A Problem with Distance Variables and Alternatives for Their Use

Abstract

Researchers commonly use distance variables to: (i) estimate the direct influence of a landmark on an outcome of interest, such as a neighborhood park on home price; or (ii) control for omitted spatial influences that affect predictions of key policy variables. While both uses continue, the use of distance as a control, such as distance to Central Business District (CBD), is now more common. Using distance to a given position such as CBD is added to multivariate analysis as a method to capture all remaining, or omitted spatial effects that influence the dependent variable. We show that there is a latent and inherent identification problem with the distance variable; and we show that this extends to the use of distance as a control. These biases affect more than the distance variable. They generate inconsistent estimates for all other spatially distributed variables in a model. We then introduce an alternative control that captures unmodeled influences that vary across space, and we show that this fully stabilizes all model parameter estimates and measures of model efficiency.

Keywords:

• Hedonic modeling
• distance variables
• CBD
• spatial estimation
• multicollinearity
• regional policy

JEL CODES:

• R30
• R31
• R20
• C21
• C18
• P25

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The data that support the findings of this paper are available from Farmer et al. (2012) and FARES (2002).

Notes

1 Triangulation of position C is exactly the condition where AB, BC and AC are all known. Given those three distances, the angular position of C, vis a vis A and B, can be found from $\mathrm{\text{tan}}(\angle \mathit{\text{BAC}})$ and $\mathrm{\text{tan}}(\angle \mathit{\text{CBA}})$ created by adding C at (x₃,y₃) Introducing position C only defines triangle ABC, thus recovering its own position but adding nothing that tells us more about position A. In fact, there is an infinite number of identical ABC triangles possible around position A, rotating in an $360°$ circle around A, and forming a sphere around A around the $x,y$ plane.

2 The familiar example is a vehicle that is either red or blue. To examine the effect of color on twilight accidents, knowledge that the range of colors for a type of vehicle is red or blue means that knowledge of the model of the vehicle observed in an accident and the observation that the vehicle is not red or is red perfectly predicts that the vehicle is blue or not blue, respectively; thus making the addition of another color variable redundant and the second color variable an unidentified explanatory variable.