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 for the robust positive correlation between prior and future criminal offending. Nagin and Paternoster (1991) have suggested that the correlation could be due to time-stable population differences in the underlying proneness to commit crimes (population heterogeneity) and/or the criminogenic effect that crime has on social bonds, conventional attachments, and the like (state dependence). Because of data and measurement limitations, the disentangling of population heterogeneity and state dependence requires that researchers control for unmeasured persistent heterogeneity. Frequently, random effects probit models have been employed, which, while user-friendly, make a strong parametric assumption that the unobserved heterogeneity in the population follows a normal distribution. Although semiparametric alternatives to the random effects probit model have recently appeared in the literature to avoid this problem, in this paper we return to reconsider the fully parametric model. Via simulation evidence, we first show that the random effects probit model produces biased estimates as the departure of heterogeneity from normality becomes more substantial. Using the 1958 Philadelphia cohort data, we then compare the results from a random effects probit model with a semiparametric probit model and a fixed effects legit model that makes no assumptions about the distribution of unobserved heterogeneity. We found that with this data set all three models converged on the same substantive result-even after controlling for unobserved persistent heterogeneity, with models that treat the unobserved heterogeneity very differently, prior conduct had a pronounced effect on subsequent offending. These results are inconsistent with a model that attributes all of the positive correlation between prior and future offending to differences in criminal propensity. Since researchers will often be completely blind with respect to the tenability of the normality assumption, we conclude that different estimation strategies should be brought to bear on the data.