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Overview

Early understandings of the cessation from crime considered desistance to be the event of moving from a state of committing crime to a state of not committing crime. Gradually, however, scholars have begun to understand desistance not as an event but as a process. Fagan (1989) was the first to recognize this, differentiating the process of desistance, defined as the reduction in the frequency and severity of offending, from the event of quitting crime. Le Blanc and Fre´chette (1989) also referred to desistance as a set of processes that leads to the cessation of crime, using the term deceleration to refer to a reduction in the frequency of offending prior to cessation. Continuing the dialog, Laub and Sampson (2001) explicitly separated the process of desistance from the termination of offending, which they viewed as the outcome of desistance. There are currently in the literature several excellent reviews of possible theoretical explanations for desistance – most notably Laub and Sampson (2003). This essay describes desistance by explicitly mapping the different processes of desistance to different stochastic time series models.

Describing Desistance

In its most basic form, a time series of individual offending can be described by the following equation, which is known as an autoregressive time series:

Desistance From Crime form 1 Formula 1

where e_t is a time series of uncorrelated shocks. A key assumption of time series analysis is that the process is stationary, which simply means that the parameters of the model are stable throughout the time period. This kind of stationary process cannot create a long-term desistance trajectory that declines to zero over time. The path described by Eq. 1 will move to an equilibrium level and then stay flat with short-term variation around the equilibrium line – the very formulation means that there can be no meaningful shift in the level of offending. State dependence (past offending causes current offending) and individual heterogeneity (differences between individuals in the stable propensity to commit crime) as captured in the lagged Y term in Eq. 1 cannot explain desistance. Therefore, desistance is inherently a nonstationary process.

There are four broad classes of nonstationary time series. The first is a series with a trend. This trend is based on age. The trend predetermines the path. With a trend, Eq. 1 becomes Eq. 2

Desistance From Crime form 2 Formula 2

This elementary model does not try to explain the existence of the trend, except in the most basic or general terms. The best example in criminology for a desistance theory that appeals to a basic trend is Gottfredson and Hirschi’s (1990) theory of self-control. In this theory, any change in an individual’s time series trend in offending over time is simply attributed to the “inexorable aging of the organism” (1990: 141). Since age is the time marker in this time series, saying age explains desistance is simply the same thing as saying that there is an undefined trend that mimics the trend in age (Bushway et al. 2001). Glueck and Glueck’s (1974) maturational theory of the decline in crime over time is but one small step removed from Gottfredson and Hirschi’s assertion about age (1990). They are careful to explicitly distinguish age from maturation – which means that the maturational process need not occur at the same age for everyone. However, all this statement does is to extend Eq. 2 to say that there is an unknown distribution of time trends in the population – there is a definitive time trend but everyone does not have the same time trend. This claim leaves open the possibility that this maturational process is preprogrammed and deterministic. Laub and Sampson (2003: 33), for example, characterize these kinds of developmental theories as being preprogrammed – essentially fixed trends: “[d]evelopmental accounts … focus on regular or law-like individual development over the life span.”

The second type of time series, a cointegrated time series, captures the counterargument to Sampson and Laub’s characterization of the developmental path. Here, Eq. 3 is developed by adding a time-varying covariate X_t. The coefficient on Xt is time constant. This variable trends in the same way as criminal propensity.

Desistance From Crime form 3 Formula 3

This basic model in which time-varying covariates can explain the long-term pattern of desistance fits with the class of theoretical models in which theorists simply extended existing theories of the onset of crime to account for its desistance. For example, Agnew (2005) argued that the bulk of offenders desist from crime simply because the strains that they experienced as adolescents that launched them into crime in the first place (school, relationship, and job strains) diminish over time, and the ability to adapt in a conventional way to existing strains increases as they entered adulthood. The movement into adulthood, then, comes with both fewer and/or less intense strains and/or an increased capability to adapt to strain in a nondeviant way. Similarly, Akers (1998: 164) argued that the most important predictor of all dimensions of offending, including desistance, is involvement with delinquent peers: “… the single best predictor of the onset, continuation, or desistance of delinquency is differential association with law-violating or norm-violating peers.” Most existing theories of crime responded to the new conceptual terrain brought about by the criminal career perspective, then, by simply insisting that they could just as easily explain desistance as they could onset or other dimensions of offending.

Developmental or maturational theories of crime can also be thought of as describing a cointegrated time series rather than a deterministic trend to the extent to which the theorist describes a variable or process that explains the change in propensity over the life course. For example, Gove (1985) posits that there are biological and psychological factors over time that peak and decline in the same manner as offending propensity. These factors are plausibly cointegrated with offending propensity.

Although they are skeptical about whether this can be done, Gottfredson and Hirschi (1990) acknowledge the possibility that timevarying covariates can explain long-term change. On the empirical side, Osgood (2005) advocates inserting time-varying covariates with time constant parameters into growth curve models in an attempt to explain the age crime curve. Within the growth curve framework, Osgood (2005) suggests testing to see if the time-varying covariates can detrend the data. This basic approach has been applied by Nieuwbeerta and Blokland (2005) where they look to see how much marriage and employment can explain the age crime curve. It is also seen in Sweelen et al. (2013) in which they look to see how much a set of time-varying covariates can explain the divergence between those who desist from and those who persist in crime. In each case, the researchers are looking to see if the time-varying covariates can make a nonstationary time series stationary – with time constant parameters, the only way this is possible is if the covariates themselves trend or track in the same manner over time as offending propensity.

The third type of time series process that can explain or accommodate nonstationarity is a time series with a structural break. A structural break implies that there are two or more sets of parameters, meaning that the causal process is different across different time periods.

Desistance From Crime form 4 Formula 4

Of course, there can be more than one structural break. There are elements of structural breaks that are harmonious with several desistance theories. For example, the notion of agegraded causal factors is entirely consistent with the idea that the value of coefficients on some time-varying variable changes over time.

A more general way of thinking about structural breaks is that some relatively time-stable component of an individual, such as self-control, changes over time. This is only relevant if life events and social context interact with self-control to affect behavior. In Thornberry’s interactional model, for example, the exact nature of state dependence depends in meaningful ways on the individual’s relatively stable characteristics (Thornberry 1987). In Thornberry’s interactional theory, those individuals who are heavily embedded in crime are less “dynamic,” in that, they are less responsive to changes in their environment, and, therefore, are also less state dependent (Thornberry and Krohn 2005). Nagin and Paternoster built on this idea in their own version of an interactional theory when they posited that the impact of sanctions depended in meaningful ways on the person’s level of self-control (Nagin and Paternoster 1994). Subsequent empirical work by Wright and colleagues (2004), as well as by Hay and Forrest (2008), have all found evidence for an interaction between life events and stable individual characteristics such as self-control. If this basic preference function shifts over time in purposeful ways, as suggested by Hay and Forrest (2008) and Giordano et al. (2007), then the same inputs and opportunities lead to different behaviors at different times – and state dependent processes can start to head people in a different direction. This situation, where a person experiences different causal processes depending on changes in their underlying personal preferences, extends interactional theories to accommodate a structural break and strengthens the ability of these types of theories to explain long-term changes in offending propensity.

Another type of desistance theory that accommodates a structural break are theories which anchors a change in crime to an offender’s change in personal identity (Giordano et al. 2002, 2007; Paternoster and Bushway 2009). The importance of identity theories from this perspective is that they provide an explanation for how fundamental individual characteristics such as selfcontrol can change from one time period to another manifesting itself as a structural break. Changes in identity can trigger fundamental shifts in how people value the future (time discounting) or value their social contacts. Simply saying that preferences change is easy – explaining the mechanism by which they change is both important and difficult (see Akerlof and Kranton 2010). Identity theorists like Giordano and her colleagues (Giordano et al. 2002, 2007) and Maruna and Farrall (Maruna 2001; Farrall 2005) offer social psychological theories of desistance which revolve around structural breaks in the process that generates crime. Basing their views on a symbolic interactionist foundation, Giordano et al. (2002) argue that desistance requires substantial cognitive transformations or “upfront” cognitive work such as the development of a general openness to change, receptivity to “hooks for change,” and consistent support from social others. In a later revisiting of this view, Giordano et al. (2007) developed a desistance theory that relies much more heavily on external, social processes – the regulation of emotions and the emotional identity (an “anger identity”) of ex-offenders as they struggle with getting out of crime. Maruna (2001) also adopted a theory of desistance that relies on notions of the actor’s identity, though not one premised on a change in identity. For Maruna (2001), “making good” does not so much involve an intentional change in the desister’s identity from bad to good as it does a reinterpretation of one’s criminal past to make it consistent with their current pro-social identity.

The fourth major type of nonstationary time series is a random walk, a well-known form that has been found occurring in many contexts, including the stock market price of a company and the financial status of a gambler. Random walks have a unit root:

Desistance From Crime form 5 Formula 5

According to Eq. 5, behavior in a given period is simply where you were in the previous period, plus a constant and a shock. The series has an infinite memory, since any shock is permanently incorporated into the time series. Random walks do not, therefore, return to any mean. The same formula can generate flat, increasing, decreasing, or U-shaped curves, depending entirely on the time series of uncorrelated shocks et.

This description of a random walk is consistent with Laub and Sampson’s (2003: 34) characterization of life course theories of desistance as the result of a series of random events or “macro-level shocks largely beyond the pale of individual choice (for example, war, depression, natural disasters, revolutions, plant closings, industrial restructuring).” Random walks are inherently unpredictable, and as described by Laub and Sampson (2003: 33–34), this lack of predictability is the key factor which distinguishes life course trajectories from predetermined developmental trajectories:

Developmental accounts.. .focus on regular or lawlike individual development over the lifespan. Implicit in developmental approaches are the notions of stages, progressions, growth and evolution… with the imagery being one of the execution of a program written at an earlier point in time. … In contrast, life-course approaches … emphasize variability and exogenous influences on the course of development over time that cannot be predicted by focusing solely on enduring individual traits. (emphasis added)

Another way to discuss the time series properties of life course theories is to consider the key life course assertion that the impact of life events depends on when they occur in a person’s life. This is the notion that “timing matters.” To the extent to which this timing dependence is predictable, it is consistent with time series models with structural breaks because the implication of timing dependence is that there are simply different models for different time periods. If there are a small number of changes, and these changes are tied to observable changes in identity, then this age-gradedness should be both predictable and identifiable. But if there are many structural breaks, and these breaks are tied to malleable social contexts, the age-gradedness becomes much more unpredictable. Indeed, a random walk can be characterized as a time series with N structural breaks, where N converges to the total number of periods in the time series.

The main difference between life course theories (random walks) and identity theories (structural breaks) is the number of breaks. In a world with many breaks, predicting long-term change is difficult. The result is a change in focus to explaining change in any given period, which is driven by these relatively exogenous life events. This conclusion is consistent with empirical practice – if a time series is a true random walk, with no trend and no cointegrated time series, the only feasible strategy is to explain period-to-period, that is, short-term, change. With a time series characterized by random walks, it is simply not possible to explain any long-term pattern because that long-term pattern is driven by random shocks. Ironically, this interpretation of life course theory implies that it is neither possible nor even interesting to study a life course “trajectory” since only period-to-period change contains interesting information – there is no meaning to a life course.

All theories of desistance must fit into one of the four basic categories of nonstationary time series models – trends, cointegrated series, series with a structural break, and random walks. Given the distinct empirical character of each of these four basic types of time series, a serious examination of individual time series characteristics should be a fruitful avenue for future empirical research. Further explication of theories within the framework provided by the extensive literature on time series processes should also help to clarify and formalize theories of desistance. Readers interested in seeing empirical examples of this approach should peruse Paternoster and Bushway (2009; Bushway and Paternoster 2012), where some basic illustrations are provided using data from the Cambridge Study in Delinquency Development (CSDD) data (Farrington et al. 2006).

Key Issues/Controversies

Bushway and Paternoster (2012) argue that the evidence shows that desistance is not inevitable as suggested by Sampson and Laub (1993; Laub and Sampson 2003) nor is it a simple part of the biological aging process as suggested by Gottfredson and Hirschi (1990). Moreover, they believe the evidence suggests that individuals stop committing crime not because they cannot physically commit crime anymore, but because they choose not to. Some choose to exit before others who wait until much later in their lives to quit crime, and as a result, there is a long right hand tail in the age distribution of offending. This long right hand tail also casts doubt on a strictly structural version of desistance which attributes the initial thrust into conformity to an acquiring of “turning points” or pro-social roles like jobs and marriages. While there is a convincing body of research that documents the ability of marriage and work to decrease crime, this work frequently does not speak very directly or clearly to the causal mechanism by which this effect occurs (Sampson et al. 2006). If the explanation is entirely or immediately structural, desistance would be highly correlated with the arrival rates of first marriages and stable employment during the 20s and into the 30s as people move into adulthood. And, indeed, a large portion of desistance clearly does occur between the ages of 20 and 40. But, it cannot be ignored that employment and marriage have been available states for 20 years by age 40. A simple matching or sorting story in which people desist when matched to jobs and spouses should not require more than 20 years before it reveals itself.

Of course, it is possible that work (and potentially marriage) has a differential impact depending on age such that work is involved in the desistance process but only when offenders reach a certain age. But this explanation would imply that something about the individual or her set of circumstances has changed with age, their identity and preferences, for example, and this change in turn leads to different choices by the individual. The typical interpretation is that the effect of these variables is age-graded, but this term simply describes what has to be explained. Another interpretation is that these factors (such as jobs and marriages) have a different impact on different kinds of people, and different kinds of people select into marriage and employment at different ages. Research on employment and crime is now increasingly showing that the established “fact” that employment is bad for youth (but good for adults) is entirely an artifact of selection. Strong controls for selection show that employment has the same modest negative impact on crime for youth as it does for adults. Entering into pro-social roles may have a role to play in desistance, but perhaps the acquisition of such roles is only part of the picture and comes later in the desistance process when other obstacles have first been overcome.

The facts of desistance state loudly and clearly that desistance cannot be explained either by strictly biological or structural explanations. If not biology and if not the immediate acquisition of prosocial roles, what then? One possible explanation lies in a person’s identity and the corresponding changes this brings in how they weigh the inputs of their decision making, their preferences, and how they make choices (Akerlof and Kranton 2010).

Theoretical Frontiers: Identity Theory

There is a long intellectual tradition in sociology and social psychology which emphasizes the importance of one’s identity (Stryker 1968). In recent years, economists have also argued that the preferences people have and ultimately the decisions that they make are influenced by who they think they are or who they want to become (Akerlof and Kranton 2010). Identity is important for numerous reasons, the most important for our concerns is that it motivates and provides a direction for behavior (Stryker 1968). A person’s actions are seen as expressions of their self-identity – people intentionally behave in ways that are consistent with who they think they are. In interaction with others, therefore, people project an identity of who they are, and a primary vehicle for communicating to others who “one is” is through one’s behavior.

Identities or selves vary in terms of their temporal orientation. Some selves are oriented toward the present as the working self (Markus 1977, 1983). The working self is that component of the self that can be accessed at the moment and is based upon the individual’s here-and-now experience. In addition to a sense of who and what one is at the moment, or a self that is fixed on the present, people also have a sense of self that is directed toward the future. This future oriented self is defined positively as the self they would like to become and negatively defined as the self they would not want to become or fear that they might become. Markus and Nurius (1987) have defined this future orientation of the self as a possible self. The possible selves “are conceptions of the self in future states” (Markus and Nurius 1987: 157) and consist of goals, aspirations, anxieties, and fears that the individual has as to what he could become. While the working self is aware of what skills the person has and does not have and what the person can and cannot do in the present, the possible self is directed toward the future and what it is possible to be and what the person would not like to be. A person may, for example, see herself currently (the working self) as a thief, drug user, poor father, unskilled worker, but may see herself in the future as working in a job (though perhaps for minimum wage), legitimately buying things for her family, owning a used car, and ceasing to use drugs and commit crime. A person may, however, also fear that she may turn out to be a burned-out addict, riddled with disease, homeless, childless, jobless, and destined to die alone.

An important consequence of a possible self is that it provides directed motivation for one’s behavior (Markus and Nurius 1987). Possible selves, both positive and negative, therefore, not only contain satisfying images of what the person would like to be or desperately fears becoming, they can also provide a specific and realistic set of instructions or a “road map” directing what one can do to achieve the positive future self and avoid the negative possible self. This is referred to as the self-regulating component of the possible self. The self is self-regulating because, among other things, it compares the past and current working self with the possible self and provides specific directions, strategies, or plans for narrowing any discrepancy between the two, thereby connecting the present with the future. Motivation is generated and is more likely to be successful, then, when the person not only has a goal of self-improvement but specific and realistic means to reach that goal. While the positive possible self is frequently a longer-term goal, an initial movement out of a deviant identity is more likely to be based on a motivation to avoid a feared self than it is a desired to achieve a positive self.

Though stable, identities clearly can and do change. A working identity as a criminal offender can change to a more conventional identity when the person thinks of a conventional identity as a positive possible self and an identity of a burned-out ex-con with no friends or possessions as a negative possible self or feared self. Contemplation of a possible self that does not include criminal offending in turn occurs when the working identity of criminal is perceived to be unsatisfying or disappointing. As one begins to find less success and satisfaction with the criminal identity, it is likely to conjure up negative possible selves – long terms in prison with young hoodlums, a violent death during a crime, small payoffs from criminal enterprises. These negative possible selves and the activation of positive selves – a working person, a person with a good spouse, a giving father, a law abider – can provide both the motivation and direction for change. Before one is willing to give up his working identity as a law breaker, then, one must begin to perceive it as unsatisfying, thus weakening one’s commitment to it. This weakening of one’s commitment to a criminal identity does not come about quickly, nor does it come about in response to one or two failures, but only gradually and only as the result of linking together of many failures and the attribution of those linked failures to one’s identity and life as a criminal.

The process of desisting from crime first requires an offender to recognize that their working identity of offender is no longer satisfactory and their attachment to this identity must be weakened. The weakening of a criminal identity comes about gradually and comes about as a result of a growing sense of dissatisfaction with crime and a criminal lifestyle. The dissatisfaction with crime is more likely to lead to a conventional possible self when failures or dissatisfactions with many aspects of one’s life are linked together and attributed to the criminal identity itself. It is not just that one has experienced failures but that diverse kinds of failures in one’s life become interconnected as part of a coherent whole which leads the person to feel a more general kind of life dissatisfaction, the kind of life dissatisfaction that can lead to intentional identity change.

It is such a new understanding of one’s life that leads to the effort to intentionally change it, or as Shover (1996: 132) put it: “[t]his new perspective symbolizes a watershed in their lives.. .[t] hey decide that their earlier identity and behavior are of limited value for constructing the future.” The importance of this is that one consequence of this linking together of diverse failures in life, or what Baumeister (1994) calls the crystallization of discontent, is that after this occurs, the dissatisfactions that one has experienced now has implications for the future. Events that seemed atypical and isolated that have been linked are now seen as interrelated and therefore both less easily dismissed and seen as likely to continue to occur in the future. The projection into the future of continued life dissatisfaction leads the person to begin to seek changes.

Kiecolt (1994: 56) has argued that intentional self-change is unlikely to be successful without what she calls “structural supports” for change. These supports “provide individuals with means and opportunities for effecting self-change” and include self-help groups and professional changers such as psychiatrists and social workers. As a separate condition for successful selfchange, Kiecolt includes the assistance of social supports such as friends, family members, and spouses and partners.

Obviously if successful self-change is going to occur, the benefits of a new identity must outweigh the costs of leaving the old one. However economically marginal a life of crime is, criminal offenders, particularly those with official records of arrest, conviction, and incarceration, find legitimate employment opportunities, even in the secondary labor market, very restricted. Some opportunity to secure a conventional job must be available for criminal offenders to desist, no matter how strong the motivation to change their identities and selves. Generally, anyone exiting one role or identity needs access to alternative sources of employment – nuns leaving religious orders no less than prostitutes leaving “the trade” must find outside employment. Without these kinds of structural supports, identity change becomes difficult. Social supports, whether in the form of friends, spouses/partners, jobs, or professional help, are important in self-change because they provide the one in the throes of a crystallization of discontent with an alternative existence or identity.

In an identity theory of desistance, changes in friendship networks and the securing of alternative jobs and vocations are important because they help maintain or bolster a fledging changed identity. To be clear, securing jobs, attracting new partners, and involvement with new friends come about after a change in identity has occurred. The change in identity has already occurred in the mind of the person; he has weighed the costs and benefits of the exiting identity and alternatives and is behaving in ways that conform to the new possible self.

Empirical Frontiers Of Desistance Research: Long-Term Hazard Models

Bushway et al. (2009) show convincingly that the main types of growth curve models largely discard as noise information about change from the individual trajectories. This finding should be particularly troubling for desistance scholars, who are fundamentally interested in studying change. But how can researchers study change if individual trajectories are too imprecise and long-term trajectory models essentially ignore the very change that desistance scholars are interested in studying? Another possibility for examining desistance processes would be to turn to a study of recidivism. Thirty years ago, recidivism and desistance were complementary measures. Those who failed after a certain period were recidivists, and those who did not were desistors.

This static approach to thinking about recidivism and desistance has been effectively rejected. Now, cutting edge recidivism studies focus on hazard rates of offending over time and cutting edge desistance studies focus on measuring trajectories of offending rates over time. But, it is a well-known fact in statistics and quantitative criminology that these two models (hazards and trajectory-type models) are actually measuring the same concept, with hazard rate models focusing on short-term change in the propensity to offend and trajectory models focusing on long-term change in the propensity to offend. For example, having noted that the hazard rate focuses on the hazard of involvement in a given criminal event, Hagan and Palloni (1988) observe that

(T)he expected number of criminal events during the age interval being examined is a unique function of these hazards. This expected number of criminal events is what Blumstein et al. are estimating when they calculate lambda (offending rate). So, lambda is a summary of the combined hazards of criminal events of various orders over a period time. (Hagan and Palloni 1988: 97)

As a result, the use of trajectories of rates to study desistance has brought the study of desistance conceptually very close to the study of recidivism.

In their article, Hagan and Palloni (1988) present arguments for focusing on the causal nature of the events, rather than on the rate of offending. At the time they made their argument, however, empirical methods only allowed for the estimation of time-stable rates for individuals. The ability to capture time variation in offending rates while controlling for individual heterogeneity, combined with the new emphasis on the process of desistance, provides a persuasive counterargument for a focus on the more long-term perspective.

The potential productivity of using hazard models with long-term data was highlighted by Barnett et al. (1989), who applied their insight about desistance and trajectories of offending to an analysis of recidivism using a hazard model. Barnett et al. (1989) examined the risk of recidivism until the 30th birthday among a small group of 88 offenders who had at least two convictions before their 25th birthday. Each offender was given a probability of a new offense as well as a desistance parameter that indicated the probability of instantaneously desisting after each event. Thus after each criminal event, the offender had the choice of continuing to offend at the given rate (l) or desisting. By dividing the offenders into two groups, “frequents” (annual m ¼ 1.14 or a 1 in 320 daily chance of offending) and “occasionals” (annual m ¼ 0.4 or a 1 in 913 daily chance of offending), they were able to quite reliably predict future patterns of recidivism. The only complication in their models was a small group of “frequent” offenders who had appeared to desist from crime according to their predictions, but actually resumed a criminal career later in life. It was this small group of offenders they deemed “intermittent” for which their basic models were not adequate. They therefore called for “more elaborate models to incorporate the concept of intermittency, whereby offenders go into remission for several years and then resume their criminal careers” (p. 384).

Kurlychek et al. (2012) have attempted to learn about desistance in the short term by using survival models which can be tied to different models of desistance. Research on survival starts with a group of active offenders and then follows them for a period of time to model the risk of recidivism as well as the time (t) to recidivism. A hazard ratio is then estimated for each time period (t) as follows:

Desistance From Crime form 6 Formula 6

Those who have not failed by the end of the follow-up period may be assumed to have desisted from crime. However, it is also possible that they would have recidivated if they had been followed for a longer period of time, meaning that the observation was merely right censored. While much current recidivism research utilize the semi-parametric Cox regression strategy which does not force a functional form on the data over time (e.g., the models are more interested in explaining the effect of covariates over time), Kurlychek et al. (2010) suggest that the use of parametric methods might be more informative if one is attempting to explain the actual form or time pattern of offending.

This approach was first introduced to criminology by Maltz (1984) and extended by Schmidt and Witte (1988). For example, Schmidt and Witte (1988) applied a variety of functional forms to two cohorts of releases from the North Carolina prison system and were unsatisfied with the fit of any of the basic models. They identified the problem to be the basic assumption that everybody in the sample will fail if only followed up for a sufficiently long period of time. To address this issue, the authors then turn to what is known as a “split-population” or mixture model which allows for the fact that everyone does not fail. That is, some people do desist.

Split-population models include an extra parameter, often referred to by biostatisticians as the “cure” factor, which estimates the portion of the risk set that will never experience a failure (in other words, they will be “cured”). The cure factor is evidence of instantaneous desistance, or a structural break, particularly for individuals who have substantial rates of offending before the current offense. In this instance, individuals somehow decide (perhaps because they have changed their identity) to quit crime immediately. When applying split-population models to their data, Schmidt and Witte found that all splitpopulation models outperformed their non-split model counterparts. However, Schmidt and Witte (1989) only follow their subjects for 5–7 years, not long enough to fully conclude that there has been desistance.

Kurlychek et al. (2012) estimated similar models using data with 18 years of follow-up from Essex County, NJ. They find that the two-parameter split-population exponential model fits the data almost as well as the more complex three-parameter lognormal counterpart and, in fact, out-performs this model in the later years of the data. It is striking how well this simple model can explain the observed behavior. Like the split-population lognormal model, the split-population exponential model assumes that there are two groups of offenders – those who have desisted at the beginning of the follow-up period and those who remain active. They find support for instantaneous desistance with the split-population lognormal and exponential model actually reaching quite similar conclusions about the size of the permanent desisting population at the outset of the follow-up period (the lognormal model is in the 20–23 % range while the exponential is 25–27 % range). This estimate is smaller than the estimates from Brame et al. (2003) looking at desistance after an arrest. However, it is still substantial. While the focus of most recidivism studies is on the high recidivism rates, the flip side here is that a full quarter of the sample of felony offenders desists after this conviction. Clearly, then, not all individuals are equally risky after a conviction. Indeed, because the exponential model assumes that the active offenders experience a constant risk of recidivism throughout the follow-up period, there is no evidence of declining hazard rates among the active offenders.

The length of the follow-up period in the Essex County dataset has a lot to do with the performance of the split-population exponential model. If the Essex County study had only followed offenders for 3, 4, or 5 years – typical follow-up periods for recidivism studies – the conclusions about the split-population lognormal and exponential models would have been different. Over this shorter window of time, the split-population lognormal model clearly performs better, but viewed over the entire 18-year follow-up period, the simpler, two-parameter split-population exponential model emerges as a formidable competitor. As more datasets with long follow-up periods are studied, it will be interesting to see how well the split-population exponential model performs, especially after the first few years of follow-up.

A final insight revolves around the concept of intermittency or reactivation of criminal careers after a period of dormancy or “temporary desistance” (Barnett et al. 1989). The concept of intermittency has been gaining ground in criminology in recent years and leads to certain theoretical and policy implications (e.g., the idea that desistance is always provisional). The Kurlychek et al. (2012) analysis is certainly consistent with the idea that a low rate offender can go for many years before committing a new offense. But intermittency is a particularly dynamic model of offending in which the offender goes from an active rate of offending to a zero rate of offending back to a fully active criminal career (what Laub and Sampson (2003) refer to as a “zigzag” criminal career). Barnett et al. (1989) moved to an intermittency explanation after they found evidence of a “fat” tail – higher rates of offending more than 5 years after the last offenses than could be explained by the exponential model. While Kurlychek et al. (2012) found support for their simple split-population exponential model, there was no fat tail even though they observed a more serious population over a longer followup period. As a result, they concluded that there is no evidence for intermittency, at least as described by Barnett et al. (1989). Replication and extension of these findings with other longterm datasets represents an important avenue for future research. In addition, there is a need to rejuvenate theoretical work in desistance. Previous efforts, while useful starting points, are not able to explain either the criminal patterns of contemporary offenders or the findings that have accumulated from recent empirical studies with different analytical models.

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