The Burglary Boost: A Note on Detecting Contagion Using the Knox Test

Objectives

A large body of literature in quantitative criminology finds that the spatio-temporal clustering of burglary is greater than one would expect from chance alone. This suggests that such crimes may exhibit a “boost” effect, wherein each burglary increases the risk to nearby locations for a short period. In this study, we demonstrate that standard tests for spatio-temporal dependence have difficulty distinguishing between clustering caused by contagion and that caused by changing relative risks. Therefore, any estimates of the boost effect drawn from these tests alone will be upwardly biased.

Methods

We construct an agent-based model to generate simulated burglary data, and explore whether the Knox test can reliably distinguish between contagion (one burglary increases the likelihood of another burglary nearby) and changes in risk (one area gets safer while another gets more dangerous). Incorporating insights from this exercise, we analyze a decade of data on burglary events from Washington, DC.

Results

We find that (1) absent contagion, exogenous changes in relative risk can be sufficient to produce statistically significant Knox ratios, (2) if risk is changing over time, estimated Knox ratios are sensitive to one’s choice of time window, and (3) Knox ratios estimated from Washington, DC burglary data are sensitive to one’s choice of time window, suggesting that long-run changes in relative risk are, in part, driving empirical estimates of burglary’s boost effect.

Conclusions

Researchers testing for contagion in empirical time series should take precautions to distinguish true contagion from exogenous changes in relative risks. Adjusting the time window of analysis is a useful robustness check, and future studies should be supplemented with new approaches like agent-based modeling or spatial econometric methods.