Open space, forest conservation, and urban sprawl in Maryland suburban subdivisions.

Rapidly urbanizing jurisdictions face substantial challenges in maintaining the provision of public goods like preservation of open space and other scenic amenities. Numerous empirical studies have demonstrated that the presence of open space increases residential property values, suggesting that households place a positive value on this public good (Cheshire and Sheppard 1995; Geoghegan, Wainger, and Bockstael 1997; Tyrvainen and Mettinen 2000; Geoghegan 2002; Irwin 2002; Thorsnes 2002; Geoghegan, Lynch, and Bucholtz 2003; Wu, Adams, and Plantinga 2004; Hardie, Lichtenberg, and Nickerson 2007). Ensuring adequate provision of these amenities is one common justification for land-use regulations like zoning as well as voluntary preservation programs such as easement purchases (Bockstael and Irwin 2000).

But some open space preservation measures might induce developers to reduce the number of lots within subdivisions. Population increases would then result in more extensive development and thus contribute to urban sprawl. Theoretical analyses using closed and semi-closed city models show how minimum lot size zoning results in more extensive, lower-density development and an equilibrium urban boundary extending farther into rural areas (Moss 1977; Pasha 1996). McConnell, Walls, and Kopits (2006) provide empirical confirmation of these theoretical results: Their econometric analysis of Calvert County, Maryland shows that zoning regulations reduce density significantly. Irwin and Bockstael (2004) present econometric evidence indicating that preservation of open space can promote development of nearby land. Wu and Plantinga (2003) use simulations based on an open city model to show that public provision of open space can result in low-density, non-contiguous ("leapfrog") development.

This article examines the effects of two regulations on the average size and number of lots in suburban residential subdivisions: minimum lot size zoning and forest planting requirements under Maryland's Forest Conservation Act (FCA). We present a conceptual model of a developer's decisions regarding average lot size and the provision of forested and non-forested open space in the presence of these two regulations. We then examine the effects of these regulations empirically using data from subdivisions developed in the Baltimore-Washington suburbs during the mid-1990s.

The Maryland Forest Conservation Act

Concerned over rapid losses of forested land from development during the preceding three decades, Maryland enacted the FCA in 1991. The Act has been described in more detail elsewhere (see for example Galvin, Wilson, and Honeczy 2000; Hardie, Lichtenberg, and Nickerson 2007; Lichtenberg, Tra, and Hardie 2007). Briefly, the FCA applies to any project involving grading on 40,000 or more square feet (slightly less than an acre). Under the Act, developers must obtain approval for a forest conservation plan, specifying: the total amount and location of forested area retained; protective measures for stand edges and specimen trees; and measures that will protect retained forested areas permanently (e.g., covenants or easements incorporated into land deeds). The FCA also specifies minimum amounts of forested area to be provided. The FCA is administered by county planning agencies as part of the overall development permit approval process.

A Model of Land Allocation within a Residential Subdivision

Our conceptual framework builds on the model of a subdivision developer presented by Hardie, Lichtenberg, and Nickerson (2007). This model considers the problem of a land developer subdividing a parcel of fixed size L into n identical lots of size s and forested and non-forested open space, z and a, respectively. Forested and non-forested open space provide amenities f(z, [phi]s, [z.sup.o]) and h(a, [a.sup.o]), where [phi] denotes the share of forested area incorporated into building lots and [z.sup.o] and [a.sup.o] denote forested and non-forested open space nearby but outside of the subdivision. Households are assumed to be identical with willingness to pay per unit of developed land given by the bid rent function

R(s, f(z, [z.sup.o]), h(a, [a.sup.o]), y, T, g, u)

= y - T - x(s, f(z, [phi]s, [z.sup.o]), h(a, [a.sup.o]), g, u)/S. (1)

Here y denotes household income, T commuting cost, x a composite of all other purchased commodities, g other public good amenities (e.g., school quality), and u the equilibrium level of utility in the metropolitan area.

The land developer's goal is to maximize the rent generated by the subdivision

V [equivalent to] R(x)ns(1 + [gamma]) - cz - ka - Q(L) (2)

where [gamma] is the amount of land per building lot needed for roads, sidewalks, and other infrastructure, assumed fixed; c is the unit cost of afforestation; k is the unit cost of developing other open space; and Q(L) is the acquisition cost of the parcel, that is, the price of raw land prior to subdivision.

Development is subject to several constraints. First, development is constrained by the total area of the subdivision

ns(1 + [gamma]) + z + a = L. (3)

Second, zoning imposes a restriction on minimum lot size

s [greater than or equal to] [sigma]. (4)

Third, the FCA requires that the developer provide a minimum amount of forested area, which can consist of forested open space z or forested area incorporated into building lots [phi]ns

z + [phi]ns [greater than or equal to] [zeta]. (5)

Developers in the Maryland suburbs typically purchase entire farms for subdivision; hence, we assume that the constraint on total land availability (3) is always binding. If both regulatory constraints are binding, the developer's problem can be concentrated in the choice of forested and non-forested open space (z, a). The necessary conditions characterizing these choices are

[partial derivative]R/[partial derivative]f[[partial derivative]f/[partial derivative]z - [partial derivative]f/[partial derivative][phi] [sigma](1 + [gamma])(L + [gamma])(L - [zeta] - a)/[(L - z - a).sup.2]] x L - z - a/1 + [gamma] - R/1 + [gamma] - c [less than or equal to] 0 (6)

[[partial derivative]R/[partial derivative]h [partial derivative]h/[partial derivative]a + [partial derivative]R/[partial derivative]f [partial derivative]f/[partial derivative][phi] [sigma](1 + [gamma])([zeta] - z) /[(L - z - a).sup.2]] x L - z - a/1 + [gamma] - R/1 + [gamma] - k [less than or equal to] 0. (7)

With an interior solution, the choice of forested open space equates the increased value of building lots due to amenities provided by forested open space [partial derivative]R/[partial derivative]f [partial derivative]f/[partial derivative]z L - z - a/1 + [gamma] with the opportunity cost of land diverted from building lots R/1 + [gamma] plus the cost of developing forested open space c adjusted for any change in the value of building lots due to the substitution of forested open space for permanent forested open space incorporated into building lots [partial derivative]R/[partial derivative]f [partial derivative]f/[partial derivative][phi] [sigma](L - [zeta] - a)/(L - z - a). The choice of non-forested open space similarly equates the increased value of building lots due to amenities provided by non-forested open space [partial derivative]R/[partial derivative]h [partial derivative]h/[partial derivative]a L - z - a/1 + [gamma] with the cost of developing that open space k plus the opportunity cost of land diverted from building lots R/1 + [gamma] adjusted for any change in the value of building lots due to the substitution of non-forested open space for permanent forested open space incorporated into building lots [partial derivative]R/[partial derivative]f [partial derivative]f/[partial derivative][phi] [sigma]([zeta] - z)/(L - z - a).

Assuming that the FCA is met entirely using forested open space and ignoring infrastructure requirements ([phi] = [gamma] = 0), Hardie, Lichtenberg, and Nickerson (2007) show that an increase in minimum lot size [sigma] decreases the average value of land in the subdivision (Rns/L), while an increase in the FCA forestation requirement [zeta] increases the average value of land in the subdivision if willingness to pay for forested open space exceeds the opportunity cost of land. Assuming in addition that utility is Cobb-Douglas, Lichtenberg, Tra, and Hardie (2007) show that an increase in minimum lot size [sigma] decreases the amount of land devoted to total open space in the subdivision z + a, while a one-unit increase in the FCA forestation requirement [zeta] decreases non-forested open space and thus increases land devoted to total open space in the subdivision by an amount less than one.

Parameter estimates from econometric studies using data from a random sample of suburban single-family residential subdivisions in the Washington-Baltimore corridor bear out predictions derived from these theoretical models. The average value of land in these subdivisions was decreasing in zoned minimum lot size and increasing in the FCA forestation requirement (Hardie, Lichtenberg, and Nickerson 2007). Total open space was decreasing in zoned minimum lot size, while a one-acre increase in the FCA forestation requirement increased total open space by an amount significantly less than one, confirming the prediction that FCA forest planting requirements crowd out other forms of open space (Lichtenberg, Tra, and Hardie, 2007). Open space nearby but outside a subdivision had no effect on either the average value of land or total open space within the subdivision, indicating that the benefits of open space are largely internalized within subdivisions.

Data