The technique used identified critical population levels (thresholds) where breaks in structure occurred without relying on a priori specification of the critical population levels. The results support the threshold hypothesis. Statistically significant shifts in expenditure functions were found when local populations reached 500 in Minnesota; 900 and 1,900 in North Dakota; and 1,800 and 2,700 in Wisconsin. When cities were grouped according to whether they lost population between 1970 and 1975, statistically significant thresholds were found for both the declining and nondeclining cities in Minnesota and Wisconsin, and they differed. Implications of these results are discussed. Tables, footnotes, and eight references are included. (Author summary modified)