Wolfers and Donohue had previously shown much of the empirics on the death penalty are fragile.
The latest from Manski and Pepper (HT: Chris Blattman) shows the results more fragile than I'd thought: you can pretty much choose your conclusion through appropriate choice of identifying assumptions.
...we study the identifying power of relatively weak assumptions restricting variation in treatment response across places and time. The results are findings of partial identification that bound the deterrent effect of capital punishment. By successively adding stronger identifying assumptions, we seek to make transparent how assumptions shape inference. We perform empirical analysis using state-level data in the United States in 1975 and 1977. Under the weakest restrictions, there is substantial ambiguity: we cannot rule out the possibility that having a death penalty statute substantially increases or decreases homicide. This ambiguity is reduced when we impose stronger assumptions, but inferences are sensitive to the maintained restrictions. Combining the data with some assumptions implies that the death penalty increases homicide, but other assumptions imply that the death penalty deters it.And so I revise: the death penalty is wrong, and it also likely has little measurable deterrent effect. There may still be a deterrent effect; we just can't show one given available data.
Update: Chris Auld has a nice intuitive explanation of the paper's results.