Alfred Blumstein, Kiminori Nakamura
Heinz College - Carnegie Mellon Univ.
March 27, 2009
1

 Old Fogy: “We shouldn’t computerize criminalhistory records because computers don’t understand the Judeo-Christian concept of redemption”
 Rejoinder: “Paper records certainly don’t understands that concept, but computers can certainly be taught”
 This paper is developing information on what to teach the computers
2

 Technology has made background checking easy - and so very ubiquitous
 Most large companies now do background checks (~80%)
 Statutes require background checks for many jobs
 Criminal records are also ubiquitous
 Lifetime probability of arrest > 0.5
 14 million arrests a year
 71 million criminal records in state repositories
 90% of the records are computerized
 Criminal records have long memories
 Many people are handicapped because of an arrest or conviction that happened long ago, and so is “stale”
3

 We know from much research that recidivism probability declines with time “clean”
 At some point in time, a person with a criminal record who remained crime-free is of sufficiently low risk that the “stale” record no longer contains useful information
 Need a basis for establishing when redemption from the prior mark of crime occurs
 We still have no measures of redemption time
 Also, we want to know how it varies with age and crime type at the prior arrest
4

 Lack of empirical evidence leaves employers to set arbitrary cut-off points
 5 or 10 years (nice round numbers)
 7 years (Biblical origins?)
 15 years (conservative)
 Forever (usually unreasonable)
 Employers vary in level of concern
 In dealing with vulnerable populations (elderly, children)
 Bank teller
 National security
 Construction worker
5

 Recidivism studies (e.g., BJS, 1997, 2002)
 Usually involve short observation period -
 Most recidivism occurs in 3-5 years
 Birth Cohort studies (e.g., Kurlychek, Brame, &
Bushway, 2006, 2007)
 Limited sample size and short follow-up
 Rap sheets:
 Criminal records from state-level repositories
 Samples ~100,000
 Permits rich disaggregation, long-term follow-up
 But no information about the never-arrested
6

 Arrest-history records from NY state repository
 Population of individuals who were arrested for the first time as adults (≥ 16) in 1980 (≈ 88,000)
 Follow-up time > 25 years
 We will report on redemption estimates for:
 Age at first arrest: A
1
 = 16, 18, 20
 Crime type of first arrest: C
1
 = Robbery, Burglary, Aggravated Assault
7

 Survival probability – S(t)
 Survive without a subsequent arrest
 Eventually saturates – only a few have more arrests after a sufficiently long time
 Provides an estimate of fraction still clean at any t
8

1
1,00
,90
,80
,70
,60
Survival
Probability
,50
,40
,30
,20
,10
,00
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Years since First Arrest
9

1
1,00
,90
,80
,70
,60
Survival
Probability
,50
,40
,30
,20
,10
,00
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Years since First Arrest
Robbery
Burglary
Aggravated
Assault
10

 Conditional probability of a new arrest
 Conditional on surviving to t
 Pr{arrest at t|survive to t} = Hazard - h(t)
 New arrest (C
2
) here could be for any crime
 Will later consider concern about specific subsequent crime types (C
2 s)
11

Hazard h(t) = Cond. Prob. of a New Arrest
(C
1
= Burglary, 3 A
1 s)
,25
,20
,15
,10
,05
,00
2 4 6 8 10 12 14
Years Since First Arrest
16 18 20
16
18
20
12

(A
Hazard h(t)
1
=18, 3 C
1 s)
,25
,20
,15
,10
,05
,00
2 4 6 8 10 12
Years Since First Arrest
14 16 18
Robbery
Burglary
Aggravated Assault
13

General Population
 The employer has a single preferred applicant
 Turn to some general measure of how common arrest is for people of the same age
 Redemption occurs when hazard crosses age-crime curve
 We denote the time to redemption as T*
The Never-Arrested
 The employer has a pool of job applicants
 Comparison would be between the risk for those with a prior vs. those without
 We don’t expect these two hazards to cross
 Redemption occurs when hazard is “close enough” to those without
 We denote the time to redemption as T**
14

 Very commonly used in criminology
 Probability of arrest as a function of age
 For our population, arrested for the first time in NY in
1980, we created a “ progressive ” age-crime curve for each value of A
1
 For A
1
=18, arrests of 19s in 1981, 20s in 1982, etc
,12
,10
,08
,06
,04
,02
,00
General population
(Age 18 in NY in 1980)
2 4 6 8 10 12 14 16 18
Years Since First Arrest
15

T*: Comparison to General Pop’n of the
Same Age by the Age-Crime Curve
 Benchmark: The age-crime curve = risk of arrest for any crime in the general population of the same age
 T* is at the intersection of h(t) and A-C curve
,25
,20
,15
T* = 7.7 years h(T*) = .096
Age 18 Robbery
,10
General population
(Age 18 in NY in 1980)
,05
,00
2 4 6 8 10 12 14 16 18
Years Since First Arrest
16

1
1
First Offense (C1)
Robbery
16
Age at First Arrest (A1)
8.5 (.103)
18 20
7.7 (.096) 4.4 (.086)
Aggravated Assault
Burglary
4.9 (.105)
4.9 (.105)
4.3 (.098) 3.3 (.086)
3.8 (.097) 3.2 (.086)
 Age effect: Younger starters need to remain crimefree longer to achieve redemption
 Crime type effect: Robbery > AA ~ Burg
17

First Offense (C1)
Robbery
16
8.5 /
Age at First Arrest (A1)
.092
18 20
7.7 / .202
4.4 / .513
Aggravated Assault
Burglary
4.9 / .291
4.9 / .257
4.3 / .429
3.3 / .556
3.8 /.
414 3.2/ .550
 Age effect: The fraction increases with age
 Crime type effect: Lowest for young robbers
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 Benchmark: The risk of arrest for those who have never been arrested
 The risk of arrest for those with a prior is likely to stay higher than that of those without
 Estimate T** when h(t) and h na
(t) are “ close enough ”
 Data to directly estimate h na
(t) for the never-arrested is not available from repositories, so must be modeled
19

 Population of the never-arrested at age A (N na
(A)):
N na
(A) = Population of New York of age A in 1980
– Σ(First-time arrestees in 1980 for all A
1
< A)
 Hazard of the never-arrested at age A (h na calculated as:
(A)) is h na
(A) =
# of first-time arrestees for A
1
= A
N na
(A)
20

na
,018
,016
,014
,012
,010
,008
,006
,004 h na
(t)
,002
,000
20 22 24 26 28 30 32 34 36 38 40 42 44
Age
21

na
,16
,14
,12
,10
,08
,06
,04
,02
,00
2 4 6 8 10 12 14 16 18 20 22
Years Since First Arrest
Age 18 Violent
Age 18 Property hna(t)
22

 Estimate T** as the time when h(t) becomes “close enough” to h na
(t)
 Simple Intersection method used for T* won’t work if h(t) > h na
(t) for all t
 Introduce risk tolerance, δ
,18
,16
,14
,12
,10
,08
,06
,04
,02
,00 hna(t)
Age 18 Violent
δ = .02
2 4 6 8 10 12 14 16 18 20 22
Years Since First Arrest
23

,12
,10
,08
,06
,04
,02
,00
2
 Use confidence interval (CI)
 We use bootstrap for the CI instead of ±z
α/2 p·q/n
 We use upper CI to be conservative : T** is the time when the upper CI of h(t) intersects (h na
(t)+δ)
,18
,16
,14
T** = 18.3 years h(T**) = .025
4 6 8 10 12 14 16 18 20 22
Years Since First Arrest hna(t)
Age 18 Violent
Lower 95% Bootstrap CI
Upper 95% Bootstrap CI
δ = .02
24

20
18
16
14
12
10
8
6
4
2
0
,02
Tradeoff of Risk Tolerance (δ ) and T**
,03 ,04 ,05 ,06
δ: Risk-tolerance difference
,07 ,08
Age 18 Violent
Age 18 Property
Age 20 Property
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 Robustness test across states
 Replicate with similar data from other states’ repositories
 Robustness across sampling years
 Add 1985, 1990
 Concern over C
2
– the next crime
 Convictions vs Arrests
 Anticipate fewer in number
 Anticipate higher hazards
 Weeded out the innocent
 Test for arrests outside New York
 Need national data from FBI – in process
26

Users of Criminal Records:
 Employers
 Inform employers of the low relevance of records older than T* or T**
 Enact statutes to protect employers from “due-diligence liability” claims if last arrest is older than T* or T**
 Pardon Boards
 Length of law-abiding period is an important factor in pardons
 Information about T* and T** provides guidance on how long a law-abiding period is long enough
27

Distributors of Criminal Records:
 Repositories
 State repositories could choose not to disseminate records older than T* or T**
 Could seal (or expunge) records older than T* or T**
 Commercial Vendors
 If states seal or expunge records older than T* or T** years, commercial vendors should do similarly
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 First use of official state repository records to produce redemption times
 Strong estimates of redemption times, T* and T**
 Provides a basis for responsiveness to user criteria in assessing redemption
⇒ T* or T**can be generated based on the specifications
(A
1
, C
1
, δ, C
2
, etc.) set by the users
29

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