A Spatial Analysis of a Rural Land Market Using Alternative Spatial Weight Matrices

Recent literature in rural land value research suggests the use of spatial econometric procedures when spatial dependence exists within the data. These procedures require the use of a spatial weight matrix to adjust for dependence in the data. This research empirically tests two forms of spatial weight matrices. The first is the Delaunay method, which represents a rigid spatial weight matrix, while the second is the nearest neighbor method, which is dependent on a decay factor and a specified number of neighbors. Empirical results suggest the nearest neighbor method is the appropriate method for data used in this study. INTRODUCTION Several factors determine the value of rural real estate, including its inherent productive capacity, location, accessibility, and alternative uses. Additionally, continued economic and population growth increases the need for land, which puts upward pressure on rural land market values. With more rural land acres being converted at the urban fringe, buyers, sellers, planners, appraisers, tax assessors, and others are expected to have an increasing need for information related to the effect of location and economic development on rural land values. Generally, research aimed at identifying the effects of location and economic development on rural land market values is expected to provide improved information for both private and public decisions. In previous studies, Vandeveer et al. (2002) showed the importance of applying spatial econometrics to a rural real estate market to estimate implicit prices. Geographical Information Systems (GIS) and spatial econometric procedures were used to model the rural land market in Louisiana. These procedures, along with spatial econometric procedures, are necessary for testing the data for spatial dependence and estimating models in the presence of spatial dependence. In addition, these procedures are important because modeling the real estate market in the presence of spatial autocorrelation using traditional OLS procedures may result in models with less than desirable statistical characteristics. Pace et al. indicated that real estate and spatial statistics complement each other, and employing spatial estimators provide benefits over ignoring dependencies in the data. The benefits include improved prediction, better statistical inference through unbiased standard errors, and better estimates because of the way that location is handled within the modeling procedure. Southwestern Economic Review 132 The general objective of this research is to empirically test two forms of spatial weight matrices in rural land market research. A spatial weight matrix in rural land markets is used in spatial econometric models to correct for spatial autocorrelation. In this analysis, spatial weight matrices are estimated using the Delaunay and the nearest neighbor methods. The Delaunay method is a rigid form of a spatial weight matrix, whereas the nearest neighbor is estimated to depend on a decay factor and a specified number of neighbors. With the nearest neighbor method it is expected that nearby rural land sales have a greater influence on a given sale than sales located farther away. In the next section, hedonic procedures for modeling rural land market values are presented and discussed. The following section presents a discussion of spatial econometric procedures including a description of the two spatial weight matrices tested in this analysis. Data for this study comes from an area in Southeast Louisiana. Final sections provide a discussion of empirical results and conclusions. HEDONIC MODEL Previous studies have demonstrated the usefulness of using hedonic analysis in rural land market research (Palmquist). In an early study, Rosen defined hedonic prices as implicit prices of attributes and notes that they are revealed to economic agents from observed prices of differentiated products and the specific amounts of characteristics associated with them. Prices of these characteristics are implicit because there is no direct market for them. Palmquist provided a discussion of the theoretical basis for using hedonic analysis in rural land value studies and Danielson used the procedure to empirically analyze the rural land market in North Carolina. This study follows the approach used by Danielson. Value in a rural land submarket is specified by the following transcendental function: