Does Death Penalty Save Lives?

Very interesting article in the New York Times discussing whether the death penalty saves lives,

"According to roughly a dozen recent studies, executions save lives. For each inmate put to death, the studies say, 3 to 18 murders are prevented.

The effect is most pronounced, according to some studies, in Texas and other states that execute condemned inmates relatively often and relatively quickly.

The studies, performed by economists in the past decade, compare the number of executions in different jurisdictions with homicide rates over time — while trying to eliminate the effects of crime rates, conviction rates and other factors — and say that murder rates tend to fall as executions rise. One influential study looked at 3,054 counties over two decades. " (from the New York Times)

It seems to me that there's a key flaw in that study and analysis.

Let's say there's a correlation between the number of executions and the crime rate. What if we randomly selected people to be executed in each district, no matter whether they were guilty of a crime or not. Would that also deter crime and 'save lives'? These studies imply that they would. It goes to the heart of one of the key arguments against capital punishment, which is the equal application of the law. (There are two additional really strong arguments against it.)