Re-examining the functional form of the certainty effect in deterrence theory

In this paper we explore the functional form of the risk-certainty effect for deterrence. Using a sample of serious youth offenders, we first estimate a simple linear model of the relationship between the perceived certainty of punishment and self-reported offending. Consistent with previous literature we find evidence of a moderate deterrent effect. We then examined whether, consistent with a linear model, the effect of perceived risk is truly constant at different ranges of the risk continuum. Estimating a nonparametric regression model that makes no a priori assumption about the functional form of the model but allows the data itself to yield the appropriate functional form, we found marked departures from linearity. Our examination showed evidence of both a tipping effect, whereby perceived risk deters only when it reaches a certain threshold (between an estimated risk of .3 and .4) and a substantially accelerated deterrent effect for individuals at the high end of the risk continuum. Perceived sanction threats did, however, have a non-trivial deterrent effect within the mid-range of risk. The implications of our findings for both theory and additional research are discussed.