The deterrence theory of capital punishment assumes that the potential capital murderer acts rationally in controlling his/her aggressive, homicidal behavior to avoid the fearful consequence of his/her own death at the hands of the State. The reasoning is that by continually impressing upon the public that certain categories of homicide will bring death to the offender, then those who would commit such acts with lesser consequences attached would refrain because of the escalated consequences of capital punishment. There is very little evidence to support this theory that those likely to commit capital murder restrain their behavior through such an analysis of the likely consequences of their behavior. Studies of the rates of capital homicides in jurisdictions where a capital punishment has been recently highly publicized do not show a deterrent effect from the offender's death for such a crime. Recognizing that many factors affect the homicide rate in a given jurisdiction over a period of time, many research scholars have sought to control for extraneous influences on the homicide rate by comparing contiguous clusters of States that differ in their capital punishment laws. None have found a deterrent effect for capital punishment. Isaac Ehrlich, however, conducted a recent econometric study that found a deterrent effect for capital punishment, but methodological criticisms of the study as well as the failure of subsequent similar studies to establish Ehrlich's conclusion has undermined confidence in his study in the research community. Overall, there is no rational basis for believing that capital punishment is a relevant response to the public's concern about the murder rate. Tabular data and 28 notes are provided.