Selective Incapacitation and Public Policy: Evaluating California's Imprisonment Crisis

Technical Appendix A

159 Technical Appendix A Data Sources and Estimation Procedures The data used for validation of the simulation model presented in chapter 7 were obtained from various sources. Arrest data were provided by the California Department of Justice, Criminal Justice Statistics Center. Data on prison and parole entrances, exits, and daily population were provided by the Research Bureau of the California Department of Corrections. Detailed data on jail and probation populations were somewhat more difficult to obtain. Limited data on these populations are available from the California Department of Justice (1980–1997), and more specific values for each of the 450 relevant subgroups were estimated. Additionally, while the prison and parole data obtained were the most complete with respect to the six relevant offender characteristics (i.e., the five indicators of the dangerousness construct and race), other data sources contain less complete information. What follows is an account of the procedures used to develop the data in order to provide validation for the model, and details of the programs that were written to produce the four projected scenarios. GENERAL FEATURES OF THE MODEL Berkeley Madonna1 (version 8.0) was used to create and estimate the simulation models. This software allows the user to represent a system as a series of differential and difference equations. Berkeley Madonna was developed by researchers in molecular and cellular biology at the University of California, Berkeley, for testing mathematical specifications of theoretical models of molecular, cellular, and developmental processes. I am unaware of other uses of this software in the social sciences. As discussed in chapters 6 and 7, the model consists of six population “states” and the pathways connecting them (e.g., the pathway by which offenders exit the state of being in jail at one time-step and enter prison at the next time-step). The simulation modeling software does not itself specify the metric of these time-steps. For this model, the incremental unit of time is one year, and validation data are annual data on the composition of populations and on transition probabilities.The transition probabilities are generally fixed, and represent the proportion of the “sending” population state that exits that state at each iteration of the model. Each transition probability is regulated over time by an informational quantity or multiplier. If a particular transition probability remains constant over time, the value of this multiplier is set to equal one. In the case of rising probabilities (e.g., the case of increasing drug arrests in the 1980s), the multipliers are set to values higher than one (and may be subject to “shocks,” delayed functions, or other stimuli to mimic changes over time). In the case of declining rates over time, multipliers have values lower than one. Generally, the transition probabilities for each population subgroup are not known. In most cases, a baseline transition probability (average, considering the entire population of both states) can be obtained, simply by dividing the size of the sending population by the size of the receiving population. In the absence of any theoretical justification to do otherwise, start values for transition probabilities for each of the four hundred fifty groups were assigned as this baseline, and altered in the course of model specification to reproduce system dynamics as represented by the validation data. For certain transition pathways, these base rates require modification, as in the case where the receiving state has more than one contributing state. For example, in the case of the transition rates that give rise to jail populations, this is done taking into account the relative proportions of sentenced and pretrial offenders in the population, and “prorating” the transition pathways to reflect these proportions. Different transition probabilities for each of the different subgroups are estimated in certain situations. If differing probabilities can be reasonably estimated from actual data using the division method, unique transition probabilities are applied for each of the population subgroups. The data on prison and parole populations are the most complete with respect to model attributes , and so many of the transition probabilities relating to these population states are estimated for each population subgroup for the transition rates between these two states, and for prison release rates. The second instance in which unique group transition probabilities are specified is when theoretical justification exists for doing so.This is most applicable in setting the transition 160 Technical Appendix A probabilities for pretrial release (arrest to street) and pretrial detention. In general...