A simultaneous model consisting of the supply of offences, police production function, and police deployment function is specified and estimated. Account is also taken of crime spillovers among observations and the daily mobility patterns of the population. The deterrent impact of police output is confirmed, but the link between police inputs and the production of deterrence is found to be weak. Consideration of the population's mobility significantly reduces the effect on crime rates of socio-economic factors such as unemployment. (Author abstract)