Segmented Regression, Threshold Effects, and Police Expenditures in Small Cities

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Abstract
Individuals projecting local government expenditures in small cities typically assume that average costs can be represented by a single, smooth, continuous function. This paper discusses why assuming piece‐wise continuity may be more realistic. Segmented regression is then used to test for discontinuities in local per capita expenditures for police protection in Minnesota, North Dakota, and Wisconsin. Three distinct segments were found for expenditures in North Dakota and Wisconsin; two for Minnesota. Minnesota and Wisconsin results improved further when cities with declining and nondeclining populations were treated separately.

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