I'm aware that there is not strong evidence of a global deterrent effect. However, if we are looking to offset something like 1 death every four years, the magnitude of a countervailing effect could be small enough to be lost in the 'noise' of the existing research studies, but still be larger than the .25 annual deaths that it's being measured against.

I would also point out that looking at state-level differences in death penalty policies isn't as likely to pick up changes in attitudes among criminals. If the federal government outlawed the death penalty, there would be much broader awareness of the change (and therefore more likelihood of a change in criminal behavior).