100 words summary

I need a summary of the article attached, approximately 100 words, also, I need your opinion of this article written by another student related to the same topic. Another 100 words

“This week’s article explains the way in which D’Alessio and Stolzenberg (1998) sought to conduct a reliable and all-encompassing study on the relationship between arrest certainty and criminal behavior. Prior to this study, there had been numerous other studies that supported the notion of a deterrence effect between criminal behavior and number of arrests made in a particular area. This means that there was an inverse relationship between the two variables; when arrests in a certain area increase, crime rates tend to decrease. This correlation ultimately gives evidence to the idea that a larger police presence and a bigger threat of punishment will cause individuals to fear the repercussions of crime and commit less of it. D’Alessio and Stolzenberg (1998) argued that, despite these studies being statistically correct, they forgot to account for a variety of other factors that could have possibly played a role in this correlation. In fact, some researchers in the past have even presented evidence to support the opposite causal effect where instead of arrests affecting the crime rate, crime rate affects the arrests that are made. A theory known as the overload effect suggests that when crime rates rise too high, law enforcement tends to feel overwhelmed and are unable to capture and commit as many offenders. 

   To begin their research, D’Alessio and Stolzenberg (1998) attempted to control for outside factors by defining three essential parts of their study. First, they tested for feedback effects which determines the accuracy of timing in criminological research. It is widely believed that crime rates affect police activity instantly while police activity affects crime rates at a much slower rate. By testing for feedback effects, the researchers can see how fast or slow data is traveled and how this affects the overall research. The second point outlined by D’Alessio and Stolzenberg (1998), and one of the most important points, is that they controlled for pretrial incarceration rates in addition to the regular arrest and crime rates.  What many previous researchers failed to account for was how the offenders being held in jail as they wait for trial impact the general crime rates in a specific area. The final point outlined for this research study was the unit of analysis being utilized. They chose to use a day as the unit of time as opposed to the standard month or year in order to obtain finer, more detailed results. 

   The results of this study, as collected by D’Alessio and Stolzenberg (1998), added more support for the deterrence theory. They found that, when controlling for pretrial detention levels, the number of daily arrests had delayed and negative effects on crime rates. Feedback data also shows that there is a split in lagged versus immediate effects. The researchers are still unsure of how this split affects the research entirely. Finally, pretrial incarceration was shown to not have any effect on crime levels. This statistic rejects the supposed incapacitation theory. Overall, the study produced a lot of interesting results despite only testing one county in the state of Florida. In the future, other studies should expand on this research by testing a multitude of counties and exploring more detailed temporal work such an hourly unit of analysis. 

CRIME, ARRESTS, AND PRETRIAL JAIL
INCARCERATION: AN EXAMINATION OF
THE DETERRENCE THESIS*

STEWART J . D’ALESSIO
LISA STOLZENBERG

Florida International University

Using longitudinal data calibrated i n daily intervals and a vector
A R M A ( V A R M A ) study design, we investigate the causal relations
a m o n g the n u m b e r of crime5 reported t o the police, the frequency of
arrest, and the n u m b e r of defendants held in pretrial jail confinement

.

Results show a lagged negative effect of frequency of arrest on reported
crime. A s the n u m b e r of wrests m a d e by police increases, the n u m b e r
of index crimes reported t o authorities decreases substantially the f o l –
lowing day. Additionally. the analysis reveals N significant positive
contemporaneous relationship between criminal activity and arrest
levels. N o feedback effects a m o n g the three variables are noted. In
s u m , o u r findings add empirical support t o the thesis that the instanta-
neous and lagged relationship between crime and clearances are of
opposite sign. That is, criniincrl activity increases arrest levels instanta-
neously, or at least relatively so, while the negative effect of arrest levels
on crime levels transpires m o r e gradually.

A fairly large and diverse body of empirical research accumulated since
the late 1960s and early 1970s reports an inverse relationship between
arrest certainty and crime rates (Blumstein et al., 1978). Studies con-
ducted at the national (Gibbs, 1968), state (Logan, 1975), county (Bailey,
1976; Brown, 1978; Tittle and Rowe, 1974), city (Chamlin, 1991; Chamlin
e t al., 1992; Tittle and Rowe, 1974), and census-tract (Kohfeld and
Sprague, 1990) levels all show this pattern. However, there are two limita-
tions to viewing these findings as unqualified support for the deterrence
hypothesis. First, a number of investigators are uncertain as to whether
arrest certainty is the cause or the effect of criminal activity (Fisher and
Nagin, 1978; Gibbs and Firebaugh, 1990). That is, if certainty of punish-
ment and crime rates are related, the causal influence could run in the
opposite direction: Criminal activity could influence certainty of punish-
ment. There are convincing theoretical expectations for such a relation-
ship. For example, it has been argued that high crime rates produce an

* This article is a revised version of a paper presented at the 49th Annual Meeting
of the American Society of Criminology, San Diego, November 19-22. 1997. We wish
to thank the anonymous reviewers for their valuable comments.

CRIMINOLOGY VOLUME 36 NUMBER 4 1998 735

736

D’ALESSIO AND STOLZENBERG

overload effect, meaning that the state’s ability to capture, convict, and
imprison offenders declines as the crime rate rises because of inelastic
police resources (Geerken and Gove, 1977). It also has been argued that
high crime rates have a desensitizing effect, thereby engendering greater
public tolerance of criminal behavior (Greenberg et al., 1979). On the
other hand, it is possible that high crime rates increase public fear, which
in turn influences the community to expend additional resources on law
enforcement and on other formal mechanisms of social control (Becker,
1968). Given the plausibility of these explanations, a compelling theoreti-
cal rationale exists for expecting that criminal activity, at least to some
degree, influences punishment levels in society.

A second and perhaps more damaging criticism of previous research is
whether the inverse relationship between arrest certainty and criminal
activity can be attributed to an incapacitative effect. Contrary to the
rationale of deterrence theory, the incapacitation thesis suggests that the
incarceration of potential offenders reduces the number of crimes perpe-
trated against the general public. To date, no study has examined the rela-
tionship between arrest certainty and crime, while simultaneously
considering pretrial incarceration levels. This neglect is problematic
because of the endemic difficulty in disentangling deterrent effects from
incapacitative effects (Blumstein et al., 1978). For example, if the crime
rate was observed to be lower in an area with a high arrest rate, one can-
not determine whether this relationship was due to deterrence or whether
it resulted from the incapacitation of pretrial defendants. The primary
reason for investigators’ failure to consider the confounding of pretrial
incarceration is because of the lack of detailed jail data. Without such
data, prior researchers have typically relied on prison incarceration or
total jail population as proxy measures of incapacitation. However,
because prison incarceration is so far removed in time from the arrest
sanction and because total jail incarceration figures include sentenced
offenders, it is exceedingly difficult to determine, with any degree of
empirical certainty, whether a negative association between arrest levels
and criminal activity resulted from an incapacitation effect.

Because all prior studies that tested the deterrence thesis at the
macrolevel are vulnerable to one or both of these criticisms, a compelling
rationale exists for questioning the validity of their conclusions. Using
daily arrest and crime data drawn from the Florida Department of Law
Enforcement and pretrial incarceration data drawn from the Orange
County Department of Corrections, we reexamine the deterrence ques-
tion. Specifically, we employ a vector autoregressive moving-average
(ARMA) procedure to examine the relations among criminal activity,
arrest levels, and pretrial incarceration levels. Our study improves on pre-
vious research in three important ways. First, in contrast to the traditional

THE DETERRENCE THESIS 737

Box-Jenkins’ methodology employed in prior research, the vector ARMA
methodology used here allows us not only to assess the contemporaneous
and lagged relationship between arrest certainty and criminal activity, but
also to directly test for feedback effects. The ability to estimate such
effects is important in macrolevel deterrence research because there is rea-
son to suspect that the instantaneous and lagged relationship between
crime and arrests is of opposite sign (Greenberg and Kessler, 1981). That
is, criminal activity most likely affects police activity instantaneously, or at
least relatively so, while the effect of police activity on crime probably
transpires much more gradually over time. The failure to model both of
these differing effects in an analysis can bias parameter estimates (Green-
berg and Kessler, 1982).

Second, we include a control for pretrial incarceration in the analysis.
Any accurate test of the deterrence thesis must control for pretrial incar-
ceration levels because deterrent and incapacitative effects are con-
founded. For example, an investigator cannot say that an inverse
relationship between arrest levels and crime levels is due to a deterrent
effect without controlling for the number of defendants held in pretrial
confinement. Likewise, an investigator cannot say that confining defend-
ants before trial reduces crime without accounting for the possibility of a
deterrent effect.

Finally, we use day as our unit of analysis. Because of ambiguity con-
cerning the appropriate lag structure between police activity and crime
levels (Loftin and McDowall, 1982), the best way to test for deterrent
effects is to calibrate data into the finest temporal aggregation possible
(Chamlin et al., 1992). By doing so, it is easier to establish time order. As
Granger (1969:430) points out: “In many economic situations an apparent
instantaneous causality would disappear if the economic variables were
recorded at more frequent time intervals.” By analyzing data calibrated in
daily intervals rather than in yearly, monthly, or weekly intervals, we are
in a better position to determine which variable, criminal activity or arrest
levels, has the more powerful effect on the other, the direction of the
effect, and the strength of the effect. Because no other study has incorpo-
rated these features in a single inquiry, our research offers a unique oppor-
tunity to assess the validity of the deterrence thesis.

BACKGROUND

Although research frequently documents an inverse association
between arrest certainty and criminal activity (see Gibbs, 1986), some dis-
agreement exists among social scientists as to what such a finding actually
means. There are currently three contrasting views of the theoretical
processes that explain this relationship: (1) the deterrence thesis, (2) the

D’ALESSIO AND STOLZENBERG

crime-punishment thesis, and ( 3 ) the incapacitation thesis. The first two of
these theses debate the causal direction of the association. While the
deterrence thesis predicts that relative increases in the certainty of punish-
ment reduce crime, the crime-punishment thesis asserts that changes in
levels of crime influence punishment levels. By contrast, the incapacita-
tion thesis assumes that the number of pretrial defendants confined in jail
affects crime rates.

Although the most widely accepted of these three interpretations is
probably the deterrence thesis, which proffers that people are free-will
actors who engage in criminal activity only after rationally weighing the
potential benefits and probable liabilities associated with such activity,
many social scientists remain skeptical of results purporting to show deter-
rent effects because of the prospect of simultaneity between the certainty
of punishment and criminal activity. Although theory concerning the
effect of crime rates on punishment certainty is broad and diverse, three
fairly distinct perspectives can be distinguished. This classification inevita-
bly simplifies some salient theore tical issues, but it does identify the essen-
tial distinctions among the perspectives.

One common thesis suggests that organizational efficiency is related to
workload. Adherents to this view maintain that because policing is consid-
ered a labor-intensive activity (Bordua and Haurek, 1971) and because
police resources tend to be relatively inelastic, at least in the short term
(McDowall and Loftin, 1986), increases in the crime rate are thought to
adversely affect police performance. As crime rates rise, the demand on
finite police resources intensifies, lowering the probability of an arrest fol-
lowing the commission of a crime. High crime rates are also thought to
decrease the state’s ability to prosecute, convict, and incarcerate offenders.
Research that has investigated this issue has generally found that
increased police workload tends to decrease the certainty of punishment
(Liska et al., 1985).

A second perspective argues that crime rates influence public attitudes,
which in turn affect law enforcement practices (Greenberg et al., 1979).
Two main variants of this argument have been advanced in the literature.
One focuses on the desensitizing aspects associated with repeated expo-
sure to crime and violence, while the other centers on the public’s concern
with rising crime levels. According to Bandura (1973), repeated exposure
to either direct or indirect violence has a desensitizing effect on individu-
als. Bandura’s claim is consistent with experimental studies showing that
frequent exposure to violence, such as watching violent television pro-
grams, not only results in a gradual blunting of emotional responses to
subsequent displays of aggression (Thomas et al., 1977), but also reduces
the speed and willingness of an individual to intervene in the violent dis-
putes of others (Drabman and Thomas, 1974).

THE DETERRENCE THESIS 739

A second variant of the public attitude thesis, commonly referred to as
public choice theory, maintains that communities respond to rising crime
levels by increasing public expenditures for law enforcement and other
crime control agencies (Becker, 1968). The allocation of additional
resources to law enforcement is thought to reduce crime by amplifying
police presence on the street and by raising the probability of an officer
being at the scene of a crime. Research findings on the relationship
between changes in crime rates and police resources (i.e., police size,
police expenditures) are mixed, however. A number of empirical studies
find that violent crime rates (Greenberg et al., 1983), property crime rates
(Chamlin, 1989), or total crime rates (Land and Felson, 1976) influence
police resources, while several other investigators report little evidence
that crime rates and police resources are related in any meaningful way
(Benson et al., 1994; Greenberg et al., 1985; Loftin and McDowall, 1982;
McDowall and Loftin, 1986). Explanations for these divergent findings
include simultaneous feedback between police resources and crime rates
(Swimmer, 1974), differences in styles of policing (Wilson and Boland,
1978), and the conversion of additional crime control resources to areas
that have little direct effect on police performance, such as higher salaries
and pensions (Blumstein et al., 1978). Differences in causal mechanisms
aside, these predictions provide a more complex view of the relationship
between the certainty of punishment and crime rates than deterrence the-
ory predicts.

Although most studies have ignored the possibility of reciprocal effects
between arrest certainty and criminal activity, some investigators have
been mindful of potential causality problems. Aggregate studies of deter-
rence typically have relied upon two research strategies to model possible
simultaneous effects. The first approach estimates panel models of recip-
rocal causation, in which arrest rates and crime rates are stipulated as both
cause and effect of each other. Studies that employ this strategy typically
include a lagged measure of arrest certainty in the analysis. The second
approach uses an autoregressive integrated moving average (ARIMA)
time-series methodology, which allows the data to aid in the determination
of the appropriate lag structure between arrest rates and crime rates.

The relative lack of correspondence in findings between panel and
ARIMA studies is quite striking. Using a multiwave panel model, which
allowed for the estimation of both instantaneous and lagged influences,
Greenberg et al. (1979) found no significant relationship between arrest
rates and crime rates in either direction. They concluded that previous
cross-sectional research examining only one-way causation had errone-
ously exaggerated the relationship between arrest rates and crime rates.
Other panel studies reached similar conclusions (Greenberg and Kessler,
1982; but see Kohfeld and Sprague, 1990; Marvel1 and Moody, 1996).

740 D’ALESSIO AND STOLZENBERG

In contrast to previous panel research, studies that used ARIMA to test
the deterrence thesis have generally evinced a strong and statistically sig-
nificant inverse lagged relationship between arrest certainty and criminal
activity (Chamlin, 1991; Chamlin et al., 1992; but see Chamlin, 1988).
Using monthly and quarterly data over 23 years (1967 to 1989), Chamlin et
al. (1992) found significant negative relationships between arrest rates and
the rates of robbery and auto theft in the monthly data. They also found a
deterrent effect for larceny crimes in the quarterly data. In another
ARIMA study that examined certainty and crime rates for seven Penn-
sylvania cities varying in population size from 5,000 to 2 million, Chamlin
(1991) reported support for the deterrence thesis for small cities, with cer-
tainty of punishment levels at about 40%.

How might the discrepancy in findings between these two different
approaches be explained? One possible explanation for these contradic-
tory findings is that the panel research design used by Greenberg and his
associates is inappropriate for testing the deterrence thesis because of
uncertainty regarding the lag structure between arrest certainty and crime
rates (Chamlin et al., 1992). Because researchers currently lack a theory
specifying how much time will pass before changes in the certainty of pun-
ishment affect crime rates (Loftin and McDowall, 1982) and because
empirical research shows both general (Ross, 1984) and specific deter-
rence (Sherman et al., 1991) effects to be short-lived, the use of fixed
yearly lags in panel studies may have underestimated the importance of
arrest certainty in reducing crime. This problem may explain in part why
panel studies, in which yearly lags were typically used, tended to find no
significant negative effect of arrest certainty on crime rates, while ARIMA
studies, in which monthly lags were employed, d o report such an effect.

However, while the findings generated from prior ARIMA studies are
clearly informative, it is questionable whether they can be adequately
interpreted as strong support for the deterrence thesis. One major short-
coming is that the traditional Box-Jenkins methodology does not allow for
the estimation of feedback relationships. The use of ARIMA in deter-
rence research is predicated on the assumption that the temporal sequenc-
ing between arrests and crime provides a sufficient basis for making
inferences about causal order. For example, Kohfeld and Sprague (1990)
maintain that the police react in time to criminal activity with immediacy,
while criminals respond in time to police sanctioning with diffusion and
delay. This delay between police activity and crime represents the time
needed for information about changes in the certainty of punishment to be
disseminated through the criminal population. If police activity and crimi-
nal activity are mutually but not simultaneous determined, it is possible to

THE DETERRENCE THESIS 741

disentangle the relationship between arrest rates and crime rates by disag-
gregating observations into highly refined temporal units (Kohfeld and
Sprague, 1990).

However, as previously discussed, the use of lags to separate out con-
temporaneous effects depends heavily upon the calibration of measure-
ment units (Granger, 1969). Even if one were to accept the theoretical
rationale of a delayed effect of arrest certainty on crime levels, the lagging
of a variable does not necessarily eliminate the problem of simultaneity
bias (Firebaugh and Beck, 1994:644). Such a bias could still be present if
the data were aggregated in large temporal units (Tiao and Wei, 1976).
Because current expectations concerning the lagged structure between
punishment certainty and criminal activity are not clearly specified in the
literature, apart from a general belief that the effect of police activity on
crime is probably not instantaneous, the use of quarterly, monthly, and
even weekly lags in prior ARIMA research may still have been too large
to separate out contemporaneous effects.

The ability to estimate not only lagged, but also instantaneous effects in
macrolevel deterrence research is relevant because there is strong reason
to suspect that these two effects are of opposite sign (Greenberg and Kess-
ler, 1981). That is, the instantaneous effect between crime and arrests is
thought to be positive and the lagged effect of arrests on criminal activity
is believed to be negative. If crime affects arrest levels contemporane-
ously and if police activity has a lagged negative influence on crime levels,
any analysis that does not allow for consideration of both of these differ-
ential effects must be rejected as inappropriate (Greenberg and Kessler,
1982). Because previous ARIMA analyses only tested for lagged arrest
certainty effects, it is questionable whether findings generated from these
studies represent the true nature of the arrest-crime relationship
accurately.

A second limitation is that prior analyses implicitly assume that any
observed inverse relationship between arrest certainty and crime is the
result of a deterrent effect. However, this assumption cannot be ade-
quately tested without also measuring pretrial incarceration because meas-
ures of deterrence and incapacitation are confounded. To date, no study
has examined the relationship between arrest certainty and crime, while
simultaneously considering pretrial jail incarceration levels. This oversight
is surprising, particularly since many arrested individuals are unable to
secure release (e.g., bail) before trial. By failing to include a measure of
pretrial confinement, previous research may have suggested a greater
direct effect of certainty of punishment on crime than is warranted. As
Sampson (1986:286) points out: “If the risk of incarceration in jail not only
deters crime but also is simultaneously influenced by the crime rate, then
estimates of the deterrent effect of sanctions will be biased.”

742 D’ALESSIO AND STOLZENBERG

Though no previous study to our knowledge has specifically controlled
for pretrial jail incarceration when examining the effect of arrest certainty
on crime, an analysis of homicide and robbery rates in 171 cities by Samp-
son (1986) suggests that the risk of jail incarceration influences crime
rates. Controlling for several known determinants of crime rates and dis-
aggregating crime-specific offending rates by age, race, and sex, Sampson
found that police aggressiveness not only had a significant deterrent effect
on robbery, but cities with higher risks of jail incarceration had dispropor-
tionately lower robbery rates. In a supplemental analysis, he also found
that the risk of jail incarceration had a significant inverse effect on bur-
glary rates. Although Sampson did not observe a relationship between the
risk of jail confinement and homicide rates, his measure of jail incarcera-
tion risk is vitiated by the inclusion of convicted offenders, who compro-
mise approximately 50% of jail populations (Perkins et al., 1995). Had
Sampson’s measure of jail incarceration been more precise, he might have
found a stronger effect on homicide rates.

Though Sampson’s study alerted us to the possible crime-reducing
effects of jail incarceration, most investigators have either ignored or
downplayed the importance of such effects in reducing crime. Some social
scientists maintain that an incapacitative effect will be relatively small
unless a high proportion of law violators are recidivists, while others assert
that the incapacitation thesis can only account for the negative relation-
ship between arrest clearance and crime if a relatively fixed pool of poten-
tial criminals exists in a given jurisdiction (Zimring and Hawkins, 1995).
Despite the hesitancy of some social scientists to consider the possibility of
an incapacitative effect, it should not be dismissed summarily. Rhodes
(1985) estimates that approximately 10% of those released pretrial in the
United States are rearrested by the police. The threat posed by this seem-
ingly small number of offenders is substantial when one considers that an
estimated 150,000 additional crimes will be committed each year by
defendants released prior to trial (Rhodes, 1985).

The purpose of this study is to investigate further the relationship
between criminal activity and arrest certainty, correcting for some of the
methodological problems encountered in earlier studies. Our focus is on
three primary questions. First, does frequency of arrest affect criminal
activity? On the basis of the deterrence assumption that people are
rational actors who weigh the likely costs and benefits of their behavior
before engaging in any given activity, we expect to find an inverse rela-
tionship between arrest levels and reported crime. Second, does criminal
activity affect arrest levels? It is possible that high crime levels may affect
police activity because of an overload effect, a desensitization effect, or a

THE DETERRENCE THESIS 743

punitive effect. Third, if causality runs in both directions, what is the rela-
tive magnitude of the effects of arrest frequency on crime and crime on
arrest levels?

In addition to analyzing the relationship between arrest frequency and
criminal activity, we attempt to determine whether the number of pretrial
defendants confined in jail has an effect on crime that is independent of
the effect of police activity. Because the number of arrests made by police
is reported to be positively related to jail incarceration levels (Welsh et al.,
1990) and because research shows that defendants charged with more seri-
ous crimes and defendants with more severe prior records are most likely
to be detained before trial (Goldkamp, 1983), it is possible that a negative
effect observed between arrest frequency and criminal activity is attributa-
ble to an incapacitative effect. To address this possibility, we derive maxi-
mum-likelihood estimates from a vector ARMA analysis that
simultaneously considers the relations among criminal activity, arrest
levels, and pretrial jail incarceration levels. We believe that the identifica-
tion of the nature and direction of the causal influences among these three
variables will enrich understanding of deterrence theory.

DATA

For our research site, we chose to focus on Orange County, Florida.
The city of Orlando, which is located in the county, is one of the largest
urban centers in the state. Practical considerations limited our analysis to
this county. Specifically, w e were constrained by the availability of pre-
trial incarceration data calibrated in daily intervals. In contrast to other
counties around the country, Orange County maintains comprehensive
and reliable jail data that are sufficiently detailed to enable us to disaggre-
gate the daily number of persons confined in the county by pretrial and
sentenced defendant classification level. The data encompass a 184-day
period, from July 1, 1991, to December 31, 1991.

Though county may be the most appropriate level of analysis of the pro-
cess of jail incarceration, since jail construction, policies, and operations
affecting pretrial incarceration are developed and implemented at the
county level, some writers argue that aggregations smaller than county or
city are most appropriate for testing the deterrence thesis. For instance,
Bursik et al. (1990) suggest that the transmission of information regarding
changes in the certainty of punishment are more likely to be enhanced by
the properties of neighborhoods than by those of larger aerial aggrega-
tions. However, while it seems reasonable to assume that people are influ-
enced more by the punishment levels of more immediate social units, we
believe that this position has been overstated in the literature. First, an
inverse relationship between arrest certainty and criminal activity has

744 D’ALESSIO AND STOLZENBERG

been observed at many different levels of aggregation (see Gibbs, 1986).
Second, it is debatable whether being receptive to social communication
regarding changes in police activity is conditioned better by smaller geo-
graphical aggregations or by other factors such as the motivation of the
individual offender (Sprague, 1982). Third, some social scientists question
whether friendship networks are actually circumscribed by bounded geo-
graphic areas. For example, Fischer (1982) and Wellman and Wortley
(1990) argue that acquaintances, friends, and kin need not necessarily live
nearby to be an important element of an individual’s personal network.
These authors argue that the frequent practice of limiting personal net-
works to bounded geographic entities is not really appropriate since the
development of effective and affordable transportation and communica-
tion networks makes long-distance relations possible and commonplace.

Our measure of criminal activity consisted of seven reported index
crimes: willful homicide, forcible rape, robbery, aggravated assault, bur-
glary, larceny-theft, and motor vehicle theft. The crime of arson was
excluded from the analysis because of problems with incomplete
reporting.

The debate about which measure to use in an analysis-number of
arrest made by police or an arrest certainty measure-remains unresolved.
Jacob and Rich (1981, 1982) believe that the raw number of arrests is the
appropriate measure of arrest certainty, whereas Wilson and Boland
(1978, 1982) maintain that risk of apprehension should be measured as a
ratio (i.e., the number of arrests made by police divided by the number of
crimes reported to police). We follow Jacob and Rich in using the fre-
quency of arrests made by police as our measure of arrest certainty. Our
use of this measure is based o n the theoretical rationale that because a
criminal’s behavior is reported to be based on fairly crude perceptions of
events (Cornish and Clarke, 1986), it is most likely that he or she is sensi-
tive to the relative frequency of the arrest sanction rather than to the mar-
ginal probability of arrest (Kohfeld and Sprague, 1990). Additionally,
Gibbs and Firebaugh (1990) suggest that there might be a problem with
what they term ”ratio correlation bias.” They maintain that because the
arrest certainty measure (i.e., arrestdcrimes) and the dependent variable
(i.e., crimes/population) used in deterrence studies have common terms
and because these common terms are likely to be measured with error, it is
possible that any observed inverse correlation between these two ratio
variables may be spurious.

The third variable of interest, pretrial jail incarceration, is measured as
the daily number of pretrial defendants incarcerated in jail in Orange
County. Drawing from the literature on incapacitation, we expect that the
number of pretrial defendants confined in jail will be inversely related to
reported crime, net of the effect of the number of arrests made by police.

THE DETERRENCE THESIS 745

The means, standard deviations, and graphs for these variables are
presented in Table 1 and Figures 1 to 5.1

Table 1. Descriptive Statistics

Mean S.D. Minimum Maximum ~- Variable

Number of Reported Crimes 169.10 24.15 98.00 240.00
Number of Arrests 53.53 22.36 8.00 104.00
Pretrial Jail Incarceration 1,493.89 66.82 1,331.00 1,651.00
Total Jail Incarceration 3,396.46 116.88 3,147.00 3,634.00
Arrest Certainty .31 .13 .06 .57

METHOD OF ANALYSIS

We used vector ARMA to estimate the relations among criminal activ-
ity, arrest levels, and pretrial incarceration levels. Although primarily
employed by statisticians and economists, vector ARMA has been used by
a few sociologists to examine trends in school victimization (Parker et al.,
1991) and to investigate the relationship between alcohol treatment and
cirrhosis mortality (Holder and Parker, 1992). Vector ARMA is a fully
recursive statistical procedure, which allows us to test for contemporane-
ous, lagged, and feedback relationships among two or more variables.
Formally, the vector ARMA model is described as: $ ( B ) Z t = e(B)E,, where
4 is a matrix of autoregressive parameters, 8 is a matrix of moving-average
parameters, 2, is a stationary vector of time series containing n observa-
tions, and E, is a vector of random shocks that are independently, identi-
cally, and normally distributed with a zero mean and stable variance.

The methodology for constructing a vector ARMA model consists of
three stages: (1) tentative model specification, in which sample cross-cor-
relation and partial cross-correlation matrices are used to specify the order
of the vector ARMA process; (2) estimation, in which efficient parameter
estimates are obtained by maximizing the likelihood function; and (3)
diagnostic checking, in which model deficiencies are identified by a cross-
correlation analysis of the residual series.

To estimate our model, we used the MTS software package from Auto-
matic Forecasting Systems (Reilly, 1986). The identification routine in
MTS computes and plots sample autocorrelation matrices and a partial lag
correlation matrix. These matrices allow us to identify the appropriate
AR and MA orders. In a VARMA (p,q) model, p is the number of

1 . The means and standard deviations for each of the variables suggest that a
sufficient degree of variability exists to expect modest effects to emerge in the analysis.

746 D’ALESSIO AND STOLZENBERG

Figure 1. Number of Reported Crimes, by Day, July 1,
1991-December 31, 1991 ( N = 184)

Number

250 1

autoregressive parameters, and q is the number of moving-average param-
eters. Once the model is identified, the MTS program uses a moment esti-
mation routine (conditional least squares) to estimate the maximum-
likelihood parameters (Spliid, 1983). If the estimated model fits well, the
residual autocorrelations for the model will be small and weakly related
(Tiao and Box, 1981).

The relations among the variables of interest can be assessed in the fol-
lowing manner. First, if the matrices for @ ( B ) and 8 ( B ) are lower triangu-
lar, it would suggest that the variables in the model are not causally related
in the sense of Granger (1969). Second, if the matrices for @ ( B ) and 8 ( B )
are block triangular, it would indicate the existence of a unidirectional
relationship. Finally, if an off-diagonal value in the error correlation
matrix ( C ) is statistically significant, it would suggest an instantaneous
relationship between two variables at the zero lag.

RESULTS
PRIMARY ANALYSIS

Initially, we analyzed each of the three series separately. Unit root
tests, following the procedure advocated by Dickey et al. (1986), led us to
analyze first differences of each of the three series. However, while the
augmented Dickey-Fuller tests indicated that each of the univariate series

THE DETERRENCE THESIS 747

Figure 2. Number of Arrests, by Day, July 1,
1991-December 31, 1991 ( N = 184)

Number

100

80

60

40

20

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181

Day

was nonstationary, it is possible that a linear combination of two or more
of the series was stationary. Such a situation is referred to as cointegra-
tion. If two or more of the series are cointegrated, differencing is not rec-
ommended. We tested for the presence of cointegration using the
procedure suggested by Engel and Granger (1987). Specifically, we com-
puted three regressions of the form:

i = l ; i # j

(‘j = 1, . . ., 3). We then estimated augmented Dickey-Fuller tests on the
residuals(&,,) of each of the regressions. Our results indicated that first
differencing was appropriate since none of the series appeared to be
cointegrated.

Table 2 reports the maximum-likelihood estimates for a VARMA (1,l)
model. The residuals for this specification satisfied all the diagnostic
requirements suggested by Tiao and Box (1981) to ensure model ade-
quacy.2 Several interesting findings emerge from inspection of the
autoregressive (5) and moving-average ( e ) matrices. First and most

2. A visual inspection of the autocorrelation and the partial lag correlation matri-
ces suggested a seasonal component in the reported crime series. Criminal activity on
Sundays was significantly lower than on the other six days of the week. To account for

748 D’ALESSIO AND STOLZENBERG

Figure 3. Pretrial Jail Incarceration, by Day, July 1,
1991-December 31, 1991 ( N = 184)

1700

1650

1600

1550

1500

1450

1400

1350

1300

important, we observe a negative and statistically significant delayed effect
of frequency of arrest on criminal activity (& < 0). As the number of arrests made by police for index crimes increases, criminal activity decreases substantially the following day. This finding provides empirical evidence for the theoretical arguments articulated by proponents of deter- rence theory.

Second and contrary to predictions derived from the incapacitation the-
sis, our findings do not lend credence to the importance of pretrial jail
confinement as a factor in reducing either crime fi13 = 0 and a,, = 0) or
arrest levels (&, = 0 and 8,, = 0). Although we suggested previously that
crime and arrest levels may be inversely related as a result of an incapaci-
tation effect, our results do not bear this prediction out. The most salient
predictor of current pretrial jail incarceration levels is past levels (& > 0
and e,, > 0). Somewhat surprisingly, our analysis demonstrates that the
daily number of arrests made by police is inconsequential in determining
pretrial incarceration levels ($32 = 0 and e,, = 0). Although previous

this systematic difference, we included a dummy coded variable (1 = Sunday, 0 = other-
wise) in the analysis as a statistical control. As expected, this seasonal variable had a
strong effect on criminal levels.

THE DETERRENCE THESIS 749

Figure 4. Total Jail Incarceration, by Day, July 1,
1991-December 31, 1991 ( N = 184)

Number
3700

3600

3500

3400

3300

3200

3100
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181

Day

research assumed that police activity was important for understanding var-
iations in jail incarceration levels, our analysis undermines this assump-
tion. In addition, criminal activity has no salient causal effect on pretrial
jail incarceration when preexisting incarceration trends are taken into
account (& = 0 and e,, = 0). The weak influence of both arrest and crime
levels on pretrial incarceration levels is probably attributable to our reli-
ance on vector ARMA, which is generally considered to be a conservative
statistical procedure. Our results also show that criminal activity has no
lagged effect on arrest levels (& = 0 and & = 0).

A third interesting finding is that an examination of the error correla-
tion matrix (2) reveals a positive, contemporaneous relationship between
criminal activity and arrest levels. As previously discussed, a contempora-
neous relationship between components of a vector series can be modeled
through the off-diagonal elements of the error correlation matrix. Using
the information provided in this matrix, w e estimated the correlation
between the residuals for crime and arrest frequency at the zero lag to be
.16. Although this correlation is somewhat small in magnitude, it is still
statistically significant at the .05 level of analysis. In contrast, the residual
correlations at the zero lag between criminal activity and pretrial incarcer-
ation and between arrest frequency and pretrial incarceration are not of
substantive importance. Our finding of an instantaneous relationship

750 D’ALESSIO AND STOLZENBERG

Figure 5. Arrest Certainty, by Day, July 1, 1991-December
31, 1991 ( N = 184)

Ratio (ArrestKrime)

0.6

0.5

0.4

0.3

0.2

0.1

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181
Day

between criminal activity and arrest levels tends to cast doubt on the argu-
ment that increased police workload reduces certainty of punishment.
Rather it appears that rising crime levels, at least in the short term, are
increasing the number of arrests made by police.

However, it is important to recognize that the contemporaneous rela-
tionship depicted in Table 2 is not entirely incompatible with deterrence
theory. After all, a contemporaneous relationship between two variables
might be (1) unidirectional (i.e., the association is entirely attributable to
the effect of one of the variables upon the other, (2) bidirectional (i.e.,
each variable affects the other significantly and equally), (3) predominant
(i.e., each variable affects the other significantly but the effect of one is
greater than the effect of the other, or (4) countervailing (i.e., the effect of
one on the other is positive while the effect of the second variable on the
first is negative). For example, it is entirely possible that criminals respond
to changes in police activity within a 24-hour period. Thus, although we
calibrated the data into the finest interval possible so as to better deter-
mine causality, w e cannot definitely say on the basis of our analysis
whether this contemporaneous relationship was solely the result of police
reacting to criminal activity. What we can say, however, is that our finding
of a contemporaneous relationship between crime and arrest levels lends

THE DETERRENCE THESIS 75 1

Crime

Arrests

Pretrial

Table 2. VARMA Maximum Likelihood Estimates of the
Relations Among Crime, Arrests, and Pretrial

Jail

Incarceration

. -.219
(3.01)

0 .
0 ,419

Crime Arrests Pretrial

,739 .
0 ,838

(11.31) . ,799
(4.71)

—
(9.53)

z x 102
Crime Arrests Pretrial —

I 4.018

,551 2.725

,075 .007 ,094

NOTE: t score in parentheses. The results are presented in matrix form. The significant coefficient
in the (1,2) position indicates that arrest levels influence crime levels at lag -1. If the coefficient in
the (2.1) position was statistically significant, it would indicate that criminal activity affects arrest
levels at lag -1. If the coefficients in the (1,2) and the (2.1) positions were both significant, it would
indicate that there was feedback between crime levels and arrest levels at lag -1. Because VARMA
uses an iterative process to derive parameter estimates, only the s i w c a n t coefficients are
reported in the final model. The results of the preliminary iterative stages of each of the VARMA
analyses conducted in this study can be obtained from the authors on the request.

more support to the thesis that criminal activity is affecting arrest levels
than to the reverse.

SUPPLEMENTAL ANALYSES

We conducted two supplemental analyses to ensure that our original
findings remained robust across different specifications. First, because an
anonymous reviewer thought it prudent to determine whether our findings
would vary depending on the incapacitation measure employed, we esti-
mated a separate vector ARMA equation using total jail incarceration
rather than pretrial jail incarceration as one of our three variables of theo-
retical interest. The results of this analysis, which are presented in Table 3,
are nearly identical to the findings generated in our original analysis. The
effects of each of the variables of interest, or lack thereof, remained stable.
We again observed a contemporaneous and a lagged relationship between
criminal activity and frequency of arrest. No substantive relationship
between total jail incarceration and criminal activity was noted. In fact,
when we considered total rather than pretrial incarceration, the magnitude
of the incapacitative effect decreased. At the zero lag, for example, the
correlation between criminal activity and pretrial incarceration was .13. In
contrast, the contemporaneous relationship between criminal activity and
total jail incarceration was .11. The most likely explanation for this
reduced effect is that the total jail incarceration measure is vitiated b y the
inclusion of offenders held for other counties, state offenders, federal
offenders, and a variety of other types of offenders. As a consequence,

752 D’ALESSIO AND STOLZENBERG

-.219 ’
(3.01)

0 e .

. . .

one might expect total jail incarceration to have a weaker overall effect on
criminal activity than pretrial jail incarceration.

.

Table 3. VARMA Maximum Likelihood Estimates of the
Relations Among Crime, Arrests, and Total Jail
Incarceration

Crime
Arrests
Jail

a, z x 102
Crime Arrests Jail

,739

0 ,838
(1 1.31)

—
(9.52)

. . .

Crime Arrests Jail —
’ 4.022

.555 2.124

,098 ,076 ,184

NOTE: t score in parentheses. Additionally, if we carried out the autoregressive and moving-
average coefficients for the crime and arrest variables more than three decimal places, they would
be slightly different from the same coefficients reported in Table 2.

A second analysis was also conducted using an arrestkrime ratio varia-
ble as our deterrence measure. This ratio variable was created by dividing
arrest frequency by the number of crimes reported to police. The robust-
ness of the results for this analysis, presented in Table 4, is clear. The
lagged effect of the arrestkrime ratio variable on criminal activity is large
in magnitude and of substantive importance. This finding buttresses the
contention that current police activity is a salient predictor of future crime
levels. Visual inspection of Table 4 also shows an instantaneous relation-
ship between certainty of punishment and crime levels, but the sign of the
coefficient is negative rather than positive. The reason that the sign of the
coefficient for arrest certainty changed direction is not clear since “the
vector ARMA model is careful not to attribute contemporaneous relation-
ships to effects in either direction” (Heyse and Wei, 1985:lSO). What is
clear, however, is that the causal processes linking crime and arrests
appear to be contingent on time. That is, one process appears to operate
instantaneously, or relatively so. and the other seems to operate more
gradually. Taken in total, our initial results-and the results of our supple-
mental analyses-all tell the same story: There is strong evidence that
police activity is an important factor in determining future crime levels,
whereas both pretrial and total jail incarceration appear to be less salient.

CONCLUSION
We began this article by noting that although a number of empirical

studies have reported an inverse association between arrest certainty and
criminal activity, several social scientists have raised important questions
concerning the bearing of this relationship on postulated processes. One

THE DETERRENCE THESIS 753

‘ 3.989

-.364 ,916

,072 -.016 ,095

Table 4. VARMA Maximum Likelihood Estimates of the
Relations Among Crime, Arrest Certainty, and
Pretrial Jail Incarceration

Crime

Certain

Pretrial

91 el z x 102
Crime Certain Pretrial Crime Certain Pretrial Crime Certain Pretrial —

I -.122 -.373
(2.04) (2.86)

. ,416
(2.68)

—
‘ ,686

,764
(10.27)

,795

(6.97)

NOTE t score in parentheses.

question centers on the reciprocal nature of the arrest-crime relationship.
Does police activity influence crime levels, or does criminal activity affect
arrest levels? Another question concerns the extent to which any inverse
relationship between arrest levels and criminal activity can be attributed to
an incapacitative effect.

Although no single study can definitely answer these complicated ques-
tions, our analysis attempted to provide a more accurate appraisal of the
relationship between criminal activity and arrest levels than previously
available. Using daily data and a vector ARMA statistical procedure, we
tested for instantaneous, lagged, and feedback effects among crime levels,
arrest levels, and pretrial incarceration levels. Results showed that con-
trolling for pretrial incarceration levels, the number of daily arrests made
by police and a certainty of punishment measure had delayed, negative
effects on criminal activity. These findings are in accord with the tenets of
deterrence theory.

Findings from the vector ARMA analyses also lend credence to the the-
oretical importance of criminal activity as a factor in determining arrest
levels. Rather than responding solely to the number of arrests made by
police, criminal activity and arrest levels were correlated at the zero lag.
Taken in total, these results speak to the validity of the claim made by
previous investigators that the causal processes linking crime and arrests
are contingent on time. That is, it appears that criminal activity has a rela-
tively immediate impact on arrest levels, while the effect of police activity
on crime levels seems to transpire more gradually (Greenberg and Kess-
ler, 1982; Kohfeld and Sprague, 1990).

These findings, tentative though they be, have important theoretical
implications for understanding the deterrence process. First, the evidence
presented here, which is based on a more sophisticated analysis than used

754 D’ALESSIO AND STOLZENBERG

in previous studies, suggests that using either frequency of arrest or a cer-
tainty of punishment ratio measure does not really make a great deal of
difference in testing for deterrent effects since both measures produced
nearly identical results. Second and somewhat surprisingly, it took only
one day for a deterrent effect to manifest itself. The question that remains
unanswered is why a one-day lag? Despite the importance of information
diffusion in the study of general deterrence, no studies to our knowledge
have assessed empirically the speed at which information regarding
changes in police activity is transmitted through the population. Even so,
our finding of a one-day lag is consistent with the operation of news diffu-
sion processes described by a number of researchers.

The rapid speed at which important news stories are disseminated
through the population is one of the most consistent findings in the com-
munication literature. Across a variety of samples, methods, and news-
worthy events, researchers have repeatedly shown that news regarding
events such as the death of Franklin D. Roosevelt (Miller, 1945), the
attempted assassinations of President Ronald Reagan (Gantz, 1983) and
Governor George Wallace (Steinfatt et al., 1973), and the Challenger
space shuttle disaster (Mayer et al., 1990) spreads rapidly through the pop-
ulation. In a meta-analysis of the results of 34 news diffusion studies, cov-
ering 45 years, from 1945 to 1990, Basil and Brown (1994) found that most
people surveyed were made aware of a given news story within a 24-hour
period. This pattern of rapid diffusion of information remained robust
despite factors such as type of news story, geographic location, and demo-
graphic characteristics of respondents. Person-to-person communication
was frequently the primary source of information rather than newspapers,
radio, or television. Even more relevant to deterrence theory is that infor-
mation regarding a “potential risk” tends t o be disseminated much more
rapidly by individuals than other types of information (Weenig and Mid-
den, 1991).

These studies’ findings have important implications, not only because
they have been replicated numerous times and across different types of
news stories, but because they bear directly on current debates regarding
the timing of deterrent effects. Because existing theory has failed to fur-
nish any basis for either the timing or longevity of deterrent effects,
researchers have generally relied on yearly, quarterly, monthly, or weekly
data to test for deterrent effects. However, based on the findings
presented here and on the findings reported in the news diffusion litera-
ture, it appears that this practice may be theoretically unjustifiable. There
is every reason t o assume that the dissemination of information is occur-
ring much more rapidly than previously thought. Thus, if one accepts the
argument that a short delay exists between changes in police activity and

THE DETERRENCE THESIS 755

changes in crime levels, one must reject the use of long lags to test for
deterrent effects.

Another interesting finding was the lack of any empirical evidence sup-
porting the incapacitation thesis. Both pretrial and total jail incarceration
levels had no statistically discernible effect on reported crime levels. It is
fruitful to ask why the hypothesized linkage was not found. We offer two
plausible explanations that warrant consideration. One possibility is that
because current practices already confine a substantial proportion of high-
risk offenders behind bars, a diminishing marginal return can be expected
by further increases in incarceration levels.3 This argument has been
articulated rather convincingly by a number of social scientists (Canela-
Cacho et al., 1997; Zimring and Hawkins, 1995). A second explanation for
our null finding relates to the prevalence of juvenile crime and the confin-
ing of juveniles in local jails. Juveniles currently account for a large per-
centage of the serious crime committed in the United States. For example,
while juveniles between the ages of 10 and 17 constituted about 25% of
the population, they accounted for 19% of the arrests for violent crimes
and 35% of the arrests for property crimes in 1994 (Federal Bureau of
Investigation, 1995). For some crimes such as homicide, the situation is
even more disturbing. Over the past decade the rate of homicide commit-
ted by teenagers between the ages of 14 to 17 has more than doubled. It
increased more than 170%, from 7.0 per 100,000 in 1985 to 19.1 in

1994

(Fox, 1996). However, while juveniles are responsible for a sizable pro-
portion of the crime experienced in society, they are typically not confined
in jail before trial. For example, although juveniles accounted for over 9%
of the arrests in Orange County during the study period, they comprised
less than 1% of the pretrial jail population.4 Thus, because juveniles are
usually not confined in local jails, it seems likely that pretrial jail incarcera-
tion levels would have relatively little effect on reducing juvenile crime.

However, certain caveats must be considered. First, the findings
reported here must be replicated with other data sets before they can be
accepted without question. Because this study focused on one large
county, it is somewhat difficult to draw inferences about the general-
izability of our findings. As a consequence, future investigators should
consider replicating this analysis in other jurisdictions. The more fre-
quently such research is conducted, the greater confidence can be placed
in the generalizability of our findings to different times and places.

Second, there will always remain a question as to whether the evidence

3. Approximately 3,572 offenders from Orange County were confined in state

4. However, approximately 1,743 juvenile offenders were detained in juvenile
prisons on June 30, 1997.

detention facilities in Orange County during fiscal year 1996-97.

D’ALESSIO AND STOLZENBERG

presented here suffices to discredit the incapacitation thesis. For example,
one could make a reasonable argument that a longer period of observation
would be needed to support an incapacitative effect. Although it would
have been desirable to extend the period of analysis, difficulties in
obtaining the data precluded extending the series.

Third, the contemporaneous relationship between criminal activity and
arrest levels should be disentangled in future empirical work. Specifying
more precisely the underlying causal mechanisms of this association will
lead to a better understanding of the deterrence process. Although such
an exploration can be addressed within the analytic framework presented
here, the data necessary for such an undertaking must be calibrated into
even finer temporal units. Unfortunately, most analysts will probably find
it difficult to obtain data calibrated in hourly intervals. Nonetheless, the
work presented here has come considerably closer to disentangling deter-
rent effects from both saturation and incapacitative effects. Additionally,
the analytic procedure employed here has the potential to advance under-
standing of a wide range of similar phenomena about which contempora-
neous, lagged, and feedback relationships are theorized to occur.

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Stewart J. D’Alessio is an Assistant Professor in the School of Policy and Manage-
ment at Florida International University. He received his Ph.D. in criminology from
Florida State University. He also served previously as a captain in the U.S. Army, and
he participated in “Operation Just Cause” and “Operation Desert Storm.” His current
research focuses on deterrence theory.

Lisa Stolzenberg is an Assistant Professor in the School of Policy and Management at
Florida International University. She also received her Ph.D. in criminology from Flor-
ida State University. Her publications have appeared in the American Sociological
Review, Criminology, Journal of Criminal Justice, Justice Quarterly, and a variety of
other scholarly journals. She is also the co-editor of Criminal Courts in the 21st Cen-
tury, which is forthcoming from Prentice-Hall.

762 D’ALESSIO AND STOLZENBERG