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Citation: 29 Criminology 163 1991-1992

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O THE RELATIONSHIP OF STTO FUTURE PARTICIPATIONIN DELINQUEN YDANIEL S. NAGIN

Carnegie Mellon UniversityRAYMOND PATERNOSTER

University of MarylandAmong the best documentedempiricalregularities n criminology is the

positive associationbetween past andfuture delinquencyand criminality.In this paper we examine alternative interpretationsof this association.One is that priorparticipation has a genuine behavioral impact on theindividual Prior participation may for example reduce inhibitionsagainst engaging in delinquent activity. Such an effect is termed statedependence. second explanation is that individuals differ in unmea-sured delinquent propensity and this unmeasuredpropensity is persistentover time. This second explanation is a consequenceofpopulation hetero-geneity. sing a three wave paneldata set we attempt to distinguish thesetwo interpretationsof the positive association between past and futuredelinquency. Our resultssuggest that the positive association isprincipallydue to a state-dependent influence. Theoretical implications and direc-tions for future researchare also discussed.

There are but a few well documented empirical regularities in criminol-ogy-males are more likely to offend and are more frequent offenders thanfemales, arrest rates are higher among blacks than whites, and aggregateoffending rates rise with age into young adulthood and decline thereafter.The interpretation of each of these regularities has been the subject of extensive empirical analysis and theorizing e.g., Greenberg 1985; Hagan 1989;Hindelang 1978, 1981; Hirschi and Gottfredson 1983). Another compara-bly documented empirical regularity is the positive association between pastand future criminality. Numerous empirical studies have documented thatthose who begin offending at an early age and those with extensive criminalhistories are more likely to commit offenses in the future see Blumstein et al.,1985; Wolfgang et al., 1972).

The observation that past experience with some specified event or behavioris highly correlated with future experience with that event or behavior hasThis work was supported by the National Science Foundation under Grant No. SES-9023109. We thank Linda Babcock, James Heckman, and David Greenberg for valuablecomments.

CRIMINOLOGY VOLUME 29 NUMBER 2 1991

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N GIN ND PATERNOSTERbeen observed in a wide range of contexts. Individuals who previously havebeen involved in accidents, experienced spells of poverty, been unemployedor moved, for example are respectively, more likely to be involved in an acci-dent, experience a spell of poverty, become unemployed, or to move in thefuture (Bates and Neyman, 1951; Goodman, 1961; Heckman, 1981b; Fein-stein and McFadden, 1988). Heckman 1981b:150) observes that there aretwo distinctively different explanations for such empirical regularities:

One is that individuals who experience the event are altered by theirexperience in that the constraints, preferences or prices (or any combi-nation of the three) that govern future outcomes are altered by pastevents. Such an effect of past outcomes is termed structural statedependence. A second explanation is that individuals differ n some unmea-sured propensity to experience the event and this propensity is eitherstable over time or, if it changes values of propensity are autocorrelated.Broadly defined, the second explanation is a consequence of populationheterogeneity (emphasis added).

In this paper we attempt to distinguish between these two interpretations ofthe relationship of past to future delinquent activity.' As will be discussedbelow, many of the leading general theories of crime can be broadly groupedinto two fundamentally different classifications-those emphasizing heteroge-neity versus those emphasizing state-dependent like effects. Thus, sorting outthe relative contributions of state dependence versus heterogeneity in explain-ing the positive association of past to future criminality has fundamentalimplications for criminological theory. Further, the paper demonstrates amethodology that has not been previously employed in criminologicalresearch despite its wide applicability to research designs based on the analy-sis of longitudinal data.

STATE DEPENDENCE ND HETEROGENEITYINTERPRETATIONS OF THE RELATIONSHIP

BETWEEN PAST ND FUTURECRIMINALITY

The population heterogeneity interpretation of the positive associationbetween past and future criminality is a fundamental premise of Gottfredsonand Hirschi's 1990) general theory of crime. They observe that competent

1 To our knowledge no prior research has attempted to disentangle the relative con-tributions of state dependency and heterogeneity in explaining the positive associationbetween past and future criminal involvement. On a somewhat related topic, Green andMartin 1973) analyzed the distribution of abscondings from an English training school.The authors attempted to distinguish between a model in which individual abscondingrates varied in the population, the analogue of heterogeneity, and a model allowing forcontagion and reinforcement, which is analogous to state dependency.

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PAST TO FUTURE DELINQUEN Yresearch regularly shows that the best predictor of crime is prior criminalbehavior. In other words, research shows that differences between people inthe likelihood that they will commit criminal acts persists over time p. 107).They go on to argue that criminal behavior is a manifestation of lack of self-control: people who lack self-control will tend to be impulsive, insensitive,physical (as opposed to mental), risk-taking, shortsighted, and nonverbal, andthey will tend therefore to engage in criminal and analogous acts p. 90).Further, they observe, after a century of research, crime theories remaininattentive to the fact that these differences appear e rly nd rem in st bleover much of the life course p. 108, emphasis added .

Likewise, Wilson and Herrnstein 1985:41-66) suggest that persons differwith respect to what might be called criminal disposition or criminal pro-pensity, which comprises such traits as impulsivity, conditionability, andconscience. Criminal disposition is a latent (unmeasured or only partiallymeasurable) characteristic that varies across individuals 2 and is presumed tobe an enduring characteristic of persons. They observe, the offender offendsnot just because of immediate needs and circumstances but also because ofenduring personal characteristics, some of whose traces can be found in hisbehavior from early childhood on . . . (p. 209, emphasis added).

Both Gottfredson and Hirschi and Wilson and Herrnstein appeal to a volu-minous literature showing a positive association between teen delinquency/adult criminality and such factors as poor parental supervision and parentalrejection in early childhood, delinquent siblings, parental criminality, and lowIQ .3

Since the ingredients of poor self-control or, alternatively, criminal propen-sity will inevitably be incompletely measured, the theories of Wilson andHerrnstein and Gottfredson and Hirschi are prototypical examples of the per-sistent, unobserved heterogeneity explanation for the positive associationbetween past and future criminality. Specifically, because differences in indi-vidual disposition to commit crime are argued to be persistent over time, pastand present lawbreaking will be positively correlated. This interpretation of

2. For example, Wilson and Herrnstein 1985) observe,The aggressive drive may occur very rarely in some of us and frequently inoth rs ... p.6).People differ in how they calculate . risks. Some worry about any chance,however slight, of being caught and would be appalled at any loss of esteem,however small or fleeting . p. 48 .Individuals differ in the degree to which they discount the future. These differ-ences are often part of a personality trait that can be measured... They may alsodiffer in their ability to conceive of the future or to plan for it (p. 54).3 For an excellent review of this literature, see Loeber and Stouthamer-Loeber1986) and Fishbein 1990).

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NAGIN ND PATERNOSTERthe positive association between past and future offending is a variant of thefamiliar omitted variable bias argument.

The alternative interpretation-state dependence-implies that the act ofcommitting a crime has a genuine behavioral influence in the sense that theexperience of crime commission increases the likelihood of future offendingby changing something about the offender s personal characteristics or lifechances. The state dependence interpretation of the positive associationbetween past and future offending implies that the initial act of crime, andperhaps subsequent criminal acts, reduces what may have been reasonablyeffective inhibitions against future crime.

The state dependence interpretation is congenial with a number of theoriesof criminality. Prior criminal involvement may, for example, weaken theindividual's social bond to conventionality (Agnew, 1985; Hirschi, 1969 .Commission of criminal acts may damage valued social relationships or mate-rial investments that once served (however imperfectly) to control criminalparticipation. These explanations for state dependency are consistent withthe findings of panel studies of delinquency which find that offending has asubsequent inverse effect on such delinquency inhibitors as attachment toschool, attachment to conventional others, perceived sanction risk, and moralbeliefs that condemn criminal behavior (Agnew, 1985; Britt and Campbell,1977; Burkett and Warren, 1987; Massey and Krohn, 1986; Meier et al.,1984; Paternoster et al., 1983 . It is also possible that criminal or delinquentacts would lead offenders into greater affinity with others who themselves areviolators, leading to additional offenses. This conjecture is consistent with thetheories of differential association and social learning (Akers, 1985; Suther-land, 1955 and the extant empirical literature (Britt and Campbell, 1977;Burkett and Warren, 1987; Ginsberg and Greenley, 1978; Kandel, 1974;Massey and Krohn, 1986; Meier et al., 1984).

A state dependence process is also compatible with the notion of labelingtheorists that reactions to instances of primary deviance create problems ofadjustment for offenders that causes them to commit additional, secondarydeviance (Lemert, 1972:62-92 . Alternatively, suppose prior criminalinvolvement is an indicator of contact with the juvenile or criminal justicesystem. In this case, state dependence may be a reflection of the diminisheddeterrent capacity of the criminal or juvenile justice system after the initialcontact. This interpretation is consistent with the idea that the preventiveeffects of punishment depend substantially on fear of censure by friends andthe community at large (Tittle, 1980; Williams and Hawkins, 1986 . If, forexample, the costs attendant to such censure are largely incurred after theinitial contact with the enforcement authorities, fear of censure will no longeract as a deterrent or, alternatively, the deterrent effect may be greatlydiminished.

If, for whatever reason, the positive association between prior criminality

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PAST TO FUTURE DELINQUENCYand future criminality is, at least in part a reflection of a genuine behavioralinfluence, then it also has important policy implications. If each additionalact of offending increases future criminal offending, the long-term crimereduction benefits of discouraging an individual from committing a crimewould include not only the avoided cost of the instant crime but also of futurecrimes. The magnitude of the long-term crime reduction savings depends onthe structure of the state dependence. If, for example the increase in criminalpropensity attendant to each additional crime diminishes with the number ofcrimes committed, the long-term savings, on average, would be greater for anintervention averting a crime by an individual who had previously committedrelatively few crimes compared with an individual who had already commit-ted many crimes. The extreme version of this case arises if only the firstcrime has an influence on subsequent criminal propensity. For this extremecase, long-term crime reduction benefits only occur if the intervention suc-cessfully averts an individual s initial crime. No such benefits would accruefrom averting the same criminal act committed by an already active offender.

IDENTIFYING ND DISTINGUISHINGHETEROGENEITY ND STATE DEPENDENCE

Heckman 1981 b) offers a constructive analogy between the problem of dis-tinguishing state dependence from heterogeneity in a social science settingwith that of distinguishing among various urn schemes. Consider two basicschemes. In both schemes, individuals are assigned urns with red and blueballs. For our purposes, it is useful to think of the event of picking a red ballas equivalent to committing crime. The proportion of red balls in an individ-ual s urn is thus analogous to that individual s criminal disposition-thelarger the proportion of red balls the greater the individual s criminaldisposition.

In the first urn scheme individuals are initially assigned urns with v ryinproportions of red and blue balls. Once assigned, however the proportionsremain constant Those individuals with a larger proportion of red balls arethose with greater criminal propensity. Such individuals would be character-ized by Gottfredson and Hirschi 1990) as having low self-control by Wilsonand Herrnstein 1985) as having high impulsivity and low conscience, and bythe biological criminologists as having a biological propensity for criminaloffending, such as low autonomic nervous system conditionability or bio-chemical imbalances (Fishbein, 1990).

Each individual samples with replacement from his or her urn. Becausethe initial proportion of red and blue balls in each urn varies across the popu-lation, some individuals will be more likely to pick a red ball. Again theseare the persons high on the unmeasured construct, criminal propensity.Observations on the number of red balls sampled by individuals are therefore

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NAGIN ND PATERNOSTERinformative in distinguishing individuals who are more likely to pick a redball in a future trial. It would be reasonable, for example, to predict that themore red balls previously sampled crimes committed) by a given individual,the higher the likelihood of that individual choosing a red ball (committing acrime) in a future trial. For this urn scheme, however, the predictive powerof past events is entirely attributable to the initi l distribution of urns withvarying compositions of red and blue balls, because for a given individual theprobability of choosing a red ball is the same from trial to trial. This first urnscheme is analogous to the (unobserved) heterogeneity interpretation of thecorrelation of past and future offending.

The state dependence interpretation can be illustrated by the following urnscheme. Suppose all individuals are initially assigned urns with the same pro-portion of red and blue balls and, like the first urn scheme, balls are sampledwith replacement. Thus, initially persons do not differ with respect to theircriminal propensity; all are equally inclined (or disinclined) to commit anoffense. Suppose, however, that whenever an individual draws a red ball asupplement of red balls is added to his or her urn. In this urn scheme, the actof drawing a red ball (committing a crime) incre sesthe probability of draw-ing a red ball (committing another crime) in future trials. This urn scheme isanalogous to the state dependence interpretation of the correlation of pastand future criminality.

This urn scheme represents the process described by labeling theorists asescalation to secondary deviance. When initial acts of primary deviance arenegatively responded to either by significant others (informal labels) or officialagents of social control formal labels), individuals may find themselves witha devalued social status, denied access to conventional roles and opportuni-ties, and censured by conventional others. Denied these normal routines oflife Becker, 1963 , such labeled persons are presumed to respond with agreater commitment to rule breaking-secondary deviance.

Urn analogies can also be constructed to illustrate two other importantpoints. First, state dependence and heterogeneity are not mutually exclusive.As amalgam of the two urn schemes above would create a situation in whichthe predictive power of past drawings stems partly from heterogeneity andpartly from state dependence. Second, state dependence can be manifested ina variety of ways. Suppose, for example, in the second scheme, red balls wereonly added after the first draw of a red ball. In this case only the first draw ofa red ball would have a state-dependent effect. This type of state dependencewould occur if the initial acts of rule breaking damaged offenders life chancesor strengthened criminogenic attitudes, but once this occurred additional actswould have little or no additional harmful effect. Still another structurewould arise if some of the supplemental red balls were withdrawn in subse-quent trials in which a red ball was not drawn. For this structure, the state-

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PAST TO FUTURE DELINQUENCYdependent effect would decay over time. This is analogous to the notion ofindividuals maturing out of crime.

The problem of distinguishing between heterogeneity and state dependencerequires that specific assumptions be made about the distribution of the(unobserved) heterogeneity and the structural form of the state 'dependence.The remainder of this section is devoted to describing the basic forms of themodels that are used to assess whether prior participation in delinquencyappears to have a genuine behavioral impact on the probability of future par-ticipation in delinquency.

Assume we observe a cohort of individuals who have not participated incrime prior to the initial period of observation, P1. Further, assume thatparticipation in P1 can be statistically characterized by the following process:

Yli Xi Eli, (la)Eli = Ti vhi lb) li = if Y* > 0, (lc)Yli 0 if Yli* < 0, 1d)

where the index i denotes the ith individual in the panel, Yli is a latent varia-ble, X1i is a lxk) vector of variables, 0 is a kx 1 vector of parameters, and Y,is a 0/1 dummy variable equal to 1 if Yi* > 0.

For our purposes, it is useful to think of Y* as an index of criminality andY1, as an indicator of participation, where individual participates in P1 i.e.,commits at least one crime if his or her index of criminality exceeds the zerothreshold. The model assumes this index is a linear function ofX1, where Xicomprises measurable individual and ecological factors thought to be associ-ated with criminal propensity, and of Eli. The disturbance Eli as defined byEquation lb, is assumed to include two components. One is Ti, where Ti is anindividual specific effect that does not vary over time. It is assumed to beindependently and normally distributed across the population with a mean ofzero and standard deviation of aF. The second component of Ei is vli, which,like T , is assumed to be independently distributed across the population but,unlike T is not assumed to be invariant over time. Rather, it is assumed to beindependently and identically distributed normal over time with a mean ofzero and standard deviation a,. The assumed structure of the disturbancedefines a model that is commonly called either a random effects e.g., Mad-dala, 1983), or one factor model e.g., Heckman, 198 lb .4 In a cross-sectional

4. This model is similar to a fixed effects model. The difference is that an individualeffect for each individual in the sample is not estimated. Instead, the proportion of thevariance in Eattributable to - is estimated. This approach has two advantages. First, farfewer parameters must be estimated. Second, as discussed in Heckman 1981a) and Mad-dala 1987) for a nonlinear model such as this, parameters from a fixed effects specificationwith state dependence are generally not consistent, whereas the estimates for a randomeffects model are consistent.

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NAGIN ND PATERNOSTERmodel, the two components o Eli are not distinguishable Heckman, 1981band the above process reduces to the familiar probit model.

The disturbance, Eli, has a number of interpretations. One that is useful forour purposes is that it captures the influence of variation across the popula-tion in unmeasured determinants of Yli*-that is, unmeasured) heterogene-ity in the population. Such unobserved heterogeneity does not, per se, giverise to ambiguity in the interpretation of the positive association between pastand future delinquency. Rather, it is the presence of a persistent componentin the unobserved heterogeneity that creates the ambiguity. As will be dis-cussed below, the Ti component of the disturbance allows for the possibility ofsuch persistent heterogeneity.

Suppose that participation in P1 i.e., li > 0) increases the likelihood ofparticipation in period 2 P2) e.g., changes the relative proportion of red andblue balls). In the context of our latent variable model such an increasecould be manifested in a number of ways. It could alter the levels of observ-ables included in x in a way that increases criminal propensity e.g., lowersattachments to conventional others). If the levels of these observables in P2are taken into account in the estimation of the P2 participation decision, sucha recursive-like structure would not give rise to state dependent-like associa-tions. This is not to say that prior participation has not increased the likeli-hood of future participation through its influence on future levels ofobservables. Rather, it is only to say that this is not a sufficient argument forexplaining a positive association between P1 and P2 participation ontrollingfor the levels of observables in P2.

A second mechanism by which P1 participation could heighten the likeli-hood of participation in P2 is by the act of participation altering the weightattached to observables in P2. Such a behavioral influence could be mani-fested by changes in the parameter vector, 0, that systematically increase thelikelihood of future participation. For example holding constant the level ofattachment to conventional others, prior experience may reduce the weightplaced on this factor in future participation decisions. Such a phenomenonmight arise from an experiential effect whereby the individual finds that theadverse reaction of significant others to participation is not as great as ini-tially feared. Such a phenomenon would give rise to a positive associationbetween P1 and P2 participation, controlling for the level of observables inP2. To capture such a manifestation of state dependence properly requires aninteractive model. Such a model, which is beyond the scope of this paper, isdiscussed in the concluding section.

Still another way that prior participation might increase the probability offuture participation is through its influence on unobservables. Here, the dis-tinction between the level of an unobservable and the magnitude of theparameter mediating its influence on criminal propensity is not material pre-cisely because the factor is unobservable. The model of P2 participation,

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PAST TO FUTURE DELINQUENCYwhich we consider next, assumes that any state-dependent influence stemsfrom the influence of prior participation on unobservables and that this influ-ence can be captured by an additive shift. Specifically, assume that the sec-ond period participation decision can be characterized by the followingmodel:

Y2i = X 2iO bY li ENi, 2a)E2 T i V2i 2b)y i = 1 if Y2i > 0, 2c)y i = 0 if Y2i < 0 (2d)

The model characterizing the participation decision in P2 parallels that forP1 but with one augmentation-Yi is included as a determinant of Y2i . If 8> 0, it implies positive) state dependence-that is, the act of participating inP1 increases the probability of participation in P2.

As previously noted, the two disturbances in the model Eli and E , can beinterpreted as capturing unobserved heterogeneity. Observe that both share acommon component, Ti Recall that i is assumed to be normally distributedacross the population but to be fixed over time. This component of the errorstructure captures the influence of any enduring, but unmeasured individualcharacteristics (e.g., impulsivity) affecting propensity to offend. By contrast,v and v2i capture the influence of unmeasured factors that vary randomly,both across individuals and over time (e.g., the availability of offendingopportunities).

The presence of r in both Eli and EN llows for the possibility of persistentheterogeneity. The magnitude of such persistent heterogeneity is captured bythe correlation p) between Eli and i which equals aT2/ U0 U, 2). Thus, pcan be interpreted as the proportion of the joint variation in Eli and E2i attribu-table to persistent heterogeneity. If such heterogeneity is negligible, p will beclose to zero. By contrast, as such enduring individual characteristicsincreasingly dominate the variation in Eli and i p approaches 1.

With this background on the interpretation of Eli and E2i,he model definedby Equations la-ld and 2a-2d can provide some additional perspective onthe problem of sorting out state dependence from heterogeneity. If Equation2a was estimated as a standard probit model the estimate of the true state-dependent influence would only be consistent in the case in which p = o.This represents the special case in which there is no persistent heterogeneity.In the general case in which p > o, the estimate of 8 will be positively biased.The magnitude of this bias will be an increasing function of p. The reason forthe positive bias is that E2i s positively correlated with l because E2 is posi-tively correlated with Eli In words, this simply means that, ceteris paribus,individuals with a high degree of unmeasured criminal propensity in P1, asmeasured by Eli, are not only more likely to participate in P1 but also aremore likely to participate in P2. This is because unmeasured propensity is

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NAGIN AND PATERNOSTERpersistent over time due to the time invariance of ri Assuming 8 0, thisargument implies that a positive estimate of 8 is simply a reflection of unmea-sured heterogeneity.

In the analyses that follow, we will attempt to sort out the state dependenceversus heterogeneity interpretations of a positive estimate of 8 by explicitlycontrolling for the type of persistent heterogeneity specified in our model.The unknown parameters of the model defined by Equations la-ld and2a-2d are 0, 6, and p These parameters can be consistently estimated bymaximum likelihood estimation, where the likelihood function is of the form: 7 f ID{[x y,.,.i+ p/ 1-p)) 2 F] [2yd- 1]) 0 ;F)d?, (3)i= .- t=1where I *) is the cumulative normal distribution, 4 *)s the standard nor-mal density function, t is an index for P1 and P2, /,, = (,, and

M THODATA

The data for this research are derived from a three wave panel study ofjuvenile delinquency. The sample consists of all tenth grade students whowere in attendance on the day the questionnaire was administered at ninelocal high schools in and around a mid-sized southeastern city. Each of thethree survey waves was administered in the students English class. The firstwave was completed in the fall of 1981, and follow-up waves were adminis-tered during the fall of 1982 and 1983. At the first administration, approxi-mately 2,700 sophomore students completed a questionnaire, whichrepresented about 99 percent of those in attendance. At the third administra-tion, approximately 1,250 senior students who had participated in waves 1and 2 completed a questionnaire (46% of the group of original sophomores).With a listwise deletion of missing data, the sample size was reduced to 1,163students who had complete data over all three waves. 6

5. See Heckman (1981b) for a derivation of this likelihood function. The model wasestimated using a programming language called Gauss.6. An examination was conducted of the source of sample attrition over time. Basedon information provided by school officials, sophomore to senior year drop-out rates werelow, approximately 5%, with little variation across different high schools. The three majorsources of sample attrition were (a) students being absent on the day of the qu estionnaireadministration at either the second or third wave (school official reported that approxi-mately 18 of the student body was absent on any given day), (b) students taking a non-traditional English class during their junior or senior year in high school (theater/drama,journalism, business English), which the research staff did not have access to, and

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PAST TO FUTURE DELINQUENCYD T DESIGN

Figure 1 illustrates the two time periods comprising the three-wave paneldesign for this research. In the first period, the outcome variable is self-reported offending that is measured at the second wave (T2) and reflects thoseoffenses committed in the one-year interval between the first and secondwaves (T1-T2). We label this period 1 P1) offending. Period 2 (P2) offend-ing is measured by self-reported offending during the one-year period betweenthe second and third waves (T2-T3), and it is measured at the third waveT3). With this design, we can examine the effect of exogenous variables mea-sured at T 1 and T2 on self-reported offending occurring, respectively, duringP1 and P2. In addition, at time 1 self-reports on offending were elicited bothfor the one year prior to T 1 and for anytime prior to T 1Figure 1 Illustration of Three-Wave Panel DesignPeriod 1 P1) Period 2 P2)Time 1 T1) -+ Time 2 (T2) - Time 3 T3)Offending Offending OffendingExogenous Variables Exogenous Variables

MEASUREMENT OF EXOGENOUS VARIABLESPrevious empirical analyses of self-reported delinquency have found thatoffending is influenced by both delinquency generators and inhibitors.Among those factors that generate specific types of delinquency say, prop-erty offending) are involvement in other types of delinquency or problembehaviors (Jessor and Jessor, 1977), involvement in or social support fordelinquency by one's peers (Akers et al., 1979; Elliott et al., 1985; Matsueda,1982; Matsueda and Heimer, 1987), being male (Elliott and Ageton, 1980;Hindelang, 1971; Hindelang et al., 1981), and residing in a broken home(Austin, 1978; Canter, 1982; Hennessy et al., 1978; Hirschi, 1969; Nye, 1958).Important factors that have been shown in previous research to inhibitinvolvement in delinquent behavior include good school performance Agnew, 1985; Hindelang, 1973; Johnson, 1979; Krohn and Massey, 1980;Wiatrowski et al., 1981), involvement in and commitment to religious activi-ties (Burkett and Warren, 1987; Burkett and White, 1974; Elifson et al.,c) students moving with their parents out of the school district. In relation to the thirdsource, two of the nine high schools were located near and served a large military installa-tion in the area. These two schools evidenced greater-than-average attrition rates over timebecause one parent was transferred to a new military base. A binary logistic regressionanalysis was conducted to identify the covariates of sample attrition. The analysis revealedthat school attended was the most important predictor of attrition. Few other variableswere significant in this analysis.

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NAGIN ND PATERNOSTER1983 , attachment to conventional others such as parents and teachers(Cernkovich and Giordano, 1987; Gove and Crutchfield, 1982; Hirschi, 1969;Liska and Reed, 1985 , parental supervision (Cernkovich and Giordano,1987; Hirschi, 1969; Matsueda and Heimer, 1987; Patterson and Dishion,1985 , informal sanctions imposed by peers and family (Grasmick and Green,1980; Paternoster et al., 1983; Tittle, 1980 , perceived risk of punishment(Bishop, 1984; Grasmick and Bryjak, 1980; Grasmick and Green, 1980 , andmoral beliefs (Akers et al., 1979; Bishop, 1984; Paternoster and Triplett,1988; Silberman, 1976 . Our measures of these delinquency generators andinhibitors are described below.DELINQUENCY GENERATORS.

Two measures of problem behaviors or previous involvement in types ofdelinquency are employed here. One is a dichotomous measure of prior par-ticipation in violent delinquent acts, wherein respondents were asked toreport whether they had ever beaten up someone badly or had ever carried ahidden weapon. The second is a dichotomous measure of drug dealing,wherein respondents were asked to report whether they had ever sold drugs.Peer participation in delinquency is measured by respondents' estimates ofthe proportion of friends who had ever committed petty theft. The fourresponse options ranged from none to all. Family intactness is measuredby a dichotomous variable coded as 1 for those who reported that they livedwith other than both of their natural parents. Finally, males are distin-guished by a dichotomous variable equal to 1 for males.DELINQUENCY INHIBITORS.

School performance is measured by the respondents' self-reported grades.The scale is based on an ordered continuum from mostly F's (coded as 1to mostly A's (coded as 9 . A measure of religious commitment wasderived from responses to the following two questions: How important arechurch group activities to you? How many hours per week do you spendattending church, Sunday school or other church groups? Scale scores werebased on a sum of the two z-scores for these items. Two indicators of attach-ment to conventional others were created. One is a measure of attachment toteachers. This summed scale is based on responses to five items that askedstudents if they had a particular teacher they thought they could go to foradvice, if they liked their teachers, if they felt that their teachers understoodthem, if their teachers' approval was important to them, and if they wanted tobe the kind of person their favorite teacher was. A second measure of con-ventional attachment is based on the strength of the emotional bond to par-ents. A summed scale measuring the degree of attachment to both parentswas derived from four questions that asked respondents to report if they felt

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PAST TO FUTURE DELINQUEN Yclose to their father (mother), if they wanted to be the kind of person theirfather (mother) is,. if their father's (mother's) approval is important, and ifthey thought it helped to talk to their father (mother) if something was both-ering them. In constructing the measure of parental attachment, we assumedthat as long as an emotional bond was forged with one parent it would serveas an effective inhibitor of delinquency. For this reason the measure ofattachment to parent employed here reflects either the father or motherparental attachment score whichever evidenced the greater amount of emo-tional bonding. A summed scale of parental supervision is based on respon-dents' reports of the extent to which their parents know who they are withand where they are when outside the home.

Three different types of informal sanctions are measured here. One is ageneral measure of informal sanctions not referencing ariy specific form ofdelinquent offending. Respondents were asked to estimate how often theywould do something that is disapproved of by their teachers, father, andmother. Responses to these three items ranged on a four-point continuumand were summed to create a composite scale. In addition to this measure,two offense-specific measures of informal sanctions are included. One ofthese is a two-item composite scale of parental sanctions wherein respondentswere asked to estimate how they thought their father/mother would react ifthey committed petty theft (theft of something under $10). A second mea-sure peer sanctions, is a composite two-item scale based on responses to thefollowing two questions: How wrong do your best friends think it is to stealsomething worth less than $10? How do you think your best friends wouldreact if they knew you had stolen something worth less than $10? The per-ceived certainty of punishment is measured by respondent estimates of howlikely it was that they would be caught by the police if they were to commitpetty theft. Finally, the moral condemnation of petty theft is measured byrespondent estimates of how wrong it is to steal something worth less than 10.

We also include in the model a dummy variable distinguishing P2 from P1observations. This variable is included to capture the influence of timeeffects, such as aging by one year, that affect all members of the cohort. Wehave no a priori prediction about the sign of the coefficient of this variablewhich equals 1 for P2 observations.MEASUREMENT OF PARTICIPATION IN PROPERTY

DELINQUENCYIn this analysis we focus on property offending-stealing something worth

less than 10, stealing something between $10 and 50, and breaking into abuilding and stealing something. Several measures of self-reported involve-ment in property delinquency were constructed. Respondents at the firstwave (T1) were asked to report if they had ever committed any of the three

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NAGIN AND PATERNOSTERdelinquent acts, and if they had committed any during the previous 12months. Respondents who reported committing any of the three propertycrimes at least once were coded as 1 and nonparticipants, those who reportednone of the behaviors, were coded 0 At time 1 then, there is both a currentpast year) and cumulative ever) participation measure of property delin-quency. Current participation measures of property delinquency were alsoconstructed at both time 2 and time 3 see Figure 1 . The T2 measure reflectsparticipation in any of the three delinquent acts during the 12-month intervalfrom time 1 to time 2 period 1 , and the T3 measure reflects those acts com-mitted in the year between time 2 and time 3 period 2). Table 1 reportssummary descriptive statistics for each of the variables used in the analysisTable 1. Summary StatisticsVariable Mean SDViolence .365 .481Drug Dealing .077 .264Male .478 .499Family Not Intact .262 .440Grades 6.420 1.400Religious Attachment 000 1.620Teacher Attachment 14.300 2.420Parental Attachment 14.800 2.450Supervision 6.220 1.370Informal Sanctions 8.550 1.540Parental Sanctions 8.640 1.060Peer Sanctions 8.280 1.600Peer Behavior 1.490 .721Perceived Certainty 2.960 1.080Morality 4.710 .627Participation in P2 .146 .353Participation in P1 .161 .367Participation 1 YearPrior to P1 .165 .371Participation EverPrior to P1 .397 .489

RESULTSThe analysis proceeds through three stages. We begin by reporting the

parameter estimates of a model of participation in periods 1 and 2 in whichprior participation is excluded from the specification. The purpose of this

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PAST TO FUTURE DELINQUENCYanalysis is to document the possibility of a positive correlation between theperiod 1 and 2 disturbances, li and E2i As discussed, such a positive correla-tion is a manifestation of unobserved heterogeneity and gives rise to the ambi-guity in the interpretation of the positive association between past and futurecriminal involvement. In the second stage of the analysis, we expand thespecification of the first-stage model by adding a dummy variable indicator ofprior participation (e.g., including P participation in the specification of theP2 participation model). Assuming the unobserved heterogeneity is ade-quately captured by a random effects/one factor error specification, theresulting coefficient estimate of 8 provides a consistent estimate of the truestate-dependent influence of prior participation on future participation. Inthe third stage of the analysis, we explore alternative state dependency struc-tures and another interpretation for the state dependent-like influence that isfound in the second-stage analysis.

ESTIMATES OF STATE DEPENDENCE AND HETEROGENEITYEFFECTSTable 2 reports the results of the first-stage analysis-a two-period model

of participation in property delinquency that does not include prior theftexperience in the specification. Inspection of the results reveals that with fewexceptions the signs of the estimated coefficients conform to expectations.Consider first those estimates that are statistically significant (one-tailed testat the 5 level). Participation in theft-related delinquency is higher formales and for those who had previously participated in violent delinquentacts or dealt drugs. Also, the probability of participation is an increasingfunction of the level of delinquent activity of peers and a decreasing functionof general informal sanctions, parental sanctions, peer sanctions, and the per-ceived certainty of arrest. Only two coefficient estimates have signs contraryto expectations-religious attachment +) and parental attachment + .Only the religious attachment estimate, however, is significant at the 5level. Taken as a whole, the results are generally consistent with both priorresearch findings and theoretical expectations.Turning now to the estimate of p, which estimates the correlation between Eliand 2i, the results reveal that the estimate is positive, as expected, and highlysignificant t 6.19). Its estimated magnitude, .38, implies that about 40of the variation in li and E2i is attributable to persistent heterogeneity. Thus,the findings suggest that unmeasured heterogeneity may account for the posi-tive association of past and future participation in property delinquency.Columns 3 and 4 of Table 2 report the results of the second-stage analysis,in which prior participation is included in the specification. Inspection of theresults reveals that the addition of this variable has no material impact on

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NAGIN AND PATERNOSTERTable 2. Models of State Dependence and Heterogeneity

Variablenter eptViolence +)Drug Dealing +)Male +)Family Not Intact +)Grades -)Religious Attachment -)Teacher Attachment -)Parental Attachment -)Supervision -Informal Sanctions -)Parental Sanctions -)Peer Sanctions -)Peer Behavior +)Perceived Certainty -)Morality -T2 Dummy ?)Participation in TI +)P

Stage 1:Heterogeneity OnlyCoefficient t-Stat

1.990 3.24.270 2.60.251 1.67.461 4.04.128 1.20-. 0226 -. 65.0524 1.82-. 0296 -1.41.0054 .26-. 0487 -1.30

-. 0907 -2.68-. 0724 -1.82-. 123 -3.46

.204 3.28-. 119 -2.60-. 101 -1.46-. 153 -1.90

.378 6.19

Stage 2:State DependenceHeterogeneity

Coefficient t-Stat.926 1.89.192 2.34.134 1.12.318 3.75.0736 .92-. 0134 -. 49.0447 2.00

-. 0231 -1.3900992 6-. 0461 -1.54

-. 0777 -2.87-. 0517 -1.63-. 0595 -2.06

.136 2.64-. 0891 -2.40-. 0456 -. 81-. 107 -1.49.804 9.33

.00001 .01either the signs or significance of the coefficient estimates of the various meas-ures of delinquency inhibitors or generators.

Consider now the estimates of p and 6 which respectively are intended tocapture the influence of persistent unobserved heterogeneity and prior partici-pation on current participation. The point estimate of p is nearly equal tozero. By contrast, the coefficient estimate of 8 is positive and highly signifi-cant (t 9.34).7

The second-stage findings have several implications. First, the results areconsistent with the idea that prior participation has a genuine behavioralinfluence on future participation in property delinquency. Further, the esti-mate of 8 suggests that the magnitude of this effect is quite large. Setting allexogenous variables at their average value at time 2 the model predicts a P2

7. Two reviewers of this paper made closely linked observations. One observed thatpredictor variables such as drug dealing violence and peer behavior may simply beanother manifestation of the underlying antisocial disposition that gave rise to the self-reported thefts. Another observed that these same variables may not be exogenous. Noneof our findings regarding the relative contributions of state dependence and heterogeneity ismaterially altered if these variables are excluded from the specification.

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PAST TO FUTURE DELINQUENCYparticipation probability of .10 for an individual who did not participate inP1. The counterpart probability for an individual who did participate is.31-more than three times higher.

Second, the results suggest that the positive estimate of p from the first-stage analysis is entirely attributable to the exclusion of prior participationfrom the model. This implies that, for the population from which this samplewas drawn, the positive association between past and future participation inproperty delinquency resulting from a simple probit model is entirely attribu-table to state dependence. W e are somewhat puzzled by this finding. Asnoted previously, there is a large literature showing a positive associationbetween teen delinquency/adult criminality and factors that are at bestimperfectly controlled for in this analysis-poor parental supervision, paren-tal rejection in early childhood, parental criminality, low IQ, and so on.Thus, we expected that unobserved heterogeneity would persist to someextent even with the inclusion of measures of prior experience. We willreturn to this issue in the concluding discussion. The finding of a negligibleamount of unobserved heterogeneity in this sample does, however, imply thatfor this sample the less cumbersome, simple probit model is adequate forexploring the influence of experience prior to P2 on behavior in P2. In ourthird-stage analyses, we follow this tack.ALTERNATIVE EXPLANATIONS ND FORMS OF THE STATEDEPENDENCE EFFECTThe purpose of the third-stage exploratory analyses is twofold. First, it is

intended to examine one additional explanation for the positive associationbetween past and future participation. Second, it is intended to explore ingreater detail the possible structure of the apparent state-dependent effect thesecond-stage analysis has identified e.g., whether the influence of prior par-ticipation on future participation decays over time).

The analyses reported in Table 2 suggest that the positive associationbetween past and future participation cannot be attributed to unobserved het-erogeneity and thus, by inference, that it is attributable to a genuine behav-ioral impact of past participation behavior on future behavior. Still another non-state dependency interpretation is a concept that we call inertia. Aspreviously discussed, the probit model assumes that participation is deter-mined by the level of the latent variable y . Suppose that, regardless ofwhether an individual participates in delinquency during a given period, thehigher the level of y in that period the more likely he or she is to participatein the subsequent period. We call this inertia. The inertia concept is consis-tent with the idea that delinquent involvement is determined not only by anindividual's current social circumstances and state of mind but also by priorlevels of those influences. The concept of inertia is congenial, for example,

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N GIN ND PATERNOSTERwith Wilson s 1987) argument that long-term social isolation in an environ-ment of extreme poverty breeds antisocial behavior such as crime.

In the context of this analysis, the inertia concept implies that the level ofy* in P1, yi*, should influence Y2 and thereby participation in P2. Althoughwe cannot observe Y , we can construct an estimator from the parameterestimates of a probit model based on the P1 data. Specifically, we first esti-mated a probit model of participation using the PI data and then for eachindividual i we computed the index w~ x1ii0 where the 1subscript denotesP1 values or estimates.8

To test whether inertia is an alternative explanation to state dependence forthe positive association of P1 and P2 participation, we re-estimated a modelof participation in P2 including i as an additional regressor. The results arereported in Table 3 column 1.9 Inspection of the results reveals thatalthough the coefficient estimate of w1i is positive and significant the coeffi-cient estimate for actual participation in P1 remains positive and is highlysignificant. We conclude from this exercise that inertia does not appear to bean alternative explanation to true state dependence for the positive associa-tion between P1 and P2 participation.

State dependence can take many forms. The results reported thus far focusonly on the effect of participation in the immediately preceding period. Ifthese results are interpreted as a reflection of an actual behavioral effect of P1participation on P2 participation, a natural next step is to probe the influenceof participation prior to P1 on participation in P2. Indeed, if we found noevidence of such an effect, it would cast doubt on a state-dependent interpre-tation of the P1 association. We say this because we can think of no plausibletheoretical reason for believing that participation during the 12 monthsimmediately preceding P2 i.e., participation in P1) should have a genuinebehavioral impact but that participation more than 12 months earlier shouldhave no such impact. The 12-month measurement period is after al larbitrary.Although we expect that participation prior to P1 should be positivelyassociated with P2 participation, we also expect that the magnitude woulddecline over time. Specifically, denoting the coefficient of participation in P1by 81 and the counterpart coefficient for the one year prior to P1 by b0, we

8. Our inertia model is very similar to a model of habit persistence discussed inHeckman 1981b). The difference is that in Heckman s formulation Y2 is a function ofyl*whereas in our formulation it is a function of w2i. Heckman s formulation is more generalthan ours but would be far more difficult to estimate.9. We do not report the results pertaining to the other exogenous variables includedin the specification because the addition of w to the specification did not appreciably altereither the magnitude or statistical significance of the coefficient estimates of these variables.

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PAST TO FUTURE DELINQUENCYTable 3 Alternative Forms of State Dependence

Multi-PeriodInertia Participation InitiationModel Model Model

Variable1) Inertia w12) .312 .203 .213(2.22) (1.39) (1.46)(2) Participation in P1 .770 .708 .887(6.21) (5.57) (4.21)3) Participation one year - .182

prior to P1 (1.26)(4) Participation any time - .233 .365prior to P1 (1.78) (2.73)

5) (2) X (4) -. 221 .88)

expect that 51 8o If 5o and 81 are interpreted as a reflection of state depen-dence, this inequality implies that the behavioral influence of prior participa-tion decays with time. Such decay is consistent with the idea that priorexperience has a persistent but not immutable influence on future behavior.We believe this is a sensible prediction. By contrast, we would be skeptical ofany state-dependent interpretation of a finding that the estimate of 8oexceeded that of 81

To test this decay hypothesis, we augmented the inertia specificationwith the addition of two variables-participation in property delinquency inthe 12 months prior to time 1 and participation at any time prior to time 1.The coefficient of participation at any time prior to time 1 is denoted by yo.We anticipate that Yo > 6o because yo measures the effect of participation inthe year prior to P1 plus all participation prior to that, whereas Yo only meas-ures the effect of participation in the one year prior to P1. We make no pre-dictions about the relative magnitudes of 81 and yo because they measure theeffects of prior participation over nonoverlapping periods of different lengthsof time (i.e. 1 year versus up to 15 years).

The results are reported in Table 3, column 2. All of the coefficient esti-mates of the prior participation variables are positive, as expected, and two ofthe three-participation in P1 and participation at any time prior to l aresignificant at the 5 level or higher. Further both of the above predictionsconcerning relative magnitudes are supported. Denoting estimates with hats,81 8 and yo go The results are thus consistent with the idea that the

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N GIN ND PATERNOSTERbehavioral impact of prior participation on future participation decays overtime.

Table 3 reports one further exploratory analysis of the possible state-depen-dent influence of prior participation. As we conjectured earlier, suppose thebehavioral impact of prior participation arises principally from the first fewacts of delinquency. First-time offenders may possibly confront greater cog-nitive barriers to delinquency than an otherwise identical counterpart whohad previously engaged in delinquency. For example deterrence researchers(Saltzman et al. 1982 have found a so-called experiential effect whereby thecommission of offenses results in a reduction of one's estimate of theprobability of apprehension. This effect has been reported to be stronger forthose committing an offense for the first time, whose estimates of theprobability of apprehension were substantially higher than average than forprevious offenders. The novelty of the behavior was then, an important con-tingency of the amount of behaviorally induced change in perceptions. If inaddition to reducing the perceived probability of apprehension the initialexperience causes the individual to attach less cost to the event of apprehen-sion a state-dependent like influence will ensue.

To test this initiation hypothesis, we estimated a modified version of themulti-period specification. The modifications are as follows. First, to sim-plify participation in the one year prior to P1 is not included in the modelspecification. Thus, prior experience is captured by two dummy variableindicators: participation in P1 and participation at any time prior to P1. Sec-ond the interaction of these two dummy variables is added to the specifica-tion. This interactive dummy variable thus equals 1 if the individual hadparticipated both in P1 and prior to P1 and equals zero otherwise. If theinitial act of delinquency has an especially large state dependent-like influ-ence the coefficient of this interaction should be negative.The results are reported in the last column of Table 3. As predicted, the

interaction coefficient estimate is negative and its absolute magnitude is about50 of the estimated effect of participation prior to P1. This suggests thatthe initiation effect may be of material magnitude. We note however thatthe interaction coefficient estimate is not even close to being statistically sig-nificant by conventional standards. We interpret the results of this finalmodel specification to be sufficiently encouraging, however to warrant fur-ther investigation of initiation effects.

DISCUSSIONAt this juncture it is useful to take stock of the findings. In the first-stageanalysis a model of participation in periods 1 and 2 was estimated that did

not include prior participation among its explanatory variables. The purpose

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P ST TO FUTURE DELINQUEN Yof this exercise was to document the possibility of persistent unobserved het-erogeneity. Consistent with this supposition, the disturbances of the period 1and 2 models were found to have a positive and highly significant correlationof about .4. In the second-stage analysis prior participation was added to thespecification. The results revealed that prior participation had a positive andsignificant association with future participation, controlling for the possibilityof unobserved heterogeneity. This finding is consistent with the hypothesisthat prior participation reduces the barriers to future participation i.e., theassociation is a reflection of a true state-dependent effect). In the third-stageanalysis, the state dependency interpretation of the second-stage findings isfurther probed. This analysis revealed that even with controls for what wecall inertia, the state dependent-like association persisted. The third-stageanalysis also explored alternative structures of the apparent state dependency.These results suggest that the state dependent-like association decays withtime. Taken as a whole we interpret these results as supporting the idea thatprior involvement in illegal activity has a genuine behavioral impact on futureinvolvement.

Throughout this analysis we have attempted to take special care in depict-ing the character of the analysis as exploratory and the interpretation of theresults as suggestive. Every social scientist is familiar with the admonishmentthat correlation is not causality. This admonishment has special meaning forthe problem of distinguishing true state dependence from heterogeneity.Results can be very sensitive to distributional assumptions about the nature ofthe heterogeneity to modeling assumptions about the structure of the statedependence and to initial-condition assumptions Heckman, 1981a;Heckman and Singer, 1985). For these reasons, considerable caution isrequired in interpreting the results. Although the results are quite consistentwith true state dependency, analyses based on alternative assumptions orother data might yield very different results.

We suggest further research should proceed along two distinct but mutu-ally reinforcing lines-one empirical and the other theoretical. On the empir-ical dimension, more analyses such as this one should be performed. To ourknowledge, ours is the first empirical analysis of the question whether priorcriminal involvement has a genuine behavioral impact on future criminalinvolvement. There is no shortage of issues concerning this question thatmight be profitably examined. Among them are the following: How quicklydo any state-dependent influences decay? Does the initial act of delinquencyor criminal involvement have a particularly large influence on subsequentcriminal involvement? Does contact with the juvenile or adult criminal jus-tice system appear to have a state-dependent influence? Does involvement inone type of crime e.g., property crime) seem to alter the propensity to engagein other types of crime e.g., violent crime)? Does prior frequency of crimecommission have a positive influence on future frequency? How sensitive are

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N GIN ND PATERNOSTERthe results to alternative assumptions about the distribution of heterogeneityand the structure of the state dependence?

Differentiation of state dependence from heterogeneity requires the use ofpanel data. At a minimum, there must be measurements on each individualfor two periods. This analysis was based on such a two-period panel. Thereason this analysis did not detect any evidence of heterogeneity may be thatthe panel was too short. The ideal panel would track a cohort from preteenyears through at least young adulthood. Such a panel would have severaladvantages. First, the number of periods of measurement would far exceedthe two-period minimum. Second it would allow measurement of relevantchildhood influences. Third, it would help to finesse what is called the initialconditions problem. In most panel data sets used by criminologists, includingthe panel used in this analysis an appreciable portion of the sampled popula-tion has already engaged in delinquency prior to the initial year of the panel.Because by definition the panel does not include data on the individual'scircumstances prior to its initial period the state-dependence versus heteroge-neity interpretation of pre-initial period involvement is not easily sorted out(Heckman, 198 la). The result is what is called the initial conditions problem.If the initial period of the panel however occurs in preteen years the initialconditions problem will be minimized because few in the panel will have beenpreviously delinquent.

Along the theoretical dimension more thinking is required on the ques-tions why and how prior involvement in -crime and delinquency may alter anindividual's propensity for future involvement. As we have suggested earlier,such an influence is congenial with any number of theories of criminality, butmuch closer thinking about this question is required. Not only would suchtheorizing be valuable in its own right, but it would be invaluable in guidingmodel specification. Previously we discussed alternative mechanisms bywhich state dependence might be manifested. One of these is by altering theparameters mediating the relationship between observables and criminal pro-pensity. As we indicated, such a mechanism suggests a model specification inwhich prior experience is interacted with specific observables. Such a modelstructure is far more complex than the simple addictive specification exploredhere. It is however more informative because it can provide direct evidenceof the mechanism by which state dependency is manifested. We did not fol-low this tack for several reasons. First, we intended this analysis to be only afirst step. Thus, a simple additive specification seemed to be the appropriatepoint of departure. Second and perhaps more important, current theory pro-vides little specific guidance on the specification of such an interactive model.The state-dependence question is certainly a prime example of an issue that isbest illuminated by the interaction between theory and empirical analysis.

Although briefly stated, we have suggested a very substantial research

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PAST T FUTURE DELINQUEN Y 185

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PAST T FUTURE DELINQUEN Y 189Wilson James and Richard Herrnstein1985 Crime and Human Nature. New York: Simon Schuster.Wilson William J.

1987 The Truly Disadvantaged. Chicago: University o Chicago Press.Wolfgang Marvin E. Robert M. Figlio and Thorsten Sellin

1972 Delinquency in a Birth Cohort. Chicago: University o Chicago Press.

Daniel Nagin is professor o management in the School o Urban and Public Affairs atCarnegie-Mellon University. His current research interests include deterrence tax compli-ance and latent variable models.Raymond Paternoster is associate professor in the Institute o Criminal Justice andCriminology at the University o Maryland. His research interests include empirical testso delinquency theory the effect of perceived sanction threats in the production of con-formity and issues related to capital punishment.