CROSS-SECTIONAL STUDIES EMPLOYING COMPARISONS OF BETWEEN-CITY VARIATIONS IN CRIME RATES AND POLICE EXPENDITURES HAVE BEEN INAPPROPRIATE FOR MEASURING THE IMPACT OF CRIME TRENDS ON POLICE EXPENDITURES. STUDIES OF LONGITUDINAL DATA FOR SINGLE CITIES HAVE USED UNREALISTIC LAG STRUCTURES OF 1, 2, OR 3 YEARS. (LAG STRUCTURE REFERS TO THE LENGTH OF TIME WITHIN WHICH A CRIME TREND IS EXPECTED TO MANIFEST ITS INFLUENCE ON POLICE EXPENDITURES). THE PROPOSED MODEL USES TIME-SERIES DATA WITHIN A MULTIPLE LAG STRUCTURE, WITH THE CONSTRAINT THAT THE IMPACT OF CRIME TRENDS ON POLICE EXPENDITURES DIMINISHES WITH INCREASING LAG TIME. CONTRARY TO THE FINDINGS OF OTHER STUDIES, ESTIMATION OF THE MODEL USING NATIONAL DATA SHOWS THAT POLICE EXPENDITURES ARE A FUNCTION OF THE CRIME RATE. THE LAG STRUCTURE BEGINS AT 2 YEARS, AND THE MEAN LAG TIME IS 3.9 YEARS. THE 'CRIME WAVE' OF THE 1960'S APPEARS TO HAVE INFLUENCED THE LEVEL OF EXPENDITURES ON POLICE PROTECTION. IT IS POINTED OUT, HOWEVER, THAT AS THE CRIME RATE DECREASES, WHOLESALE REDUCTIONS IN POLICE APPROPRIATION WOULD BE UNWISE. THE RECIPROCITY OF THE RELATIONSHIP BETWEEN CRIME RATES AND POLICE EXPENDITURES SHOULD BE KEPT IN MIND, PARTICULARLY THE FACT THAT CHANGES IN THE LEVEL OF POLICE EXPENDITURES AFFECT INDIRECTLY THE RATE OF CRIME. DETAILS OF THE MODEL AND ITS ESTIMATION, MATHEMATICAL FORMULATIONS, GRAPHS, AND A LIST OF REFERENCES ARE INCLUDED. (LKM)