The Value of Rural and Urban Public Infrastructure

Abstract

The authors estimate the value of public infrastructure using a panel of rural and urban counties in the United States from 1970 to 2012. Regression estimates imply public infrastructure increases employment more in urban counties, while improving property values more in rural ones; positive effects on income are similar. Spatial equilibrium modeling suggests public capital has similar quality-of-life and productivity benefits in urban and rural areas but does more to reduce costs of providing housing in urban ones. While public investments in rural and urban counties appear to pass conventional cost–benefit tests, dollar-per-dollar they are more valuable in urban counties.

Keywords

infrastructure public goods employment income capitalization valuation spatial equilibrium cost–benefit analysis

In their proposals on public infrastructure, both Presidents Trump and Biden gave special attention to rural areas.¹ This raises questions as to whether infrastructure policy should treat rural areas differently than urban areas.

In this paper, we analyze and compare the value of local infrastructure spending in rural and urban counties. We construct a panel of public capital stocks—we use the terms “public capital” and “infrastructure” interchangeably—for U.S. counties from 1970 to 2012. This public capital stock includes funding for parks, roads, schools, utilities, hospitals, and buildings and equipment for administration, justice, and public safety. While local governments are responsible for these outlays, much of their funding is provided by federal and state governments through various grants.

We estimate how changes in public capital affect several local economic outcomes in rural and urban counties. We consider whether public capital raises local incomes, employment levels, and property values, both residential and agricultural. Using a theoretical model of spatial equilibrium, we interpret how these estimates reflect underlying changes in the productivity of local businesses, as well as quality-of-life benefits received directly by households.

From one perspective, prioritizing rural investments appears sensible. According to our calculations, public capital expenditures per person are much lower in rural counties than in urban ones. Yet, 97% of American land is rural, even if only 19% of the American population lives on that land (U.S. Census Bureau, 2010). If the law of diminishing returns holds for public capital, and either land or population is fixed, we can expect the return may be lower in urban areas than in rural ones.

On the other hand, rural areas, by definition, have lower population densities. Having fewer people in an area means fewer may share in the public-good nature of infrastructure, whereby the benefits to one do not diminish the benefits to others. Furthermore, new investments—public or private—are typically more valuable in faster-growing areas, and this principle tends to favor urban areas. In 1980, the census counted a rural population of just under 60 million; in 2010, the rural population was roughly the same (although the rural land area fell slightly). Meanwhile, the urban population (which includes suburbs) rose from 167 million to 249 million.

These census numbers may be misleading as they apply to a changing definition of rural: rural areas that grow can become urban simply by increasing population density, which is a defining factor of urban versus rural. In Figure 1, we compare the ratio of rural to urban populations based on an urban–rural classification of counties we construct that is fixed over time and that is used in our subsequent analysis.² This shows a decrease of population in rural counties relative to urban ones: from 33 to 30 rural residents for every 100 urban residents, which is a gentler decline than shown in the census data. Figure 1 also shows that employment is relatively lower than population in rural areas, although this disparity has shrunk since 1970.

Figure 1.

Relative population, employment, and public capital: fixed rural and urban counties. Note. See Data and Descriptive Statistics section and for our definition of fixed rural and urban counties. The census definition is based on block groups that change over time, gradually becoming more urban.

As noted earlier, the share of public-capital spending in rural counties is decidedly lower than in urban counties. The total spending has remained unchanged at a ratio of $19 rural to every $100 urban. The relative dollar amount per capita has also remained around $60 rural to every $100 urban.

However, these ratios are based on expenditures and ignore the possibility that rural infrastructure may come at a lower cost (Brooks & Liscow, 2019). If infrastructure in rural areas is only 60% of the cost of infrastructure in urban areas, which housing-price differences show to be plausible, then the amount of actual public capital per person would be similar. As rural areas receive greater proportional representation in Congress (Atlas et al., 1995), especially the Senate, there is concern that “pork-barrel” politics may even overallocate public capital to rural areas.

Whatever the case, an important question for an infrastructure policy that targets rural areas is whether infrastructure affects a rural economy any differently than an urban one. It is worth investigating whether public infrastructure investments are as valuable, dollar-per-dollar, in rural areas as in urban areas.

Infrastructure Benefits in Spatial Equilibrium

Context in the Existing Research on Valuing Infrastructure

Our theoretical and empirical approaches build off of Haughwout (2002) and Albouy and Farahani (2017) successively. Haughwout (2002) estimated the value of public infrastructure through its effects on wages and housing prices, interpreting these effects through the lens of the Roback's (1982) spatial equilibrium model.³ This price-oriented approach contrasts with quantity-oriented approaches, such as Aschauer (1989).⁴ An advantage of the price-oriented approach is that it can account for quality-of-life benefits that accrue directly to households, and not just in productivity benefits for producers (i.e., “firms”). Quality-of-life benefits do not show up in income accounts and may indirectly lower local incomes through spatial-equilibrium forces. However, both quality-of-life and productivity benefits will typically raise local land values.

Albouy and Farahani (2017) integrated quantities into the price-oriented approach by modeling total employment, working from Albouy (2016) and Albouy and Stuart (2020). Thus, while Haughwout (2002) made a cost–benefit assessment based solely on how much housing prices appreciate, Albouy and Farahani (2017) considered how infrastructure could lower housing prices by making housing cheaper to build. Lower housing costs will attract new workers from other communities and thus boost local employment and population levels. This mechanism proves to be quite important in our model, as the results suggest this effect is stronger in urban counties than in rural ones. Our model also features federal taxation and imperfect household mobility, which are novel to infrastructure valuation. Together, these features help to measure the full benefits of infrastructure, while steering clear of possible issues involving double counting.

Our model is largely an extension of the one in Albouy and Farahani (2017), except that it accounts for agricultural production and simplifies nonagricultural production.⁵ The spatial-equilibrium model treats each county as a local economy containing land, public capital, private (mobile) capital, and a population of employed worker-households.

Lacking data within counties, we use data consisting of single measures per county, indexed by j in our equations. Note that smaller geographic units would capture fewer spillovers across areas, either positive or negative. For instance, a major highway passing through one village is likely to have considerable positive spillovers for other nearby villages. As the model is static, we omit the time index t. However, we do consider possible dynamic effects in a section of the online Appendix (Dynamics: New Public Infrastructure versus Old).

The key empirical inputs of the model are various elasticities, which we estimate from the data panel. Namely, an elasticity such as $β_{N}$ provides the elasticity of county population with respect to infrastructure. $β_{m}$ is a similar elasticity for income, and $β_{p}$ is for housing prices. Based on logarithmic transformations for each variable, these elasticities are akin to percentage effects for small numbers.

Assumptions about the mobility of households and firms allow us to transform these estimated elasticities into measures of how infrastructure affects fundamental economic features of the local economy, together with the well-being of households, and the profitability of firms and property owners. Below, we provide an intuitive overview of the theory in log-linearized form. Parameter values used to properly combine the elasticities are substituted directly into the equations below, so as not to overburden the reader with notation. The full model, with free parameters, is derived in the Parameterization section of the online Appendix. The values shown are for a representative national average. In practice, we use numbers that differ (typically slightly) for urban and rural economies, as detailed in the Additional Data Details section of the online Appendix.

Theoretical Framework and Assumptions

Land is categorized into three different uses: residential (Y), agricultural (Z), and wilderness. In each of these uses, land has a separate value: an observed agricultural value $r_{Z}^{j}$ , or an unobserved, but inferable, residential value, $r_{Y}^{j}$ . The value of wilderness land is not only unobserved, but unobservable, and so is left out of further analysis.

Private firms belong to three sectors, each producing a different type of good: an agricultural good, which may be traded across counties (Z); a nonagricultural good, similarly traded (X); and a nonagricultural good, which is not traded (Y). This latter type is referred to as a “home good” and consists mainly of residential housing.

All three goods are produced with mobile capital, which has a price that is the same across counties and is therefore safely ignored.⁶ All three goods are produced with local labor, which has an observable wage, $w^{j}$ . This wage does vary by location, but unlike the price of land, we assume that it does not vary by sector. The agricultural sector, Z, uses agricultural land, while the home-good sector, Y, uses residential land. The nonagricultural traded good X does not use land.⁷

Quality of Life Benefits

Infrastructure confers quality-of-life benefits that directly benefit households, but do not show up in income measures. Spatial-equilibrium reasoning allows us to infer these benefits through two components. The first is a willingness-to-pay component that measures how much households sacrifice in private consumption to live in a county due to how high local costs of living are relative to local wage levels. The reasoning is that lower quality-of-life counties must offer residents a higher real income, which translates into higher private consumption, to keep them from leaving.

The second component depends on population growth and local attachment to an area. It considers how the willingness-to-pay to live in a county varies across the population. A county that grows increasingly brings in people who, absent material considerations, would otherwise choose not to live there. Those incoming residents essentially pay a psychic moving cost by leaving attachments from their origin. The heterogeneity in costs generates a downward-sloping demand curve of population in terms of willngness-to-pay, or equivalently, an upward-sloping supply curve of employment in terms of real income. Assuming markets are competitive—the law of one price holds in both housing and labor markets—movers and existing residents are paid the same and face the same costs. This is true even as firms bid up real wages to attract new residents. The more population growth a county sees, the more private consumption must rise to attract a (supra-)marginal resident into a county. Greater growth implies greater welfare gains for existing (infra-marginal) residents, who also see their private consumption rise, but do not pay moving costs.⁸

Given measures of the elasticities of population, income, and housing prices, we infer the quality-of-life elasticity by adding up these two components:

β_{Q} = \underset{Willingness - to - Pay}{\underset{⏟}{0.33 β_{p} - 0.67 β_{m}}} + \underset{Growth Premium}{\underset{⏟}{0.07 β_{N}}}

(1)

The willingness-to-pay term assumes that home goods make up 33% of consumption, while 33% of income gains are taken by federal taxes. The value of 0.07 measures the rate at which psychic cost grows as a county attracts more, less likely, residents.⁹

Productivity Benefits

To infer the productivity of firms in a county, we measure how much each input is paid relative to output prices. In a standard competitive model, the ratio of input to output prices reveals the marginal productivity of each factor. For firms that produce output traded across counties, the output price is taken as constant. In that case, we can measure the productivity of each factor in terms of input prices directly (i.e., the nominal wage or the rental value of the land). This is the case for agriculture (Z) and the traded good (X). Following standard production theory, we weighted the elasticity of each input price in proportion to its share of costs in production.

As we lack exact data on wage changes, we infer them through household income changes. We assume that nonlabor income is diversified, so that its return does not depend on local wage levels. All variation in local income is then driven by local wages. Thus, if 71% of income derives from labor, $β_{m} = 0.71 β_{w}$ , or inversely $β_{w} = 1.42 β_{m}$ .

For nonagricultural traded output, the measure of productivity is simply proportional to the wage, considering that wages are around 85% of costs. This measure is then:

β_{A X} = 0.85 β_{w}

(2)

The remaining 15% of costs are assigned to mobile private capital, whose price should have an elasticity of zero.

For agricultural productivity, the measure factors in wages and agricultural land values. Thus,

β_{A Z} = 0.38 β_{w} + 0.25 β_{r Z}

(3)

This assumes that 38% of costs are due to local labor, accounting for nonlabor inputs (e.g., materials) supplied locally by other nontradable firms using labor. Twenty-five percent of costs are from land (and, in practice, farm buildings). The remaining 37% belong to mobile capital, including seed, fuel, and machinery.

For home productivity, we account for differences in the output price, using the price of housing. In the log-linearization, the house-price elasticity is simply subtracted from the weighted input-price elasticities:

β_{A Y} = \underset{Input Costs}{\underset{⏟}{0.50 β_{w} + 0.25 β_{r Y}}} - \underset{Output Price}{\underset{⏟}{β_{p}}}

(4)

The issue here is that we do not observe the value of residential land directly. Instead, we must infer

β_{r Y}

through changes in housing supply and demand.¹⁰

The Theoretical Derivations section of the online Appendix details how to infer home productivity and residential land-value changes. In short, the model considers how residential populations grow from quality-of-life and productivity improvements in tradable sectors. If the observed population rises more than this predicted amount, then the model infers that home productivity must have risen to account for the gap. Put into concrete numbers, home productivity is inferred from a weighted sum of population and wage growth relative to housing-price growth:

β_{A Y} = 0.35 β_{N} + 0.84 β_{w} - 0.95 β_{p}

(5)

Simultaneously, changes in residential land prices are inferred from a weighted sum of increases in population, wages, and housing prices:

β_{r Y} = 1.38 β_{N} + 0.60 β_{w} + 0.22 β_{p}

(6)

Through the lens of a correctly specified model, population estimates can serve as a substitute for unmeasured residential land values.

The Form and Distribution of Benefits

As covered above, the effects of infrastructure on the local economy take on four different forms: quality of life for households and three different productivities for firms. To determine the effect on total productivity, the productivities must be added, each weighted by its output share. The quality-of-life effect is already in units comparable to total income. The weighted sum of quality-of-life and productivity elasticities produces a total-value elasticity, $β_{Ω}$ , written as

β_{Ω} = β_{Q} + 0.65 β_{A X} + 0.33 β_{A Y} + 0.02 β_{A Z}

(7)

The benefits of local infrastructure accrue ultimately to four, possibly overlapping, parties. As firms and capital are fully mobile in the model, they do not earn additional profits or returns.¹¹ Property owners come in two kinds. Residential landowners include those in owner-occupied homes and those who lease housing. Agricultural landowners either produce agricultural output directly or lease it to others. We infer these make up about 8.3% and 0.5% of total income. The third party consists of residents who are renters. They gain insofar as their quality of life and private consumption grows. As explained above, this is measured for the infra-marginal residents, who see a gain equal to the growth premium

0.07 β_{N}

. Homeowners (i.e., owner-occupiers) gain both this benefit of renters, as well as that of residential landowners. Finally, the federal government gains through greater tax receipts when incomes rise, given by

β_{τ} = 0.33 β_{w}

Taken together, using the proper weights, this means that the sum of benefits may be written as

β_{Ω} = 0.083 β_{r Y} + 0.005 β_{r Z} + 0.07 β_{N} + 0.360 β_{m}

(8)

Through income accounting identities, the numbers implied by

β_{Ω}

are the same in (7) as in (8). This neat accounting system provides a lens on how infrastructure can benefit parties beyond traditional income measures, which would simply look at

β_{m}

To determine the value of benefits per dollar invested, we must consider the ratio of the value of outcome variable relative to the cost of the infrastructure. In the case of total value, the elasticity $β_{Ω}$ must be multiplied by income and divided by the cost of public capital.

β_{Ω} \frac{N m}{G} = \frac{d Ω}{d G}

(9)

A challenge in doing this is that income is measured as a flow, while the cost of public capital is accrued over time and subject to discounting.

Internal and External Sources of Funding

Note that the model does not account for changes in tax rates. Our data do not tell us how much the funds used to pay for public capital investments are internal to the county. While local governments are largely responsible for overseeing the projects we consider, a large proportion of them are often paid for by state and federal grants. Since counties are small relative to the federal government and most states, federal and state tax increases to pay for these grants can be safely ignored. However, for many projects some amount is paid for by taxes levied within the county. Depending on how they are levied, such taxes are likely to have effects like quality-of-life or productivity decreases and lower the welfare of residents and property owners.

On average, the omission of local taxes from the model means that the estimates are a lower bound on the effects of infrastructure. A positive effect of a project that is being paid for by a local tax is more notable than a positive effect of a project paid for exclusively by external grants. Bear in mind that the form and distribution of estimated benefits may be affected by the mix of taxes: property taxes will likely reduce property values, while sales taxes will likely reduce residents’ (as renters) welfare.

Data and Descriptive Statistics

Our panel consists of observations of all 3,105 continental U.S. counties in years 1970, 1980, 1990, 2000, 2007, and 2012, using minor adjustments for county boundary changes to match them to 2000 definitions. Data on these counties come from several census sources. Population, employment, and housing data are from the Decennial Census of Population and Housing for 1970, 1980, 1990, and 2000, and the American Community Survey (ACS) for 2007 and 2012. Farm and land value data are retrieved from Haines et al. (2018), which aggregates county-level data of the Census of Agriculture survey conducted by the U.S. Department of Agriculture. We use 1969 and later years ending in 2 and 7, until 2012. We use state and local government outlays of capital from the Census of Governments in years ending in 2 and 7, starting in 1902, to estimate the public capital stock, as described below.¹²

County Panel of Public Capital

The census data provide measures of public-capital outlays or investment flows. We add up these flows over time to create a public infrastructure stock using a perpetual inventory method. County-area capital outlay measures aggregate expenditures of all local (nonstate and nonfederal) governments within a county, including county, city, township, special district, and school district governments. This includes public funding for parks, roads, schools, utilities, hospitals, and buildings and equipment for administration, justice, and public safety. We combine all these outlays to construct a single measure of the public-capital stock, a term we use interchangeably with public infrastructure. Changes in the data over time limit how much this capital can be differentiated by its functional purpose or by character and object.

The perpetual inventory method adds up investment flows every year to ever-depreciating public capital stock. Specifically, we follow procedures by Haughwout and Inman (1996) and Haughwout (2002), with only minor adjustments. As finance data are provided every 5 years, we geometrically interpolate the outlays for years in between, if they follow a smooth pattern. Investments are deflated over time using the Producer Price Index (PPI). We depreciate these investments geometrically using three depreciation rates depending on whether they are allocated to land and existing structures (L&ES; 1.64%), construction (1.82%), and equipment (11.0%). Construction accounts for roughly three-quarters of investments and four-fifths of the capital stock, as equipment depreciates much more quickly.

Less than half of the capital stock refers to core infrastructure, which consists of highways, utilities, sewerage, solid waste management, and air and water transportation. Noncore infrastructure consists largely of buildings for education, hospitals, parks, and public housing. A section in the online Appendix (Core versus Noncore Infrastructure) examines the composition of infrastructure in greater detail.

Table 1 presents the average value of our public-capital measures by county, broken down for urban and rural areas in 2012. It also includes national aggregates. In 2012, the aggregate value of public capital financed at the county level and all other local governments was $6.38 trillion in urban and rural areas combined. The value financed at the state level was $3.27 trillion, for a sum of $9.65 trillion. In comparison, the Bureau of Economic Analysis (BEA)—using different accounting methods—estimates the total value of public capital financed by state, county, and all other local governments at $9.40 trillion.¹³ This 3% discrepancy seems minor given the differences in methodology. In relative terms, rural counties have a lower percentage of core infrastructure compared to urban counties.

Table 1.

Aggregate Value of Public Capital, Labor, and House Values by County in 2012.

	Rural counties		Urban counties
	County	National	County	National
	Mean	Sum	Mean	Sum
	($M)	($B)	($M)	($B)
Panel A: Values in 2012
Public capital stock, local	414	1,012	8,148	5,370
Core infrastructure, local	156	381	3,758	2,477
Noncore infrastructure, local	257	630	4,389	2,892
Public capital outlays (flow), local	14	34	265	175
Public capital outlays + maintenance (2%)	22	54	428	282
Family income (flow)	515	1,261	7,856	5,177
House value	1,298	3,175	22,328	14,714
House value × user cost (7%)	90	222	1,562	1,029
Gross rent (flow)	23	58	618	407
Inferred value of housing services (flow)	114	280	2,181	1,437
Farm value	693	1,695	910	562
Panel B: Income shares
Public capital share (G/Nm)		0.043		0.055
Inferred housing services share (pY/Nm)		0.222		0.278

Note. All amounts in 2012 U.S. dollars, deflated by the Consumer Price Index for family income, house value, and gross rent, and Producer Price Index for public capital outlays. County mean and national sum are unweighted. Core capital is comprised of air and water transportation, highway, solid waste, sewerage, and utilities. Noncore infrastructure includes all other functions. Family income, house value, and gross rent are aggregate values.

We calculate the ratio of public-capital outlays to household income to be 4.3% in rural counties and 5.5% in urban counties. This is less than a quarter of what households spend on housing (22.2% and 27.8%), based on adding up gross rents and an inferred user cost of housing. All these percentages may be seen as expenditure shares, which are useful for the cost–benefit analysis in The Value of Rural and Urban Infrastructure section of this paper.

Rural and Urban County Definition

The U.S. Census Bureau defines urban areas at the block group level, using contiguous groups that add up to 2,500 people or more, at a density of 1,000 per square mile (Brown et al., 1994). As our data are at the county level, we cannot perfectly divide them along these lines. Most counties contain both urban and rural block groups. Thus, we were required to make our own classification of counties.¹⁴

We classify counties as rural if they meet either one of two criteria, using 2000 data:

More than 40% of the county's population lives in a rural (i.e., nonurban) block group.

The population density over the entire county is under 64 per square mile (10 acres per person).

This second definition applies even if less than 40% of the population lives in rural block groups. This counts as large those rural counties that may have a smattering of people in small, isolated urban clusters, but are largely surrounded by large tracts of sparsely populated land. These counties, shown in Figure 2, are mostly west of the Mississippi.

Figure 2.

Map of U.S. counties by urban and rural classification using 2000 data.

Rural and Urban Differences and Trends

Figure 3 maps out two different ways of visualizing county infrastructure density. The map in Figure 3a shows infrastructure density per person. This tends to be higher in some states than others, and typically, but not always, in urban counties. The density of infrastructure over land is displayed in Figure 3b, which is generally higher in urban counties, although less so in very large urban counties, such as in Arizona.

Figure 3.

Infrastructure by county, per capita and per square mile. (a) Infrastructure per capita. (b) Infrastructure per square mile.

Table 2 reports the means and standard deviations of our key variables, separating rural and urban counties. Unlike our later regressions, these statistics are unweighted, giving a sense of the variation across counties. We also present additional figures showing trends in these variables, in rural versus urban aggregates, as in our first figure.

Table 2.

Descriptive Statistics, All Counties and Years 1970 to 2012, Urban versus Rural.

	Rural counties		Urban counties
	Mean	SD	Mean	SD
Variable of interest
Public capital stock, local ($ M)	271	445	5,260	16,768
Core capital stock, local ($ M)	108	270	2,542	8,869
Noncore capital stock, local ($ M)	163	236	2,717	8,087
Public capital stock, per square mile ($ K)	391	575	14,823	62,686
Public capital stock, per capita ($ K)	11	10	13	9
Main outcomes for theoretical analysis
Population	25,491	27,334	301,300	611,528
Family income, average ($)	56,392	13,588	73,650	20,361
Housing value, average ($)	111,862	60,431	176,454	105,890
Farm value per acre ($)	2,164	1,650	6,592	18,932
Other outcomes
Farmland, percent of total land	0.56	0.31	0.39	0.29
Employment	10,650	12,183	137,471	276,443
Agricultural share of employment	0.09	0.09	0.02	0.02
Manufacturing share of employment	0.17	0.11	0.17	0.1
Additional variables
Land area (sq. mi)	1,014	1,333	726	1,156
Average gross rent	6,492	1,726	9,139	2,688
Public capital stock, state ($ M)	50,993	48,203	67,955	54,913
Number of counties	2,446	-	659	-

Note. All amounts in 2012 U.S. dollars, deflated by the Consumer Price Index for family income, housing value, and gross rent, and Producer Price Index for public capital outlays. Averages and standard deviations are at the county level, and unweighted. Public capital in millions. Additional statistics reported in online Appendix Table A3.

Several features of the data are worth noting, in addition to what we saw earlier. First, rural counties report family incomes that are only between 70% and 80% lower than those of urban families. As seen in Figure 4, this ratio has fluctuated a bit, with a rise and fall between 1980 and 1990, a particularly difficult period for family farms.¹⁵ Housing values and rents in rural counties are just over half of what they are in urban counties. Although rural housing values saw a steeper decline in the 1980s, by 2012 the urban/rural ratio was comparable to what it had been in 1970.

Figure 4.

Income, housing value, agricultural land value.

Figure 5 looks at agricultural land, which is defined broadly to include pastureland as well as other nonfarming agricultural uses. It reflects the fact that urban counties, while only having a minority of residents outside of dense urban clusters, still generally have most of their land devoted to agriculture. In 2012, the percentage of all land devoted to farms was only 40% higher in rural counties than urban counties, although that difference has grown over the period our data cover. Meanwhile, the average value of farmland per acre in rural counties—seen in Figure 4—is closer to that of farmland in urban counties than are the housing values.¹⁶ The relative trend has been upward: per acre rural county farms are worth 90% of their urban counterparts by 2012.

Figure 5.

Employment and farmland percentage.

As seen earlier, employment in rural and urban counties is roughly proportional to population, as the employment-to-population rate rose in rural areas. In Table 2, we see that in rural counties, agricultural workers make up about 10% of the workforce, while in urban counties it is scarcely 2%. Manufacturing employment is higher than agricultural employment in rural counties at 17%. The trends in Figure 5 show that over time, rural counties have become relatively more reliant on manufacturing jobs. Meanwhile, the proportion of farmland in urban counties has fallen relative to the amount in rural counties. This reflects faster urban development in urban counties.

Empirical Model

To estimate the impact of infrastructure on various outcomes, we use panel regressions across counties j and time periods t. The dependent variables are the logarithm of the outcome $O^{j t}$ . These variables include incomes, housing prices, agricultural land values, and population. Public capital, $G^{j t}$ , is entered as the independent variable, also in logarithm, so that the coefficients refer to the elasticities required of the model. Public capital is interacted with a rural indicator $R_{j}$ , or an urban indicator $U_{j} = 1 - R_{j}$ , to provide separate elasticities $β_{O R}$ and $β_{O U}$ for rural and urban counties. Thus, the panel regression equation takes the form

\ln O^{j t} = β_{O R} R^{j} \ln G^{j t} + β_{O U} U^{j} \ln G^{j t} + \sum_{l} C_{l}^{j t} (R^{j} β_{l R} + U^{j} β_{l U}) + μ^{j} + R^{j} ξ_{R}^{t} + U^{j} ξ_{U}^{t} + ε^{j t}

where µ^j are county indicators (i.e., fixed effects) and

ξ_{R}^{t}

and

ξ_{U}^{t}

are time indicators. The variables

C_{l}^{j t}

correspond to an array of time-varying control variables that are also interacted with the rural and urban indicators. They include state income (top and bottom), sales, and corporate tax rates; the gender ratio; shares in various age and race groups; shares that are or have ever been married; and shares educated with less than high school, exactly high school, or some college.

$ε^{j t}$ is an error term that is exogenous based on the presumption that infrastructure investments are exogenously targeted, conditional on the controls. This assumption has some credibility if infrastructure differences are determined by formulae that ignore future growth, and/or fluctuating political power imbalances and pork barrel spending. The most typical concern is that infrastructure may be targeted toward areas that expect future growth in population and income, which would bias the estimates upward.

A limitation of the data is that they are not at the household level. To make the results comparable to those using such data, we weigh the observations using current county population. To address possible correlation in the error terms, the standard errors are clustered by county and year.¹⁷

The Impact of Infrastructure on Rural and Urban Economies

Base Elasticities: Population, Income, and Property Values

In Table 3, we present the estimates of how infrastructure affects economic outcomes in rural (Panel A) and urban (Panel B) counties. The difference is shown in Panel C. The results in the first four columns also inform the model, for which we provide the notation. A visual comparison of the rural and urban estimates is shown in Figure 6.

Figure 6.

Elasticity of outcomes with respect to infrastructure. (a) Total population and rural population. (b) Family income, house value, and farm value per acre. (c) Employment.

Table 3.

Estimated Elasticities of Public Capital on Outcomes, County Panel, 1970 to 2012.

Outcomes for theoretical analysis				Other outcomes
Populaion	Family income	Housing value	Farm value per acre	Rural percent pop.	Employment, total	Agric. emp.	Manuf. emp.
$β_{N}$	$β_{m}$	$β_{p}$	$β_{r Z}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Panel A: Rural counties
0.288	0.034	0.092	0.099	−0.067	0.286	0.077	0.215
(0.029)	(0.008)	(0.021)	(0.038)	(0.011)	(0.028)	(0.047)	(0.026)
Panel B: Urban counties
0.519	0.035	0.007	0.150	−0.087	0.520	0.265	0.666
(0.027)	(0.013)	(0.040)	(0.095)	(0.010)	(0.027)	(0.039)	(0.044)
Panel C: Rural vs urban difference
−0.231	−0.001	0.085	−0.051	0.020	−0.234	−0.188	−0.451
(0.034)	(0.017)	(0.044)	(0.098)	(0.009)	(0.035)	(0.057)	(0.049)

Note. Dependent (outcome) and independent (public capital stock, county) variables entered in logarithmic form. All regressions include county and year fixed effects as controls, as well as time-varying covariates listed in Table A3 including public capital at the state level, each interacted with a rural indicator. All regressions are weighted by current county population and include 18,630 county-year observations. Two-way clustered standard errors (county and year) in parentheses. Unweighted estimates are reported in online Appendix Table A4, which also shows less conservative (smaller) Conley (2008) standard errors in addition to clustered ones.

In column 1, infrastructure is associated with a considerable increase in population (i.e., new residents). The elasticity for urban counties, near one-half, is almost twice as high as for rural ones, at just over a quarter.

Results in the second column show that infrastructure also has significant associations with income in both urban and rural counties, just over 3%; the estimates are statistically indistinguishable from one another.

In column 3, we see a considerable association with housing values in rural areas, at 10 points, but almost none in urban areas. In column 4, we see that the effect on farm values is slightly higher in urban counties, but the difference with rural counties is not statistically significant.

The results in columns 1 and 3, taken together, would suggest that housing supply is more elastic in urban counties than in rural ones. Demand increases generally raise prices in inelastic counties and less so in elastic ones. However, this reasoning presumes a stable housing supply curve. The more general spatial-equilibrium model we use allows for the housing supply curve in urban areas to, instead, shift outward from increased infrastructure.

In the Core versus Noncore Infrastructure section in the online Appendix, we consider whether core infrastructure yield stronger or weaker effects than noncore. Statistically, the fraction of capital that is core is insignificant for all the outcomes, implying the effects are roughly similar. Thus, further breakdowns seem unlikely to be fruitful, at least given the data quality we have.

The Dynamics: New Public Infrastructure versus Old section in the online Appendix considers the possible role of dynamic issues related to investments. It shows that in the short run, price effects are slightly larger, while population effects are slightly weaker. Although the differences are generally small, these findings are qualitatively consistent with standard dynamic predictions.

Additional Elasticities: Employment Effects and Urbanization

The results in columns 1 and 5 in Table 3 may also be interpreted to examine how infrastructure encourages urbanization. The results in column 5 suggest infrastructure reduces rural population within both types of counties. However, since these coefficients are smaller than the overall population measure, the total rural population will still grow overall if we consider rural counties in isolation.

A fuller analysis requires looking at urbanization shifts across and within counties. Importantly, the elasticity for population in column 1 is larger for urban counties than rural ones. Increasing infrastructure in all counties simultaneously requires the population effects to average out to zero—assuming infrastructure does not affect the total population. Thus, greater infrastructure everywhere would likely increase population in urban counties at the expense of rural counties. Thus, infrastructure investments distributed equally nationwide are likely to grow urban populations across counties, as well as within them.

The employment estimates in column 6 are nearly identical to those for population in column 1, so there does not appear to be any effect of infrastructure on the employment-to-population ratio. To evaluate how much infrastructure adds to local employment, it is meaningful to consider the ratio of employment elasticity relative to the income share of public capital from Table 1. These shares are 4.3% and 5.5% for rural and urban counties, respectively. The ratios of employment elasticities to shares are 6.8 and 9.5, respectively. These ratios may seem large, although one must be reminded that they represent employment being moved from one county to another—the employment-to-population rate hardly changes at all. Economically, these ratios are similar in magnitude to those estimated by Bartik (1991), who looked at how employment changes with local tax burdens, holding expenditures constant.¹⁸ Accordingly, if the federal government uses funds to finance local infrastructure, it may have an effect on employment similar to using those funds to finance local tax relief.

In column 7, we see that agricultural employment grows with infrastructure, but less than total employment. This means that, while infrastructure does grow the agricultural sector, its share of the overall labor force diminishes. Finally, in column 8, we see that infrastructure investments have a stronger association with manufacturing employment in urban counties than in rural ones.

Elasticities Inferred from Spatial Equilibrium

Table 4 displays elasticities inferred from the spatial-equilibrium model, all of which turn out to be positive. Wage increases, seen in column 1, exceed income increases seen previously, based on our assumptions. The concomitant federal tax revenue shows both urban and rural areas contribute roughly 1 percentage point more of total income.¹⁹

Table 4.

Estimated Elasticities of Public Capital on Quality of Life and Productivities, County Panel (1970 to 2012).

	Wage	Fed. tax	Quality of life	Trade prod	Home prod	Resid land	Agric prod	Total value
	$β_{w}$	$β_{τ}$	$β_{Q}$	$β_{A X}$	$β_{A Y}$	$β_{r Y}$	$β_{A Z}$	$β_{Ω}$
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Rural	0.048	0.010	0.023	0.041	0.022	0.422	0.043	0.059
	(0.011)	(0.002)	(0.005)	(0.010)	(0.020)	(0.040)	(0.011)	(0.006)
Urban	0.049	0.012	0.015	0.041	0.184	0.665	0.056	0.107
	(0.017)	(0.004)	(0.007)	(0.015)	(0.031)	(0.034)	(0.029)	(0.007)
Difference	−0.001	−0.002	0.008	−0.001	−0.162	−0.243	−0.013	−0.048
	(0.023)	(0.006)	(0.007)	(0.020)	(0.034)	(0.049)	(0.032)	(0.010)

Quality-of-life increases are also measured in units corresponding to total income. Both rural and urban counties see quality-of-life increases of roughly 2%. Referring to equation (1), in rural counties this is mainly reflected in willingness-to-pay, as housing-value growth exceeds income growth. In urban counties, it is reflected more in population growth (i.e., the growth premium).

Infrastructure is associated with higher trade productivity in both types of counties, as implied by the wage increases. Urban counties see much larger increases in home productivity, which explains how their populations grew along with income, while housing values did not. Column 6 shows large increases in inferred residential land values in both urban and rural counties. In urban counties, this results from large quantities of homes being built on available land, which then becomes more valuable. In rural counties, it has more to do with the greater value of the homes built on that land.²⁰ Column 7 shows increases in agricultural productivity commensurate with increases in traded productivity.

The results in column 8 of Table 4 show the elasticity of total value, measured in total income units. Here we see an elasticity of roughly 6% for rural areas and 11% for urban areas. The difference is largely accounted for by differences in home productivity growth. It stems from how the spatial model interprets the larger population elasticity in urban counties.

The Value of Rural and Urban Infrastructure

The question of whether infrastructure spending is worthwhile depends greatly on its economic return. The returns estimated here capture both consumption in market goods and nonmarket goods. They capture increases in real income generated by firms, as well as the nonmarket benefits not captured by typical income statistics. The returns do not capture spillover benefits, positive or negative, to other counties. At the highest level of aggregation, nonmarket benefits would be invisible to our methodology. Presumably, total population and housing values would not change if all areas got uniformly better quality of life through infrastructure.

To determine the return on public capital, the elasticities in Table 4 need to be compared with their outlays as a share of income in Table 1 (i.e., 4.3% for rural counties and 5.5% for urban counties). The final column of Table 5 shows that the ratio of the total-value elasticity to this share is roughly 1.4 in rural counties; in urban counties, it is just less than 2. Thus, in both cases, the ratio is over 1, although the aggregate return appears higher in urban counties. These numbers are shown as the total heights of the bars in Figure 7.

Figure 7.

Form of benefits of public capital per dollar invested. (a) Values across households and firms. (b) Benefits across agents.

Table 5.

The Inferred Value of Infrastructure in Rural and Urban Counties.

Expressed in dollars of return per dollar of public capital investment
Panel A: Partition across households and firms
	Quality	Trade	Home	Agricultural	Total
	of life	productivity	productivity	productivity	value
Rural	0.532	0.574	0.146	0.099	1.350
	(0.103)	(0.135)	(0.133)	(0.024)	(0.132)
Urban	0.282	0.486	1.180	0.010	1.959
	(0.135)	(0.174)	(0.200)	(0.005)	(0.124)
Difference	0.250	0.087	−1.034	0.088	−0.609
	(0.143)	(0.250)	(0.221)	(0.025)	(0.198)
Panel B: Distribution of benefits across landowners, residents, and federal government
	Residential land	Agricultural land	Local residents	Federal govt	Total value
Rural	0.593	0.057	0.465	0.235	1.350
	(0.056)	(0.020)	(0.047)	(0.055)	(0.132)
Urban	1.067	0.007	0.666	0.220	1.959
	(0.055)	(0.004)	(0.035)	(0.079)	(0.124)
Difference	−0.473	0.050	−0.201	0.016	−0.609
	(0.073)	(0.020)	(0.050)	(0.109)	(0.198)

Note. Ratio of capitalized income to capital costs of 23.35 (18.36) in rural (urban) counties.

Panels A and B of Table 5 provide two different breakdowns of the total estimated value of public infrastructure in rural and urban counties. Panel A monetizes the economic effects, also shown in Figure 7a, while panel B looks at the breakdown of gains to economic agents, also shown in Figure 7b.

In rural counties, infrastructure provides most of its benefits in terms of quality of life. This finding is strikingly close to findings by Lewis and Severnini (2020) on rural electrification. The remainder of benefits accrues to producers of traded goods in both agricultural and nonagricultural sectors. This may be due to improvements in transportation networks, allowing firms to import inputs and export outputs more cost effectively. The benefits to agricultural productivity are rather high, especially relative to the sector's still modest size in rural county economies. We do not find any measurable impact on home productivity. It may be that home productivity is less of an issue in rural counties, so that infrastructure improvements do not ease housing costs as they do in urban counties. The total benefit per dollar of investment is $1.35. Unless the marginal cost of public funds is high, more than $0.35 per dollar raised, this finding suggests that, on average, public infrastructure investments in rural areas should pass a standard cost–benefit test.

The results for urban counties show benefits distributed in a somewhat different manner. Most of the benefits take the form of home productivity, as infrastructure helps to keep housing prices from spiraling upward. Benefits to traded nonagricultural firms are also quite large, almost enough on their own to justify the investments. In total, the benefits are about $0.60 higher per dollar than rural investments. It is remarkable that the return on infrastructure is higher in urban counties, even though the amount spent on public capital there is higher relative to both income and population. While the law of diminishing returns may hold, the need for public infrastructure may be higher in more densely populated areas.

The distribution of benefits is somewhat more even between urban and rural counties. Residential landowners benefit considerably in both, although somewhat more in urban areas. Agricultural landowners, not surprisingly, benefit more in rural counties, as land ownings are relatively more important. Local residents, taken as renters, also seem to gain from these infrastructure improvements in both types of counties. The federal government receives a substantial benefit of over $0.20 per dollar invested.

In some ways, these estimates constitute lower bounds on the return to infrastructure as they presuppose that funding is external to the county, namely from the state or federal level. A self-financed project could pass the cost–benefit test so long as its calculated value surpasses the marginal cost of funds alone. Furthermore, our conclusion that urban investments yield a larger return remains valid if urban counties fund an equal fraction or more of their public infrastructure relative to rural counties. At the same time, the estimates may be overstated if infrastructure investments are largely made in anticipation of new growth of population, income, and property values.

Conclusion

Taken at face value, this model finds that infrastructure investments typically yield positive value, net of costs, with higher returns in urban counties. This conclusion is based on how urban counties saw significantly greater employment growth, even though rural areas saw greater housing-price appreciation. However, a simpler model, one that ignores how infrastructure can make housing more affordable, could lead to the opposite conclusion that infrastructure is more valuable in rural counties. Taken together, our analysis produces results that make sense economically.

In the first and simplest interpretation, this analysis can support the idea that public infrastructure in the United States is underprovided. This is a fair conclusion, insofar as the empirical model identifies the marginal investment, and if the marginal cost of public funds is less than roughly $1.40 per dollar raised. While infrastructure may be more expensive to provide in urban counties, the return per dollar spent is still larger than in rural counties. Most importantly, our estimates are, at best, merely that of an average treatment effect. The returns to a specific project may be much higher or lower than this average, depending on its function, the characteristics of the local area, how it is planned, and how well it is implemented.

Nonetheless, these results should be interpreted cautiously, given the possible endogeneity of infrastructure spending. Planners and politicians may initiate infrastructure investments to anticipate increases in growth of population, income, or property values. Such endogenous processes may differ substantially in rural areas relative to urban ones. Hopefully, future researchers will make progress in isolating increases in public infrastructure exogenous to the many outcomes we consider. In the meantime, we caution readers at taking our urban–rural distinctions too seriously.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

David Albouy

Heejin Kim

Supplemental Material

Supplemental material for this article is available online.

Notes

Author Biographies

David Albouy is professor of economics at the University of Illinois at Urbana-Champaign. His research is primarily in urban and public economics, focusing on federal taxation and spending, and quality-of-life issues.

Heejin Kim is a Ph.D. candidate at the University of Illinois at Urbana-Champaign. Her research interests are in urban and public economics.

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