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8 The Impact of Changes in Sentencing Policy on Prison Populations Alfred Blumstein THE NEED FOR ESTIMATES Widespread activity oriented toward structuring sentenc- ing policy has generated a need for the development of improved methodology for estimating the impact of changes in sentencing policies on prison populations. The need for such estimates is particularly intense today because prisons in the United States are now effec- tively filled and are likely to get more crowded even in the absence of a policy change. Since changes in sen- tencing policy tend much more often to be directed at increasing rather than decreasing prison populations, failure to account for the impact of a policy change will result in two kinds of undesirable consequences: (1) Judges will adhere to the policy change, and prisons will become severely overcrowded, with the attendant dehumanr ization and associated risks of violence, misconduct, riot, and recidivism; and (2) Judges will adhere to existing capacity limits, and will do so by accommodating in ways they choose, which may well violate the mandated policies adopted. If a proposed policy change does involve a need for significant new prison capacity, then it is important that the body adopting the policy, and certainly the legislature, weigh the desirability of the policy change against the cost of that increment of capacity. If the policy change is worth that cost, then the legislature should appropriate the funds for the extra capital cost 460
461 and consider the anticipated operating cost of the extra capacity. If not, then adoption of an empty policy is likely to serve only to further discredit the criminal justice system. Thus, finding reliable means for esti- mating the prison impact--and the corresponding budget impact--of a sentencing policy is a necessary part of ensuring responsible consideration of such policies. The resulting "prison impact statement" and its associated "budget impact statement" can then be as helpful in this case as it is with many other kinds of legislation. In determining sentencing policies, only rarely is any consideration given to the downstream implications of such policies by the judiciary or by legislative judi- ciary committees, perhaps because such considerations of impact seldom enter their concerns. That limited per- spective may have been satisfactory when resources were available to accommodate any reasonable policy adopted, when the increment of resources are costless, or when they can be expanded rapidly and easily to accommodate the demand imposed by the court. It is certainly not the situation that prevails in the criminal justice system of today, and the situation is likely to become even more severe throughout the decade of the 1980s. On one hand, such impact estimates are necessary because those capacity limits, which are being severely pressed, should enter into any consideration of sentenc- ing policy. A policy that fails to take such considera- tions into account will simply be violated, but on the basis of ad hoc considerations of individual judges or prosecutors in individual cases, rather than on the basis of the considerations of those responsible for establish- ing policy. This accommodation could take the form of shifts in plea bargaining, greater use of mitigating circumstances, and the development of various "front door" diversion strategies and "back door" early-release strategies to accommodate the resource or capacity con- straint in prison space. Even if the body establishing the sentencing policy chooses to ignore such capacity considerations in reach- ing their policy choices--and there are many who insist not only that such considerations can be ignored but also that they should be ignored--it is necessary to be able to estimate the impact of their choices on prison resource requirements. Such estimates enable legislatures charged with reviewing or adopting such policies to assess the reasonableness of any sentencing policy. Then, when a policy is adopted and implemented,
462 impact estimates are necessary to begin to plan for the resources to accommodate the new policy. In many cases a body charged with establishing sen tencing policy is specifically mandated to establish that policy without generating any increase in prison popula- tions or capacity. The Minnesota legislature, for exam- ple, in establishing the Minnesota Sentencing Guidelines Commission, suggested that they "take into substantial correctional resources . . ." and the consideration . . commission took that suggestion as a constraint, so that any sentencing schedule it adopted would have a zero net aggregate prison impact. The Pennsylvania Commission on Sentencing did not adopt current populations as a con- straint on its eventual schedule but did try to keep informed of the estimated effect of the evolving sen- tencing schedule on Pennsylvania's prison population. Any impact estimate is associated with a future time after the sentencing policy is adopted and implemented. The impact estimate must therefore use as a baseline a projection of future prison populations under current The policy change, or alternative changes being considered, can then be viewed as a perturbation to that projected baseline level. The difference between the two projections is the estimated impact associated with the policy change. In developing the estimate of the impact projection, the time dimension must be taken into account. That is, _ policies prior to the policy change. different policies involve different build-up rates of prison populations, and those differences can be very important. For example, a policy that involves a large increase in numbers of prison commitments will display a more rapid growth in prison populations compared with a policy that involves a similar fractional increase in time served. Even though both policies will require the same capacity eventually, in the latter case, the build- up will take place more slowly over time as release dates are extended. Any impact estimate must take account of compliance with the planned policy. This requires some behavioral assumptions about how judges, prosecutors, and defense counsel respond to the imposition of the changed policy. The simplest--and most simplistic--assumption is that they will fully comply with the policy. Another simple assumption is that they will ignore the policy and con- tinue their prior practices. Even though this assumption is not so simplistic, the associated impact estimate is
463 zero, and the estimate of future prison populations is merely the baseline projection. Most often, of course, the response is somewhere between the two extremes. There does tend to be some compliance with a policy change, but it often is less than total compliance. In considering a 5-year mandatory minimum sentencing law for rape, for example, it is entirely possible that introduction of the law will bring about no Change in charging behavior by the prosecutor and that everyone charged under the law will be sent to prison with certainty for a sentence no less than the specified 5-year mandatory minimum sentence; this would represent total compliance. It is more likely, however, that under the new law a larger fraction of the rape arrests would appear as assault cases, or that judges faced with a rape indictment would be more likely to dismiss the charge or to find mitigating circumstances that would enable them to assign probation if the only available prison sentence is 5 years or more. These kinds of accommodation behaviors must somehow be reflected in any impact assessment that is made. In discussing impact assessment, therefore, we begin first with a discussion of approaches to the projection of future prison populations, then consider means of incorporating policy changes into those projections. PROJECTION OF FUTURE PRI SON POPULATIONS AS A BASELINE FOR THE IMPACT ESTIMATE In considering approaches to estimating future prison populations, it is useful to organize them roughly in order of increasing complexity of the projection model and the associated increase in the richness or subtlety of the assumptions involved in generating a projection. Naive Projection--Current Situation as a Baseline The simplest, most simplistic projection is the naive one that suggests that any subsequent year's prison popula- tion will be the same as that of the current year. This has the obvious benefit of requiring only one assumption (however gross), instead of many more complex and challenging, subtle and simple ones. (Clearly, the number of assumptions is not necessarily a good indicator of the parsimony of a model).
464 Such an assumption can be invoked even in the absence of any conviction that it represents a good approximation of reality. This form of projection is implied, for example, when current practice is used as a baseline on which to estimate the impact of a policy change. This clearly avoids the many concerns that arise in attempting to project the baseline to reflect continuation of cur- rent practice in the absence of a policy change. This is probably a very reasonable approach when there are no external changes affecting criminal justice operations. When there are such important influences in progress-- demographic shifts, for example--then it does become important to have an accurate baseline projection, espe- cially when saturation of prison capacity becomes rele- vant. If current practice results in a prison population well below current prison capacity, and if the external changes in the absence of policy shifts would generate prison populations that exceed prison capacity, then it is important to have that baseline estimate to plan future resource requirements. The cost of a policy is appreciably greater if it requires creating new capacity than if it can be accommodated within existing capacity. This approach of using current practice as the base- line level was used by the Pennsylvania Commission on Sentencing in estimating the impact of its sentencing schedule. The commission collected a sample of con- viction cases in Pennsylvania in 1977 and assigned each case to the appropriate cell of the sentencing guideline grid.2 Then, with Ni cases assigned to the ith cell in the sentencing grid and Mi of them given prison sen- tences, the sentences imposed in that sample of cases provide estimates of the principal sentencing parameters in each cell, Qi' the probability of imprisonment, and Si, the sentence served. The probability of imprisonment, Qi' is estimated as Qi = Mi/Ni, and the mean sentence, Si, is estimated as Mi Si = ~ Sip 3=1 where Sij is the sentence assigned to the jth case (j = 1, 2, . . . , Mi) that falls in the ith cell. The prison capacity associated with cell i in the baseline case is then NiQi Si '
465 and the total prison capacity required would be n n C = ~ C i - ~ NiQiSi i=1 i=1 where the summation is taken over the n cells in the sentencing grid. The impact of a recommended guideline structure can then be estimated as a change in this baseline. If a prison sentence of Si' years is recommended for cell i (with Si' - 0 for cells in which no imprisonment is recommended), then the prison capacity for cell i under the recommended schedule is Ci' = NiSi ' and the total capacity required is n C' = ~ NiSi' i-1 If the sentence recommendation for cell i is a range, Sio ~ Si1 (e.g., 3-4 years), then one can generate a conservative estimate of capacity requirements by using the upper Si1 value in each cell, a risky estimate by using the lower Sio value, or a median estimate by using the average, (Sin + Sil)/2 . For a heterogeneous jurisdiction with diverse sentenc- ing practices across its counties (as is certainly the case in Pennsylvania), a better estimate can be obtained by assuming that the lower values are applied in the metropolitan counties and the upper values in the rural counties. This additional refinement--as is the case with most refinements--requires additional information. The extra information required is the distribution of cases across counties, Nik, the number of cases falling within cell i from the kth type of county. Extrapolation of the Time Series of Prison Populations One of the least helpful approaches to projecting future prison populations is linear extrapolation of recent trends. After a number of years of fairly steady increases (or decreases) in prison populations, it can be
466 particularly tempting to simply draw a line through the points and extrapolate that line into the future. This approach has a number of serious pitfalls. If the points were following a downward trend, even the most naive extrapolator would know enough not to draw that line far enough so that it took on negative values for prison population. Projecting an increasing trend does not yield such obviously absurd results, but it could be equally inaccurate. Simple linear extrapolation--even though widely used--fails to recognize the fact that most trends at some point saturate and reverse themselves, and are certainly more likely to do that than to continue indefinitely. While a linear extrapolation may be rea- sonable for a short-term projection of one or two years, going beyond that can be very risky. The underlying model of the linear extrapolation is: Yt= aO* + al*t, to be fit from recent data. (1) where t represents time, Yt represents the prison population at time t, and aO* and al* are two parameters ~ ~ ~ Here, aO is the prison population in the year when t is set at 0, and a1 is the average annual increase in prison population. So simple a model, of course, invokes only one vari- able, time, and no other information about the other factors influencing imprisonment. Most important, from the viewpoint of using this projection as a policy tool for impact estimation, such a model contains no policy variables, reflecting sentencing practice (the Qi and S of the previous section) whose impact on prison popu~a tion can be directly measured. If the time series of imprisonment has been moving in other than a linear way, one might become somewhat more elaborate in the extrapolation by adding additional terms involving higher powers of t for example, be adding a term, a2*t2, to equation (1). , . _ Such an elaboration of t~ng a n~gner-uegree polynomial to the data can be very risky. Even though adding terms can give a closer fit to the data, that higher-degree polynomial is much more vulnerable to radical deviation outside the fitted data points. In contrast, one of the virtues of the linear equation is the severe limitation on how rapidly it can change. ~ much more sophisticated form of extrapolation in- volves the use of ARIMA models, introduced by Box and Jenkins (1976; see also McCleary and Hay, 1980), as a
467 means of using data on a time series (Y1, Y2, · · · , Yt) to forecast future values, (Yt+l, Yt+2, , Yt+k) The basic approach in developing such a forecast involves first identifying the form of the underlying process that generated the original series, then estimating the param- eters of that process, and finally, by assuming that the same underlying process continues into the future, gener- ating estimates of the expected future values of the series. As with all such forecasts, the farther the look into the future, the more sources of error there are that can lead to an erroneous forecast, and the more likely it becomes that the underlying assumption of a continuation of the prior underlying process will be violated by a distortion of the process. Such univariate time series have the limitation that they do not include the relevant policy variables. Multivariate ARIMA processes, which are used to establish the link between two or more time series--for example, prison population Y and the sentencing policy variables, Q (the probability of imprisonment given conviction) and S (the average sentence imposed)--can then be used to test the effect of a change in one of those policy variables. . Multivariate Regression One can go beyond models that use only the single vari- able time as an exogenous determinant of future prison populations by invoking a variety of other variables known to be causally related to prison populations. This equation takes the following form: Yt = aO + alXlt + a2X2t = . · + anXnt i (2) where Yt is the prison population in year t and the x vector, {xit I i = 1, 2, . . . , n} , includes exogenous determinants of prison population in year t. Factors that have been proposed for x include unemployment rates (see Greenberg, 1977, for example) consumer price index (see Fox, 1978,), or demographic variables (e.g., population of men ages 20-30) and other such variables. They could also include sentencing parameters, Qt (the probability of imprisonment in year t) and St (average sentence imposed in year t).
468 Such a model could be estimated by collecting data on the specified xt variables and on the associated Yt over a period of years, using standard multivariate techniques to estimate the values of the coefficients (aO *, al*, a2 *, · , an*) Using such a model for projecting future prison popu- lations obviously requires projections of the values of the x vector (xl, . . . , xn). For many variables that would be important candidates for inclusion in x, it may be far more difficult to generate a projected esti- mate of that variable than of prison population itself. If that is the case for the unemployment rate, for exam- ple, then a model that depends strongly on a projection of the unemployment rate contributes little to the capability of projecting prison population (Y). Some variables, such as demographic variables, are more easily projected. For example, the number of men in a particular high-imprisonment age group (for example, ages 20-29), is relatively easy to project for at least 20 years into the future. Aside from migration, all individuals who will be in that age group are already born, so the only uncertainty is that associated with death and migration. Death rates are fairly small for ages 1-20 and are also reasonably predictable. Migration can be a major distorting factor in a small region like a city or in a rapidly growing state, and it must certainly be taken into account in projecting the demographic variables. . Some variables can reasonably serve as leading indi- cators of Y (e.g., xt_k is one of the components of the Xt vector in equation (2) for Yt). When that is the case, then such a variable can be helpful for projecting as many as k years ahead. An important limitation of the multivariate regression approach, especially for estimating the effect of changes in the sentencing policy variables, is the anticipated insensitivity of the regression equation to those vari- ables. First, as with most complex phenomena, one can expect only limited success in accounting for the factors contributing to the variation in prison population through a linear regression equation. Second, the regression of Yt on the sentencing policy variables, Q and S. must involve, in addition to Qt and St, (Q,S)t_l, (Q,S)t_2' etc., since the prison population in year t (Yt) includes people sentenced one or more years earlier, and so was determined by sentencing poli- cies more than several years prior to t. One might try
469 to avoid this complexity by considering only commitments during t, but that strategy would fail to recognize the effects of sentence length, S. or changes in S. Finally, in the context of the other exogenous politi- cal, demographic, and socioeconomic factors that influ- ence prison populations, each of which is difficult to capture totally, it is likely to be very difficult to discern the separate effects of sentencing policy through a multiple regression model. Thus one cannot have strong confidence that the coefficients associated with the sentencing policy variables will be reliably estimated. Projections Based on Demographic-Specific Incarceration Rates It is well known that different age, race, and sex groups differ markedly in many aspects of their involvement with the criminal justice system. This is particularly true in prison populations: in 1979 females made up only 4 percent of the total state prison population; the incar- ceration rate for males (i.e., prisoners per capita) was disproportionately large by a factor of 25 to 1 compared with females; black males made up 46 percent of the total U.S. male prison population, a disproportionate represen- tation of 6.7 to 1 compared with white males; and the incarceration rate by age was also markedly different across the different age groups.3 Table 8-1 shows the incarceration rate by race and age for males in U.S. state prisons in 1979.4 The peak incarceration rate for white males occurs at age 23 and is 2.2 times that at ages 35-39 and 8.8 times that at age 40 or older. The incarceration rate for black males reaches its peak at ages 25-29 and is 7.5 times the peak for white males (at age 23). The age falloff for blacks is comparably fast, the peak being 2.5 times the rate at ages 35-39 and 9.1 times the rate at age 40 or older. These striking age, race, and sex differences suggest another approach to projecting prison populations. The current prison population can be partitioned into demo- graphic subgroups and the incarceration rate calculated for each subgroup; if that rate is assumed constant (or projected), that incarceration rate can then be applied to any projection of the general population. Thus, for example, one can generate a vector of incar- ceration rates, g i = Yi/Ni
470 TABLE 8-1 Demographic-Specific Incarceration Rates (prisoners per 100,000 population) in 1979 for U.S. Males by Race and Age Total Age U.S.WhiteBlack 18-19 4322421,657 20 6784272,234 21 7344362,826 22 8194763,208 23 8895133,485 24 8314653,543 25-29 7964163,856 30-37 5262802,716 35-39 3622331,515 40+ 9258424 Total 2541451,062 NOTE: Incarceration rates were calculated from Yi/N i, where Yi is the number of prisoners in demographic group i at time of the 1979 survey of the Bureau of Justice Statistics and the Bureau of the Census, and Ni is the number of persons in the general population in demographic group i in 1979. SOU=E: U.S. Bureau of the Census (1980). where Yi is the number of prisoners in the ith demogra- phic group, Hi is the number in the general population within the ith demographic group, and gi is the incar- ceration rate for the ith subgroup. Then, if one has a demographic projection of the population for time t' say, N i* ( t' ), then the estimate of the pr ison popu- lation in demographic group i at time t' is given by Yi*(t') = giNi*(tt) and Y* (t') = ~ Yi* (t')
471 The crucial assumption is that the incarceration rate, gi, remains fairly constant within any demographic group over time. That is not necessarily the case, as is suggested by Table 8-2, which presents estimates of the incarceration rates based on two estimates of prisoner demographics5 from two surveys, one in 1974 and one in 1979. It is striking to note the significant growth in incarceration rates between the two surveys. The aggre- gate growth is 40 percent over the entire population and is between 20 and 40 percent for most age groups. In aaa~zon, there Goes not appear to be important differ- ences between the growth rate for blacks and that for the population generally. If values of incarceration rates were available at several points in time, and if those values displayed a trend instead of a constant rate, then one might try to extrapolate the incarceration rates to generate estimates gi*(t') for time t'. One would expect gi(t) to be more stable than Yi(t) [because Yi(t) also reflects demo ~ ~ .. . .. TABLE 8-2 Age-Specific Incarceration Rates (prisoners per 100,000 population) Estimated for U.S. Males in 1974 and 1979 Percentage I nc reas e 1974 Rates 1979 Rates 1974-197 9 . To tat Total Total Age U . S . Blac k U . S . Blac k U . S . Blac k 18-19 8253,497 9023,60093 20 7203,009 8853 ,3912313 21 6642,627 8893,7343442 22 7243,286 9443 ,6023010 23 6983,078 9413,9123527 24 5802,620 8493 ,676464 0 25-29 4552,168 6813,2115048 30-34 3071,368 4081,8683337 35-39 231901 3031, 1583129 40+ 58263 703242123 Total 182771 2541,0624038
472 graphic shifts occurring in Ni(t)], and if that stability is displayed, then extrapolating gi(t) may be reasonable. If gi(t) follows a trend, however, all the cautions necessary in extrapolating a trending variable (see the section on time series above, for example) must be taken into account. This projection approach based on demographic-specific incarceration rates is particularly attractive when the incarceration rates, especially for the high-rate demo- graphic groups (e.g. males in their 20s), are found to be fairly constant over time. This approach is particularly important when significant demographic changes are taking place in the high-rate groups and when one has fairly reliable projections of those demographic changes. This approach allows anticipation of the effects of the demographic changes. An important shortcoming of this approach, as with the others involving extrapolation of prison population estimates, is the absence of any sentencing policy vari- ables from the projection model. This could be remedied by generating instead a demographic-specific conviction rate by offense, then applying the corresponding sentenc- ing variables, Q and S. to those conviction rates. (This is the basic approach associated with flow models, and these are developed in more detail in the next section.) Unfortunately, while the data systems in most jurisdic- tions will support calculation of incarceration rates because of good records on prison populations, the data based on court records are sufficiently inadequate that estimates of demographic- and offense-specific conviction rates will be extremely difficult to generate. Disaggregated Flow Models The data problems become much more manageable in those jurisdictions in which some form of offender-based tran- saction statistics (OBTS) system is operational. These data permit a much more detailed and disaggregated exami- nation of prison population projections. In the OBTS system, an individual record is created at each arrest or court filing, and that record is augmented by each subse- quent transaction as the case moves through successive processing stages in the criminal justice system. Col- lection of these individual records of terminated cases at the end of a year permits highly disaggregated estim- ates of the processing parameters through the system.
473 With the support of such a data base, highly detailed flow models of the criminal justice system become pos- sible. One such illustration is the JUSSIM models that has seen fairly widespread implementation. In this program the criminal justice system is represented as a sequence of stages processing defendants or "units of flown These flow units impose work loads, consume various types of resources, and incur costs at each processing stage. The flow through the processing net- work can be represented by a matrix of "branching ratios" or transition probabilities, {Pij(V); ~ Pij(V) = 1} , representing the fraction of the cases at stage i that go to stage j next: these transition probabilities are disaggregated by crime type v (or any other relevant attribute of the units of flow that influences the flow process), since different crime types generally flow differently through the system. For reasons of simplicity, the JUSSIM model was de- signed as a steady-stage flow model that takes no account of the passage of time but simply averages the flow through any stage in any year. It is thus somewhat too simplistic for dealing with the time accumulation of prisoners in prison, although an extension to incorporate that feature has been introduced by Lettre et al. (1978). Another important limiting feature is the fact that the parameters of the model (e.g., the branching ratios) are treated deterministically in the model as fixed quan- tities rather than as functions of state variables describing the condition of the criminal justice system. The model is designed to operate interactively. The user can then change any of the parameters, but must decide which parameters to change and by how much. Thus, if any of the parameters is trending over time, that trend can simply be projected. In particular, there is no behavioral model built into the program that, as the prison population builds up beyond the prison's capacity, reduces the flow rate from a sentencing stage to prison (by reducing the probability of prison given conviction), even though such accommodation is likely. The problem in doing that lies in the difficulty of learning the nature of the behavioral response and incorporating its conse- quences. One approach to the use of such flow models involves treating the flow structure of the criminal justice
474 system rather simply and directing attention to achieving greater disaggregation of the demographic structure of the offenders. Then, by focusing particular attention on the sentencing stage of the process, an effective and valuable sentencing-impact-assessment instrument can be developed. This demographic disaggregation becomes particularly necessary when demographic changes are important factors influencing prison populations, as they certainly are in many regions of the United States and in other countries experiencing the postwar baby boom of 1947 to 1962. Thus, a flow model like JUSSIM, augmented by retaining demographic disaggregation of Processing parameters, could be used to generate a projection ot prison popu- lations that was sensitive to demographic shifts. Such a model was formulated and estimated by Blumstein et al. (1980). They found, using data for Pennsylvania for 1970 through 1975, that most of the criminal justice processing parameters (i.e., arrest rates, probability of indictment given arrest, and probability of being sen- tenced to prison given conviction) were fairly constant within demographic groups and offense types. Their model first estimated commitments to prison by Ctjo = Ntj x at;O x ctjo x Qtio where: Ctjo = number of commitments to prison in year t for offense o of people in demographic group (age, race, sex combinations) j; Ntj = number of people in the general population in year t in demographic group j; atj0 = demographic-specific arrest rate for offense o in year t; ctjo = probability of conviction given arrest; and Qtjo = probability of commitment to prison given conviction. (3) Then, Pt. the number of prisoners in any year t, de- pends on the number of prisoners in the previous year, Pt_l, the average time served per commitment, S. and the number of commitments, C. The basic equation for their model thus consists of two terms, one to account for last year's prisoners still serving time and one for the current year's commitments still left at the end of the
475 year. Carrying the same subscripts forward, Ptjo is given by Ptjo = P(t(ll)jo-l/se /StDo + Ctjo x Stjo (4) The total prison population is then found by summing over the offense types and demographic groups: Pt= ~ ~ Ptjo (5) Their analyses provided a basis for projecting numbers of arrests, commitments to prison, and prison populations to the year 2000. Those projections reflected the strong effects of the postwar baby boom on the criminal justice system as the trailing edge of that group (the 1962 birth cohort) moves out of the high-crime ages of 16-18. The results suggested that arrest rates should reach a peak about 1980. They projected, however, that prison commit- ments would not reach their peak until 1985: They are lagged because juveniles are rarely sent to prison, and most adult arrestees do not go to prison until they have accumulated several convictions, by which time they are in their mid-20s. They also projected that prison popu- lations would peak about five years later still, about 1990; this lag reflects the fact that prison population will still accumulate even after the input flow has peaked because it will take several more years before the departure rate (reflecting time served) exceeds the declining arrival rate.7 This projection of prison population pointed out that Pennsylvania was expected to exceed the prison capacity in 19798 and to reach a peak in 1990 of 10~200, about 2s percent in excess of the 1977 caDacitv. In making d ~_ _ ~ . , these projections, the model ignores the effects of such saturation by keeping the behavioral parameters unchanged through that saturation period. It is likely, of course, that some form of behavioral response would result. The capacity could be increased by constructing additional cells (and that would take several years to accomplish), or by expanding the nominal capacity by crowding more prisoners into the same number of cells. Alternatively, if the capacity is kept fixed, then adaptation could occur by introducing diversion programs (i.e., reducing Q) or by lowering time served (i.e., reducing S) through shorter sentences or earlier parole release. Since the nature of the choice among such behavioral responses is
476 extremely difficult to predict, and since the actual choice in any case will be idiosyncratic to a particular jurisdiction or to a particular decision maker, it is extremely difficult to incorporate them into the projec- tion model. The role of the projection analysis in such a situation is to call attention to the impending satura- tion and thereby to highlight the need for some form of response: Either capacity must be increased or policy must be changed to accommodate to the existing capacity. After that, the issue is one of political decision making. The model can help in that process, however, by helping to illuminate the impact of those choices on prison populations. This approach of analyzing the demographically disag- gregated flow process is particularly attractive because of the disaqareqation of the Flow units (by the changing ~ ,, _ _, ~ demographic variables of age, race, and sex as well as by crime type) and because of the potential for isolating whatever processing stages in the criminal justice system are available for policy control. In particular, the model of equation (4) contains the primary policy vari- ables: Q,10 the probability of imprisonment given conviction, and S. the time served for those who are sent to prison. Here, Q and S are disaggregated by crime type and by demographic group (which might be related to prior record) for independent testing of alternative policy changes. Microsimulation Models The flow models discussed in the previous section simply treat average flow rates at each stage of the criminal justice system and examine the distribution of those units of flow across the processing network. This is efficient computationally, but it looks only at average statistics. Estimates of total distributions can be developed by simulating the flow of individual offenders through the system and combining their individual experi- ences to generate aggregate statistics. In this approach, a sample of individual simulated offenders are generated with their individual demographic attributes: type of current offense, prior record, and any other attribute relevant to their processing through the crimi- nal justice system. One could generate this sample of offenders by taking a group of actual case records, extracting their relevant attributes, and using those as _
477 the simulated sample.ll If the demography of the population was anticipated to be undergoing a shift (for example, more blacks), that subset of the sample could be replicated at an appropriate rate to match whatever future mix was projected. Alternatively, one could collect statistics on the joint distribution of offender attributes and use Monte Carlo sampling methods to syn- thesize a simulated sample of offenders from that distri- bution. The former method has the benefit of avoiding explicit worry about the particular joint distribution of offender attributes; the sample of cases provides that distribu- tion directly. The latter approach has the flexibility of permitting the joint distribution, or any aspect of it, to be changed analytically, something that can be done easily. In the operation of such a simulation, the sentencing policy decision rules (including the possibility of a probabilistic choice that would be realized by the results of a process of random-number generation) would be established, and the sentences would be imposed on each of the simulated cases that arrive for sentencing. Then, the aggregate consequences in terms of impact on prison populations of any sentencing policy can be examined over the years that policy is expected to be in effect. IMPACT ESTIMATION In the discussion of the projection of prison populations in the previous section, some attention was focused on manipulating the sentencing policy variables, Q and S. in order to estimate the consequences of those changes in sentencing policies on prison populations. Even though a number of models can project prison population reason- ably, only the subset that specifically contains the sentencing policy variables Q and S can also serve the policy-impact-estimation function. The approaches that are most appropriate are likely to be the disaggregated flow models and the microsimulations. Development of such an impact involves four basic steps: 1. Characterizing the subset of court cases to which the policy applies; 2. Translating the policies into corresponding values of the policy variables in the projection models;
478 3. Formulating the behavioral model characterizing the response of the court to the sentencing policy; and 4. Calculating the projected change in prison popula- tion resulting from the response to the changed policy. Identification of Population Subsets Any sentencing policy ordinarily specifies at least the following attributes of those to whom it applies: (1) offense type; (2) particular aspects of the offense type (e.g., use of a weapon, causing of bodily harm, vulnera- bilities of the victim such as age); and (3) prior record of the offender. If one had a rich data base characterizing each case in terms of each of the attributes invoked in the policy, then it would be easy to identify each case in terms of whether each specific provision of the policy applied. Each case could then be assigned the specified imprison- ment policy associated with its attributes, and the consequences under the old and the new policies could be compared. In the sample-case simulation, this requires that the records associated with each of the sampled cases include each of those attributes. In the flow model, it requires that the units of flow be adequately characterized in terms of each of the attributes invoked in the sentencing policy. Since it is almost always the case that the available data set is not sufficiently rich and satisfactory, then other approaches must be used as an approximation. First, for those relevant variables that are available, the data set can be partitioned according to those vari- ables. Then, within those variables, some independent sampled estimates must be obtained to estimate the joint distribution with the variables already recorded of the variables not adequately recorded. This can generate the fraction associated with each of the other policy vari- ables. Establishment of Values of Policy variables With a sufficiently fine characterization of the offenders into identified subsets, {Gi}, the task in characterizing a sentencing policy for analysis lies in determining for each
479 such {Gi} the corresponding sentencing variables, Qi and Si. For example, those groups for whom a policy calls for mandatory imprisonment should have Qi set equal to 1.0. For those groups that remain unaffected by the law or policy, then Qi can remain at its prior value. A similar approach pertains to sentence under a manda- tory minimum sentencing policy. For those offenders whose prior sentence was below their mandatory minimum, Sol, their sentences should be moved up to the manda- tory minimum itself. Those whose sentence is above the mandatory minimum would presumably remain unaffected. Those subgroups whose offense is not addressed by the mandatory minimum law should remain unaffected. Thus, using (Qi', Si') to denote the sentence of group i under the new policy and (Qi' Si) under the old, we can summarize: (Qj', Sj') = (Qj, Sj) for groups j unaffected by the mandatory minimum law; Qi' = 1 for groups i for whom imprisonment is mandatory; So; for groups i affected by the law if sit = v ~ - _ Si < Soi; Si for groups i affected by the law if Si > Soi Behavioral Response to the New Policy The previous discussion has attempted to translate into the policy the Q and S variables precisely as prescribed by the policy. Actually, however, there are likely to be many forms of adaptation by the practitioners within the court work groups. Some examples follow: 1. The judge, faced with imposing an excessively large mandatory minimum sentence on someone who might otherwise have received a shorter prison term might conform to the law (i.e., raise Si to Sol), or the judge might decide to assign such an individual to probation instead. 2. The judge could adhere to the minimum for all who are sent to prison (i.e., if Qi = 1, then Si' > Sol) but could ignore the mandatory requirement by retaining probation when that was done before (i.e., Qi' = Qi)
480 3. The prosecutor could revise charging behavior so that individuals for whom the mandatory minimum sentence seems excessively severe could be charged under one of the many related offense types, there- by decreasing the fraction charged with a pre- scribed offense and correspondingly increasing some of the other offenses. In all of these cases, the response could be characterized in terms of a corresponding change in Qi or Si as well as in changes in the number of persons associated with each subset, {Gi}. Calculation of the Effects of the Sentencing Policy Change Once the parameters in the estimation models have been formulated to generate estimates of the numbers in each subset, {Gi}, and their associated Qi and Si under each of the alternative sentencing policies being considered, and for each of the behavioral adaptation assumptions, it then becomes possible to calculate the prison populations associated with each sentencing policy. That calculation could be accomplished using a disaggregated flow model (equations (3) to (5)) or a microsimulation, each with the appropriate sentencing policy variables, Qi and Si. By comparing Pt', the prison population in year t under the new policy to the corresponding Pt under the old, the difference (Pt' - Pt) represents the incremental cost (or savings) associated with the policy change. Estimation of the Impact of a Mandatory Minimum Sentencing Bill In order to illustrate some of the methodological issues discussed earlier and also to convey some of the substan- tive insights that emerged, this section summarizes the results of an impact analysisl2 in Pennsylvania, build- ing on projections of prison populations in Pennsylvania through the demographic-specific flow model discussed above. The particular policy change examined is a mandatory minimum sentencing bill, S.B. 995, that was one of sev- eral such bills being considered by the Pennsylvania legislature during its 1976 session. The bill addressed 10 felony offenses ranging from murder to sale of nar
481 cotics and burglary. Recidivists with one prior con- viction were to receive a one-year mandatory minimum sentence upon reconviction, and those with two or more prior convictions were to receive a two-year minimum.13 If a firearm was used in the current offense, an addi- tional year was to be added to the minimum sentence. These provisions of the bill provided the necessary guidance for generating the offense and offender subsets that fall under its provisions. The relevant offenses were clearly specified in the bill and also were avail- able in the court OBTS records. _ The prior record provi- s~ons were clear in the bill but, as is often the case, were not available in the individual records from the court; court records, at best, might include a single number (such as prior felony convictions) but are not likely to provide more detailed information on convic- tions for a specified group of felonies. Thus it became necessary to draw a separate sample of convicted persons and to examine their prior records in detail in order to determine the fraction associated with each combination of current offense type and prior record that were speci- fied by the bill. A similar partition was conducted for the offenses involving firearms. This information provided the basis for partitioning convicted offenders in any year into appropriate subsets, {Gi}, corresponding to each of the combinations of conditions specified in the bill. For each such group, the fraction of cases involved and the sentencing pattern prior to enactment of the bill, Qi and Si, could be determined. For each such group, the provisions of the bill indicated Qi' (either Qi' = Qi if the group was not relevant to the bill or Qi' = 1 if imprisonment was mandatory). The average sentence under the bill, Si', depended on the distribution of sentences in prior practice. For the groups not addressed by the bill, Si' = Si. For those for whom prison was mandated, the lower tail (below Sol, the group's relevant mandatory minimum) of the sentence distribution was set at Sol, those previously assigned to probation were set at Sol, and the upper tail of the sentence distribution (above Sol) remained unaffected. These statements reflect literal interpretation of the bill's provisions. The next step involved characterizing the judges' behavioral responses to those provisions. Since the bill afforded judges the opportunity to avoid imposing a sentence if they found that mitigating factors warranted such an action, three possible scenarios were considered:
482 1. Mandatory Prison Scenario: Literal interpretation of the bill so that anyone who satisfied the condi- tions of the bill was sent to prison for the speci- fied mandatory minimum sentence. 2. Conforming to Minimum Only Scenario: Only those who formerly were sent to prison but served less than the specified minimum had their sentences raised to the minimum; others,-and particularly those who formerly were assigned to probation-- remained unaffected by the bill. 3. Undermining Scenario: Those who were formerly sent to prison for a sentence less than the mandatory minimum were put on probation in order to avoid having to increase their sentences; others remained unaffected by the bill. Analysis was carried out only on the first two of these scenarios, and their effects on state prison popu- lations were examined. Since the impact will accumulate over a number of years as new offenders are convicted under the new bill, the impact estimate was calculated over time as a perturbation to the population projections assuming continuation of current practice. These effects under the two scenarios, reflecting the different beha- vioral responses to the bill, are shown in Figure 8-1. The striking observation is that full implementation of the legislation as written (the mandatory prison sce- nario) would have involved an increase of about 50 per- cent in prison populations at the peak. A much less dramatic change is associated with the conforming to ~ninimum only scenario, in which the prior probation decisions remain unaffected. Under this scenario, prison population would increase only about 10 percent, certain- ly well within any forecasting or impact estimation error and certainly a tolerable impact on any prison system. This also indicates that the major change called for by the bill is the increase in the use of imprisonment for people who otherwise are put on probation, and it does not call for major increases in time served by those who already do go to prison. These two scenarios undoubtedly encompass the judicial response that would be anticipated. The results also suggest that if the bill were passed, most judges would probably invoke the mitigating factors option, at least for a sizable fraction of the cases they had formerly put on probation.
483 1 5,000 LL At: 1 0,000 - o U) Ct: Cal On mandatory prison scenario / / 5,000 - - conforming to minimum only scenario - current sentencing scenario of 1 1 1 1 1 1 1 970 1 97 5 1 980 1 985 YEAR 1990 1995 2000 FIGURE 8-1 Pro jec ted Pr ison Populations Under Alternative Sentencing Scenarios (S.B. 995) It was also interesting to identify the offenses that contributed to the major growth in prison populations under the mandatory minimum scenario. The changes in the number of commitments for five offense categories are shown in Table 8-3. It is clear from the table that th e bill would have very little effect on those convicted of murder and rape--virtually all of them go to prison already. The major influence would be on those convicted of relatively minor offenses, burglary in particular. The predominant portion of those new commitments would be those convicted of burglary with relatively few prior
484 TABLE 8-3 Changes in Commitments to State Prison Under S.B. 995 Number of Number of Increase Current Commit- in Percentage Commit- ments Number of Increase meets Under Commit- in Commit (1975) S.B. 995 meets meets Burglary 685 1,626 941 137 Robbery 686 1,148 462 67 Drugs 401 582 181 45 Murder 406 436 30 7 Rape 120 145 25 21 convictions, largely because they were not committed under prior policy. In view of the considerable disparity in sentencing practice across a state as heterogeneous as Pennsylvania, the predominant increase in sentences to state prison comes from Philadelphia. For example, Philadelphia would provide 58 percent of the new commitments for robbery. This is partly a result of the disproportionate number o f robbery convictions in Philadelphia, partly a result of the greater leniency with which Philadelphia treats robbery--many of its convicted robbers go to the county jail for sentences less than the mandatory minimum, and S.B. 995 would require that they be sent to the state prison. The results of this analysis were presented in testi- mony to the Pennsylvania legislature in 1977 and in 1978, when it was considering a number of mandatory minimum bills, along with a proposal to create a sentencing commission. The sentencing commission was intended, at least in part, as a means of heading off the politically attractive mandatory minimum bills. The magnitude of the estimated impact estimate of S.B. 995 was surprising to many of the legislators; that provided one basis for arguing for the necessity of formulating sentencing policy in a forum like a sentencing commission, which they hoped would be more deliberative than is normally the case on the floor of a state legislature. The sew
485 fencing commission bill was passed with a majority of only one vote. SUMMARY AND FURTHER RESEARCH NEEDS This paper has focused on the importance and the feast bility of providing estimates of the impact on prison populations of proposed changes in sentencing policy and of the need to develop improved methods for generating them. Such estimates are necessary to ensure that the debate over sentencing policy is balanced and that the political attractiveness of a tougher policy is respon- sibly weighed against the costs of such a policy. This issue will be particularly important in the coming decade, when prisons, already largely filled to capacity, can expect significant growth in sentenced populations. It is also important that the impact be examined in the context of projections of prison popula- tions over an interval of at least 20 years in order to estimate the degree to which the anticipated future prison population growth warrants provision of additional prison capacity. At least in those states of the North- east and the Midwest in which prison populations can be expected to reach a peak and to decline after about 1990, there may be a serious question about the advisability of creating that extra capacity, especially if one considers the limited excess demand after it is finally con- structed. The availability of impact estimates provides legislatures and the public generally the opportunity to make responsible and explicit trade-offs between the desired level of punitiveness and its cost. There are a number of research approaches that could make important contributions to the ability to develop such impact estimates: 1. A number of readily available models for calculat- ing prison impact should be formulated and made available to criminal justice planning agencies for their use in assisting a legislature or sentencing commission in estimating the impact of their policy choices. 2. Some pilot trials ought to be undertaken in states with OBTS systems to develop good means for pro- jecting future prison populations and to estimate impacts. 3. In jurisdictions that have adopted significant new sentencing policies, the impact should be estimated
486 using data that were available prior to the policy changes, and these projections should be compared with the changes that actually occurred. 4. Cros~jurisdictional studies should be conducted to discern how judges respond to changes in sentencing policy. It is particularly important to be able to compare courts in jurisdictions in which the prison system is fully saturated with those in which there is slack capacity in the prison. NOTES 1. In this paper, the term sentencing policy is used generically to refer to guidance or mandates to sentenc- ing judges, whether that guidance is established by a legislated determinate sentencing schedule as embodied in California's SB-42, by a mandatory minimum sentencing law, or by sentencing guidelines established by a judi- cial council or by a legislatively created sentencing commission. Statutory sentence maximums are also a form of sentencing policy, but they are largely ignored in this paper, partly because their role in the courtroom is insignificant, but primarily because the questions of prison impact addressed here are much more related to concerns over the effects of sentences that are con- strained from below than from above. 2. The grid was created by generating an offense score of 12 levels based on a ranking of offense seriousness and an offender score of 7 levels based on the prior conviction history of the defendant. 3. The estimates of number of prisoners by sex and race are based on Tables 2 and 3 (for sex) and Table 7 (for race of males) of U.S. Department of Justice (1981). The general population estimates are based on U.S. Bureau of the Census (1980:Table 2). 4. The rates in Table 8-1 were calculated on the basis of the age and race of the male prisoners responding to a survey in 1979 conducted by the U.S. Bureau of the Census (1980) for the Bureau of Justice Statistics, and the demographic composition of the U.S. population was deter- mined from U.S. Bureau of the Census (1980).
487 5. These are not the same incarceration rates presented in Table 8-1. The values in Table 8-2 are based on the demographic features of interviewed prisoners at the time of their admission to prison. The more appropriate numerators are the demographic features at the time of the survey, which were used in Table 8-1. That numer- ator, however, was available only for the 1979 survey, and so, for comparability, the less appropriate measure of age at admission is used in Table 8-2. 6. For a description of the JUSSIM model, see Blumstein (1980). That article contains detailed references on the program and its operation. 7. These substantive observations are, of course, pre- cisely true only for Pennsylvania. The important role of the demographic shifts associated with the baby boom, however, is likely to apply broadly to the states of the Northeast and the Midwest, with their numerically stable and aging populations. Even within those states, the large cities would have to be examined separately because of their large rates of migration and the strong effect those migration patterns could have on demographic struc- tures. At the state level, however, the level at which concern over prison population is most relevant, demogra- phy is less sensitive to shifting migration patterns. In contrast to the Northeast, the rapid population growth in the West and the Southwest could dominate the age shifts that cause the peaking observed in Pennsylvania. 8. In 1981, Pennsylvania's prison population was about 300 prisoners over capacity. 9. These projections were based on the processing parameters remaining constant throughout the period, a situation that did prevail in the early 1970s. In the late 1970s, however, sentences were observed to increase, thereby intensifying the anticipated saturation. 10. Literally, C enters equation (4), but Q influences C through equation (3). 11. This is the approach used by the Minnesota Sentenc- ing Guidelines Commission in estimating the effect of any guideline sentencing schedule on prison populations, enabling the commission to adhere to the policy it adopt- ed of avoiding any policy that would lead to an increase in prison populations (see Knapp and Anderson, 1981).
488 12. The details of the impact analysis are reported in Blumstein et al. (1979). The results are summarized in Miller (1981). 13. One interesting indication of the shift in attitudes since 1976 is the fact that the mandatory minimum bills considered by the Pennsylvania general assembly in 1981 call for minimum sentences of five years rather than one or two years. REFERENCES Blumstein, Alfred 1980 Planning models for analytical evaluation. Pp. 237-257 in Malcolm W. Klein and Katherine S. Teilmann, eds., Handbook of Criminal Justice Evaluation. Beverly Hills, Calif.: Sage _ Publications. Blumstein, Alfred, Jacqueline Cohen, and Harold D. Miller 1980 Demographically disaggregated projections of prison populations. Journal of Criminal Justice 8(1):1-25. Blumstein, Alfred, Harold Miller, Wendy Bell, Deborah Kahn, and Stewart Szydlo 1979 The Impact of New Sentencing Laws on State Prison Populations in Pennsylvania: Final Report. Urban Systems Institute, Carnegie- Mellon University. Box, George E.P., and Gwilym M. Jenkins 1976 Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day. Fox, James A. 1978 Forecasting Crime Data: An Econometric Analysis. Lexington, Mass.: Lexington Books. Greenberg, David F. 1977 The dynamics of oscillatory punishment processes. Journal of Criminal Law and Criminology 68(4):643-651. Knapp, Kay A., and Ronald E. Anderson 1981 Minnesota Sentencing Guidelines Projection Program--User's Manual. Minnesota Sentencing Guidelines Commission, St. Paul. 55101. Lettre, Michel A., et al. 1978 A Jurisdiction-Based Description of the Maryland Criminal Juvenile Justice System. Maryland Governor's Commission on Law Enforcement and Administration of Justice.
489 McCleary, Richard, and Richard A. Hay, Jr. 1980 Applied Time Series Analysis for the Social Sciences. Beverly Hills, Calif.: Sage Publications. Miller, Harold 1981 Projecting the impact of new sentencing laws on prison populations. Policy Sciences 13:51-73. U.S. Bureau of the Census 1980 Estimates of the population of the United States by age, race, and sex: 1976 to 1979. Report No. 870, Series P-25, Population Estimates and Projections. Washington, D.C.: U.S. Department of Commerce. U.S. Department of Justice 1976 Survey of Inmates of State Correctional Facili- ties 1974. National Prisoner Statistics Special Report SD-NPS-SR-Z. Washington, D.C.: U.S. Department of Justice. 1981 Prisoners in State and Federal Institutions on _ . . ~ . December 31, 1979. National Prisoner Statistics - Bulletin No. NPS-PSF-7, NCJ-73719. Washington, D.C.: U.S. Department of Justice, Bureau of Justice Statistics.
