On Terrorist Attacks and Estimation Methods

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## Abstract

In my thesis I propose a theoretical model of terrorist attacks and anestimation strategy which I compare to existing methods in the literature. The modeling approach was designed with terrorism in mind, but can be applied to other discrete dynamic decision processes with a latent component and a random payoff variable that is measured when the agent exits a state of waiting. Chapter 1 briefly describes the structure of the thesis.

Chapter 2 provides a literature review of empirical studies of terrorist attacks. The primary focus is the series hazard model that estimates the effect of policy interventions on the risk of terrorist attacks. Recent contributions include LaFree et al. (2009), Dugan (2011), Carson (2014) Argomaniz and Vidal-Diez (2015), and Carson (2017). A major limitation of the series hazard approach is that it is unable to evaluate the impact of a policy intervention on the outcomes of attacks (e.g., the number of fatalities) even if these are measured during each event.

Chapter 3 introduces the sequence hazard model of a terrorist groupdeciding when to attack. The model links the outcome of terrorist attacks to the choice of when to attack by taking the amount of time elapsed since the last attack as an input into the planning of the next attack. The agent trades off the desire to improve their attack against the risk that their plans are sabotaged before they are able to carry them out. The sequence hazard model is dynamic because agents take into account the potential size of future attacks when deciding whether or not to attack today. As a consequence, the hazard implied by the sequence approach is non-proportional in time. This distinguishes the sequence hazard model from the proportional hazard assumed by the series (Cox) approach.

The sequence model implies a data generating process for attack outcomes that takes into accountthe probability the agent attacks. Chapter 3 derives the implied mathematical expectation and variance of attack outcomes which allows researchers to extend the notion of deterrence to allow for the possibility that counterterrorist policies that reduce the frequency of attacks, but increase the expected severity of attacks that do take place. Two types of attack outcomes are considered, a mixed Poisson-beta model for the number of casualties and a mixed Bernoulli-beta model for attack success or failure.

Chapter 4 presents a Monte Carlo study demonstrating the validity ofestimating the sequence hazard model by maximum likelihood. In contrast, when the underlying data are generated according to the simple behavioral model presented in Chapter 3, the series hazard fails to estimate the true effect of a policy intervention on the risk of attacks. Moreover, the standard tests fail to reject the null hypothesis that the data are generated according to a proportional model. The simulation implies that if planning time and uncertainty over attack outcomes are important elements in terrorist decision making, then methods of policy evaluation based on the assumption of proportionality may not be appropriate. In contrast, by modeling both the timing of attacks as well as their size, the sequence hazard offers a straightforward way of incorporating terrorist attack outcomes into the analysis of counterterrorism policy.