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

Abstract

Researchers have 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. This paper asks how research should proceed. We seek to make transparent how assumptions shape inference. We study the identifying power of relatively weak assumptions restricting variation in treatment response across places and time. We perform empirical analysis using state-level data in the United States in 1975 and 1977. The results are findings of partial identification that bound the deterrent effect of capital punishment. 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. Imposing certain assumptions implies that adoption of a death penalty statute increases homicide, but other assumptions imply that the death penalty deters it. Thus, society at large can draw strong conclusions only if there is a consensus favoring particular assumptions. Without such a consensus, data on sanctions and murder rates cannot settle the debate about deterrence. However, data combined with weak assumptions can bound and focus the debate.