A randomized controlled trial of the impact of body-worn camera activation on the outcomes of individual incidents

Abstract

Objectives

Evaluate the impact of body-worn cameras (BWCs) on officer-initiated activity, arrests, use of force, and complaints.

Methods

We use instrumental variable analysis to examine the impact of BWC assignment and BWC activation on the outcomes of individual incidents through a randomized controlled trial of 436 officers in the Phoenix Police Department.

Results

Incidents involving BWC activations were associated with a lower likelihood of officer-initiated contacts and complaints, but a greater likelihood of arrests and use of force. BWC assignment alone was unrelated to arrests or complaints; however, incidents involving officers who were assigned and activated their BWC were significantly more likely to result in an arrest and less likely to result in a complaint.

Conclusions

Future researchers should account for BWC activation to better estimate the effects of BWCs on officer behavior. To maximize the effects of BWCs, police agencies should ensure that officers are complying with activation policies.

Appendices

Appendix 1. Using path models to estimate TOT

The purpose of this appendix is to show how path models can estimate treatment on the treated impacts equivalent to typical econometric instrumental variable regression. Our example employs two dichotomous treatment indicators, but these derivations apply to any IV model. Our exposition was kept general in order to be helpful to a broader set of readers.

To estimate the so-called “treatment on the treated” impact, researchers often employ the local average treatment effect (LATE). This impact estimate involves three key variables: the outcome Y, the randomly assigned binary treatment indicator Z, and the observed treatment behavior (X).

Given an exogenous (uncorrelated with any other factors) treatment predictor z where control and treatment conditions are randomly assigned and coded as z = {0, 1}, the instrumental variable (IV) estimate is the ratio of the mean difference in the outcome by the mean difference in the instrumented behavior variable (as noted in Cameron and Trivedi (2005) as the Wald Estimator based on Wald's (1940) paper).

$$ {\tau}_{IV}=\frac{{\overline{y}}_{z=1}-{\overline{y}}_{z=0}}{{\overline{x}}_{z=1}-{\overline{x}}_{z=0}} $$

Two-stage-least-squares

In the parlance of two-stage-least-squares, the first stage estimates

$$ x= az+{\varepsilon}_2 $$

which produces predicted values of $\hat{x}$, namely ${\overline{x}}_{z=1}$ and ${\overline{x}}_{z=0}$ where $a={\overline{x}}_{z=1}-{\overline{x}}_{z=0}$. The second stage uses these predicted values in the model

$$ y=b\hat{x}+{\varepsilon}_1 $$

hence the name “2SLS.”

Path models

In the below, we show that the IV LATE estimate can also be achieved using path models estimated with structural equation model software. Essentially, x completely mediates the relationship between z and y (through model constraints). Path models estimate constrained covariance structures to sets of variables. We can visually represent the LATE model with the path model shown in Fig. 4.

Fig. 4

Basic LATE path model

In Fig. 4, the two endogenous variables, x and y, are proposed to relate to each other through two paths. The first is that the predicted value of $\hat{y}$ is a linear function of the predicted value of $\hat{x}$, or $\hat{y}=f\left(\hat{x}\right)=b\hat{x}$. The second relationship is that the residuals of y, or ε₁, are correlated with the residuals of x, or ε₂. This figure also includes a representation of the major reason IV models are sometimes required: there is a relationship between the predictor (which is composed of both the prediction and residual, $x=\hat{x}+{\varepsilon}_2$) and the outcome residuals from the model, ε₁.

An indicator of the result of random assignment, z, is exogenous by definition and thus not correlated with the observed outcome, y. However, it is a good predictor of behavior, x, and thus the third relationship in this model is $\hat{x}=g(z)= az$.

Much of the literature on path models (e.g., Davis and Weber, 1985) note that the total impact of a chain between two variables, say z and y, are the product of the paths. Thus, the total impact of z on y in this model is the product of the first path and second path, namely $\hat{y}=f\left(g(z)\right)= abz$ since $\hat{y}=f\left(\hat{x}\right)$ and $\hat{x}=g(z)$.

Two-stage-least-squares and path models

To connect 2SLS and path models, we note that another equivalent parameterization of this estimate comprises two stages of covariances, namely the ITT impact $\mathit{\operatorname{cov}}\left(z,y\right)={\overline{y}}_{z=1}-{\overline{y}}_{z=0}$ and the covariances between behavior x and treatment assignment z, $\mathit{\operatorname{cov}}\left(z,x\right)={\overline{x}}_{z=1}-{\overline{x}}_{z=0}$, namely

$$ {\tau}_{IV}=\frac{\mathit{\operatorname{cov}}\left(z,y\right)}{\mathit{\operatorname{cov}}\left(z,x\right)} $$

which can be rewritten as

$$ {\tau}_{IV}=\frac{f\left(g(z)\right)}{g(z)}=\frac{ab}{a}=b $$

In other words, the path, b, from x to y in Fig. 4 is the IV estimate τ_IV.

Example

Table 4 provides an example of data to be analyzed such as the above discussion. Those assigned control have a value of z = 0, and those assigned treatment have a value of z = 1. The mean of x for the control observations is .2, and the mean of x for the treatment observations is .9; ${\overline{x}}_{z=1}-{\overline{x}}_{z=0}=.7$. The mean of y for the control observations is 57, the mean of y for the treatment observations is 53.1; ${\overline{y}}_{z=1}-{\overline{y}}_{z=0}=-3.9$. This can be confirmed with the regression.

Table 4 Example data

The ITT impact is thus − 3.9, and the IV impact is ${\tau}_{IV}=\frac{{\overline{y}}_{z=1}-{\overline{y}}_{z=0}}{{\overline{x}}_{z=1}-{\overline{x}}_{z=0}}=-\frac{3.9}{.7}=-5.571429.$

This result can be confirmed by running a model in Stata using the instrumental variable regression package (ivregress; note the coefficient for x and its standard error).

We can also fit a path model to estimate this impact, as shown in Fig 5.

Fig. 5

Path LATE model on example data

The sem procedure in Stata can be used to fit the path model (gsem can be employed for non-linear outcomes). This produces the same results as the instrumental variable regression procedure above; note the output for the coefficient of x and compare it and its standard error to the output from ivregress.

Also note that the coefficient for z predicting x is ${\overline{x}}_{z=1}-{\overline{x}}_{z=0}=.9-.2=.7$ as expected.

Appendix 2. Predicted probabilities based on varying levels of contamination (with 95% confidence intervals)

	Proportion of responding officers assigned to wear a BWC
	0%	33%	50%	66%	100%
Officer-initiated	11.31%	11.47%	11.56%	11.64%	11.82%
Arrest	26.42%	26.48%	26.51%	26.54%	26.60%
Use of force	0.04%	0.05%	0.05%	0.05%	0.06%
Complaint	0.01%	0.02%	0.02%	0.02%	0.02%

1. Note: Results based on Model 1 for each outcome, holding all other covariates at their means