Hedonic valuation of land protection methods: implications for cluster development

Abstract

This study estimates a generalized spatial hedonic pricing model to assess how residential property values are impacted by inclusion within cluster developments and by proximity to various types of protected land. The estimated model simultaneously controls for the spatial dependence of residential housing prices and for the presence of spatial autocorrelation. The sample includes 4,008 single-family housing sales transactions within the non-urban portions of Larimer County in northern Colorado. The empirical framework accounts for topographical diversity across the study region, as well as distinguishing between several distinct types of publicly and privately protected land. The key findings of the study are: (i) proximity to national or state park land and to city or county open space has a significant positive impact on property values, while proximity to national forest land or to privately conserved land exhibits no significant effects; and, (ii) inclusion of a property within a cluster development decreases its value by 17 to 26 %. These findings are robust to different estimation techniques and model specifications, which suggests important considerations for policymakers who design development rules and alternative land protection measures aimed at preserving open space in non-urban areas.

Appendix: Marginal price impact calculations

A complication arises in measuring the marginal impact of an open space variable in the spatial lag/autoregressive model (SAR) and in the generalized spatial model (SAC), given that the price vector is not specified explicitly in terms of the explanatory regressors in (2) and (4). As such, it is necessary to first present the models in explicit form. Following Kim et al. (2003), a series of algebraic rearrangements yields the marginal benefit (implicit price) of an arbitrary spatial variable,

$$ \frac{\partial \mathbf{P}}{\partial \mathbf{l}_{l}^{\prime}}=\left|\left| \begin{array}{cccc} \partial P_{1}/\partial l_{1m} & \partial P_{1}/\partial l_{2m} & \dots & \partial P_{1}/\partial l_{nm} \\ \partial P_{2}/\partial l_{1m} & \partial P_{2}/\partial l_{2m} & \dots & \partial P_{2}/\partial l_{nm} \\ \dots & \dots & \dots & \dots \\ \partial P_{n}/\partial l_{1m} & \partial P_{n}/\partial l_{2m} & \dots & \partial P_{n}/\partial l_{nm} \end{array}\right|\right| =\gamma_{l}[\mathbf{I}-\rho \mathbf{W}_{r}]^{-1}, $$

(A1)

where $\mathbf {l}^{\prime }$ is a 1×n row vector of one spatial characteristic, I is n×n identity matrix, and $r= \overline {1,2}$ in our setup. The Jacobian matrix in (3) implies that a price at one point in space is affected by a marginal change in one unique locational characteristic at that particular point and by the marginal changes of locational characteristics at all other points. To obtain the overall impact, we sum across the space such that $\frac {\partial \mathbf {P} }{\partial \mathbf {l}_{l}^{\prime }}\mathbf {i}=\gamma _{l}[ \mathbf {I }-\rho \mathbf {W}_{r}]^{-1}\mathbf {i}$ reduces to $\gamma _{l}\left ( \frac {1}{1-\rho }\right ) \mathbf {i}$, where i is a given column of the I matrix and where 1/(1−ρ) is a spatial multiplier (Kim et al. 2003).