Deterrence and the Death Penalty: Partial Identification Analysis Using Repeated Cross Sections

Researchers have long used repeated cross sectional observations of homicide rates and sanctions to examine the deterrent effect of the adoption and implementation of death penalty statutes. The empirical literature, however, has failed to achieve consensus. A fundamental problem is that the outcomes of counterfactual policies are not observable. Hence, the data alone cannot identify the deterrent effect of capital punishment. How then should research proceed? It is tempting to impose assumptions strong enough to yield a definitive finding, but strong assumptions may be inaccurate and yield flawed conclusions. Instead, 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.