Does increased police deployment decrease crime? According to these results, "a 10% increase in police leads to a 3% fall in crime." [Alex Tabarrok of Marginal Revolution is cited in the references]:
Policing and crime: evidence from the London bombings re-deployment, by Mirko Draca, Stephen Machin, and Robert Witt, Vox EU: Debate over law and order policy in most countries is often characterised by calls for ‘more police’. Compared with debates over the efficacy of incarceration or increases in criminal sanctions, a call for more police is much less controversial. Indeed, politicians from both left and right-wing parties are often eager to make commitments to increase police resources, particularly those related to the visible deployment of police officers in community areas or prominent public places.
However, in empirical terms very little is known about the effects of increased police deployment on crime. ...[S]pending on law and order is a major area of public expenditure. Furthermore, the intuition that extra police must deter crime is as appealing... However, in practice the realisation of this intuition can face obstacles. In the case of crime, the deployment of police in one area or at one time can shift or displace criminal activity thereby reducing the net effect of the deployment. And like all types of investment, the provision of extra police resources faces inevitable diminishing returns.
Crime, terror and police deployment – evidence from London
The forthcoming study ‘Panic on the Streets of London’ by myself, Stephen Machin and Robert Witt attempts to estimate the causal impact of the central and inner London police deployments that followed the July 2005 terrorist attacks. In general, research on crime and police faces an endogeneity problem – governments allocate more police resources to high crime areas thereby creating a positive correlation between the levels of crime and police resources across geographical areas. The policy deployments that occurred after the attacks effectively broke this endogenous relationship by temporarily re-allocating police resources in an unanticipated pattern that was unrelated to prior crime levels or trends.
The scale of the post-attacks police deployment in London makes it a unique case amongst similar studies in the crime-police area. There was a 34% increase in hours worked by police in central-inner London in the six weeks that followed the attacks. In turn, we find that this increase was associated with an 11% fall in crime. Together, these estimates imply an elasticity of approximately -0.3 between crime and police deployment. Taken literally this says that a 10% increase in police leads to a 3% fall in crime. This is broadly consistent with previous casual estimates of the impact of police on crime.
The timing of the ‘policy on’ period is crucial to our estimates. In principle, it is plausible that the terrorist attacks could have affected crime through channels other than the increased police deployment. For example, the attacks changed commuter travel patterns across London and there was a general increase in public safety awareness in the period after the attacks. Either of these changes could also have had an impact on the pattern of crime in London. However, we find that the pattern of the deployment and the fall in crime match each other very closely – no other factor can account for the 6-week timing of the reduction in crime.
Overall, it is interesting that similar estimates of the effects of police on crime are being reached across studies that take place in very different settings. Furthermore, these studies have considered very broad increases in police resources rather than assessing the effects of specific police strategies and policies. This leaves the field open for further research investigating the impact of specific crime reduction initiatives.
... Di Tella, R. and E. Schargrodsky (2004) Do Police Reduce Crime? Estimate Using the Allocation of Police Forces After a Terrorist Attack, American Economic Review, 94, 115-133 and Klick, J and Tabarrok, A (2005) Using Terror Alert Levels to Estimate the Effect of Police on Crime, The Journal of Law and Economics, 48, 267-279.
 Levitt, S. (1997) Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime, American Economic Review, 87, 270-290 and Corman, H and H. Mocan, (2000) A Time Series Analysis of Crime , Deterrence and Drug Abuse, American Economic Review, 87, 270-290.