A whole series of studies (e.g. Thorstin Sellin; 1998 UN study) have failed to uncover any evidence whatsoever that the death penalty acts as a deterrant.
The opposite may be true
There is some evidence that the death penalty actually increases the murder rate. It has a brutalizing effect on society, increasing society's tolerance of violence. The murder rate tends to rise slightly after an execution has taken place, according to the Bowers-Pierce study.