Assessing Stability and Change in Criminal Offending: A Comparison of Random Effects, Semiparametric, and Fixed Effects Modeling Strategies

An important theoretical problem for criminologists is an explanation forthe robust positive correlation between prior and future criminaloffending. Nagin and Paternoster (1991) have suggested that the correlationcould be due to time-stable population differences in the underlyingproneness to commit crimes (population heterogeneity) and/or thecriminogenic effect that crime has on social bonds, conventionalattachments, and the like (state dependence). Because of data andmeasurement limitations, the disentangling of population heterogeneityand state dependence requires that researchers control for unmeasuredpersistent heterogeneity. Frequently, random effects probit models havebeen employed, which, while user-friendly, make a strong parametricassumption that the unobserved heterogeneity in the population follows anormal distribution. Although semiparametric alternatives to the randomeffects probit model have recently appeared in the literature to avoid thisproblem, in this paper we return to reconsider the fully parametric model. Viasimulation evidence, we first show that the random effects probit modelproduces biased estimates as the departure of heterogeneity from normalitybecomes more substantial. Using the 1958 Philadelphia cohort data, we thencompare the results from a random effects probit model with a semiparametricprobit model and a fixed effects logit model that makes no assumptions aboutthe distribution of unobserved heterogeneity. We found that with this dataset all three models converged on the same substantive result—evenafter controlling for unobserved persistent heterogeneity, with models thattreat the unobserved heterogeneity very differently, prior conduct had apronounced effect on subsequent offending. These results are inconsistentwith a model that attributes all of the positive correlation between priorand future offending to differences in criminal propensity. Sinceresearchers will often be completely blind with respect to the tenabilityof the normality assumption, we conclude that different estimationstrategies should be brought to bear on the data.