all of Western Europe has abolished the death penalty. But the USA has a higher murder rate per capita than all of Western Europe. Canada, the USA's closest neighbour has a much lower murder rate.

Look at the following table and see who's above the USA for mureder rate: Murders (per capita) statistics - countries compared - NationMaster

None of those countries are fully developed, to what we would call "first world" countries. Jamaica comes in at 3rd and they still have the death penalty. Russia's quite high up and they still have the death penalty.

The USA has the highest murder rate of any developed country, yet they have the death penalty.

The figures show that capital punishment is not a deterrant to murder. This is because everybody thinks they won't get caught. The deterrant is getting caught.