Klick and Tabarrok use changes in the terror alert levels in Washington to infer a variation in police deployment, and provide an estimate of the police crime elasticity as -0.3 which is similar to the results got by Levitt（1997）， Di Tella and Schargrodsk (2004) and Draca et al.(2008).
Although Di Tella and Schargrodsk is creative by using a terrorist bomb which lead to police deployment and get statistically significant result, one concern here is that a single shock does not generally allow a researcher to use critical values from standard asymptotic theory to judge the statistical significance of observing a given test statistic. However, Klick and Tabarrok use terror alert level which varies four times in the period, and it reduces the possibility of spurious correlation. Furthermore, they use the daily data and the treatment window is short, so their results are less likely to be due to changes in other factor.
Comparing the earlier studies like Levitt(2002), Kovandzic and Sloan(2002), Corman and Mocan(2005) which use observational study, Klick and Tabarrok use natural experiment that usually allow firmer causal conclusions to be drawn than observational studies, so they provide better evidence for a general link between police number and crime rates. Klick and Tabarrok also find no deterrence effect for homicide while Levitt found the largest deterrence effect for homicides in earlier studies, this is notable.
One significant shortcoming of Klick and Tabarrok research is its reliance on single jurisdiction. Although strong designs require this and it can provide a better identification, there is a concern about external validity. For example, Klick and Tabarrok reveals a statistically significant result applying the data from one single city Washington DC, but it is unclear whether this effect observed in Washington DC could be expected in other cities. In particular, this research does not provide any evident about the actual variation in terms of the police number and it does not examine how police are allocated to reduce crime. Therefore, use of this design in other cities and more detailed information on police allocation has the potential to increase confidence in these results substantially.
This research uses IV method, so a possibly excessive faith in instrumental variable can really be a problem. Robustness of the IV used is far from proven, which means that issues of endogeneity may not have been fully dealt with as the author claim. In this case, the change in transport usage pattern and the police effort can really affect criminal rate.
As Draca, Machin and Witt(2009) explain, the indirect effect from adopting IV may rely on two displacement: spatial displacement and temporal displacement. But Klick and Tabarrok does not involve it.
Draca, M., Machin, S. and Witt, R. (2008) Panic on the Streets of London: Police, Crime and the July 2005 Terror Attacks. CEP Discussion Paper no. 852. Levitt, S.D. (1997) Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime, The American Economic Review 87(3): 270-290
Levitt, S.D. (2002) Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime: Reply, The American Economic Review 92(4): 1244-1250. Di Tella, R. and Schargrodsky, E. (2004) Do Police Reduce Crime? Estimates Using the Allocation of Police Forces after a Terrorist Attack, The American Economic Review 94(1): 115-133.