European Observatory to Combat Radicalization – EOCR
Arrests and convictions but not sentence length deter terrorism in 28 European Union member states
nature – While countries differ in how they handle terrorism, criminal justice systems in Europe and elsewhere treat terrorism similar to other crime, with police, prosecutors, judges, courts and penal systems carrying out similar functions of investigations, apprehension, charging, convicting and overseeing punishments, respectively. We address a dearth of research on potential deterrent effects against terrorism by analysing data on terrorism offending, arrests, charges, convictions and sentencing over 16 years in 28 European Union member states. Applying both count and dynamic panel data models across multiple specifications, we find that increased probability of apprehension and punishment demonstrate an inverse relationship with terrorism offending, while the rate of charged individuals is associated with a small increase in terrorism. The results for sentence length are less clear but also indicate potential backlash effects. These findings unveil overlaps between crime and terrorism in terms of deterrent effects and have implications for both the research agenda and policy discussion.
Main
In recent years, criminologists have increasingly devoted attention to the study of terrorism, making important contributions to a field that suffered from severe stagnation1,2. These contributions show that while differences certainly exist, ordinary crime and terrorism display extensive overlaps. These include socio-demographics of offenders, with most offenders being relatively young males, especially those with criminal backgrounds, as well as psychological characteristics such as low self-control3. Overlaps have also been identified in terms of spatial and temporal clustering4,5,6,7, patterns of recidivism8, cycles of violence4, target selection9 and network organization10. Importantly, strategies found to be effective in combatting crime also appear effective in combatting terrorism, particularly situational prevention11,12,13,14,15,16.
An extensive array of factors can account for variation in the occurrence of terrorism, including but not limited to cultural, political and socio-economic conditions17,18,19. However, the role of criminal justice factors has remained under-researched, despite the relatively consistent role of the criminal justice system in combatting terrorism: police are responsible for arrests, prosecutors are responsible for proceedings, judges are responsible for convicting/acquittal and sentencing, and the prison service is responsible for managing prison sentences20,21. Whether a country experiences terrorism or not (or how much) is a function of its socio-political climate, the differential opportunities that exist and the effectiveness of authorities in both prevention and deterrence22.
These considerations underpin the deterrence model, which holds that decisions to engage in offending are the product of weighing the risks of offending against the rewards, against the background rewards for abstaining from offending. Here, the risks of an individual being subject to punishment, whatever its severity, depend on the risks of apprehension, prosecution and conviction. Accordingly, deterrence is a function of the probability of arrest, the probability of conviction given arrest, the probability of imprisonment conditional on conviction and the expected severity of punishment conditional on imprisonment23,24.
However, evidence for this model is mixed, with punishment severity displaying small effects and in some cases even a positive relationship, in which it is associated with an increase in crime25,26,27,28,29. Even where punishment severity is associated with reduced crime, it has been suggested that this is an artefact of incapacitation effects and not deterrence30. While there is also mixed evidence concerning the effects of certainty of apprehension and punishment, a meta-analysis found that certainty operates in the hypothesized direction and is of a meaningful magnitude29.
Analytically, many issues, such as measurement31 and specification biases32, may impact results. Few studies examine the full range of deterrence factors in a single model, with most limited to analysing certainty of punishment32. This is especially problematic given the theorized negative correlation between certainty and severity33. In the cross-national research context, while in some countries greater likelihood of punishment is associated with a reduction in crime, in others the opposite is true, and differences exist across crime categories as well34. Other studies have found that police performance, which includes case clearance, has a negative relationship with homicide rates35. There are no real examples of cross-national studies that test the full deterrence model, in part due to a lack of data36.
With regard to measurement, using the probability of conviction ignores the likelihood of being charged as a function of arrest. There is evidence that the omission of this variable is a potential source of specification bias, as its inclusion has been found to impact the statistical significance of other deterrence variables32,37,38. In light of these challenges, much of deterrence research focuses on policies conceptualized as proxies for either certainty or severity of punishment. For example, researchers focused on how laws targeting gangs, which resulted in wide-scale arrests—thereby increasing the likelihood of punishment—impact a range of crime outcomes. Classically, research on the severity of punishment has focused on the effects of the death penalty, which can also be characterized by mixed results, and studies of policies such as California’s (no longer practised) ‘three strikes and you’re out’ approach. While these avenues of research are certainly important, they are limited methodologically and in terms of what they can tell us about deterrence39.
Returning to the issue of terrorism, while various overlaps with crime have been found, there are also important differences. Ordinary offenders are primarily motivated by the maximization of financial gains. Even the maximization of power is more a means of achieving financial goals than a goal in and of itself. Terrorism is motivated more by grievances and seeks to maximize changes to social, political or other norms and systems viewed as the sources of those grievances40,41,42. As a result, terrorists more often act out of altruistic motivations than ordinary offenders do. Relatedly, whereas most ordinary offenders seek to avoid detection, terrorism has traditionally been used as a means of garnering maximum attention43.
These differences have led some to theorize that terrorists are irrational and therefore undeterrable44, mirroring some positions on homicide that view general or marginal deterrence through increasing the costs of offending as unachievable45. However, as in the case of homicide45, there is evidence that (potential) terrorism offenders engage in rational choice making, weighing potential rewards against potential risks12,13,14,46,47,48. Some argue that this is the point at which terrorism and crime are most similar, at least as much as the overlaps between general crimes (for example, ordinary violence) and specialty crimes such as hate crime or gang violence49. Evidence for rational choice making in terrorism, like in the case of crime, has been further deduced from how it responds to situational prevention efforts, with findings that increasing the difficulty of successful attacks and increasing apprehension are associated with reductions in terrorism12,14,15,50. Additional evidence for this claim can be deduced from the impact of routine activities on incident rates. During the recent coronavirus pandemic, lockdowns were found to be associated with decreases in crime, due to changes in routine activities leading to fewer opportunities for crime51. This similarly reduced opportunities for terrorism, with a lack of crowds at public venues and increased police presence52,53,54.
Most deterrence studies on terrorism follow the approach of analysing policies as proxies for deterrence, partly due to data availability issues. These studies generally rely on time-series analyses in which specific interventions are treated as dummy variables. Methodologically, these approaches can be quite problematic39, and there are statistical issues in assessing these results when some countries experience no terrorism due to other factors, such as the socio-political environment and opportunities22. Nevertheless, these studies can still be informative. In reviewing the results, indiscriminate policies (such as wide-scale crackdowns) generally have no effect on terrorism or produce backlash effects, increasing terrorism. Conversely, policies conceptualized as representing ‘soft’ approaches are regularly associated with decreases in the risk of terrorism11,55,56,57.
Few studies have tested the likelihood of arrest in a way that is comparable to general deterrence research. These studies partially overcome some of the statistical issues that exist when there is an absence of terrorism due to background characteristics, since there is at least time variation in the independent variables22. The first such study examined how a small number of annual arrests (between 11 and 17) of Palestinian Liberation Organization terrorists impacted the number of attacks carried out by the group outside of Israel (international attacks). The study found evidence that higher arrest rates (the number of arrests per incident) displayed a small deterrent effect58. Another study focused on Israel found that increased arrests reduced the likelihood of suicide bombings59. It should be noted, however, that for both studies, the data for arrests were derived from open sources, and their dependent variables were both limited to very specific types of terrorism activity. The only known study that used counts of arrests, as derived from official sources, was a thesis study that found that increased terrorism-related arrests in Pakistan were associated with lower terrorism60.
One observation that can be made from the above noted literature is that whether measuring deterrence through dummy variables representing specific counterterrorism actions or through more traditional measures such as the numbers of arrests, different types of terrorism in different contexts may respond differently61. What the overall effects may be also remains unknown, as reflected by the ongoing debate as to whether terrorism can be deterred by the criminal justice system. As above, some have argued that since terrorists are willing to die for their cause or group, deterrence is not a relevant factor. However, others reject this proposition as representing a narrow understanding of terrorism, and such notions may be limited to the now relatively rare case of suicide bombings62. Much of the ‘new terrorism’ experienced in Europe involves actors engaging in extensive planning for survival, even if they are prepared to die. Many terrorists, including Osama bin Laden, have sought to evade capture and punishment63. Moreover, the willingness to die for a cause is not unique to terrorists. Many ordinary offenders may prefer to ‘get away with it’ while at the same time being prepared to accept the possibility of capture or death64. As such, differences in motivations and objectives do not necessarily lead to differences in the theorized impact of deterrence.
Most deterrence research has focused on high-volume crimes such as assault and property crime, whereas most cross-national research has focused on homicide34,35,36. Terrorism is more similar to homicide in that it is a low base-rate crime, and a relatively small proportion of the population are ever at risk of offending65,66. While police resources can become overwhelmed by high-volume crime, reducing the likelihood of capture and punishment32, extensive resources are dedicated to dealing with homicide and terrorism, which also have small non-reporting rates67.
Additional issues with how the criminal justice systems in democratic and semi-democratic countries treat terrorism could lead to differential deterrent effects. For example, compared with ordinary crime, the rate of release without charge may be quite high. According to the United Kingdom’s Home Office, some years have seen more than 50% of those arrested under the Terrorism Act (2000) released without charge68. Our own review of these statistics shows that this rate increases commensurate with the volume of arrests. Similarly, in the United States, while arrests for terrorism have increased and have been viewed as having led to a decrease in successful attacks, the rate of declination (in which charges are dropped) has increased, possibly indicating that authorities are identifying terrorism threats early enough to prevent them but too early to gather sufficient evidence for successful prosecution69. Additionally, conviction rates may be lower than for ordinary crime, although they have increased in recent years as terrorism cases have increasingly been tried as criminal cases70,71.
In the absence of any rigorous tests of the deterrence theory model with respect to terrorism, it is still only possible to theorize about how it may respond to the criminal justice system. There are both theoretical and empirical reasons to assume that it will respond in ways similar to ordinary crime, as well as reasons to suggest that it may respond differently. A direct test comparing terrorism and crime would be ideal, but as described above, there is a lack of cross-national data for deterrence variables as they relate to crime. As such, the current study tested whether the criminal justice system has a deterrent effect on terrorism and whether the effects follow similar patterns to what extant literature has found in the case of ordinary crime. Our study draws on data from Europol’s annual Terrorism Situation and Trends reports (TE-SAT) from 2006 to 2021, testing how arrests, charges, convictions and sentence length for terrorism offences impact gross terrorism offending. Our analytic strategy employs a dynamic panel-data framework in which we treat the data according to different modelling specifications—namely, as offending rates (as is common in the criminological literature) and counts (as is common in the terrorism literature). All models include multiple fixed effects and theoretically relevant control variables. Extensive robustness checks were also performed to test the impact of model specification and measurement bias and the influence of alternative explanatory variables.
Results
Our analysis sought to explain the variation in terrorism incident rates across 28 European Union (EU) member states. As shown in Figs. 1 and 2, which depict the raw number of incidents (Fig. 2 displays the inverse hyperbolic sine (IHS) transformed measure), there are high degrees of between-country variability and within-country variability over the observation period. The between-country variability is further illustrated in Fig. 3 in the form of a heat map.The highest peaks of attacks are France in 2006 (N = 294), Spain in 2007 (N = 279), France in 2007 (N = 267) and Spain in 2008 (N = 263). Both countries, which are among the ones with the highest prevalence of incidents in the dataset, experienced substantial decreases after heightened levels of terrorism in the early years of the analysis. The only countries that experienced terrorism increases in more recent years are Belgium, Italy and the United Kingdom, although all three reported decreasing trends during the COVID-19 pandemic.
France (N = 1,419), Spain (N = 1,175) and the United Kingdom (N = 745) reported the highest counts of incidents throughout the period under consideration. Nine countries reported no attacks (Croatia, Cyprus, Estonia, Latvia, Luxembourg, Malta, Romania, Slovakia and Slovenia). Map credit: Eurostat package in R, under a Creative Commons licence CC BY 4.0.The results of the primary generalized method of moments (GMM) analysis are displayed in Table 1. Model Ia (without controls) and Model IIa (with controls) present the results in which arrests are treated as exogenous. Between both models, the size of the coefficients remains relatively similar. We use B to report coefficients with 95% confidence intervals and P values. Relying on Model IIa, the largest effect is for the lagged terrorism incident rate, in which a one-unit increase is associated with a 0.909% increase (B = 0.909 (0.789, 1.069), P = 0.000) in the subsequent rate.
In terms of deterrent effects, a 1% increase in the arrest rate is associated with a 0.017% reduction in the terrorism rate (B = 0.017 (−0.029, −0.006), P = 0.004), while for the conviction rate, a 1% increase is associated with an approximately 0.09% reduction (B = −0.095 (−0.168, −0.023), P = 0.010). Two variables were associated with an increase in terrorism. A 1% increase in the rate of charged individuals was associated with a 0.16% increase in the terrorism rate (B = 0.016 (0.006, 0.026), P = 0.001), whereas a one-unit increase in the average sentence length was associated with a 0.12% increase (B = 0.012 (0.005, 0.019), P = 0.001). In Model IIIa, where arrests are treated as endogenous, the coefficients were smaller for all factors, except for the charge rate. That is, the reduction in the terrorism incident rate for a 1% increase in the arrest rate was 0.011% (B = −0.011 (−0.020, −0.001), P = 0.018), and for a 1% increase in the conviction rate, it was 0.057% (B = −0.057 (−0.092, −0.021), P = 0.002). There was a slight increase in the size of the coefficient for the charge rate (B = 0.019 (0.007, 0.030), P = 0.002), whereas the coefficient for sentence length was not statistically significant (B = 0.005 (0.004, 0.014), P = 0.246). Drawing on Model IIa, these effects are further illustrated in Fig. 4, which displays the predicted margins with 95% confidence intervals for each of the primary predictor variables. The plots vary in their scales as they relate to the effects from the minimum to maximum values of each of the variables.
Average predictive margins (black line) along with 95% confidence intervals (in grey) of the lagged (yt−1) terrorism incident rate and the lagged (yt−1) deterrence variables based on GMM Model IIa as reported in Table 1.These models were replicated using count models, where raw counts of terrorism events served as the dependent variable. The results are displayed in Table 2. In Model Ib, all independent variables were measured as counts (for example, number of arrests, number of charges and number of convicted individuals), except sentence length, which was the average number of years. Here, the estimates for arrests, charges and convictions follow the same direction as the effects observed in the GMM models, while the direction of the effects for sentence length is reversed. In Model Ib, each additional arrest was associated with a 0.2% decrease in the number of terrorism incidents (B = −0.002 (−0.002, −0.001), P = 0.000), and each additional conviction with 1.6% fewer incidents (B = −0.016 (−0.019, −0.013), P = 0.000). Each additional charge was associated with 1.7% more incidents (B = 0.017 (0.014, 0.020), P = 0.000).
A one-unit increase in sentence length was associated with approximately 3.5% fewer incidents (B = −0.036 (−0.051, −0.021), P = 0.000). In Model IIb, the number of convictions was replaced with the conviction rate, for which a one-unit increase was associated with 62.8% fewer incidents (B = −0.990 (−1.207, −0.772), P = 0.000). While the estimate for arrests remained the same as in Model Ib, the estimate for charges decreased to 0.4% (B = 0.004 (0.004, 0.004), P = 0.000) and that for sentence length to 2.4% (B = −0.024 (−0.033, −0.015), P = 0.000). In Model IIIb, all factors were treated as rates (as in Models Ia–IIIa). Here, a one-unit increase in the arrest rate was associated with 1% fewer incidents (B = −0.010 (−0.014, −0.005), P = 0.000), conviction rate with 60.9% fewer incidents (B = −0.940 (−1.220, −0.659), P = 0.000), charge rate with an 8.9% increase (B = 0.086 (0.071, 0.100), P = 0.000) and sentence length with a 2.3% decrease (B = −0.023 (−0.038, −0.007), P = 0.000).
Robustness checks
Several robustness checks were performed. First, we estimated an alternative specification of our equations in which we used contemporaneous values of control variables. This specification addresses the fact that economic variables could affect crime differentially between lagged and contemporaneous effects. Here, there were no substantive differences in the effects of the main explanatory variables, and none of the control variables demonstrated statistically significant effects (Extended Data Tables 1 and 2). Second, we carried out a series of robustness checks in which we assessed the potential for omitted variable bias as an issue in the analysis of deterrence, as it has been found to be an issue in criminological research32. These tests revealed a good degree of stability in the effects of the explanatory variables; however, we note that when arrest rates are assessed on their own, the estimate falls below the level of statistical significance (Extended Data Tables 3 and 4).
This is not surprising, as one of the criticisms of deterrence research mentioned above is the risk of type II errors in the context of examining deterrence variables in isolation32. Third, we added additional, time-varying control variables of theoretical relevance: gross domestic product, population density, urbanity, violent crime rate, the number of asylum seekers and rule of law (a composite measure that captures confidence in and abidance by the law, the quality of law enforcement measures, property rights, police and judicial quality and efficiency, and the likelihood of crime and violence). All data were derived from official sources such as the World Bank. For all of these tests, the jackknife estimation method was employed to identify whether the estimates of the explanatory factors were also sensitive to the iterative exclusion of panels. Lags of the control variables were used so that the models would be more closely related to the specification of the main models (Extended Data Tables 5 and 6). Across all of these analyses, the results remained robust and fairly consistent. There was, however, a notable difference in the count model in which the violent crime rate was included. Here the estimate for sentence length was positive, indicating an association of a 1% increase in incidents (B = 0.010 (0.001, 0.018), P = 0.032). This differs from the effects of sentence length in Models Ib–IIIb but points in the same direction as in Models Ia–IIIa (Extended Data Table 6).
As an additional robustness check, we conducted a series of zero-inflated Poisson models. Across these models, the effects for convictions and charges were consistent with the main models. However, the estimates for arrests were statistically significant only when measured as a rate but not as a count. The estimates for sentence length demonstrated a statistically significant negative relationship across all models (Extended Data Table 7).
Discussion
The objective of this work was to test the deterrence model in the case of terrorism, an especially important line of inquiry given the central and consistent role of the criminal justice system in dealing with the phenomenon. Whereas most prior research has been limited to testing the effects of specific counterterrorism policies or actions (usually modelled using dummy variables), our goal was to test the effects of arrests, charges, convictions and sentencing. Our study relied on official data reported to Europol by 28 EU member states over a 16-year period. To summarize the major findings, increased convictions have the most consistent and salient relationship with terrorism offending. Increased arrests also have a consistent negative relationship, but the relationship is smaller; this is to be expected as arrests are more frequent than convictions, and issues of scale must therefore be considered. Conversely, charges almost always have a significant positive relationship.
The results for sentence length are less clear, with the GMM models demonstrating positive (backlash) relationships and the count models producing negative (deterrence) relationships. The robustness checks indicate that for the count models, the addition of certain control variables can change the sign of the effects. The consistent findings for arrests, charges and convictions are noteworthy given that the effects for many factors may differ when terrorism is measured variously as rates or counts72. This can also explain the divergent findings for sentence length.
The results regarding arrest are consistent with the few studies that have found that increased arrests are associated with reductions in terrorism. However, like much of the criminological literature, these studies focused on single contexts58,59,60. Despite the fact that the broader deterrence literature widely discusses whether potential offenders are aware of the risk of apprehension, the case of terrorism may be somewhat unique. Terrorism events are rare, their outcomes are highly publicized and, at least within ideological milieus, there is a high degree of information sharing. This could increase the potential ability for the criminal justice system to exert a general deterrent effect against terrorism, at least in comparison with ordinary crime.
Our results also broadly overlap with findings pertaining to ordinary crime and particularly homicide, as demonstrated by the results of a meta-analysis in which certainty of punishment was found to have a pooled estimate of r = −0.15. In contrast, the pooled estimate of r = −0.032 for sentence length was not statistically significant29. Drawing on our GMM models, our results for both likelihood of arrest and charge would be equivalent to correlations of r = −0.13, and for conviction rate, r = −0.10. With regard to sentence severity, the results would be equivalent to r = 0.03 and, combined with our divergent results from the count models, would provide a similar, non-significant pooled result. Here the degree of overlap even in the relative magnitudes of the estimates is quite striking.
Beyond the more substantive findings, these results point to possible policy implications. In this regard, counterterrorism tactics, like police methods against gang violence, often involve large-scale crackdowns in which there may be extensive arrests but many arrestees are eventually released without charge. As noted above, some research indicates that these types of crackdowns can have backlash effects. In synthesizing our own results with those of these prior studies, we are able to offer some insights into those findings that wide-scale crackdowns can have potential backlash effects. In our study, we found that increased arrests are associated with a deterrent effect. However, the evidence also points to a potential backlash effect when there is a larger number of arrests that do not lead to charges. Policymakers and law enforcement should consider the chances of charge and conviction when making arrests if they want to reduce the potential for iatrogenic effects.
While we have endeavoured to conduct a study using the most robust data and methods available, and our analytic approach and models follow the contemporary approaches in both the deterrence and terrorism research fields, caution is still warranted in how the results are interpreted, and there are also several limitations of note. One issue, for example, is the potential impact of unobserved confounders. While we endeavoured to include theoretically relevant controls, we were limited in the number of controls that could be included owing to methodological reasons, as the number of instruments could not exceed the number of panels. Furthermore, some of our controls were imperfect. For example, the dummy variable representing the years in which there were changes to counterterrorism laws cannot capture the nature or extent of these changes or the elements of deterrence they affected (that is, certainty or severity of punishment). Additionally, a key component of the deterrence model that we were unable to address at a high level of specificity in the current study is celerity, or the swiftness of punishment. We were able to include a general measure of celerity, yet it did not relate specifically to the terrorism cases included in the data, as such a measure was not available. Ideally, future research will be able to identify appropriate data for assessing the role of celerity in deterrence research on terrorism. This may be particularly important as it has previously been argued that the small effects observed for the likelihood of punishment and punishment severity on crime may be related to the swiftness—or lack thereof—of punishment.
A further limitation of our study is that the external validity of our findings is limited given our use of TE-SAT data, which pertain only to EU member states. It is possible that in other regions of the world, such as the United States, Canada, Australia and elsewhere, the results may be different. Such differences may be related to variations in the nature of the criminal justice system, the level of terrorist activity and the nature or ideology of terrorist organizations, groups and adherents in operation in different contexts (which may influence deterrent versus backlash responses). Of course, we would highly encourage additional studies in a broader set of contexts, and we caution against assuming that deterrence patterns would be universal.
Relatedly, although the TE-SAT reports provide for reporting events disaggregated by ideological motivation (for example, Islamist, right-wing or left-wing), not all countries report such data. Additionally, this option does not exist for charges, convictions and sentence length, precluding the ability to conduct analyses across and between ideological strains. Such analyses would seem pertinent given that different types of terrorism may respond to deterrence in different ways.Our study measured the impact of the certainty and severity of punishment on terrorist activity in the next year. Future research might consider shorter time frames, such as monthly ones, to dig deeper into analysing the longevity of effects. Additionally, our study does not examine other issues relevant to deterrence, such as perceptions of the likelihood of punishment and expected punishment severity. These areas of research are prominent in the criminological literature and may be applicable to terrorism as well.
While acknowledging these limitations and cautioning against assuming the generalizability of our findings at this stage in the development of the body of knowledge, we do believe that they should serve as encouragement for further integrating terrorism and deterrence research more generally. This line of inquiry offers promise for informing more evidence-based policy.
Methods
Our study follows what could be referred to as a classic deterrence framework, in which the expected deterrent effect on terrorism activity is a function of the probability of arrest (PA), the probability of charge conditional on arrest (PC|A), the probability of conviction conditional on being charged (PP|C) and the severity of punishment as expected prison sentence length (S). This approach follows economic models of crime deterrence, and it includes the background environment against which terrorism occurs and the resources available to police that constrain their potential effectiveness.
Data sources
The primary data for our study come from the annual TE-SAT reports published by Europol between 2006 and 2022 that collect verified information provided by member states, which it cross-references with the Eurojust system73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88. One advantage of this data source is that contributing countries have all adopted the EU’s counterterrorism strategy and associated definitions. To the best of our knowledge, these data have yet to be exploited by researchers.
The TE-SAT reports aggregate counts of the annual completed, failed and foiled terror attacks in each country, which offers several advantages over other data sources. First, as Nagin27,28 explains, deterrence is achieved through the (perceived) probability of apprehension given both completion and non-completion of an offence. Second, while it is common to observe no terrorism in a given year for a given country, this does not mean that the country is free of terrorism. Rather, police may have simply been effective in that year in preventing or deterring terrorism, perhaps through arrest, and as such, these are not “true zeroes”89. Our data therefore more accurately capture the “gross plot production” and not just the number of attacks that succeeded in avoiding detection90. While Europol does not define ‘failed’ or ‘foiled’ plots, examples are given throughout the reports. For instance, on 16 January 2016, counterterrorism police in Belgium conducting a raid killed two suspects and arrested a third who were suspected of preparing an immediate attack. Also, on 19 June 2017, an offender in Paris, France, died from fumes generated by explosive materials in his vehicle that failed to detonate.
While these specific examples are also included in the widely used, open-source Global Terrorism Database (GTD), “The GTD does not include plots or conspiracies that are not enacted, or at least attempted. For an event to be included in the GTD, the attackers must be ‘out the door,’ en route to execute the attack. Planning, reconnaissance, and acquiring supplies do not meet this threshold”91. Additionally, many events recorded in the GTD are not recorded as terrorism by EU member states, perhaps being classified as some other form of sub-terroristic violent extremism, such as hate crime92. The GTD includes a filter for whether there is doubt that the incident was terrorism; however, with few exceptions, research often overlooks this option93. About 17% of GTD incidents for our country list from 2006 to 2020 (the GTD is not updated to 2021) are classified as ‘in doubt’. Filtering out these incidents, the GTD provides 7.48 incidents per observation (s.d. = 19.10), whereas our data have 8.97 (s.d. = 33.75). While the differences are small (t(419) = 1.37, P = 0.086), they could be meaningful. Additionally, whereas the GTD includes counts of offenders arrested or killed per attack, it does not include all terrorism-related arrests or post-arrest data, such as convictions.
In line with terrorism trends in Europe and other democratic countries94, the majority of events were ‘domestic’, with perpetrators being residents of the target country, and there were only a small number of cases that can be defined as truly ‘international’, in which the offenders travelled to the country from elsewhere specifically to engage in an attack. There was however heterogeneity in terms of the distribution of ideologies attached to the incidents (for example, Jihadist, right-wing or left-wing); however, as noted above, not all countries report disaggregated data.
Dependent variable
Terrorism studies commonly use raw counts of events as the dependent variable. However, terrorism is known to increase with population size18,72. As there are justifications for modelling terrorism as either a count or a rate, and these measurement choices can substantially impact results72, we calculated terrorism incidents both as a raw count of the number of events and as a rate per 100,000 residents, with population data retrieved from the World Bank95. For the incident rate, we applied the IHS transformation (see the ‘Model specifications’ subsection for further details).
Independent variables
Our main independent variables were (1) the probability of arrest, (2) the probability of being charged, (3) the probability of conviction and (4) sentence severity (average number of years), representing a fully specified model. Like our approach for the dependent variable, we measured these variables both as counts and as rates. For the latter, we calculated (1) the number of arrests divided by the number of terrorism events, (2) the number of charges divided by the number of arrests and (3) the number of convictions divided by the number of charges. In line with our objective of testing deterrent effects, the first lag of all variables was used. This also inherently reduces the risk of reverse causality.
Control variables
There is no shortage of macro-level factors that demonstrate important relationships with the occurrence of terrorism19. However, “the direction and nature of these relationships vary substantially across studies”17, and the relative importance of the factors has not been determined. We have therefore included a variety of control variables in our models.A key deterrence variable is swiftness of punishment. Unfortunately, neither TE-SAT nor any other identifiable data source provides such data for terrorism cases. However, the European Commission for the Efficiency of Justice Council of Europe provides data on the average disposition time for all criminal cases96. While it is imperfect, we included this variable to provide at least a partial control for the variation in the overall celerity of punishment in the different included countries.
We also controlled for the Human Development Index (HDI) given its highly time-variant nature. The HDI provides a composite measure of multiple relevant socio-economic dimensions: (1) life expectancy at birth, (2) education (mean years of schooling for adults aged 25 years or more and expected years of schooling for children of school-entering age) and (3) standard of living (measured by gross national income per capita). As per the United Nations Development Programme, from which data on HDI were retrieved, the HDI utilizes the logarithm of income to better reflect the diminishing importance of income with increasing gross national income97.
Furthermore, we controlled for security expenditure as a proportion of gross domestic product, which should reflect the constraints of counterterrorism resources89. Criminological studies have used measures of police resources as proxies for deterrence, finding that they impact arrest rates98,99. Data for this factor were retrieved from the International Monetary Fund100. We also included a dummy variable for years in which new counterterrorism policies were enacted as reported in the TE-SAT reports, capturing the effects of the types of factors that have been examined in deterrence in terrorism research to date.The descriptive statistics for the above noted factors can be found in Supplementary Table 1. Intercorrelations and multicollinearity statistics can be found in Supplementary Tables 2 and 3, respectively.
Analytic strategy
Several methodological considerations should be considered when developing an appropriate analytic strategy for identifying deterrent effects on crime. Many of these are relevant for terrorism as well.
First, one of the most important predictors of crime is crime in a previous period101,102,103. In many approaches, the reliance on aggregated data gives rise to a lack of exogeneity, rendering it difficult to identify causal effects for law enforcement efforts. Additionally, an exogenous increase in crime may come to outweigh police resources, which are finite. This leads to a reduction in the likelihood of arrest, or the number of arrests per event, which is itself meant to be a regressor on the crime rate. This can give rise to issues of reverse causality or simultaneity32. The first issue is also true for terrorism4,104; however, with respect to the second issue, terrorism offending is unlikely to outweigh police resources to the degree that it negatively impacts the arrest rate in such a way. As in the case of ordinary homicides, resources dedicated to counterterrorism are known to be quite substantial. In contrast to high-volume crimes such as general violence, there are more prevented terrorism incidents than successful ones. This, however, introduces an issue of ratio bias, in which there is a negative correlation between the arrest rate and the offending rate105,106, and, like homicide, terrorism is known to be a low-base-rate problem65.
Another issue relates to measurement error. Such error is known to be present in aggregated crime data, which do not capture actual offending rates and may suffer from temporal alignment issues. For example, if offenders’ decisions are theorized to be impacted by the likelihood of punishment but punishment for crimes in a given period are for crimes that occurred some time ago, then it may be difficult to capture the deterrent effects, if they exist. However, in the case of terrorism, the dark figure is exceptionally small107. And unlike other forms of crime, the detection of terrorism offences is not sensitive to victim reporting. Additionally, official data sources—such as TE-SAT—suffer from lower levels of bias than open-source datasets108,109. Temporal alignment is also less of an issue in annualized data32, such as in the current study.
Lastly, like other types of crime, there are unobserved, time-invariant characteristics of different geographical units. It has previously been said that differences between countries’ legal and political cultures, institutional arrangements, and constitutional traditions and values shape both crime and punishment in ways that no one has yet figured out how to quantify110,111,112. With this being the case, country-specific fixed effects serve to account for unobserved heterogeneity and enable more accurate estimation of the time-varying factors of core interest.
Model specifications
Given the aforementioned issues, we implemented two types of panel regression models with fixed effects.
GMM models
We first implemented a GMM dynamic panel model113, widely considered to be the gold standard practice in deterrence research32,38,114,115 and particularly in cross-national research on crime rates116,117,118,119,120. In first-differenced GMM, the dependent variable is the terrorism incident rate, which is calculated as the number of incidents in a given country i at time t (labelled as Territ) divided by the country’s population size for each year (Popit). The terrorism incident rate is modelled as a function of the probability of arrest, the probability of charge given arrest, the probability of conviction given charge and the length of prison sentence given conviction, giving rise to the following model specification:
The error terms in equation (1) allow for country-specific fixed effects (ηi), which could be correlated with the main explanatory factors, as well as time (yearly) fixed effects (λt), which are specified to capture common variations in the terrorism incident rate across countries. Following previous works, a time trend variable was also included32,121. The coefficient for the lagged value of the terrorism incident rate (α) is specified to measure the combined effects of both the short-run dynamics and omitted, time-varying factors that may be hidden within the endogenous, lagged terrorism incident rates. Regarding the probability of arrest, we also estimated a model in which it was specified as strictly exogenous, as arrest rates can be assumed to depend on the number of offences32. Conversely, charge and conviction rates, as well as sentence lengths, are unlikely to be endogenous to incident rates and even to arrest rates. The same holds true for police expenditure. While time-invariant characteristics of countries that may impact the likelihood of terrorism are modelled by the fixed-effects components, time-varying social and socio-economic conditions may impact the attractiveness of terrorism offending. As noted above, we included the HDI and security expenditure to model the background opportunity structure against which offending decisions are made.
Because the dependent and main independent variables include observations with zeroes, for the calculation of the event rate we used the IHS transformation, which is common in economics in situations where the presence of zeroes prohibits the calculation of the logarithm of the variable. It has previously been demonstrated that the IHS is conceptually and statistically comparable to the logarithm and superior to other approaches such as log(y + 1), more closely maintaining the original properties of the data122,123,124, including in the case of terrorism data61,89. Figures 1 and 2 display the raw numbers of incidents and transformed incident rates (normalized to population size). A visual examination of the plots demonstrates that the original properties of the data are preserved following normalization and transformation. To provide an additional level of appreciation of the variation in incidents, Fig. 3 provides a heat map of the number of incidents per country over the whole observation period.
We assessed the validity of the estimated model specification with Hansen’s J test of overidentifying restrictions and its associated P value124. We also implemented a two-step model with robust standard errors, using Windmeijer’s finite-sample correction for the two-step covariance matrix125. All analyses were conducted in Stata v.17 using the XTABOND2 command126.
Count models
As noted above, we considered it important to also adopt the standard approach in the terrorism literature, which has been to rely on count models127,128,129,130 or at least conduct them for comparison with linear models128, in part due to the relatively small number of cases and skewed distributions. Some claim that terrorism event data characteristically suffer from an issue of ‘two types of zeroes’, as some countries never experience terrorism, while others experience some years with no events either following or prior to years with at least one event. Some suggest that this is the outcome of different underlying processes, and therefore, these zeros are ‘structural’131,132. However, others hold that the zeroes are not necessarily structural but ‘random’ in that they are being generated by deterrence or police efficiency89.
Additionally, there is a debate about the utility of using the ‘clearance rate’, or the number of arrests divided by the number of crime events. One key criticism is that crime ends up serving as both the numerator of the dependent variable and the denominator of the independent variable, leading to negative correlations being statistical artefacts133,134,135. However, others have demonstrated that even when ‘over controlling’ for the potential partial correlation, there are no substantive differences in the correlations, and thus the measure remains appropriate136,137,138,139,140. At least in the case of terrorism data, which have relatively few arrests, charges and convictions, this issue may extend to the charge and conviction rate. As such, we use both the counts of these main predictors and their likelihoods.
We followed Wooldridge141,142, estimating Poisson pseudo-maximum likelihood models with multiple fixed effects143,144,145. While some scholars have suggested the utility of a zero-inflated model, others hold that such models may not offer any substantial benefits in the context of panel models in which zeros are not structural146,147, and it is difficult to claim that countries with no events have zero likelihood of experiencing an event130,148. Moreover, even if we assume that the zeroes are not entirely random, the heterogeneity is at least partially accounted for by the country-level fixed effects, as in recent studies from both criminology149 and terrorism research150 implementing similar procedures. Furthermore, to deal with the two-zeroes issue, this approach allows us to include the no-event dummy as an additional fixed effect at the level of countries that have never experienced an event151. In addition to the fixed effects, we employed clustered standard errors to account for heteroskedasticity and serial correlation.
As in the GMM models, the first-differenced lag of the dependent variable is entered into the model as a regressor, further accounting for the two-zeroes issue118, and the model is expressed as: In equation (2), Territ is the number of terrorism events in country i in year t. Arrit, Charit, Convit and βSentit are the arrests, charges, convictions and sentence lengths, respectively, whereas σEit is an indicator variable that equals 1 when there was at least one event in it and 0 if otherwise. δCountry is the country-level fixed-effects component, θCountry–t is the country–year fixed-effects component and εit is the idiosyncratic error term. As it is virtually impossible to interpret the coefficients for these dummy variables, and there is little utility in doing so, we suppress them from the tables displayed in the Results section152.
