Did Abolition of Parole Impact the Reported Crime Rates? A Comparison of Intervention Time Series Methods Using Arma and Structural Time Series Approaches

Richard McCleary, University of California, Irvine
Sanjeev Sridharan, WESTAT
Siem Koopmans, Free University Amsterdam

Virginia abolished parole and reformed sentencing for all felony offenses committed after January 1, 1995 in a special legislative session in Fall 1994. Parole abolition was accompanied with substantially enhanced sentences for both violent offenses and violent offenders. For non-violent offenders the new "truth-in-sentencing" attempted to preserve the time-served practices from the prior system. In this presentation, we will examine the impact of the abolishing parole on reported violent and property crimes. We specifically examine the differences between ARIMA (McCleary and Hay, 1980) and structural time series methods (Koopmans and Durbin, 2001) in estimating the impacts of abolishing parole on reported crimes.

Exhibits 1 and 2 describe the reported crimes for both property and violent crimes. The curious aspect is that reported crimes were already declining when parole was abolished in January 1995. Intervention Time series methods will model the trajectories of the reported crimes both before and after the abolition of parole.

This presentation will be a contribution to time series methods. This involves a collaboration between leading practitioners of ARIMA and Structural Time Series methods.

METHODS Intervention time series methods have been primarily implemented in applied criminology using ARIMA methods. The strength of ARIMA intervention time series methodology are its ability to discern the form of the impact. Structural time series models are formulated directly in terms of components of interest (e.g., the trend, seasonal, cycle, and the residual-irregular-components). Modeling explanatory variables are often more straightforward in a Structural Time Series framework as compared to ARIMA. The explanatory variables enter the models along with the unobserved components. These models gain their flexibility because the stochastic formulation allows the mean, trend and seasonality to evolve over time.

We will compare the results of the ARIMA and structural time series analysis. Both methodological and substantive implications of the results will be discussed.


The intervention ARIMA models will be implemented using the SCA software. The structural time series models will be implemented in STAMP and SSFPACK.

Exhibit 1 Time Series of Reported Property Crimes: Pre and Post Parole Abolition

Exhibit 2 Time Series of Reported Violent Crimes: Pre and Post Parole Abolition

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Updated 05/20/2006