Correlation and regression techniques are applied to aggregate data on imprisonment and crime rates. Certainty of imprisonment shows a negative and possibly curvilinear association with crime rate; contrary to recent criticisms, this relation cannot be accounted for by an artifice in the indexes of these two variables. Severity of imprisonment shows a negative correlation with crime rate after controlling for the effects of certainty. Some evidence is found of interaction between certainty and severity in effects on crime rate.
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Caroline Logan (1972) studied this question.