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 t he 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 co mmit crimes (population heterogeneity) and/or the criminogenic effect that crime has on social bonds, conventional attachments, and the like (state de pendence). Because of data and measurement limitations, the disentangling o f population heterogeneity and state dependence requires that researchers c ontrol 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 avo id this problem, in this paper we return to reconsider the fully parametric model. Via simulation evidence, we first show that the random effects prob it model produces biased estimates as the departure of heterogeneity from n ormality becomes more substantial. Using the 1958 Philadelphia cohort data, we then compare the results from a random effects probit model with a semi parametric probit model and a fixed effects legit model that makes no assum ptions about the distribution of unobserved heterogeneity. We found that wi th 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 ha d a pronounced effect on subsequent offending. These results are inconsiste nt with a model that attributes all of the positive correlation between pri or and future offending to differences in criminal propensity. Since resear chers will often be completely blind with respect to the tenability of the normality assumption, we conclude that different estimation strategies shou ld be brought to bear on the data.