Semi‐nonparametric competing risks analysis of recidivism

Abstract

SUMMARYIn this paper we specify a semi-nonparametric competing risks (SNP-CR) model of recidivism, for misdemeanors and felonies. The model is a bivariate mixed proportional hazard model with Weibull baseline hazards and common unobserved heterogeneity. The distribution of the latter is modeled seminonparametrically, using orthonormal Legendre polynomials on the unit interval, and integrated out to make the two durations dependent, conditional on the covariates. The SNP-CR model involved corresponds to a Logit model for felony arrest; hence the validity of the SNP-CR model can be tested by testing the validity of the implied Logit model. The latter will be done by using the integrated conditional moment (ICM) test. In the first instance we have estimated and tested two versions of the SNP-CR model, without and with fixed state effects. However, the ICM test rejects these models. Therefore, we have estimated and tested the model for each state separately. These state models are not rejected by the ICM test. Indeed, the estimation results vary substantially per state.

Consistency and Asymptotic Normality of Sieve Ml Estimators Under Low-Level Conditions

“…See Newey (1990) for a general review of efficiency bounds, and Hahn (1994) and Ridder and Woutersen (2003) for the efficiency bound of the MPH model. On the other hand, Hahn (1994) has also shown that, in general, the multiple spell MPH model does not suffer from this problem, which is confirmed by the estimation results in Bierens and Carvalho (2007). Thus, Assumptions 6.7 and/or 6.8 may not hold for the single spell MPH model, and the same applies to Assumption 3(a) in Chen et al (2006) (cf.…”

“…The model then becomes fully parametric, and, therefore, asymptotic normality can be derived in a standard way, provided that the SNP parameters involved are unique. This is the approach followed by Bierens and Carvalho (2007).…”

“…Heckman and Singer (1984) propose to estimate the distribution function of the unobserved heterogeneity variable by a discrete distribution. Bierens (2008) and Bierens and Carvalho (2007) use orthonormal Legendre polynomials to model seminonparametrically the unobserved heterogeneity distribution of interval-censored mixed proportional hazard models and bivariate mixed proportional hazard models, respectively.…”

Reoffending among serious juvenile offenders: A developmental perspective

“…In the recidivism literature, failure is often defined as reentry to the criminal justice system, whereas recidivism time is often measured examining the time between release from prison and the first rearrest (Bierens & Carvalho, 2007). In studying recidivism with survival analysis, an assessment of the hazard function of recidivism is needed as well (Gruenewald & West, 1989).…”

The Et Interview: Herman Bierens

“…We used that technique in the application for the JAE, and I also managed to squeeze in an ICM test for the correctness of the Weibull baseline hazards. It became a nice paper [19], an empirical application with theoretical innovations as required by the JAE. That is how I got interested in semi-nonparametric econometrics.…”