit of observation is the group-month. Various cross-checks have been carried out to make this dataset arguably less subject to reporting bias compared with relying on a single data source. Balance checks substantiate the assertion that drone hits and misses are quasi random.

Drone Strikes

To construct a dataset of successful and failed targeted killings of terrorist leaders, I code 443 narratives about individual drone strikes between 2004 and 2015, collated by the Bureau of Investigative Journalism (BIJ),Footnote ¹¹ and cross-check these with data from the New America Foundation (NAF)Footnote ¹² and information on terrorist leaders from the Mapping Militants Project at Stanford University (Crenshaw Reference Crenshaw2012).

For each drone strike reported by the BIJ, I code whether a terrorist leader was targeted and whether this leader died. The terrorist group(s) the drone strike targeted is also recorded. This results in 379 strikes for which the group targeted can be determined from BIJ reports,Footnote ¹³ including 137 targeting a named individual designated by BIJ reports as “leader.” For full coding rules, see Appendix A2.

The resulting data on terrorist leaders was cross-checked with data from the NAF. This organization also provides information on terrorist leaders targeted by drone, which was used by previous studies (e.g., Abrahms and Mierau Reference Abrahms and Mierau2017; Johnston and Sarbahi Reference Johnston and Sarbahi2016). These data have substantial downsides. The NAF for unknown reasons does not report unsuccessful strikes on leaders between 2012 and 2015 and is extremely broad-brushed when classifying terrorist groups. For example, the Afghan Taliban, local (Pakistani) Taliban, Tehrik-i-Taliban Pakistan (TTP), and the Punjabi Taliban are all coded as “Taliban.” This forces authors using NAF leaders data to consider all groups targeted as a single unit and truncate the data in 2011 (Abrahms and Mierau Reference Abrahms and Mierau2017), creating a single short time series. By contrast, coding BIJ narratives results in information on 13 different terrorist groups, forming a panel dataset covering a longer period. An overview of these 13 groups can be found in Appendix A1. Note that two of these 13 groups do not exist for part of the research period.

Cross-checking data between the BIJ and the NAF gives insight into how information from single data sources might be biased. Although both BIJ and NAF are nonpartisan and construct their data on the basis of (often the same) reputable news sources, when reading between the lines, the NAF appears to have a more positive outlook on use of drones than the BIJ. This gives the NAF a stronger tendency to portray those killed by a drone strike as a leader. I cross-check all named individuals the NAF classifies as “leaders killed.” Deaths of all but one of these individuals are also found in the BIJ data, within 2 days of the NAF-recorded data. However, the BIJ does not always classify these individuals as “leaders.”

To mitigate bias in the interpretation of who is a leader, I cross-check data coded with leaders mentioned by the Stanford Mapping Militants project. United States counterterrorism agencies have an incentive to inflate the importance of individuals once they are killed by drone strike, which affects both NAF and BIJ data, as these are based on strike reports. By contrast, the Mapping Militants project creates profiles of terrorist groups independent of drone strikes, based on open-source information it selects to “maximize veracity and reliability.” Names of the group’s leaders are a fixed element of each profile.

Confirming the suspicion that the importance of individuals is inflated by drone strike reports, the “leader” as classified by BIJ is only recognized as such by the Mapping Militants Project for approximately one-third of strikes (45 out of 137). In the preferred specification, only the 45 strikes involving leaders who are considered as such by the Stanford project are coded as a drone strike targeting a leader. Fifteen of these succeeded in killing the target. Ten leaders were both missed and hit (see Appendix A3 for details). Results using the BIJ definition, giving 137 drone strikes targeting a leader, are included as a robustness check.

Note that it is the rule rather than the exception for the death of a leader, especially those leaders recognized by the Stanford project, to be confirmed by both sources in the US government and the terrorist organization. Terrorist organizations commonly publish statements about the death of their leader, put out eulogies, or place online pictures of his funeral. This does not hold for those marked as “leaders” by the NAF or BIJ only, who are sometimes only identified by some less-than-unique nickname.

It is possible that a terrorist group has leaders that are not publicly known. These would not be included in reports by BIJ, NAF, or Mapping Militants, which are all based on open-source information. Drone strikes on these individuals are counted as strikes not involving a group’s leader in the present analysis. As results are driven by the difference between drone hits and misses on a leader, this is not likely to bias the analysis.

I supplement the dataset of terrorist leaders with information on the importance of a leader within a terrorist group. Two metrics are used. The first is an indicator equaling 1 if the Stanford Mapping Militants Project indicates an individual was ever “first in command” or similar of a terrorist group. The second is the maximum reward amount offered for information on a terrorist leader by the US Department of State’s Reward for Justice Program.

The identification strategy of this paper relies on the quasi randomness of hits and misses: indeed, there is virtually no evidence that there is a pattern to hits and misses. Table 2 displays the mean of a large set of variables for group-months with a drone hit and a drone miss, respectively, and the $ p $ -value for a $ t $ -test of the difference between both. Results indicate that the probability of a hit is not driven by prior drone activity, Pakistani military action, or peace agreements between the terrorist groups and the Pakistani government, all of which could reveal information about terrorist leaders and make a hit more likely. Table 2 also finds no evidence that the probability of a hit is statistically significantly different when Pakistani military action or a peace agreement might be anticipated. The probability of a hit does not significantly differ by importance of the leader, number of leaders involved, district, target type, or terrorist group. Hits do not cause a significantly higher or lower number of (civilian) casualties. There is some evidence that terrorist groups are less likely to be the target of a drone strike after a drone hit on their leaders. Therefore, all specifications will control for drone strikes not targeting leaders. There is strong evidence that the probability of a hit increased over time. This highlights the importance of including time-fixed effects, which will be included in all specifications.

TABLE 2.

Difference between Group-Months with a Drone Hit and a Drone Miss

Anecdotally, drone misses seem to be mostly driven by chance. They fall into three broad categories: drone strikes hitting locations where the targeted leader is not yet or no longer present, instances when the targeted leader is merely wounded, and instances when reports of a leader’s death are credible enough to be taken up by reputable news sources only for the leader to later show up alive. To mitigate concerns that misses are underreported, results using an alternative definition of a “miss” will be presented as a robustness check.

Terrorist Violence and Other Data

Data on drone strikes targeting the 13 terrorist groups mentioned by BIJ is linked to data on terrorist attacks by these groups from the Global Terrorism Database (GTD). The GTD relies on open-source media accounts of terrorist attacks, and attributes terrorist incidents to a group based on these accounts where possible. Hence, unclaimed terrorist attacks are attributed to a group if media reports name the group as perpetrator, and “lone wolf” attacks claimed by some terrorist group are not attributed to this group if open-source media accounts judge this claim not to be credible. The GTD also records instances of infighting—terrorists fighting other terrorists.

Relying on open-source reports introduces possible biases, but simulations suggest that the extent of these biases would have to be substantial to completely drive this paper’s main results. First, bias could arise if media are more likely to report terrorist attacks by a group in the 6 months after a hit on its leader, compared with after a miss. Appendix B.2.1 suggests that, if drone hits in fact had no effect on terrorist violence, media would have to report all terrorist attacks by a group for 6 months after a drone hit on its leader and only approximately 65% of attacks after a drone miss to obtain a single statistically significant coefficient with 95% certainty. The actual analysis obtains three significant coefficients. Secondly, measurement error might bias the analysis, as attacks committed by an unknown perpetrator are excluded from the analysis. This may introduce bias if there is a group-specific time trend in the likelihood that GTD ascribes an attack to a particular group that correlates to the probability of a drone hit. Appendix B.2.2 shows that drone hits are uncorrelated to the logged number of unattributed terrorist attacks. Furthermore, it gives results of simulations that attribute attacks by unknown perpetrators to the groups in the main dataset: 88% of simulated regressions still give at least one statistically significant coefficient.

The main dataset is restricted to the 13 groups subject to drone strikes, because the identification strategy in this paper hinges on comparing groups that had their leader hit and missed at different times. Including terrorist groups not subject to drone strikes in the sample does not contribute to the identification of the coefficients of interest, but it does artificially inflate the sample size and introduce needless heteroskedasticity. Appendix B.5 illustrates that, unsurprisingly, including all terrorist groups that committed more than one attack in Afghanistan or Pakistan in the sample does not affect the main results.

To investigate group splintering, I identify all terrorist groups (other than the included 13) in the GTD that ever committed a terrorist attack in Afghanistan or Pakistan. Using a web search, I code these as having an affiliation to one or more of the 13 terrorist groups in the drone strike dataset or as unaffiliated (see Appendix A.4 for details). These groups have typically committed a small number of terrorist attacks (median 2), and anecdotally many of these groups are splinter groups of the main terrorist groups. The first attack by such a terrorist group recorded by the GTD is taken as a proxy for splintering.

Data on peace agreements between the Pakistani government and terrorist groups and Pakistani military action against particular terrorist groups up to March 2013 were collected by Staniland, Mir, and Lalwani (Reference Staniland, Mir and Lalwani2018).

Table 3 provides descriptive statistics for the main outcome variables of interest at the group-month level. For ease of interpretation, it displays counts of terrorist attacks. In the main analysis, all count outcome variables are logged. Note that the number of observations included in the main analysis is smaller than that in Table 3, due to the inclusion of leads and lags of variables. Appendix B.1 plots terrorist attacks and drone hits and misses by group over time. Terrorist attacks fluctuate strongly over time, and no definitive pattern can be discerned by eye-balling the resulting graphs.

TABLE 3.

Descriptive Statistics

Empirical Strategy

The main specification of interest is the following:

(1) $$ {Y}_{it}=\sum \limits_{k=-6}^6{\beta}_{i,t-k}{hit}_{i,t-k}+\sum \limits_{k=-6}^6{\delta}_{i,t-k}{targeted}_{i,t-k}+\sum \limits_{k=-6}^6{\gamma}_{i,t-k}{X}_{i,t-k}+{\mu}_i+{\theta}_t+{\varepsilon}_{it}, $$

where subscript $ t $ indicates a month and subscript $ i $ a terrorist group, $ {Y}_{it} $ is the outcome variable of interest, most commonly a logged count ( $ \mathit{\ln}\left( count+1\right) $ ) of the number of terrorist attacks, and $ hit $ is an indicator equaling 1 if a group’s leader was targeted by drone and killed. The variable $ targeted $ equals 1 if a leader was targeted by drone and killed or if a leader was targeted by drone and survived, and $ X $ denotes any group-specific control variables. All specifications unless otherwise indicated control for the number of drone strikes on a group regardless of whether they targeted a leader, and $ {\mu}_i $ and $ {\theta}_t $ are vectors of group and month-fixed effects, respectively. Standard errors are Newey-West standard errors with bandwidth 12, although Appendix B.5 investigates the robustness of results to using different standard errors and bootstrapping test statistics using randomization inference.

Specification 1 is estimated using an ordinary least squares (OLS) model. As OLS assumes normally distributed standard errors to determine the level of statistical significance of coefficients, Appendix B.4 shows that residuals obtained using specification 1 are indeed approximately normally distributed. Alternatively, negative binomial models are commonly used in the literature to analyze unlogged counts of terrorist attacks (e.g., Reese, Ruby, and Pape Reference Reese, Ruby and Pape2017). This is not the model of choice here, as results from negative binomial models are inconsistent and subject to bias in the presence of a large number of fixed effects (Allison Reference Allison2012; Hilbe Reference Hilbe2011). However, as the extent of this bias in the present case is unclear, Appendix B.5 also presents alternative results using two fixed-effect negative binomial models.

The individual coefficients on the lags of $ hit $ —and the $ p $ -value from a Wald test of their joint significance—are the main coefficients of interest. These reflect the effect of a drone hit on a terrorist leader compared with that of a drone miss.Footnote ¹⁴ In experimental terms, group-months for which $ hit=1 $ and $ targeted=1 $ are the treatment group, and group-months for which $ hit=0 $ and $ targeted=1 $ form the control group. The coefficients on the lags of $ targeted $ reflect the effect of a drone miss.Footnote ¹⁵

To credibly identify the causal impact of targeted leader killing, the probability of a hit must not be driven by prior trends in the outcome variable. This would, for example, be the case if counterterrorist organizations would accept a higher or lower probability of a hit for terrorist groups that commit an increasing number of terrorist attacks. To verify the parallel trends assumption, each specification includes six leads of $ targeted $ and $ hit $ , in addition to six lags. If the coefficients on the leads of $ hit $ are statistically significant, this provides evidence that the parallel trends assumption has been violated. The $ p $ -values for the joint significance of leads of $ hit $ will be provided for all regressions.

Speed-Up of the Timing of Terrorist Attacks

The main results presented would not necessarily imply an increase in terrorist attacks overall if terrorist groups merely change the timing of already planned attacks after a drone strike has hit their leader so that attacks are concentrated in the 6 months after the strike. I find some evidence of this, but the effects are not statistically significant and too small to explain the main results.

There is no evidence that terrorist groups commit their next attack substantially sooner after a drone hit on their leader compared with after a miss (Table 4). If the duration to the first terrorist attack after the drone strike is decreased, this effect is small: point estimates suggest the first attack occurs about 13 days earlier after a hit compared with after a miss (column 1). The Cox hazard model presented in column 2 similarly suggests that the hazard of a first attack occurring is not significantly higher after a drone hit compared with after a drone miss.

TABLE 4.

Duration in Days to First Terrorist Attack

Note: Clustered (group) standard errors in parentheses; *p < 0.1, **p < 0.05, ***p < 0.01.

On a longer time scale, there is some evidence of displacement of terrorist attacks over time, but this effect is not statistically significant for drone hits on a terrorist leader. Figure 2 displays results from specification 1, including 15 leads and lags of all variables. For readability, only the coefficients on the lags of $ hit $ and $ targeted $ are displayed, in addition to a cubic trend and 95% confidence intervals. Results suggest that the number of terrorist attacks is somewhat lower in earlier and higher in later months after a drone miss compared with similar periods not preceded by a drone strike aimed at a leader. Coefficients are significant for months 3, 10, and 13. Although coefficients on $ hit $ follow the opposite trend, there is no statistically significant decline in the number of terrorist attacks in months 8 to 15 after a drone hit on a terrorist leader, as we might expect if terrorist attacks planned for later periods were committed earlier in response to the hit. On average, the 15 coefficients in the extended model still suggest a 17% increase in terrorist attacks after a drone $ hit $ .Footnote ¹⁶

FIGURE 2.

Timing of Terrorist Attacks

Alternative Econometric Specifications

Main results are robust to including leader-fixed effects, omitting control variables, including several additional control variables, and estimating $ p $ -values for lags of $ hit $ through randomization inference. Similar but somewhat weaker results are also obtained when employing an alternative definition of “leader.” Main results are sensitive to varying which Al-Qaida branches are considered part of Al-Qaida but not to other alternative treatments of terrorist groups.

Table 5 investigates the robustness of the main results, which are reproduced in column 1. Only lags of the variable of interest are presented to promote readability.

TABLE 5.

Robustness of Main Results

Note: Newey-West standard errors in parentheses; *p < 0.1, **p < 0.05, ***p < 0.01.

Omitting the number of drone strikes targeting a terrorist group as a control variable does not meaningfully affect the main results (column 2). Results are robust to including leader-fixed effects (column 3) and to controlling for six leads and lags of an indicator for Pakistani military action against a terrorist group and the existence of a peace agreement between the terrorist group and the Pakistani government (columns 4 and 5). The latter two variables are only available up to March 2013, leading to a substantial loss in observations, so these variables are not included in the baseline specifications.

The next columns of Table 5 investigate the sensitivity of main results to alternative ways of aggregating terrorist groups. The dependent variable for Al-Qaida in the baseline specification is an aggregation of terrorist attacks by all Al-Qaida branches.Footnote ¹⁷ I argue that this is the most appropriate set-up to analyze Al-Qaida terrorist attacks for several reasons. First, leaders of several of these branches are at times present in FATA. Presence of leaders of Al-Qaida in Iraq, Al-Qaida in the Arab Peninsula, and Al-Qaida in the Indian Subcontinent in FATA is recorded by the BIJ.Footnote ¹⁸ Second, Al-Qaida leaders based in FATA at least attempt to control its branches (Crenshaw Reference Crenshaw2012; Shapiro Reference Shapiro2013). Third, reducing attacks by branches is one motivation for drone strikes against Al-Qaida. The 2018 US counterterrorism strategy explicitly mentions that targeting key terrorists will “disrupt, degrade and prevent reconstruction of terrorist networks.”Footnote ¹⁹ Nevertheless, column 6 presents results obtained if only attacks by Al-Qaida proper and Al-Qaida in the Indian Subcontinent are “counted” as Al-Qaida terrorist attacks. Main results are clearly sensitive to this alternative treatment of Al-Qaida branches. The reader unconvinced by the arguments above may have to conclude that drone strikes on a terrorist group’s leader do not affect the number terrorist attacks this group commits. However, considering Al-Qaida branches as independent organizations affiliated to Al-Qaida only strengthens the results obtained in Appendix C.1, indicating that drone strikes hitting a terrorist group’s leader increase the number of terrorist attacks committed by this group’s affiliates.

Main results are robust to recoding “local Taliban” as TTP from December 2007 onwards. The GTD appears to code all terrorist attacks by the Taliban in Pakistan after this date as committed by TTP, whereas the BIJ distinguishes the TTP from the “local Taliban.” This recoding does not affect the main results (column 7).

Lastly, column 8 presents results when using an alternative coding rule for who constitutes a terrorist leader. Under this alternative rule, all individuals marked by the BIJ as “leader,” “commander,” “senior figure,” or similar are considered leaders. This coding rule plausibly considers as drone hits strikes on some individuals whose status as leader was exaggerated in the media after they have been hit. Despite this, the second lag of $ hit $ remains individually and all coefficients on $ hit $ jointly significant. Although the observed effect is somewhat weakened, which may be unsurprising if the alternative coding rule counts as “hits” strikes on some individuals who may in reality not have a leading role, it is still in evidence.

Appendix B.3 suggests that the lack of statistical significance of individual leads and lags of $ hit $ in the main results is not an artifact of small sample size, implying that the first, fourth, and fifth lag of $ hit $ , as well as all leads of hit, are indeed null. Simulations thus suggest that the sample size would have to be radically expanded to make a meaningful difference to the main results.

Appendix B.5 furthermore shows that results are robust to restricting the analysis to periods within 6 months of a hit or a miss, using a group-time trend instead of period-fixed effects, using Discroll-Kraay standard errors, dropping two small terrorist groups, including all terrorist groups that have committed more than one attack in Afghanistan or Pakistan in the sample, and restricting the period under analysis to periods prior to Pakistan acquiring its own drone capability. Results are also robust to using alternative counterfactuals that are less subject to measurement error. To investigate concerns that results are driven by trends over time specific to world regions terrorist groups are active in, Appendix B.5 also shows results from region-group-month-level regressions, including region-fixed effects, region-group fixed effects, and region-period fixed effects, respectively. Results are somewhat sensitive to using HAC instead of Newey-West standard errors.

However, calculating the main test statistic using randomization inference leaves results qualitatively unchanged (Appendix B.6). As randomization inference necessitates no assumptions regarding the distribution of the standard errors, this further mitigates the concern that statistically significant coefficients in the main result are an artifact of nonnormally distributed residuals. Although there are doubts about whether these are consistently estimated (Allison Reference Allison2012; Hilbe Reference Hilbe2011), Appendix B.5 provides results from two fixed effects negative binomial models. In these models, most individual coefficients lose statistical significance, but the coefficients on the lags of $ hit $ are still jointly significant.

Problems of Control

Principal-agent models of terrorist organizations suggest that the main results may be driven by a loss of control of terrorist leaders over operatives. I find evidence in favor of most hypotheses derived from theoretical models of problems of control.

The increase in terrorist attacks after a drone hit on a leader is driven by those types of attacks that leaders plausibly do not favor. Consistent with the idea that terrorist operatives may have a greater preference for violence against civilians than the leader (H1.1a), the number of attacks against civilian and private targets is statistically significantly higher after a drone hit on a leader compared with after a drone miss (Table 6, columns 1 and 2). This result echoes that obtained by Abrahms and Mierau (Reference Abrahms and Mierau2017). Furthermore, the number of unclaimed attacks increases significantly for 3 out of 6 months after a drone hit (column 3). This is consistent with the idea that leaders may strategically not claim attacks by operatives that they fear will have negative repercussions for the terrorist group’s long-term goals (H1.1b).

TABLE 6.

Effects on Attack Type and Organizational Changes

Note: Newey-West standard errors in parentheses; *p < 0.1, **p < 0.05, ***p < 0.01.

A decrease in control may also be expressed in a change in the organizational structure of the terrorist group. If all ties between leaders and operatives break down, a terrorist group may splinter (H1.1c) or operatives may start fighting among themselves (H1.1d). Indeed, a drone hit is associated with an increase in the third and fifth lag of a proxy for group splintering (Table 6, column 4). If the first attack by a small affiliated group in Afghanistan and Pakistan is a credible indicator for splintering of the parent group, terrorist groups are more likely to splinter after a drone hit on their leader. Finally, a drone hit is associated with an increase in infighting (column 5). These results should be treated with some caution for two reasons. First, infighting is rare, there are only forty instances of infighting in 26 periods. Second, in this specification, leads of $ hit $ are also strongly jointly statistically significant. However, Appendix B.8 shows that this is driven by a single coefficient and not necessarily by consistently differing trends between a hit and a miss prior to the drone strike.

If the main results of these study are due to aggravated problems of control, we may furthermore observe heterogeneous effects across terrorist groups and leaders. Specifically, terrorist groups that rely more strongly on central control may be more strongly affected (H1.2a), and the drop in control may be largest for the first leader killed, as they were initially not subject to incentives to trade off control for secrecy (H1.2b). Results on heterogenous effects, displayed in Table 7, should be interpreted with some caution: given the limited number of drone strikes targeting a terrorist leader and limited number of groups, statistical power to detect any interaction effects may be lacking.

TABLE 7.

Heterogeneous Effects

Note: Newey-West standard errors in parentheses; *p < 0.1, **p < 0.05, ***p < 0.01.

Keeping this in mind, the first three columns of Table 7 suggest that the effect of a drone hit on a terrorist leader is greater for terrorist groups that rely more strongly on central control. I employ a classification by Staniland (Reference Staniland2014), in which integrated and vanguard terrorist groups have strong central control. Staniland considers the Taliban an integrated group (140). Al-Qaida is not explicitly classified, but its strategy of making alliances closely resembles Staniland’s (Reference Staniland2014) description of a vanguard group (44–46). No other groups subject to drone hits and misses on their leaders are classified by Staniland as having strong central control.Footnote ²⁰ Column 1 reveals that the effect of a drone hit on terrorist attacks is indeed stronger for these two organizations. This heterogeneous effect holds both for the Taliban, the one integrated organization (column 2), and for Al-Qaida, the only vanguard organization (column 3).

Lastly, column 4 of Table 7 provides some very tentative support for the hypothesis that the effect of a drone hit is stronger for the first leader hit. Coefficients on the second to fifth lag of the interaction term are positive and of substantial size compared with their noninteracted counterparts. They are not individually or jointly statistically significant however.

Capacity

There is no evidence that terrorist groups, in response to a drone strike hitting their leader, substitute a small number of high-impact attacks with a large number of low-impact attacks, as capacity models would suggest (H2.1).

A low-impact attack might be an “unsuccessful” terrorist attack—that is, the planned attack type was foiled or an attack with a small number of victims (H2.1a and H2.1b, respectively). Table 8 provides no evidence that these attack types increase after a drone hit on a terrorist leader. If anything, the percentage of “successful” terrorist attacks (column 1) is lower for some individual months after a hit.

TABLE 8.

Substitution of Terrorist Attack Types

Note: Newey-West standard errors in parentheses; *p < 0.1, **p < 0.05, ***p < 0.01.

Furthermore, there is no evidence that terrorist groups substitute attacks against “softer” targets for attacks against “hard” targets (H2.1c). Even though the number of attacks against civilian or private targets does increase (Table 6), Table 8 shows no significant decline in the number of terrorist attacks against military targets (column 3) or attacks with US casualties or injured (column 4).Footnote ²¹

Finally, Table 8 provides no evidence that terrorist groups are concentrating their attacks in their “homebase” of Pakistan at the expense of attacks in Afghanistan or the rest of the world (excluding Western Europe, the US, and Australia) after a drone hit on their leader (H2.1d). In fact, the main results are driven by terrorist attacks in the rest of the world (ROW, column 5).Footnote ²² Although it would be interesting to investigate the effect of a drone hit on terrorist attacks in “the West,” there have been only eight such attacks over the research period, making this impossible.

The observation that the increase in terrorist attacks after a drone hit is concentrated in the rest of the world rather than in Pakistan or Afghanistan is interesting in light of the other three families of theoretical models. We might speculate that a new leader taking the place of a leader killed by drone has greater trouble exerting control over far-away operatives than operatives close to home. This contrasts with the backlash or signaling perspective. From either of those perspectives, we might expect a stronger reaction in Pakistan, as most civilians killed are Pakistani and because operatives closer to the leader killed may have a greater incentive to signal strength.

Signaling

There is some evidence that a drone hit on a terrorist leader induces terrorist groups to signal their strength and resolve by committing an increasing number of attacks (H3.1).

Attacks that send a strong signal may include attacks that quickly follow the drone strike, are claimed, and hit high-profile targets. From the main results, the timing of the increase in terrorist attacks is not obviously consistent with the signaling mechanism: statistically significant increases in the number of terrorist attacks are only observed from 2 months after the drone hit onward (Figure 1). Table 8 furthermore shows no increase in terrorist attacks on US citizens, which would be a high-profile target.

Consistent with the signaling mechanism however, Column 6 of Table 6 does show a statistically significant increase in the number of claimed terrorist attacks in months 1 and 3 after a drone hit compared with after a drone miss. Coefficients are jointly statistically significant. Furthermore, Table 8 column 3 also shows a significant increase in attacks on military targets, also high-profile, after a drone hit.

Lastly, the incentive to signal strength may be greater after the death of more prominent leaders (H3.2). The final columns of Table 7 explore this hypothesis. Results in these columns provide some tentative support in favor of this hypothesis. Terrorist attacks are significantly higher in the second month after a drone hit on a leader who is designated “first in command” according to the Stanford project (column 6) or for whom the US Department of Justice ever offered a reward (column 5). However, lags on neither set of interaction terms are jointly statistically significant.

In sum, there is evidence in favor of some hypotheses following from the signaling mechanism. Alternatively, we might think that patterns observed arise out of terrorist groups’ desire for revenge. However, not all hypotheses are supported with evidence and this mechanism cannot explain the results on unclaimed attacks, group splintering, or infighting.

Backlash

There is no evidence that drone strikes killing civilians are associated with an increase in terrorist attacks, as backlash would suggest (H4.1).

Even if drone strikes cause backlash, this effect does not necessarily coincide with the effect of targeted leader killing. Backlash would affect the analysis only if drone hits on a leader killed more civilians than drone misses, and Table 2 does not provide any evidence for this. There is also no evidence that terrorist organizations specifically use drone strikes on terrorist leaders in their recruitment propaganda: propaganda refers to drone strikes as a “failing” policy and does not emphasize hits on terrorist leaders (Ludvigsen Reference Ludvigsen2018).

Nevertheless, I test whether drone strikes killing civilians are associated with an increase in terrorist attacks. To do so, I estimate two variations on Equation 1. The first variation replaces $ {hit}_{it} $ with the number of civilian casualties from drone strikes targeting group $ i $ in month $ t $ and $ {targeted}_{it} $ with the total number of casualties from drone strikes in month $ t $ on group $ i $ . The second variation replaces $ {hit}_{it} $ with an indicator that equals 1 if some drone strike in month $ t $ targeting terrorist group $ i $ instead killed only civiliansFootnote ²³ and $ {targeted}_{it} $ with an indicator for any drone strike in month $ t $ on group $ i $ . These specifications do not control for the total number of drone strikes to avoid multicolinearity. The BIJ provides maximum and minimum casualty estimates. Table 9 shows results from maximum casualty estimates, but similar results are obtained when using minimum casualty estimates (not shown).

TABLE 9.

Drone Strikes with Civilian Casualties

Note: Newey-West standard errors in parentheses; *p < 0.1, **p < 0.05, ***p < 0.01.

Table 9 provides no evidence that drone strikes hitting only civilians, or done strikes hitting many civilians, are associated with an increase in terrorist attacks compared with other drone strikes (H4.1). If anything, it shows a decrease in the number of terrorist attacks, by the terrorist group itself and by an aggregation of all terrorist groups in the study.Footnote ²⁴ The sign on virtually all coefficients is negative, although coefficients on the lags of the dependent variable of interest are not jointly statistically significant in each instance.

This study by no means convincingly shows that drone strikes causing civilian casualties decrease terrorist violence. In two of the specifications shown, the leads of the dependent variable are jointly statistically significant. As this provides evidence that the parallel trends assumption is violated, these results should be interpreted with due caution. The sole purpose of this exercise is to show the lack of evidence in favor of backlash.