Estimating effects of short-term imprisonment on crime using random judge assignments

Figures & data

Table 1. Prior studies using random judge assignment to estimate effect of custodial versus noncustodial sanctions on recidivism.

Study name	Sample size	Custodial sanction	Noncustodial sanction	Offender type	Specific crime	Follow-up period	Significant effect (p < .05)
Green & Winik, 2010	1,003	prison	probation	adult	drug crime	4 years	n.s.
Loeffler, 2013	20,297	prison	probation	adult	no	5 years	n.s.
Nagin & Snodgrass, 2013	6,515	prison	noncustodial sanction	adult	no	10 years	n.s.
Aizer & Doyle, 2015	37,692	prison	probation	juvenile	no	10 years	sig. positive effect for homicide, violence, property crime, and drug crime
Mueller-Smith, 2015	431,422-887,019	prison	noncustodial sanction	adult	felony/misdemeanor	5 years	sig. positive effect for violence, property, drug crime and DWI (felony sample), sig. positive effect drug crime (misdemeanor sample)
Harding et al., 2017	111,110	prison	probation	adult	no	5 years	sig. positive effect technical violations and felony convictions
Harding et al., 2019	111,110	prison	probation	adult	no	5 years	n.s. violent crime
Bhuller et al., 2020	23,373	prison	noncustodial sanction	adult	no	5 years	sig. negative effect 15-60 months after release
Eren & Mocran, 2021	7,371	prison	nonsecure custody, probation	juvenile	no	16 years	n.s. all crime and violent crime, sig. negative effect property crime, sig. positive effect drug crime
Rahman & Weatherburn, 2021	11,282	prison	suspended sentence	adult	driving under the influence	5 years	n.s.

Figure 1. First stage—The probability of imprisonment by judge. Notes: The horizontal dashed line is the sample mean imprisonment probability. The size of the circle is proportional to the number of cases sentenced by each judge.

Table 2. Estimated effects of imprisonment versus noncustodial sanctions on recidivism prevalence by time since release and IV estimator.

	Model 1: 2SLS						Model 2: LIML						Model 3: stringency
	1yr		3yr		5yr		1yr		3yr		5yr		1yr		3yr		5yr
Prison	.171***		.103***		.068**		.193***		.109***		.070**		.195***		.113***		.081**
	(.019)		(.022)		(.023)		(.022)		(.025)		(.025)		(.027)		(.028)		(.028)
Social demographics
Non-Dutch	.004		.009		.002		.001		.008		.002		.001		.008		.001
	(.005)		(.005)		(.006)		(.005)		(.006)		(.006)		(.005)		(.006)		(.006)
Woman	−.014*		−.022**		−.023**		−.013*		−.022**		−.023**		−.012*		−.021***		−.022***
	(.006)		(.007)		(.007)		(.006)		(.007)		(.007)		(.005)		(.006)		(.006)
Age (/10)	−.520***		−.636***		−.733***		−.527***		−.638***		−.734***		−.529***		−.641***		−.738***
	(.094)		(.108)		.111		(.094)		(.108)		(.111)		(.096)		(.109)		(.113)
Age_squared (/10)	.140***		.167***		.197***		.143***		.167***		.197***		.143***		.168***		.199***
	(.029)		(.034)		(.035)		(.029)		(.034)		(.035)		(.030)		(.034)		(.035)
Age_cubed (/10)	−.013***		−.016***		−.019***		−.013***		−.016***		−.019***		−.013***		−.016***		−.019***
	(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)
Case characteristics
#crimes	.018***		.021***		.023***		.017***		.020***		.023***		.017***		.020***		.023***
	(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)
Severity of offense	−.011***		−.008***		−.007***		−.011***		−.008***		−.007**		−.012***		−.009***		−.007***
	(.002)		(.002)		(.002)		(.002)		(.002)		(.002)		(.002)		(.002)		(.002)
Criminal/ punishment history
#prior criminal cases	.003***		.005***		.006***		.003***		.005***		.006***		.003***		.005***		.006***
	(.001)		(.001)		(.001)		(.001)		(.001)		(.001)		(.001)		(.001)		(.001)
#prior prison spells	.030***		.039***		.039***		.029***		.039***		.039***		.028***		.039***		.039***
	(.002)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)		(.003)
#prior prison spells_squared	−.001***		−.002***		−.002***		−.001***		−.002***		−.002***		−.001***		−.002***		−.002***
	(.000)		(.000)		(.000)		(.000)		(.000)		(.000)		(.000)		(.000)		(.000)
#prior CSO’s	.062***		.112***		.142***		.062***		.112***		.142***		.062***		.112***		.142***
	(.007)		(.008)		(.008)		(.007)		(.008)		(.008)		(.007)		(.008)		(.008)
#prior CSO’s_squared	−.013***		−.023***		−.032***		−.013***		−.023***		−.032***		−.013***		−.023***		−.032***
	(.003)		(.004)		(.004)		(.003)		(.004)		(.004)		(.004)		(.004)		(.003)
#prior CSO’s_cubed	.001**		.001***		.002***		.001**		.001***		.002***		.001*		.001**		.002***
	(.000)		(.000)		(.000)		(.000)		(.000)		(.000)		(.000)		(.000)		(.000)
#prior fines	.009***		.020***		.021***		.009***		.020***		.021***		.009***		.020***		.021***
	(.002)		(.002)		(.002)		(.002)		(.002)		(.002)		(.002)		(.002)		(.002)
Constant	.775***		1.050***		1.213***		.785***		1.053***		1.213***		.788***		1.057***		1.220***
	(.098)		(.112)		(.116)		(.098)		(.112)		(.116)		(.101)		(.115)		(.119)
Offense effects?	yes
District effects?	yes

Notes: Model includes controls for 16 different offense types and 11 district-specific effects. Standard errors in parentheses. The two-stage least squares (2SLS) and limited information maximum likelihood (LIML) estimators rely on judge dummy variables as the instrument. The judge stringency instrument relies on one measure, namely the proportion of all cases that come before a particular judge that result in a custodial sanction, excluding the index case.

***p < .001; **p < 0.01; *p < 0.05 (two-tailed test).

Table 3. Estimated effects of imprisonment versus noncustodial sanctions on recidivism incidence by time since release and IV estimator.

	Model 1: 2SLS						Model 2: LIML						Model 3: stringency
	1yr		3yr		5yr		1yr		3yr		5yr		1yr		3yr		5yr
Prison	.717***		1.072***		1.145***		.816***		1.186***		1.227***		.772***		1.104***		1.175***
	(.065)		(.124)		(.164)		(.073)		(.140)		(.184)		(.116)		(.206)		(.231)
Social demographics
Non-Dutch	.018		.017		−.032		.007		.005		−.041		.013		.014		−.035
	(.016)		(.030)		(.040)		(.016)		(.031)		(.041)		(.020)		(.036)		(.044)
Woman	−.084***		−0.226***		−.345***		−.079***		−.220***		−.341***		−.080***		−.223***		−.342***
	(.019)		(.037)		(.049)		(.019)		(.037)		(.049)		(.015)		(.028)		(.034)
Age (/10)	−1.067**		−1.813**		−2.146**		−1.101**		−1.851**		−2.173**		−1.081**		−1.818**		−2.164**
	(.317)		(.606)		(.804)		(.318)		(.607)		(.805)		(.316)		(.612)		(.786)
Age_squared (/10)	.286**		.457*		.543*		.296**		.469*		.551*		.290**		.460*		.549*
	(.098)		(.188)		(.250)		(.099)		(.189)		(.250)		(.097)		(.188)		(.242)
Age_cubed (/10)	−.028**		−.045*		−.056*		−.029**		−.046*		−.057*		−.028**		−.045*		−.057*
	(.010)		(.019)		(.025)		(.010)		(.019)		(.025)		(.010)		(.019)		(.024)
Case characteristics
#crimes	.008***		.157***		.227***		.057***		.153***		.224***		.058***		.155***		.225***
	(.002)		(.017)		(.022)		(.009)		(.017)		(.022)		(.012)		(.023)		(.032)
Severity of offense	−.042***		−.067***		−.076***		−.045***		−.072***		−.079***		−.045***		−.070***		−.078***
	(.005)		(.010)		(.014)		(.006)		(.011)		(.014)		(.006)		(.011)		(.014)
Criminal/ punishment history
#prior criminal cases	.008***		.017***		.027***		.009***		.018***		.027***		.008**		.018**		.027***
	(.002)		(.004)		(.005)		(.002)		(.004)		(.005)		(.003)		(.006)		(.007)
#prior prison spells	.101***		.285***		.435***		.096***		.279***		.430***		.099***		.284***		.434***
	(.008)		(.016)		(.021)		(.008)		(.016)		(.021)		(.013)		(.024)		(.031)
#prior prison spells_squared	−.002***		−.007***		−.011***		−.002***		−.007***		−.011***		−.002**		−.007***		−.011***
	(.000)		(.001)		(.001)		(.000)		(.001)		(.001)		(.001)		(.001)		(.002)
#prior CSO’s	.068**		.260***		.424***		.068**		.259***		.424***		.069**		.259***		.423***
	.023		(.043)		(.057)		(.023)		(.043)		(.057)		(.025)		(.049)		(.064)
#prior CSO’s_squared	.007		−.014		−.027		.007		−.015		−.028		.007		−.015		−.027
	(.010)		(.020)		(.026)		(.010)		(.020)		(.026)		(.013)		(.026)		(.033)
#prior CSO’s_cubed	−.002		−.001		−.001		−.002		−.001		−.001		−.002		−.001		−.001
	(.001)		(.002)		(.003)		(.001)		(.002)		(.003)		(.002)		(.003)		(.004)
#prior fines	.016**		.068***		.099***		.015**		.068***		.098***		.015*		.068***		.099***
	(.005)		(.010)		(.014)		(.005)		(.010)		(.014)		(.007)		(.014)		.018
Constant	1.662***		3.147***		3.971***		1.711***		3.201***		4.010***		1.685***		3.156***		3.994***
	(.329)		(.629)		(.834)		(.330)		(.630)		(.835)		(.333)		(.648)		(.826)
Offense effects?	yes
District effects?	yes

Notes: Model includes controls for 16 different offense types and 11 district-specific effects. Standard errors in parentheses. The two-stage least squares (2SLS) and limited information maximum likelihood (LIML) estimators rely on judge dummy variables as the instrument. The judge stringency instrument relies on one measure, namely the proportion of all cases that come before a particular judge that result in a custodial sanction, excluding the index case.

***p < .001; **p < 0.01; *p < 0.05 (two-tailed test).

Figure 2. Mean recidivism rate during 1 yr, 3 yr, and 5 yr follow-up period, by judge’s tendency to incarcerate. Notes: The horizontal dashed lines are sample mean recidivism probabilities, while the angled solid lines are linear fits. The size of the circle is proportional to the number of cases sentenced by each judge.

Figure 3. Pre- to posttreatment incidence of criminal behavior, 1 yr, 3 yr, and 5 yr.

Table 4. Estimated effects of prison sentences up to one year versus noncustodial sanctions on recidivism prevalence and incidence by time since release and IV estimator.

	Model 1: 2SLS			Model 2: LIML			Model 3: stringency
	1yr	3yr	5yr	1yr	3yr	5yr	1yr	3yr	5yr
Recidivism prevalence
Prison	.167***	.098***	.063**	.188***	.104***	.064*	.188***	.106***	.073**
	(.019)	(.022)	(.023)	(.021)	(.024)	(.025)	(.027)	(.027)	(.028)
Recidivism incidence
Prison	.703***	1.048***	1.116***	.798***	1.154***	1.190***	.748***	1.068***	1.129***
	(.064)	(.123)	(.163)	(.073)	(.139)	(.183)	(.115)	(.204)	(.230)

Notes: Models include all variables shown in table 2 plus controls for district and offense type. Standard errors in parentheses.

***p < .001; **p < 0.01; *p < 0.05 (two-tailed test).

Table 5. 2SLS estimates of effects of imprisonment versus noncustodial sanctions on recidivism prevalence and incidence.

	Model 1: Recidivism prevalence			Model 2: recidivism incidence
	1yr	3yr	5yr	1yr	3yr	5yr
Punishment history
First-timers	.104***	.083**	.072**	.345***	.411***	.333*
	(.021)	(.026)	(.028)	(.059)	(.113)	(.149)
Repeated prisoners	.173***	.064*	.011	.943***	1.287***	1.516***
	(.031)	(.231)	(.029)	(.122)	(.232)	(.309)
	[1.843]	[.082]	[1.513]	[-4.413]	[-3.395]	[-3.448]
Age
Young adults (18-25)	.055	.039	.037	.321**	.472*	.687**
	(.031)	(.035)	(.036)	(.100)	(.189)	(.250)
Adults (25+)	.201***	.110***	.070**	.822***	1.210***	1.240***
	(.022)	(.025)	(.025)	(.074)	(.142)	(.188)
	[-3.841]	[-1.651]	[-.753]	[-4.027]	[-3.122]	[-1.768]
Recidivism severity
Serious crimes	.167***	.110***	.074**	.589***	.842***	.887***
	(.019)	(.022)	(.022)	(.055)	(.104)	(.137)
Very serious crimes	.002	.002	-.004	.002	.007	.002
	(.007)	(.010)	(.012)	.007	(.015)	(.019)
	[11.951]	[4.469]	[3.113]	[10.587]	[7.947]	[6.399]

Notes: Models include all variables shown in Table 2 plus controls for district and offense type. Standard errors in parentheses. T-stats for difference between coefficients between square brackets.

***p < .001; **p < 0.01; *p < 0.05 (two-tailed test).

Table A1. Randomization checks—global F-tests

	F
Social demographics
Age	1.34
Female	1.19
Non-Dutch	5.31
Case characteristics
Number of crimes	2.52
Severity of offense	7.40
Criminal/ punishment history
Number of prior criminal cases	1.90
Number of prior prison spells	2.22
Number of prior CSO’s	1.55
Number of prior fines	1.51
Offense type
Threatening	1.28
Assault	2.39
Aggravated theft with violence	1.36
Sex and other violent crimes	1.30
Forgery	5.36
Theft	3.64
Aggravated theft	1.41
Other aggravated theft	2.52
Other property	1.33
Public order	2.32
Offense against authority	1.32
Destruction	1.22
Traffic	8.89
Drug	4.02
Firearms	1.18
Other	1.47

Note: All models condition on district court fixed effects as cases are randomly distributed within courts.

Table A2. Measurement properties for all variables

Variable	Possible values	Description
Outcomes
Prevalence of recidivism	0, 1	Coded 1 if an offense was registered after the index offense at 1, 3, and 5 years after conviction and after prisoners are released from prison
Incidence of recidivism	[0, ∞)	Number of offenses registered after the index offense at 1, 3, and 5 years after conviction and after prisoners are released from prison
Social demographics
Age	[0, ∞)	Years of age of adult arrestees (/10)
Female	0, 1	Coded 1 for female arrestees
Non-Dutch	0, 1	Coded 1 for arrestees not born in the Netherlands
Case characteristics
Number of crimes	[0, ∞)	Number of crimes in the case
Severity of the offense	[0, 20)	Offense severity is based on the maximum penalty
Criminal/ punishment history
Number of prior criminal cases	[0, ∞)	Number of previous criminal cases
Number of prior prison spells	[0, ∞)	Number of previous prison spells
Number of prior CSO’s	[0, ∞)	Number of previous Community Service Orders
Number of prior fines	[0, ∞)	Number of previous fines
Offense type
Threatening	0, 1	Coded 1 if the most serious offense consists of an offense against personal safety, such as stalking (Art. 285 Dutch Penal Code)
Assault	0, 1	Coded 1 if the most serious offense consists of assault
Aggravated theft with violence	0, 1	Coded 1 if the most serious offense consists of aggravated theft with violence
Sex and other violent crimes	0, 1	Coded 1 if the most serious offense consists of a sex offense or another violent offense
Forgery	0, 1	Coded 1 if the most serious offense consists of falsity, such as forgery of documents (e.g. Art. 208, 209, 210, 219, 225, 227, 231, 232 Dutch Penal Code)
Theft	0, 1	Coded 1 if the most serious offense consists of theft
Aggravated theft	0, 1	Coded 1 if the most serious offense consists of aggravated theft
Other aggravated theft	0, 1	Coded 1 if the most serious offense consists of another aggravated theft offense
Other property	0, 1	Coded 1 if the most serious offense consists of another property offense
Public order	0, 1	Coded 1 if the most serious offense consists of a public order offense
Offense against authority	0, 1	Coded 1 if the most serious offense consists of an offense against authority
Destruction	0, 1	Coded 1 if the most serious offense consists of destruction, such as damaging someone else’s property (e.g. Art. 350, 351, 352, 354 Dutch Penal Code)
Traffic	0, 1	Coded 1 if the most serious offense consists of a traffic offense
Drug	0, 1	Coded 1 if the most serious offense consists of a drug offense
Firearms	0, 1	Coded 1 if the most serious offense consists of a weapons act offense
Other	0, 1	Coded 1 if the most serious offense consists of other crimes

Notes: No variable contained missing values. To control for outliers all continuous variables were winsorized at the 99th percentile. We also coded dummy variables for the different Dutch district courts. These dummy variables are omitted from the table in the interest of space. The Dutch court districts include the following: Amsterdam, Den Haag, Limburg, Midden-Nederland, Noord-Holland, Noord-Nederland, Rotterdam, Oost-Brabant, Oost-Nederland Gelderland, Oost-Nederland Overijssel, and Zeeland-West-Brabant.

Table A3. Estimated effects of imprisonment versus noncustodial sanctions on recidivism prevalence and incidence without covariates (other than fixed effects).

	Model 1: 2SLS			Model 2: LIML			Model 3: stringency
	1yr	3yr	5yr	1yr	3yr	5yr	1yr	3yr	5yr
Recidivism prevalence
Prison	.220***	.158***	.116***	.229***	.152***	.104***	.229***	.157***	.114**
	(.016)	(.019)	(.019)	(.017)	(.020)	(.021)	(.031)	(.035)	(.035)
Recidivism incidence
Prison	.896***	1.576***	1.914***	.947***	1.617***	1.883***	.918***	1.576***	1.869***
	(.053)	(.104)	(.140)	(.058)	(.116)	(.156)	(.125)	(.241)	(.290)

Notes: Model includes controls for 11 district-specific effects. Standard errors in parentheses. The two-stage least squares (2SLS) and limited information maximum likelihood (LIML) estimators rely on judge dummy variables as the instrument. The judge stringency instrument relies on one measure, namely the proportion of all cases that come before a particular judge that result in a custodial sanction, excluding the index case.

***p < .001; **p < 0.01; *p < 0.05 (two-tailed test).

Table A4. Estimated effects of imprisonment versus noncustodial sanctions on recidivism prevalence and incidence using different caseload thresholds

	Model 1: 2SLS			Model 2: LIML			Model 3: stringency
	1yr	3yr	5yr	1yr	3yr	5yr	1yr	3yr	5yr
Recidivism prevalence
≥ 10 cases handled by each judge
Prison	.189***	.108***	.064**	.210***	.114***	.0641*	.205***	.112***	.075*
	(.020)	(.023)	(.024)	(.022)	(.026)	(.026)	(.027)	(.029)	(.030)
≥ 25 cases handled by each judge	.164***	.087**	.040	.180***	.089**	.036	.175***	.092**	.056
Prison	(.023)	(.026)	(.027)	(.025)	(.029)	(.030)	(.032)	(.033)	(.034)
Recidivism incidence
≥ 10 cases handled by each judge	.817***	1.201***	1.240***	.922***	1.323***	1.328***	.843***	1.219***	1.265***
Prison	(.069)	(.131)	(.074)	(.077)	(.146)	(.192)	(.118)	(.211)	(.242)
≥ 25 cases handled by each judge	.711***	1.223***	1.241***	.791***	1.358***	1.340***	.713***	1.276***	1.322***
Prison	(.077)	(.147)	(.195)	(.085)	(.164)	(.217)	(.137)	(.241)	(.286)
F-statistic (≥ 10 cases)	6.12	6.10	6.08	6.12	6.10	6.08	892.81	897.60	898.80
F-statistic (≥ 25 cases)	6.03	6.03	6.01	6.03	6.03	6.01	647.19	650.25	651.27

Notes: Model includes controls for 11 district-specific effects. Standard errors in parentheses. The two-stage least squares (2SLS) and limited information maximum likelihood (LIML) estimators rely on judge dummy variables as the instrument. The judge stringency instrument relies on one measure, namely the proportion of all cases that come before a particular judge that result in a custodial sanction, excluding the index case.

***p < .001; **p < 0.01; *p < 0.05 (two-tailed test).

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Data Availability Statement

Restrictions apply to the access of the data that support the findings of this study as these data can only be reused if permission has been granted by all relevant authorities, i.e. Statistics Netherlands (CBS), Public Prosecutor’s Office, and the Research and Documentation Centre of the Netherlands Ministry of Justice and Security (WODC). The CBS and WODC only grant data access to institutions, services and organizations that are located in countries that fall under the scope of the GDPR (the European Economic Area) or to which an adequacy decision of the European Commission applies.