County Spending and the Implicit Subsidy to
"Urban Sprawl"
This paper examines county spending patterns in Wisconsin, to determine whether that spending provides an implicit subsidy to urban- type development outside of any city or village limits. I estimate that counties spend around $180 less per person on their city and village residents that they do on their town residents. Or stated differently, a Wisconsin county typically spends $500 more on public services provided to a town household than it does for a city or village household. As a result, most urban households are paying a tax penalty of between $150 and $350 annually, providing most town households with a tax subsidy of between $150 and $350 annually, due to the difference in county services provided to them. This creates a strong incentive for the growth of residential developments in rural areas, i.e. in urban sprawl. A reform in the way town and city/village residents are taxed for county services is therefore warranted.
M. Kevin McGee
Department of Economics
U Wisconsin Oshkosh
Oshkosh WI 54901
mcgee@uwosh.edu
phone: 920-424-7155
fax: 920-424-1734
February, 2000
To some, it's a waste of natural resources, an ugly blight on our countryside. To
others, it's the market at work, converting low value farmland into high value homesteads.
Its proponents call it development; its opponents malign it as "urban sprawl".
To an economist, converting land from rural to urban/suburban use is efficient and
appropriate if, but only if, the developers and homebuyers who enjoy the benefits of the
land conversion also bear all of its costs. However, if some of the costs of their
decision to develop are borne by others, through higher taxes or a lower quality of life,
then the land conversion is being implicitly subsidized, and an inefficiently high level
of low density development would be occurring.
This paper explores one potential form of implicit subsidy: the possibility that the local
government services provided to those developers and homebuyers are being underpriced.
Much of the "sprawl" occurring here in Wisconsin takes place outside of any
incorporated city limits, in the "urban towns" that have sprung up across the
state.1 These towns retain the political and governmental structure of a rural
town. However, although a few of them provide a complete array of services to their
constituents, including police protection, the vast majority receive most of their
governmental services from the county. In contrast, most city and village residents get
many of their local government services provided by their city or village.
The costs of those county provided services are for the most part shared equally by all
the county's taxpayers, whether they live in a city, a village or a town. As a result,
city and village taxpayers pay not only for their own police protection, provided by their
city/village tax financed police department, but also for the town dweller's police
protection, through the portion of their county taxes going to the County Sheriff's
Department. The town taxpayers in contrast pay for only a portion of their own police
protection. This tax shifting increases the property taxes that city/village residents
must pay, reduces the property taxes of town residents, and therefore increases the
attractiveness of housing developments built out into the countryside.
The extent to which this subsidization of rural development occurs should be apparent in
the spending patterns of Wisconsin's 72 counties. If counties are providing services to
town residents that cities and villages supply to their own residents, then county
spending on those services should be higher, the more the county's residents live outside
of cities and villages. Indeed, by looking at the relationship between county spending and
town population, we should be able to determine not only whether such a subsidy occurs,
but also how large the subsidy typically is.
The Model
County spending can vary from one county to the next for a number of reasons. Wealthier
counties could spend more, because they can afford to. Larger counties, providing services
over a greater geographic area, may need to spend more to provide the same level of
service to its more disperse population. And more populous counties may need to spend
more, because there are more to serve.
This last relationship, between county spending and population, may be complicated by the
presence of either economies or diseconomies of scale. Economies of scale imply
that there are cost advantages to larger population, typically in the form of some
"fixed" cost that can be spread out over a larger number of people. If economies
of scale exist, we should observe the relationship
Spending = a + ß Population
where a and ß are constants, and a, representing fixed costs, would be positive.
Diseconomies of scale imply cost disadvantages to a more populous county. As the county's
population grows, the size of the various county departments will grow. These larger
departments may in turn develop more complex, and costly, management hierarchies. If such
diseconomies of scale exist, we should observe the relationship
Spending = ß Popn + y Popn2
where y would be a positive constant. A negative y is also possible, and would be an
alternative indication of economies of scale.
In the absence of any differences in county spending on city, village, and town residents,
the relationship to estimate would be
Spending = a + ß Popn + y Popn2 + 8 Wealth + Ø Area
where the coefficients 8 and Ø would presumably be positive constants. To determine
whether a spending difference (and therefore implicit subsidy) exists, I need to add an
additional explanatory variable, measuring the number of city and village residents. The
coefficient of the population variable, ß, will then reflect the level of spending for a
town resident. If ß is the city/village population coefficient, (ß+¥) will measure the
level of spending for a city/village resident; so ¥ will measure any difference between
county spending on town residents versus city/village residents. If an implicit subsidy is
occurring, ¥ will be negative.
To also explore whether county spending on village residents differs from spending on city
residents, a village population variable will also be added. This variable's coefficient u
will be positive if counties provide village residents with more services than city
residents, negative if counties provide village residents with fewer services than city
residents, and zero if village and city residents receive the same set of county services.
Finally, I've divided both sides of the spending relationship by county population,
expressing all of the variables in per capita terms. This was done both to simplify the
interpretation of the results, as well as to eliminate the problem of heteroskedasticity.2
The resulting model is
Spend=a 1
+ ß + y Popn + 8 With + Ø Area
+ ¥ (Cit+Vil)+ µ Vill
This model will be estimated using ordinary least
squares regression. My hypothesis, that counties spend more on town residents than on
either city or village residents, implies that the estimated values for ¥ will be
negative and for µ will equal zero.
The Data
My measures of county spending were taken from Comparing County Expenditures, compiled
by the Wisconsin Taxpayers Alliance. Their report, based on unaudited annual financial
reports filed by each county with the Wisconsin Department of Revenue, listed county
spending levels in each of 6 categories -- General Government, Highway Maintenance and
Construction, Judicial, Public Safety, Health & Human Services, and
"Extracurricular" (i.e. cultural, educational, and recreational services) -- for
the years 1994 through 1998. I used their 1998 spending levels.
The measures of the other variables were taken from the State of Wisconsin 1999-2000
Blue Book. The population figures, for both counties and their subjurisdictions, are
official state population estimates for January 1,1999. County wealth is measured as the
county's full value property assessment, for 1997.3
The ResuIts: Total County Spending
My initial analysis aggregates all 6 of the Wisconsin Taxpayer Alliance's 6 spending
categories together. This allows me to examine whether there are any overall spending
differences on town versus city/village residents.
Table 1: Total County Spending
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Table 1 shows the estimated coefficients for my Total
County Spending model.4 Because there is considerable multicollinearity among
the explanatory variables, I've reported results both including and excluding the
variables with very statistically insignificant coefficients. In addition, estimated results for a data set excluding Milwaukee County are reported. Because Milwaukee CountY's population and its %(City+Village) are significantly larger that any other county, there is a possibility that this single county may act as an outlier, giving it an undue influence on the results. Throughout the paper, I will report any case where the inclusion or exclusion of Milwaukee County has a significant impact on the estimated coefficients. My results show first of all that there are clearly significant economies of scale in county spending, and that there may be some diseconomies of scale as well. In all four regressions, the 1/Population coefficient is statistically significant at the 0.1% level. The coefficient suggests that counties have around $1 million in fixed costs that they must incur, regardless of their population size. As my later results will demonstrate, these fixed costs appear to be concentrated in 3 of the 6 spending categories: Judicial, Health & Human Services, and General Government. |
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The two regressions that include Milwaukee Co. have
positive and significant coefficients for the Population variable, implying that there are
also diseconomies of scale in county spending. When Milwaukee Co. is excluded from the
data set however, the Population coefficient is no longer statistically significant. That
may imply that only Milwaukee County is large enough to experience these diseconomies, or
it could merely reflect some other reason, such as local public preferences, that
increases county spending in Milwaukee County.
Figure 1 shows the estimated relationship between county spending and population, drawn
through a scatterplot of the data.5 As you can see, the line fits the pattern of data
points well, clearly demonstrating the presence of economies of scale in county
governmental spending.
More importantly, both the reduced variable regressions (the second and fourth columns) in Table 1 have a statistically significant negative coefficient for the %(City+Village) variable. These coefficients suggest that counties spend around $180 less per person on their city and village residents that they do on their town residents.6 The coefficients for %Village are statistically insignificant, implying that county spending on city residents and on village residents are equal. Figure 2 shows this estimated relationship between county spending and percent city and village residents.7
It might be easiest to interpret this result on a
household basis. According to the U.S. Census Department, the average American household
has 2.62 persons.8 Using the $189.29 coefficient from the second column of
Table 1, a Wisconsin county typically spends almost $500 more on public services provided
to a county household than it does for a city or village household. If these town, city
and village households are paying the same county taxes for those services, this spending
differential does indeed constitute arather substantial tax subsidy to town households, as
well as a rather substantial tax penalty on city/village households.
The size of the subsidy or penalty that an individual household faces depends in part on
the degree to which the county is urbanized. Suppose for simplicity that we have a county
with a total population of just 1000 households. If only 10% of them live in cities or
villages, the county will spend $500 x 900 = $450,000 on the "extra" services to
its town residents. If the cost of these services is spread out evenly over all of the
county's residents, the 100 urban households will each be paying $450 for services they
don't receive their tax penalty for living in a city or village -- while the 900 town
households will each be paying only $450 in taxes for their $500 in extra services -- a
$50 subsidy.
If instead, 90% of the households live in cities or villages, by the same analysis the
county will spend $50,000 on the extra services to its town residents; the urban
households will each be paying $50 for those services they don't receive, while the town
households will each be receiving a $450 taxes subsidy.
Since (as Figure 2 shows) in two thirds of Wisconsin's
counties, from 30% to 70% of the population resides in cities and villages, most urban
households are paying a tax penalty of between $150 and $350 annually, providing most town
households with a tax subsidy of between $150 and $350 annually, due to the difference in
county services provided to them.
To complete the discussion of the results in Table 1, note that the Assessed Value
coefficients are not statistically significant, so county spending does not appear to be a
function of the tax base. As will be seen below however, increased property values do
appear to result in a reallocation of county spending among the various spending
categories. Observe also that the Area coefficients are significant only at the 10% level.
This weak evidence that greater area increases county spending will reappear below, when
we look at the areas of public safety spending and highway maintenance spending.
General Government Spending
To further explore the above differences in county spending, and in particular to identify
what additional services counties typically supply to their town residents, I've estimated
the spending relationship described earlier for each of the Wisconsin Taxpayer Alliance's
six spending categories. The first category, General Government Spending, includes
"spending for legislative, legal, general and financial administration, general
buildings and plant, and property records and control."9 Since many of
these functions will have similar costs independent of population size, I would expect to
find substantial economies of scale in this category.
Table 2: General Govt Spending
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Table 2 presents the estimated
coefficients for my General Government Spending model. As in Total County Spending, the
1/Population coefficient is positive and statistically significant, showing that there are
indeed economies of scale in General Government. Somewhat surprisingly, the coefficient
for Assessed Value per capita is also positive and significant: apparently, wealthier
counties devote more resources to general government than poorer counties. Since Assessed Value has no apparent impact on total county spending, this suggests that wealthier counties pay for the additional administrative services -- or expensive administrative structures-- by reducing other forms of county spending. As will be seen below, this additional administrative spending appears to come at the expense of in spending on health and human services. None of the other variables have significant coefficients, using the standard 5% significance level, The %(City+Village) coefficient is negative however, as would be expected if a spending subsidy in this category exists, and is significant at the 10% level if a one tail test is employed. This can probably best be interpreted as positive but very weak evidence that counties provide some addititional administrative services to their town residents, that are not prwided to their city/village residents.10 The most likely area of differential senrices would be in "property control," that is, zoning and building inspection services. Tvpically, cities and villages have their own planning and inspection departments. Towns typically do not, and therefore their planning and. inspections are done mostly at the county level. The size of the coefficient, at around $19 per person, is consistent with this interptetation: in 1998, the City of Oshkosh, where I reside, spent about $15 per person in its Planning and Inspections Divisions. |
| Since these divisions typically collect fees for many of these services,
the net subsidy to town residents wilt be less than $19 per person. Assuming that exactly
half of these costs am paid for by user fees, these extra property services represent
about a $25 benefit per household to town residents.11 Highwav Maintenance Spending Highway Maintenance Spending includes the "net cost of county highway administration, maintenance and construction financed from both general and proprietary funds." I would expect this spending to be greater per person, the lower the county's population density. Table 3 presents the estimated coefficients for my Highway Maintenance Spending model. There is no evidence of either economies or diseconomies of scale, and only weak evidence that area affects highway spending: the Area coefficients, estimating about $300 of additional annual highway spending for each additional square mile of area, are not statisticatly significant in either of the regressions including that variable. The %(City+Village) coefficient is negative and statistically significant, implying that counties spend more highway dollars on town residents than on either city or village residents. The %Village coefficient is not significant, implying that |
Table 3: Hwy Maintenance Spending
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there is no spending difference between city and village residents. The %(City+Village) coefficient, of around $70 when area is controlled for, implies that counties typically supply town households with $180 more in highway construction and maintenance services than city residents.
| This result is not particularly surprising, since
county roads are generally located outside of cities, and frequently cease to be county
roads after they have crossed the corporate boundary. The magnitude of the difference may
be surprising however: the fitted equations imply that counties typically spend around
$300 per household on town residents for highway construction and maintenance, and only
about 40% of that amount, $120 per household, on city/village residents. Judicial Spending Judicial Spending includes "spending for the courts, the law library, public defenders and coroner." As Table 4 shows, there is no evidence that judicial spending per capita varies by town, city or village residency. There do appear to be significanl economies of scale, with around $50,000 in fixed costs per county. There may also be diseconomies of scale, although the Population coefficient that suggests these diseconomies is only statistically significant when Milwaukee County is included in the data set. |
Table 4: Judicial Spending
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Table 5: Public Safety Spending
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Public Safety Spending Public Safety Spending includes the "costs of law enforcement, ambulance, inspection and emergency communications [as well as] expenditures for the operation of jails and other correctional facilities." Since cities and villages typically have their own police forces, I would expect significantly more county public safety spending on town residents than on city/village residents. Table 5 presents the estimated coefficients for my Public Safety Spending model. The first three columns include Milwaukee County in the data set, the last column does not. In all four columns, both Assessed Value and Area have positive and significant coefficients: an additional million dollars of assessed value increases annual public safety spending by around $0.60, while an additional square mile of area increases that spending by around $400. There do not appear to be any economies or diseconomies of scale. The last two columns measure the impact of the %(City+ Village) variable, when it is incorporated linearly into the model. I estimate that counties spend about $30 to $48 more on town residents, or about $80 to $120 per household, depending on whether I include Milwaukee Co. in the data set; this estimated difference is statistically significant only when Milwaukee Co. is excluded. When %(City+Village) is added nonlinearly, by adding %(City+Village)2 as an explanatory variable, an interesting and perhaps surprising pattern emerges, as shown in Figure 3.12 For counties with little or no urban population, the spending difference between town and city/village residents is large: e.g., at 10% city/village, the spending difference (calculated as the slope of the estimated curve) is $159. As the city/village population proportion rises, this spending difference falls: at 40% city/village it equals $64, and by 60% city/village it has fallen to zero. |
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One possible interpretation of the curving spending pattern is that, as the county's city/ village population increases, the county spends less per capita on those services which only benefit town residents, and more per capita on services beneficial to city/ village residents. As the appendix demonstrates, if either per capita spending on town services were falling, or per capita spending on city/village services were rising, or both, a quadratic pattern is exactly what we should observe in the data.
This explanation is also consistent with a "public choice"
interpretation: as the city/village population proportion rises, those city/village
residents will have increasing political power in the county, and county spending patterns
will change in response to the altered balance of power. It should be noted however that
this shifting pattern of resource allocation was only detected in this public safety
category of spending; in particular, it was not found in total county spending. That
suggests either that any reallocation of spending in this category was offset by an
opposite reallocation in some other category, or, more likely, the small amount of
reallocation that may be occurring here is not replicated elsewhere, and is no longer
visible when all of the spending categories are combined together.
Health & Human Services Spending
Health & Human Services Spending includes the "costs of public and mental
health services, income maintenance, social services, aging services, veterans services,
and other health and human services financed from general funds." Since cities and
villages typically do not provide these types of services to their residents here in
Wisconsin, I would not expect this spending to be related to %(c+v).
| Table 6 presents the estimated coefficients for my
Health & Human Services model. Menominee County, which is a reservation for the
Menominee tribe, was excluded from the data set, since its per capita spending level in
this category was nearly twice as high as the next highest county. Its observed H&HS
spending per capita was $953.71; its predicted H&HS spending, using the estimated
coefficients in the first column of Table 6, was only $443.96. As the table shows, there are significant economies of scale in health and human service spending. Per capita spending is also influenced by assessed property value, but in the opposite direction from what I had expected: additional wealth results in less spending, not more. This undoubtedly reflects need: counties with lower property values most likely have lower average income levels, and therefore a greater need for human service spending. This would also explain why assessed value has no significant impact on total county spending. As county wealth rises, spending on general government and public safety increases (because it can be afforded), while spending on human services falls (because it is not needed). The net effect is therefore small, and statistically insignificant. The table also shows that, as predicted, the percent city and village residents has no significant impact on per capita health and human service spending. |
Table 6: HIth & Hum Svc
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Extracurricular Spending
Extracurricular Spending includes the "costs of library, museum,... other cultural
and educational services [and] parks and recreational programs and facilities."
Table 7: Extracurricular Spending
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As Table 7 shows, this category of spending appears to
have no significant relationship to any of the explanatory variables, with the possible
exception of Population. The coefficient on that variable is however extremely sensitive
to whether Milwaukee Co. is included in the data set, switching from positive
(diseconomies of scale) and not quite significant at the 10% level in the first column, to
negative (economies of scale) and significant at the 5% level in the third column. Summary The results above give clear evidence that
counties provide more services, about $500 per household, to their town residents than to
their city/village residents. These additional services are primarily concentrated in the
categories of general government spending (around $50 per household), highway construction
and maintenance spending (around $180 per household), and public safety spending (around
$120 per household). |
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APPENDIX
In this appendix I show that, whenever the spending per capita on town residents or on
city/village residents is a linear function of the proportion of the population residing
in cities or villages, total per capita spending will be a quadratic function of that
proportion. This result is useful in interpreting the statistically estimated pattern of
county public safety spending.
Let St and Scv represent spending per person on town and
city/village residents respectively. Let nt and ncv be the
numbers of town and city/village residents. Then total county spending will be
S = stnt + scvncv = stn +(scv-st)ncv
where n = nt+ncv. Suppose now that spending per capita on town
residents is a decreasing linear function of the proportion of the population residing in
cities or villages, %(c+v). That assumes that as the proportion of the population residing
in cities or villages rises, the level of service provided to town residents declines, or,
noting that %(c+v) =ncv/n,
st = a - b ncv/n
Suppose also that spending per capita on city/village residents is
an increasing linear function of the proportion of the population residing in cities or
villages,
scv = c + d ncv/n
Then
S = an - bncv + (c-a) ~ +(b+d)ncv (ncv/n)
and spending per capita, S/n, is
S/n = a+ (c-a-b)(ncv/n) + (b+d)(ncv/n)2
= a + (c-a-b) [%(c+v)] +(b+d)[%(c+v)]2,
a quadratic function of %(c+v).
Note that spending per capita is a quadratic function whenever either b or d is nonzero,
that is, whenever either per capita spending on town residents or on city/village
residents is a linear function of %(c+v). Note also that, when we observe the coefficients
of %(c+v) and %(c+v)2, the individual slopes b and d cannot be identified,
since all we can estimate from the data is their sum b+d.
Therefore, when we observe that spending per capita follows a quadratic curve, as it
appears to do for public safety spending, all we can conclude is that per capita spending
on town residents may be falling, or per capita spending on city/village residents may be
rising, or both.
REFERENCES
Pindyck, Robert S. and Rubinfeld, Daniel L., Econometric Models and Economic
Forecasts, 4th Edition, Irwin McGraw-Hill, Boston MA, 1998.
Wisconsin Legislative Reference Bureau, State of Wisconsin 1999-2000 Blue Book, Wisconsin
Department of Administration, Madison WI, 1999.
Wisconsin Taxpayers Alliance, Comparing County Expenditures, Madison WI, 1999.
ENDNOTES
1. In 1998, Wisconsin had 6 towns-- Caledonia and Mount Pleasant in Racine County, Grand
Chute in Outagamie County, Menasha in Winnebago County, Pewaukee in Waukesha County, and
Bellevue in Brown County -- with populations over 10,000 persons, larger than 70% of
Wisconsin's cities and 95% of its villages.
2. Heteroscedasticity exists when the variances of the error terms are systematically
related to the explanatory variables. It reduces the model's efficiency, and biases the
t-statistics. See Pindyck and Rubinfeld (1998), or any other econometrics text. Both a
Breusch-Pagan test and a White test of the errors showed significant heteroskedasticity in
the unadjusted data. The conversion to per capita values corrected the problem.
3. Area is measured in square miles, Assessed Value in millions of dollars.
4. I have adjusted the total spending level for Menominee Co. to generate these results.
As I will discuss below, the health and human service spending for this county is
dramatically higher than any other county, exceeding its predicted level (based on the
coefficients in the first column of Table 6, estimated from the other 71 counties) by
$509.75 per capita. Menominee County's total spending was therefore reduced by that
figure, to obtain total spending coefficients that are unaffected by its unusual human
service spending.
5. The estimated relationship depicted in Figure 1 uses the coefficients from the third
column in Table 1, that is, including all of the variables and excluding the data from
Milwaukee County.
6. When the original, unadjusted total spending measure for Menominee Co. is used all four
regressions yield statistically significant negative coefficients for %(c+v). The
coefficients range from -176 to -241, and generally imply that counties spend around $220
less per person on their city and village residents that they do on their town residents.
7. Again, the estimated relationship uses the coefficients from the third column in Table
1.
8. U.S. Census, March 1998 Current Population Survey. It can be accessed on line at http
://www.ce nsus.gov/popu lation/socdemo/h h-fam/98ppla.txt.
9. Comparing County Expenditures, page 1.
10. I routinely looked for nonlinearities in all the relationships between county per
capita spending and %(City+Village). I only detected significant nonlinearities relative
to general government spending and public safety spending. In general
