An Application of Trend Surface Analysis to a Rural-Urban Land Market

Abstract

In past issues of this journal, the analytical technique of trend surface analysis (TSA) has been utilized in the investigation of population density gradients and their spatial characteristics. Schroeder and Sjoquist (1976) and Barnbrock and Green (1977) employed TSA in their studies of population density patterns in Atlanta and Baltimore, respectively. These articles and the comment by Jackson (1977) provide a fairly detailed discussion of TSA and its inherent strengths and weaknesses in specific empirical applications. One common point raised by these authors is an emphasis on the need to use TSA as a search or exploratory process-due in part to its identified limitations-accompanied by a hope for studied expansion of its use by economists as a viable empirical technique. In this paper we employ TSA to estimate the distribution of land value over space or land-value surfaces, specifically those for a six-year period in a ruralurban fringe county of the Lexington, Kentucky, SMSA. In the first section, traditional land-value approaches and studies with specific applicability to the rural-urban fringe are reviewed and our conceptual framework is outlined. TSA is shown to directly reflect this framework in its application as a form of analysis complementary to conventional regression analysis. The emphases of this spatial analysis are the interdependence of spatial phenomena and distance. The second section reviews the basic conast i sues of this journal, the l tical technique of trend surface l sis (TSA) has been utilized in the stigation of population density grats and their spatial ch racter stics. cepts and aspects of TSA and the rationale for its use; it also identifies limitations and constraints in empirical pplication. The third section presents the results of the analysis and their interpretation, and the final section presents some concluding remarks. The general emphasis of this paper, as was true of the above-cited efforts, is methodological in nature. Traditional land-value studies, utilizing some form of regression analysis, are implicitly (if not explicitly) based on the assumption of land-value gradients exhibiting monotonically decreasing values as distance from the urban center or central business district increases. This assumption is then maintained in a multicentric milieu, wherein it is hypothesized that at some point between any two such centers the lowest level of the land-value surface occurs at the intersection of the two respective land-value gradients. The interpretation of estimated coefficients from regression analyses (those particular coefficients related to distance from the urban centers in question) reflects the original assumption on which the empirical technique was based. Since the interpretation of distancerelated variables has spatial connotations or implications via land-value gradients