Disproportionate agglomeration and scaling in regional socioeconomic analyses: Alabama counties as a case study

Figures & data

Table 1. The 58 Alabama counties used in the case study and their 2016 estimated populations

County	Population 2016	County	Population 2016	County	Population 2016
Autauga	55,416	Dale	49,226	Macon	18,963
Barbour	25,965	Dallas	40,008	Marengo	19,673
Bibb	22,643	DeKalb	70,900	Marion	29,998
Blount	57,704	Elmore	81,799	Marshall	95,157
Bullock	10,362	Escambia	37,728	Monroe	21,530
Calhoun	114,611	Etowah	102,564	Morgan	119,012
Chambers	33,843	Fayette	16,546	Perry	9,574
Cherokee	25,725	Franklin	31,628	Pickens	20,324
Chilton	43,941	Geneva	26,614	Pike	33,286
Choctaw	12,993	Greene	8,422	Randolph	22,652
Clarke	24,392	Hale	1,4952	Russell	58,172
Clay	13,492	Henry	17,164	St. Clair	88,019
Cleburne	14,924	Houston	104,056	Sumter	13,040
Coffee	51,226	Jackson	52,138	Talladega	80,103
Colbert	54,216	Lamar	13,918	Tallapoosa	40,727
Conecuh	12,395	Lauderdale	92,318	Walker	64,967
Coosa	10,581	Lawrence	33,244	Washington	16,756
Covington	37,458	Limestone	92,753	Wilcox	10,986
Crenshaw	13,913	Lowndes	10,358	Winston	23,805
Cullman	82,471

Table 2. Power laws* associated with the population numbers of 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties*	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
Population (no.)	Paid employees (no.)	0.029	1.193	89.3	1.29
	Highly educated (no.)	0.026	1.167	94.7	1.24
	Payroll ($)	0.001	1.163	83.6	1.24
	GDP ($)	0.005	1.153	88.5	1.22
	Enterprises (no.)	0.003	1.149	94.6	1.22
	Total income ($)	0.006	1.123	98.2	1.18
	Households (no.)	1.155	0.917	98.6	0.89
	Poor people (no.)	1.468	0.813	88.2	0.76
	Enterprise richness	0.130	0.696	93.8	0.62
	EDI**	291.85	−0.149	22.6	−0.10

* Associated characteristic = constant(population^coefficient); ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 3. Power laws* associated with the enterprise numbers of 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
Enterprises	Highly educated (no.)	11.50	1.1419	90.4	1.21
	Total income ($)	2.14	1.0993	92.6	1.14
	Paid employees (no.)	10.86	1.0359	93.9	1.05
	Payroll ($)	0.45	1.0109	88.1	1.02
	GDP ($)	1.60	0.9855	90.3	0.98
	Poor people (no.)	94.57	0.8605	87.1	0.82
	Population (no.)	187.79	0.8232	94.6	0.77
	Households (no.)	134.28	0.7620	95.0	0.70
	Enterprise richness	4.07	0.6053	98.9	0.52
	EDI**	187.79	−0.1770	44.5	−0.12

* Associated characteristic = constant(population^coefficient); ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 4. Power laws* associated with the enterprise richness of 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
Enterprise richness	Paid employees (no.)	1.12	1.686	92.2	2.22
	Payroll (no.)	0.05	1.638	85.6	2.11
	Enterprises (no.)	0.11	1.634	98.9	2.10
	GDP ($)	0.19	1.599	88.1	2.03
	Highly educated (no.)	1.30	1.583	90.2	2.00
	Total income ($)	0.27	1.508	91.6	1.84
	Population (no.)	29.79	1.347	93.8	1.54
	Households (no.)	24.41	1.247	94.2	1.37
	Poor people (no.)	20.41	1.119	86.5	1.17
	EDI**	276.14	−0.287	43.6	−0.18

* Associated characteristic = constant(enterprise richness^coefficient); ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 5. Power laws* associated with the gross domestic products (GDPs) of 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
GDP (2012 chained $)	Payroll ($)	0.31	1.0064	93.9	1.01
	Paid employees (no.)	9.58	0.995	93.2	0.99
	Enterprises (no.)	1.19	0.9161	90.3	0.89
	Highly educated (no.)	11.44	0.9102	84.9	0.88
	Total income ($)	2.28	0.8593	86.4	0.81
	Population (no.)	197.79	0.7678	88.5	0.70
	Households (no.)	143.31	0.7081	88.3	0.63
	Poor people (no.)	90.60	0.6508	86.5	0.57
	Enterprise Richness	4.64	0.5507	88.1	0.46
	EDI**	166.36	−0.1482	0.337	−0.10

* Associated characteristic = constant(GDP^coefficient); ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 6. Power laws* associated with the number of highly educated people in 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
Highly educated persons (no.)	Paid employees (no.)	1.68	0.984	87.4	0.98
	Payroll ($)	0.07	0.960	81.9	0.95
	GDP ($)	0.24	0.951	86.5	0.93
	Enterprises (no.)	0.18	0.937	90.4	0.91
	Total income ($)	0.29	0.918	94.4	0.89
	Population (no.)	33.16	0.812	94.7	0.76
	Households (no.)	29.20	0.742	92.8	0.67
	Poor people (no.)	25.99	0.657	82.7	0.58
	Enterprise Richness	1.43	0.569	90.2	0.48
	EDI**	180.09	−0.125	23.0	−0.08

* Associated characteristic = constant(no. degreed persons)^coefficient; ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 7. Power laws* associated with the size of payrolls in 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
Total payroll	Paid employees (no.)	31.90	0.978	97.2	0.97
	GDP ($)	4.40	0.934	93.9	0.91
	Enterprises (no.)	4.22	0.872	88.1	0.83
	Highly educated (no.)	43.30	0.853	81.9	0.81
	Total income ($)	8.14	0.802	81.2	0.74
	Population (no.)	610.72	0.719	83.6	0.65
	Households (no.)	402.25	0.664	83.7	0.58
	Poverty (no.)	228.61	0.615	81.6	0.53
	Enterprise Richness	9.98	0.523	85.6	0.44
	EDI	144.81	−0.153	38.7	−0.10

* Associated characteristic = constant(county payroll^coefficient); ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 8. Power laws* associated with total income in 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
Total income ($)	Paid employees (no.)	8.14	1.036	86.4	1.05
	Highly educated (no.)	5.83	1.028	94.4	1.04
	Payroll ($)	0.34	1.012	81.2	1.02
	GDP ($)	1.07	1.005	86.4	1.01
	Enterprises (no.)	0.74	1.003	92.6	1.00
	Population (no.)	106.78	0.875	98.2	0.83
	Households (no.)	84.05	0.802	96.7	0.74
	Poverty (no.)	78.18	0.684	80.1	0.61
	Enterprise Richness	3.39	0.608	91.6	0.52
	EDI	144.00	−0.128	21.6	−0.09

* Associated characteristic = constant(county income^coefficient); ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 9. Power laws* associated with the number of officially poor people in 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
No. of poor persons	Paid employees (no.)	0.044	1.357	86.5	1.56
	Payroll ($)	0.002	1.328	81.6	1.51
	GDP ($)	0.008	1.305	84.9	1.47
	Enterprises (no.)	0.007	1.274	87.1	1.42
	Degrees (no.)	0.071	1.260	82.7	1.40
	Total income ($)	0.022	1.172	80.1	1.25
	Population (no.)	2.23	1.086	88.2	1.12
	Households (no.)	2.303	1.0003	87.9	1.00
	Enterprise Richness	0.195	0.773	86.5	0.71
	EDI**	329.0	−0.189	27.2	−0.12

* Associated characteristic = constant([no. poor people]^coefficient); ** EDI = enterprise dependency index; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Table 10. Power laws* associated with the enterprise dependency indices of 58 small (<120,000 persons) Alabama counties

Primary characteristic	Associated characteristics of counties	Constant	Coefficient	Variation explained (R^2 in %)	Scaling***
Enterprise dependency index**	Poor people (no.)	2,583,597	−1.442	27.2	−0.63
	Households (no.)	7,394,485	−1.494	25.6	−0.64
	Enterprise Richness	92,880	−1.516	43.6	−0.65
	Population (no.)	16,758,726	−1.519	22.6	−0.65
	Total income ($)	693,500	−1.681	21.6	−0.69
	Degrees (no.)	9,288,399	−1.838	23.0	−0.72
	GDP ($)	8,830,806	−2.272	33.7	−0.79
	Enterprises (no.)	16,758,726	−2.519	44.5	−0.83
	Payroll ($)	8,405,857	−2.530	38.7	−0.83
	Employees (no.)	291,423,731	−2.579	40.9	−0.83

* Associated characteristic = constant([county EDI]^coefficient); ** enterprise dependency index = EDI; *** a value larger than one indicates super-linear scaling and a value smaller than one indicates sub-linear scaling. A negative value indicates a decrease in one characteristic when the other increases, and vice versa.

Figure 1. The requirement for new and existing entrepreneurial types in Alabama counties of different sizes (measured as total enterprise numbers). Triangles (new entrepreneurs) and circles (existing entrepreneurs) represent actual entrepreneurial activities in the counties.

Figure 2. The potential impact of a single additional enterprise type on additional enterprises (circles) and additional jobs (triangles) in Alabama counties of different sizes. Power laws were used to calculate the values.

Figure 3. The levels of poverty, unemployment and higher education in relation to the population sizes of Alabama counties. Power laws were used to calculate values, which were then expressed as percentages of the total population. 

Figure 4. The total income of and payrolls in Alabama counties relative to the magnitude of their gross domestic products (GDPs). Power laws were used to calculate values, which were then expressed as fractions.