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Although several economic theories of crime postulate that crime rates and police strength are simultaneously determined, empirical research on the issue has produced highly divergent results. The need for strong assumptions about temporal patterning, which the theories do not supply, is probably responsible for these findings. A statistical technique which permits a more flexible approach to temporal analysis is described and applied to data on crime and police strength in Detroit. We find no evidence for the systematic relationships envisioned in economic theory and attribute this to important organizational and political variables which are omitted from these theories.