This always strikes me as a very interesting question. It presupposes that the goal of the death penalty is and always has been the deterrence of further or future crime. If this is not and has not historically been the goal of death penalties, then the question of whether it does or does not deter crime has no bearing upon the larger question of should the death penalty continue as a judicial practice.
I'd suggest that the idea of crime deterrence is a newly overlaid goal that clouds the historical goal of the death penalty. Though not an historian nor an anthropologist, I believe I speak correctly in saying that the historic goal, throughout eras and civilizations, has been punishment for crimes against individuals or society. Again, being none of the above, I think I speak correctly in saying that the goal of deterring crimes came about after 20th century attempts at prison reform and the humanistic rejection of "punishment" as a justifiable stance against crime and criminals.
Whether more states should have the death penalty, previously called "capital punishment," really depends upon the actual goal being pursued. If a state's goal is to punish for crimes against individuals or society, then, yes, for fitting crimes (not petty larceny!), the state should enact the death penalty. If, on the other hand, the state's goal is to deter further and future crime, then perhaps not, perhaps using one human being, who is not undergoing just social punishment, to deter other human beings is an unjust manipulation of the first human being.
This argument evades the question of whether the death penalty does or does not deter crime because the argument is predicated on an altogether different moral argument, one to which effective deterrence is immaterial. As a final note, when death rates are reduced after one execution, as Pepperdine discloses, the question has to be asked whether the drop in rates is due to judges actions in withholding the death penalty or due to criminals being much more judicious in their crime choices.