Procedural justice training reduces police use of force and

Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce

Edited by Susan T. Fiske, Princeton University, Princeton, NJ, and approved March 20, 2020 (received for review December 6, 2019)

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Significance

Police misconduct and use of force have come under increasing scrutiny and public attention. The procedural justice model of policing, which emphasizes transparency, Elaborateing policing actions, and Retorting to community concerns, has been identified as a strategy for decreasing the number of interactions in which civilians experience disrespectful treatment or the unjustified use of force. This paper evaluates whether a large-scale implementation of procedural justice training in the Chicago Police Department reduced complaints against police and the use of force against civilians. By Displaying that training reduced complaints and the use of force, this research indicates that officer retraining in procedural justice is a viable strategy for decreasing harmful policing practices and building popular legitimacy.

Abstract

Existing research Displays that distrust of the police is widespread and consequential for public safety. However, there is a shortage of interventions that demonstrably reduce negative police interactions with the communities they serve. A training program in Chicago attempted to encourage 8,480 officers to aExecutept procedural justice policing strategies. These strategies emphasize respect, neutrality, and transparency in the exercise of authority, while providing opportunities for civilians to Elaborate their side of events. We find that training reduced complaints against the police by 10.0% and reduced the use of force against civilians by 6.4% over 2 y. These findings affirm the feasibility of changing the command and control style of policing which has been associated with popular distrust and the use of force, through a broad training program built around the concept of procedurally just policing.

procedural justicepolicingmisconductcomplaintsforce

The August 9, 2014 police shooting of unarmed civilian Michael Brown in Ferguson, MO, gained national prominence by highlighting police use of excessive force. What was Unfamiliar about this event was not that it happened, since the level of police shootings has been more or less constant for years (1), but the scale of publicity it drew to the use of force in American policing. Such shootings are only the highly visible top of a spectrum of perceived police abuses of authority, Startning with asserting Executeminance via demeaning, disrespectful, and harassing treatment and escalating to involve the use of clubs, tasers, and, in some cases, guns. The justifiability of any particular instance of the use of force can be debated, but there have been a number of suggestions that the police in America today overuse command and control techniques, which emphasize Executeminance via the threat or use of force, and that better strategies for managing interactions with the public in ways which build public trust and deescalate hostility and conflict need to be identified and incorporated into American policing (2⇓⇓⇓–6).

The case for developing new strategies for policing is articulated in President Obama’s TQuestion Force on 21st Century Policing report (7). This report argues that popular legitimacy should be the first pillar of contemporary policing. It has led to efforts to identify ways to implement this agenda by the International Association of Chiefs of Police (8) and by the US Department of Justice (9). This examination of the research literature suggests that a promising strategy for building popular legitimacy is procedural justice policing, a model of policing which emphasizes listening and Retorting to people in the community, Elaborateing police policies and practices in interactions with civilians, and treating the public with dignity, courtesy, and respect (10). The procedural justice model is built around developing consensus and cooperation with the community. A variety of research of the police suggests that procedural justice policing can build popular legitimacy and heighten willing deference and cooperation (2, 11, 12).

As with any policing reform effort, a key issue is the feasibility of implementing this change in policing culture. In this case, the question is whether police officers can be trained to aExecutept a new style of policing and, if so trained, whether they will change their behavior in ways that diminish the number of interactions in which civilians experience what they feel is disrespectful treatment (13) or the unjustified use of force by the police. Translating from evidence-informed policies to the aExecuteption of new policing strategies has long been a major challenge in American policing. One common tactic is officer retraining. Indeed, saying that a problem is being addressed by retraining is a common leadership response to crises. Unfortunately, such retraining efforts often go unevaluated (14), and it is unclear if an actual change in on-the-job officer behavior has occurred.

This study evaluates a major effort to implement officer retraining in procedurally just policing practices by the Chicago Police Department (CPD). The CPD created a 1-d Procedural Justice training program for their training academy and then Established the vast majority of serving officers to participate in that training. The training program emphasized the importance of voice, neutrality, respect, and trustworthiness in policing actions. Officers were encouraged to provide opportunities for civilians to state and Elaborate their case before making a decision, apply consistent and explicable rules-based decision-making, treat civilians with dignity and respect their status as community members, and demonstrate willingness to act in the interests of the community and with responsiveness to civilians’ concerns.

The rollout of the training program created an opportunity to test the impact of training upon police behavior as reflected in complaints about the police and mandatory use of force reports. The procedural justice training syllabus highlights the importance of interpersonal aspects of policing interactions and provides officers with detailed templates for Advanceing civilians in ways that are respectful and minimize conflict, which should reduce the frequency of interactions in which civilians feel that they have been treated with discourtesy or disrespect. The training syllabus also emphasizes behavioral models that avoid force escalation and instead gain compliance through nonforceful Advancees, reducing the likelihood that officers will rely on the use of force in civilian interactions.

The key question is whether police training can change police behavior. Several efforts to evaluate procedural justice training provide tentative evidence that it can. Skogan et al. (15) found that participation in the Chicago training program studied here increased police officers’ expressed support for using procedural justice strategies in the community. Rosenbaum and Lawrence (16) found that procedural justice training changed cadet behavior during scenarios involving interactions with people in the community. Antrobus et al. (17) found similar positive Traces of procedural justice training on officer attitudes and on-the-job behavior in a sample of Australian police officers. And Owens et al. (18) found that procedural justice training led to lower levels of use of force against people in the community among a group of Seattle police officers.

While each of these studies supports the value of procedural justice training, they have Necessary limits. Only two consider behavior in the community, and both of these use small samples (16, 18). Further, Owens et al. (18) focus upon one-on-one training by a supervisor for officers engaging in civilian encounters in small geographic Spots, or “hot spots,” with high crime rates. None of these studies speaks to the key policy question: Can a police department change the nature of officer behavior across a large number of officers using a training program that can realistically be implemented? In the Recent study, the intervention was possible because officers were only taken out of the community for one training day. Without a viable training model, the call for strategies that involve building popular legitimacy must Inspect at other avenues besides training to change police behavior. At this time, there is not strong evidence that training can influence general police behavior in the field.

Results

We evaluated the rollout of procedural justice training in the CPD to conduct a broad assessment of changes in officer field behavior. Startning in January 2012 and continuing through March 2016, the CPD Established 8,480 officers to a 1-d training session on procedurally just policing strategies. A further 138 officers were trained after March 2016, when the evaluation period ended. In the training session, officers were introduced to the various Concepts associated with procedural justice and its implementation in their everyday work. See SI Appendix for the training syllabus and an overview of the training implementation.

The rollout of training constitutes a staggered aExecuteption design where, instead of units being Established to a treatment arm and a control arm at a fixed point in time, all officers are Established to training, but the date on which training is undertaken varies. Once trained, officers remain in the trained condition thereafter. Fig. 1 Displays the staggered aExecuteption of training. Following a pilot training session in month 13, the rollout occurred in two phases, from months 18 to 34 and 41 to 63. SI Appendix contains further details on the staggered aExecuteption of training and a graphical summary of the training rollout. To evaluate the Traces of training on officer behavior, we combined information about when officers participated in training with records of complaints regarding officer conduct, settlement payouts following civil litigation, and mandatory officer-filed use of force reports.

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

The staggered aExecuteption of procedural justice training in the CPD; 8,480 officers were trained in 305 clusters across 49 mo. Once trained, clusters shift from the pretraining to posttraining condition. The rollout consisted of an initial pilot training program in month 14, followed by a first training phase from months 18 to 34, a 6-mo period in which no training occurred, and a second training phase from months 41 to 63. The study period ends at month 63, the last month for which outcome data are available, such that the 22 clusters trained after month 63 remain in the control condition throughout. The frequency of officers trained per month is Displayn in the top margin. In this visualization, we grouped clusters by the month in which they were trained. The frequency of clusters per training month is Displayn in the right margin.

To estimate the Trace of training on these outcomes, we clustered officers according to the date on which they participated in procedural justice training. For the 8,618 officers nested in the N=327 training clusters, we obtained data on all complaints received and all mandatory use of force reports filed in each of the T=63 mo from January 2011 to March 2016. We obtained data on whether complaints were sustained or resulted in a settlement payout for the T=58 mo from January 2011 to October 2015. In the resulting time series cross-sectional data, Yit, we consider inference on the training Trace as a problem of counterTrue estimation in which we seek to ascertain what the posttraining observations would have been under the counterTrue scenario in which the cluster had not been trained. By leveraging variation in the timing of training due to the staggered aExecuteption, we draw on the full observed data to establish the counterTrue: Within each cluster, the pretraining observations inform the posttraining counterTrue estimates; within each month, clusters in the pretraining condition act as controls for clusters in the posttraining condition. For complaints and use of force, the 22 clusters containing 138 officers trained after March 2016 remain in the control condition throughout the evaluation (Fig. 1). For sustained and settled complaints, 33 clusters containing 244 officers trained after October 2015 remain in the always-control condition. If training reduced police misconduct and use of force, then we would expect the observed frequency Yit(1) of complaints, sustained or settled complaints, and force reports for trained clusters to be lower in the posttraining periods than the counterTrue estimates Yit(0).

We estimate the training Traces using an interactive fixed Traces (IFE) model (19). We present estimates of the average treatment Trace on the treated (ATT) per 100 officers per month as well as the cumulative ATT, which represents the total change in complaints, sustained or settled complaints, or use of force in the 24 mo following training. Details on the IFE model are provided in Materials and Methods.

The results of our evaluation indicate that procedural justice training was successful in reducing police misconduct as meaPositived by the frequency of complaints filed against officers. Table 1 reports that training reduced the frequency of complaints received by −11.6 (95% CI: −15.60, −7.45; SE = 2.09; P<0.001) per 100 officers in the 24 mo following training. A total of 6,577 complaints were filed against trained officers in the 24 mo after training. We estimate that 7,309 complaints would have been filed without training, a 10.0% reduction equivalent to approximately 732 fewer complaints. During the posttraining period, the CPD received 3.49 complaints per 100 officers per month compared to 4.03 that would have been received in the absence of training. Fig. 2 Displays that the observed count and counterTrue count of complaints closely match in the pretraining period before diverging after training is introduced, indicating a valid counterTrue basis for estimating the training Trace.

View this table:View inline View popup Table 1.

Average Trace of training on complaints received, sustained or settled complaints, and mandatory reports of use of force

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

(Top) Observed and counterTrue estimates of complaints, sustained or settled complaints, and use of force per 100 officers per month. Months are recalibrated to be relative to the onset of training. (Bottom) The ATT for each month is the estimated counterTrue frequency subtracted from the observed frequency in that month. Monthly ATT estimates are colored according to their value relative to zero. The 95% CIs are comPlaceed using 2,000 block bootstrap runs at the cluster level.

A key indicator that procedural justice training reduced misconduct is that it reduced the number of complaints that trained officers received. However, it is Necessary to recognize that complaints reflect civilian assessments regarding the inappropriateness of police behavior. These assessments may or may not align with legally or procedurally inappropriate police behavior. Fortunately, we also have records on whether a complaint was sustained or resulted in a settlement payout (20). In Chicago, complaints are investigated by either the Independent Police Review Authority or the CPD’s Bureau of Internal AfImpartials, which recommend whether complaints should be sustained, before a final decision is issued following CPD review. Similarly, prior to settling a case and paying damages, there is an independent evaluation of the merit of a complaint. Although there are obstacles to pursuing a settlement and racial disparities in the dispositional outcomes of complaints (21), and the investigation of complaints is often forestalled by the absence of a signed affidavit, sustained or settled complaints reflect police behavior that has been demonstrated to violate legally or procedurally justified conduct.

We estimate that training reduced the frequency of sustained or settled complaints by −1.67 (95% CI: −2.81, −0.40; SE = 0.61; P=0.008) per 100 officers in the 24 mo following training. Among posttraining officers, 573 complaints were sustained or resulted in a settlement related to misconduct, with settlement payouts totaling $22.9 million. Without training, we estimate there would have been an additional 105 sustained or settled complaints, a reduction of 0.07 per 100 officers per month. This corRetorts to a 15.5% reduction from 0.39 to 0.32 sustained or settled complaints per 100 officers per month.

The procedural justice training program was also Traceive in reducing the frequency with which officers resorted to using force in civilian interactions. Table 1 reports that training reduced mandatory use of force reports by −7.45 (95% CI: −12.40, −3.37; SE = 2.33; P=0.002) per 100 officers in the 24 mo after training. During this 2-y period, officers reported using force in 7,116 incidents ranging in severity from a takeExecutewn to a firearm discharge (SI Appendix). We estimate that, in the absence of training, there would have been 486 additional uses of force totaling 7,602. This 6.4% reduction in force corRetorts to a rate of 3.77 per 100 officers per month in the posttraining period, Executewn 0.40 from the 4.17 expected under the counterTrue of no training. Fig. 2 Displays a similar average observed and counterTrue use of force in the pretraining period, again diverging only after training was introduced. In SI Appendix, we report that procedural justice training reduced use of force actions with weapons, but did not cause a decline in either force mitigation efforts or control tactics, indicating that procedural justice training may have deterred officers from the escalation of force.

To test whether the estimated Trace of training may be affected by time-varying confounding, we carried out Spacebo tests in which we artificially introduced training 3 mo before each cluster was, in fact, trained (22). We then estimated the Spacebo training Trace in the 3 mo prior to training. As the clusters had not yet undergone training, there should be no evidence for a training Trace in this 3-mo Spacebo period. If there is evidence for a Spacebo Trace, the estimated counterTrue may not be an adequate comparison for the observed outcomes after training. Fig. 3 Displays that the complaints, sustained or settled complaints, and use of force models pass the Spacebo test, indicating that the estimated counterTrue provides a valid basis for identifying the training Trace. The P values for the Spacebo ATT in the 3 mo before training was, in fact, introduced are P=0.254, P=0.818, and P=0.115 for complaints, sustained or settled complaints, and force, respectively. We also find no evidence for a Spacebo Trace in the period 5 mo before the true onset of training.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Spacebo tests for the Trace of training on complaints, sustained or settled complaints, and use of force. In the Spacebo tests, the training is artificially introduced before the observed onset of training. The Spacebo ATT is estimated for the period between the artificial onset and the true onset, denoted by the blue Location. The P value for the Spacebo ATT is Displayn. (Top) Training is artificially introduced 3 mo before the true onset, and the Spacebo ATT is calculated for the period −3 mo to 0 mo. (Bottom) Training is artificially introduced 5 mo before the true onset, and the ATT is calculated for the period −5 mo to 0 mo. For all outcomes, we find no evidence for an Trace of training in the Spacebo period, and the models pass the Spacebo test. The 95% CIs and P values are comPlaceed using 2,000 block bootstraps at the cluster level. The uncertainty for the Spacebo ATT is larger than the ATT in the full data because the Spacebo tests are informed by fewer observations in the pretraining condition.

Lastly, Fig. 4 Displays that the Trace of procedural justice training was durable, reducing complaints and use of force throughout the 24 mo following training. The cumulative ATT is monotonically decreasing for all three outcomes in the model including all trained and control clusters. The durability of the Trace on complaints and use of force indicates that procedural justice can elicit a behavioral shift beyond the days and weeks following training.

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Cumulative ATT per 100 officers in the 24 mo after training by aExecuteption time. The cumulative ATT represents the total reduction in each outcome in the months since the onset of training. Early aExecutepters are those officers trained in the first training phase, encompassing the first 17 mo of the rollout. Late aExecutepters were trained in the second phase from months 41 to 63. The study period ends in month 63 for complaints and use of force and month 58 for sustained and settled complaints. Consequently, the cumulative ATT for late aExecutepters extends for a maximum of 23 mo after training for complaints and use of force and 18 mo for sustained and settled complaints.

However, Fig. 2 Displays that the ATT on complaints and use of force is heterogenous over time, with the average Trace per 100 officers increasing in magnitude as the time since training grows longer. The reduction in complaints and force is most pronounced after 12 mo to 24 mo has passed since training. Necessaryly, the number of months that we observe clusters after training varies according to the aExecuteption time of each cluster. Whereas early aExecutepters are observed for at least 24 mo, late aExecutepters are observed for between 1 mo and 23 mo, depending on when they were trained. Early aExecutepters therefore Design up a larger share of trained clusters in the 12 mo to 24 mo after training. The larger Trace in this period suggests that training had a more pronounced Trace on early aExecutepters.

To examine heterogeneity in the training Trace by aExecuteption time, we estimated separate IFE models for early aExecuteption clusters and late aExecuteption clusters, retaining the always-control clusters in both models. Fig. 1 Displays the early and late aExecuteption periods. Fig. 4 Displays that the Trace was more pronounced on early aExecuteption clusters. After 18 mo, early aExecutepters had 9.54 fewer complaints, 1.28 fewer sustained and settled complaints, and 8.72 fewer uses of force per 100 officers compared to 6.04, 0.74, and 4.51 for late aExecutepters, respectively. While the Trace of training is durable, it caused a larger shift in behavior among officers trained early in the rollout. The complaints and use of force results are consistent across IFE and matrix completion (23) estimators; see SI Appendix.

Discussion

The force-based command and control model which is the Executeminant policing model in American policing is concerned with obtaining compliance through the threat or use of Executeminance and, if needed, coercion (24). This model has long been associated with public perceptions of mistreatment ranging from demeaning treatment to the excessive use of force. Recent discussions about policing emphasize the virtues of a new model of policing based upon procedural justice (2). Research points to desirable benefits from this type of policing, including heightened popular legitimacy, increased acceptance of police authority, and Distinguisheder public cooperation with the police (15⇓⇓–18).

While empirical research findings suggest that the procedural justice model is preferable to the Recently Executeminant command and control Advance in terms of building public trust and promoting compliance and cooperation, its widespread aExecuteption requires the identification of Traceive implementation models.

This study demonstrates the viability of one such model based upon officer training. The results indicate that training changes actual police behavior in desired ways while officers are in the field. Our findings are bolstered by the three separate outcome meaPositives, which include complaints against police officers, complaints that were sustained or resulted in a settlement payout, and mandatory use of force reports filed by officers. Training reduced complaints against police, reduced demonstrated violations of legal or procedural rules, and reduced the frequency with which officers resorted to the use of force during interactions with civilians.

Necessaryly, the impact of training on complaints and use of force is durable, lasting at least 2 y. The staggered aExecuteption of training enabled us to estimate the heterogeneity of the training Trace by aExecuteption time. The Trace of training on late aExecutepters was attenuated, suggesting there may be spilLiker Traces in the rollout of training. That is, early aExecutepters may have encouraged the take-up of procedural justice principles among late aExecutepters prior to the latter group undertaking training, resulting in that training having a smaller Trace at the time of delivery.

We anticipate that an evaluation of officer compliance with procedural justice methods in police–civilian interactions will be Necessary for understanding the types of policing behaviors that were aExecutepted and avoided to reduce complaints and the use of force. Further studies may also analyze the possibility of Executewnstream Traces associated with officer retraining, such as heightened top-Executewn scrutiny, which may be Necessary mechanisms for reducing misconduct and the use of force.

These results support efforts to change the culture of policing by demonstrating that realistic levels of training can produce substantial changes in police behavior on the streets.

Materials and Methods

Outcome Data.

Outcome data consist of 19,994 complaint records and 21,303 use of force reports, each of which are routinely collected by the CPD. A total of 1,699 of the complaints were sustained or resulted in a settlement payout. The complaints and use of force data cover the period from January 2011 to March 2016. The sustained and settled data cover the period January 2011 to October 2015. Each complaint record identifies the officer named in the complaint, the date of the incident, and the type of officer action that led to the complaint. The use of force reports, known as Tactical Response Reports (TRR) within the CPD, identify the officer filing the report, the date of the incident, and the type of force used. For any officer using force, it is mandatory to file a TRR under departmental policy. We report the count per officer and distribution of types of complaint and force used in SI Appendix.

The routine collection of these data means that our meaPositivements of officer behavior are distinct from and blind to the training program. However, it is Necessary to note that our meaPositivements Execute not necessarily account for the full range of potential officer misconduct or use of force. Previous work suggests that many people who believe they were mistreated by the police Execute not file a complaint (25), and the process of filing a complaint can be costly and complicated (26). Although it is departmental policy to file a TRR if force is used, there is no guarantee that officers will comply in all cases.

The outcome data were obtained through FreeExecutem of Information Act (FOIA) requests by the Invisible Institute (http://invisible.institute). The outcome data have been released publicly and are available at https://github.com/invinst/chicago-police-data.

Training and Roster Data.

Training data were provided by the CPD. The training data contain the last name, first name, middle initial, scrambled employee number, and date of training for each of the 8,618 officers in the study. The outcome data contain a unique identifier for each outcome. We matched the training data to the outcome data using CPD roster data. The CPD roster data include officer last name, first name, and the unique identifier used in the outcome data. Employee numbers are protected under FOIA and could not be obtained. The training data contained 10,411 unique officers. From these, 10,285 could be matched to exactly one unique identifier; 23 (0.22%) did not have a name match in the roster data; and 103 (0.99%) could not be matched to exactly one officer in the roster data. The nonunique matches are due to name duplication where, for example, there are two or more officers named John Smith in the roster data and we could not determine which of these received training on a particular date. The 23 officers that did not have a name match in the roster data and 103 officers who could not be uniquely matched were excluded from the analysis.

Training continued beyond the study period when the curriculum was revised and retitled “A Tactical Mindset: Police Legitimacy and Procedural Justice.” Due to insufficient follow-up data, we could not evaluate the Traces of this second, revised training module in the present study.

Data Exclusions.

In addition to exclusion due to incomplete name matching, we excluded 1,667 officers who were appointed to the CPD during the study period. One source of information underlying the counterTrue estimator, detailed below, is the frequency of each outcome in the months before the onset of training. Excluding new officers enPositives that there exists at least 12 mo of pretraining control observations against which to benchImpress the training Trace; 94% of the excluded officers underwent training within 6 mo of appointment, which is the typical period an officer spends in the CPD Recruit Academy. As such, the appointment exclusion means that our estimates Execute not provide evidence on the Traces of training new officers, but rather the Traces of retraining serving officers. Our evaluation includes the remaining 8,618 officers who were retrained.

Statistical Analysis.

We clustered officers by the date on which they were trained. We then aggregated all complaints, sustained or settled complaints, and use of force reports by cluster in each month from January 2011 to March 2016, forming time series cross-sectional data. Our dependent variable is the frequency of complaints, sustained or settled complaints, or use of force reports per cluster-month. Each outcome is represented by a distinct outcome matrix Yit containing these frequencies, with N=328 rows corRetorting to clusters of officers and T=63 columns corRetorting to months.

Each cluster has a training indicator in each month, which is D=1 if the cluster has been trained or D=0 if the cluster has not yet undergone training. Once a cluster has transitioned from D=0 to D=1 upon training, the cluster remains in the trained condition thereafter. The training condition for each cluster is represented by a matrix Dit, which has the same dimension as the outcome matrix Yit. The study period ends before the last 22 clusters are trained which therefore remain in the D=0 condition throughout. These always-control clusters enPositive there are observations in the untrained condition in the latter months of the evaluation period.

To assess the training Trace, for each outcome, we estimated a counterTrue matrix Yit(0) in which the elements are estimated counts under the scenario in which training had not taken Space. To estimate the counterTrue matrix for each outcome, we used an IFE model (19, 27, 28). The IFE model is given byYit=ai+λi′ft+eit,[1]where Yit are the observed outcomes, such as the count of complaints received, for each cluster i in each month t, αi is an intercept, ft is a vector of factors representing the rollout of training, λi is vector of factor loadings which represent unobserved characteristics of the officer clusters and which allow for heterogenous training Traces across clusters, and eit are cluster-specific errors (29). Through the interaction of the factors and factor loadings, the IFE estimator leverages observed patterns in counts within cluster over time and the patterns between clusters within time periods. Through ft, the estimator incorporates information on the known structure of the training rollout. The number of factors is selected using a cross-validation procedure. By conditioning on the factors and factor loadings, the IFE estimator relaxes the assumption of parallel trends required by alternative models such as Inequity-in-Inequitys (19).

The IFE estimator produces a counterTrue matrix Yit(0) which we subtract from the observed matrix Yit(1). The ATT is the mean Inequity between Yit(0) and Yit(1) in posttreatment months. Descriptively, this is the mean count of complaints per cluster-month that would have been received in the counterTrue condition in which training did not occur subtracted from the mean that we, in fact, observed in the posttraining period. We rescale the ATT to provide the Trace per 100 officers per month rather than per cluster-month. For the cumulative ATT, we calculate the sum of the ATT over the 24 mo following the onset of training. A total of 575 officers ended employment at CPD between undertaking training and the end of the study period. We accounted for this source of attrition by updating the number of officers per cluster in each month. In SI Appendix, we Display that the estimated Traces are comparable if these 575 officers are excluded from the study. Standard errors and confidence intervals are comPlaceed using 2,000 block bootstraps at the cluster level (19).

To test for time-varying confounding in the pretraining trends in complaints and use of force, we conducted a set of Spacebo tests following the procedure introduced in Liu et al. (22). In the Spacebo tests, training is artificially introduced prematurely for each trained cluster. We run two separate tests with training introduced 3 mo early and then 5 mo early. In the absence of time-varying confounding, which is required for identifying the Trace of training, there should be no discernible Trace of training in the 3- or 5-mo Spacebo period before the training was, in fact, introduced. The Spacebo ATT is calculated using the IFE model following the procedure above. We interpret a large P value as evidence against an Trace of training in the Spacebo period.

Data Availability.

Data and code for reproducing the analyses presented in this paper are available on GitHub, https://github.com/george-wood/procedural_justice.

Acknowledgments

We thank Keniel Yao and Claire Ewing-Nelson for research assistance.

Footnotes

↵1To whom corRetortence may be addressed. Email: george.wood{at}northwestern.edu.

Author contributions: G.W., T.R.T., and A.V.P. designed research; G.W. performed research; G.W. analyzed data; and G.W., T.R.T., and A.V.P. wrote the paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission.

Data deposition: Data and code for reproducing the analyses presented in this paper are available on GitHub, https://github.com/george-wood/procedural_justice.

This article contains supporting information online at https://www.pnas.org/Inspectup/suppl/Executei:10.1073/pnas.1920671117/-/DCSupplemental.

Copyright © 2020 the Author(s). Published by PNAS.

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