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«This PDF is available from The National Academies Press at The Growth of Incarceration in the United ...»

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Research on incapacitation effects derives from what has come to be called the “criminal career” model first laid out in a seminal paper by AviItzhak and Schinnar (1973). These authors assume that active offenders commit crimes at a mean annual rate (denoted by λ) over their criminal career (averaging τ years in length).10 The extent of punishment is described by the probability of arrest, conviction, and incarceration for a given crime and the length of time spent in prison.

At the level of the population, this framework yields an accounting model that calculates the hypothetical level of crime in society in the absence of incarceration and the fraction of that level prevented by incarceration as a function of the probability of incarceration and the average length of the sentence served. The theory, as already noted, is appealingly simple.

The model has no behavioral component. It views the prevention of crime not as a behavioral response to punishment, as in deterrence, but as the result of the simple physical isolation of offenders. We return to the implications of these behavioral assumptions below, but first consider two other key assumptions of the Azi-Itzhak and Shinnar framework that has been so influential in research on incapacitation. The first concerns the assumption that λ is constant across offenders, and the second is that it remains unchanged over the duration of the criminal career.

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Copyright © National Academy of Sciences. All rights reserved.

The Growth of Incarceration in the United States: Exploring Causes and Consequences

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Inmate Survey, for which a sample of 2,190 incarcerated respondents in California, Michigan, and Texas was interviewed in the 1970s. The survey recorded respondents’ criminal involvement in the 3 years before their current incarceration (Petersilia et al., 1978). The most important finding of this survey was that λ is far from being constant across inmates; to the contrary, it is highly skewed. Table 5-1 is taken from Visher’s (1986) reanalysis of the RAND data. For robbery, the mean to median ratio is 8.3, 12.6, and 5.2 for California, Michigan, and Texas, respectively. For burglary, these respective ratios are 15.9, 17.2, and 11.0. The difference between the median and the 90th percentile is even more dramatic. With the exception of robbery in Texas, that ratio always exceeds 20 to 1. The skewness of the offending rate distribution has crucial implications for the calculation of incapacitation effects: as a matter of accounting, the estimated size of incapacitation effects will be highly sensitive to whether the mean, median, or some other statistic is used to summarize the offending rate distribution.

Skewness in the offending rate distribution also has important implications for projecting the marginal incapacitation effect of changes in the size of the prison population. This is due to the important concept of “stochastic selectivity” (Canela-Cacho et al., 1997). Stochastic selectivity formalizes the observation that unless high-rate offenders are extremely skillful in avoiding apprehension, they will be represented in prison disproportionately relative to their representation in the population of nonincarcerated

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Copyright © National Academy of Sciences. All rights reserved.

The Growth of Incarceration in the United States: Exploring Causes and Consequences

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offenders. This is the case because they put themselves at risk of apprehension so much more frequently than lower-rate offenders.

Thus, surveys of offending among the incarcerated will overstate the crime prevention benefits of further increases in the imprisonment rate. The basis for this conclusion is straightforward: because most of the high-rate offenders will already have been apprehended and incarcerated, there will be relatively few of them at large to be incapacitated by further expansion of the prison population. The implication is that the crime control benefits of incapacitation will decrease with the scale of imprisonment.

Canela-Cacho and colleagues (1997) use the RAND Second Inmate Survey to estimate the actual magnitude of the model’s prediction. Their findings are dramatic—they conclude that offending rates of the incarcerated are on average 10 to 50 times larger than those of the nonincarcerated. Figure 5-2 compares projections of the distribution of robbery offense rates for offenders who are and are not incarcerated. The distributions are starkly different—few high-rate robbers are at large because most have already been apprehended and represent a large share of the prison population.

Direct evidence of stochastic selectivity is reported by Vollaard (2012), who studied the introduction of repeat-offender sentence enhancements in the Netherlands. These enhancements increased sentences from 2 months to 2 years for offenders with 10 or more prior convictions—mainly older men with histories of substance abuse who were involved in shoplifting and other property crimes. The sentence enhancements initially had a large crime-reducing effect, but the effect declined as they were administered to less serious offenders with fewer prior convictions. Recent work by Johnson and Raphael (2012) on the crime prevention effect of imprisonment also suggests that the size of the effect diminishes with the scale of imprisonment. They estimate substantial declines in the number of crimes averted per prisoner over the period 1991 to 2004 compared with 1978 to 1990.





This finding also is consistent with the results of an earlier analysis by Useem and Piehl (2008), who conclude that crime reduction benefits decline with the scale of imprisonment, and with Owens’ (2009) finding of modest incapacitation effects based on her analysis of 2003 data from Maryland.

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Copyright © National Academy of Sciences. All rights reserved.

The Growth of Incarceration in the United States: Exploring Causes and Consequences

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decline sharply with age. The implication is that estimates of offending rates of prison inmates based on self-reports or arrest data for the period immediately prior to their incarceration will tend to substantially overstate what their future offending rate will be, especially in their middle age and beyond. This conclusion is reinforced by the criminal desistance research of Blumstein and Nakamura (2009), Bushway and colleagues (2011), and Kurlychek and colleagues (2006). Blumstein and Nakamura (2009), for example, find that offending rates among the formerly arrested are statistically indistinguishable from those of the general population after 7 to 10 years of remaining crime free.11

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11 Most active career offenders also desist from crime at relatively early ages—typically in their 30s (Farrington, 2003). The “age-crime curve” and the short residual lengths of criminal careers are among the principal reasons why it can be difficult to implement ideas about “selective incapacitation” of high-rate offenders—it is easy to identify high-rate serious offenders retrospectively but not prospectively.

12 We also note that in their reanalysis of the RAND data, Marvell and Moody make further adjustments for many of the other factors already discussed. The adjustments result in a 77 percent reduction in their estimate of the incapacitation effect compared with the RAND estimate.

Copyright © National Academy of Sciences. All rights reserved.

The Growth of Incarceration in the United States: Exploring Causes and Consequences

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Copyright © National Academy of Sciences. All rights reserved.

The Growth of Incarceration in the United States: Exploring Causes and Consequences

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incarceration rates affect crime rates because an increase in crime may increase the numbers of arrests and prison admissions. Under these conditions, a coefficient from a regression of crime rates on imprisonment rates will reflect both the reductions in crime due to incapacitation and deterrence and the increase in incarceration due to increased crime. Estimates of the negative incarceration effect that do not adjust for this endogeneity will thus be biased toward zero, underestimating the degree to which imprisonment reduces crime.

Adjustment for endogeneity of this kind usually involves instrumental variables. In this problem context, an instrumental variable is a variable that (1) is not affected by the crime rate but (2) does affect the incarceration rate, and (3) has no effect on the crime rate separate from its effect on the incarceration rate. Although instrumental variables generally are difficult to find, researchers have argued that some policy changes meet these three conditions. Such policy changes may thus be useful instruments for identifying the causal effect of incarceration on crime, purged of the influence of crime on incarceration. We discuss these studies below.

A review by Donohue (2007) identifies eight studies of the relationship of crime rates to incarceration rates. Six of the eight studies use data from all or nearly all of the 50 states for varying time periods from the 1970s to 2000, and the remaining two use the RAND inmate surveys and countylevel data from Texas. All find statistically significant negative associations between crime rates and incarceration rates, implying a crime prevention effect of imprisonment. However, the magnitudes of the estimates of this effect vary widely, from nil for a study allowing for the possibility that prevention effects decline as the scale of incarceration increases (Liedka et al., 2006) to –0.4 percent for each 1 percent increase in the incarceration rate (Spelman, 2000). Apel and Nagin (2011), Durlauf and Nagin (2011a, 2011b), and Donohue (2007) discuss the main limitations of these studies.

Western (2006) performed a Bayesian sensitivity analysis that adjusted regressions not accounting for endogeneity according to different beliefs about the effect of crime on incarceration. In an analysis of 48 states for the period 1971 to 2001, the assumption that crime had no effect on incarceration yielded an elasticity of the index crime rate to state incarceration rates of –0.07. Assuming strong endogeneity—that a 1 percent increase in crime produced a 0.15 percent increase in incarceration—yielded an elasticity of –0.18 that was more than twice as large, although this estimate was statistically insignificant. In short, the estimated elasticity of crime with respect to incarceration is acutely sensitive to beliefs about the dependence of incarceration on crime. The highest estimates of crime-incarceration elasticity imply that crime has a large effect on incarceration rates.

Explicit adjustment for endogeneity with instrumental variables is provided by Levitt (1996), Spelman (2000), and Johnson and Raphael (2012).

Copyright © National Academy of Sciences. All rights reserved.

The Growth of Incarceration in the United States: Exploring Causes and Consequences

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Levitt (1996) uses court-ordered prison releases and indicators for overcrowding litigation to form a set of instrumental variables. (Spelman [2000] uses the same instruments applied to a slightly longer time series.) Levitt argues that such court orders meet the test for providing a valid estimate of the effect of the incarceration rate on the crime rate. The orders are not affected by and have no direct effect on the crime rate, affecting it only insofar as they affect the imprisonment rate. Levitt’s instrumental variablesbased point elasticity estimates vary by specification and crime type, but some are as large as –0.4.

Even if one accepts Levitt’s arguments about the validity of the prison overcrowding instrument, the estimated effects have only limited policy value. The instrument, by its construction, likely is measuring the effect on crime of the early release of selected prisoners, probably those nearing the end of their sentenced terms. It may also reflect the effect of diverting individuals convicted of less serious crimes to either local jails or community supervision. In either case, the estimates are not informative about the crime prevention effects, whether by deterrence or incapacitation, of sentence enhancements related to the manner in which a crime is committed (e.g., weapon use), to the characteristics of the perpetrator (e.g., prior record), or to policies affecting the likelihood of incarceration. More generally, the uncertainty about what is actually being measured inherently limits the value of the estimated effects for both policy and social science purposes.

A more recent instrumental variables-based study by Johnson and Raphael (2012) specifies a particular functional dependence of prison admissions on crime and uses this information to identify the incarceration effect. Identification is based on the assumption that prison populations do not change instantaneously in response to changes in the size of the criminal population. As in the non-instrumental variables-based analysis of Liedka and colleagues (2006), Johnson and Raphael conclude that the crime prevention effect of imprisonment has diminished with the scale of imprisonment, which was rising steadily over the period of their analysis (1978 to 2004). Their conclusion also is consistent with previously discussed findings of Canala-Cacho and colleagues (1997), Vollaard (2012), and Owens (2009).

In light of the incapacitation studies, evidence reported by Johnson and Raphael (2012) that the crime-incarceration elasticity is smaller at higher incarceration rates suggests that relatively low-rate offenders are detained by additional incarceration when the incarceration rate is high. However, even the incapacitation interpretation is cast in doubt by the aging of the U.S. prison population. Between 1991 and 2010, the percentage of prisoners in state and federal prisons over age 45 nearly tripled, from 10.6 percent to 27.4 percent (Beck and Mumola, 1999; Guerino et al., 2011). Thus, the apparent decline in the incapacitative effectiveness of incarceration with Copyright © National Academy of Sciences. All rights reserved.

The Growth of Incarceration in the United States: Exploring Causes and Consequences

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