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OCR for page 129
The Role of Extralegal
Factors In Determining
Criminal Case Disposition
Steven Garber, Steven Klepper,
and Daniel Nagin
INTRODUCTION
The major participants in the criminal justice process
exercise substantial discretion. An issue that has
received considerable attention is the degree to which
the existence of such discretion results in systematic
inequities in the disposition of criminal cases. In
particular, numerous empirical studies have examined the
extent to which members of racial minority groups and/or
disadvantaged social classes are treated more harshly
because of their race or socioeconomic status.
Most of the empirical studies on case disposition use
regression and related statistical techniques.
Correlations between outcomes of the various processing
stages in the criminal justice system and measured case
and defendant characteristics are examined.
Discrimination is analyzed by testing for an empirical
association between extralegal characteristics, such as
race and socioeconomic status, and various decisions in
the criminal justice system, holding constant observable,
legally relevant case and defendant characteristics.
A fundamental problem with this approach is that many
of the important factors affecting case disposition are
We thank Alfred Blumstein, Jacqueline Cohen, and Franklin
Fisher for their helpful comments.
129
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130
extremely difficult to measure. In particular, the
seriousness of an offense and the quality of the
evidence, perhaps the two most important factors
affecting case disposition, involve important elements
for which researchers typically can observe no data.
When seriousness and case quality are correlated with
race and social status, the techniques currently being
employed yield biased estimates of the effects of
extralegal factors on case disposition.
This possibility is particularly troublesome for
studies of discrimination in the criminal justice system
because even if discrimination is present and of
sufficient concern to warrant reform, extralegal factors
are undoubtedly of secondary importance in explaining
variations in case disposition. Under these circum-
stances, biases attributable to measurement error may
dominate the estimated effects of extralegal factors.
Thus inferences about the incidence of discrimination
based on standard regression techniques may be seriously
distorted and are unlikely to provide a reliable basis
for policy reform.
One response to this problem is to measure more
accurately the primary determinants of case disposition.
However, the inherent unobservability of a number of the
components of the primary determinants suggests strongly
that this strategy is unlikely to resolve the ambiguities
that plague existing studies. We propose an alternative
approach known as structural equation modeling. It
involves explicit mathematical representation of the
fundamental mechanisms believed to generate the data.
For the study of discrimination in the criminal justice
system, it involves modeling the fundamental relation-
ships linking observable case outcomes to both their
observable and unobservable causes. If a sufficient
number of decisions affected by the unobservable
principal determinants of case disposition are observed,
it is possible to control fully for forces that cannot be
observed. It is then possible in principle to make
inferences about the extent of discrimination that are
not distorted by the inevitable lack of accurate
measurements of the primary determinants of case
disposition. The methods we propose are relatively
complex, but we know of no simpler way to control for the
effects of unobservable variables.
The paper is organized as follows. First we review
nine recent and influential empirical studies of
discrimination in the criminal justice system. The major
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131
purpose of the review is to provide motivation and
background for the discussion that follows. In the next
section we discuss statistical implications of the
impossibility of measuring accurately the primary
determinants of criminal case disposition. We then
illustrate the import of these statistical issues by
presenting alternative interpretations of various results
reported in the literature.
We then illustrate the
proposed approach by presenting a structural equation
model of criminal case disposition. We model nine
decisions affecting the criminal process, taking explicit
account of the measurement difficulties discussed. The
next section is a discussion of the estimability of the
parameters of our illustrative structural model and an
example that illustrates how the effects of unobserved
variables can be estimated. We then provide a heuristic
discussion indicating how our illustrative model aids in
the effort to obtain less ambiguous data summaries. In
the next section we indicate briefly how future studies
might take account simultaneously of the measurement
issues emphasized here and the sample selection issues
discussed in Klepper et al. (in this volume). The next
section is a brief discussion of the trade-offs in
specifying alternative structural models of the criminal
justice system. The final section contains concluding
remarks.
EMPIRICAL STUDIES OF DISCRIMINATION
I N THE CRIMINAL JUSTICE SYSTEM
This section reviews nine recent and influential studies
on the incidence of discrimination in the criminal
justice system. The studies are of three kinds: studies
of the choice of sentence given conviction, studies of
case disposition] given arrest andVor indictment, and
one longitudinal study of forcible sex offenses from
arrest through sentencing. Some of the studies analyze
samples combining dissimilar offenses, whereas others
concentrate on specific offenses ranging from theft to
murder.
We first discuss the studies of sentence given
conviction and case disposition given arrest. This is
followed by a review of studies on the various stages
preceding sentencing, beginning with the conviction
process and working backward to the choice of plea,
release on and setting of bail, choice of legal
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132
representation, charge, and the decision to prosecute.
Since only LaFree (1980a) examines separately the stages
preceding sentencing, it was necessary to supplement the
nine studies with a few additional studies of the stages
preceding sentencing. We conclude with a summary of the
major findings of the various studies.
Case Disposition and Sentencing Studies
The various studies of case disposition and sentencing
focus on a small number of common forces. They include:
(1) Seriousness of the offense. Nearly all the
studies include a measure of the charge to control for
seriousness of the offense. The exceptions are Farrell
and Swigert (1978), Swigert and Farrell (1977), and
Chiricos and Waldo (1975), which concentrate on specific
offenses.
Some of the studies also try to use characteristics of
the offense to control more completely for seriousness.
For example, Lizotte (1977:569) takes account of such
factors as whether the defendant resisted arrest, the
number of defendants, the sobriety of the defendant,
injury to the victim, and the value of property taken.
For forcible sex offenses, LaFree (1980a) considers such
factors as whether a weapon was used and the type of
offense (i.e., rape or attempted rape).
(2) Prior record. All of the studies include a
variable to represent the criminal history of the
defendant. Measures of prior record range from a dummy
variable indicating whether the defendant was ever
arrested to the total of the maximum statutory penalties
of the defendant's prior convictions.
(3) Type of legal representation. A number of
studies examine the choice of legal representation,
distinguishing no attorney, a public defender, and
privately retained counsel. The choice of legal
representation is expected to affect primarily the
probability of conviction and the sentence resulting from
a plea bargain. Legal representation is not generally
viewed as affecting sentence if the defendant is
convicted at trial, although Tiffany et al. (1975)
include a measure of legal representation in their
sentencing study of defendants convicted at trial.
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133
(4) Release on bail. A number of the studies include
a variable indicating whether the defendant was released
on bail. Being out on bail is expected to improve the
defendant's ability to develop an effective defense,
which is expected to be helpful both at trial and in plea
bargaining.
(5) Type of conviction. Some of the studies that
combine guilty pleas and trial convictions include an
additive dummy variable denoting whether the defendant
pleaded guilty. In studies of case disposition, a plea
of guilty is generally expected to lead to a worse
outcome in that it precludes acquittal. In studies of
convictions, guilty pleas are generally assumed to be the
result of plea bargains and hence are expected to result
in lighter sentences, ceteris paribus.
(6) Miscellaneous factors. Some of the studies
include the age of the defendant, whether the defendant
is employed, and the type of county (urban versus rural)
in which the defendant is convicted.
(7) Discriminatory or extralegal factors. Various
characteristics of the defendant that are not legally
relevant are included in all the studies. They include
race, socioeconomic status (SES), sex, and the racial
composition of the victim-defendant dyed. In addition,
Clarke and Koch (1976) use the average income in the
Census tract in which the defendant resides as a measure
of the defendant's income, while other studies use SES as
a proxy for income. Swigert and Farrell (1977)
distinguish a characteristic they label "normal
primitive" to denote particularly lower class, black
defendants who are (stereotypically) thought to be
disposed toward violent behavior.
The conclusions of the various studies of final case
outcome can be summarized as follows. First, virtually
all the studies that include a variable measuring the
charge found that the seriousness of the offense is the
most important factor affecting case outcome. This is
most evident for studies that analyze only convictions.
Second, all the studies conclude that the prior record of
the defendant is important. Third, all the studies that
include a variable denoting whether the defendant makes
bail infer that it is an important factor in case
outcome. Fourth, most of the studies that include legal
representation found that it affects case outcome, but
the nature of this effect varies considerably among the
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134
studies. Clarke and Koch (1976) and Tiffany et al.
(1975) conclude that for some types of cases legal
representation affects the sentence received, while Hagan
(1975), Lizotte (1977), Farrell and Swigert (1978), and
Swigert and Farrell (1977) infer that legal represen-
tation matters principally through making bail and
secondarily through choice of plea. Fifth, type of
conviction generally seems to be important: Defendants
who plead guilty fare worse on average than those who
plead not guilty (Hagan, 1975:541; Farrell and Swigert,
1978:449; Swigert and Farrell, 1977:26) but fare better
than defendants who are convicted at trial (LaFree,
1980a:850).
The inferences concerning the role of extralegal
characteristics differ considerably across the studies.
One point of agreement is that if extralegal character-
istics affect case outcome, their quantitative signi-
ficance is small compared with the other factors
discussed above. This view is consistent with Hagan's
(1974) review of earlier studies. Most of the studies
find a role for some extralegal characteristics, and
different characteristics appear to be important in
different studies. Swigert and Farrell (1977) and
Farrell and Swigert (1978) infer that for murder cases,
SES has a significant effect on case outcome, holding
constant a number of other factors. LaFree (1980a) found
that for forcible sex offenses, cases involving white
victims and black defendants are generally treated more
harshly. Clarke and Koch (1976) infer that for
burglaries and larcenies, defendants with lower incomes
are more likely to be imprisoned. They attribute most of
this effect to the correlations between income and making
bail and income and the choice of legal representation.
Tiffany et al. (1975) found that for defendants with no
prior record, blacks receive significantly more severe
sentences, holding constant a number of other factors.
Some studies that did not find a direct role for
extralegal characteristics in determining case dispo-
sition suggest an indirect role for such factors.
Hagan's (1975) results suggest that individuals with
lower socioeconomic status in Canada are charged with
more serious offenses and that charge directly affects
case outcome. Lizotte (1977) infers that race and SES
play important roles in determining whether the defendant
is released on bail, which in turn has an important
effect on case outcome. Only the results of Gibson
(1978) and Chiricos and Waldo (1975) suggest a role
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135
neither for race nor SES, although Gibson does present
some evidence of racial discrimination on the part of
some judges.2
Overall the studies suggest that low-status blacks
fare worse in the criminal justice system than other
defendants. Below we examine the information provided by
the various studies concerning the extent to which this
disadvantage is attributable to events prior to the
sentencing decision.
The Conviction Process
LaFree (1980a, 1980b) focuses on factors affecting
conviction at trial for forcible sex offenses. None of
the other studies focuses directly on the conviction
process, although Clarke and Koch t 1 qlh) nr~vi ~" =~m"
~ ~, ,= ~
evidence concerning tne conviction Process tor burglaries
. _ .
_ _ ~of: ~ _ ~. t · . ~
ana larcenies. 1nalrect evidence about the conviction
process is also provided by the studies of Lizotte
(1977), Hagan (1975), Farrell and Swigert (1978), and
Swigert and Farrell (1977), all of whom examined case
outcome following arrest or indictment.
The various studies emphasize two types of factors:
quality of the evidence and prior record of the
defendant. For forcible sex offenses, LaFree (1980b)
constructed measures of the quality of the prosecution
case and the quality of the defense case. He included
other variables, such as misconduct on the part of the
defendant and the victim's living arrangement, to proxy
for whether the alleged act was voluntary. Lizotte
(1977) also recognizes the importance of such factors.
He constructed an index that represents the availability
of 10 different types of evidence, including such factors
as the number of eye witnesses, length of time between
arrest and the incident, the recovery of a weapon, etc.
(Lizotte, 1977:568-9). Clarke and Koch (1976) also
constructed an admittedly crude measure of the quality of
the evidence using the length of time elapsed between the
offense and the arrest. LaFree (1980b) used a measure of
promptness of the report of the offense to the police.
Prior record is also cited in some of the studies.
LaFree (1980b:843) notes that despite legal procedures
intended to conceal from the jury the defendant's prior
record, it was often inferred by jurors from other
testimony or through the defendant's failure to testify.
Clarke and Koch (1976:72) conjecture that prior record
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136
might affect the prosecutor's efforts to convict the
defendant. Swigert and Farrell (1977) and Farrell and
Swigert (1978) also consider the role of prior record in
the conviction process.
The findings of the various studies suggest that both
the quality of the evidence and the defendant's prior
record affect the likelihood of conviction. LaFree
(1980a, 1980b) infers that both factors are relevant in
forcible sex offenses. Lizotte's (1977) results
concerning the role of the quality of the evidence are
inconclusive, but he attributes this to the equivocal
nature of his index when applied to different types of
crimes (Lizotte, 1977:57). Clarke and Koch (1976) found
a minor role for the promptness of arrest and an
insignificant effect of prior record, although their
results are difficult to interpret since cases settled by
guilty plea as well as at trial were considered jointly.
Only LaFree (1980a) examined the role of the race of
the defendant in affecting the likelihood of conviction
at trial. He did not find a significant role for race.
The Plea Decision
A number of the studies examined the choice of plea.
None of the studies proposes an explicit theory of the
plea bargaining process. The choice of plea is
approached in an exploratory fashion, with different
researchers examining the role of different factors.
LaFree's (1980b) analysis is the most detailed
investigation of the plea decision. He found that the
amount of evidence assembled by the defense is an
important factor in the choice of plea, with the
accumulation of more evidence lowering the probability of
a guilty plea. Concerning the role of race, he found
that black defendants were less likely to plead guilty,
regardless of the race of the victim. He was unable to
determine whether this is attributable to the attitude of
the prosecutor or the defendant or both.
Hagan (1975) also analyzed the choice of plea. He
concludes that defendants charged with more serious
offenses and represented by private counsel are less
likely to plead guilty. He found no role for race or SES.
The other study that considered the choice of plea is
Swigert and Farrell (1977). They conclude that the
single most important factor affecting the choice of plea
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137
is the perceived characteristics of the defendant, and
those classified as normal primitive are more likely to
plead guilty.
Release on Bail
Three factors are cited as affecting the decision to make
bail: the amount of bail, the income of the defendant,
and the defendant's legal representation.3 The role of
the first two factors is obvious. The role of legal
representation is less obvious and differs across the
studies that consider it.
The importance of bail amount is supported by Lizotte
(1977:5711. Clarke and Koch (1976:83) found that the
defendant's income is an important factor in the ability
to make bail. Lizotte (1977:571) provides evidence of a
role for race and SES in making bail, which he interprets
as proxies for the defendant's income. Lizotte
(1977:572) and Swigert and Farrell (1977:25) found
significant but somewhat opposite roles for legal
representation.
Setting of Bail
Only Lizotte (1977) analyzed the setting of bail,
although other studies contain speculation concerning the
determinants of the bail amount. Lizotte (1977:571)
found that seriousness of the offense, the defendant's
prior record, and the defendant's legal representation
influence the bail amount. Defendants represented by
courtroom regulars and public defenders on average are
required to post lower bonds. Lizotte (1977:566) offers,
but is not able to test, the hypothesis that the quality
of the evidence also affects the level of bail. He did
not find a significant effect of race or SES on bail
amount, although the results of Swigert and Farrell
(1977:25) on making bail suggest possible discrimination
against "normal primitives" in the determination of the
level of bail.
Choice of Legal Representation
Defendants can choose either no attorney, a public
defender, or a private attorney. (Lizotte further
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138
distinguishes between courtroom regular and nonregular
private attornies.) This choice was studied by Lizotte
(1977), Hagan (1975), Farrell and Swigert (1978), and
Swigert and Farrell (1977). Four factors are cited: the
seriousness of the offense, the prior record of the
defendant, the quality of the evidence, and extralegal
characteristics of the defendant. The seriousness of the
offense and the prior record of the defendant are
included as predictors of the sentence the defendant
would receive if convicted. The quality of the evidence
is included as a predictor of the probability of
conviction. It is expected that the greater the
probability of conviction and the more serious the
offense, the greater the incentive of the defendant to
retain higher-quality legal representation. A private
attorney is assumed to mount the best defense and no
attorney the worst. The primary extralegal character-
istic that is expected to affect the choice of attorney
is the defendant's income. Other characteristics of the
defendant are included only to proxy for income when
income is not observed.
The results of the various studies suggest that
seriousness of the offense is the most important
determinant of choice of attorney (Lizotte, 1977:570;
Clarke and Koch, 1976:83; Hagan, 1975:541). None of the
researchers was able to measure the quality of the
evidence and hence none can test its effect on choice of
attorney. However, Clarke and Koch (1976:83) found that
case outcome and choice of attorney are highly corre-
lated, those who choose no attorney having a much smaller
probability of conviction and imprisonment. Prior record
appears to affect the choice of attorney in Lizotte
(1977) and, to a lesser degree, in Swigert and Farrell
(1977): Those with more extensive prior records are more
likely to choose either no attorney or a private
nonregular attorney in Lizotte (1977:570) and a public
defender in Swigert and Farrell (1977:23). Hagan's
(1975:541) results, however, suggest that the effect of
prior record is insignificant. As for extralegal
characteristics of the defendant, the results of Clarke
and Koch (1976:83) suggest a role for income, and Farrell
and Swigert (1978:448) and Swigert and Farrell
(1977:23-24) found a role for SES, which they interpret
as a proxy for income. In contrast, Hagan (1975:541) and
Lizotte (1977:571) found no role for race or SES in the
choice of attorney.4
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139
The Charge Decision
The charge decision was analyzed in detail only by LaFree
(1980a). The role of race (alone) was considered by
Hagan (1975). For forcible sex offenses, LaFree
(1980a:850) found that the type of offense (i.e.,
attempted rape or rape), the use of a weapon, and victim
preference are important elements of the charge
decision. These variables are interpreted primarily as
measures of the seriousness of the offense (LaFree,
1980a:852). LaFree (1980a:850) also found that the
racial composition of the victim-defendant dyed affects
the charge decision; cases involving a black defendant
and a white victim led to a more serious charge. Hagan
(1975:541) also found that SES is correlated with
charge: Individuals with lower SES were charged with
more serious crimes. Hagan did not control for other
factors (such as seriousness), presumably because of a
lack of data.
The Decision to Prosecute
The only study that focused on the decision to prosecute
is LaFree (1980a). He found that for forcible sex
offenses, the charge, the presence of witnesses, the use
of a weapon, and the defendant's age are important
determinants of the decision to prosecute. These
findings generally agree with Frase's (1980) detailed
investigation of the reasons given by U.S. attornies for
dismissals. Frase found that the three factors cited
most often for dismissing a case are the seriousness of
the offense, the quality of the evidence, and the
defendant's prior record.
LaFree (1980a:850) also found that the racial
composition of the victim-defendant dyed affects th e
decision to prosecute; cases involving a white victim and
a black defendant less likely to be dismissed. Frase did
not consider the role of race or other extralegal
characteristics in his study.
Sublunary of the Major Findings
Virtually all the studies suggest that three factors ar
of particular importance in the processing of cases
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173
bargain decision into the model because most convictions
result from guilty pleas. Using the plea bargain theory
in Klepper et al. ~
. . .
(in this volume), an additional
unobservable variable representing culpability might be
introduced into the model.
Another desirable extension of the illustrative
structural model would involve use of an explicit theory
to structure the suspected correlations between race and
seriousness and case quality. In the present formu-
lation, for example, a positive estimate Of 611 would
~na~cate the existence of a correlation between race and
seriousness but would provide no information concerning
the source of such a correlation. Recall from the
discussion that the literature contains at least three
reasons to expect race and seriousness to be correlated.
If the source of the correlation is labeling, as
emphasized by Lizotte, then we might interpret this as
legislative discrimination. If the economic basis to
expect a correlation is operative, we might interpret 611
as reflecting discrimination in the labor market.
v~s~ngu~sn~ng among such possibilities would seem to be
quite desirable for policy purposes.
Finally, we might not be able to observe directly
anything about the financial capabilities of defendants.
If so, wealth could be modeled as an unobservable. Then
variables such as the average income in the census tract
containing the residence of the accused might be regarded
as a classical proxy and hence an indicator of the wealth
of the defendant. When other indicators of wealth are
observable (e.g., level of bail, release on bail, choice
of attorney) models treating wealth as an unobservable
are likely to be identified.
Finally, we briefly mention specification issues
relating to the fact that some of the indicators we have
defined may not be directly observable. In some
instances such variables are modeled as direct causes of
other indicators or latent variables. An interesting
specification issue is whether such variables should be
viewed identically in their roles as both indicators and
causes. For example, consider Y2, which was defined as
an index determining the probability that the victim
cooperates with the prosecution. This variable also
appears in equation (13) as a factor contributing to case
quality. One might interpret Y2 in equation (13) as a
dichotomous outcome determined-by the continuous-index
version Of Y2. But victim cooperation might be more
plausibly viewed as a continuous variable representing
_ . . . . . .
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174
the enthusiasm with which the victim cooperates. Similar
remarks apply to Y6 (i.e., attorney choice), which
appears as an indicator in equation (8) and a cause of
the trial outcome in equation (9). It seems clear,
however, that y3 (i.e., charge) and y5 (i.e., release on
bail) are most plausibly viewed as qualitative outcomes
of the indexes defined in equations (5) and (7) when they
appear as observable causes in equations (8) (i.e.,
choice of attorney) and (15) (i.e., the case Duality at
trial), respectively.
A useful paper in this regard is
Beckman (1978), which presents an estimation scheme for
situations involving endogenous qualitative regressors.
Finally, the fact that we observe only partial
information about various indicators raises estimation
issues, even if these variables do not also appear as
causes of other variables. Estimation would require
explicit modeling of the links between the observed data
and the indicators of the illustrative model. For
example, Muthen (1979) discusses latent variable models
with qualitative indicators. Maximumrlikelihood
techniques, while somewhat complex in this context, are
likely to provide a feasible approach to estimation
CONCLUDING REMARKS
, ~
In our view, the empirical literature on the criminal
justice system has evolved in a natural and appropriate
way. Total correlations between case disposition and
race and YES suggest an alarming degree of discri-
mination. Studies aimed at probing the source of these
correlations have attempted to control for the effects of
legally relevant variables using crude, albeit the best
available, proxies for such factors.
reviewed are of this variety.
The studies we
For the most part, they
still find evidence of discrimination, although less than
is suggested by the total correlations between case
disposition and race and SES.
The fact that inclusion of legally relevant variables
reduces the correlations between case outcomes and
variables such as race and SES provides empirical support
for theories that predict correlations between legal
factors and personal characteristics of defendants.
Under such circumstances, failure to control fully for
the effects of legally relevant factors implies that
inferences about the extent of discrimination are likely
to be erroneous. For this reason the techniques
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175
currently being used offer little hope of providing a
reliable basis for policy reform. The approach proposed
here seems like a logical next step.
Satisfactory resolution of the role of extralegal
factors in determining criminal case disposition will be
difficult. Structural equation mode ;na chest helm hill
it is not a panacea.
The restrictions in any identified
structural model are likely to be controversial. The
possibility of compatible indications emerging from a
broad range of structural models raises the hope of
developing a consensus.
NOTES
1. By case disposition we mean the outcome of a case
following arrest andVor indictment. The alternative
outcomes include acquittal, dismissal, and various types
of sentences (given conviction). Case disposition is
generally measured by an index that (arbitrarily) is
commensurate to the different types of outcomes.
2. Klepper et al.
~ . ~ . .
nine squares, these two are the most sensitive to
statistical biases due to sample selection. Conse-
quently, the extent of discrimination may be particularly
underestimated in these two studies because of the
specially selected nature of their samples.
(in this volume) argue that among the
-
3. Other factors such as prior record and extralegal
characteristics of the defendant are also cited (for
example, Swigert and Farrell, 1977:25; Farrell and
Swigert, 1978:447), but it seems these factors are
expected to operate through bail amount (only Lizotte
holds constant the effect of bail amount).
4. Although Lizotte (1977) used a strange ordering for
the quality of different types of legal representation.
5. For convenience, throughout this paper all random
variables are expressed as deviations from their means.
6. An estimator is unbiased for a parameter if its
mathematical expectation is equal to that parameter. An
estimator is consistent if in the limit as the sample
size goes to infinity, the estimates are arbitrarily
close to the parameter of interest. ~ ~
Strictly speaking,
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176
consistency of least squares requires additional (but in
this context uninteresting) assumptions concerning the
sampling process on x* and z.
7. When ~ equals one and ~ is independent of x*, z, and
u, x is called a classical measurement of x*. The
results discussed here are straightforward extensions of
results discussed by Garber and Klepper (1980) for the
case of classical measurements.
8. Formally, f = V(£)/V(xlz).
9. This result is due independently to McCallum (1972)
and Wickens (19721. For cases in which more than one
variable is measured with error, this result does not
generalize straightforwardly (see Garber and Klepper,
1980).
10. These conditions follow from
faD/8 = fPx~z[Py~x*lzV(ylx*)/py~zlx*v(ylz)] ,
where P ~x*lz and Py~zlx* are respectively the
correlation coefficients of y and x* given z and y and z
given x* and Px~z is the correlation coefficient of x
and z. This result can be derived by exploiting the
relationship between regression coefficients and-the
second moments of the respective conditional distri-
butions.
11. An especially valuable collection of theoretical and
empirical studies is Goldberger and Duncan (1973). Our
discussion borrows from Goldberger (1973), the introduc-
tory essay in this volume.
12. We consider residential thefts to include the crimes
of breaking and entering, petit larceny, grand larceny,
second-degree burglary, first-degree burglary, etc.
We avoid the plea bargain issue, despite its
importance, because of the apparent lack of any widely
held views concerning the determinants of the plea
bargain decision. Incorporation of especially contro-
versial relationships in the illustrative model could
seriously compromise our objectives.
13. In the Washington, D.C., superior court about 50
percent of all arrests are rejected at the initial
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177
screening or subsequently nailed by the prosecutor (Forst
et al., 1977).
14. We use 0's throughout for coefficients of
unobservable variables and B's for coefficients of
observable variables. The first subscript of each
coefficient refers to the indicator and the second to the
respective unobservable or observable exogenous variable.
15. Discrimination is presumed to be on the basis of
race and wealth. The two variables together can be
interpreted as the primary components of the SES of the
defendant. Alternatively, we might have introduced
another observable variable to represent the SES of the
defendant. The additon of an accurate measure of SES
would not alter the model in any fundamental way. We
assume discrimination on the basis of race and wealth
alone only to simplify the exposition.
16. Typically, the bail is paid by a bail-bonding
agency. The accused pays a nonrefundable fee based on
the amount of the bail. Equation (7) can be interpreted
as describing the decision to pay this fee.
17. Recall that we model only those cases of residential
theft disposed by a dismissal or trial verdict.
18. As will become clear with the introduction of
equation (15) below, we distinguish between case quality
before and at trial to examine the claim that release on
bail is an important determinant of the quality of the
defense.
19. As will be more clear when equation (13) and the
stochastic assumptions pertaining to £1 are introduced,
we attempt to use observable variables to control
entirely for correlation between xl* and x2*. Education
is viewed as an important correlate of each of these
variables.
20. In the section on additional specification issues,
we consider treating prior record, or more precisely all
the determinants of prior record, as known and observable.
21. Since xl*, x2*, X3*, and X4* are never observed, the
scales on which these variables are measured are
arbitrary. Until these scales are specified, the
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magnitudes of their coefficients are trivially indeter-
minate. In order to remove such indeterminacies it is
necessary to "normalize" these coefficients by directly
or indirectly specifying the units of measurement of each
of the unobservable variables. Specific normalizations
are chosen for analytic convenience. The coefficient of
x2* in equation (15) is chosen as one to specify the
scale on X4*, given the normalization (presented below),
which defines the scale of x2*.
22. Note that y5 was specified as an index variable in
equation (7) but as a dichotomous outcome in the present
equation. The complications associated with this type of
specification issue are discussed in a later section.
23. Inspection of equations (3) through (15) reveals
that w77 and V(£4) are not identified. This is obvious
since both X4* and U7 appear only in equation (9). Thus
in this model randomness in convictions (represented by
U7) cannot be distinguished empirically from random
influences on the quality of the evidence at trial
(represented by E4). This lack of identifiability is of
minimal concern since neither all nor V(~4) is of direct
interest.
2 4. The second step involves solving for the structural
parameters as functions of the reduced-form parameters
(this is illustrated by equation (7)). Use of Slutsky's
Theorem (see Goldberger, 1964:118-119) establishes that
these solutions provide a basis for consistent estimation
of the structural parameters.
25. This follows from the fact that the reduced-form
disturbances are uncorrelated with the independent
variables of the reduced form.
26. These population variances and covariances can be
computed quite simply from Table 3-2 since the ui (i = 1,
2, . . . , 9) and ej (j = 1, 2, 3, 4) are mutually
uncorrelated.
27. Various symbols (such as Y1, v1, etc.) are
redefined here in order to emphasize the analogies
between the simplified model employed here and our
illustrative model of the criminal justice process
.
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179
28. These features are the ones that enable us to
estimate the various mixtures of structural parameters
appearing in the reduced-form disturbances of our model.
29. To see how these expressions are computed, consider
for example equation (19d). Since all variables are
assumed to have zero means, the covariance of Y1 and
Y2 can be computed as
E(yl~y2) = E(8lz + Dlx* + Ul)(02Z + 02x + u2)
Equation (19d) then follows from the assumptions that z,
x*, ul, and u2 are independent and V(x*) = 1.
30. The apparently trivial nature of equation (19;)
merely reflects the fact that since z is observable its
variance can be estimated directly.
31. This expression for 81 results from the use of
equations (led), (lee), (19f), (leg), (19h), (19i), and
(19j). It can be verified straightforwardly by
substitution of these equations into equation (20)
.
32. For example, consider how we checked that y54 is
identified. Table 3-1 indicates that the coefficients of
Z3 in the reduced-form equations for y5 and y4 are
respectively Y541042023 and \042623 Division of t
former coefficient by the latter provides a solution for
r 54 and thus a basis for consistently estimating y54.
33. The assumption that r~1 exists says merely that
values of the x* and z variables and the values of the
structural disturbances uniquely determine the values of
the indicators.
34. It might be argued that race would enter into this
decision: Perhaps anticipation of racial discrimination
would affect the accused's decision concerning testi-
fying. If that is the case, however, this indicator
would still be quite valuable. Suppose that defendants
anticipate discrimination in the way described by the
other structural equations. In that case race will
affect the testimony decision through its effect on
expected sentence. This would provide other restrictions
that would be useful in disentangling the various
structural parameters associated with race.
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180
35. Dealing with sample selection requires the use of a
specific distribution because the observed sample is
viewed as a random sample from a truncated distribution.
Assuming normality per se is not required.
36. The expressions in equation (23) correspond to those
in equation (19) and are derived using results reported
in Johnson and Kotz (1970:81-83; 1972:70).
37. Perhaps the easiest way to verify this is to solve
the expressions in equation (23) for the unconditional
moments given by the expressions in equation (19). As
reported above, knowledge of these moments is sufficient
to identify all of the structural parameters. A
particularly helpful fact in checking identification here
is that a = V(yl) can be consistently estimated by the
sample variance of Y1 computed from all of the
observations on Y1.
38. Although it does complicate the form of these
moments.
39. Formally, they can be eliminated by substitution of
y4 from equation (6) into equation (7) and substitution
of Ye from equation (10) into equation (11).
40. We did not invoke these restrictions in the
illustrative model because incorporation of controversial
assumptions would compromise the major purpose of this
paper.
41. Formally, this involves assuming that the variance
of £3 (see equation (14)) is zero. The attractiveness of
such an assumption certainly depends on the extensiveness
of the available information concerning prior record.
42. Note, however, that one would not want to delete
equations representing decisions resulting in sample
selections because it is precisely the structure provided
by these equations that allows us to correct the sample
selection bias.
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181
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Representative terms from entire chapter:
criminal justice
