Americans undoubtedly sleep more soundly with more cops on the beat, but academics have turned up surprisingly little evidence that police reduce crime. The crux of the problem is that rising crime rates spark police hiring, so the two variables are often positively related even if police reduce crime. Similarly, large police forces are typically found in cities with high crime rates.
In a National Bureau of Economic Research study, economist Steven D. Levitt has come up with a way to circumvent this problem. His study indicates that increases in police forces in large cities are concentrated in mayoral and gubernatorial election years. Thus, changes in crime rates during such years (after controlling for other influences) provide an independent measure of the impact of police on crime.
Levitt's analysis of data from 59 cities from 1970 to 1992 indicates that adding a police officer eliminates about 8 to 10 serious crimes in a year (mostly auto thefts). Based on past estimates of crime costs, Levitt calculates that this translates into at least $100,000 in social benefits per cop--suggesting that hiring more police remains cost-effective.