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David S. Abrams, Marianne Bertrand and Sendhil Mullainathan

David S. Abrams, Marianne Bertrand and Sendhil Mullainathan, Do Judges Vary in Their Treatment of Race? , 41 Journal of Legal Studies 347 (June, 2012) (21 Footnotes)


In 2008, 38 percent of sentenced inmates in the United States were African American, with African American males incarcerated at six and a half times the rate of white males (Sabol, West, and Cooper 2010). Do these differences in incarceration rates merely reflect racial differences in criminal behavior, or are they also partly an outcome of differential prosecution or sentencing practices? A long-standing principle embedded in our system of justice is that defendants should not be treated differently because of their race. This principle is codified in the equal protection clause of the Fourteenth Amendment to the Constitution. Differential sentencing or conviction rates by race are presumably a violation of this clause, which makes this an important question to answer on legal grounds. Establishing whether courts treat minority defendants differently also has important social implications: such practices might further exacerbate social inequalities and might even lead to a self-confirming equilibrium in which expectations of racial discrimination affect criminal behavior.

Numerous studies examine this question, and most encounter empirical hurdles, particularly small sample sizes and omitted-variables biases. Although almost all proceedings in U.S. courts are a matter of public record, as a practical reality it is quite challenging to obtain a statistically significant sample size. The studies using small samples of archival data have produced mixed results. Of equal concern is the fact that cross-sectional studies suffer from a potentially severe omitted-variables bias. Apparently significant effects of the defendant's race may actually be due to omitted case characteristics that are correlated with race, such as criminal history or attorney quality. Thus, there are two potential reasons for finding a significant coefficient on race in a cross-sectional regression: discriminatory sentencing on the part of judges or juries or unobservable characteristics that drive the sentencing gap. The central difficulty with a cross-sectional methodology is that race is not randomly assigned. Therefore, any regression and interpretation thereof is likely to suffer from an omitted-variables bias.

In this paper, we take a new approach to studying the impact of race in judicial sentencing, one that avoids some of the methodological pitfalls just discussed and helps to shed light on the central issue. We attempt to determine whether there are systematic differences across judges in the racial gap in sentencing. At the heart of our research strategy is the ability to exploit the random assignment of cases to judges. This random assignment ensures that unobservable characteristics of cases and defendants are the same across judges. It allows us to distinguish between unobservable variables pertaining to cases and defendants, on the one hand, and judicial behavior, on the other hand, as explanations for a racial gap in sentencing.

Under the unobserved-variables explanation, in which no judge is discriminatory, we may see an overall difference in sentencing by race, but we do not expect systematic variation in that difference across judges, as random assignment ensures that each judge receives the same mix of cases and defendants. Under the discriminatory-sentencing explanation, as long as there is some between-judge heterogeneity in the level of differential treatment, we have the opposite prediction; that is, some judges will systematically sentence African Americans at a higher rate, and some will sentence them at a lower rate. This logic underlies the examination in this paper of whether there is significant interjudge disparity in the racial gap in sentencing.

To proceed, we use data from felony cases to compute the racial gap in the sentence length and the incarceration rate for each judge. The main empirical challenge is to identify the correct counterfactual, in which interjudge variation is due solely to sampling variability. The asymptotic F-distribution is inappropriate for this data set because of the small number of observations at the level at which random assignment occurs. This is a problem that occurs frequently in data sets involving randomization procedures for which data are collected over a long period of time. We address this problem by employing a Monte Carlo methodology to explicitly construct the counterfactual in which race has the same impact on sentencing for all judges. Besides its application to the current study, this technique could benefit a large array of empirical studies facing similar constraints without a great deal of learning costs.

We find evidence of significant interjudge disparity in the racial gap in incarceration rates, which provides support for the model in which at least some judges treat defendants differently on the basis of their race. The magnitude of this effect is substantial. The gap in incarceration rates between white and African American defendants increases by 18 percentage points (compared with a mean incarceration rate of 51 percent for African Americans and 38 percent for whites) when moving from a judge at the 10th percentile to one at the 90th percentile in the racial gap distribution. The corresponding sentence-length gap increases by 10 months, but this cannot statistically be distinguished from a situation in which race plays no role in sentence length.

Although judges differ in the degree to which race influences their sentencing, we do not find evidence that observable characteristics such as judges' gender or age group significantly predict this differential treatment by race. Similarly, no systematic pattern emerges with respect to work history (such as whether the judge ever worked as a public defender). However, there is somewhat stronger evidence that the racial gap in sentencing is smaller among African American judges. Further, judges who are harsher overall (as measured by incarceration rate) are more likely to sentence African Americans than whites to jail. We also explore an important potential confounding factor: that the heterogeneity we observe in the racial sentencing gap may actually be due to heterogeneity in treatment of the type of crime. The results of this analysis indicate that there may be a difference in treatment of drug and nondrug crimes but that there is still a heterogeneous treatment of race within nondrug crimes.

One limitation to our approach is that while we can statistically establish that race matters in the courtroom, we cannot formally detect whether this is due to some judges discriminating against African Americans or some judges discriminating against whites or a mixture of both. In itself, though, the evidence we uncover on the importance of race in judicial decision making should be of direct relevance to legal policy.

The rest of the paper proceeds as follows. Section 2 provides a brief overview of prior work on the role of race in judicial decisions. In Section 3, we describe the data from the courts of Cook County, Illinois. We discuss our econometric methodology, including the simulation procedure, in Section 4. In Section 5, we report our basic results, and we discuss the influence of the crime category in Section 6. Section 7 concludes.

. DAVID S. ABRAMS is Assistant Professor of Law at the University of Pennsylvania. MARI-ANNE BERTRAND is Professor of Economics in the Booth School of Business at the University of Chicago, SENDHIL MULLAINATHAN is Professor of Economics at Harvard University.