Likelihood Based Inference and Prediction in Spatio-Temporal Panel Count Models for Urban Crimes

Abstract

We develop a panel data count model combined with a latent Gaussian spatio-temporal heterogenous state process to analyze monthly severe crimes at the census tract level in Pittsburgh, Pennsylvania. Our data set combines Uniform Crime Reporting data with socio-economic data from the 2000 census. The likelihood of the model is accurately estimated by adapting recently developed efficient importance sampling techniques applicable to high-dimensional spatial models with sparse precision matrices. Our estimation results confirm socio-economic explanations for crime and, foremost, the broken-windows hypothesis, whereby less severe crimes in a region is a leading indicator for severe crimes. In addition to ML parameter estimates, we compute several other statistics of interest for law enforcement such as elasticities (idiosyncratic, total, short-term as well as long-term) of severe crimes w.r.t. less severe crimes, one-month-ahead out-of-sample forecasts, predictive cumulative distribution functions and validation test statistics based on these cdf's.