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The economics behind detecting terror plots

Editor’s note: This post was written by Edward H. Kaplan before the Charlie Hebdo terrorist attacks in Paris on 7th January 2015.

How many good guys are needed to catch the bad guys? This is the staffing question faced by counterterrorism agencies the world over. While government officials are quick to proclaim “zero tolerance” for terrorism, unlimited resources are not made available to prevent terror attacks, nor should that be the case. Indeed, as with most public policy decisions, the appropriate staffing level depends upon both the benefits and costs of fielding counterterrorism agents.

The benefits derive from successfully interdicting terror attacks and averting the damage such attacks impose in deaths, injury, property and infrastructure damage, and more generally population fear and anxiety. While intensifying both covert and overt counterterror intelligence efforts does lead to greater detection, as with many other economic activities, there are diminishing returns to effort: doubling the number of agents will not lead to a doubling of the detection rate, and indeed the marginal detection rates fall rapidly as the number of counterterror agents grows.

And as the number of counterterror agents grows, so does the cost of detecting terror plots. However, unlike detection levels, the marginal cost of adding additional agents stabilizes, for all agents must be trained, outfitted, and compensated. These simple economic considerations are sufficient to suggest that there is a socially optimal counterterror staffing level, which in turn implies a socially efficient detection level for terror plots. So, while government officials contend that even one terror attack is one too many, economics suggests that there is an optimal fraction of terror attacks to prevent that equates the marginal benefits and costs of detection, and this optimal fraction could be significantly less than unity.

How to operationalize the concepts described above is another matter, for unlike many production processes, it is not easy to observe the relationship between counterterror agent staffing on the one hand, and terror plot detection on the other. However, progress in this area has been made thanks to methods borrowed from queueing theory, which is applied widely to study staffing problems in situations ranging from telephone call centers to hospitals to manufacturing facilities to air traffic control. As shown in the figure below, newly hatched terror plots can be construed as “customers” who “arrive” to a service system.

Terrorism graph, by Edward Kaplan. . Used with permission.
Terrorism diagram, by Edward H. Kaplan. Used with permission.

Upon arrival, a new plot is undetected, and will remain so until it is detected, or matures to an actual terror attack, whichever happens first. The number of counterterror agents drives the rate with which plots are detected, but of course the total number of detected plots also depends upon the actual number of plots that exist. Once a plot is detected, it can be interdicted, thus this terror queue framework provides the link between the number of counterterror agents fielded on the one hand, and the number of terror plots that are detected and interdicted on the other.

There are still details that must be specified to complete the analysis, and it is in these details that a recent ten year study of all Jihadi terror plots in the United States provides important data. From an analysis of court records including the testimony of undercover operatives in addition to suspect confessions or observed attack details, it was possible to approximate the starting dates for a sample of terror attacks in addition to the observed dates of actual attack or plot detection, whichever came first. From these data, an interesting hypothesis emerged: when is a terror plot more likely to be detected? The answer is that as a plot edges closer to the moment of execution as a terror attack, there is more activity on the part of would be attackers, and this increased level of activity provides more opportunities for counterterror agents to detect an attack. This idea can be formalized by stating that the instantaneous chance that an undetected plot is detected is proportional to the instantaneous chance this same plot executes as an attack. In language more familiar to economists and statisticians alike, the plot detection hazard is proportional to the attack hazard, which gives rise to what is known as a proportional hazards model. The Jihadi plot data mentioned above are consistent with this hypothesis, which greatly simplifies the relationship between agent staffing levels on the one hand and the fraction of terror plots that are detected on the other.

FBI headquarters in Washington D.C., by Aude. CC-BY-SA-2.5 via Wikimedia Commons.
FBI headquarters in Washington D.C., by Aude. CC-BY-SA-2.5 via Wikimedia Commons.

With this new model in hand, what remains is a valuation step – what is the marginal benefit of preventing a terror attack, and what is the marginal cost of assigning an additional agent? Both of these quantities can be estimated from the terrorism literature. For example, data suggest the typical number of persons killed and injured in terror attacks in Europe, Israel and the United States, well-known economic studies have estimated the value of a statistical life, and a more recent study has established that on average, the disability adjusted life years (DALYs) lost per terrorism injury are equivalent to 0.57 of the DALYs lost due to a death from terrorism. On the cost side, the United States Federal Bureau of Investigation (FBI) provide information regarding the salaries and benefits received by FBI special agents, who comprise the principal counterterror detection force in the United States.

Applying the model to the United States leads to an interesting and perhaps counterintuitive result. The Jihadi plot data report that 80% of these plots were interdicted prior to attack. If one uses this observation to calibrate the proportional hazards relation between attack and detection discussed above, the model suggests an optimal staffing level of only 2,080 agents. It is interesting that in 2004, the FBI reported that 2,398 of 11,881 special agents were devoted to counterterrorism. As of October 2013, the FBI reported that their total number of special agents increased to 13,598, though the number allocated to counterterrorism was not stated.

There are additional analyses one can conduct using the framework developed above. For example, while most of the plots in the United States sample discussed above were “lone wolf” attempts by individuals or small groups to wreak havoc, it is well known that many terrorist organizations behave in strategic fashion and are able to adapt their behavior to counterterror policy and tactics. This leads to a game theoretic model where strategic terrorists who understand how socially efficient staffing works modify their own attempted attack rates in accord with their own benefit-cost calculus. In this game, the resulting optimal terror plot detection level depends upon the costs and benefits that terrorists assign to terror attacks, which provides yet another example of how strategic terrorists can manipulate counterterror agencies (or governments more broadly) to achieve their objectives.

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