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V. Results

Results of the estimation procedure are presented in Table 2 and 3. Time series cross sectional model structure was evaluated using a fixed effects model, a constrained OLS estimator, and a random effects estimator using generalized least squares. The fixed effects model was inferior to either the constrained OLS estimator or the random effects model based on F-tests calculated for all equations. The constrained OLS model was tested against the random effects model using a Hausman (1978) test where the null hypothesis was that the random effects model was the best model. The preferred specification is presented in Table 3. The random effects specification was chosen because it performed better than the others.

Table 2: Statistical results of the choice of model

Lagrange multiplier test
Chi-square statistic (p value)
Null Hypothesis: Ho County Revenue County Expenditures School Revenue School Expenditures
Error components do not exist
127.0399
75.2547
155.8269
95.2267
(0.000)
(0.000)
(0.000)
(0.000)
Error components model is the correct specification
36.6892
95.182
28.172
14.567
(0.000)
(0.000)
(0.000)
-0.0022

Table 3: Fiscal impact model results

Coef. Std. Error t-Stat P-Value R2 F df
County Revenues
0.000
0.941
398.83
125
Constant
0.9062
0.6929
1.3077
0.193
Rural Personal Inc ($000)
0.2333
0.0502
4.645
0.000
City Personal Inc ($000)
0.2948
0.0482
6.1182
0.000
Agric. Land (acres)
0.1006
0.0332
3.0283
0.003
Non-min assessed val.
0.1084
0.071
1.5273
0.129
Mineral assessed val.
0.2837
0.0149
19.017
0.000
County Expenses
0.000
0.928
324.31
125
Constant
1.1294
0.7674
1.4717
0.144
Rural Personal Inc ($000)
0.257
0.0556
4.6195
0.000
City Personal Inc ($000)
0.2998
0.0534
5.6185
0.000
Agric. Land (acres)
0.1011
0.0368
2.7502
0.007
Non-min assessed valuation
0.0835
0.0786
1.0628
0.29
Mineral assessed valuation
0.2774
0.0165
16.792
0.000
School Revenues
0.000
0.94
661.02
127
Constant
4.1856
0.364
11.5
0.000
Rural Personal Inc ($000)
0.3891
0.0311
12.513
0.000
City Personal Inc ($000)
0.3449
0.0372
9.2653
0.000
Total assessed valuation
0.2082
0.0256
8.1432
0.000
School Expenses
0.000
0.933
588.02
127
Constant
4.0645
0.3908
10.401
0.000
Rural Personal Inc ($000)
0.4203
0.0334
12.589
0.000
City Personal Inc ($000)
0.3048
0.04
7.6258
0.000
Total assessed valuation
0.2211
0.0274
8.0568
0.000

Evaluating the other sets of coefficients across equations indicates some expected and some interesting relationships. The coefficient on county revenues for urban residents is not significantly different than the coefficient on the expenditure equations. This suggests that city dwellers payment to county tax rolls is not an unencumbered source of revenues. Urbanites pay taxes to counties but receive services from both the county and cities (and pay taxes to cities also). The implication is that city population increases should benefit county government. Counties do indeed view city population growth as a draw on their resources. The county sometimes can end up providing law enforcement, health, and other public services that very small communities cannot.

The results suggest that at face value the marginal contribution of rural residential population to county revenue (revenue equation for both county government and schools) is less than the marginal contribution to county expenditures. The results also show that for agricultural and rangelands, the marginal contributions to expenditures are practically equal than those to revenues. It remains to be determined if the relationship between the two sets of parameters is statistically significant. This would validate the supposition that rural residential development is always a net fiscal loss to the county government and schools while agricultural land is a net fiscal gain.

The following statistic was used to test the hypothesis that rural residential development costs county taxpayers more than it contributes to county revenues at the margin, (10), as suggested by Mittelhammer (2001). The estimated parameter for rural personal income from the revenue equation is subtracted from the estimated parameter for rural personal income from the expenditure equation. The difference then is divided by a weighted average of the standard errors of the coefficients and the covariance between the two coefficients (calculated by estimating the equations as a seemingly unrelated regression). A test statistic greater than the student t distribution for the number of degrees of freedom would suggest that expenditure coefficients are significantly higher than revenue the coefficients. A similar test statistic was developed to test the hypothesis that agricultural land contributes more in revenues than in expenditures (11).

Formula 10

(10)

Formula 11

(11)

The results indicate that the differences between both pairs of coefficients are not significant, Table 4. The null hypothesis and alternative hypothesis for each test is presented in Table 4. The null hypothesis stating that the revenue generation of rural populations is equal to or greater than the expenditure generation of rural populations could not be rejected at a 95 percent confidence level. Likewise, the null hypothesis for agricultural land coefficients could not be rejected either at a 95 percent confidence level. The notion that rural residential development does not pay while agricultural land does pay is not corroborated with any degree of confidence by the statistical relationship from the model estimated. An AFT-type ratio cannot be validated as a general planning concept at the margin. One cannot claim, as a general rule, that rural residential development is a net fiscal loss to counties.

Table 4: Fiscal impact model results

Hypothesis test t-test
Hypothesis test 1
0.864899
Hypothesis test 2
0.049849

The inability to show a general result as presented above does not imply the opposite, i.e., rural residential development always pays for itself. It simply suggests that there may be scenarios where it might pay for itself. The outcomes then are a function of the specified scenario. A particular scenario is identified and used with the estimated equations to calculate AFT-type ratios. Thirty-five acres of agricultural land are replaced by one new rural household in the county to evaluate the relative role that rural residential development plays in a county fiscal structure.

The addition of one rural household is assumed to earn the county-wide average income and possess a house with a county-wide average assessed valuation. Thirty-five acres are used for two reasons. First, a smaller acreage expansion (e.g. one or even five acre expansions) is usually connected with subdivision development which, while fragmentation nonetheless, can begin to approximate cluster development. This can allow for population growth without the more egregious consequences of fragmentation. The second reason for using a 35-acre size is that anything under 35 acres in Wyoming has to be designated as a subdivision. This level of fragmentation then is a less regulated development (Wyoming State Statutes, 1999). Baseline analysis uses family sizes for rural populations equal to the average family size specific to the county. Likewise, county-wide average incomes are used. The scenario assumes a new rural resident that is approximately the same size and generating the same income as the average household in the specific county.

The models are used to calculate changes in revenues and expenditures for both county government and schools. County population, personal income, and assessed valuation rise as a result of the new household. Agriculture's contribution through total assessed valuation declines by a small amount. The predicted net changes in both revenues and expenditures are used to calculate average ratios of total county expenditure changes to total county revenue changes. The results are displayed in Table 5. Residential development at the expense of agricultural land costs county government and schools on average across counties 1.14 of expenditures for every dollar of new revenue received when incorporating both general government and schools into the equation. The average ratio is $1.08 when looking at only general government and excluding schools. This is generally consistent with the AFT (1999) findings. The results for the overall ratio vary considerably from county to county: Hot Springs County has the highest ratio at 1.45 and Weston County the lowest with 1.03.

The results suggest the AFT claims are provisionally valid, being highly dependent upon the characteristics of the scenario chosen. Changing those assumptions (county average household income, county average residential assessed valuation, county average family size, and inclusion of schools) can change the ratios. Policy makers are right to be concerned about rural residential development. The abundance of AFT-type studies and this research also, suggest that rural residential development in the aggregate is a net fiscal loss to county governments. What these results suggest though is that the character and type of development should be studied before one can say that a particular development is itself a net fiscal loss.

Table 5: Population mix, revenue change, and ratios of public expenditures to revenues for Wyoming Counties with a replacement of 35 acres of agricultural land with one average size family.

Wyoming Counties Urban population Rural Population Household size Ave. Assessed Valuation per person Revenue Change Net Expense Change County Government Ratio (excluding schools) Total Government Ratio (including schools)
Albany Co.
26,526
3,849
2.23
1,889
809
992
1.10
1.21
Big Horn Co.
7,049
4,007
2.60
2,086
2,429
2,779
1.04
1.13
Campbell Co.
20,249
11,293
2.73
2,219
2,344
2,779
1.07
1.17
Carbon Co.
13,755
2,174
2.39
2,559
1,620
1,717
1.06
1.04
Converse Co.
8,151
3,844
2.55
2,801
1,989
2,257
1.06
1.12
Crook Co.
2,653
3,030
2.51
3,067
3,426
3,730
1.09
1.08
Fremont Co.
19,273
16,269
2.58
1,179
2,774
3,116
1.11
1.11
Goshen Co.
7,014
5,685
2.38
1,250
2,039
2,301
1.07
1.12
Hot Springs Co.
3,406
1,253
2.25
1,264
1,807
2,644
1.05
1.45
Johnson Co.
3,828
2,797
2.36
1,623
2,153
2,409
1.05
1.11
Laramie Co.
54,922
23,271
2.45
1,839
1,439
1,626
1.08
1.12
Lincoln Co.
7,233
6,500
2.75
1,905
3,359
3,919
1.05
1.15
Natrona Co.
53,432
10,082
2.42
1,509
1,245
1,429
1.09
1.13
Niobrara Co.
1,684
923
2.28
1,594
2,217
2,440
1.10
1.09
Park Co.
14,751
10,459
2.42
1,724
1,667
1,908
1.09
1.13
Platte Co.
5,074
3,320
2.40
2,007
2,255
2,551
1.08
1.12
Sheridan Co.
16,098
8,838
2.31
2,197
1,670
1,872
1.10
1.11
Sublette Co.
2,461
3,041
2.47
2,222
3,965
4,252
1.10
1.06
Sweetwater Co.
33,929
6,313
2.62
1,341
1,534
1,874
1.04
1.20
Uinta Co.
15,020
5,148
2.84
1,393
2,062
2,313
1.07
1.11
Washakie Co.
6,222
2,349
2.47
1,454
1,647
1,831
1.10
1.10
Weston Co.
4,139
2,395
2.42
1,690
2,188
2,268
1.10
1.03

The implications of this change can be seen using the AFT estimates of ranchland at risk for one county. Fremont County had an annual budget of $10 million. AFT estimates that there are 296,960 acres of ranch and farmland threatened by development. Following the results of Table 5, conversion of this acreage to 35-acre ranchettes with households earning average incomes in the county and average sizes would generate almost 8,500 dispersed family households. This would mean a $2.9 million net increase in cost to county residents with the same level of service.

page 28

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