More Evidence on the Spatial Scale of Cities (McGrath, 2005)

Summary

"More evidence on the spatial scale of cities" by Daniel T. McGrath (University of Illinois at Chicago), Journal of Urban Economics 58(1), 2005, pp. 1–10, is a research note that re-estimates the determinants of metropolitan urbanized land area using a much larger panel than the classic Brueckner & Fansler (1983) study: the 33 largest US metropolitan statistical areas across the five censuses from 1950 to 1990 (153 observations).[1] It is cited here because it is exactly the kind of metro-level spatial-structure evidence the sprawl outcome page flags as thin — and one of its findings bears on the mechanism through which land taxation is argued to contain sprawl.

McGrath regresses the log radius of each urbanized area on population, real per capita income, a transportation-cost index, and agricultural land value (the opportunity cost of fringe land, r_a), plus a time trend. The standard economic factors are highly explanatory: "Changes in population, income, transportation costs, and agricultural land values determine nearly 90% of the variation of urbanized land areas within the data."[1] Consistent with monocentric-city theory, "urban spatial size is increasing in population and income and decreasing in transportation costs and agricultural rent."[1]

The Result That Bears on the Sprawl Mechanism

The variable most relevant to the Georgist case is agricultural land rent at the fringe (r_a), whose coefficient is negative and statistically significant in both specifications (−0.0000467, t = 2.01; and −0.0000547, t = 2.42 with the time trend).[1] Higher opportunity cost of holding land at the urban edge is associated with a smaller urbanized footprint. This is the monocentric-model analogue of the land value tax carrying-cost argument: raising the cost of holding fringe land — whether through market land rent here, or through a tax on land value in the LVT case — pushes the development margin inward and contains the spatial expansion of the city. It is metro-level, not tract-level, evidence, addressing the outcome the page says is under-tested.

Two further findings matter for honest interpretation. First, McGrath's central message is deflationary about sprawl-as-pathology: the results "strongly support Brueckner and Fansler's assertion that 'sprawl is the result of an orderly market process rather than a symptom of an economic system out of control.'"[1] Second, even so, a time-trend variable is positive and significant, implying "urban land areas are on average 2.3% larger per year than can be explained by standard economic factors" — a large unexplained residual (about 26% per decade) that McGrath attributes to decentralized employment and possible market failures in the development process.[1] Among the candidate market failures he cites is Brueckner's "failure of municipal governments to accurately estimate the fiscal burden of development" — a fiscal channel adjacent to, though not identical with, the land-tax case.[1]

Why It Supports the Outcome — and the Limits on That Support

• What it supports: a metro-level, peer-reviewed empirical result that raising the opportunity cost of fringe land significantly reduces urbanized land area — the direction the LVT carrying-cost mechanism predicts — plus a documented, large excess-sprawl residual that leaves room for corrective instruments.
• What it does not show (rent-gradient honesty): McGrath includes no property-tax or LVT variable at all; he does not test any tax. The r_a channel is a market-price effect, and its estimated elasticity is small (0.10, the least important of the significant factors — population, elasticity 0.76, dominates). The paper is therefore mechanism-consistent metro-level evidence, not a test of land taxation, and its headline finding — that sprawl is largely an orderly economic process — is itself a bound on how much any single policy could be expected to reshape metropolitan form. Scan depth Medium (full text read).

Bears On

• Outcome: LVT reduces urban sprawl — metro-level evidence on the fringe-land-cost mechanism; caveated as non-tax, small-magnitude.
• Research: Song & Zenou (2006) and Brueckner & Kim (2003) — the property-tax-and-sprawl theory in the same monocentric tradition.

See Also

• Song & Zenou (2006)
• Spatial Misallocation
• Land Value Tax

Sources

1. Daniel T. McGrath (2005), "More evidence on the spatial scale of cities," Journal of Urban Economics 58(1):1–10. DOI · free full-text PDF at coolclimate.berkeley.edu — used for the sample (33 largest US MSAs, 1950–1990, 153 obs.), the "nearly 90%" explanatory-power figure, the negative and significant agricultural-land-rent coefficient (Table 3), the monocentric sign pattern, the quoted "orderly market process" conclusion, and the 2.3%-per-year unexplained excess-sprawl trend (B/C-claims); directly fetched and read this pass.