Spatio-Temporal Crime Processes

Crime as a Spatio-Temporal Process

Butry and Prestemon (2005) and Prestemon and Butry (2005) found that wildland arson is a crime that may be particularly suited to hotspotting. Wildland arson, like other crimes, is concentrated in space and in time, due to concentrations of criminals and fuel quantities in space and the concentration of amenable fire-setting weather and dry fuel in time. Genton and others (2006) showed how this clustering in space can last many years, whereas Prestemon and Butry (2005) showed concentrations at the daily time scale, and Butry and Prestemon (2005) showed concentrations at the daily time scale in relatively limited geographical areas.

Wildland Arson as a Spatio-Temporal Process

Prestemon and Butry (2005) found that, for small county aggregates in Florida, wildland arson is concentrated in time, with an elevated risk for more such ignitions for up to 11 days after an initial ignition. This kind of temporal clustering is consistent with models of serial and copycat criminal activity, patterns, and behaviors observed for other crimes (Brandt and Williams 2001, DiTella and Schargrodsky 2004, Surrette 2002). Also important are weather, as measured by the Keetch-Byram Drought Index, which indexes fuel conditions on fine temporal scales and captures the effect of fuel moisture on ignition success rates or the cost of igniting a wildfire; historical wildfires and prescribed fire in the location, which reduce fuels and usually reduce arson risk by making fire setting more difficult or costly; and intra-annual patterns of weather, as measured by month dummy variables, which are probably also related to fuel conditions and therefore fire setting cost or success. Other explanatory variables, which fit an economic model of crime, include police per capita, the retail wage rate, and poverty. Daily variations were also found to matter, with arson more common on Saturdays and sometimes holidays.

Butry and Prestemon (2005) evaluated wildland arson patterns in Florida, where ignitions were geolocated to the Census Tract. This analysis related wildland arson ignitions in a single day to, in addition to the same set of variables used in Prestemon and Butry (2005) at the county level, wildland arson ignitions in previous days in the same and neighboring Census tracts in six high-arson tracts in the State. Their analysis found that wildland arson ignitions in the Census tract are related positively to ignitions in the same tract in the previous several days and in local (immediately surrounding) and regional (an outer shell of) neighboring tracts in the previous 11 days. They found that a current day’s count of ignitions could be explained by local neighbors for up to 11 days, regional neighbors for up to 4 days, and ignitions in the same tract for up to 10 days. Thus, it appears that short-term arson ignition process propagates like a contagion (although the exact pattern in space-time was not identifiable).

National forests and wildland arson

In research similar to that reported by Prestemon and Butry (2005), we report here an analysis of arson ignitions on national forests in California (see figure at right). We estimate daily and annual models of arson fires at the national forest level. Models use wildfire data from the USDA Forest Service National Interagency Fire Management Integrated Database (NIFMID), unemployment and population data from the California Department of Finance (2005), law enforcement data from the California Department of Justice (2005), and climate and weather data from the National Oceanic and Atmospheric Administration (2005) and the National Climatic Data Center (2004). The models are generally specified as in Prestemon and Butry (2005), capturing temporal autocorrelation and not directly quantifying spatio-temporal patterns, but omit information on wages and poverty. Also, unlike in Prestemon and Butry (2005), the number of sworn full-time equivalent police officers, a measure of law enforcement effort, is lagged one year to avoid issues of simultaneous determination with crime and to allow for lagged perceptions among potential arsonists on arrest probability (Lochner 2007). As in Prestemon and Butry (2005), a Poisson autoregressive model of order p (Brandt and Williams 2001) is specified for the daily ignitions for the San Bernadino, Sierra, Cleveland, and Angeles National Forests, 1994-2002 (Table: Poisson autoregressive models of order p of daily wildland arson fire occurrences for selected high-arson California national forests, 1994-2002). An annual panel fixed effects Poisson model (Greene 2003) is specified using data from all 18 national forests in the State, 1993-2002 (Table: Fixed-effects panel Poisson model of wildland arson fire occurrences, 18 California national forests, 1993-2002).

In the daily model, significant variables (at 5 percent) influencing arson ignitions on the two national forests studied include up to 5 ignition lags (positively); alternative models that drop these lags (i.e., non-autoregressive alternative versions) explain significantly less variation in daily wildfire at high significance (last row of Table: Poisson autoregressive models of order p of daily wildland arson fire occurrences for selected high-arson California national forests, 1994-2002). This result is consistent with serial or copycat fire setting activity. The model also found that many month dummy variables are significant, which indicates that arson, like other fire causes, has a seasonal pattern that may be related to seasonal weather and fuel moisture variations that affect the difficulty or costs of successfully igniting arson fires. Also, for these national forests, the coefficient on the Saturday dummy is significant and positive in two cases (Sierra N.F. and Cleveland N.F.) and the coefficient on the holiday dummy variable is significant and positive in one case (Sierra N.F.), both results indicating higher arson fire probability, which, in the context of an economic model of crime, is consistent with lower opportunity costs of time faced by arsonists those days. In contrast, dummy variables for weekdays are not significant, indicating that those days of the week have the same arson probabilities as Mondays. The average annual Palmer Drought Severity Index is not significantly related to fires. The unemployment rate is negatively related to arson ignitions in two cases (Sierra N.F. and Angeles N.F.), which conflicts with expectation, but positive in two cases (San Bernadino N.F. and Cleveland N.F.), which does fit with expectation. A similar conflicting result occurs for law enforcement: higher law enforcement levels are significantly and negatively related to arson rates in one case (the Cleveland N.F.) but are positively related to arson in another (Sierra N.F.). The latter finding is not expected and could be a consequence of omitted variables related to wages or other justice-related expenditures, (e.g., sanction levels). But, the former finding for the Sierra N.F. would be expected based on the opportunity costs of being caught and convicted of setting an arson wildfire. Finally, lagged wildfire area (the running total of the area burned by wildfire in the national forest in previous years) is negatively related to arson wildfire in all cases where statistical significance is found. This is consistent with our expectations, as wildfires can reduce landscape fuels, providing the prospective arsonists with greater difficulty or higher costs of successful arson fire setting. In summary, the majority of these findings are consistent with those of Prestemon and Butry (2005), supporting an economic model of crime and one that confirms the temporal clustering of arson ignitions on these forests. However, some conflicting results indicate further research into the daily arson fire setting process for California National Forests is necessary.

In contrast with uncertainty about the role of law enforcement and socioeconomic factors in wildland arson, the annual models provide results consistent with expectations (Table: Fixed-effects panel Poisson model of wildland arson fire occurrences, 18 California national forests, 1993-2002). Here, law enforcement officers per capita are significantly and negatively related and unemployment is significant and positively related to wildland arson ignitions. The finding of the deterrent (negative) effect of policing on wildland arson is entirely consistent with crime theory, indicating that either (i) arsonists perceive higher opportunity costs of being caught, or (ii) more arsonists are caught and convicted and, hence, are removed from the arson fire setting population.

Biophysical variables also explain significant variation in annual levels of wildland arson ignitions on national forests: lagged wildfire (positively for 2-, 3-, 11-, and 12-year lags and negatively for 1-, 4-, 8-, and 10-year lags); the Pacific decadal oscillation (positively); the Palmer Drought Severity Index (positively for 2- and 3-quarter lags and negatively for 1- and 4-quarter lags); and the Niño-3 SST anomaly (negatively) (Table: Fixed-effects panel Poisson model of wildland arson fire occurrences, 18 California national forests, 1993-2002). Population is negatively related to wildland arson risk, a finding that cannot be fully explained, except in the context of omitted variable bias. Nor is there an explanation for the unusual statistical correlations between arson ignitions and longer lags of wildfire activity, thus left to future research.

What these results for the California National Forests show is broad consistency with the results found for Florida: wildland arson ignitions are clustered in time (5 days in two high-arson national forests in California, up to 11 days in Florida); law enforcement is generally negatively related to arson rates; climate and weather variables matter, in a more complex intra-annual pattern in California than in Florida; and fuel levels matter, although in a more complicated way in California than in Florida. Left uninvestigated are the influences of other labor market variables, poverty, and other measures of criminal sanctions.