Do Judges Vary in Their Do Judges Vary in Their Treatment of Race?Treatment of Race?

David Abrams (U of Chicago)David Abrams (U of Chicago)

Marianne Bertrand (U of Chicago)Marianne Bertrand (U of Chicago)

Sendhil Mullainathan (Harvard)Sendhil Mullainathan (Harvard)

June 5, 2007June 5, 2007

Research QuestionsResearch Questions

Does the legal system discriminate?Does the legal system discriminate?

Are African-Americans more likely to be Are African-Americans more likely to be incarcerated?incarcerated?

Do they receive longer sentences?Do they receive longer sentences?

Standard ApproachStandard Approach

sentencesentenceijtijt = = αα + + ββraceraceijtijt + X + Xijtijt + + εεijtijt

jailjailijtijt = = αα + + ββraceraceijtijt + X + Xijtijt + + εεijtijt

Problem: Race is not randomly assigned, so Problem: Race is not randomly assigned, so betas may be biased due to unobservables!betas may be biased due to unobservables!

Our ApproachOur Approach

Use random assignment of cases to judges to Use random assignment of cases to judges to answer a related question: answer a related question:

Do judges vary in their treatment of race?Do judges vary in their treatment of race?

sentencesentenceijtijt = α + βrace = α + βraceijtijt + X + Xijtijt + Σδ + ΣδjjDDjj + + ΣγΣγjjDDjj*race*raceijtijt + mo + mott + ε + εijtijt

Test for equality of the γTest for equality of the γjj

Why is this interesting?Why is this interesting? Large variance of sentencing disparities may have Large variance of sentencing disparities may have

negative implications for perceptions of fairness of negative implications for perceptions of fairness of judicial systemjudicial system

Could also help explain different findings in different Could also help explain different findings in different studiesstudies

Legally importantLegally important Would such variation violate constitutional rights? Would such variation violate constitutional rights?

No State shall…deny to any person within its jurisdiction the No State shall…deny to any person within its jurisdiction the equal protection of the laws. equal protection of the laws. (14(14thth Amendment) Amendment)

ObjectivesObjectives

Test that cases are randomly assigned to judgesTest that cases are randomly assigned to judges

Establish counterfactual where judges don’t Establish counterfactual where judges don’t vary in treatment of racevary in treatment of race

For Both: Use Monte Carlo SimulationFor Both: Use Monte Carlo Simulation Allows for small cell sizesAllows for small cell sizes Allows for skewed Bernoulli variablesAllows for skewed Bernoulli variables

Monte Carlo SimulationMonte Carlo Simulation Use for both test of random assignment and Use for both test of random assignment and

heterogeneity in racial gapheterogeneity in racial gap Create cells at the Create cells at the monthmonth level level Simulate each observation 500 times, draw Simulate each observation 500 times, draw

simulated data from same cell, with replacement.simulated data from same cell, with replacement. For inter-judge heterogeneity in racial gap in For inter-judge heterogeneity in racial gap in

sentencing:sentencing: Create cells at the Create cells at the month-racemonth-race level level

Data Description-Chicago DataData Description-Chicago Data Circuit Court of Cook County Circuit Court of Cook County

Largest unified court system in the countryLargest unified court system in the country Main Chicago location handles 85% of casesMain Chicago location handles 85% of cases

Assignment procedure:Assignment procedure: Daily assignment of cases uses random number generatorDaily assignment of cases uses random number generator Exceptions include drugs, murder, some sex crimesExceptions include drugs, murder, some sex crimes Suburban court locations perform their own random Suburban court locations perform their own random

assignmentassignment Data includes all felony cases from 1985-2004Data includes all felony cases from 1985-2004

Over 500,000 casesOver 500,000 cases Includes charge(s), judge(s), defendant characteristics, plea, Includes charge(s), judge(s), defendant characteristics, plea,

disposition, sentencedisposition, sentence We use small subset of the dataWe use small subset of the data

MeanStandard Deviation Minimum Median Maximum

Sample: Dataset only with African Americans and WhitesNumber of Charges 2.4 5.1 1 1 266Disposition (Guilty =1) 0.92 0.27 0 1 1Plea 0.69 0.46 0 1 1Length of Incarceration (Months) 20 36 0 0 720Length of Incarceration (Conditional on Non-Zero) 42 42 0.032 36 720Fraction African American 0.86 0.35 0 1 1Fraction Female 0.17 0.38 0 0 1Age 29 10 16 27 89Probation 0.25 0.44 0 0 1Incarceration (Dummy) 0.49 0.5 0 1 1

Case CharacteristicsCase Characteristics

Judges 80Cases 34298

Case types and outcomesCase types and outcomesMean

Standard Deviation Minimum Median Maximum

By Type of ChargeDrugs 0.39 0.49 0 0 1

Violent Crime 0.16 0.37 0 0 1Embezzlement, Fraud, Theft 0.19 0.39 0 0 1

Other 0.26 0.44 0 0 1Sentence Length by Type of Charge

Drugs 15 22 0 0 360Violent Crime 24 43 0 0 480

EFT 23 31 0 3 360Other 24 48 0 0 720

Sentence Length by RaceAfrican American 21 36 0 0.19 720

White 16 33 0 0 420Sentence Length on Non-Zero by Race

African American 42 41 0.032 36 720White 42 43 0.032 36 420

Incarceration by RaceAfrican American 0.51 0.5 0 1 1

White 0.38 0.48 0 0 1Cases/Judge 432 419 10 281 1308

Judges 80Cases 34298

Bootstrapping (I) Bootstrapping (I) Testing for Random AssignmentTesting for Random Assignment

Real Data Simulation 1 Simulation …Judge Case # Date Race Race RaceWapner 1001 1/1/2000 Black Black White

1414 1/15/2000 White Black Black…

Judy 3141 1/5/2000 Black Black Black6789 3/12/2000 White White Black

…Dredd 2718 1/20/2000 Black White Black

8765 2/29/2000 Black Black White

25% 75%

25% 75%

Random Assignment ChecksRandom Assignment Checks

RaceRace GenderGender AgeAge Total Number of ChargesTotal Number of Charges Charge TypeCharge Type

Also use 10%-90% and 5%-95% rangesAlso use 10%-90% and 5%-95% ranges

Bootstrapping (II)Bootstrapping (II)Testing for Racial gap HeterogeneityTesting for Racial gap Heterogeneity

Real Data Simulation 1 Simulation …Judge Case # Date Race Sent. Length Sent. Length Sent. LengthWapner 1001 1/1/2000 Black 666 30

1414 1/15/2000 White 0 365…

Judy 3141 1/5/2000 Black 30 73006789 3/12/2000 White 3650 0

…Dredd 2718 1/20/2000 Black 7300 1095

8765 2/29/2000 Black 10500 0

Numerical ImplicationsNumerical Implications How much does the sentencing gap between black How much does the sentencing gap between black

and white defendants vary across judges?and white defendants vary across judges?

Judge Percentile Judge Percentile shiftshift

Change in Change in Incarceration GapIncarceration Gap

Change in Change in Sentence Length Sentence Length (months)(months)

25%-75%25%-75% .11.11 33

10%-90%10%-90% .18.18 1010

Robustness CheckRobustness Check

Perhaps race is a proxy for other characteristics, (such Perhaps race is a proxy for other characteristics, (such as charge) that receive heterogeneous treatment by as charge) that receive heterogeneous treatment by judges.judges.

Address this concern by looking at subsets of the dataAddress this concern by looking at subsets of the data Drug crimesDrug crimes EFTEFT ViolentViolent OtherOther

InterpretationsInterpretations

Evidence of “too much heterogeneity” in Evidence of “too much heterogeneity” in Chicago incarceration data need not imply Chicago incarceration data need not imply discrimination against Blacks.discrimination against Blacks. Suppose the “appropriate” gap is 25%Suppose the “appropriate” gap is 25% Variation in judges between 15 and 25% would be Variation in judges between 15 and 25% would be

a sign of reverse discriminationa sign of reverse discrimination

Possible approaches to deal with this issue in Possible approaches to deal with this issue in the future:the future: Recidivism? Recidivism?

Focus on Restricted SampleFocus on Restricted Sample

Eliminate “drug” judgesEliminate “drug” judges 8 judges receive only drug cases8 judges receive only drug cases Overflow drug cases are randomized among remaining judgesOverflow drug cases are randomized among remaining judges

Keep only central locationKeep only central location Can expand to other locations, but central location accounts Can expand to other locations, but central location accounts

for 85% of casesfor 85% of cases Restrict to initial appearance of defendantRestrict to initial appearance of defendant

Subsequent appearances often assigned to the same judgeSubsequent appearances often assigned to the same judge Restrict to judges known to have been regular judges Restrict to judges known to have been regular judges

under current judicial administration (through under current judicial administration (through consultation with presiding judge’s office)consultation with presiding judge’s office)