"One of the first of these studies was conducted by Ehrlich. Using aggregate homicide data for the United States for the period 1933-70, Ehrlich analyzed the effect of the probability of execution upon homicide rates. Ehrlich also controlled for a variety of other factors, including unemployment, age distribution, and per capita income. Based upon this analysis, Ehrlich concluded that executions did have a deterrent effect and, specifically, that between seven and eight homicides were deterred by each execution...

... Attempted replications of Ehrlich's work using similar methods (multivariate analyses and econometric methods) have failed, however, to find a deterrence effect. For example, Loftin did an elaborate ecological analysis of crime rates and social characteristics in the United States. When social and economic variables such as poverty, education, and family structure were controlled, Loftin's study found little or no evidence for the deterrence hypothesis. Similarly, Brier and Fienberg used econometric models to test for a deterrence effect, and they concluded that the claims made in Ehrlich's 1975 study were not supported by the evidence. Finally, some of the most interesting longitudinal evidence involves separate time-series analyses from five different states examining the relationship between execution risk and homicide rates. Here, again, the evidence runs counter to deterrence theory in three of the five states examined...."

Archer, Gartner and Beittel notes, also, that "[i]n recent research, there is even some evidence for what might be called an "antideterrent" effect. A fine-grained study by Bowers and Pierce examined monthly homicide rates in New York State between 1907 and 1963 and found an average increase of two homicides in the month after an execution. This finding led Bowers and Pierce to postulate, in direct opposition to the deterrence hypothesis, a "brutalizing" effect, that is, that executions might increase rather than deter homicides. In summary, recent studies of the de facto issue do not contradict the long-standing conclusion from de jure research that the death penalty has no consistent, demonstrable deterrent effect...."

Their own research, Archer, Gartner and Beittel note, fails to support and, indeed, repeatedly contradicts the proposition that "If capital punishment is a more effective deterrent than the alternative of life imprisonment, its abolition ought to be followed by homicide rate increases." In their "cross-national sample, abolition was followed more often than not by absolute decreases in homicide rates. Further, the homicide rates of these nations also decreased relative to the rates of noncapital offenses after abolition. Both of these findings hold true whether comparisons are made for short, medium, or the longest feasible time periods.

This cross-national research design controls for some possible defects in previous studies, including vicarious deterrence, the alleged jurisdictional nonspecificity of capital punishment. The results of this comparative analysis contradict general deterrence theory, and also reject specific hypotheses derived from this theory, such as residual deterrence and offense deterrence. These findings lend new weight to the body of research running counter to deterrence theory." [Dane Archer, Rosemary Gartner and Marc Beittel, "Homicide and the Death Penalty: a Cross-National Test of a Deterrence Hypothesis" (Symposium on Current Death Penalty Issues), 74 J. Crim. L. & Criminology 991, 999-1001, 1011-1012 (1983)].