Research on Sentencing The Search for Reform, Volume II (1983) / Chapter Skim
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2 DISCRIMINATION IN THE CRIMINAL JUSTICE SYSTEM: A CRITICAL APPRAISAL OF THE LITERATURE
2 DISCRIMINATION IN THE CRIMINAL JUSTICE SYSTEM: A CRITICAL APPRAISAL OF THE LITERATURE
Pages 55-128
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From page 55... ...
The discretionary of the principal actors -- the police, prosecutors, judges -- are considerable and allow ample latitude unfair treatment of persons of a specific race or powers and for social background. A large empirical literature has emerged concerning the extent of discrimination in the criminal justice process.
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From page 56... ...
In order to model decisions at each stage of the criminal justice system, a theory of the important decision criteria of each of the major actors and their interaction is required. Without such a theory, estimating equations are likely to be misspecified, which in turn is likely to result in serious biases in the estimated effects of included variables and an inability to discern the effects of more subtle influences.
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From page 57... ...
(2) Sample Selection Biases Resulting from Screening and Processing Decisions The criminal justice system has been likened to a leaky sieve.
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Next we review selected studies in the context of the sample selection phenomenon and the model developed. We then discuss alternative models of the sentencing decision that do not require the use of arbitrary severity indices.
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Under these assumptions, it is well known that ordinary least squares provide consistent and unbiased estimates of the coefficient vector $. The assumptions of the classical regression model are appropriate in cases in which the dependent variable has a large, approximately continuous range of possible values.
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Most models for binary variables that have been proposed in the statistical literature can be written as p(x)
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From page 61... ...
= z if z < 0 if 0 < z < 1 if z > 1 , the PROBIT model, where F(z) is set equal to the cumulative standard normal distribution function, and the LOGIT model, with F(z)
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From page 62... ...
It can be shown that neither o2 nor b can be estimated because they are not uniquely defined.2 But the coefficient vector ~ can be estimated directly from a sample of observations on the binary variable y and x. One widely employed estimation procedure is called maximum likelihood estimation.
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From page 63... ...
. SELECTION Selection Bias The criminal justice process can be thought of as a series of stages, each involving a different set of actors.
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From page 64... ...
This introduces the possibility of sample selection bias. The type of biases that may arise can be illustrated best with an example.
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From page 65... ...
This will suggest that judges discriminate against high-SES individuals, even though there is no discrimination at the sentencing stage and there is discrimination against low-SES individuals at the stages preceding sentencing. More generally, this example points out that if there does exist discrimination against low-SES individuals at the sentencing stage, then the biases induced by sample selection might mask the true extent of the discrimination.
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From page 66... ...
Equation (ll) is the regression equation of interest: x is a K x 1 vector of nonstochastic regressors, ~ is a K x 1 vector of coefficients, and £ iS an unobserved disturbance, where the subscript i denotes the ith observation in the sample.
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From page 67... ...
The specification of I in the example would then relate the probability of conviction to a set of observable characteristics z and a set of characteristics unobservable to the investigator, represented by the disturbance u. The literature suggests that some of the factors influencing whether a criminal act ultimately results in a conviction, such as the seriousness of the crime, will also affect the sentence length.
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From page 68... ...
thus implies that the regression of y on x will not consistently estimate ~ unless x and G(-z'y) are uncorrelated.
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From page 69... ...
Of SES that is consistently estimated by the regression of y on x will be greater than or equal to Hi and will be positive if -~Ipo£rj > -hi. Thus this regression is biased toward understating the true extent of discrimination at the sentencing stage and may in fact suggest the presence of reverse discrimination at the sentencing stage if discrimination exists at the earlier stages.
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From page 70... ...
It is only in the selected population of crimes from which we sample that a correlation is induced between the observed and unobserved factors affecting the processing of a crime. It is this induced correlation that gives rise to sample selection bias.
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From page 71... ...
which measures the characteristic on which discrimination occurs, an unobservable variable x, which commonly enters each equation, and a disturbance, which represents the effects of all other unobservable factors specifically affecting each of the three stages. The presence of the unobserved factor x in each equation is what gives rise to a nonzero covariance between the unobserved variables entering each of the three equations.
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From page 72... ...
J Selection bias occurs because Y2i and Y3i are observed in selected instances and the same unobservable factor affects each of Yl, Y2, Y3. We are interested in comparing the magnitude of the inconsistency in the estimate of the coefficient of S from the regression of Y2 on S versus the regression of y3 on S
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From page 73... ...
The whites who do pass to the next stage must on average have a larger value of x than the blacks who pass to the next stage. The difference between the expected value of x for the blacks who reach the imprisonment stage and the whites who reach the imprisonment stage is equal to 82, the inconsistency in the regression of Y2 on S using the selected sample.
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From page 74... ...
finding reverse discrimination relative to regressions using less selected populations, when in reality the same amount of discrimination occurs at each stage. More generally, it might be expected that we would estimate a greater amount of discrimination at the imprisonment stage than at the punishment stage given imprisonment.
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From page 75... ...
Whether this is true depends critically on the distribution of x and the various parameters of the model. Procedures to Deal with Selection Bias If sample selection bias is operative, it is essential to consider how its effects might be isolated in order to estimate the true extent of discrimination in the criminal justice system.
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From page 76... ...
indicates that variables that enter the selection equation but not the regression equation of interest will have a nonzero coefficient in the regression equation if a selected sample is used to estimate the regression equation. But if the investigator is willing to specify that at least one of the included variables is included only because of its role in the selection of the sample, then it is possible to get a consistent m.~tim~ - of R - ~ - n i n The presence Of sample selection.
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From page 77... ...
This suggests that an attempt to measure some of these factors, by means of, for example, interviews of the relevant individuals involved in each of the cases in the sample, would reduce the magnitude of the selection bias. Experiments might be helpful in identifying the most prominent factors giving rise to a nonzero covariance between the unobserved factors affecting both selection and the regression process of interest.
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The ideal approach is to measure the relevant factors well enough to eliminate the nonzero covariance between the disturbances in the selection and the regression equations. This will eliminate the sample selection bias entirely.
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A MODEL OF THE CRIMINAL JUSTICE SYSTEM The processing of cases through the criminal justice system is a complex process, involving a number of different actors, each with individual objectives. In order to make inferences about the role of extralegal factors in the various stages of processing, it is essential to have a model of the criminal justice system.
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From page 80... ...
For example, in the Washington, D.C., superior court (which is different from the district court) only 16 percent of arrests were indicted and prosecuted as felonies in 1974 (Forst et al., 1977)
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From page 81... ...
, while not directly applicable because their estimation data set includes guilty pleas, also illustrate the important influence of case quality on the likelihood of conviction. Probably the single most important factor affecting the sentence of those convicted is the seriousness of the offense.
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Otherwise, the plea bargaining process would not persist. The high rate of guilty pleas shown in Table 2-1 suggests that plea bargaining is a common practice in the Washington, D.C., district court.
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There are no official statistics on the proportion of convictions resulting from guilty pleas. But most observers believe plea bargaining is common.
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If extralegal factors play a major role in determining case disposition, their most important influence may be at this highly discretionary and low-visibility decision point. While extralegal considerations may affect the charging decision, clearly relevant factors also have a major influence.
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From page 85... ...
These two equations form the basis of our model of prosecutorial decision making and the plea bargaining process. Our model of prosecutorial decision making borrows from Landes (1971)
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From page 86... ...
Its presence in SP reflects the assumed prosecutorial objective of maximizing expected punishment. Note that since the term u is not observed by the prosecutor, it is not included in the prosecutor's estimate of expected sentence at trial.
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From page 87... ...
Intuitively, SP < 0 implies that the expected sentence at trial less the shadow price of the resources expended in prosecution is negative. Assuming that the prosecutor's objective is to maximize expected punishment, it is rational for the prosecutor to dismiss the case and not proceed into plea negotiations when SP < 0.
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From page 88... ...
The parameter ~ measures the shadow price of defense resources. A value of ~ strictly greater than zero implies that a defendant will be willing to accept a sentence greater than the expected sentence at trial in order to avoid expending the additional time and money required to prepare and present a case at trial.
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From page 89... ...
In such cases the expected sentence if convicted at trial may not closely approximate the seriousness of the crime. However, the purpose of this model is not to provide a literal characterization of the motives and decision rules of the
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From page 90... ...
Third, the model implies that an analysis of the determinants of conviction should not mix guilty pleas and trial convictions. The model suggests that the probability of the defendant's pleading guilty is not related to the attributes of case quality known to both the defendant and the prosecutor.
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Sample Selection Bias Sample selection is a natural aspect of the criminal justice system. Cases are screened from the system at various stages.
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From page 92... ...
Two general comments can be made about these studies with regard to sample selection bias. First, if there exists discrimination at the detection and arrest stages (particularly the latter)
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From page 93... ...
Consequently, studies that account for a larger portion of the variation in sentence in the selected sample are likely to be less subject to selection bias. The second factor affecting the magnitude of the covariance is the extent to which specific unobservable case or defendant characteristics commonly affect the sentence length decision and prior selection decisions.
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From page 94... ...
. may be attributable to selection bias.
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From page 95... ...
Diserimination on the basis of race found, but only for eases where the defendant had no prior record. Discrimination found against black defendants when the victim is white at a number of processing stages, including the sentencing stage.
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While their conclusion is certainly reasonable, sample selection is an alternative explanation for their findings that we feel is equally plausible. As we argued above, studies analyzing a specific type of sanction for a specific offense are particularly susceptible to selection bias.
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As with Chiricos and Waldo, this sort of sample specificity makes the analysis particularly vulnerable to selection bias. The specifics of Gibson's findings also suggest sample selection.
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Thus their estimates of discrimination are subject to selection bias only if (1) there is some discrimination at the detection and arrest stages and (2)
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From page 99... ...
This has the advantage of mitigating the selection bias attributable to the specific charging decision of the prosecutor. Second, they did not find evidence of discrimination in the process from arrest to conviction.
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From page 100... ...
Whatever the interpretation of this variable, however, our arguments about selection are still applicable. We argued earlier that selection bias would reduce the estimate of discrimination at the sentencing stage among a sample of cases resulting in imprisonment if there was some type of discrimination occurring at the stages preceding sentencing.
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From page 101... ...
Our discussion of selection bias is at best suggestive, but it does illustrate the role that selection bias may play in the various studies. Generally, selection bias is likely to cause all the studies to underestimate the magnitude of discrimination in sentencing decisions.
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From page 102... ...
More important, guilty pleas generally dominate trial convictions in samples of convictions. Since the great proportion of guilty pleas are tendered as the result of plea bargaining, sentencing equations that are estimated on samples of all convictions primarily provide information about the factors affecting sentence in successful plea negotiations.
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From page 103... ...
We specified above that a case would result in a negotiated settlement whenever the prosecutor offered the defendant a settlement that was less than the sum of the defendant's expected sentence and a positive term reflecting the cost to the defendant of waging a trial. In many instances, the settlement that is acceptable to the defendant may be greater than the minimum settlement the prosecutor would be willing to offer (assuming no discrimination)
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From page 104... ...
Our model of the plea bargaining process also provides some guidance on how the sentence received from a negotiated settlement should be analyzed. The model suggests that the sentence in negotiated guilty pleas is a function of the seriousness of the offense and the legal and extralegal characteristics of the defendant as they interacted with the probability of conviction.
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From page 105... ...
As we noted earlier, it also provides guidance on how guilty pleas should be treated. The one issue we have not yet addressed is the implication of using an artificial index to scale the different types of sentences that are typically dispensed by judges.
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From page 106... ...
These sentence severity indices are in some respects uncomfortably arbitrary. Are there alternative approaches for analyzing sentencing decisions that do not require the investigator ex ante to impose a severity index?
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From page 107... ...
Is a prison sentence of 55 months twice as harsh as a sentence of 20 months, and is a 20 month prison sentence 2.5 times as harsh as a sentence of 18 months of supervised probation? The arbitrary cardinality of the scales may increase the difficulty of detecting more subtle influences on sentencing decisions by introducing (unnecessary)
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From page 108... ...
This constrains the decision on sanction type to be a function of the same factors that influence the decision on sentence length within each sanction type. It also greatly constrains the functional form of the two relationships.
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109 Z* lo: 111 > He On LL He Prison ~ 72 months ~~ TJ 60 months < Prison 6 72 months T]
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The width between the Tj'S coupled with a and ~ determines the range of values of the explanatory variables in _ and x that map into each sanction type. Both the coefficient vectors a and ~ and the threshold parameters Tj, j = 1, 2, .
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From page 111... ...
It also constrains considerably the way the case-specific factors can affect the choice of sanction type and the choice of sentence length within the sanction type. The model can be generalized considerably if we model the sentencing decision as a two-step decision, the first step corresponding to the choice of sanction type and the second step corresponding to the length of sentence given the sanction type.
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, K The second step can be modeled as a regression equation.
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1. The seriousness of the offense, the defendant's prior record, and his perceived threat to society may in the judge's opinion require at least some minimum term of incarceration.
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This uncertainty may be particularly great when the defendant has no prior record but has committed a serious crime. Uncertainty about the defendant's potential for reform may affect the spread between the minimum and the maximum.
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115 This notion of disparity can be extended by noting that identical cases tried by the same judge might result in different sentences (one might imagine a judge trying the same case repeatedly and having his recollection of the previous trial erased before each new trial)
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= 0 is rarely justified; as a result, it is very difficult, if not impossible, to obtain consistent estimates of the parameters from these observations alone. The problems in dealing with observational data are due primarily to the lack of comparability in the observed cases.
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117 the discriminatory variable, then the imposed sentences might be written as Yijk = H*
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118 to act out the hearing. This could be done once and recorded on video tape or it could be done repeatedly with each judge in the experiment acting as the presiding judge.
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From page 119... ...
119 seriousness of these problems. To protect against this kind of bias, an experimental format, such as personal interviews, can be used to minimize the nonresponse rate.
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This point illustrates one way in which experiments can be used in conjunction with nonexperimental data. Experiments can be used to validate results obtained from nonexperimental data or to provide alternative estimates with different biases.
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From page 121... ...
Experiments might also be useful aids for constructing models of the plea · ~ Bargaining process. In addition to providing data for analysis, experiments may also have a beneficial side effect, especially if they are conducted on a regular basis.
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From page 122... ...
failure to consider the sample selection biases that result from the many screening decisions in the criminal justice system, and (3) the use of arbitrary scales for scaling qualitatively different dispositions.
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and f2(r) are proper probability density functions.
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From page 124... ...
The imprisonment decision is made by the judge who also determines the length of the sentence. The formal distinction between the imprisonment decision and the determination of the sentence length is thus somewhat artificial.
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9. The factors giving rise to selection bias involve the stages preceding the sentence length decision and thus are not related to the true extent of discrimination in the sentence length decision of each judge.
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Sons. New York: John Wiley & 1980 Abnormal Selection Bias.
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From page 127... ...
:536-544. 1979 Sample selection bias as a specification error.
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From page 128... ...
OtMalley 1976 Punishing homicide in Philadelphia: perspectives on the death penalty. University of Chicago Law Review 43(2)
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