Net reductions or spatiotemporal displacement of intentional wildfires in response to arrests? : evidence from Spain

Net reductions or spatiotemporal displacement of intentional wildfires in response to arrests? Evidence from Spain Jeffrey P. Prestemon A , E ,David T. Butry B ,Marı´a L. Chas-Amil C and Julia M. Touza D A Forest Policy and Economics Research, Southern Research Station, USDA Forest Service, Forestry Sciences Laboratory, PO Box 12254, Research Triangle Park, NC 27709, USA. B Applied Economics Office, Engineering Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Mailstop 8603, Gaithersburg, MD 20899-8603, USA. C Departamento de Economı´a Cuantitativa, Universidade de Santiago de Compostela, Avenida Xoa ´n XXIII s/n, 15782, Santiago de Compostela, Spain. D Department of Environment and Geography, University of York, Wentworth Way, Heslington, York, YO10 5NG, UK. E Corresponding author. Email: [email protected] Abstract. Research to date has not examined how the impacts of arrests manifest across space and time in environmental crimes. We evaluate whether arrests reduce or merely spatiotemporally displace intentional illegal outdoor firesetting. Using municipality-level daily wildfire count data from Galicia, Spain, from 1999 to 2014, we develop daily spatiotemporal ignition count models of agricultural, non-agricultural and total intentional illegal wildfires as functions of spatiotemporally lagged arrests, the election cycle, seasonal and day indicators, meteorological factors and socioeconomic variables. We find evidence that arrests reduce future intentional illegal fires across space in subsequent time periods. Additional keywords: arson, autoregression, elections, negative binomial, panel data, spatiotemporal, zero inflation. Received 13 June 2018, accepted 16 April 2019, published online 31 May 2019 Introduction Natural resource managers worldwide face a challenge of how to limit the occurrence of accidentally and intentionally ignited wildfires that destroy property, damage resources and harm people. A changing climate is projected to increase wildfire potential, severity and extent (e.g. Krawchuk et al. 2009;Liu et al. 2010;Jolly et al. 2015), potentially exacerbating the damages and raising the urgency of addressing human-ignited wildfires (Balch et al. 2017;Bowman et al. 2017). Among the strategies and tactics available to policy-makers in response to heightened wildfire risks is to boost law enforcement efforts (e.g. Donoghue and Main 1985;Butry and Prestemon 2005; Prestemon and Butry 2005;Prestemon and Butry 2010;Abt et al. 2015) aimed at apprehending and deterring intentional firesetters. 1 With only a few exceptions (e.g. Thomas et al. 2011; Prestemon et al. 2012), research has not evaluated how and whether arrests, a discrete measure of law enforcement efforts, are linked to reductions in the occurrence of intentional fires or whether such efforts have broader impacts across space and time. The effects of law enforcement efforts are potentially complex, considering motivated offenders’ dynamic responses. Criminologists have long recognised that actions by law enforcement or other groups intended to reduce crime in one time or place or of one type might be at least partially offset by compensating shifts in behaviours of prospective offenders in response to those efforts (e.g. Cornish and Clarke 1987;Barr and Pease 1990;Eck 1993;Clarke and Weisburd 1994;Guerette 2009). Although spatiotemporal concentrations in arson are evident in maps of wildfires (e.g. Mothershead 2012), no study has sought to characterise the effects of arrests on these fires at fine spatial scales or over longer time scales than detected by Prestemon et al. (2012). Understanding how law enforcement efforts affect the timing and locations of future offending, including illegal firesetting, is critical to enacting effective policies and in the design of more effective law enforcement strategies (e.g. Weisburd and Eck 2004) aimed at reducing the occurrence of unwanted wildfires. The primary objective of our study is to assess whether there is evidence of spatiotemporal displacement effects of law 1 In this study, we define all intentional firesetting as illegal and so refer to intentional illegal firesetting as ‘intentional firesetting’. CSIRO PUBLISHING International Journal of Wildland Fire 2019,28, 397–411 https://doi.org/10.1071/WF18234 Journal Compilation ÓIAWF 2019 Open Access CC BY-NC-ND www.publish.csiro.au/journals/ijwf enforcement in intentional outdoor firesetting. To do this, we develop statistical models that control for hypothesised driving factors in addition to arrests. Among the driving factors we include are variables describing the seasonality of intentional firesetting, which likely stems from regular variations in fuel flammability and ignition attempts related to agricultural or other seasonal activities (e.g. hunting) and daily human routines (days of the week and holidays). Additionally, we include variables explaining firesetting variation at longer time scales, which capture associations with slowly changing aggregate wildland fuels and demographic and economic conditions. Finally, we include a set of indicators of election seasons, which have been shown in other research to be criminogenic for firesetting in Europe (e.g. Seijo 2005;A ´lvarez-Dı´az et al. 2015;Ramos and Sanz 2018). 2 With the inclusion of election season indicators, we are able to quantify the daily time scale imprint of one form of politically based protest actions (Pyne 1995), extending existing research and providing additional policy-relevant insights. Their inclusion also helps to explain variation in observed intentional wildfires, increasing the power of our statistical inferences regarding law enforcement spatiotemporal effects. This study advances the earlier work by Prestemon et al. (2012) by including spatiotemporal lags of arrests in the equation specifications. Although those authors allowed for effects of arrests at long temporal scales, their models did not include arrests lagged as long as in the present study. Furthermore, their models were not specified in a way that quantified how intentional fires in one location could be associated with arrests in nearby locations in previous time periods. Finally, Prestemon et al. (2012) ignored the potentially differing firesetting processes across reported motivations, which we find are distinct in their responses to arrests, a potentially important distinction with implications for law enforcement resource allocation decisions. The study also advances research into the role of elections on wildfires in Spain conducted by A ´lvarez- Dı´az et al. (2015), who used reduced-form vector error correction modelling methods to identify the association between the total numbers of forest fires during ‘intense’ electoral years. Our study, in contrast, estimates count data structural equations of intentional wildfires in Spain, controlling for the many factors that influence wildfire ignition processes, including the motivations of firesetters, arrests and elections. Our equations are estimated at fine temporal (daily) and spatial (municipality) scales, measuring how specific phases of elections affect the daily pattern of firesetting in the run-up to elections. Theory and methods Theory of intentional firesetting Cohen and Felson (1979) describe a Routine Activities (RA) theory of crime that forms the foundation on which we build our empirical model of the numbers of intentional wildfires. These authors contend that criminal activities vary over time and space according to variations in the simultaneous overlap of three essential elements of crime occurrence: (1) a motivated offender, (2) a suitable target, and (3) the absence of capable guardians against a violation; if one of these elements is missing, then a crime will not occur. It is straightforward to design an empirical modelling framework around RA theory because motivated offenders and suitable targets are simple to define. Geographers, philosophers and criminologists dating back several centuries have recognised that persistent criminal activity has evident spatial components related to societal and landscape features (see Cohen 1941 and Cohen and Felson 1979 for informative syntheses). As Cohen and Felson (1979) argue, defining RA theory, persistent spatial and temporal concentrations of offending may be attributed to fine- and coarse-scale spatial and temporal (hourly, daily, seasonal) features of landscapes and routine human behaviours as well as to temporally trending variations in the relative abundances of motivated offenders, suitable targets and capable guardians. Here, we propose that RA theory is an amenable framework for understanding these observed spatial and temporal patterns. In the development of an empirical version of an RA theory of intentional firesetting, we identify candidate physical, biological and societal variables that vary over space and time that can be mapped to one (or more) of the three elements of RA theory. With this empirical framework, we are able to test for spatiotemporal displacement and uncover the effects of other policyrelevant phenomena on intentional firesetting. We summarise the variables connected to each of these three elements of RA theory as it relates to intentional firesetting: Motivated offenders Variations in the numbers of motivated firesetters in a location are likely related to several demographic, social and economic factors, including the size of the human population, historical efforts to remove known offenders from the location and factors that influence motivations to offend. Such motivational factors can be broadly defined as incentives to commit a crime (e.g. utility gained or pecuniary benefits acquired). In the case of intentional wildland firesetting, greater incentives might exist during times of political discord (Dyke 2007), when firesetters protest by igniting wildfires (e.g. Pyne 1995;Kull 2002;Seijo 2005,2009;Hovardas 2014,2015;Skouras and Christodoulakis 2014;A ´lvarez-Dı ´az et al. 2015;Ramos and Sanz 2018); when agricultural areas may be prepared for planting by (illegally) burning them; and when the opportunity costs of time for firesetters are low (e.g. in times and places where they are unemployed) (e.g. Prestemon and Butry 2005; Sebastia´n-Lo´pez et al. 2008), which reduces the pecuniary cost of spending time trying to ignite fires and the expected costs of being arrested and imprisoned for igniting a fire. Suitable targets Variations in suitable targets for intentional wildfires can be explained by variations in the availability of flammable 2 Mechanisms proposed or identified for how electoral cycles could influence intentional firesetting include election-related adjustments in law enforcement effectiveness – law enforcement budgets (Efthyvoulou 2012) and police force levels (Levitt 1997) – and the scope or severity of criminal sanctions (Smith 2004;Dyke 2007;Berdejo´ and Yuchtman 2013). 398 Int. J. Wildland Fire J. P. Prestemon et al. wildland fuels and in the weather suitable for successful ignition and spread. Capable guardians Variations over time and space of capable guardians could be indexed by law enforcement efforts: the number of patrol officers or the effectiveness of law enforcement actions (e.g. arrests). Measures of political discord, which can induce reallocations of law enforcement resources across space and time, could further be proxies for short-run changes in capable guardianship. Our introduction of arrests into an RA-based theory of intentional firesetting bears further exploration. Because offenders who are caught are often sanctioned by imprisonment, an arrest actually affects two elements of RA theory. First, the arrest can shrink the pool of motivated offenders by removing spatially stationary serial criminals from the landscape (e.g. Canela-Cacho et al. 1997;Ratcliffe and Rengert 2008). Second, an arrest, if observed widely across space, potentially raises the perceived strength of capable guardianship. 3 Guardianship adjustments may be more likely to occur close to the location of the arrest (e.g. Levitt 1998;Pogarsky et al. 2004), we hypothesise, because arrest information may be more readily communicated locally to motivated offenders, achieving a local crime reduction subsequent to the arrest. If the arrest information is more broadly disseminated across space, then this adjustment could result in a deterrent effect across a larger spatial domain, revealed, in the case of intentional firesetting, as a reduction in the number of fires in subsequent time periods in surrounding locations. The motivated offender may also be induced by an arrest to change their ‘domestic base’ of operation in order to avoid localities where capable guardianship has increased (e.g. Telep et al. 2014). The result of this dynamic response by motivated offenders may be higher overall crime rates farther from the arrest location in subsequent time periods, revealing how law enforcement actions could displace crime in space–time (e.g. Eck 1993;Bowers and Johnson 2003;Guerette and Bowers 2009;Bowers et al. 2011). Displacement caused by an arrest would be revealed by, all other things being equal, higher numbers of intentional fires in subsequent time periods in areas more distant from the arrest location. Application of RA theory to intentional firesetting should comprehend existing evidence of positive temporal autocorrelation in intentional firesetting (e.g. Butry and Prestemon 2005; Prestemon et al. 2012). The cited studies attribute positive autocorrelation to a combination of serial and copycat firesetting. Kocsis and Irwin (1997) find that serial arsonists (along with rapists and burglars) tend to commit their crimes close to their domestic base but also exhibit an occasional ‘commuter pattern’, ranging farther from the domestic base to carry out some of their offending. Such spatiotemporal clustering of firesetting is consistent with the near repeat hypothesis in crime victimisation tested by many analysts of certain property crimes (e.g. Townsley et al. 2003;Bowers and Johnson 2005;Bernasco 2008;Ratcliffe and Rengert 2008;Bernasco et al. 2015) and identified as well for non-wildland arson (Prestemon et al. 2013; Grubb and Nobles 2016). Empirical specifications The study location chosen is the region of Galicia, Spain, where intentional wildfires are the dominant cause attribution (Ponte Pintor and Bandı´n Buja´n 2008). Galicia is also a region with a large enough number of intentional wildfires (half of Spain’s) and associated arrests to permit statistical identification of spatiotemporal effects of arrests. Accurate quantification of the spatiotemporal displacement of intentional firesetting due to arrests might depend on the type of motivated offender who is being modelled. Therefore, we test for the spatiotemporal effects of arrests and the effects of elections and other driving variables by partitioning our data according to whether a fire is classified as agriculturally or nonagriculturally motivated. Separate evaluation of these two broad categories of intentional firesetting could reveal the potential biases of modelling that ignores their different nature and uncovers their distinct spatiotemporal dynamics. Also, separate modelling by motivation could potentially yield more accurate assessments of the overall effects of changes in law enforcement efforts and elections on firesetting in the region and reveal how prevention efforts might be differently focused on these two categories of intentional fires. More formally, we express the probability of Iintentional wildfires started for motivation min location jin period tas a function of a vector of variables affecting the number of motivated offenders in period t(Y j,t ), a vector of variables measuring the availability of suitable targets in period t(W j,t ), and vectors of measures (A j,t ) of the presence of (effective) capable guardians in location jand nearby locations kover l lagged time periods as: PrðIm j;tÞ¼fðYj;t;Wj;t;Aj;t;Ak;tÞð1Þ Vector Y j,t , the number of motivated offenders in our study, comprises the human population in the location (P j,t ); incomeearning (G j,t ) potential for residents of location j; the unemployment rate (U j,t ); dummies measuring holidays (H t ) and each of two weekend days (Rt¼ðRSat t;RSun tÞ), when the opportunity costs of firesetting are lower (and motivations higher) (Gill et al. 1987;Prestemon and Butry 2005;Prestemon et al. 2012); and a subvector of variables describing the occurrence of an election (E j,t ), Ej;t¼ðEc j;t;Ec j;tþ15;Ec j;tþ30;Ec j;tþ45;Es j;t;Ed j;tÞ, where Ec j;tis a dummy variable ¼1 during the next 15 days (also called campaign days) in advance of an election, 0 otherwise; Es j;tis a dummy variable ¼1 during the single silence day before an election, 0 otherwise; and Ed j;tis ¼1 for the single day of the election. Note that the tþ15, tþ30 and tþ45 leads of the election campaign days dummy variable are intended to capture 3 Another way to view ‘motivation’ is in terms of the prospective offender’s expected net psychic or monetary benefits of crime commission, in the form advanced by Becker (1968). Hence, an increased probability of arrest would be expected to lower the expected net benefits of crime commission. Wildfire spatiotemporal displacement Int. J. Wildland Fire 399 the potentially long criminogenic temporal footprint of elections. Also, note that the last lead only occurs to 52 days, which covers only the last week of the 52-day statutorily required number of days from the announcement of an election and the election’s actual occurrence. The motivated offender vector is therefore Yj;t¼ðPj;t;Gj;t;Ut;Ht;Rt;Ej;tÞ. The vector W j,t , the number of suitable targets in location jin period t, is described as a function of available flammable fuels, which can be quantified by a vector of meteorological variables (Zj;t), consisting of minimum daily relative humidity (Z1 j;t), total daily precipitation (Z2 j;t), the Keetch–Byram Drought Index (Keetch and Byram 1968)(Z3 j;t), the Fire Weather Index (Fosberg 1978)(Z4 j;t), daily maximum hourly wind speed (Z5 j;t) and maximum daily temperature (Z6 j;t) (e.g. Prestemon et al. 2012), so that Zj;t¼ðZ1 j;t;Z2 j;t;Z3 j;t;Z4 j;t;Z5 j;t;Z6 j;tÞ. It also includes seasonal variation in firesetting (e.g. Fuller 1996), as a set of 11 month dummy variables, DMt¼ðDMJan t;DMFeb t;...;DMNov tÞ, with the effect of December included in the intercept. The suitable targets vector is Wj;t¼ðZj;t;DMtÞ. Finally, vectors of variables indexing capable guardianship in location jin period tare measured by successive lags of arrests for intentional firesetting (of either motivation, because we lack specific information about the motivations of arrestees). We include running sums of the count of arrests lagged t1 to t365 and t366 to t545inlocationj,sothat Aj;tl¼P365 l¼1Aj;tl;P545 l¼366 Aj;tl  . Recognising the recommendations about choice of buffer distances (Phillips 2011), we use a proportionate size criterion, with buffer radii at 10, 15 and 25 km. These radii are also justified by observed firesetting behaviour by serial arsonists in Spain (Sotoca Plaza 2016). Variables on the neighbouring arrests were also generated using running sums; these occurring in three successively more distant ‘doughnuts’ around the municipality: 10, 15 and 25 km, with vector Ak;tl¼ðA5km k;t;A15km k;t;A25km k;tÞ,A5km k;t¼P365 l¼1A5km k;t1;P545 l¼366 A5km k;t1  , A15km k;t¼P365 l¼1A15km k;tl;P545 l¼366 A15km k;tl  ,A25km k;t¼P365 l¼1A25km k;tl;P545 l¼366 A25km k;tl  . The number of intentional wildfires is hypothesised to follow a count process, distributed as Poisson but with a variance s 2 that is a function of its expected value (m j ) and a scale parameter, a, i.e. a negative binomial model (Cameron and Trivedi 1998, p. 70), sj¼mjþm2 j. Adding the time subscript (t), indicating the motivation mand consolidating the independent variables shown in Eqn 1 into a single vector (X j,t ) and a conforming vector of parameters (b m ), we have: mm j;t¼expðX0 j;tbmÞð2Þ Eqn 2 assumes that all spatial units have independently and identically distributed errors, a situation not likely to be met. Therefore, a fixed-effects process is considered, allowing for variations across municipalities in the average rates of intentional wildfires due to time-invariant unobservable factors. Therefore, Eqn 2 is augmented to include indicator parameters representing locations, a j-dimensional vector D m : mm j;t¼expðX0 j;tbmþDm jÞð3Þ The likelihood function for Eqn 3 is: ln Lðam;bm;DmÞ¼XN j¼1XT t¼1ln tþam1  n ln Im j;t!Im j;tþam1  ln 1 þamexp X0 j;tbmþDm j  þIm j;tln amþIm j;tX0 j;tbmþDm j o ð4Þ A random-effects version of this same general model for cross-sectional data is also available, but in the interest of brevity, we do not show its specification or likelihood equation. To account for temporal autoregressivity in intentional wildfires, we adopt a method recommended by Zeger and Qaqish (1988) and elaborated in Cameron and Trivedi (1998, p. 239–240). Their approach entails specifying two variables, Im j;t1and dm j;t, constructed from lags of the dependent variable: Im j;t1¼Im j;t1and dm j;t¼0;Im j;t140; Im j;t1¼1 and dm j;t¼1;Im j;t1¼0ð5Þ Lags of the variables specified in Eqn 5 accommodate higher orders of autoregression in the count process. In estimation, X0 j;tbmcan be augmented to include r-dimensional subvectors Im trand dm trþ1, where ris the order of autoregression. Coefficients on the elements of Im trare estimates of autoregressive components, and those in dm trþ1rescale the effect of the lagged dependent variable in cases in which Im j;t1¼0. The presence of significant autoregression in the dependent variable implies that there are short-run and long-run effects of a change in the elements of X j,t besides Im trand dm trþ1. The longrun effect of any non-autoregressive variable iin X j,t on Im is calculated as ^ bm;LR i¼^ bm i=ð1Pr u¼1 ^ bm uÞ, where ^ bm uis the estimated autoregressive component u(u¼1,y,r), quantified as the coefficient of Im tufrom the estimate of Eqn 3 or Eqn 4, augmented by Im trand dm trþ1. Following Leamer (1983), and with examples of the importance of his recommendations (e.g. Levine and Renelt 1992), it has now become standard practice in many economics journals to test inferences across multiple specifications in order to evaluate whether these inferences are robust to specification. We follow this practice by testing for the effects of arrests, elections and other hypothesised variables using several specifications that carry with them different assumptions about the intentional wildfire data generation process. In addition to a fixed-effects negative binomial and a random-effects negative binomial, we model intentional wildfires using four alternative estimators, which each make differing assumptions about the intentional wildfire data-generating process. These include (i) a pooled (across municipalities) negative binomial model that controls for municipality-level differences in error variance; (ii) a pooled negative binomial (NB) model with municipality indicators that also controls for municipality-level differences in error variance; and two specifications that recognise potential zero inflation in the count of intentional wildfires: (iii) a pooled zero-inflated negative binomial (ZINB) model that controls for municipality-level differences in error variance, and (iv) a pooled ZINB with municipality indicators that also controls for municipality-level differences in error variance. 400 Int. J. Wildland Fire J. P. Prestemon et al. Evaluation of the magnitudes of the effects of the variables of interest – arrests and elections – was done with a counterfactual analysis. In the case of arrests, we can quantify the long-run average effects of an arrest by, say, simulating an increase in the number of arrests by 1% and observing how the predicted counts of intentional wildfires changes, or tm;A¼PT t¼0PJ j¼0ð^ Im;Ajt¼Ajt j;t^ Im;Ajt¼Ajt j;tÞ. Arrest effects are measured with an elasticity. To evaluate the non-marginal effects of elections, we compare the predicted counts of intentional wildfires with the counts predicted with all election dummy variables set to zero, tm;E¼PT t¼0PJ j¼0ð^ Im;Ejt¼0 j;t^ Im;Ejt¼Ejt j;tÞ. Election effects are measured as changes in total numbers and percentage. Given that our data are spatially arranged, maximum likelihood estimation of any of our model specifications could produce spatially autocorrelated residuals deriving from omitted spatially correlated factors (e.g. Dormann et al. 2007), which would have the effect of attenuating standard errors. Although more complex methods of bounding of our model coefficient estimates do exist (e.g. Hall 1985;Liu and Singh 1992), and these could be tried in future studies to uncover any residual spatial autocorrelation remaining, Monte Carlo bootstrapped generation of the effects size confidence limits provides a view of the statistical significances of the overall effects of arrests and elections, regardless of any possible standard error attenuation in model estimates. Data and estimation Weassembleddataontotaldailycountsofreportedignitions of agricultural (Im¼agricultural j;t) and non-agricultural intentional wildfires (Im¼non-agricultural j;t) in Galicia, covering a 16-year period between 1 January 1999 and 31 December 2014. The spatial unit of observation is the municipality (Fig. 1), of which there are 313. The wildfire database compiled by the Spanish Forest Service contains observations on 108 527 fires over the 16-year span, burning 431 956 ha. Data on each wildfire include a general cause attribution (lightning, negligence and accidents, intentional, reignition and unknown), the majority of which (81%) are classified as intentional. Intentional wildfires are further subcategorised by ‘motivation’, i.e. as either agriculturally related (i.e. started by farmers to eliminate brush and agricultural debris) or non-agricultural. In our econometric estimates of the fixed effects, random effects and ZINB models, separate equations are reported for each motivation 0 5 10 20 30 km N Fig. 1. A map of Galicia and its municipalities. Wildfire spatiotemporal displacement Int. J. Wildland Fire 401 (m¼agricultural, non-agricultural) as well as their sum, as mentioned. Population data were obtained from municipal administrative records. The population figure was divided by the area of the municipality (P j,t ), with daily changes computed by interpolation. As a proxy of income level (G j,t ), we used the change in the average income declared in annual income tax per year in the municipality, which was provided by the Spanish Tax Agency, and deflated with the annual average of the Consumer Price Index by province (base year 2016); daily values were found by interpolation. The unemployment rate (U j,t ) was the change in the average 30-day centred average rate calculated from monthly municipality unemployment data, with daily changes computed by interpolation. Collected from the Public Employment Service, it was the seasonally adjusted number of unemployed persons aged 16 to 64 years, divided by the total population; daily values were found by interpolation. Holidays (H t ) were official days recognised across Spain and those official days recognised across Galicia only. Data on the meteorological variables for each municipality (Z j,t ) were based on a network of weather stations distributed across Galicia; the centre of each municipality was used as the reference location for computing distances to each weather station, and values were generated with an inverse-distance-weighted spatial averaging process. Daily data on the numbers of arrests, Aj;t, were employed as daily sums of arrests made by the Guardia Civil (gendarmerie) and local police service. Neighbourhood arrest data, Ak;t¼ A5km k;t;A15km k;t;A25km k;t  and their temporal lags were generated for three circular buffers around the centroid of the municipality. Centroid distance was determined using a 1 : 25 000 map of municipalities obtained from the Galician Territorial Information System. Note that buffers for municipalities on the edges of the region can extend into the Atlantic Ocean, where there are no arrests, and into Portugal and neighbouring regions of Spain, where no consistent daily data are available on arrests. To avoid potential biases, the sample of municipalities used was limited to those that did not have a regional border with the rest of Spain or an international border with Portugal within the outermost ring of neighbourhood arrests of the municipality. Municipalities with buffers that reached into the ocean were kept in the sample. Finally, elections variables are defined as representing the various phases of the election cycle of any of four possible levels: local (council), regional, national or European parliamentary. Owing to their individual infrequency, identification of the effects of the different levels of elections was usually not possible (likelihood maximisation failed) if separately modelled, compelling their aggregation. In all models, we attempted to specify autoregressive orders as high as five, but it was clear on estimation that high orders prevented many longer-order autoregressive specifications from converging. Given the convergence problems, we limited our models to control for only first-order autocorrelation. The long lags of arrest data (back to t– 545) effectively shortened the usable dataset by 1.5 years, meaning that parameter estimates cover mid-2000 through December 2014. Effects are reported for the short run, which ignores the autoregressive effect of wildfires within a municipality, and the long run, which incorporates the autoregressive effect. When estimating separate agricultural and non-agricultural intentional fire models, we included the lagged count and lagged zero count indicators (Eqn 5) of both categories. When calculating the longrun effects of elections and arrests, we used only the lagged count of the own type (i.e. the coefficient on agricultural intentional lagged fires was used to make the long-run adjustment, and the same for the non-agricultural category). Maximum likelihood estimation of some of the alternative specifications of the intentional fire count models failed when the sample of municipalities included those with fewer than 200 intentional wildfires, probably a result of lack of model parameter identification. To allow for greater comparability in model results and effect size estimates, models were estimated only for the 113 municipalities with at least 200 total intentional wildfires over the time span. Data sources and descriptions of variables included in models are shown in Table 1. Results Equation estimates Equation estimates for the fixed-effects NB models and the random-effects NB models are shown in Tables 2 and 3 respectively. Estimates with alternative estimators are available from the authors. Summary estimation statistics indicate that the model specifications are significant compared with constantonly model estimates, as measured by the Wald Statistic, distributed chi-squared(i). For total, agricultural and nonagricultural fires, the random-effects NB specification (allowing for differences in variances across municipalities) is preferred over a pooled NB specification with municipality-level heteroscedasticity, according to a chi-squared statistic and according to the significance of the dispersion parameters, which were all significant at a#0.01. Model estimates indicate that nearly all included variables are statistically significant at a#0.01. Nearly all variables intended to account for suitable targets are highly statistically significant in all model estimates, including relative humidity, precipitation, wind speed, maximum daily temperature, the Keetch–Byram Drought Index and the Fire Weather Index. Forest area, however, a measure of aggregate fuels available as ignition targets, is positively related to intentional fires, in total and then also for agricultural intentional wildfires, though not significant for non-agricultural intentional fires. Variables intended to account for temporal variations in the number of motivated offenders are typically also highly statistically significant in all models. Month indicators quantify a seasonal pattern in firesetting for both rural agricultural (possibly related to field preparation) and non-agricultural activities (possibly related to hunting), and they are nearly all highly statistically significantly different from the reference month of firesetting (December), with peak rates observed in February, March and April, an ebb in June and July, more fires in August, and then somewhat more in autumn. In all model estimates, variables controlling for lower opportunity costs for carrying out firesetting at the daily time scale on non-work days, indicators of Saturdays, Sundays and holidays, are statistically significant 402 Int. J. Wildland Fire J. P. Prestemon et al. at a#0.01 and positively signed, as expected (e.g. Prestemon and Butry 2005;Prestemon et al. 2012). Population density generally is associated with more intentional firesetting, as expected (more motivated firesetters per unit area) in most of the model estimates. Unemployment, modelled as the change in rate, meant to capture how the opportunity cost of carrying out and getting caught setting intentional fires affects the number of motivated offenders, is usually not statistically significant. The rate of change in real personal income, expected to be negatively related to the numbers of motivated offenders owing to the higher opportunity costs of being caught intentionally igniting wildfires, demonstrates unexpected sign differences between intentional agricultural and non-agricultural firesetting. In the fixed-effects NB specifications (Table 2), agricultural intentional fires respond negatively to income changes, as expected, while non-agricultural respond positively, counter to expectations (and also positively for total intentional fires). In the random-effects NB specification (Table 3), agricultural fires have the expected negative sign on income changes, while not significant for non-agricultural fires and having an unexpectedly positive association with the total number of intentional fires. Variables intended to model spatial and temporal variations in capable guardianship are nearly all highly significant explainers of variation in intentional firesetting. Arrests at all lag orders evaluated are strongly statistically significant (a#0.01) and negatively signed. These results are found for within the municipality and at progressively greater spatiotemporal lags around the municipality, and they are found for both the fixedeffects and random-effects NB specifications. The negative signs on the spatiotemporal lags of arrests support a hypothesis that arrests do not simply displace intentional fires in space or time; rather, they work to decrease occurrence of such fires for long periods and across broad geographical areas near the arrests, presumably by increasing perceived capable guardianship both within the municipality and in surrounding municipalities. The modelled effects of elections, hypothesised to measure both the numbers of motivated offenders (because elections Table 1. Data sources and summary statistics of model variables for municipalities with at least 200 intentional wildfires, 1999–2014 Variable name Units Reporting frequency Minimum Maximum Mean Source Intentional wildfire ignitions Count Daily 0 16 0.0778 General Statistics of Forest Fires, Spanish Ministry of Agriculture, and Fisheries, Food and Environment Agricultural intentional wildfires Count Daily 0 10 0.0252 General Statistics of Forest Fires, Spanish Ministry of Agriculture, and Fisheries, Food and Environment Non-agricultural intentional wildfires Count Daily 0 12 0.0526 General Statistics of Forest Fires, Spanish Ministry of Agriculture, and Fisheries, Food and Environment Lightning ignitions Count Daily 0 4 0.0006 General Statistics of Forest Fires, Spanish Ministry of Agriculture and Fisheries, Food and Environment Other ignitions Count Daily 0 6 0.0155 General Statistics of Forest Fires, Spanish Ministry of Agriculture and Fisheries, Food and Environment Relative humidity Percentage Daily 18 100 59 Spanish Meteorological Agency (AEMet) Precipitation mm Daily 0 265 4.24 Spanish Meteorological Agency (AEMet) Keetch–Byram Drought Index Index number Daily 0 702 83 Spanish Meteorological Agency (AEMet) A Fire Weather Index Index number Daily 0.36 38.52 7.78 Spanish Meteorological Agency (AEMet) A Average daily windspeed m s 1 Daily 0.05 10.66 2.69 Spanish Meteorological Agency (AEMet) Average daily maximum temperature 8C Daily 3.68 40.76 17.50 Spanish Meteorological Agency (AEMet) Arrests Count Daily 0 6 0.0010 Guardia Civil Population less than 16 years No. persons Annual 19 41 707 2056 Galician Statistical Institute (Instituto Galego de Estatistica) Population less than 16 years Density Persons ha 1 Annual 0.001 8.163 0.262 Galician Statistical Institute (Instituto Galego de Estatistica) Land area ha 3236 37 882 11 508 Fourth Spanish Forest Inventory Average income Thousand euros Annual 4.35 29.59 11.31 Galician Statistical Institute (Instituto Galego de Estatistica) Unemployment rate Percentage Monthly 1.00 16.40 5.84 Galician Statistical Institute (Instituto Galego de Estatistica) Forest land area ha 1050 23 848 7500 Third Spanish Forest Inventory, Fourth Spanish Forest Inventory A Calculated by the authors, using AEMet data. Wildfire spatiotemporal displacement Int. J. Wildland Fire 403 encourage political protest fires) and the numbers of capable guardians (shifting policing intensities), are consistently associated with intentional fire counts across all motivations and model specifications. Results reveal the temporal pattern of election-associated firesetting. First, election days either do not have greater numbers of intentional fires (agricultural in particular) or have fewer such fires (non-agricultural). Second, silence day has a pronounced higher rate of intentional firesetting for total, agricultural and non-agricultural intentional fires. Third, campaign day periods have generally no effects or positive effects on intentional firesetting. For both the fixed-effects NB (Table 2) and the random-effects NB, higher firesetting rates are found in the 32 to 46 days and the 47 to 52 days before the election day but not in the month just before the election. Finally, we find that for total, agricultural and nonagricultural intentional wildfires, intentional wildfires are Table 2. Fixed effects negative binomial model estimates for all intentional, agricultural intentional and non-agricultural intentional wildfires in Galicia *** indicates significantly different from zero at a#0.01, ** at a#0.05, * at a#0.10. Ag., agricultural; non-ag., non-agricultural All intentional Agricultural intentional Non-agricultural intentional Relative humidity 0.58*** 1.39*** 0.028 Precipitation 1.68*** 1.72*** 1.71*** Keetch–Byram Drought Index 0.0033*** 0.0033*** 0.0028*** Fire Weather Index 0.21*** 0.16*** 0.26*** Wind speed 0.65*** 0.48*** 0.80*** Maximum daily temperature 0.021*** 0.029*** 0.017*** January 0.20*** 0.062 0.288*** February 0.93*** 1.04*** 0.83*** March 1.11*** 1.27*** 1.00*** April 0.79*** 0.92*** 0.65*** May 0.20*** 0.32*** 0.061 June 0.44*** 0.50*** 0.42*** July 0.52*** 0.47*** 0.58*** August 0.74*** 0.81*** 0.78*** September 0.75*** 0.83*** 0.75*** October 0.17*** 0.38*** 0.10* November 0.07 0.12 0.045 Arrests, t1tot365 0.016*** 0.028*** 0.0035 Arrests, t365 to t545 0.0092*** 0.017*** 0.0042** Neighbour 1 arrests, t–tot365 0.013*** 0.012*** 0.0103*** Neighbour 2 arrests, t–tot365 0.022*** 0.017*** 0.021*** Neighbour 3 arrests, t–tot365 0.021*** 0.019*** 0.018*** Neighbour 1 arrests, t365 to t545 0.008*** 0.012*** 0.0071*** Neighbour 2 arrests, t365 to t545 0.0074*** 0.007*** 0.009*** Neighbour 3 arrests, t365 to t545 0.011*** 0.008*** 0.012*** Saturday 0.15*** 0.14*** 0.15*** Sunday 0.22*** 0.21*** 0.21*** Holiday 0.16*** 0.11*** 0.18*** Campaign day (2 to 16 days before) 0.019 0.0034 0.0055 Campaign day (17 to 31 days before) 0.0036 0.0896* 0.037 Campaign day (32 to 46 days before) 0.13*** 0.13*** 0.25*** Campaign day (47 to 52 days before) 0.074*** 0.11*** 0.08*** Silence day, t0.57*** 0.62*** 0.55*** Election day, t0.13 0.045 0.253* Population density change, all persons, t0.0017*** 0.002*** Not included Forest area, t0.0094** 0.038*** 0.0039 Unemployment rate change, t0.082 4.34 2.01 Real total personal income change, t5.13*** 4.32** 9.57*** Intentional fire count, t1 0.22*** No intentional fires, t11.15*** Non-ag. intentional fire count, t1 0.045*** 0.21*** No non-ag. intentional fires, t10.65*** 1.22*** Ag. intentional fire count, t1 0.25*** 0.12*** No ag. intentional fires, t11.13*** 0.57*** Constant 0.67*** 0.22 0.72*** Observations 576 074 576 074 617 319 Model Significance (Wald Test) 59 074*** 20 658*** 45 263*** 404 Int. J. Wildland Fire J. P. Prestemon et al. positively first-order autocorrelated at the daily time step. Findings are similar for all model specifications, with all parameter estimates significant at a#0.01. For total intentional fires, the coefficient on the intentional fire count from day t1 is 0.22 in both the fixed- and random-effects specifications. For agricultural intentional fires, the coefficient is 0.25 on its own type in both specifications and 0.045 and 0.046 on the nonagricultural fire count day t1 in the fixed-effects and randomeffects NB specifications respectively. For non-agricultural intentional fires, the coefficient is 0.21 on its own type and Table 3. Random effects negative binomial model estimates for all intentional, agricultural intentional and non-agricultural intentional wildfires in Galicia *** indicates significantly different from zero at a#0.01, ** at a#0.05, * at a#0.10. ag., agricultural; non-ag., non-agricultural All intentional Agricultural intentional Non-agricultural intentional Relative humidity 0.58*** 1.4*** 0.26 Precipitation 1.68*** 1.72*** 1.67*** Keetch–Byram Drought Index 0.0033*** 0.0033*** 0.0034*** Fire Weather Index 0.21*** 0.16*** 0.24*** Wind speed 0.65*** 0.48*** 0.73*** Maximum daily temperature 0.022*** 0.029*** 0.019*** January 0.20*** 0.060 0.27*** February 0.93*** 1.05*** 0.85*** March 1.11*** 1.27*** 0.98*** April 0.79*** 0.92*** 0.68*** May 0.21*** 0.32*** 0.080 June 0.44*** 0.5*** 0.35*** July 0.53*** 0.48*** 0.47*** August 0.74*** 0.82*** 0.64*** September 0.75*** 0.84*** 0.66*** October 0.17*** 0.38*** 0.012 November 0.067 0.12 0.0011 Arrests, t1tot365 0.016*** 0.028*** 0.011*** Arrests, t365 to t545 0.009*** 0.018*** 0.007*** Neighbour 1 arrests, t1tot365 0.013*** 0.012*** 0.014*** Neighbour 2 arrests, t1tot365 0.022*** 0.016*** 0.025*** Neighbour 3 arrests, t1tot365 0.021*** 0.019*** 0.022*** Neighbour 1 arrests, t365 to t545 0.008*** 0.011*** 0.0069*** Neighbour 2 arrests, t365 to t545 0.007*** 0.0068*** 0.0081*** Neighbour 3 arrests, t365 to t545 0.011*** 0.0081*** 0.013*** Saturday 0.15*** 0.14*** 0.15*** Sunday 0.22*** 0.21*** 0.23*** Holiday 0.16*** 0.11*** 0.18*** Campaign day (2 to 16 days before) 0.019 0.0035 0.029 Campaign day (17 to 31 days before) 0.0038 0.090* 0.044 Campaign day (32 to 46 days before) 0.13*** 0.13*** 0.14*** Campaign day (47 to 52 days before) 0.074*** 0.11*** 0.058*** Silence day, t0.57*** 0.62*** 0.51*** Election day, t0.14 0.045 0.28** Population density change, all persons, t0.0016*** 0.0020*** 0.0015*** Forest area, t0.0134*** 0.040*** 0.0024 Unemployment rate change, t0.12 4.304 3.262 Real total personal income change, t 5.17*** 4.32** 0.26 Intentional fire count, t1 0.22*** No intentional fires, t11.16*** Non-ag. intentional fire count, t1 0.046*** 0.21*** No non-ag. intentional fires, t10.65*** 1.18*** Ag. intentional fire count, t1 0.25*** 0.12*** No ag. intentional fires, t11.13*** 0.54*** Constant 0.69*** 0.23 0.54*** Natural log of overdispersion parameter a(rho) 3.22*** 2.30*** 3.29*** Natural log of overdispersion parameter a(sigma) 2.29*** 0.60*** 2.23*** Observations 576 074 576 074 576 074 Model significance (Wald Test) 59 707*** 20 713*** 44 031*** Likelihood ratio test vs pooled 4285*** 6183*** 2606*** Wildfire spatiotemporal displacement Int. J. Wildland Fire 405