This study examines the contextual effect of arrest clearance rates, over time, on the arrest-crime relationship. The bivariate autoregressive integrated moving average (ARIMA) analyses of monthly crime and arrest data for seven Pennsylvania cities for robbery, burglary, larceny, and auto theft suggest that the deterrent effect of arrests on crime is probably limited to smaller cities whose police department are able to clear an appreciable proportion of crimes over time, through arrests.
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Mitchell B. Chamlin (1991) studied this question.