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IV. Method

Model development

The conceptual framework for this research is motivated in part from Heikkila (2000). Government is modeled as a firm providing a vector of services to the public. These services can be likened to outputs paid for by county revenues. The analysis consists of changes in the distribution of revenues and expenses arising from a change in land use. The model given here cannot replicate Heikkila's approach exactly because he uses a proxy for a specific government services (e.g. inverse of the number of crimes in a community). The proposed model focuses on the entire array of services. This analysis begins with a total operating revenue function and a total variable cost function for a particular county.

Formula 1


Total operating revenues for a county (TRc) are defined in (1) where "mri" is the marginal revenue for tax instrument "i" and "u" is the taxpayer type. "S" is the number of users in class "u". There is no actual market for the public services. The services are nonexclusive, congestible, and lack private sector substitutes. Government service providers then are by law public monopolies, thus marginal revenue is used in place of price. This analysis does not distinguish between types of tax instruments, i.e. property taxes, sales taxes, or use taxes. The overall tax burden charged by the local government is the value of interest.

The total operating revenue function then is a marginal revenue burden "mbu" multiplied by the number of users in the county "S" where mbu = Si * mri. This relation is represented in (2). The difference here is that each user group is charged for the entire array of government services.

Formula 2


Total variable cost is represented in (3). Total variable cost for county “c” is the marginal service unit service cost multiplied by the number of service units, where “mucju” is the marginal service cost for user “u” using service “j”.

Formula 3


Generally all services in government are provided without a unique service price. It is assumed that changes in the number of service units, expand the demand for the entire array of government services, and thus total variable cost. Equation (3) collapses into cost as a function of service units (4). Total variable cost then is the sum of each marginal unit cost of service multiplied by the number of service users.2 “TVCc” then is a function of the service users where the coefficient “usercst” represents the unit demand for government expenditures by user type Su.

Formula 4


The goal of the policy maker is to allocate expenditures across different groups and interests in a county subject to a revenue constraint. If the service burden of each user group is growing proportionally, then the job of the policy maker is simplified. The problem occurs when various groups' burdens change differentially. The array of services required by user types may differ. One user group may view another as taking a disproportionate level of public resources. It is assumed in this analysis that access and availability to public services across different geographic groups remains the same. There may be public choice aspects to rural versus urban residents, but the data cannot be used to adequately address it.

If county expenditure requirements increase as dispersed rural residential development increases, then this would impose a higher tax burden on the rest of the user groups. Government must either increase tax revenues and shift resources away from traditional users to the newcomers (rural homeowners) or reduce services to at least some users.

Population changes in rural areas contribute both to revenues and expenditures. More households located further away from urban public service centers increases the cost of providing public services and spreads out available maintenance operating resources to a larger area. Land used in agricultural or forestland is hypothesized to require a lower level of public services than land used for residential purposes. The expectation then is that rural residential development exacts a higher cost to the taxpayer as land is moved from agriculture or forest to residential uses.

The conversion of private ranch and farmland to rural residential use however is expected to increase revenue generation, which generates some of the skepticism for rural land use controls. Residential land is generally taxed at a higher rate than agricultural land, so conversion is viewed as a revenue enhancement to taxpayers. What matters to public services providers and taxpayers alike is ultimately the net, not the gross, revenue generated. Empirical studies using AFT methodology indicate that, on average, residential development is a net loss to a county's tax base. However, the issue is framed as a general result and not a case-by-case basis. The hypothesized relationship can be stated as in (5).

Formula 5


This statement implies that rural residential development is a breakeven or net loss prospect to county governments. Many AFT type studies suggest that the ratio of expenditures to revenues for rural residential development is greater than unity. However, there are other factors that can account for changes in the fiscal impacts of residential development that AFT methodology cannot effectively incorporate. Income, wealth, and unique aspects of the land base itself can all affect the kind of ratios the AFT methodology generates. Higher assessed valuation or higher income generally means higher taxes paid out.

The approach utilized here first tests the general hypothesis formulated in (5) with a complete model for both county and school revenues and expenditures. The AFT-type ratios are calculated using the estimated model for a representative scenario of ranch land conversion common in Wyoming (and throughout the inter-mountain west): replacement of 35 acres of ranchland with a one unit residential parcel. This latter procedure first calculates the net fiscal impacts on county governments and schools from the representative scenario. Predicted changes in revenues and expenditures are then converted to percent changes from the baseline. The percent changes from the baseline are then used to calculate actual average revenue and expenditure changes for each county. The aforementioned procedure permits AFT-type expenditure-to- revenue ratios to be calculated.

The fiscal impact model developed for this analysis predicts total county government operating revenues and expenditures as well as school district revenues and expenditures. Municipal government is not considered in this modeling framework since the issue relates to policies in unincorporated areas of counties.3 School districts and county governments have jurisdictional control in rural areas.

Four equations are estimated for each county: total county government operating revenues, total county government operating expenditures, total school operating revenues, and total school operating expenditures. Revenues come from the following categories of sources: property taxes, sales tax recapture, and intergovernmental transfers (Wyoming Statutes 39-1-21). Intergovernmental transfers and sales tax recapture are for the most part a function of population (e.g. Wyoming Statutes 39-15-111,39-15-112, 39-14-211). Changes in the level of all types of user groups affect the revenues that are received by a county. Fluctuations in mineral activities (coal, oil, gas, trona, and other minerals) and the resulting taxes (severance and federal mineral royalties) are collected but are not repatriated to the county of origin. They are distributed based upon changes in population. The larger urban population areas then receive most of these sources of funds.

Property taxes are the largest source of revenue for counties . Land uses are assessed at four tiers: mineral, commercial and industrial, residential, and agricultural. Minerals are taxed at 100 percent of the value of production. Commercial and industrial lands are taxed at 11 percent of assessed valuation. Residential land is taxed at 9 percent of assessed valuation. Finally agricultural land is taxed at 9 percent of the value of production as determined by the State. The local mill levy is then applied to the assessed value.

The State of Wyoming preempts all local jurisdictions in levying income or earnings taxes (Wyoming Statutes 39-12-101). State personal or business income taxes do not currently exist in Wyoming.

Statistical procedure

Total revenue and expenditure equations were estimated for each county governmental unit in Wyoming using time series cross-sectional models. The four dependent variables are county government operating revenue (CREV), county government operating expenses (CEXP), school operating revenues (SCHREV), and school operating expenses (SCHEXP). All variables, in dollar terms, both dependent and explanatory variables were represented as real 1998 dollars.

County revenues and expenditure equations are estimated as a function where "CREV" and "CXPE" for county "i" and time "t" is a function of rural personal income, urban personal income, acres of agricultural land, residential and commercial assessed valuation, and mineral assessed valuation, (6) and (7). Similarly, "SCHREV" and "SCHEXP" county "i" and time "t" are a function of rural personal income, urban personal income, and total assessed valuation. The arguments in each function are proxies that represent the user groups who contribute to revenues and exact a demand for services.

Formula 6


Formula 7


Formula 8


Formula 9


The explanatory variables are defined in Table 1. Two population base variables are "rupi" or rural personal income and "urpi", the incorporated area personal income. The other three variables represent the important land uses: agriculture, commercial, and mineral. The number of acres of agricultural land is "agland"; "asval" is total assessed valuation excluding mineral valuation; and "mval" is the assessed valuation of minerals. Rural and urban personal income is used instead of rural and urban population in order to capture both income and population effects without incurring statistical problems. Urban population and personal income exhibit multi-collinearity when they are used as separate arguments in the equations.

Table 1: Explanatory variables for the estimated equations

Variable Definition Expected Sign
CREV County operating revenue Endog.
CXPE County operating expenditure Endog.
SCHREV School district revenues Endog.
SCHXPE School district expenditures Endog.
RUPI Rural personal income +
URPI Urban personal income +
AGLAND Acres of agricultural land +
ASAL Assessed valuation of commercial and residential property +
MIN Assessed valuation of mineral property +
TOTVAL Total assessed valuation in county +

Mineral assessed valuation was separated out from the other components of assessed valuation because of the large contribution of minerals to most county budgets in the State. County government revenue and expenditure equations separated the effects of mineral assessed valuation while for school districts a total assessed valuation was used. Ad-valorem taxes are levied against both structures and on the value of the mineral. The mill levy charged to structures and improvements are set and collected by the county. The mill levy on the value of production are set by the State and collected by the county.

The log-log structure is used to account for governmental economies of scale between large communities and small communities. Natrona County and Laramie County, with the largest populations, have 66,000 and 81,000 respectively. Niobrara County conversely has approximately 2,400 in population. This structure was compared with linear and semi-log forms. The log-log format performed best based on a comparison of F-statistics for each specification.

Data Sources

Data sources come from information collected and summarized by the State Department of Audit (Wyoming Dept. of Audit; 2000) from 1993 to 1998. Total expenditures are solely operating expenditures. Urban and rural personal income variables are estimated based upon the 1990 Census estimates of per capita income in rural versus urban census tracts. The difference between per capita income in rural census tracts and urban census tracts was less than one percent. School district variables are collected from the State Department of Education (Wyoming Department of Education; 1993-1998).

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