Post on 21-Dec-2015
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)