Measuring the Impacts of Everyday Police Proactive Activities: Tackling the Endogeneity Problem



To examine how the practice of daily proactivity affects and responds to changes in crime at micro geographic and temporal scales.


Police calls for service and automated vehicle location data from a large suburban jurisdiction were used to create comprehensive measures of police proactivity. Panel data and the generalized method of moments framework were applied to tease out the endogenous relationships between crime and police proactivity and understand the unique impact of proactive patrol and crime upon one another.


Daily police proactivity in this locality was highly stable at micro places, although police did intensify their activities very briefly in response to recent changes in crime. In turn, increases in proactive patrol generated immediate increases in crime reporting, followed by fleeting residual deterrent effects that were weaker and less robust. The patterns remained relatively consistent when varying the units of analysis or focusing on hot spots with different profiles of proactivity, but the deterrent effects appeared more sensitive to model specification. Of all measures of proactivity, patrols of medium length and non-traffic enforcement activities were associated with stronger evidence of crime reduction effects.


Short-term adjustments in hot spot patrols appear to produce both reporting effects and temporary residual deterrent effects as measured through calls for service and police vehicle location data. Police could potentially enhance and prolong their deterrence by adopting more deliberate strategies with their daily proactive behaviors, including making their proactive activities more targeted and sustained.

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  1. 1.

    Information retrieved from Koper et al. (2020).

  2. 2.

    Assuming that an officer calls in for a proactive activity (as noted, this can be uncertain), the length of a call as recorded by CAD could overestimate or underestimate the actual length of officer presence on scene for various reasons. Officers might close out a call after they have left the scene while writing their report elsewhere. They might also close out a call yet continue to stay in the area. Conversely, officers might mark out for proactive work at a hot spot as they are driving to the location. To provide some tentative insight into this issue, we looked at instances in which CAD suggests that officers were in the hot spot on a proactive call, but the AVL shows that they were somewhere else (either a non-hot spot location or another hot spot) for at least part of the “on scene” time record in CAD. We found that this happened in about 55% of proactive calls recorded in CAD. Determining the precise extent of this error in the measurement of time on-scene would require extensive calculations and may be a useful subject for future methodological research. Nonetheless, this basic illustration underscores the caveat that CAD-based time measures should be viewed as approximations of time on scene.

  3. 3.

    Hence, our focus is on police actions and impacts in the hot spots that were most active and stable during the study year.

  4. 4.

    Under the standard definition of Granger (1969) causality, for each individual \(i\in [1, N]\), a stationary variable \({x}_{i,t}\) is deemed to be “causing” another stationary variable \({y}_{i,t}\), if past values of \({x}_{i,t}\) increase the predicting power of the model on \({y}_{i,t}\) compared to using only past values of \({y}_{i,t}\). The original Granger Causality test was spelled out for individual time series data only, but scholars have extended the formula to panel data given the proliferation over time of panel data with large N and large T (Dumitrescu and Hurlin 2012). Individual effects are fixed in the time dimension, controlling for the effect of time-invariant variables (Allison 2005). Lag orders are assumed to be identical for all cross-section units of the panel and the panel should be balanced with an equal number of time points for each cross-sectional unit.

  5. 5.

    Panels with small T and large N are particularly susceptible to such biases. Judson and Owen (1999) suggest a 20% downward bias in the coefficient of a lagged dependent variable using within group transformation even when T = 30. That being said, the current study is likely less affected by the dynamic bias due to the relatively long time series (T = 52).

  6. 6.

    Depending on the underlying autocorrelation structure in the outcome series, one or several lagged terms of the dependent variable are included in the GMM models. Two test statistics are conducted specifically to assist with model identification. The Arellano-Bond test for ARs in first differences detects autocorrelation left in the differenced residuals. The test for an AR(1) process in first differences is expected to be significant, since the residuals of the differenced equation should possess serial correlation by construction (i.e., \({y}_{i,t-1}\) is correlated with \({v}_{i,t-1}\) in the error term in differences, \(\Delta {\varepsilon }_{it}={v}_{it}-{v}_{i,t-1}\), by construction). The test for an AR(2) process, however, should not reject the null hypothesis because it tests for serial correlation in levels (e.g., when the AR(2) term is significant, \({y}_{i,t-2}\) would be endogenous to \({v}_{i,t-1}\) in the error term in differences, \(\Delta {\varepsilon }_{it}={v}_{it}-{v}_{i,t-1}\), and therefore becomes an invalid instrument). Adding higher-order lags of the dependent variable (and occasionally the independent variables) as regressors typically removes the serial correlation. In addition, the Sargan/Hansen and the difference-in-Hansen tests are part of the standard output following system GMM estimation and are typically used to understand the validity of the model specification and whether the instruments or subsets of instruments are exogenous. Insignificant test statistics are preferred as they suggest that the model specifications are valid.

  7. 7.

    Back-up activities, in particular, occurred in about 17% of officer-initiated calls in the jurisdiction, with an average of 1.3 officers attending a proactive officer CAD call (these back-ups are not included in the CAD measure of proactivity). Adjusting for this, roughly 24 of the 31 lengthier AVL visits might have been independent in nature.

  8. 8.

    Note that any impact of the lagged independent variable is a partial effect, namely, the effect of a one-unit change in past week’s crime or proactivity on current proactivity or crime, holding everything else in the model unchanged. Past proactivity, for example, might also affect past crime, which, in turn, affects current crime. While it may be possible to quantify the long run effect of the predictor, the study focuses on the direct impact of crime and proactivity that go beyond the first week.

  9. 9.

    The grid cell approach is tested with CAD data only to limit to a reasonable extent the extensiveness of the robustness analysis.


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Correspondence to Xiaoyun Wu.

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Appendix A

See Table 6.

Table 6 Types of calls included in the measure of crime and disorder, serious crime, and proactivity

Appendix B

See Table 7.

Table 7 Unit root test for crime and proactivity series

Appendix C

See Table 8.

Table 8 Granger causality tests for serious crime and proactivity (adjusted z values reported)

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Wu, X., Koper, C. & Lum, C. Measuring the Impacts of Everyday Police Proactive Activities: Tackling the Endogeneity Problem. J Quant Criminol (2021).

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  • Police proactivity
  • Police everyday practice
  • Deterrence
  • GMM
  • Reverse causality