From the Chronicle of Higher Education:
"Statistical evidence for the idea that the death penalty deters homicide is "at best weak and inconclusive," write John J. Donohue, a professor at Yale University Law School, and Justin J. Wolfers, an assistant professor of business and public policy at the Wharton School at the University of Pennsylvania.
"While it remains possible that the death penalty may deter murderers, the available data are "simply too noisy, and the conclusions from any study are too fragile," they write."
Funny how Donohue and his research partner Steven D. "Freakonomics" Levitt ignored how noisy the data were when they popularly proclaimed that legalizing abortion had lowered the crime rate!
My guess is that the recent lengthening of sentences for non-homicides, such as the life sentences for a third felony, means that the death penalty can play a role in deterring a particular kind of murder: witness-murdering. If your state has a three strikes rule but no death penalty, a two-time loser engaging in a felony like armed robbery has a rational incentive to murder his victims to prevent them from identifying him. If he lets them live and they identify him, he goes to prison for life. If he kills them, he reduces the chance he will be convicted, and if convicted he still merely goes to prison for life.
Unfortunately, I've never heard of anyone studying this particular possibility. Indeed, this logic seldom seems to come up in discussions of the death penalty.
Also, having a death penalty gives the district attorneys more leverage, especially in a prisoner's dilemma situation where they've arrested two suspects who worked together but can't convict either one unless one confesses. Avoiding the death penalty gives one the incentive to roll over on the other. (Of course, this also means that sometimes the accomplice who didn't pull the trigger gets framed by his partner who actually was the killer.)