Previous analyses of the determinants of per capita police expenditures have assumed that the set of cities being used as an object set are properly observed through single equation least squares techniques. This analysis shows that such a practice is likely to lead to incorrect results. Regression equations fitted to broad population size ranges produce heteroscedastic residuals. Further, cities growing in population have significantly different regression equations than those declining in population. As a result, future determinants analyses as well as the comparative study of urban political and bureaucratic processes must be prepared to deal with different types of cities.
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W. Patrick Beaton (1974) studied this question.