This word is all you have - no actual evidence, just assertions.
You forgot to include the link that demonstrates correlation. You can't, or else rich Western states without the death penalty wouldn't have lower crime rates than the US.
No, the word is not all I have. I have the numbers. Looking at all states, by the numbers of GDP per capita and by murder rate, you will see a pattern.
Low GDP per capita, regardless of death penalty or not = Murders will happen.
High GDP per capita and loose death penalty or no death penalty = Variates. Iceland is great and peaceful, USA is dangerous.
High GDP per capita and strict death penalty = Almost guaranteed no murders (examples, Brunei and Singapore).
Very small nations and islands where everyone knows each other, regardless of death penalty or not = Almost guaranteed no murders.
If you should find some numbers to prove my claim (factually based on numbers) wrong, then try.
A nation can be peaceful with or without the death penalty, as Iceland proves, but no rich countries with a strict death penalty system posseses any significant murder problems at all. The numbers don't lie.
Please read up, bro.
Oh, and in Singapore and Brunei, murderes actually do get executed. In USA, there are almost no executions despite the massive amount of murders. Don't call USA a nation with "the death penalty", unless you remember to call it "butter death penalty" or "loose death penalty", be specific so you don't misinform people.