Methodology

Carruthers & Ulfarsson (2003), “Urban Sprawl and the Cost of Public Services,” published in the Journal of Planning Education and Research, analyzed how urban development patterns are associated with per capita public service costs across 283 metropolitan counties in 14 fast-growing US states.

The study used 1982–1992 data drawn primarily from the USDA National Resources Inventory (NRI) for land-use variables and the Census of Governments for fiscal data. The key independent variable was “density,” defined as the sum of population and employment divided by urbanized land area.

The authors estimated a semilog OLS model with state fixed effects (13 dummies for the 14 states, Texas omitted) and White’s HC1 heteroscedasticity-consistent standard errors. The dependent variable was the natural log of per capita expenditure in each of 12 service categories, and observations with zero expenditure were dropped prior to the log transformation.

Key finding: Higher density was associated with lower per capita costs for most public services. The density coefficient was negative and statistically significant in categories such as total direct expenditure, roadways, police protection, and education.

This project replicates the original analysis using updated data from the same 14 fast-growing states: Arizona, California, Colorado, Florida, Georgia, Idaho, Nevada, New Mexico, North Carolina, Oregon, Tennessee, Texas, Utah, and Washington.

Key differences from the original

• Time period: 2012, 2017, and 2022 (three Census of Governments waves), compared to the original’s 1982–1992 data.
• Data sources: Census Bureau data throughout — American Community Survey (ACS), County Business Patterns (CBP), Census of Governments finance and organization files, and CBSA delineation files — rather than the USDA NRI used in the original.
• Sample: 394 metropolitan counties (defined using 2023 CBSA delineations; 393 in 2012/2017, 362 in 2022), yielding 1,148 county-year observations across the 3-year panel.
• Inflation adjustment: All dollar amounts are deflated to real 2022 dollars using CPI-U annual averages, allowing valid comparison across the three panel years.
• Methodology upgrade: A 6-specification robustness ladder replaces the single original specification, adding county fixed effects, clustered standard errors, demographic controls, and endogeneity tests.

Regression equation

Where:

• ln(e_it) — natural log of per capita expenditure in category for county i in year t
• α — intercept
• λ_j — fixed effects (state or county, depending on specification)
• τ_t — year fixed effects (2012 omitted as reference)
• X_it — vector of independent variables
• ε_it — error term

Independent variables

Interpreting the coefficients

Rather than reporting a single regression, we estimate six progressively different specifications for each of the 12 expenditure categories (72 regressions total). This “spec ladder” approach reveals how sensitive the density–spending relationship is to modeling choices and helps distinguish robust findings from specification-dependent artifacts.

Summary comparison

Why deflation is necessary

Our panel spans three Census of Governments waves: 2012, 2017, and 2022. Over this period, the general price level rose substantially — CPI-U increased by approximately 29% from 2012 to 2022 and by 21% from 2017 to 2022 alone. Comparing nominal dollar amounts across these years would confound real changes in service costs with general inflation, biasing year fixed effects and any variable correlated with the price level.

Method

We use CPI-U annual averages from the Bureau of Labor Statistics (series CUUR0000SA0) to deflate all dollar-denominated variables to real 2022 dollars. The deflator for each year is:

Variables deflated

All expenditure amounts (12 categories), local tax revenue, intergovernmental revenue, and aggregate property values are multiplied by the deflator before per-capita computation. This ensures that per-capita figures are in constant 2022 dollars and comparable across years.

The problem

An earlier implementation of this replication used 2020 Urban Area data for all panel years, making urban land area time-invariant. Under county fixed effects (Specs 2–5), a time-invariant variable is perfectly absorbed by the county dummy and contributes nothing to identification. This also meant that the density variable (population + employment divided by urban land area) varied over time only through changes in population and employment, not through changes in the built environment.

The original paper used USDA NRI data, which did vary over time (1982 vs. 1992 observations of developed land).

The solution

We assign each panel year to the nearest Census Urban Area vintage:

This gives meaningful within-county variation in urban land area for counties observed in both 2010 and 2020 UA vintages. In turn, the density variable varies over time through both numerator changes (population and employment) and denominator changes (urban land area), as in the original study.

All Census API calls use the Census Bureau’s public REST API for ACS 5-Year and CBP data. Census of Governments files are downloaded as bulk fixed-width or Excel archives directly from the Census Bureau website.

To assess the sensitivity of our main findings, we re-estimate two key specifications (Spec 1: state FE + HC1, and Spec 3: county FE + clustered SEs + demographic controls) on four expenditure categories that are central to the sprawl–cost debate: Total Direct expenditure, Roadways, Sewerage, and Police Protection. Each check modifies the sample or a key variable to test whether the density coefficient is robust to the change.

The four checks

Interpretation

Each check produces 8 regressions (4 categories × 2 specs). If the density coefficient retains a similar sign, magnitude, and significance level across checks, the finding is considered robust. If a check substantially alters the coefficient, it signals sensitivity to that particular modeling choice and warrants further investigation.

Full robustness results are available in the dashboard robustness section, which provides an interactive table with coefficient estimates, standard errors, and p-values for each check.